Thermohydrauiic relationships for advanced water cooled ...

XAO100970

IAEA-TECDOC-1203

Thermohydrauiic relationships foradvanced water cooled reactors

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April 2001

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IAEA-TECDOC-1203

Thermohydraulic relationships foradvanced water cooled reactors

INTERNATIONAL ATOMIC ENERGY AGENCY

April 2001

The originating Section of this publication in the IAEA was:

Nuclear Power Technology Development SectionInternational Atomic Energy Agency

Wagramer Strasse 5P.O. Box 100

A-1400 Vienna, Austria

THERMOHYDRAULIC RELATIONSHIPS FOR ADVANCEDWATER COOLED REACTORS

IAEA, VIENNA, 2001IAEA-TECDOC-1203

ISSN 1011-4289

© IAEA, 2001

Printed by the IAEA in AustriaApril 2001

FOREWORD

This report was prepared in the context of the IAEA's Co-ordinated Research Project(CRP) on Thermohydraulic Relationships for Advanced Water Cooled Reactors, which wasstarted in 1995 with the overall goal of promoting information exchange and co-operation inestablishing a consistent set of thermohydraulic relationships which are appropriate for use inanalyzing the performance and safety of advanced water cooled reactors. For advanced watercooled reactors, some key thermohydraulic phenomena are critical heat flux (CHF) and postCHF heat transfer, pressure drop under low flow and low pressure conditions, flow and heattransport by natural circulation, condensation of steam in the presence of non-condensables,thermal stratification and mixing in large pools, gravity driven reflooding, and potential flowinstabilities.

Thirteen institutes co-operated in this CRP during the period from 1995 to 1999.

The IAEA acknowledges the strong efforts of the following persons in preparing thisreport: N. Aksan (Paul Scherrer Institute, Switzerland), F. D'Auria (University of Pisa, Italy),D.C. Groeneveld (AECL Research, Canada), P.L. Kirillov (Institute of Physics and PowerEngineering, Russian Federation) and D. Sana (Bhabha Atomic Research Centre, India). TheIAEA officers responsible for this publication were A. Badulescu and J. Cleveland of theDivision of Nuclear Power.

EDITORIAL NOTE

The use of particular designations of countries or territories does not imply any judgement by thepublisher, the IAEA, as to the legal status of such countries or territories, of their authorities andinstitutions or of the delimitation of their boundaries.

The mention of names of specific companies or products (whether or not indicated as registered) doesnot imply any intention to infringe proprietary rights, nor should it be construed as an endorsement orrecommendation on the part of the IAEA.

CONTENTS

CHAPTER 1. INTRODUCTION 1

1.1. Overview of advanced water cooled reactors 11.2. Background for the co-ordinated research project 41.3. Objectives 51.4. Participants 51.5. Summary of activities within the co-ordinated research project 61.6. Structure of this report 6

References to Chapter 1 6

CHAPTER 2. THERMOHYDRAULIC PHENOMENA OF INTEREST TO

ADVANCED WATER COOLED REACTORS 9


CHAPTER 3. A GENERAL CHF PREDICTION METHOD FORADVANCED WATER COOLED REACTORS 15

Nomenclature 15

3.1. Introduction 163.2. CHF mechanisms 18

3.2.1. General 183.2.2. DNB (departure from nucleate boiling) 183.2.3. Helmholtz instability 193.2.4. Annular film dryout 193.2.5. Unstable or periodic dryout 203.2.6. Slow dryout 20

3.3. CHF database 203.3.1. General 203.3.2. Tube database 223.3.3. Bundle database 24

3.4. CHF prediction methodology 243.4.1. General 243.4.2. Analytical models 263.4.3. Empirical CHF prediction methods 263.4.4. Application to bundle geometries 28

3.5. Recommended CHF prediction method for advanced water-cooled reactors 303.5.1. Tubes 303.5.2. Rod bundles 313.5.3. Correction factors 31

3.6. Assessment of accuracy of the recommended prediction methods 373.6.1. CHF look up table assessment 373.6.2. Accuracy of bundle CHF prediction methods 373.6.3. Impact of accuracy of CHF model on cladding temperature prediction 39

3.7. CHF concerning accident conditions 393.7.1. General 393.7.2. Effect of the axial/radial node size 393.7.3. Transient effects on CHF 42

3.8. Recommendations and final remarks 42


CHAPTER 4. GENERAL FILM BOILING HEAT TRANSFERPREDICTION METHODS FOR ADVANCEDWATER COOLED REACTORS 49

Nomenclature 49

4.1. Introduction 504.2. Description of post-CHF phenomena 52

4.2.1. General 524.2.2. Transition boiling 534.2.3. Minimum film boiling temperature 554.2.4. Flow film boiling 56

4.3. Film boiling data base 604.3.1. General 604.3.2. Tube and annuli 614.3.3. Bundle 61

4.4. Overview of film boiling prediction methods 614.4.1. General 614.4.2. Pool film boiling equations 664.4.3. Film boiling models 704.4.4. Flow film boiling correlations 754.4.5. Look-up tables for film boiling heat transfer in tubes 86

4.5. Recommended/most recent film boiling prediction methods 884.5.1. Pool film boiling 884.5.2. Flow film boiling 894.5.3. Radiation heat transfer in film boiling 904.5.4. Correlations for single phase heat transfer to superheated steam 914.5.5. Application to rod bundles 91

4.6. Application to film boiling prediction methods codes 934.6.1. General 93

4.7. Conclusions and final remarks 94


CHAPTER 5. PRESSURE DROP RELATIONSHIPS 109

Nomenclature 1095.1. Introduction 1105.2. Survey of situations where pressure drop relationships are important I l l

5.2.1. Distinction between core and system approach 1135.2.2. Geometric conditions of interest 113

5.3. Correlations for design and analysis 1155.3.1. Components of pressure drop 1155.3.2. Configurations 1175.3.3. Friction pressure drop correlations 1185.3.4. Local pressure drop 1285.3.5. Importance of void fraction correlations 1325.3.6. Review of previous assessments 134

5.3.7. Proposed assessment procedure for diabatic vertical flow 1425.3.8. Results of assessment 142

5.4. Comparisons of correlations as they stand in codes 1465.4.1. Physical models in system codes 147

5.5. Final remarks 149


CHAPTER 6. REMARKS AND FUTURE NEEDS 163References to Chapter 6 165

APPENDICES I-XIX

APPENDIX I: ACTIVITIES CONTRIBUTED TO THE CRP BY THERESEARCH GROUPS AT THE PARTICIPATING INSTITUTES.... 169

APPENDIX II: THE 1995 LOOK-UP TABLE FORCRITICAL HEAT FLUX IN TUBES 175

APPENDIX III: CHF PREDICTION FOR WWER-TYPEBUNDLE GEOMETRIES 183

APPENDIX IV: AECL LOOK-UP TABLE FORFULLY DEVELOPED FILM-BOILINGHEAT-TRANSFER COEFFICIENTS (kW m'2 K"1) 190

APPENDIX V: IPPE TABLE OF HEAT TRANSFER COEFFICIENTS FORFILM BOILING AND SUPERHEATED STEAM FOR TUBES 241

APPENDIX VI: CIAE METHOD FOR DETERMININGFILMBOILING HEAT TRANSFER 271

APPENDIX VII: TWO-PHASE VISCOSITY MODELS FOR USEIN THE HOMOGENEOUS MODEL FORTWO-PHASE PRESSURE DROP 273

APPENDIX VIII: TWO-PHASE PRESSURE DROP CORRELATIONSBASED ON THE MULTIPLIER CONCEPT 274

APPENDIX IX: DIRECT EMPIRICAL TWO-PHASEPRESSURE DROP CORRELATIONS 281

APPENDIX X: FLOW PATTERN SPECIFIC PRESSURE DROPCORRELATIONS FOR HORIZONTAL FLOW 283

APPENDIX XI: FLOW PATTERN SPECIFIC PRESSURE DROP FORVERTICAL UPWARD FLOW 288

APPENDIX XII: INTERFACIAL FRICTION MODELSGIVEN BY SOLBRIG (1986) 291

APPENDIX XIII: SLIP RATIO MODELS FOR CALCULATION OFVOID FRACTION 294

APPENDIX XIV: Kp MODELS FOR THE CALCULATION OFVOID FRACTION 295

APPENDIX XV: DRIFT FLUX MODELS FOR THE CALCULATION OFVOID FRACTION 296

APPENDIX XVI: MISCELLANEOUS EMPIRICAL CORRELATIONS FOR

VOID FRACTION 304

APPENDIX XVII: COMPILATION OF DATA 305

APPENDIX XVIII: DETAILED RESULTS OF ASSESSMENT OFVOID FRACTION CORRELATIONS 310

APPENDIX XIX: DETAILED RESULTS OF ASSESSMENT OFFLOW PATTERN DATA 319

ANNEX A: INTERNATIONAL NUCLEAR SAFETY CENTER DATABASE 331

ANNEX B: PREPARED METHODOLOGY TO SELECT RANGES OFTHERMOHYDRAULIC PARAMETERS 335

CONTRIBUTORS TO DRAFTING AND REVIEW 343

Chapter 1

INTRODUCTION

1.1. OVERVIEW OF ADVANCED WATER COOLED REACTORS

In the second half of the 20th century nuclear power has evolved from the research anddevelopment environment to an industry that supplies 17% of the world's electricity. In these50 years of nuclear development a great deal has been achieved and many lessons have beenlearned. At the end of 1998, according to data reported in the Power Reactor InformationSystem, PRIS, of the IAEA, there were 434 nuclear power plants in operation and 34 underconstruction. Over eight thousand five hundred reactor-years of operating experience hadbeen accumulated.

Due to further industrialization, economic development and projected increases in theworld's population, global energy consumption will surely continue to increase into the 21stcentury. Based on IAEA's review of nuclear power programmes [IAEA (1998)] and plans ofMember States, several countries, especially in the Far East, are planning to expand theirnuclear power capacity considerably in the next 15-20 years.

The contribution of nuclear energy to near and medium term energy needs depends onseveral key issues. The degree of global commitment to sustainable energy strategies andrecognition of the role of nuclear energy in sustainable strategies will impact its future use.Technological maturity, economic competitiveness and financing arrangements for new plantsare key factors in decision making. Public perception of energy options and relatedenvironmental issues as well as public information and education will also play a key role inthe introduction of evolutionary designs. Continued vigilance in nuclear power plantoperation, and enhancement of safety culture and international co-operation are highlyimportant in preserving the potential of nuclear power to contribute to future energystrategies.

To assure that nuclear power remains a viable option in meeting energy demands in thenear and medium terms, new reactor designs, aimed at achieving certain improvements overexisting designs are being developed in a number of countries. Common goals for these newdesigns are high availability, user-friendly features, competitive economics and compliancewith internationally recognized safety objectives.

The early development of nuclear power was to a large extent conducted on a nationalbasis. However, for advanced reactors, international co-operation is playing an important role,and the IAEA promotes international co-operation in advanced reactor development andapplication. Various organizations are involved, including governments, industries, utilities,universities, national laboratories, and research institutes.

Worldwide there is considerable experience in nuclear power technology and especiallyin light water reactor (LWR) and heavy water (HWR) technology. Of the operating plants,346 are LWRs totaling 306 GW(e) and 31 are HWRs totaling 15 GW(e). The experience andlessons learned from these plants are being incorporated into new water cooled reactordesigns. Utility requirements documents have been formulated to guide these activities byincorporating this experience with the aim of reducing costs and licensing uncertainties byestablishing a technical foundation for the new designs.

The full spectrum of advanced water cooled reactor designs or concepts covers differenttypes of designs — evolutionary ones, as well as innovative designs that require substantialdevelopment efforts. A natural dividing line between these two categories arises from thenecessity of having to build and operate a prototype or demonstration plant to bring a conceptwith much innovation to commercial maturity, since such a plant represents the major part ofthe resources needed. Designs in both categories need engineering, and may also needresearch and development (R&D) and confirmatory testing prior to freezing the design ofeither the first plant of a given line in the evolutionary category, or of the prototype and/ordemonstration plant for the second category. The amount of such R&D and confirmatorytesting depends on the degree of both the innovation to be introduced and the related workalready done, or the experience that can be built upon. This is particularly true for designs inthe second category where it is entirely possible that all a concept needs is a demonstrationplant, if development and confirmatory testing is essentially completed. At the other extreme,R&D, feasibility tests, confirmatory testing, and a prototype and/or demonstration plant areneeded in addition to engineering. Different tasks have to be accomplished and theircorresponding costs in qualitative terms are a function of the degree of departure fromexisting designs. In particular, a step increase in cost arises from the need to build a reactor aspart of the development programme (see Figure 1.1).

Advanced designDifferent types of new nuclear plants are being developedtoday that are generally called advanced reactors. Ingeneral, an advanced plant design is a design of currentinterest for which improvement over its predecessors and/orexisting designs is expected. Advanced designs consist ofevolutionary designs and designs requiring substantialdevelopment efforts. The latter can range from moderatemodifications of existing designs to entirely new designconcepts. They differ from evolutionary designs in that aprototype or a demonstration plant is required, or thatinsufficient work has been done to establish whether such aplant is required.

Evolutionary designAn evolutionary design is an advanced design that achievesimprovements over existing designs through small tomoderate modifications, with a strong emphasis onmaintaining proven design features to minimisetechnological risks. The development of an evolutionarydesign requires at most engineering and confirmatorytesting.

Innovative designAn innovative design is an advanced design whichincorporates radical conceptual changes in designapproaches or system configuration in comparison withexisting practice. Substantial R&D, feasibility tests, and aprototype or demonstration plant are probably required.

Advanced Designs

-.tEvolutionary designs Designs requiring substantial development

o i Engineering i

and/orDemonstration plant

+Confirmatory testing

+Engineering

"Substantial R&D~

Departure From Existing Designs(A prototype Is normally a scaled down unit, whereas a demonstration plant is a more

substantial plant that can be as large as fu8 size.)

Figure 1.1. Efforts and development costs for advanced designs versus departure fromexisting designs (Terms are excerpted from IAEA-TECDOC-936).

Large water cooled reactors with power outputs of 1300 MW(e) and above, which possessinherent safety characteristics (e.g. negative Doppler and moderator temperature coefficients,and negative moderator void coefficient) and incorporate proven, active engineered systemsto accomplish safety functions are being developed. Other designs with power outputs from,for example, 220 MW(e) up to about 1300 MW(e) which also possess inherent safetycharacteristics and which place more emphasis on utilization of passive safety systems arealso being developed. Passive safety systems are based on natural forces such as convectionand gravity, making safety functions less dependent on active systems and components likepumps and diesel generators. Table 1.1 presents a list of advanced water cooled reactors underdevelopment1.

TABLE 1.1. SURVEY OF ADVANCED WATER COOLED REACTOR DESIGNSUNDER DEVELOPMENT

Evolutionary,large-sizeplants

Evolutionary,medium-sizeplants

Designconceptsrequiringsubstantialdevelopment

Name

APWRABWR

BWR90EP10003

EPRESBWR2

KNGR

Sizewell CSystem 80+SWR 1000WWER-1000(V-392)

CP-1300

CANDU9AC-600

AP-600HSBWRMS-600WWER-640 (V-407)CANDU6AHWR4

ISISJPSR

PIUSSPWR

VPBER-600

Type

PWRBWR

BWRPWRPWRBWRPWR

PWRPWRBWRPWR

PWR

HWRPWR

PWRBWRPWRPWRHWRHWR

PWRPWR

PWRPWR

PWR

Power,MW(e)

13001300

12001000154511901350

1250135010001000

1300

900-1300600

600600600640670220

300630

650600

630

Supplier/designer

Westinghouse, USA& Mitsubishi, JapanGeneral Electric, USA in co-operationwith Hitachi and Toshiba, JapanABB Atom, SwedenWestinghouse, USA, Genesi, Italy, EURNuclear Power International (NPI)General Electric, USAKorea Electric Power Corp., Republic ofKoreaNational Nuclear Corp. (NNC), UKABB Combustion Engineering, USASiemens, GermanyAtomenergoprojekt/Gidropress, RussiaKorea Advanced Institute of Science andTechnology, Republic of Korea

Atomic Energy of Canada, Ltd

China National Nuclear Corp. (CNNC)ChinaWestinghouse, USAHitachi Ltd., JapanMitsubishi, JapanAtomenergoprojekt/Gidropress, RussiaAtomic Energy of Canada, Ltd.Bhabha Atomic Research Centre, India

Ansaldo Spa., ItalyJapan Atomic Energy Research Institute(JAERI), JapanABB Atom, SwedenJapan Atomic Energy Research Institute(JAERI), JapanOKBM, Russia

Design status1

Conceptual designDetailed design

Detailed designBasic designBasic designPreliminary designBasic design

Conceptual designDetailed designConceptual designBasic designConceptual design

Detailed design

Conceptual design

Detailed designBasic designDetailed designDetailed designDetailed designBasic design

Conceptual designDesign study

Basic designConceptual design

Conceptual design

1 The design status classification refers to the IAEA (1997a), Terms for Describing New, Advanced NPPs.2 ESBWR (and JSBWR in Japan) is an enlarged version of GE's SBWR design.3 EP 1000 (in Europe) represents an enlarged version of AP-600.4 Boiling light water cooled, heavy water moderated.

1 For detailed descriptions of these designs see IAEA (1997c and 1997d).

1.2. BACKGROUND FOR THE CO-ORDINATED RESEARCH PROJECT

The nuclear industry and regulatory bodies have developed thermohydraulics codes forpredicting the performance of water cooled reactors under normal, transient and accidentconditions. These codes are used for plant design, evaluation of safety margin, establishmentof emergency procedures and operator training. These codes essentially solve mass,momentum and energy balance equations and include detailed representations ofthermohydraulic relationships and thermophysical properties.

Extensive validation programmes have been carried out to demonstrate the applicabilityof the codes to plants, considering the stated objectives. These have been conducted innational and international contexts at four levels, involving the use of:

— fundamental experiments;— separate effects test facilities (SETF);— integral test facilities (ITF);— plant data.

Experimental data have been extensively compared with code predictions includingInternational Standard Problems of the OECD Committee on the Safety of NuclearInstallations (CSNI) and IAEA standard problem exercises.

The present situation in relation to the development, validation and use of system codes,can be summarized as follows:

— the codes have reached an acceptable degree of maturity though the reliable applicationis still limited to the validation domain;

— the use of qualified codes is more and more requested for assessing the safety ofexisting reactors, and for designing advanced reactors;

— code validation criteria and detailed qualification programmes have been established[OECD-NEA-CSNI (1989, 1987, 1994 and 1996b)];

— methodologies to evaluate the 'uncertainty' (i.e. the error) in the prediction of nuclearplant behaviour by system codes have been proposed and are being tested;

— problems like user effect (i.e. influence of code users on the predictions) [OECD-NEA-CSNI (1995)] nodalization qualification, quantification of code accuracy (i.e. ranking ofthe error in the comparison between measured and calculated trend), have been dealtwith and experience is currently available;

— relevant activities have been recently completed that are coordinated by the OECDCommittee on the Safety of Nuclear Installations (CSNI). These include:

• the state of the art report on themalhydraulics of emergency core cooling [OECD-NEA-CSNI (1989)];

• the set-up of the ITF code validation matrix [OECD-NEA-CSNI (1987, 1992 and1996b)];

• the set-up of the SETF code validation matrix including the identification and thedefinition of the phenomena that must be predicted by codes [OECD-NEA-CSNI(1994)];

• the characterization of relevant plant status;• the lessons learned from the execution of the International Standard Problem

exercises [OECD-NEA-CSNI (1996a and 1996b)].

Clearly the performance of these codes is dependent on the accuracy and consistency ofthe representations of the thermohydraulic relationships and thermophysical properties datacontained in the codes.

On the recommendation of the IAEA's International Working Group on AdvancedTechnologies for Water Cooled Reactors (IWG-ATWR) a Coordinated Research Project(CRP) to establish a thermophysical properties database for light and heavy water reactormaterials was organized with the objective to collect and systematize a thermophysicalproperties database for reactor materials under normal operating, transient and accidentconditions. This CRP has been completed with the publication of IAEA (1997b). Also, on therecommendation of the IWG-ATWR, the CRP on Thermohydraulic Relationships forAdvanced Water Cooled Reactors began in January 1995 with a duration of 4-years.

1.3. OBJECTIVES

The objectives of the CRP are (i) to systematically list the requirements forthermohydraulic relationships in support of advanced water cooled reactors during normal andaccident conditions, and provide details of their database where possible and (ii) torecommend and document a consistent set of thermohydraulic relationships for selectedthermohydraulic phenomena such as CHF and post-CHF heat transfer, pressure drop, andpassive cooling for advanced water cooled reactors.

~"~" Key collaborative activities of the participating institutes within the CRP include:

— preparation of internationally peer reviewed and accepted prediction methods for CHF,post CHF heat transfer and pressure drop;

— establishment of a base of non-proprietary data and prediction methods available on theInternet.

1.4. PARTICIPANTS

The participating institutes and chief scientific investigators are:

Atomic Energy of Canada Ltd (AECL), Canada (D.C. Groeneveld)China Institute of Atomic Energy (CIAE), China (Hanming Xu and Yuzhou Chen)Nuclear Research Institute (NRI), Czech Republic (J. Macek)Forschungszentrum Karlsruhe (FZK), Germany (F. J. Erbacher and X. Cheng)Bhabha Atomic Research Centre (BARC), Mumbai, India (D. Saha)University of Pisa, Italy (F. D'Auria)Ente per le Nuove tecnologie, l'Energia e l'Ambiente (ENEA), Italy (S. Cevolani)Korea Atomic Energy Research Institute (KAERI), Republic of Korea (M.K. Chung)Korea Advanced Institute of Science and Technology (KAIST), Republic of Korea (S.H.Chang)Institute of Physics and Power Engineering (IPPE), Russia (P. Kirillov)Paul Scherrer Institute (PSI), Switzerland (N. Aksan)Middle East Technical University, Turkey (O. Yesin)Argonne National Laboratory, United States of America(J. Roglans-Ribas)

The programme has been co-ordinated through annual meetings of the chief scientificinvestigators from the participating institutes.

1.5. SUMMARY OF ACTIVITIES WITHIN THE CO-ORDINATED RESEARCHPROJECT

Brief summaries of CRP related activities contributed to the CRP by the research groupsat the participating institutes are given in Appendix I.

1.6. STRUCTURE OF THIS REPORT

This chapter provides a brief discussion of the background for this CRP, the CRPobjectives and lists the participating institutes. Chapter 2 provides a summary of importantand relevant thermohydraulic phenomena for advanced water cooled reactors on the basis ofprevious work by the international community. Chapter 3 provides details of the database forcritical heat flux, and recommends a prediction method which has been established throughinternational co-operation and assessed within this CRP. Chapter 4 provides details of thedatabase for film boiling heat transfer, and presents three methods for predicting film boilingheat transfer coefficients developed by institutes participating in this CRP. Chapter 5compiles a range of pressure drop correlations, and reviews assessments of these relations andthe resulting recommendations. Chapter 6 provides general remarks and conclusions, andcomments on future research needs in thermohydraulics of advanced water cooled reactors.

Nomenclature is provided at the beginning of each chapter for which it is necessary, andreferences are provided at the end of each chapter. Chapter appendices present relevantinformation in more detail. The report contains two annexes. Annex A identifies the contentsof a base of thermohydraulics data which has been contributed by institutes participating inthe CRP and made openly available on the internet site which is maintained by InternationalNuclear Safety Center at Argonne National Laboratory. Annex B discusses a methodology toselect the range of interest for parameters affecting CHF, film boiling and pressure drop inadvanced water cooled reactors.

REFERENCES TO CHAPTER 1

IAEA, 1998, Energy, Electricity and Nuclear Power Estimates for the Period up to 2020,Reference Data Series No. 1, Vienna.

IAEA, 1997a, Terms for Describing New, Advanced Nuclear Power Plants, IAEA-TECDOC-936, Vienna.

IAEA, 1997b, Thermophysical Properties of Materials for Water Cooled Reactors, IAEA-TECDOC-949, Vienna.

IAEA, 1997c, Status of Advanced Light Water Cooled Reactor Designs: 1996, IAEA-TECDOC-968, Vienna.

IAEA, 1997d, Advances in Heavy Water Reactor Technology, IAEA-TECDOC-984, Vienna.

OECD-NEA-CSNI, 1987, CSNI Code Validation Matrix of Thermal-Hydraulic Codes forLWR LOCA and Transients, Report No. 132, Paris.

OECD-NEA-CSNI, 1989, Thermohydraulics of Emergency Core Cooling in Light WaterReactors, a State-of-the-Art Report, (SOAR) by a Group of Experts of the NEA Committeeon the Safety of Nuclear Installations, Report No. 161, Paris.

OECD-NEA-CSNI, 1992, Wolfert, K., Glaeser, H., Aksan, N., CSNI validation matrix forPWR and BWR Codes, RL(92)12 (Proc. CSNI-Specialists Mtg on Transient Two-Phase flow,Aix-en-Provence), M. Reocreux, M.C. Rubinstein, eds.

OECD-NEA-CSNI, 1994, Aksan N., et al., Separate Effects Test Matrix for Thermal-Hydraulic Code Validation, R(93)14, Part 1 and Part 2, Volume I: PhenomenaCharacterization and Selection of Facilities and Tests, Volume 2: Facility and ExperimentsCharacteristics.

OECDNEA-CSNI, 1995, Stadtke H., User on the transient system code calculations, R(94)35.

OECD-NEA-CSNI, 1996a, Annunziato A., et al., CSNI Integral Test Facility ValidationMatrix for the Assessment of Thermal-Hydraulic Codes for LWR LOCA and Transients,R(96)17.

OECD-NEA-CSNI, 1996b, Lessons Learned from OECD/CSNI ISP on Small Break LOCA,R(96)20, OECD/GD(97)10.

Chapter 2

THERMOHYDRAULIC PHENOMENA OF INTEREST TO ADVANCEDWATER COOLED REACTORS

This chapter will provide a short summary on the important and relevant thermal-hydraulic phenomena for advanced water cooled reactor designs in addition to the relevantthermal-hydraulic phenomena identified for the current generation of light water reactors(LWRs). The purpose of these relevant phenomena lists is that they can provide someguidance in development of research plans for considering further code development andassessment needs, and for the planning of experimental programs.

All ALWRs incorporate significant design simplifications, increased design margins,and various technical and operational procedure improvements, including better fuelperformance and higher burnup, a better man-machine interface using computers andimproved information displays, greater plant standardization, improved constructability andmaintainability, and better operator qualification and simulator training.

Design features proposed for the ALWRs include in some cases the use of passive,gravity-fed water supplies for emergency core cooling and natural circulation decay heatremoval. This is the case, for example, for the AP600 and ESBWR. Further, naturalcirculation cooling is used for the ESBWR core for all conditions. Both plants also employautomatic depressurization systems (ADSs), the operation of which are essential during arange of accidents to allow adequate emergency core coolant injection from the lower pressurepassive safety systems. The low flow regimes associated with these designs will involvenatural circulation flow paths not typical of current LWRs. These ALWR designs emphasizeenhanced safety by means of improved safety system reliability and performance. Theseobjectives are achieved by means of safety system simplification and reliance on immutablenatural forces for system operation. Simulating the performance of these safety systems iscentral to analytical safety evaluation of advanced LWRs with passive safety systems.

Specifically, the passive safety principles of the next generation ALWR designs include:

(1) low volumetric heat generation rates,(2) reliance solely on natural forces, such as gravity and gas pressurization, for safety

system operation,(3) dependence on natural phenomena, such as natural convection and condensation, for

safety system performance.

The engineered safety features which incorporate these passive safety principles achieveincreased reliability by means of system redundancy, minimization of system components,non-reliance on external power sources, and integral long term decay heat removal andcontainment cooling systems. In the design of the current generation of operating reactors,redundancy and independence have been designed into the protection systems so that nosingle failure results in loss of the protection function. Since the new ALWR designsincorporate significant changes from the familiar current LWR designs and place higherreliance on individual systems, a thorough understanding of these designs is needed withrespect to system interactions. These interactions may occur between the passive safetysystems e.g. the core makeup tanks and accumulators in the AP600, and the ADS system and

isolation condensers in the ESBWR. In addition, there is a close coupling in both plantdesigns between the reactor coolant system and the containment during an accident.

It can also be noted that in order to fully profit from the safety benefits due to theintroduction of the passive safety systems, the behaviour of plants in which engineering safetyfeatures involving active components have been replaced with completely passive devicesmust be carefully studied to ensure the adequacy of the new design concepts for a widespectrum of accident conditions. In fact, choice of passivity is an advantage in reducing theprobability of the wrong operator interventions, especially in the short-term period after anaccident, although passive systems require more sophisticated modelling techniques toascertain that the natural driving forces that come into play can adequately accomplish theintended safety functions. Hence, there is also the need for an in-depth study of the basicphenomena concerning the design of ALWRs which make use of passive safety features.

Thermalhydraulic phenomena relevant to the evolutionary type ALWRs can beconsidered the same as those valid for the current generation LWRs. A suitable review ofapplicable phenomena can be found in [OECD-NE-CSNI (1987, 1989, 1994 and 1996)] and[NUREG (1987)]. For completeness, the list is reported in Table 2.1. A limited specificresearch activity in this area appears necessary, if one excludes new domains like AccidentManagement and special topics like instability in boiling channels where the interest iscommon to the present generation reactors.

In the case of advanced cooled reactors the foreseeable relevant thermalhydraulicphenomena can be grouped into two categories [see OECD-NEA-CSNI (1996)]:

a) phenomena that are relevant also to the present generation reactors (Table 2.1)b) new kinds of phenomena and/or scenarios.

For the category a) the same considerations apply as for the evolutionary ALWRs andthe phenomena of concern are therefore well documented in [OECD-NEA-CSNI (1987 and1989)] and [NUREG (1987)]. However, it has to be noted that significance of variousphenomena may be different for the passive and advanced reactors. Nevertheless, it isbelieved that the data base, understanding and modelling capabilities acquired for the currentreactors are adequate for phenomena in category a.

Phenomena of the category b can be subdivided into three classes:

bl) phenomena related to the containment processes and interactions with the reactorcoolant system

b2) low pressure phenomenab3) phenomena related specifically to new components, systems or reactor configurations

In current generation LWRs the thermalhydraulic behaviour of the containment systemand of the primary system are studied separately. This is not any more possible in most of thenew design concepts; suitable tools must be developed to predict the performance of theintegrated system.

A speciality common to almost all the advanced design reactors is the presence ofdevices that depressurize the primary loop essentially to allow the exploitation of largeamount of liquid at atmospheric pressure and to minimize the risk of high pressure core melt.

10

TABLE 2.1. RELEVANT THERMALHYDRAULIC PHENOMENA IDENTIFED FOR THECURRENT GENERATION REACTORS*0

1

2

345

6

7

g

9

10

11

12

13141516171819202122232425

BASIC PHENOMENA

CRITICAL FLOW

PHASE SEPARATION/VERTICAL FLOW WITH AND WITHOUTMIXTURE LEVEL

STRATIFICATION IN HORIZONTAL FLOWPHASE SEPARATION AT BRANCHESENTRAINMENT/DEENTRAINMENT

LIQUID-VAPOUR MIXING WITHCONDENSATION

CONDENSATION IN STRATIFIEDCONDITIONS

SPRAY EFFECTS

COUNTERCURRENT FLOW/COUNTERCURRENT FLOW LIMITATION

GLOBAL MULTIDIMENSIONALFLUID TEMPERATURE, VOIDAND FLOW DISTRIBUTION

HEAT TRANSFER: NATURAL OR FORCED CONVECTIONSUBCOOLED/NUCLEATE BOILINGDNB/DRYOUTPOST CRITICAL HEAT FLUXRADIATIONCONDENSATION

QUENCH FRONT PROPAGATION/REWET

LOWER PLENUM FLASHINGGUIDE TUBE FLASHING (BWR)ONE AND TWO PHASE IMPELLER-PUMP BEHAVIOURONE AND TWO PHASE JET-PUMP BEHAVIOUR (BWR)SEPARATOR BEHAVIOURSTEAM DRYER BEHAVIOURACCUMULATOR BEHAVIOURLOOP SEAL FILLING AND CLEARANCE (PWR)ECC BYPASS/DOWNCOMER PENETRATIONPARALLEL CHANNEL INSTABILITIES (BWR)BORON MIXING AND TRANSPORTNONCONDENSABLE GAS EFFECT (PWR)LOWER PLENUM ENTRAINMENT

1234567g9123

123

11123456

1234561234

123

123456

1234123456

12

Evaporation due to DepressurisationEvaporation due to Heat InputCondensation due to PressurisationCondensation due to Heat RemovalInterfacial Friction in Vertical FlowInterfacial Friction in Horizontal FlowWall to Fluid FrictionPressure Drops at Geometric DiscontinuitiesPressure Wave PropagationBreaksValvesPipes

Pipes/PlenaCoreDowncomer

PipesBranchesCoreUpper PlenumDowncomerSteam Generator TubeSteam Generator Mixing Chamber (PWR)Hot Leg with ECCI (PWR)

CoreDowncomerUpper PlenumLower PlenumSteam Generator Mixing Chamber (PWR)ECCI in Hot and Cold Leg (PWR)Pressuriser (PWR)Steam Generator Primary Side (PWR)Steam Generator Secondary Side (PWR)Horizontal Pipes

Core (BWR)Pressuriser (PWR)Once-Through Steam Generator Secondary Side (PWR)

Upper Tie PlateChannel Inlet Orifices (BWR)Hot and Cold LegSteam Generator Tube (PWR)DowncomerSurgeline (PWR)

Upper PlenumCoreDowncomerSteam Generator Secondary SideCore, Steam Generator, StructuresCore, Steam Generator, StructuresCore, Steam Generator, StrucutresCore, Steam Generator, StrucutresCoreSteam Generator, Structures

Fuel RodsChannel Walls and Water Rods (BWR)

* This table is applicable to LWRs and is expected to be applicable to WWERs as well.

11

TABLE 2.2. RELEVANT THERMALHYDRAULIC PHENOMENA OF INTEREST IN THEADVANCED WATER COOLED DESIGN REACTORS

bl. Phenomena occurring due to the interaction between primary system and containment

1. Behaviour of large pools ofliquid:

2. Tracking of non-condensibles (essentiallyH2, N2, air):

3. Condensation on thecontainment structures:

4. Behaviour of containmentemergency systems (PCCS,external air cooling, etc.):

5. Thermofluiddynamics andpressure drops in variousgeometrical configurations:

- thermal stratification- natural/forced convection and circulation- steam condensation (e.g. chugging, etc.)- heat and mass transfer at the upper interface (e.g.

vaporization)- liquid draining from small openings (steam and gas

transport)

- effect on mixture to wall heat transfer coeficient- mixing with liquid phase- mixing with steam phase- stratification in large volumes at very low velocities

- coupling with conduction in larger structures

- interaction with primary cooling loops

3-D large flow pths e.g. around open doors and stair wells,connection of big pipes with pools, etc.gasliquid phase separation at low Re and in laminar flowlocal pressure drops

b2. Phenomena occurring at atmospheric pressure

6. Natural circulation:

7. Steam liquid interaction:

8. Gravity driven reflood:

9. Liquid temperaturestratification:

interaction among parallel circulation loops inside andoutside the vesselinfluence of non-condensables

direct condensationpressure waves due to condensation

heat transfer coefficientspressure rise due to vaporizationconsideration of a closed loop

lower plenum of vesseldowncomer of vesselhorizontal/vertical piping

b3. Phenomena originated by the presence of new components and systems or special reactorconfigurations

10. Behaviour of density locks: -

11. Behaviour of check valves: -

12. Critical and supercritical -flow in discharge pipes and -valves: _

13. Behaviour of Isolation -Condenser

14. Stratification of boron: -

stability of the single interface (temperature and densitydistribution)interaction between two density locks

opening/closure dynamicspartial/total failure

shock wavessupercritical flow in long pipesbehaviour of multiple critical section

low pressure phenomena

interaction between chemical and thermohydraulic problemstime delay for the boron to become effective in the core

12

In this case, the phenomena may be similar (or the same) as those reported for currentgeneration LWRs (Table 2.1) but the range of parameters and their safety relevance can bemuch different.

hi addition to the concerns specific to light-water-cooled reactors, the followingconcerns are specific to HWRs:

I. Thermalhydraulics related to short fuel bundles located in long HWR-type horizontalchannels, and on-line fuelling,

II. Thermalhydraulics related to radial and axial pressure-tube creep.Finally, the presence of new systems or components and some geometric specialities ofadvanced design reactors require the evaluation of additional scenarios andphenomena.

A list of identified phenomena belonging to subclasses bl, b2 and b3 is given inTable 2.2.


OECD-NEA-CSNI, 1987, CSNI Code validation Matrix of Thermal-Hydraulic Codes forLWR LOCA and Transients, Rep. No. 132, Paris, France.

OECD-NEA CSNI, 1989, Thermohydraulicsof Emergency Core Cooling in Light WaterReactors, a State-of-the-Art Report, (SOAR) by a Group of Experts of the NEA Committee onthe Safety of Nuclear Installations, Rep. No. 161, Paris.

OECD-NEA-CSNI, 1994, Aksan, N., D'Auria, F., Glaeser, H., Pochard, R., Richards, C ,Sjoberg, A., Separate Effects Test Matrix for Thermal-Hydraulic Code Validation, R(93)14,Vol. I: Phenomena Characterization and Selection of Facilities and Tests; Vol. 2: Facility andExperiments Characteristics.

OECD-NEA-CSNI, 1996, Aksan, N., D'Auria, F., Relevant Thermalhydraulic Aspects ofAdvanced Reactor Design, CSNI Status Report OCDE/GD(97)8, Paris.

NUREG, 1987, Compendium of ECCS Research for Realistic LOCA Analysis, USNRC Rep.1230, Washington, DC.

13

Chapter 3

A GENERAL CHF PREDICTION METHOD FOR ADVANCEDWATER COOLED REACTORS

NOMENCLATURE

cCHFCpDe, Dhy

DheDdEgGHhK,FLsp

LPPqT

uX

z

ConstantCritical heat fluxSpecific heatHydraulic equivalent diameterHeated equivalent diameterTube inside diameterFuel element diameterEntrainment rateAcceleration due to gravityMass fluxEnthalpyHeat transfer coefficient kCorrection factorDistance to upstream spacer planeHeated lengthPressureElement pitchSurface heat fluxTemperatureVelocityQualityAxial co-ordinate

-kW/m2

kJ/(kg °Cmmmmkg/(m2s)m/s2

kg/(m2s)kJ/kgW/(m2 °C-mmkPamkW/m2

°Cm/s-m

GREEK SYMBOLS

a8

<f>XPayAHAXAT

e

Void fractionInter element gapSurface heat fluxLatent heat of evaporationDensitySurface tensionDimensionless mass fluxLocal subcooling, hs - hBundle quality imbalanceLocal subcooling, Ts - TAngle

SUBSCRIPTS

aavgbBLA

Actual valueAverage valueBubble, bulk, boilingBoiling length average

-mkW/m2

kJ/kgkg/m3

N/m-

kJ/kg-°Cdegrees

15

cCHFDOffgh,HhorngI, in1mmax.minnuP/B0

radssubUV

Critical, convectionCritical heat fluxDryoutSaturated liquid valueDifference between saturated vapour and saturated liquid valueHeatedHomogeneousSaturated vapourInside, inletLiquidMaximumMaximum

MinimumNon-uniform AFDPool boilingOutside, outletRadiationSaturation valueSubcoolingUniform (AFD)Vapour

ABBREVIATIONS

AFDBLACHF

Axial flux distributionBoiling length averageCritical heat flux

c/s Cross sectionDNBDOFBPDORFD

Departure from nucleate boilingDryoutFilm boilingPost-dryoutRadial flux distribution

3.1. INTRODUCTION

The objective of this chapter is to recommend a validated CHF prediction methodsuitable for the assessment of critical power at both normal operating conditions and accidentconditions in Advanced Water Cooled Reactors (AWCRs). This method can be implementedinto systems codes such as RELAP, CATHARE, CATHENA as well as subchannel codessuch as COBRA, ASSERT and ANTEO. The requirement of this prediction method has beendiscussed in more detail in previous CRP RCM meetings and expert meetings.

The two main applications for CHF predictions are:

(i) to set the operating power with a comfortable margin to avoid CHF occurrence.This margin to CHF can be expressed in terms of Minimum Critical Heat FluxRatio (MCHFR, ratio of CHF to local heat flux for the same pressure, mass fluxand quality), Minimum Critical Heat Flux Power Ratio (MCHFPR, the ratio ofpower at initial CHF occurrence to the operating power for the same pressure mass

16

flux and inlet temperature), or Minimum Critical Power Ratio (MCPR, the ratio ofreactor or fuel channel power at initial dryout occurrence to normal operatingpower for the same system, pressure and inlet temperature); the definition of theseratios is illustrated in Fig. 3.1. A detailed discussion has been provided byGroeneveld (1996). Most CHF prediction methods address this concern; theseprediction methods provide best-estimate values of the initial CHF occurrence in areactor core or fuel bundle.

q, CHF

NOP = fq.Phdl

MCHFR = CHF1/q1

Margin to CHF

CHF = f(X)

(a) Schematic representation of definition of MCHFR

q.CHF

N O P = Jq aPhdl

CP, = J<fc Ph dl

CHFPR = CP,/NOP

Xin X, X c X

( b) Schematic representation of definition of MCHFPR

FlowNOP NOP

Hydraulic curve^ .

Reactor flowat NOP

Reactor flowat CHF

1111

CHF, v(constant G)\

VX/1\

.1 \& 1 1| Margin to CHF |

J^- CP=f(G)(transformed fromCHF = fl;X) curve)

\

constant P, Tjn

Fixed pump curve

^.NOP CP2 CP, Power

(c) Schematic representation of definition of MCPR

FIG. 3.1. Definition of margins to CHF as defined by MCHFR, MCHFPR and MCPR.

17

(ii) to evaluate the thermalhydraulic and neutronic response to CHF occurrence in a reactorcore. This requires knowledge of how CHF spreads in the reactor core, which in turnrequires a best-estimate prediction of the average CHF for a section of the core and/orprediction of the variation of fuel surface area in dryout as a function of power.

This chapter is subdivided as follows: Section 3.2 discusses various CHF mechanisms,followed by a description of the CHF database in Section 3.3. In Section 3.4, CHF predictionmethodologies are reviewed for both tubes and bundle geometries, ranging from correlations,subchannel codes, analytical models and look up tables. In Section 3.5, the recommendedprediction methods for CHF in AWCRs are described, together with correction factors toaccount for various CHF separate effects. The assessment of the accuracy of therecommended prediction method when applied to steady state conditions is described inSection 3.6. Finally in Section 3.7 the prediction of CHF during transients such as LOCAs,flow and power transients are discussed.

The topic of CHF has been extensively researched during the past 30 years. Excellentreviews may be found in text books by Collier (1981), Tong (1965), Tong and Weisman(1996), Hewitt (1970) and Hetsroni (1982), and review articles by Bergles (1977), Tong(1972), Groeneveld and Snoek (1986), Weisman (1992) and Katto (1994).

3.2. CHF MECHANISMS

3.2.1. General

In forced convective boiling, the boiling crisis2 occurs when the heat flux is raised tosuch a high level that the heated surface can no longer support continuous liquid contact. Thisheat flux is usually referred to as the critical heat flux (CHF). It is characterized either by asudden rise in surface temperature caused by blanketing of the heated surface by a stablevapour layer, or by small surface temperature spikes corresponding to the appearance anddisappearance of dry patches. The CHF normally limits the amount of power transferred, bothin nuclear fuel bundles, and in conventional boilers. Failure of the heated surface may occuronce the CHF is exceeded. This is especially true for highly subcooled CHF conditions. Athigh flows and positive dryout qualities, the post-dryout heat transfer is reasonably effectivein keeping the heated surface temperatures at moderate levels, and operation in dryout may besustained safely for some time.

In flow boiling the CHF mechanisms depend on the flow regimes and phasedistributions, which in turn are controlled by pressure, mass flux and quality. For reactorconditions of interest, the flow quality generally has the strongest effect on CHF: the CHFdecreases rapidly with an increase in quality. The change in CHF with pressure, mass flux andquality is illustrated in the tables of Appendix II. The following sections describe the CHFmechanisms encountered at different qualities and flow conditions.

3.2.2. DNB (departure from nucleate boiling)

(i) Nucleation induced. This type of CHF is encountered at high subcooling (negative flowqualities) where heat is transferred very efficiently by nucleate boiling. Here the bubblesgrow and collapse at the wall; between the bubbles some convection will take place.

2 Other terms used to denote the boiling crisis: burnout, dryout, departure from nucleate boiling (DNB).

18

The CHF (or DNB) occurs at very high surface heat fluxes. It has been suggested[Collier (1981); Tong (1972)] that the CHF occurrence is due to the spreading of adrypatch following microlayer evaporation under a bubble and coalescence of adjacentbubbles although no definite proof of this is yet available. The occurrence of CHF hereonly depends on the local surface heat flux and flow conditions and is not affected bythe upstream heat flux distribution. The surface temperature excursion occurring onceCHF is exceeded is very rapid (fast dryout) and usually results in a failure of the heatedsurface.

(ii) Bubble clouding. In subcooled and saturated nucleate boiling (approximate qualityrange: from - 5 % to +5%) the number of bubbles generated depends on the heat flux andbulk temperature. The bubble population density near the heated surface increases withincreasing heat flux and a so-called bubble boundary layer [Tong (1965), Weismann(1983)] often forms a short distance away from the surface. If this layer is sufficientlythick it can impede the flow of coolant to the heated surface. This in turn leads to afurther increase in bubble population until the wall becomes so hot that a vapour patchforms over the heated surface. This type of boiling crisis is also characterized by a fastrise of the heated surface temperature (fast dryout). Physical failure of the heatedsurface frequently occurs under these conditions.

3.2.3. Helmholtz instability

In saturated pool boiling, the CHF is limited by the maximum vapour removal rate.Zuber's theory of CHF [as reported by Hsu and Graham (1976)] assumes the heated surface tobe covered by a rising vapour column with countercurrent liquid jets flowing downwards tocompensate for the removal of liquid by evaporation. Ultimately at very high heat flux levels(vapour removal rates) the relative velocity between liquid and vapour will be so high that anunstable flow situation is created, resulting in a CHF condition. This was recognized byKutateladze (1952) who based his hydrodynamic theory of the boiling crisis on thisinstability. A similar situation can be considered at very low flow rates or flow stagnationconditions. This type of CHF is accompanied by a rapid rise in surface temperature (fastdryout).

3.2.4. Annular film dryout

In the annular dispersed flow regime (high void fraction and mass flow) the liquid willbe in the form of a liquid film covering the walls and entrained droplets moving at a highervelocity in the core. Continuous thinning of the liquid film will take place due to thecombined effect of entrainment and evaporation. Near the dryout location the liquid filmbecomes very thin and due to the lack of roll waves (which normally occur at higher liquidfilm flow rates) entrainment is suppressed. If the net droplet deposition rate does not balancethe evaporation rate the liquid film must break down. The temperature rise accompanying thisfilm breakdown is usually moderate (stable dryout). The liquid film breakdown may bepromoted by one of the following mechanisms:

(i) Thermocapillary effect: If a significant amount of heat is transferred by conductionthrough the liquid film and the interface is wavy, the temperature of the liquid vapourinterface will have a maximum in the valley of the wave and large surface tensiongradients will be present. The surface tension gradients tend to draw liquid to areas ofhigh surface tension. Under influence of this "thermocapillary effect" the liquid film

19

will eventually break down in the valley of the wave. This mechanism is thought to beimportant at low flows and high qualities.

(ii) Nucleation induced film breakdown: Hewitt et al. (1963) noticed that nucleation andsurface evaporation could occur simultaneously in the annular flow regime. If the liquidfilm thickness is close to the maximum bubble size, then the bubble may rupture theliquid vapour interface and a momentary drypatch could occur. At high heat flux levelsthe liquid film may be prevented from rewetting this spot by the high drypatchtemperatures. This mechanism will only occur for local heat flux spikes, or a highlynon-uniform axial heat flux distribution.

3.2.5. Unstable or periodic dryout

The critical heat flux can be considerably reduced due to the hydrodynamiccharacteristics of the experimental equipment. Flow oscillations are frequently encountered inparallel channels, channels experiencing slug flow or in systems having a compressiblevolume near the inlet. During an oscillation the velocity at the wall is periodically sloweddown, thus permitting the boundary layer to become superheated which may lead to apremature formation of a drypatch. Unstable dryouts are accompanied by an oscillation insurface temperature.

3.2.6. Slow dryout

During a slow dryout the heated surface does not experience the usual dryouttemperature excursions; instead, a gradual increase in surface temperature with power isobserved. A slow dryout is usually encountered in flow regimes where the phases aredistributed homogeneously such as froth flow or highly dispersed annular flow at high massvelocities (>2.7 Mg m"2 s"1) and void fractions >80%. At these conditions liquid-wallinteraction is significant thus limiting the temperature rise at dryout. Calculations based oncooling by the vapour flow only indicate that post-CHF temperatures are below the minimumfilm boiling (Leidenfrost) temperature; hence depositing droplets may wet the surface thusincreasing the heat transfer coefficient.

3.3. CHF DATABASE

3.3.1. General

Since the CHF usually limits the power output in water cooled reactors, accurate valuesof CHF are required. The CHF has been measured extensively in simple geometries such asdirectly heated tubes. Such measurements have helped us to understand the CHF mechanisms.However to obtain accurate values of the CHF at reactor conditions of interest, experiments intest sections closely simulating the reactor fuel bundles are required. Such experiments arevery expensive; e.g., CHF tests in Canada alone have cost over 30 million dollars over thepast 20 years.

To reduce the expense and complexity of CHF testing of full-scale fuel bundles withhigh pressure steam-water, low-latent-heat modeling fluids have been used. Freons have beenused successfully in many heat transfer laboratories as a modeling fluid for simulating theCHF of water. Reliable CHF predictions for water can be made based on CHF measurementsin Freons at considerably lower pressures (e.g. 1.56 MPa in Freon-12 compared to 10 MPa inwater), temperatures (e.g. 50°C in Freon-12 compared to 300°C in water) and powers (e.g.

20

685 kW in Freon-12 compared to 10 MW in water), resulting in cost savings of around 80%compared to equivalent experiments in water.

In Sections 3.3.2 and Section 3.3.3, the available databases will be discussed. Particularattention is given to the CHF data in tubes as:

(i) the tube database is most complete and covers a much wider range of flow conditionsthan any other geometry, and

(ii) bundle geometries can be broken down into subchannels (see Section 3.4.4) which aretraditionally assumed to behave as tubes with correction factors applied to account forsubchannel specific effects.

TABLE 3.1. RANGES OF CONDITIONS COVERED BY VARIOUS SETS IN THE AECLDATABANK

References

AlekseevfKirillov, 1992]

Becker et al.T1962,1963]

Becker et al. [19651

Becker and Ling[19701

Becker et al. [19711

Bennett et al. [19651

Bergelson [19801

Bergles [19631

Bertoletti et al. [19641

Borodin and MacDonald[19841

Cheng et al. [19831

DeBortoIietal. [1958]*

Dell etal. [19691

Era etal. [19671

Griffel [19651

Griffel [1965]SRL data

Groeneveld 119851

Hassidetal. [1967]

Hewitt et al. [19651

Jens and Lottes [19511

Judd and Wilson [19671

Kirillov et al. [19841

Landislau [1978]

Lee and Obertelli[1963]*

Diameter(mm)

10.0

3.94-20.1

3.93-37.5

2.40-36.0

10.0

9.22-12.6

8.00

0.62-6.21

4.90-15.2

8.92

12.3

4.57-7.77

6.17

5.98

6.22-37.5

6.35-25.4

10.0

2.49-2.51

9.30

5.74

11.3

7.71-8.09

4.00

5.59-11.5

Length(m)

1.000-4.966

0.400-3.750

0.216-3.750

0.500-1.880

1.000^1.966

1.524-5.563

0.241-0.400

0.011-0.155

0.050-2.675

3.690-3.990

0.370-0.740

0.229-0.589

0.914-5.512

1.602-^1.800

0.610-1.972

0.597-1.105

1.000-2.000

1.590-2.391

0.229-3.048

0.625

1.829

0.990-6.000

0.200

0.216-2.007

Pressure(MPa)

9.80-19.6

0.22-8.97

1.13-9.91

3.05-7.10

3.00-20.0

6.61-7.48

0.17-3.08

0.14-0.59

4.88-9.88

8.20-10.4

0.10-0.69

6.90-13.8

6.90

6.78-7.05

3.45-10.3

0.41-8.41

7.90-20.0

2.94-6.09

0.10-0.21

3.45-13.8

6.86-13.9

6.37-18.1

0.42-1.00

4.14-11.0

Mass Flux(Mg.rrfV)

0.216-7.566

0.100-3.183

0.160-5.586

0.093-2.725

0.156-8.111

0.624-5.844

1.927-7.078

1.519-24.27

1.051-3.949

1.194-6.927

0.050-0.400

0.651-6.726

1.329^1.136

1.105-3.015

0.637-18.58

0.664-11.39

0.282-2.805

0.369-3.858

0.091-0.301

1.302-10.60

0.674-3.428

0.494^t.l54

0.884-5.504

0.678^1.421

Dryout Quality(-)

-0.866-0.944

-0.069-1.054

-0.005-0.993

0.207-0.903

-0.866-1.061

0.026-0.948

-0.295-0.090

-0.137-0.111

-0.083-0.774

0.105-0.570

0.187-1.227

0.052-0.768

0.144-0.779

0.374-0.952

-0.209-0.592

-0.253-0.484

-0.097-0.805

-0.035-0.838

0.161-1.083

-0.464—0.150

0.016-0.776

-0.494-0.981

-0.051—0.01

0.000-0.910

InletSubcooling

(kJ.kg"1)

57-1398

-50-1640

-16-2711

371-1065

26-1414

21-691

96-853

25-534

-28-769

31^156

42-210

0-874

79-365

-1211-565

45-1209

66-1224

622-1733

0-467

^11-383

279-1310

33-730

7-1537

104-638

9-690

Critical HeatFlux

(MW.m-!)

0.134-4.949

0.278-7.477

0.503-6.620

1.026-5.130

0.135-5.476

0.590-3.300

3.511-14.57

4.957^14.71

0.199-7.503

0.542-2.304

0.331-2.115

1.609-5.805

0.493-3.340

0.109-1.961

1.401-8.107

3.186-11.83

1.133-5.479

1.427-3.433

0.144-4.013

2.965-11.92

0.593-2.669

0.110-7.700

1.860^.631

1.104-8.107

No. ofData

1108

2664

1343

116

1496

201

336

117

386

465

150

54

82

163

402

85

118

238

442

48

49

2470

136

295

21

TABLE 3.1. (CONT.)

References

Lee R9651*

Lee fl9661

Leung et al. [1990]

Leung et al. [19901

Lowdermilk et al.[19581

Matzner[1963]*

Matzneretal. [1965]

Mayinger [19671

Menegus [19591***

Nguyen and Yin [19751

Rudzinski [1992[**

Smolin et al.[1962,19641

Smolin et al. [19791

Snoek [1988]

Swenson [19621*

Tapucu [1992]**

Thompson and Macbeth[19641+

Tong [19641

Yin et al. [19881

Zenkevich et al. [19691

Zenkevich et al. [19711

Zenkevich [19741++

Overall

Diameter(mm)

9.25-11.8

14.1^14.7

5.45

8.94

4.00-4.80

12.8

10.2

7.00

3.6-92.4

12.6

8.00

3.84-10.8

3.84-16.0

11.9

10.5

8.00

1.02-37.5

6.22-12.9

13.4

3.99-15.1

7.80-8.05

4.80-12.6

0.62-92.4

Length(m)

0.841-3.658

0.635-1.524

2.511

2.490

0.119-0.991

1.930

2.438^1.877

0.560-0.980

.

2.438^1.877

1.745

0.776-4.000

0.690-6.050

1.500

1.753-1.803

0.940-1.840

0.025-3.660

0.380-3.660

3.658

0.250-6.000

7.000-20.00

1.000-6.000

0.011-20.00

Pressure(MPa)

6.45-7.17

8.24-12.6

5.03-9.71

7.03-9.58

0.10

6.86

6.89

1.92-10.2

0.19-6.80

6.65-8.40

3.07-10.1

7.84-19.6

2.94-17.7

9.46-9.61

13.8

0.49-3.01

0.10-19.0

5.17-13.8

1.03-21.2

5.88-19.6

6.86-17.7

5.89-19.6

0.10-21.2

Mass Flux(Mg.rrfV1)

1.961-5.722

0.332-3.410

1.168-9.938

1.956-7.611

0.027-4.866

0.933-1.978

1.193-9.560

2.233-3.734

0.006-13.70

0.930-3.838

1.232-7.832

0.498-7.556

0.490-7.672

0.980-5.060

0.678-1.763

0.876^t.061

0.010-18.58

0.678-14.00

1.938-2.081

0.498-9.876

1.008-2.783

0.497-6.694

0.006-24.27

DryoutQuality

(-)

-0.002-0.462

-0.110-0.780

0.210-0.578

0.106-0.414

0.030-1.236

0.075-0.592

0.008-0.693

0.098-0.405

-0.21-0.000

0.216-0.738

0.038-0.727

-0.132-0.795

-0.136-0.789

0.034-0.543

0.178-0.502

0.164-0.779

-0.820-1.577

0.002-0.502

0.075-0.431

-1.652-0.964

0.262-0.876

-0.221-0.969

-1.652-1.577

InletSubcooling(kJ.kg"1)

12-584

60-451

6-316

13-229

317-331

54-947

48-1183

-239-314

0-600

52^113

19-495

5-1329

4-1362

^81-356

41-565

31-809

0-1659

5-1060

0-493

2-1644

18-1549

5-1381

-1211-2711

Critical HeatFlux (MW.rrf

2)

1.000-4.306

0.871-3.738

0.656-3.058

0.904-2.328

0.167-9.525

1.686-3.372

0.643^1.041

0.924-5.618

1.56-11.70

0.677-2.024

1.388^4.512

0.230-5.652

0.245-5.626

0.423-3.037

0.587-1.063

1.193^1.680

0.113-21.42

0.587-6.139

0.583-1.864

0.136-14.76

0.470-1.283

0.230-4.740

0.109-44.71

No. ofData

274

435

66

39

113

25

99

128

129

56

106

666

3009

33

25

68

2356

266

287

5641

392

840

28 017

* These data have already been included in Thompson and Macbeth's compilation.

** These data are used for validation only.

*** These data have not been used since the heated-length values of channels were not provided.

+ Duplicated data of Becker (1963) have been removed.

++ Duplicated data of Zenkevich et al. (1969) have been removed.

3.3.2. Tube database

Table 3.1 lists a summary of data collected jointly by AECL and IPPE, and used in thedevelopment of the CHF prediction methods, including the CHF look up table [Groeneveld etal. (1996)]. Figure 3.2(a) shows that the conditions covered, although extensive, do leaveopen several gaps in the data. The non-proprietary part of the CHF databank, containing over30 000 CHF data, obtained in directly heated tubes, has recently been deposited in theInternational Nuclear Safety Center Database at Argonne National Laboratory, described inAnnex A.

22

u-

3

3000020000

10000 -

1000 -

100

10000

1000

•0.5 0 0.5

DRYOUT QUALITY

100 -

10 -

• WPB

*1

1 1

*KNNH|IE3|HH

-0.5 0 0.5DRYOUT QUALITY

0.1 -

0.01

0.001 -

0.0001

-0.5 0 0.5

DRYOUT QUAUTY

FIG. 3.2 (a). Ranges of test conditions for the combined AECL-IPPE tube-CHF data bank.

The parameters controlling the CHF in tubes (for steady state conditions, and a uniformheat flux distributions) are:

(i) Primary: thermodynamic quality, mass velocity, pressure and diameter(ii) Secondary: heated length, surface roughness, conductivity and tube wall thickness.

As the secondary parameters usually have a insignificant effect on CHF for conditionsof interest, they may be ignored.

23

3.3.3. Bundle database

A large number of CHF experiments in bundles have been performed ranging fromcrude simulations of fuel bundles (e.g. annuli or 3-rod bundles) to full-scale simulations ofactual fuel bundles. The following parameters have been found important in controlling CHFin fuel bundles:

(i) Flow parameters (pressure, mass flow, and quality). This includes cross section averageflow conditions (this is usually reported) and distribution of flow parameters (i.e.distribution of enthalpy and flow across a bundle as evaluated by subchannel codes orother empirical means),

(ii) Bundle geometric parameters (number of rods, rod spacing, unheated flow boundaryand heated length),

(iii) Rod bundle spacing devices and CHF enhancement devices (grids, appendages andmixing vanes) and their axial spacing,

(iv) Heat flux distribution (axial and radial heat flux distributions, and flux tilt acrosselements).

A number of surveys of bundle CHF data have been made. However because of theproprietary nature of bundle CHF data, these reviews are usually restricted as most bundledata (especially the recent ones) are unavailable or can only be obtained under specialagreements. An earlier paper by Hughes (1974) provides a compilation of bundle CHF datasources. A more recent example of the ranges of conditions covered by specific bundle datasets is given in Figure 3.2(b) for the WWER bundle geometry [Macek (1998)], as can be seenthe coverage is reasonably wide. However, as most bundle experiments still use fixedthermocouples, the reliability of the experimental CHF data as representing the initialoccurrence of CHF may well be too optimistic (i.e. overpredicts the CHF). The moreadvanced sliding thermocouple technique (Schenk, 1990) has demonstrated that largedifferences (up to 20%) in bundle CHF can occur around the circumference of the mostcritical rod at the axial location corresponding to the initial CHF.

3.4. CHF PREDICTION METHODOLOGY

3.4.1. General

Because of the many possible fuel bundle geometric shapes, a wide range of possible flowconditions and the various flux distributions for AWCRs, it is impossible to predict the CHFfor all cases with a single CHF prediction method and a reasonable degree of accuracy. Thecomplexity of predicting the CHF in a nuclear fuel bundle may be best understood by firstconsidering the prediction of CHF of a simplest experimental setup; a uniformly heated tubecooled internally by a fluid flowing at a steady rate vertically upwards. Here the CHF is afunction of the following independent variables:

CHF = f(LH,De,G,AHin,P,E) (3.1)

where E takes into account the effect of the heated surface, i.e. surface roughness, thermalconductivity and wall thickness.

24

WWER CHF DATA BANK

250

-0.3

-0.6Inlet Quality

2 0 1 8 1 6

Pressure(MPa)

I

250

200

150

100

3500Pressure(Mpa)

4500

15002500 Mass Flow

(kg/m2-s)

§45003500

5001500

2500 M ass Flow(kg/m2-s)

FIG. 3.2(b). Ranges of test conditions covered by the WWER CHF databank.

Despite the simplicity of the experimental setup, over 400 correlations for CHF in tubesare currently in existence. The present proliferation of correlations illustrates the complexstate-of-the-art in predicting the CHF phenomenon even for a simple geometry at steady-stateflow conditions. The complexity in predicting the CHF increases significantly for fuel bundlegeometries during severe transients, when additional parameters characterizing the transientare required. This demonstrates the need to categorize the important CHF-controllingparameters and their ranges of interest. A methodology to categorize these parameters forthermalhydraulic parameters of interest has been proposed in Annex B.

25

In the following sections, analytical CHF prediction methods are discussed in Section3.4.2, followed by empirical prediction methods in Section 3.4.3 which include empiricalcorrelations as well as the CHF look up table. In Section 3.4.4 the application of CHFprediction methods to bundle geometries is described.

3.4.2. Analytical models

Analytical CHF models are based on the physical mechanisms and satisfy the conservationequations. They generally require a two-fluid model approach but occasionally must use athree-field approach (e.g. dispersed annular flow). Although the models have been improvedsignificantly and usually predict the correct asymptotic trends, the evaluation process iscomplex and time-consuming. Furthermore, because of our limited understanding of themechanisms involved, and the lack in measurements of interfacial parameters, the models arestill less accurate than empirical correlations over the range of their database. An excellentreview of the analytical CHF models has been presented by Weisman (1992). The mostcommon CHF models that have met with some success are:

Annular film dryout model. This model is based on a mass balance on the liquid film inannular flow, and postulates that CHF corresponds to the depletion of the liquid film.Equations for droplet entrainment and deposition have been proposed. The model provides areasonable predictions of CHF for the annular flow at medium to high pressures and flowsand void fractions exceeding 50% [Hewitt and Hall-Taylor (1970)].

Bubbly layer model. This model postulates that CHF occurrence in the lower quality regimefirst occurs when the bubble layer covering the heated surface, becomes so thick and saturatedwith bubbles that liquid mixing between the heated surface and the cooler core liquidbecomes insufficient. This model as proposed by Weisman and Pei (1983); and Ying andWeisman (1986) appear to predict the CHF with reasonable accuracy at high pressure, highflow and low quality conditions.

Helmholtz instability model. In pool boiling, the boiling crisis is reached when the flow ofvapour leaving the heated surface is so large that it prevents a sufficient amount of liquid fromreaching the surface to maintain the heated surface in the wet condition. The phenomenon thatlimits the inflow of liquid is the Helmholtz instability, which occurs when a counter-currentflow of vapour and liquid becomes unstable. Zuber (1959) and Kutateladze (1952) havederived equations for the CHF based on the Helmholtz instability theory- their predictionsagree with the CHF values measured in pool boiling systems. For very low flows, a modified

version of this model as expressed by the Zuber-Griffith CHF correlation \CHFPB(l - a))

appears reasonable for up- and down flow at flows less than 0.1 Mg.m^.s"1 and a <0.8.However for a > 0.8 this correlation significantly underpredicts the CHF. At these conditionsthe \ — a correction is not recommended [Griffith et al. (1977)].

3.4.3. Empirical CHF prediction methods

Empirical CHF prediction methods may be subdivided into those based on inletconditions and those based on local cross-sectional average (CSA) conditions.

26

3.4.3.1. Inlet-conditions-type prediction methods

These prediction methods are all in the form of empirical correlations, based on CSAinlet conditions (P, G, Tjn or AH in) and usually assume the "overall power" hypothesis. Thishypothesis states that, for a given geometry and inlet conditions, the critical power NDo(power corresponding to the first occurrence of CHF for that geometry) is independent ofaxial or radial heat flux distribution or

NDO = f(Pin,Gin,Tin,c/ S,LH) (3-2)

This will permit the use of CHF correlations derived from uniformly heated bundle data forthe prediction of dryout power in non-uniformly heated bundles of identical geometry (i.e.identical cross section and heated length).

This technique is a reasonable one for obtaining a first estimate of dryout power; itgives reasonable estimate of dryout power in the annular flow regime for symmetric fluxprofiles and form factors ( qmax/qavg) close to unity. However it is not recommended for formfactors significantly different from unity.

This approach can also be used to predict the critical power of fuel channels with a fixedcross section, heated length, axial flux distribution (AFD) and radial flux distribution (RFD),irrespective of the form factor. If the experimental AFD and RFD represent the worst fluxshapes from a CHF point of view, then the empirical correlations can be used for lower-boundpredictions.

The Inlet-Conditions-Method cannot be used for predicting the location and magnitude of theCHF except when CHF initially occurs at the downstream end.

3.4.3.2. Local-conditions-type prediction methods

This type of prediction methods follow the local-conditions hypothesis which states thatthe local CHF is dependent only on the local conditions and not on upstream history. Inprinciple, the local conditions hypothesis is sound if it is based on the true local conditions(which must include radial distribution of void, liquid and vapour velocity, liquid temperatureand turbulent velocity fluctuation near the wall). Hence ideally

CHF =f(P,G,XD0,c/s) (3.3)

In practice only the local cross section average pressure, flow and quality are knownand the assumption

CHF = f(a.(r),Ti(r),Ui(r),Uy(r),Uv(r),'",P,(c/s)) (3.4)

that is often made. The local conditions approach, or variations thereof, is probably the mostcommon method for predicting CHF. This form is more convenient than Eq. 3.1 since itdepends on fewer parameters and permits the prediction of the location of CHF. Onecomplication with this method is its ability (or lack of it) to account for the effect of AFD.

27

Two methods are frequently used to account for the effect of a non-uniform AFD on CHF: theboiling-length-average (BLA) approach, and the F-factor approach [Tong (1965, 1972),Kirillov and Yushenko (1996)]. The F-factor approach tends to modify CHF correlationsdesigned for uniform heating, while in the boiling- length-average (or BLA) heat fluxapproach the heat flux distribution is modified. Lahey and Moody (1977) have shown that thetwo techniques are similar, yield similar answers and are reasonably successful in predictingthe CHF for various non-uniform AFDs. Section 3.5.3.6 will describe the recommendedapproach for correcting for the effect of AFD.

Local conditions based empirical correlations. The large majority of the CHF predictionmethods proposed are of this type. It is conservatively estimated that there are over400 empirical correlations of this type proposed in the literature for directly heated tubes.Their main disadvantage is their limited range of application.

CHF table look up method. Since most empirical correlations and analytical models have alimited range of application, the need for a more general technique is obvious. As a basis ofthe generalized technique the local conditions hypothesis was used for the reasons given inSection 3.4.3.2 The initial attempt to construct a standard table of CHF values for a givengeometry was made by Doroshchuk (1975), using a limited database of 5000 data. The CHFtable approach, which is basically a normalized databank, has been continued at CENG-Grenoble, University of Ottawa, IPPE, and Chalk River using a much more extensivedatabase (30 000 data). The recently completed International CHF table look up method[Groeneveld et al. (1996)] provides CHF values for water cooled tubes, at discrete values ofpressure (P), mass flux (G), and quality (X), covering the ranges of 0.1-20 MPa, 0-7500kg-irf^.s"1 (zero flow refers to pool-boiling conditions) and -50 to 100% vapour quality(negative qualities refer to subcooled conditions). Linear interpolation between table values isused for determining CHF. Extrapolation is usually not needed as the table covers a range ofconditions much wider than any other prediction method. The CHF look up table and itsderivation are presented in Appendix II.

Compared to other available prediction methods, the tabular approach has the followingadvantages: (i) greater accuracy, (ii) wider range of application, (iii) correct asymptotic trend(iv) requires less computing time and (v) can be easily updated if additional data becomeavailable. Although tabular techniques were initially developed for tubular geometries, andhave been successfully used in subchannel codes, their greatest potential for application is inpredicting the consequences of postulated Loss of coolant-Accidents (LOCA). To apply thetables to transient heat transfer in bundles requires the use of adjustment factors to correct forgeometry, flux shape, and possibly transient effects. Here the advantages of the tabulartechnique (wide range of application, greater accuracy and more efficient in computing) areparticularly important to the user.

Although promising, the look up table approach has certain disadvantages such as (i) itis a purely empirical prediction method and hence it does not reflect any of the physics, and(ii) could introduce erroneous trends if the underlying database is subject to experimentalerrors. Despite these reservations, the look up table approach is currently considered to bemore accurate than other prediction methods for the CHF for most situations of interest.

3.4.4. Application to bundle geometries

Prediction of the critical power in untested fuel bundle geometries remains unreliable. Effectsof flux distribution, grid spacers and bundle array dimensions are not well understood. The

28

next two approaches are commonly used, while the third one has more recently been proposedand an alternative.

(1) Empirical approach: The empirical CHF predictions methods use cross-sectionalaverage conditions to predict the CHF or critical power and are designed for tubes orbundles. For bundles for which experimental data can be obtained (using an electricallyheated fuel bundle simulator, having a fixed axial and radial flux distribution) a variantof the following methodology is frequently employed:

— obtain sufficient data for deriving an empirical CHF correlation for conditions ofprimary interest;

— extrapolate the empirical correlations (which are usually based on a given axialand radial flux distribution) to other flux distributions of interest using the changein CHF as predicted by (i) subchannel codes (see below) or (ii) empirical methodsto account for changes in the upstream flux shape (as described in the previoussection;

— similarly extrapolate to other conditions not tested in the full scale simulation testsusing trends observed in simpler geometries, or as predicted by subchannel codes.

(2) Subchannel approach: The subchannel approach is basically different from theempirical approach as it predicts the axial variation in flow and enthalpy for eachsubchannel. It is particularly useful for bundles for which no direct experimental dataare available. The following methodology is normally followed for bundleCHF prediction based on the subchannel analysis approach:

— employ subchannel codes to predict the flow and enthalpy predictions across thebundle

— employ subchannel CHF models (basically modified tube CHF predictionmethods) for predicting the initial CHF occurrence anywhere in the bundle.

Two definitions of subchannels are currently in use. The conventional approach definessubchannel boundaries by lines between rod centre and is used in subchannel codessuch as ASSERT [Carver et al. (1993)], COBRA [Owen 1971)]; ANTEO [Cervolani(1995)] or HAMBO [Bowring (1967)]. The rod centered approach defines subchannelboundaries by lines of zero stress between rods and is used primarily to predict CHF inthe annular flow regime [using Hewitt and Hall-Taylor's (1970)] annular flow model oran equivalent CHF correlation. A thorough review of subchannel prediction methods ispresented by Weisman (1975).

(3) Enthalpy imbalance approach. An alternative to the subchannel approach has beendescribed by McPherson (1971) (applied to various bundle geometries contained inpressure tubes), Bobkov (1995, 1997) (applied to excentric annuli and bundlesubchannels), and Leung (1997) (applied to 37 element bundle CHF predictions). Thisapproach, which was recently reviewed by Kirillov et al. (1996b), considers thedifferences in enthalpy rise rates among bundle subchannels, and based on this defines aquality imbalance, AX for that bundle. This quality imbalance (a variation of this is theenthalpy imbalance number specified by McPherson(1971) ) represents the difference inqualities between the cross section average bundle quality and the maximum bundlesubchannel quality for a given cross-section. The difficulty is in predicting theAX value; no general expression for the enthalpy imbalance is yet available but ad hocexpressions for specific bundle geometries have been proposed. In general,

29

AH =f\51 d, AXmaxJ where 81 d is the element gap/diameter ratio, and AXmaxis the

maximum quality imbalance, which depends on the difference between the subchannelenthalpy of the critical subchannel for zero cross flow and the cross-sectional averageenthalpy. Once a general expression for AX is found (this may well require a fit of arandomly-generated database using a subchannel code) the bundle CHF can be obtainedfrom the tube CHF look up table [Groeneveld et al. (1996)] for the critical subchannel,hi equation form this bundle CHF methodology is as follows:

CHF bundle (P, G, X) = CHF tube (P, G, Xo). K,.K$.K4'K5- (3.5)

where:

Xo = X + AXand Ki, K3, etc. are correction factors described in Section 3.5.3. Theimpact of flow imbalance on CHF is usually assumed to be negligible or assumed to beincorporated in AX.

3.5. RECOMMENDED CHF PREDICTION METHOD FOR ADVANCEDWATER COOLED REACTORS

To provide precise predictions of CHF for advanced water cooled reactors fuel bundlesis a nearly impossible task as advanced water cooled reactors designs include a variety ofbundle cross sections as well as element spacer designs. This section therefore willrecommend a generic approach of predicting CHF in untested bundle geometries. The basis ofalmost any generic bundle prediction method is a tube CHF prediction method, because (i) theparametric trends with P, G, and X are similar in tubes and in bundles, and (ii) tube CHFprediction methods are generally used in subchannel codes to predict the CHF in bundles.

hi this section we will first discuss the recommended tube CHF prediction method andwill subsequently describe how this method can be used for predicting the CHF in bundlegeometries.

3.5.1. Tubes

The recommended CHF prediction is the recently published CHF look up table for tube[Groeneveld et al. (1996)] which was based on cooperation of several international groups,notably AECL in Canada and IPPE in Russia. This CHF prediction method is a slightmodification from previous tables [Groeneveld et al. (1993)], has been validatedindependently by others as described in Section 3.6.1 and has resulted into better CHFpredictions compared to other existing CHF correlations, both in accuracy and range ofvalidity. Groeneveld et al. (1996) have presented a complete description of the new tableincluding its derivation, and accuracy with respect to the world database, and a comparisonwith other widely used CHF prediction methods.

30

3.5.2. Rod bundles

The tube CHF look up [Groeneveld et al. (1996), see also Appendix II] needs to beconverted into a prediction method for bundle geometries. To do this, two approaches may beused:(1) Subchannel based approach, as described in Section 3.4.4 item 2, and(2) Cross-sectional average bundle approach as described in Section 3.4.4 item 3.

Ideally a subchannel code should be used to predict the CHF for bundle geometry.Several subchannel codes are currently in existence [see review article by Weisman (1975) formore details] but their validation tends to be limited to a narrow range of bundle geometriesand flow conditions for which their constitutive relations have been tuned to agree with theexperimental database. With time this limitation is expected to be resolved as moreappropriate constitutive relations are being derived and the robustness of the codes iscontinuously being improved.

In both of the above approaches the CHF needs to be modified to account for bundlespecific or subchannel specific effects. The following correction factor methodology isadopted to evaluate the bundle or subchannel CHF:

CHFbundle = CHFtablexK1xK2xKsxK4xK5xK6xK7xK8 (3.6)

where

is cross section average value of the heat flux at which the CHF first occurs at thecross-section, CHFtabie is the CHF value for a tube as found in the look up table for the samecross-sectional average values of P and G, and Ki to Kg are correction factors to account forspecific bundle effects. Note that the form of this equation implies that all correction factorsare independent. Many factors are somewhat interdependent, but these interdependencies areassumed to be second order effects unless indicated otherwise in the following sections. Thecorrection factors are described in Section 3.5.3.

3.5.3. Correction factors

Table 3.2 lists the most common bundle specific or subchannel specific effects whichare expected to affect the CHF. As these effects are not reflected by the database for the tubelook up table, correction factors have been derived. Table 3.3 lists approximate relationshipsfor the correction factors. The sections below elaborate on the more important correctionfactors.

3.5.3.1. Diameter

Experiments in tubes have shown a strong effect of tube diameter on CHF. A number ofinvestigators have discussed this effect. Recently Wong (1996) has made a thoroughsystematic study of this effect and concluded that the original approach using the equation:

31

K, =CHFD

CHF' D=8mm 8

(3.7)

where

n is between -1/3 and -1/2 and appears to be valid for the majority of the data. Slightimprovements could be made by assuming n = f (P, G, X) but the improvements were minorand limited to the range of experimental data on which the new n-function was based. Chengand Erbacher (1997) have recently performed additional experiments in Freon and noticedthat the change in CHF with diameter according to Eq. 3.7 appears to valid (with n —1/2) fordiameters equal or smaller than 8 mm but no effect of diameter (or a very small effect) onCHF was observed for diameters greater than 8 mm. Note that Cheng's data were obtainedprimarily at subcooled or low quality conditions. Kirillov and Yushenka (1996) also noteddisagreements in the diameter effect on CHF for negative qualities but the general agreementfor D 8mm with n between -1/3 and -1/2. Despite this disagreement, the recommendation byGroeneveld (1996) using n = -1/2 , and subsequently confirmed by Wong (1996), appears tobe a simple compromise which agrees reasonably with the bulk of the available data.

Although Ki was derived empirically from tube data, the diameter correction factor hasbeen applied directly to subchannels as well where the Dhy is used. Because of lack of data onCHF in various sizes of subchannels, the validity of the approach as applied to subchannelshas not been confirmed.

TABLE 3.2. CHF SEPARATE EFFECTS ENCOUNTERED IN FUEL BUNDLES

GENERAL

Global Flow Area Effects:

Subchannel Effects

Length Effects

Spacers/Bundle Appendages Effects

Flow Orientation Effects

Axial/Radial Flux Distribution Effects

Flow Parameter Effects

Transient Effects

Effect of Fluid Type

DETAILS OF SEPARATE EFFECTS

- n-rod bundle where n » 3 and all subchannels identical except corners orcold-wall-adjacent subchannels (e.g., square or triangular arrays ofsubchannels)- n-rods where n » 3 and adjacent subchannels are generally not equal (e.g. 37-rod bundle geometries inside round tubes)

- Subchannel size/shape (similarity to tube)- Cold wall effect- Distorted subchannels (due to bowing, clad strain, pressure tube creep)- Misaligned bundles (CANDU case)

Similar to appendage effects

- mixing grids- attached spacers/ bearing pads/ endplates (CANDU)

- Vertically upward- Vertically downward- Horizontal

- Axial flux distribution (flux peaking/global flux distribution)- Radial Flux Distribution (global RFD effect, cold wall effect, flux tilt acrossan element)

- mass flow (incl. zero flow or pool boiling / flow stagnation case)

- Power/Flow/Pressure transients- Combined transients

- Light water- Heavy water- Modelling fluids (Freons) in conjunction with a CHF Fluid-to-fluid modellingtechnique

32

TABLE 3.3. SUMMARY OF CORRECTION FACTORS APPLICABLE TO THE CHFLOOK-UP TABLE

FACTOR FORM COMMENTS

Kj, Subchannel or Tube- For 2 < Dh < 25 m m :

Diameter Cross-Section _ m n n R i -.1/2Geometry Factor K l ~ (0-008/D»y)

For Dhy > 25 mm:K, = 0.57

Includes the observed diameter effect onCHF. This effect is slightly qualitydependent.

K2, Bundle-Geometry FactorK2 = mm[l,(0.5 + 2S/d)exp(-0.5x

1/3JThis is a tentative expression, an empiricallyderived factor is preferred. K2 is also aweak function ofP, G andX.

A = 1.5 KL05(G/1000 f2

B = 0.10

This factor has been validated over a limitedrange of spacer geometries.

K4, Heated-Length Factor For L I D hy > 5 :

K4 =

ah =

exp(2afl)]

Inclusion of ah correctly predicts thediminishing length effect at subcooledconditions.

, Axial Flux Distribution For X < 0 : K5= 1.0Factor For X > 0: Ks =

Tong's F-factor method (1972)may also be used within narrow ranges ofconditions.

K6, Radial or Circumferential For X > 0: K6 = q(z)avg/ q(z)max

Flux Distribution Factor For X < 0: Ke = 1.0Tentative recommendation only and to beused with well-balanced bundle. May beused for estimating the effect of flux tiltsacross elements. Otherwise method of Yin(1991) is recommended.

K7, Flow-Orientation FactorK? = l-exp(-(Ti/3rj)

This equation was developed by Wong andGroeneveld (1990) based on a balance ofturbulent and gravitational forces. The voidfraction is evaluated with the correlation ofPremolietal. (1970).

-a) gDhyPf(pf-pg)d0.5

fi, is the friction factor of the channel

Kg, Vertical Low-Flow Factor G<-400 kg.m'2.s"! or X « 0 :

Ks = 1-400 <G < 0 kg.m'2.s'': Use linear interpolation betweentable value for upward flow and value predicted from

CHF = CHFG=o,x=o (1 - ahom) C,

For ah(0.S :

Cl = 1.0

c, =0.8 + 0.2 pf/ p.

+ O-CChom) Pf/ P,

Minus sign refers to downward flow.G=0, X=0 refers to pool boiling.

3.5.3.2. Bundle

Prediction of the critical power in untested fuel bundle geometries such as many of theproposed advanced water cooled reactor fuel bundles has a higher uncertainty especially if theflux distribution, grid spacer shape and bundle array dimensions are different from thosetested previously. The most reliable approach aside from ad hoc testing, is to employ asubchannel analysis as described in Section 3.4.5 (at a limited range of conditions of interest)to valuate the bundle CHF analytically, and to derive a bundle correction factor expressed as

33

for use inside a systems code. In the absence of any test data Eq. 3.8is the simplest one available and follows the correct asymptotic trends.

K2 = Min/7.0,(0.5 + 2S/d)exp(-0.5x1/3)] (3-8)

Note that further work in this area is required and that the approach based on theenthalpy imbalance as embodied in Equation 3.5 [Kirillov (1996b)] is the most promising

K^_CHFtube,ab!e(P,G,X + AX) (3.9)

CHFtube-tab!e(P>G,X)

one. This would then simply change the bundle correction factor to the form of Equation 3.9,but requires an empirical expression for AX (see also Section 3.4.4 item 3 and the referencesof Appendix III for further details).

3.5.3.3. Spacer

A number of researchers have investigated the effect of spacing devices on CHF orcritical power. Figure 3.3 shows the various types of spacers used in these studies. In generala significant increase in local CHF was observed just downstream of the spacers. Thisincrease usually decays slowly with distance downstream as illustrated in Fig. 3.4. Theincrease is primarily due to the higher turbulence level of the two-phase flow, which canstrongly suppress the occurrence of CHF and the improved intersubchannel mixing. Inexperiments on CANDU fuel bundles, this increase in CHF is most pronounced justdownstream of spacer planes and bundle junctions, where increases in local CHF of over150% have been observed.

The strong CHF-enhancement effect has been confirmed by others, e.g. Tong (1972). Ithas been expressed by the enhancement factor:

(3.10)

where

A = 1.5 K0'5 (0.001 G)02 (K is the pressure loss coefficient of the spacing device) and B = 0.1were proposed by Groeneveld (1989).

Subsequent studies at CRL and IPPE have noted that using the pressure loss coefficientitself may not be sufficient because of the apparent insensitivity of the CHF enhancement tostreamlining of the grid spacer, and an expression using the flow blockage area may be moreappropriate [Kirillov (1997)]. Note that these values will still be approximations as the shapeof the spacer and the element gap are also important parameters.

In bundles the length factor is no longer needed as this effect is already incorporated inthe spacer correction factor (hence K4 = 1).

34

WffJU

TTi

U

ffll

HONEYCOMBTYPE SPACER

EGG CRATE

TYPE SPACER

FERRULE TYPE CANDU TYPE HELICAL PLATE TYPE

SPACER SPACER &WEAR PADS WIRE WRAP SPACER

u13uo

F/G. 3.3. Different types of rod spacing devices.

CHF for bundle with rod spacing devices

Rod spacing devices

FIG. 3.4. Exponential decaying CHF enhancement downstream of a spacing device.

35

3.5.3.4. Axial flux distribution

Many experimenters have studied the effect of axial flux distribution (AFD) on criticalpower [e.g. Collier (1981); Tong (1972); Todreas and Rohsenow (1965); Groeneveld (1975),Kirillov (1997)]. The common observation in all these studies is that the AFD has a strongeffect on the CHF in the annular flow regime but this effect tends to disappear altogether forthe DNB-type of CHF. The effect of AFD on CHF can be accounted for by using the boiling-length-average (BLA) heat flux instead of the local heat flux. The BLA heat flux is definedas:

( 3 ' n )

T _ GHfsDhe (3-12)4 X DO <} BLA

where the BLA heat flux has been incorporated in the AFD correction factor K5 defined as:

K5=P l o c a l /pB L A for X> 0.0K5 = 1.0 for X< 0.0

3.5.3.5. Radial flux distribution

The ideal tool for evaluating the RFD effect on dryout power or CHF is a reliablesubchannel code. Subchannel codes can also consider the effect of flux tilt across elements byaccounting for the different heat flux values around the circumference of a fuel pin. Howeversubchannel codes are complex, expensive to run and have usually a limited range validity.Hence a more empirical approach is often preferred. The RFD correction factor falls betweentwo extreme values: (i) for open bundles where the subchannel flow and enthalpy imbalanceis small, and the maximum heat flux controls the initial occurrence of CHF. For such a caseK2 is close to unity (or AX is close to zero) and K6 is approximately equal to qavg(z)/qmax (z),where qmax represents the maximum heat flux for the subchannel and qavg is the cross sectionaverage heat flux, and (ii) for very tight bundles (8/D < 0.1) where the communicationbetween subchannels is severely hampered and K$ (if used in conjunction with K2 asexpressed by Equation 3.8) depends also on the subchannel and flow imbalance. For this casea technique for obtaining a K6 value based on RFD was proposed by Yin et al. (1991), but thisstill requires knowledge of the RFD corresponding to simultaneous CHF occurrence acrossthe bundle (this could possibly be obtained from subchannel codes). However if the K2 valueis obtained from Equation 3.9 (based on AX), no further correction for K^ beyond the qaVg/qmaxvalue is required.

3.5.3.6. Flow orientation

The effect of orientation is important for CANDU reactors, where the fuel channels areoriented horizontally, and for conventional boilers, where many of the boiler tubes areinclined. The approach taken is to correct the vertical flow CHF by a penalty factor to accountfor the deleterious effects of flow stratification. For fully stratified flow, the CHF = 0 (i.e.K7=0), while for a flow regime unaffected by flow stratification, CHFver = CHFhor orK7= 1.0. Using a mechanistically based flow regime map [e.g. Taitel and Dukler (1975)]

36

permits the determination of the mass flux threshold Gi, corresponding to the onset ofcomplete flow stratification (where liquid no longer touches the top of the channel, i.e. theCHF = 0) and the mass flux threshold G2, corresponding to the first noticeable effect ofstratification on the phase distribution. Table 3.3 shows a simple expression for the correctionfactor K7 having the correct asymptotic trends. A more rigorous expression for the flowstratification correction factor was derived by Wong et al. (1990), based on both the flowregime and a force balance on the phases. Their expression for the correction factor K7resulted in accurate predictions of the CHF in horizontal flow in various fluids over a widerange of conditions.

3.6. ASSESSMENT OF ACCURACY OF THE RECOMMENDEDPREDICTION METHODS

3.6.1. CHF look up table assessment

The CHF look up table described in Section 3.5.1 and presented in Appendix II as wellas earlier versions of the look up table have been assessed extensively. The most recentassessment was made at KAIST, Korea, by Baek et al. (1996) using their database. Theirassessment confirms the error statistics reported by Groeneveld et al. (1996), and confirms theimproved prediction capability compared with the 1986 AECL-University of Ontario (UO)Look-up Table [Groeneveld et al. (1986)]. In addition the distribution of CHF data and theerror distribution of the CHF look up table as a function of pressure, flow and qualityintervals are given in Table 3.4.

Earlier assessments by Smith (1986) and Weaver (1995) indicated the suitability of thetable look up approach and has resulted in its use in systems codes such as CATHARE[Bestion (1990)], THERMOHYDRAULIK [Ulrych (1993)], ASSERT [Kiteley (1991),Carver (1993)] and RELAP [Weaver (1995)]. Assessments were also made by Aksan etal.(1995) and Faluomi and Aksan (1997) where an earlier version of the look up table (CHF-UO table) was compared to other leading CHF correlations and the impact of the differencesin CHF predictions on nuclear plant transients of interest was assessed.

3.6.2. Accuracy of bundle CHF prediction methods

As indicated in the previous sections, the prediction of bundle CHF is much moredifficult than the tube-based predictions. In addition the database has a much greateruncertainty because of the relatively crude fixed thermocouple technique for detecting initialCHF occurrence. Prediction accuracy for a well tested bundle geometry is usually quitereasonable (frequently within 5% at a 2cr confidence level for a given inlet conditions) butthis is due to the fine-tuning of the correlation/subchannel code with empirically derivedcoefficients. For new AWCR geometries the accuracy is significantly reduced and could wellbe greater than 10% at 2<x.

An independent assessment was made by Chun et al. (1997) of the CHF look up table asa prediction method for bundles in conjunction with a subchannel code (COBRA-TV-1). Theycompared the look up table with six leading CHF prediction methods [Biasi et al. (1967)];W-3, EPRI-1 as referred to by Chun et al. (1997); Katto and Ohno (1984); and two CHFmodels [Weisman and Ying (1985); Lin et al. (1989)]. They concluded that, for AWCRdesign applications, in the absence of a database, the look up table has the greatest potential asa general predictor for CHF in rod bundles. The CHF look up table has also been used andassessed in conjunction with the ASSERT subchannel code [Carver (1993,1995)] and theANTEO subchannel code [Cervolani (1995)].

37

For specific bundle geometries a bundle specific look up table can be used. Goodsuccess has been reported with the recent IPPE bundle CHF look up table for WWERgeometries. This table is reproduced in Appendix III where a brief description of its potentialuse is also provided.

TABLE 3.4. ERROR-DISTRIBUTION TABLE FOR LOCALIZED RANGES OF FLOWCONDITIONS

Pressure Range (kPa)

Mass FluxRange(kg.nT2.s-')

0

to

1000

1000

to3000

3000to

4500

4500to

6000

6000

to

8000

No. of Data

Avg. Error (%)

Rms Error (%)

No. of Data Set

No. of Data

Avg. Error (%)

Rms Error (%)

No. of Data Set

No. of Data

Avg. Error (%)

Rms Error (%)

No. of Data Set

No. of Data

Avg. Error (%)

Rms Error (%)

No. of Data Set

No. of Data

Avg. Error (%)

Rms Error (%)

No. of Data Set

Pressure Range (kPa)

0

to1000

1000to

3000

3000to

4500

4500

to

6000

6000to

8000

No. of Data

Avg. Error (%)

Rms Error (%)

No. of Data Set

No. of Data

Avg. Error (%)

Rms Error (%)

No. of Data Set

No. of Data

Avg. Error (%)

Rms Error (%)

No. of Data Set

No. of Data

Avg. Error (%)

Rms Error (%)

No. of Data Set

No. of Data

Avg. Error (%)

Rms Error (%)

No. of Data Set

100 to 1000

Quality Range

-0.5-

-0.1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

3

3.8

4.7

3

3

3.2

3.7

2

0

0

0

0

0

0

0

0

-0.1-

0.2

1

31.9

31.9

1

0

0

0

0

1

14.3

14.3

1

0

0

0

0

0

0

0

0

8000 to

27

1.3

5.0

5

671

0.4

4.8

18

538

1.4

4.7

18

272

0.9

5.6

12

143

4.9

13.6

11

0.2-

0.5

55

4.7

16.7

4

115

12.3

25.7

6

33

9.9

20.1

2

0

0

0

0

0

0

0

0

12 000

249

1.8

11.9

12

1457

2.5

9.1

23

392

0.2

6.2

12

193

0.9

7.8

10

124

3.6

8.3

7

0.5-

1

523

0.4

8.8

5

21

2.1

18.5

4

0

0

0

0

0

0

0

0

0

0

0

0

535

-0.6

8.4

13

216

3.1

10.7

12

0

0

0

0

0

0

0

0

0

0

0

0

1000 to 5000

Quality Range

-0.5-

-0.1

0

0

0

0

0

0

0

0

1

13.3

13.3

1

0

0

0

0

0

0

0

0

-0.1-

0.2

0

0

0

0

45

-2.5

4.1

5

67

1.2

12.7

7

34

4.9

10.3

7

19

24.9

61.9

3

0.2-

0.5

87

-8.1

10.2

7

766

-2.7

10.2

10

248

4.8

12.0

7

28

5.7

11.9

5

22

11.9

17.3

2

0.5-

1

1755

-3.5

7.2

8

416

-1.9

10.8

8

0

0

0

0

0

0

0

0

0

0

0

0

12 000 to 16 000

0

0

0

0

86

-0.4

5.2

8

25

2.2

5.6

3

28

4.0

5.4

3

0

0

0

0

178

-0.6

6.1

7

1234

1.2

4.7

15

513

2.5

5.7

10

221

4.1

6.9

9

47

6.2

14.9

6

621

1.2

6.1

13

1763

1.8

6.0

13

337

-0.4

5.2

8

124

3.5

6.4

7

18

-1.8

3.6

3

388

0.7

10.4

10

15

-4.2

5.3

4

0

0

0

0

0

0

0

0

0

0

0

0

5000 to 8000

Quality Range

-0.5-

-0.1

0

0

0

0

2

-4.2

4.2

2

0

0

0

0

6

3.0

8.3

3

0

0

0

0

32

1.5

4.8

3

135

1.1

5.5

8

59

2.3

6.4

5

14

0.9

1.6

3

6

-1.5

1.9

2

-0.1-

0.2

1

4.6

4.6

1

454

0.0

10.4

17

486

1.9

9.9

18

228

1.0

5.3

13

95

7.2

11.0

9

0.2-

0.5

141

-1.0

5.4

12

1340

0.7

4.4

22

493

0.3

3.8

19

126

2.1

5.6

9

15

9.6

12.3

5

6 000 to 20 000

154

-0.3

4.4

8

570

0.7

4.1

9

255

4.6

8.6

9

134

6.6

9.3

7

34

7.5

12.1

6

333

0.2

5.0

9

1031

-0.5

4.8

9

272

1.3

5.7

8

106

2.6

5.9

7

9

-2.7

6.0

5

0.5-1

776

-1.4

5.9

15

747

0.0

8.2

15

0

0

0

0

0

0

0

0

0

0

0

0

215

0.7

8.9

8

16

0.3

3.8

3

3

-6.7

10.6

2

0

0

0

0

0

0

0

0

38

3.6.3. Impact of accuracy of CHF model on cladding temperature prediction

CHF prediction methods are usually integrated in reactor safety codes and are used topredict the cladding temperature. This brings up the concern whether the same CHFprediction method is used for maximum cladding temperature prediction and for predictingthe hydraulics response in a channel (see Section 3.7.1 for more details). Various investigatorshave considered the sensitivity of the CHF model in their codes on the cladding temperaturetransient. Belsito and D'Auria (1995) used an earlier version of the CHF look up table[Groeneveld et al. (1986)] and concluded that the discrepancies between pre-test and post-testanalysis is due to the uncertainty in the boundary conditions and the calculation of thepressure at CHF.

3.7. CHF CONCERNING ACCIDENT CONDITIONS

3.7.1. General

In the previous discussion of CHF prediction methods it was assumed that theprediction of the initial occurrence of CHF is of paramount importance (as it is for setting theoperating power for a reactor). However to predict the proper thermalhydraulic/neutronicresponse (they are linked) to a more massive occurrence of CHF across the core, knowledgeof how CHF occurrence spreads across the reactor core is required. This will permit anevaluation of how much of the heat generated by the fuel is used for evaporation (usually100% for saturated boiling if the CHF has not been exceeded), and how much is used forheating up the fuel (this could be close to 100% during fast transients where the fuel claddinghas just experienced CHF and is heating up to the corresponding film boiling temperature).Systems codes ideally should be based on this more detailed (3-D) approach of evaluating thespread of CHF occurrence (or drypatch size) across the core.

The drypatch size predictions depends directly on the choice of the time steps, axialnode size and size of nodes across the core. Detailed experiments on 37-rod fuel bundlesimulators using sliding thermocouples [Schenk et al. (1990)] have clearly indicated that itrequires a significant rise in power (10-25%) just to spread the CHF around one element,while the same measurements indicated that fuel element supports (spacers, endplates, grids)usually have a large local impact (-100-200%) on CHF (e.g. see Section 3.5.3).

A number of papers have been published where an assessment was made of theimplementation impact of the CHF look up table [Faluomi and Aksan (1997); Aksan et al.(1995); Weaver (1991)]. They generally confirm the difficulty of individual CHF correlationsin following the complex CHF variations with flow conditions.

3.7.2. Effect of the axial/radial node size

It is now known that CHF is strongly affected by fuel element supports such as gridspacers (which frequently are equipped with mixing vanes), and spacers/endplates in CANDUreactors. Increases in CHF of over 100% (for the same local flow conditions) due solely to thepresence of an upstream fuel rod support have been measured. This increase in CHF decreasesexponentially with distance downstream from the rod spacer as shown by Equation 3.10. Thenet impact of this depends on the specifics of the bundle geometry and rod support type:decreases in CHF by up to 50% over a distance of 12 cm have been measured [Doerffer

39

(1996)]. It is recommended to use as small an axial node length as practically possible (lessthan 5 cm) for those types of safety analysis where the size of the drypatch is important.

CHF does not occur simultaneously across a bundle, and in fact even across a37 element bundle, it requires typically 50% increase power (for the same local flowconditions P, G and X) to have the CHF spread across the half the bundle geometry, and over100% to spread across the whole geometry. Figures 3.5 and 3.6 [D'Auria (1997)] alsoillustrate the non-uniformity in CHF occurrence as measured in the LOBI and BETHSY testfacilities [Faluomi and Aksan (1997)]; for square array bundle geometries. This limits the useof a 1-D system code in representing the CHF behaviour and its impact on void generationand neutron flux behaviour for PHWR.

r o»uu -

3000:

S, :

2 2000^

> :

y :

1000:

BAF 0-

•

m

•m

A A

•A

—.A

•A

• A• • •

• • • •

• •

A

1 1 1 i 1 1 1 1 i i l i I 1 I 1 1 1 1 1

• •A

• A

A

1 1 1 1 I 1 I 1 1 1 1 1 1 1

560 580 600 620 640TEMPERATURE (K)

ooooooooo *o o"_o_p_ p 61 o

^!O'r6"o o ojo'ooroia[p"61o;o;oO;O;O'LO OjO!O|O

ô'o'o'ojoioO L ° _ O O O O O Jo o o"o"6~6"o o

Figure 3.5. Axial and radial distribution of rod surface temperatures during intial CHFoccurrence measured in the LOBI small break LOCA experiment BL-34.

40

TAF 3660H

3000-

sg 2000 :

5

1000

A

•O

DO

O

D Ooa

DO• • A

•oDm*

B A F 0 | i i i i i i i i i | i i i i i i i i i | i i i i i i i i i j i i i i r i i i i i i i i i i i i i r j

560 580 600 620 640 660TEMPERATURE (K)

HOT LEG— ' ~~BROKEN LOOP

/HOT LEG 2:——^

oooooQOOOOOOOQ.'

OOOOOOOOOO O'O OOOOOO OOOOO'OOOOO

<poooooooooobo[bo ooOOORQOoo ooooo opoooooooooo oXoooooo o'ocooo ooo

OOOOOO 0 O-QOO OOOOOOOOOOCoooopooo o]o~6!o Q'O ooooo t

j OOOOO b o o OOOOiOOOOO OOttC.- ....fooooooooo Q[o_pjoo o ooooo oloojc

OOOOOOO OOCLOOÔ.OOO OOOOOO OO ]1 .O_0;0 |ocro o oofoôtoo 6b"Do-ooQ.o oo

3 0 0 0 O O obO OjO\0 OOOOOOOO 0"O /o'o O|O O O O O O <TO Q O Q O O O O O O O O O?O OOO OOOOOOOOOiDO OOOOO O Ooooooooo/oooooo'O o(5~olopo0000000000000.00 O|O OjO 6 O

ooooo oh o o o o o o o. oJo oreoooo aooooooooot

OOQOOOOOOOQOO O-Oo op oooooooooo/ooooooooo

OOOOO

Figure 3.6. Axial and radial distribution of rod surface temperatures during initial CHFoccurrence measured in the BETHSY small break LOCA experiment.

Three possible options are proposed to resolve the concerns of properly representing thethermalhydraulic/neutronic response to massive CHF occurrence.

(1) use subchannel codes to evaluate the spread of CHF occurrence in a core across a fuelcell or bundle;

(2) predict the average (not initial) CHF for a fuel cell or bundle and use this for predictingthe fraction of fuel in dryout (this requires knowledge of the variation in flow conditionsamong fuel bundle/fuel cell);

(3) use subchannel codes and/or experimental data to relate the bundle/core drypatchfraction to heat flux beyond the initial CHF occurrence and use this in systems codecalculations to predict the thermalhydraulic and neutronic response.

The choice of which option is appropriate depends on the application, the availability ofrelevant data and the type of subchannel and systems code.

41

3.7.3. Transient effects on CHF

3.7.3.1. Flow transient

During a LOCA or pump rundown scenario, the flow decay phase can frequently becharacterized by G = Go e"1701, during which time CHF will occur. The impact of the flowtransient on CHF depends strongly on the flow decay constant Ci: This permits a subdivisionof the transients into:

(i) slow transients, where the channel transit time is much smaller than the flow decay timeconstant Cl. These are mild transients, which can be considered as pseudo-steady-statecases. Here, the CHF is assumed to be unaffected by the flow transient. For normalreactor flow conditions, the core transit time is roughly about 1 sec.

(ii) fast transients where the transit time is greater than the flow decay time constant Cl.Here the CHF is expected to be affected noticeably by the transient and any effect dueto AFD is considered secondary.

As a first order approximation, it may be assumed that for 1/G (dG/dt) < 0.1 (i.e. adecay time constant Cl > 10 seconds) no effect of the transient on CHF is noticeable and theBLA heat flux (or any other methods which correctly account for upstream AFD) should beused. For a time constant Cl of 1 second or less, however, the BLA effect is no longerrelevant as it is overshadowed by transient effects. It is generally assumed that the CHF isenhanced during fast transients but no reliable predictions are available. The assumption that

= CHFsteady state for the same instantaneous local flow conditions is frequently made.

3.7.3.2. Power transients

Power transients will also accompany a LOCA. The power transient can be either in theform of a power decay , or a power spike. The easiest methodology for representing the powerchange is by employing the "Lagrangian" approach. The similarity between the variation inupstream heat flux as experienced by a fluid parcel while travelling along a non-uniformlyheated channel, and the change in heat flux experienced by a fluid particle during a powertransient can be used in evaluating the impact of a power transient on CHF [see also Chang(1989)]. If the fluid is in the annular flow regime (void fractions >60%), a methodologysimilar to the BLA approach can be used, provided that the time a fluid particle sees a changein heat flux is transformed properly into an equivalent AFD. A previous study of axial fluxspikes [Groeneveld (1975)] has shown that a BLA-type of approach can handle flux spikeswith a magnitude of 2-3 times the average heat flux.

3.8. RECOMMENDATIONS AND FINAL REMARKS

(1) Based on the arguments presented in Sections 3.4-3.6, the CHF look-up table aspresented in Appendix II is currently recommended for use as the reference predictionmethod for CHF in advanced water-cooled reactors. As an alternative for fuel bundles inwhich the rods are arranged in a triangular array, the WWER-based look-up table ofAppendix III is recommended.

(2) For new bundle geometries, and in the absence of any relevant bundle CHF data,corrections for radial and axial flux shapes should be applied to account for differencesbetween CHF values in tubes and bundle or bundle subchannels. These corrections can

42

best be obtained from a reliable subchannel code; without the complexity of asubchannel code, the method of applying correction factors based on element spacing,axial and radial flux distribution may be utilised.

(3) Supercritical water is currently being considered as a coolant medium for several Advanced WaterCooled Reactor concepts. The heat transfer characteristics of reactor cores cooled by supercritical waterneeds further investigation. Specifically the pseudo-CHF and post-CHF behaviour of supercritical waterhas received very little attention in the literature.

(4) Over 90% of the CHF literature is concerned with the prediction of initial CHF. Thereare currently no expressions for determining the average CHF or the spread of CHFavailable, even though this can be very important for predicting the thermalhydraulicand neutronic response to massive CHF occurrence during severe LOCAs. Themethodology described in Section 3.7 may be used for evaluating the average CHF orthe size of the drypatch.

(5) As shown in Figure 3.2 there exists currently a scarcity of CHF data at low flows/lowqualities and at or high flows/high qualities. In addition relatively little is known of theeffect of fast flow and power transients on CHF. Additional experiments are required toimprove our knowledge of CHF in these areas.


ADORNI, N., et al.. 1966, Heat Transfer Crisis and Pressure Drop with Steam-WaterMixtures: Experimental Data with 7-Rod Bundles at 50 and 70 kg/cm2, CISE Report R170.

AKSAN, S.N., D'AURIA, F., FALUOMI, V., 1995, "A comparison and asessment of somechf prediction models used in thermalhydraulic systems codes", paper presented at FirstResearch Coordination Mtg on Thermalhydraulic Relationships for Advanced Water-CooledReactors, IAEA-RC-574.

BAEK, W.-P., KIM, H.-C, CHANG, S.H., 1996, An Independent Assessment of Groeneveldet al.'s 1995 CHF Look up Table, Nuclear Engineering and Design.

BECKER, K.M., FLINT A, J., NYLUND, O., 1967, "Dynamic and static burnout studies forthe full-scale Marviken fuel elements in the 8 MW Loop FRIGG" (Proceedings, Symp. onTwo-Phase Flow Dynamics, Eindhoven, Netherlands), Vol. 1, 461-474.

BELSITO, S., D'AURIA, F., 1995, Comparison of Advanced Computer Codes in theSimulation of CHF Occurrence in the PKF Facility, Report on Expert Group Meetings onCHF and Post-CHF Heat Transfer, New Orleans, IAEA-CT-2991 and 2992.

BERGLES, A.E., 1977, Burnout in boiling heat transfer. Part II: Subcooled and low qualityforced-convection systems, Nuclear Safety 18 2 154-167.

BESTION, B., 1990, The physical closure laws in the CATHARE code, Nuclear Eng. Design124 229-245.

BEZRUKOV, Y.A., ASTACHOV, V.I., SALII, L.A., 1974, "Study of CHF in rod bundles forWWER type reactors", Proc. Thermophysical Mtg TF-74, Moscow (57-66).

43

BEZRUKOV, Y.A., ASTACHOV, V.I., BRANTOV, V.G., 1976, Experimental study andstatistical analysis of CHF data for WWER type reactors, Teploenergetika 2 80-82.

BOBKOV, V.P., VINOGRADOV, V.N., ZYATNINA, O.A., KOZINA, N.V., 1995, Amethod of evaluating the critical heat flux in channels and cells of arbitrary geometries,Thermal Engineering 42 3 (221-231).

BOBKOV, V.P., VINOGRADOV, V.N., ZYATNINA, O.A., KOZINA, N.V., 1997,Considerations in describing burnout in rod bundles, Thermal Engineering 44 3 (2-7).

BOWRING, R.W., 1967, HAMBO, A Computer Programme for the Subchannel Analysis andBurnout Characteristics of Rod Clusters, Part I. General Description, UKAEA Rep. AEEW-R524.

BURCK, E., HUFSCHMIDT, W., DE CLERQ, E., 1968, Der Einfluss KuenstlicherRauhigkeiten auf die Erhoehung der Kritischen Waermestromdichte von Wasser inRingspalten bei erzweigener Konvektion, EUR 4040d.

CARVER, M.B., KITELEY, J.C., ZHOU, R.Q.N., JUNOP, S.V., 1993, Validation ofASSERT Subchannel Code for Standard and Non-Standard Geometries, ARD-TD-454P,2nd Int. Seminar on Subchannel Analysis, EPRI, Palo Alto.

CHANG, S.H., LEE, K.W., GROENEVELD, D.C., 1989; Transient-effects modeling ofcritical heat flux, Nuclear Eng. Design 133 51-57.

CHUN, T.H., HWANG, D.H., BAEK, W.P., CHANG, S.H., 1997, "Assessment of the look-up table method for bundle CHF predictions with a subchannel code" (Proc. ISSAC-4 MtgTokyo.

CERVOLANI, S., 1995, "Description and validation of ANTEO, an optimized PC code forthe thermalhydraulic analysis of fuel element bundles" (Proc. 2nd Regional Mtg on NuclearEnergy in Central Europe, Portoroz, Slovenia).

CHENG, X., ERBACHER, F.J., 1997, this publication, Chapter 3.

COLLIER, J.G., 1972 and 1981, Convective Boiling and Condensation, McGraw-Hill,London.

D'AURIA, F., 1997, this publication, Figures 3.5 and 3.2.

DEBORTOLI, R.A., GREEN, S.J., LETOURNEAU, B.W., TROY, M., WEISS, A., 1958,Forced-Convection Heat Transfer Burnout Studies for Water in Rectangular Channels andRound Tubes at Pressures Above 500 Psia, Westinghouse Electric Corp. Rep. WAPD-188.

DOERFFER, S., GROENEVELD, D.C., SCHENK, J.R., 1996, "Experimental study of theeffects of flow inserts on heat transfer and critical heat flux", (Proc. 4th Int. Conf. on NuclearEngineering, New Orleans, Vol. 1 — Part A (41^9).

DOROSHCHUK, V.E., LEVITAN, L.L., LANTZMAN, F.P., Investigation into Burnout inUniformly Heated Tubes, ASME Publication 75-WA/HT-22.

44

DURANT, W.S., TO WELL, R.H., MIRSHAK, S., 1965, "Improvement of Heat Transfer toWater Flowing in an Annulus by Roughening the Heated Wall", Chem. Engrg. ProgressSymposium Series 6 60 106-113.

FALUOMI, V., AKSAN, S.N., 1997, "Analysis and assessment of some selected CHFmodels as used in Relap5/Mod3 code", (Proceedings Fifth Int. Conf. on Nuclear Engineering(ICONE 5), Nice, France).

GASPARI, G.P., HASSID, A., VANOLI, G., 1969, "An experimental investigation on theinfluence of radial power distribution on critical heat flux in a nuclear rod cluster", (Proc.European Two-Phase Flow Group Mtg, Karlsruhe).

GASPARI, G.P., et al , 1968, Heat Transfer Crisis and Pressure Drop with Steam WaterMixtures: Further Experimental Data with Seven Rod Bundles, CISE Rep. R-208.

GROENEVELD, D.C., et al., 1996, The 1996 look-up table for critical heat flux in tubes,Nuclear Eng. Design 163 1-23.

GROENEVELD, D.C., 1996, On the definition of critical heat flux margin, Nuclear Eng.Design 163 245-247.

GROENEVELD, D.C., LEUNG, L.K.H., 1989, "Tabular approach to predicting critical heatflux and post-dryout heat transfer", Proc.Thermalhydraulics, Karlsruhe), Vol 1, 109-114.flux and post-dryout heat transfer", Proc. 4th Int. Top. Mtg on Nuclear Reactors

GROENEVELD, D.C., YOUSEF, W.W., 1980, "Spacing devices for nuclear fuel bundles: Asurvey of their effect on CHF, post-CHF heat transfer and pressure drop", (Proc.ANS/ASME/NRC Int. Top. Mtg on Nuclear Reactor Thermal-Hydraulics, Saratoga Springs),NUREG/CP-0014, Vol. 2,1111-1130.

GROENEVELD, D.C., 1975, The Effect of Short Flux Spikes on the Dryout Power", AtomicEnergy of Canada Ltd Rep. AECL-4927.

GROENEVELD, D.C., 1974, "The occurrence of upstream dryout in uniformly heatedchannels", (Proc. Fifth Int. Heat Transfer Conf.), Vol. IV (265-269).

GROENEVELD, D.C., 1972, The Thermal Behaviour of a Heated Surface at and BeyondDryout", Atomic Energy of Canada Ltd Rep. AECL-4309.

GROENEVELD, D.C., SNOEK, C.W., 1986, "A comprehensive examination of heat transfercorrelations suitable for reactor safety analysis", Multiphase Science and Technology,Volume II (181-274).

GROENEVELD, D.C., et al., 1986a, "Analytical and experimental studies in support of fuelchannel critical power improvements", Proc. Canadian Nuclear Society Annual Mtg, Toronto.

GROENEVELD, D.C., et al., 1992, "CHF fluid-to-fluid modelling studies in threelaboratories using different modelling fluids", (Proc. NURETH-5, Salt Lake City), Vol. 2,531-538.

45

HERON, R.A., et al., 1969, Burnout Power and Pressure Drop Measurements on 12-ft., 7-rodClusters Cooled by Freon-12 at Ispra, UKAEA Rep. AEEW-R655.

HETSRONI, G., 1982, "Handbook of multiphase systems", Hemisphere, McGraw-Hill.

HEWITT, G.F., HALL-TAYLOR, N.S., 1970, Annular Two-Phase Flow, Pergamon Press,Oxford.

HEWITT, G.F., KEARSEY, H.A., LACEY, P.M.C., PULLING, D.J., 1963, Burn-Out andNucleation in Climbing Film Flow, UKAEA Rep. AERE-R437.

HSU, Y.Y., GRAHAM, R.W., 1976, Transport Processes in Boiling and Two Phase Systems,McGraw-Hill.

HUGHES, E.D., et al., 1974, A compilation of rod array critical heat flux data sources andinformation", Nuclear Engrg. & Design 30 20-35.

JENSEN, A., MENNOV, G., 1974, Measurement of Burnout, Film Flow and Pressure Dropin a Concentric Annulus 3500 x 26 x 17 mm With a Heated Rod and Tube, European Two-Phase Flow Group Meeting, Harwell, UK.

KATTO, Y., 1994, Critical heat flux, Int. J Multiphase Flow 20 (53-90).

KIRILLOV, P.L., YUSHENKO, S.S., 1996, "Diameter effect on CHF", Second ResearchCoordination Meeting, IAEA Coordinated Research Program on ThermalhydraulicRelationships for Advanced Water-Cooled Reactors, Vienna, Austria.

KIRILLOV, P.L., BOBKOV., V.P., SMOGALEV, I.P., VINOGRADOV, V.N., 1996,Prediction of Critical Heat Flux in Channels Relevant to Water Cooled Reactors, IAEAContract 8219R1.

KIRILLOV, P.L., BOBKOV. V.P., 1997, Working Material Related to the WWER-typeBundle CHF Look-up Table, Presented at the Third Research Coordination Meeting,Coordinated Research Program on Thermalhydraulic Relationships for AdvancedWater-Cooled Reactors, Obninsk, Russia.

KITELEY, J.C., CARVER, M.B., LINER, Y., BROMLEY, B.P., MCCRACKEN, I.K., 1991,"ASSERT-FV thermalhydraulics subchannel analysis code simulation of dryout power andpressure drop in a horizontal 37-rod bundle fuel channel including the effect of pressure tubecreep", Proc. 16th Annual CNA Nuclear Simulation Symp. St. John, New Brunswick.

KRUZHILIN, G.N., 1949, Experimental data on heat transfer boiling at natural convection",Izvestiya Akademii Nauk SSSR, Otdel Technik. Nauk 5 (701-702).

KUNSEMILLER, D.F., 1965, Multi-Rod, Forced Flow Transition and Film BoilingMeasurements, General Electric Rep. GEAP-5073.

KUTATELADZE, S.S., 1952, Heat Transfer in Boiling and Condensation, USAEC Rep.AEC-tr-3770.

46

KUTATELADZE, S.S., BORISHANSKII, V.M., 1966, A Concise Encyclopedia of HeatTransfer, Pergamon Press.

KYMALAINEN, O., et al , 1993, "Heat flux distribution from a volumetrically heated poolwith high Rayleigh number", (Proc. NURETH-6 Conf. Grenoble), Vol. 1 (47-53).

LAHEY, R.T., GONZALEZ-SANTOLO, J.M., 1977, "The effect of non-uniform axial heatflux on critical power", Paper C219/77 presented at the Inst. of Mech. Engineers Conf. onHeat and Fluid Flow in Water Reactor Safety, Manchester.

LAHEY, R.T., Jr., MOODY, F.J., 1977, The Thermal Hydraulics of a Boiling Water NuclearReactor, ANS Monograph.

LIN, W., LEE, C.H., PEI, B.S., 1989, An improved theoretical critical heat flux model forlow quality flow", Nuclear Technol. 88 (294-306).

LEE, D.H., OBERTELLI, J.D., 1963, An Experimental Investigation of Forced ConvectionBoiling in High Pressure Water, UKAEA Rep. AEEW-R213.

LEUNG, L.K.H., 1997, AECL Report.

MACEK, J., 1998, Private Communication.

MCPHERSON, G.D., 1971, The Use of the Enthalpy Imbalance Number in Evaluating theDryout Performance of Fuel Bundles, AECL Rep. AECL-3968.

NORMAN, W.S., MCINTYRE, V., 1960, Heat transfer and liquid film on a vertical surface,Trans. Inst. Chem. Engineers 38 301-307.

PARK, H., DHIR, V. K., et al., 1994, Effect of external cooling on the thermal behavior of aboiling water reactor vessel lower head, Nuclear Technol. V. 108 2 266-282.

POLOMIK, E.E., 1967, Transition Boiling, Heat Transfer Program, Final Summary Report onProgram for Feb. 63-Oct. 67, General Electric Report GFAP-5563.

ROWE, D.S., 1971, COBRA III, A Digital Computer Program for Steady State and TransientThermal-Hydraulics Analysis of Rod-Bundle Nuclear Fuel Elements, Battelle-NorthwestReport BNWL-B-82.

SCHENK, J.R., GROENEVELD, D.C., 1990, "Measurement of thermalhydraulic parametersinside multi-element bundles", Proc. Int. Symp. on Multi-Phase Flow, Miami.

SMITH, R.A., 1986, Boiling Inside Tubes: Critical Heat Flux for Upward Flow in UniformlyHeated Tubes, ESDU Data Item No. 86032, Engineering Science Data Unit International Ltd,London.

SULATSKI, A.A., EFIMOV, V.K., GRANOVSKY, V.S., 1997, "Boiling crisis at the outersurface of WWER vessel", Proc. Int. Symp. on the Physics of Heat Transfer in Boiling andCondensation, Moscow (263-268).

47

TAITEL, Y., DUKLER, A.E., 1975, A Model for Predicting Flow Regime Transitions inHorizontal and Near Horizontal Gas/Liquid Flow, ASME 750WA/HT829 (1975); AIChE J.22(1976)47855.

TIPPETS, F.E., 1962, "Critical Heat Fluxes and Flow Patterns in High Pressure Boiling WaterFlows", ASME Paper 62-WA-162 presented at the Winter Annual Meeting of the ASME,New York.

TODREAS, N.E., ROHSENOW, W.M., 1965, The Effect of Non-uniform Axial Heat FluxDistribution, Rep. 9843-37, M.I.T. Dept. of Mech. Engineering.

TONG, L.S., HEWITT, G.F., 1972, Overall Viewpoint of Flow Boiling CHF Mechanisms,ASME paper 72-HT-54.

TONG, L.S., 1972, Boiling Crisis and Critical Heat Flux, USAEC Rep. TID-25887.

TONG, L.S., WEISMAN, J., 1996, Thermal Analysis of Pressurized Water Reactors, ThirdEdn, American Nuclear Society.

TONG, L.S., 1965, Boiling Heat Transfer and Two-Phase Flow, John Wiley & Sons.

TO WELL, R.H., 1965, Effect of Spacing on Heat Transfer Burnout in Rod Bundles, ReportDP-1013.

ULRYCH, G., 1993, "CHF table applications in KWV PWR design", Paper presented at theInt. Workshop on CHF Fundamentals — CHF Table Improvements, Braunschweig.

WATERS, E.O., FITZSIMMONS, D.E., 1963 DNB varies with rod spacing in 19-rodbundles, Nucleonics (96-101).

WEAVER, W.L., RIEMKE, R.A., WAGNER, R.J., JOHNSON, G.W., 1991, "TheRELAP5/MOD3 code for PWR safety analysis", (Proc. NURETH-4". 4th Int. Top. Mtg onNuclear Reactor Thermalhydraulics, Karlsruhe", Vol. 2 (1221-1226).

WEISMAN, J., BOWRING, R.W., 1975, Methods for detailed thermal and hydraulic analysisof water-cooled reactors, Nuclear Science Engineer. 57 (255-276).

WEISMAN, J., 1992, The current status of theoretically based approaches to the prediction ofthe critical heat flux in flow boiling, Nuclear Technol. 99 (1-21).

WEISMAN, J., PEI, B.S., 1983, Prediction of critical heat flux in flow boiling at low qualityconditions, Int. J. Heat Mass Transfer 26 (1463).

WEISMAN, J., YING, S.H., 1985, A theoretical based critical heat flux prediction for rodbundles, Nucl. Eng. Design 85 (239-250).

YING, S.H., WEISMAN, J., 1986, Prediction of critical heat flux in flow boiling atintermediate qualities, Int. J. Heat Mass Transfer 29 (1639).

WONG, Y.L., GROENEVELD, D.C., CHENG, S.C., 1990, CHF predictions in horizontaltubes, Int. J. Multiphase Flow 16 (123).

ZUBER, N., 1959, Hydrodynamic Aspects of Boiling Heat Transfer, Atomic EnergyCommission Report AECU-4439.

48

Chapter 4

GENERAL FILM BOILING HEAT TRANSFER PREDICTION METHODS FORADVANCED WATER COOLED REACTORS

NOMENCLATURE

ACp

CDdFGgh1NuPPrqRerSTtVXxa

GREEK SYMBOLS

area of surfacespecific heatconcentrationhydraulic diameterdrop diameterempirical functionmass fluxacceleration of gravityenthalpylengthNusselt numberpressurePrandtl numberheat fluxReynolds numberlatent heat of evaporationvelocity slip ratio; pitch of rod bundlestemperaturetimespecific volumemass qualityactual quality

n J- min

asX

xc

Pa^ 0

0

perimeterA 1 m j n 1 min 1 s

heat transfer coefficientemissivitythermal conductivitycritical wave lengthvoid fractiondynamic viscositydensitysurface tensionStefan-Boltzman constantinclination angle in degrees

49

SUBSCRIPTS

accr, CHFefgh£minQsstsubtotTBV

vdwwvwd

actualcriticalcritical heat fluxequilibriumfront of wettinggas (vapour)hydraulic; heatliquidminimumquenchsaturationstabilisationsubcooledtotaltransition boilingvapourvapour-to-dropwallwall-to-vapourwall-to-drop

ABREVIATIONS

AWCRCHFCRPDFFBECCIAFBLOCALWRMFBTMHFPDOQFRCM

advanced water cooled reactorcritical heat fluxcoordinating research projectdispersed film flow boilingemergency cooling of coreinverted annular film boilingloss of coolant accidentlight water reactorminimum film boiling temperatureminimum heat fluxpost-dryout heat transferquench frontresearch coordination meeting

4.1. INTRODUCTION

Post-CHF (or post-dryout) heat transfer is encountered when the surface temperaturebecomes too high to maintain a continuous liquid contact, and the surface becomes covered by acontinuous or intermittent vapour blanket. Post-CHF heat transfer includes transition boiling,where intermittent wetting of the heated surface takes place, and film boiling, where the heated

50

surface is too hot to permit liquid contact. The boundary between these post-CHF heat transfermodes is the minimum film boiling temperature, or TMFB. Due to the poor heat transportproperties of the vapour, high heated surface temperatures are often encountered during filmboiling.

Although nuclear reactors normally operate at conditions where dryout does not occur,accidents can be postulated where dryout occurrence is possible. The most serious of thepostulated accidents is thought to be the loss-of-coolant accident (LOCA) caused by a rupture inthe primary coolant system. Accurate prediction of the consequences of a LOCA requiresprecise calculation of foel-coolant heat transfer during (i) the blowdown phase (when the fuelchannel is voided), and (ii) the subsequent emergency-core-cooling (ECC) phase. Although thetime-in-dryout may be short, nevertheless this interval, when the primary mode of heat transferis film boiling, can be of crucial importance in maintaining core integrity.

The post-CHF cladding temperature can be predicted from empirical correlations or fromtheoretical models. Since theoretical models are rather complex and the physical mechanismson which they are based are not yet fully understood, predictions are usually based on empiricalcorrelations. The main three methodologies considered by IPPE, AECL and CIAE have beenpresented in this chapter.

Film boiling heat transfer has been extensively investigated during the past 30 years.Excellent reviews may be found in text books by Tong (1965), Collier (1980), Delhaye et al.(1981), Stryikovitch et al. (1982), a handbook by Hetsroni (1982), and articles by Ganic et al.(1977), Mayinger (1978), Tong (1978), Sergeev (1978, 1987), Groeneveld and Snoek (1986),Groeneveld (1992), Yadigaroglu (1989), Sakurai (1990a), Andreoni and Yadigaroglu (1994)and in the proceedings of the 1st International Symposium on Fundamental Aspects of Post-CHF Heat Transfer (1984).

The objective of this chapter is to review and recommend film boiling predictionmethods suitable for the assessment of LOCAs and other disruptive accidents in AWCRs andfor implementation into systems codes such as RELAP, CATHARE, and CATHENA, as wellas subchannel codes such as COBRA, ASSERT, and MIF. The requirements for thisprediction method have been discussed in more detail in CRP RCM meetings and expertmeetings.

This chapter is subdivided as follows:

(i) Section 4.2 discusses the mechanisms of the post-CHF heat transfer;

(ii) Section 4.3 describes the film boiling data base in tubes and rod bundles;

(iii) Section 4.4 provides an overview of the prediction methodology for film boiling heattransfer;

(iv) Section 4.5 presents the recommended prediction methods for film boiling heat transfer;

(v) Section 4.6 discusses the film boiling prediction methodologies used in reactor safetycodes; and

(vi) Section 4.7 provides final remarks related to the use of film boiling prediction methodsin the thermal analysis of advanced water cooled reactors.

51

4.2. DESCRIPTION OF POST-CHF PHENOMENA

4.2.1. General

Post-CHF heat transfer is encountered when the surface temperature becomes too high tomaintain a continuous liquid contact. As a result the heated surface becomes covered by acontinuous vapour blanket as is the case in the film boiling regime, or an intermittent vapourblanket, as is the case in the transition boiling regime. The boundary between these post-CHFheat transfer modes is the minimum film boiling temperature, or TMFB .

Post-CHF heat transfer is initiated as soon as the critical heat flux condition isexceeded; it persists until quenching or rewetting of the surface occurs. Depending on theparticular scenario and flow conditions present, various heat transfer modes of the boilingcurve of Fig. 4.1 may be distributed along a heated surface, or a series of heat transfer modescan succeed each other in time at the same location as is the case during transients.

uX

M3

qCHF

*• Posf-CHF flegfon

Onset of ONB

Crftica! HeatTransition when

Flux Increasing

*" '"•Întcrmedia-fe Fittn Boiling RegfonFilm Boiling \ ^Minimum Heat Flux Film 8oili'ng Region

I Tronsition whenj Heat Flux Decreasingi

Surface Temperature - Saturation Temperature

FIG. 4.1. Typical boiling curve.

The occurrence of film boiling depends on surface temperature and flow conditions.Figure 4.2 is a three-dimensional representation of the variation of the heat flux with walltemperature and quality at constant mass flux and pressure, the so-called boiling surfaceconcept described by Nelson (1975) and Collier (1980). The flow quality introduces a thirddimension to the problem that was not present in pool boiling. This 3-D boiling surface ormap shows the nucleate, transition and film boiling surfaces (regimes) as well as the criticaland minimum heat flux lines for a given pressure and mass flux.

52

FIG. 4.2. The boiling surface [Nelson, 1975].

The post-CHF heat transfer modes in flow boiling can be classified as:

(i) transition boiling (also referred to as "sputtering");(ii) inverted-annular film boiling (IAFB) associated with subcooled or low quality flow; and(iii) dispersed-flow film boiling (DFFB) associated with intermediate and high quality flow.

In the following sections concise descriptions of the mechanisms controlling these post-CHF heat transfer regimes will be presented.

4.2.2. Transition boiling

As the name implies, transition boiling is an intermediate boiling region. Berenson (1962)has provided a concise description of the transition boiling mechanism: Transition boiling is acombination of unstable film boiling and unstable nucleate boiling alternately existing at anygiven location on a heating surface. The variation in heat transfer rate with temperature isprimarily a result of a change in the fraction of time each boiling regime exists at a givenlocation.

53

Quench flegion \

Low flooding rate

Forced convectionto vapor

0

°o * !Quenchregion

High flooding rate

FIG. 4.3. Post-CHF reflooding heat transfer modes [Yadigaroglu, 1978]

rv 1 ^ ? f § feCtl°n ° f t h e b 0 i l i n g c u r v e i s b o u n d e d by t h e critical heat flux(Fig. 4.3) and the minimum heat flux. The critical heat flux has been extensively studied andcan be predicted by a variety of correlations. The minimum heat flux has undergone less

^Zi^^^^^^r fluid—d J

™rf i f SUrfaC!, temfratureu

S " 6XCeSS ° f t h e C H F t e m P e r a toe , the heated surface will bepartially covered with unstable vapour patches, varying with space and time. Ellion (1954)studied forced convective transition boiling in subcooled water and observed frequenrep acement of vapour patches by liquid. Although this may seem similar to transition poolboi ing as described above, the introduction of the convective component will improve the filmboiling component by reducing the vapour film thickness and changing the heat transfer modewhether dry or wet, from free convection to forced convection. This will result in an mcreTeTnqmin and also can increase ATfflfb (if ATmfb is hydrodynamically controlled). For low qualities andsubcooled conditions the slope of the transition boiling is always negative, just i i n T i

54

The amount of heat transfer in the transition boiling region is primarily governed byliquid-solid contact. At the critical heat flux point the contact-area (or time) fraction F is closeto unity and, therefore, the liquid contact heat flux q^ is close to the CHF. The value of F

strongly decreases with increasing wall temperature, hi the high quality region for example,most of the heat transferred during transition boiling will be due to droplet-wall interaction.Initially, at surface temperatures just in excess of the boiling crisis temperature, a significantfraction of the droplets will deposit on the heated surface but at higher wall superheats thevapour repulsion forces become significant in repelling most of the droplets before they cancontact the heated surface. The repelled droplets will contribute to the heat transfer bydisturbing the boundary layer sufficiently to enhance the heat transfer to the vapour.

The periodic contacts between liquid and heated surface in the transition boiling regionof the boiling curve result in the formation of both large amounts of vapour, which forcesliquid away from the surface, and creates an unstable vapour film or blanket. Because of this,the surface heat flux and the surface temperature can experience variations both with time,and position on a heater. However, the average heat transfer coefficient decreases as thetemperature increases, because the time of contact between the liquid and the heater surface isdecreased.

To gain a better understanding of the transition boiling mechanism, the phenomenaoccurring at the interface between fluid and a heated surface (i.e. the mechanism of fluid-solidcontact including the frequency of this contact; heat transfer in the contact areas; time historyof such contact) need to be considered. Comprehensive reviews of these phenomena havebeen presented by Kalinin et al. (1987) and Auracher (1987, 1990).

Transition boiling has received less attention than nucleate or film boiling. Only inrecent years has the interest in this boiling regime increased because of its potentialimportance during a LOCA in a nuclear reactors. Overviews of the mechanisms andprediction methods for transition boiling have been provided by Bankoff and Mehra (1962),Groeneveld and Fung (1976), Auracher (1987, 1990), Winterton (1982), Groeneveld andSnoek (1986) and Johannsen (1991).

4.2.3. Minimum film boiling temperature

The minimum film boiling temperature (TMFB) separates the high temperature regionwhere inefficient film boiling or vapour cooling takes place, from the lower-temperature region,where much more efficient transition boiling occurs. It thus provides a limit to the application oftransition boiling and film boiling correlations. Knowledge of the minimum film boilingtemperature is particularly important in reactor safety assessments.

A large number of terms have been used for the minimum film boiling temperature orTMFB- They include rewetting temperature, quench temperature, Leidenfrost temperature, filmboiling collapse temperature and others.

During quenching of a surface (such as emergency core cooling), rewetting commences atthe minimum film boiling temperature and, as a rule, rapidly proceeds until nucleate boiling isestablished at a much lower wall temperature. Predicting the minimum film boiling temperatureas a function of the system parameters is thus very important since heat transfer coefficients on

55

either side of the minimum film boiling temperature can differ by orders of magnitude.Generally, TMFB is defined as the temperature at the minimum heat flux.

The TMFB also represents a temperature boundary beyond which surface properties andsurface conditions generally do not affect the heat transfer. Wettability or contact anglealthough important in nucleate and transition boiling, are not applicable in the film boilingregime, and conduction along the surface becomes less important when nucleate and filmboiling no longer occur side-by-side.

Two theories have been proposed for the analytical prediction of the minimum filmboiling temperature. One theory says that the minimum temperature is a thermodynamicproperty of the fluid (i.e. maximum liquid temperature) and thus is primarily a function ofpressure. The other theory suggests that rewetting commences due to hydrodynamic instabilitieswhich depend on the velocities, densities, and viscosities of both phases as well as the surfacetension at the liquid-vapour interface. During fast transitions, where insufficient time isavailable to fully develop the hydrodynamic forces, rewetting is expected to bethermodynamically controlled while for low flows and low pressures, where sufficient time isavailable and the volumetric expansion of the fluid near the wall is large, rewetting is morelikely to be hydrodynamically controlled. Once rewetting has occurred locally, the rewettingfront can then propagate at a rate which is primarily controlled by axial conduction. Thesetheories can be modified to include the thermal properties of the surface.

There is no general consensus on the effect of the various system parameters on theminimum film boiling temperature under forced convective conditions. These effects areincluded in correlations for the minimum temperature which have been tabulated by Groeneveldand Snoek (1986).

4.2.4. Flow film boiling

4.2.4.1. General

Film boiling is generally defined as that mode of boiling heat transfer where only thevapour phase is in contact with the heated surface. The term film boiling was originallyapplied to pool boiling where the stagnant liquid was separated from the heated surface by avapour film. The term has been used in forced convective boiling to refer to conditions wherethe liquid does not contact the heated surface but is usually in one of the following forms:

(i) a dispersed spray of droplets, normally encountered at void fractions in excess of 80%(liquid-deficient or dispersed flow film boiling regime);

(ii) a continuous liquid core (surrounded by a vapour annulus which may contain entraineddroplets) usually encountered at void fractions below 40% (inverted annular filmboiling or IAFB regime); or

(iii) a transition between the above two cases, which can be in the form of an inverted slugflow for low to medium flow.

Figure 4.3 illustrates the above flow regimes. Of these, the dispersed flow film boiling(DFFB) regime is most commonly encountered and has been well studied. Its heated surfacetemperature is moderate while in the inverted annular and the inverted slug flow regimes,excessive surface temperatures are frequently encountered.

56

Radiation heat transfer, although unimportant in transition boiling, becomesincreasingly important in film boiling, particularly at low flows, low void fractions andsurface temperatures in excess of 700°C.

The main parameters controlling the film boiling heat transfer are: pressure, equilibriumquality (or subcooling), and mass flux. At low flows, strong non-equilibrium effects can bepresent which will need to be considered. In addition at locations just downstream of (or "justsubsequent to" during fast transients) the CHF or quench occurrence, upstream/history effectsare important. These effects frequently are not included in film boiling models [see alsoGottula et al. (1985); Shiralkar et al. (1980); Kirillov et al. (1982)].

Due to the high surface temperatures frequently encountered during film boiling withwater, studies using cryogenic and refrigerant fluids and pool boiling studies have beenextensively employed to improve our understanding of film boiling and to extract parametrictrends and derive correlations.

Reviews of the film boiling literature have been prepared separately for the higherquality DFFB regime [Mayinger (1978); Collier (1981); Groeneveld (1975a & 1977);Andreoni and Yadigaroglu (1994)]; the IAFB regime [Groeneveld (1984, 1992); Andreoniand Yadigaroglu (1974)] and for pool film boiling [Hsu (1972); Kalinin (1987)].

4.2.4.2. Inverted annular film boiling

IAFB refers to the film boiling type characterized by a vapour layer separating thecontinuous liquid core from the heated surface. Figure 4.3 (RHS) shows schematically thephase distribution during IAFB. IAFB resembles pool film boiling superficially, but the actualheat transfer mechanisms are considerably more complex.

In the inverted annular flow regime few entrained droplets are present while the bulk ofthe liquid is in the form of a continuous liquid core which may contain entrained bubbles. Atdryout the continuous liquid core becomes separated from the wall by a low viscosity vapourlayer which can accommodate steep velocity gradients. However, the velocity distributionacross the liquid core is fairly uniform. Once a stable vapour blanket has formed, the heat istransferred from the wall to the vapour and subsequently from the vapour to the wavy liquidcore. Initially, for very thin vapour films, heat transfer from the wall to the liquid is primarilyby conduction across a laminar vapour film. When the vapour film thickness increases,turbulent flow will occur in the film, and the liquid-vapour interface becomes agitated. Heattransfer across the wavy vapour-liquid interface takes place by forced convection. This modeof heat transfer is much more efficient than the single-phase convective heat transfer betweena smooth wall and the vapour; hence it is assumed that the bulk of the vapour is at or close tothe liquid core temperature (i.e. saturation temperature). The low-viscosity, low-densityvapour-flow experiences a higher acceleration than the dense core flow. This results in anincreased velocity differential across the interface which may lead to liquid entrainment fromthe wavy interface. It may also lead to more interaction of the liquid core with the heatedsurface through dry collisions and will increase the turbulence level in the vapour annulus.The resulting increase in wall-vapour and wall-core heat transfer will lower the walltemperature; if the wall temperature drops below the minimum film boiling temperaturerewetting may occur. Rewetting can also occur at higher temperatures if it is caused by apropagating rewetting front.

57

Modeling of IAFB requires proper relationships for the interfacial heat and momentumtransfer between the superheated vapour blanket and the subcooled or saturated liquid core.The net interfacial heat transfer determines the rate of vapour generation and, therefore, thefilm thickness.

The heat transfer process in IAFB can be considered by the following heat fluxcomponents:

(i) convective heat transfer from the wall to vapor (qW; v);(ii) radiation heat transfer from the wall to liquid (qrad);(iii) heat transfer from vapor to the vapor-liquid interface (qv, 0;(iv) heat transfer from the vapor-liquid interface to the liquid core (qi, i).

In the case of subcooled film boiling, the last heat flux component is used for bothvaporization and reducing liquid subcooling. For saturated liquid, qy is used only forvaporization, thus increasing the vapor film thickness more rapidly.

A significant increase in heat transfer coefficient with an increase in liquid subcoolinghas generally been observed in pool film boiling and flow film boiling [e.g. see Groeneveld(1992)]. The effect of subcooling on the film boiling heat transfer coefficient may beexplained as follows: heat is transferred primarily by conduction across a thin vapour film tothe interface (convection and radiation may also be significant). Here a fraction of the heatreceived is used for heating up the liquid core, while the remainder is used for evaporation.Higher subcoolings results in less evaporation, and hence a thinner vapour film, whichconsequently increases the heat transfer coefficient h. During tests on heated bodies immersedin water, Bradfield (1967) observed that subcooled film boiling with subcoolings less than35°C resulted in a calmer interface with a wavelike motion compared to saturated boiling.Most experimental studies show an increase in h with an increase in Xe at the high massvelocities (G > 1000 kg/m2s at P > 6 MPa [Stewart (1981); Laperriere and Groeneveld(1984)] and G > 100 kg/m2s at P = 0.1 MPa, [Fung (1981)]) although at times this increase inh may not be evident near zero qualities. At lower mass velocities, a decrease in h (=qw/(Tw-Ts)) with an increase in Xe is frequently observed. The above effect is due to the gradualthickening of the vapour film with increasing Xe. This will increase the resistance toconduction heat transfer which may still be dominant at low G and Xe values. It also increasesthe convective heat transfer coefficient, defined as hc = q/(Tw-Tv). Since at low flows thevapour temperature Tv may rise significantly above saturation, the Tw may still increasedespite the increase in hc. At high mass velocities (G > 2000 kgm^s"1) Tv is usually nearsaturation and h generally increases with Xe. With an increase in quality or void fraction theIAFB regime breaks up at void fraction of about 30-60% and the transition to the DFFBregime occurs.

The recent reviews on IAFB published by Groeneveld (1992), Johannsen (1991) andHammouda (1996) include description or tabulations of new or modified models for IAFBheat transfer related to reflood heat transfer of water-cooled nuclear reactors. These reviewsare based on publications by Analytis et al. (1987), Klyugel et al. (1986), Mosaad (1986), Hsuet al. (1986), Wang et al (1987,1988), Yan (1987), and Lee et al. (1987).

4.2.4.3. Slug flow film bo iling

Slug flow film boiling is usually encountered at low flows and void fractions which aretoo high to maintain inverted annular film boiling but too low to maintain dispersed flow film

58

boiling. In tubes, it is formed just downstream of the inverted annular flow regime when theliquid core breaks up into slugs of liquid in a vapour matrix. The prediction of the occurrenceof slug flow during bottom flooding ECC is important because of the change in heat transferrate long before the arrival of the quench front.

Several theories for the break-up of the IAFB regime have been proposed. Data of Chi(1967) suggest that the liquid core will break up into slugs which are equal in length to themost unstable wavelength of interfacial waves. Subcooling tends to stabilize the liquid-vapourinterface, and thus inhibits the formation of slug flow. Smith (1976) assumes the location ofslug flow to correspond to the point of minimum heat transfer coefficient in the film boilingregion. In doing so, he is suggesting that if the vapour velocity is high enough to break up theliquid core, then it is also high enough to considerably improve the heat transfer coefficient.Kalinin (1969) observed another possible mechanism for the onset of slug flow in transienttests. Immediately after the introduction of liquid to their test section, the sudden increase invoid due to vapour generation at the leading edge of the liquid caused a back pressure whichdecelerated the flow. The higher pressure and lower flow rate caused a decrease invaporization and the flow surges forward. The cycle was repetitive with a liquid slugseparating from the liquid core with each cycle.

4.2.4.4. Dispersed flow film boiling (DFFB)

The DFFB regime is characterized by the existence of discrete liquid drops entrained ina continuous vapor flow. This flow regime may be defined as dispersed flow film boiling,liquid deficient heat transfer, or mist flow. It is of importance in nuclear reactor cores for off-normal conditions such as the blowdown or ECCS phase of a LOCA, as well as in steamgenerators.

The DFFB regime usually occurs at void fractions in excess of 40%. No exact lower-bound value for the onset of DFFB is available as the transition from IAFB or slug flow filmboiling is likely to be gradual. According to Levitan and Borevskiy (1989), the beginning ofthe dispersed regime is determined by the following correlation

l/3

where

Xad represents the onset of annular dispersed flow.

In the DFFB regime the vapour temperature is controlled by wall-vapour and vapour-droplet heat exchange. Due to the low superheat of the vapour near the dryout location orrewetting front the vapour droplet heat exchange is small and most of the heat transferred fromthe wall is used for superheating the vapour. At distances further downstream, however, an"equilibrium" vapour superheat can be reached, i.e. the amount of heat transferred from the wallto the vapour may approximately balance the amount of heat absorbed by the droplets (from thevapour) and used for evaporation of the droplets.

59

Near the heated surface the heat exchange between vapour and droplets is enhanced dueto the temperature in the thermal boundary layer being well above that of the vapour core[Cumo and Farello (1967)]. If the temperature of the heated surface is below the minimumtemperature, some wetting of the wall may occur resulting in an appreciable fraction of thedroplets being evaporated [Wachters (1965)]. At temperatures above the minimum temperatureonly dry collisions can take place (collisions where a vapour blanket is always present betweensurface and droplet). Little heat transfer takes place to small droplets which resist deformationand bounce back soon following a dry collision [Wachters (1965); Bennett et al. (1967)].However, the dry collisions disturb the boundary layer thus improving the wall-vapour heattransfer. Larger droplets are much more deformable and tend to spread considerably thusimproving both the wall-vapour and vapour-droplet heat exchange [Cumo and Farello (1967);Wachters (1965)]. This spreading may lead to a breakup into many smaller droplets if theimpact velocity is sufficiently high [McGinnis and Holman (1969)]. The vapour film thicknessseparating the stagnated droplets from the heated surface is difficult to estimate but must begreater than the mean free path of the vapour molecules in order to physically separate theliquid from the heated surface.

Attempts to evaluate the direct heat flux to the droplets due to interaction with the heatedsurface have resulted in the postulation of many simplifying assumptions, e.g. Bailey (1972),Groeneveld (1972), Plummer et al. (1976). These assumptions may be questionable whenapplied to liquid deficient cooling. However, due to lack of direct measurement of droplet-wallinteraction during forced-convective film boiling conditions no other approach can be taken.

The heat flux encountered during DFFB can be partitioned as follows:

(i) Heat transfer from wall to liquid droplets which reach the thermal boundary layerwithout wetting the wall (dry collisions) — qWdd;

(ii) Heat transfer from wall to liquid droplets which temporarily wet wall (wet collisions) —Iwdwj

(iii) Convective heat transfer from wall to vapor — q^;(iv) Convective heat transfer from steam to droplets in the vapor core — qvd;(v) Radiation heat transfer from wall to liquid droplets — qra(i;(vi) Radiation heat transfer from wall to vapor — qrad.

The most important unknown in DFFB is the thermal non-equilibrium or vapoursuperheat. The vapour superheat increases with heat flux (its main driving force) anddecreases with interfacial area and interfacial drag. Both the interfacial area and the interfacialdrag are dependent hydrodynamic parameters controlled by the dynamics of interfacial shear,droplet generation, break-up, and coalescence mechanisms, and evaporation history. There arebasic difficulties in determining experimentally important parameters such as the interfacialdrag coefficient. Since the spectrum of droplet sizes may vary from case to case, and theclosure laws depend on droplet diameter, the formulation of universally valid closure laws isdifficult. This has been investigated in more detail analytically and experimentally byAndreoni and Yadigaroglu (1991, 1991a, 1992), and Kirillov and Smogalev (1973).

4.3. FILM BOILING DATA BASE

4.3.1. General

Because of the importance of film boiling heat transfer and reactor accident analysis,there has been a significant interest in providing a good film boiling data base for reactor

60

conditions of interest. The high CHF and generally low heat transfer coefficients in film boilingresults in high surface temperatures and this restricts the range of conditions at whichmeasurements are feasible under steady state conditions. Hence many of the earlierexperimental data were obtained in cryogenics and refrigerants, in temperature controlledsystems [Smith (1976); Ellion (1954)] or from transient tests [Newbold et al. (1976); Cheng andNg (1976); Fung (1977)]. However, a novel approach has been developed at Chalk River forobtaining subcooled film boiling data [Groeneveld and Gardiner (1978)]. Using the so-calledhot-patch technique steady-state subcooled and low-quality film boiling data can be obtained ina heat flux controlled system at heat flux levels well below the CHF. This approach haspermitted a much more extensive study of film boiling especially at IAFB conditions [e.g.Stewart (1981); Fung (1981); LaPerriere and Groeneveld (1984); Gottula et al. (1985);Johannsen(1991)].

4.3.2. Tube and annuli

Tables 4.1 and 4.2 summarize the test conditions of film boiling data obtained in tubesand annuli, respectively. Although the coverage is extensive, there is still a scarcity of filmboiling data at low pressures and low flows. Recent data obtained by CIAE have helped toresolve this lack of data [Chen and Chen (1998)].

4.3.3. Bundle

Table 4.3 summarizes the film boiling data available for rod bundles. Many otherbundle data have been obtained but these are inaccessible because of their potentialcommercial value and because of licensing concerns. The film boiling bundle data base ismore limited than the CHF bundle data base because of the higher temperatures which makestesting much more difficult. The hot patch approach, used successfully in tubes, cannot beused in bundles and this further restricts this data base.

4.4. OVERVIEW OF FILM BOILING PREDICTION METHODS

4.4.1. General

Accurate prediction of the wall temperature in the film boiling regime is of vitalimportance in accident analysis of the core and steam generators of advanced water cooledreactors. The following four methods for estimating the film boiling heat transfer arecommonly used:

(i) Semi-theoretical equations for pool film boiling (Section 4.4.2);(ii) Semi-theoretical models to predict flow film boiling. They are based on the appropriate

constitutive equations, some of which are empirical in nature;(iii) Purely empirical correlations for flow film boiling, which do not account for any of the

physics, but instead assume a forced convective type correlation;(iv) Phenomenological equations for flow film boiling, which account for the thermal non-

equilibrium and attempt to predict the "true" vapour quality and the vapour temperature.

Because of the proliferation of film boiling prediction methods (there are currently over20 film boiling models available and well over 50 correlations) tabular methods have recentlybeen proposed. Tabular methods are well accepted for the prediction of CHF and are basedmore closely on experimental data. They will be discussed in Section 4.4.5.

61

ON

TABLE 4.1. EXPERIMENTAL DATA ON FILM BOILING IN TUBES

Year

1950

1960

19611961

1961

19631964

1965

1967

1967

1967

1967

1967

1969

1969

19701971

Reference

Me Adams

Hemann

CollierParker

Swenson

MiropolskiyBertoletti

Bishop et al.

Bennett et al.

Era et al.

Herkenrath et al.

Mueller

Polomik

Brevi

Kutcukcuoglu

LeeKeeys

P,MPa

0.8-24

2.1 - 10.3

0.1-7.40.2

20.7

3.9-21.67

16.6-21.5

6.89

6.89 - 7.28

14 - 20.5

6.9

6.9

5

1-3.3

14-186.9

G,kg/m2s

70 - 230

190 - 1070

580-138050-100

949 - 1356

398-21001000-4000

2000 - 3377

380-5180

1090-3020

693 - 3556

700 - 1000

700-1350

470 - 3000

1000-4000700-4100

d,mm

3.3

2.5 - 8.4

4.3-6125.4

14

85; 9

2.5-5.1

12.6

6

10-20

15.7

15.7

6.5; 9.3

7-14

12.7

Lm

0.5

1.5

9; 13

X

0.89-1.0

0.08-0.98

-2.43-3.420.4 - 0.90

0.07-0.91

0.229-1.48

0.456-1.24

-0.117-1.32

0.62-1.0

0.8-1.0

0.40-1.0

0.3 - 0.70.15-0.90

MW/m2

0.03 - 0.54

0.16-0.92

0.16-0.410.01-0.06

0.297-0.581

0.07-2.330.1-1.60

0.905-1.92

0.383-2.07

0.20-1.65

0.253 - 1.666

0.5-0.85

0.55-1.10

0.38-1.5

0.03 - 0.57

0.3 - 1.40.8-1.5

T°c

379-499

390-610

454 - 840

295 - 630

374 - 592

n,number of

points

5500

Notes

L/d=14.7 - 80

L/d=36-100

L/d=35 - 170rewetting of wall

unstable temperature

L/d=50, 150

heated by sodiumcosine heatflux distribution

TABLE 4.1. (CONT.)

Year

1972

1973

1974

1975

1981

1982

1983

1983

1983

1983

1985

1987

1988

1988

1988

1989

1996(b)

Reference

Bailey

Sutherland

Grachev etal.

Janssen et al.

Fang

Stewart, Groeneveld

Becker et al.

Borodin

Chen and Nijihawan

Laperriere

Gottula et al.

Remizov et al.

Chen, Fu, Chen

Mosaad

Swinnerton etal.

Chen Yu-Zhou et al.

Chen and Chen

P,

MPa

17.8

6.9

7-14

0.683 - 7.07

0.089 - 0.145

1.94-9.05

2.98-20.1

8.2 - 8.34

0.226 - 0.419

3.95 - 9.63

0.290 - 0.79

4.9 -19.6

0.15-1.02

0.11

0.2-1.92

0.41 - 6

0.1-6.0

G,

kg/m2s

668 - 2690

24 - 175

350-1000

16.6 -1024

50 - 495

114-2810

4.96-3110

1350 - 6870

18.7-69.5

962-4510

1.21 - 19.3

350-3000

100-512

100 - 500

200 -1000

47.6 - 1462

23-1462

d,

mm

12.7

38

11.12

12.6

11.8-11.9

8.9

10-24.7

8.9

14.1

9

15.7

10

7; 12

9

9.75

12

6.8; 12

L,

m

2.1-9.0

1.71

1.5-10.2

0.99

0.28

0.92

2.2

1.2-2.6

X

0.391 - 0.95

0.35-1.3

0.584-1.63

-0.026-0.138

-0.12-0.736

-0.042-1.65

0.133-1.07

0.072 - 0.838

-0.119-0.597

0.319-0.87

0 - 2.48

-0.12-0

0 - 0.46

-0.05 - 0.24

-0.05-1.36

q>

MW/m2

372 - 454

0.016 - 0.063

0.05 - 0.3

0.034 - 0.997

0.025 - 0.257

0.064 - 0.459

0.083 - 1.29

0.90 - 2.7

0.0027 - 0.088

0.069 - 0.736

0.003 - 0.044

0-1.28

0.005 - 0.5

0.028 - 0.260

0.015-0.49

T

°C

341-

362-1

306-

279-

378-

229-

308-

175-

727

148

780

722

720

648

781

789

n

number of

points

414

1023

37298

38

2100

273

3568

Notes

U-tube

L/d=120-220

heated by

sodium

ON

OS

TABLE 4.2. EXPERIMENTAL DATA ON FILM BOILING IN ANNULI

Year

1961

196419671969

1971

1971

1980

Reference

Polomik

BennettEraGroeneveld

Polomik

Era

OKB GidropressReport No 431-0-047

P,Mpa

5.5-9.7

3.5-6.97

4.1-8.3

6.9

5

1.5-15.9

G,kg/m2s

1000-2560700 - 2700

800 - 38001350-4100

350 - 2700

600 - 2200

8.9- 148

4mm

9.1do= 15.5

L,m

3.24

X

0.15-1.00.2-1.0

0.3 - 1.0

0.15-0.65

0.2 - 0.9

0.5 - 1.96

q ' 2MW/m2

0.6-2.2

0.6-1.80.13-1.00.5-1.4

0.75 - 2.3

0.2 - 0.6

0.03 - 0.275

T°c

nnumber of

points

1154

Notes

de= 1.52; 3.05

de = 2; 5 spacerstwo heated sectionsseparated by unheatedsectionde=3.3spacersde = 3 uniformly andnonuiformly heated

TABLE 4.3. EXPERIMENTAL DATA ON FILM BOILING IN ROD BUNDLES

Year

1963

196419651966

1968

19701971

1973

1976

Reference

Matzner

HenchKunsemillerAdorni

Matzner

Groeneveld et al.Me Pherson

Groeneveld andMe PhersonOKB GidropressReport No 213-0-084

P,MPa

6.9

4.1-9.74.1-9.75-5.5

3.4-8.3

6.310.9-2.17

6.8 - 10.2

1-6

G,kg/m2s

700 - 2700

390 - 2700390-1350800-3800

700 - 1400

1100-2200700-4100

630-1350

130-700

dr,mm

15.2

13.8

9.1

s,mm

16.2

14.8-15.8

L,m

0.5

0.5

1.75

n,numberofrods

19

237

19

328

36

7

X

0.17-0.60

0.2 - 0.90.3 - 0.70.2 - 0.9

0.23 - 0.38

0.3 - 0.60.28 - 0.53

0.35 -s-1

0.6-1.24

MW/m2

0.8-2.35

0.45-1.90.55-1.00.2-1.5

0.033-1.160.6-1.45

0.08-1.2

0.1-0.35

nnumberof points

160

301

Notes

de = 8.3 mm,mainly stabletemperaturede= 10.3 mmde = 11.2mmmainly stabletemperaturede = 6.7 mmsegmented bundleinpile test trefoilde = 7.8mmmainly stabletemperatureinpile testTw = 650°Cd e

=2.5 mmspacers

4.4.2. Pool film boiling equations

4.4.2.1. Horizontal surfaces

Pool film boiling from a horizontal surface has been investigated for over 50 years, andcan be reasonably well represented by analytical solutions. Most pool film boiling and lowflow film boiling prediction methods [e.g. Bromley (1950); Borishanskiy (1959, 1964);Berenson (1961)] are of the following form:

a = CXv

3 -r -pv(p^ - pv)arad{z,Tw,Ts)

where

r* is an equivalent latent heat and includes the effect of vapour superheat, sometimesexpressed as r* = r + 0.5(Cp)vAT. The velocity effect on the heat transfer coefficient is takeninto account by the F-function. The symbol / represents either a characteristic length (e.g.diameter) of the surface or the critical wave length which is usually defined as:

Other relations for pool film boiling have been proposed by Epstein and Hauser (1980),Klimenko (1981), Dhir (1990), and Sakurai (1990a, 1990b). Table 4.4 gives the correlationsfor the film boiling heat transfer on horizontal surfaces in pool boiling based on the followingdimensional groups

N u = a l / X v (4.4)

4.4.2.2. Vertical surfaces

Saturated pool film boiling on vertical surfaces has been investigated experimentallyand theoretically by many researchers including Hsu, and Westwater (1960), Suryanarayana,and Merte (1972), Leonardo, and Sun (1976), Andersen (1976), Bui, and Dhir (1985).Frequently equations similar as those for horizontal surfaces are proposed for verticalsurfaces; the main difference is usually in the constant C in front of the equation and thecharacteristic length. Sakurai (1990a, 1990b, 1990c) developed new equations for film boilingheat transfer on surfaces with different configurations. In particular, correlations for verticalplates and tubes, spheres and horizontal plates were derived by the same procedure as thatused for horizontal cylinders. The latter was derived by slightly modifying the correspondinganalytical solution to get agreement with the experimental results.

66

TABLE 4.4. CORRELATIONS FOR FILM BOILING HEAT TRANSFER ON HORIZONTAL SURFACES IN POOL BOILING

References Correlations Notes

1

Chang1959 Nu = 0.295

where

a/3

C -ATP

= g/3(pv-p^Pr/pvv

/ =

r =r + 0.5 C AT

PJ

(1)

(2)

(3)

(4)

Laminar flow in vapor film.

Berenson1961 Nu = 0.672

\l/2

Ra-C -AT

P

(5) Laminar flow in vapor film; Ra, /, and r according toEqs. 2, 3 and 4.

Frederkinget al. 1966

Nu = 0.20

1/3

Ra-C -AT

P

(6) Turbulent film boiling; Ra, /, and r according toEqs. 2, 3 and 4.

HamillBaumeister, 1967

(cited by Klimenko1981)

Nu = 0.648 Ra-C AT

P

1/4

r =r + 0.951 C ATPJv

(7)

7.1

Turbulent film boiling; Ra and / according toEqs. 2 and 3.

Clark, 1968(cited by Klimenko

1981)Nu = 0.612 Ra-

C -ATP )

111

(8) Turbulent film boiling; Ra, /, and r according toEqs. 2, 3 and 4.

OS00

TABLE 4.4. (CONT.)

1Lao, 1970

(cited by Klimenko1981)

Nu = 185Ra

x-0.09

C ATv P J

(9)

(10)

Turbulent film boiling; Ra, r according to Eqs. 2 and4.

Klimenko1981

= 0.19Ar1/3Pr1/3-f1C -AT

Pv

Here

Pv-v

(11) Laminar flow in vapor film; / according to Eq. 3

(12)

r

C •\ Pv AT

1

0.89-r

C •

{ pvAT

)

forC -AT

pv

• < 1 . 4

forCpv-AT

(13)

TABLE 4.4. (CONT.)

1

Klimenko1981

Nu = 0.0086Ar1/2Pr1/3-f2

Here Ar>0.8

C AT(14) Turbulent film boiling.

/ \

V C pV A T

1

0.71

at

CP V A T ;

1/2CpvAT

<2

(12)

atCpvAT

>2

Granovskyetal1992

Nu = 0.031 -(lgA)3-5<p2/3

(Ar)<

Cp-AT~* I + *r -Pr r -Pr

(13)

(14)

Turbulent film boiling; / and r* according to Eq. 3 and 4.

9 = +

(15)

(16)

4.4.2.3. Downward-facing surfaces

Recent experiments by Kaljakin et al. (1995) on curved down-facing surfaces havedemonstrated that in many cases the heat transfer coefficient prediction for pool film boilingor for low mass velocities can be based on the modified Bromley formula (1950):

(4.6)Y U- v A 1 • X

where

(3 = 0.8 + 0.00220; 0 is a surface inclination angle, in degrees;AT = Tw - Ts; is a characteristic length along the vessel surface, andr* is defined as in Equation 4.2.

Eq. 4.6 is reportedly valid for a pressure range of about 0.1 - 0.2 MPa.

4.4.3. Flow film boiling models

4.4.3.1. General

The first flow film boiling models were developed for the DFFB regime. In thesemodels, all parameters were initially evaluated at the dryout location. It was assumed that heattransfer takes place in two steps: (i) from the heated surface to the vapour, and (ii) from thevapour to the droplets (see also Section 4.2.4.4). The models evaluate the axial gradients indroplet diameter, vapour and droplet velocity, and pressure, from the conservation equations.Using a heat balance, the vapour superheat was then evaluated. The wall temperature wasfinally found from the vapour temperature using a superheated-steam heat transfer correlation.Improvements to the original model have been made by including droplet-wall interaction, bypermitting a gradual change in average droplet diameter due to the break-up of droplets, andby including vapour flashing for large pressure gradients.

Subsequent to the development of models for the DFFB regime, models have also beendeveloped for the IAFB regime. They are basically unequal-velocity, unequal-temperature(UVUT) models which can account for the non-equilibrium in both the liquid and the vapourphase. Most of the models are based on empirical relationships to predict interfacial heat andmomentum transfer. Advanced thermalhydraulic codes employ similar models to simulate thepost-CHF region. Universal use of film boiling models is still limited because of unresolveduncertainties in interfacial heat transfer, interfacial friction and liquid-wall interactions, aswell as the difficulty in modelling the effect of grid spacers.

4.4.3.2. IAFB regime

A large number of analytical models have been developed to simulate the IAFBconditions [e.g. Analytis and Yadigaroglu (1987); Kawaji and Banerjee (1987); Denham(1983); Seok and Chang (1990); Chan and Yadigaroglu (1980); Takenaka (1989); Analytis(1990); de Cachard (1995); Mosaad (1988), Mosaad and Johannsen (1989); Hammouda,Groeneveld, and Cheng (1996)]. The salient features of many of these models have been

70

tabulated by Groeneveld (1992) and Hammouda (1996). Table 4.5 provides an overview ofsome of the current IAFB models. The majority is based on two-fluid models and employsome or all of the assumptions listed below:

(i) at the quench front the liquid is subcooled and the vapour is saturated;(ii) vapour will become superheated at the down stream of the quench front;(iii) both the vapour and liquid phases at the interface are at saturation;(iv) the interfacial velocity is taken as the average of the vapour and liquid velocities;(v) there is no entrainment of vapour in a liquid core or of the liquid in the vapor film;(vi) the vapour film flow and the liquid core flow are both turbulent.

The above assumptions clearly indicate differences from the classical Bromley-typeanalysis for pool film boiling, and there is no smooth transition between these two cases.

The main challenge in implementing IAFB models into two-fluid codes resides in theproper choice of the interfacial heat and momentum exchange correlations. Interfacial heatexchange enhancements may be due to turbulence in the film, violent vaporization at thequench front, liquid contacts with the wall near the quench front, upstream grid spacers orapproaching quench front, and the effect of the developing boundary layer in the vapour film.The large amount of vapour that may be generated right at the quench front (release of theheat stored in the wall due to quenching) must also be taken into account. Refloodingexperiments clearly show an exponential decay of the heat transfer coefficient with distancefrom the quench front for a length extending some 20 or 30 cm above the quench front.

The constitutive relations employed are based on the simplifying assumptions. Ingeneral, there are too many adjustable parameters and assumptions made by different authorswhich results in a multitude of IAFB models. A part of the reason is the difficulty in verifyingthe proposed interfacial relationships with experimental-based values. Despite this, relativelygood agreement was reported by the model developers between their model prediction and theexperimental data, but no independent review of their models was ever made.

During high-subcooling film boiling the vapour film at the heated surface is very thinover most of the IAFB length. Here the prediction methods or models tend to overpredict thewall temperature, presumable because the conduction-controlled heat transfer across a verythin film was not properly accounted for.

4.4.3.3. DFFB regime

Significant non-equilibrium between the liquid and vapor phases is usually present inthe DFFB regime, except for the high mass velocities. Mixture models are intrinsically notable to predict this non-equilibrium and hence the need for two-fluid models. As theinterfacial heat transfer is easier to determine either experimentally or analytically for theDFFB regime vs. the IAFB regime, these models tend to be somewhat more accurate thanthose simulating IAFB.

As discussed in Section 4.2 the heat transfer in DFFB is a two-step process, i.e. (i) wallto vapour heat transfer and (ii) vapour to entrained droplets heat transfer. Enhancement ofheat transfer due to the interaction of the droplets with the heated wall are usually smallexcept for low wall superheats, near the TMFB , where transition boiling effects becomeimportant.

71

TABLE 4.5. SUMMARY OF IAFB MODELS

1.

2.

3.3.1

3.23.3

3.4

4.4.1

4.2

4.3

4.4

5.5.1

5.2

6.

7.7.1

7.2

7.3

CHARACTERISTICS

Dimensional ( I D — one-dimensional;2D - two-dimensional)

Flow Structure (h - homogeneous;t - two fluids)

Vapour Generationfrom liquid surface

evaporation of drops in a vapour filmevaporation of drops on a wall

wall-liquid interaction

Vapour Filmflow regime (/ - laminar; t - turbulent)

presence of drops

boundary of liquid (s - smooth;w - wavy)Radiation through a vapour film

Central Flow1 - one phase flow; 2 — two-phase flow

flow regime (/ - laminar; t - turbulent)

Accuracy by author (%)

VerificationPressure, MPa

Velocity, m/s

Subcooling, K

REFERENCES

OO

as

iI1

ID

t

+

—-

-

t—w

+

1

/, t

1

0.025

0.17<70

OO

t—1

ID

t

+

—-

-

t—s

-

1

l,t

20-25

1-20

0.85

735-200

OOOS

1

ID

t

++-

-

t-s

+

1

t

<1

0.1

10

O\OOON

|

o1—>

1

ID

t

+

—-

-

t-w

+

1

tRMS12

0.1-8

0.1

1020-60

OOas

1I1bS

PH

ID

t

+

—-

-

/, t

-s

-

1

t

0.1

0.2

0.3<20

il| |

ID

t

+

—-

-

/, t-s

+

1

t

OO

as

tJ

2D

t

+

—-

+

t-w

+

1

t

11

2; 4

OOONI - H

I&ID

t

+

++

-

l,t+s

+

2

t

72

TABLE 4.6. SUMMARY OF DFFB MODELS

CHARACTERISTICS

REFERENCES

00ON r

ONON

oo

ON

1

1

11

O N

*—r

<D

O

su>

O\

p00ON

10

2.

3.

4.4.1

4.2

4.3

4.4

4.5

5.

6.6.1

6.2

6.3

Dimensional (ID - one-dimen-sional; 2D - two-dimensional;3D - three-dimensional)

Flow Structure (h - homoge-neous; dv - drops + vapour)

Scheme of Heat Transfer*

EffectsDeposition of drops

Spectrum of dropsEffect of drops on transportproperties of mediumSlip

Radiation


VerificationPressure, MPa

Mass Flux, kg/m2-s

Quality

2D,3D

dv

II

ID ID

dv

n

ID

dv

II

ID

dv

III

ID

dv

III

ID

RMS

12.315 RMS

6.93

0.1-6

24

1000

0.05

1.4

0.7

21.5

130

5200

0.08

1.6

ID

dv

II

2D

II

* Scheme of Heat Transfer I - heat transfer wall to vapourII -1 + wall to dropletIII -1 + II + wall to drops.

73

TABLE 4.6. (CONT.)

1

1

1.

2.

3.

4.4.1

4.2

4.3

4.4

4.5

5.

6.

6.1

6.2

6.3

CHARACTERISTICS

2

Dimensional (ID - one-dimen-sional; 2D - two-dimensional;3D - three-dimensional)

Flow Structure (h - homoge-neous; dv - drops + vapour)

Scheme of Heat Transfer*

EffectsDeposition of drops

Spectrum of drops

Effect of drops on transportproperties of mediumSlip

Radiation


Verification

Pressure, MPa

Mass Flux, kg/m2-s

Quality

REFERENCES

Osr—<

Iao

12

ID

h

II

-

-_

+

-

CNOOOs

6t»OO

13

ID

dv

m

+

+_

-

-

OOOs

OOOs

1• 1—<

14

ID

dv

m

+

-_

-

+

20

400

1600

OOOs

Vl

15

ID

dv

III

-

-—

-

-

oOs

u

e?<D

VI

16

ID

dv

II

-

-_

-

+

RMS

10

1-18

100

1500

Os

17

ID

dv

n

-+_

+

-

OOOs

1CO

%Pi

1

18

ID

dv

III

+

-+

-

-

CNOOOs»—1

I

19

ID

h

II

+

-_

-

-

3-12

300

1400

0.3

0.1

OOOs1—1

1

i

20

ID

dv

II

--+

-

-

24

0.1-7

12

100

0

0.99

CNOOOst—<

'S•4-*U

>%

21

ID

dv

II

-

+_

-

-

30

60

OOOs

11

22

ID

dv

II

-

+_

+

-

* Scheme of Heat Transfer I - heat transfer wall to vapourII -1 + wall to dropletHI -1 + II + wall to drops.

74

At high mass velocities, the droplet size is small, the interfacial area is large and theinteraction between the vapor and droplets is sufficiently intensive to keep the vaportemperature close to the saturation temperature. Here a Dittus-Boelter type equation, based onthe volumetric flow rate and vapour properties, provides a reasonable estimate of the overallheat transfer coefficient, and an analytical model is not required.

A large number of models have been developed for the DFFB regime. The first DFFBmodels were developed for the liquid deficient regime by the UKAEA [Bennett (1967)] andMIT [Laverty and Rohsenow (1967)]. In these models, all parameters were initially evaluatedat the dryout location. The models evaluated at the axial gradients in droplet diameter, vapourand drop velocity, and pressure, from the conservation equations. Using a heat balance, thevapour superheat was then evaluated. The wall temperature was finally found from the vapourtemperature using a superheated-steam heat transfer correlation. Bailey (1972), Groeneveld(1972), and Plummer et al. (1976) have suggested improvements to the original model byincluding droplet-wall interaction, by permitting a gradual change in average droplet diameterdue to the break-up of droplets, and by including vapour flashing for large pressure gradients.Additional expressions for the vapour generation rate have also been suggested by Saha(1980), and Jones and Zuber (1977).

The various models tend to have the same basic structure but differ in the choice ofinterfacial relationships and separate effects. The following variants have been used in themodels:

(i) droplet size: based on various Weber number criteria for the initial droplet size and forsubsequent break-up; Weber number may be ignored; subsequent droplet break-up isoften ignored

(ii) droplet size distribution: various assumptions have been made, e.g. constant size,gaussian distribution

(iii) droplet drag force: depends on drag coefficient and assumed shape of the droplet(iv) interfacial heat transfer: depends on phase velocity differential: various equations are

possible(v) droplet-wall heat transfer qdw." this may be expressed by a separate heat flux qjw = 0 or

qdw = f(Tw-TsAT); may be ignored (qaw = 0) or may be incorporated by enhancement ofthe convective heat transfer.

Despite these variants the agreement between the predictions of most DFFB models isquite good at steady-state conditions, and medium flows and pressures (G = 0.3-6 MgnrV1 ,P = 5-10MPa).

Details of the models and the equations on which they are based may be found inAndreoni and Yadigaroglu (1994), Groeneveld and Snoek (1986), Chen and Cheng (1994),and Hammouda (1996). Table 4.6 provides an overview of the major features of the DFFBmodels.

4.4.4. Flow film boiling correlations

4.4.4.1. IAFB correlations

For the IAFB regime many equations have been proposed, including the classicBromley (1950) equation for the vertical surface, the Ellion (1954) equation, the Hsu and

75

Westwater (1960) equation, the modified Bromley equation for pool film boiling: [Leonard(1978); Hsu (1975)], and various other ones. Groeneveld (1984, 1992) later updated byHammouda (1996) have tabulated the proposed equations for IAFB. None of the proposedprediction method appears to have a wide range of application as far as flow conditions isconcerned or as far as geometry is concerned. Most are derived for tube flow or for poolboiling conditions and none has been derived for application in a bundle geometry equippedwith rod spacing devices. Hence caution should be exercised before applying them toAWCRs.

4.4.4.2. DFFB correlations

4A.4.2A. Correlations based on equilibrium conditions

Most of the equilibrium-type equations for film boiling are variants of the single-phaseDitrus-Boelter type correlation. These equations were empirically derived or simply assumethat there is no non-equilibrium and hence use the same basic prediction method as forsuperheated steam except that the Reynolds number is usually based on the homogeneous (noslip) velocity. These equations usually have a very limited range of application, or are validonly for the high mass velocity regime where non-equilibrium effects are small. The mostcommon correlations of this type are tabulated in Table 4.7. Among these the DougallRohsenow (1963), the Miropolskiy (1963) and the Groeneveld (1973) equations are the morepopular ones. The latter two are both based on Miropolskiy's Y-factor as defined in Table 4.7.This factor is particularly significant at lower pressures and qualities. Groeneveld optimizedhis coefficients and exponents based on a separate data base for tubes, annuli and bundles.

4.4.4.2.2. Phenomenological equations based on non-equilibrium conditions

Phenomenological equations attempt to predict the degree of non-equilibrium betweenthe liquid and vapour phase. These equations are a compromise between the empiricalcorrelations discussed in the previous section and the film boiling models described inSection 4.4.3. The phenomenological equations generally predict an equilibrium vapoursuperheat corresponding to fully developed flow and based on local equilibrium conditions.They generally do not require knowledge of upstream conditions, such as location of thequench front. An overview of the phenomenological film boiling equations is given in Table4.8.

The non-equilibrium equations are based on film boiling data for water and have beendeveloped by Groeneveld and Delorme (1976), Plummer et al. (1977), Chen et al. (1977,1979), Saha (1980), Sergeev (1985a), Nishikawa (1986). Most of them use the of the Dirtus-Boelter type equation e.g. Equation 4.7:

~ 2 ~ v v (4-7)V

where

a, b, and c are constants and a is the two-phase heat transfer coefficient in a tube with aninside diameter D.

76

TABLE 4.7. EMPIRICAL FLOW FILM BOILING HEAT TRANSFER CORRELATIONS

References

Collier1962

Collier1962

Swenson et al.1961

Miropolskiy1963

Dougall1963

Bishop et al.1964

Correlations

q-[D0-2/(G-X)08] = c0[(Tw-Ts)]m (1)

whereco=[exp(O.O1665-G)]/389;m= 1.284-0.00312G;Tw- Ts<200°C; [G]-kg/m2-s; rD]-m; [q]-kW/m2; [T]-K or °C;q-[D02/(G-X)0'8] = 0.018(Tw- Ts)

0921 (2)whereTw-Ts<200°C;[G]-kg/m2-s; |"D]-m; [q]-kW/m2; [T]-Kor°C;

Nuw= 0.076{Rew[X + ( p v / p , ) (l-X)](pw/pv)}08Prw

04 (3)

Nu = 0.023Rev° 8Prw08[X +(pv /pt) (1-X)]° 8-y (4)

where

y=l-0 .1[ (p , /p v ) - l ) ] ( l -X) 0 - 4 ;

Nu==as-d/A^; Rev=G-D/(Xv;

0.23^ q< 1.16MW/m2;8 < D <24 mm;

Nu = 0.0203{Re[X + (p v /p^) (l-X)]}a8Pr04 (5)

Nuw=0.098{Rew(pw/pv)[X+ (p v / P i ) ( l -X) ]} 0 8 Pr w0 8 3 ( p v / p ^ ) a 5 (6)

Ranges of ParametersP

MPa7.03

7.03

20.6

3.9-21.6

<3.5

16.8-21.9

Gkg/m2-s>1000

<10b

945-1350

800-4550

1660-3650

1350-3400

X

0.15-1

0.15-1

<0.5

0.1-1

TABLE 4.7. (CONT.)

References

Bishop et al.1964

Bishop et al.1965

Bishop et al1965Tong 1965Quin1966

Kon'kov et al.1967

Henkenrath et al.1967

Brevi et al.1969

Lee1970

Correlations

Nuv=0.055{Rev(p£/pv)[X+(pv/p£)(l-X)]}°-82Prw0-96(pv/p^)0-35

(1+26.9-D/L) (7)

Nu, = 0.0193 Re?-8 Pr |2 3 (pv /p^)0 0 6 8 pC+(p v / P / ) ( l -X)f68 (8)

Nu, =0.033 Re?'8 Pr |2 5 (pv/p^)0197[X+ (pv/p,)(l -X)f738 (9)

Nuw= 0.005(D-G/JV)° 8Prv05 (10)

Nuv = 0.023 {Rev [X + (p v /p^)( l -X)]}°- 8Prw0 - 4 ( |a v /^^) a 1 4 (11)

Nu = 0.019-{Rev[X + ( p v / p ^ ) ( l -X)]}08Prw (12)

where0.29 <q < 0.87 MW/m2;D = 8 mm;

Nuw = 0.06{Rew[X+ ( p v / p ^ ) ( l -X)] (pv/p£)Prw}08(G/1000)04(P/Pcr)27(13)

Nu^ = 0.0089(Ree X/cp)°'84 p r / 3 3 3 [(1 - Xcr)/(X - Xcr)]0124- (14)

wherecp - void fraction.

Tw - T 8 = 1.915-

q-W/m2

q

2

(15)

PMPa

16.8-21.9

4.08-21.9

4.08-21.9

>7006.9

2.94-19.6

14.2-22.3

5.06

14.2-18.2

Gkg/m2-s

350-3400

700-3140

700-3140

>141150

500-4000

750-4100

500-3000

1000-4000

X

0.1-1

0.07-1

0.07-1

<0.10.72-0.79

0.1-1

0.4-1

0.30-0.75

TABLE 4.7. (CONT.)

References

Slaughterbecketal. 1973

Groeneveld1973

Cumo et al.1974

Tong, and

Young1974

Mattson1974

Mattson1974

Correlations

Nuv=1.604-10-4{Rev[X+(pv/p^)(l-X)]}a838PrwL81q0-278(V^rr0-508

(16)

where

[qj-Btu-h-'-fr2;

Nuv= 0.052Rev0668Prw

126[1 - 0.1 ( p , / p v -1)0"4 (1 - X)04]'106 (17)

where

Nuv = a,-DAv; Rev= (G D/p,) [X + (p v /pe) (1 - X)]

0.03< q <2MW-m'2; 2.5 < D <12.8 mm; annuli.

Nuv=0.0091RevL154 (18)

q = qcr+ 0.023(Tw- TyXK/d^GJ)/^)0 -8Pr°333 (19)

asD/?w=3.28-10-4{RevU5[X+ ( p v / p / ) ( l -X)]}0777

TJ^ 1.69 0.18 |S / i \-0-294 n mPrV;W q [kY/k£) (20)whereD is equivalent hydraulic diameter, ft;M-Btu-h^ft^F^ql-Btu-h^-ft-2;

ccsD/Xv= 1.6-10-4{Rev[X+ ( p v / P i ) ( l -X)]}°-838Prv,w1-8Iq0i78(^v A^)"0"508

(21)whereD is equivalent hydraulic diameter, ft;[A,]-Btu-hJ-ft"1-FI;[q]-Btu-h'1-ft-a;

PMPa

6.88-20.2

0.07-21.5

4.05-10.1

6.9-22

<20.8

Gkg/m2s

1050-5300

130-4000

400-5150

710-5170

710-5170

X

0.12-0.9

-0.12-3.09

0.20-1.65

0.1-0.9

0.1-0.9

00o TABLE 4.7. (CONT.)

References

Groeneveld1975(a)

Groeneveld1975 (a)

Groeneveld1975 (a)

Groeneveld1975 (a)

Campolunghietal. 1975

Vorob'ev et al.1981

Correlations

Nuv= 1.09-10-3{Rev[X+ (p v / p* ) ( l -X)]}°-989Prv>wL41Y-115 (22)

where

Y=[ l -0 . l (p^ /p v - l ) ° - 4 ( l -X) 0 4 ]

0.12 < q <2.1 MW-m"2; 2.5 < D <25 mm; Tubes;

Nuv= 1.85-10"4Rev [X + ( p v / p j ) ( 1 -XJJPTW^'Y"1-1^0 '1 3 1 (23)

where

Y = [ l - 0 . l ( p ^ / P v - l ) a 4 ( l - X ) 0 4 ]

[qj-Btu-h^ff2; Tubes;

Nuv = 7.75-10"4{Rev [X + (pv /p e)(1 - X ) ] } 0 - 9 0 ^ 1 - 4 7 ^ 1 ^ 0 1 1 2 (24)

where

Y = [ l - 0 . l ( p ^ / P v - l ) a 4 ( l - X ) 0 4 ]

[qJ-Btuh^-ft"2; Tubes and annuli

Nuv = 3.27-10"3{ Rev [X + (p v / p^ ) (1 - X)]}0-901?^1-32^1-5 (25)

where

Y = [ l - 0 . l ( p ^ / P v - l ) a 4 ( l - X ) 0 - 4 ]

[ql-Btu-h^-ft"2; Tubes and annuli

Nuw= 0.038[RewPrw(x/(p)(pw/pv)(G /1000)]04(P/Pcr)27 (26)

Nuw= 0.0228{Rew[X+ (p v / p^ ) ( l -X)]}°-8Prw°-4[(l-Xcr)/(X-Xcr)f28

[ (G . r /q ) ( P v / P , ) r o 4 . ( v v / v w ) 0 - 6 8 6 (27)

where2 < q <1 MWm2; D =10 mm;vv and vw is specific vapor volume at saturation and wall temperatures.

PMPa

6.8-21.5

5.5-21.5

3.4-21.5

3.4-21.5

9.8-17.6

Gkg/m2s

700-5300

700-5300

700-5300

700-5300

350-1000

X

0.1-0.9

0.1-0.9

0.1-0.9

0.1-0.9

Xcrto 1

Xcrto 1

TABLE 4.7. (CONT.)

References Correlations PMPa

Gkg/m2s

X

Remizov1987

7-14 350-700 Xcrto

s

14.5 + 0.0296-G(54()0-9.38GXX-Xc

(X +0.001)-Xc

where[as]-W-m'2-K;0.2 < q < 0.7 MW-rn2;D = 10mm;And for narrow range data P is 16.0-18.OMPa

(as)-as

(28)

where [q ]-W-m

(29)

oo

to TABLE 4.8. NON-EQUILIBRIUM PDO HEAT TRANSFER CORRELATIONS

References Correlations

Ranges of Parameters

P

MPa

G

kg/m -s

X

Plummer1976

Nuv = ^ ^ - = 0.023 Re°v8- Prf • F

or

= 0.023A,, GD

0.8 v0.14

. P r V 3 . 1 + 0.3D

L + 0.01D

where

L is a length from CHF section and S is a slip ratio, which is given as

= l + 0.5I I \0.205(P</Pv) 1

,0.016

where

y=A/KB and K is the degree of non-equilibrium

= C,ln\V2

o- — d-xj + c,

for water A=2.5; B=0.264; Ci=0.07 and C2=0.40.

(1)

(2)

TABLE 4.8. (CONT.)

References

Groeneveldand

Delorme1976

Marinov1977

Correlations

Nuf= 0.008348{(G -D/u^) [Xa+ (pv /p*)( l - Xa)]}0-8774Pf°-6112

Xa can be found from (hVa-hve)/r = exp(-tan\|/) where hVa=hi>s+Xar

i|/=f(P,G,X,q)

where the functional relationships my be found in Groeneveld and Delorme 91976

the subscript "f' refers to the temperature between wall and bulk of vapour flow;0.03 < q <2 MW-m"2, 5 < D < 20 mm;

Nuv= 0.023(G-d/|av)°-8[X+ (p v /p , ) ( l - X)f8Prw0-8 ( 4 )

for the wall surface temperature from

Tw=Tv+(q/ocv)

0.06 < q < 0.75 MW-m'2;

D=12 mm;

P

MPa

0.7-2.15

0.1-7

G

kg/m2-s

130-4000

30-850

X

-0.12-3.09

0.65-1.1

oo

TABLE 4.8. (CONT.)

References

Remizovand Sergeev

1987

Correlations

Method of calculation of Tw from the differential equation:

^ = 1.75mXv (pv/p£)2(G/q)2x2[(l -Xa)/Xa][(X-Xa)/Xa]n

where

m and n are the functions of D; AT; Xa is found from boundary conditions

X = Xcr and Tv = Ts;

The wall temperature Tw = Tv + q/ocn, is defined from (hv - h ^ ] / r = (X - Xa)/Xa—> hv;

where

an is calculated from the correlation

Nuv= 0.028Rev°-8Prv°'4(Pw/pv)L15, at q < 1 MW-nV2.

P

MPa

5-18

G

kg/m2-s

100-1000

X

x>xcr

The equations are based on a vapour Reynolds number which is usually based on theactual quality Xa instead of the equilibrium quality Xe. Some of the equations [e.g. Plummeret al. (1977)] also permit slip to exist between the phases as shown in Equation 4.8:

Rev =G D

X a + S ( l - X a ) V

p. (4.8)

where S is the slip ratio which in this case depends on the degree of non-equilibrium.

However most of the phenomenological equations are based on the assumption ofhomogeneous flow. Further details of the equations are provided in Table 4.8.

The main difference between the various phenomenological equations is primarily inthe relation between the equilibrium quality Xe and the actual quality Xa. For exampleGroeneveld and Delorme (1976) recommended the following relationship:

[Xe /XJ - max(l, Xe) = exp(-tam[/) (4.9)

where

\\r = f(ReV;hOm, P, q, Xe)

The non-equilibrium correlation developed by Plummer et al. (1977) was based anexpression for (Xa - XdO)/(Xe - Xd0) = f(G) while Tong and Young (1974) expressed Xa/Xe =f(Xe, G) and Chen et al. (1977) expressed Xa/Xe = f(P, Tw). Plummer based his equation ondata for water, nitrogen and freon-12 and takes into account the wall-to-drop heat transfer ocWdas well. The heat flux from the wall to vapor and from the wall to droplets is given as,

q = a w v ( T w - T v ) + a w d ( T w - T . ) (

where the heat transfer coefficient to the vapour ocwv is given in Table 4.8 and the wall-to-droplet heat transfer coefficient ocwd is given as,

and 8f = 1.2-1CT4 and the void fraction q> is based on the actual quality.

Sergeev's method (1978, 1985a, 1985b, and 1987) evaluates the wall temperature and isvalid for G < 1000 kg/m2-s; P = 3 ^ 18 MPa; X>Xcr; AT=TW-Ts< 500°C. It is based on aknown critical quality and the assumptions that:

(i) the radiation heat transfer coefficient is small,(ii) the interaction of drops with a wall is insignificant.(iii) the heat transfer coefficient can be found from a single-phase convection equation (e.g.

see Section 4.5.4).

85

The relation between Xe and Xa can be found by solving the following differentialequation:

y - y ""m " v • - — ^ s - • x „ (l - x * e a

C m A „ 11 A „ I

where

C is an empirical constant; C = 1.5 for tubes, rod bundles, and annuli at the PDO regime ontwo surfaces; C - 3 for annuli at the PDO regime on one surface. Besides, m and n arefunctions of pressure; Uw and Uth are the wetted and thermal channel perimeters. Eq. 4.12 canbe integrated from XCT (at Tva = Ts) to the given channel section for given Xe. This method hasbeen used for tubes, annuli (with a gap of 2 mm and more) and rod bundles (without heattransfer enhancement due to spacing devices).

4.4.5. Look-up tables for film boiling heat transfer in tubes

The high interest in film boiling heat transfer over the past 30 years has led to aproliferation of filmboiling models and prediction methods, many of them film-boiling-regime specific, applicable only over the range of test conditions investigated by theindividual investigator. Hence it has become increasingly more difficult to select film boilingprediction methods which can be used with confidence over a wide range of conditions andgeometries as will be encountered in AWCRs. In addition, these prediction methods,particularly the models and phenomenological equations, are very time consuming even withthe use of fast computers. This is because of (i) frequent iteration, (ii) the large number ofequations involved, and (iii) evaluation of many different fluid properties during eachiteration.

To simplify the film boiling prediction process, and to make it more universallyapplicable, the film boiling table look-up method has been developed. This approach issimilar to the CHF table look-up method, and is basically a methodology which is based on acombination of all available film boiling data and predicted values covering a very wide rangeof conditions. It contains a tabulation of normalized heat transfer coefficients for fullydeveloped film boiling at discrete values of pressure, mass flux, quality, and heat flux.Because the world's film boiling data base still has significant gaps, particularly at conditionswhere experiments are difficult (i.e. high surface temperatures), the tables are based partiallyon extrapolation using the observed trends from the better film boiling models or correlationsand of known asymptotic trends. Ideally the tabulated heat transfer coefficient should bebased on the wall superheat with respect to the actual vapour temperature, but since thistemperature is almost always difficult to evaluate, the equilibrium vapour temperature or thesaturation temperature are usually used as reference temperatures.

The look-up table method for film boiling was first suggested by Groeneveld (1988) andhas since been refined into an improved method [Leung et al. (1997)], based on over 15 000film boiling data for a wider range of conditions. Leung's most recent look-up table is givenin Appendix IV (Table IV.I), where the fully developed heat transfer coefficient with respect

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8.00 —i

6.00

S

Oo

S2 4.00

OQPH

2.00

0.00

-1.00 0.00 1.00X, Steam quality

2.00 3.00

FIG. 4.4. PDO heat transfer coefficient as a function of steam quality; P=16 MPa, G=1000kg/(m2s), q=0.6 MW/m ; the line presents the look-up table-1999 values, the pluses areexperimental points.

to the equilibrium vapour temperature is tabulated for discrete values of mass velocities (0 to7 Mgm s"1 in 12 steps), pressures (0.1 to 20 MPa in 14 steps), quality (-0.2 to +1.2 in11 steps) and heat flux (0.05 to 3 MWnT2 in 9 steps). In the development of this table thedeveloping heat transfer coefficients close to the dryout point or quench point were not used,as these values depend on prior history which is different in accident scenarios (where filmboiling prediction methods are most often applied) then in steady state conditions. This tablewas compared extensively with the data base and the rms error was 6.73% in surfacetemperature. The error and data distribution for Leung's table [Appendix IV (Table IV.II)]show significant gaps in the data base at low flows and medium pressures. Some of these gapsin the data have since been partially filled by the CIAE [Chen and Chen (1998)].

Recently Kirillov et al.(1996) have taken parts of the Leung/Groeneveld table,experimental data and combined them with measurements and predictions from the Sergeev etal.(1985a) model, and added a gradual transition between. There heat transfer coefficients

87

were tabulated for pressures of 0.1 to 20 MPa, mass flux values of 250 to 2000 kgm 2s l,thermodynamic qualities from -0.2 to +2.2 in intervals of 0.1 and heat flux values of 0.2, 0.6and 1.0 MWnT2 and is presented in Appendix V. Kirillov however defined his heat transfercoefficient based on a saturation temperature but extended his tabulated values up tothermodynamic qualities of 2.2, which corresponds to equilibrium bulk steam temperaturesover 1000 °C at low pressures. This representation suppresses the effect of mass velocities,particularly at the highest qualities as can be seen in Appendix V. An example of the variationof the heat transfer coefficient is shown in Fig. 4.4.

Chen and Chen (1994) measured film boiling at low flows and low to mediumpressures, and noted the presence of strong inlet effects at these conditions. SubsequentlyChen and Chen (1998) proposed a new method for predicting the film boiling heat transferbased on finding the Plummer (1976) non-equilibrium factor K = (Xa - Xc)/(Xe- Xc) which isa function only of P, G, and Xc.. The K value can be derived using the method ofAppendix VI. This permits the vapour temperature to be found from iteration after which,using a pure steam heat transfer equation, the heat transfer coefficient and wall temperaturecan be found. The table is suitable for finding the heat transfer coefficient in the developingheat transfer region downstream of the CHF location. This method differs significantly fromthose discussed above as it requires also knowledge of the critical quality; as expected thiswill improve the prediction accuracy particularly for the low flow cases where developingnon-equilibrium effects are significant (the Leung table look-up method does not predict thedeveloping heat transfer, only fully developed heat transfer coefficients were used in itsdevelopment). For low flow Chen's data and table, as presented in Appendix VI [Chen andChen (1998)] make a significant contribution as they fill a gap in both the data base and in ourunderstanding of the non-equilibrium effects during low flow film boiling. However in manycases the non-equilibrium is still an inferred value as actual vapour temperature measurementsare difficult to measure and have only been obtained successfully over very limitedconditions.

The above table prediction methods partially complement each other but can result insignificantly different predictions. These differences in predictions need to be resolved andwork is in progress to wards this.

4.5. RECOMMENDED/MOST RECENT FILM BOILING PREDICTION METHODS

4.5.1. Pool film boiling

There is a general agreement that the modified Bromley equation for film boiling maybe used for horizontal surfaces:

1/4 (4.13)

For vertical surfaces, changes to the constant in front of the equation and thecharacteristic length are required as indicated in Section 4.4.2.

4.5.2. Flow film boiling

4.5.2.1. Film boiling table

Because of the large number of film boiling methods presently available, it would bedesirable to have more universal prediction method. The bundle look-up table method appearsto be a more promising approach because of the following reasons:

(i) simplicity

(ii) correct asymptotic, and parametric trends

(iii) most universal method with the best overall fit to the fully developed film boiling database

(iv) with modifications now being introduced, it can be used to account for effects such asgeometry, spacer devices etc.

A similar approach has recently been adopted for predicting the CHF in safety analysis[e.g. in RELAP and CATHARE (Section 3.6.1)]. The current look-up tables do not yetproperly account for the developing flow effects, in particular as it is encountered duringaccident scenarios, but a combination of the approach proposed by Chen and Chen (1998) andan appropriate transformation from a time dependent heat transfer coefficient [e.g. a = f(t -tc)] to a length dependent heat transfer coefficient [a = f(z - zc)] is expected to resolve thisshortcoming. Current work in progress will also account for the effects of upstream flowobstructions (such as grids or endplates), which are known to have a significantdesuperheating effect.

The film boiling look-up table and other film-boiling prediction-methods are leastreliable in areas where data are unavailable, and this is particularly true if strong non-equilibrium effects are present. At high flow this problem disappears and the equilibrium-typecorrelations will apply, i.e. the equations of Table 4.8 will apply but with the vapourtemperature based on equilibrium conditions (Tv = min [Tsat, Tb]).

The film boiling look-up table method has been used for the following applications

(i) as a normalized database for validation of film boiling models;

(ii) as an alternative to film boiling models which cover only limited ranges of flowconditions.

For application in AWCR condition, correction factors may eventually be incorporatedin the look-up table to account for the effects of the heat flux distribution and transmissions.They are not available at present. The mechanistic models may also be used to account forthese effects [e.g.: Analytis and Yadigaroglu (1987); Analytis (1989, 1990) and Chen andChen (1997)].

4.5.2.2. Inverted annular film boiling

The film-boiling prediction methods are least accurate for the IAFB regime. The database coverage in IAFB is much more sparse compared to DFFB. Upstream effects, priorhistory effects and spacer effects will affect the heat transfer prediction. No properly validated

89

method covering all conditions of interest is available for this regime. At the low flow end ofthe IAFB regime the pool boiling prediction method will provide a lower-bound prediction.The look-up table method for the IAFB regime is based both on experimental data (whereavailable) and on the model of Hammouda and Groeneveld (1996).

4.5.2.3. Dispersed flow film boiling

High mass flux

The prediction accuracy for flow film boiling is most accurate at high mass-velocities(G > ~3 MgmT^s"1) where non-equilibrium effects are unimportant. For these conditionsexisting equations for heat transfer to superheated steam may be used. Section 4.5.4 presentssome of these equations. The film boiling look-up tables (Appendix IV, Table IV.I andAppendix V) at high mass velocities are based primarily on single phase heat transferequations.

Low mass flux

At low mass velocities non-equilibrium effects become significant and the predictionaccuracy reduces. Also the effect spacers will complicate the prediction accuracy. Furtherwork on the look-up table is required as the recent data of Chen and Chen (1994) has not yetbeen used in updating the AECL look-up table. The upstream history effect is also moreimportant at these conditions as film boiling may never become fully developed; a methodsuch as the one suggested by Chen and Chen (1998) may need to be combined or incorporatedin the look-up table. No single validated prediction method is available covering allconditions of the low mass velocity DFFB regime.

4.5.3. Radiation heat transfer in film boiling

The radiation heat transfer coefficient is usually evaluated separately and added to theconvection heat transfer coefficient, i.e.:

a = aconv + ocrad (4.14)

It should be noted that the radiation heat transfer is particularly significant for the IAFBregime. In this case, the heat transfer at the wall-to-liquid radiation is expressed according toSiegel and Howell (1972) as,

S (T W +T S ) (TJ+T S2 )

a r a d = 5.67 • lO"8 ^ ^ ^

where:

Tw and Ts are the surface and the saturation temperatures, respectively in K; sw and s i arerespectively the emissivity of the heated surface and the liquid.

90

At Tw < 700 °C the radiation heat transfer is relatively small for the DFFB regime.Nevertheless, it is added to the convection heat transfer coefficient. The following simpletwo-gray-plane method may be used:

8 ( T W + T S ) ( T J + T S2 )

a r a d = 5.67 • 10"8 V w x

s ; y '-L (4.16)

'V

The emissivity of the heated surface sw is dependent on both surface material andsurface temperature. The surface emissivity is affected by oxidation, particularly for Zr withthin ZrC>2 coatings, while the vapour emissivity can be indirectly affected by the dropletconcentration.

4.5.4. Correlations for single phase heat transfer to superheated steam

Single phase heat transfer to superheated steam is important as it provides an asymptoticvalue to the film boiling heat transfer for cases when the actual quality approached 1.0 . Anumber of tube-based correlations have been proposed; all of them are of the Dittus-Boeltertype and give similar predictions. The following two equations are frequently used:

(i) Miropolskiy (1975) equation, valid for P = 4 - 22 MPa, G = 0.4 - 2 MgmV 1 and pw/pv

= 0.5 - 0.9, range of Re = 105 - 2 x 106

Nuv = av-D/Xv= 0.028Rev°-8-Prva4(pw/pv)115 (4.17)

where

Rey ~ KJ'J

(ii) Colborn equation:

Nuv = 0.023Reva8-Prv

a4(Tva/Tw)0-5 (4.18)

4.5.5. Application to rod bundles

Virtually all film boiling prediction methods are based on correlations derived for tubes.Applying them to the prediction of fuel-bundle cladding temperatures is common practice; indoing so the following bundle-specific factors should be considered:

(i) bundle enthalpy and flow imbalance(ii) heat transfer enhancement downstream of grids or spacers

91

(iii) adjacent wet surface or cold wall

(iv) narrow gaps between elements

(v) change in wall friction in dry portion of bundle (resulting in higher flow in drysubchannels)

(vi) non-circular subchannel cross section shape

(vii) presence of axial dry-streaks in partially dry bundles.

Reactor safety computer codes may account for some but not all of the above effects.Bundle enthalpy and flow imbalance can be evaluated using subchannel codes (see alsoSection 3.4.4) to predict the flow conditions in individual subchannels. The flow conditions,in turn, will permit the evaluation of the local CHF as described in Chapter 3. When the heatflux of a rod surface facing a given subchannel exceeds the local CHF, both the wall-fluidheat transfer coefficient and the wall friction factor will be reduced drastically. By keepingtrack of the circumferential drypatch fraction (CDF) and the axial drypatch length (ADL) foreach rod facing each subchannel, the flow and enthalpy distribution as well as the distributionin film-boiling heat transfer coefficient can be evaluated. This will permit the evaluation ofthe fuel temperature distribution and the prediction of the extent of fuel melting. The aboveapproach is being incorporated in some of the subchannel codes to permit a detailedprediction of the cladding temperature distribution.

As was noted also in Chapter 3, the change in geometry from tubes to bundlesconsiderably complicates the thermalhydraulic analysis. Aside from the cross-sectiondifferences, the global and local effects of the grid or spacers on the wall heat transfer, quenchbehaviour and interface mass and energy transport are usually unknown, or at best areincluded via an empirical fix for each grid spacer configuration. In general (grid) spacers canhave the following effects:

(viii) promotes rewetting downstream of the grid due to the larger turbulence level (i.e.encourages multiple quench fronts)

(ix) acts as a cooling fin

(x) causes desuperheating of the vapour

(xi) results in an increase of interfacial area by breaking up the droplets or liquid core(xii) homogenizes the flow.

No satisfactory models are available to model the film boiling heat transfer in bundlesequipped with grid spacers and hence most of the codes neglect the presence of the spacergrids. This is despite the fact that experimental studies by Yao et al. (1982), Yoder et al.(1983), Lee et al. (1984), Ihle et al.(1984) and others have demonstrated the beneficial effectof grid spacers, particularly during a reflooding phase where grid spacer can considerablereduce cladding temperatures.

92

4.6. APPLICATION TO FILM BOILING PREDICTION METHODS CODES

4.6.1. General

Most system analysis codes used in LWR and HWR safety analysis represent the coreor bundle by an equivalent tube. Bundle specific effects as discussed in Section 4.5.4 aboveare frequently ignored. Also the axial node size used is frequently so large that it skips thetransition boiling IAFB region. Thus the details of spatial variation of the heat flux cannot beconsidered properly, unless the size of the nodes is drastically reduced.

4.6.1.1. RELAP

Different geometrical configurations (more than 10) can be accommodated in theRELAP5 code. For each of these, various options for heat transfer modes and correlations areavailable. Here reference is made to the "default" geometry, that is a standard cylinderexternally cooled, [see RELAP5 (1995)].

In the reference geometry, at least three types of flow patterns are distinguished,namely, inverted annular flow, slug flow and dispersed flow. The mechanisms of the wall-to-fiuid heat transfer include conduction across a vapor film, convection to flowing vapor,convection between vapor and the droplets, and radiation across the vapor film.

For pool film boiling and IAFB conditions where forced convection is not important,the Bromley (1950) equation is basically adopted in this case. However, the Berenson (1961)wave length concept was introduced in this equation, together with a factor to account for thevoid fraction effect, and a correction for the liquid subcooling proposed by Sudo and Murao(1975). For higher vapour velocities, the wall-vapour heat transfer coefficient is predictedusing the well-known Dittus-Boelter type correlation for single phase heat transfer. TheAnalytis and Yadigaroglu (1987) model has also been implemented in RELAP5/MOD 2 andwas reported to successfully predict reflooding transients [Analytis (1989,1990)].

Radiation heat transfer will be evaluated using Sun's (1976) methodology byconsidering the radiative heat transfer between wall-to-liquid, wall-to-vapor, andvapor-to-liquid and their respective emissivities.

4.6.1.2. CATHARE

In the CATHARE code the heat transfer from the wall across the vapour film ispredicted with either

(xiii) Bromley-type equation modified to account for the effect of subcooling,(xiv) a pure heat conduction equation,(xv) Dittus-Boelter type equation, used primarily at higher vapor velocities and void

fractions, and(xvi) natural convective equations at high void fraction and low velocities.

93

If in doubt which equation applies, the maximum predicted heat transfer coefficientshould be used. Further details of the CATHARE equations can be found in Groeneveld(1982), Bestion (1990) and Groeneveld and Rousseau (1982). The radiation from wall to bothphases is modeled using equations proposed by Deruaz and Petitpain (1976), which strictlyspeaking are applicable only for DFFB.

4.7. CONCLUSIONS AND FINAL REMARKS

(1) The prediction of film boiling heat transfer is much more complex than that of CHF.Aside from requiring a 4th parameter (heat flux) in the look-up table, non-equilibriumeffects should also be considered, especially in the region just down steam of thequench, near flow obstructions, and at low flows.

(2) Current film boiling models and correlations appear to be flow regime specific. Nosingle prediction method can currently provide a satisfactory prediction for both theIAFB and the DFFB regime.

(3) All film boiling prediction methods are derived or validated based on data obtained indirectly heated tubes. They have generally not been validated for bundle geometriesexperiencing severe transients. Effects such as differences in flow cross sections(subchannels vs. tubes), presence of narrow gaps and cold walls are usually notaccounted for.

(4) Fuel bundles are equipped with bundle appendages (as in HWRs) or grid spacers. Theseappendages have a CHF and heat transfer enhancing effect, as well as a desuperheatingeffect thus reducing the non-equilibrium. They also result in having multiple quenchfronts. Current film boiling prediction methods usually ignore these important effects.

(5) The current proliferation of film boiling prediction methods, and their limited range ofvalidity, has reinforced the need for universal prediction methods. Several suchprediction methods are now under development.

(6) Despite the ever increasing speed of computers, the evaluation of film boilingtemperatures is still time-intensive requiring coarse nodalization. The main reasons forthis are: (i) frequent iteration, (ii) the large number of equations involved, and (iii)evaluation of many different fluid properties during each iteration. Table look-upmethods vastly simplify this prediction process, and permit direct evaluation of the filmboiling heat transfer coefficient.

(7) Caution should be exercised when extrapolating steam heat-transport properties to hightemperatures (>1500°C). In addition to the uncertainty in extrapolating to hightemperatures, the dissociation of steam will also affect the steam properties.

(8) The film boiling prediction methods discussed in this chapter were based primarily onsteady state conditions. Transient can have a significant effect on film boiling. Asidefrom affecting the region over which film boiling will occur (by affecting the CHF)IAFB or pool film boiling can be destabilized, possibly resulting in a momentary returnto transition boiling. Increases in heat transfer coefficient of 10-40 times have beenrecorded due to small pressure pulses or by passing through shock waves.

94

(9) During the past three years progress has been made in developing look-up tables forfilm boiling heat transfer. This has been embodied in this chapter. No finalrecommendation for any specific prediction method for film boiling has been made aswork on combining the most promising methods into a single, fully validated method isstill in progress.

(10) The table prediction methods discussed previously partially complement each other butcan result in significantly different predictions. Further research activities to resolvethese differences in prediction methods are currently in progress.

(11) Table IV.I (see Appendix IV) and Table V.I (see Appendix V) contain values for filmboiling heat transfer for all heat flux values including those where the heat flux value isbelow the CHF but above the minimum heat flux. The data base for these table usuallycomes from the "hot patch" type of experiments or from predictions of models.

(12) The differences between the three main prediction methods for film boiling heat transferappear exaggerated as the reference temperatures of the heat transfer coefficients differ;a table based only on surface temperature will result in a convergence of theseprediction methods.

(13) The heat transfer coefficient <% applied in Table 4.1 and Fig. 4.4 is referred to atemperature difference (Tw - Ts). This results in seeming absence of the mass flux effecton the heat transfer intensity at high qualities. However, such definition of as isconvenient for engineering calculations. It is preferred to use only the value Ts as thereference temperature because that allows to simplify considerably the prediction of theFFB heat transfer coefficient. It should be borne in mind that the recalculation betweenthe values of as and cc? leads to as/cXv - (Tw — TV)(TW — Ts) improper results and thedistortion of function as(G). During recalculation cCs-xxv we discovered that the effectis negligible and as & G0'8. The calculation was carried out by the method based onMiropolsky's work (1975) where it was found that Nu &Re°-8and a?« G08. Two FFBheat transfer regimes should be distinguished: 1) PDO (post-CHF) heat transfer, 2)before-CHF heat transfer. At the present time it is not obvious yet whether the heattransfer correlations will be the same for both regimes or not. The FFB heat transferprediction in a rod bundle is performed by both the CHF look-up table for bundles andthe LUT for FFB in tubes with appropriate correction factors.


ADORNI, N., 1966, Heat Transfer Crisis and Pressure Drop with Steam-Water Mixtures:Experimental Data with Seven Rod Bundles at 50 and 70 kg/sm2, CISE R-170.

ANALYTIS, G.Th., 1989, Implementation of a Consistent Inverted Annular Flow Model inRELAP5/MOD2, Trans. ANS 60, 670-671.

ANALYTIS, G.Th., 1990, Implementation and Assessment of an Inverted Annular FlowModel in RELAP5, ICAP Meeting, Madrid.

95

ANALYTIS, G.Th., YADIGAROGLU, G., 1987, Analytical modelling of inverted annularfilm boiling, Nucl. Eng. Design V. 99 201-212.

ANDERSEN, J., 1976,Low-Flow Film Boiling Heat Transfer on Vertical Surfaces, AJChESymp. Ser., V.73 (2-6).

ANDREONI, M., YADIGAROGLU, G., 1991a, Study of Two-Dimensional Effects on DFFBby Eulerian-Lagrangian Model, Proc. of the 27th ASME/ANS National Heat Transfer Conf.,July 28-31, Minneapolis.

ANDREONI, M., YADIGAROGLU, G., 1991b, A Mechanistic Eulerian-Lagrangian Modelfor DFFB, in Phase-Interface Phenomena in Multiphase Flow, Hemisphere Publ. (Hewitt,G.F., Mayinger, F., Eds), London.

ANDREONI, M., YADIGAROGLU, G., 1992, Effect of the Cross-sectional DropletDistribution in DFFB at Low Mass Flux, Proc. NURETH-5 3, 823-831.

ANDREONI, M., YADIGAROGLU, G., 1994, Prediction methods for dispersed flow filmboiling, Int. J. of Multiphase Flow 20 1-51.

AURACHER, H., 1987, Partielles Filmsieden in Zweiphasenstromungen, Fortschritt-Ber.VDI, R. 3, No 142, VDI-Verl., Dusseldorf.

AURACHER, H., 1990, Transition Boiling, Proc. 9th Int. Heat Transfer Conf., Jerusalem 1(69-90).

AVDEEV, A.A., 1986, Heat transfer and pressure drop at film subcooled boiling in channels,Teploenergetika 4 39-42 (in Russian).

BAILEY, N.A., 1972, Dryout and Post Dryout Heat Transfer at Low Flow in a Single TubeTest Section, Europ. Two-Phase Group Meeting, Riso.

BANKOFF, S.G., MEHRA, V.S., 1962, A quenching theory for transition boiling, Ind. Eng.Chem. Fund. 1 38^0 .

BARZONI, G., MARTINI, R., 1982, Post-dryout Heat Transfer: an Experimental Study inVertical Tube and a Simple Theoretical Method, Proc. 7th Int. Heat Transfer Conference,Munich 5 401^10.

BECKER, K.M., 1983, An Experimental Investigation of Post Dryout Heat Transfer, Dep. ofNucl. Reactor Engn., Roal Institute of Technology, Stockholm, KHT-NEL-33.

BENNETT, A.W., 1964, Heat Transfer to Mixtures of High Pressure Steam and Water in anAnnulies, Rep. AERE-R-4352.

BENNETT, A.W., HEWITT, G.F., KEARSEY, H.A., KEEYS, R.K.F., 1967, Heat Transferto Steam Water Mixtures Flowing in Uniformly Heated Tubes in which the Critical Heat Fluxhas been Excluded, Rep. AERE-R-5373.

BERENSON, P.J., 1961, Film boiling heat transfer from a horizontal surface, J. Heat Transfer83 3 (351-358).

96

BERENSON, P.J., 1962, Experiments on pool-boiling heat transfer, Int. J. Heat MassTransfer 5 (985-999).

BERTOLETTI, S., 1961, Heat Transfer and Pressure Drop with Steam-Water Spray, Rep.CISE R-36.

BESTION, D., 1990, The physical closure laws in the CATHARE code, Nucl. Eng. Des. 124.

BISHOP, A.A., SANDBERG, R.O., TONG, L.S., 1964, High Temperature SupercriticalPressure Water Loop. Part V: Forced Convection Heat Transfer to Water After the CriticalHeat Flux at High Supercritical Pressures, WCAP-2056 (Pt. 5).

BISHOP, A.A., SANDBERG, R.O., TONG, L.S., 1965, Forced Convection Heat Transfer atHigh Pressures After the Critical Heat Flux, ASME Paper 65-HT-31.

BORISHANSKIY, V.M., KUTATELADZE, S.S., 1959, Reference Book on Heat Transfer,Gosenergoizdat, Moscow (in Russian).

BORISHANSKIY, V.M., FOKIN, B.S., 1964, "Heat transfer film pool boiling at naturalconvection", Heat Transfer in Single and Two-Phase Flows, Energy a, Moscow, 221-235 (inRussian).

BRADFIELD, W.S., 1967, On the effect of subcooling on wall superheat in pool boiling,J. Heat Transfer 89 3 (87-88).

BREVI, R., CUMO, M., PALMIERI, A., PITIMADA, D., 1969, Heat Transfer Coefficient inPost Dryout Two-Phase Mixtures, Europ. Two-Phase Group Meeting, Karlsruhe.

BROMLEY, L.A., 1950, Heat transfer in stable film boiling, Chem. Eng. Progress 46 5.

BUI, T.D., DHIR, V.K., 1985, Transition boiling heat transfer on a vertical surface, J. HeatTransfer 107 (756-763).

CAMPOLUNGI, F., CUMO, M., FERRARI, G., 1975, On the thermal design of steamgenerators for LMFBRs, Trans. ANS 20 (137-139).

CHAN, K.C., YADIGAROGLU, G., 1980, Calculations of Film Boiling Heat Transfer Abovethe Quench Front During Reflooding, Proc. 19th Nat. Heat Transfer Conf., Orlando 7 (65-72).

CHANG, YAN-PO, 1959, Wave theory of heat transfer in film boiling, J. Heat Transfer 81 1(1-12).

CHEN, Y., FU, X., CHEN, S.P., 1988, "Experimental and analytical study of inverted annularfilm boiling of water", Experimental Heat Transfer Fluid Mechanics and Thermodynamics(Shah, R. K. et al., Eds.), Elsevier (1438-1443).

CHEN, YU., CHEN, H.Y., 1994, A Model of Dispersed Flow Film Boiling Heat Transfer ofWater, Proc. 10th Int. Heat Transfer Conference, Brighton 7 18-FB-3 (419-424).

97

CHEN YUZHOU, CHENG, P., WANG, J.W., YANG, M., 1989a, Experimental Results ofSubcooled and Low Quality Film Boiling Heat Transfer of Water in Vertical Tubes atModerate Pressure, Proc. NURETH-4, Karlsruhe (1105-1110).

CHEN, YUZHOU, 1989b, Experimental Measurement of the Minimum Film Boiling of FlowWater in Multiphase Flow and Heat Transfer (Chen, X., Veziroglu, T.N., Tien, C.L., Eds)393^00.

CHEN, J.C., OZKAYANAK, F.T., SUNDARAM, R.K., 1979, Vapor Heat Transfer in Post-CHF Region Including the Effect of Thermodynamic Non-Equilibrium, Nucl. Eng. Design 51(143-155).

CHEN, J.C., SUNDARAM, R.K., OZKAYNAK, F.T., 1977, A PhenomenologicalCorrelation for Post-CHF Heat Transfer, Rep. NUREG-0237.

CHEN Y.Z., CHEN, H.Y., 1994, "An experimental investigation of thermal non-equilibriumin dispersed flow film boiling of water", Proc. Int. Conf. on New Trends in Nuclear SystemThermohydraulics, Pisa 1 (31-38).

CHEN Y., CHEN, H., 1996a, Forced convection heat transfer to steam in tubes with differentdiameters, Chinese J. Engineering Thermophysics 17 (107-110).

CHEN Y., CHEN, H., 1996b, "Experimental results of steady-state film boiling of forcedflowing water", Paper presented at 2n Research Co-ordination, Vienna.

CHEN Y., CHEN, H., 1997, "Assessment of RELAP5/MOD2.5 with staedy-state dispersedflow film boiling experiments", Proc. 5th Topical Meeting on Nuclear Thermal Hydraulics,Operation and Safety.

CHEN Y.Z., CHEN, H.Y., Aug 1998, "A tabular method for prediction of the heat transferduring saturated filmSeoul, Rep. of Korea.during saturated film boiling of water in a vertical tube", Proc. 111 Int. Heat Transfer Conf.

CHENG, S.C., NG, W., 1976, Transition boiling heat transfer on forced vertical flow via ahigh thermal capacity heating process, Lett. Heat and Mass Transfer 3 (333-342).

CHENG, S.C., RAGHEB, H., 1979b, Transition boiling data of water on Inconel surfaceunder forced convection, Int. J. Multiphase Flow 5 (281-291).

CHI, J.W.H., 1967, Slug flow and film boiling of hydrogen, J. Spacecraft and Rockets 4(1329-1332).

CLARK, J.A., 1968; Cryogenic heat transfer, Advances in Heat Transfer 5.

COLLIER, J.G., et al., 1961, Heat Transfer to Mixtures of High Pressure Steam and Water inan Annulus. Pt. I: Single Phase Experiments: Superheated Steam, AERE-R 3653.

COLLIER, J.G., et al., 1962, Heat Transfer and Fluid Dynamic Research as Applied to FogCooled Power Reactors, AECL-1631.

COLLIER, J.G., 1980, Convective Boiling and Condensation", McGraw-Hill, London.

98

COLLIER, J.G., 1981, "Post dryout heat transfer", Two-Phase Flow and Heat Transfer in thePower and Process Industries (Bergles, A.E., Collier, J.G., Delhaye, J.M., Hewitt, G.F.,Mayinger, F., Eds) Hemisphere Publishing Corporation (282-324).

CUMO, M., FARELLO, G.E., 1967, "Heated wall droplet interaction for two phase flow heattransfer in liquid deficient region", Proc. Symp. on Two Phase Flow Dynamics, Eindhoven,vol. II (1325-1357).

CUMO, M., URBANI, G.C., 1974, Post-burnout Heat Transfer, CNEN/RT/ING.

DE CACHARD, F., 1995, "Development, Implementation and Assessment of Specific, Two-Fluid Closure Laws for IAFB", Proc. NURETH-7, Saratoga Springs 1 4 (166-191).

DELHAYE, J.M., GIOT, M., RIETHMULLER, M.L., 1981, Thermohydraulics of Two-PhaseSystems for Industrial Design and Nuclear Engineering, Hemisphere Publishing Co.

DENHAM, M.K., 1983, IAFB and Bromly Model, Rep. AEEW-1590.

DERUAZ, R., PETITPAIN, B., 1976, "Modelling of heat transfer by radiation duringreflooding in a PWR", OECD Spec. Meet, on the Behavior of Water Reactor Fuel Elementsunder Accident Conditions, Spain.

DHIR, V.K., 1990, "Nucleate and transition boiling heat transfer under pool and external flowconditions", Proc. 9th Int. Heat Transfer Conf., Jerusalem, 139-155.DOUGALL, R.S., ROHSENOW, W.M., 1963, Film Boiling on the Inside of Vertical Tubeswith Upward Flow of Fluid at Low Qualities, MIT-TR-9079-26.

ELLION, M.E., 1954, A Study of the Mechanism of Boiling Heat Transfer, IPL-20-88, Cal.Inst. Technol.

EPSTEIN, M., HAUSER, G.M., 1980, Subcooled forced convection film boiling in theforward stagnation region of a sphere or cylinder, Int. J. Heat & Mass Transfer 23 2 (179—189).

ERA, A., 1967, Heat Transfer Data in the Liquid Deficient Region for Steam-Water Mixturesat 70 kg/sm2 Flowing in Tubular and Annular Conduits, CISE R-184.

ERA, A., GASPARL G.P., PEOTTI, M., ZAVATARELLI, Z., 1971, "Post dryout heattransfer measurements in an annulus with uniform and non-uniform axial heat fluxdistribution", Europ. Two-Phase Group Meeting, Riso.

FORSLUND, R.P., ROHSENOW, W.M., 1968, Dispersed flow film boiling, J. Heat Transfer,Trans. ASME 90, 399-407.

FREDERKING, T.H., WU, Y.C., CLEMENT, B.W., 1966, Effects of interfacial instabilityfilm boiling of saturated liquid helium-i above a horizontal surface, AIChE J. 12 (238-244).

FUNG, K.K., 1977, Forced Convective Transition Boiling, MSc Thesis, University ofToronto.

99

FUNG, K.K, 1981, Subcooled and Low Quality Film Boiling of Water in Vertical Flow atAtmospheric Pressure, PhD Thesis, University of Ottawa; ARNL Rep. NUREG/CR-2461.

FUNG, K.K., GROENEVELD, D.C., 1982, "A Physical Model of Subcooled and LowQuality Film Boiling of Water in Vertical Flow at Atmosphere Pressure", Proc. 7th Int. HeatTransfer Conf. Munich, 381-386

GANIC, E.N., ROHSENOV, W.M., 1977, Dispersed flow heat transfer, Int. J. Heat MassTransfer 20, 8(855-866).

GOTTULA, R.P.,et al., 1985, Forced Convective, Nonequilibrium, Post-CHF Heat TransferExperiment Data and Correlation Comparison Rep., NUREG/CR-3193 (1985).

GRACHEV, N.S., IVASHKEVITCH, A.A., KIRILLOV, P.L., PROHOROVA, V.A.,TURCHIN, N.M., 1974, "DNB in Steam Generators Sodium-Water and PDO Heat Transfer",Proc. USA-USSR Seminar on Development of Sodium Cooled Fast Breeder Reactor SteamGenerators, Los Angeles (302-331).

GRANOVSKI, V.S., SULATZKY, A.A., HABENSKI, V.B., SHMELEV, S.M., 1992, Filmboiling heat transfer from a horizontal surface, Inzhenerno-fizicheskiy Zhurnal 63 3, 259-269(in Russian).

GROENEVELD, D.C., THIBODEAU, M., MCPHERSON, G.D., 1970, Heat TransferMeasurements on Trefoil Fuel Bundles in the Post-Dryout Regime with Data Tabulation,AECL-3414.GROENEVELD, D.C., 1972, The Thermal Behaviour of a Heated Surface and BeyondDryout, AECL-4309.

GROENEVELD, D.C., 1973, Post-Dryout Heat Transfer at Reactor Operating Conditions,AECL-4513.

GROENEVELD, D.C., MCPHERSON, G.D., 1973, In Reactor Post-Dryout Experimentswith 36-Element Fuel Bundles, AECL-4705.

GROENEVELD, D.C., 1975a, PDO Heat Transfer: Physical Mechanisms and a Survey ofPrediction Methods, Nucl. Eng. Design 32 3, 283.

GROENEVELD, D.C., 1975b, The Effect of Short Flux Spikes on the Dryout Power,, ChalkRiver, Rep.,AECL-4927.

GROENEVELD, D.C., DELORME, G.G.J., 1976, Prediction of thermal non-equilibrium inthe post-dryout regime, Nucl. Eng. Design 36, 17-26.

GROENEVELD, D.C., FUNG, K.K., 1976, Forced Convective Transition Boiling — Reviewof Literature and Comparison of Prediction Methods, Rep. AECL-5543.

GROENEVELD, D.C., GARDINER, S.R.M., 1977, Post-CHF Heat Transfer under ForcedConvective Conditions in Thermal and Hydraulic Aspects of Nuclear Reactor Safety 1, LightWater Reactors, 43^47 (Jones, O.C. et al., Eds).

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GROENEVELD, D.C., GARDINER, S.R.M., 1978, A method of obtaining flow film boilingdata for subcooled water, Int. J. Heat & Mass Transfer 21, 664-665

GROENEVELD, D.C., 1982, Prediction Methods for Post-CHF Heat Transfer andSuperheated Steam Cooling Suitable for Reactor Accident Analysis, Rep.DRE/STT/SETRE/82-4-E/DGR,CEA-CENG.

GROENEVELD, D.C., ROUSSEAU, J.C., 1982, "CHF and Post-CHF heat transfer: Anassessment of prediction methods and recommendations for reactor safety codes", NATOAdvanced Research Workshop of Two-Phase Flows and Heat Transfer, Aug. 31-Sep. 3,Germany, Vol. 1, 203-238.

GROENEVELD, D.C., 1984, "An inverted annular and low quality film boiling: a state-of-artreport", Int. Workshop on Fundamental Aspects of PDO Heat Transfer, Salt Lake City.

GROENEVELD, D.C., SNOEK, C.W., 1986, "A comprehensive examination heat transfercorrelations suitable for reactor safety analysis", Multiphase Science and Technology (Hewitt,G.F. et al eds.) 181-271.

GROENEVELD, D.C., October 1988, "Recent Developments in Thermalhydraulic PredictionMethods", Proc. Int. Top. Mtg on Thermalhydraulics and Nuclear Reactors, Seoul.

GROENEVELD, D.C., 1992, A Review of Inverted Annular and Low Quality film Boiling,Post-dryout Heat Transfer (Hewitt, Delhaye, Zuber, Eds), CRC Press (327-366).

HAMMOUDA, N., GROENEVELD, D.C., CHENG, S.C., 1996, Two-fluid Modelling ofInverted Annular Film Boiling.

HAMMOUDA, N., 1996, Subcooled Film Boiling in Non-Aqueous Fluids, PhD Thesis,University of Ottawa.

HEINEMANN, J.B., 1960, An Experimental Investigation of Heat Transfer to SuperheatedSteam in Round and Rectangular Channels, ANL-6213

HENCH, G.E., 1964, Multi-Rod (Two Rod) Transition and Film Boiling in ForcedConvection Heat Transfer to Water at 1000 psia, GEAP-4721.

HERKENRATH, H., MORK-MORKENSTEIN, P., JUNG, U., WECKERMANN, F.J., 1967,Warmeubergang an Wasser bei Erzwungener Stromung in Druckbereich von 140 bis 250 Bar,EUR-3658d.

HETSRONI, G., 1982, Handbook of Multiphase Systems, Hemisphere PublisingCo/McGraw-Hill.

HSU, Y.Y., WESTWATER, J.W., 1960, Approximate theory for film boiling on verticalsurfaces, Chem. Eng. Prog. Symp. Ser. 56, 15-24.

HSU, Y.Y., 1972, "A Review of film boiling at cryogenic temperatures", Advances inCryogenic Engineering, Vol. 17 (361-381).

101

HSU, Y.Y., 1975, "A Tentative Correlation for the Regime of Transient Boiling and FilmBoiling During Reflood", Proc. 3rd Water Reactor Safety Review Meeting.

HSU, C.C., GUO, Z.C., YAN, A., BI, H.R., 1986, "Low pressure and subcooled water flowfilm boiling research by visual method", 4th Miami Int. Symp. On Multi-Phase Transport andParticulate Phenomena, Miami Beach.

HSU, CHI-CHUN, YANG, YAN-HUA, CHEN, F., 1989, "Two-dimensional mathematicalmodel and numerical study of IAFB heat transfer", Proc. NURETH-4, Karlsruhe, 1099-1104.

IHLE, P. et al, 1984, "Grid Spacer Effects in Reflooding Experiments Using Rod Bundles ofDifferent Fuel Rod Simulator Design", First Int. Workshop on Fundamental Aspects of Post-Dryout Heat Transfer, Salt Lake City, Utah, 1984, NUREG/CP-0060.

JANSSEN, E., KERVINEN, J.A., 1975, Film Boiling and Rewetting, NEDO-20975.JOHANNSEN, K., 1991, Low quality transition and inverted annular flow film boiling ofwater: an updated review, Experim. Thermal and Fluid Science 4, 497-509.

JONES, O.C., ZUBER, N., 1977. Post-CHF heat transfer: A non-equilibrium, relaxationmodel. ASME paper 77-HT-79.

KALININ, E.K., 1969, "Investigation of the Crisis of Film Boiling in Channels, a Two-PhaseFlow and Heat Transfer in Rod Bundles", ASME Ann. Mtg Los Angeles (89-94).

KALININ, E.K., BERLIN, I.I., KOTYUK, V.V., 1987, Transition boiling heat transfer,Advances in Heat Transfer 18, 241-323.

KALJAKTN, S.G., GRABEZHNAJA, V.A., GRACHEV, N.S., 1995, "Experimental studiesfor the computer code verification in supporting corium retention in WWER vessel",Thermophysics-90/Thermophysical Aspects of WWER Safety (Proc. Int. Symp. Obninsk 2),210-221 (in Russian).

KAWAJI, M., BANERJEE, S., 1987, Application of a multifield model to reflooding of a hotvertical tube: Part 1 — Model structure and interfacial phenomena", J. Heat Transfer, Trans.ASME 109, 204-211.

KEEYS, R.K.F., RALPH, G.C., ROBERTS, 1971, Post Burnout Heat Transfer in HighPressure Steam-Water Mixtures in a Tube with Cosine Heat Flux Distribution, AERE-R-6411.

KIRILLOV, P.L., SMOGALEV, I.P., 1973, Effect of droplet size on mass transfer in two-phase flow", Teplophysika Vysokikh Temperatur 11, 1312-1313 (in Russian).

KIRILLOV, P.L., KOKOREV, B.V., REMIZOV, O.V., SERGEEV, V.V., 1982, "PDO HeatTransfer", Proc. 7th Int. Heat Transfer Conf., Munich 4, 437-442.

KIRILLOV, P.L., et al., 1996, The Look-Up Table for Heat Transfer Coefficient in Post-Dryout Region for Water Flowing in Tubes (the 1996-Version), Preprint FEI-2525, Instituteof Physics and Power Engineering, Obninsk (in Russian).

102

KLIMENKO, V.V., 1981, Film boiling on horizontal plate- new correlation, Int. J. Heat MassTransfer 24 1,69-79.

KLYUGEL, E.V., KABANOV, L.P., 1986, Film boiling with weting of heated sufaces,Therma. Eng. 33,218-221.

KON'KOV, A.S., ZUPERMAN, D.A., 1967, The experimental investigation of heat transferto moisture steam, Teploenergetika 3, 54-56 (in Russian).

KUNSEMILLER, D.F., 1965, Multi-Rod Forced Flow Transition and Film BoilingMeasurements, GEAP-5073.

KUDRYAVTSEVA; A.A., YAGOV; V.V., ZUDIN, YU,B., 1987, A method of calculatingthermohydraulic characteristics of dispersed film boiling regime, Teploenergetika 10, 65-69(in Russian).

LAO, Y.J., BARRY, R.E., BALZHISER, R.E., 1970, "Study of film boiling a horizontalplate", Proc. 4th Int. Heat Transfer Conf. Paris 5, B 3.10.

LAPERRIERE, A., GROENEVELD, D.C., 1984, "A study of low quality film boiling at highpressures and flows", AIChE Symposium Series 236, 80, 440-445.

LAVERTY, W.F., ROHSENOW, W.M., 1967, Film Boiling of Saturated Liquid NitrogenFlowing in a Vertical Tube, J. Heat Transfer 89, 90-98.

LEE, D.H., 1970, "Studies of heat transfer and pressure drop relevant to subcritical once-through evaporators", Proc. Symp. on Progress in Sodium-cooled Fast Reactor Engineering,Monaco.LEE, D.H., SHEEN, H.J., CHO, S.K., ISSAPOUR, I., 1984, "Measurement of dropletdynamics across grid spacer in mist cooling of subchannel of PWR", Proc. First Int.Workshop on Fundamental Aspects of Post-Dryout Heat Transfer, Salt Lake City,NUREG/CP-0060.

LEE, Y., KIM, K.H., 1987, Inverted Annular Flow Boiling, J. Multiphase Flow 13, 345-355

LEONARD, J., SUN, K.H., 1976, "Low flow film boiling heat transfer on vertical surfaces;empirical formulations and applications to BWR LOCA analysis", AJChE Symp. 73, 7-13.

LEONARD, J., SUN, K.H., ANDERSEN, J., 1978, Calculation of Low Flow Film BoilingHeat Transfer for BWR LOCA Analysis, GE Rep. NEDO-20566-1.

LEUNG, L.K.H., HAMMOUDA, N., GROENEVELD, D.C., 1997, "A look-up table for film-boiling heat transfer coefficients in tubes with vertical upward flow", Proc. Eighth Int. Top.Mtg on Nuclear Reactor Thermal-Hydraulics, Kyoto, Japan, Sept. 30-Oct. 4.

LEVITAN, L.L., BOREVSKY, L.YA., 1989, "Holographia Steam-Water Flow", MoscowEnergoatomizdat.

MARINOV, M.J., KABANOV, L.P., 1977, Study of PDO heat transfer at low pressure andlow mass flux, Teploenergetika 7, 81-83 (in Russian).

103

MATTSON, R.J., CONDIE, K.G., BENGSTON, S.J., OBENCHAIN, C.F., 1974,"Regression analysis of post-CHF flow boiling data", Proc. 5th Heat Transfer Int. Conf.Tokyo 4, B.3.8, 115-119.

MATZNER, B., 1963, Experimental Studies of Boiling Fluid Flow and Heat Transfer atElevated Pressures, Columbia University Monthly Progress Report MPR-XIII-2-63.

MATZNER, B., GASTERLINE, G.E., KOKOLIS, S., 1968, Critical Heat Flux and FlowStability in a 9 ft. 19-rod Test Section Simulating a Setting of Short Discrete Rod Bundles,Columbia University Topical Report, No 10.

MAYINGER, F., LANGER, R., 1978, "PDO heat transfer", Proc. 6th Int. Heat TransferConf., Toronto 6, 181.

MCADAMS, W.H., et al, 1950, Heat transfer to superheated steam at high pressure, Trans.ASME 72, 421^28.

MCGINNIS, F.K., HOLMAN, J.P., 1969, Individual droplet heat-transfer rates for splatteringon hot surfaces, Int. J. Heat Mass Transfer 12, 95-108.

MCPHERSON, G.D., MATZNER, B., GASTERLINE, F., GASTERLINE, J.E.,WIKHAMMER, G.A., 1971, "Dryout and post- dryout behaviour of a 28-element fuelbundle", American Nucl. Society Winter Meeting, Miami Beach.

MIROPOLSKIY, Z.L., 1963, Heat transfer at film boiling steam-water mixture in tubes,Teploenergetika 5, 49-52 (in Russian).

MIROPOLSKIY, Z.L., 1975, heat transfer to superheated steam at heat supply and heatremoval", Teploenergetika 3, 75-78 (in Russian).

MOOSE, R.A., GANIC, E.N., 1982, On the calculation of wall temperatures in the post-dryout heat transfer region, Int. J. Multiphase Flow 8, 525—542.

MOSAAD, M., 1986, "A theoretical analysis of film boiling heat transfer from verticalsurfaces to subcooled liquid", 4th Miami Int. Symp. On Multi-Phase Transport and ParticulatePhenomena, Miami Beach.

MOSAAD, M., 1988, Subcooled Film Boiling Transfer to Flowing Water in Vertical Tube,Thesis, Techn. Univ. Berlin, Berlin.

MOSAAD, M., JOHANNSEN, K., 1989; "A new correlation for subcooled and low qualityfilm boiling heat transfer of water at pressures from 0.1 to 8 Mpa". Proc. 4th Int. Top. Mtg onNuclear Reactor Thermal-Hydraulics, Karlsruhe.

MUELLER, R.E., 1967, Film Boiling Heat Transfer Measurements in a Tubular Test Section,EURAEC-187 l/GEAP-5423.

NELSON, R., 1975, "The heat transfer surface technique", LOCA Heat Transfer Workshop,Idaho Falls, Idaho.

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NEWBOLD, F.J., RALPH, J.C., WARD, J.A., 1976, "Post dryout heat transfer under lowflow and low quality conditions," Paper presented at the European Two Phase Flow GroupMeeting, Erlangen.

NIJHAWAN, S., CHEN, J.C., SUNDERAM, R.K., LONDON, E.J., 1980, Measurements ofvapour superheat in post-critical heat flux boiling, J. Heat Transfer 102, 465-470.NISHIKAWA, K., YOSHIDA, S., MORI, H., TAKAMATSU, H., 1986, PDO heat transfer tofreon in a vertical tube at high subcritical pressure, Int. J. Heat Mass Transfer 29, 1245-1251.

QUIN, F.P., 1966, Forced Flow Heat Transfer to High Pressure Water beyond the CriticalHeat Flux, ASME Paper 66-WA/HT-36.

PARKER, Y.D., GROSH, R.Y., 1962, Heat Transfer to a Mist Flow, ANL-6291.

PLUMMER, D.N., GRIFFITH, P., ROHSENOW, W.M., 1976, "Post-Critical Heat Transferto Flowing Liquid in a Vertical Tube," Presented at the 16th National Heat TransferConference, 76-CSME/CSChE-13, St. Louis.

POLOMIK, E.E., LEVY, S., SAWOCHKA, S.G., 1961, Heat Transfer Coefficients withAnnular Flow During Once Through Boiling of Water to 100% Quality at 800, 1000 and 1400psia, GEAP-3703.

POLOMIK, E.E., 1971, Deficient Cooling 7th Quarterly Report, GEAP-10221-7.

REMIZOV, O.V., 1978, Study of temperature operating conditions of heat generating surfaceat crisis, Teploenergetika 2, 16-21 (in Russian).

REMIZOV, O.V., VOROB'IEV, V.V., SERGEEV, V.V., 1987, The design PDO heat transferin tubes, Teploenergetika 10, 55-56 (in Russian).

Rep., 1976, Study of Heat Transfer in Rod Bundles after CHF, OKB Gidropress, No 213-0-084 (in Russian).

Rep., 1980, Study of Heat Transfer of Moistured and Superheated Steam at Low MassVelocity, OKB Gidropress, No 431-0-047 (in Russian).

SAHA, P., 1980 A nonequilibrium heat transfer model for dispersed droplet post-dryoutregime, Int. J. Heat Mass Transfer 23, 483-492.

SAKURAI, G., 1990a, " Film boiling heat transfer", Proc. 9th Int. Heat Transfer Conf.,Jerusalem 1,157-186.

SAKURAI, G., SHIOTSU, M., HATA, K., 1990b, A General correlation for Pool FilmBoiling Heat Transfer, J. Heat Transfer 112 2, 430-451.

SAKURAI, G., SHIOTSU, M., HATA, K., 1990c, Correlations for subcooled pool filmboiling heat transfer from large surfaces with different configurations, Nucl. Eng. Design 120,N 2-3,271-280.

Seok, H., Chang, S.H., 1990, "Mechanistic model of the inverted annular film boiling", Proc.9th Int. Heat Transfer Conf., Jerusalem 3,431-435.

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SERGEEV, V.V., 1978, PDO Heat Transfer in Annulis and Rod Bundles, Analytical ReviewFEIOB-67, Institute of Physics and Power Engineering, Obninsk (in Russian).

SERGEEV, V.V., GALCHENKO, E.F., REMIZOV, O.V., 1985a, Engineering Method ofDesign PDO Heat Transfer, Preprint FEI-1649, Institute of Physics and Power Engineering,Obninsk (in Russian).

SERGEEV, V.V., 1985b, The Dynamic Entrainment of Liquid from Film Surface, PreprintFEI-1750, Institute of Physics and Power Engineering, Obninsk (in Russian).

SERGEEV, V.V., 1987, PDO Heat Transfer in Vertical Tubes, Preprint FEI-1836, Institute ofPhysics and Power Engineering, Obninsk (in Russian).

SHIRALKAR, B.S., HEIN, R.A., YADIGAROGLU, G., 1980, "The 'boiling curve' in highquality flow boiling", Proc.of ANS/ASME/NRC Int. Top. Mtg on Nucl. Reactor Thermal-Hydraulics, Saratoga Springs, NUREG/CP-0014 2, 1131-1141.

SIEGEL, R., HOWELL, J.R., 1972, Thermal Radiation Heat Transfer, McGraw Hill.

SLAUGHTERBECK, D.C., YBARRONDO, L.J., OBENCHAIN, C.F., 1973, Flow FilmBoiling Heat Transfer Correlations: A Parametric Study with Data Comparison, ASMERep.73-HT-50.

SMITH, T.A., 1976, Heat Transfer and Carryover of Low Pressure Water in a Heated VerticalTube, M.Sc Thesis, MIT

STEWART, J.C., 1981, Low Quality Film Boiling at Intermediate and Elevated Pressures,MSc Thesis, University of Ottawa.

STEWART, J.C., GROENEVELD, D.C., 1982, Low quality and subcooled film boiling atelevated pressure, Nucl. Eng. Design 67, 254-272.

SWENSON, H.S., CARVER, J.R., SZOEKE, G., 1961, The Effects of Nucleate BoilingVersus Film Boiling on Heat Transfer in Power Boiler Tubes, ASME Rep. 61-WA-201.

SWINNERTON, D., MOOD, M.L., PERSON, K.G., 1988, Steady State Post-DryoutExperiments at Low Quality and Medium Pressure, Rep. AEEW-R2267, Winfrith.

STYRIKOVICH, M.A., POLONSKIY, V.S., ZIKLAURI, G.V., 1982, Heat and mass transferand hydrodynamic two-phase flow for nuclear power, Nauka 368.

SUDO, Y., MURAO, Y., 1975, Study on Film Boiling Heat Transfer During Reflood Process,JAERI Rep. JPNRSR-15.

SUN, K.H., GONZALES-SANTALO, J.M., TIEN, C.L., 1976, Calculation of combinedradiation and convection heat transfer in rod bundles under emergency cooling conditions", J.Heat Transfer 98 3.

TAKENAKA, N., FUJII, T., AKAGAWA, K., NISHIDA, K., 1989, Flow pattern transitionand heat transfer of inverted annular flow, Int. J. Multiphase Flow 15, 767-785.

106

TONG, L.S., 1965, Boiling Heat Transfer Two-phase Flow, J. Wily & Sons Inc., London,Sidney, No. 4 (344).

TONG, L.S., YOUNG, J.D., 1974, "A phenomenological transition and film boiling heattransfer correlation", Proc. 5th Int. Heat Transfer Conf. Tokyo IV, B. 3.9.

TONG, L.S., 1978, " Heat transfer in reactor safety", Proc. 6th Int. Heat Transfer Conf.,Toronto 6, 285-309.

TRUSHIN, I.M., BEZRUKOV, YU.A., LOGINOV, S.A., BRANTOV, V.G., 1978,"Investigations of heat transfer to damp and superheated steam at low mass fluxes and lowpressures", Thermophysical Investigations Relevant to Ensuring of Reliability and Safety ofWater Cooled Reactors, Seminar TF-78, Budapest 1, 305-318 (in Russian).

VARONE, A.F., ROHSENOW, W.M., 1984, "Post-dryout heat transfer prediction", Proc. 1stInt. Workshop on Fundamental Aspects of Post-dryout Heat Transfer, Salt Lake City,NUREG/CP-0060.

VOJTEK, J., 1982, "Investigation of transient CHF phenomena and forced convection filmboiling heat transfer", Proc. 7th Int. Heat Transfer Conference Munich 4, 557-563.

VOROB'IEV, V.V., LOSCHININ, V.M., REMIZOV, O.V., SERGEEV, V.V., 1981."Generalization of PDO heat transfer experimental data with using nonequilibrium model",Heat Transfer and Hydrodynamics at Steam Generation, Nauka, 181-187, (in Russian).

WACHTERS, L.H.J., 1965, De Warmte Overdracht van een Hete Wand Naar Druppels in deSferoidale Toestand, PhD Thesis, Technological University, Delft.

WANG, B.X., PENG, X.F., 1987, An advanced study of forced turbulent flow film boilingfor subcooled liquid with high velocity in a circular tube, Warme-Stoffubertrag 21,139-144.

WANG, B.X., LIN, Z.Z., PENG, X.E., YUAN, H.J., 1988, Experimental study of steadyturbulent flow film boiling of subcooled liquid R 11 flowing upward in a vertical circulartube, Sci. Sinica31.

WEBB, S.W., CHEN, J.C., SUNDARAM, R.K., 1982, "Vapour generation rate in non-equilibrium convective film boiling", Proc. 7th Int. Heat Transfer Conf. Munich 4, 437-442.

WHALLEY, P.B., et al., 1982, "A physical model for two phase flows with thermo-dynamicand hydrodynamic non-equilibrium", Proc. 7th Int. Heat Transfer Conf. Munich 5, 181-188.

WINTERTON, R.S., 1982, Transition Boiling, Rep. AEEW-R1567.

YADIGAROGLU, G., ANDREANI, M., 1989, "Two-fluid modeling of thermal-hydraulicphenomena for best-estimate LWR safety analysis", Proc.NURETH-4, Karlsruhe, V.2,980995 (Mueller, U.,Rehme, K., Eds).

YAN, D.M., 1987, "Subcooled forced convection film boiling heat transfer", Heat TransferScience and Technology, Hemisphere, Washington.

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YAO SHI-CHUNE, HOCHREITER, L.E., LEECH, W.J., 1982, Heat transfer augmentationin rod bundles near grid spacers, J. Heat Transfer 104 1.

YODER, G.L., MORRIS, D.G., MULLINS, G.B., 1983, Dispersed flow film boiling heattransfer data near spacer grids in a rod bundle, Nucl. Technol. 60 2, 304.

YODER, G.L., Jr., ROHSENOW, W.M., 1983, A solution for dispersed flow heat transferusing equilibrium fluid, J. Heat Transfer 105 1.

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Chapter 5

PRESSURE DROP RELATIONSHIPS

NOMENCLATURE

AAr

Ag

cfQCv

CoD,deFFrffiftGGSL

gHhhfgIjKLPtP>PqRe

sTtuVV

v f gWX

Z

flow areaflow area ratio ( < 1)projected grid cross sectionfriction coefficientdrag coefficientmodified loss coefficientdistribution coefficientdiameterabsolute roughnesscorrection coefficientFroude Numberfriction factorlaminar friction factorturbulent friction factormass fluxsuperficial liquid mass flux (PL JL)gravitational accelerationwire pitchheat transfer coefficientlatent heatspecific enthalpyvolumetric fluxloss coefficientlengthrod pitchpressureheat fluxReynolds Numberslip ratiotemperaturethicknessvelocityvelocityspecific volume

mass flow ratemass qualitylength, elevation

GREEK SYMBOLS

a void fraction0 angle of direction of flow with vertical

109

pA5

42

Pa

X

homogeneous void fractiondifferencethickness of annular filmtwo phase friction multiplierdynamic viscositydensitysurface tensionMartinelli parameter

SUBSCRIPTS

aavBbcircritefGGOhiLLO1m0

RsSPFTP, TPFtotw

accelerationaveragebundlebulkcircularcriticalelevationfilm, frictionalvapourgas onlyhydraulicinletliquidliquid onlylocalmeanoutletrelativespacersingle-phase flowtwo-phase flowtotalwall

5.1. INTRODUCTION

In the nuclear industry, pressure drop correlations find extensive application for design andanalysis of many systems and components. For example, validated pressure drop correlations(PDCs) are required to determine the extent of orificing needed to match the channel flow to thepower, pumping power required, the riser height required to achieve a certain circulation rate innatural circulation BWRs, recirculation ratio in natural circulation type steam generators,stability analysis, transient and accident analyses, etc. Some of the above applications requirecorrelations for both single-phase and two-phase flows. Two-phase flows are encountered duringnormal operation of BWRs, transients and accidents in PWRs and PHWRs, and in certaincomponents like the steam generators.

110

Two-phase flow pressure drop depends on a large number of independent parameters likegeometric configuration of the duct, mass and volume fractions of the individual phases,pressure, fluid properties, mass flux, orientation of the duct (i.e. horizontal, vertical or inclined),flow direction (i.e. vertical upflow, downflow or counter-current flow) and flow patterns.Further, in many engineering applications, two-phase flow systems can be adiabatic, diabatic,one-component, two-component or multi-component. To cater to the needs of these diverseapplications, a very large number of two-phase flow pressure drop correlations are reported inliterature. Many of these correlations, being empirical in nature, are applicable only for limitedparameter ranges. Even mechanistic models are based on certain assumptions and carefulexamination of the particular application is necessary to ensure that the assumptions made inderiving the model hold good. For many practical situations, designers and analysts often requiresome guidance to choose the appropriate correlation.

The parameter ranges of two-phase flow in some of the above applications can be quitedifferent. For example, natural circulation reactors are characterised by relatively low mass fluxand driving pressure differential compared to forced circulation systems. Therefore, correlationschosen for the analysis of natural circulation systems require improved accuracy at low massfluxes. For the analysis of critical flow, following a break in high pressure systems, pressuredrop correlations valid for very high mass fluxes (10-20 Mg/m2s) are required. Forinvestigations on the start-up procedure for natural circulation boiling water reactors,correlations valid over a wide range of pressures starting from atmospheric pressure are required.

In this document, some of the commonly used and often-cited pressure drop correlationsare compiled along with their range of application. Later on assessments of these PDCs reportedin literature are reviewed and their recommendations summarized. Limitations of the reportedassessments are brought out and a rational assessment procedure for diabatic flow is proposed.As per this procedure assessment of pressure drop correlations cannot be carried out in isolation.For example, a rational assessment of diabatic flow pressure drop requires pre-assessment ofmodels for the onset of nucleate boiling (ONB) and void fraction. Assessment of flow patternspecific pressure drop correlations also require pre-assessment of the criteria for flow patterntransitions.

5.2. SURVEY OF SITUATIONS WHERE PRESSURE DROP RELATIONSHIPS AREIMPORTANT

In a nuclear reactor, the generated power, QG, is extracted from the core by means of afluid coolant. The first purpose of the thermohydraulic design of the reactor is to ensure that,during the nominal steady state reactor operating conditions, the extracted power, QE, is equal tothe generated one. Secondly, for accidental conditions, the evaluation of the difference betweenQG and QE is necessary for predicting the behaviour of the plant. The evaluation of the extractedpower is performed by means of the well known relationship:

where

AI is the enthalpy difference between the core outlet and inlet and W is the mass flow rate.

For the evaluation of the extracted power, it is then necessary to know the flow rate. Insome cases, it can be measured (total flow rate in the main loop) but generally at design level, it

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has to be computed and this calculation requires a knowledge of the pressure loss through thedifferent parts of the plant.

It is necessary to take into account the fact that the total pressure loss is due to differentcomponents, namely distributed pressure loss due to friction, local pressure losses due to suddenvariations of shape, flow area, direction, etc. and pressure losses (the reversible ones) due toacceleration (induced by flow area variation or by density change in the fluid) and elevation(gravity effect).

A general purpose relationship for the evaluation of the pressure loss in any possible casedoes not exist up to now and thus it becomes necessary to collect a set of relationships applicableto the different configurations, conditions, etc. A list of the factors on which the pressure lossdepends is shown in Table 5.1.

An important factor affecting the pressure loss is the geometry. In a reactor plant, we haveto deal with several basic geometrical shapes (circular pipes, annuli, etc.) and with a number ofspecial devices, like rod bundles, heat exchangers, valves, headers, plenums, pumps, pools, etc.Other factors are then concerned with the fluid status (single or two phase/one component, two-component or multi-component), the flow nature (laminar or turbulent), the flow pattern(bubbly, slug, annular, etc.), the flow direction (vertical upflow, downflow, inclined flow,horizontal flow, counter-current flow, etc.) and the operating conditions (transient or steadystate).

TABLE 5.1. FACTORS ON WHICH THE PRESSURE DROP DEPENDS

Geometry basic shapes circular pipe, rectangular channel,annulus, etc.

other shapes & rod bundle, spacer, valve,devices heat exchanger, orifice,

plenum, header, pump etc.

fluid status

flow nature

flow patterns

flow direction

operatingconditions

driving force

single phase

two phase

laminar

turbulent

bubbly, slug,annular, etc.

vertical upflow,downflow,inclined flow& horizontalflow

steady statetransient

forced convection

natural convection

one-component,two-componnet &multi-component

co-current &counter-current flow

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A final, very important issue, is concerned with the driving force depending on whetherthe flow is sustained by a density difference in the fluid (natural convection) or by a pump(forced convection), or whether there will be feedback between the pressure loss and theextracted power or not. Once more, in case of natural convection, some differentiation couldarise from what is called microscopic natural convection: normally the pressure loss inside adevice does not depend on the fact that the flow is sustained by a pump or by a densitydifference (macroscopic natural convection); however, in some circumstances, local effectscould happen and, as a consequence, the pressure loss will be influenced by the driving force.

By looking at Table 5.1, it appears clearly that it generates a very big matrix of conditionsand to fill all the matrix cells is a very hard job. At the same time, it becomes immediately clearthat the filling of the whole matrix is not necessary. For example, with respect to the geometry,mainly the basic geometrical shapes have to be taken into account. Some of the geometricconditions of interest are identified in the next section. The pressure loss correlation for specialdevices is usually given by the manufacturer.

5.2.1. Distinction between core and system approach

The term Xhermalhydraulic analysis is often used to identify two widely differentanalytical approaches. The first one can be called core approach and is mainly concerned withthe reactor core, hi this case, a very detailed analysis is performed at subchannel level and,consequently, only the basic geometrical shapes are taken into account. For instance, thepressure drop in rod bundles is usually computed by subdividing them into subchannels ofsimple shape. The bundle pressure drop is then computed based on the pressure drop in singlesubchannel and, in principle, no special pressure drop correlation for bundles is needed. Thespecial devices are limited to the spacers, a relatively limited class. Due to the fact that theanalysis is a very detailed one, it is normally performed for steady state conditions or for slowtransients, computed as subsequent steady states. This approach is the basic one for designpurposes.

The second one can be called system approach and deals with the whole plant. In thiscase, each component is represented by a small number of mesh points. For instance, no detailedgeometrical description of the core is considered. All the subassemblies are usually representedby means of one pin, from a thermal point, and the pressure drop is then computed by means of abundle pressure drop correlation. Again, basic geometrical shapes are needed (circular pipe,annulus, etc.) but the several complex geometries of interest are represented by means of adhocempirical relationships. This approach is mainly used in safety analysis and consequently dealswith transient conditions.

5.2.2. Geometric conditions of interest

Geometric conditions of interest to nuclear power plants (NPPs) only are considered here.Emphasis is made on geometric conditions that are relevant to the primary loop of NPPs. Thesecondary loop of NPPs (the steam generator and the piping up to the main steam isolation valve(MSIV) and the feedwater valves in case of PWRs and PHWRs) is also important and is to beconsidered. In addition, the emergency core cooling (ECC) lines from the ECC pumps to theinjection point along with the different types of valves may also be considered. Also, there arequite a few advanced designs to be dealt with (examples are SBWR, AP-600, CANDU-3,CANDU-9, EPR, AHWR, etc.). Again, it becomes a difficult task to cover typical geometries

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relevant to all these designs. For the purpose of this report, the various geometries relevant toNPPs can be classified into two categories:

5.2.2.1. Simple geometry for steady state and design calculations

In case of NPPs, the attention is generally limited to the nuclear fuel. The geometries ofinterest for local pressure drop are the spacer grids, tie plates, etc. Similarly for distributedpressure drop the geometries of interest are the channel and subchannels (various types, i.e.central, lateral, middle-lateral) for the square and the triangular array.

TABLE 5.2. LOCATIONS IN A PWR WHERE LOCAL AND DISTRIBUTED PRESSURELOSSES ARE IMPORTANT

Local pressure drop in the RPV: Cold leg to downcomerDowncomer to lower plenum entryCore inletSpacersCore outletUpper plenum to hot legBypasses: Lower plenum to core bypass

Core bypass to upper plenumDowncomer to hot legDowncomer to upper headUpper head to upper plenum (direct)Upper head — Control Rod Guide (CRG)CRG-Upper Plenum (different positions)

Local pressure drops in the primary loop:Hot leg bends

Hot leg to steam generator inlet water box entryU-tube bendsU-tube exitSteam generator outlet water box to cold leg entry

Loop seal bendsPump inletPump (inside with various situations for the rotor)Pump outletPressurizer to surge line entryHot leg to surge line connectionSurge line bends if anyAccumulator to pipe entryAccumulator pipe bendsAccumulator line check valve

Similarly distributed (due to skin friction) pressure drops are important for the following locations in a PWR:

Distributed pressure drops in the RPV: DowncomerCore and Core bypassUpper PlenumCRG

Distributed pressure drops in the primary loop: Hot legSurge lineU-TubesCold leg — loop sealCold leg — horizontal

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In addition, the reactor system consists of pipes of various sizes, annulus, etc. The flowpaths on the secondary side of the steam generators and the water boxes could be consideredseparately.

5.2.2.2. Complex geometry (or system) for safety — transient-analysis

During a transient, both direct (i.e. the nominal direction of the flow) and reverse flowdirections are relevant. Both transient and steady state knowledge is relevant (as alreadymentioned). Both single phase (liquid or steam only) and two phase flows are relevant. Flowswith phase opposition including counter current flow limit (CCFL) may happen in anydiscontinuity.

A knowledge of local and distributed pressure drops is necessary for transient analysis,(e.g. LOCA calculations). For example, in a typical PWR, local loss coefficients for direct andreverse flow must be supplied by the code user for each of the locations identified in Table 5.2.Table 5.2 also identifies the locations where distributed pressure drops are important.

Similar tables can be prepared for other reactors. For example, in a pressure tube typeheavy water reactor, additional local loss coefficients required are listed in Table 5.3.

TABLE 5.3. LOCATIONS IN A PHWR WHERE ADDITIONAL LOCAL PRESSURELOSSES ARE IMPORTANT

Entry loss from steam generator outlet pipes to headerHeader to feeder entry lossInlet feeder bendsInlet graylocInlet grayloc to Liner tube entryLiner tube to channel entryFuel locatorJunction between two bundlesChannel to liner tube entryLiner tube to outlet graylocOutlet graylocOutlet feeder bendsFeeder to header entry lossHeader to steam generator inlet pipe entry

5.3. CORRELATIONS FOR DESIGN AND ANALYSIS

5.3.1. Components of pressure drop

The overall static pressure drop, Ap, experienced by a fluid while flowing through a ductcomprises of the following components:

Ap = Ap f+ Ap,+ Apa+ Ape (5.2)

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where

APf, APi, APa and APe are the components of pressure drop due to skin friction, form friction(also known as local friction), acceleration and elevation respectively. The skin friction pressuredrop is also known simply as friction pressure drop.

5.3.1.1. Friction pressure drop

This is the irreversible component of pressure drop caused by shear stress at the wall andcan be expressed as:

fL W2 (5.3)

where

Dh is equal to 4 times flow area/wetted perimeter.

The pressure drop occurs all along the length and hence referred to as distributed pressuredrop sometimes. This equation is applicable for single-phase and homogeneous two-phaseflows, although, the method of calculation of the friction factor, f, and density, p, differ in thetwo cases. Pressure drop across tubes, rectangular channels, annuli, bare rod bundle (i.e. withoutspacers), etc. are examples of this component.

5.3.1.2. Local pressure drop

This is the localized irreversible pressure drop component caused by change in flowgeometry and flow direction. Pressure drop across valves, elbows, tee, spacer, etc. are examples.The local pressure drop is given by

„ W2 (5.4)A p ' = K

where

K is the local loss coefficient, the correlations for which differ for different geometries and forsingle-phase and two-phase flows.

5.3.1.3. Acceleration pressure drop

This reversible component of pressure drop is caused by a change in flow area or density.Expansion, contraction and fluid flowing through a heated section are the examples. Theacceleration pressure drop due to area change for single-phase and two-phase flow can beexpressed as

(5.5)

116

where Ao = smaller flow area

(j) = 1 for single-phase flow and for two-phase flow <j) is given by:

= f x3 + (1 -x ) 3 "\ ( pQ pL ~) (5-6)

lp2G a2 p2

L(l-a)2){x pL + (l-x)pJ

The acceleration pressure drop due to density change for single-phase and two-phase flowscan be expressed as:

(5.1)

For single-phase flows, this component is negligible, but can be significant in two-phaseflows. For two-phase flow, the above equation can be used with pm given by:

1 , x2 , (1-x)2 (5.8)— = ( + —r, z)Pm PG

a Pdl-a)

To evaluate the acceleration pressure drop due to density change, accurate prediction ofthe density of fluid is necessary. For single phase flow, density of fluid can be predictedreasonably well with established relationships for thermophysical properties of the fluid. For twophase flow, it is necessary to predict void fraction accurately to determine density and in turnacceleration pressure drop. Hence, correlation for void fraction needs to be chosen judiciously.

5.3.1.4. Elevation pressure drop

This reversible component of pressure drop is caused by the difference in elevation andcan be expressed as:

Ape = /?gAz cos 9 (5.9)

where

0 is the angle with the vertical in the direction of flow. For two phase flow,

p = pL (1-a) + pG a (5.10)

In many instances with vertical test sections, the elevation pressure drop is the largestcomponent. For such cases, accurate prediction of the void fraction is essential which again callsfor a judicious choice of the correlation for void fraction.

5.3.2. Configurations

For the purpose of design of advanced reactors, the required correlations mainly cover thefollowing configurations. For friction pressure loss, circular pipe, annulus, rectangular channelsand rod cluster and for local pressure loss, spacer, bottom and top tie plates, flow area changeslike contraction, expansion, bends, tees, valves etc. are most common. For CANDU type fuel

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bundles, the alignment of two adjacent fuel bundles also is important in estimating the pressuredrop. In addition, in-core effects like radiation induced creep, blister formation, swelling,corrosion, etc. are also important factors affecting the pressure drop which are not dealt withhere. Following is an account of the pressure drop correlations described configuration-wise andgenerally used for design.

5.3.3. Friction pressure drop correlations

The present compilation of pressure drop correlations is applicable to steady state fullydeveloped flow. Fully developed flow conditions are expected to occur in long components likethe steam generator U-tubes.

5.3.3.1. Circular pipe

5.3.3.1.1. Adiabatic single-phase flow

For fully developed laminar flow, the friction factor is given by:

f=64/Re (5.11)

which is valid for Reynolds number less than 2000. For turbulent flow in smooth pipes severalfriction factor correlations are proposed and in use. A few commonly used correlations forsmooth pipe are given below.

Blasius (1913) proposed the following equation:

f = 0.316 Re"025 (5.12)

valid in the range 3000 < Re < 105. The following equation valid in the range of 3000 < Re < 106

is also often used for design.

f = 0.184 Re"02 (5.13)

Drew et al. (1932) proposed the following equation:

f = 0.0056+0.5 Re"032 (5.14)

valid in the range 3000 < Re <3xlO6. The following equation proposed by Nikuradse (1933)

-]= = 0.861n(ReVf) - 0.8 (5>15)

Vf

is valid over the entire range of Reynolds number. Colebrook (1938) proposed the followingequation

Vf v 3.7 Re Vf

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valid for smooth and rough pipes for the whole range of Reynolds number above 3000. Thefollowing explicit equation proposed by Filonenko (1948) is a good approximation of Colebrookequation for smooth tube in the range 4 x 103 < Re < 1012.

f = [1.82 log(Re) - 1 .64f2 (5.17)

An explicit form of the Colebrook equation valid for smooth and rough tubes has beenobtained by Selander (1978) for use in computer codes.

f = 4 [3.8 log(10/Re + 0.2e/D)]"2 (5.18)

It may be noted from the above that well established correlations for friction factor do notexist in the transition region between 2000 < Re < 3000. Further, in many transients, the flowmay change from laminar to turbulent, or vice versa, necessitating a switch of correlations.Numerical calculations, often encounter convergence problems when such switching takes placedue to the discontinuity in the friction factor values predicted by the laminar flow and turbulentflow equations. A simple way to overcome this problem is to use the following criterion forswitch over from laminar to turbulent flow equation.

ifft>fithenf=ft (5.19)

where

ft and fi are friction factors calculated by turbulent and laminar flow equations respectively. Thisprocedure, however, causes the switch over from laminar to turbulent flow equation at Re «1100. Solbrig's (1986) suggestion to overcome the same is to use friction factor as equal to

greater of (ftUooo and f] below Reynolds number of 4000. (ft)4ooo is the friction factor calculatedby the turbulent flow equation at Re = 4000. Effectively this leads to

f=(ft)4ooo for 2000 < Re < 4000 (5.20)

In addition, a condition to avoid infinite friction factor is required to take care of flowstagnation (i.e. Re « 0).

5.3.3.1.2. Diabatic single-phase flow

Generally isothermal friction factor correlations are used with properties evaluated at thefilm temperature Tf = 0.4 (Tw - Tb) + Tb, where T\y and Tb are the wall and bulk fluidtemperatures [Knudsen & Katz (1958)]. Sometimes the friction factor for non-isothermal flow isobtained by multiplying the isothermal friction factor with a correction coefficient, F. Thecorrection coefficient accounts for the temperature gradient in the laminar layer and theconsequent variation in physical properties of the fluid. The correction coefficient can beexpressed as a function of the temperature drop in the laminar layer, ATf as given below:

F = l±CATf (5.21)

The negative sign shall be used for heat transfer from wall to the fluid, and

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AT f =q/h (5.22)

Different values of the constant C are given by different investigators. El-Wakil (1971)gives a value of 0.0025, while Marinelli and Pastori (1973) give a value of 0.001.

An alternative approach is to express the correction factor in terms of the viscosity ratio.This approach is more widely used and the following empirical equation proposed by Leung andGroeneveld (1993) is recommended.

Ta28 (5-23)

where

the subscripts b and w refer to the bulk fluid and wall respectively.

5.3.3.1.3. Adiabatic two-phase flow

A large number of two-phase flow pressure drop correlations can be found in literature.These correlations can be classified into the following four general categories.

(1) Empirical correlations based on the homogeneous model,

(2) Empirical correlations based on the two-phase friction multiplier concept,(3) Direct empirical models,

(4) Flow pattern specific models.

hi addition, computer codes based on the two-fluid or three-fluid models requirescorrelations for the partitioning of wall friction between the fluids and interfacial frictioncorrelations.

Some of the widely used and often cited correlations in each of the above category aregiven below.

Homogeneous flow model

In the homogeneous flow model, the two-phase frictional pressure gradient is calculated interms of a friction factor, as in single-phase flow. The friction factor is calculated using one ofthe equations given in Section 5.3.3.1.1, with the use of the two-phase viscosity in calculatingthe Reynolds number. Several models for two-phase viscosity are available some of which aregiven in Appendix VII.

Many of the models for mixture viscosity do not yield significantly different results.Further, homogeneous models are expected to give good results for high mass flux flows withlow and high void fractions where the bubble diameter is small compared to the duct diameter.Hussain et al. (1974) recommend a value of G = 2700 kg/m2-s (« 2 x 106 lb/h-ft2) above whichhomogeneous models are applicable.

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Correlations based on the multiplier concept

In this case, the two-phase pressure drop is calculated from the single-phase pressure dropby multiplying with a two-phase friction factor multiplier. The following definitions of two-phase friction multipliers are often used.

2 __ (dp/dz)TPF 2 _ (dp/dz)TPFj

^LO (dp/dz) L 0 ' 9GO (dp/dz)G 0 '

, (dp/dz)^ f Wtoh* (5-24)^ (dp/dz)L

VG (dp/dz)G

where

the denominators refer to the single-phase pressure gradient for flow in the same duct with massflow rates corresponding to the mixture flow rate in case of §\o and §QO and individual phasesin case of ^ and <J>G2. Among these, <J)LO2 is the most popular friction multiplier. Some of themultiplier based correlations are briefly described in Appendix VIII.

There are many more empirical correlations (other than those in Appendix VIII) givenunder the multiplier concept, inclusion of all of which is outside the scope of the present report.Care has been taken to include all those correlations which are of interest to current andadvanced reactor designs. In passing, it may be mentioned that all of the homogeneous modelsgiven in the previous section can also be expressed in terms of a two-phase friction multiplier.

Direct empirical models

In this category, the two-phase friction pressure drop is directly expressed as a function ofmass flux, mixture density, length, equivalent diameter, etc. without reference to single-phasepressure drop. Examples in this category are the models proposed by Lombardi-Pedrocchi(1972), Lombardi-Ceresa (1978), Bonfanti et al. (1982) and Lombardi-Carsana (1992). Thesecorrelations also specify the use of the homogeneous model for the calculation of thegravitational and accelerational pressure drop. Such correlations are expected to provide accuratevalues of the calculated total pressure drop rather than the individual components of the pressuredrop. Since Lombardi-Carsana is the latest in this series only this correlation is given inAppendix IX.

Flow pattern specific models

In general, two methods are being used to generate flow pattern specific correlations. Inthe first, empirical correlations are obtained by correlating the data for each flow pattern. In thesecond method mechanistic models which take into account the distribution of phases in eachflow pattern have been developed. Examples of the first approach are those due to Baker [seeGovier and Aziz (1972) and Hoogendoorn (1959)] for horizontal flows and Hughmark (1965)for horizontal slug flow. Examples of mechanistic models are those due to Taitel and Dukler(1976a) and Agrawal et al. (1973) for stratified flow; Wallis and Dobson (1973) and Dukler andHubbard (1975) for slug flow and Hewitt and Hall-Taylor (1970) for annular flow. Some of theempirical and mechanistic models for calculating pressure gradient for horizontal and verticalflows are given in Appendices X and XI respectively.

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To apply flow pattern specific correlations, we must also have a method to identify flowpatterns. This can be done by the use of flow pattern maps proposed by different authors forhorizontal, vertical and inclined flows.

Interfacial friction models

The two-fluid model used in many of the advanced system codes require correlations forinterfacial friction in addition to wall friction. Complete description of the models used incomputer codes like TRAC-PFI/M0D1 [Liles and Mahaffy (1984)] and RELAP5/MOD3.2 [theRELAP5/MOD3 development team (1995)] are readily available in the open literature. Forspecific flow patterns, models are proposed by Wallis (1970), Coutris (1989), Putney (1991) andStevanovic and Studovic (1995). For use in computer codes, it is also essential that suchcorrelations for the various flow patterns be consistent. For example, when the flow patternchanges from bubbly to slug, the interface force predicted at the transition point by correlationsfor the bubbly and slug flow should be same. A consistent set of interfacial and wall frictioncorrelations for vertical upward flow has been proposed by Solbrig (1986) along with a flowpattern map for use in two-fluid models (Appendix XII).

5.3.3.1.4. Diabatic two-phase flow

The correlations discussed so far are applicable to adiabatic two-phase flow. The effect ofheat flux on two phase pressure drop has been studied by Leung and Groeneveld (1991),Tarasova (1966) and Koehler and Kastner (1988). Tarasova (1966) observed that two phasefriction pressure drop is higher in a heated channel compared to that in an unheated channel forsame flow condition. However, Koehler and Kastner (1988) concluded that two phase pressuredrops are same for heated and unheated channels. Studies conducted by Leung and Groeneveldindicate that the surface condition is significantly influenced by heat flux. Effective surfaceroughness increases due to the formation of bubbles at heated surface leading to larger pressuredrop. They concluded that for the same flow conditions, the two phase multiplier is larger forlow heat flux than high heat flux. They further observed that maximum value of two phasemultiplier is obtained when heat flux approaches critical heat flux value. In the absence ofestablished procedure to take the affect of heat flux into account the following procedure forcalculation of two phase diabatic pressure drop is generally followed.

For diabatic two-phase flow, the quality, void fraction, flow pattern, etc. change along theheated section. To calculate the pressure drop in such cases, two approaches are usuallyfollowed. In the first approach, the average (J>LO2 is calculated as:

(525)

The approach can be used in cases where the (|>LO2(Z) is an integrable function. Numericalintegration is resorted to in other cases. An example of such an approach is proposed by Thom(1964). Thom has derived average values of <|>LO2(Z) which are reproduced in Table 5.4. Similarintegrated multiplication factors for diabatic flow as a function of outlet quality are alsoavailable for the Martinelli-Nelson method. Thom has also obtained multiplication factors forcalculating the acceleration and elevation pressure drops for diabatic flow in this way.

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hi the second approach the heated section is subdivided into a large number of smallsegments. Based on average conditions (i.e. x;, oti and flow pattern) in that segment, the pressuredrop is calculated as in adiabatic two-phase flow using one of the models described previously.

TABLE 5.4. VALUES OF FRICTION MULTIPLIER FOR DIABATIC FLOW [THOM(1964)]

Outlet Pressure (bar)Quality 17.24 41.38 86.21 144.83 206.9

0.0000.0100.0150.0200.0300.0400.0500.0600.0700.0800.1000.1500.2000.3000.4000.5000.6000.7000.8000.9001.000

1.001.491.762.052.633.193.714.214.725.256.309.0011.4016.2021.0025.9030.5035.2040.1045.0049.93

1.001.111.251.381.621.862.092.302.502.703.114.115.087.008.8010.6012.4014.2016.0017.8019.65

1.001.031.051.081.151.231.311.401.481.641.712.102.473.203.894.555.256.006.757.508.165

--_1.0201.0501.0701.1001.1201.1401.1901.2101.3301.4601.7202.0102.3202.6202.9303.2303.5303.832

--_------1.0501.0601.0901.1201.1801.2601.3301.4101.5001.5801.6601.740

hi many cases, the pressure drop is to be calculated for a component with subcooled inletflow (for example rod bundles in BWRs). For such cases a single-phase friction model is used inthe non-boiling part of the test section and a two-phase model is used in the boiling zone. Amodel is also required to establish the onset of boiling in such cases. Usually, the thermalequilibrium model is used. But in many cases a model taking into account the effect ofsubcooled boiling is also used. The Saha and Zuber (1974) model is preferred by manyinvestigators for this purpose [Marinelli & Pastori (1973), Vijayan et al. (1981), Snoek &Ahmad (1983)].

Comparison of diabatic two-phase pressure drop predictions with experimental data bySnoek and Leung (1989) showed that the Saha & Zuber model is not adequate to predict theonset of nucleate boiling (ONB) in 37-rod bundles with non-uniform heat flux due to enthalpymaldistribution in the subchannels. They found that the Saha and Zuber correlationoverpredicted the single-phase region length by as much as 50%. They modified the Saha &Zuber correlation for the case of Peclet number >70 000 as:

x 0 N B Ghfg

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Knowing the thermodynamic quality, xe, the true quality, xt, is obtained as:

e „ (5-27)Xt

^ O N B

They also tested this correlation with the available data and found that better agreementis obtained in the prediction of single-phase length in case of nonuniform heat flux. Withuniform heat flux, however, the single-phase length is underpredicted to some extent.

5.3.3.2. Annulus

Correlations for circular pipe are normally used for the calculation of single phase pressuredrop in annulus using the hydraulic diameter concept. For two-phase pressure drop, the sameconcept is expected to be applicable. The accuracy of this method can be checked by comparisonwith experimental data. Examples of available experimental data are those due to Adorni (1961),CISE (1963), Moeck (1970), etc.

5.3.3.3. Rod bundle

The rod bundle geometries used in advanced designs differ in several ways, hi PWRs andBWRs, the fuel bundles are long (»1.8 to 4.5 m) whereas in CANDU type heavy water reactorsshort fuel bundles of about 0.5 m are used. Generally grid spacers are used in PWRs and BWRswhile split-wart spacers are used in CANDUs. hi certain fast breeder reactors wire-wrappedbundles are still used. In PWRs and BWRs, the total pressure drop is obtained by summing upthe pressure drop in bare rod bundle and the spacers. For wire-wrapped bundles empiricalcorrelations for the pressure drop in the bundle considering the geometric details of the wirewraps are available. For prototype CANDU type bundles, the total pressure drop is sometimesexpressed in terms of an overall loss coefficient due to the closeness of the spacers and thecomplex geometry of the end plates [Vijayan et al. (1984)] and alignment problem at thejunction between two bundles [Pilkhwal et al. (1992)].

5.3.3.3.1. Pressure drop in wire wrapped rod bundles

hi the case of wire wrapped rod bundles, the geometry and shape of the system is quiterigid and the development of a general correlation for predicting the pressure drop is areasonable task. Such a correlation proposed by Rehme (1968 and 1969) is given below:

L pu U (5.28)AP = fR ——

Dh 2 UG

where

UB = Us + UD is the bundle perimeterUG = Us + UD + UK is the total perimeterUK, US and UD are the shroud perimeter, pins perimeter and wire perimeter respectively. Thereference velocity, UR, is defined as:

UR = UVF (5.29)

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where

u is the average velocity in the rod bundle

The geometrical factor F depends on the pitch to diameter ratio and on the ratio betweenthe mean diameter and the wire pitch (H).

n °'5 d D , 2 1 6 (

where

dm is the mean diameter of wire wraps. The reference friction factor fR is calculated by means ofthe following correlation based on Rehme's experimental data.

= _64_ 0.0816 fo r2x l0 3 <Re R <5xl0 5 (5.31)R = ReR

+ Re-3 3

where

ReR = Re VF and Re = (uR Dh)/v (5.32)

These are valid in the range 1.12 < pt/D < 1.42 and 6 < H/dm < 45. Later on Dalle Donneand Hame (1982) extended the validity of the correlation to lower pt/D ratios by multiplying Fwith a correction factor C for p/D < 1.03.

(5.33)C = 1.6-e 005873

The measurements on wire wrapped bundles performed in ENEA when compared with thegeneral correlation were found to be in very good agreement for a wire pitch of 140 mm. Thediscrepancy in the whole Reynolds number range was about 4-5 per cent. The agreement for the160 mm pitch was a little worse, up to 13 per cent which is attributed to measurementuncertainty. Later on, pressure drop measured by ENEA in prototype fuel elements of thePEC reactor were found to be in good agreement with the predictions of Rehme's correlationthus confirming its general validity [Cevolani (1996)].

5.3.3.3.2. Pressure drop in CANDU type fuel bundles

Several short bundles are stacked end to end in CANDU type PHWRs compared to a longsingle fuel bundle used in PWRs and BWRs. Due to the basic change in design concept some ofthe problems and geometries are unique to the design.

Snoek& Ahmad (1983)

Snoek & Ahmad suggested the following empirical correlation for friction factor based onexperiments on a 6 m long electrically heated horizontal 37 rod cluster.

f = 0.05052 Re"005719 for 108,000 < Re < 418,000 (5.34)

125

Venkat Raj (1993)

Venkat Raj proposed the following equations based on a set of experiments with prototypehorizontal 37 rod clusters for PHWRs with split-wart type spacer which includes the junctionpressure drop.

f = 0.22 Re"0163 10,000 < Re < 1,40,000 (5.35)

f= 0.108 Re"0108 1,40,000 < Re < 5,00,000 (5.36)

5.3.3.3.3. Pressure drop in bare rod bundles

Single-phase

Correlations for circular pipes are commonly used to calculate pressure drop usinghydraulic diameter of the rod bundle in the absence of experimental data. Some of thecommonly used correlations are:

Kays (1979)

For rod clusters

f=fcirK1 (5.37)

where

Ki •— is provided as a function of p/D (pitch to diameter ratio) based on the work by Diesslerand Taylor (1956).

fcir — can be calculated using correlations given for circular pipe.

Rehme (1980)

For non-circular channels

Laminar flow;

fRe = K (5.38)

where K is a geometry parameter that only depends on the configuration of the channel.

Turbulent flow;

V(8/f) = A[2.5 In ReV(f/8) + 5.5]-G* (5.39)

where

the empirical factors A & G* can be determined from the diagrams given in Rehme (1973a)

126

Grillo and Mannelli (1970)

Grillo and Marinelli proposed the following equation based on their measurements on a4 x 4 square array rod bundle with rod diameter of 15.06 mm and p/D of 1.283

f= 0.1626 Re"02 (5.40)

Two-phase

In the absence of experimental data, the method used for diabatic two phase flow inSection 5.3.3.1.4 can be used with hydraulic diameter of the bundle in place of pipe diameter.Lombardi-Carsana (1992) (CESNEF-2) correlation discussed in Appendix DC is also applicablefor rod bundles, hi addition, there are some empirical equations proposed for rod bundles someof which are given below.

CNEN correlation (1973)

= 1.7205X10"6 (L Ma852)/DhU42 (5.41)

where

M is given by:

M = [xvG+(l-x)vL]G2 (5.42)

where

M is in [N/m2]L & Dj, are in metres,

is obtained in metres of water at 25°C.

This equation is applicable for square array fuel bundles with pitch to diameter ratio =1.28, Dh = 1.31 cm, peripheral rod-channel gap = 0.55 x pitch, 8 < P < 70 kg/cm2 and 680 < G <2700kg/m2s.

Grillo and Marinelli (1970)

1-N

<f(G) = 0.56 + 0.315-^-

where ((|)LO2)M-N is calculated using the Martinelli-Nelson method (Appendix VIII).

127

Una! (1994)

For rod cluster

f = 0.1 Reav"03 (5.45)

Reav=GD/u.av (5.46)

where jum corresponds to average of inlet and outlet under post CHF dispersed flow condition.

5.3.3.4. Steam generator secondary side

Two-phase pressure drop calculations are important for natural circulation type steamgenerators. The driving force for natural circulation flow is resisted by pressure losses whichoppose the flow. The natural circulation driving force is provided by the difference between thedensity of the water in the downcomer and that of the steam-water mixture in the heating zoneand riser. Calculation of pressure losses in a steam generator is therefore an integral part ofevaluating the circulation and flow rate through the heating zone. Pressure drop correlationsspecific to steam generator tube banks are not readily available. For design and analysispurposes, however, the frictional pressure losses can be calculated by the procedure listed fordiabatic two-phase flow discussed in Section 5.3.3.1.4 with the hydraulic diameter of the tubebank used in place of the pipe diameter [ORNL-TM-3578 (1975)].

5.3.4. Local pressure drop

5.3.4.1. Grid spacers

Because of variation and complexity of geometry, it is extremely difficult to establish apressure loss coefficient correlation of general validity for grid spacers. But methods ofcalculation reasonably accurate for design purpose can be achieved. For more precisedetermination of pressure drop across spacers, experimental studies are required. Somecorrelations used to determine pressure drop across grid spacers are discussed below.

5.3.4.1.1. Single-phase flow

Single-phase pressure drop is calculated using a spacer loss coefficient, K, as:

Ap = KpVB2/2 (5.47)

In some cases, it may be possible to obtain a reasonable value of the spacer loss coefficientif its geometry can be approximated to one of those considered in Idelchik (1986). For othercases, the different empirical models for K, described below may be used.

Rehme (1973b)

K = Cvs2 (5.48)

where

s =

128

For ReB > 5 x 104, Cv = 6 to 7 and for Res < 5 x 104 Cv values are given in graphical formas a function of Res. Subsequently Rehme (1977) studied the effect of roughness of rod surfaceon the pressure drop across spacers. Cevolani (1995) proposed Cv - 5 + 6133Re"0789 for squarebundles and ln(Cv) = 7.690-0.9421 ln(Re) + 0.0379 ln2(Re) for triangular bundles with an upperlimit of K = 2 if the calculated value is greater than 2.

Mochizuki & Shiba (1986)

K = 2.7-1.55(log ReB-4) for ReB < 8 x 104 (5.49)

K=1.3 forRe B >8xl0 4 (5.50)

This correlation is valid only for the specific spacer used for the experimental studies with37 rod cluster.

Kimetal. (1992)

K = (Cd + 2LQ/t) s/(l-s)2 (5.51)

where

Cd the drag coefficient varies from 0.8 to 1.0 for a thin rectangular plate depending on theaspect ratio of the plate,

Cf the friction coefficient can be obtained from the flat plate flow solution. For turbulentboundary layer preceded by laminar region.

Cf = 0.074 (ReB L/Dhf2 - 1740 (ReB L/Dh)"1 (5.52)

For fully laminar flow

C f - 1.328(Dh/L)°-5(ReB)-0-5 (5.53)

Transition Reynolds number is assumed to be 5 x 10 .

5.3.4.1.2. Two phase flow

In general, the homogeneous model or the slip model is used for the estimation of the two-phase pressure drop across grid spacers.

Homogeneous model

Ap = K(Resat)vG2/2 (5.54)

where

K(Resat) is the form loss coefficient for single phase flow estimated at the Reynolds numbercorresponding to the total flow in the form of saturated liquid and v is the specific volume givenby

129

v = xvG + (l-x)vL (5.55)

This model may be used when experimental data are not available. Beattie (1973) hasprovided the following equation to calculate the pressure drop in rod spacers, sudden expansion,etc. if the flow is churn-turbulent at the obstruction.

o02 (5.56)

]A > [ ( ) ] [ F ) ]Pa PG

Slip model

According to this model, the form loss coefficient for two phase flow can be obtainedfrom

KSPFG2 = PL G2 _ G2 (5-57)

JS-SPF JVTPF"2p p 2pL 2pL

where

p is given by

P = ^pG + (l-a)pL ; a =

x J pL

It may be noted that this equation reduces to the homogeneous model if S = 1. Grillo andMarinelli (1970) recommend a value of S = 2 for grid spacers.

Tie plate

Generally, tie plates are used at the ends of rod cluster fuel elements which structurallyjoins all the fuel pins. Unlike spacers, the flow areas at the downstream and upstream sides ofthe tie plates are different. Also, these are generally located in the unheated portion of thebundle. Reported studies on pressure drop for the tie plates are few in number. An approximatecalculation for design purposes can be made using the contraction and expansion model for localpressure losses, hi addition the friction losses in the thickness of the tie plates can be calculatedusing the hydraulic diameter concept. For two-phase pressure losses, the homogeneous or theslip model described above can be employed in the absence of experimental data.

5.3.4.2. Area changes

Single-phase

The pressure losses due to area changes are calculated by Equation 5.4 with losscoefficients calculated for the relevant geometry from Idelchik (1986).

130

Two-phase

In general, the irreversible pressure drop due to area changes is estimated from theknowledge of single-phase loss coefficient using the homogeneous model. When details of theslip ratio are available, then the slip model given above can be used.

Sudden expansion

Romey [see Lottes (1961)] expresses the two-phase pressure drop across suddenexpansion by the following equation:

PL

Beattie (1973) model given above can also be used (Eq. 5.56).

Fitzsimmons (1964) provides the following equation to calculate the pressure change acrossabrupt expansion

PL [PG WiAr ai)\ [" ' V(l-ai)A r (l-a2)>

where

subscripts 1 and 2 refer respectively to the upstream and downstream locations of the abruptexpansion. An assessment carried out by Husain et al. (1974) suggests that better agreement withdata is obtained when ai and 0C2 are calculated by assuming slip flow.

5.3.4.3. Bends and fittings

The single-phase pressure drop due to bends and fittings can be calculated using theappropriate loss coefficients from Idelchik (1986).

Two-phase pressure drop

Chisholm (1969) provides the following general equation for the calculation of two-phasepressure drop in bends and fittings.

(5.60)

(5.61)

where

Vfg = vG-vL , andC2 is a constant.

131

Bends

For bends C2 is a function of R/D, where R is the radius of curvature of the bend and D isthe pipe diameter.

C2 for normal bend

C2 for bend with upstreamdisturbance within 50 L/D

4.35

3.10

3.40

2.50

2.20

1.75

1.00

1.00

Chisholm provided the above values of C2 by fitting Fitzsimmons (1964) data.

Chisholm & Sutherland (1969)

For 90° bends: C2 = l + 35 N (5.62)

For 180° bends: C2 = l +20N (5.63)

N is the number of equivalent lengths used for calculating single-phase pressure drop.

Tees:

C2 =1.75

Valves:

C2 = 1.5 for gate valves= 2.3 for globe valves

Alternatively the homogeneous model may be used.

Orifices:

For separated flow (stratified) at obstruction, Beattie (1973) obtained the following

02 (5.64)

expression for (|)LO2-

5.3.5. Importance of void fraction correlations

Void fraction plays an important role, not only in pressure drop calculation, but also inflow pattern determination and neutron kinetics. All the four components of pressure dropdirectly or indirectly depend on the void fraction. For certain situations of practical interest,accurate prediction of all the components are required. For example, steady state flow prevails ina natural circulation loop when the driving pressure differential due to buoyancy (i.e. the

132

elevation pressure drop) balances the opposing pressure differential due to friction andacceleration. For natural circulation loops, therefore, the largest contribution to pressure droparises from the elevation pressure drop. Also, the acceleration pressure drop can be 10-15% ofthe total core pressure drop. For such cases, accurate estimation of each component of pressuredrop is required. Therefore, it is very important to have a reliable relationship for the mean voidfraction. Significant deviations are observed between the predicted flow rate using differentmodels for friction and void fraction.

In many experiments with diabatic vertical test sections, the friction pressure loss isobtained as shown below:

g + G V G + v

TPF m \yG yL ) d z U G \-a L)

where

(dp/dz)m is the measured pressure drop.

It is observed from the above equation that the void fraction, a, and quality, x, play animportant role in deducing the frictional term from the measured static pressure drops. Usually,the acceleration and elevation drops are calculated with the help of a void fraction value, whichmay not be measured but calculated by a correlation.

The stability predictions of natural circulation loops are also strongly influenced by thefriction and mean void fraction model [see Furutera (1986)]. The use of certain friction modelscan completely mask the stability phenomenon. In coupled neutronic thermalhydrauliccalculations, the void fraction plays an important role in the calculation of reactor power[Saphier and Grimm (1992)]. For such calculations, it is essential to use the best models for eachcomponent of pressure drop which indirectly also implies the use of the best void fractionmodel. Hence, it is necessary to make a judicious choice of the void fraction correlations. Someof the commonly used void fraction correlations are described briefly in the following section.

5.3.5.1. Void fraction correlations

In general, the void fraction correlations can be grouped into three; viz.,

(a) slip ratio models,(b) K.p models and(c) correlations based on the drift flux model.

In addition, there are some empirical correlations, which do not fall in any of the threecategories. Some of the commonly used correlations in all the above categories are describedbelow.

5.3.5.1.1. Slip ratio models

These models essentially specify an empirical equation for the slip ratio, S (=UG/UL)- Thevoid fraction can, then be calculated by the following equation:

133

(5.66)

x J pL

For homogeneous flow, UQ = UL and S = 1. At high pressure and high mass flow rates thevoid fraction approaches that of homogeneous flow, and can be calculated by setting S = 1 in theabove equation. But usually, the slip ratio is more than unity for both horizontal and verticalflows. For vertical upward flows, the buoyancy also assists in maintaining S > 1. The commonslip ratio models are given in Appendix XIII.

5.3.5.1.2. Kp models

These models calculate a by multiplying the homogeneous void fraction, p, by a constantK. Well-known models in this category are due to Armand (1947), Bankoff (1960) andHughmark (1965) which are given in Appendix XTV.

5.3.5.1.3. Correlations based on the drift flux model

By far the largest number of correlations for void fraction reported in the literature arebased on the drift flux model. The general drift flux formula for void fraction can be expressedas

a = Jo <5-67>Co[jG + jL] + VGj

where

VQJ is the drift velocity (= UQ-J, where j is the mixture velocity) and for homogeneous flow Co =1 and VQJ = 0. The various models (see Appendix XV) in this category differ only in theexpressions used for Co and VQJ which are empirical in nature.

The Chexal and Lellouche (1996) correlation is applicable over a wide range ofparameters and can tackle both co-current and counter-current steam-water, air-water andrefrigerant two-phase flows. The correlation is used in RELAP5 [the RELAP5 DevelopmentTeam (1995)] and RETRAN [Mcfadden et al. (1992)] and is given in Appendix XV for steam-water two-phase flow.

5.3.5.1.4. Miscellaneous correlations

There are a few empirical correlations which do not belong to the three categoriesdiscussed above. Some of the more common ones are given in Appendix XVI.

Significant differences exist between the void fraction values obtained using differentcorrelations. This necessitates a thorough assessment of the void fraction correlations.

5.3.6. Review of previous assessments

Several assessments of pressure drop and void fraction correlations reported in literatureare reviewed and their recommendations summarized in this section.

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5.3.6.1. Pressure drop correlations

hi general, two different approaches are followed while assessing the predictive capabilityof pressure drop correlations, hi one of these, a particular correlation is chosen and comparedwith all available two-phase flow pressure drop data disregarding the flow pattern to which thedata belong. This approach is adequate for adiabatic flows while assessing correlations valid forall flow patterns, and is followed by Idsinga et al. (1977), Friedel (1979 & 1980), Beattie andWhalley (1982), Snoek & Leung (1989) and Lombardi & Carsana (1992).

In the other approach correlations are chosen for a particular flow pattern and comparedagainst data obtained for that flow pattern. Since flow pattern specific pressure drop data arelimited, the flow pattern to which the data belong is identified with a flow pattern map tofacilitate the selection of the correlation. This approach requires a pre-assessment of flow patternmaps. Examples of such assessments are those due to Mandhane et al. (1977), Hashizume &Ogawa (1987) and Behnia (1991). Some assessments like those of Dukler et al. (1964) andWeisman & Choe (1976) combine both these approaches.

Some limited assessments for investigating parametric effects are also reported. Forexample, Simpson et al. (1977) and Behnia (1991) assessed data from large diameter pipes whileD'Auria and Vigni (1984) studied the effect of high mass velocity flows. Most assessmentsemployed statistical methods, but the parameter and the correlations chosen for assessment arewidely different. Some salient results of these assessments are presented here.

5.3.6.1.1. Homogeneous model

Beattie and Whalley (1982) compared 12 pressure drop correlations including5 homogeneous models using the HTFS (Heat transfer and fluid flow services) databankcontaining about 13500 adiabatic data points for steam/water and non-steam water mixtures.This study used roughly about 8400 horizontal flow data points and 5100 vertical flow datapoints. They used the homogeneous void fraction model to calculate the elevation head for thehomogeneous friction models whereas an unpublished void fraction correlation (HTFS-1981)was used for the other models. From this study Beattie and Whalley conclude that thehomogeneous model is as good as the others in predicting the two-phase flow pressure drop overthe range of parameters considered. The main results of Beattie and Whalley are summarized inTable 5.5.

Idsinga et al. (1977) compared 18 different correlations (4 homogeneous models) against 3500steam-water pressure drop measurements under both adiabatic and diabatic flow conditions.Most of the data were from vertical pipes ranging in diameter from 0.23 to 3.3 cm. Also, theamount of low mass flux data (less than 300 kg/m2s) was much less. They used thethermodynamic equilibrium model for the calculation of single-phase length in case of diabaticdata. The void fraction model used is the homogeneous model for all homogeneous frictionmodels and for other models, consistent void fraction correlations recommended by the originalauthors were used. Assessment by Idsinga et al. (1977) shows that best results are obtained fromthe homogeneous models proposed by Owens (1961) and Cicchitti (1960). Incidentally, thesemodels were also considered for assessment by Beattie and Whalley (1982) and were found togive reasonable results for steam/water flow, although not as good as that of Beattie and Whalleymodel.

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Assessment by Weisman and Choe (1976) showed that the homogeneous models ofMcAdams (1942) and Dukler et al. (1964) give better results in the homogeneous flow regime(G > 2712.4 kg/m2s). Interestingly, the homogeneous model by Dukler (1964) gave consistentlygood results for all flow regimes except the separated (stratified) flow regime.

5.3.6.1.2. Correlations based on the multiplier concept

Several comparisons of these correlations have been reported previously. One of theearliest assessment was carried out by Dukler et al. (1964). They also compiled a databankconsisting of about 9000 data points. They have selected 5 correlations [Baker (1954), Bankoff(1960), Chenoweth and Martin (1955), Lockhart and Martinelli (1949) and Yagi (1954)] forassessment. Their assessment showed that the Lockhart and Martinelli correlation is the best outof the five correlations for two-component two-phase flow.

Idsinga et al. (1977) assessed 14 multiplier based models against 3500 steam-waterpressure drop data. The multiplier based models recommended by Idsinga et al. (1977) are theones due to Baroczy (1966) and Thorn (1964).

Friedel (1980) compared 14 pressure drop correlations against 12 868 data points obtainedby 62 authors from circular and rectangular channels. Both horizontal and vertical flow adiabaticdata in pipes ranging from 1 to 15 cm in diameter were studied. While applying the correlationsno distinction is made as to whether they were derived for horizontal or vertical two-phase flow.Overall, the Chisholm (1973) and the Lombardi-Pedrocchi (DIF-1) correlations were found to bethe most accurate. However, these two correlations are equivalent and are unexpectedlyinadequate for prediction of the measured values in gas/water and gas/oil flows.

TABLE 5.5. MAIN RESULTS OF BEATTIE AND WHALLEY

Fluid used

Non steam-water

Non steam-water

Steam-water

Steam-water

NDP(a)

7168

2011

1236

3095

Orientation

horizontal

vertical

horizontal

vertical

Recommended Correlation

HTFS, L-M(b) & B-W(c)

L-M, HTFS & B-W

Dukler et al, B-W & Isbin

B-W, HTFS, & Friedel

(a) NDP: No. of data points,00 L-M: Lockhart-Martinelli (1948),(c) B-W: Beattie and Whalley (1982).

Friedel (1979) derived two-phase friction pressure drop correlations for horizontal, verticalupflow and downflow based on his databank. He has also compared the predictions of thesecorrelations with the Chisholm (1973) and DIF-2 correlations using an enhanced databankconsisting of about 25 000 data points. The data pertain to one-component and two-componentmixtures flowing in straight unheated sections with horizontal, vertical upflow and downflow intubes, annular and rectangular ducts under widely varying conditions. The Friedel correlationwas found to be better than the other two.

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5.3.6.1.3. Flow pattern specific models

To assess flow pattern specific pressure drop correlations, the first step is to select a flowpattern map applicable to the geometry. Previous review of flow pattern specific pressure dropcorrelations have been carried out by Weisman and Choe (1976), Mandhane et al. (1977),Hashizume & Ogawa (1987) and Behnia (1991) for horizontal two-phase flow. In the reviews byMandhane et al. and Behnia, the flow pattern to which the data belong has been obtained withthe help of Mandhane's flow pattern map. Hashizume and Ogawa (1987) used a modified Bakermap in their assessment. Weisman and Choe used their own flow pattern map.

Using the AGA-API databank (enhanced by the addition of Fitzsimmons (1964), Petrick(1961) and Miropolski (1965) data), Weisman and Choe made a flow pattern specificassessment for horizontal two-phase flow. Their assessment covers four basic flow patternsreferred to as separated flow (Stratified flow), homogeneous flow, intermittent (slug) flow andannular flow. The transition criteria used by them are given in Table 5.6.

Based on their assessment the correlations recommended for different flow patterns aregiven in Table 5.7. Their assessment shows that the scatter obtained using the differentcorrelations (11 in all) for separated flow is substantially large. Ten different correlations wereassessed for the homogeneous flow pattern and in this regime, the homogeneous models givebetter predictions. Most of the correlations tested for the intermittent flow regime were found togive reasonably good values, although the best predictions are obtained with the Dukler et al.(1964) correlation followed by Lockhart-Martinelli correlation. These two correlations are alsoseen to give consistently good results for annular flow.

TABLE 5.6. TRANSITION CRITERIA FOR HORIZONTAL FLOW (WEISMAN & CHOE)

Flow pattern Transition criteria

Separated flow JG* < 2.5 exp [-12(l-a)J + 0.03awhere J*G = pG°-5JG/[g D(pL-pG)a5]

Annular flow G > 10(GL)"° 285 (D/Dc)

0-38

where GL is in ib/fPhr and Dc= 1.5" (0.0381 m)Homogeneous flow G > 2712.4 kg/m2s (2 x 106 lb/h ft2)

Mandhane et al. (1977) compared 16 pressure drop correlations against the University ofCalgary Pipe Flow Data Bank containing about 10 500 data points. The data were grouped bypredicted flow pattern using the Mandhane et al. (1974) flow pattern map. Each correlation wasthen tested against all the data points contained within each flow pattern grouping. Thecorrelations recommended by Mandhane et al. are given in Table 5.8. Hashizume and Ogawa(1987) also carried out an assessment of 5 pressure drop correlations using selected data (only2281 data) from the HTFS databank. This, however, contained some very low mass flux data. Inthis analysis they have used the modified Baker (1954) map for flow pattern identification. Theyconcluded that their correlation gives the best prediction for refrigerant data.

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TABLE 5.7. CORRELATIONS RECOMMENDED BY WEISMAN & CHOE (1976)

Flow pattern Recommended correlation No. of correlations tested

Separated flow Agrawal et al. (1973) and 11Hoogendoorn(1959)

Homogeneous flow McAdams (1942), Dukler et al. 10(1964) &Chisholm (1968)

Intermittent flow Dukler (1964), Lockhart- 7Martinelli (1949) & Hughmark(1965)

Annular flow Dukler (1964) & Lockhart- 6Martinelli (1949)

TABLE 5.8. CORRELATIONS RECOMMENDED BY MANDHANE ET AL. (1977)

Flow pattern Correlation

Bubble, elongated bubble Chenoweth and Martin (1956)

Stratified Agrawal et al. (1973)

Stratified Wavy Dukler et al (1964)

Slug Mandhane et al. (1974)

Annular, annular mist Chenoweth and Martin (1956)

Dispersed bubble Mandhane et al. (1974)

5.3.6.1.4. Assessment for diabatic flow

With modified Saha and Zuber correlation for the onset of nucleate boiling and theArmand correlation for void fraction, Snoek & Leung (1989) carried out an assessment of 9different correlations using diabatic pressure drop data from horizontal 37 and 41 rod clustersrelevant to CANDU type reactors. The databank consisted of 1217 measurements using eitherwater or refrigerant-12. The correlations compared are the Beattie model (1973), Levy model(1974), Lombardi and Pedrocchi correlation, Martinelli-Nelson separated flow model (1948,1949), Chisholm and Sutherland model (1969), Chisholm (1983), Reddy et al. (1982) andBeattie and Whalley model (1982). The acceleration pressure drop was calculated using Eqs. 5.6and 5.7 given in Section 5.3.1 Friedel (1979) correlation was found to predict the experimentalresults best. Either of the Beattie models were found to yield small errors. Levy model wasfound to be good for water, but poor for refrigerant-12 data. Results of similar studies forvertical clusters are not available in open literature.

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5.3.6.1.5. Parametric effects

Effect of diameter

Simpson et al. (1977) compared six pressure drop correlations with data from largediameter (12.7 and 21.6 cm) horizontal pipes. None of the pressure gradient correlationspredicted the measured pressure drop accurately, suggesting the need for considering the effectof pipe diameter. Behnia (1991) has compared seven pressure drop correlations with datagenerated from large diameter pipe lines ranging in diameter from 7.6 cm to 48.4 cm. In order toidentify the flow pattern to which the data belong he has used the Mandhane et al. (1974) flowpattern map. He concludes that the best predictions are obtained using the Beggs and Brill(1973) correlation followed by Aziz et al. (1972) correlation. However, it may be noted that themajority of the data is from large oil pipe lines of about 0.5 m in diameter.

Effect of high mass velocity two-phase flow

An assessment to identify a correlation suitable for predicting friction pressure losses inhigh velocity two-phase flows (characteristic of critical flow in long channels) has been carriedout by D'Auria and Vigni (1984). The pressure drop measurements obtained in the exit nozzle ofa pressure vessel was used to assess different pressure drop correlations. The investigations werein the range of pressures from 0.1 to 7.0 MPa and flow rate between 500 to 20 000 kg/m2s. Theassessments were carried out in two-phases; first 17 different correlations were compared withexperimental data adopting a homogeneous equilibrium model. Later on a two-velocity modelaccounting for slip was considered and the correlations were compared with the sameexperimental data. Results from these studies indicate that practically none of the correlations isable to predict the measured (Ap)tot for high values of mass velocities (G > 8000 kg/m2s) whilefor low values of the same quantity (G < 2000kg/m2s) nearly all correlations produce resultswhich are within the experimental error band.

5.3.6.2. Assessment of void fraction correlations

Assessment of void fraction correlations are comparatively few in number. The reportedassessments are due to Dukler et al. (1964), Friedel (1980), Chexal et al. (1991) Diener andFriedel (1994) and Maier and Coddington (1997). Dukler compared three holdup (i.e. 1-a)correlations, viz., Hoogendoorn (1959), Hughmark (1962) and Lockhart-Martinelli (1949).Hughmark correlation was found to give the best agreement with data.

Friedel (1980) compared 18 different correlations for mean void fraction using a databankhaving 9009 measurements of void fraction in circular and rectangular channels by 39 differentauthors. In his assessment no distinction was made as to whether the correlations were derivedfor horizontal or vertical two-phase flow. The mean void fraction correlation of Hughmark(1962) and Rouhani (I and II) (1969) were found to reproduce the experimental resultsconsiderably better than the other relationships, regardless of the fluid and flow directions.However, Rouhani equation II was found to reproduce the measured values more uniformly overthe whole range of mean density. Hence, Friedel recommends Rouhani II relationship.

Chexal, Horowitz and Lellouche (1991) carried out an assessment of eight void fractionmodels using 1500 steam-water data points for vertical configurations representative of severalareas of interest to nuclear reactors such as: (1) high pressure — high flows, (2) high pressure —

139

low flows, (3) low pressure — low flow, (4) counter current flooding limitation, (5) naturalcirculation flows and (6) co-current downflows. The data were representative of PWR and BWRfuel assemblies and pipes up to 18 inches in diameter. The correlations assessed and statisticalcomparision are given in Table 5.9.

Diener and Friedel (1994) made an assessment of mean void fraction correlations usingabout 24000 data points. The data consists of single-component (mostly water & refrigerant 12)and two-component systems (mostly air-water). In this assessment, they had compiled 26 mostoften used and cited correlations. These correlations were then checked for the limitingconditions [i.e. zero and unity value of void fraction for single-phase liquid (x = 0) and single-phase vapor (x = 1)]. Only 13 correlations were found to fulfill the limiting conditions and wereselected for further assessment. In this assessment they have not differentiated the data on thebasis of flow direction, although, in vertical upward flow the mean void fraction is expected tobe lower than in case of horizontal flow under identical conditions (due to larger velocitiescaused by buoyancy effect). Most of the void fraction correlations reproduce the data with arather acceptable accuracy. The three best correlations in the order of decreasing predictionaccuracy are listed in Table 5.10 for various fluid conditions.

Maier and Coddington (1997) carried out an assessment of 13 wide range voidcorrelations using rod bundle void fraction data. The database consisted of 362 steam-water datapoints. The data is from level swell and boil-off experiments performed within the last 10-15 years at 9 experimental facilities in France, Japan, Switzerland, the UK and the USA. Thepressure and mass flux of the data range frm 0.1 to 15 MPa and from 1 to 2000 kg/m2-srespectively. Of the 13 correlations considered, 5 were based on tube data. The remainingcorrelations either are specific to rod bundles or include rod bundle option.

TABLE 5.9. STATISTICAL COMPARISION OF THE EIGHT VOID FRACTION MODELS[CHEXAL, HOROWITZ AND LELLOUCHE (1991)]

Void fraction model Mean error Standard deviation

Chexal-Lellouche (1986)

Liao, Parlos and Griffith (1985)

Yen and Hochreiter (1980)

Wilson etal. (1965)

Ohkawa and Lahey (1980)

Dix(1971)

GE ramp (1977)

Katoka and Ishii (1982)

All 13 correlations except Gardner (1980) are based on drift flux model. Some of thecorrelations e.g. Ishii (1977), Liao, Parlos and Griffith (1985), Sonnenburg (1989), Takeuchi etal. (1992), Chexal-Lellouche (1992) require iterations to calculate the void fraction. Theimportant results of this assessment are:

140

-0.0041

0.002

0.050

0.013

0.025

0.023

0.012

0.031

0.049

0.094

0.142

0.099

0.057

0.094

0.062

0.101

(1) Two of the tube based correlations i.e.Liao, Parlos and Griffith (1985) and Takeuchi(1992), produce standard deviations which are as low as the best of the rod bundlecorrelations.

(2) Comlpex correlations like Chexal et al. (1992), or others requiring iterative solutionsproduce no significant improvement in mean error or standard deviation compared to moredirect correlations of Bestion (1990), Inoue et al. (1993) and Maier and Coddington(1997).

TABLE 5.10. VOID FRACTION CORRELATIONS RECOMMENDED BY DIENER &FRIEDEL(1994)

Fluid Total number ofData points

Recommended Correlation

Water/air mixture

1-component mixtures2-component mixtures

2-component mixtureswith G> 100 kg/m2s

10991

982714521

11394

Rouhani I, Rouhani II, HTFS-Alpha®

HTFS-Alpha, HTFS®, Rouhani IIHTFS-Alpha, Rouhani I, Rouhani

IIRouhani II, Rouhani I, HTFS

! proprietary correlations belonging to HTFS.

5.3.6.3. Limitations of the previous assessment procedure

Most of the well documented assessments of pressure drop correlations have beenreviewed in the Section 5.3.6.1. Some limitations of these assessments are given below:

(1) To the best of our knowledge, none of the prior assessments of the two-phase frictioncorrelations concentrate on low mass flux two-phase flows. Analysis using limited numberof data (see Vijayan & Austregesilo) shows that there is considerable scatter in thepredictions at the low mass fluxes typical of advanced designs. Hence it is desirable toassess the predictive capability of correlations reported in literature for use in the design ofadvanced reactors where better accuracy of prediction at low mass flux is the criterion ofacceptability.

(2) Most assessment of PDCs are based on statistical approach. The correlations selected by astatistical method need not necessarily reproduce the parametric trends as shown by Leung& Groeneveld (1991). Reliable reproduction of parametric trends by PDCs is important tocapture certain thermalhydraulic phenomena. An example in this regard is the flow patterntransition instability occurring near slug flow to annular flow transition [Boure et al.(1971)].

(3) Effect of pressure has not been studied separately. It is of interest to study this aspect forthe advanced designs.

(4) Effect of pipe diameter needs to be assessed as the pipe diameters in advanced designs canbe large. In this case, there is a need to generate additional data as most of the availabledata on steam water mixture are for small diameter pipes.

(5) Most assessments are for pipe flow data. The only assessment for rod bundles in the openliterature is that reported by Snoek and Leung (1989) for CANDU type reactors.

141

(6) The database for vertical downflow is less extensive.

(7) In deriving certain empirical friction models, a specific void correlation is used to derivethe experimental friction pressure drop data. Such empirical models, are to be used withthe specified void correlation to predict the pressure drop. Such correlations may not beacceptable for natural circulation reactors where the flow rate is a dependent variablegoverned by the balance of the driving pressure differential due to elevation and thepressure losses. Therefore, applicability of such correlations needs to be assessed fornatural circulation flow.

(8) To our knowledge, assessment of flow pattern specific pressure drop correlations forvertical flow are not reported so far. For the assessment of flow pattern specificcorrelations, the flow pattern to which the data belong is identified with the help of a flowpattern map which is different for different orientations of the duct. Therefore, separateassessments are required for identifying the best flow pattern map.

5.3.7. Proposed assessment procedure for diabatic vertical flow

For adiabatic vertical flows, the gravitational pressure drop is significant and therefore avoid fraction correlation is necessary to derive the experimental friction pressure drop from themeasured total pressure drop. For diabatic vertical two-phase flows with subcooled inletconditions, which is relevant to nuclear reactors, a model for the onset of nucleate boiling isnecessary in addition to void fraction correlation. This suggests that the factional Pressure DropCorrelations (PDCs) cannot be assessed in isolation, hi fact, a rational assessment of PDCs fordiabatic flow requires a preassessment of models for onset of nucleate boiling (ONB), voidfraction and flow pattern transitions. Therefore, a rational assessment procedure consists of thefollowing steps:

(1) To review the literature and compile a set of correlations for ONB, void fraction, flowpattern and pressure drop,

(2) To compile a databank consisting of raw data for ONB, void fraction, flow patterns andpressure drop for forced and natural circulation conditions of one-component two-phaseflow,

(3) Assessment of models for ONB, void fraction, flow pattern transitions and pressure drop.

This assessment also aims to investigate the parametric effects due to mass flux, pressure,quality, diameter, flow direction and geometry relevant to the advanced designs. An assessmentis in progress in BARC. Some of the results available at this stage are given below.

5.3.8. Results of assessment

5.3.8.1. Compilation of databank

Several databanks exist for the pressure drop in two-phase flow. Examples are those dueto Dukler et al. (1964), Friedel (1980), AGA-API, University of Calgary multiphase pipe flowdatabank, HTFS databank and MID A [Brega et al. (1990)]. A databank has been compiled byFriedel (1994) for void fraction. Some databanks for flow patterns are also available. Thesedatabanks are not available to us at present and therefore a Avo-phase /low Jata frank(TPFDB) consisting of raw experimental data on the following phenomena is being compiled.

142

(a) Adiabatic and diabatic pressure drop in ducts of various geometry,(b) Void fraction,(c) Flow patterns,(d) Flow pattern specific pressure drop.

In this compilation, special emphasis is given to steam-water flows although some dataon air-water and refrigerant two-phase flows are included. The databank is being updatedcontinuously. Currently, this databank consists of about 4000 data on pressure drop, 5000 dataon void fraction, 3000 data on flow pattern and 500 data on flow pattern specific pressuredrop. The sources from where the original data were compiled are shown in Appendix XVII.

5.3.8.2. Assessment of void fraction correlations

An assessment of the void fraction correlations given in Section 5.3.5.1 was carried outusing a part of the void fraction data (about 3300 entries) contained in the TPFDB. The dataused for assessment pertains to vertical upward flow of steam-water mixture in circular,annular and rectangular channels. Further details of the assessment are given in AppendixXVIII.

The present assessment showed that Chexal-Lellouche correlation performs better thanother correlations. Clearly, all the statistical parameters considered above are minimum forthis correlation, followed by Hughmark, Modified Smith and Rouhani correlations(Table 5.11). Previous assessments by Dukler et al. (1964) and Friedel (1980) have alsoshown that the Hughmark correlation to be the best. Assessment by Diener and Friedel (1994)have shown the Rouhani correlation to be among the best three correlations for predictingvoid fraction.

A generic problem of all good correlations mentioned above except Modified Smithcorrelation is that they overpredict the void fraction. This is clear from the mean error given inthe table-11, which is positive for almost all the correlations (except Nabizadeh and ModifiedSmith correlations). Among the top four correlations only the Chexal-Lellouche and themodified Smith correlations satisfy the three limiting conditions (i.e. at x = 0, a = 0 ; at x = 1,a = 1 and at P = Pcrjt; a = x) over a wide range of parameters (see also Appendix XVIII).Therefore, these correlations may be used in computer codes used for thermalhydraulicanalysis.

5.3.8.3. Assessment of flow pattern maps for vertical upward two-phase flow

A large number of flow pattern maps are found in the literature. Many of these are basedon experiments. Examples are those due to Griffith and Wallis (1961), Hosier (1967),Spedding and Nguyen (1980) and Weisman and Kang (1981). Since such flow pattern mapsare based on limited data, these cannot be assumed to be of general validity. Therefore,theoretical flow pattern maps have been proposed by a few authors. In such maps, thetransition criteria are physically based and can be considered to be of general validity.Examples of such maps are those proposed by Taitel et al. (1980), Mishima-Ishii (1984),Solbrig (1986), Bilicki and Kestin (1987) and McQuillan and Whalley (1985). In the presentassessment, only three theoretical flow pattern maps for vertical upward flow, proposed by

143

Taitel et al. (1980), Mishima and Ishii (1984) and Solbrig (1986) are considered as they formthe basis of the flow pattern maps used in computer codes for the thermal-hydraulic analysisof nuclear reactors.

A fairly large number of flow regimes are reported in literature. Examples are bubbly,dispersed bubbly, slug, churn, annular, wispy annular, wavy annular, annular mist, sprayannular, droplet flow, etc. However, most investigators categorised the flow pattern data intomainly three regimes. These are the bubbly, slug and annular flow regimes. Even computercodes like RELAP5 consider only these as independent flow regimes. Therefore, in ourassessment only these three flow patterns are considered. Corresponding to these threepatterns the relevant transitions are bubbly-to-slug and the slug-to-annular.

Detailed results of this assessment are given in Appendix XVIII. Table 5.12 shows asummary of the comparison of the data with bubbly-slug together with slug — annulartransition criteria. The characterization of bubbly flow data using the different transitioncriteria yield comparable results. Since it uses a = 0.52, 95% of all bubbly flow data ischaracterized as bubbly by the Solbrig criterion. However, a large amount of slug flow dataalso fall in the bubbly flow regime.

The slug-annular transition criteria together with bubbly-slug transition criteria arerequired to assess the slug flow data. Table 5.13 shows the results of such an assessment. Asseen all the criteria fare badly in characterizing slug flow data even though the Solbrigcriterion I is somewhat better than others.

TABLE 5.11. COMPARISON OF VARIOUS VOID FRACTION CORRELATIONS

Correlation name

Chexal-Lellouche

Hughmark

Modified Smith

Rouhani

Zuber-Findlay

Bankoff

Osmachkin

Bankoff-Jones

Thorn

Nabizadeh

Armand

GE-Ramp

Bankoff-Malnes

Dix

Homogeneousmodel

mean error(%)5.10

6.85

-5.44

10.76

11.20

9.08

1.32

12.50

6.72

-21.17

21.54

27.30

30.98

17.81

44.90

absolute mean error

(%)15.25

16.72

18.13

18.42

19.32

19.21

18.91

20.78

21.11

24.40

27.75

32.60

36.57

39.92

49.03

r. m. s. error(%)

22.74

23.81

24.19

25.97

26.15

26.58

26.59

27.95

28.88

30.00

34.75

39.10

44.15

48.52

55.51

standard deviation(%)

22.16

22.60

23.58

23.64

23.64

24.98

26.56

25.00

28.08

21.35

27.27

28.08

31.45

45.14

32.65

144

TABLE 5.12. CHARACTERIZATION OF BUBBLY FLOW DATA USING THE VARIOUSTRANSITION CRITERIA

Item Taitel et al. Mishima-Ishii Solbrig

PBB

PBS+

PBA**

PSB®

PAB#

72.3

21.1

6.7

13.0

0.7

77.7

17.8_

4.6

17.7

1.6

95.1

4.9

0.0

39.6

4.0

*PBB:+PBS:** PBA:@PSB:#PAB:

Percentage of bubbly data characterized as bubbly;Percentage of bubbly data characterized as slug;Percentage of bubbly data characterized as annular;Percentage of slug data characterized as bubbly;Percentage of annular data characterized as bubbly.

TABLE 5.13. CHARACTERIZATION OF SLUG FLOW DATA USING VARIOUSTRANSITION CRITERIA

Item

PSS*

PSB

PSA**

PBS

PAS#

Taitel et al.

40.2

13.0

47.0

21.1

9.4

Mishima-Ishii

43.2

17.7

39.2

17.8

16.0

Solbrig I

46.6

39.6

13.5

4.9

47.8

Solbrig II

34.4

24.6

40.5

11.8

12.1

*PSS:#PAS:** PSA:

Per cent of slug data characterized as slug;% of annular data characterized as slug;Per cent of slug data characterized as annular.

TABLE 5.14. CHARACTERIZATION OF ANNULAR FLOW DATA WITH VARIOUSTRANSITION CRITERIA

Item

PAA*

PAS

PAB

PBA

PSA

Taitel et al.(1980)

90.1

9.4

0.7

6.7

47.0

Mishima-Ishii(1984)

82.7

16.0

1.6

4.6

39.2

Solbrig I(1986)

48.1

47.8

4.0

0.0

13.5

Solbrig II(1986)

85.5

12.1

2.4

0.7

40.5

PAA: Percentage of annular data characterized as annular.

145

Limiting our attention to only the characterization of annular flow data shown inTable 5.14, Taitel et al. Mishima-Ishii and the Solbrig II criterion are found to perform well.However, an acceptable criterion shall not characterize slug flow data as annular and that iswhere all the three criteria fail.

5.3.8.4. Assessment of pressure drop correlations

A part of the pressure drop data from TPFDB for vertical upward two-phase flow indifferent geometries has been assessed against some of the correlations described earlier inthis report. In the present assessment 2156 data points collected from literature for diabaticsteam-water flow were assessed against the correlations listed in Table 5.15. ExceptingChisholm and Turner-Wallis the other correlations belong to the homogeneous model. Theassessment is based on Colebrook equation for single-phase friction factor, Zuber-Findlay(1965) correlation for void fraction and Saha and Zuber (1974) model for the onset of nucleateboiling. The results are also given in Table 5.15. The table shows that the Chisholmcorrelation is the one with least R.M.S. error (37%) and least standard deviation (28%)followed by the homogeneous model given by Dukler et al. (1964) with 48% R.M.S. error and46% standard deviation which suggests that the simple homogeneous models can givereasonable predictions for design purposes. Earlier assessment by Friedel (1980) had shownthat the Chisholm (1973) correlation to be most accurate for adiabatic steam-water flow. Priorassessment by Weisman and Choe (1976) showed that the Dukler et al. (1964) gaveconsistently good results for all flow regimes.

5.4. COMPARISON OF CORRELATIONS AS THEY STAND IN CODES

Reference is made hereafter to system codes used in the safety and design analysis ofnuclear power plants. The attention is focused toward RELAP5 and CATHARE owing to thedirect experience gained in the use of these codes. The physical phenomenon addressed is thewall-to-fluid (steam and/or liquid) pressure drop excluding other phenomena that may contributeto the overall (steady state or transient) pressure drop.

TABLE 5.15. COMPARISON OF PRESSURE DROP CORRELATIONS

Correlation

Dukler etal. (1964)

Me Adams (1942)

Beattie&Whalley(1982)

Cicchittie (1960)

Chisholm (1973)

Tumer-Wallis(1965)

Mean error

(%)

12

20

21

31

24

21

R.M.S.

error%

48

54

55

65

37

61

Standard Deviation

%

46

50

51

57

28

57

146

The comparison among correlations as they stand in the codes, implies two different steps:

(a) description of the physical models or constitutive equations or closure equationsimplemented in the codes;

(b) comparison among results produced by the code in terms of pressure drops, eventuallyincluding experimental data.

The item a) constitutes the objective of the Section 5.4.1, while item b) is addressed in thefollowing discussion.

The calculation (better, the results of calculations) of pressure drop by system codes is afunction of different types of parameters including :

- nodalization details,

- user assumptions,

- physical models for wall-to-fluid pressure drops (Section 5.4.1),

- general code hydraulic model and coupling with physical models other than pressure drops(e.g. heat transfer coefficient),

- numerical structure of the code.

The role of each set of parameters may be extremely different in the various codeapplications; i.e. user assumptions may be very important in one situation and (almost) notimportant in the another case; clearly, physical models are always important.

A huge amount of comparison among calculation results by system codes (includingcomparison with experimental data), is provided in the open literature (e.g. InternationalStandard Problems organized by OECD/CSNI or Standard Problem Exercise organized by theIAEA), hi the case of natural circulation, a detailed comparison among system codes, includingevaluation of the effects of nodalization details, of boundary and initial conditions and of userchoices can be found in D'Auria and Galassi (1992). In the framework of the present CRP somepresentations focused on this item too [D'Auria and Frogheri (1996)].

Considering all of the above, it was preferred not to include results of time trendspredicted by the code.

5.4.1. Physical models in system codes

The attention is focused hereafter to the two-phase wall-to-fluid friction inRELAP5/MOD3.2 [the RELAP5 Development Team (1995)] and CATHARE 2 vl.3 [Houdayeretal. (1982)] codes.

5.4.1.1. RELAP5

The wall friction model is based on the Heat Transfer and Fluid Flow Service (HTFS)modified Baroczy correlation, [see Chaxton et al (1972)]. The basic equation is

147

f(5.68)

where

2 < C = - 2 + fi(G)Ti(A,G)

where

fi(G) = 28-0.3VG;T I ( A , G ) = exp [{log10A + 2.5}2/{2.4-G(l()-4)}], andA = (pG/pL)(iaL/u<})

0-2

The same derivation implies the use of the Lockhart-Martinelli parameter, i.e. Eqs 1 to 3in the Appendix VIII.

The partition between contributions to the total pressure drop due to liquid and steam isobtained following the theoretical basis proposed by Chisholm using the Z parameter defined as:

aLW

(5.69)

Z 2 = «,

a

such that

dP

'dz

dPGdz~

aG+ahZ2

[aG+aLZ2

(5.70)

(5-71)

In the last formulae (other than the already defined quantities) PL and po are the sectionperimeters contacting with liquid and steam, respectively; in addition, CCLW and OCQW are theliquid and the vapor volume fraction respectively, in the wall film:

PL/P = aLw

pG/p = aGW

(5.72)

(5-73)

These are defined from the flow regime maps, on the basis of what can be referred asRELAP5 approach [the RELAP5 Development Team (1995)].

The single phase coefficient (Darcy-Weisbach friction factor) is computed fromcorrelations for laminar and turbulent flows with interpolation in the transition regime. Thelaminar zone coefficient is obtained from the well known "64/Re" formula. The turbulent

148

friction factor is obtained from the Zigrang-Sylvester approximation, [Zigrang and Sylvester(1985)], that is introduced into the already discussed Colebrook correlation. The transitionregion is computed by a linear interpolation that, again, can be reported as RELAP5 approach.Finally the heated wall effect is accounted for, by introducing the correlation adopted in theVIPRE code [Stewart (1985)].

5.4.1.2. CATHARE

hi relation to two-phase wall-to-fluid friction, a simpler approach is included in theCATHARE Code [Bestion (1990)]. The complex interaction of this model with terms includedin other code models (e.g. dealing with momentum transfer : interfacial friction, stratificationcriterion, drift velocity, droplet diameter) should be recalled: the overall result of the codepredicted pressure drop comes from the combination of the effects of all the above mentionedmodels.

The wall friction is computed from the following formula (the index "K" may indicateeither the liquid phase, K = L, or the vapor phase, K = G):

K "K (5.74)

where

CFK is the single-phase friction coefficient

CFK = CFK (Rek) with ReK = ctRpsmP^^ ( 5 ' 7 5 )

and CKIS the two phase flow multiplier deduced from the experiments.

In the case of stratified flow, this is the relative fraction of the wettable perimeter occupiedby the phase K; CK is only a function of the void fraction. In the other flow patterns, the vapourfriction is assumed as negligible and only the liquid-to-wall friction is computed. This isassumed true in all cases except the case of very high void fraction. Specifically, theLockhart-Martinelli (Appendix VIII) correlation for liquid was adopted for pressure below2 MPa; for pressure larger than this value a slightly different correlation was adopted whichcorrects the pressure effect.

This approach was demonstrated to be acceptable with the exception of the situation ofhigh quality in the annular-mist flow regime. A special correlation for CK=L is developed in sucha case. It should be mentioned that an extensive experimental database was utilized todemonstrate the validity of the approach.

5.5. FINAL REMARKS

The performed activity gave an idea of the difficulty in synthesizing the currentunderstanding of a fundamental phenomenon in thermohydraulics: the occurrence and themodelling of various components of pressure drop. Making only reference to the modelling,different approaches can be pursued for calculating friction pressure drops, hi addition, a number

149

of correlations, different from each other, have been developed and are currently in use. Theareas and the modalities of application of the correlations are also different; in this context,system geometry (e.g. tubes, bundles), fluid status (single-phase, two-phase with or withoutinteraction of phases), flow type (transient, steady state, fully developed or not), flow regime(e.g. in two-phase flow, bubbly or annular flow), can be distinguished. This makes it difficult toidentify an 'agreeable' (or widely accepted) approach or to recommend a particular one.

The recommendations should also suit the objectives and the framework of the use of thecorrelations. Requirements of subchannel analysis codes and system codes should bedistinguished. Detailed plans for future development are outside the purpose of the CRP,specifically the need to distinguish between the various applications. However, a few genericrequirements that should be the basis of any future development are listed below.

(a) To identify the conditions for a suitable experiment (i.e. quality of facility design, of testdesign, of instrumentation and of recorded data)

(b) To identify "reference data sets"(c) To define acceptable errors (as a function of application)(d) To compare code and/or correlation results with selected "reference data sets".

hi addition, a few specific requirements which need to be considered for future work arelisted below.

The correlations selected based on assessment by statistical method need not necessarilyreproduce the parametric trends. Therefore, future assessment should also examine theparametric trends for mass flux, pressure, quality and diameter.

Most of the reported assessments are for adiabatic pipe flow data. Assessment of pressuredrop correlations for diabatic flow requires pre-assessment of the models for the on-set ofboiling and void fraction. For flow pattern specific pressure drop correlations, a pre-assessmentof flow pattern transition criteria is also required.

Only limited data are available for complex geometries like rod bundles, grid spacers, tieplates, etc. in the open literature. More data are required in this area.

The available database in the open literature is limited and further work is required togenerate more pressure drop data for the following range of parameters:

Low (<500 kg/m2 s) and high (>8000 kg/m2s) mass flux two-phase flowLarge diameter pipe (>70 mm)Low pressure (<10 bar)Vertical down flow.

Simultaneous void fraction measurement is required along with pressure dropmeasurement to calculate individual components of pressure drop. The availability of flowpattern specific pressure drop data is very limited. More data are required to be generated in thisarea.

As final remarks, from a methodological point of view, we can limit ourselves to list thefollowing various approaches for modelling pressure drops that can be considered whendeveloping advanced thermohydraulic models (capabilities intrinsic to CFD — Computational

150

Fluid Dynamics or DNS — Direct Numerical Simulation are excluded from the present review)suitable for system codes.

Two-phase flow multiplier (developed having a boiling channel as reference): An averagevalue of the two-phase pressure drop can be calculated. Users must be aware of the conditionsunder which the correlations are developed or tested (e.g. length of the channel, consideration ofacceleration pressure drops, etc.).

Interfacial drag: The lack of knowledge of the interfacial area may noticeably lower the qualityof such an approach.

Use of drift flux: The calculation of void fraction, based on correlations not tuned to thecalculation of pressure drops may limit the validity of the approach.

Use of 6-equation model: The same observations as above applies here.

Calculation of pressure drop considering subchannels: Lack of appropriate knowledge oftwo- or three-dimensional flows, may limit the validity of the approach.


ADORNI, et al., 1961, Results of Wet Steam Cooling Experiments: Pressure Drop, HeatTransfer And Burnout Measurements in Annular Tubes with Internal and Bilateral Heating,CISE-R-31.

ADORNI, N., GASPARI, G.P., 1966, Heat Transfer Crisis and Pressure Drop with Steam-Water Mixtures, CISE-R-170.

AGRAWAL, S.S., GREGORY, G.A., GOVIER, G.W., 1973, An analysis of stratified two-phase flow in pipes, Can. J. Chem. Eng. 51, 280-286.

ARMAND, A.A., TRESCHEV, G.G., 1947, Investigation of the resistance during themovement of steam-water mixtures in heated boiler pipes at high pressure, Izv. Ves. Teplotekh.Inst. 4, 1-5.

AZIZ, K., GOVIER, G.W. FOGARASI, M., 1972, Pressure drop in wells producing oil and Gas,J. Can. Petroleum Technol, 38-48.

BAKER, O., 1954, Simultaneous flow of oil and gas, Oil Gas J. 53, 185.

BANKOFF, S.G., 1960, A variable density single-fluid model for two-phase flow withparticular reference to steam-water flow, J. Heat Transfer 82,265-272.

BAROCZY, C.J., 1966, A systematic correlation for two-phase pressure drop, Chem. Eng.Progr. Symp. Ser. 62,232-249.

BEATTIE, D.R.H., 1973, "A note on calculation of two-phase pressure losses", Nucl. Eng.Design, 25, 395^02.

151

BEATTIE, D.R.H. WHALLEY, P.B., 1982, A simple two-phase frictional pressure dropcalculation method, Int. J. Multiphase Flow 8, 83-87.

BECKER, K.M., HERNBORG, G., BODE, M., 1962, "An experimental study of pressuregradients for flow of boiling water in vertical round ducts", (part 4) AE-86.

BEGGS, H.D., BRILL, J.P., 1973, A study of two-phase flow in inclined pipes, J. PetroleumTechnol 25, 607-617.

BEHNIA, M., 1991, Most accurate two-phase pressure drop correlation identified, Oil & Gas J.,90-95.

BENNETT, A.W., HEWITT, G.F., KEARSEY, H.A., KAY, R.K.F., LACEY, P.M.C., 1965,Flow Visualisation Studies of Boiling at High Pressure, UKAEA Rep. AERE-4874.

BERGLES, A.E., CLAWSON, L.G., GOLDBERG, P., SUO, M., BOURNE, J.G., 1965b,Investigation of Boiling Flow Regimes and Critical Heat Flux, NYO-3304-5.

BERGLES, A.E., DOYLE, E.F., CLAWSON; SUO, M., 1965a, Investigation of Boiling FlowRegimes and Critical Heat Flux, NYO-3304-4.

BERGLES, A.E., GOLDBERG, P., CLAWSON, L.G., ROOS, J.P., BOURNE, J.G., 1965c,Investigation of Boiling Flow Regimes and Critical Heat Flux, NYO-3304-6.

BERGLES, A.E., ROOS, J.P., ABRAHAM, S.C., GOUDA, S.C., MAULBETSCH, J.S.,1968a, Investigation of Boiling Flow Regimes and Critical Heat Flux, NYO-3304-11.

BERGLES, A.E., ROOS J.P., 1968b, Investigation of Boiling Flow Regimes and Critical HeatFlux,NYO-3304-12.

BERKOWITZ, L. et al., 1960, Results of Wet Steam Cooling Experiments: Pressure Drop,Heat Transfer and Burnout Measurements with Round Tubes, CISE-R-27.

BESTION D., 1990, The physical closure laws in the CATHARE code, J. Nucl. Eng. Design124.

BILICKI, Z., KESTIN, J., 1987, Transition criteria for two-phase flow patterns in verticalupward flow, Int. J. Multiphase Flow 13, 283-294.

BLASIUS, H., 1913, Mitt. Forsch. Geb. Ing.-Wesen 131.

BONFANTI, F., CERES A, I., LOMBARDI, C, 1982, "Two-phase densities and pressure dropsin the low flow rate region for different duct inclinations", Proc. 7th hit. Heat Transfer Conf.Munich.

BOURE J.A., BERGLES, A.E., TONG L.S., 1971, Review of two-phase flow instability,ASME Preprint 71-HT-42.

152

BREGA, E., BRIGOLI, B., CARSANA, C.G., LOMBARDI, C, MARAN, L., 1990, "MIDA:Data bank of pressure and densities data of two-phase mixtures flowing in rectangular ducts",8th Congresso UIT, Ancona.

CARLSON, K.E., et al., 1990, RELAP5/MOD3 Code manual, NUREG/CR-5535, EGG-2596.

CEVOLANI, S., Sept. 5-8, 1995, "ENEA Thermohydraulic data base for the advanced watercooled reactor analysis", 1st Research Co-ordination Meeting of IAEA CRP onThermohydraulic Relationships for Advanced Water Cooled Reactors, Vienna.

CHAWLA, J.M., 1967, VDI-Forsc-Heft, No. 523.

CHAXTON K.T., COLLIER J.G., WARS J.A., 1972, "HTFS Correlation For Two-PhasePressure Drop and Void Fraction in Tubes", AERE Rep. R7162.

CHENOWETH, J.M., MARTIN, M.W., 1956, Pressure drop of gas-liquid mixtures inhorizontal pipes, Petroleum Eng. 28, C-42-45.

CHEXAL, B., LELLOUCHE, G., 1986, A Full Range Drift Flux Correlation for Vertical Flows(Revision 1), EPRI-NP-3989-SR.

CHEXAL, B., et al., 1996, Understanding Void Fraction in Steady and Dynamic Environments,TR-106326/RP-8034-14, Electric Power Research Institute.

CHEXAL, B., LELLOUCHE, G., HOROWITZ, J., 1992, A void fraction correlation forgeneralized applications, Progress in Nuclear Energy 27 4, 255-295.

CHEXAL, B., HOROWITZ, J., LELLOUCHE, G., 1991, An assessment of eight void fractionmodels, Nucl. Eng. Design 126, 71-88.

CHISHOLM, D., 1973, Pressure gradients due to friction during the flow of evaporatingtwo-phase mixtures in smooth tubes and channels, Int. J. Heat Mass Transfer 16,347-358.

CHISHOLM, D., 1968, "The influence of mass velocity on friction pressure gradient duringsteam-water flow", Proc. Thermodynamics and Fluid Mechanics Conf., Institute of MechanicalEngineers, 182,336-341.

CHISHOLM, D., SUTHERLAND, L.A., 1969, "Prediction of pressure gradient in systemsduring two-phase flow", Proc. Inst. of Mechanical Engineers Symp. on Two-phase FlowSystems, Univ. of Leeds.

CICCHITTI, A., LOMBARDI, C, SILVESTRI, M., SOLDAINI, G., ZAVATTARELLI, R.,1960, Two-phase cooling experiments: pressure drop, heat transfer and burnout experiments,EnergiaNucleare 7,407-425.

CISE; 1963, A research programme in two-phase flow.

COLEBROOK, C.F., 1938, Turbulent flow in pipes with particular reference to the transitionregion between the smooth and rough pipe laws, J. Inst. Civ. Eng. Lond., 133-156.

153

COOK, W.W., 1956, Boiling Density in Vertical Rectangular Multichannel Sections withNatural Circulation, ANL-5621.

COUTRIS, N., DELHAYE, J.M., NAKACH, R., 1989, Two-phase flow modelling: The closureissue for a two-layer flow, hit. J. Multiphase Flow 15, 977-983

DALLE DONNE, M., HAME, W., 1982, A Parametric Thermalhydraulic Study of an AdvancedPressurized Light Water Reactor with a Tight Fuel Rod Lattice, KfK 3453-WUR 7059e.

D'AURIA, F., VIGNI, P., 1984, "The evaluation of friction pressure losses in two-phase highvelocity flow using non-homogeneous models", 1984 European Two-Phase Flow GroupMeeting, Rome.

D'AURIA, F., GALASSI, G.M., 1992, Relevant Results obtained in the analysis of LOBI/mod2Natural Circulation Experiment A2-77A, US NRC, NUREG/IA-0084.

DIESSLER, G., TAYLOR, M.F., 1956, Analysis of Axial Turbulent Flow Heat TransferThrough Banks of Rods or Tube, Reactor Heat Transfer Conference, TID-7529, Vol. 2.

DffiNER, R., FRIEDEL, L., 1994, Proc. German-Japanese Symp. on Multiphase Flow,Karlsruhe, Germany.

DEX, G.F., 1971, Vapour Void Fraction for Forced Convection with Subcooled Boiling at LowFlow Rates, NEDO-10491.

DREW, T.B., KOO, E.C., MCADAMS, W.H., 1932, Trans. AIChE 28, 56.

DUKLER, A.E., HUBBARD, M.G., 1975, A model for gas-liquid slug flow in horizontal andnear horizontal tubes, hid. Engrg. Chemistry Fundamentals 14, 337-347.

DUKLER, A.E., WICKS, M., CLEVELAND, R.G., 1964, Frictional pressure drop and holdupin two-phase flow, Part A — A Comparison of existing correlations for pressure drop andholdup, B An approach through similarity analysis, AIChE J. 10, 38-43 and 44-51.

EL-WAKIL, M.M., 1971, Nuclear Heat Transport, International text book company, 233-34.

EPRI, 1986, Advanced Recycle Methodology Program-02 Documentation, EPRI-NP-4574.

FILONENKO, G.K., 1948, On Friction Factor for a Smooth Tube, All Union ThermotechnicalInstitute (Izvestija VTI, No 10), Russia.

FITZSIMMONS, D.E., 1964, Two-phase Pressure Drop in Piping Components, HanfordLaboratory Rep., HW-80970.

FRIEDEL, L., 1979, "Improved friction pressure drop correlations for horizontal and verticaltwo-phase flow", European two-phase flow group mtg, Ispra.

FRIEDEL, L., 1980, Pressure drop during gas/vapor-liquid flow in pipes, hit. ChemicalEngineering 20, 352-367.

154

GARDNER, G.C., 1980, Fractional vapour content of a liquid pool through which vapour isbubbled, Int. J. of Multiphase Flow. 6, 399-410.

GENERAL ELECTRIC COMPANY, 1978, Qualification of the one-dimensional core transientmodel for boiling water reactors, NEDO-24154,78 Nucl. Eng. Design 290.

GOVIER, G.W., AZIZ, K., 1972, The Flow of Complex Mixtures in Pipes, Van NostrandReinhold Company, New York, 538.

GRIFFITH, P., 1963, The slug-annular flow regime transition at elevated pressure", ANL-6796.

GRIFFITH, P., WALLIS, G.B., 1961, Two-phase slug flow, J. Heat Transfer 83 C (3), 307.

GRILLO, P., MARINELLI, V., 1970, Single and two-phase pressure drops on a 16-RODbundle, Nuclear Applications & Technol. 9, 682-693.

HASHIZUME, K., 1983, Flow pattern, void fraction and pressure drop of refrigerant two-phaseflow in a horizontal pipe, Int. J. Multiphase Flow 9, 399-410.

HASHIZUME, K., OGAWA, N., 1987, Flow pattern, void fraction and pressure drop ofrefrigerant two-phase flow in horizontal pipe — III Comparison of the analysis with existingpressure drop data on air/water and steam/water systems, Int. J. Multiphase Flow 13, 261-267.

HASHIZUME, K., OGIWARA, H., TANIGUCHI, H., 1985, Flow pattern, void fraction andpressure drop of refrigerant two-phase flow in horizontal pipe — II: Analysis of frictionalpressure drop, Int. J. Multiphase Flow 13,261-267.

HEWITT, G.F., HALL-TAYLOR, N.S., 1970, Annular Two-Phase Flow, Pergamon Press, NewYork.

HEWITT, G.F., OWEN, D.G., 1992, "Pressure and entrained fraction in fully developedflow", Multiphase Science and Technology, Vol. 3 (G.F. Hewitt, J.M. Delhaye and N. Zuber,Eds), Hemisphere Publishing, New York.

HOGLUND, B., et al., 1958, Two-phase Pressure Drop in a Natural Circulation BoilingChannel, ANL-5760.

HOOGENDOORN, C.J., 1959, Gas-liquid flow in horizontal pipes, Chem. Eng. Sci 9, 205-217.

HOSLER, E.R., 1967, Flow Patterns in High Pressure Two-Phase (Steam-Water) Flow withHeat Addition, WAPD-TM-658.

HOUDAYER G., et al., 1982, "The CATHARE code and its qualification on analyticalexperiments", 10th Water Reactor Safety Information Mtg, Washington.

HUGHMARK, G.A., 1965, Holdup and heat transfer in horizontal slug gas-liquid flow,Chemical Eng. Sci. 20,1007-1010.

155

HUSSAIN, A., CHOE, W.G., WEISMAN, J., 1974, The applicability of the homogeneous flowmodel to pressure drop in straight pipe and across area changes, COO-2152-16.

IDELCHIK, I.E., 1979, Hand Book of Hydraulic Resistances, Hemisphere Publishing Company,New York.

IDSINGA, W., TODREAS, N., BOWRING, R., 1977, An assessment of two-phase pressuredrop correlations for steam-water mixtures, Int. J. Multiphase Flow 3,401^413.

ISHII, M., 1977, One-dimensional Drift-flux Model and Constitutive Equations for RelativeMotion Between Phases in Various Two Phase Flow Regimes, ANL-77-47.

INOUE, A., et al., 1993, "In bundle void measurement of a BWR fuel assembly by an X-ray CTscanner: Assessment of BWR design void correlation and development of new voidcorrelation", Proc. ASME/JSME Nuclear Engineering Conf., Vol. 1, 39-45.

ITO, A., MOWATARI, K., 1983, Ring Grid Spacer Pressure Loss Experimental Study andEvaluation Method, American Nuclear Society, 972-978.

JANSSEN, E., KERVINEN, J.A., 1971, Developing Two-phase Flow in Tubes and Annuli,Part-I: Experimental Results, Circular Tubes, GEAP-10341.

JANSSEN, E., KERVINEN, J.A., 1964, Two-phase Pressure Drop in Straight Pipes andChannels: Water-Steam Mixtures at 600 to 1400 psia, GEAP-4616.

JONES, A.B., DIGHT, D.G., 1962, Hydrodynamic Stability of a Boiling Channel, KAPL-2208, Knolls Atomic Power Laboratory.

KATAOKA, I., ISHII, M., 1982, Mechanism and Correlation of Droplet Entrainment andDeposition in Annular Two-Phase Flow, NUREG/CR-2885 and ANL-82-44.

KAYS, W.M., 1975, Convective Heat and Mass Transfer, Tata-McGraw Hill PublishingCompany Ltd., New Delhi.

KHARE, R., VIJAYAN, P.K., SAHA, D., VENKAT RAJ, V., 1997, Assessment of TheoreticalFlow Pattern Maps for Vertical Upward Two-Phase Flow, BARC/1997/E010.

KIM, NAE-HYUN; LEE, S.K., MOON K.S., 1992, Elementary model to predict the pressureloss across a spacer grid without a mixing vane, Nuclear Technol. 98,349-353

KING, C.H., OUYANG, M.S., PEI, B.S., WANG, Y.W., 1988, Identification of two-phaseflow regimes by an optimum modeling method, Nuclear Technol. 82, 211-226.

KOEHLER, W., KASTNER, W., 1988, Two Phase Pressure Drop in Boiler Tubes, Two-PhaseFlow heat Exchangers: Thermalhydraulic Fundamentals and Design (S. Kakac, A.E. BerglesE.O. Fernandes, Eds), Kluwer Academic Publishers.

KNUDSEN, J.G., KATZ, D.L., 1958, Fluid Dynamics and Heat Transfer, McGraw-Hill, NewYork, 178.

156

LAHEY, R.T., Jr., 1984, Two-phase Flow In Boiling Water Reactors, NEDO-13388, 59-70.

LAHEY, R.T., Jr., LEE, S.J., 1992, "Phase distribution and two-phase turbulence for bubblyflows in pipes", Multiphase Science and Technology, Vol. 3 (G.F. Hewitt, J.M. Delhaye, N.Zuber, Eds), Hemisphere Publishing, New York.

LAHEY, R.T., Jr., SHIRALKAR, B.S., RADCLIFFE, D.W., 1970, Two-phase Flow and HeatTransfer in Multirod Geometries, Subchannel Flow and Pressure Drop Measurements in a 9-Rod Bundle for Diabatic and Adiabatic Conditions, GEAP-13040.

LEUNG, L.K.H., GROENEVELD, D.C., 1991, "Frictional pressure gradient in the pre- andpost-CHF heat-transfer regions", Multiphase flows' 91, Tsukuba, 1991, Tsukba, Japan.

LEUNG, L.K.H., GROENEVELD, D.C., AUBE, F., TAPUCU, A., 1993 New studies of theeffect of surface heating on frictional pressure drop in single-phase and two-phase flow,NURETH-3, Grenoble, France.

LIAO, L.H., PARLOS, A., GRIFFITH, P., Heat Transfer Carryover and Fall Back in PWRSteam Generators During Transients, NUREG/CR-4376, EPRINP-4298.

LILES, D.R., MAHAFFY, J.H., 1984, TRAC PF1-MOD1 An advanced best-estimate computerprogram for pressurised reactor thermal-hydraulic analysis, Los Alamos National Laboratory.

LOCKHART, R.W., MARTINELLI, R.C., 1949, Proposed correlation of data for isothermaltwo-phase, two-component flow in pipes, Chem. Eng. Prog. 45,39-48.

LOMBARDI, C, CARSANA, C.G., 1992, A dimensionless pressure drop correlation for two-phase mixtures flowing upflow in vertical ducts covering wide parameter ranges, Heat andTechnol. 10,125-141.

LOMBARDI, C, CERESA, I., 1978, A generalized pressure drop correlation in two-phase flow,EnergiaNucleare25 4,181-198.

LOMBARDI, C, PEDROCCHI, E., 1972, A pressure drop correlation in two-phase flow,EnergiaNucleare 19 2, 91-99.

LORENZINI, E., SPIGA, M., TARTARINI, P., 1989, "Some notes on the two-phase flowfriction multiplier", 7th Seminar on Thermal Non-equilibrium in Two-Phase Flow, Roma.

LOTTES, P.A., FLINN, W.S., 1956, A method of analysis of natural circulation boiling systems,Nuclear Science Eng. 19 2,91-99.

LU ZHONGQI ZHANG XI, 1994, Identification of flow patterns of two-phase flow bymathematical modelling, Nuclear Eng. and Design 149,111-116.

MAIER, D., CODDINGTON, P., 1997, "Review of wide range void correlations against anextensive database of rod bundle void measurements", Proc. ICONE, 5th Int. Conf. onNuclear Engineering, Nice.

157

MALNES, D., 1979 "Slip ratios and friction factors in the bubble flow regime in verticaltubes, KR-110, Kjeller Norway (1966) and A new general void correlation", European two-phase flow group Mtg., Ispra (1979).

MANDHANE, J.M., GREGORY, G.A., AZIZ, K, 1977, Critical evaluation of frictionpressure-drop prediction methods for gas-liquid flow in horizontal pipes, J. Petroleum Technol.29,1348-1358.

MANDHANE, J.M., GREGORY, G.A., AZIZ, K., 1974, A flow pattern map for gas-liquid flowin horizontal pipes, Int. J. Multiphase Flow 1, 537.

MARCHATERRE, J.F., 1956, The effect of pressure on boiling density in multiplerectangular channels, ANL-5522.

MARCHATERRE, J.F., PETRICK, M., LOTTES, P.A., WEATHELAND, R.J., FLINN,W.S., 1960, Natural and Forced Circulation Boiling Studies, ANL-5735.

MARTINELLI, R.C., NELSON, D.B., 1948, Prediction of pressure drop duringforced-circulation boiling of water, Trans. ASME 70, 695-702.

MARINELLI, V., PASTORI, L., 1973, AMLETO — A Pressure drop computer code for LWRfuel bundles, RT/ING(73)11, Comitato Nazionale Energia Nucleare (CNEN).

MCADAMS, W.H., WOODS, W.K., HEROMAN, R.H., Jr., 1942, Vaporization insidehorizontal tubes. II. Benzene-oil mixtures, Trans ASME 64,193.

MCFADDEN, J.H., et al., 1992, RETRAN-03: A program for Transient Analysis of ComplexFluid Flow Systems, Volume 1: Theory and Numerics, Electric Power Research institute, EPRINP-7450.

MCQUILLAN, K.W., WHALLEY, P.B., 1985, Flow patterns in vertical two-phase flow, Int.J. Multiphase flow 11, 161-175.

MIROPOLSKL EX., SHITSMAN, M.E., SHNEENOVA, R.I., 1965, Thermal Eng. 12 5, 80.

MISHEVIA, K., ISHII, M., 1984, Flow regime transition criteria for upward two-phase flow invertical pipes, hit. J. Heat Mass Transfer, 723-739.

MOCHIZUKI, Y., ISHII, Y., 1992, "Study of thermalhydraulics relevant to natural circulation inATR", Proc. 5th Int. Top. Mtg on Reactor Thermal Hydraulics, Vol. I, Salt Lake City, 127-134.

MOCHIZUKI, H., SHIBA, K., 1986, "Characteristics of natural circulation in the ATR plant",2nd hit. Top. Mtg. Nuclear Power Plant Thermal Hydraulics and Operations, Tokyo, 132-139.

MOECK, E.O., 1970, Annular Dispersed Flow and Critical Heat Flux, AECL-3656.

NABIZADEH, H., 1977, Modellgesetze and Parameteruntersuch fur den volumetrichenDampfgehalt in einer zweiphasen Stroemung, EIR-Bericht, Nr. 323.

158

NIKURADSE, J., 1932, Mitt. Forsch Geb. Ing.-Wesen, 356,1.

OHKAWA, K., LAHEY, R.T., Jr., 1980, The analysis of CCFL using drift-flux models, Nucl.Eng. Design 61.

ORNL-TM-3578, 1975, Design Guide for Heat Transfer Equipment in Water Cooled NuclearReactor Systems, Oak Ridge National Laboratory and Burns and Roe Incorporated, Term.

OSMACHKIN, V.S., BORISOV, V., 1970, Paper B4.9, IVth Int. Heat Transfer Conf, Versailes.

OWENS, W.S., 1961, "Two-phase pressure gradient", Int. Developments in Heat Transfer,PartlLASME.

PETERSON, A.C., Jr., WILLIAMS, C.L., 1975, Flow patterns in high pressure two-phaseflow: A visual study of water in a uniformly heated 4 — rod bundle, WAPD-TM-1199.

PETRICK, M., 1961, Two-phase Water Flow Phenomena, ANL-5787.

PETRICK, M., 1962, A Study of Vapour Carryunder and Associated Problems, ANL-6581.

PILKHWAL, D.S., VIJAYAN, P.K., VENKAT RAJ, V., 1992, "Measurement of pressure dropacross the junction between two 37 rod fuel bundles for various alignments of the bundles",Proc. 19th National Conf. on Fluid Mechanics and Fluid Power, IIT, Powai, Bombay.

RANSOM, V.H., et al., 1987, RELAP5/MOD2 Code Manual, Volume 1: Code structure,System Models And Solution Methods, NUREG/CR-4312, EGG-2396, Rev. 1.

REHME, K., 1968, Systematische experimenetelle Untersuhung der Abhngigkeit desdruckverlustes von der geometrischen Anordnung fur langs durchstromte Stabbundel mitSperaldraht-Abstandshaltern, KfK, Rep. 4/68-16.

REHME, K., 1969, Druckverlust in Stabbundeln mit Spiraldraht-Abstandshaltern, Forsh. Ing.-Wes.35 Nr.4.

REHME, K., 1973a, Simple method of predicting friction factors of turbulent flow in non-circular channels, Int. J. Heat Mass Transfer 16, 933-950.

REHME, K., 1973b, Pressure drop correlations for fuel element spacers, Nuclear Technol. 17,15-23.

REHME, K.., 1977, Pressure drop of spacer grids in smooth and roughened rod bundles, NuclearTechnol. 33, 313-317.

REHME, K., TRIPPE, G., 1980, Pressure drop and velocity distribution in rod bundles withspacer grids, Nuclear Eng. Design 62, 349-359.

ROUHANI, S.Z., 1966, Void Measurements in the Regions of Sub-cooled and Low QualityBoiling, AE-238.

159

ROUHANI, S.Z., 1966, Void Measurements in the Regions of Sub-cooled and Low QualityBoiling, AE-239.

ROUHANI, S.Z., 1969, Subcooled Void Fraction, AB Atomenergi, Rep. AWE-RTV-841.

ROUHANI, S.Z., BECKER, K., 1963, Measurement of Void Fractions for Flow of BoilingHeavy Water in a Vertical Round Duct, AE-106.

SAHA, P., ZUBER, N., 1974, "Point of net vapour generation and void fraction in subcooledboiling", Paper B4.7, Proc. 5th Int. Heat Transfer Conf., 175-179.

SAPHIER, D., GRIMM, P., 1992, Bypass Channel Modelling and New Void Correlations forthe BWR Option of the SILWER Code, PSI-BerichtNr.-l 19.

SEKOGUCHI, K., SAITO, Y., HONDA, T, 1970, JSME Preprint No. 700-7, 83.

SELANDER, W.N., 1978, Explicit Formulas for the Computation of Friction Factors inTurbulent Pipe Flow, AECL-6354.

SIMPSON, H.C., et al., 1977, "Two-phase flow studies in large diameter horizontal lines",European two-phase flow meeting, Grenoble.

SNOEK, C.W., AHMAD, S.Y., 1983, A Method of Predicting Pressure Profiles in Horizontal37-Element Clusters, AECL-8065, Chalk River, Ontario (1983).

SNOEK, C.W., LEUNG, L.K.H., 1989, A model for predicting diabatic pressure drops in multi-element fuel channels, Nucl. Eng. Design 110, 299-312.

SOLBRIG, C.W., 1986, "Consistent flow regime map and friction factors for two-phase flow",AIChE Annual meeting, Miami Beach, Florida.

SONNENBURG, H.G., 1989, "Full-range drift-flux model based on the combination of driftflux theory with envelope theory", NURETH-4 Proceedings, Vol. 2 (1003-1009).

SPEDDING, P.L., NGUYEN, V.T., 1980, Regime maps for air-water two-phase flow, Chem.Eng. Sci. 35, 779.

STEINER, D., 1987, Pressure drop in horizontal flows, Multiphase Science and Technology,Vol. 3 (G.F. Hewitt, J.M. Delhaye, N. Zuber, Eds), Hemisphere Publishing, New York.

STEVANOVIC, V., STUDOVIC, M., 1995, A simple model for vertical annular and horizontalstratified two-phase flows with liquid entrainment and phase transitions: one-dimensional steadystate conditions, Nucl. Eng. Design 154, 357-379.

STEWART C.W., 1985, VIPRE-01: A Thermalhydraulic Code For Reactor Cores, EPRINP-2511-CCM

SUO, M., BERGLES, A.E., DOYLE, E.F., CLAWSON, L., GOLDBERG, P., 1965,Investigation of Boiling Flow Regimes and Critical Heat Flux", NYO-3304-3.

160

TAITEL, Y., BORNEA, D., DUKLER, A.E., 1980, Modelling flow pattern transitions forupward gas-liquid flow in vertical tubes, AIChE J. 26, 345-354.

TAITEL, Y., DUKLER, A.E., 1976, A model for predicting flow regime transitions inhorizontal and near horizontal gas-liquid flow, AIChE J. 22,47-55.

TAITEL, Y., DUKLER, A.E., 1976a, A theoretical approach to the Lockhart-Martinellicorrelation for stratified flow, Int. J. Multiphase Flow 2, 591-595.

TAKEUCHI, K., YOUNG, M.Y., HOCHREITER, L.E., 1992, Nucl. Sci. Eng. 112,170-180.

TARASOVA, N.V., et al., 1966, "Pressure drop of boiling subcooled water and steam watermixture flowing in heated channels", Proc. of 3rd Int. Heat Transfer Conf. 178, ASME.

TAKEUCHI, K., YOUNG, M.Y., HOCHREITER, L.E., 1992, Generalized drift flux correlationfor vertical flow, Nucl. Sci. and Eng. 112,170-180.

RELAP5 DEVELOPMENT TEAM; 1995, RELAP5/MOD3 Code Manual, Vol. 1 CodeStructure, System Models and Solution Methods, NUREG/CR-5535 or INEL-95/0174, IdahoNational Engineering Laboratory, Idaho Falls.

THOM, J.R.S., 1964, Prediction of pressure drop during forced circulation boiling of water, Int.J. Heat Mass Transfer 7, 709-724.

TIPPETS, F.E., 1962, Critical heat flux and flow pattern characteristics of high pressureboiling water in forced convection, GEAP-3766.

TURNER, J.M., WALLIS, G.B., 1965, The Separate Cylinders Model of Two-Phase Flow",NYO-3114-6, Thayer School of Engg. Darmouth College, Hanover, New Hampshire.

TUTU, N.K., 1982, Pressure fluctuations and flow pattern recognition in vertical two-phasegas-liquid flows, Int. J. Multiphase Flow 8, 443-447.

UNAL, C, BADR, O., TUZLA, K., CHEN, J.C., NETI, S., 1994, Pressure Drop at Rod BundleSpacers in the Post-CHF Dispersed Flow Regime, Int. J. of Multiphase Flow 20, 515-522.

VENKAT RAJ, V., 1993, "Experimental thermal hydraulics studies for pressurised heavy waterreactors — An Update and Review, 3rd World Conf. on Experimental Heat Transfer, FluidMechanics and Thermodynamics, Hawaii.

VIJAYAN, P.K., PRABHAKAR, B., VENKAT RAJ, V., 1981, "Experimental measurement ofpressure drop in diabatic two-phase flow and comparison of predictions of existing correlationswith the experimental data", H-13, 6th National heat and mass transfer conf. Madras.

VIJAYAN, P.K., SAHA, D., VENKAT RAJ, V., 1984, Measurement of Pressure Drop inPHWR Fuel Channel with 19 Rod Bundles (Wire-Wrap Type) at Low Reynolds Numbers',BARC/I-811.

161

VIJAYAN P.K., AUSTREGESILO, H., 1993, Predictive Capability of the Models used in theATHLET Code for the Estimation of Frictional Pressure Loss, Technical Note No.TN-VIJAYAN-93-1, Gesellschaft fur Reaktorsicherheit, Garching.

WALLIS, G.B., 1970, J. Basic Eng. Trans ASME Ser. D. 92, 59.

WALLIS, G.B., 1969, One-Dimensional Two-Phase Flow, McGraw-Hill, New York.

WALLIS, G.B., DOBSON, J.E., 1973, The onset of slugging in horizontal stratified air-waterflow, Int. J. Multiphase Flow 1,173-193.

WEISMAN, J., KANG, S.Y., 1981, Flow pattern transitions in vertical upwardly inclinedlines, Int. J. Multiphase Flow 7,271.

WEISMAN, J., CHOE, W.G., 1976, "Methods for calculation of pressure drop in cocurrent gas-liquid flow", Proc. Two-phase Flow and Heat Transfer Symp. Workshop, Fort Lauderdale, Two-Phase Transport and Reactor Safety. Vol. 1.

WILSON, S.F., LITTLETON, W.E., YANT, H.W., MAYER, W.C., 1965, PreliminarySeparation of Steam from Water by Natural Separation, Part 1, Allis-Chalmers Atomic EnergyReport No. ACNP-65002.

YEH, H.C., HOCHREITER, L., 1980, Mass effluence during FLECHT forced refloodexperiments, Nucl. Eng. Design 60, 413^-29.

ZHAO, L., REZKALLAH, K.S., 1995, Pressure drop in gas-liquid flow at microgravityconditions, Int. J. Multiphase Flow 21 (1995) 837-849.

ZIGRANG, D.J., SYLVESTER N.D., 1985, A review of explicit friction factor equations,Trans. ASME, J. Energy Res. Technol. 107.

ZUBER, N., FINDLAY, J.A., 1965, Average volumetric concentration in two-phase flowsystems, J. Heat Transfer, Trans. ASME 87,453^68.

162

Chapter 6

REMARKS AND FUTURE NEEDS

The content of this TECDOC is based on work done and related activities carried out bythe institutes within Member States contributing to the Co-ordinated Research Project (CRP)on Thermohydraulic Relationships for Advanced Water Cooled Reactors as well asinformation presented at two IAEA Technical Committee meetings [IAEA (1996 and 2000)].During the process of preparing this TECDOC, the maturity of knowledge forthermohydraulic phenomena of advanced water-cooled reactors (AWCRs) and the widedegree of usage of the prediction methods for the phenomena have been considered. As aresult, emphasis within this CRP has been on the following topics:

• CHF prediction methods for AWCRs;• General film boiling heat transfer methods for AWCRs; and• Pressure drop relationships for AWCRs.

While the CRP examined the above phenomena in detail, it is important to note that itwas not possible within this CRP to examine in detail other very important thermohydraulicphenomena of interest to AWCRs. For example, transition film boiling, condensation withnon-condensables, natural circulation, and heat transfer in large pools are very importantphenomena but have not been reviewed in detail in this activity. The performed activity alsogave an idea of the difficulty in synthesizing the current understanding of the abovementioned fundamental phenomena which were addressed.

The recommendations and future needs for the phenomena addressed in this TECDOCare provided in each of related chapters in some detail. Therefore the reader should refer tothe individual chapters for the details of the conclusions and remarks. In this chapterrecommendations for the most reliable prediction methods, and comments on future needs areprovided in generic form. Detailed plans for future development are outside the purpose of theCRP.

The following are general remarks and comments on future needs:

Some years ago, it was considered that application of passive safety systems foradvanced water cooled reactor designs was limited to small to medium size plants (less thanabout 700 MW(e)). Now, as a result of further design and testing activities, passive systemsare being incorporated into designs of 1000 MW(e) and above [IAEA (1996, 1999 and2000)]. Uncertainties in phenomenology typically result in incorporation of extra margins intosystem designs. Thorough knowledge of thermohydraulic phenomena for passive systems canhelp both to achieve economical designs and to assure that the passive systems will functionas intended. For passive systems, developers of nuclear power plants need to assure thatsufficient data exist for validation of thermohydraulic codes, and that the effects ofdegradation mechanisms on system performance are well understood.

For advanced water cooled reactors with passive systems, the importance of certainphenomena (e.g. tracking of non-condensable gases, condensation of steam in the presence ofnon-condensable gases, mixing and steam condensation in large pools, natural circulation,temperature stratification and turbulence) is greater than in current designs. For suchphenomena, qualification of the associated thermohydraulic codes and methodologies relyingon best-estimate predictions and uncertainty analyses is highly important.

163

A considerable base of data for condensation heat transfer in the presence of non-condensable gases has been accumulated over fifty years. Although there had been increasedactivity in recent years in this field, because of the importance of this phenomenon toadvanced water cooled reactors, there remains a need for a thorough literature survey, and fora review and assimilation of the existing data. Because such data are very dependent onthermohydraulic conditions and system geometry, a proper review should start with plantdesign and anticipated operational and accident conditions. If it is found necessary,appropriate experiments could be carried out to extend the database for the relevant conditionswhere current data are insufficient.

For natural circulation phenomena (both single phase and two-phase naturalcirculation), there is a need for a thorough literature survey and a review and assimilation ofthe existing data for relevant geometries of the new designs. Specific aspects that should beaddressed include both establishment of natural circulation and transition from forced flow tonatural circulation.

For heat transfer in large pools of water, there is a need for a thorough literature surveyand a review and assimilation of the existing data for conditions relevant to the new designs.Specific aspects that should be addressed include mixing, condensation, and stratification.

International standard problems (ISPs) are an effective way to assess thermohydrauliccomputer codes versus experimental data. Further work in this area is recommended, as somepast ISPs have experienced large differences in predictions made with the same code. Factorswhich can be addressed within the frame of ISPs include "user effect", analyses of codeuncertainties, deficiencies in models, and needs for further experimental work. In order to useexperimental data for code validation, it is important to have proper instrumentation to collectthe needed data for important phenomena, and for use in performing uncertainty analyses ofthe experimental results.

Specifically as a result of the collaboration within the Co-ordinated ResearchProgramme, the following remarks and comments on future needs are made:

(1) The look up table (Appendix II) based on CHF in tubes is recommended as thereference method for predicting critical heat flux in advanced water cooled reactors;methods are presented for predicting CHF in rod bundles and in bundle sub-channelsusing these data for CHF in tubes together with correction factors obtained either from asub-channel codes or from correlations which account for rod geometry and neutronflux distributions. As an alternative for fuel bundles in which the rods are arranged in atriangular array, the WWER-based look-up table of Appendix III is recommended.Further efforts are needed for combining these two cited methods to develop aprediction method for CHF in rod bundles of various shapes. Further work in CHF isalso needed for predicting how the CHF spreads in the reactor core, which is necessaryin predicting the coupled thermohydraulic — neutronic response of the core.Experimental work is needed to improve knowledge of CHF especially in low flow/lowquality conditions and in high flow/high quality conditions.

(2) The prediction methods for film boiling are less advanced than those for CHF. Whilethis TECDOC reviews various methods for predicting film boiling, norecommendations for specific methods are given because important work on combiningthe most promising methods into a validated method is still in progress. The currentproliferation of film boiling prediction methods, and their limited range of validity,indicate the need for universal prediction methods, e.g. look up tables based on

164

qualified experimental data. The current status of development of such methods isreflected in the methods presented in Appendices IV, V and VI.

(3) Many prediction methods in use for the various components of pressure drop arereviewed and summarized in this TECDOC. No single unified method can berecommended due to the wide range of conditions (geometry, fluid status, flow type,flow regime) which must be addressed. It is to be noted that forced and naturalcirculation conditions should be clearly distinguished. In the latter case, the influence ofpressure drops upon the system performance is much higher. Therefore, care must beexercised in selecting proper correlations for calculating the pressure drops of theindividual components.

(4) Areas in which future work should be considered include acquisition of data forcomplex geometries (e.g. new design rod bundles and grid spacers), and for conditionsfor which the current openly available database is limited (e.g. two phase flow at lowand high mass flux; pressure drop in large diameter pipes; pressure drop at lowpressure; and vertical down flow).

(5) Supercritical water is currently being considered as a coolant medium for severaladvanced water cooled reactor concepts. The heat transfer characteristics of reactorcores cooled by supercritical water needs further investigation. Specifically the pseudo-CHF and post-CHF behaviour of supercritical water has received very little attention inthe literature.

(6) During the course of this CRP, there has been extensive experimental data exchange.Some of these data, including look-up tables for CHF and post-CHF are integrated intothe database at the International Nuclear Safety Center (INSC) at the Argonne NationalLaboratory (ANL). A sizeable database is maintained at the Heat and Mass TransferInformation Center (HEMATIC) in the State Scientific Center of the Russian Federation— Institute for Physics and Power Engineering, Obninsk, Russian Federation. Theestablishment of a distributed database which can join the contents of local databasesusing standard network connections would be useful and convenient. The use of suchdatabanks would contribute to the exchange of technical information and know-how,and to the sharing of research results among various organizations.


IAEA, 1996, Progress in Design, Research and Development and Testing of Safety Systemsfor Advanced Water Cooled Reactors, IAEA-TECDOC-872, Vienna.

IAEA, 1997, Status of Advanced Light Water Cooled Reactor Designs, IAE-TECDOC-968,Vienna.

IAEA, 1999, Evolutionary Water Cooled Reactors: Strategic Issues, Technologies andEconomic Viability, IAEA-TECDOC-1117, Vienna.

IAEA, 2000, Experimental Tests and Qualification of Analytical Methods to AddressThermohydraulic Phenomena in Advanced Water Cooled Reactors, IAEA-TECDOC-1149,Vienna.

165

APPENDICES I-XIX

Appendix I

ACTIVITIES CONTRIBUTED TO THE CRP BY THERESEARCH GROUPS AT THE PARTICIPATING INSTITUTES

AECL, Canada

Atomic Energy of Canada Ltd (AECL) has performed experimental and analyticalstudies on CHF. They have combined the AECL and the IPPE databank of CHF up to 1993,and constructed the interim 1993 tube CHF lookup table. Since then additional CHF data havebeen added to the CHF databank. The expanded CHF databank has a total of 30 417 CHFpoints and covers a wider range of conditions.

Using the expanded CHF data, the AECL and IPPE have proposed a new CHF lookuptable covering a wider range of thermohydraulic conditions. They incorporated amultidimensional (pressure, dryout quality, mass flux and inlet subcooling) smoothingprocedure based on weighted polynomial fitting method in the CHF lookup table. The newCHF lookup table for tubes shows improved smoothness and accuracy.

In addition, the AECL has developed an interim post-dryout databank which contains atotal of 21 525 post-dryout data for vertical upward flow in tubes, and a corresponding lookuptable for post-dryout heat transfer using direct interpolation of experimental data because itusually provides good prediction accuracy and reduces computing time. The databank is beingexpanded by additional post CHF data from IPPE and CIAE.

CIAE, China

CIAE has conducted studies on film boiling, vapour convection and CHF. The filmboiling experiments with flowing water have been performed at steady-state condition usingthe directly heated hot patch technique. A great number of wall heat transfer and vapoursuperheat data have been obtained in stainless steel tube and Inconel tube with differentdiameter, covering a wide range of thermohydraulic conditions. The data fill the gap ofdatabase which are interest for the reactor accidents. The experiments involved invertedannular flow and dispersed flow, showing complicated effects of pressure, mass flux, quality,heat flux, diameter and significant history-dependence. Based on the data of wall heat transferand vapour superheat the mechanistic model has been proposed. An assessment ofRELAP5/MOD2.5 has been made based on the CIAE data. The data have been used for thelook-up table. The minimum film boiling temperatures were also measured using the samesteady-state technique. The pressure and subcooling showed appreciable effects on thistemperature, but the effect of mass flux was not appreciable. An empirical correlation wasformulated on the basis of experiment.

The experiment on the vapour convection heat transfer has been performed in tubes withdifferent diameter. The change of flow regime from turbulent to transition regime wasevidenced by a substantial decrease of heat transfer coefficient. The Reynolds number at thistransition was the function of Gr number, and varied significantly with the diameter andpressure. The correlation of heat transfer in folly developed turbulent flow and the criteria forthe transition of regimes have been proposed.

169

Low pressure subcooled CHF experiment has been conducted in tubes with differentdiameter. The effect of diameter was found to be related to the flow condition. The subcoolingand velocity had strong effects on the CHF, but the effect of pressure appeared not appreciable

NRI Czech Republic

NRI activities have involved experimental research on CHF for water cooled rodbundles modelling WWER type reactors; CHF databank for tubes, annuli and rod bundles; acomputational system based on CHF databank; and subchannel analysis code based on rodbundle data for coolant behaviour in the WWER type cores.

The SKODA Plzen a large water loop has been designed for research on CHF in waterflow through a WWER fuel bundle.

The NRI collected CHF experimental data of tubes, annuli and rod bundles into NRICHF databank. The number of data points in the NRI databank was more than 20 000.Besides, they have developed their original CHF correlations.

The NRI also develop a software enabling evaluation of CHF correlations with CHFdatabank by means of statistical methods.

The NRI has carried out system analyses covering axial distribution of DNBR(departure from nucleate boiling ratio) using their CHF correlations to compare the analyticalresults each other. They also compare results of subchannel analyses and isolated channelanalyses.

FZK, Germany

FZK has conducted experimental and analytical investigations on critical heat flux(CHF) in circular tubes of different diameters, ranging from 2 mm to 16 mm, and in tighthexagonal 7 and 37 rod bundles. The model fluid Freon-12 was used as working fluid due toits low latent heat, low critical pressure, well known properties and intensively investigatedfluid-to-fluid modelling for water and Freon-12. More than 1700 data points in tubes and1300 data points in rod bundles have been obtained in a large range of parameters: pressure1.0 MPa to 3.0 MPa, mass flux 1.0 Mg/m2s to 6.0 Mg/m2s and exit steam quality -0.75 to+0.60.

The effect of different parameters on CHF have been studied, especially the effect oftube diameter and spacers. The test data have been compared with different CHF predictionmethods, e.g. CHF look-up table, and with the CHF data available in the literature.Comparison of the CHF data in Freon-12 with that in water was made, to investigate the fluid-to-fluid scaling laws for circular tubes as well as for rod bundles.

hi the 7-rod bundles experimental investigations have also been performed on two-phase turbulent mixing. The effect of different parameters on the turbulent mixing has beenstudied.

170

BARC, India

BARC has performed studies on friction pressure drop under low mass flow conditionsfor advanced heavy water reactors (AHWR), which uses natural circulation in the primary andthe safety systems. Extensive studies are being carried out on natural circulation flow as wellas instability of natural circulation. Pressure drop experiments have been conducted on 19-rodand 37-rod fuel bundles of PHWRs and 52-rod fuel bundle of AHWR. Experimentalinvestigations have been carried out to study the effect of alignment of bundles at junctionsand creep of fuel channel on the pressure drop in PHWR fuel channels. Studies also coveredvarious components of the fuel channel like the fuel locator, end fittings, and refueling tools.

Under this CRP, BARC has compiled correlations for single-phase and two-phasepressure drop, void fraction and flow pattern transitions. A two-phase flow databank has alsobeen compiled using published data on pressure drop including flow pattern specific pressuredrop, void fraction and flow patterns. Using this databank the compiled correlations have beenassessed.

University of Pisa, Italy

Activities at University of Pisa have involved development and assessment of thespecial codes, large-system-code assessment, evaluation of experimental data, planning andconduct of experiments, code application to nuclear plants, and studies on uncertainties ofCHF predictions.

They have developed and assessed three special codes which are used for integralthermohydraulic analyses of advanced water cooled reactors, for evaluation of "isolationcondenser" performance, and for evaluation of fission product transport inside the primarycircuit and the containment vessel. Assessment and evaluation of large-system-codes havebeen carried out by comparing with test results from integral test facilities (ITF) and separateeffect test facilities (SETF). Accident analyses including severe accident are performed foradvanced water cooled reactors. Besides, they have been planning and conductingexperiments using their facilities.

Studies on uncertainties of CHF predictions have been also carried out at University ofPISA. UMAE (Uncertainty Methodology based on Accuracy Extrapolation) was developed toevaluate uncertainties in prediction of transient and accident scenarios by thermohydraulicsystem codes. Since the use of UMAE is limited to only the ITF, UMAE-SETF is beingdeveloped to use vast data from the SETF. The UMAE-SETF considers only a specificphenomenon in a transient or an accident condition. Then similarity analyses and grouping ofexperimental data are performed to establish calculational database. Using the database andsame methodology in the UMAE, extrapolation of accuracy and uncertainty are estimated forsingle phenomenon.

ENEA, Italy

ENEA activities have involved the development of computer codes for the thermohydraulicdesign of reactor cores and experimental researches supporting both the core design and thecodes development.

171

The reference code is the ANTEO code, a subchannel model for the steady-stateanalysis of reactor core rode bundles. The wide experience available in the field of subchannelcodes has allowed to develop a simple, fast and user-oriented code running on a PC machine.Due to its characteristics, the code can be used for comparison among different models, forinstance for comparing different CHF models.

Experiments were performed mainly in the field of pressure drop and flow distributionin different geometries of interest for the reactor core design. Particularly, pressure drop in rodbundles with helical wire wraps system were measured. Part of the investigations wereextended down to the low flow region, in order to cover the natural circulation range.

KAERI, Republic of Korea

KAERI has conducted experiments on CHF and on natural circulation including a singlerod CHF test, a 3x3 bundle CHF test and a natural circulation test. Objectives of the single rodCHF test are to obtain fundamental CHF data and to understand thermal hydraulic phenomenaunder abnormal conditions such as LOCA and pump trip. In the 3 x 3 rod bundle test, twotypes of tests were made; steady state test under low flow and under boil off conditions, andtest of power or flow rate transient. The objective of the natural circulation test is tounderstand fundamental characteristics of natural circulation, heat transfer capability of theheat exchanger and characteristics of boiling phenomena.

A study on hydraulic characteristics in rod bundles has been also carried out by theKAERI. Heat transfer improves near spacer grids in the rod bundles. To understand thisbehaviour, hydraulic characteristics near the spacer grids should be clarified before thermalcharacteristics. Besides, hydraulic characteristics are useful to develop the local thermaldiffusion coefficient in a subchannel analysis code.

Furthermore, heat/mass transfer study has been performed using Naphthalenesublimation technique, which measures mass transfer coefficients in the complex geometrywhere the conventional heat transfer measurement is impossible. The objective of this study isto investigate mechanism and analogy of heat/mass transfer at the complicated flowconditions.

KAIST, Republic of Korea

CHF at low pressure and low flow (LPLF) conditions is a key thermohydraulicphenomenon which may limit thermal power under natural circulation and accidentconditions. KAIST has performed a series of LPLF CHF experiment for both stable andoscillating flow conditions. Totally 523 stable CHF data have been obtained with verticalround tubes of various diameters and heated lengths for low pressure, low flow, and highquality conditions. Parameteric trends were examined and existing prediction models wereassessed against the data. KAIST also performed some tests to identify the effects of flowoscillations and circulation modes on LPLF CHF.

In addition to the LPLF CHF study, an independent assessment was conducted for theapplicability of the AECL-IPPE CHF table to predicting CHF in round tubes and bundles.Some works on the development of a length correction factor was also conducted.

172

IPPE, Russian Federation

It is significantly important to know CHF for water flowing in various channels forsafety analyses of water cooled reactors. An international collaboration with IPPE, AECL,Technical University of Branschweig and KfK has led to joint studies on CHF. In that way, aJoint International Data Bank (JIDB) on CHF in tubes has been established covering the mostavailable data in the world. Then the lookup table 1996 version was proposed and containsabout 30 000 data points for tubes.

The lookup table has been tested against the JIDB for the 8 mm tubes to show that thelookup table has satisfactory features of accuracy and smoothness. The CHF at low flow rateand low pressure, however, show complicated behaviour possibly due to complicated role ofbuoyancy, flow instability, geometry effects on flow stability, and near sound velocity.Besides, there are a few amounts of data in the regions so that accuracy of the CHF predictionis insufficient.

A post-dryout heat transfer table was developed and covers a wide range ofthermohydraulic conditions. The number of data points is 42 800. The heat transfercoefficients are expressed as a function of pressure, mass flux, quality and heat flux. In IPPEhas been developed Look-Up Table CHF WWER rod bundles for wide range parameters.

PSI, Switzerland

PSI has developed together with institutes in some other OECD countries a methodology toestablish SET (Separate Effect Tests) validation matrix. The SET validation matrix is aninformation which collects the best set of test data available for calculational code validation,assessment and improvement. The SET validation matrix report can be used for codedevelopment and quantitative uncertainty analyses.

In the SET matrix, a particular attention has been paid in definition of each phenomenonsince the level of the state of knowledge for different phenomenon varies. Internationallycoordinated works are necessary to compensate the short of the knowledge. The first volumeof the SET matrix report provides cross references between test facilities and thermalhydraulic phenomena, and list of tests classified by phenomena. Presently 67 phenomena and2094 tests have been identified and selected in the matrix.

Different CHF correlations and CHF lookup tables have been examined and analyzed bythe PSI. The correlations were tested in thermohydraulic analyses under low mass flow andlow pressure conditions like small break LOCA, and under high mass flow and high pressureconditions like large break LOCA. The influences of major physical and geometricalparameters on CHF are investigated. The behaviour in a correlation based on local conditionswas compared with that in the CHF lookup table.

Middle East Technical University, Turkey

Condensation heat transfer in the presence of a non-condensable gas such as air oftendominates the cooling performance of the safety systems used in advanced water cooledreactors. Since there is a need for more experimental data on in-tube condensation in thepresence of non-condensable gas, an experimental research has been carried out by Middle

173

East Technical University in collaboration with Turkish Atomic Energy Authority which waspartially sponsored by International Atomic Energy Agency.

A test facility with a vertical single-tube, once-through type of heat exchanger wasconstructed to examine the non-condensable gas effect on heat transfer associated with in-tube condensation.

In this research work, in-tube condensation in the presence of air has been investigatedexperimentally for different operating conditions, and inhibiting effect of air is analyzed bycomparing the experimental data of air/steam mixture with the data of corresponding puresteam cases, with respect to temperature, heat flux, and heat transfer coefficient. The testmatrix covered the range of; Pn = 2-6 bar, Rev = 45000 - 94000, and Xj = 0% - 52%.

The inhibiting effect of air manifests itself as a remarkable decrease in centerlinetemperature (10°C-50°C), depending on inlet air mass fraction. However, the measuredcenterline temperature is suppressed compared to the predicted one, from the Gibbs-DaltonLaw, which indicates that the centerline temperature measurements are highly affected byinner wall thermal conditions, possibly due to narrow channel and high vapour Reynoldsnumber.

Even at the lowest air quality (10%) the reduction of the heat flux is 20% while itreaches up to 50% for the quality of 40%. Maximum percent decrease of the heat transfercoefficient was observed in runs with the system pressure of 2 bar; 45% and 65%, for the airmass fraction of 10% and 28%, respectively. The film Reynolds number of cases with purevapour and air/vapour mixture lies in the range of turbulent region (Ref > 300).

The RELAP5 code, using Shah-Colburn-Hougen model, overestimates the heat fluxdata from about 5% to 50%. However, the majority of the predicted values of the Nusseltnumber fall in the uncertainty band (±24%) of experimental data.

Argonne National Laboratory, USA

Argonne National Laboratory (ANL) hosts the US Department of Energy (DOE) InternationalNuclear Safety Center (INSC). One of the main goals of the INSC is to promote theinternational exchange of information and data to enhance the safety of nuclear installations.The INSC has developed a database, accessible on the World Wide Web, to support theCenter activities and facilitate the exchange of information among international organizations.The database contains nuclear installation and nuclear safety information. Argonne NationalLaboratory contributes the INSC database facility, its support and maintenance structure to thepresent IAEA Coordinated Research Project. ANL has offered the INSC database to become acommon repository of data on thermohydraulics of nuclear reactors-look-up tables, rawexperimental data, software tools, correlations and prediction methods, and references -provided by organizations participating in the CRP that have experimental programs in thisarea. The data and information contributed by these organizations are stored in the INSCdatabase and maintained by ANL. Data related to thermophysical material properties, incoordination with another IAEA Coordinated Research Project is already being stored in theINSC database (http://www.insc.anl.gov). The addition of thermohydraulics datacomplements the existing nuclear safety related information in the INSC database(http://www.insc.anl.gov/thrmhydr/iaea/chf).

174

Appendix II

THE 1995 CHF LOOK-UP TABLE FOR CRITICAL HEAT FLUX IN TUBES

Table ILL has been published previously by Groeneveld et al. (1996). It contains CHF valuesin kW/m2 as a afunction of pressure, mass flux and thermohydraulic quality. The shadednumbers refer to CHF values having a less sound basis (based either on questionable data oron extrapolation.

175

TABLE ILL THE 1995 CHF LOOK-UP TABLE FOR CRITICAL HEAT FLUX IN 8 mmTUBES (in kW.rrr2)1.Pressure(kPa)

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

300

300

300

300300300300300300300300300300

300300300300300300300

500500500500500500500500500500500500500500500500500500500500

Mass Flux(kg.m-2.s-l)

0501003005001000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

0501003005001000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

0501003005001000

1500

2000

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4000

4500

5000

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6000

6500

7000

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8000

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2888

2975

3293

3406

3527

3662

3652

3485

3404

2840

2816

3079

3093

3096

3116

3135

0.25 0.3

142 130

620 609

1093 1084

1536 1502

1798 1725

2129 2028

2195 2084

2212 2054

2217 1985

2245 1941

2282 1937

2327 1960

2353 2026

2401 2097

2454 2156

2492 2167

2502 2208

2507 2251

2530 2291

2550 2326

317 234

813 745

1230 1211

1895 1828

2185 2072

2388 2283

2424 2301

2462 2320

2444 2282

2426 2245

2407 2154

2389 20442405 2064

2489 2200

2572 2259

2610 2269

2625 2291

2649 2337

2670 2376

2697 2407

374 278

1005 921

1566 1525

2527 2409

2695 2498

2923 2629

3154 2782

3261 2790

3335 2696

3428 2621

3350 2426

3154 2345

3064 2352

2783 2354

2690 23622727 2371

2749 2389

2791 2408

2811 2426

2832 2463

0.35

1206001078

1475

1714

1870

1905

1950

1846

1738

1684

1638

1696

1798

1863

1912

1968

2019

2066

2108

1947081190

1771

1869

1968

2021

2066

1916

1806

1692

17181846

1867

1914

1970

2073

2115

2152

2185

2268651492

2050

2187

2277

2260

2184

1991

1871

1700

1798

1871

1903

1964

2025

2084

2147

2190

2236

0.4

1115911070

1378

1615

1655

1857

1918

1779

1596

1449

1316

1378

1496

1587

1662

1731

1792

1848

1898

1786861168

1636

1700

1766

1834

1771

1700

1577

1390

1372

1490

1536

1667

1742

1809

1868

1920

1966

2078261440

1799

1887

1911

1811

1696

1535

1427

1330

1428

1483

1577

1676

1760

1837

1901

1958

2010

0.45

1035821060

1243

1486

1632

1856

1889

1693

1472

1264

1098

1145

1262

1355

1437

1511

1577

1638

1693.

1716601118

1494

1539

1586

1615

1571

1524

1380

1258

1166

1203

1303

1402

1488

1565

1634

1697

1753

1917931391

1552

1593

1547

1453

1383

1290

1224

1214

1234

1261

1337

1434

1519

1599

1670

1734

1791

0.5

995701037

1151

1463

1631

1856

1815

1582

1315

1059

8919391054

1149

1230

1305

1374

1436

1495

1706421081

1418

1447

1545

1525

1410

1327

1180

1043

9359781088

1187

1273

1351

1422

1486

1545

1837541292

1489

1414

1385

1268

1164

1067

9729639731016

1111

1210

1300

1379

1451

1517

1577

0.6

845139619791188

1434

1597

1466

1162

8426105035916937768539259931056

1116

1496011026

1203

1155

1174

1103

1029

957777581545

610

7107998799541024

1089

1150

1516111158

1188

959962911852605570541555624719810893971

.1042

1109

1171

0.7

74401747751752850839674494341220239324398466530592651708763

143472857866764677568490407333264275340411477543608669728784

1504931045

1049

774635543335298283271301358420482548

,615

678738795

0.8

68288550626.

558428348183806170108151194238282326369413458

143391669695574439220143746177111

152191237283329374420465

149476875919622445271130726182115153190235282330376423469

0.9

6725341655041520610962121533517192113135157179201223

"903004735645212881316023.19345169,90112136159' 182

204227

14035953960755430123265292135516888111135159182206

- 229

1

00000000000000000000

000000000000

0

0000000

00000000000000000000

Note: shaded are denotes less relaible data.

176

TABLE ILL THE 1995 CHF LOOK-UP TABLE FOR CRITICAL HEAT FLUX IN 8 mmTUBES (in kW.nT2).(Continued)

Pressure Mass Flux(kPa) (kg.m-2.s-l)

Quality

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

3000

3000

3000

3000

3000

3000

3000

3000

3000

3000

3000

3000

3000

3000

3000

3000

3000

3000

3000

3000

5000

5000

5000

5000

5000

5000

5000

50005000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

0501003005001000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

0501003005001000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

0501003005001000

1500

20002500

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

-0.5

. 6583

' 7307

• 7888

8463

8655

9003

9523

10680

11975

12932

13887

14813

15714

16584

17426

18238

19035

19813

20584

21353

' 5951

6644

7234

7680

7918

8364

9068

10362

11531

12458

13348

J4214

15045

15844

16626

17388

18126

18845

19549

20238

-0.4

5927

. 6575

7106

7476

7674

7776

8313

9563

10928

11900

12661

13379

14077

14778

15454

16101

16814

17464

18107

18730

5460

6095

6636

' 6990

7164

7454

8009

9287

1OS9911530

12271

12958

13625

14283

14896

15495

16100

16707

17296

17880

-0.3

5619

6371

6981

7492

7577

7594

7700

8187

8962

9731

10456

11146

11816

12447

13033

13573

14101

14608

15109

15629

5252

5972

6580

7307

7578

7660

7824

8427

9397

10414

11230

11939

12608

13200

13765

14321

14849

15350

15834

16299

' 4941

5629

6223'

6769

6943

7171

7470

81599179

10191

10990

11651

12254

12804

13352

13856

14340

14796

15245

15671

-0.2

4685

5523

62S2

7295

7464

7466

7468

7552

7788

8149

8659

9203

9746

10239

10745

11285

11770

12172

12524

12866

4544

5386

6114

7303

7560

7598

7647

7706

8034

8640

9396

10174

10862

11500

12044

12489

12926

13332

13724

14090

4459

5224

5891

6737

6900

7014

7142

73467837

8483

9196

9917

10566

11186

11741

12319

12662

12961

: -0.15

4058

4991

5685

7089

7327

7329

7349

7424

7544

7728

8005

8342

8754

9182

9599

10064

10479

10857

11194

11463

4205

5107

5897

7302

7554

7560

7578

7640

7681

7947

8434

9013

9586

10262

10824

-0.1 -0.05

3564

4436

5281

6901

7177

7192

7230

7281

7314

7370

7450

7591

7750

78598124

8595

8933

9325

9725

9958

3891

4857

5708

7300

7541

7548

7560

7567

7634

7643

7824

8028

8292

8818

9249

1138510063

1194610878

1205311351

1242911527

1278911585

4230

5030

5734

6722

6882

6944

7025

7139

74587761

8178

8669

9102

9669

10379

11076

4011

4840

5573

6686

6819

6829

6859

6944

71957353

7551

7764

7980

8443

8952

9876

1177310800

1197111295

13320 12236 11413

13711 1270111561

2859

3928

4851

6766

7110

7124

7153

7192

7202

7206

7179

7143

7141

6988

6794

6647

6351

6654

7272

7773

3536

4570

5479

7298

7627

7518

7471

7453

7441

7439

7437

7418

7365

7348

7402

7735

8193

8542

8891

9157

3762

4626

5387

6677

6812

6743

6707

6593

65656543

6527

6476

6502

6655

6807

7558

8118

8492

8865

9151

0

2175

3323

4268'

6620

7048

7022

7013

7012

6979

6966

6910

6778

6500

5900

5800

5530

5228

4850

5409

6039

3022

4135

5057-

7255

7621

7512

7436

7298

7158

7069

6995

6832

6566

6039

6188

6382

6446

6507

6526

7075

3360

4294

5065

6619

6739

6595

6441

6110

58495664

5421

5139

5044

4986

5334

5744

5954

6049

6189

6556

0.05

1910

2944

3386

6215

6818

6705

6604

6401

6100

5900

5800

5752

5537

5107

4822

4654

4460

4232

4227

4447

2429

3478

,4121

6954

7496

7444

7250

6723

6226

5966

5829

5753

5570

5258

5134

5070

5002

4694

4644

4971

2628

3606

4165

6280

6395

6107

5779

5262

49154750

4581

4421

4317

4255

4253

4314

4356

4363

4478

4717

0.1

1438

2469

2799

5289

S771

5694

5532

5196

5028

4920

4849

4757

4627

4361

4239

4096

3913

3734

3683

3684

2009

3061

3502

5922

7000

6846

6661

6026

5599

5339

5131

4966

4792

4610

4431

4332

4181

3888

3817

3980

2234

3225

3609

5401

5734

5662

5317

4779

45154321

4144

3916

3784

3723

3656

3627

3603

3613

3749

3975

0.15

1030

2071

2651

4760

5094

5042

4989

4720

4668

4647

4628

4584

4477

4211

4085

3966

3804

3547

3525

3536

1564

2653

3326

5380

6400

6208

5980

5315

4880

4712

4586

4471

4348

4242

4136

4061

3931

3705

3643

3715

1791

2837

3458

5007

5296

5289

4899

440539S13782

3693

3540

3457

3454

3421

3415

3397

3445

3547

3695

0.2

7171752

2531

4456

4660

4634

4422

4404

4397

4391

4385

4380

4304

3924

3729

3625

3484

3336

3287

3341

1145

2266

3186

5211

5660

5620

5043

4507

4175

4094

4067

4021

3945

3867

3794

3753

3693

3557

3459

3548

1346

2450

3315

4907

5178

4957

4530

3984

3594

3428

3380

3317

3260

3251

3240

3239

3235

3291

3350

3482

0.25 0.3

519 389

1559 1414

2415 2292

4120 3432

4233 3856

3953 3264

3952 3236

3952 3143

3924 2999

3898 2880

3865 2765

3794 2723

3715 2689

3338 2581

3112 2523

3050 2519

2973 2497

2867 2461

2851 2478

3061 2571,

892 '699

2041 1865

3051 2926

4936 4635

5269 4807

4728 4200

4364 3792

3991 3485

3702 3152

3619 2963

3540 2705

3424 2463

3273 2302

3121 2196

3006 2155

3042 2265

3067 2360

3084 2530

3103 2699

3291 2904

1083 877'

2224 2047

3174 3061

4741 4509

5027 4588

4676 4166

4074 3623

3610 3206

3401 30673268 2855

3109 2510

2945 2221

2799 2059

2745 1990

2717 1992

2688 2091

2711 2303

2801 2510

3051 2667

3290 2882

0.35

3121307

2184

2600

2754

2670

2429

2259

2081

1955

1797

1891

1953

1978

2017

2063

2115

2178

2246

2306

'568

1722

2796

3997

4297

3745

3422

2958

2369

2085

1715

1474

1514

1610

1712

1853

2043

2209

2390

2413

7311896

2936

4202

4244

3759

3337

2865

24742024

1688

1437

1425

1470

1583

1812

2034

2189

2329

2405

0.4

286'

1230

2041

2151

2284

2035

1557

1373

1281

1234

1252

1484

1498

1579

1703

1767

1852;

1945

2006

2062

5021614

2625

3322

3392

3079

2691

2279

1726

1423

1329

1234

1311

1505

1650

1738

1876

2008

2073

2112

6381774

2803

3881

3975

3447

2983

2557

18611406

1195

1140

1247

1385

1504

1679

1869

1951

2021

2074

0.45

2701157

1891

1924

1979

1741

1145

9809259081059

1292

1327

1363

1469

1555

1633

1707

1774

1834

4521521

2475

3177

3376

2910

2130

1686

1252

1037

1127

1228

1306

1405

1500

1542

1622

1755

1825

1885

5711666

2655

3659

3803

3322

2569

1973

1301948

9581108

1242

1295

1459

1529

1611

1689

1764

1829

0.5

2561076

1703

1708

1659

1516

9307136907011000

1021

1034

1126

1235

1325

1406

1480

1548

1612

4131418

^2367

3173

3324

2618

1728

1211

8677721020

1118

1145

1173

1252

1311

1388

1514

1588

1654

5151553

2476

3315

3503

3086

2134

1332

921793

8741049

1187

1205

1234

1296

1370

1444

1519

1588

0.6

1988761312

1343

1035

958637541512510595605643726816902983'

1057

1126

1190

3211409

2191

2865

2745

1925

1080

6084315206786997137668468769821062

1138

1205

4051532

2300

2973

3040

2066

1194

668401584

6456887347868048509139891064

1130

0.7

1888061291

1289

825592411343306349-

356375401438484546616681744802

2751400

1936

2078

1841

1242

626373308374431440445466493532589656724787

3451512

2148

2543

2459

1433

913650313420

441441453472481500531592656717

0.8

1818041250

1215

7674523701378495108134159188227275326375

"423

470

2661392

1587

15361

1320

83049933089129137147163179197234282333385437

3419451757

1823

1769

1034

899650117132

149151167:

164182211239282328379

0.9

175"

700.

7326605893382668625303651~6583104129155'

180204227

2561000

1015

953835471312

'216

- .25

4544

' 54

63.' 72

83103129 .

155181207

323 "

8301080

1215

1118

7637445265353

555S61667694110 .

130154178

1

600000000000000000

60

000000000000

b0000000

0000

6000000d

0,

600000

177

TABLE ILL THE 1995 CHF LOOK-UP TABLE FOR CRITICAL HEAT FLUX IN 8 mmTUBES (in kW.m"2).(Continued)


Quality

6000

6000

6000

6000

6000

6000

6000

6000

6000

6000

6000

6000

6000

6000

6000

6000

6000

6000

6000

6000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

8000

8000

8000

8000

8000

8000

8000

8000

8000

8000

8000

8000

8000

8000

8000

8000

8000

8000

8000

8000

0

50

100

300

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

0

50

100

300500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

0

50

100

300

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

-0.5

'5626

6300

6873

7318

7573

8080

8817

10109

11237

12123

12969

13791

14582

15341

16091

16823

17524

18210

18884

19548

5361

: 6002'

6539

6998

7264

7798

8557

9793

10882

11730

12535

13317

14070

14792

15509

16208

16875

17529

18170

18806

I 5101

^5714

;': 6229;

6685

6958

7518

8280

9465

10508

11320

12091

12839

13559

14251

14934

15597

16235

16859

17470

18075

-0.4

5219

5838

6366

6710

6883

7185

7758

9053

10324

11219

11949

12626

13274

13920

14489

15039

15635

16212

16771

17309

5010-.

5599

6094

6441

6617

6930

7520

8774

9986

10850

11558

12216

12839

13465

14000

14521

15091

15640

16174

16673

4795

•.; 5359:

5«34*

6179

6354

6668

7266

8470

9633

10465

11136

11763

12361

12945

13466

13983

14521

15043

15550

16026

-0.3

4798

5443

5999

6451

6586

6742

7023

7842

8947

9913

10669

11288

11857

12372

12910

13396

13826

14268

14706

15140

/4651

5236

5738

6104

6233

6386

6715

7597

8709

9620

10344

10929

11469

11954

12474

12931

13336

13763

14182

14610

"4484^

5025

\5487'

" 5792'

5920

6144

6556

7416

8457

9316

10017

10584

11093

11568

12056

12477

12879

13288

13689

14098

-0.2

4387

5092

5708

6395

6512

6576

6667

6970

7698

8360

8979

9594

10119

10555

11165

12151

12525

12743

13013

13347

4293

"4926

5474

6015

6123

6216

6339

6676

7496

8170

8740

9320

9769

10124

10713

11464

12214

12432

-0.15

4185

4920

5567

6379

6480

6502

6585

6796

7356

7693

7986

8324

8549

8820

9671

10623

-0.1

3995

4760

5434

6330

6364

6256

6331

6559

7038

7264

7458

7679

7682

7811

8416

9568

1157510720

1183811239

1206311299

12447 11537

4118

4778

5355

6002'

6088

6135

6253

6480

7142

7523

7757

8041

8188

8354

9223

10460

3954

4644

5245

5947

5953

5799

5886

6142

6690

6953

7135

7398

7399

7427

8025

9338

1143210650

1171811183

12682 1174011185

12995

4175

' 4744:

"5235;

5654

5763

5919

6124

6490

7323

7976

8489

9021

9494

9938

10488

11140

11791

12019

12260

12584

1206711187

;,4022;

4615

:5132

5637

5718

5765

5911

6179

6937

7376

7576

7836

8078

8351

9083

10142

10678

.3883

•4503:

5039

55771

5605

5314

5334

5626

6335

6702

6794

7014

7215

7424

7990

9265

9903

1121410542

1123510544

1155510546

-0.05

3777

4575

5273

6310

6316

6114

6146

6167

6235

6241

6243

6245

6247

6336

6533

7356

8043

8441

8839

9144

:3762

4483

5105'

5886

5940

5604

5603

5684

5806

5816

5848

5938

6061

6225

6409

7226

7804

8065

8202

8424

3716

4362

4916

5512

5597

5072

5042

5178

5386

5426

5461

5626

5921

6106

6213

6851

7172

7253

7292

7482

0

3415

4272

4973

6255

6261

6008

5787

5531

5383

5237

4962

4590

4578

4701

4793

5118

5370

5556

5779

6019

;;3426

. 4198

[ 4818

5865

5887

5505

5145

4952

4876

4724

4567

4372

4410

4552

4682

4752

4867

5055

5208

5405

3403

U4081

•4650

5484

5544

5040

4774

4623

4575

4348

4205

4145

4248

4394

4479

4526

4629

4766

4874

4967

0.05

2669

3564

4079

5942

5978

5633

5138

4716

4543

4449

4218

3787

3624

3674

3751

3824

3900

4010

4287

4481

;2692'

• 3498

3957

5582

5690

5318

4673

4275

4104

3981

3834

3469

3347

3378

3454

3483

3535

3745

3974

4172

7 2547

31;70.

: 3796

5250

5324

4997

4459

4015

3816

3609

3479

3241

3137

3169

3283

3352

3419

3593

3748

3931

0.1

2291

3191

3530

5126

5371

5334

4703

4227

4030

3882

3651

3318

3133

3115

3148

3169

3211

3305

3660

3966

2336

3137

3401

4834

5134

5070

4301

3785

3537

3369

3199

2928

2743

2696

2710

2714

2784

3006

3339

3727

'2044

;2622

3239

4549

4784

4755

4066

3483

3144

2906

2798

2592

2403

2420

2478

2510

2556

2843

3136

3490

0.15

1859

2812

3377

4783

5005

4857

4326

3875

3545

3340

3219

3038

2922

2918

2936

2946

2979

3095

3411

3675

1918

2769

3239

4494

4682

4472

3874

3407

3147

2940

2786

2645

2515

2458

2471

2470

2519

2708

3032

3483

1674

2374

3086

4207

4306

4106

3562

3039

2769

2535

2381

2238

2116

2120

2177

2237

2432

2558

2935

3380

0.2

1416

2431

3237

4679

4822

4429

3964

3532

3244

3043

2961

2893

2814

2795

2816

2843

2886

2988

3187

3423

1485

2397

3093

4247

4316

3892

3486

3122

2922

2714

2565

2490

2418

2380

2382

2415

2466

2595

2913

3384

1295

2169

2969

3911

3829

3452

3137

2749

2551

2340

2179

2084

2037

2031

2070

2159

2391

2466

2820

3376

0.25 0.3

1150 941

2204 2023

3089 2966

4496 4269

4683 4333

4177 3788

3637 3309

3229 2919

3054 2797

2876 2560

2696 2235

2570 1995

2470 1863

2432 1792

2475 1877

2506 2049

2586 2247

2795 2492

2980 2635

3262 2860

1212 996

2165 1981

2941 2820

4046 3862

4157 3900

3626 3347

3189 2964

2890 2731

2723 2445

2491 2133

2294 1896

2201 1730

2139 1640

2105 1591

2146 1673

2213 1840

2330 2140

2464 2260

2779 2541

3259 2846

1195 994

2006 1871

2837 2708

3759 3642

3583 3411

3103 2847

2863 2639

2551 2345

2319 1899

2093 1694

1947 1616

1893 1528

1867 1475

1821 1450

1878 1570

1998 1721

2207 2027

2287 2179

2611 2287

3257 2798

0.35

787

1871

2854

4066

4077

3528

3056

2640

2311

1887

1522

1376

1358

1319

1459

1755

2026

2169

2268

2359

8341826

2707

3632

3634

3136

2735

2451

1983

1570

1323

1228

1200

1193

1308

1539

1879

2014

2199

2288

8381761

2601

3458

3248

2749

2355

2014

1514

1253

1128

1063

1066

1147

1300

1519

1794

1832

1980

2157

0.4

6861749

2724

3800

3812

3418

2839

2383

1632

1093

871

988

1154

1237

1363

1621

1760

1822

1901

1981

7231706

2595

3430

3469

3031

2523

2023

1367

967

782

840

9301010

1154

1385

1599

1687

1773

1851

731

1667

2507

" 3328

3096

2560

2001

1559

1099

811

696702

783

923

1076

1256

1514

1585

1654

1718

0.45

"608

1645

2598

3584

3707

3263

2550

1789

930571

582952

1133

1183

1345

1405

1468

1545

1632

1717

641

1604

2489

3318

3366

3028

2250

1445

789553

519734

872

949

1102

1228

1311

1401

1489

1576

'653

1579

2417

3212

2964

2331

1661

1068

655

524

501

603

738859988

1136

1225

1316

1402

1479

0.5

5471537

2431

3283

3468

2964

2068

1096

519

477

5769521124

1130

1149

1192

1250

1314

1394

1479

5751501

2302

3065

3157

2838

1728

844

424

425

490732

854888

9521032

1108

1186

1269

1353

591

1490

2281

2893

2629

2069

1209

656

396

397

470

577676756850

938

1025

1111

1193

1272

0.6

439

1229

1833

2663

2874

1965

1029

532

370

472505580

622650

698

756

818

887

9601034

4661200

1710

2402

2596

1774

805

432

261

346

409

470

492

521

582655

725

795

866

936

542

1183

1678

2144

2068

1413

643

388

237

307

385

401

425

470535

607678

747

814

881

0.7

3489891647

2330

2374

1257

785518

305

353

382

384

386

390

411

438472

528

587

646

369984

1515

2144

2213

1121

488

322

204

263

317

317

317

326

348379

422

476

530

581

'456

980

1457

1877

1858

944

364

250

178

225

258

258

259

275304

346

396

447

498

548

0.8

344'

942

15111766

1636

803

714

439

107

122

145

146

147

148

167196223

260299

341

3579401479

1735

1587

735273

19699112

135

136

137138

153179

210

243

277

312

423

938

1449

1538

1427

554

205

154

96111

122

122

122

125139

165

197

228

260

295

0.9

327

823

1070

1193

1061

735

707

435

52

52

57

596064'74

90

105

123"

142

162

339

774

1060

1179

1029

613

259

190

"51

5257

58

5963

7084

99

116'

132

149

364

720

1050

1083

917511195134

4950555657596577

93

108124

140

1

0

000

00000

0

0

000

00000

0

00

0

0

00

0

0000

0

00

000

p00

00

00000

0

000

0q00000

60

178

TABLE ILL THE 1995 CHF LOOK-UP TABLE FOR CRITICAL HEAT FLUX IN 8 mmTUBES (in kW.m-2).(Continued)


Quality

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

11000

11000

11000

11000

11000

11000

11000

1100011000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

0

50100

300

5001000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

0501003005001000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

050

100

300

500

1000

1500

20002500

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

-0.5

4836

5422

5916

6366

6641

7221

7976

9111

10108

10887

11622

12336

13022

13683

14332

14962

15570

16165

16748

17323

1 4568

5126'

5597

6039

6318

6912

7650

8720

9664

10400

11099

11783

12444

13081

13694

14268

14835

15399

15952

16496

4294'

• 4821,

' 5267

5694

5966

6553

72SI

82859166

9861

10518

11153

11765

12351

12922

13495

14034

14562

15082

15594

-0.4

4571

5114

5571

5916

6100

6432

7023

8171

9252

10041

10683

11283

11857

12418

12927

13402

13909

14403

14881

15340

4337

4857

5296

5642

5831

6184

6747

7826

8829

9580

10200

10775

11327

11867

12355

12772

13236

13708

14166

14588

4095

4588

5006

5346

5534

5906

6484

74698371

9055

9636

10169

10675

11158

11622

12064

12509

12953

13381

13784

-0.3

4301

4813

5251

5527

5668

5947

6356

7160

8185

8998

9660

10200

10680

11127

11580

11998

12387

12779

13166

13551

'4103

4591

5007

5266

5417

5732

6118

6896

7895

8648

9259

9774

10230

10655

11078

11467

11837

12204

12567

12938

3891

4356

4752

5002

5145

5430

5794

66007589

8268

8798

9265

9696

10092

10478

10871

11220

11560

11899

12241

-0.2

4034

4547

4988

5300

5412

5625

5856

6258

7162

7755

8227

8756

9235

9685

10180

10758

11336

11578

11824

. -0.15

3902

4432

4892

5260

5332

5398

5535

5863

6749

7210

7395

7669

7924

8259

8872

9759

10230

10702

10747

12107 10954

.3874

4336

' 4734

4961

5074

5328

5570

6030

7010

7587

8008

8533

8989

9402

9834

10320

10808

11028

11253

11536

3694

.4124

4492

4672

4765

4911

5105

573268077343

7680

8151

8592

8934

9284

9741

10197

10403

10634

10923

3760

4230

4637

4891

4965

5073

5212

5591

6589

7077

7253

7582

7824

8114

8616

9342

9713

10083

10103

10351

3599

4017

4379

4560

4640

4665

4739

52706361

6854

7019

7358

7672

7863

8203

8840

9174

9509

9563

9825

-0.1

3783

4335

4811

5239

5205

4936

4958

5299

6025

6399

6453

6674

6936

7305

7818

8777

9257

9737

9739

9741

3658

4146

4565

4870

4855

4676

4712

5000

5726

6149

6254

6503

6787

7092

7476

8224

8600

8975

8977

8979

3513

3938

4303

4526

4516

4365

4389

46755371

5785

5939

6242

6551

6753

7035

7663

7996

8328

8334

8435

-0.05

3639

4213

4704

5236

5147

4705

4693

4835

5004

5097

5140

5266

5469

5645

5764

6149

6353

6355

6394

6556

3534

4040

4472

4868

4800

4463

4476

4575

4678

4779

4797

4841

4940

5116

5265

5687

5912

5926

5940

5955

3407

3844

4217

4505

4468

4197

417i

42214332

4446

4491

4605

4757

4892

5020

5414

5637

5655

5673

5692

0

3352

3960

4462

5194

5114

4703

4467

4196

4119

4045

3995

3983

4047

4183

4272

4331

4416

4542

4637

4714

3274

3814

4253

4832

4765

4376

4178

3974

3901

3891

3830

3728

3754

3898

4034

4147

4241

4267

4279

4484

3175

3646

4027

4452

4393

4035

3806

36953676

3668

3619

3503

3566

3707

3849

4024

4157

4188

4209

4231

0.05

2503

3071

3658

4944"

4925

4697

4189

3569

3339

3240

3155

3066

3026

3080

3210

3303

3344

3482

3660

3838

2464"

3002

3512

4636

4599

4328

3843

3349

3191

3089

3005

2909

2892

2977

3114

3227

3275

3390

3559

3783

2437

2917

3358

4236

4218

3837

3390

31223005

2920

2843

2761

2765

2890

2985

3128

3262

3347

3497

3680

0.1

1977

2528.

3134

4270

4243

4204

3730

3097

2797

2604

2487

2349

2245

2249

2355

2421

2492

2788

3076

3419

1922

2482

3015

4016

4013

3822

3402

2872

2623

2444

2327

2178

2087

2088

2208

2286

2378

2707

2995

3325

1880

2416

2892

3709

3706

3389

2982

26192461

2257

2127

1952

1999

2004

2108

2210

2360

2669

2915

3152

0.15

1637

2304

2976

3692

3625

3520

3227

2746

2521

2289

2124

1931

1827

1836

1963

2126

2346

2527

2877

3342

1596

2256

2865

3506

3353

3225

2958

2468

2258

2030

1877

1686

1605

1612

1742

1927

2206

2422

2729

3120

1560

2184

2727

3392

3250

2981

2564

21951970

1695

1570

1471

1476

1540

1677

1846

2118

2349

2635

2836

0.2

1290

2110

2841

3478

3364

3118

2850

2448

2241

2038

1896

1750

1719

1755

1856

2045

2317

2402

2745

3299

1276

2057

2728

3393

3165

2936

2559

2106

1901

1701

1591

1470

1476

1562

1692

1902

2200

2309

2594

2988

1270

1985

2589

3301

3083

2693

2201

17721537

1311

1251

1266

1336

1491

1645

1823

2112

2256

2511

2703

0.25 0.3

1179 992

1945 1810

' 2697 2575

3344 3257

3160 2999

2854 2661

2712 2495

2312 1931

1942 1373

1724 1354

1643 1276

1604 1375

1631 1385

1663 1416

1760 1542

1937 1699

2197 1985

2245 2070

2567 2142

3162 2736

1163 991

1890 1750

2582 2457

3315 3233

3038 2871

2680 2484

2393 2102

19121402

1601 1035

1419 1001

1361 1062

1345 1147

1410 1262

1539 1383

1663 1496

1821 1641

2098 1895

2182 2003

2483 2092

2864 2621

1146 '989

1820 1673

2441 2299

3207 2996

2957 2761

2389 2153

1934 1567

1484 9721265 818

1109 802

1101 820

1160 962

1256 1133

1440 1299

1578 1416

1716 1518

2032 1743

2110 1824

2375 2020

2634 2467

0.35

8431699

2458

3065

2887

2545

2034

1428

1028

9679529821037

1152

1290

1500

1710

1785

1800

2042

8491641

2347

2987

2644

2171

1655

9726666477238701016

1130

1261

1440

1687

1720

1733

2015

8541579

2230

2872

2395

1682

1212

738529

457

524

733

922

1057

11811326

1521

1591

1689

1976

0.4

7391610

2373

2894

2741

2118

1429

1027

809

708

650664771908

1071

1219

1431

1497

1557

1620

7481555

2266

2781

2239

1342

938677533

478

5256417688769931183

1382

1432

1484

1596

7571510

2182

2516

1926

919

675554399

322

407

572

699

804

9361115

1302

1396

1451

1595

0.45

6601536

2317

2713

2351

1553

1081

745570

508457558670816

9351072

1170

1258

1339

1420

6801482

2213

2593

2002

1033

647480399388414492590686796993

1133

1212

1287

1393

6931451

2146

2259

1663

791458345283

277

349

4344895506649201104

1178

1248

1383

0.5

608• 1457

2165

2334

1983

1143

892603348393419

499

615717

801

8929771058

1140

1218

6251415

2105

2240

1651

802547355280

300364429

545

639703842

9421021

1097

1182

6431375

2048

1687

1311

696361305241

276

331

359

408

462

534

780

9229941061

1159

0.6

"560

1152

1554

1672

1583

984546345211

282

305331381445512

578646712

778

842

5621139

1551

1383

1137

636451

303

195256274291359430

490

553620686750

812

565"

1101

1471

1316

959477

295228192

237

247

274

338

397450

529

602

666729790

0.7

471

9711306

1380

1282

729

350186136

169184

190

205

239

281329378426475

525

' 474

9651296

1076

848

460253155126147

151

160

188

229274

317

363

410

459

507

4939381039

963

728

363209

135115

126

129

151

186

226

272

307

351399447

493

0.8

4319381300

1197'

904346

1319796103107108109,

116

130

157186

216248

281

410

8861211

1021

796

29812795'959799101

105

112

126150179208

240272

389837960652550

245'

124

9490

90

92

97

104, '

112

126"

146173

203

233-

265

0.9

349

6501040

,899

626311119-48484954555657627388

103118

134

282645897674522250864647485153-54565970

8599114129

267565741548344189654647

4849.50,

51

53576882-97111126

1

00

0

00000000000

0000

00

000000000000000000

60

, 0

00000000

0

0.0,0

00"00000

179

TABLE ILL THE 1995 CHF LOOK-UP TABLE FOR CRITICAL HEAT FLUX IN 8 mmTUBES (in kW.m-2).(Continued)

Pressure Mass Flux(kPa) (kg.m-2.s-1)

Quality

12000

12000

12000

12000

12000

12000

12000

12000

12000

12000

12000

12000

12000

12000

12000

12000

12000

12000

12000

12000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

14000

14000

14000

14000

14000

14000

14000

14000

14000

14000

14000

14000

14000

14000

14000

14000

14000

14000

14000

14000

0

50100

3005001000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

0

50

100

300

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

0

50

100300

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

-0.5

4022

4511

4924

5311

5533

6063

6852

7804

8606

9263

9873

10395

10866

11303

11820

12614

13206

13689

14161

14662

3766

4208

4575

4843

4923

5355

6344

7337

8056

8688

92109436

9495

9545

10034

11456

12458

12882

13246

13772

3493

3895

4229

4448

4497

4928

5911

6752

7369

8033

8543

8724

8731

8733

9100

10544

11595

11986

12314

12821

-0.4

3849

4309

4699

5011

5172

5518

6169

7104

7926

8483

8929

9339

9735

10049

10479

11227

11751

12152

12534

12943

3617

4039

4391

4613

4655

4921

5777

6773

7515

7876

8021

8108

8197

8199

8609

10012

11078

11431

11713

12145

3365

3750

4072

4260

4278

4533

5399

6229

6879

7236

7311

7332

7377

7394

7685

9148

10306

10624

10864

11286

-0.3

3671

4111

4488

4728

4848

5083

5458

6246

7227

7798

8209

8589

8953

9228

9563

10153

10530

10841

11149

11474

3465

3883

4236

4448

4500

4614

5070

5836

6896

7317

7365

7419

7536

7622

7982

9157

9915

10179

10405

10756

3232

3620

3948

4142

4181

4349

4821

5421

6351

6834

6865

6886

6942

6999

7266

8464

9186

9429

9636

9967

-0.2

3501

3909

4261'

4435

4467

4489

4626

5206

6161

6682

7076

7553

7997

8306

8588

9051

9514

9715

9952

10247

3317

3712

4030

4050

4070

4095

4197

4656

5685

6269

6395

6533

6741

7067

7400

8347

8897

9113

9314

9606

' 3106

3476

3794

3958

3970

4004

4046

4413

5379

6001

6069

6137

6292

6618

6926

7715

8230

8450

8641

8893

-0.15

3419

3809

4147

4333

4300

4119

4129

4596

5502

6060

6416

6877

7296

7473

7674

8222

8530

8838

8942

9213

3247

3624

3947

4030

4000

3769

3817

4124

4865

5533

57665984

6225

6480

6731

7605

8120

8280

8405

8630

3046

3402

3708

3862

3832

3659

3724

3994

4639

5227

5420

5545

5734

6103

6363

7010

7474

7655

7821

8043

-0.1

3349

3729

4058

4239

4185

3776

3854

4089

4523

4884

5166

5668

6103

6374

6576

7070

7357

7643

7712

7919

3184

3555

3870

4018

3803

3369

3594

3820

4126

45094775

5113

5464

5834

6064

6635

6995

7180

7305

7448

2994

3343

3641

3800

3618

3197

3394

3672

4017

4390

4584

4794

5054

5568

5822

6223

6512

6686

6853

7029

-0.05

3259

3634

3957

4176

4097

3577

3569

3659

3768

3885

4024

4293

4504

4628

4720

5076

5290

5346

5403

5460

3111

3463

3762

3934

3654

3032

3201

3363

3471

3631

3802

4060

4230

4420

4489

4586

4727

4812

4870

4957

2930

3266

3551

3706

3453

2864

3020

3200

3363

3551

3679

3790

3846

4075

4241

4288

4416

4467

4610

4837

0

'3053

3462

3791

4057'

3919

3372

3177

3172

3225

3274

3319

3390

3487

3605

3697

3873

3991

4035

4054

4075

2935

3302

3597

3831

3560

2832

2766

2852

2940

3022

3091

3223

3342

3429

3515

3609

3679

3703

3742

3776

2779

3123

3403

3630

3399

2705

2650

2739

2826

2931

3013

3086

3189

3321

3364

3456

3503

3523

3613

3735

0.05

2397

2826

3213

3775

3659

3118

2823

2712

2688

2659

2654

2687

2735

2874

2952

3098

3239

3319

3404

3533

2352

2728

3067

3536

3358

2644

2390

2361

2403

2449

24912622

2784

2879

2935

3029

3121

3206

3310

3396

2271

2618

2933

3411

3267

2530

2255

2230

2300

2372

2439

2620

2929

3081

3088

3126

3132

3169

3242

3362

0.1

1859"

2360

2789

3401

3254

2733

2464

2281

2203

2064

1983

1935

1952

2068

2165

2268

2429

2652

2855

3020

1850

2293

2675

3175

3019

2307

2013

1983

1965

1962

19782024

2106

2232

2324

2384

2471

2607

2761

2923

1812

2211

2560

3099

2963

2189

1886

1847

1938

1959

2039

2184

2368

2520

2583

2613

2665

2673

2682

2870

0.15

1535

2111

2599

3187

3004

2496

2101

1898

1707

1477

1395

1384

1450

1598

1738

1877

2116

2326

2556

2664

1530

2039

2463

2868

2708

1992

1697

1637

1567

1434

1413

1493

1604

1789

1949

2027

2174

2298

2431

2537

1510

1958

2336

2800

2612

1791

1534

1520

1477

1498

1546

1688

1828

1993

2156

2254

2333

2344

2356

2481

0.2

1258"

1910

2447

3099

2866

2232

1764

1497

1262

1064

1053

1160

1285

1465

1625

1799

2091

2225

2423

2570

1255

1827

2279

2663

2485

1724

1396

1277

1149

1031

10651222

1362

1532

1726

1894

2110

2192

2305

2427

1248

1756

2169

2552

2295

1508

1287

1188

1078

1089

1190

1356

1489

1648

1850

1996

2149

2172

2240

2313

0.25 0.3

1130 988

1745 1598

2293 2152

2966 2695

2685 2402

1947 1675

1474 1094

1168 747

949 640

850 620

900 682

1038 867

1176 1020

1359 1211

1501 1343

1673 1456

2020 1664

2106 1800

2286 1948

2496 2307

1115'987

1658 1496

2106 1909

2492 2124

2193 1864

1540 1361

1182 937

962 638

797 504

777 562

874 681

1050 882

1188 1023

1324 1139

1520 1303

1714 1449

2016 1658

2090 1791

2191 1898

2360 2161

1089 963

1588 1423

2005 1804

2404 1967

1941 1605

1359 1209

1089 877

902 629

782 529

826 589

943 696

1106 871

1240 1067

1390 1164

1596 1343

1776 1472

2002 1646

2079 1741

2133 1870

2243 2034

0.35

8591505

2088

2591

2057

1318

7935684574024856878639951135

1281

1445

1576

1653

1914

8651404

1830

1896

1584

1136

699455362385462

695

866950

1094

1265

1431

1573

1640

1859

8511327

1708

1669

1318

980629

425

351

388

4967028749881148

1280

1413

1567

1623

1810

0.4

766" 1436

2036

2227

1673

8155364743633103765596847779141109

1280

1390

1433

1594

7751326

1749

1746

1320

721476387290309364

586

7127699041098

1278

1369

1434

1592

7671253

1636

1554

1124

6273963162662853835967468409851152

1270

1364

1444

1588

0.45

'706

1383

2008

2034

1341

6194083452752633354194625406508941076

1150

1223

1374

7201237

1618

1454

1069

471361307231235331

452

5265306408901053

1137

1217

1365

7141168

1509

1263

950434307248200218312471586685803

9421053

1136

1217

1357

0.5

6601309

1916

1389

940

514

320

257

221

253

309

342

3634335187499039731037

1140

' 677

1143

1446

1179

716351293243192228287

342

387403

4737358829551022

1126

6951070

1300

986626334273220170202257330394

480568721866

942

1012

1116

0.6

5651069

1415

1132

716338235221176209220260318376424513588652714774

5881005

1234

931473254229206161186201

244

298355403499578641703763

598974992757381223205195148166185227282

338382484568633695757

0.7

494 ,

933985820537262175119107113116145181226265299343390437484

518926940

' 746

397202162113105111112

139

178

218

255292336383

431

477

509'

807764563322190150109104108111135172210246286332379427474

0.8

376'

818946636263128'

1149187878894101 "

109

123

142

169

198

228

260

373752933622

2451221128684'84

86--90

97105

119139.

165194225257

351'

632615378224116

93

80

82

83

848794101116136163192222255

0.9

22450770854522896544444484950515255668094109123

18744463650620872'50444445

• 4 6

47

4849

54'65,78

. 93

107122

175355350246164704741

• 43

43" 44

44454753647791106121

1

00000

000000000

0

0000

0

000000

0-0000

0

00

00_00

0

0

00

00000000000

00

00

000

180

TABLE ILL THE 1995 CHF LOOK-UP TABLE FOR CRITICAL HEAT FLUX IN 8 mmTUBES (in kW.nT2).(Continued)

Pressure Mass Flux Quality(kPa) (kg.m-2.s-l)

15000

15000

15000

15000

15000

15000

15000

15000

15000

15000

15000

15000

15000

15000

15000

15000

15000

15000

15000

15000

16000

16000

16000

16000

16000

16000

16000

16000

16000

16000

16000

16000

16000

16000

16000

16000

16000

16000

16000

16000

17000

17000

17000

17000

17000

17000

17000

170001700017000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

0501003005001000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

0501003005001000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

0501003005001000

1500

2000

25003000

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

-0.5

3196

3566

3874

4082

4184

4678

5402

5890

6438

7244

7886

8278

8512

8629

8926

9942

10615

10992

11337

11774

2883

,3213

3486

3649

3683

4042

4726

5241

5901

6667

7252

7734

8088

8350

8669

9148

9555

9926

10287

10652

2551

2800

2998

2970

2817

3054

3874

4639

55656358

6917

7403

7593

7689

7871

8132

8472

8820

9163

9480

-0.4

3087

3437

3730

3878

3933

4287

4961

5387

5806

6348

6597

6675

6767

6956

7284

8684

9447

9718

9941

10337

2793

3103

3359

3441

3473

3623

4312

4790

5360

5912

6155

6288

6346

6494

6857

7890

8478

8738

8963

9312

2479

"2707

2886

2769

2549

2719

3538

4218

5074

5769

6047

6224

6226

6228

6397

6991

7405

7664

7907

8235

-0.3

2976

3319

"3611

3747

3790

4068

4532

4879

5478

6122

6342

6445

6565

6681

6913

7860

8361

8592

8797

9087

"2700

3009

3268

3336

3359

3491

4002

4395

5038

5709

5907

6048

6193

6277

6463

7094

7462

7682

7885

8130

2406

2619

2789

2607

2374

2452

3124

3790

46385238

5368

5569

5723

5814

5943

6277

6535

6746

6947

7110

-0.2

2868

3207

3497

3630

3638

3724

3891

4196

4946

5596

5765

5899

6179

6504

6707

7163

7475

7676

7866

8074

2612

2911

3163

3210

3236

3323

3586

3873

4546

5190

5393

5561

5888

6217

6376

6537

6654

6811

6963

7145

2335

2530

2685

2439

2227

2318

2722

3214

39634406

4467

4621

4953

5285

5432

5506

5600

5718

5876

6148

-0.15

2815

3149

3434

3543

3517

3482

3586

3805

4365

4858

5039

5239

5561

5999

6217

6512

6767

6946

7112

7319

2571

2857

3101

3159

3112

3149

3329

3538

4031

4449

4622

4834

5220

5695

5903

5988

6074

6188

6314

6495

2300

2485

2631

2347

2138

2233

2518

2860

34163758

3874

4012

4355

4769

4936

4986

5049

5133

5271

5620

-0.1

2772

3098

3373

3442

3315

3068

3155

3351

3686

4010

4226

4502

4808

5383

5673

5863

5984

6098

6222

6455

2530

2816

3054

3080

2886

2725

2901

3050

3307

3540

3772

4052

4407

4991

5268

5386

5402

5423

5492

5785

2276

2439

2566

2260

2044

2074

2320

2568

29113197

3398

3528

3694

3933

4086

4123

4154

4169

4622

5075

-0.05

2720

3033

3295

3358

3195

2708

2674

2833

3083

3336

3459

3517

3552

3789

3984

4029

4103

4135

4282

4633

2489

2759

2983

3009

2775

2366

2360

2500

2724

2937

3075

3170

3270

3561

3783

3873

3928

3952

4090

4413

2235

2398

2521

2175

1917

1850

2043

2288

25292726

2844

2931

3017

3247

3463

3557

3656

3754

3853

4230

0

2595

2910

3163

3274

3115

2468

2312

2464

2705

2854

2904

2916

3057

3255

3297

3339

3419

3443

3522

3670

'2380

2664

2888

2934

2673

2089

1945

2166

2446

2617

2660

2824

2980

3223

3344

3367

3388

3406

3520

3660

•2146

2319

2439

2102

1774

1597

1753

2018

22832415

2588

2765

2902

3128

3458

3471

3485

3498

3517

3649

0.05

2165

2485

2768

3111

3003

2251

1955

2071

2224

2322

2340

2615

2953

3188

3216

3221

3228

3286

3297

3309

2020

2329

2593

2818

2545

1853

1655

1841

2112

2282

2440

2668

2932

3209

3321

3321

3321

3395

3414

3434

1849

2046

2196

1972

1661

1407

1526

1757

19912218

2526

2746

2863

3110

3330

3370

3374

3415

3434

3455

0.1

1750

2114

2430

2884

2739

1897

1649

1843

1912

1974

2055

2270

2472

2657

2744

2785

2823

2826

2831

2836

1647

1998

2295

2597 "

2268

1528

1419

1688

1888

2058

2199

2401

2554

2774

2940

2993

3003

3020

3039

3050

1547

1734

1878

1755

1487

1205

1305

1533

17902081

2337

2519

2619

2821

3024

3080

3087

3116

3135

3155

0.15

1456

1873

2229

2667

2384

1523

1367

1501

1559

1595

1670

1815

1951

2131

2295

2397

2440

2450

2461

2470

1379

1756

2072

2432

1963

1251

1235

1477

1628

1745

1859

2011

2118

2307

2470

2586

2611

2629

2650

2669

1327

1473

1S84

1532

1308

1045

1187

1448

16371832

1993

2134

2245

2406

2545

2673

2708

2719

2738

2757

0.2

1221

1695

2087

2393

1923

1286

1179

1178

1171

1225

1339

1483

1607

1774

1947

2063

2165

2179

2194

2218

1162

1586

1940

2194*

1580

1076

1071

1188

1298

1408

1554

1691

1807

1979

2116

2242

2301

2340

2359

2380

1144

1299

1423

1399

1151

9121020

1223

14081562

1685

1807

1935

2092

2203

2311

2349

2357

2367

2388

0.25 0.3

1047 923

1514 1341

1906 1686

2193 1807

1657 1425

1204 1147

1025 850

918 664

891 618

954 675

1062 769

1217 939

1355 1103

1495 1250

1676 1419

1838 1539

2010 1656

2030 1754

2120 1845

2166 1988

997 873

1404 1228

1741 1521

2016 1688

1362 1198

992 948

907 743

943 704

1031 754

1139 849

1254 947

1412 1104

1543 1240

1684 1391

1814 1519

1942 1627

2033 1704

2040 1774

2110 1830

2141 1969

993 866

1154 1022

1286 1150

1286 1107

1048 958

839 744

859 685

993 780

1148 8851289 1006

1399 1114

1533 1246

1681 1380

1833 1539

1931 1643

1984 1694

2037 1733

2050 1785

2100 1825

2120 1952

0.35

8311223

1537

1514

1191

9275954243954615577509341083

1232

1321

1421

1570

1610

1784

7691076

1333

' 1438

1051

8045414624955976988671026

1174

1289

1389

1481

1572

1598

1749

7619221054

1000

868635527567618719

8319781120

1273

1365

1457

1526

1580

1593

1722

0.4

' 745"

1152

1472

1251

1038

6063682812723444546738419441065

1180

1300

1400

1458

1576

674' 975

1226

1124

9345873573123394655887639019901084

1211

1339

1405

1473

1554

6728581007

941802483361405462568

6948329471048

1135

1277

1395

1435

1490

1537

0.45

6941073

1355

1128

895420

2592021932573605496767628559671079

1160

1230

1349

614'888

1114

9788034072282012443704856347368038851009

1121

1199

1249

1342

608798946821685354223273

358483

6097027758499381069

1174

1237

1269

1334

0.5

6939681123

8665973122331901491802663774555246057398559381013

1111

612791907747574288172147

1972713694765435976677658579401018

1107

598726806659534273155180288407

5336156466857438218729471023

1104

0.6

645900871644368200176163139154185231291352406484558623689753

537693695508333190125120165190247297343395449499557618686751

494581587429291180104125218302

462489499508530577597629683748

0.7

501712648482299174

135107103107116132164204244283328375424471

383"

' 482

550428272154115105120123129136163201244283328373422470

"354 "

40749039024313683108

136148

193212216242275307340376420468

0.8

297520494351213-

10892"76808182838895113135162191221253

260 "

38336032520310280727678798081,89109134161190220253

257347350295194957469 '

7273767780 .

89 .

109135161189219

251

0.9

172332327227134604339414242

' 42

434552637791105121

16731931121012759393637393939404250637690105120

1562922581921185239333536363737404962'7690104120

1

00000000000000000000

00000000000000000

- 000

00

q000000.000000

b0000

181

TABLE ILL THE 1995 CHF LOOK-UP TABLE FOR CRITICAL HEAT FLUX IN 8 mmTUBES (in kW.nr2).(Continued)

Pressure Mass Flux(kPa) (kg.m-2.s-1)

Quality

18000

18000

18000

18000

18000

18000

18000

18000

18000

18000

18000

18000

18000

18000

18000

18000

18000

18000

18000

18000

19000

19000

19000

19000

19000

19000

19000

19000

19000

19000

19000

19000

19000

19000

19000

19000

19000

19000

19000

19000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

0

50

100

300

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

050

100

300

5001000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

050100

300

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

-0.5

2189

2382

2524

2378

2137

2484

3354

4160

5115

5776

6200

6698

6863

6894

6982

7157

7437

7750

8065

8347

Vi786-.";1935

;\2032

1682

1364

1882

2838

3670

4468

4747

4918

5285

5496

5668

5862

6118

6389

6653

6916

7164

:i36i\

2 1628'

1806

~1524

1167

1538

2411

3269

3945

4169

4171

4173

4233

4436

4687

4915

5129

5338

5548

5757

-0.4

2133

2308

2435

2223

1930

2220

3048

3773

4671

5147

5263

5557

5589

5600

5726

6118

6468

6724

6948

7225

'1744

1889

1983

1612

1264

1752

2604

3283

3900

4016

4106

4443

4642

4833

5120

5409

5636

5832

5989

6190

1333

1593

1774.

1476

1090

1403

2193

2881

3350

3514

3606

3765

4009

4270

4581

4686

4688

4706

4808

4976

-0.3

2078

2239

2357

2101

1790

1960

2648

3358

4271

4697

4751

5016

5164

5215

5328

5497

5657

5829

6031

6182

1699

.:1843

1940

1549

1167

1537

2302

2917

3580

3725

3813

4086

4166

4311

4534

4659

4757

4906

5136

5284

1304

• 1576

.1772

1461

1024

1259

1966

2536

2983

3182

3286

3426

3596

3812

4048

4148

4157

4158

4185

4232

-0.2

2022

2172

2282

2002

1698

1832

2304

2874

3613

3919

3952

4100

4349

4608

4726

4754

4756

4805

5039

5286

1656,

• 1802

1903

1545

1123

1372

2033

2593

3169

3315

3355

3441

3493

3646

3738

3748

3765

3883

4275

4511

1277

1552

1752

1461

9971142

1766

2229

2597

2767

2850

2954

3034

3193

3320

3416

3492

3532

3586

3614

-0.15

1997

2137

2239

1936

1657

1759

2097

2589

3118

3353

3428

3547

3817

4132

4258

4297

4302

4340

4556

4858

:1639

1777

:1872i

1528

1099

1286

1827

2380

2832

2968

3013

3077

3159

3301

3375

3396

3426

3540

3911

4158

1261

1522

1715

1449

9781086

1640

2049

2338

2442

2522

2639

2742

2893

3002

3109

3206

3242

3298

3338

-0.1

1976

2103

2192

1854

1582

1689

2004

2408

2736

2939

3073

3146

3236

3365

3473

3667

3860

4053

4247

4441

1628

1752

1830

1462

1067

1241

1702

2218

2523

2642

2717

2773

2813

2910

3017

3107

3162

3240

3493

3826

1255

1477

1633

1379

9629961468

1812

2012

2077

2154

2294

2472

2659

2825

2950

3018

3051

3110

3135

-0.05

1950

2070

2152

1777

1487

1587

1862

2176

2410

2529

2613

2683

2917

3148

3458

3478

3524

3580

3770

3952

1618

1711

1760

1358

9801189

1623

2014

2261

2332

2393

2470

2534

2760

2879

3059

3134

3160

3268

3509

1235

1396

1508

1253

9059361328

1633

1864

1949

2014

2174

2308

2489

2661

2733

2820

2840

2861

2882

0

1885

2004

2077

1693

1377

1399

1606

1855

2108

2224

2476

2602

2828

3069

3348

3399

3399

3437

3511

3525

'1567

1660.

1706

1290

911

1085

1428

1679

1905

1977

2047

2158

2280

2757

2877

3058

3123

3143

3164

3204

1193

1314

1394

1173

858

873

1194

1469

1692

1770

1854

2013

2123

2485

2657

2728

2815

2835

2854

2876

0.05

1647

1782

1880

1600

1275

1195

1377

1637

1885

2092

2473

2600

2795

2992

3313

3334

3355

3374

3393

3414

1393

1503

1570

1218

8339091225

1498

1694

1769

1917

2021

2130

2546

2796

3028

3069

3087

3119

3139

1092

1222

1310

1072

7507811161

1396

1534

1566

1763

1960

2096

2256

2428

2611

2697

2717

2736

2755

0.1

1398

1532

1632

1481

1210

1049

1204

1484

1730

2088

2291

2432

2504

2578

2865

2885

2904

2924

2945

2965

1207'.

1316

1388

1115

810

890

1170

1465

1672

1768

1890

2014

2127

2342

2587

2756

2775

2797

2815

2836

9881094

1165

9046857131161

1360

1369

1380

1669

1959

2096

2120

2146

2172

2220

2260

2329

2443

0.15

1213

1325

1410

1325

1096

9791165

1435

1680

1863

1953

2107

2176

2354

2532

2620

2640

2659

2680

2701

1069

•1154-

1208

974799889

1114

1402

1531

1610

1742

1875

2125

2151

2350

2485

2505

2526

2545

2566

9211001

1044

7215927121096

1198

1252

1294

1581

1870

2008

2038

2068

2100

2116

2147

2179

2255

0.2

1060 '

1183

1278

1192

9648541011

1259

1431

1569

1645

1808

2020

2132

2295

2357

2363

2383

2404

2423

•:m:

1055;:

1113

8547248009861226

1393

1472

1595

1753

1902

1963

2135

2290

2348

2367

2388

2409

8469511014

6675727119491153

1250

1293

1522

1720

1892

1927

1962

1999

2040

2083

2114

2164

0.25

9301062

1168

1112

8957478491077

1241

1328

1395

1584

1761

1877

2023

2031

2038

2060

0.3

8129371040

9918546526958971010

1104

1186

1341

1486

1636

1768

1778

1789

1799

2090 1809

2114

•"856:

;974

1056

' 867

6957058381101

1246

1328

1391

1455

1593

1934

V74p843.;918;;

763671646737

9451064

1169

1216

1280

1455

1762 1648

1945

1948

1950

2070

2080

2090

7618819576525726677691029

1153

1771

1775

1779

1800

1800

1919

6657477976095396106819391124

1292 1227

1331

1371

1253

1264

1473 1425

1576

1678

1571

1669

1832 1671

1891

1937

1983

1674

1725

1776

2075 1912

0.35

7268499408717495435546757578609661080

1188

1342

1410

1494

1535

1580

1590

1710

;664::;

'.: 760 T

'646'

575529605746840929

9931098

1212

1414

1509

1531

1546

1580

1585

1703

5736236515474874856118259391033

1128

1188

1280

1374

1519

1521

1534

1548

1561

1697

0.4

657796892

' 759

6534203834475326537648811000

1113

1167

1312

1417

1451

1464

1515

63a •

::; 660

:«66 •

"534'

508409406470618735

821

883

1021

1127

1211

1328

1439

1458

1461

1502

5225475534324303935335938089059621035

1044

1150

1230

1335

1438

1463

1478

1493

0.45

5957528656885453502292884135136407057778879831126

1227

1261

1275

1321

•57D'

•'.• 6 5 5

485447340303335481

587

671

710

8238979961170

1257

1265

1294

1311

4724764804003753303854116116728138568719001021

1178

1273

1287

1296

1304

0.5

5776917575804572691982343524656066436647208178698989651034

1103

"528;:

^ 59<j;

.624

452'

381

263

244

249

3734906466466737408368939299851048

1102

4184214243182692592502834285586716906957508579359589981053

1102

0.6

444525542392274170112138268368526583585628635651654667697746

402460'483;;

•342"

250160137150279388

550587

588638692693695696716745

'321

345371292210

150139167291390582601611692693694696700726744

0.7

31540047837523112673115147158209238239260291324356387423468

281369;423

33320711983116156173

225258

262288301333365396430468

228270

' 369

29 i

185103102129159184232272278300302333366399433467

0.8

228

314

340

271

184

88

71 .

66686972747688109135162190218249

1942783322481748363606667

71

72

75 '

88109135

162~

190

219

248

15421522422316577.63,62646570727588109135163'

190220247"

0.9

13924823317411547353132333434353949627589104120'

1162142201561123331293031

3132

3339486175 •

89103119

901521871407231292728292929313748607488103119

1

0

0

00

0000

0000

0000

0000

0

00

00

00

0000

0

0000

0000

00

0

060

00

0000

0

.0

0

q0

0

0

0

182

Appendix III

CHF PREDICTION FOR WWER-TYPE BUNDLE GEOMETRIES

The CHF look-up table for the WWER-type bundles has been derived at IPPE, Obninskand is included in this appendix as an alternative to calculate CHF in bundles of the WWER-type. This look-up table is based on (i) experimental data for bundles, and (ii) predictionsusing a semi-empirical model described in detail by Bobkov (1993, 1995) and Bobkov etal.(1993, 1995a-b, 1997a-b) in which the data on CHF in other geometries (tubes, annuli) andthe look-up table for CHF in tubes were used that helped to expand the ranges of applicability.More than 4000 CHF data were used, obtained for 22 bundle geometries that were taken fromthe unified Czech-Russian CHF data bank [Kostalek et al. (1990)] (3, 7, 19 and 37 rods,triangular shape with p/d ratio of 1.16-1.52, ranges of flow conditions are: 1.5 < P < 20 MPa;220 < G <5 04 kg/m2s;-0.52 < X < 0.9). A 3-dimensional smoothing procedure was applied toremove irregular trends.

This version of look-up table is derived for the WWER-type rod bundles with thefollowing applicability conditions:

— bundle with triangular rod array ;— smooth channel with no effect of spacers;— uniform axial and radial heating;— heated-equivalent diameter is 9.36 mm;— pitch to rod diameter ratio is 1.4;— pressure: from 0.1 to 20 MPa;— mass flux: from 50 to 5000 kg/m s;— relative enthalpy (steam quality): from -0.5 to 0.9.

The range of application of the look-up table can be expanded by using the followingcorrection factors:

CHF = CHF(P,G,X,Dhe= 9.36 mm>KrK2-K3-K4

where— CHF(...) refers to the look-up table value;— K!=(9.36/Dhe)

1/3;— for p/d < 1.1: K2 = 0.90 - 0.7exp[-35(p/d-l)];— for p/d > 1.1: K2 = 0.26 + 0.57 p/d;— K3 = 0.95 + 0.6exp(-0.01 Lh/Dhe).— K4 = 1 + 1.5^°-5(G/1000)°-2-exp(0.1Lgs/ Dhe), where % is spacer grid friction factor, Lgs -

distance from outlet to the nearest grid spacer.

These correction factors permit to expand the application range of look-up tablepresented in this appendix up to:

— heated-equivalent diameter range, Dhe, - from 2.8 to 21 mm;— heated length/diameter ratio, \j Dhe, - from 40 to 300;— pitch to rod diameter ratio, p/d, - from 1.02 to 1.52;— effect of rod spacing devices.

In the look-up table, strongly shaded cells are connected with the data on bundles,lightly shaded - with the data on simpler geometries (tubes, annuli).

183

TABLE DLL THE LOOK-UP TABLE FOR CHF IN REGULAR TRIANGULAR RODBUNDLES OF WWER-TYPE (HEATED EQUIVALENT DIAMETER IS 9.36 mm, THEPITCH TO ROD DIAMETER RATIO IS 1.4), CHF IS IN kW/m2

pMPa100100100100100100100100100100100100

200200200200200200200200200200200200

300300300300300300300300300300300300

400400400400400400400400400400400400

Gkg/m2s -0.5

50100200300500750100015002000300040005000

50100200300500750100015002000300040005000

50100200300500750100015002000300040005000

50100200300500750100015002000300040005000

-0.4 -0.3 -0.2- 628- 694- 747- 799- 902- 1039- 1184- 1432- 1660- 2136- 2711- 3461

- 632- 707- 770- 834- 943- 1081- 1227- 1475- 1710- 2217- 2903- 3734

- 636- 720- 794- 869- 984- 1124- 1270- 1517- 1760- 2297- 3095- 4009

- 648- 746- 834- 925- 1048- 1195- 1350- 1611- 1871- 2459- 3293- 4276

-0 124232441751665276488510721247162020242471

29237247157772484597511691357175921872648

341421525637796925106412661467189923502825

3754675857118671007115713771595205725473036

00136214279349434531640802950127816462083

1962523213945016037168821038137617532169

2562913624395686767939631125147518612256

28331241552465576287610501223165820162351

X0.1123223287356457552657804946125416141985

152238316400512605706852999130916562028

180253345444567658756|9001051136416992072

20028940052063572682110281218163419612129

0?126232292357449539636772885106413121685

140246318395491579674810939114113421727

154259343433533619711849993121813721769

1722933924985876747669351086131514681828

031302432913434414975557378799309321270

1402533123754525105707278409229541289

1502643344084645235857178029149761307

1652953594274875466067107828719981326

04131248275303421494573770868797661942

140253295339419485556699770757679958

149259315374416476539628672718697975

161283332383410460511575614654712986

0.512423925527035543352068l|720528390648

134248274301351410473576614509408657

145257293 [331347|386426471508490425666

147274302[331319354389432464426430671

06101195207219238278321372343220194388

111210223235240265290313297219209395

120225238252242252259253251217224402

123250265279244250252248212201234407

0777151171192185179169160984192198

901671184202189183173132874193197

104| 183197|212193187176104774295195

115I 211228]245201192178117744296195

0861110124138133129123117753771142

7012113314413613212598683772141

7913214115113813412779613873140

8715016217314413812888593874140

09

457077848180767352335086

507581878381776449345185

548186908482785445345185

5890961018784795944345285

184

TABLE III.I. (CONT.)

pMPa500500500500

500500

500500

500500500500

600

600

600

600

600600600600600600600600

700700

700700700700700700

700700

700700

800

800

800

800

800

800

800800

800800

800

800

Gkg/m2s

X-0.5 -0.4 -0.3

50 - - 932

100 - - 1067

200 - - 1166300 - - 1265

500 - - 1396750 - - 1552

1000 - - 17091500 - - 2025

2000 - - 23513000 - - 32434000 - - 45215000 - - 6060

50 - - 931

100 - - 1072

200 - - 1183

300 - - 1296

500 - - 1436

750 - - 15951000 - - 1756

1500 - - 2079

2000 - - 2418

3000 - - 3337

4000 - - 4645

5000 - - 6216

50 931100 - - 1076

200 - - 1200

300 - - 1327500 - - 1475750 - - 16371000 - - 18021500 - - 2133

2000 - - 24863000 - - 3430

4000 - - 47695000 - - 6372

50 - - 930100 - - 1080200 - - 1217300 - - 1358500 - - 1514750 - - 16801000 - - 18471500 - - 21872000 - - 25523000 - - 35224000 - - 48925000 - - 6527

-0.266077287498111111267143017051982262134914542

678802925105411951353151818082104277036444684

695832975112612791440160619122225291737964825

712

862

1026

1199

1363

1526

16932015

2347

3065

3947

4965

-0 1

410514645785

9381089

12491487

1723221627443249

440

559

717

886

1053

1205

1365

1621

1876

24022950

3388

470604

7899871166132014811755

20292590

31573527

500

649

860108812801435

15961888

21822777

3364

3666

00309334467610

741848

9591137

1322184021712445

336

372

533

707

8559671082

1272

14511952

2309

2585

363411

600805969108612061407

15812064

24472725

391

449

667

903

1083

1205

13291542

1711

2176

2586

2865

01220326456596

703792

8861156

1384190422232186

244

362

512

675

7888839811233

1463

19782336

2344

268399

569754

875

975

1076

1311

15422052

24502504

291

435

626

833

961

1066

11731389

1622

2127

2564

2665

0?190326441564

642729

8211021

1181141215641888

210

359

480

611

70978486010541211

1442

1615

1925

230391

5206587768409001087

12411472

16661963

251

424

560706845896

9401121

12721502

1717

2001|

03181326385447

512569

628703

76382710201345

198

353

407

4655345866386837338031029

1347

216380

430483556603647664

704780

10381349

234

407

453

501

579

620

657644

675757

1047

1351

0.4 0.5173 148

308 291349 311392 331

•H)5 291•U-1 321

482 352523 392

556 420590 362

727 435

997 677

188 161

328 299365| 320

404 340

419 320

456 324492| 352

495 369

513 391559 356735 444

1001 679

203 174347 307

381 328

415 349433 300468 327501 352467 346

470 361527 349

744 4531005 682

218 187

366 315

397 337

427 358

447| 305

480 329

511 352440 323

428 332

4951 343

752 462

1009 684

06127275291307

247248

244244

173186

245

412

143

289

305

321

270249242233174195258416

159302

319336254249239

223

176204

271420

175316333350258250236212177|214284425

071272392582"8209197

179130

714298195

145

259

278

296

2302031801397247102195

162280

297314228208181149

7352

105195

180

301

317332237214

182158

7456

109

195

0.8 0.9Q4 62169 99

182 106195 113

149 89141 85

129 7997 63

57 4338 3475 53140 85

106 68

183| 106195 1122<r 1 18

155 92

145 87130 80

103 66

58 44

41 3578 54

140 85

118 740.8 0.9

118 74

197 113208 119219 124162 96149 89

130 80109 69

58 4444 37

80 55

140 85

130 80

211 120

221 125

231 130

168 99153 91

131 80

115 72

59 44

47 39

185


pMPa1000

100010001000

1000

1000

1000

1000

1000

10001000

1000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

20002000

300030003000

30003000

3000

3000

3000

3000

3000

3000

3000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

Gk£/m2s

50100200300

500

750

1000

1500

2000

30004000

5000

50

100

200

300

500

750

1000

1500

2000

3000

40005000

50100200

300500

7501000

1500

2000

3000

4000

5000

50

100

200

300

500

750

1000

1500

2000

3000

4000

5000

-0.5

-

-

---

1120

1256

1361

1465

1636

1827

2022

2553

3388

5411

7486 [9876

1032

11601270

14211609

1813

2023

2588

3476 [5610

7829

1039[

9451084

1216

1364

1571

1811

2058

2679

3634

5857

8113

I 10631

-0.4

1072

121713361456

1614

1792

19712363

2904

4416

6226

8320

1044

1186

1312

1439

1615

1797

1981

2385

2957

4600

64918630

93910741207

13821592

1798

2053

2530

3360

49756962

9287

873

1015

1154

1317

1577

1818

2117

2658

3598

5291

72889521

-0.3

9291088

12491417

1590

1763

1937

2292

2684

3706

5138

6837

924

1083

1248

1421

1602

1779

1957

2322

2715

3834

54497316

8489991167

13801579

1778

2019

2417

3063

4291

5965

8101

811

961

1120

1311

1559

1788

2065

2513

3259

4588

6265

8325

-0.2

74692111251342

1531

1699

1868

2220

2589

33594249

5245

788

964

1167

1383

1571

1742

1916

2273

2642

342843935615

7659331132

13791566

1758

19862342

2844

3716

4850

6258

753910

108913071542

1757

2013

2398

2960

3895

5037

6417

-0.1

56174010041288

1505

1665

1824

2152

24863154

3778

3941

634

819

1076

1353

1566

1728

1890

2221

2547

3205

38274021

6558311074

13721533

1716

1926

2230

2606

3185

3822

4305

675835

1043

1297

1500

1699

1924

2234

2619

3177

3776

4173

0.04465268011100

1313

1446

1578

1814

1973

2403

2864

3143

504

594

872

1173

1463

1606

1748

20102142

2511

29313235

520620889

11351385

1566

1741

19612186

2550

2948

3265

544

646

8811086

1367

1576

1754

1979

2183

2506

2858

3091

0.1339508740991

1133

1250

1366

1546

1783

2278

2793

2991

391

575

817

1079

1261

1393

1525

1665

1814

221526992996

413596836

10581240

14011525

16681817

2087

2432

2924

446

618

833

1017

1278

1431

1587

1732

1848

2046

2326

2802

X0.2292489640802

983

1009

1020

1190

1334

15641822

2077

339

558

750

957

1125

1161

1180

1314

1434

162317741955

359582802

10061131

1211

1286

1371

1 44315641719

1819

390

606

819985I ITS

1332

1421

1507

1544

1600

1710

1848

0.3269461499538

623

653

675

6056177121065

1355

312

529

60"

689

782

S23

857S428387829831335

329555674

775925

1011

1031

1024

992

986

1109

1287

357590

77183510781159

1214

1221

1133

1073

1146

1286

0.4248405428451

476

505

530

384342 f4317691017

2894875666-48724731

731

55ft

4664578161050

305528656

771839

852840735

632615[8061073

331554

710

786f940

1015

1005

9U3

743

678

820[1133

0.5214331354376

31.5

335

352

277272329480689

279

442

513

589

579

565

537378

2931336524718

318515633

738710

700638504

393409561744

339539

674

~^746l821825

773

614

468

440

591

796

0.6207343361378

265

251

230

189179233309433

283

428

161

495

•129

401359240191248344457

332479531

570557

522456

338

263271364478

352

529

600

629

657634

552

424

318

301

388

511

0.7216|343356369

256

226

183

1777566116195

296395410

424

352

31426321013181125195

347413434

442419

383325

253

185152182200

247462

170

485

501

462

396

313

237|

187

205212

0.8154239248256

181160

132

128605487140

207

273

283

292

244

219

185150976493140

241286299

304288

261223

17913296110143

174

318

325

333

342

314

268

224

171

118

123

152

0.992134139143

105

95

81

7945425885

118151156161

137

1251079063476185

135158164

167160

147129

98

80526687

102

174

176

181

187172

149

134

114

57

72

91

186

TABLE IILI. (CONT.)

pMPa600060006000(600060006000600060006000600060006000

800080008000800080008000800080008000800080008000

100001000010000100001000010000100001000010000100001000010000

120001200012000120001200012000120001200012000120001200012000

Gkg/m2s

50100200300500750100015002000300040005000

50100200300500750100015002000300040005000

50100200300500750100015002000300040005000

50100200

300

500

750

1000

15002000

3000

4000

5000

X-0.5

980

1131

1279

14701734

205523783138

4260

6573

8635

10591

1158

1338

1524

1761

2090

24832872376949947246

8833

9819

1398

1612

1830

2108

2488

2939

3383

4355

5607763786718671

1617

18512076

23662738

31873625

46615833

7445

7824

6913

-0.4

914

1064

1212

14021707

200023613001

40565793

7599

9447

1087

1259

1429

16451982

2329

2755

3487

4618

6286

7693

8812

1325

1526

1721

1968

2300

2680

3147

3931

5064

654574517812

1545

17691972

2233

2514

2874

3328

41075144

631866736264

-0.3

855

1011

1176

13831663

192922532777

3625

5010

6497

8118

1026

1198

1372

1590

1892

2198

2569

3162

4089

5443

6621

7648

1253

1445

1623

1848

2157

2482

28763502

4439568664786935

1473

16861867

2099

2348

2640

3000

35954473

5455

5835

5685

-0.2

800

964

1144

13701626

186321442571

3200

4149

5145

6088

973

1151

1336

1567

1822

20832378283634914448

5228

5825

1193

1384

1561

1785

2040

22952591

3034

3712

15735139

5475

14031601177219902179237726303027360543564676]4746

-0.17288931098135415671783200423202675320436853908

90110831285153717571962217824412806326"36563855

11261319152217741912212422882539

2839

32883516

3301

1332152316961915

19912089

222624292"?70

312232562890|

0.0585693934116314531636182420122189240926122465

6518381107136516041823

1933

2090

2195

23--1

2446

2055

83910501336161017601891

2013

2073

220223192326

1873

1055

12661495

17041724

1833

1873197421002279

2243

1771

0.1 0.2 0.3 0.4

482 419 382 355

655 639 624 592

877 858| 824 767

1090 1071 1018 9381324 1272 1160 1017

1506 1379 1252 10901641 1483 1317 10891794 1602 1314 99|

1852 1587 1220 7931951 1575 1085 680

2094 1596 1091 780

2273 1707 1148 1104

547 497 467 442

774 754 737 717

998 971 946 908

I 1214 1181 1151 10941477| 1348 1245 1072

1612 1-152 1279 1071I70S 1511 1270 10291793 1539 1256 9001829 1521 1132 726185') 1157 1024 608

1816 1419 960 653

1645 1376 925 766

697 626 581 557

949 911 883 876

1160 1145 1091 1023

1356 1372 1292 11571516 1408 1226 1010167"7 14'12 1207 927

1709 1429 1137 822

172-1 1398 1033 682

1721 1333 930 5581"37 12~0 841 49')1646 1223 828 533

1208 1198 890 608

856 756 698 6781113 1046 1019 10321345 1292 1217 10891566 1533|1408 11241522|1321 1156 887

1522 1309 1042 ~bb

1565 1260 936 623

1571 1197 823 1981627 1159 "43 425

1647 1137 700 410

1568 1090 719 454

1102 994 755| 436

0.530448464"809889

907844676492437550738

382587735881890868775603436379451540

494734786819766703594454346315376476

608882841

772

646

542427

329

270

277322354

0.6257443589735T51716615461339302370461

329511(vU775746689564399285257304339

433616623612601535421304227219255295

543661652621•no

392301228196195227266

0.7 0.8249 176425| 293515 353601 410591 409537 366440 296336 238250 180197 129208 130209 149

318 222516 354601| 410678 462605 426525 363398 267272 181195 133168 111182 119178 129

406 280581 397584 399569 389485 339401 278297| 200200 135152 103144 99159 107158 115

499 342581 397545 373490 336361 248281 192211 145160 111135 95134 94146 101152 111

0.9103161192220237208162163124668289

1261922202462662221558170667679

1552132142091891571127159636672

18621320118311599777060616570

187


pMPa14000

1400014000

14000

14000

14000

14000

14000

140001400014000

14000

16000

16000

16000

16000

16000

16000

16000

1600016000

16000

1600016000

18000

18000

18000

18000

18000

1800018000

18000180001800018000

18000

20000

20000

200002000020000

20000200002000020000200002000020000

Gkg/m2s

50100200

300

500

750

1000

1500

200030004000

5000

50

100

200300

500

7501000

15002000

3000

40005000

50

100

2003005007501000

1500200030004000

5000

50

100

200300500

750100015002000300040005000

-0.5

1760

19882170

24132652

3014

3362

4469

547266146263

4740

1748

1950

2074

2254

2408

2649

2879

36334181

5184

50673896

1496

1607

1582

1548

I4U51540

UiS7

232628T t

.".•5 5

3661

3650

1135

1259

11431027749

82388712571536164915321657

-0.4

1699

19232097

2330

2498

2788

3175

3889

474655445420

4245

1694

1889

1995

2152

21732354

2642

31883818

4423

142563318

1452

1554

1509

1454

ps:13941502

2082259033563126

3100

1115124411231001701

75880611391354141713861561

-0.3

1638

18582024

2245

2367

2584

2895

3392

4066

47784762

4016

1643

1835

1934

2079

2056

2193

2407

28183345

382937533242

1411

1506

14471370

1 100

12791353

1810ir;

2970

2728

2628

1103

1240

1118995666

699

72610221191126912431370

-0.2

1573

17821937

2141

J2190

2319

2475

2794

324937243855

3587

1589

1773

1867

J200619141965

2107

23262686

3050

30892980

1369

1457

1386

13061140

12021258

154410052356?. 152

1900

1081

1216

1104991647

6536579071034106810461138

-0.1151017061857|2054

1956

1957

2040

2191

245927742816

2380

1536

1708

1790

1912

1708

] 16641692J8652111235723501918

1328

1401

13061202

HJ33

10901142

13641600I"7I1634

11534

1008

1097

993889fiO9

589

570

"43

831

830

8 H)

966

001249

14561678

1883

1715

1647

1675

1764

195021092116

1800

1356

1547

1678

1794

14781392

1391

14961704

190319101665

1207

1286

12051116

014913006

1059

1211

in1559

1500

908967

871776532

51 1496643709699"65006

011003

12451456

1656

1429

1388

13631400

150316u21559

1248

1094

1323

1496

1663

12841144113512021366

151015131307

969

1046

10271004

8458U"7692711391121I-K)3

1403

803842

717593452

i58•1626586~3002"88855

X0?

86711371326

1508

1235

1116

107310451069

II01

108(i929

932

1185

1332

1473

1061

9388748961007

110011261015

820

909

001

888731689612

"ISOil10951120

1220

750806

663523438

•157173526612624666"55

0377210321084

1120

982

892

782fSOO

6806O(i725

702

760

966

1049

1125

855

739658621656743774752

695

780

767"50650

5SI502

526650"71830

930

590620

552483413

K).:303-1215255"()5606"S

04718959934889

753

636

50941U376121477

511

661

851

835808

648

547434358380

450536547

644

746

6866225151313 12

2*2308485

574

674

468471420369142

?0S27631.2300416450191

05

664769719

651

533

447

3352612412"1326324

581

648

603549

456

375285219224300361356

561611544•17 1

369300227

165106400501

581

390

398

345293228

206185160167290346381

06608620577

518

388

305

238190

\-\191218228

490529

482427

328

262196158160

202

241227

449492

•136

377

25"

209158

102135284385

450

333

381

335290

103

15311799110198276315

07515512456

3872842211711 11

128130139

135

376

409

389362

254192148121116132144117

363

425

38734522317412179105128157

200

275352

31"282170

130

S67481941221366

08353351314268

196

152121102929296100

261283

269251

180

1391089086919488

252

293

26824015912690

638095115

135

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221198129976759647291100

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19119017214910189

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6759616365

14515614914110086685957625959

14116214913594786046556272102

1111371251147963484447516065

188

REFERENCES TO APPENDIX III

BOBKOV V.P.; 1993, "Burnout in Channels of Various Cross-Section", Preprint of IPPE -2313, Obninsk (in Russian).

BOBKOV V.P., ZYATNINA O.A., KOZINA N.V., SUDNITSIN O.A., 1993, "Burnout inChannels of Various Cross-Section (Model and Statistical Results)". Preprint of IPPE - 2314,Obninsk (in Russian).

BOBKOV V.P.; 1994, "The Features of Burnout in Rod Bundles and Other ComplexChannels", Proc. of 1st Russian Conference on Heat Transfer, Moscow, vol. 4, p.p. 32-37 (inRussian).

BOBKOV V.P., VINOGRADOV V.N., ZYATNINA O.A., KOZINA N.V.; 1995a,"Description of Critical Heat Flux in Rod Bundles and Other Complex Channels", Proc. ofIntern. Conference on Thermophysical aspects of WWER's Safety, Obninsk, v.l, p.p.143-154(in Russian).

BOBKOV V.P., VINOGRADOV V.N., ZYATNINA O.A., KOZINA N.V.; 1995b, "Methodof Burnout Description in Channels of Complex Cross-Section", Teploenergetika, v.3, p.p.37-46 (in Russian).

BOBKOV V.P., VINOGRADOV V.N., ZYATNINA O.A., KOZINA N.V.; 1997a, "RelativeDescription of Burnout in Rod Bundles and Other Complex Channels", Teploenergetika, v.3p.p. 1-7 (in Russian).

BOBKOV V.P., KIRILLOV P.L, SMOGALEV I.P., VINOGRADOV V.N.; 1997b, "Look-UpTables Developing Methods for Critical Heat Flux in Rod Bundles", Proceedings, NURETH-8,Vol3pp. 1581-1589,1997.

KOSTALEK YA., CIZEK J., LISTSOVA N.N., MAKHOV D.N., SUSLOV A.I.; 1990, "DataBank on Burnout in Rod Bundles". Proc. of Seminar "Thermohydraulics-90", Obninsk, p. 182,1990 (in Russian).

189

Appendix IV

AECL LOOK-UP TABLE FOR FULLY DEVELOPED FILM-BOILING HEAT-TRANSFER COEFFICIENTS (kW m 2 KT1)

This Appendix contains two tables. The first table contains the filmboiling heat transfercoefficients as a function of pressure, mass flux, quality and heat flux for a 8 mm ID tube. Ithas been described in Section 4.4.5 and should be used only with the following qualifications:

- the heat transfer coefficients at low flows and qualities are based on extrapolation fromHammouda's model (except for zero flow and X<0 where the data are based on poolfilm boiling conditions).

- the conditions where data are available can be found in the second table of thisappendix. This table also specifies the number of data points and the errors for eachsubset of flow conditions.

Legend:

Non-shaded

Lightly-shaded

1 le:iv:lv-siukL"d

: Areas where data exist;

: Areas where data are not available, values come from models;

Areas where data are not available,(predicted surface-temperature is greater than l,450°C).

190

TABLE IV.I. AECL TABLETRANSFER COEFFICIENTS

FOR FULLY-DEVELOPED FILM-BOILING HEAT

p

(kPa)

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100100

100100

100

100100

100

100

100

100

100

100

100

100

100

100

G

(kg m-2 s-1)

0

0

0

0

0

0

0

0

0

0

0

0

50

50

50

50

50

50

50

50

50

50

50

50

100

100

100

100

100100

100100

100

100

100

100

200

200

200

200

200

200

200

200

200

Xe

(-)-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20 I

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

50

C.174

0.173

0.161

0 142

0.101

0.069

0 046

0.046

CC68

0 079

0 071

0 057

0.222

0.218

0.180

0 129

0.087

0.068

0.056

0.081

0 105

0118

0 136

0 202

0 303

0 286

0.257

0.134

0 091

0 093

0 1 i4

0.137

0.155

0 162

0.215

0 378

0.3 .

0.311

0.288

0.140

0.111

0.145

0.241

0.275

0.278

100

0 2G5

0 203

0.185

0 162

0.124

0.096

0.065

0 005

0.094

C107

0 10'

'J O."3

0 251

0.243

0 208

0.153

0.112

0.093

0.083

0.112

0.127

0 139

0.157

0 22;

0.347

0 323

0.290

0.165

0 122

0 120

0.139

0.170

0.175

0.184

0.233

0 391

401

0.391

0.329

0.179

0.146

0.171

0.259

0.341

0.344

150

0.237

0.226

C218

0 1S2

0.153

0.130

:C97

C CCO

0.125

0.137

0 133

'J 10°

0.279

0 271

0 241

C 177

0 133

0116

0.113

0.134

0.150

0.168

0 187

0 242

0 375

0 355

0.338

0.205

0 152

0 M90.166

0.185

0.189

0.209

0 265

0 406

0 455

0.445

0.367

0.219

0.181

0.188

0.278

0.365

0.368

200

q (kW m-2)

400 600 800

Heat Transfer Coefficient (kW m-2 K-2)

0.269

C252

C238

0 218

0.182

C 157

C \?.O

•J126

0 155

C 168

C 162

Z 1X9

0 307

C295

0 25,-

0 198

0 155

0 140

0 13/

0 156

0 170

0 188

0 211

0 25/.

0.385

0 3/0

0.354

0.226

0. iS9

0 iG'i

0 179

0 199

0 205

0.228

0.289

0.422

C 472

0 463

0.389

0.252

0.215

0.214

0.283

0.372

0.376

0.400

0 3-38

0 347

0 320

0?34C :-84

C ?o4

o.r'i-g0.279

0 288

0 236

c?e.3

0.414

0 382

0 3-43

C2S3

0 25?

0 235

0.23C

0 2b2

Q2;'

0 2S3

C:i45

0.447

0.420

0.398

0 306

C;?5£

0 r?.6

0 24!

0 ?b3

0 264

0.29/

0.361

0.480

0.503

0 488

0.456

0.350

0.304

0.270

0 316

0 379

0 382

0.531

0 484

0 4C3

0 44'J

0 4??.

C410

C 394

0 385

0 4^3

C 3£'?

0 522

0 471

0^23

0 3':

0.326

0 322

0 31b

C 219

C 32b

C306

0 3SS

C 4j'

0 547

0 4G5

0 445

0 308

C 'iC'S

C ? 3 ••

0 2ii9

0 31?

0 330

0 368

C £33

0.543

0 553

0 535

0 481

0 383

0.3?8

0 317

C 353

C4C3

0.-33

0 654

0.602

o.becC5'iC

0 US

OK.C -24

0 518

0.5?V

0 532

Oi:Zd

C £ I9

0 628

0 5r«

CiCO

C.-ibb

0 i.2?.

C iZC

0 39?;

O33r5

Q4!H

0 440

0 47?.

C 515

0 644

C 57v

0 494

0 41"'

0 3/1

C JC-'J

0 3b;'

0.36'

C.3S1

C435

az?.0 6:5

0 580

0.6C3

ObbO

C 44C

0 33-

0.3S4

C3S5

C 440

C 4S •

1000

0 303

0 72G

0 ,7:4

C 68?

as '40 66/

Cfjf-4

C £4=

G 65"

0 66!

C3C0

:G49

0 7?u

0 643

CiS4

C5?.'

C41'9

0 4Sfr

0 4'6

0.4;'.'

0 4S4

0 513

0 51-3

C i-3-3

C /23

C640

G 47?

0 47b

0 414

0.412

0 4?3

0 443

0 430

0 5S4

0 faO2

0.755

0 672

0 635

0.489

C437

C411

0 44?

C 8f;

0=324

2000

1 502

1 345

1 324

: 32'

1 31c1 315

' ?C7

-.3Z3

1 3Cii

: 5Cb

' 30C

' 23S

1.20"

1 0bJ

C06'

C 004

0 6T2

0 662

0 5'.;/

0 55-1

0 6/4

C 'i'C'i

0 942

0 Si;"

* '54

C 954

GS4U

C /4£

C53?

C 'JS5

0 682

COS?

0/32

0 754

0 3/1

C 9HC

: "8?

' 012

0 853

0 720

C 6b?.

C.64S

G 5^

0 .'26

C50C

3000

?'S31 .E'b4

1 934

* GJI

. 929

'• S2J

• 920

: sis' S??

' <5OS

• 9 3 '

• 936

1 /Oc1 i77

' 3b'

1.2i"6

1 ?.i~S

1 ?.<r.C

' ;Jf:7

\?!b'

J y?3

• 31?

'. 3rib

' 40^

1 33S

! :=8

' 03S

0 9'8

c -jiy

0.9U&

C ii~d

;.O33

1.1101 "H&

',.25-1

i 62b1

' 3G:"-

• '49

0 081

0 925

CX4

0S16

0 3-T5

;.o.'3

191

p

(kPa)

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100100100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

G

(kgm-2s-1)

200

200

200

500

500

500

500

500

500

500

500

500

500

500

500

1000

1000

1000

1000

10001000

1000

1000

1000

1000

1000

1000

1500

1500

1500

1500

1500

1500

1500

1500

1500

1500

1500

1500

2000

2000

2000

2000

2000

2000

2000

2000

Xe

(-)0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.050.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

50

0.319

0.496

0.804

0.296

0.277

0.263

0.149

0.151

0.215

0.346

0.478

0.595

0.904

1.425

1.997

0.300

0.252

0.188

0.1620.2090.319

0.539

0.894

1.469

2.345

3.192

3.669

0.341

0.265

0.190

0.173

0.262

0.464

0.867

1.666

2.678

3.846

4.782

5.174

0.381

0.286

0.197

0.187

0.343

0.664

1.302

2.544

100

0.349

0.505

0.814

0.331

0.357

0.295

0.179

0.179

0.232

0.386

0.510

0.617

0.908

1.429

2.003

0.333

0.281

0.231

0.1850.2340.349

0.565

0.904

1.459

2.321

3.174

3.680

0.371

0.291

0.214

0.197

0.282

0.478

0.874

1.650

2.641

3.808

4.765

5.189

0.409

0.312

0.222

0.210

0.358

0.672

1.297

2.511

150 200

q (kW m-2)

400 600 800


0.373

0.523

0.823

0.362

0.417

0.334

0.215

0.204

0.240

0.398

0.531

0.639

0.916

1.432

2.009

0.365

0.310

0.267

0.217

0.2610.371

0.582

0.917

1.456

2.304

3.161

3.690

0.401

0.318

0.240

0.223

0.303

0.493

0.882

1.639

2.611

3.776

4.750

5.204

0.437

0.338

0.248

0.232

0.374

0.682

1.296

2.484

0.381

0.542

0.832

0.393

0.445

0.364

0.247

0.230

0.269

0.413

0.543

0.654

0.924

1.435

2.017

0.397

0.341

0.302

0.247

0.2890.395

0.600

0.926

1.445

2.274

3.135

3.702

0.430

0.347

0.268

0.251

0.327

0.510

0.887

1.618

2.566

3.730

4.727

5.219

0.464

0.364

0.275

0.257

0.391

0.690

1.287

2.442

0.444

0.6000.874

0.513

0.501

0.451

0.347:

0.314'

0.335'„_

0.449

0.574

0.700

0.964

1.444

2.040

0.526

0.451

0.394

0.345.

0.3660.473

0.646

0.963

1.454

2.235

3.099

3.745

0.551

0.453

0.367

0.332L0.389

0.567

0.923

1.606

2.495

3.636

4.682

5.278

0.582

0.467

0.371 _

0341. ,

0.453

0.733

1.296

2.372

0.504..

0.6560 316

0.630

0.562

0.493;

0.385

0.348

. .0.400

0.482. .

0.611

0.751

1.010

1.471

2.065

0.652

0.554___

_O464

0.419

JJ.4330.528_

0.688

1.016

1.480

2.219

3.079

3.786

0.672

0.555_

. ..0,461

.0,4.130.455;

0.620

0.961

1.613

2.453

3.571

4.646

5.336

0.701

0.566_

0.461

0.513,;

0.776

1.313

2.329

0,560

0.7110 9=8

0.741

0.647;-

0.572

0.44?

0.403

0.432

...0.523

0.653

0.804

1.060

1.506

2.091

0.776

0.657

0.553

0.4740.4700.581

0.735

1.066

1.516

2.216

3.065

3.825

0.793

0.656

0.551

0.490

0516

0.673^

1.004

1.628

2.428

3.520

4.620

5.388

0.822

0.665

0.543

0.494

0.57.3

0.823

1.334

2.296

1000

. .0,6170.7671 005

0.838

•0.728

0.616

0.480

0.450

0.472

0.S63

0.701

0.858

1.113.

1.549

2.123

0.890

0.751

0.628

0.533

0.5170.604

0.782,

1.122

1.566

2.244

3.080

3.861

0.910

_ 0.748'

0.622

0.543

0.561

0,71.7

1.052,

1.678

2.463

3.524

4.625

5.434

0.943

0.756

0.619

0.547

0.6180.866

1.377

2.327

2000

0.904

1,048

• riv

~ 1.341

1.131

0,927

0.745

0.6690.694

0.761

0.933

1.132

1.385

1.758'

2.277__

1.455

•I .2130.998

0.814

0.7490.822

1.011

1.402

1.820

2.382

3.141

4.042

1.493/

• 1.208

0.9810.814

0.793

0.944

.1-28.71.915;

2.616

3.544

4.635

5.681

1.546;

'-' 1.211

0^974

0.819

0.852

. 1.087.

1.5691'

2.459

3000

1 204

1.345• 4«^

1.818

1.524;

1-245

1.005

0.894;

0.904J

0.965j

1.170,

1.397]

1.643J

1.969J

2.438

2 , 0 . •

1 .G6''j1.357

1.C93O.P-'S1.0 iC

1.6'?

2.CW2.i>21

3.214

4.21 '•

2.073

1.66S1.350

1.101;

' 1.039

1.180,

1.5182.135:

2.748

3.548

4.637

5.928

2.140

1.664'

1.339

1.108;

1.102

1.314

1.75?

2.564

192

Xe 50 100 150 200

q (kW m-2)

400 600 800 1000 2000

(kPa) (kgm-2s-1) Heat Transfer Coefficient (kW m-2 K-2)

3000

100

100

100

100

2000 0.60

2000 0.80

2000 1.00

2000 1.20

3.863 3.815 3.7725.169 5.131 5.0976.178 6.167 6.1566.638 6.654 6.669

3.714 3.5905.054 4.9486.143 6.1106.685 6.747

3.4994.8636.0856.809

3.4284.7936.0826.871

3.4394.7876.0806.926

3.465 3.4654.731 4.6526.079 6.0667.208 7.496

100

100

100

100

100

100

100

100

100

100

100

100

3000

3000

3000

3000

3000

3000

3000

3000

3000

3000

3000

3000

-0.20-0.10-0.050.000.050.100.200.400.600.801.001.20

0.4180.2990.2030.2300.5481.0852.1104.0035.7987.4608.7829.477

0.4460.3260.2280.2500.5581.0872.0963.9665.7567.4328.7789.492

0.4730.3530.2530.2700.5691.0902.0863.9315.7157.4068.7749.506

0.5020.3800.2790.2930.5801.0902.0693.8905.6717.3798.7699.522

2.2443.5065.0186.8928.731

10.066.. 10.373

100

100

100

100

100

100

100

100

100

100

100

100

4000

4000

4000

4000

4000

4000

4000

4000

4000

4000

4000

4000

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

0.435

0.296

0.205

0.278

0.749

1.458

2.770

5.171

7.452

9.591

11.310

12.193

0.4640.3250.2310.2960.7571.4582.7595.1457.4229.569

11.30412211

0.4910.3530.2560.3150.7661.4602.7495.1207.3939.548

11.29912 225

0.5220.3830.2830.3360.7741.4622.7375.0947.3659.527

11.29112.239

0.634

0.489

0.378

0.413

0.816

1.474

2.711

5.012

7.270

9.462

11.277

12 2S5

0.7490.5900.4700.489,0.8611.4942.7094.9567.1909.409

11.26812.354

0.8620.6890-558.

0.974

0.908

1.517

2.690

4.890

7.1189.361

11.26212.412

0.956;;1.5552.7034.8667.080

9.33711.25012.471

1.532" "

1.222 "fjtfef1.00? -1.387

1.7362.7704.7436.882

9.213

11.244

12 768

.1.448

2.823

4.6066.684

9.083

11.230

13 070

100

100

100

100

100

100

100

100

100

100

100

100

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

-0.20-0.10-0.050.000.050.100.200.400.600.801.001.20

0.458

0.285

0.208

0.334

0,943

1.798

3.360

6.2349.009

11.648

13.764

14.832

0.488

0.316

0.234

0.350

0.951

1.800

3.3566.221

8.989

11.62813.75414.845

0.5160.3460.2590.3670.9591.803

3.353

6.2098.970

11.609

13.74614.858

0.5490.3790.2870.3880.967

1.804

3.3496.199

8.954

11.590

13.734

14.872

0.6630.489

0.382

0.4601.004

1.820

3.342

6.1578.894

11.53213.71014.926

0.777

0.594

0.474"

0.534

1.045

1.840

3.337

6.1208.843

11.486

13.69214.982

0.8890.695

0.994 1.524

0.607,,1.0881.8623.3346.0858.795

11.446

13.67815.039

1.134'

1.896

3.347

6.060

8.75811.424

13.67015.096

s " 1.020 1.40®. .gjKis. . JJM8

3.4005.9358.576

11.314

13.66515.382

3.4395.805

8.403

11.201

13.658

15.670

100

100

100

100

100

100

100

6000 -0.20

6000 -0.10

6000 -0.05

6000 0.00

6000 0.05

6000 0.10

6000 0.20

0.505

0.277

0.212

0.387

1.117

2.112

3.940

0.535

0.310

0.238

0.402

1.124

2.115

3.939

0.565

0.341

0.263

0.418

1.132

2.118

3.938

0.599

0.375

0.291

0.438

1.140

2.120

3.935

0.719

0.493

0.387

0.506

1.174

2.137

3.935

0,9600.605i:0.480

0.5771.212

2.155

3.937

0.569*0.6471.251

2.1763.942

1.076P0.807.

0.7051.2902.2033.953

1-.658

• 1.285

1.008';

1.4912.3344.010

Z2S01.78?

1.708

2.480

4.064

193

p

(kPa)

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

200

200

200200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

G

(kgm-2s-1)

6000

6000

6000

6000

6000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

0

0

00

0

0

0

0

0

0

0

0

50

50

50

50

50

50

50

50

50

50

50

50

100

100

100

100

100

100

Xe

(-)0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.050.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

50

7.335

10.619

13.716

16.172

17.406

0.546

0.267

0.217

0.447

1.284

2.421

4.522

8.430

12.204

15.739

18.520

19.935

0.198

0.196

0.1800.161

0.120

0.089

0.050

0.066

0.099

0.102

0.094

0.068

0.236

0.229

0.195

0.149

0.108

0.087

0.087

0.111

0.127

0.131

0.144

0.212

100

7.323

10.596

13.692

16.160

17.419

0.577

0.301

0.242

0.461

1.292

2.425

4.521

8.416

12.179

15.714

18.509

19.947

0.222

0.220

0.2040.181

0.142

0.112

0.077

0.079

0.126

0.129

0.124

0.097

0.264

0.253

0.223

0.172

0.133

0.113

0.113

0.144

0.152

0.154

0.165

0.231

._

150 200

q (kW m-2)

400 600

Heat Transfer Coefficient (kW

7.312

10.575

13.669

16.150

17.432

0.608

0.333

0.267

0.475

1.300

2.430

4.520

8.403

12.156

15.689

18.498

19.959

0.252

0.244

0.2350.209

0.172

0.148

0.119;

0.116...0.150

0.162

0.155

0.128

0.290

0.279

0.253

0.194

0.153

0.137

0.147

0.170

0.183

0.196

0.198

0.250

•

7.300

10.556

13.647

16.137

17.446

0.641

0.368

0.295

0.495

1.309

2.433

4.517

8.390

12.135

15.667

18.486

19.973

0.282

0.268

0.2560.235

0.201

0.175

0.147

.0..143

0.174.

0.186

0.183

0J59 .

0.318

0.302

0.271

0.217

0.176.

0.158

0.165

0.185

0.191'

0.203.

0.220

0.272;

• • •

7.266

10.491

13.578

16.103

17.500

0.771

0.492

0.394

0.563

1.347

2.454

4.518

8.353

12.066

15.592

18.449

20.027

0.408

0.384

0.3630.338

0.313

0.302

0.281

0.274

., 0.297

0.306

0.304

. 0,285

0.421

0.389

0.354'

0.305

0.271

0.251

0.2510.260 .

0.273

0.288

.. P.-30.5

0.352

.:

7.238

10.440

13.524

16.077

17.557

0.904

0.612.

0.492

0.635

1.388

2.478

4.522

8.326

12.015

15.533

18.418

20.084

0.534

0.498

0.479'0.458

0.440Q.428

0.410

0.404

0.418

0.425

0-424

0.409

0.524

0.478

0.4330.383

0.350

0.335

0-325

0.328

0.342

0.362

0.391

0.435

. •

800

m-2 K-2)

7.214

10.395

13.476

16.054

17.614

1.038

QJ29.0.588

0.708

1.431

2.504

4.529

8.304

11.969

15.479

18.390

20.141

0.662

_0.616

0.5960-576

. 0.5610.552

0.5380.531

0.541

0.547

0.548

0.533

0.625

0.566

0.515

0.467

0.4360.421

0.4070.406

0.420

0.444

0.475

0.518

" - . •

1000

7.200

10.369

13.453

16.052

17.671

1.175!

, .0-838

0.674...

0.773

1.476

2.537

4.547

8.299

11.947

15.449

18.379

20.198

0.795

Q.741

0,7210.704

0.691

0.682

aess0.662

0.671

0.676

0.675

0.664

0.719

0.649

0.593

0.543

0.511

0.498

0.483

„ 0.482

0.4S7

- 0.521 •

0.554

, 0.597

• :

:

. : .

.•

2000

7.132

10.239

13.340

16.043

17.959

"7.8601.382

1.109

1.110:

1.703

2.698

4.630

8.275

11.840

15.302

18.319

20.488

1.462

' 1.3661.350•1.3431.338

1.334

1.324

1.3181.323

1.324

1.321.

1.317

1.178

1.058

0.972

0.913

0.878

0.86S0.858

0.853

0.870

0.897

0.938

0.983

• •

3000

7.068

10.116

13.220

16.019

18.251

2.<S4

1J.'\'1.£>£9

1.S51

2.87 3

8.250

11 .-VL3

15/5318.24520.V83

2. 2 '

1.LE,

1 . ! ; • • - '

1.!.6=.

1.C---'.-

1.L .'

t.-i'O

1.--V.

1. • • ' •« :

1.-6-V

1.--:.a

1 • - • ' • > -

1.6571

1.482:

1.367

1.301:1.267

1.2561.251

1.243

1.262!

1.293J

1.343

1.38&;

•

194

Xe 50 100 150 200

q (kW m-2)

400 600 800

(kPa) (kg m-2 s-1) Heat Transfer Coefficient (kW m-2 K-2)200

200

200

200

200

200

100 0.20

100 0.40

100 0.60

100 0.80

100 1.00

100 1.20

0.1260.1510.1690.1730.2180.382

0.1610.1920.1950.2000.239

0.1920.2180.2260.2360.271

0.2060.233C.2340 2420.29!

0.2J:s

0 ,\>37

0312

0 363

0 3C30 321C 337C3/2C 43-

0 JOG

0 3/40.3-J5

0 433

C (3C2

1000

0i?80 4020 4LC-

2000

0 684

o beeo r;:--C7S2

Cc!i:

C M '

3000

0 9C5!

' Cb9

200

200

200

200

200

200

200

200

200

200

200

200

200 -0.20

200 -0.10

200 -0.05

200 0.00

200 0.05

200 0.10

200 0.20

200 0.40

200 0.60

200 0.80

200 1.00

200 1.20

0.3090.3000.2860.1560.1350.1520.2070.2390.2740.3080.4990.810

0.343

0.372

0.322

0.193

0.174

0.192

0.256

0.321

0.325

0.329

0.502

0.820

0.370

0.423

0.358

0.229

0.206

0.206

0.273

0.365

0.368

0.370

0.521

0.827

0.397

0 446

0.383

0.263

0.239

0.239

0 306

0.406

0410

C415

0 536

0 835

0 4930 4830 4550 3590.3220.2870.3520 4280 4350 4450 5950.371

0 585

C53-

0 484

0 -1C6

C3b-'

C33--

0.38/

0 42C

0 AA2

0 506

0 655

0.912

0.675

0 599

C5b;

C 453

0.410

o 38::

0 415

C46*

C £8G

0 713

0 955

0 752

C 6C4

0.40-i0.4280.46'0 5100 54-

0 767

1 C01

' -4?

G84'

o /?:.

1 bbii

1 3'i'

0 5b?.C5S"C /31-

OSSS

1 C401.232

0 967* f\ *» -i

v O •

• 152

1 332

200

200

200

200

200

200

200

200

200

200

200

200

500 -0.20

500 -0.10

500 -0.05

500 0.00

500 0.05

500 0.10

500 0.20

500 0.40

500 0.60

500 0.80

500 1.00

500 1.20

0.325

0.289

0.261

0.171

0.188

0.219

0.311

0.461

0.593

0.921

1.428

2.016

0.359

0.332

0.292

0.202

0.220

0.267

0.367

0.488

0.610

0.922

1.430

2.020

0.389

0.400

0.332

0.230

0.240

0.282

0.388

0.526

0.640

0.929

1.434

2.024

0.418

0.441

0.362

0.260

0.263

0.314

0.444

0.574

0.665

0.931

1.436

2.028

0.528

0.505

0.453

0.361

0.350

0.398

0.486

0.599

0.710

0.973

1.461

2.046

0.638

0.563

0.496

0.425

0.424

0.480

0.535

0.634

0.762

1.021

1.485

2.068

0.740

0 5cG

0 43S

0 492

0 549

0 670

0 817

1 075

1 519

2 093

0.830S-

0 726! '"•'

0 614

0 533

0 484

0 53?

0 bS--"

C716

0 87C

1 127

1 562

2 125

0219

C /5"

0 552

0 .'C-'

C7C6

CE3C

• 143

1 40?

• 773

2 273

; 1.740

- '/?••

I 030!

G.892

O.ZZo

O-Jbe1 :f,S

"• 404

'• 80S

' 03:;

2 <i;is

200200200200200200200200200200200200

100010001000100010001000100010001000100010001000

-0.20-0.10-0.050.000.050.100.200.400.600.801.001.20

0.3400.2820.2530.2100.2640.3350.5470.9131.5062.4263.2973.703

0.3710.3080.2650.2380.3010.3700.5810.9171.4942.3953.2723.713

0.3990.3330.2960.2680.3360.4040.5980.9381.4842.3733.2533.723

0.4300.3600.3250.3000.3690.4530.6220.9521.4692.3363.2203.735

0.5460.4630.4250.4230.4960.5980.6750.9741.4732.2833.1683.775

0.661 0.7750.561 0.6630.539-;:i"

0.881 0.753' 1-20Q

1.9331.642

: 0-7.68

1.02

0.799JC

1.577 1.836,-^2.(388.2.267 2.411 2.5573.100 3.178 3.2463.886 4.056 4.223

200

200

200

200

200

1500 -0.201500 -0.101500 -0.051500 0.001500 0.05

0.3940.2980.2260.2130.304

0.421

0.321

0.248

0.237

0.328

0.4470.3450.2720.2680.360

0.4720.3700.2980.2960.391

0.5780.4700.3850.373;0.442

0.683 0.7900.567 twJ16630.474 — # : ^ 2 '

'i|?442"v- Q. 040.493*"

0.897 1.427-vg0.752-'-"T.W:"

..0.556'.. . 0:820.-- f.'tqq0,577 ~ llSGOV 1.037-

195

p

(kPa)

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

200

G

(kgm.2 8-1)1500

1500

1500

1500

1500

1500

1500

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

30003000

3000

3000

3000

3000

3000

3000

3000

3000

3000

3000

4000

4000

4000

4000

4000

4000

4000

4000

4000

4000

4000

4000

5000

5000

5000

5000

Xe

(")0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

50

0.479

0.892

1.704

2.760

3.994

4.943

5.215

0.446

0.328

0.225

0.208

0.355

0.680

1.332

2.613

3.998

5.374

6.384

6.685

0.5070.357

0.239

0.250

0.562

1.115

2.169

4.134

6.023

7.768

9.080

9.544

0.553

0.367

0.247

0.298

0.773

1.506

2.862

5.357

7.753

9.996

11.701

12.284

0.588

0.364

0.253

0.355

100

0.492

0.895

1.685

2.715

3.948

4.920

5.231

0.471

0.352

0.249

0.230

0.371

0.687

1.325

2.574

3.941

5.329

6.368

6.701

0.5310.382

0.264

0.270

0.571

1.114

2.153

4.092

5.973

7.733

9.070

9.558

0.577

0.395

0.272

0.317

0.780

1.504

2.848

5.326

7.715

9.966

11.689

12.297

0.614

0.394

0.278

0.371

150 200

q(kW

400

m-2)

600 800


0.511

0.902

1.672

2.681

3.909

4.900

5.246

0.495

0.376

0.273

0.253

0.388

0.696

1.323

2.543

3.891

5.287

6.353

6.717

0.5540.406

0.287

0.289

0.581

1.112

2.141

4.052

5.924

7.699

9.061

9.572

0.600

0.420

0.296

0.335

0.787

1.503

2.835

5.296

7.678

9.937

11.679

12.310

0.638

0.422

0.302

0.388

0.529

0.903

1.643

2.627

3.853

4.871

5.262

0.518

0.400

0.299

0.278

0.405

0.702

1.310

2.493

3.824

5.235

6.334

6.733

0.5760.432

0.313

0.312

0.590

1.113

2.119

4.003

5.869

7.661

9.048

9.586

0.623

0.448

0.322

0.356

0.793

1.497

2.817

5.262

7.640

9.905

11.66312.324

0.664

0.452

0.330

0.4C9

0.598

0.939

1.628

2.543

3.738

4.806

5.321

0.617

0.494

0.390

0.354

0.460

0.740

1.316

2.413

3.679

5.104

6.282

6.795

0.6710.524

0.403

0.391

0.640

1.130

2.086

3.880

5.712

7.547

9.014

9.641

0.711

0.541

0.412

0.433

0.833

1.504

2.780

5 :S1

7 516

9 836

'.: 623

'2 3V9

C 75S

0.551

0.421

0 4S2

0.649

0.976

1.625

2.486

3.648

4.754

5.378

0.718

0.585,,..

... JMZT"

. -.Q,431

0.519..

0.783

1.327

2.353

3.568

5.000

6.240

6.855

0.7670.614

0.488

0.467..

0.690

1.153

2.061

3.781

5.582

7.451

8.983

9.699

0.799

0.630

0.498

0.509:

0.876

1.518

2.748

5 072

74109 /2C

11 537

'2.435

0 84-3

0.645

0.509

0.555

0.689

1.017

1.641

2.455

3.579

4.709

5.435

0.821

0.677

0.561

0.508

...0-582

0.831

1.348

2.319

3.483

4.911

6.203

6.915

0.865_ 0.702

0.571

05400.741

1.181

2.050

3.698

5.469

7.364

8.955

9.757

0.887

0.717

0.581

0.583

0.922

1.537

2.731

4.39S

7.312

9 640

i 1.554

12 491

0 931

0.736

0.593

0 630

1000

1.064....,

1.691

2.489

3.577

4.704

5.481

0.929r

0.764

O.S30

0.560

0.626

0.875

1.389

2.351

3.493

4.898

6.200

6.970

0.970-0.786

0-640

0-596

0.788

1.221,

2.076

3.694

5.439

7.329

8.949

9.817

0.979'

0.795.

0.651

0.642-

0.970',

1.575

2.7504 9"<4

7 263

9 :599

1- 547

i2=oC

1 024

0.664c t'isr.

2000

0-951-1 ,298

1.933..2.646

3.574

4.700

5.712

1.4661.198

0.976

0.829

0.859

1.09$

1.588

2.489

3.511

4.807

6.166

7.249

1.4921.205

0.989

0.881

1.027

... 1-417.2.185

3.639

5.256

7.135

8.907

10.117

1.436

1.188

0.998

0.943

.... .1-2J21.755.

2.818

4.830

7.004

9.379

11.493

12.842

1.467

1.211

1.021

3000

1.'-'J

1.&2i

2.7/9

3.53'4.66"

5.6^3

2.014

1-639

. 1.335;

1.114

1.10®

1.320

.....1.-77$'2.597

3.515

4.687

6.104

7.532

2,0191.628;1.349

1.183

1.277,

1-61?2.278

3.552

5.053

6.923

8.841

10.420

1,'JJ?

1.L.S-'

1.3^S

1 :/">/

1.1-J?2.855

4.c5b

6.T33

9.145

11.4,6

13.13=:

1W3

1.01.:

I.'il?

196

Xe 50 100 150 200

q (kW m-2)

400 600 800 1000 2000


3000

200

200

200

200

200

200

200

200

5000

5000

5000

5000

5000

5000

5000

5000

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

0.976

1.862

3.481

6.466

9.375

12.141

14.237

14.936

0.982

1.861

3.473

6.448

9.349

12.113

14.223

14.949

0.990

1.860

3.466

6.431

9.323

12.086

14.210

14.962

0.996

1.858

3.456

6.413

9.298

12.056

14.189

14.976

1.029

1.866

3.434

6.351

9.211

11.965

14.140

15.030

1.068

1.879

3.417

6.296

9.133

11.886

14.093

15.085

1.110

1.895

3.404

6.243

9.060

11.813

14.051

15.140

1.157

1.928

3.414

6.211

9.008

11.770

14.039

15.196

2.087'"

3.453

6.042

8.745

11.549

13.960

15.473

1-833

3.477

5.868

8.487

11.313

13.857

15.749

200

200

200

200

200

200

200

200

200

200

200

200

6000

6000

6000

6000

6000

6000

6000

6000

6000

6000

6000

6000

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

0.633

0.360

0.258

0.406

1.153

2.186

4.081

7.606

11.047

14.289

16.719

17.526

0.661

0.392

0.284

0.421

1.159

2.187

4.076

7.588

11.018

14.258

16.704

17.539

0.688

0.423

0.308

0.437

1.166

2.188

4.071

7.572

10.989

14.228

16.690

17.552

0.716

0.456

0.336

0.457

1.172

2.189

4.062

7.552

10.961

14.196

16.669

17.566

0.822

0.567

0.431

0.528

1.206

2.196

4.048

7.496

10.869

14.095

16.612

17.620

0.927

0.673

0.523

0.600

1.242

2.210

4.037

7.447

10.791

14.008

16.557

17.676

200

200

200

200

200

200

200

200

200

200

200

200

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

0.663

0.348

0.261

0.465

1.325

2.506

4.681

8.733

12.687

16.384

19.128

20.068

0.692

0.382

0.287

0.480

1.332

2.508

4.676

8.714

12.656

16.352

19.115

20.081

0.721

0.415

0.313

0.494

1.339

2.511

4.672

8.697

12.625

16.321

19.101

20.093

0.750

0.448

0.341

0.514

1.346

2.511

4.663

8.676

12.595

16.289

19.080

20.107

0.867

0.569

0.440

0.583

1.383

2.526

4.652

8.619

12.498

16.182

19.021

20.161

0.986

0.684

0.537

0.657

1.423

2.544

4.644

8.571

12.417

16.088

18.962

20.216

1.105

0.796^

0.631 ; |

0.731

1.466

2.566

4.640

8.528

12.344

16.000

18.904

20.271

1.232

0.900."

0.797i;

1.512

2.598

4.651

8.510

12.301

15.944

18.870

20.327

1.864

•1-420,;*s

i.%r1.137J

1.746*;:

2.754

4.702

8.413

12.085

15.653

18.678

20.608

2.501

2.908

4.740

8.305

11.864

15.350

18.464

20.891

500

500

500

500

500

500

500

500

500

500

500

500

0 -0.20

0 -0.10

0 -0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

0.246

0.233

0.214

0.198

0.173

0.152

0.122

0.124

0.147

0.155

0.148

0.118

0.272

0.257

0.238

0.221

0.197

0.176

0.150

0.145

0.173

0.182

0.177

0.147

0.299

0.283

0.266

0.247

0.226

0.211

0.186

0.178

0.194

0.209

0.204

0.178

0.439

0.417

0.401

0.383

0.369

0.358

0.338

0.328

0.340i

0.348?;

0.347

500

500

500

50 -0.20

50 -0.10

50 -0.05

0.276

0.258

0.299

0.279

0.323

0.300

0.346

0.322

0.436

0.4040.527

0.488

0.617:.

0.571"

197

p

(kPa)

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

G

(kgm-2s-1)

50

50

50

50

50

50

50

50

50

100

100

100

100

100

100

100

100

100

100

100

100

200

200

200

200

200

200

200

200

200

200

200

200

500

500

500

500

500

500

500

500

500

500

500

500

1000

1000

Xe

(-)0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

50

0.202

0.1570.142

0.'20

0.125

0 133

0 150

0 173

0 242

0 3C2

0 252

0 263

0213

0.163

0.130

0 115

0.1 OS

0.107

0.163

0 2'-7

0 4C1

0.342

0.321

0.303

0.216

0.162

0.122

0.148

0.172

0.180

0.293

0.506

0.827

0.407

0.361

0.307

0.227

0.210

0.188

0.245

0.377

0.543

0.975

1.556

2.058

0.454

0.398

100

0.225

0 ISO

C '65

C 143

0 i53

0 155

C'72

Z '93

0 25C

0 223

C334

0.286

0 2^2

0.191

0 158

0 156

0.148

0.131

0 193

0 264

0 412

0.369

0.343

0.322

0.238

0.197

0.158

0.182

0.234

0.238

0.311

0.511

0.831

0.437

0.386

0.345

0.259

0.255

0.242

0.275

0.384

0.549

0.973

1.540

2.055

0.482

0.422

150 200

q (kW m-2)

400 600 800


C.241

0 2 3

0 '?.9

C ' " '

C i ' " '

0 192

0 iC6

C220

C278

:S48C.324

C.293

0.252

0.2'4

0.179

C ' 35

0 13'

0 198

C 2 i 6

Q.233

0^24

0.392

0.362

0.334

0.248

0.220

0.185

0.195

0.264

0.313

0.344

0.529

0.834

0.462

0.412

0.378

0.286

0.302

0.310

0.328

0.415

0.551

0.970

1.530

2.053

0.507

0.437

C261

C 233

0212

0 189

3 194

C 21-

C.215

0 243

:.297

0 3^3

C.346C 31?

C 2~2C224

0.19S

C.I 86

C 203

C 223

0 236

C 202

0 435

0.419

0.386

0.357

0.275

0.241

0.208

0.214;0.282

0.349

0.368

0.543

0.836

0.492

0.439

0.405

0.318

0.333

0.360

0.392

0.452

0.554

0.958

1.509

2.040

0.536

0.454

0 340

C3I4

C.2C2

G2SS

0 ?CA

C 2 'S

C •>:-4

0 322

0 372

0.457

0419

0 3~7

c:s3c

0 2Sf:

C7- 'C

<y/A7:

C .V56

C 2 • '

0 3C50 371

O/iSS

0=03

C.460

0.416__0.358

0.326

0.291

.0.289

0.329!

0.387;.

0.429

0.597

0.860

0.588

0.519

0.493

0.440

0.452

0.457

0.464

0.519

0.656

1.007

1.508

2.039

0.632

C 529

0.4 IEfJ JS4

C 3~?

C242

0 33E

C 3L-4

0 37::

G&~Q

C43'

C542

0 491

G.OSE;

C JU3

0 3"'-"

0 2Z4

0 3:>

Coi8

C3'!-l

C-4 '

0 543

0 556

0.528

0.466

0.411

0.375

o.3ei0.3330.374

<W38

0.497;...0.656

0.897

0.681

0.599

0.533

0.539'

0.547

0.555i .

0.560^.

0.583

0.738

1.051

1.526

2.038

0.729

0.629

c.so:0 47 j

0 45/c 4? :

C*1?

C42E

C4C:!5

C 48R

C =?.'

0 624

0 b--'

Cu iJ

C^DS

0 4 1S

C3L4

C 3r5-C3C4

OSS'

0*4?

ciii:

C6C?

0.666

0.587

0.527

0.455

0.417

0.405

0.391

0.423

0.480

. .0.5690.720

0.944

0.769

0.679

0.585

0.642

0.548

0.560

. ...0.5.650.651,,

0.814

1.107

1.553

2.074

0.825

0 /18

1000

Ct73

C 549

J-;c

C 487

C5C4

G b2a

0 6C6

CGi?

C.o3J

Cb(:9

Gi 'T

C-.'2

C 44!"

C41fcC 41 •'

0 4L;'

C 4SS

coo;-

• 0.728

0.656

0,579

0.502

0.461

0.448

.0.4350.468

O.530

0-623

0.773.

0.991 _

0.842

0.747

0.642

0.591

0.568- 0.568

• 0.586

..._ 0-697

0.869

1.161,

1.598

2.110

0.916

0.803

2000

C S45

C ECs

C 5S::

G S6r:

C 6C3

C £-31

C953

' .03"

C '343

0 ."L-!3

0 W

0.^:9

0 6»?

C 6;'fc

G .'!•'.

C77'

C 84--'

C •)'.£

1.0480.954

0.843

0.743

0.684

0.666

0.657

0.698

0.781

O.S90

1.036

...1-221

1^3T

1.104

0.933

0.776

0.707

0.7200.767

0.944

1.162

1.43$

1.804

2.272!

1.381• ;-J2a

3000

1.33'

" 2r5i

• 2 = 1

' 22'd

• •>&$

' 2" 3

• 521}

' M^

- ? s •

i ;L-3

• c-:-;i C1b

Z 'S./0:-4J

0.3t4

' C63

i i£0|

' ??:;

1.402

1.27&

1.12811.005'

0.92S

0.908^

0.900J0.947'

1.052'

1.181;1.3251

1.614

1.44©

1.215

0.997

0.881

0.8970.956;

1.171;

1.427.

1.697

2.022

1.843:

' 542

198

Xe 50 100 150 200

q (kW m-2)

400 600 800 1000 2000 3000


500

500

500

500

500

500

500

500

500

500

1000 -0.05

1000 0.00

1000 0.05

1000 0.10

1000 0.20

1000 0.40

1000 0.60

1000 0.80

1000 1.00

1000 1.20

0.3480.2880.2910.3860.5670.9171.5872.6383.5623.792

0.3830.3230.3400.4140.5900.9241.5692.5923.5193.797

0.4000.3620.3970.4810.6230.9451.5462.5563.4843.802

0.4140.4020.4520.5310.6540.9621.5232.5053.4343.809

0.5340.5290.5720.6180.7111.0101.5252.4133.3253.824

0.5900.587!;.0.625E0.6940.7541.037

1.5292.3393.231

3.845

0.626..

0.665|;0.793

1.1051.554

2.297

3.1663.870

0.834|

1.161|1.6062.3223.1643.905

1.040

1.434

1.875:-

2.475

3.242

4.064

'1.073

0.789 "s»0.:9&4j

1:705;

2.6333.3094.227

500

500

500

500

500

500

500

500

500

500

500

500

1500

1500

1500

1500

1500

1500

1500

1500

1500

1500

1500

1500

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

0.5190.4070.3200.3080.3650.5350.9451.7892.9694.3695.3615.362

0.5430.4280.3400.3300.3940.5530.9481.7682.9134.3045.3175.339

0.5640.4470.3780.3770.4390.5770.9581.7562.8714.2475.2775.351

0.5870.4670.4050.4040.4690.6020.9601.7252.8064.1715.2275.366

0.6700.5520.4600.4550.4990.6440.9921.7072.6954.0015.0955.409

0.7271.0581.7082.5553.7324.8805.505

500

500

500

500

500

500

500

500

500

500

500

500

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

-0.20-0.10-0.050.000.050.100.200.400.600.801.001.20

0.5830.4380.3120.2760.4060.7311.4112.7794.3385.8996.9186.920

0.6030.4600.3340.2960.4190.7341.4002.7354.2685.8356.8866.890

0.6210.4790.3560.3300.4400.7411.3942.7004.2065.7776.8556.860

0.6400.5010.3810.3510.4550.7461.3772.6424.1225.7046.8186.853

0.7140.5790.4590.4100.4990.7811.3732.5463.9365.5136.7106.910

1.1191.6232.5573.6264.9976.3687.347

500

500

500

500

500

500

500

500

500

500

500

500

3000

3000

3000

3000

3000

3000

3000

3000

3000

3000

3000

3000

-0.20-0.10-0.050.000.050.100.200.400.600.801.001.20

0.6800.4860.3320.3160.6151.1922.3144.4646.6028.5659.8429.845

0.6970.5080.3550.3350.6221.1892.2964.4146.5358.5109.8189.820

0.7120.5270.3760.3520.6291.1882.2824.3686.4698.4569.7959 800

0.7250.5470.3990.3730.6371.1802.2544.3066.3948.3969.7639.7/0

0.7850.6200.4780.4500.6831.1912.2134.1536.1738.2069.6699 798

0.847

0.6920.5540.522..0.7301.209

2.167

4.018

5.9818.042

9.5799.848

0.9100.764

,0.628.

J-593;.;0.7791.2342.1613.9095.8157.8909.4959.902

0.988.-;..

0.837" .

0.694..-«

0.827p1.271,.2.1793.8925.7637.816

9.4549.960

3CS34 1.233

2.2583.7745.4587.4249.221

10 254

2.3253.6135.1166.9998.950

10 551

500 4000 -0.20 0.782 0.796 0.809 0.819 0.866 0.912 0.960 1.022L-4^225-__..!,

199

p

(kPa)

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

500

G

(kg m-2s-1)

4000

4000

4000

4000

4000

4000

4000

4000

4000

4000

4000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

50005000

6000

6000

6000

6000

6000

6000

6000

6000

6000

6000

6000

6000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

Xe

(-)-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.001.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

50

0.520

0.349

0.369

0.847

1.628

3.088

5.829

8.531

11.041

12.695

12.700

0.852

0.535

0.364

0.430

1.073

2.031

3.791

7.069

10.331

13.415

15.44515.450

0.904

0.541

0.372

0.481

1.264

2.389

4.456

8.320

12.174

15.786

18.126

18.130

0.922

0.528

0.376

0.544

1.453

2.739

5.106

9.548

13.980

18.090

20.713

20.720

100

0.543

0.373

0.387

0.851

1.622

3.072

5.790

8.474

10.988

12.669

12.680

0.867

0.560

0.387

0.446

1.076

2.024

3.775

7.038

10.285

13.364

15.41715.420

0.923

0.571

0.398

0.497

1.267

2.382

4.438

8.287

12.125

15.734

18.100

18.105

0.946

0.560

0.402

0.559

1.457

2.735

5.091

9.514

13.927

18.038

20.689

20.692

150 200

q (kW m-2)

400 600 800


0.564

0.394

0.403

0.856

1.618

3.058

5.752

8.419

10.937

12.643

12.650

0.881

0.584

0.410

0.464

1.081

2.018

3.761

7.009

10.241

13.315

15.38915.392

0.943

0.599

0.422

0.512

1.271

2.377

4.422

8.255

12.077

15.683

18.074

18.080

0.969

0.591

0.427

0.573

1.461

2.732

5.077

9.480

13.877

17.988

20.665

20.670

0.585

0.418

0.424

0.860

1.608

3.033

5.705

8.358

10.880

12.606

12.615

0.892

0.607

0.435

0.485

1.084

2.007

3.739

6.974

10.193

13.259

15.34615.350

0.958

0.626

0.448

0.533

1.274

2.368

4.399

8.215

12.025

15.625

18.031

18.040

0.988

0.620

0.454

0.593

1.466

2.724

5.054

9.440

13.823

17.929

20.625

20.630

0.657

0.498

0.499

0.892

1.602

2.990

5.571

8.163

10.693

12.501

12.591

0.943

0.687

0.519

0.555

1.109

1.997

3.690

6.865

10.034

13.081

15.23015.292

1.033

0.725

0.540

0.604

1.301

2.357

4.344

8.100

11.860

15.439

17.911

17.928

1.078

0.732

0.551

0.663

1.495

2.719

5.004

9.321

13.645

17.735

20.504

20.510

0.725

0.575

0.573

0.930

1.609

2.916

5.426

7.996

10.528

12.397

12.642

0.992

0.761

0.599

0.629

1.142

1.995

3.651

6.767

9.891

12.918

15.11115.342

1.108

0.818

0.628

0.679

1.333

2.353

4.296

7.995

11.711

15.266

17.786

17.979

1.167

0.834

0.645

0.739

1.530

2.719

4.958

9.212

13.486

17.552

20.372

20.561

0.791

0.649

0.645-..

0.973

1.624

2.913

5.337

7.839

10.369

12.299

12.695

1.042

0.832

0.676

0.703

1.180

2.000

3.620

6.676

9.754

12.763

14.99915.391

1.186

0.909

0.714

0.753

1.370

2.354

4.255

7.898

11.573

15.104

17.665

18.030

1.258

0.934

0.737

0.815

1.569

2.724

4.919

9.112

13.338

17.377

20.243

20.612

1000

0.856

0.712

.0,7.041.022

1.656

2.928

5.294

7.754

10.280

12.246

12.751

1.106

0.899

0-742

0.7S4

1.227.

2.029

3.617

6.619

9.659

12.663

14.93615.443

1.286

0.998

0.791'

0.816

1.412

2.376

4.248

7.840

11.474

14.991

17.585

18.081

1.364

1.030;

0.819

0.881.

1.613

2.747

4.908

9.048

13.233

17.245

20.146

20.663

2000

1.174

1.030

1.00?

1.-266

1.820

2.953

5.059

7.320

9.804

11.954

13.029

1.418

1.229

1.073

1,081

.,1.4632.169:.

3.596

6.315

9.175

12.141

14.58215.700

__ 1.768

1.4361.176

1.142

1.629-.

2.479

4.191

7.526

10.979

14.403

17.143

18.337

1.881

1.5021.236

. .. J.^301.840,

2.854

4.839

8.715

12.698

16.570

19.621

20.918

3000

1.504

1.360:1.323

1.518

... 1.8872.956

4.789

6.868

9.298

11.616

13.306

• 1.732

1.564!

1.416

1.412'

1.7032.305

3.564

6.005

8.687

11.588

14.17915.951

2.210

1.848

1.565,1.484!

... 1-837.2.554

4.095

7.180

10.470

13.792

16.664

18.588

2.376

1.8531.65$

1.595

2.052

2.919

4.707

8.318

12.127

15.869

19.066

21.167

200

Xe 50 100 150 200

q (kW m-2)

400 600 800 1000 2000

(kPa) (kgm-2s -1 ) Heat Transfer Coefficient (kW m-2 K-2)

3000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

0 -0.200 -0.100 -0.05

0.000.050.100.200.400.600.801.001.20

0.3290.2960.2700.2470.2280.2150.1760.1680.1910.2050.2010.169

0.3530.3200.2930.2690.2500.2380.2020.1850.2150.2300.2280.199

0.3780.3450.3190.2960.2770.2640.2320.2190.2360.2560.2550.229

0.4010.3670.3410.3200.3070.2940.2640.2470.2590.2790.2810.258

0.5070.4740.4500.4300.4200.4090.3820.3670.3790.3890.3930.378

0.6130.5790.5560.5390.5310.5220.497*

0.481 '•

0.488*'

0.7220.6890.6690.654§0.6470.638 s

0.502: 0.616

0.8390.810-;

0.794-

N0-73.7*."0.^43''

1-423'

-1*41 ^

1.372

1-

-2,042:2.0391

2.01CJ1.S' "

"2:003Z002!

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

50 -0.20

50 -0.10

50 -0.05

50 0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

50

50

50

50

50

50

50

50

0.3590.3240.2960.2680.2340.2030.1550.1440.1650.1800.2120.274

0.3810.3450.3150.2880.2540.2220.1840.1680.1850.2000.2310.289

0.4020.3650.3350.2980.2730.2450.2020.196•0.2140.2210.2490 305

0.4230.3850.3540.3160.2900.2660.220'0.212^

0.5050.463...0.4310.3970.373|0345^

0.242 0.317'-

0.269 0.345p§

0.321 0 391

0.587 0.669-0.542^0.621^0.508' 0.5S57[f

. 0.555'0.531

.. 0.736

0JS96.**

0.8C(7

jH#q.93d

0 542

0.573

0 618

0.940 s

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

100 -0.20

100 -0.10

100 -0.05

100 0.00

100

100

100

100

100

100

100

100

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

0.385

0.352

0.324

0.300

0.245

0.195

0.139

0.121

0.154

0.195

0.274

0.419

0.407

0.373

0.342

0.305

0.264

0.222

0.183

0.159

0.174

0.215

0.289

0.425

0.429

0.392

0.355

0.309

0.265

0.237

0.199

0.185

0.221

0.236

0.303

0.433

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

200 -0.20

200 -0.10

200 -0.05

200 0.00

200

200

200

200

200

200

200

200

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

0 439

0 406

0.37 i

0.325

0.260

0 178

0.136

0.156

0.245

0 345

0.544

0 79C

0 465

0.428

0416

0.345

0.283

0.222

0.185

0.236

0 279

0.363

0.54-'-

0.794

0 487

0 449

0 425

0.351

0.306

0.259

0.212

0.275

0.349

0 388

0.5c4

C7S8

0.511

0 475

0 441

0.357

0.325

0 27'

0.238

0.295

0.377

0 414

0.565

C8X

0 595

0 542

0 505

0.405

0.369

0.337

0 239

0 335

G 409

0 502

C622

0.8i4

0.667

0 604

0 541

•0.-457

0 406

03/'

0 331

Q2<~>

C 457

0 564

0 585

0 823

0/^0

0 867

G i": i 7

0 4a6

0 435

0 3D1

0.418

0.717

0.372

0.790

C71G

C ?43

O.bca

0.1) 1*

O.-i.'S

0.434

0.540COL-'.C •'•"!0.926

C »840 8J.G

0 80SC 739c bsa

C.GG3

C 534

0 733

C.faO*1 CAZ

' 'S i -

! i/S

i 07?;

0 L'Sf;

0 940

0 69!)C 9^8

' 'S31 33c

201

P G Xe

(kPa) (kgm-2s-1) (-)

q (kW m-2)

SO 100 150 200 400 600 800 1000


2000 3000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

500500

500

500

500

500

500

500

500

500

500

500

1000

1000

1000

1000

1000

1000

1000

1000

10001000

1000

1000

1500

1500

1500

1500

1500

1500

1500

1500

1500

1500

1500

1500

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

-0.20-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.600.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

0.5400.502

0.478

0.320

0.277

0.224

0.204

0.343

0.610

1.124

1.690

2.074

0.625

0.584

0.539

0.376

0.345

0.418

0.562

0.921

1.7222.941

3.921

3.924

0.677

0.604

0.504

0.409

0.430

0.615

0.999

1.866

3.225

4.866

5.938

5.940

0.706

0.586

0.462

0.403

0.496

0.821

1.511

2.962

4.762

6.585

7.630

6.965

0.5710.542

0.521

0.339

0.298

0.268

0.247

0.361

0.605

1.114

1.661

2.050

0.655

0.622

0.585

0.391

0.358

0.420

0.593

0.948

1.6942.864

3.833

3.878

0.702

0.628

0.538

0.425

0.444

0.597

0.997

1.857

3.159

4.761

5.837

5.840

0.728

0.608

0.486

0.424

0.507

0.823

1.495

2.922

4.678

6.490

7.560

6.974

0.5950.574

0.544

0.359

0.318

0.309

0.306

0.410

0.593

1.100

1.650

2.029

0.679

0.648

0.599

0.426

0.396

0.441

0.613

0.974

1.6592.797

3.751

3.857

0.723

0.646

0.563

0.458

0.480

0.617

1.004

1.853

3.107

4.666

5.740

5.745

0.747

0.627

0.507

0.448

0.529

0.825

1.487

2.889

4.602

6.402

7.493

6.983

0.6240.589

0.560

0.384

0.351

0.348

0.367

0.454

0.593

1.152

1.646

2.020

0.710

0.673

0.600

0.454

0.453

0.504

0.620

0.980

1.6272.707

3.642

3.833

0.752

0.706

0.628

0.519

0.533

0.669

1.012

1.839

3.030

4.541

5.620

5.624

0.770

0.658

0.552

0.488

0.553

0.825

1.467

2.840

4.512

6.302

7.415

6.993

0.7140.652

0.610

0.457

0.430

0-421 ]

0.441

0.552

0.682

1.154

1.576

1.918

0.799

0.724

0.631

0.570

0.568

0.592

0.679

1.030

1.5852.501

3.374

3.749

0.830

0.775

0.686

0.587

0.596

0.716

1.045

1.838

2.876

4.239

5.286

5.413

0.843

0.728

0.623

0.555

0.597

0.846

1.443

2.740

4.264

6.009

7.180

7.026

0.7990.717

0.637

0.500/

0.462

.. P-4570-480;,.,

0.594

0.733

1.156

1.507

1.861

0.886

0.791

0.685

0.576

0.569

0.614

0.743

1.251

1.5822.322

3.108

3.698

0.911

0.828

0.715

0.600

0.597

0.726

1.086

1.979

2.803

3.984

4.852

5.389

0.918

0.802

0.692

0.619

0.647

0.871

1.453

2.735

4.092

5.731

6.953

7.088

0.8760.785

0.687

0.542

0.503

0.498

0.660

0.796

1.159

1.509

1.925

0.972

0.866

0.736

0.630

G.S20

0.6541

0.813

1.307

1.5652.246

2.919

3.620

0.991

0.897

0.778^

0.663.

0.643:

0.771

1.126

1.980

2.679

3.870

4.638

5.251

0.994

0.874

0.758

0.679.

0.697

0.898

1.458

2.689

3.901

5.500

6.759

7.120

0.941_..0.848.

0.742

O.5S9

0.543

0.5360.572

0.710

0.866

1.166

1.571

1.975

1.055

0.945

0.797

0.671

0.650

. ..0-691

0.863;

1.365

1.6222.286

2.917

3.618

1.076

0.979

_ 0.840

0.707.

0.680

0.810

1-165,_

2.001

2.696

3.875

4.686

5.321

1.076

0.957-

0.823

0.728

0.737

0.937:

1.488,,

2.658

3.799

5.432

6.738

7.171

1.2911.1800.999

0.8200.732

0.734

- 0.791

0.S86

1.182

1-443

1.791

2.206...

1.475

1.341

1.105

0.886

,0.809

0.880

......1.1001.604

1.9262.432

3.130

3.950

1.501

1-384

1.146

0.928

0.8711.008

_ 1-3512.075'...

2.801

3.877

4.?""

5." '

1.«\

• 1.367

1.147

0.S64

0.948

1.135

, 1.S42

2.573

3.673

5.136

6.553

7.454

1.61 a1.490

1.265

1.051-

0.932

0.S29

0.993

1.21S,

1.457

1.719

2.045"2,459

1.88$

1.6601.408

1.111

0.990

1.07f

1.313

1.769

2.152,2.620

3.289

4.196:

1.«:»•:•

1.?3.-:

1>DS

.i.'CL-

1.C-'1

1-21'J

t.^b

2.KJ2.808

3.880A nnn

1.660

1.475!

1.215J

i.16S

1.326

ijpse2.410

3.395

4.736

6.240

7.6951

202

P G Xe

(kPa) (kgm-2s-1) (-)

q (kW m-2)

50 100 150 200 400 600 800 1000 2000 3000


1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

3000

3000

3000

3000

3000

3000

3000

3000

3000

3000

3000

3000

-0.20-0.10-0.050.000.050.100.200.400.600.801.001.20

0.7770.5930.4350.4180.7131.2982.4674.8437.3259.570

10.7959.915

0.7940.6140.4590.4380.7191.2992.4624.7967.2429.496

10.7579.930

0.8090.6330.4790.4560.7261.3002.4614.7527.1619.425

10.7209.946

0.8230.6540.5050.4820.7371.3032.4514.6997.0779.352

10.6749.958

0.8810.7240.5810.5540.7771.3212.4454.5356.7929.096

10.52710.024

0.9410.7950.6550.6250.8231.3542.4404.5016.6188.898

10.40410.084

1295' 1.651

2.3585-

3.820

5.641

7.819

9.668

10.483

3.3724.9897.0769.148

10.777

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

4000

4000

4000

4000

4000

4000

4000

4000

4000

4000

4000

4000

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

0.881

0.6250.4530.4770.9641.7663.3076.378

9.50312.35713.932

12.775

0.892

0.6470.4750.4940.9681.771

3.322

6.3509.428

12.27713.88312.737

0.9030.6670.496

0.512

0.9711.779

3.339

6.324

9.35612.19913.841

12 799

0.910

0.687

0.5200.5340.9791.783

3.347

6.2899.280

12.117

13 782

12.810

0.9510.7570.5970.6051.0041.813

3.406

6.1909.015

11.83513.60012.802

0.9910.8240.6700.6761.0431.8573.6756.1808.791

11.585

13.423

12.915

1.035

0.8890.741

0.746

1.0861.910

3.740

6.1738.554

11.361

13.253

12.972

1.087: 1.344

0.951 -1.261'

0.806. 1.129

1.131L.1.9143.7455.9548.427

11.166

13.13913.020

1.990-3.7505.2907.666

10.320

12.527

13.273

3 0904 7325 8839 469

11.8V5

'3.538

100010001000100010001000100010001000100010001000

500050005000500050005000500050005000500050005000

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

0.9690.6520.4740.5451.2192.2444.154

7.81711.549

15.028

16.95515.549

0.9770.6740.4960.5611.219

2.237

4.148

7.783

11.478

14.945

16.902

15.556

0.9S6

0.6950.5180.578

1.2212.2314.1437.750

11.40914.86616.85215.563

C.9G0

0.715

0.541

0.5971.221

2.219

4.127

7.709

11.338

14.777

16.780

15 572

1.023

0.787

0.622

0.6691.2382.2074.1067.576

11.09214.48716.57215 604

1.0570.8550.7000.7441.2642.208

4.093

7.460

10.873

14.22016.361

15 640

1.0940.9200.7750.8161.2972.2204.0917.346

10.66313.969

16.16515 676

1.1440.980:0.840K

0.879!

1.339,.

2.226

4.0527.221

10.576

13.78416.03515.724

2.291

3.8306.6099.688

12.844

15.333

15 982

2.3653.6085.9468.787

11.86314.572"6.190

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

6000 -0.20

6000 -0.10

6000 -0.05

6000 0.006000

6000

6000

6000

6000

6000

6000

0.050.100.200.400.600.801.00

1.050

0.6620.478

0.6001.4492.686

4.9649.252

13.628

17.695

19.894

1.059

0.687

0.5030.617

1.447

2.6664.926

9.195

13.55017.61219.848

1.068

0.709

0.5260.6331.4462.6484.8919.140

13.475

17.53119.802

1.0710.7300.5520.6561.4462.6264.8469.077

13.39717.44419.737

1.108

0.8090.6400.729

1.455

2.5664.7208.880

13.135

17.148

19.536

1.1490.8840.7250.8051.4672.5144.6078.696

12.894

16.87219.328

1.1960.9580.8070.8791.4812.4684.5048.521

12.66516.608

19.125

3.880

6.97110.517

14.25617.335

203

P G Xe

(kPa) (kgm-2s-1) (-)

q (kW m-2)

50 100 150 200 400 600 800 1000


2000 3000

1000 6000 1.20 18.238 18.248 18.258 18.269 18.311 18.356 18.400 18.442 18.659 18.874

10001000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

70007000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

0

0

0

0

0

0

0

0

0

0

0

0

50

50

50

50

50

50

50

50

50

50

50

50

100

100

100

100

100

100

100

100

-0.20-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

1.0740.647

0.483

0.674

1.671

3.087

5.695

10.637

15.679

20.296

22.726

20.886

0.531

0.428

0.373

0.335

0.329

0.315

0.245

0.220

0.251

0.276

0.280

0.244

0.545

0.458

0.410

0.372

0.344

0.309

0.219

0.173

0.201

0.231

0.270

0.329

0.561

0.484

0.445

0.407

0.374

0.315

0.206

0.133

1.0870.674

0.507

0.688

1.669

3.069

5.657

10.571

15.591

20.213

22.684

20.896

0.551

0.450

0.388

0.355

0.351

0.341

0.262

0.220

0.272

0.299

0.306

0.273

0.565

0.478

0.436

0.387

0.361

0.330

0.235

0.177

0.214

0.249

0.287

0.341

0.583

0.506

0.482

0.419

0.385

0.333

0.227

0.153

1.1000.700

0.531

0.702

1.667

3.051

5.621

10.508

15.507

20.130

22.643

20.906

0.572

0.474

0.412

0.379

0.368

0.354

0.304

0.258

0.300

0.324

0.331

0.302

0.584

0.498

0.453

0.403

0.370

0.337

0.271

0.211

0.235

0.267

0.302

0.354

0.604

0.527

0.492

0.421

0.386

0.346

0.263

0.183

1.1070.723

0.558

0.725

1.668

3.030

5.575

10.438

15.422

20.042

22.582

20.916

0.592

0.494

0.435

0.402

0.391

0.376

0.324

0.297

0.325

0.349

0.357

0.333

0.604

0.518

0.469

0.420

0.390

0.357

0.281

0.243.

0.259

0.281

0.315

0.363

0.625

0.549

0.504

0.430

0.394

0.361

0.270

0.206'

1.1570.813

0.650

0.794

1.673

2.969

5.440

10.204

15.123

19.731

22.386

20.960

0.686

0.595

0.539

0.509

0.500

0.487

0.441

0.415

0.433

0.441

0.457,

0.441'

0.682

0.596

0.545

0.496

0.466

0.429

0.352:

0.311

0.330:

0.369!

0.392:

0.436

0.704

0.619

0.569

0.489

0.441 _

0.407.

0.327

0.269

1.2080.897

0.739

0.869

1.682

2.913

5.310

9.980

14.848

19.439

22.179

21.004

0.780

0.695

0.644

0.614

0.606

0.595

0.556

0.529

0.537

0.540

0.558

,, 0.663

0.762

0.675

0.620

0.572_

0.542

0.500

0.420

0.381

0.4040.447

0.470

0.504

0.784

0.691

0.627

0.554-

0.506-

0.454

0.3570.324

1.2630.979

0.826

0.942

1.691

2.859

5.186

9.765

14.584

19.156

21.973

21.050

0.877

0.800

0.753

0.724

0.717

0.705

0.670

0.643

0.646

0.657

0.673

0.674

0.840

0-754

0.700:

0.651

0.621

0.577

0.492

0.450

0.476

0.511

0!635

,...0.566.

0.860

0.761

0.693,

0.622

0.574

0.516

0.414

0.376

1.3371.059.

0.901;

1.000

1.699

2.827

5.112

9.597

14.366

18.922

21.806

21.088

0.981'

0.915

0.874

0.849.'

0.843'

0.831;

0.795

0.768

0.772

0.781

0.796

0,796

0.902

0.826;

0.776

0.731

0.700

0.652

0.5620.518

0.544

0.581

0.60$

..J0.642.

0.914

......9.329'0,751

0.682

0.632

' 0.570

0.461

0.420

1.6951.452

. 1.284

1.310

1.740'

2.699

4.701

8.743

13.267

17.739

20.926

21.288

"""l502 '14881.483

; .-1.474".. 1.469

1.4571.4191.3971.3991.401 .1406.1,406

1.208

1.180

1.152

1.126

1.083.

1.019

0.901 :

0.844

0.874

0.919

0.968

1.010

1.193' 1.114

1.0410.978

• 0.918

•' 0,835

. 0.689

0.633

2.054

1JS1-

1.668!1.60S

.1-74.2=2.501

4.160

7.779

12.092

16.527

20.028

21.489

2T69Q2.0882.084i2.0822.078

2.Q65J2.0202.008:2.003:1.9981.996

1.997J

1.:

. 1 . •

1 . ••

1.1.'-

1.1 . •

1.

1..

1..1 . •

1. '

1,'-1,1, •

1.1.

\ : ••

0.

0.

204

p

(kPa)

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

G

(kgm-2s-1)

100

100

100

100

200200

200

200

200

200

200

200

200

200

200

200

500

500

500

500500

500

500

500

500

500

500

500

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1500

1500

1500

1500

1500

1500

1500

Xe

(-)0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

50

0.172

0 242

0 325

0.458

0.605

0.558

0.545

0.466

0.365

0.282

0.186

0.161

0.267

0.426

0.593

0 8'4

0.713

0.672

0.632

0.448

0.348

0.293

0.222

0.331

0.757

1.395

1.894

2.061

0.837

0.823

0.719

0.556

0.488

0.510

0.625

0.940

1.944

3.357

4.362

3.950

0.881

0.910

0.888

0.704

0.630

0.760

1 10/

100

0.183

0 259

C 33V

C457

0.628

0.600

0.610

0.486

0.384

0.307

0.217

0.219

0.300

0.452

0.594

0.802

0.740

0.719

0.667

0.463

0.373

0.328

0.266

0.379

0.779

1.393

1.853

2.018

0.868

0.861

0.729

0.536

0.471

0.509

0.624

0.938

1.912

3.240

4.212

3.889

0.911

' 0.940

0.899

0.705

0,631

0.764

1 133

150

0 199

0 275

0 3^8

0 459

0.650

0.616

0.616

0.488

0.400

0.339

0.253

0.256

0.325

0.483

0.599

0.793

0.762

0.743

0.681

0.476

0.389

0.360

0.313

0.408

0.780

1.394

1.841

1 985

0.893

0.886

0.730

0.547

0.481

0.515

0.665

1.035

1.881

3.132

4.065

3.827

0.936

0.967

0.929

0.717

0.643

0.765

1.140

200

q (kW m-2)

400 600 800


0 233

0 292

0.352

0 454

0.671

0.617

0.632

0.497

0.417

0.367

0.279

0.279

0.348

0.575

0.599

0.773

0.759

0.756

0.673

0.485

0.416

0.396

0.365

0.463

0.865

1.636

1.839

1.983

0.916

0.902

0.732

0.549

0.522

0.580

0.667

1.040

1.816

2.972

3.888

3.790

0.971

1.173

1.037

0.815

0.739

0.847

1.141

0 ?&'

0.395

0 435

0 522

0.754

0.683

0.677

0.539

0.458

0.409

0.331

0.353

0.433

0.695

0.700

0.796

0.848

0.804

0.705

0.534

0.480

0.466

0.461

0.590

0.863

1.473

1.683

1.768

1.011

0.958

0.733

0.569

0.565

0.638

0.732

1.162

1.653

2.509

3.289

3.497

1.062

1.200

1.074

0.881

0.801

0.884

1.167

C369

C*G8

0 504

0 561

0.826

0 748

0 690

0.533

0.503

0 403

0 3SS

0*15

0 48'

0.749

0.750

0.801

0.935

0.850

0.754

0.573

0.509

0.493

0 491

0 653

0 791

1.253

1 584

1 679

1 100

1 045

0 779

0.6 IS

0 5S6

0.664

0 857

1 738

1.740

2.346

2.843

3.303

1.150

1.205

1.113

0.896

0.805

0.886

1.347

0.426

0 490

0 5?8

C.fB

0.900

0 811

0 736

C625

0 =4S

0 493

0 404

0 420

0511

0 758

0 769

0 860

1 029

0.923

0 808

0 632

CM59

0^3

C558

0 779

0.797

1.255

1.599

1.776

1.189

1.089

0.833

0G6y

C537

0.713

1.000

1.740

1.742

2.311

2.622

2.978

1.233

1.208

1.133

0.942

0.843

0.906

1.439

1000

GAt">.

C541

0 L-S-

CS39

0-947,.,.

0 862?*

C 7S"7

0.677

0 bS7

0.536

0 447

0.443

0.1)61

0 i'-Z

0 82C

0 919

1 088s-

0.983

0 864

0 633

0 510

0 5P7

oece0.832

0.863

1.260

1.667

1.846

1.261

1 158

0 8S8

o ns0 576

0 e'49

1.052

1.840

1.841

2.367

2.776

3.053

1.306

1.278 S

1-177U0.971 "

0.873^"

0.940^

1.445"'

2000

C702

C .'8ii

0 £C7

C S3i

;. .1.19?

: C43

0.S34

CS4-

0 769

C3;-C

CSTS

C 704

" 01 =

• C.'G

' is:;

•-1 4ilP

1 3C •'

I 11?

oi'ie0 812

0 .'9.'

O.SL'-,

1 11?

' 1=j4

' 42'

' 764

2.117

1 531

" bOC1 Z?A

0 88C

C.95G

1 252

2.031

2.16C

2.541

2 356

3 687

1.680

Lin C"1\445 *;

3000

GSaS

' CE61 '-3LJ

• ?z?

?fpi34141

1.3C3

! ?35

' '0:

' C18

C&l?

G P^2

'. 0=3

' PCS

1 36S

• •-: G

4"70'i

' 504

" 3-2

•• til

'• 02LJ

• on

• 08?

• 3C8

1 5C:J

1 759

2.G2S

? 405

1 iuZ-

'.828

: 513

! M !

' 083

;. I-J6

1.44"

1 8d?

?'61

2.542

3 161

4.145

1..9g4t.skf

1.2«P?j"1.485

205

p

(kPa)

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

20002000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

G

(kgm-2s-1)

1500

1500

1500

1500

1500

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

3000

3000

30003000

3000

3000

3000

3000

3000

3000

3000

3000

4000

4000

4000

4000

4000

4000

4000

4000

4000

4000

4000

4000

5000

5000

5000

5000

5000

5000

Xe

(-)0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.050.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

50

2.021

3.644

5.597

6.787

5.642

0.873

0.798

0.692

0.621

0.689

1.030

1.752

3.326

5.491

7.734

8.768

7.189

0.897

0.722

0.5630.573

0.915

1.566

2.817

5.596

8.567

11.266

12.359

10.226

0.967

0.740

0.587

0.648

1.201

2.066

3.636

7.302

11.205

14.582

15.975

13.221

1.052

0.768

0.625

0.754

1.535

2.668

100

2.049

3.571

5.436

6.575

5.594

0.901

0.821

0.700

0.642

0.706

1.027

1.728

3.307

5.382

7.568

8.625

7.192

0.918

0.744

0.5670.585

0.928

1.571

2.847

5.547

8.460

11.158

12.308

10.268

0.981

0.764

0.607

0.663

1.205

2.089

3.753

7.315

11.088

14.466

15.909

13.239

1.060

0.792

0.645

0.765

1.528

2.664

150 200

q (kW m-2)

400 600 800


2.086

3.508

5.285

6.359

5.544

0.924

0.842

0.732

0.666

0.714

1.025

1.713

3.305

5.282

7.405

8.484

7.194

0.938

0.766

0.5950.605

0.930

1.581

2.883

5.507

8.361

11.056

12.260

10.310

0.996

0.788

0.627

0.678

1.207

2.116

3.898

7.347

10.975

14.354

15.845

13.258

1.070

0.815

0.665

0.778

1.521

2.659

2.120

3.407

4.982

6.049

5.503

0.955

0.914

0.961

0.836

0.801

1.023

1.704

3.304

5.153

7.215

8.317

7.199

0.958

0.785

0.6340.637

0.936

1.604

2.933

5.432

8.242

10.951

12.201

10.352

1.009

0.808

0.647

0.694

1.208

2.138

3.995

7.348

10.861

14.237

15.764

13.278

1.077

0.842

0.685

0.789

1.512

2.644

2.240

3.157

4.5435.279

5.231

1.044

0.980

0.970

0.919

0.853

1.020

1.703

3.303

4.795

6.663

7.826

7.209

1.036

0.867

0.7150.711

0.966

1.622

3.017

5.311

7.892

10.606

12.027

10.511

1.070

0.894

0.723

0.756

1.229

2.241

4.406

7.359

10.452

13.846

15.511

13.352

1.120

0.922

0.764

0.849

1.503

2.640

2.550

3.156

4.173

4.356

4.972

1.131

1.035

0.972

0.920

0.855

0.983

1.700

3.302

4.658

6.122

7.136

7.219

1.110

0.954

0.7980.778

0.995

1.785

3.463

5.309

7.674

10.291

11.832

10.677

1.127

0.976

0.798

0.820

1.240

2.527

5.655

8.060

10.241

13.481

15.229

13.434

1.163

0.991

0.839

0.913

1.508

2.639

2.550

3.028

4.165

4.170

4.451

1.215

1.104

1.006

0.922

0.862

0.973

1.600

3.300

4.349

5.867

6.755

7.147

1.183

1.033

0.8740.846

1.049

1.750

3.213

5.252

7.452

9.980

11.628

10.863

1.186

1.054

0.871

0.888

1.302

2.704

5.586

7.736

10.001

13.189

14.985

13.514

1.208

1.063

0.916

0.981

1.523

2.638

1000

2.555

3.020

3.895

4.168

4.569

1.286

1.179-

1.063,

0.945

0.894,

1-040...1.590

3.169

4.194

5.576

6.750

7.235

1.241

1.102: '

0.944: '0.905

1.088-1.708

2.906

4.782

6.934

9.790

11.532

10.912

1,232:

1.113

0.940

0.957

1-349:..2.547

4.982

7.096

9.261

12.881

14.785

13.544

1.248-

1.118;

0.982'-

1.045'

1.550

2.609

2000

2.556| .

3.019

3.794

4.165

5.418

1,656

1.560

1.347

1.13?1.074

..1J251.414J

2.7431

3.997

5.359

6.649

7.501

1.542

1.45812931.201

1.297

1.682;

2.421

3.951

6.054

8.601

10 335

10.972

1.473

1.419

1.287

1.28?

,1577

2.257-

3.660

5.510

7.973

11.410

13.661

13.698

t.452

- 1.401

1.311

,1,362

1.703;

2.481:

3000

2J88

2.951

4.074

5.012

5.814

2.C"?

1.i3<:

1-Okt

1.3'^1.249

1.?"^

1.543

2.1 e-i

3.154

4.483

6.223

7738

1.858

1.817J

1.6471.50&1.522;

' .t-514;1.800

2.703

4.681

7.329

9.697

11.152

1.723;1.731]

1.637J

1.626|

1.817;

1,9952.556

3.970

6.541

9.868

12.528

13.909

1.862;

1.694

1.643

1.682

1.8601

2.380

206

p

(kPa)

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

50005000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

G

(kg m-2 8-1)

5000

5000

5000

5000

5000

5000

6000

6000

6000

6000

6000

6000

6000

6000

6000

6000

6000

6000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

00

0

0

0

0

0

0

0

0

0

0

5050

50

50

50

Xe

(-)0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20-0.10

-0.05

0.00

0.05

50

4.818

9.135

13.665

17.764

19.451

16115

1.159

0.768

0.631

0.847

1.854

3.263

5.860

10.871

16.158

20.959

22.852

18.914

1.197

0.749

0.642

0.950

2.135

3.761

6.751

12.537

18.628

24.071

26.106

21.673

1.2230.845

0.661

0.534

0.518

0.510

0.413

0.351

0.405

0.435

0.433

0.383

1.2520.877

0.702

0.584

0.552

100

4.816

9.078

13.542

17.635

19.367

15.112

1.163

0.790

0.654

0.859

1.837

3.219

5.795

10.771

16.019

20.819

22.770

18.918

1.202

0.773

0.665

0.959

2.116

3.713

6.675

12.419

18.479

23.932

26.033

21.679

1.2230.853

0.668

0.545

0.530

0.542

0.4590.356

0.421

0.451

0.452

0.407

1.2520.885

0.712

0.595

0.563

150

4.814

9.020

13.423

17.511

19.285

16 109

1.168

0.811

0.676

0.871

1.821

3.176

5.733

10.676

15.884

20.682

22.689

18.923

1.208

0.797

0.687

0.969

2.097

3.666

6.602

12.304

18.334

23.794

25.959

21.686

1.2240.863

0.679

0.562

0.545

0.552

. 0.4790.396

0.445

0.470

0.470

0.431

1.2550.896

0.726

0.605

0.569

200

q (kW m-2)

400 600


4.812

8.957

13.303

17.376

19.178

18 109

1.168

0.829

0.702

0.892

1.808

3.129

5.657

10.572

15.752

20.545

22.589

18.930

1.210

0.815

0.713

0.988

2.083

3.616

6.516

12.186

18.198

23.658

25.869

21.696

1.2250.867

0.688

0.575

0.562

0.556

0.492

0.432

0.461

0.485

0.486

0.454

1.2560.898

0.730

0.613

0.581

4.810

8.714

12.868

16.927

18.851

16.108

1.193

0.906

0.788

0.949

1.752

2.973

5.433

10.224

15.272

20.041

22.248

18.957

1.235

0.898

0.800

1.038

2.015

3.437

6.237

11.758

17.678

23.145

25.548

21.728

1.2530.933

0.768

0.665

0.653

0.643

0.584

0.534

0.555

0.562

0.571

0.552

1.2860.960

0.793

0.676

0.641

4.809

8.618

12.490

16.535

18.52016 117

1.222

0.977

0.872

1.011

1.703

2.830

5.200

9.878

14.827

19.567

21.905

18.989

1.264

0.974

0.886

1.095

1.953

3.269

5.950

11.328

17.195

22.656

25.222

21.763

1.2830.993

0.847

0.753

0.739

0.727

0.675

0.633

0.644

0.645

0.656

0.650

1.3161.017

0.856

0.742

0.704

800

m-2 K-2)

4.805

8.445

12.136

16.166

18.226

'6 1:3

1.256

1.047

0.952

1.069

1.654

2.696

5.009

9.556

14.393

19.108

21.563

19.026

1.296

1.049

0.968

1.148

1.888

3.102

5.671

10.915

16.719

22.177

24.889

21.805

1.3301.070

0.937

0.852

0.838

0.824

0.773

0.734

0.743

0.751

0.761

0-764*1

1.3591.084

0.929

0.815

0.772

1000

4.656

7.902

11.558

15.803

17.983

16 154

1.296,

LHo"'1.016^

1.113s;..

i.6ia_2.623

5.000

9.447

14.069

18.732

21.294

19.053

1.337

1.118-

LOSS-

L I 88.,.

1.830L,2.987

5.514

10.589

16.300

21.774

24.604

21.821

1.403^1.17lJ1.0521

0.972p:i

0.958;**

°-944S0.892^

0.855;-

0.862

0.868j

^0,878*'

** 0.886

1.420

1.164;';'

1.012."

0.897;;;

0.851

2000

3.917

6.508

9.916

14.049

16.680

13 388

i.§oT'\L425 r ;

' X$$s< 1v34$V

,;f~L42$2.002;;

4.559

7.933

12.117

16.825

19.901

19.193

1.53©-]

1.461-;-:

.. 1-S41-V2.173^

4.658

8.776

14.219

19.728

23.141

21.910

1.757- •

.4,571

7*4 .-55^-"uSil

1.4S5J1.454^t.453%5

1.459^

•14?6....

1.718. <-

-t4|9 ;^" 1,29$"i-!L23f

3000

3.375

5.345

8.211

12.285

15.353

16 586

'* ~1.761

*1.665v-1.558!

i.ssd

îlool3.865

6.275

10.142

14.864

18.434

19.350

- 1 . 7 M

~'v'?i>.-'9' 1.58b

2.C142

3.730

6.929

12.112

17.650

21.63C

22.03C

- 1.08^.2/148;

-'--sBsd;~J?.14$"

2.128J

"'Modw.2.<M6j

3:2.032)¥§2.Q24i

^2 ;0i4l

. 1.99S• tM%

" 1.701)

1-614

207

p

(kPa)

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

50005000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

G

(kgm-2s-1)

50

50

50

50

50

50

50

100

100

100

100

100

100

100

100

100

100

100

100

200

200

200

200

200

200

200

200

200

200

200

200

500

500

500

500

500

500

500

500

500

500

500

500

1000

1000

1000

1000

Xe

(-)0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

50

0.531

0.411

0.313

0.324

0.350

0.405

0.465

1.269

0.899

0.736

0.627

0.588

0.563

0.423

0.291

0.290

0.351

0.467

0.500

1.2960.937

0.814

0.704

0.625

0.560

0.434

0.369

0.390

0.565

0.789

0.998

1.358

1.027

0.892

0.725

0.616

0.532

0.450

0.487

0.915

1.731

2.259

2.192

1.390

1.109

0.947

0.850

100

0.554

0.443

0.317

0.332

0.362

0.416

0.471

1.273

0.909

0.753

0.645

0.590

0.588

0.446

0.308

0.299

0.364

0.475

0.602

1.3030.952

0.860

0.730

0.650

0.562

0.434

0.390

0.413

0.582

0.790

0.982

1.371

1.053

0.937

0.766

0.665

0.589

0.495

0.530

0.935

1.707

2.185

2.145

1.407

1.116

0.985

0.914

150 200

q (kW m-2)

400 600 800


0.555

0.451

0.347

0.348

0.376

0.427

0.480

1.277

0.925

0.769

0.645

0.591

0.590

0.457

0.330

0.313

0.376

0.483

0.603

1.3090.967

0.871

0.730

0.650

0.563

0.434

0.391

0.423

0.611

0.793

0.975

1.384

1.085

0.959

0.769

0.667

0.590

0.497

0.535

0.949

1.687

2.136

2.101

1.423

1.144

0.984

0.871

0.556

0.452

0.365

0.366

0.390

0.445

0.489

1.281

0.926

0.774

0.651

0.595

0.592

0.458

0.345

0.340

0.397

0.510

0.605

1.3180.998

0.878

0.731

0.652

0.564

0.440

0.400

0.454

0.701

0.858

0.970

1.446

1.127

0.960

0.770

0.668

0.595

0.543

0.552

1.039

1.686

2.130

2.197

1.476

1.188

0.955

0.816

0.604

0.498^

0.420^

0.420

0.462

0.503

0.544

1.316

0.988

0.826

0.696

0.631

0.593

0.481

0.398:

0.387

0.488

0.568

0.649

1.3511.052

0.907

0.741

0.656

0.587

0.475

0-4401..

0.531

0.835

0.876

0.965

1.490

1.181

0.962

0.783

0.697

0.642

0.611

0.638

1.102

1.685

1.899

1.939

1.533

1.208

0.976

0.845

0.657

0.543'

0.469

0.471

0.527:

0.567

0.602

1.350

1.047

0.879

0.753

0.697

0.634

•0.501

0.421

0-433

0.550

0.623

0.686

1.3821.084

0.941

0.799

0.715

0.646

0.512

.JL448 .0.693

0.910

0.913

0.978

1.509

1.199

1.008

0.844

0.757

0.692

0.643

0.758

1.479

1.680

1.839

1.870

1.569

1.257

1.031

0.896

0.719,'

0.597

0.522

0.531

0.574

0.615

0.654

1.391

1.110

0.943

0.811

0.750

0.678

0:5340.45S

0.480

0.553

0.624

0.688

1.4161.140

0.982

0.833

0.747.

0.671

0.538

.0,484

0.716;

0.920

0.945

0.999

1.516

1.229

1.056

0.891

0.803

0.734

0.701 .

0.842

1.406

1.671

1.835

1.869

1.611

1.296

1.073

0.938

1000

0.793

0.659

0.581

0.5S8

0.641

0.6.85

0.725 •

1.446

1.179

1.011

0.875'.

0.809

0.731

0.572-

0.488

0.623

' 0,6010.676

0.744

1.4501.192

1.037

0.890

0.802

0.720

0.576

0.520

0.717

0.922

0.969

1.045

1.527

1.270

1.108

0.931'

_,_0.8_49:

0.787

0.744

0.879

1.346

1.655"

1.834

1.867

1.628

1.342

1.128

0.990'

2000

1.1500.959

0.861

6.895

0-949

1.008.1.067_

1.721.

1.52$

1-34$

1.188

1.098

0.990

0.754

0.642

0.717

0.817

0.921

1.014

1.6221.452

1-313

1.1701.071

0.966

0.784

0.702

0.828

1.071

1.158

1.230

1.613 .1.471

1.338

. 1.206

1.113

1.040

1.018

1.223

1,263

1-.5.84

1.806

1.865_

1.722;

1.580

•1.408

1.256

3000

1.506;

1.268

1.156

1.208

1.274

1.347:

1417]

1.i

1.J

1.i •1.]

1.;

1 . ; •

O . i ••••

OJ

OJ1.1 :

1.

1.:

1.7fcS

%:,-[•.

1 .!jt-C

1.-45r.

1 Mb1.2=4O.T'-i

O.£;-J

1.J4?

1.22c

I . J i f r

1.1.1 •

1 ; •

1 . -

1.

1 / "

1.

1 - •

1-

1 :

1, -

1.

1.

1_.

1. -

1-

1.

1 . '

208

Xe SO 100 150 200

q (kW m-2)

400 600 800

(kPa) (kg m-2 s-1) Heat Transfer Coefficient (kW m-2 K-2)

5000

5000

5000

5000

5000

5000

5000

5000

1000

1000

1000

1000

1000

1000

1000

1000

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

0.784

0.771

0.813

1.143

2.634

4.362

5.294

3.917

0.854

0.835

0.880

1.250

2.553

4.142

5.030

3.807

0.814

0.825

0.879

1.249

2.469

3.934

4.780

3.702

0.777

0.800

0.859

1.212

2.272

3.475

4.340

3.653

0.815

0.846

0.888

1.278

1.970

2.768

3.534

3.302

0.856

0.877

1.027

1.907

1.950

2.435

2.854

2.984

0.898

0 922

1 134

1.917

1.953

2.457

2.714

2.980

1000

0.945

0.959

1 199

1 993

1.994

2.461

2.823

2.830

2000

'• 2C:-i

• -is:

2.129

2.170

2.665

2.825

3000

• £ 3 '

? 130

?330

2 700

2 826

2 920

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

1500

1500

1500

1500

1500

1500

1500

1500

1500

1500

1500

1500

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

1.377

1.206

1.156

1.016

0.932

1.051

1.453

2.767

5.012

7.450

8 486

5 807

1.395

1.229

1.172

1.055

0.980

1.085

1.452

2.742

4.816

7.109

8 100

5 890

1.412

1.250

1.193

1.058

0.982

1.092

1.450

2.732

4.634

6.779

5 576

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

1.361

1.145

0.979

0.870

0.953

1.427

2.463

4.617

7.503

10.475

11.389

7.822

1.380

1.166

1.027

0.882

0.935

1.398

2.397

4.493

7.211

10.075

11.056

7.731

1.397

1.184

1.034

0.902

0.936

1.376

2.339

4.385

6.928

9.673

10.720

7.627

1.416

1.245

1.209

1.066

1.044

1.361

2.231

4.223

6.339

8.882

10.264

7.565

1.488

1.305

1.265

1.113

1.090

1.331

2.020

3.854

5.132

7.310

9.103

7.203

1.555

1.342

1.265

1.114

1.092

1.218

1.954

3.711

4.627

6.015

7.393

6.472

1.622

1.400

1.266

1.130

1.095

1.183

1.789

3.420

4.399

5.876

6.917

6.082

1.663

1.452__

1.311|~

1.173}.-

1.132^;

1.180

1.661

3.190

4.423

5.734

6.900

6.302

1.884|;

2.W0.

1.70XJ

1.324

2.542.

4.175

5.353

6.248

6.262

3 300

4 449

5 573

5.764

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

3000

3000

3000

3000

3000

3000

3000

3000

3000

3000

3000

3000

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

1.351

1.087

0.870

0.851

1.267

2.242

4.143

. 7.909

11.861

15.562

16.380

11.068

1.369

1.111

0.922

0.872

1.239

2.207

4.073

7.674

11.508

15.174

16.160

11.142

1.386

1.131

0.932

0.887

1.226

2.178

4.019

7.441

11.152

14.773

15.935

11.221

1.404

1.151

0.935

0.895

1.188

2.100

3.946

7.123

10.458

14.037

15.676

11.320

1.476

1.227

1.008

0.936

1.209

2.025

3.663

6.298

9.224

12.388

14.842

11.524

1.543

1.302

1.089

1.014

1.248

2.020

3.599

5.736

8.044

10.745

13.363

11.720

1.611

1.375

1.163

1.079

1.287

1.966

3.210

5.450

7.943

10.565

12.890

11.574

1.654

1.430^

1.228;

1.142*

1.

1.8861

1.729*

3.025

5.091

7.588

10.501

12.786

11.563

2.186)

4.123

6.861

9.514

11.735

10.960

3.600

6.000

8.800

10.536

10.722

5000

5000

5000

4000 -0.20

4000 -0.10

4000 -0.05

1.354

1.042

0.868

1.369

1.069

0.885

1.385

1.094

C9C1

1.400

1.118

0.915

1.469

1.212

0.991

1.533

1.299

1.067

1.598

1.383

1.144

1.637

1.435

1.213

1.849""'

1.715 v

JJ4G

209

p

(kPa)

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

7000

7000

G

(kgm-2s-1)4000

4000

4000

4000

4000

4000

4000

4000

4000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

6000

6000

6000

6000

6000

6000

6000

6000

6000

6000

6000

6000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

0

0

Xe

(-)0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

50

1.008

1.805

3.124

5.526

10.502

15.613

20.057

21.028

14.335

1.375

1.008

0.908

1.218

2.390

4.047

7.059

12.883

19.006

24.437

25.547

17.443

1.419

0.957

0.940

1.410

2.907

4.848

8.329

15.079

22.379

28.851

30.083

20.558

1.447

0.928

0.974

1.589

3.343

5.600

9.595

17.260

25.708

33.145

34.395

23.579

1.570

1.073

100

1.007

1.773

3.092

5.503

10.276

15.289

19.801

20.895

14.361

1.386

1.036

0.921

1.205

2.341

3.985

6.953

12.634

18.706

24.199

25.414

17.430

1.426

0.991

0.954

1.395

2.857

4.792

8.248

14.865

22.065

28.573

29.928

20.547

1.452

0.963

0.987

1.570

3.291

5.531

9.498

17.097

25.454

32.882

34.237

23.573

1.545

1.064

150 200

q (kW m-2)

400 600 800


1.006

1.748

3.068

5.500

10.056

14.963

19.553

20.765

14.386

1.399

1.064

0.936

1.197

2.297

3.928

6.847

12.380

18.407

23.967

25.283

17.418

1.435

1.023

0.969

1.384

2.814

4.745

8.174

14.656

21.754

28.298

29.773

20.536

1.458

0.998

1.001

1.554

3.245

5.469

9.406

16.939

25.206

32.622

34.080

23.567

1.529

1.061

1.004

1.705

3.060

5.459

9.800

14.604

19.292

20.608

14.421

1.412

1.099

0.951

1.186

2.237

3.860

6.723

12.141

18.141

23.745

25.118

17.408

1.443

1.055

0.984

1.373

2.751

4.669

8.080

14.442

21.461

28.035

29.595

20.529

1.465

1.031

1.016

1.540

3.181

5.381

9.288

16.770

24.973

32.373

33.902

23.568

1.503

1.046

1.043

1.660

3.050

5.395

8.994

13.560

18.375

20.090

14.501

1.471

1.200

1.025

1.201

2.12'-

3.6676 29ri

11.180

16.860

22.909

24.565

17.379

1.488

1.172

1.053

1.371

2.649

4.551

8.075

13.773

20.157

27.014

28.928

20.509

1.498

1.153

1.085

1.527

3.067

5.199

8.964

16.223

24.117

31.412

33.222

23.557

1.487

1.079

1.08S

1.6'. 6

3 048

5 391

8 333

'2.126

17 326

19-154

14=90

1 527

1 287

1.C98

1.232

2 046

3 5015 r;'i8

10.161

15.666

22.156

24.043

17.407

1.531

1.277

1.125

1.396

2.598

4.475

8.700

13.185

18.996

26.079

28.250

20.483

1.534

1.262

1.159

1.546

3.008

5.071

8.666

15.734

23.356

30.486

32.502

23.544

1.466

1.106

' '46

' 522

3C45

5 390

7 951

11.865

16.331

18.827

K 5 2 6

1 58^

1 374

'. '.76

• 276

2 CCO

3 37?

5 <54*

9.465

14.856

21.327

23.491

17.411

1.575

1.377

1.199

1.433

2.583

4.433

8.068

12.840

17.853

25.171

27.569

20.475

1.571

1.364

1.235

1.580

2.984

4.979

8.452

15.268

22.584

29.617

31.785

23.538

1.472

1.157

1000

1 2*0

i 5^1

3 045

5.389

7.14?

10.425

16.219

'3.435

14.526

I 615

1.420

1 245

\.7At2 0^2

3 1V2

5 393

8.740

12.519

20.565

22.872

17.438

1.605

1.439__

1.270:

1.512

2.668

4.843

8.060

12.839

16.108

24.163

26.743

20.537

1.604

1.433

1.313

1.666

3.097

5.050

8.450

15.114

21.970

28.826

31.094

23.531

1.530__

1.250

2000

i 543

1 724

2 411

3 837

5.730

9 204

14 271

15 b271*273

1.797

: 702

1 5C5

1 .<3S4

2 '.582 734

4.309

7.023

10.641

17.478

20.299

17.522

1.764

_ 1 . 7 6 3 j

. 1 -64.11.929

3.207

5.097

7.747

11.109

13.980

20.612

23.655

20.513

1.773;-

1.772:

1.709

2.097

3.631

5.605

7.938

13.817

19.319

25.009

27.625

23.467

_ 1.803

1.700

3000

- $.-•£.

: «v.' 56?

2.151

3 679

7 200

'1 b.'*

'4.2-13

"4 285

' 97?

' <J8O

' 974

2 C " •'•

2:'18i

2 4 i : :

3.056

5.700

9.772

14.234

17.681

17.540

1.919J

2^70,

2.040'

2390

3.736

4.900

6.481

9.223

12.882

17.018

20.503

20.511

1.934)

Z10S!

2.139

2.589

4.154

6.057

9.120

12.389

16.765

21.198

24.031

23.451

2J601

2.158

210

Xe 50 100 150 200

q (kW m-2)

400 600 800 1000 2000


3000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

0 -0.05

0 0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

0.8380.6680.6380.6290.5630.5040.5240.5370.518

0.8340.6670.6420.6410.5830.5150.5290.5460.529

0.8330.6730.6530.6550.6050.5320.5340.5580.540

0.8270.6750.6550.6580.6070.5450.5470.5620.542

0.8820.7510.7340.7230.6690.6210.6240.6350.607

0.9320.8220.8050.7900.7390.6980.7050.7090.699

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

1.6251.1820.9530.8090.7830.739

1.6141.2161.0060.8750.847

50 -0.20 1.761 1.741 1.726 1.693 1.666

50 -0.10 1.185 1.175 1.172 1.153 1.173

50 -0.05 0.907 0.897 0.895 0.885 0.92150 0.00 0.718 0.718 0.727 0.730 0.765

50 0.05 0.683 0.690 0.696 0.699 0.73850 0.10 0.656 0.686 0.686 0.689 0.70350 0.20 0.556 0.596 0.596 0.599 0.60050 0.40 0.445 0.464 0.473 0.473 0.50050 0.60 0.403 0.409 0.417 0.437 0.479^4.0-51250 0.80 0.407 0.412 0.418 0.434 0.491 0.541'

50 1.00 0.471 0.476 0.486 0.544 0.580 0.614 ftfijif

50 1.20 0.527 0.533 0.541 0.577 0.614 0.659 0.716

0.528'"

0.5S2v:

1.648

1.279'-1.079

0.9550.926^

0.863r:

0.022

0.680

1.787 ,,..,1.890

*f.722

-42611

0.783 1.438;

700070007000700070007000700070007000700070007000

100 -0.20

100 -0.10

100 -0.05

100 0.00100100100100100100100100

0.050.100.200.400.600.801.001.20

1.872

1.244

0.946

0.754

0.748

0.746

0,658

0.477

0.361

0.381

0.536

0.665

1.8571.2380.9340.7610.7580.7570.7260.5090.3730.3810.5360.667

1.843

1.234

0.930

0.760

0.755

0.754

0.707

0.511

0.383

0.384

0.541

0.671

1.8151.2160,9170.7590.7500.7490.6270.5120.4150.4200.7200.776

1.8151.2310.9450.7870.7800.7610.6280.5140.4630.4680.7210.778

1.8161.2360.9810.8270.7940.765 _

°-629S0.516JH{5.475|. •0.526r"0.7230.780

1.818

1.313L

1.0840.9440.905'

1.817

1.264

1.027

0.882

0.844

JT781J;

o.7251' ...jyw0.793 ., 0.84? .1,114

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

200 -0.20

200 -0.10

200 -0.05

200 0.00200

200

200

200

200

200

200

200

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

1.9531.2680.9730.8330.7670.7280.6160.4890.4590.5681.0571 400

1.S451.2670:9940.8550.8060.7540.6290.5190.4670.5691.0571.39G

1.9401.2661.0200.8930.8130.7550.6300.5200.4940.5751.0791.39:

1.9381.2650.9780.8400.7800.7270.6060.5040.5890.7251.3101.390

1.937

1.298

0.996

0.840

0.790

0.732

0.616

0.542

0.622

0.782

1.315

1.276

1.8.'/'1.3241 0530 9230.8560 79"0 5480 5490 5980 8571.3251.195

',.8061.325' 0780.9370.8840 812

0 !i"20 752

0.893

1 3301.153

1.802

1 -359*"

1 127*

0.994

0.939

C857

C 59 =

C 559

C753

0 894

1.331

1.193

1^761,.

'MJ2q"1.373

' 283

: 2 1 /

' 083

0 cb3

C.712

C 64C

1 0C0

1 334

1 4C?

-1.717

! 2H"

C 'J88

CS73

1 i C •'

1.542

7000 500 -0.20 2.068 2.094 2.124 2.361 2.345 2.242 2.094 2.057 1.719 ' ?5C

211

p

(kPa)

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

70007000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

G

(kgm-2s-1)

500

500

500

500

500

500

500

500

500

500

500

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

10001000

1500

1500

1500

1500

1500

1500

1500

1500

1500

1500

1500

1500

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

Xe

(-)-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.001.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

50

1.297

1.022

0.832

0.727

0.684

0.655

0.644

0.940

1.749

2.647

2.483

1.993

1.351

1.105

0.892

0.846

0.885

1.001

1.331

3.068

5.149

6.0924.181

1.953

1.320

1.088

0.979

1.007

1.225

1.554

2.774

5.920

9.007

10.015

6.248

1.955

1.361

1.220

0.943

0.968

1.437

2.345

4.514

8.688

12.476

13.540

8.414

100

1.324

1.080

0.890

0.780

0.723

0.689

0.694

0.981

1.750

2.556

2.417

1.997

1.361

1.149

0.973

0.930

0.963

1.064

1.424

2.971

4.866

5.7614.028

1.944

1.321

1.146

1.012

1.027

1.252

1.602

2.713

5.666

8.540

9.506

6.080

1.944

1.434

1.342

1.001

0.971

1.411

2.314

4.391

8.298

11.953

13.060

8.249

150

1.347

1.114

0.931

0.814

0.744

0.690

0.700

0.990

1.754

2.475

2.356

2.000

1.384

1.202

1.018

0.950

0.964

1.075

1.427

2.864

4.6005.4423.884

1.933

1.330

1.198

1.020

1.022

1.229

1.597

2.688

5.421

8.082

8.997

5.914

1.936

1.433

1.322

0.985

0.970

1.381

2.239

4.288

7.915

11.427

12.566

8.069

200

q (kW m-2)

400 600 800


1.384

1.115

0.935

0.818

0.756

0.720

0.712

1.021

1.821

2.470

2.355

2.117

1.372

1.155

0.994

0.948

0.951

1.031

1.362

2.593

3.952

4.8053.771

1.93.

1.329

1.177

1.002

1.021

1.189

1.570

2.660

4.678

7.208

7.982

5.706

1.926

1.394

1.222

0.920

0.944

1.281

2.245

3.919

7.060

10.405

11.889

7.924

1.426

1.137

0.987

0.918

0.825

0.764

0.751

1.122

1.823

2.300

2.147

2.087

1.373

1.225

1.157

1.122

1.069

1.049

1.460

2.651

3.442

4.0223.241

1.343

1.208

1.088

1.112

1.242

1.568

2.659

4.428

5.505

6.173

5.158

1.900

1.393

1.234

0.939

0.979

1.264

2.105

3.611

5.528

8.352

10.014

7.204

1.444

1.238

1.138

1.055

0.916

0.820

0.896

1.596

1.853

1.969

1.853

2.009

1.380

1.284

1.261

1.217

1.124

1.162

1.943

2.256

2.633

3.0022.911

1.358

1.222

1.131

1.146

1.243

1.567

2.655

3.446

4.175

4.579

4.541

1.883

1.395

1.244

1.001

1.063

1.305

2.122

3.546

4.519

6.641

7.814

5.842

1.443

1.210

1.078

1.016

0.904

0.819;

0.895

1.494

1.850

1.967

1.850

1.926

1.379

1.283

1.236

1.194

1.139

1.224

1.960

2.103

2.5092.9502.906

_.

1.400

1.258

1.163

1.172

1.263

1.551

2.650

3.349

3.990

4.519

4.468

1.872

1.440

1.285

1.048

1.120

1.333

2.132

3.340

4.379

6.280

7.350

5.205

1000

1.473-.

1.268:

1.170

1.092'

_ 0-.?77;

0.05$

0.928

1.394

1.733

1.960;

1.849

I 339

1 415

1 315

1.266.

1.222

1.155

1 -254.,.

2.135

2.137

2.449

2.9363.152

1.438

1.300

1.204

1.207

1.271

1.550..

2.596

3.332

3.991

4.603

4.823

1.880

1.487

1.337.

1.108:

1.163;

1.484;

2.188

3.280

4.313

5.972

7.116

5.539

2000

. .1.521

1.450

1.386

1.304

1.179

1.071

• 1.2301.264

1.336

' 1.680

1.8.40,

_ 1.721-

1.552

1.488

1.432

1.381

1.326

... 14942.181i

2.235

2.427..

2.7283.655

1.631

1.512

1.41?

1402

1.431

1.5012.217

3.128

3.825

4.468

5.157

1.920

1.724'

1.590

1.422

1.440

.... 1,4.861.715:

2.601;..,

3.716

4.847

5.864

5.513

3000

1XCJ

1.61 C

1.1-•'

1.353

1.?i6

1 . ; » • : • • •

t.5.-. 1

i.r.y.

1.87.4

2,?y.

t.fii.3

1.t-.-_

1.L6*1.62?

1.1:1 i

1,015

1.fc 'J

2.C3

_?,/"':•2.7? 13.23G

1.T?:!

1 .kj'1724

1.632

i.bi>

i.f"-:

•* OiS

? - J :

2 '"69

3 443

4.302

5 583

1.L-.2

1.15"

1.K 'S

1.T5C

1.V29

1.L-J

i.r:c. 2.?0C

3.026

4.00C

5.223

5.4CQ

212

Xe 50 100 150 200

q (kW m-2)

400 600 800 1000 2000 3000


7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

3000 -0.20

3000 -0.10

3000 -0.05

3000 0.00

3000 0.05

3000 0.10

3000 0.20

3000 0.40

3000 0.60

3000 0.80

3000 1.00

3000 1.20

1.947

1.4601.3071.072

1.215

2.130

4.1298.359

13.76718.454

19.355

11.887

1.937

1.546

1.434

1.1311.200

2,073

4.031

8.09713.280

17.86318.93011.874

1.9311.545

1.414

1.1181.2272.0323.829

7.85712.79217.243

18.47811.862

1.930

1.502

1.3261.0631.1821.8593.7447.236

11.85416.08817.942

11.899

1.9111.5021.3401.075

1.2041.8133.4976.2929.849

13.35416.16611.687

1.9001.5221.342

1.136

1.281

1.851

3.363

5.8558.402

10.80213.21511.358

1.894

1.5291.379

1.172

1.3301.8653.2125.5858.133

10.53512.61410.587

1.9141.579^1.435>~1.235'1-367*2.0563.2005.3997.817

10.34712.20510.285

2.009, >2.092

1.909;.j2.689|;4.3456.9319.547

11.2889.752

3.5005.7708.2259.8449.736

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

4000

4000

4000

4000

4000

4000

4000

4000

4000

4000

4000

4000

-0.20-0.10-0.050.000.050.100.200.400.600.801.001.20

1.9431.4561.167

1.2491.8973.5356.731

12.50618.460

23.63824.451

1.9361.4661.211

1.2661.8593.4206.535

12.11517.990

23.243

24.216

1.929

1.474

1.218

1.270

1.831

3.310

6.340

11.714

17.50722.845

23.980

1.921

1.4861.228

1.2751.727

3.0686.038

11.253

17.007

22.463

23.721

1.9021.5091.249

1.280

1.6422.8555.527

10.08415.39920.86622.737

1.891

1.534

1.2801.2851.5962.6735.2248.379

13.122

18.941

21.638

1.886

1.5721.3411.2871.5702.5045.2448.457

12.67016.972

20.304

1.904

1.618

1.397?

1.366J;1.613\;3.137

5.575

7.651

11.909

17.058

19.748

1.995!:1.845'

2.378f

4.383

6.460

10.84615.33117.598

1 J

2.8234.5308.600

12.80015.500

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

1.9451.4391.174

1.460

2.5174.7488.845

15.61422.43728.66529.532

18.563

1.937

1.4531.175

1.461

2.4544.591

8.60615.25122.04928.342

29.35018.546

1.929

1.467

1.198

1.4672.3924.441

8.373

14.88321.65628.02029.16818.531

1.918

1.489

1.2331.468

,2.2674.0638.035

14.52421.32527.72728.943

18.517

1.8991.5311.2661.470

2.127

3.784

7.360

13.287

19.918

26.526

28.128

18.482

1.8861.5731.3151.472

•2.054

3.5526.520

11.759

18.288

25.285

27.385

18.512

1.880

1.6161.3761.4762.0263.3836.289

11.265

17.192

23.841

26.50418.561

1.894

1.6571.4361.5322.136

3.6596.738

10.61715.64623.16925.59618.561

1.965..1.866;1.761;

1.870:"

3.235

5.097

8.904

14.992

20.114

22.575

18.301

12.091:

2.818

3.327

6.423

13.49317.100

19.600

17.997

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

6000

6000

6000

6000

6000

6000

6000

6000

6000

6000

6000

6000

-0.20-0.10-0.050.000.050.100.200.400.600.801.001.20

1.9611.352

1.1571.5933.3015.881

10.212

17.94726.26033.73534.73921.895

1.9521.3781.164

1.571

3.245

5.838

10.121

17.689

25.900

33.41534.55821.865

1.943

1.402

1.169

1.555

3.207

5.812

10.042

17.433

25.542

33.098

34.377

21.837

1.933

1.4291.171

1.5273.123

5.7309.935

17.18225.20932.797

34.164

21.814

1.911

1.5151.214

1.5273.117

5.7279.806

16.30323.61831.618

33.360

21.731

1.898

1.5931.2691.5743.209

6.054

10.022

15.37722.21430.57632.52321.645

1.8931.6671.3301.6423.3696.653

10.032

14.666

20.850

29.56631.683

21.572

1.9141.716

1.417

1.7863.6667.536

11.132

14.66018.346

28.182

30.55421.624

2.011

2 064^

1.720f2.488

4.8989.140

12.100

14.113

18.07423.988

26.17921.445

' 2.11$

3.2556.310

10.80013.80013.81717.153

20.417

23.442

21.292

213

P G Xe

(kPa) (kgm-2s-1) (-)

q (kW m-2)

50 100 150 200 400 600 800 1000


2000 3000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

70007000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

0

0

0

0

0

0

0

0

00

0

0

50

50

50

50

50

50

50

50

50

50

50

50

100

100

100

100

100

100

100

100

100

100

100

100

-0.20-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.600.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

1.9681.300

1.194

1.807

3.906

6.827

11.648

20.367

30.108

38.764

39.741

25.116

1.775

1.239

0.988

0.799

0.754

0.732

0.655

0.604

0.6000.595

0.590

0.589

2.215

1.495

1.129

0.866

0.806

0.748

0.598

0.482

0.457

0.466

0.520

0.554

2.473

1.632

1.200

0.904

0.843

0.831

0.710

0.516

0.414

0.439

0.558

0.628

1.9591.333

1.200

1.773

3.845

6.779

11.565

20.209

29.829

38.455

39.542

25.088

1.736

1.217

0.969

0.789

0.745

0.731

0.665

0.604

0.6000.598

0.591

0.590

2.191

1.475

1.106

0.852

0.801

0.765

0.635

0.503

0.460

0.467

0.521

0.556

2.456

1.614

1.175

0.886

0.865

0.894

0.780

0.560

0.426

0.430

0.550

0.625

1.9511.364

1.202

1.748

3.807

6.749

11.489

20.061

29.561

38.150

39.342

25.062

1.709

1.206

0.963

0.785

0.752

0.743

0.679

0.620

0.6300.637

0.638

0.640

2.170

1.462

1.096

0.850

0.800

0.766

0.635

0.507

0.465

0.471

0.526

0.562

2.436

1.598

1.163

0.884

0.864

0.880

0.768

0.568

0.441

0.434

0.551

0.629

1.9421.394

1.206

1.708

3.729

6.671

11.388

19.891

29.302

37.859

39.116

25.042

1.668

1.183

0.945

0.775

0.743

0.733

0.671

0.617

0.6200.632

0.633

0.634

2.134

1.424

1.062

0.827

0.783

0.744

0.613

0.504

0.482

0.482

0.553

0.579

2 ^05

1 54=

i 115

u.o61

0.845

0.853

0.739

0.561

0.474

0.453

0.634

0.677

1.9241.499

1.239

1.692

3.712

6.659

11.130

19.414

28.401

36.734

38.234

24.960

1.627

1.194

0.980

0.836

0.810

0.794

0.728

0.682

0.6860.689

0.690

0.693

2.079

1.421

1.077

0.859

0.822

0.769

0.618

0.520

0.511

0.522

0.590

0.624

2.336

1.537

1.109

0.880

0.840

0.829

0.642(

0.522:

0.500;.

0.488

0.650

0.705

1.9171.589

1.296

1.730

3.794

6.941

10.898

19.143

27.672

35.686

37.264

24.883

1.583

1.200

1.010

0.889

0.867

0.848

0.789

0.750

0.7530.762

0.762

0.772

2.006

1.399

1.085

0.888

0.856

0.797

0.637

0.539'

0.541

0.568.

0.628

0-667'.__

2.252

1.512

1.135

0.910

0.875

0.830

0.650.

0.523

.0,502

0.539'

0.654

0.709

1.9161.673

1.363

1.798

3.944

7.536

10.633

19.100

26.947

34.738

36.320

24.799

1.574

1.236

1.069

0.966

0.947

0.929

0.867

0.830

0.8350.846

0.848

0.857

1.961

1.409

1.121

0.946

0.915

0.841

0.669

0.572

0.582

0.611

0.674

0.726

2.189

1.512

1.163

0.957

0.921

0.835

0.655

0:52$

0.525

0.570

0.681

0 7=~

1.9451.729

1.458

1.959

4.292

8.312

10.757

19.328

26.171

33.714

35.348

24.764

1.628

1.325_

1.176r

1.083''

1.067;

1.045. '

0.981

0.945

0.9550.961,

0.962

0.969

1.983

1.463'

1.191

1.028.

0.998-

0.919-

0.729

0.627

0.632

0.871

0.7330.788

2.188

1.546

1.214

1.022''

0.987

0.894

•0.6650.544

0.550 ,:

0.611

0.723

0 8C-i

2.1502.101

1 .807; .

2.731

5.623

9.521

10.810

20.200

24.802

28.932

30.153

24.656

1.874

JJ531.6911.656

1.649

1.618

1.543

1.515

1.5241.527

1.528

1.529 __

2.046

1.702

1.5181.426

1.399

1.272

0.996

0.872

0.009

0.94$

1.017

1.076

2.142

1.6901.458

1.339

1.305

1.152

0.806

-'0.655' 0.714

0402

0.924

1.037

2.4102.35Q

...2-244

3.591

6.026

10.043

10.900

20.210

22.784

25.119

26.915;

24.538

2 X '?•

2.13'-

2.'-v3

2 ' 9"

2: i •

2/>i

2X'-9

2.CJ'.:

2.CC"2.C-J'

2.t'.-9

2.CS •;

2V;9I f Or.

1.6?'

1.K-1

1.754

1.6!/

1.P-S

iM>

1 . •••:

1.7 Jo

1.J12

2.CL--

1.eC:.

1.6. ?

1X4.;

I .OL"

1.392

0.0-3

Q.H- '

O.fi-'s

1.CC-

1. V

1.7S"

214

P G Xe

(kPa) (kgm-2s-1) (-)

q (kW m-2)

50 100 150 200 400 600 800 1000


2000 3000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

200 -0.20

200 -0.10

200 -0.05

200 0.00

200 0.05

200 0.10

200 0.20

200 0.40

200 0.60

200 0.80

200 1.00

200 1.20

2.6061.6571.2050.9570.8790.8290.7140.5770.5470.6660.9551.032

2.5901.6401.1891.0120.9220.8780.7680.6100.5550.6110.9311.019

2.5691.6251.1851.0100.9200.8650.7420 6050.5530.6080.9231.011

2.5401.5811.1620.9650.9000.8390.7120.6000.6530.7241.1741.141

2.4511.5901.1710.9600.8970.8260.6890.5990.6320.7231.1451.088

2.3181.5961.2341.0380.9780.897

2.363

1.593

1.217

1.0360.9720.8810.7230.613:"F;;!p36;0.662L '/'US?!'0.713 0.8410.957 1.0381.002 1.010

i , \ : ^ N v

2.302

1.277k

1.0931.034

'^0.97%x t-21/C

1,342;

1.17f

1.045

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

500 -0.20

500 -0.10

500 -0.05

500 0.00

500 0.05

500 0.10

500 0.20

500 0.40

500 0.60

500 0.80

500 1.00

500 1.20

2.6751.6231.2110.9560.8610.8630.8520.8251.0871.7972.2S42.201

2.6601.6241.2491.0130.9040.8760.8770.8791.0591.7122.2052.122

2.6431.6301.2801.0560.9360.8870.8780.8661.0301.6342.1072.059

2.6561.6361.2841.0690.9710.9030.8800.8501.0291.5952.1462.089

2.6061.6541.3451.2001.1020.9660.8880.8791.0251.4981.8891.825

2.4971.6801.4621.3891.2641.0690.9800.9521.0971.5521.7271.625

2 4521 5~41 3971.2921 2031.0930.9900.9761.1391 7601.9621.765

2 41/.1 6631.4461.3391 2311 0940 5951 22C

1.225

1.634

1.876

1.835

2 192

1. ,'23

1 586

' 499

' £03

' 263

i '/b

1 22-

1 338

1.793

2 0~3

2 01b1 TVS

: 7io

i .64b

1 b^£

1 3C.9

1 23c

'. 319

• /no

2 074

'-J1H3

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

-0.20-0.10-0.050.000.050.100.200.400.600.801.001.20

2.5791.6241.2570.9360.9481.0781.3031.6012.9224.8145.5074.245

2.5501.6161.2941.0251.0201.1251.3331.7202.9164.5595.1624 039

2.5201.6151.3201.0681.0321.1311.3451.6572.7664.3234.8803.895

2.4591.6141.3131.0631.0251.0981.3041.5312.2513.7134.1713.549

2.4101.5611.3901.2921.2281.2301.2851.5111.9623.0633.3122.996

2.3391.5501.4571.4431.3271.3381.4061.6001.9822.7943.1852.940

2.3071.5451.4371.3741.3281.3401.4461.6712.0402.7263.1753.226

2.259

1.587

1.459:

1.343f*Ss»

2.014

2.325

2.663

3.023

3.385

2.0'.&

2.519

2.552

3.020

3.878

2 270

2 51:3

3019

3 510

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

1500

1500

1500

1500

1500

1500

1500

1500

1500

1500

1500

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

2 5711.5481.18C1.2041.3421.6941.9382.4555.6479.693

11.164

2 6451 5221.2241.2401.3941.6901.9182.4515.4489.182

10.593

26151 4971.2201.1591.3431.6551.8902.4295.199

' 8.67510.026

2 542

1.462

1.164

1.064

1.212

1.578

1.889

2.145

3 850

7 238

8 858

2 4431.3821.1531.0601.2081.5031.7652.1273.5195 6055.559

2.3731.4451.1861.1161.2491.5041.7102.1253.3644.3544.993

2 3C91 4721 2111 1441.2491.5041.7152.3113.5614.3654.994

2 272

i 504

1 2-30

1.194

1.272

1 505

1.720

2.411

3.692

4.398

4.995

2.0831 68"

'• 4-3'J

1 4 : J 6

1 bZi'

1.S35

2.240

3.540

4.354

4.927

" DO?

. BE5

1 8C8

1 7T

1.660

• 54/

3 237

4 IOC

4 800

215

p

(kPa)

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

90009000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

G

(kgm-2s-1)

1500

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

3000

3000

3000

3000

3000

3000

30003000

3000

3000

3000

3000

4000

4000

4000

4000

4000

4000

4000

4000

4000

4000

4000

4000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

Xe

(-)1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.200.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

50

6.942

2.712

1.568

1.314

1.116

1.362

1.864

2.5153.782

9.458

14.336

15.750

9.235

2.705

1.810

1.483

1.225

1.526

2.535

3.9098.187

15.841

21.528

22.605

13.004

2.688

1.982

1.454

1.507

1.918

3.943

7.883

14.372

21.335

27.272

28.017

16.754

2.683

2.062

1.484

1.737

2.300

5.216

10.961

18.466

25.880

32.836

100

.6.743

2.693

1.539

1.325

1.179

1.413

1.845

2.512

3.671

9.068

13.784

15.200

9.044

2.686

1.792

1.486

1.261

1.563

2.465

3.8287.811

15.277

20.904

22.054

12.925

2.669

1.966

1.482

1.527

1.920

3.750

7.590

13.914

20.801

26.825

27.732

16.701

2.660

2.063

1.516

1.753

2.274

4.934

10.540

18.067

25.480

32.485

150 200

q(kW400

m-2)

600 800


6.541

2.669

1.538

1.321

1.131

1.376

1.840

2.485

3.5888.698

13.244

14.635

8.838

2.664

1.790

1.485

1.247

1.560

2.410

3.6307.427

14.731

20.260

21.438

12.849

2.644

1.965

1.530

1.571

1.914

3.524

7.222

13.450

20.254

26.375

27.443

16.651

2.633

2.074

1.568

1.791

2.262

4.607

10.105

17.663

25.074

32.134

6.251

2.644

1.515

1.221

1.028

1.275

1.839

2.480

3.252

7.772

12.437

13.946

8.656

2.649

1.819

1.434

1.169

1.502

2.400

3.6296.283

13.697

19.552

20.967

12.758

2.623

1.964

1.529

1.481

1.714

3.011

6.555

12.646

19.744

25.958

27.148

16.604

2.611

2.075

1.624

1.735

2.049

3.704

9.290

17.248

24.687

31.798

5.517

2.537

1.406

1.179

1.024

1.240

1.719

2.317

3.000

6.461

10.516

11.915

7.925

2.555

1.681

1.392

1.160

1.466

2.2933.4055.457

11.912

17.205

18.643

12.413

2.535

1.910

1.447

1.350

1.578

2.692

5.787

11.357

17.889

24.238

25.924

16.437

2.524

2.042

1.542

1.577

1.916

3.362

8.185

15.785

23.220

30.453

4.789

2.462

1.407

1.214

1.074

1.286

1.685

2.211

2.950

5.472

8.234

9.358

6.639

2/-S8

1.582

1.392

1.213

1.519

2.212

3.1445.400

9.569

13.594

14.864

11.839

2.463

1.855

1.416

1.349

1.540

2.380

5.210

9.591

14.956

22.437

24.471

16.278

2.454

2.009

1.540

1.564

1.915

3.163

6.502

13.986

21.666

29.178

4.882

2.376

1.480

1.265

1.126

1.299

1.648

2.126

2.900

5.224

7.569

8.610

6.083

2.4'.',

1.671

1.458

1.262

1.530

2.132

3.0345.390

9.201

12.428

13.864

11.247

2.393

1.856

1.488

1.364

1.541

2.390

5.345

10.048

14.331

20.652

23.035

16.140

2.389

1.983

1.594

1.600

1.935

3.117

6.225

13.524

20.362

27.803

1000

5.275

2.346

1.527

1.324

1.189|"1.3301.627

2.078

2.850

5.157

7.227

8.296

6.436

2.3=4

1.715

1.513

1.328.

1.550

2.133

3.1235.744

8.977

11.837

13.220

11.039

2.375

1.884

1.548

1.459

1.600

2.887

5.972

8.780

13.324

19.160

21.886

16.028

2.371

1.998

1.640

1.682

2.049

3.592

7.784

12.756

19.145

26.558

2000

5.270

2.179;

1.767

1.631

1.5101 531

1 5s3?

1.649

2.680

4.420

6.257

7.154

6.504

2.239

1.929

_!,.7S31.6':4

...1,7-;31.855

2.4814.697

8.035

10.730

12.171

10.613

2.269

2.027

1.819

1.749

1.766

2.390

4.419

7.403

12.177

16.673

19.038

15.384

2.262'

2.097

1.899.

1.997;

2.517.

3.306

5.221

10.613

18.106

22.493

3000

5.265

2.1.8

2.C;r-1.? e1.81 -1 &.E

- c2<:1 7i?2 M43 8005 2C06*00

•> ; / ;

2 "4^

• 9SD

' S21.}

' litC

."• JDO

4.C9-

6 382

8 3^1

1CCS41051C

2 / :.•>'

1X3b1.S201.b2u1.81''

.. 2tyx3.20C

5//C0

9.4CC

13.60C

16.C00

15.30C

2.1455

2.162

2.170

231Q

. 2.$!2j2.951

4.300

8.800

15.000

19.600

216

Xe 50 100 150 200

q (kW m-2)

400 600 800 1000 2000 3000


90009000

5000 1.005000 1.20

33.61820.389

33.40320.339

33.19020.290

32.91220.245

31.95920.083

30.98920.001

29.93019.921

28.95019.801

24.90219.189

21.30019.000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

6000

6000

6000

6000

6000

6000

6000

6000

6000

6000

6000

6000

-0.20-0.10-0.050.000.050.100.200.400.600.801.001.20

2.705

1.933

1.3521.6393.6067.155

12.51121.05930.30538.76739.64123.990

2.6831.9401.3521.6223.5257.070

12.36820.79829.94738.418

39.42923.934

2.6591.9491.3551.612

3.457

6.99912.23520.54529.59838.07339.21623.881

2.637

1.948

1.352

1.5963.329

6.823

12.116

20.317

29.28937.74938.96523.833

2.5551.9691.379

1.6013.2776.680

11.76919.482

27.99136.46838.018

23.656

2.4921.9871.422

1.6553.381

6.86011.46818.72326.89435.28537.02723.485

2.436

2.010

1.472

1.7353.5497.355

11.051

18.04025.851

34.14736.03923.326

2.4342.0431.5541.8723.8318.279

11.99418.03124.49532.97634.93023.239

2.4162.295^.1.9952.5544.6779.1359.136

15.97322.60627.758

29.74222.635

2.692

2.344

2.951

4.467

7.734

7.735

14.92820.24826.50028.840

22.084

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

9000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

-0.20-0.10-0.050.000.050.100.200.400.600.801.001.20

2.7091.906

1.3761.8654.4058.319

14.183

23.92934.844

44.596

45.35227.527

2.6881.9051.3691.8194.3228.250

14.06423.72234.51344.241

45.125

27.469

2.6671.900

1.3671.788

4.2608.201

13.94523.52834.194

43.887

44.895

27.413

2.6471.8951.3481.746

4.1708.130

13.86323.30033.90843.56244.63927.363

2.5781.9561.3791.7454.1058.009

13.444

22.663

32.832

42.26143.61321 Ml

2.528

2.000

1.422

1.789

4.1588.179

13.06722.20031.91741.028

42.488

27.004

2.4862.0451.484

1.8644.2758.634

12.56821.88231.05539.85141.39326.833

2.493

2.088

1.577

2.019

4.573

9.30812.45221.96730.36938.72240.27626.716

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

0 -0.200 -0.100 -0.050 0.000 0.050 0.100 0.200 0.400 0.600 0.800 1.000 1.20

1.8471.3071.0530.8620.8080.7760.6910.6400.6460.6540.6560 611

1.8061.2811.0310.8480.7990.7700.6910.6420.6460.6560.6560 550

1.7771.2681.0230.8470.8010.7740.6990.6500.6540.6640.6720 569

1.7351.2410.9990.8290.7880.7640.6940.6470.6440.6630.6670 5G4

1.6901.2491.0300.8830.8500.8260.7580.7150.7190.7290.7370.745

1.6441.2511.0560.9300.9030.8790.8150.7750.7790.7880.7960 812

1.6311.2841.1121.0040.9810.9580.8940.8540.8590.8690.8800 898 2 048

10000

10000

10000

10000

10000

10000

10000

10000

10000

50 -0.20

50 -0.10

50 -0.05

50 0.00

50 0.05

50 0.10

50 0.20

50 0.40

50 0.60

2.4261.6551.2510.9470.8620.7660.5580.4520.480

2.4051.6331.2220.9220.8450.7580.5590.4580.483

2.3871.6191.2090.9150.8450.7590.5590.4610.492

2.3561.5831.1760.8890.8240.7430.5540.4600.490

2.2981.5691.1750.9170.8630.7790.5790.484I0.511

2.2211.5351.1730.9380.8920.808

2.1701.5341.2020.9930.9510.856

2.1851.5841.274^

1.081b

..0.515. .;,<- 0.5530.543*

217

p

(kPa)

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

1000010000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

G

(kgm-2s-1)

50

50

50

100

100

100

100

100

100

100

100

100

100

100

100

200

200

200

200

200200

200

200

200

200

200

200

500

500

500

500

500

500

500

500

500

500

500

500

1000

1000

1000

1000

1000

1000

1000

1000

Xe

(-)0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.050.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

50

0.517

0.564

0.573

2.767

1.849

1.356

0.993

0.894

0.778

0.530

0.404

0.449

0.513

0.600

0.616

2.926

1.911

1.385

1.002

0.8770.764

0.547

0.488

0.623

0.797

0.935

0.917

2.953

1.871

1.413

0.959

0.817

0.796

0.819

0.892

1.175

1.797

2.139

1.931

2.962

1.866

1.397

1.001

1.040

1.213

1.458

1.712

100

0.513

0.558

0.572

2.755

1.829

1.325

0.966

0.878

0.798

0.583

0.442

0.467

0.513

0.590

0.610

2.911

1.890

1.371

1.001

0.8850.781

0.586

0.518

0.653

0.782

0.911

0.891

2.930

1.868

1.452

1.041

0.876

0.803

0.827

0.937

1.152

1.740

2.068

1.859

2.928

1.855

1.437

1.093

1.103

1.246

1.484

1.839

150 200

q(kW

400

m-2)

600 800


0.517

0.561

0.576

2.738

1.813

1.309

0.958

0.878

0.799

0.584

0.450

0.472

0.515

0.591

0.610

2.889

1.870

1.351

1.019

0.9010.792

0.614

0.552

0.685

0.757

0.887

0.872

2.906

1.859

1.440

1.063

0.884

0.814

0.850

0.937

1.132

1.674

1.995

1.800

2.890

1.846

1.431

1.092

1.077

1.232

1.482

1.754

0.513

0.549

0.576

2.713

1.773

1.270

0.931

0.856

0.773

0.549

0.437

0.479

0.517

0.575

0.602

2.817

1.808

1.316

0.987

0.8870.788

0.614

0.555

0.715

0.943

1.047

0.844

2.818

1.868

1.461

1.076

0.902

0.826

0.864

0.945

1.245

1.926

2.089

1.661

2.791

1.854

1.450

1.085

1.027

1.156

1.469

1.626

0.548

0.593

0.61

2.638

1.743

1.262

0.948

0.884

0.784

0.552

0.443

0.489.

0.534

0.606

0.629

2.749

1.786

1.292

1.000

0.9110.793

0.600

0.550

0.627

0.766

0.940

0.882

2.834

1.868

1.461

1.205

1.038

0.882

0.827

0.874

1.153

1.497

1.736

1.609

2.722

1.787

1.477

1.269

1.174

1.202

1.407

1.622

0.584;

0.638

2.549

1.694

1.247

0.961

0.905

0.801

0.556;

0.448

0.557'

0.640.

0.670,

2.676

1.761

1.326

1.060

0.9780.825

0.624

0.566

0.624.

0.753

0.839

0.819

2.756

1.870

1.565

1.382

1.207

0.998

0.928

0.923

1.150

1.454

1.586

1.543

2.651

1.775

1.560

1.431

1.330

1.331

1.442

1.664

0.625

0.681

2.478

1.677

1.262

1.004

0.952

0.832

0.575

0.463

0.5090.57S

0.666

0.709 .

2.625

1.744

1.326

1.065

0.9820.875

0.664

0.586

0.654

0.794

0.947

0.926

2.741

1.869

1.494

1.298

1.144

0.979

0.916

0.962

1.268

1.600

1.880

1.846

2.615

1.781

1.513

1.363

1.283

1.332

1.467

1.709

1000

0.687

0.745'

2.468

1.705

1.315

1.076

1.025

0.897

0.614

0.494

0.548

.0.624

0.716

0.765

2.606

1.763

1.369

1.125

1.047.0.905;

0.666

0.565

0.630

0.743

0.884

__o.9ijL

2.712

1.880

1.531:

1.354

1.220

1.071

0.966'

1.030

1.268

1.607,

1.886

1.850

2.578

1.784

1.533

1.389

1.306

1.333:

1.482

1.846

2000

0.954

1.020

2.356

1.807i

1.5611.424

1.378

1.183

0.780

0.622

0.706

0.805

0.914

_0.987.

2.487

1.839

- 1.568

' 1.401

1.3231.135

0.807

0.696

0.8130.966

1.127

1,221,

2.537

1.880

1.648-

1.504

1.3961.244

1.080

1.144

1.333

.........l$$o1.889

2.128:

2.399

1.824

1.642

1.533

1.474

"1.4481.520

16S3

3000

1.235

1.310

2J210J

1,874;

1.781-

1.75Q

1.704:

1.453;

0.854;

0.761=

0.^69

0.994

1.12$

_1.224j

2.3'1

1.<..!J

1.7^3

1.CSJ

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1.£.M

1.52:1

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218

Xe 50 100 150 200

q (kW m-2)

400 600 800 1000 2000


3000

10000

10000

10000

10000

1000 0.60 2.763 2.800 2.683 2.241 2.240 2.240 2.261 2.376 2.142*'1000 0.80 4.374 4.149 3.945 3.470 2.800 2.801 2.813 2.955 2.701 2.9241000 1.00 5.046 4.730 4.490 3.599 3.120 3.201 3.270 3.270 3.269 3.6721000 1.20 4.180 4.026 3.875 3.451 3.059 3.195 3.390 3.391 3.390 4.576

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

1500

1500

1500

1500

1500

1500

1500

1500

1500

1500

1500

1500

-0.20-0.10-0.050.000.050.100.200.400.600.801.001.20

3.0721.7171.2661.3151.5131.8882.1412.3535.5709.629

11.2527.275

3.0451.6801.2651.3141.5121.8852.1272.5085.3999.151

10.7477.113

3.0131.6431.2391.2321.4581.8472.0892.5255.1768.680

10.2526.956

2.9621.5911.1901.0951.3011.7452.0852.5263.8197.2469.1686.753

2.8211.5041.1681.0941.2731.6121.9592.6563.7995.6887.0005.970

2.7311.5631.2371.1491.3181.6131.9592.8213.6914.7975.8375.723

2.6551.5841 2571 1741 3181 5931.8842.7983.6904.6895.6805.685

2.6031.6121.3051 2241 3291 5921.8572.6823.6874.6885.6785.888

2.3301.762"! 50:/

'.•18'

1.bS1

1 694

1.944

3.235

4.543

5.6^'

6.126

' S48• 73;

1 67/

1 516" soC' c.'O

2 390

3 9995 171

5 530

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

-0.20-0.10-0.050.000.050.100.200.400.600.801.001.20

3.1191.7081.2351.2601.5502.0592.7443.8459.863

15.10016.5919.637

3.1001.6361.2341.2561.5452.0272.7363.7429.454

14.52716C7C9.534

3.0731.5801.2131.2031.5112.0222.6153.6939.055

13.96115.5469.438

3.0561.5501.1461.0761.3962.0202.6773.4588.092

13.16414 9239 322

2.9351.4491.1101.0611.3441.8632.4803.2936.645

11.20413 0849 008

2.8361.4671.1551.1081.3811.7862.3603.4785.7529.099

11.0768.667

2.7271.5421.2171.1591.3871.7332.2413.6045.7308.2259 9308 383

2.6741.5871.284,1.2211.4111.7042.0273.4335.7298.2239.9288 385

2.391

2.535$;5.1477.3789 1008 161

"5:8

4.1756.6008 3008 083

100001000010000100001000010000100001000010000100001000010000

3000

3000

3000

3000

3000

3000

3000

3000

3000

3000

3000

3000

-0.20-0.10-0.050.000.050.100.200.400.600.801.001.20

3.1101.9591.3581.3021.702

2.804

4,225

8.65216.833

22.82923.806

13 755

3.C9i

1.8981.3811.3221.7352.7174,1228.253

16.288

22.288

23.402

13 679

3.0671.8421.3651.3061.734

2.685

3.960

7.83515.77821.75422.97513612

3.0541.7641.3091.2241.6812.6803.9586.379

14.73921.19722.739'3.500

2.9471.6541.2491.1841.6032.4753.6726.350

13.224

19.334

21.125

13.280

2.8561.6261.280

1.2451.6452.3493.3586.325

11.430

17.09018.862

'3.054

2.757

1.713

1.3461.2831.6472.2353.2656.300

10.89315.333

17.10512.818

2.7 i 51.7551.413

1.352'1.661="2.189-'2.9856.242

11.010

15.082

16.52512.557

2.4891.964;

1.766-

2.25,2.

1.8104.663

10.15413.90015.100'2.5C0

2.63d4.5007.300

10.60012.000

'.2 000

10000100001000010000100001000010000

4000 -0.20

4000 -0.10

4000 -0.05

4000 0.00

4000 0.05

4000 0.10

4000 0.20

3.0912.2391.5571.600Z0414.3508.685

3.0692.2131.5811.6192.0474.1248.357

3.0412.1991.6111.6652.0483 8667.932

3.023 2.917 2.828 2.735 2.695 2.4781

2.190 2.0901.610 1.4871.577 1.4311.837 1.7183.225 2.941

2.0091.4841.4301.6902.659

2.0101.5521.4441.6922.660

2.0251.6121.5441.7663.162

2.122

1.881

: 9752 582

2.1

?5C?7.145 6.302 5.876 6.042 6.298 4.077 3 457

219

p

(kPa)

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

1000010000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

10000

11000

11000

11000

11000

11000

11000

G

(kg m-2 s-1)

4000

4000

4000

4000

4000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

6000

6000

60006000

6000

6000

6000

6000

6000

6000

6000

6000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

0

0

0

0

0

0

Xe

(-)0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.050.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

50

15.444

22.769

29.057

29.793

17.798

3.086

2.385

1.618

1.820

2.417

5.709

12.080

19.917

27.653

34.951

35.706

21.694

3.113

2.2601.4431.644

3.809

7.917

13.813

22.769

32.465

41.375

42.197

25.498

3.121

2.198

1.466

1.888

4.699

9.197

15.650

25.939

37.394

47.614

48.269

29.262

1.919

1.376

1.118

0.925

0.863

0.824

100

14.965

22.244

28.628

29.523

17.725

3.060

2.380

1.654

1.842

2.398

5.396

11.613

19.513

27.267

34.604

35.489

21.616

3.088

2.255

1.4421.631

3.711

7.789

13.629

22.500

32.103

41.008

41.966

25.425

3.097

2.196

1.455

1.841

4.597

9.092

15.493

25.685

37.020

47.232

48.030

29.185

1.881

1.350

1.094

0.907

0.851

0.816

150 200

q (kW m-2)

400 600 800


14.479

21.717

28.201

29.251

17.656

3.030

2.378

1.735

1.880

2.389

5.022

11.122

19.110

26.879

34.261

35.273

21.539

3.060

2.251

1.4411.624

3.621

7.672

13.454

22.241

31.750

40.644

41.733

25.354

3.071

2.195

1.449

1.811

4.513

9.005

15.333

25.443

36.657

46.852

47.789

29.111

1.853

1.336

1.085

0.905

0.852

0.819

13.597

21.207

27.809

28.978

17.585

3.010

2.354

1.730

1.830

2.160

3.954

10.201

18.689

26.502

33.926

34.985

21.465

3.038

2.243

1.4391.615

3.488

7.448

13.298

22.010

31.441

40.303

41.459

25.290

3.048

2.193

1.431

1.772

4.416

8.912

15.218

25.170

36.335

46.504

47.521

29.044

1.816

1.308

1.058

0.885

0.8370.807

12.186

19.384

26.242

27.841

17.354

2.905

2.276

1.635

1.664

2.031

3.631

8.860

17.211

25.127

32.613

34.031

21.197

2.933

2.222

1.4671.621

3.342

7.095

12.627

21.051

30.176

38.945

40.435

25.044

2.958

2.210

1.458

1.765

4.240

8.599

14.626

24.317

35.066

45.093

46.449

28.789

1.772

1.313

1.085

0.933

0.894

0 8G7

10.683

17.111

24.737

26.716

17.141

2.816

2.224

1.628

1.642

2.030

3.413

6.589

15.471

23.894

31.422

33.020

20.975

2.846

2.203

1.5051.665

3.343

6.870

11.930

20.202

29.049

37.654

39.346

24.822

2.884

2.225

1.500

1.797

4.182

8.373

14.106

23.594

33.934

43.740

45.293

28.560

1.734

1.315

1.107

0.973

0.9420S17

10.533

16.383

23.400

25.408

16.977

2.728

2.190

1.676

1.678

2.068

3.370

6.089

14.765

22.635

30.223

32.031

20.756

2.760

2.195

1.5521.730

3.392

6.721

11.372

19.286

27.954

36.380

38.261

24.607

2.814

2.247

1.556

1.855

4.176

8.179

13.552

22.802

32.865

42.407

44.132

28.338

1.728

1.349

1.161

1.044

1.018

0.9W

1000

9.401

15.373

22.038

24.487

16.829

2.688

2.186

1.719

1.753

2.160

3.616

7.859

13.655

21.205

29.020

31.100

20.588

2.725

2.219

1.6241.836

3.575

6.786

11.507

18.897

26.970

35.196

37.193

24.418

2.790

2.284

1.639

1.971

4.337

8.207

13.155

22.351

31.996

41.164

42.993

28.137

1.777

1.432

1.263

1.159-

1.13/

1111

2000

7.566

13.878

'8 530

20 529

'.6 00'

2.465:

2.229:

1.956

2.040;

2.556

3.540

5.635

11.144

17.784

23.68326.237

19.758

2.541.

2.325

1.979,.2.375

4.434

7.872

9.235

15.824

22.676

29.313

31.754

23.490

2.663;

2.456.

2.050.

2.565

5.209

9.365

11.537

20.127

27.369

34.922

37.162

27.170

2.012

1.833

- 1.7S9

1.720

1.713• -JK4

3000

5.700

9.400

14.000

15.976

15.600

2.240

2.232

2.207J

2.324:

2.754

3.715

5.888

9.200

13.957

18.299

21.283

18.909

23m2.372;

2.372;2.979

4.467

7.079

10.000

13.612

18.4171

23.456

26.198

22.576

-.2.556.

'. 2:55a

2,51$3.248

5.248

8.710

12.000

17.884

22.881

28.740

31.184

26.221

2.197:

2.197

2.214

2JZ41'

2.251

' 2.217J

220

Xe

(kPa) (kg m-2 s-1) (-)

50 100 150 200

q (kW m-2)

400 600 800 1000 2000


3000

11000

11000

11000

11000

11000

11000

0 0.200 0.400 0.600 0.800 1.000 1.20

0.737 0.735 0.7420.672 0.671 0.6800.649 0.647 0.6540.660 0.658 0.6650.687 0.685 0.694

0.735 0.7970.675 0.7450.621 0.7250.639 0.7280.687 0.760

0.8520.8010.7860.7970.825

0.9270.8790.8700.8830.910

1.040

0.989

1.016- ' 1.5

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

50 -0.20

50 -0.10

50 -0.05

50 0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

50

50

50

50

50

50

50

50

2.6401.8161.3781.0350.9240.7870.5160.4310.5410.5950.6140.584

2.6321.7991.3491.0070.9030.7730.5100.4300.5400.5920.6050.579

2.6251.7881.3350.9960.8990.7730.5120.4340.5460.5990.6090.582

2.6081.7601.2990.9620.8720.7540.5090.4370.5750.6200.6220.587

2.5821.7501.297

0.982

0.9080.7950.5460.461 K

0.5760.6220.6320.624

2.5321.7171.2840.9950.9340.8270.5861

0.578!0.6310.659:

0.664

2.682

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

100 -0.20

100 -0.10

100 -0.05

100 0.00

100 0.05

100 0.10

100 0.20

100 0.40

100 0.60

100 0.80

100 1.00

100 1.20

3.0752.0721.5221.0950.9560.7670.4020.3310.5570.6540.6470.574

3.0802.0571.4911.0630.9340.7560.4020.3410.5710.6570.6480.565

3.0782.0461.4721.0480.9280.7540.4050.3470.5880.6780.6490.564

3.0742.0191.4351.0110.8980.7360.4060.3590.6850.7750.6700.586

3.0411.9901.4131.0150.9220.7680.4380.3670.6910.7790.6750.606

2.985

1.942

1.386

1.016

0.938

0.793

0,39?0.6990.7830.679

2.9331.9161.3891.0490.9820.839_

0.712"'-0.790-*0.683

2.9321.9421.4401.121,1.058*

2.9302 .03 | |1.669'1.467

2.860

0.771

0.623, ....0,658

110001100011000110001100011000110001100011000110001100011000

200 -0.20

200 -0.10

200 -0.05

200 0.00

200 0.05

200 0.10

200 0.20

200 0.40

200 0.60

200 0.80

200 1.00

200 1.20

3.3052.1941.5901.1200.9520.7460.3920.4320.8981.0560.8900.700

3.3082.1771.5601.0910.9320.7380.3990.4481.0361.1550.8900.686

3.3012.1611.5391.0780.9290.7400.4080.4601.0791.1670.9090.686

3.2912.1291.5041.0480.9040.7290.3590.5121.2581.2340.9570.690

3.2362.071

1.461

1.039

0.918

0.750

0.43110.5650.8570.9410.825

0.692

3.1912.0361.4461.0520.9460.786

0.582

0.784

0.936 0.878 -0.a?#l|fÔ|§*.0.820 0.819o.75o o.8ie; ^ . a i e s a a

3.1372.027

1.48551.135

1.045

0.716T

11000

11000

11000

11000

11000

500 -0.20 3.453 3.439 3.419 3.351 3.293 3.247 3.235 3.218 3.122 3.015500 -0.10 2.262 2.238 2.215 2.157 2.112 2.073 2-059 2.070 2.500 -0.05 1.615 1.609 1.585 1.608 1.535 1.562 1.537 1 .569^*^500 0.00 1.118 1.115 1.109 1.086 1.170 1.224 1.186 1.235 " ^ j j500 0.05 0 929 0.927 0 912 C 888 0 S82 1068 1.054 1.105 ~i.

221

p

(kPa)

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

1100011000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

G

(kgm-2s-1)

500

500

500

500

500

500

500

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

15001500

1500

1500

1500

1500

1500

1500

1500

1500

1500

1500

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

3000

3000

3000

3000

Xe

(-)0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

50

0.854

0.767

0.914

1.427

1.693

1.501

1.341

3.481

2.267

1.590

1.153

1.162

1.410

1.880

1.921

2.496

3.398

3.770

3.853

3.5222.223

1.539

1.247

1.506

2.035

2.805

3.378

4.478

7.268

9.787

7.717

3.540

2.207

1.485

1.253

1.702

2.556

3.337

5.700

9.572

14.869

16.703

10.341

3.533

2.334

1.517

1.356

100

0.833

0.754

0.932

1.505

1.722

1.489

1.316

3.462

2.238

1.585

1.150

1.160

1.370

1.792

1.920

2.458

3.302

3.636

3.749

3.5112.192

1.517

1.264

1.521

2.035

2.815

3.421

4.333

6.926

9.365

7.568

3.530

2.170

1.443

1.281

1.683

2.424

3.218

5.514

9.173

14.303

16.183

10.297

3.522

2.302

1.492

1.350

150 200

q(kW400

m-2)

600 800


0.818

0.782

0.950

1.489

1.691

1.488

1.303

3.436

2.212

1.569

1.147

1.121

1.336

1.762

1.877

2.429

3.252

3.562

3.662

3.4902.168

1.490

1.229

1.482

1.995

2.810

3.420

4.206

6.618

8.962

7.421

3.512

2.141

1.392

1.256

1.647

2.312

3.093

5.348

8.798

13.748

15.666

10.274

3.504

2.272

1.461

1.345

0.802

0.820

1.144

1.541

1.779

1.516

1.265

3.383

2.162

1.568

1.141

1.119

1.332

1.992

1.994

2.496

3.240

3.167

3.050

3.4792.056

1.389

1.144

1.358

1.981

2.800

3.419

3.910

5.598

7.793

7.427

3.512

2.029

1.266

1.133

1.509

2.186

3.086

5.257

7.661

12.127

14.647

10.248

3.504

2.212

1.375

1.290

0.824

0.821

1.234

1.286

1.386

1.481

1.415

3.268

2.075

1.534

1.140

1.118

1.329

1.970

1.972

2.313

2.842

3.278

3.408

3.3831.987

1.361

1.137

1.320

1.852

2.786

3.154

3.827

5.280

6.415

6.753

3.42'

1.925

1.234

1.118

1.435

1.926

2.896

4.521

6.511

10.035

12.232

10.095

3.419

2.094

1.325

1.243

0.913

0.911

1.162

1.164

1.288

1.437

1.471

3.212

2.042

1.530

1.135

1.115

1.325

1.851

1.857

2.221

2.828

3.312

3.414

3.3002.012

1.414

1.157

1.321

1.856

2.787

3.154

3.973

5.410

6.466

6.473

3 335

1.917

1.327

1.158

1.466

1.909

2.712

4.166

6.393

9.274

10.987

10.151

3.339

2.041

1.427

1.309

0.974

0.934

1.265

1.286

1.504

1.701

1.730

3.193

2.039

1.524

1.130

1.110

1.324

1.828

1.870

2.261

2.867

3.494

3.620

3.2151.996

1.439

1.189

1.319

1.743

2.420

2.902

3.877

5.147

6.023

6.208

3 239

1.955

1.410

1.221

1.454

1.679

2.295

3.859

6.252

9.130

11.179

10.616

3.249

2.059

1.501

1.374

1000

1.001

0.886

1.209:'

1.210'

1.449

1.571

1.671

3.156

2.044

1.555

1.262,

1.223

1.335,.

1.829

1-8711

2.262

3.096

3.495

3.621

3.1522.006

1.480"

1.241

1.350

1-691..2.313

2.681

3.748

5.200

6.385

6.461

3 !69

1.975

1.462

1.283'

1.495!

1.584..

1.921

3.602

6.588

9.826

11.166

10.181

3.186

2.079

1.561

1.442

2000

1.209

1.013

1.210

- 1.271

1,542

1.866,

2.m_

2.969

2.070

1.714

1.484

1.415

1.405

1.490

... .1,5201.925;

2.723

3.496

4.073

2.8272.044;

1.688

1.4991.511

1-618.

1.897

1.898

3.147

4.775

6.300

6.485

2 305

2.067

1,725

1.580

1.684

1.368

2.378

5.745

8.489

10.300

9.800

2.857

2.1^5

1.854

1.800

3000

1.346

1.202

1.212

1.515

1.8512.265

. 2-141

2.775

2.C3:

1-«L-2

1.6-.-:

1.5"'

1/-3vl

i.*n1.18-

1.-S-2

2.729

3.730

4.649

2/-: 32.0-L1.8: b

1X-:J3

1.1 IE

1 .& z1.-5;

2754

4.252

5.806

6.682

2/4.2.0'-.:i.b-:;1.fj?2

1 1 - . ' .

i bSb

2 30J

-1243

6 432

9 20C

9 800

2 = K

2 24.i

" .<..?,

1.C.C::

222

p

(kPa)

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

11000

G

(kgm-2s-1)3000

3000

3000

3000

3000

3000

3000

3000

4000

4000

4000

4000

4000

4000

4000

4000

4000

4000

4000

4000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

6000

6000

6000

6000

6000

6000

6000

6000

6000

6000

6000

6000

7000

7000

7000

Xe

(-)0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

50

2.185

3.911

6.432

10.719

18.099

24.185

25.173

14.779

3.522

2.474

1.583

1.559

2.757

5.695

9.734

16.778

24.295

30.916

31.670

19.138

3.523

2.568

1.594

1.651

3.321

7.273

13.066

21.270

29.450

37.053

37.828

23.335

3.536

2.562

1.511

1.650

4.138

8.795

15.206

24.647

34.769

44.061

44.833

27 AW

3.545

2.523

1.537

100

2.083

3.733

6.264

10.370

17.630

23.635

24.765

14.702

3.511

2.455

1.572

1.556

2.668

5.542

9.619

16.325

23.801

30.498

31.402

19.037

3.508

2.555

1.594

1.666

3.201

7.086

12.803

20.884

29.078

36.728

37.627

23.222

3.518

2.549

1.506

1.635

4.043

8.647

14.982

24.333

34.370

43.664

44.581

27.317

3.526

2.522

1.526

150 200

q (kW m-2)

400 600 800


2.038

3.558

5.968

10.044

17.191

23.096

24.357

14.632

3.492

2.438

1.568

1.554

2.570

5.390

9.542

15.871

23.311

30.090

31.137

18.941

3.488

2.544

1.597

1.700

3.062

6.899

12.552

20.494

28.710

36.407

37.426

23.111

3.498

2.537

1.505

1.626

3.957

8.506

14.763

24.028

33.977

43.269

44.328

27.225

3.505

2.520

1.522

1.901

3.461

5.941

8.777

16.256

22.474

24.030

14.533

3.489

2.418

1.564

1.553

2.348

. 5.076

9.473

15.035

22.685

29.702

30.863

18.843

3.480

2.540

1.612

1.710

2.802

6.464

12.257

20.099

28.422

36.078

37.168

22.996

3.487

2.517

1.504

1.622

3.874

8.324

14.493

23.739

33,615

42.903

44.029

27.142

3.489

2.508

1.520

1.781

2.973

5.363

8.775

15.612

20.291

22.513

14.338

3.402

2.345

1.548

1.497

2.155

4.610

9.170

13.953

21.285

28.259

29.827

18.514

3.391

2.475

1.614

1.715

2.574

5.876

11.371

18.667

27.206

34.914

36.238

22.584

3.398

2.470

1.529

1.636

3.658

7.827

13.664

22.581

32.157

41.405

42.930

26.816

3.409

2.492

1.519

1.809

2.751

4.665

8.014

14.200

18.615

20.991

14.302

3.321

2.288

1.562

1.502

2.158

.. 4.860

9.458

12.819

19.650

26.884

28.772

18.222

3.310

2.420

1.635

1.724

2.520

5.450

10.774

17.316

25.915

33.765

35.318

22.156

3.316

2.431

1.570

1.677

3.521

7.385

12.855

21.502

30.852

39.983

41.759

26.530

3.3359 477

1.814

2.545

3.946

7.463

14.150

18.420

19.979

14.131

3.230

2.248

1.594

1.531

2.159

4.575

8.319

12.505

19.630

25.785

27.615

17.969

3.221

2.370

1.663

1.733

2.546

5.242

10.131

16.399

24.878

32.515

34.249

21.804

3.229

2.400

1.617

1.727

3.418

6.992

12.156

20.457

29.548

38.605

40.616

26.237

3.260? 4RR

1000

1.867

2.236

3.004

6.971

14.100

18.400

20.018

13.536

3.168

2.253

1.657

1.621

2.258

3.901

6.380

10.507

19.600

25.412

26.970

17.674

3.157

2.369.

1.722

1.751

2.620

5.177

9.254

14.821

23.752

31.296

33.213

21.653

3.163

2.412

1.685

1.803

3.419

6.812

11.724

19.608

28.347

37.279

39.496

25.941

3.205

2000

1.790*

1.780**

1.47%

4.211

12.854

16.000

16.969

12.703

2.842

2.277'

1.954J*

1.933"'

2.322(

2.623[;

3.110

7.970

17.076

21.000

22.389

16.599

2.8231*

3000

"'"1.862•<x\1.726i

aSyoo-4.500

9.600

13.800

15.000

13.000

•2J506

' 2.450

153400

;2.-3i2

Jf. 2.455

3.800

6.800

11.695

17.500

18.800

16.800

' 2.484'

2.368s J2.343-

2.01V2-070^

2.707

4.239

6.389

11.476

18.683

25.097

27.691

20.478

2.825

2.453«

2.032.

2.192^

3.424

5.794

9.216

15.354

22.712

30.758

33.825

24.580

2.921p2.594^

2.116'.

' ?i81!

2.813

3.240

4.800

8.700

13.535

19.042

22.187

19.237

12.381:

3.452

4.689

6.600

11.075

17.154

24.276

27.986

23.249

Z6-3J

J-"'2.518

223

p

(kPa)

11000

11000

11000

11000

11000

11000

11000

11000

11000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

G

(kgm-2s-1)

7000

7000

7000

7000

7000

7000

7000

7000

7000

0

0

0

0

0

0

0

0

0

0

0

0

50

50

50

50

50

50

50

50

50

50

50

50

100

100

100

100

100

100

100

100

100

100

100

100

200

200

Xe

(-)0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

50

1.872

4.967

10.122

17.322

28.216

40.110

50.735

51.298

31.459

2.124

1.548

1.271

1.063

0.989

0.934

0.826

0.725

0.664

0.688

0.741

0.760

3.156

2.188

1.665

1.241

1.081

0.891

0.544

0.479

0.694

0.759

0.725

0.683

3.796

2.575

1.894

1.340

1.128

0.857

0.374

0.375

0.830

0.922

0.797

0.660

4.143

2.782

100

1.837

4.853

9.972

17.100

27.893

39.680

50.314

51.039

31.362

2.082

1.519

1.242

1.040

0.971

0.922

0.824

0.723

0.612

0.639

0.735

0.759

3.148

2.167

1.629

1.204

1.053

0.871

0.533

0.479

0.755

0.810

0.730

0.673

3.799

2.555

1.854

1.297

1.096

0.833

0.365

0.382

1.066

1.130

0.798

0.664

4.137

2.754

150 200

q (kW m-2)

400 600 800


1.814

4.756

9.833

16.880

27.578

39.257

49.896

50.777

31.267

2.050

1.501

1.228

1.032

0.969

0.920

0.823

0.731

0.621

0.647

0.737

0.760

3.138

2.152

1.607

1.184

1.043

0.857

0.532

0.481

0.756

0.810

0.740

0.672

3.791

2.535

1.823

1.270

1.082

0.829

0.362

0.388

1.111

1.188

0.863

0.680

4.120

2.726

1.793

4.665

9.655

16.612

27.241

38.859

49.519

50.482

31.180

2.013

1.470

1.197

1.007

0.947

0.905

0.817

0.731

0.628

0.666

0.740

0.763

3.118

2.118

1.563

1.140

1.006

0.842

0.531

0.472

0.675

0.725

0.720

0.671

3.780

2.501

1.775

1.218

1.040

0.802

0.358

0.380

1.018

1.046

0.825

0.693

4.101

2.683

1.782

4.401

9.141

15.744

26.089

37.336

47.945

49.353

30.845

1.951

1.460

1.209

1.040

0.993

0.956

0.873

0.796

0.718

0.751

0.810

0.838

3.062

2.079

1.532

1.135

1.025

0.876

0.570

0.498

0.678

0.728

0.720

0.690

3.699

2.426

1.710

1.190

1.045

0.834

QAM

0.392

0.871

0.915

0.775

0.675

3.976

2.554

1.809

4.223

8.668

14.843

24.993

35.952

46.446

48.138

30.552

1.901

1.450

1.216

1.066

1.028

0.996

0.921

0.848

0.807

0.825

0.875

0.905

2.973

2.012

1.487

1.121

1.031

0.897

0.613.

0,53.30.680'

0.730

0.725

0.711

3.585

2.325

1.637

1.157

1.048

0.8480.458

0.418

0.715!

0.796

0.729

0.665^

3.863

2.460

1.854

4.079

8.230

14.061

23.901

34.586

45.018

46.962

30.250

1.880

1.471

1.258

1.125

1.094

1.064

0.990

0.923

0.893

0.911

0.954

0.982

2.897

1.973

1.480

1.148

1.073

0.9470.667

0.572

0.683

0.735

0.750

0-751. _

3.470

2.246

1.600

1.165

1.065

0.889

0.511

0.439

.... 0.6720.751.0.727

0J>91 _

3.737

2.368

1000

1.931

4.051

8.009

13.606

23.098

33.416

43.674

45.824

29.919

1.916

1.545

1.353

1.234

1.206

1.176-

1.098

1.029!

1.002

1.017

1.056!

1.078

2.896

2.006

1.539

1.230!

1.160

1.029

0.729

0.630

0.736

0.792

0.810

_JL-8±3_._

3.426

2.241

1.631'

1.228 .

1.137;'

0.957

0.555

0.477

0.7030.788

0.774

. - O J i S „

3.677

2.350

2000

2.338

3.946

6.824

10.841

18.434

27.486

36.982

40.040

28.445

2.082

1.901

1.811

1.758

1.750

'1.721

1.621

1.565

1.557

1.S84

1.578

1.581

2.837

2.119!

1.794'

1.610

1.571

1.421

1.028

0.875

0.945

1.001

1.049

...J.-Q79

3.139

2.154

1.746

1.522

. 1.467

1.279

0.776

Q.614

0.7$8

0.869

0.931

..P-951

3.315

2.211

3000

2.775

3.896

5.554

7.970

13.899

21.710

30.332

34.061

27.028

2.:

2.: •

2.. .2.: '•2.. .2:. •

2 . •

2.-

2:

2 . •

2.

2.

2.

2.1

1 . . •

1 . •••

1 . •

1.

1 . . '-.

1.1

1.

1..

1.294

.-JL33I

2.788

2.170

1.814

1.775,

1.767!

1.573

1.024!

GJ«9

0.812

0.928j

1.085J

_..U6?i

2.881

2.140;

224

Xe 50 100 150 200

q (kW m-2)

400 600 800 1000 2000


3000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

200 -0.05

200 0.00

200

200

200

200

200

200

200

200

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

2.011

1.385

1.134

0.843

0.315

0.506

1.689

1.736

1.031

0.688

1.965

1.338

1.096

0.823

0.316

0.587

2.242

2.159

1.220

0.672

1.926

1.300

1.081

0.820

0.320

0.641

2.224

2.124

1.214

0.681

1.8751.2521.039

0.790

0.321 |

0.743

1.873

1.6701.0640.835

1.767

1.192

1.019

0.800

0.6691.4451.3260.9500.789

1.701

1.169

1.023

0.819_

Q.433'0-641 -

1.169

1.226

0.947

0.845

1.651

1.165

1.044

0855

OSOQ

0.966

1.080

0.946^

0.858p

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

500 -0.20

500 -0.10

500 -0.05

500 0.00

500

500

500

500

500

500

500

500

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

4.383

2.931

2.077

1.398

1.140

0.991

0.708

1.158

1.792

1.864

1.307

0.929

4.351

2.889

2.036

1.360

1.111

0.963

0.710

1.227

2.055

2.053

1.378

0.972

4.310

2.845

1.988

1.326

1.082

0.940

0.717

1.258

2.057

2.055

1.378

1.041

2.884

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

4.407

2.954

2.041

1.412

1.403

1.670

2.344

2.553

2.755

3.367

3.397

3.533

4.374

2.909

2.001

1.381

1.370

1.598

2.277

2.473

2.739

3.388

3.437

3.542

4.3302.8651.9571.3511.3251.5562.2722.3552.7003.3993.5223.566

4.281

2.795

1.923

1.301

1.231

1.746

2.350

2.355

2.725

3.400

3.585

3.508

4.080

2.634

1.808

1.272

1.210

1.730

1.985

1.990

2.382

3.255

3.982

3.988

3.0054.1664.874

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

1500

1500

1500

1500

1500

1500

1500

1500

1500

1500

1500

1500

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

4.411

2.952

1,975

1.452

1.816

2.689

3.686

4.323

4.873

6.259

8.876

8.906

4.387

2.908

1.936

1.431

1.769

2.564

3.495

4.184

4.813

6.195

8.778

8.905

4.352

2.866

1.895

1.399

1.720

2.475

3.404

4.079

4.773

6.180

8.714

8.919

13000 2000 -0.20 4.415 4.391 4.358 4.346 4.187 4.036 3.866 3.734 3.059k

225

p

(kPa)

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

1300013000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

G

(kg m-2 s-1)

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

3000

3000

3000

3000

3000

3000

3000

3000

3000

3000

30003000

4000

4000

4000

4000

4000

4000

4000

4000

4000

4000

4000

4000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

Xe

(-)-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.001.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

50

2.957

1.914

1.490

2.180

3.615

4.870

6.739

9.087

14.402

17.265

12.430

4.409

3.024

1.876

1.609

2.946

5.596

8.575

12.391

19.481

26.193

27.83117.616

4.400

3.107

1.881

1.754

3.644

7.473

12.177

19.260

27.447

34.409

35.459

22.716

4.398

3.166

1.871

1.879

4.354

9.175

15.653

24.625

33.531

41.581

42.357

27.654

100

2.907

1.854

1.464

2.098

3.404

4.630

6.517

8.783

13.930

16.807

12.380

4.383

2.978

1.832

1.574

2.810

5.333

8.259

11.981

18.987

25.268

27.39117.585

4.376

3.073

1.855

1.730

3.528

7.311

12.004

18.844

26.846

33.989

35.206

22.607

4.371

3.140

1.851

1.858

4.224

9.025

15.411

24.186

33.130

41.268

42.173

27.488

150 200

q (kW m-2)

400 600 800


2.859

1.800

1.438

2.035

3.219

4.406

6.317

8.519

13.488

16.352

12.327

4.350

2.932

1.794

1.558

2.726

5.070

7.920

11.603

18.532

24.287

26.96417.548

4.342

3.040

1.834

1.721

3.418

7.154

11.870

18.464

26.236

33.593

34.963

22.495

4.336

3.115

1.834

1.852

4.085

8.879

15.177

23.744

32.738

40.958

41.988

27.324

2.755

1.719

1.367

1.932

2.874

4.219

6.305

8.096

11.463

15.289

12.556

4.335

2.864

1.732

1.519

2.597

4.869

7.648

10.570

16.964

22.652

26.46717.428

4.328

3.000

1.810

1.707

3.267

6.902

11.775

17.695

25.115

33.099

34.642

22.357

4.317

3.086

1.822

1.850

3.909

8.659

14.962

23.297

32.453

40.727

41.839

27.215

2.584

1.655

1.331

1.776

2.552

3.734

5.563

7.174

9.447

13.245

12.648

4.180

2.684

1.671

1.480

2.392

4.277

6.860

10.568

15.737

17.187

23.87817.427

4.175

2.868

1.769

1.666

3.055

6.315

12.004

17.368

23.939

31.377

33.750

21.931

4.166

2.975

1.795

1.820

3.634

8.052

14.005

21.601

31.250

39.759

40.948

26.567

2.471

1.666

1.339

1.699

2.159

2.887

4.801

7.870

11.010

13.541

12.805

4.033

2.550

1.711

1.508

2.272

3.743

5.646

9.957

15.976

18.786

22.68117.115

4.032

2.754

1.757

1.663

2.888

6.310

11.959

16.123

23.751

30.299

32.327

21.606

4.027

2.878

1.792

1.815

3.477

7.545

13.948

20.890

29.324

38.237

40.100

26.005

2.394

1.669

1.363

1.659

1.832

2.295

4.239

7.869

12.172

14.219

13.765

3.869

2.465

1.720

1.542

2.214

3.358

4.733

9.086

16.424

22.286

23.65817.299

3.873

2.652

1.756

1.660

2.850

6.285

10.563

15.312

23.748

30.250

32.273

21.055

3.875

2.785

1.790

1.810

3.388

7.150

13.422

19.746

29.411

37.137

38.775

25.226

1000

2.378

1.658

1.414 .

1.881

2.268

2.078

3.862

8.641

14.272

15.901

13.459

3.740

2.474

1.722

1.595

2.608

3.350

3.797

8.276

17.899

25.601

24.77816.467

3.764

2.619

1.750

1,620_

2.845

5.356

8.049

13.224

23.740

30.180

32.119

20.256

3.773

2.761

1.785'

1.800

3.350

6.709

11.438

17.529

29.027

35.895

37.727

24.960

2000

2.147

1.765

... .1-8731.982

2.154!

1.422; ,

2.072

7.450

13.647

15.200

12.300

3.092

2.269

1.880

1.890;

2.610

2.987s

1.748

4.582

16.108

23.164

23.20015.500

3.183

2.448"

. 1.740

.....1.-5802.794,,.

3.453

3.890

10.274

23.515

28.065

29.800

18.117

3.228

_ 2.622

1.775

1.793

3.082

5.008

7.520

13.801

23.016

28.833

31.303

22.945

3000

1.885,

1.842

1.698

1.69$

1.73S

1.862

2.800

6.660

11.419

13.600

12.400

2.396:

2.007

1.73a1.738

1.8201-9.S5

2.754

6.000

13.000

18.000

19.10013.800

2.555'

2.2211

1.735-

1.738

2.18S

3.236

5.495

9.600

16.000

19.900

23.000

18.400

2.04$

2.18a1.77d

1.905J

2.45$

3.631

5.700

10.000

15.566

22.035

25.105

20.8301

226

Xe 50 100 150 200

q (kW m-2)

400 600 800 1000 2000


3000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

6000 -0.20

6000 -0.10

6000 -0.05

6000 0.00

6000 0.05

6000 0.10

6000 0.20

6000 0.40

6000 0.60

6000 0.80

6000 1.00

6000 1.20

4.402

3.204

1.824

1.933

5.093

10.767

18.235

28.579

39.447

49.435

50.424

32 676

4.3703.178

1.807

1.908

4.97910.593

17.97128.217

39.007

48.99750.12432 513

4.334

3.151

1.793

1.887

4.87110.421

17.71027.86338.574

48.56049.82232 362

4.308

3.113

...1.785

1.880

4.787

10.213

17.394

27.537

38.170

48.133

49.452

32 129

4.1593.008

1.779

1.870

4.471

9.547

16.379

26.181

36.523

46.45248.16231.634

4.019

2.913

1.772

1.869

4.225

8.915

15.362

24.847

35.080

44.932

46.792

31 C90

3.870

2.828

1.768

1.853

4.000

8.315

14.458

23.562

33.530

43.299

45.5?5

30 616

3.7572.811^

1.76ii

1.846

3.851

7.922

13.64922.349

32.124

41.77644 22R30 C87

3.170H2.683

1.8411"

3.134j>*

5.452

10.143

16.725

24.911

34.257

37 799

27 515

2.089

...1..751J

4.0006.39410.89817.94526.77231 16225 173

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

13000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

-0.20-0.10-0.050.000.050.100.200.400.600.801.001.20

4.408

3.182

1.846

2.1625.984

12.310

20.840

32.817

45.512

56.90657.71237.488

4.371

3.1671.828

2.1225.854

12.122

20.555

32.42145.017

56.427

57.400

37.339

4.334

3.152

1.814

2.091

5.73311.939

20.26932.031

44.53055.95357.08937.191

4.300

3.121

1.8072.0805.637

11.715

19.913

31.619

44.05555.48056.70737.037

4.1543.0461.803

2.075

5.27410.995

18.777

30.183

42.248

53.60455.39236.496

4.017

2.973

1.800

2.058

4.988

10.292

17.514

28.65040.710

52.025

53.98235.961

3.8772.9081.792

2.0494.7239.623

16.408

27.24538.89650.42152.73435.506

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

0 -0.20

0 -0.10

0 -0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

2.536

1.949

1.646

1.412

1.315

1.209

1.015

0.860

0.808

0.845

0.891

0.864

2.481

1.909

1.606

1.378

1.287

1.190

1.010

0.861

0.753

0.791

0.8880.869

2.433

1.878

1.579

1.357

1.272

1.182

1.012

0.869

0.760

0.795

0.877

0.879

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

50 -0.20

50 -0.10

50 -0.05

50 0.00

50 0.05

50 0.10

50 0.20

50 0.40

50 0.60

50 0.80

50 1.00

50 1.20

4.184

3.013

2.370

1.814

1.554

1.265

0.793

0.668

0.913

1.006

1.019

0.982

4.150

2.978

2.321

1.761

1.511

1.234

0.773

0.659

0.970

1.051

.0.999

0.962

4.109

2.944

2.280

1.723

1.482

1.216

0.765

0.655

0.963

1.042

1.003

0.946

4.050

2.888

2.215

1.657

.1.424"

1.175

0.751

0.639

0.934

0.998

0.986

0.945

3.887

2.778

2.118

1.586

1.382

1.162

0.762

0.643

0.880

0.948

0.953

0.927

2.943

;i-i .j is;: 1.290

227

P G Xe

(kPa) (kgm-2s-1) (-)

q (kW m-2)

50 100 150 200 400 600 800 1000


2000 3000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

100

100

100

100

100

100

100

100

100

100

100

100

200

200

200

200

200

200

200

200

200200

200

200

500

500

500

500

500

500

500

500

500

500

500

500

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

5.261

3.687

2.809

2.052

1.692

1.304

0.687

0.621

1.113

1.234

1.185

1.117

5.910

4.078

3.043

2.169

1.753

1.387

0.819

0.839

2.055

2.091

1.471

1.209

6.468

4.403

3.210

2.253

1.867

1.666

1.336

1.440

2.090

2.108

1.681

1.534

6.511

4.460

3.185

2.276

2.261

2.475

2.391

3.256

3.527

4.230

4.194

5.216

5.223

3.645

2.750

1.988

1.641

1.269

0.662

0.615

1.351

1.439

1.166

1.089

5.847

4.019

2.971

2.096

1.697

1.349

0.739

0.904

2.597

2.523

1.597

1.204

6.366

4.319

3.123

2.174

1.802

1.611

1.217

1.453

2.304

2.313

1.807

1.634

6.403

4.374

3.101

2.196

2.169

2.359

2.253

3.132

3.501

4.338

4.459

5.358

5.170

3.598

2.695

1.936

1.604

1.246

0.650

0.608

1.384

1.486

1.215

1.065

5.771

3.953

2.903

2.036

1.652

1.313

0.714

0.939

2.590

2.504

1.694

1.222

6.258

4.233

3.046

2.108

1.750

1.555

1.144

1.434

2.268

2.348

1.921

1.754

6.291

4.286

3.025

2.129

2.100

2.260

2.115

3.006

3.457

4.434

4.763

5.522

5.100

3.530

2.616

1.857

1.535

1.200

0.635

0.585

1.281

1.347

1.218

1.113

5.688

3.874

2.814

1.948

1.577

1.251

0.706

0.907

2.142

2.061

1.650

1.428

6.171

4.147

2.950

2.023

1.669

1.426

0.927

1.488

1.965

2.136

1.967

2.028

6 POO

4.196

2.938

2.050

1.999

1.932

2.027

2.949

3.503

4.399

4.895

5.577

4.852

3.350

2.457

1.740

1.463

1.165

0.632

0.556

1.087

1.188

1.129

1.058

5.331

3.602

2.579

1.769

1.452

1.168

0.657

0.740

1.698

1.743

1.477

1.347

5.744

3.824

2.699

1.830

1.521

1.290

0.662

1.061

1.498

1.971

2.275

2.408

5 7~3

3.868

2.695

1.865

1.796

1.621

1.632

2.262

3.135

4.914

6.539

6.853

4.560

3.138

2.286

1.617

1.375

1.123

0.647:

0-550....

0.886

0.994

0.979

0.92-4

5.03'

3.387

2.413

1.658

1.380

1.119

0.653

0.702,.

1.4501.609

1.428

1.322

5.357

3.542

2.487

1.689

1.409

1.179

0.612

1.013

1.636

2.164

2.566

2.635

5 392

3.587

2.500

1.738

1.646

1.491

1.362

1.770

3.035

5.109

6.716

6.769

4.2942.960

2.160

1.546

1.336

1.112

0-872

_ 0,557

0.831, .

0.944

0.957

0S27

4 720

3.175

2.265

1.573

1.330

1.097

0.815

0,611

1.1151.283

1.267

1.131

5.009

3.308

2.343

1.622

1.371

1.155_

0.944 .

1.171

1.620

2.113

2.247

2.550

5.015

3.326

2.345

1.662

1.544

1.789

1.818

1.854

3.527

5.633

7.030

7.117

4.1882.916

2.156

1.573

1.379;

1.156-

0.701

0.574 •

...0.33$0.948:

0.969:

0 94*

t- 531

3.108

2 .249^

1.595'-;

1.367':-"

1.134 .

0.675

...0-845

1.1661.371

1.355'

1-257*....

4.804

3.196

2.303

1.635

1.396

1.204

0.78,3

1.09Q:

1.478 ..

1.832

1.932

2.446

4.778

3.189

2.293

1.669

1.553:;'

1.518'

1.702

1-845',;....

3.452

5.655

6.754

6.631

3.5322.598;

_2.051:

1.648

' 1.543

'1.342

0.842

0.653

0.815

0.938

1-013

1.01$

3.793

2.697

2.114

1.670

1.511

1.294

0.855

0,781

1.1831.32$

' 1.358

1,380

3.616f

2.540

2.003

1.041

1.471

1.281

0-923

1.012

1.578

2.019;2 331

2 505

2 607

2.620.

2.037

1.707

1.560

1,444

1.415

J.-&60

3.204

4.921

5.527

5.401

2.7552.2001.868;

1.659

1.646

1.487

1.00i'

0-745

0.76$,0.898

1.041;

. 1-08JL

_ 2.8982.M-1.S/21.7 iC1.6/21.4 iJ

1.0:40.03 i1.0?31 / -V1.?'.'1.4 V

2.0432.031.-191.CS1-

1.553

1.-'5C

1. : ~

1 .'x 5

. . ! - • - * '

2.791

- "}J?

2,'b..

1.-S/3

1.--5

1.bdD

1.J54

1. J 2 '1:

1.600,3.162

4.960

5.336

4.933

228

P G Xe

(kPa) (kgm-2s-1) (-)

q (kW m-2)

50 100 150 200 400 600 800 1000


2000 3000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

150015001500150015001500150015001500150015001500

200020002000200020002000200020002000200020002000

300030003000300030003000300030003000300030003000

40004000400040004000400040004000400040004000

-0.20-0.10-0.050.000.050.100.200.400.600.801.001.20

-0.20-0.10-0.050.000.050.100.200.400.600.801.001.20

-0.20-0.10-0.050.000.050.100.200.400.600.801.001.20

-0.20-0.10-0.050.000.050.100.200.400.600.801.00

6.4574.5053.0952.3022.9834.3115.8806.3826.4447.435

10.54612.020

6.4444.5583.0242.3833.8266.5458.5779.385

11.62217.04420.48317.814

6.4364.6072.9362.5755.1369.812

14.58019.19724.68631.87534.20025812

6.4214.6442.8582.7316.209

12.28219,10927.35335.41742.47544.100

6.3574.4213.0242.2242.8604.1045.6716.1986.3907.497

10.54311.921

6.3454.4752.9662.3113.6796.2388.1929.112

11.38816.63420.33617.909

6.3384.5272.8802.5084.9839.469..

14.07818.61024.05830.65633.75025 866

6.3264.5732.7962.6586.059

12.04318.75626.65434.64442.00443.869

6.2504.3352.9572.1642.7613.9185.4656.0086.3527.607

10.56811.827

6.2414.3882.9122.2533.5505.935

- 7.8378.878

11.21016.25320.25418.040

6.2364.4432.8292.4494.8319.122

13.61818.05923.47129.32933.29725.885

6.2264.4982.7392.5935.920

11.80918.43825.95633.84041.55343.640

6.1584.2542.8932.0912.5973.9885.5315.9796.4147.660

10.20411.421

6.1474.3022.8582.2033.4185.4387.5538.821

10.69813.74819.60218.057

6.1414.3502.7812.4014.7058.656

12.75816.43321.61627.20232.72026.089

6.1354.4112.6802.5375.807

11.54617.83724.75232.78441.01143.383

5.7473.9292.6801.9352.3273.4324.6675.0116.2448.455

11.00711.364

5.7483.9752.6772.0593.0084.7426.6588.383

10.55812.50017.73017.587

5.7524.0402.6292.2754.2367.652

11.75615.64119.24518.89929.38726 283

5.7584,1292.5262.4155.396

10.76517.15022.36330.45538.51642.337

5.3863.6382.5101.8302.1252.6493.4834.1496.1719.542

12.20611.761

5.3943.6832.5321.9682.7113.8595.1847.931

11.51414.86719.93519.359

5.4093.7562.5162.2003.8396.745

10.20814.90520.82822.27529.39526 509

5.4353.881..2.4302.3465.025

10.54517.05920.88528.58237.30141.228

5.0243.3732.3581.7521.9862.4683.1203.6766.090

10.16112.37611.358

5.0423.4062.3931.8992.5303.1714.3227.332

11.64916.11618.45017.755

5.0703.4892.4122.1473.5635.8789.167

14.21621.24125.32428.40825.613

5.1183.6512.3542.3074.724

10.25316.17720.31828.94537.28739.962

4.8063.2552.3201.7691.9992.6333.1083.6876.521

10.86112.92611.382

4.8173.3212.3121.9142.8633.6013.9326.768

11.96016.94019.55818.095

4.8613.3922.3852.1783.6665.6167.954

13.24221.85127.74230.62825.994

4.9493.6082.3372.3384.8969.888

14.52319.47429.30737.87439.517

3.6882.616*2-1 04i1.829-1

2.217-2.2101.9715.5519.9949.5547.801

3.672J.;2.65iJ»2.127-

1.9991"'

2.708> x

3.256lx

2.415

3.841

9.928

15.970

16.159

12.288

3.7811V,.2 ' 7 7 9 t2.3152.318

3.312L4.0124.5439.044

18.96226.12726.62019.270

4.0803.145!2.477",2.528(J*4.0426.4839.313

15.37225.60432.99333.614

2.§97

j||.S5';

1.L&41^2;

-< SC5

k C6D

2.63C

4.898

8 128

9419

5 62C

^2.138"'Ti'CH

i:|jp73JIJ138J*2344

2.8184.1698.574

14.17814.30011.00C

"2Jssa2.455

"?2i|3$^•2.630

3.2364.6007.000

16.54823.20024.60017.600

3J47

2.683

2.72753.1644.0006.000

10.27818.00026.00027.066

229

(kPa) (kgm-2s-1)

q (kW m-2)

Xe 50 100 150 200 400 600 800 1000

(-) Heat Transfer Coefficient (kW m-2 K-2)

2000 3000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

17000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

4000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

6000

6000

6000

6000

6000

6000

60006000

6000

6000

6000

6000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

7000

0

0

0

0

0

0

0

0

0

0

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.200.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

33.153

6.411

4.656

2.814

2.946

7.366

14.605

23.318

33.650

43.217

51.672

53.017

40.402

6.410

4.674

2.781

3.185

8.587

17.159

27.44439.236

50.741

61.462

63.452

48.131

6.415

4.623

2.801

3.537

9.902

19.491

31.456

45.296

58.564

70.658

72.570

55.134

2.690

2.254

1.989

1.766

1.644

1.481

1.192

1.025

1.010

0.997

33.064

6.318

4.598

2.753

2.866

7.211

14.437

23.013

33.097

42.701

51.317

52.815

40.138

6.316

4.628

2.727

3.107

8.411

16.947

27.11638.782

50.225

60.940

63.032

47.808

6.323

4.598

2.753

3.449

9.720

19.265

31.094

44.792

57.985

70.092

72.151

54.860

2.638

2.212

1.941

1.718

1.602

1.452

1.183

1.028

1.010

0.996

32.958

6.222

4.539

2.696

2.794

7.068

14.276

22.708

32.540

42.187

50.958

52.608

39.879

6.222

4.531

2.678

3.038

8.244

16.740

26.79038.334

49.717

60.423

62.613

47.488

6.234

4.570

2.709

3.371

9.544

19.042

30.731

44.298

57.419

69.534

71.732

54.583

2.592

2.177

1.904

1.684

1.574

1.434

1.181

1.035

0.956

0.942

32.933

6.132

4.460

2.641

2.737

6.949

14.099

22.494

32.115

41.821

50.697

52.412

39.579

6.128

4.511

2.637

2.995

8.106

16.478

26.38937.895

49.243

59.906

62.129

47.177

6.139

4.516

2.680

3.335

9.408

18.767

30.264

43.779

56.863

68.966

71.258

54.352

2.550

2.139

1.858

1.635

1.526

1.395

1.161

1.024

0.938

0.926

32.337

5.778

4.228

2.499

2.608

6.510

13.422

21.114

29.902

39.904

49.572

51.443

38.601

5.789

4.313

2.525

2.862

7.619

15.635

25.08636.238

47.395

57.897

60.376

45.964

5.817

4.373

2.593

3.190

8.888

17.847

28.819

41.996

54.837

66.705

69.489

53.252

2.459

2.081

1.804

1.589

1.494

1.388

1.190

1.075

1.056

1.050

31.744

5.478

4.023

2.417

2.546

6.176

12.706

20.334

27.610

37.228

47.520

49.880

37.405

5.496

4.130

2.470

2.810

7.250

14.803

23.73034.628

45.734

56.122

58.707

44.862

5.533

4.222

2.563

3.142

8.488

16.924

27.258

40.363

53.177

64.888

67.834

52.239

2.394

2.034

1.754

1.540

1.452

1.367

1.204

1.099

1.081

1.084

30.854

5.188

3.833

2.360

2.512

5.873

11.951

19.765

26.100

36.138

45.971

49.017

36.665

5.217

3.961

2.435

2.782

6.921

14.00322.40032.998

43.889

54.214

56.872

43.672

5.265

4.079

2.550

3.118

8.124

16.036

25.694

38.641

51.242

63.007

65.909

51.069

2.361

2.021

1.746

1.534

1.454

1.386

1.246

1.157

1.145

1.153

29.930

5.047

3.778

2.410

2.548

5.649

11.359

18.518

25.225

35.532

45.254

47.642

35.770

5.064

3.902

2.481

2.817

6.700

13.358

21.32031.413

41.985

52.210

55.188

42.610

5.085

4.008

2.590

3.144

7.854

15.327

24.470

36.848

49.264

60.990

64.250

49.922

2.387

2.067

1.804

1.598

1.525

1.465

1.332

1.247

1.235

1.241'

24.361

4.302

3.441

2.637

2.746

4.647

7.980

12.222

19.405

28.801

36.821

39.840

31.212

4.266

3.544

2.718

3.041

5.665

10.156

15.51023.709

33.433

43.206

46.923

37.394

4.178

3.592

2.826

3.357

6.582

11.691

18.130

28.494

40.447

52.075

55.934

44.199

2.507'

2.276

2.071

1.890'

1.854;

1.838

1.742

1.671

1.664

1.662

21.700

3.496

3.023

2.842

2.954

3.642

4.411

7.200

13.100

21.476:

28.995]

32.526

26.920

3.418

3.113

2.946

3.291

4.647

6.818

9.62116.106

24.943

34.112

38.389

32.105

3.228

3.104

3.071

3.622

5.342

7.917

13.000

20.307

31.734

42.972

47.280

38.357

2.605

2.454

2.292-

2.125;

2.123:

2.090;

2.109;2.054

2.054

2.053:

230

(kPa) (kgm-2s-1)

q (kW m-2)

Xe 50 100 150 200 400 600 800 1000

J-) Heat Transfer Coefficient (kW m-2 K-2)

2000 3000

20000

20000

1.00

1.201.016 1.015 0.963 0.948 1.075 1.110 1.177 1.261 |2?§i;666v'

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

50 -0.20

50 -0.10

50 -0.05

50 0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

50

50

50

50

50

50

50

50

4.7503.6463.0322.4402.0861.6651.0080.7500.9681.1781.3021.141

4.7413.6282.9862.3742.0231.6190.9790.7290.9391.1391.2591.109

4.722

3.607

2.945

2.319

1.974

1.585

0.961

0.720

1.000

1.194

1.300

1.082

4.6813.5612.8762.2351.8921.5270.9410.7090.9801.1651.2671.029

4.6163.5082.7772.1031.7791.4640.9270.7010.8661.0201.1110.991

4.4983.4092.6461.9521.6431.3860.9270.723:0.8530.9791.0620.968

4.4183.3522.5681.8581.5641.3500.945

0.835s

0.9451.0230.962

4.477

3.416

2.612

1.876

1-590J

1.391U

0.983V

4.6983.6602.7581.892

1.189

4.7573.7742.7951.034

f.187i1.047l!0.990* 1.129 1.280

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

100 -0.20

100 -0.10

100 -0.05

100 0.00100

100

100

100

100

100

100

100

0.050.100.200.400.600.801.001.20

6.1624.5423.6682.8432.3511.8020.9820.7101.1061.4731.6381.274

6.1624.5263.6152.7622.2751.7450.9420.6741.0631.4171.5751.228

6.1434.4993.5602.6902.2121.7010.9120.6551.2701.6481.7681.186

6.1004.4473.4792.5892.1121.6320.8870.6421.2471.6101.7241.096

6.0014.3593.3282.3941.9451.5310.8420.5900.9101.1901.3051.026

5.8414.2263.1532.1901.7601.4200.8220.5920.8531.0821.1890.968

5.7144.1343.0302.0441.6341.3500.819

0.874

0.774;.

0.9661.074

0.934

5.7474.1833.0532.0331.634 s

JLj3§Zk

0JJ320.5810.7780.966;.1.0760.948

5.7974.3283.074^1.887P

1.410

5.6844.336

J2.979

0.637...0.786'"

,..Q.9551.0681.018

0.883-

1,05s1

200002000020000200002000020000200002000020000200002000020000

200 -0.20

200 -0.10

200 -0.05

200 0.00200200200200200200200200

0.050.100.200.400.600.801.001.20

7.1705.1074.0143.0432.4942.0491.4681.3382.1102.5502.5411.501

7.1505.0703.9452.9512.4051.9711.3881.2492.0502.5092.5201.460

7.1165.0253.8742.8652.3291.9121.2791.2502.5403.0873.1191.426

7.065

4.959

3.782

2.755

2.220

1.825

1.181

1.122

2.302

2.888

2.936

1.472

6.8824.7813.5452.4821.9731.6241.0680.8941.5501.8191.8441.259

6.7464.6663.3912.2971.8021.491

0.9620.694;;1.3221.8011.784

1.075

6.6014.5563.2532.1371.6561.3870.824;

0.868

1.1451.2721.044

6.606 6.5334.598 4.7153.280 3.3312.135 2.064;1.1.384 1,339

1.004*^*023*1 361 ¥"*?$?§*

6.2794.6893.2931.S82

1.247;

1.192 :. 1,316'

20000

20000

20000

20000

20000

20000

20000

20000

20000

500 -0.20

500 -0.10

500 -0.05

500 0.00

500 0.05

500 0.10

500 0.20

500 0.40

500 0.60

8.3295.6774.2603.1672.7782.8602.9133.1393.569

8.2685.6034.1743.0692.6692.7262.7442.9793.475

8.2075.5304.0892.9772.5702.6072.5812.8343.464

231

p

(kPa)

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

2000020000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

G

(kgm-2s-1)

500

500

500

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1000

1500

1500

1500

1500

15001500

1500

1500

1500

1500

1500

1500

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

2000

3000

3000

3000

3000

3000

3000

3000

3000

Xe

(-)0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.050.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

50

3.573

3.258

3.056

8.670

5.829

4.237

3.247

3.584

4.438

4.689

6.274

6.129

5.452

5.491

8.818

8.613

5.779

4.172

3.470

4.8296.857

7.785

9.053

9.535

12.145

17.141

18.819

8.568

5.732

4.115

3.748

6.199

9.919

13.368

16.127

19.748

26.162

28.919

24.627

8.550

5.796

3.986

3.994

8.063

14.376

21.334

28.922

100

3.584

3.350

3.108

8.587

5.744

4.145

3.139

3.431

4.235

4.509

6.209

6.207

5.813

5.952

8.911

8.532

5.708

4.080

3.347

4.6386.613

7.654

9.112

9.667

12.115

16.966

18.594

8.493

5.675

4.022

3.611

5.985

9.646

13.189

15.828

19.296

25.541

28.436

24.492

8.476

5.750

3.893

3.848

7.834

14.117

21.051

28.275

150 200

q (kW m-2)

400 600


3.737

3.683

3.187

8.512

5.665

4.060

3.042

3.293

4.050

4.358

6.137

6.281

6.240

6.559

9.091

8.462

5.641

3.999

3.241

4.4736.393

7.575

9.203

9.842

12.156

16.827

18.400

8.426

5.618

3.942

3.498

5.803

9.391

13.058

15.570

18.875

24.913

27.965

24.390

8.409

5.699

3.815

3.736

7.644

13.869

20.790

27.633

3.727

3.658

3.379

8.430

5.561

3.972

2.934

3.093

3.627

4.431

6.316

6.288

6.310

6.654

8.712

8.379

5.543

3.908

3.119

4.2385.788

7.314

9.281

9.617

11.759

14.813

17.075

8.345

5.538

3.845

3.360

5.565

9.012

12.605

13.868

15.788

22.533

26.828

24.071

8.330

5.633

3.716

3.601

7.433

13.611

20.448

26.534

3.423

3.631

3.698

8.169

5.303

3.718

2.658

2.711

3.093

3.835

5.739

6.924

8.738

10.274

11.217

8.135

5.320

3.676

2.827

3.7295.458

7.959

10.641

11.916

13.243

16.288

18.820

8.113

5.336

3.631

3.055

4.948

8.588

13.673

15.128

16.682

20.069

24.662

23.998

8.101

5.440

3.519

3.324

6.836

12.646

19.782

24.063

3.1123 524

3 =93

7.950

5.110

3.537

2.458

2.424

2.874

3.801

5.294

6.828

9.353

11.031

11.003

7.927

5.145

3.512

2.618

3.3415.271

7.956

10.050

12.259

15.845

18.560

17.860

7.914

5.171

3.486

2.841

4.459

8.270

13.215

15.664

17.865

21.098

24.978

24.673

7.904

5.273

3.398

3.133

6.275

12.318

19.314

23.525

800

m-2 K-2)

3.253

3.470

3 5^0

7.753

4.956

3.390

2.296

2.193

2.904

4.161

5.905

8.063

10.122

11.320

11.167

7.737

4.998

3.377

2.459

3.0784.528

7.061

9.313

12.063

15.703

17.885

17.039

7.733

5.031

3.375

2.681

4.067

7.678

12.002

15.153

18.406

21.614

24.652

24.454

7.725

5.125

3.313

3.005

5.843

11.515

17.950

22.677

1000

2.467

3.148

3.348

7.648

4.947

3.391

2.285

2.166

2.635

3.672

4.756

6.200

8.609

9.893

9.588

7.650

5.005

3.403

2.464

3.0364.267

6.291

8.410

11.062

14.994

17.210

15.088

7.646

5.047

3.390

2.684

4.113

6.632

9.874

13.673

17.984

21.698

23.714

22.212

7.638

5.127

3.341

3.004

5.774

10.697

15.916

21.400

2000

2.450:

2 54C

2 368

7.139

4.898

3.404

2.237

1.960

2.188;

2.823'

3.623,

5.063

6.175

6.601

6.348

7.195

4.988

3.490

2.450

2.651^3.385*

3.560,.

4.789

8.805

11.309

11.363

10.753

7.187

4.992

3.507

2.668:

3.467"

4.685'

4.555

7.705

14.382

19.025

19.678

17.082

7.182

4.993

3.550

2.999

4.435

7.272

10.581

15.906

3000

2.048

2.41?

2.467

6.747

4.942

3.502

2.26Q

1.793

1.971,

2.2141

.2,525

3.872

4.631

4.807

4.259

6.699

4.883

3.533

2.413

2.16S2.159

2.570:3.548

6.134

9.800

10.000

8.400

6.685

4.807

3.632

2,636-2.3941

,2.36d3.236

6.300

11.800

15.684

16.500

13.800

6.683

4.760

3.739

2.999

3.040

4.000

6.400

12.000

232

p

(kPa)20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

20000

G

(kgm-2s-1)30003000

3000

3000

4000

4000

4000

4000

4000

4000

4000

4000

4000

4000

4000

4000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

5000

6000

6000

6000

6000

6000

6000

6000

6000

6000

6000

6000

6000

7000

7000

7000

7000

7000

7000

7000

Xe

(-)0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

0.40

0.60

0.80

1.00

1.20

-0.20

-0.10

-0.05

0.00

0.05

0.10

0.20

50

35.285

40.509

41.121

33.556

8.536

5.951

3.836

4.080

9.571

18.108

27.360

36.363

43.875

50.590

52.185

43 616

8.523

6.061

3.713

4.247

11.166

21.716

32.806

43.074

52.002

60.475

63.129

53.729

8.508

6.078

3.630

4.582

13.075

25.725

39.447

51.762

62.448

72.689

75.319

63.370

8.504

5.983

3.637

5.084

15.001

29.085

45.234

100

34.497

39.900

40.764

33.484

8.460

5.905

3.743

3.941

9.340

17.913

27.042

35.813

43.348

50.214

51 948

43 419

8.449

6.018

3.631

4.123

10.928

21.515

32.533

42.665

51.590

60.114

62.821

53.353

8.438

6.047

3.559

4.456

12.814

25.444

39.009

51.156

61.795

72.056

74.803

62.946

8.439

5.981

3.571

4.943

14.738

28.803

44.765

150

33.682

39.251

40.365

33.385

8.392

5.854

3.666

3.835

9.144

17.729

26.700

35.227

42.796

49.818

51 691

'13 204

8.382

5.971

3.562

4.023

10.713

21.321

32.248

42.232

51.164

59.748

62.513

52.980

8.373

6.013

3.498

4.349

12.569

25.170

38.573

50.564

61.157

71.429

74.288

62.526

8.376

5.975

3.513

4.819

14.486

28.525

44.295

200q (kW m-2)400 600 800


32.397

38.780

40 301

33 480

8.311

5.785

3.577

3.720

8.939

17.505

26.339

34.710

42.385

49.573

51 538

43 034

8.304

5.897

3.494

3.941

10.508

21.035

31.958

42.010

50.930

59.397

62.075

52.549

8.299

5.944

3.447

4.282

12.365

24.816

38.069

49.979

60.537

70.804

73.734

62.120

8.309

5.928

3.478

4.761

14.294

28.182

43.761

28.852

35.756

38.097

32.872

8.078

5.586

3.391

3.479

8.356

16.761

25.438

32.662

40.208

47.915

50 182

42 COO

8.075

5.706

3.338

3.728

9.874

20.138

30.552

40.319

49.380

57.871

60.703

51.183

8.077

5.783

3.328

4.074

11.63023.637

36.293

47.794

58.186

68.426

71.627

60.482

8.096

5.838

3.382

4.527

13.528

26.961

41.831

28.547

32.801

36.191

32.797

7.879

5.411

3.277

3.332

7.889

15.954

24.958

30.893

38.509

46.229

48 746

40 942

7.880

5.532

3.253

3.615

9.372

19.177

29.047

38.225

47.266

56.422

59.139

49.524

7.886

5.625

3.283

3.982

11.048

22.414

34.480

45.795

56.100

66.117

69.532

58.969

7.911

5.721

3.367

4.441

12.918

25.681

39.893

27.806

30.237

32.191

32.033!

7.699

5.252

3.204

3.225

7.394

15.970

25.355

29.965

37.078

44.080

46 619

39 753

7.702

5.377

3.202

3.543

8.930

18.229

28.089

35.792

44.669

53.943

57.249

48.058

7.713

5.483

3.268

3.928

10.518

21.213

32.659

43.917

54.100

64.096

67.546

57.431

7.742

5.612

3.379

4.392

12.353

24.406

37.852

1000

28.394

33.131

34.994

31.851

7.615

5.262

3.222

3.228

7.436

15.586

23.119

29.368

37.652

44.279

45 775

33^02

7618

5.351

3.264

3.544

8.559

17.431

27.082

35.146

43.769

52.641

55.798

46.668

7.620

5.454

3.337

3.930

10.085

20.156

30.925

41.830

52.018

61.859

65.503

55.943

7.632

5.580

3.450

4.388

11.863

23.270

35.933

2000

24.177

29.833

29.722

24.426

7.179

5.093

3.489

3.263

5.842

11.218

17.205

24.748

33.491

37.872

37.923

30.778

7.172

5.145

3.570

3.609

6.804

12.657

19.715

27.701

35.561

42.936

46.460

39.478

7.135

5.228

3.714

4.045

8.058

14.771

22.434

31.785

41.676

51.518

55.840

48.631

7.080

5.331

3.863

4.522

9.574

17.425

26.757

3000

19.998

24.407

25 5C0

20.000

6.700

4.804

3.769

3.331

4.133

6.106

10.300

17.805

26.060

30.400

31 7C0

23.021

6.683;

4.852

3.862

3.713

5.141

7.785

11.805

18.321

25.467

33.239

37.535

32.652

6.614

4.911

4.094

4.223

6.118

9.210

13.854

21.992

31.677

41.178

45.891

41.238

6.501

4.989

4.311

4 766

7.401

11.348

17.384

233

q (kW m-2)

P G Xe 50 100 150 200 400 600 800 1000 2000 3000

(kPa) (kgm-2s-1) (-) Heat Transfer Coefficient (kW m-2 K-2)

60.115 59.415 58.733 58.066 55.592 53.443 51.439 49.106 38.518 28.25072.301 71.573 70.866 70.207 67.635 65.447 63.447 61.206 50.626 40.49883.546 82.907 82.272 81.687 79.270 76.875 74.802 72.575 62.027 51.44585.966 85.497 85.021 84.553 82.527 80.460 78.432 76.389 66.423 56.13072.450 72.078 71.705 71.377 69.847 68.430 66.940 65.403 57.746 49.991;

2000020000

20000

20000

20000

700070007000

7000

7000

0.400.60

0.80

1.00

1.20

234

TABLE IV.II. DISTRIBUTION OF DATA AND ERRORS FOR WALL TEMPERATURES IN DEGREES C FOR THE AECL FILMBOILING LOOK-UPTABLE.

Pressure Range (kPa) = 100 to 1000

Mass Flux Range (kg/(m2s))

Heat Flux Range(kW/m2)

50 to 200

200 to 600

600 to 1000

1000 to 3000

235

No. of DataAvg. Error (%)RMS Error (%)No. of Data Set




-0.20to-0.05

0000

0000

0000

0000

-0.05to0.00

770-4.217.3

1

145-1

12.61

0000

0000

50 to 500

Quality Range

0.00 0.10to to0.10 0.40

15836.18.8

1

871.66.9

1

0000

0000

0000

0000

0000

0000

0.40to1.00

0000

0000

0000

0000

-0.20to-0.05

0000

0000

0000

0000

-0.05to0.00

0000

0000

0000

0000

500 to 2000

Quality Range

0.00to0.10

0.10to0.40

0000

0000

0000

0000

0000

0000

0000

0000

0.40to1.00

0000

0000

0000

0000

-0.20to-0.05

0000

0000

0000

0000

-0.05to0.00

0000

0000

0000

0000

2000 to 4000

Quality Range

0.00to0.10

0000

0000

0000

0000

0.10to0.40

0000

0000

0000

0000

0.40to1.00

0000

0000

0000

0000

-0.20to-0.05

0000

0000

0000

0000

-0.05to0.00

0000

0000

0000

0000

4000 to 7000

Quality Range

0.00to0.10

0000

0000

0000

0000

0.10to0.40

0000

0000

0000

0000

0.40to1.00

0000

0000

0000

0000

TABLE IV.II. (CONT.)


Mass Flux Range (kg/(m2-s))


50 to 200

200 to 600

600 to 1000

1000 to 3000





-0.20to-0.05

0000

0000

0000

0000

-0.05to0.00

2-4.95.1

2

2-4.2

52

0000

0000

50 to 500

Quality Range

0.00 0.10 toto 0.400.10

273242

90.91.3

2

0000

0000

332-0.76.3

2

13-1.13.3

2

0000

0000

0.40to1.00

9-6.8

72

42-2.35.3

2

0000

0000

-0.20to-0.05

0000

2-14.614.6

2

0000

0000

-0.05to0.00

53-3.97.2

2

1310.35.7

2

0000

0000

500 to 2000

Quality Range

0.00to0.10

2051.43.2

2

1731.33.1

2

0000

0000

0.10to0.40

330.71.2

2

370.71.9

2

0000

0000

0.40 -0to to1.00 -0

0000

56.56.6

2

173-0.35.7

2

411.5

32

.20

.05

0000

0000

0000

0000

-0.05to0.00

0000

0000

0000

0000

2000 to L1000

Quality Range

0.00to0.10

0000

0000

0000

0000

00

.10 to

.40

0000

0000

211

4.72

17-1.92.5

2

0.40to1.00

0000

0000

34.75.6

2

9-0.42.2

2

-0.20to-0.05

0000

0000

0000

0000

-0.05to0.00

0000

0000

0000

0000

4000 to 7000

Quality Range

0.00to0.10

0000

0000

0000

0000

0.10to0.40

0000

0000

0000

0000

0.40to1.00

0000

0000

0000

0000





50 to 200

200 to 600

600 to 1000

1000 to 3000

237





-0.20to-0.05

0000

93

3.82

0000

0000

-0.05to0.00

6-1.22.8

2

382.94.8

2

0000

0000

50 to 50()

Quality Range

0.00to0.10

630.72.6

2

644.14.7

2

0000

0000

0.10 to0.40

1131.85.7

4

116-2.24.3

5

0000

0000

0.40to1.00

26-2.14.4

3

500.8

43

0000

0000

-0.20to-0.05

0000

700.054.1

2

0000

0000

-0.05to0.00

38-2.13.2

2

100-0.27.9

2

0000

0000

500 to 2000

Quality Range

0.00to0.10

710.82.3

2

170-1

7.12

0000

0000

0.10to0.40

223.63.8

2

106-1.83.5

4

0000

0000

0.40 -0to to1.00 -0

0000

401.47.4

2

3540.94.9

4

1991.83.3

3

.20

.05

0000

0000

0000

0000

-0.05to0.00

380.24.3

2

453.9

10.32

0000

0000

2000 tc)4000

Quality Range

0.00to0.10

20-0.41.7

2

431.62.3

2

0000

0000

0.10 to0.40

0000

0000

0000

96-0.93.5

3

0.40 -0to to1.00 -0

0000

40.81.8

1

254-1.64.5

4

419-1.1

43

.20

.05

0000

0000

0000

0000

-0.05to0.00

0000

0000

0000

0000

4000 to 7000

Quality Range

0.00to0.10

0000

0000

0000

0000

0.10to0.40

0000

0000

0000

96-3.69.2

2

0.40to1.00

0000

0000

0000

142.35.5

2





50 to 200 No. of DataAvg. Error (%)RMS Error (%)No. of Data Set




-0.20to-0.05

0000

0000

0000

0000

-0.05to0.00

0000

0000

0000

0000

50 to 500

Quality Range

0.00 0.10to 0.400.10

0000

0000

0000

0000

to

0000

0000

0000

0000

0.40 to1.00

0000

0000

0000

0000

-0.20to-0.05

0000

1085.27.9

2

0000

0000

-0.05to0.00

311.22.4

2

1261.28.6

2

0000

0000

500 to 2000

Quality Range

0.00to0.10

190-0.52.7

2

3310.67.3

2

8-2

2.42

0000

0.10to0.40

1410.14.2

4

5600.02

64

841.76.1

2

2-2.52.6

1

0.40to1.00

0000

730.74.7

3

295-0.92.1

3

25-2.93.8

2

-0.20to-0.05

0000

169.4

11.52

0000

0000

2000 to 4000

Quality Range

-0.05to0.00

310.72.3

2

1072.6

10.42

0000

0000

0.00to0.10

78-0.94.42

2

2371.5

52

191.1

32

0000

0.10to0.40

72.6

31

1801.84.7

3

84-2

4.73

733

4.42

0.40to1.00

0000

0000

260.21.3

2

930.63.3

2

-0.20to-0.05

0000

0000

0000

0000

4000 to 7000

Quality Range

-0.05to0.00

0000

125.96.3

2

0000

0000

0.00 0.10to to0.10 0.40

23-1.43.4

2

101-0.23.9

2

191.6 52.9 5.

2

0000

0000

0000

1.7.71

0000

0.40to1.00

0000

0000

0000

0000





50 to 200

200 to 600

600 to 1000

1000 to 3000

239





-0.20to-0.05

0000

0000

0000

0000

-0.05to0.00

0000

0000

0000

0000

50 to 500

Quality Range

0.00to0.10

0.10!0.40

0000

0000

0000

0000

to

0000

0000

0000

0000

0.40 to1.00

310.8

32

58-3.15.1

2

0000

0000

-0.20to-0.05

0000

0000

0000

0000

-0.05to0.00

0000

0000

0000

0000

500 to 2000

Quality Range

0.00to0.10

0000

0000

0000

0000

0.10to0.40

0000

68-1.13.4

4

95-5.57.8

3

0000

0.40to1.00

0000

955-1.34.9

5

812-2.14.7

5

0000

-0.20to-0.05

0000

0000

0000

0000

2000 to 4000

Quality Range

-0.05 0.00to to0.00 0.10

0000

0000

0000

0000

0000

0000

0000

0000

0.10to0.40

0000

19-0.11.9

3

361-4.66.9

3

1306.79.2

2

0.40 -0to to1.00 -0

0000

17-0.65.3

3

2370.042.5

3

169-0.4

42

.20

.05

0000

0000

0000

0000

-0.05to0.00

0000

0000

0000

0000

4000 to 7000

Quality Range

0.00to0.10

0000

0000

0000

0000

0.10 0.40to to0.40 1.00

0000

0000

0000

0000

0000

0000

0000

0000

to



Mass Flux Range (kg/(ni2-s))


50 to 200

200 to 600

600 to 1000

1000 to 3000





-0.20to-0.05

0000

0000

0000

0000

-0.05to0.00

0000

0000

0000

0000

50 to 500

Quality Range

0.00to0.10

0.100.40

0000

0000

0000

0000

to

0000

0000

0000

0000

0.40 to1.00

33-0.03

1.13

0000

0000

0000

-0.20to-0.05

0000

0000

0000

0000

-0.05to0.00

0000

0000

0000

0000

500 to 2000

Quality Range

0.00to0.10

0000

0000

0000

0000

0.10to0.40

0000

32-5

8.22

464

3.81

55.15.3

1

0.40to1.00

11-1.61.7

1

786-1.73.7

3

362-2.34.5

3

33-2.32.4

1

-0.20to-0.05

0000

0000

0000

0000

2000 to 4000

Quality Range

-0.05 0.00to to0.00 0.10

0000

0000

0000

0000

0000

0000

0000

0000

0.10to0.40

0000

0000

94-0.52.8

1

44-4

4.71

0.40to1.00

0000

10-0.10.3

1

3240.41.3

1

178-1.52.4

1

-0.20to-0.05

0000

0000

0000

0000

-0.05to0.00

0000

0000

0000

0000

4000 to 7000

Quality Range

0.00to0.10

0000

0000

0000

0000

0.10 0.40to to0.40 1.00

0000

0000

0000

0000

0000

0000

0000

0000

Appendix V

IPPE TABLE OF HEAT TRANSFER COEFFICIENTS FOR FILM BOILING AND SUPERHEATED STEAM FOR TUBES

TABLE V.I. IPPE TABLE OF HEAT TRANSFER COEFFICIENTS (kW/m2-K) FOR FILM BOILING AND SUPERHEATED STEAM FORA TUBE OF DIAMETER 10 mm AT q = 0.2 - l.OMW/m2; Tinkt< Ts; [P] MPa; [G] kg/ m2-s, x < 1

Bold lines are approximate borderlines between film boiling and post-dryout regimes.

pMPa

0.1

Gkg/m2s

250

0.1 500

0.1 750

0.1 1000

0.1 1500

0.1 2000

0.1 3000

qMW/m2

0.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.0

X-0.20.42g0.60g1.18g0.42g0.60g1.18g0.42g0.60g1.16g0.42g0.60g1.18g0.50g0.60g1.18g0.43g0.60g1.18g0.43g0.60g1.18g

-0.10.37gO.53gO.95gO.37gO.53gO.95gO.37gO.53g0.95g0.37gO.53g0.95g0.37gO.53g0.95g0.37gO.53gO.95g0.37gO.53gO.95g

0.00.24g0.50g0.75g0.24g0.50g0.75g0.24g0.50g0.75g0.24g0.50g0.75g0.24g0.50g0.74g0.24g0.50a0.74g0.24g0.50g0.74g

0.10.19g0.45g0.71g0.21g0.45g0.72g0.26g0.46g0.72g0.32g0.47g0.72g0.24a0.49a0.76g0.30a0.47a0.65g0.34a0.55a0.73a

0.20.19g0.43g0.72g0.26g0.46g0.72g0.40g0.56g0.77g0.53g0.66g0.82g0.23a0.48a1.06g0.33s0.45a0.62a0.44s0.62s0.73a

0.30.22g0.45g0.72g0.33g0.53g0.75g0.51g0.69g0.87g0.34s0.55a0.99g0.23s0.48a0.73a0.34a0.44a0.58a0.56s0.64s0.73a

0.40.25g0.47g0.72g0.42g0.60g0.78g0.26s0.72a0.97g0.18s0.44a0.70a0.21s0.35a0.49a0.34a0.41a0.51a0.65s0.74s0.79a

0.50.28g0.49g0.74g |0.31s0.68g0.86g0.16s0.41a0.67a0.15s0.31a0.48a0.22s0.32a0.42a0.35s0.43a0.50a0.70s0.82s0.88s |

0.60.32g0.52g0.76g0.18s0.52a0.85a0.13a0.30a0.48a0.14s0.26a0.38a0.23s0.31a0.39a0.37s0.45s0.51a0.72s0.88s|0.95s

0.70.30a0.56g0.77g0.13a0.37a0.60a0.12a0.25a0.38a0.14s0.24a |0.33a0.24s0.32a|0.39a0.38s0.48s|0.54a0.70s|0.91s1.00s

0.80.28s0.61g0.82g0.11a0.29a0.47a0.11a0.22a0.33a0.14s10.22a0.30a0.25s0.33a0.39a0.37s0.49s0.56a|0.66s0.91s1.03s

0.90.19s0.56a0.87g0.10a0.24a0.38a0.10a0.20a0.29a0.14s0.22a0.29a0.24s0.33a0.39a0.36s0.50s0.57a0.59s0.88s1.03s

1.00.14a0.43a0.71a0.09a0.21a0.33a0.10a0.18a0.26a0.14s0.21a0.28a0.24s0.34a0.40a0.33s0.50s0.58a0.51s0.84s1.02s

to

g - Groenevelda - approximations - Sergeev

TABLE V.I. (CONT.)

pMPa

0.1

Gkg/m s

250

0.1 500

0.1 750

0.1 1000

0.1 1500

0.1 2000

0.1 3000

qMW/m2

0.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.0

X1.10.12a0.35a0.58a0.08a0.19a0.29a0.10a0.18a0.25a0.14s0.21a0.27a0.22s0.34a0.40a0.30s0.49s0.59a0.42s0.78s0.98s





1.60.07a0.18a0.30a0.07a0.13a0.20a0.09a0.16a0.21a0.12a0.21a0.26a0.14s0.31a0.40a0.15s0.38s0.53a0.15s0.44s0.68s

1.70.06a0.17a0.27a0.06a0.13a0.19a0.09a0.16a0.20a0.11a0.20a0.26a0.13s0.29a0.39a0.13s0.35a0.50a0.13s0.39s0.62a

1.80.06a0.15a0.25a0.06a0.12a0.18a0.09a0.15a0.20a0.10a0.20a0.26a0.12s0.28a0.38a0.12s0.33a0.48a0.12s0.35a0.56a

1.90.05a0.14a0.23a0.06a0.12a0.17a0.08a0.15a0.20a0.10a0.20a0.26a0.10a0.27a0.37a0.11a0.30a0.45a0.11a0.31a0.51a





TABLE V.I. (CONT.)

pMPa

0.2

Gkg/m s

250

0.2 500

0.2 750

0.2 1000

0.2 1500

0.2 2000

0.2 3000

qMW/m2

0.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.0

X-0.20.41g0.66g0.95g0.41g0.66g0.95g0.41g0.66g0.95g0.41g0.66g0.95g0.47g0.66g0.95g0.56g0.66g0.95g0.56a0.66g0.95g

-0.10.37g0.55g0.84g0.37g0.55g0.84g0.37g0.55g0.84g0.37g0.55g0.84g0.37g0.55g0.84g0.42g0.55g0.84g0.48g0.58g0.84g

0.00.27g0.52g0.77g0.27g0.52g0.77g0.27g0.52g0.77g0.27g0.52g0.77g0.27g0.52g0.77g0.27g0.52g0.77g0.27g0.52g0.77g

0.10.23g0.45g0.72g0.24g0.45g0.72g0.28g0.46g0.73a0.33g0.47g0.73g0.47g0.60g0.76g0.30a0.55a0.74a0.40a0.60a0.81a

0.2(U9g0.44g0.73g0.30g0.47g0.72g0.42g0.57g0.77g0.54g0.68g0.82g0.85g0.96g1.08g0.33a0.51a0.71a0.54s0.68a0.85a

0.30.22g0.46g0.73g0.36g0.49a0.75g0.52g0.70g0.88g0.42a0.86gl.OOg0.34s0.80s1.26a0.35s0.51a0.68a0.66s0.77s0.90a

0.40.26g0.47g0.73g0.43g0.51g0.78g0.39a0.82g0.97g0.30s0.78s1.17g0.27s0.48a0.70a0.38s0.51s0.66a0.77s0.87s0.95s

0.50.29g0.50g0.75g0.49g0.70g0.87g0.27s0.73al . l lg0.20s0.47a0.73a0.27s0.41a0.55a0.41s0.52s0.62a0.83s0.96s1.03s

0.60.32g0.52g0.77g0.35s0.76g0.96g0.18s0.47a0.75a0.18s0.36a0.54a0.28s0.39a0.49a0.44s0.54s0.62a0.85s1.03s1.11s

0.70.37g0.57g0.80g0.22s0.61a1.01a0.15s0.35a0.56a0.17s0.31a0.45a0.28s0.38a0.47a0.44s0.56s0.63a0.83s1.06s1.17s

0.80.42g0.62g |0.83g0.16s0.44a0.72a0.14s0.30a0.45a0.17s0.28a0.40a0.28s |0.39a0.47a0.43s0.57s0.65a0.77s1.05s1.19s

0.90.35s|0.70g0.88g0.13a0.35a0.56a0.13a0.26a0.39a0.16s |0.27a0.36a|0.28s0.39a0.47a0.41s0.58s0.67a0.69s1.01s1.19s

1.0|0.23s0.70a0.94g0.11a0.29a0.47a0.12a0.24a0.35a|0.16s0.26a0.34a0.27s0.39a0.47a0.38s0.57s0.67a0.58s0.96s1.16s


TABLE V.I. (CONT.)

pMPa

0.2

Gkg/m s

250

0.2 500

0.2 750

0.2 1000

0.2 1500

0.2 2000

0.2 3000

qMW/ra2

0.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.0

X1.10.18s0.53a0.88a0.10a0.25a0.40a0.12a0.22a0.32a0.16s0.25a0.33a0.25s0.39a0.47a0.34s0.56s0.67a0.48s0.88s1.11s





1.60.08a0.24a

L0.40a0.08a0.17a0.25a0.10a0.19a0.25a0.13s0.23a0.30a0.15s0.34a0.45a0.16s0.41s0.58a0.16s0.47s0.73s

1.70.08a0.22a0.36a0.07a0.16a0.24a0.10a0.18a0.24a0.12a0.23a0.30a0.14s0.32a0.43a0.14s0.38a0.55a0.14s0.41s0.66s




2.10.06a0.16a0.26a0.07a0.14a0.20a0.08a0.17a0.23a0.09a0.21a0.28a0.09a0.25a0.38a0.09a0.27a

L0.42a0.09a0.27a0.45a



TABLE V.I. (CONT.)

pMPa

0.5

Gkg/mM s250

0.5 500

0.5 750

0.5 1000

0.5 1500

0.5 2000

0.5 3000

qMW/m2

0.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.0

X




0.10.26g0.46g0.74g0.26g0.46g0.74g0.3 lg0.47g0.75g0.36g0.48g0.75g0.50g0.62g0.78g0.68g0.77g0.87g0.50a1.12g1.22g

0.20.20g0.45g0.74g0.34g0.48g0.74g0.46g0.59g0.79g0.58g0.70g0.84g0.88g0.99gl . l lg1.30g1.30g1.40g0.70a1.16a1.26a

0.30.23g0.47g0.74g0.39g0.56g0.78g0.56g0.72g0.91g0.73g0.88g1.04g1.19g1.28g1.41g0.96s1.71gl-81g0.90s1.21s1.30a

0.40.27g0.49g0.75g0.45g0.64g0.81g0.66g0.85g1.02g0.87g1.07g1.23g0.61s1.52s2.43s0.55s0.93s1.33s1.03 s1.23a1.35s

0.50.31g0.51g0.77g0.52g0.73g0.90g0.78g0.99g1.16g

0.60.34g0.54g0.79g0.58g0.82g0.99g0.78s0.99a1.30g

0.76s 10.36s1.25g1.42g0.40s0.79s1.18a

0.92s1.47a0.38s0.62s0.87a

0.55s 10.57s0.76s0.99s1.11s1.27s1.39s

0.74s0.90s1.13s1.33s1.45s

0.70.39g0.57g0.82g0.56a0.93gl.lOg0.36s1.00s1.17a0.28s0.62s0.97a0.37s0.56s0.74a0.57s0.74s0.87s1.08s1.35s1.50s

0.80.44g0.64g0.85g0.53s1.04g1.21g0.26s0.66s1.07a0.24s0.50a

0.90.55g0.82g0.91g0.32s0.92s1.39g0.21s0.51a0.81a0.22s0.43a

0.75a 10.63a0.36s ||0.35s0.53s 10.52s0.68a0.55s0.74s0.86s1.00s1.32s1.51s

0.65a0.51s0.73s0.86s0.87s1.26s1.48s

1.00.49a0.82g0.96g0.23s0.65a1.07a0.18s0.42a0.66a0.21s0.39a0.55a0.33s0.50s0.63a0.46s0.71s0.85s0.71s1.17s1.42s


TABLE V.I. (CONT.)

pMPa

0.5

Gkg/m s

250

0.5 500

0.5 750

0.5 1000

0.5 1500

0.5 2000

0.5 3000

qMW/m2

0.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.0

X1.10.42s0.82g0.98g0.19s0.51a0.83a0.17s0.37a0.56a0.20s0.36a0.50a0.30s0.49s0.61a0.40s0.68s0.83s0.56s1.05s1.34s

1.20.29s0.74a0.97g0.16s0.42a0.69a0.15s0.33a0.50a0.19s0.34a0.47a0.27s0.48s0.60a0.34s0.64s0.81s0.43s0.93s1.24s

1.30.22s0.66a0.91a0.14s0.36a0.58a0.14s0.30a0.45a0.18s0.33a0.44a0.24s0.46s0.58a0.29s0.60s0.78s0.33s0.80s1.13s

1.40.18s0.54a0.89a0.12a0.32a0.51a0.14s0.28a0.41a0.17s0.31a0.42a0.22s0.44s0.57a0.24s0.55s0.74s0.25s0.69s1.01s

1.50.15s0.45a0.75a0.11a0.29a0.46a0.13s0.26a0.38a0.15s0.30a0.41a0.19s0.41s0.55a0.20s0.50s0.70a0.21s0.59s0.90s




1.90.10a0.28a0.46a0.09a0.21a0.33a0.10a0.22a0.32a0.11a0.26a0.36a0.12a0.32a0.47a0.12s0.34a0.53a0.12a0.35a0.57a





TABLE V.I. (CONT.)

pMPa

1.0

Gkg/m2s

250

1.0 500

1.0 750

1.0 1000

1.0 1500

1.0 2000

1.0 3000

qMW/m2

0.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.0

X-0.20.55g0.71g0.88g0.84g0.82g1.02g0.84g0.82g1.02g0.84g0.82g1.02g0.84g0.82g1.02g0.84g0.82g1.02g0.84g0.82g1.02g

-0.10.47g0.61g0.82g0.70g0.69g0.91g0.70g0.68g0.91g0.70g0.68g0.91g0.65a0.68g0.91g0.65g0.68g0.91g0.70g0.69g0.91g



0.20.25g0.47g0.77g0.44g0.57g0.80g0.55g0.80g0.84g0.66g0.75g0.89g0.94g1.04g1.15g1.38g1.37g1.41g1.21a1.58a2.10g

0.30.28g0.49g0.76g0.47g0.62g0.82g0.63g0.95g0.96g0.79g0.99gl.lOg1.27g1.40g1.48g1.10a1.86a1.88g1.24s1.57a1.96a

0.40.31g0.50g0.76g0.50g0.67g0.83g0.71g1.05g1.07g0.92g1.23g1.30g0.96a1.40a1.43a0.83s1.60a1.62a1.34s1.56s1.84s

0.50.34g0.53g0.79g0.56g0.76g0.93g0.83g1.15g1.19g0.86a1.34g1.46g0.65s1.35a1.39a0.72s1.08s1.46s1.44s1.63s1.80s

0.60.36g0.56g0.81g

0.70.42g0.61g0.84g

0.61g 0.77g0.85g J0.98g1.02g0.96g1.35g1.32g0.81s1.20a1.62g0.50s

1.14g0.88s1.26a1.51g

0.80.48g0.67g0.87g0.69al.lOg1.27g0.43s1.18s1.38a

0.43s 1 0.33s1.07s 10.74s1.38a0.47s

0.92s ||0.76s1.34s 11.04a0.72a0.96s1.21s1.46s1.69s1.85s

0.72s0.94s1.13s1.39s

1.15a0.45s0.69s0.91a0.68s0.92s1.09s1.26s

1.70s 11.65s1.88s 11.87s

0.90.59g0.74g0.93g0.61s1.08a1.46g0.31s

1.00.70g0.81g0.99g0.37s1.06s1.35a0.25s

0.79s 10.61s1.28a 10.97a0.29s l|0.26s0.60s 10.52s0.90a0.43s0.65s0.84a0.62s0.90s1.07s1.08s1.55s1.82s

0.76a0.40s0.62s0.79a0.52s0.86s1.04s0.87s1.40s1.72s


to

to00

TABLE V.I. (CONT.)

pMPa

1.0

Gkg/m s

250

1.0 500

1.0 750

1.0 1000

1.0 1500

1.0 2000

1.0 3000

qMW/m2

0.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.0

X

1.10.63s0.81gl.Olg0.27s0.76s1.25a0.21s0.50a0.79a0.24s0.46a0.67a0.36s0.60s0.76a0.47s0.81s1.01s0.66s1.24s1.59s

1.20.39s0.79gl.Olg0.21s0.59a0.98a0.19s0.44a0.67a0.23s0.43a0.61a0.32s0.57s0.73a0.39s0.75s0.97s0.48s1.07s1.45s





1.70.14a0.41a0.68a0.12a0.30a0.48a0.13s0.29a0.43a0.14s0.33a0.46a0.16s0.41a0.59a0.16s0.45s0.69a0.16s0.47s0.77s

1.80.12a0.36a0.60a0.11a0.28a0.44a0.12s0.27a0.40a0.13s0.31a0.44a0.14s0.38a0.56a0.14s0.40a0.63a0.14s0.41s0.68a

1.90.11a0.33a0.54a0.10a0.26a0.41a0.11s0.26a0.38a0.12a0.29a0.42a0.12a0.35a0.52a0.12a0.36a0.58a0.12a0.37a0.61a





TABLE V.I. (CONT.)

pMPa

2.0

Gkg/m2s

250

2.0 500

2.0 750

2.0 1000

2.0 1500

2.0 2000

2.0 3000

qMW/m2

0.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.0

X

-0.20.88g0.90g0.99g0.90g0.90g0.97g0.90a0.90g

l . l lg0.19a0.90gl . l lg0.90a0.90g

l . l lg0.90a0.90gl . l lg0.90a0.90gl . l lg

-0.10.75g0.76g0.90g0.77g0.76g0.91g0.76a0.76g0.97g0.76a0.76g0.97g0.77a0.77g0.97g0.77a0.77g0.97g0.78a0.78g0.97g

0.00.48g0.63g0.84g0.50g0.70g0.85g0-53g0.70g0.94g0.55g0.70g0.97g0.73g0.74a0.97g0.73g0.81g0.97g0.73g0.81g0.97g

0.10.39g0.59g0.82g0.42g0.63g0.84g0.49g0.65g0.90g0.56g0.66g0.97a0.76g0.78g1.00a0.85g0.88g0.98g1.35a1.37g1.37g

0.20.28g0.53g0.80g0.40g0.63g0.88g0.55g0.75g0.92g0.70g0.86gl.OOg1.05g1.17g1.22g1.30a1.35a1.38g2.25a2.30a2.32g

0.30.34g0.55g0.80g0.49g0.71g0.93g0.66g0.97g1.08g0.84g1.23g1.27g1.42g1.60a1.64g1.95a2.00a2.03g2.34a2.55a2.60a

0.40.39g0.56g0.80g0.57g0.78g0.98g0.77g1.10a1.24g0.97g1.35a1.44a1.78g1.90a2.06g1.70a2.13a2.68g |2.30a2.55a2.65a |

0.50.41g0.58g0.82g0.67g0.80g1.02g0.94g1.14g1.25g1.21g1.48g1.52g1.32a2.01a2.36g |1.17s1.91s

|2.28a2.28s2.55a2.71s

0.60.43g0.59g0.84g0.78g0.82g1.16gl . l lg1.21a1.27g1.07a1.36g1.61a0.85s1.71s

|2.02a1.11s1.47s1.88s2.28s2.55s2.73s

0.70.54g0.65g0.89g0.90a0.98g1.29g1.04a1.29g1.45g |0.92s1.33a1.74g0.71s1.19s1.68s1.08s1.36s1.65s2.16s2.52s2.75s

0.80.64g0.72g0.94g1.10a1.14g1.50g0.98s1.34a

|l.63g0.54s1.29s1.57a0.66s1.00s1.35s1.00s1.31s1.55s

11.92s2.40s2.69s

0.90.71g0.73g0.98g1.02a1.33g1.71g0.52s1.40s1.58a0.42s0.92s1.41s0.60s0.92s1.19s0.90s1.25s1.49s1.59s2.20s2.55s

1.00.72a0.74g1.02a0.67s1.27a1.65g0.37s0.95s1.53a0.37s0.75s1.12a0.54s0.86s1.10s0.77s1.17s1.43s1.22s1.94s2.36s

g-Groenevelda - approximations - Sergeev

TABLE V.I. (CONT.)

pMPa

2.0

Gkg/m2s

250

2.0 500

2.0 750

2.0 1000

2.0 1500

2.0 2000

2.0 3000

qMW/m2

0.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.0

X1.10.71g0.72g1.04a0.42s1.21s1.58g0.30s0.74s1.17a0.33s0.65s0.95a0.48s0.80s1.03s0.63s1.08s1.36s0.87s1.65s2.12s

1.20.54s0.70g1.05a0.31s0.88s1.44a0.26s0.61s0.96a0.29s0.58s0.84a0.41s0.75s0.98s0.50s0.98s1.27s0.60s1.36s1.86s

1.30.37s0.69a1.08a0.25s0.69s1.13a0.23s0.53a0.82a0.26s0.53s0.76a0.34s0.69s0.92s0.39s0.87s1.18s0.42s1.10s1.61s

1.40.28s0.68a1.11a0.21s0.57a0.93a0.21s0.47a0.72a0.24s0.49s0.70a0.29s0.64s0.87s0.30s0.77s1.09s0.31s0.89s1.37s




1.80.14a0.43a0.71a0.13a0.35a0.56a0.14s0.34a0.51a0.15s0.38a0.55a0.15s0.44a0.67a0.15s0.45s0.73a0.15s0.46s0.76s






TABLE V.I. (CONT.)

pMPa

3.0

Gkg/m s

250

3.0 500

3.0 750

3.0 1000

3.0 1500

3.0 2000

3.0 3000

qMW/m2

0.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.0

X

-0.20.98g1.06g1.20gl.OOg1.06g1.28g1.06a1.06g1.28g1.06a1.06g1.28g1.06a1.06g1.28g1.06a1.06g1.28g1.06a1.06g1.28g

-0.10.84g0.88g1.05g0.86g0.88gUOg0.88a0.88gl.lOg0.88a0.88g1-lOg0.88a0.88gl.lOg0.88a0.88gl.lOg0.89a0.89gUOg

0.00.56g0.69g0.88g0.58g0.76g0.96g0.60g0.76g0.98g0.63g0.76gl.OOg0.78g0.86gl.OOg0.78g0.86gl.OOg0.78g0.86g1.02g

0.10.45g0.64g0.85g0.48g0.68g0.89g0.55g0.70g0.94g0.63g0.72gl.OOg0.83g0.83gl.OOg0.95g0.96g1.05g1.35a1.40a1.44g

0.20.32g0.56g0.82g0.45g0.68g0.88g0.61g0.79g0.96g0.76g0.91g1.05g1.16g1.24g1.29g1.35a1.40a1.46g2.30a2.35a2.39g

0.30.37g0.57g0.82g0.53g0.75g0.92g0.71g1.02g1.12g0.89g1.29g1.33g1.56g1.82g1.71g1.90a2.00a2.11g3.10a3.35a3.36g

0.40.42g0.59g0.83g0.61g0.82g0.97g0.82g1.15a1.29g1.03g1.55a1.60gl-97g2.05a2.13g1.85a2.70a2.76g3.15a3.72s

0.50.44g0.60g0.84g0.72g0.86g1.02gl.Olg1.22g1.31g1.28g1.59g1.61g1.63a2.20a2.42g1.78s2.60a2.71a3.24s3.62a

3.80a ||3.78s

0.60.46g0-61g0.86g0.83g0.89gl-07g1.19g1.30a1.34g1.15a1.52g1.61g1.29s2.32a2.37a1.57s2.07s2.66s3.23s3.57s3.78s

0.70.58g0.68g0.90g1.02a1.02g1.15g1.19a1.40g1.49g1.00a1.44a1.81g0.98s1.64s2.32s1.50s1.86s2.22s3.03s3.50s3.76s

0.80.70g0.74g0.94g1.10a1.16g1.23g1.19a1.60g1.64g0.83s1.36a1.90a0.88s1.33s1.78s1.38s1.75s2.05s|2.66s3.28s3.63s

0.90.75a0.77g0.99g1.21a1.34g1.44g0.81s1.47a1.95g0.58s1.29s1.99s0.79s1.19s1.54s1.20s1.65s1.94s2.16s2.94s3.38s

1.00.76a0.80g1.04g1.04s1.53g1.65g0.51s1.34s1.75a0.48s0.99s1.48s0.69s1.09s1.40s1.00s1.52s1.84s1.60s2.52s3.05s


TABLE V.I. (CONT.)

to pMPa

3.0

Gkg/m2s

250

3.0 500

3.0 750

3.0 1000

3.0 1500

3.0 2000

3.0 3000

qMW/m2

0.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.0

X1.10.77a0.78g1.06g0.56s1.32a1.58g0.39s0.97s1.55s0.41s0.83s1.21s0.59s1.00s1.29s0.78s1.37s1.71s1.08s2.07s2.67s

1.20.65s0.75g1.06g0.39s1.12s1.53g0.32s0.78s1.22a0.36s0.73s1.05a0.49s0.92s1.21s0.59s1.20s1.58s0.70s1.64s2.27s

1.30.43s0.75a1.06a0.30s0.85s1.39a0.28s0.66s1.02a0.32s0.66s0.94a0.39s0.84s1.13s0.44s1.04s1.44s0.47s1.28s1.90s





1.80.16a0.48a0.79a0.15s0.40a0.65a0.16s0.40a0.60a0.16s0.43a0.64a0.16s0.48s0.75a0.16s0.49s0.81s0.16s0.49s0.82s

1.90.14a0.42a0.70a0.14a0.37a0.59a0.14s0.37a0.56a0.15s0.40a0.61a0.14s0.43a0.69a0.15s0.44s0.72a0.15s0.44s0.73a





TABLE V.I. (CONT.)

pMPa

4

Gkg/m2s

250

4 500

4

4

750

1000

4 1500

4 2000

4 3000

qMW/m2

0.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.0

X-0.21.08g1.22g1.42gl.lOg1.22g1.46g1.20g1.22g1.46g1.30g1.22g1.46g1.30g1.22g1.46g1.30g1.22g1.46g1.30g1.22g1.46g

-0.10.85a0.89g1.20g0.96g0.99g1.22g0.99g0.99g1.22g1.02g0.99g1.22g1.03g0.99g1.22g1.03g0.99g1.22g1.03gl.OOg1.22g

0.00.63g0.75g0.92g0.65g0.82gl.Olg0.68g0.82g1.02g0.70g0.82g1.03g0.84g0.90g1.04g0.84g0.90g1.04g0.84g0.90g1.07g

0.10.50g0.68g0.88g0.53g0.73g0.93g0.61g0.75g0.99g0.70g0.78g1.05g0.90g0.88g1.05g1.00a1.03g1.12g1.40a1.45a1.50g

0.20.36g0.59g0.84g0.50g0.72g0.92g0.66g0.84gl.Olg0.82g0.96gl . l lg1.27g1.32g1.36g1.45a1.50a1.54g2.35a2.40a2.46g

0.30.40g0.60g0.85g0.58g0.79g0.96g0.76g1.07g1.17g0.95g1.34g1.39g1.71g1.74a1.77g2.10a2.15a2.19g3.30a3.40a3.45g

0.40.44g0.61g0.85g0.66g0.86gl.Olg0.87g1.30g1.34g1.08g1.60a1.67g2.00a2.10a2.19g2.72a2.80a2.83g4.19s4.35a4.45g |

0.50.47g0.63g0.87g0.77g0.91g1.06g1.07g1.31g1.37g1.38g1.62a1.68g2.15a2.30a2.49g2.66s3.09a3.34g4.40s4.74s|5.08s

0.60.49g0.64g0.88g0.89g0.96g1.12g1.28g1.32g1.41g1.50a1.68g1.70g2.14s2.53a2.78g2.12s2.80s3.59s4.37s4.80s5.04s

0.70.62g0.71g0.91g0.95a1.07g1.14g1.31a1.51g1.53g1.33a1.95g1.92g |1.34s2.28s3.26s2.01s2.44s2.88s4.08s4.67s4.98s

0.80.76g0.78gl.OOg1.00a1.17g1.20a1.35g1.60a1.65g1.18s1.81a

|2.14g1.17s1.74s2.32s1.83s2.28s2.63s|3.55s4.33s4.75s

0.90.78a0.82g1.07g1.30a1.36g1.38g1.17s1.71a1.95g0.76s1.68s2.00a1.03s1.51s1.94s1.57s2.11s2.46s2.84s3.81s4.36s

1.00.80a0.85g1.08g1.47s1.55g1.59g0.66s1.73s1.93a0.60s1.23s1.85s0.89s1.37s1.74s1.27s1.91s2.29s2.04s3.19s3.85s


to

toTABLE V.I. (CONT.)

pMPa4

Gkg/m2s250

4 500

4 750

4 | 1000

4 1500

4 2000

4 3000

qMW/m2

0.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.0

X

1.10.78a0.88a1.09g0.71s1.44g1.56g0.48s1.20s1.91s0.51s1.01s1.47s0.73s1.24s1.59s0.96s1.68s2.11s1.31s2.54s3.28s

1.20.76s0.88a1.32a0.47s1.35s1.52g0.39s0.93s1.46s0.44s0.87s1.26s0.59s1.12s1.47s0.70s1.44s1.91s0.80s1.94s2.71s







1.90.15a0.46a0.76a0.15a0.41a0.66a0.15s0.41a0.64a0.16s0.44a0.68a0.16s0.47s0.76a0.16s0.47s0.78a0.16s0.47s0.78s


2.10.12a0.37a0.62a0.12a0.34a0.55a0.13a0.36a0.56a0.13a0.37a0.59a0.13a0.38a0.63a0.13s0.38a0.63a0.13s0.38a0.64a

2.20.11a0.34a0.57a0.11a0.32a0.51a0.12a0.33a0.52a0.12a0.34a0.55a0.12a0.35a0.58a0.12s0.35a0.58a0.12a0.35a0.58a


TABLE V.I. (CONT.)

pMPa

6

Gkg/m2s

250

6 500

6 750

6 1000

6 1500

6 2000

6 3000

qMW/m2

0.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.0

X


-0.11.15g1-lOgl-29g1.13a1.26g1.39g1.21g1.27g1.40g1.25g1.28g1.42g1.25g1.28g1.42g1.25g1.28g1.42g1.25g1.28gl-42g

0.00.77g0.88gl.Olg0.81g0.98g1.14g0.85g1.03g1.18g0.89g1.07g1.22g0.95gl.lOg1.22g0.95gl . lOg

1.22g0.98gl.lOg1.25g


0.20.48g0.66g0.90g0.64g0.82gl.Olg0.80g0.95g1.12g0.96g1.08g1.22g1.51g1.44g1.49g2.32g2.01g1.74g4.16g3.31g2.71g

0.30.50g0.67g0.90g0.71g0.83a1.05g0.81g1-17S

1.28gl . l lg1.45g1.50g2.00g2.02g1.90g3.22g2.76g2.38g5.88g4.51g3.77g

0.40.53g0.68g0.90g0.78g0.85g1.09g1.02a1.39g1.44g1.28g1.83g1.78g2.49g2.59g2.32g4.00a3.52g3.03g6.84s5.70g4.82g |

0.50.55g0.69g0.91g0.87g1.02g1.14g1.23g1.46g1.49g1.60g1.90g1.85g3.22g2.89g2.82g3.75a4.07g3.59g |7.00s|6.93g|6.00g

0.60.58g0.70g0.91g0.96gl.lOg1.19s1.45g1.54g1.55g1.93g1.98g

1.91s2.68g3.20g2.93g |3.38s|4.12a|4.14g6.94s7.60s7.17g

0.70.70g0.78g0.93g1.20g

l-17s1.25a1.72g1.69g1.60g2.00a2.20g2.06g2.15s3.30a|3.36g3.17s3.74s4.33s6.45s7.33s7.70s

0.80.82g0.87a0.97a1.42g1.24g1.30a2.00g1.84g1.66g |2.06s2.43g |2.20g1.80s2.60s3.43 s2.85s |3.43s3.86s5.59s6.72s7.26s

0.91.03g0.94g1.02g1.84g1.47g1.36g1.50a2.15s11.97s1.15s2.40a2.58g1.56s2.19s2.76s|2.41s3.13s3.56s4.41s5.81s6.54s

1.01.05al.Olgl-12g1.42a1.69g1.40a1.00s1.91a2.28g0.86s1.73s2.58s1.31s1.94s2.41s1.89s2.77s3.26s3.09s4.73s5.64s


to

TABLE V.I. (CONT.)

pMPa6

Gkg/m2s250

6 500

6 750

6 1000

6 1500

6 2000

6 3000

qMW/m2

0.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.0

X

1.1

o era

1.03a1.13g1.00s1.54g1.47a0.68s1.68s2.06g0.70s1.37s1.99s1.04s1.72s2.17s1.37s2.36s2.93s1.88s3.62s4.65s

1.20.94g1.08a1.14g0.62s1.42g1.55g0.52s1.25s1.87g0.59s1.16s1.65s0.80s1.51s1.97s0.94s1.96s2.58s1.07s2.63s3.69s

1.30.62s1.14a1.15a0.45s1.27s1.57a0.43s1.01s1.56s0.49s1.01s1.44s0.60s1.31s1.78s0.64s1.59s2.23s0.66s1.88s2.86s

1.40.44s1.08a1.15a0.36s0.99s1.62a0.36s0.86s1.31a0.40s0.90s1.28s0.45s1.13s1.59s0.46s1.28s1.91s0.46s1.38s2.22s



1.70.24s0.70a1.17a0.22s0.60a0.98a0.23s0.60s0.92a0.24s0.64s0.97a0.24s0.71s1.12s0.24s0.72s1.18s0.24s0.72s1.20s



2.00.16a0.48a0.79a0.16s0.44a0.71a0.16s0.46a0.72a0.16s0.47a0.76a0.16s0.49s0.80a0.16s0.49s0.81a0.16s0.49s0.81s


2.20.13a0.39a0.65a0.13a0.37a0.60a0.13a0.39a0.62a0.13a0.40a0.65a0.13a0.40a0.66a0.13a0.40a0.67a0.13a0.40s0.67a


TABLE V.I. (CONT.)

pMPa

8

Gkg/m2s

250

8 500

8 750

8 1000

8 1500

8 2000

8 3000

qMW/m2

0.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.0

X



0.00.89g0.98g1.08g0.98g1.17g1.30gl.Olg1.24g1.34g1.03g1.32g1.38g1.03g1.32g1.38g1.03g1.32g1.38g1.13g1.32g1.40g

0.10.75a0.88g1.02g0.89g1.10a1.16g0.94g1.09g1.21g0.98g1.18g1.28g1.19g1.18g1.31g1.49g1.36g1.46g2.33g1.99g2.04g

0.20.59g0.73g0.98a0.78g0.93gl . l lg0.98g1.07g1.19g1.14g1.21g1.29g1.74g1.50g1.54g2.53g2.08g1.94g4.33g3.24g2.87g

0.30.60g0.73g0.95g0.84g0.96g1.14g1.09g1.21g1.34g1.33g1.47g1.54g2.09g1.96g1.95g3.34g2.72g2.57g5.92g4.47g4.14g |

0.40.61g0.73g0.95g0.91g0.99g1.16g1.22g1.36g1.49g1.52g1.72g1.78g2.44g2.42g2.36g4.14g3.36g3.20g7.50g5.69g|5.32g

0.50.64g0.73a0.94g0.95g1.02g1.18g1.42g1.44g1.55g1.90g1.86g1.92g3.00a2.81g2.78g |5.60a4.28g |3.92g10.3g7.41g6.65g

0.60.66g0.75a0.93gl.OOg1.04g1.19g1.52a1.52g1.62g2.00a2.00g2.05g3.30a3.20g|3.20g5.24s5.20g4.64g10.5s9.13g7.98g

0.70.73g0.77g0.93g1.10al.lOg1.25a1.62a1.67g1.66g2.30a2.24g2.18g3.32s3.84g3.62g 14.90s |5.81s5.72g9.73s |10.9g9.05g

0.80.80g0.83g0.92g |1.20a1.16g1.30a |1.72a1.82g1.71g 12.25a2.48g |2.31g2.78s |3.89s4.03g|4.38s5.33s5.90s8.40s10.4s11.0g

0.90.84a0.93g|l.01g1.30a1.32a|l.36g1.80a2.17g|2.06g1.71s

|2.46a2.76g|2.38s3.26s3.99s3.65s4.79s5.40s6.59s8.85s10.0s

1.00.88a1.95gl . l lg1.35a1.45a1.55a1.43s2.30a2.41g1.26s2.43s2.72a1.95s2.85s3.46s2.80s4.14s4.85s4.50s7.02s8.43s


tooo

TABLE V.I. (CONT.)

pMPa8

Gkg/m2s250

8 500

8 750

8 1000

8 1500

8 2000

8 3000

qMW/m2

0.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.0

X

1.10.92al.OOg1.15g1.44s1.48g1.63g0.94s2.26s2.24g1.01s1.88s2.68s1.50s2.47s3.08s1.95s3.42s4.24s2.60s5.16s6.70s

1.20.97g1.10a1.18g0.84s1.35g1.64g0.71s1.64s2.10g0.81s1.57s2.20s1.09s2.11s2.73s1.26s2.72s3.61s1.39s3.55s5.07s

1.30.78s1.30a1.94a0.59s1.30a1.84a0.57s1.30s1.99s0.65s1.34s1.89s0.77s1.76s2.40s0.81s2.10s3.00s0.82s2.40s3.73s





1.80.24s0.71a1.18a0.23s0.65a1.04a0.24s0.66s1.02a0.24s0.70s1.09s0.24s0.72s1.19s0.24s0.72s1.20s0.24s0.72s1.20s



2.10.17a0.50a0.83a0.17s0.48a0.77a0.17s0.49a0.79a0.17s0.50a0.82a0.17s0.50s0.84a0.17s0.50s0.84a0.17s0.50s0.84s

2.20.15a0.45a0.75a0.15a0.44a0.71a0.15s0.45a0.73a0.15s0.46a0.75a0.15s0.46a0.76a0.15s0.46a0.76a0.15s0.46s0.76s


TABLE V.I. (CONT.)

pMPa

10

Gkg/m2s

250

10 500

10 750

10 1000

10 1500

10 2000

10 3000

qMW/m2

0.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.0

X



0.00.86g0.93g1.07g1.08g1.29g1.36g1.08g1.33g1.41g1.08g1.38g1.47g1.08g1.38g1.47gl.lOg1.38g1.47g1.26g1.38g1.47g

0.10.77g0.82gl.OOg0.87g1.03g1.19g0.98g1.14g1.21gl.lOg1.26g1.23g1.53g1.33g1.41g1.90g1.62g1.69g2.89g2.40g2.26g

0.20.46g0.59g0.88g0.77g0.88g1.08gl.lOgl.lOg1.18g1.42g1.32g1.29g2.02g1.63g1.64g2.76g2.22g2.00g4.56g3.39g2.88g

0.30.48g0.60g0.89g0.82g0.89g

l.Hg1.20g1.18g1.28g1.58g1.47g1.46g2.23g2.06g1.99g3.48g2.78g2.62g |5.77g4.63g 14.32g |

0.40.50g0.61g0.90g0.86g0.90g1-14R

1.30g1.26g1.38g1.74g1.62g1.63g2.44g2.48g2.34g |4.20g3.34g ||3.23g6.99g|5.86g|5.76g

0.50.54g0.61g0.91g0.89g0.87g1.14g1.42g1.33g1.49g1.95g1.80g1.85g2.85a2.90g|2.81g6.45g|4.40g4.15g11.0g8.43g7.64g

0.60.58g0.62g0.93g0.89a0.88a1.16a1.55g1.40g1.60g2.16g1.98g2.07g3.30a3.31g3.28g7.73s5.46g5.07g15.0s11.Og9.52g

0.70.67g0.66g0.96g0.89a0.89g1.21g1.70a1.54g1.78g2.30a2.20g2.35g4.00a4.10g3.87g7.27s7.43g6.39g13.9s14.0g11.7g

0.80.75g0.71g0.99g0.90a0.95g1.29g1.80a1.68g1.96g2.50a2.42g2.62g|4.17s4.90g4.45g6.48s8.18s7.70g12.0s15.6sH.Og

0.90.85g 10.83g |1.08g1.10a |1.12g1.49g1.90a |1.94g2.19g2.42s2.77g2.89g3.58s4.87s5.54g5.38s7.30s8.27s8.46s13.2s15.2s

1.00.90a|0.95g1.17g11.20a1.29g1.69g|l.83s2.20g2.43g1.83s3.12g3.16g2.88s4.25s5.08s4.07s6.19s7.32s6.43s10.3s12.6s


to

toO

TABLE V.I. (CONT.)

pMPa10

Gkg/m2s

250

10 500

10 750

10 1000

10 1500

10 2000

10 3000

qMW/m2

0.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.0

X1.10.85a0.90g1.17g1.15a1.16g1.66g1.24s2.02g2.44g1.45s2.59s3.20g2.16s3.62s4.47s2.76s4.99s6.24s3.60s7.38s9.72s

1.20.82a0.86g1.18g1.02a1.04g1.64g0.94s1.86g2.45g1.14s2.15s2.94s1.50s3.00s3.88s1.70s3.81s5.14s1.83s4.85s7.06s

1.30.80a0.86a1.18a0.76s1.04a1.64a0.74s1.65s2.47s0.88s1.82s2.51s1.01s2.41s3.32s1.05s2.81s4.10s1.06s3.13s4.96s






1.90.24s0.73a1.18a0.24s0.69s1.11a0.24s0.71s1.12a0.25s0.74s1.20s0.25s0.74s1.23 s0.25s0.74s1.24s0.25s0.74s1.24s



2.20.18s0.52a0.87a0.18s0.52a0.84a0.18s0.52a0.86a0.18s0.53s0.88a0.18s0.53s0.88a0.18s0.53s0.88s0.18s0.53s0.88s


TABLE V.I. (CONT.)

pMPa

12

12

Gkg/m s

250

500

12 750

12 1000

12 1500

12 2000

12 3000

qMW/m2

0.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.0

X


-0.12.78g2.20g2.11g2.78g2.20g1.07g2.78g2.20g2.11g2.78g2.20g2.1 lg2.78g2.20g2.11g2.78g2.20g2.11g2.78g2.20g2.11g

0.00.90g0.88g1.07g0.87a0.90g1.02g0.94g0.93g1.07g0.95g0.96g1.08g1.04g1.02g1.15g1.15g1.12g1.26g1.33g1.30g1.45g

0.10.80g0.84g1.02g0.83a0.85g0.95g1.06g0.94g1.07gl-27g1.04g1.13g2.05g1.45g1.42g2.90g1.88g1.50a5.11g3.27g2.30a


0.30.42g0.59g0.88g0.79g0.79gl.lOg1.33g1.07g1.24g1.86g1.34g1.47g3.30g2.17g1.90g

0.40.49g0.61g0.91g0.84g0.82gl.lOg1.37gl . l lg1.31g1.90g1.39g1.52g3.70g2.55g2.28g

4.99g |6.20g3.06g|2.52g8.49g6.62g4.98g

3.97g3.32g9.86g8.67g6.98g

0.50.62a0.65g0.93g1.03g0.80gl.lOg1.64g1.21g |1.42g2.26g1.63gl-74g4.18g3.19g3.03g7.82g5.28g4.93g13.6g11.3g10.2g

0.60.67a0.68g0.96g

1.21g0.77g1.19g1.91g1.32g1.53g2.62g1.87g

0.70.70a0.72g|0.98g1.44g

|0.88g1.29g2.23g1.56g1.80g

0.80.75a0.76gl.OOg1.66g0.99g1.48g2.54g1.81g2.07g

3.02g ||3.42g2.25g

1.96g |2.41g4.65g3.84g3.78g9.44g6.58g6.53g17.3g13.9g13.4g

5.68g4.82g4.73s10.5s8.29g8.54g19.3s15.8g16.2g

2.63g2.86g6.22s5.81g5.67g9.41slO.Og10.5g16.8s17.6g18.9g

0.9 11.00.78a j|0.75a0.80g J0.83g1.06g1.70g1.17g1.68g2.70g2.16g2.49g3.41s3.15g3.50g5.35s7.02g7.11g7.83s11.2s12.0g13.3s19.4s20.2g

1.12g1.73g1.36g1.50g2.58s2.51g2.91g2.69s3.67g4.14g4.28s6.53s7.77s5.91s9.41s11.3s9.04s15.1s18.8s


ON

K>TABLE V.I. (CONT.)

pMPa12

Gkg/m2s

250

12 500

12 750

12 1000

12 1500

12 2000

12 3000

qMW/m2

0.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.0

X1.10.73g0.80g1.12g1.40g1.16g1.45a1.80s2.18g2.68g2.14s3.15g3.73g3.15s5.48s6.78s3.94s7.43s9.46s4.99s10.6s14.3s

1.20.66g0.76g1.13g1.15g0.96g1.32a1.37s1.90g2.48g1.64s2.73g3.38g2.13s4.41s5.76s2.35s5.51s7.56s2.48s6.78s10.1s

1.30.66a0.76a1.13a0.98s0.96a1.32a1.06s1.90a2.43a1.22s2.57s3.19a1.38s3.42s4.78s1.41s3.90s5.80s1.42s4.21s6.78s

1.40.66a0.76a1.13a0.74s0.96a1.32a0.83s1.88s2.38a0.89s2.14s3.01s0.93s2.59s3.88s0.93s2.75s4.37s0.93s2.79s4.64s








2.20.21s0.62a1.03a0.2 IS0.61s1.00a0.21s0.63s1.04a0.21s0.63s1.04a0.21s0.63s1.05s0.21s0.63s1.05s0.21s0.63s1.05s


TABLE V.I. (CONT.)

pMPa

14

Gkg/m2s

250

14 500

14 750

14 1000

14 1500

14 2000

14 3000

qMW/m2

0.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.0

X

-0.23.53g4.31g3.47g5.53g4.31g3.47g5.53g4.31g3.47g5.53a4.31g3.47g5.53g4.31g3.47g5.53g4.3 lg3.47g5.53g4.31g3.47g


0.01.13g0.91g1.21g1.13g0.92g1.21g1.13g0.95g1.21g1.13g0.99g1.21g1.22g1-lOg1.26g1.31g1.23g1.35g1.54g1.45g1.57g

0.10.94g0.89gl . l lg0.97g0.90gl . l lg1.32g1.04g1.19g1.66g1.17g1.27g2.93g1.79g1.78g4.23g2.49g2.00a6.91g4.64g2.90a

0.20.42g0.60g0.88g0.87g0.79g0.99g1.45gl.Olg1.26g2-04g1.22g1.52g3.74g2.05g1.92g5.36g2.74g2.26g9.29g6.10g4.25g


0.40.56g0.62g0.93g1.08g0.81g1.15g1.76g1.09g1.36g2.44g1.37g1.57g4.60g2.92g2.69g7.67g5.12g4.30g12.7g11.lg8.91g


0.6l.OOg0.76gi.oig1.53g0-95g1.19g2.35g1.53gl-75g3.17g2.10g2.30g5.64g4.63g4.86g10.7g8.29g8.49g19.5g16.6g16.6g

0.71.03g0.83g1.04g1.50e1.12g1.32g2.65g1.89g2.07g3.57g2.66g2.82g6.44g5.88g6.25g12.8glO.lg10.9g22.0g18.2g20.2g

0.81.05g0.88g1.07g1.40e |1.28g1.45g2.95g2.25g2.39g3.98g3.22g3.34g7.24g7.14g7.64g13.2s11.9g13.4g22.5s20.4g23.9g

0.90.98g |0.91g1.12g

|l.30e1.50g1.64g3.07g2.69g2.89g4.21g3.86g4.14g7.81s8.33g9.17g11.1s14.5g15.0g18.0s25.0g25.5g

1.0|0.90g0.94g1.18g1.30e1.73g1.83g3.20g3.13g3.39g4.07s4.54g4.94g6.28s9.93g10.7g8.41s14.2s16.7g12.4s21.9s27.1g


toON

TABLE V.I. (CONT.)

pMPa14

Gkg/m s

250

14 500

14 750

14 1000

14 1500

14 2000

14 3000

qMW/m2

0.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.0

X1.10.91e0.90g1.18g1.30e1.46g1.74g2.56g2.70g3.07g3.26s3.88g4.36g4.61s8.16g8.91g5.61s11.1s12.9g6.91s15.4s18.8g

1.20.84e0.86g1.19g1.30e1.22g1.64g2.04s2.32g2.78g2.47s3.33g3.86g3.06s6.67s7.52g3.32s8.11s10.3g3.44s9.65s13.8g

1.30.81e0.86a1.19a1.20e1.22a1.64a1.56s2.32a2.78a1.78s3.23a3.86a1.94s5.02s7.16s1.96s5.58s8.49s1.97s5.89s9.60s

1.40.78e0.86a1.19aUOe1.22a1.64a1.18s2.32a2.78a1.25s3.12s3.86a1.28s3.67s5.61s1.28s3.82s6.16s1.28s3.85s6.40s

1.50.72a0.86a1.19a0.82s1.22a1.64a0.89s2.23s2.78a0.90s2.49s3.70s0.91s2.70s4.34s0.91s2.73s4.51s0.91s2.73s4.55s


1.70.53s0.86g1.19a0.53s1.22a1.64a0.54s1.55s2.40s0.54s1.61s2.60s0.54s1.63s2.71s0.54s1.63s2.72s0.54s1.63s2.72s

1.80.44s0.86g1.19a0.44s1.22a1.64a0.45s1.31s2.08s0.45s1.34s2.19s0.45s1.34s2.23s0.45s1.34s2.23s0.45s1.34s2.24s


2.00.32s0.86a1.19a0.33s0.95a1.53a0.33s0.98s1 60s0.33s0.98s1.63s0.33s0.98s1.63s0.33s0.98s1.63s0.33s0.98s1.63s




TABLE VJ. (CONT.)

pMPa

16

Gkg/m2s

250

16 500

16 750

16 1000

16 1500

16 2000

16 3000

qMW/ni2

0.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.0

X

-0.26.41g4.63g3.29g6.41s4.63g3.29g6.41g4.63g3.29g6.41g4.63g3.29g6.41g4.63g3.29g6.41g4.63g3.29g6.41g4.63g3.29g

-0.14.25g2.90g2.43g4.25s2.90g2.43g4.25g2.90g2.43g4.25g2.90g2.43g4.25g2.90g2.43g4.25g2.90g2.43g4.25g2.90g2.43g

0.01.44g0.96g1.39g1.44g0.97g1.39g1.44gl.Olg1.39g1.44g1.06g1.39g1.46g1.21g1.41g1.52g1.36g1.46g1.80g1.63g1.72g

0.11.12g0.93g1.21g1.13g0.96g1.21g1.50a0.99a1.34g2.00a1.08a1.47g4.05g2.26g2.27g5.82g3.38g3.35g9.04g6.31g3.90a

0.20.55g0.64g0.90g1.03g0.81g1.06g1.57g0.96g1.29g2.11gl.lOg1.52g4.70g2.56g2.52g7.46g3.91g3.19g12.3g6.54g6.12g

0.30.62g0.64g0.93g1.24g0.84g1.13g1.93g1.07g1.40g2.62g1.30g1.66g5.31g3-llg2.99g8.53g5.43g4.58g14.4g11.4g

0.40.70g0.64g0.95g1.46g0.88g1.20g2.29g1.19g

0.5 10.60.92g J1.14g0.75g j|0.86gl.OOg1.68g1.06g1.27g2.63g1.54g

1.50g 1.81g3.13g 3.58g1.49g l|2.01g1.80g |2.33g5.92g3.66g3.46g9.60g6.94g5.97g16.6g14.4g

|8.86g | l l .6g

6.36g4.68g4.88g11.0g8.74g8.23g19.4g17.4g15.7g

1.06g1.91g1.24g1.34g2.70a1.89g2.12g|4.04g2.53g2.90g6.80g5.70g6.29g12.4g10.5g10.7g22.2g20.5g19.8g

0.71.15g0.93gl.lOg2.10e1.44g1.49g2.80e2.38g2.54g4.62g3.32g3.59g7.51g7.17g8.07a14.0g12.6g13.1g24.5g23.3g24.2g

0.8 10.91.16g0.98g1.14g2.00e1.63g1.63g3.00e2.87g2.95g5.20g4.11g4.27g8.21g8.65g9.85g15.5g14.6g15.6g27.0a26.1g28.6g

1.14g1.03g1.20g2.00e1.91g1.82g3.20e3.41g3.43g5.48g4.92g5.05g10.4glO.lgH.lg15.5s18.5g17.8g24.1s22.0a3L8g

1.0l . l lg1.06gl-25g2.00e2.00a2.01g4.02g3.86g3.92g5.75g5.75g5.82g9.17s11.6g12.4g11.9s17.7a20.0g17.0s31.5s35.0g


OS

toONO\

TABLE V.I. (CONT.)

pMPa16

Gkg/m s

250

16 500

16 750

16 1000

16 1500

16 2000

16 3000

qMW/m2

0.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.0

X1.11.08gl.Olg1.26g2.00e1.87g1.91g3.50g3.38g3.59g4.64g4.87g5.23g6.79s9.94g10.6g8.06s16.9s16.2g9.64s22.4s25.6g

1.21.05g0.97g1.27g1.90e1.58g1.82g3.17s2.90g3.29g3.80s4.14g4.70g4.53s8.08g9.05g4.82s12.3s13.5g4.94s14.2s19.6g

1.31.05a0.97a1.27a1.70e1.58a1.82a2.42s2.90a3.29a2.70s4.14a4.70a2.87s7.72s8.83a2.89s8.39s13.1s2.90s8.69s14.3s

1.41.05a0.97a1.27a1.60e1.58a1.82a1.78s2.90a3.29a1.86s4.14a4.70a1.89s5.51s8.62s1.89s5.65s9.25s1.89s5.68s9.46s

1.51.05a0.97a1.27a1.40e1.58a1.82a1.30s2.90a3.29a1.32s3.75s4.70a1.32s3.96s6.45s1.33s3.98s6.61s1.33s3.98s6.64s

1.60.94s0.97a1.27a1.20e1.58a1.82a0.98s2.73s3.29a0.98s2.89s4.59s0.98s2.94s4.88s0.98s2.95s4.91s0.98s2.95s4.92s




2.00.43s0.97a1.27a0.43s1.28s1.82a0.43 s1.30s2.15s0.43s1.30s2.16s0.43s1.30s2.17s0.43s1.30s2.17s0.431.30s2.17s


2.20.33s0.97a1.27a0.33a0.99s1.63a0.33s0.99s1.66s0.33s0.99s1.66s0.33s1.00s1.66s0.33s1.00s1.66s0.33s1.00s1.66s


TABLE V.I. (CONT.)

pMPa

18

Gkg/m s

250

18 500

18 750

18 1000

18 1500

18 2000

18 3000

qMW/m2

0.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.0

X




0.11.41g1.03g1.24g1.47gl.lOg1.29g2.05a1.19a1.48a2.35a1.35a1.67a5.40g3.35g3.07g7.92g5.33g4.59g12.0g9.56g7.36g


0.30.79g0.71g0.97g1.72g0.97g1.22g2.79g1.46g1.77g3.87g1.96g2.32g7.60g5.54g5.24g12.0glO.lg8.09g19.0g18.6g13.5g

0.40.84g0.72gl.OOg1.94gl.Olg1.29g3.43g1.72g2.01g4.92g2.43g2.73g9.13g6.66g6.16g13.7g12.3glO.lg21.8g22.1g |16.6g

0.51.03g0.84g1.06g2.21g1.28g1.41g3.45a1.92a2.43g5.91g3.20g3.44g10.3g8.23g7.87g15.5g14.9g12.8g24.5g|25.9g21.1g

0.61.22g

|0.86g1.12g2.48g1.54g1.53g3.47a |2.16g2.84g6.20e3.97g4.15g11.4g9.80g9.59g17.2g17.5g15.6g27.1g |29.7g25.6g

0.71.25g1.04g1.17g2.68g |1.79g1.69g

|3.50e3.46g3.23g6.70e5.12g4.77g12.9g11.6g11.2g18.8g19.9g18.1g

|29.1g33.1g30.6g

0.81.27g1.12g1.22g

|2.50e2.04g1.86g4.10e4.16g3.62g9.27g6.27g5.39g14.3g13.4g12.8g20.3g22.3g20.5g31.lg36.4g35.7g

0.91.34g1.18g1.28g2.50e2.38g2.06g4.60e4.86g4.34g9.97g7.33g6.63g16.5g14.7g13.9g23.9s25.6g22.2g34.0g42.0g38.4g

1.01.40g1.24g1.34g2.50e2.72g2.26g5.00e5.56g5.06g10.6s8.39g7.87g14.9s16.0g14.9g18.8s28.8g24.0g25.9s47.6g41.0g

g-Groenevelda - approximations - Sergeev

toCT\00

TABLE V.I. (CONT.)

pMPa18

Gkg/m s

250

18 500

18 750

18 1000

18 1500

18 2000

18 3000

qMW/m2

0.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.0

X1.11.36g1.21g1.35g2.60e2.40g2.14g4.50e4.89g4.69g8.72s7.20g7.19g11.3s13.7g13.0g13.1s23.4g20.4g15.2s35.1g32.3g

1.21.31g1.18g1.36g2.50e2.10g2.02g3.80e4.28g4.33g6.69s6.36g6.57g7.69s11.9gH.5g8.06s19.6g17.4g8.18s23.8s26.1g

1.31.31a1.18a1.36a2.30e2.10a2.02a3.00e4.28a4.33a4.78s6.36a6.57a4.98s10.8a11.5a5.01s14.7s16.9a5.02s15.0s24.9s

1.41.31a1.18a1.36a2.00e2.10a2.02a2.30e4.28a4.33a3.29s6.36a6.57a3.31s9.79s11.5a3.32s9.95s16.4s3.32s9.97s16.6s

1.51.31a1.18a1.36a1.80e2.10a2.02a2.00e4.28a4.33a2.30s6.36a6.57a2.31s6.91s11.4s2.31s6.93s11.5s2.31s6.94s11.6s

1.61.31a1.18a1.36a1.60e2.10a2.02a1.67s4.28a4.33a1.67s4.99s6.57a1.68s5.03s8.36s1.68s5.04s8.40s1.68s5.04s8.40s






2.20.49s1.18a1.36a0.49s1.46s2.02a0.49s1.46s2.43s0.49s1.46s2.43s0.49a1.46s2.43s0.49s1.46s2.44s0.49s1.46s2.44s


TABLE V.I. (CONT.)

pMPa

20

Gkg/m s

250

20 500

20 750

20 1000

20 1500

20 2000

20 3000

qMW/m2

0.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.0

X

-0.28.40g6.31g6.25g8.41g7.79g|6.67g8.41g7.79g6.67g8.41g7.79g6.67g8.41g7.79g6.67g8.41g7.79g6.67g8.41g7.79g6.67g

-0.15.58g4.04g4.57g5.58g4.44g4.37g5.58g4.44g|4.57g5.58g4.44g4.57g |5.58g4.44g4.57g5.58g4.44g4.57g5.58g4.44g4.57g

0.02.56g1.46g1.38g |2.56g1.46g1.38g2.56g1.46g1.38g2.56g1.46g

|l.38g2.56g1.56g1.56g2.59g1.90g1.91g2.56g2.39g2.41g

0.11.80g1.17g|l.20g2.00g1.26g |1.28g3.19g1.60a1.79g3.36a1.90a2.30g6.96g5.09g4.18g |10.6g8.33g6.36g15.8g14.4g10.3g

0.20.97g0.79gl.OOg2.28g|l.l6g1.25g3.22g1.75g |1.94g4.15g2.35g2.64g7.83g7.69g|7.29g14.0g14.4g ,11.0g |20.8g26.1g17.7g

0.30.98g0.82g |1.03g2.40g1.19g1.33g4.20g|2.23g2.42g5.99g3.26g3.31g11.0g9.80g9.03g17.0g17.9g

|l3.8g24.6g30.2g20.6g |

0.40.99g|0.84g1.07g2.52g1.21g1.40g5.17g2.70g2.89g7.82g4.18g4.38g14.2g11.9g10.8g20.0g21.3g16.6g28.4g34.4g|23.8g

0.51.12g0.95g1.12g2.88g1.54g1.58g6.33g3.42g3.40g9.76g5.31g5.21g16.9g14.4g12.8g22.7g25.2g ]

20.0g31.4g39.3g28.8g

0.61.24g1.06g1.19g3.24g |1.87g1.76g7.47g4.15g3.90g11.7g6.43g6.05g19.6g16.9g14.7g25.3g29.2g23.3g34.4g |44.3g33.8g

0.71.32g1.16g1.24g

|3.47g2.18g1.94g7.80a5.13g4.15g14.0g8.07g6.37g22.5g19.1g15.6g27.2g32. lg25.6g|35.9g47.8g39.5g

0.81.40g |1.26g1.29g3.71g2.50g2.12g8.20e6.11g4.40g16.2g9.71g6.68g25.4g21.3g16.5g29.2g34.9g27.9g37.4g51.4g45.1g

0.9|l.58g1.37g1.38g3.96g2.92g2.35g9.30e7.02g5.62g17.7g

H.lg8.88g27.3g22.2g17.4g30.4g35.7g28.4g39.2g51.9g45.2g

1.01.76g1.48g1.46g4.21g3.35g2.58g9.30e7.93g6.83g19.2g12.5g11.lg29.1g23.1g18.2g31.8g36.4g28.8g41.0g52.4g45.3g


N>

too

TABLE V.I. (CONT.)

pMPa

20

Gkg/m2s

250

20 500

20 750

20 1000

20 1500

20 2000

20 3000

qMW/m2

0.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.00.20.61.0

X

1.11.68g1.48g1.47g4.15a3.08g2.42g8.10e7.28gOOOlg16.8g11.4g10.4g24.1g20.2g16.7g25.5g31.6g25.6g32.7g46.3g39.4g

1.21.59g1.49g1.47g4.10e2.82g2.27g6.40e6.65g6.00g14.8g10.4g9.68g20.3g17.6g15.2g20.8g27.4g22.6g26.7s41.lg34.0g

1.31.59a1.49a1.47a3.80e2.82a2.27a5.10e6.65a6.00a13.5a10.4a9.68a18.1s17.6a15.2a18.2s26.5a22.6a18.2s39.1a34.0a

1.41.59a1.49a1.47a3.30e2.82a2.27a4.10e6.65a6.00a12.3s10.4a9.68a12.3s17.6a15.2a12.4s25.7a22.6a12.4s37.1s34.0a

1.51.59a1.49a1.47a2.80e2.82a2.27a3.40e6.65a6.00a8.28s10.4a9.68a8.30s17.6a15.2a8.31s24.9s22.6a8.32s24.9s34.0a

1.61.70e1.49a1.47a2.40e2.82a2.27a2.90e6.65a6.00a5.64s10.4a9.68a5.65s17.0s15.2a5.66s17.0s22.6a5.66s17.0s28.3s

1.71.50e1.49a1.47a2.40a2.82a2.27a2.60e6.65a6.00a3.95s10.4a9.68a3.96s11.9s15.2a3.96s11.9s19.8s3.97s11.9s19.8s

1.81.40e1.49a1.47a2.40a2.82a2.27a2.10e6.65a6.00a2.87s8.60s9.68a2.87s8.61s14.4s2.87s8.62s14.4s2.88s8.63s14.4s

1.91.40a1.49a1.47a2.14s2.82a2.27a1.80e6.45s6.00a2.15s6.46s9.68a2.16s6.47s10.8s2.16s6.48s10.8s2.16s6.48s10.8s

2.01.40a1.49aI Ala.1.67s2.82a2.27a1.60e5.01s6.00a1.67s5.02s8.36s1.67s5.02s8.37s1.68s5.03s8.38s1.68s5.03s8.38s

2.11.33s1.49a1.47a1.33s2.82a2.27a1.30e4.00s6.00a1.34s4.01s6.68s1.34s4.01s6.69s1.34s4.02s6.69s1.34s4.02s6.70s

2.21.09s1.49a1.47a1.09s2.82a2.27a1.20e3.28s5.47s1.10s3.29s5.48s1.10s3.29s5.48s1.10s3.29s5.49s1.10s3.29s5.49s


Appendix VI

CIAE METHOD FOR DETERMINING FILMBOILING HEAT TRANSFER

The non-equilibrium factor is defined as [Plummer (1976)]:

and

xe-xc

where

kd,kq and kx are the correction factors to account for the effects of tube diameter,

heat flux and local quality, respectively.

0.008J

The k0 is a function of P, G and XQ and its values are obtained from the calculation onthe mechanistic model [Chen and Chen (1994)] and provided in this appendix in tabular form.

Then the vapour temperature is calculated by the heat balance equation:

= xs- 1

Hfg

Finally, the wall temperature is obtained by:

T -T q

W ~ " V ( \

[K+K)with

K = Nuf0F

and

Nu f0 = 0.0175 • Ref 0812 Prf °-333 [Chen and Chen (1996a)].

where the subscript /refers to properties evaluated at the film temperature, Tf = ~\TW + Tvj

and P is in bar.

The non-equilibrium is primarily determined by the inlet flow condition, as accountedby the k0, but the effect of P and X are less important. With Kq - 1 and Kx=\ and without

considering the radiation heat transfer (hr = 0). 2192 CIAE film boiling data (L>0.1m and

(G-X)2DWe = > 10) are calculated for the wall temperature with an average error of 1.4%

PgCT

and a RMS error of 7.2%.

271

TABLE VI.I. THE TABLE OF NON-EQUILIBRIUM FACTORS "k0" OF CHENAND CHEN (1998)

p

(MPa)

0.1

0.3

0.5

1.0

2.0

4.0

6.0

G

(kg/m2s)255010020040060010001500

25501002004006001000

1500

255010020040060010001500

2550100

2004006001000

1500

25501002004006001000

150025501002004006001000

1500

255010020040060010001500

0.00.68

0.690.74

0.780.810.82

0.830.840.72

0.74

0.760.78

0.80

0.820.83

0.830.74

0.760.78

0.790.800.810.820.82

0.760.770.79

0.800.80

0.800.81

0.82

0.81

0.810.810.810.82

0.83

0.83

0.81

0.810.82

0.830.83

0.84

0.81

0.820.82

0.830.840.84

0.05

0.58

0.590.63

0.730.81

0.880.92

0.96

0.60

0.610.64

0.710.78

0.800.86

0.90

0.56

0.580.600.62

0.670.800.84

0.870.62

0.630.66

0.660.68

0.770.80

0.84

0.68

0.710.690.70

0.730.74

0.81

0.72

0.72

0.72

0.770.78

0.79

0.72

0.730.76

0.770.78

0.80

0.10.44

0.450.60

0.750.86

0.920.960.98

0.45

0.460.540.66

0.79

0.84

0.890.950.44

0.450.500.63

0.650.81

0.860.92

0.530.560.58

0.600.66

0.74

0.790.85

0.65

0.680.650.68

0.710.74

0.80

0.62

0.63

0.630.73

0.760.78

0.63

0.64

0.670.700.74

0.77

Xcr0.20.31

0.420.64

0.78

0.890.940.98

0.990.40

0.430.57

0.700.81

0.880.92

0.960.35

0.380.440.64

0.770.83

0.890.94

0.420.460.53

0.500.65

0.730.82

0.87

0.54

0.62

0.530.560.64

0.74

0.80

0.45

0.50

0.55

0.610.71

0.78

0.450.52

0.550.60

0.690.76

0.40.280.48

0.680.77

0.900.960.98

0.990.31

0.360.52

0.680.83

0.90

0.93

0.980.29

0.330.40

0.610.74

0.830.900.95

0.250.280.33

0.450.62

0.71

0.800.84

0.320.350.52

0.610.71

0.80

0.30

0.34

0.490.56

0.70

0.77

0.35

0.42

0.510.58

0.680.74

0.60.260.36

0.560.74

0.890.95

0.980.99

0.170.300.47

0.63

0.75

0.860.92

0.970.23

0.22

0.360.56

0.700.800.880.94

0.100.140.22

0.380.56

0.63

0.730.82

0.16

0.280.44

0.530.65

0.71

0.21

0.26

0.41

0.480.60

0.69

0.200.25

0.390.48

0.610.68

0.80.180.25

0.44

0.600.81

0.900.970.98

0.100.160.33

0.47

0.630.75

0.87

0.950.12

0.14

0.260.400.54

0.670.78

0.890.08

0.090.130.250.40

0.45

0.57

0.70

0.08

0.160.290.360.47

0.55

0.08

0.14

0.26

0.330.42

0.53

0.110.14

0.26

0.310.43

0.53

1.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.0

0.00.00.00.00.00.0

0.00.00.00.00.00.0

0.00.00.00.00.00.0

272

Appendix VII

TWO-PHASE VISCOSITY MODELS FOR USE IN THEHOMOGENEOUS MODEL FOR TWO-PHASE PRESSURE DROP

McAdams (1942)

1 = JL + IlliO (1)M MG ML

Cicchitti (1960)

M = * MG + ( l -x) / /L (2)

Owens (1961)

M= ML (3)

Dukler (1964)

/ / = (1-P) ML + PMG (4)

Weisman and Choe (1976)

suggested the following equation for a frothy mixture

f 2.5 1 (5)

l-39/?/64j

and

1 V (6)+ (MC -

for a misty mixture at high void fraction. Choe (1975) suggested a value of 3 for the constant kand |Oc is the mean of ^G and HL-

Beattie and Whalley (1982)

ju= ML{\-/3)(\ + 2.5 0) + MGP (7)

Beattie and Whalley also proposed some flow pattern specific models. For example, forbubbly flow

<u= juL (1 + 2.5J3) (8)

and for annular flow

273

Appendix VIII

TWO-PHASE PRESSURE DROP CORRELATIONSBASED ON THE MULTIPLIER CONCEPT

Martinelli-Nelson (1948)

Based on tests conducted using steam-water mixture, values of (|)LO2 are presented ingraphical form as a function of pressure and quality by Martinelli and Nelson. Table VIII.I hasbeen obtained from these graphs.

Accuracy of this correlation at high mass fluxes, i.e. G > 1500 kg/m2s is not good.

Lockhart-Martinelli (1949)

The authors defined a parameter %, generally known as the Martinelli parameter, as below.

, = £ = fdP/dz)L

& (dp/dz)G K)

The following expressions were obtained for the two phase multiplier

£ = 1 + - + (2)X X

2$1 = i+ cz+ z

Values of C are dependent on the nature of flow (i.e. laminar or turbulent) of individualphases and are given below:

C =20 for turbulent flow of both phases= 12 for laminar liquid and turbulent gas flow= 10 for turbulent liquid and laminar gas flow= 5 for laminar flow of both phases.

This correlation is mainly based on tests conducted at near atmospheric pressure with massvelocities less than 1500 g/m2s.

Lottes-FHnn (1956)

Correlation for annular upward flow through heated channels is

( 4 )

i -

Thorn (1964)

Thorn presented the two-phase friction multiplier, <J)LO25 in tabular and graphical form as a

function of quality and pressure for water-steam mixtures (Table VIILII).

274

TABLE VIII.I. VALUES OF THE TWO-PHASE FRICTIONAL MULTIPLIER <t>L02 FOR

STEAM-WATER SYSTEM FROM THE MARTINELLI-NELSON MODEL

Steam

Quality

0.01

0.05

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

Pressure (bar)

1.01

5.6

30.0

69.0

150.0

245.0

350.0

450.0

545.0

625.0

685.0

720.0

525.0

6.89

3.5

15.0

28.0

56.0

83.0

115.0

145.0

174.0

199.0

216.0

210.0

130.0

34.4

1.8

5.3

8.9

16.2

23.0

29.2

34.9

40.0

44.6

48.6

48.0

30.0

68.9

1.6

3.6

5.4

8.6

11.6

14.4

17.0

19.4

21.4

22.9

22.3

15.0

103.0

1.35

2.4

3.4

5.1

6.8

8.4

9.9

11.1

12.1

12.8

13.0

8.6

138.0

1.20

1.75

2.45

3.25

4.04

4.82

5.59

6.34

7.05

7.70

7.95

5.90

172.0

1.10

1.43

1.75

2.19

2.62

3.02

3.38

3.70

3.96

4.15

4.20

3.70

207.0

1.05

1.17

1.30

1.51

1.68

1.83

1.97

2.10

2.23

2.35

2.38

2.15

221.2

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

Turner-Wallis (1965)

The following relationships are provided by Turner-Wallis for annular two-phase flow

1 + X

45-n

5-n2

• 2 - 1A4r

5-n

(5)

where

n is the exponent of Re in the single-phase friction factor correlation and % is the Martenelliparameter.

Tarasova (1966)

The correlation applicable for adiabatic flow in the range of 49 < P < 195.9 bar and 515 <G < 2575 kg/m2s is:

-7.35io5

(6)

where

Fr = UL2/gD. SI units are used for the various parameters and A is a constant dependent on P.

P(bar)

A

49.0

3.1

98.000

1.628

147.000

1.313

196.00

1.14

275

Baroczy (1966)

Baroczy introduced a "physical property index" which is given below:

TABLE VIII.II. VALUES OF FRICTION MULTIPLIER 4>Lo2 FOR FLOW OF WATER AND

STEAM IN UNHEATED TUBES, REPRODUCED FROM THOM (1964)

Steam

Quality

0.000

0.010

0.015

0.020

0.030

0.040

0.050

0.060

0.070

0.080

0.090

0.100

0.150

0.200

0.300

0.400

0.500

0.600

0.700

0.900

1.000

Pressure (bar)

17.24

1.00

2.12

2.71

3.22

4.29

5.29

6.29

7.25

8.20

9.15

10.10

11.10

15.80

20.60

30.20

39.80

49.40

59.10

68.80

88.60

98.86

41.38

1.00

1.46

1.60

1.79

2.13

2.49

2.86

3.23

3.61

3.99

4.38

4.78

6.60

8.42

12.10

15.80

19.50

23.20

26.90

34.50

38.30

86.21

1.00

1.10

1.16

1.22

1.35

1.48

1.62

1.77

1.92

2.07

2.2

2.39

3.03

3.77

5.17

6.59

8.03

9.49

10.19

13.80

15.33

144.83

1.060

1.110

1.160

1.210

1.260

1.310

1.370

1.420

1.480

1.750

2.020

2.570

3.120

3.690

4.270

4.860

6.050

6.664

206.9

1.020

1.030

1.040

1.050

1.060

1.080

1.160

1.240

1.400

1.570

1.730

1.880

2.030

2.330

2.480

Baroczy supplied <|)LO2 at a reference mass velocity of 1356.2 kg/m2s (106 lb/h ft2) intabular form as a function of steam quality and property index (Table VIII.III). Using this,<1>LO2(G) (i.e. <))LO2 at any mass velocity G) is calculated by multiplying with a correction factor.Correction factors for different mass velocities are provided in graphical form as a function ofquality and property index and are reproduced in Tables VIII.IV to VIII.VII. The method is validin the range of 340 <G <4070kg/m2s.

276

TABLE VIII.III. VARIATION OF FRICTION MULTIPLIER (j)L02 AT G = 1356 kg/m2s (106

lb/ft2h) WITH PROPERTY INDEX AND QUALITY REPRODUCED FROM BAROCZY(1966)

Prop-

erty

index

xlOO

0.01

0.10

0.40

1.00

3.00

10.0

30.0

Quality (%)

0.1

2.2

2.15

2.08

1.59

1.12

1.04

1.01

0.5

5.8

5.60

4.90

3.30

1.55

1.12

1.02

1

9.2

8.80

7.80

4.80

1.81

1.22

1.06

2

16.0

14.8

11.9

7.00

2.57

1.48

1.13

3.5

26.5

22.8

16.3

9.60

3.45

1.78

1.26

5

47

34.2

22.8

12.4

4.70

i 2.05

1.36

7.5

99

48.2

29.0

16.0

6.10

2.50

1.50

10

163

70.0

36.0

20.0

7.90

2.80

1.59

15

376

108

49.5

27.0

11.0

3.60

1.77

20

630

148

63.0

33.5

13.2

4.20

1.93

30

1300

86.0

86.5

43.5

17.3

5.50

2.25

40

2050

330

110

53.0

21.2

6.5

2.48

60

4300

538

155

69.0

26.0

8.00

2.86

80

6600

760

203

85.0

30.0

9.10

3.20

100

10000

1000

250

100

33.3

10.0

3.33

TABLE VIII.IV. TWO-PHASE MULTIPLIER CORRECTION FACTOR FOR MASS FLUXOF 339 kg/m2s (0.25 x 106 lb/ft2h) REPRODUCED FROM BAROCZY (1966)

Property

index

(PC/PL)-

(HiAta)0'2

0.000461

0.0065

0.055

0.0775

0.3551

1.0

Quality (%)

0.1

1.6690

1.1717

1.2000

1.2130

1.1180

1.0000

1

1.6688

1.1717

1.2702

1.2915

1.1532

1.0000

5

1.6000

1.0319

1.2957

1.3864

1.5532

1.0000

10

1.5850

1.4212

1.3723

1.5340

1.7750

1.0000

20

1.5851

1.4212

1.3723

1.5340

1.7750

1.0000

40

1.4938

1.2404

1.3128

1.3362

1.4106

1.0000

60

1.3587

1.1489

1.1570

1.1574

1.1872

1.0000

80

1.1745

1.0979

1.0830

1.0819

1.0681

1.0000

100

1.0

1.0

1.0

1.0

1.0

1.0

TABLE VIII.V. TWO-PHASE MULTIPLIER CORRECTION FACTOR FOR MASS FLUXOF 678.1 kg/m2s (0.5 x 106 lb/ft2h) REPRODUCED FROM BAROCZY (1966)

Property index

(PG/PO.WHG) 0- 2

0.000461

0.0065

0.055

0.0775

0.3551

1.0

Quality (%)

0.1

1.3000

1.1289

1.1051

1.1000

1.0737

1.0000

1

1.3316

1.2479

1.1705

1.1516

1.0895

1.0000

5

1.3000

1.1289

1.1895

1.2160

1.3105

1.0000

10

1.3000

1.2692

1.2284

1.2263

1.4277

1.0000

20

1.3105

1.2362

1.2400

1.2645

1.5610

1.0000

40

1.2474

1.1567

1.2158

1.2316

1.3105

1.0000

60

1.2000

1.1103

1.1158

1.3116

1.1579

1.0000

80

1.1030

1.0722

1.0737

1.0790

1.0526

1.0000

100

1.0

1.0

1.0

1.0

1.0

1.0

277

TABLE VIII.VI. TWO-PHASE MULTIPLIER CORRECTION FACTOR FOR MASS FLUXOF 2712.4 kg/m2s (2.0 x 106 lb/ffh) REPRODUCED FROM BAROCZY (1966)

Property index

(PG/PLMHI/HG)02

0.000461

0.0065

0.055

0.0775

0.3551

1.0

Quality (%)

0.1

0.4526

0.7737

0.9000

0.9095

0.9674

1.0000

1

0.4526

0.6737

0.8368

0.8632

0.9158

1.0000

5

0.7526

0.6926

0.7790

0.8000

0.7657

1.0000

10

0.7526

0.7268

0.7947

0.8137

0.7152

1.0000

20

0.7326

0.7567

0.7684

0.7632

0.6400

1.0000

40

0.7716

0.8053

0.7263

0.7053

0.5895

1.0000

60

0.9126

0.8611

0.7474

0.7147

0.5895

1.0000

80

0.9084

0.9316

0.8474

0.8179

0.7150

1.0000

100

1.0

1.0

1.0

1.0

1.0

1.0

TABLE VIII.VII. TWO-PHASE MULTIPLIER CORRECTION FACTOR FOR MASSFLUX OF 4068.6 kg/m2s (3.0 x 106 lb/ft2h) REPRODUCED FROM BAROCZY (1966)

Property index

( P G / P L M ^ I M / 2

0.000461

0.0065

0.055

0.0775

0.3551

1.0

Quality (%)

0.1

0.6368

0.7842

0.8526

0.8768

0.9474

1.0000

1

0.6105

0.5000

0.7326

0.8000

0.8968

1.0000

5

0.6368

0.5211

0.6591

0.7000

0.7158

1.0000

10

0.6368

0.5947

0.6796

0.7000

0.6586

1.0000

20

0.6000

0.6211

0.6424

0.6324

0.5700

1.0000

40

0.6526

0.7053

0.5842

0.5474

0.4823

1.0000

60

0.7211

0.7737

0.6000

0.5474

0.4823

1.0000

80

0.8389

0.8720

0.7326

0.6889

0.6000

1.0000

100

1.0

1.0

1.0

1.0

1.0

1.0

Sekoguchi (1970)

= 0.38 ReL 0o.i 1 + vG

0.95

vL

Lystsova Correlation [Osmachkin & Borisov (1970)]

\\i, the in-homogeneity parameter is defined as

- 0 . 2 x

(1 + 0.57 xul25>0.125\

uopG/(pLVgD)

where

UQ = G/pL

(7)

(8)

(9)

278

Becker (1973)

i n = 1+ 10 —^~ X (]Q\

The correlation is valid up to 70 bar.

Chisholm (1973)

Chisholm suggested that the equation

(11)

is rather unsatisfactory for use with evaporating flows where the liquid flow rate varies along theflow path. He suggested that the equation can be transformed with sufficient accuracy forengineering purposes to

GT2-i)

2"n

B x 2 1-x 2 + x2-n2 2-n (12)

where n is the exponent in Blasius equation; the following formulae apply for B

T G (kg/m2s) B

<500

500 <G< 1900

>1900

<600

>600

4.8

2400/G

55/G0-5

520/(rG05)

2i/r

15 000/(r2G05)

<9.5

9.5<r<28

>28

and F = (APGO/APLO)° 5, which for turbulent flow can be written as

0.5 r T n/2

r=m mFriedel (1979)

The correlation valid for horizontal and vertical upward flow in circular, rectangular andannular ducts has the form

^LO2 = E + F H / (Frmi Wem2) (14)

where

E = (1-x)2 + x2 pLfGo/(pGfLo); F = 3.24 x078(1-x)0224

279

H = (pi/po)09 W W / 1 9 ( 1 - U G / U I / 7 ; Fr = G2/(p2 g D)

We = DG2/(pa) ; mi = 0.0454 and m2 = 0.035

f<3o and ô are the friction factors computed for single-phase gas and liquid flows of mass flowequal to the two-phase flow and p is the density computed from the homogeneous model. Forvertical downward flow F, H, mi and ni2 are to be replaced by the values given below:

F = 48.6 X05 (1-x)0-29; H =

mi= 0.03 and m2 = 0.12

280

Appendix IX

DIRECT EMPIRICAL TWO-PHASE PRESSURE DROP CORRELATIONS

CESNEF-2 [Lombardi-Carsana (1992)]

This correlation is the last version of four different correlations [Lombardi-Pedrocchi(1972) DIF-1, Lombardi-Ceresa (1978) DIF-2, Bonfanti et al. (1982) DIF-3 and the present one]developed first at the CISE laboratories and then at the Department of Nuclear Energy —CESNEF of Polytechnic of Milan. This correlation is the result of a wide research work carriedout at CISE with different fluids, geometries and boundary conditions and assessed with a databank, named MID A, prepared at the Department of Nuclear Energy — CESNEF. Here only theCESNEF-2 correlation will be presented, because it is the logical generalization of the previousones. This correlation is fully dimensionless, continuous between two-phase and single-phaseflow and is valid only for vertical upflow (both for adiabatic and diabatic conditions). Itcalculates the total pressure drop as the sum of the elevation, acceleration and friction termsobtained by an energy balance instead of a momentum balance approach. Therefore in thisapproach the elevation term is proportional to the homogeneous density of the two-phasemixture and not to the actual density in the vertical duct, as in the case of a momentum balanceapproach. The acceleration term is obtained by the assumption of homogeneous flow. Thefriction term is given by an equation similar to that for single-phase flow, where the frictioncoefficient (Fanning type) is empirically correlated and the specific volume is assumed equal tothe homogeneous value. By defining dimensionless numbers as follows:

(1)

Ce ={pL g (D-Do)2/ <T} (UG/ nO where Do = 0.001 m (2)

Ce = 0forD<D o (3)

where

vm = x VG + (1-x) VL. One obtains the friction coefficient of the two-phase mixture, frp, asfollows:

_ |0 .046( l o r 0 2 5 for l o > 3 0 C e (4)f i p = (0.046(30Ce)(lo)""1-25 for l o < 3 0 C e

and the total friction coefficient is obtained as

f=fGbG + fLbL + frpbTP (5)

where

f*G and fi are the single-phase friction coefficients (Fanning type), calculated at the same totalflow rate by usual correlations, be bL and bTp are the weight functions as follows:

(6)l - b G - b L

281

Then

AP f =-G 2 v m Az ; A P e = ^ A z ; APa = G2(Avm)2fD

where

APf, APe and APa are the friction, elevation and acceleration terms respectively. The totalpressure drop is given by

Ap = APf+APe + APa (8)

To calculate the pressure drop, the channel is subdivided into sections, the number ofwhich is problem dependent: diabatic or adiabatic conditions, high or low pressures, etc. Startingwith a given subdivision (typically two sections), the above terms are calculated for each section,assuming average data for friction and elevation terms and true specific volume variations acrossthe section for the acceleration term. Then all these terms for the different sections are summedup to obtain the channel overall pressure drop. The channel is then subdivided into a largernumber of sections till the overall pressure drop converges to a definite value. The total pressuredrop, when lo < Ce, is limited to the liquid weight of the channel (gAzM,).

282

Appendix X

FLOW PATTERN SPECIFIC PRESSURE DROP CORRELATIONSFOR HORIZONTAL FLOW

(a) Stratified flow

The empirical model for the pressure gradient for stratified flow as given by Baker [Govier& Aziz (1972)] is as follows:

15400^, - ,0 .8CJSL

(1)

where

GSL = PL JL and % is the Martinelli parameter. No separate equation is provided by Baker for thestratified wavy flow pattern.

Hoogendoorn (1959) proposed the following relation for x < 0.8 in case of stratifiedsmooth and wavy flow patterns.

Ap

Azx145G2

(2)

The constant C depends weakly on the diameter and the fluid used. For the purpose ofengineering calculations, C can be given a value of 0.024 for smooth tubes (if 0.05 m < D <0.14 m). For rough pipes, the following table shall be used to calculate C.

Relative roughness, e/D

C

0.0012

0.0260

0.0039

0.0320

0.0190

0.0450

0.0300

0.0520

Dukler et al. [see Govier & Aziz (1972)] gave the following mechanistic model forstratified flow

f Api = fTpG2

(3)

where

"032frp = Fr|f; f = 0.0056+0.5 Re"032 ; Re =

F = 1+ y/[1.281- 0.478y + 0 . 4 4 4 / " O ^ y 3 + 0.00843y4]

and y = - In ( 1 - p) ; TI = (pi7pm)(l- P)2/(l - a) + ( pG/pm)p2/a ; \xm= u.L(l- P) +P) + PGP

; Pm = P L ( 1 -

283

Chawla (1967)

Apl = 0.3164 G V " (l-x)p 19/g

U z J ^ (GD//*O)M52DV XP

where

sc = 9.1 [(1- x)/x](ReLf rL)- 1/6(PG/PL)0-9

2 / (p 2ReL = DG(1- x)/ \xh and FrL= G2(l- x)2/(pL2gD)

In addition, mechanistic models for stratified flow are provided by Agrawal et al. (1973)and Taitel and Dukler (1976a).

Agrawal et al. (1973)

pG is the perimeter of the portion of the wall that is in contact with the gas phase.

•ttW.VAr. (6)

where212 ; TWL = ILPIML 12 with fG and ^ calculated by Blasius equation using Reo and

defined as

ReG = PGUG Dho/(J<}; ReL = P^LOM/ML with Dho = 4 AG /(PG+W0 and DhL = 4AI7PL

where

W; is the width of the gas-liquid interface.

xi = (0.804ReG-a285)2pGuG2 (7)

The calculations can be carried out if the geometric quantities appearing in the aboveequations are calculated. The following equations can be used to evaluate the geometricquantities.

= 0.5 {1- Cos(y/2)} ; a = AG/A = 1 - (y Sin y )/(2TT) ; and

i/D = 2{hIyD-(hL/D)2}0-5; Pi/p = y/27i ; pG /p=l-pL/p;

where

y, is the angle subtended by the interface at the pipe central line and h^ is the depth of liquidphase at the pipe central line.

DhG/D = 4AG/{D(PG+ WJ)}= ap/(pG+ W;) and DMTD = 4AI/(PLD) = (1 - a)p/pL

284

Computations can be made for laminar or turbulent liquid layer. Also, the average velocityin the liquid layer is calculated using the velocity distribution corresponding to the laminar orturbulent flow regime.

Taitel & Dukler (1976a)

This procedure assumes the pressure drop in the liquid and gas phass to be equal. Furtherit requires the calculation of the nondimensional liquid level , h L (= hi/D, where, IIL, is thedepth of liquid phase at the pipe central line), in the horizontal pipe, which can be calculatedknowing the Lockhart-Martinelli parameter from the following equation;

(UGDG)"1 AL AG fo AL AG

where

A - _ A - _ A L - _ A G - _ D G _ 4 A; = A = ; A = ; D = ; D =A V D ;

- A _

G

; hL = ^

AG = 0.25[COs-1(2hL-l)-(2hL-l)Vl-(2hL-l)2

pL = ^•-cos"1(2hL-l) ; pG = cos"1(2hL-l) ; Pi =

-n

1 Ll\ / 5 I G^G VG Vh

Equation 8 can be solved for laminar or turbulent flow by specifying the values of Q,CQ, n and m.

Knowing h L, the pressure drop can be calculated using the following equation;

,2 i -2 f f a a i ) - ] f- . f. -1 (9)

(b) Bubbly flow

^ P = ^^mVm ( 1 Q)

Az 2D

where

Vm = G/pm and f is calculated from single-phase correlation using Re=DVmpL/|u,L and

p m = ( l - a ) p L + a p G .

285

(c) Elongated bubbly flow

Baker /Govier & Aziz(1972)] gave the following empirical equation for elongated bubble

fG = 27.315% ' /GSL ' (11)

Hoogendoorn gave the following equation valid for elongated bubble, slug and froth flowpatterns

Ap _ fTpG2

Az 2D/?L

(12)

Hoogendoorn and Buitelaar (1961) provided a graphical correlation for fn>/f as function ofquality and density ratio where f is the friction factor calculated using single-phase liquidReynolds number given by Re =

(d) Slug flow:

Baker /Govier & Aziz (1972)]

(13)

(14)

Hughmark (1965)

TPF 2D

f is the single-phase friction factor based on Re = DULPI/|J.L

where

UL = JL ( 1 - oc), a = JG/{(1 + K) j} and K is a function of Rem(= D j PI/UL)- A graph of K vs. Ren

is given by Hughmark from which the following table has been obtained.

Rem

K

103

0.92

104

0.63

5x104

0.40

105

0.33

2x105

0.25

3xl05

0.23

>4xlO5

0.22

Dukler andHubbard (1975)

I A z J TPF 2Do)(15)

frp is calculated using the following single-phase correlation.

= 0.0056+ 0.5Rem032 (16)

286

where

DipRem = -; Pm = pGa + pL(l-a); j = j L + j G ; ftm = fiGa +ftL(l-a)

Gregory and Scott (1969) proposed the following correlation for ro

/ \-il.2

co = 0.0226j

JJ(17)

For the constant C a value of 0.25 was proposed by Hubbard and Dukler whereas 0.35was proposed by Gregory and Scott (1969).

where

B = 0.2. No equation for the void fraction, a, was proposed by Hubbard and Dukler.

(e) Annular mist flow:

Baker [Govier & Aziz (1972)]

<PG = (4.8-0.3125D) %

FPS units are used in all the equations given by Baker.

Hoogendoorn (1959)

[AP | _LAzJ™, 2D/?G

where

fTp = 0.025 (GGS)~°0 2 5 with GGS (= PQJG) given in kg/m2s.

(20)

287

Appendix XI

FLOW PATTERN SPECIFIC PRESSURE DROP CORRELATIONS FORVERTICAL UPWARD FLOW

(a) Bubbly flow:

The pressure gradient in bubbly flow is calculated by essentially single phase methods

Apl = fL/?LJ (1)Azj^p 2D

where

fi is given by conventional single-phase friction factor with Re = DJPL/UL- The homogeneousmodel is expected to give good results for bubbly flow.

Beattie (1973)

0.8 c / N 1 0.2

(b) Slug flow:

The pressure gradient in slug flow is calculated by

[AzJTPF 2D

where

f~L and Re are as defined for bubbly flow above.

(c) Froth flow (churn flow):

No equations are reported for this flow regime. The pressure gradient in this regime can becalculated using the homogeneous model as described for bubbly flow above.

(d) Pure annular flow (without entrainment):

Chawla (1967)

(Ap\ 0.3164 _ .. ^

I Az J TPF

where

l/ccc3 = 1/ai3 + l/a2

3

log a 7 = 0.960 + log B; loga2 =

288

0.168-0.055 l o g - log B- 0.67

{-i -0.9 r 1 -0.5

M \M ;ReL = G(l-x)D/^L;FrL = (G2(l-x)2)/(pL2gD).

The correlation is valid in the range 0.006 < D < 0.154 m, 5.9 10"6 < (e/D) < 6.8 10"2,102< ReL< 3 105,10"5 < FrL< 102,30 < (pi7pG)) < 850,40 < (\HJ\XG) 7000 and10"4<x<0.98.

Wallis (1970)

J^pl f/?GJo (5)J25UzJTPF 2Da

where

f = 0.005[l + 75(1 - a)] and JG is the superficial velocity of gas.

Beattie (1973)

** - HtfH^-f(e) Dry wall (post dryout flow):

Beattie (1973)

Lorenzini et al. (1989)

This correlation applicable for the transition between annular and fog flow pattern is givenby

A, = kR* (8)

where

k = 0.45 ln(100 xe), the subscript "e" refers to the final conditions in the section and R* is givenby

R = GR2 if ae < ax and xe > XT ,

R = GRi if cce < ax and xe < XT ;

289

where

GRi= ^ — ' ' * J ; GR2 = (1-A2)CD

B =

XT VG

1067.6

P is in bar.

XT = j 1067'622413-0.308424[{0.476615-0.442864 exp(-0.014721P)} where

If G > 3461 kg/m2s, then XT — 1/G. Friction factors fLo and fix} are calculatedcorresponding to ReLo and ReLG respectively. ReLo is the Reynolds number of the saturatedliquid and ReLG is given by

C X T H A I ifcce>aT (9)ReLG = ReL0 - ^ f^ (S-l)

fx. 1U1 ifae<aT (10)ReLG = ReLO ^ f^ (S-l)

290

Appendix XII

INTERFACIAL FRICTION MODELS GIVEN BY SOLBRIG (1986)

(a) Bubbly flow:

F i=-A iB i(uG-uL) (1)

where

Fi is the interface force, Aj is interface area per unit volume and B, is the coefficient of interfacefriction.

Ai=3 a/rb,

where

fb - Tb,we (1 - P) + rb>m P ; P = exp [(- Db/rb5we)/xt] and xt is normalized liquid induced bubbleoscillation distance,

x t =l if ReL< 2,000;

xt = exp (1 - 2,000 / ReL) if ReL > 2,000;

rb>We= 0.06147 {(Web>crit/2) (a/(p uR2)}

where

UR = UG- UL and Web>Crit = 1 -24

rb,m = rb,we/0.06147

I ]/8, f is obtained from the Colebrook equation, with Re defined as:

Dh = 2 rbX if rbX < R ;

Dh = 2R if rbx>R,

R is tube radius and x - Dh/2 rb;we-The roughness is set by setting e = rb.

(b) Slug flow

Since the slugs are assumed to be made up of a combination of hemispherical end capsand a cylindrical center section, contributions to the interface friction are obtained by summingboth of the components, i.e.

(2)Fi=(A;;heBi)he+Ai>acBj,ac)UR, v '

291

where

Ai;he= (a/D)(4/7i)°-5[4/{(2/3) + K}],

AUc= (a/D)(4/7i)a5[4K/{(2/3) + K}]

where subscripts "he" and "ac" refer to hemispherical ends and annular center portionrespectively and K = {(2/3)Ki2- a}/{cc-Ki2}; Kj = (7t/4)05« 0.886.

The friction coefficient of the hemispherical ends is calculated as BC;he = f [pi, I UR | ]/8,where f is calculated using Moody friction factor correction with Dh = 2 rb,m and the roughnessdefined as e = rb,m ; i.e. calculation of friction coefficient Be> he is carried out by the sameequations used for bubbly flow.

The friction coefficient for the annular center section based on the gas phase friction termis Bcac= fb[pG I UR I ]/8, where the friction is assumed to be that of annular flow plus an entrancelength correction due to the developing velocity profile in the gas and liquid phase to give fc =f<j,fd + fe ,where the fully developed friction factor fc, fd is obtained from Moody friction factorcorrelation with Reynolds number defined as Re = Dh PG UR / UQ with Dh = 2 rb;m and theroughness is given by e = 4 8, where 8 is the thickness of the liquid film. The thickness of film inSolbrig(1986) model is 8 = 0.114 R, where R is the tube radius. The entrance length frictionfactor is given as fe= 10 e^10.

(c) Annular flow regimes

cl. Annular flow

Fi = A;B iUR, A;= (4Voc)/D, B;=f G [pG I uR | /8 (3)

where

fo calculated from the Moody diagram with Re = DhPGUR/uo; Dh = Va D and the roughness isgiven by e = 4 8 = 2( 1 - Va )D, The maximum value of film thickness is limited to 0.1 R, i.e. if ecalculated is greater than this value, then e = 0.1 R is used.

c2. Annular mist regime

The interface force for annular mist flow is

Fi,am= Ai>am Bj;amUR (4)

where

A i j a m = 4 V { l - ( l - a ) ( l - E ) } / D

where E is the entrainment fraction given by

E = tanh (4.5x10"7 WeL25ReLa25)

where We is the Weber number for entrainment and ReL is the total liquid Reynolds numberdefined as

292

We = (PGaG2uR2D/a){(pL- PGVPG} 0 3 3 , ReL = PLOCLURD/UL (5)

In both of these definitions, the liquid velocity to be used in the calculation of UR is that ofthe liquid film and not of the droplets. The friction coefficient is obtained from Moody diagramwith the hydraulic diameter given by:

D h = D V { l - ( l - a X l - E ) } .

The roughness is defined as e = 2 [1 - V{1 - (1 - a)(l - E)}]D with the maximum valuelimited to 0.1 R.

c3. Droplet regime

The interface force between the gas phase and the droplets is calculated in a mannersimilar to that of bubbles in the liquid phase except that the role of the continuous anddiscontinous phases are reversed.

(6)

where

Ai,d= {3(1 - cc)E/D ; Bi;d= fG p I uR | /8 and

UR = UQ— UL in a two-fluid model,

= UG- UD in a three-fluid model where UD is the droplet velocity.

293

Appendix XIII

SLIP RATIO MODELS FOR CALCULATION OF VOID FRACTION

Osmachkin (1970)

5 = 1

,0.5

(1)0.25

Bankoff and Jones (1962)

\-aS =

(1 - KK

where

K = 0.71 + 0.00131 P and r - 3.33 + 2.61xlO"5P + 9.67xlO"3 P2, P is in bar.

Bankoff and Malnes (1979)

S = (l-a)/(C-a) for a < C - 0.02

and

S = 50[1.02 - C + 50(a - C + 0.02)(l - C)] for a > C - 0.02

where

UQ = SuL+ u0 with uo =0.174 m/s and C = 0.904.

Modified Smith [Mochizuki and Ishii (1992)]

0.5

+ KfI-l]PG

(2)

1 + K I - -.x

where

K = 0.95 tanh (5.0 x) +0.05

(3)

(4)

(5)

294

Appendix XIV

MODELS FOR THE CALCULATION OF VOID FRACTION

Armand (1947)

K = 0.833 +0.167x (1)

Bankoff(1960)

K -0.71 +0.00131 P (2)

where

4.9 < P < 206.2 bar

Hughmark (1961)

K = -0.16367 + 0.31037 Y - 0.03525 Y2+ 0.0013667 Y3 for Y<10 (3)

K = 0.75545 + 0.00358Y-0.1436.10~4Y2 for Y>10 (4)

Y = Re1 / 6Fr1 / 8( l-a)-1 / 4 (5)

Re = GD/[a^G+(l-a) |aL] (6)

Fr = (G2/gD)(x/pG + (1 - x)/pL)2 (7)

295

Appendix XV

DRIFT FLUX MODELS FOR THE CALCULATION OF VOID FRACTION

Zuber-Findlay (1965)

»0.25

1.13 and VGj=1.41 (1)

Rouhani (1969)

Co = 1 + 0.2(1- x)\

-\0.25

A

Dix(1971)

IO.I

V - 2 0 (A.

°j 1

(2)

(3)

(4)

(5)

Nabizadeh (1977)

where

GE-Ramp (1970)

C0=l.lfora<0.65

= 1 + 0.1(1 - a)/0.35 for a >0.65

(6)

(7)

and the drift flux velocity is given by,

296

0.25

and R = 2.9 for a < 0.65(9)

= 2.9 (1 - a) / 0.35 for a > 0.65

EPRI(1986)

C- âJO (10)K0+(l-K0)ar

L(«,P) = f £ (11)l-expC-Cj)

where the constants are given by,

/ \ 1/4

and the drift velocity is given by

PI

°-25 n s(1~a) (12)

1

Chexal-Lellouche (1996)

The correlation valid for steam-water flow is presented here. For refrigerant two-phaseflow or Air-water two-phase flow reference may be made to the original report.

1. Distribution parameter (Co)

The distribution parameter, Co, for a two-phase mixture flowing at any angle, where theangle is measured from the vertical axis, is the weighted average of values for horizontal andvertical flow.

Co = FrCov + ( l -F r )C o h (13)

where

C and C u are the distribution parameters evaluated for vertical and horizontal flow and Fr isov oh

a flow orientation parameter defined as

for ReG > 0

297

F =r(90°-e)

90°for (0°< G < 90°)

(14a)

for ReG < 0

(14b)

for (6 < 80°)

(90°-B)

10°for (80°<e<90°)

where

0 = pipe orientation angle measured from the vertical axis

VA) local vapour superficial Reynolds numberRe =

Note that in all cases, the pipe orientation angle 0 = 0° for a vertical pipe and 0 = 90° fora horizontal pipe. The angle is always in the limits of (0 < 0 < 90°).

1.1. Vertical flow

For vertical pipe (0 = 0°), the volumetric fluxes, ji,and jo, are taken as positive if bothphases are flowing upward and negative if both phases are flowing downward. Forcountercurrent flow, the vapour velocity is always positive (upward) and the liquid velocity isalways negative (downward). Countercurrent flow is only considered for vertical flows. Thedistribution parameter for vertical flow is given by

forReG >0

L (15a)

for ReG < 0

(15b)

[K0+(l-K>r]

(IJLI+IJGI)

where

298

V°. = defined later by Eq. (30)

L = Chexal-Lellouche fluid parameter.

Different forms of L are used with different fluids. For steam-water mixtures the formof L is selected to ensure proper behavior as the pressure approaches the critical pressure,

" l-expf-Q)

where

4 ?L (17)C,=

P-cnt

[P(P--P)1

Other variables in the distribution parameter correlation are defined as,

( V /4

(18)

(1.0+1.57 pG/ph)

d-BOr= r^" (w)Bj =min(0.8,A1) (20)

A i _ l on[l + exp(-Re/60,000)] V ^

Re G if ReG > ReL or ReG < 0.0R e = •!

ReL if ReG < ReL

Rej^ = local liquid Reynolds number = h

= local vapour Reynolds number =

The sign convention for all Reynolds numbers, Re, ReL, and ReG is the same as the sign

convention for the individual flows.

1.2. Horizontal flow

For horizontal flow (6 = 90°), the void fraction correlation considers only cocurrentflows. Horizontal countercurrent flow has not yet been included in the database. Thevolumetric fluxes for horizontal flow are always taken as positive; negative volumetric fluxesshould not be used. The distribution parameter for horizontal flow is given by

299

(25)

where

C o v is defined by Eq. (15a) above, and is evaluated with positive vapour Reynolds numbers,

using the horizontal fluid parameter, L^, defined as follows:

1 - exp(- Cja)steam water Lh = —, r- (26)

l - e x p ^ - C j

All other parameters are defined as for vertical flows, with positive fluxes.

For both vertical and horizontal flows, the steam-water parameter is a function ofpressure and void fraction.

2. Drift velocity (VGj)

The drift velocity, VGJ, for cocurrent upflow and pipe orientation angles (0° < 0< 90°) isdefined as:

VGj = FrVgjv + ( l -F r )V g j h (27)

where

Vgjy and Vgjh are the drift velocities for vertical and horizontal flow and F r is the flow

orientation parameter defined by Eqs (14a) and (14b). For cocurrent downflow, the driftvelocity is defined as:

VGj = F rVg jv + (F r - l )V g j h (28)

2.1. Vertical flow

Like the distribution parameter, the drift velocity for a vertical pipe0°), V :v, covers cocurrent upi

velocity for vertical flow is given by:

(0 = 0°), V^v, covers cocurrent upflow and downflow and countercurrent flow. The drift

Vgjv = VGjC9 (29)

where

V°=1.41 2

0.25

C2C3C2C3C4PL

C 9 =( l -a ) B l forReG>0 (31)

C9 = (1 - a) °5 for ReG < 0 (32)

300

Other parameters are defined as:

for • ^ - <18 C2 =0.4757

0.7

for \£±-1 - exp

ifC5>l

ifC5<l

where:

Cd —

C 7 = l

l-exp(-Cg)

if

if C7<

C8 =1-C7

D2 = Normalizing diameter, 0.09144 m

(33)

(34)

(35)

(36)

(37)

(38)

(39)

The parameter C3 is determined based on the direction of the gas and liquid flows. It iscontinuous as the two directional boundaries are crossed, but has a particularly strongderivative when coming across the j L equals zero plane. The values of C3 for the three typesof flows (cocurrent upflow, cocurrent downflow, and countercurrent flow) are given as:

The upflow C3 expression has been modified to decrease the rate of change of C3 in the1 Quadrant as it approaches zero liquid flow rate. This change improves the ability of thesystem dynamic models to utilize the inferred interface friction factor. From a steady statestandpoint, the expression can be modified as long as the proper end point characteristics aremaintained and good statistical compositions with the data result.

The upflow C3 expression is as follows:

r 0.5C3 - maxj 2exp(-JReLj/300,000) (40)

1 water and steam both flowing upwards.

301

A single C3 expression covers the 2nd quadrant2 and 3rd quadrant3 and the CCFL4 line.Only a portion of the original C3 expression has been modified, C3, B2, and Di remain asdesigned in NSAC-139. The original NSAC-139 countercurrent/downflow C3 expression is

as follows:

C,=2 '10

2

= 2 exp •

(41)

\0.25

ReT

0.4

0.001

0.03

exp-ReT

50,000

D,

(42)

where

0.4

and2 (l+0.05(|ReL|/350,000))

)j = Normalizing diameter = 0.0381 m(43)

For clarity, the revised expression for C10 is broken into the three constituent terms

which are summed to form C10.

jK i 0.4

350,000C10(Term l) =

C10(Term 2) = -1.7{ R e L | P « q , { 7 JwK ' X L | / F [(35,000 JLIX +25,000) \D

5

where

•\r

-10

ReT

and

in the 2 n d Quadrant

in the 3rd Quadrant

in the 2 n d Quadrant

in the 3 r d Quadrant

JL(ccfl)ls ^ suPerficial liquid velocity at CCFL for vapour velocity j G , and

1 -JL

(44)

(45)

(46)

(47)

(48)

2 water flowing downwards and steam flowing upwards.3 water and steam both flowing downwards.4 counter current flow limit.

302

0.8- f.0.8

JL — 0.3

for

for

JL

JL(ccfl)

JL

-<0.3

>0.3 (49)V JL(ccfl) J JL(ccfl)

The new terms Y, Z, and J work together in the countercurrent quadrant to fit both therd

data and the CCFL line. In the 3 quadrant, term 1 reduces to its original form and term 2 hasonly slight differences in the coefficients. The magnitude of Term 3 is small relative to theother two in the 3 quadrant.

2.2. Countercurrent flow

For countercurrent flow, a large hydraulic diameter model is included to accommodate

the behavior of the large diameter blowdown tests. The large diameter model is applicable

when hydraulic diameter is greater than 0.3048 m (1 ft). A transition from the normal to thelarge diameter model is made from Dj (0.0381 m/0.125 ft) to 0.3048 m. The following

equations illustrate the large diameter model:

0.6XTS+C3N(1.0-XT)'D,-0.3048V

0.6-0.27

0.06S0.3048 J

xS

for 0.3048m > Dh > Di

for 0.9144m > Dh > 0.3048m

forDh> 0.9144m

(50)

where

C3N = the normal C3 as defined by Eq. (41)

, 0 . 5

S=JLIX+(1.O-JL ,and

XT=(Dh-D1)/(0.3048-D1)

2.3 Horizontal flow

For horizontal flow only cocurrent flows are considered. The drift velocity forhorizontal flow, V -h, is evaluated with Eq. 29, using positive values of the volumetric fluxes.

3. Units

Tl

units of a velocity and should be consistent with the units used for the volumetric flux.

The correlation is the same in either British or SI units. Co has no units and V . has the

303

Appendix XVI

MISCELLANEOUS EMPIRICAL CORRELATIONS FOR VOID FRACTION

Thorn (1964)

y is a constant at any pressure and assumes the following values for water.

Martinelli-Nelson (1948)

a =

(1)

P(bar)

Y

1.014

246.0

17.24

40.0

41.38

20.0

86.21

9.8

144.83

4.95

206.9

2.15

221.1

1.0

(2)

where

C = (pi/pa)0'5

Baroczy (1966)

Baroczy has expressed in graphical form, the void fraction as a function of the Martinelliparameter, Xtt, and the property index:

1-x

X

0.9 , , 0 . 5 , 0.1 (3)

Based on these graphs Marinelli and Pastori (1973) have obtained the following best fitequation valid only for 70 kg/cm

a = 0.1800285 +4.2049x- 11.523x2+ 14.856x3 - 6.7624x4 (4)

304

Appendix XVII

COMPILATION OF DATA

The compiled data are shown in Tables XVII.I, XVII.II, XVII.III and XVII.IVrespectively for pressure drop, void fraction, flow pattern and flow pattern specific pressuredrop.

TABLE XVII.I. TWO-PHASE FLOW PRESSURE DROP DATA — A COMPILATION

Author

(year)

Adorni(1961)

-do-

Hoglund(1958)

Hashizume(1983)

Hashizume(1983)

Cicchitti(1960)

Cicchitti(1960)

Janssen(1964)

Janssen(1964)

Janssen(1964)

Janssen(1964)

Janssen(1964)

Janssen(1964)

Test

sec-

tion

A

A

P

P

P

P

P

P

P

P

RC

RC

RC

Flow

direc-

tion

V-U

v-u

V-U

H

H

V-U

V-U

V-U

H

V-D

V-U

V-U

V-U

adiabatic/

diabatic

adiabatic

diabatic

diabatic

adiabatic

adiabatic

adiabatic

diabatic

adiabatic

adiabatic

adiabatic

adiabatic

adiabatic

adiabatic

Forced/

Natural

forced

forced

natural

natural

natural

forced

forced

forced

forced

forced

forced

forced

forced

Fluid

used

S-W

S-W

S-W

R-12

R-22

S-W

S-W

S-W

S-W

S-W

S-W

S-W

S-W

No.

of

Data

pts.

97

376

87

85

85

52

18

37

65

37

67

87

26

Hydra-

ulic-

dia

(mm)

3.23

3.23

11.65

10.0

10.0

5.1

5.1

19.7&11.1

18.8,24.3&32.3

24.3

19.7&11.1

19.7&11.1

19.7&

Pres-

sure

range

(MPa)

6.83-7.07

6.83-7.58

1.14-4.24

0.57-1.22

0.92-1.96

2-7.8

3.6-5.2

4.1-9.6

4.1-9.6

4.1-9.6

4.1-9.7

4.1-7.0

4.1-6.9

Mass

Flux

(kg/

m2s)

961-3799

976-3828

717-935

88-354

88-354

2000-6000

2200-4000

271-1492

271-2306

271-1492

678-2848

678-2848

271-2848

Quality

range

0.0-0.75

0.0-0.85

0.01-0.065

0.1-0.81

0.08-0.81

0.05-0.8

0.4-0.7

0.09-0.9

0.09-0.9

0.09-0.9

0.02-0.99

0.05-0.92

0.02-0.79

305

TABLE XVII.I. (CONT.)

Author

(year)

Lahey(1970)

Steiner(1988)

Berkowitz(1960)

Adorni(1966)

CISE(1963)

CISE(1963)

CISE(1963)

Marchattern(1956)

Cook(1956)

Moeck(1970)

Vijayan(1981)

Test

sec-

tion

RB

P

P

RB

P

A

A

RC

RC

A

P

Flow

direc-

tion

V-U

H

V-U

V-U

V-U

V-U

V-U

V-U

V-U

V-U

V-U

adiabatic/

diabatic

diabatic

adiabatic

diabatic

diabatic

adiabatic

adiabatic

diabatic

diabatic

diabatic

diabatic

diabatic

Forced/

Natural

forced

forced

forced

forced

forced

forced

forced

natural

natural

forced

forced

Fluid

used

S-W

R-12

S-W

S-W

S-W

S-W

S-W

S-W

S-W

S-W

S-W

No.

of

Data

pts.

36

158

920

314

525

280-

843

30

62

972

22

Hydra-

ulic-

dia

(mm)

12.0

14.0

5.2-10.1

5.07-11.61

5.2-10.1

3.23-7.0

3.23-7.0

16.23

16.23

4.06

6.2

Pres-

sure

range

(MPa)

7.0

0.15-0.31

4-8.36

5-6.96

4-7.06

6.8-7.13

6.8-7.58

0.79-4.24

4.23

3.47-7.25

7.2

Mass

Flux

(kg/

m2s)

271-2984

50-240

1044-4088

80-3800

1038-4398

961-4570

976-4581

366-500

173-443

150-3350

2740-4044

Quality

range

0.03-0.45

0.1-0.81

0.018-0.97

0.0-0.5

0.018-0.8

0.001-0.836

0.0-0.98

0.019-0.461

0.016-0.087

0.066-0.69

0.01-0.28

P - Pipe; A - Annulus; RC - rectangular channel; RB - rod bundle; V-U - vertical upward; V-Dvertical downward; H - horizontal; S-W - steam-water; R-12 - Refrigerant-12; R-22 - Refrigerant-22.

306

TABLE XVII.II. DETAILS OF STEAM-WATER VOID FRACTION DATA

Author Test

(year) sec-

tion

Rouhani P(1963)

Merchattere RC(1956)

Cook et al. RC(1956)

Petrick P(1962)




Rouhani A(1966)

Flow adiabatic/ Forced/ Fluid No. Hydra- Pres- Mass Quality

direc- diabatic Natural used of ulic- sure Flux range

tion Data dia range (kg/

pts. (mm) (MPa) m2 s)

V-U diabatic

V-U diabatic

V-U diabatic

V-U diabatic

V-U diabatic

V-U diabatic

V-U diabatic

V-U diabatic

forced S-W 149 6.1

natural S-W 675 16.2


forced S-W 108 49.3


forced S-W 237 11.3


forced S-W 535 13.0

0.7-6.0

0.8-4.3

4.2

4.1-10.3

1.12-4.23

1.12-4.23

1.12-4.23

1.0-5.0

650-2050

360-502

173-457

163-1256

490-1112

490-1455

289-744

650-1450

0.0-0.38

0.082-0.0

0.0-0.141

0.0-0.11

0.0-0.076

0.0-0.0.65

0.0-0.076

0.0-0.12

A — Annulus; V-U — vertical upward; S-W — steam-water; P — pipe; RC — Rectangular Channel.

307

TABLE XVII.III.WATER

DETAILS OF THE FLOW PATTERN DATA COMPILED FOR STEAM-

Author

Bennett et. al.(1965)

Hosier (1967)

Griffith(1963)

Suo et al.(1965)

Janssen &Kerivinen

(1971)

Peterson &Williams

(1975)

Bergles et al.(1965a)

Bergles et al.(1965b)

Bergles et al.(1965c)

Bergles et al.(1968a)

Bergles et al.(1968b)

Tippets(1962)

Test sectionGeometry

Tube

Rectangularchannel

Tube

Tube

Tube

Rod bundle

Tube

Tube

Tube

Tube

Rod bundle

Rectangularchannel

Pressure(MPa)

3.44 & 6.9

1.034 to13.79

1.483 to2.862

6.9

7

2.758 to13.79

3.45

3.45 & 6.89

6.89

3.45

&6.89

6.89

6.9

hydraulicdia.(mm)

12.638

6.003

9.525 to22.225

10.16

17.06

7.06

101.6

9.652

10.31

20.93

14.2

20.6

Method ofidentification of

flow pattern

High speed cine-photography X-ray photography

High speedphotography

Electricalresistance probe


Electricalconductance

probe

Visualobservations






High speedmotion picture

No. ofdata

points

109

683

344

61

94

98

56

65

55

88

301

25

308

TABLE XVII.IV.DATA

COMPILATION OF FLOW PATTERN SPECIFIC PRESSURE DROP

Author Test

(year) sec-

tion

Flow adiabatic/ Forced/ Fluid No. Hy-

direc- diabatic Natural used of draulic-

tion Data dia

pts. (mm)

Pres-

sure

range

(MPa)

0.57-1.22

0.92-1.96

0.151-0.309

6.89

Mass

Flux

(kg/

m2s)

80-320

80-320

80-320

510-2800

Quality

range

0.1-0.8

0.1-0.8

0.1-0.8

0.01-0.322

Hashi-Zume P(1983)

Hashi-Zume P(1983)

Steiner C P(1979)

Suo et al. P(1965)

Zhao & PRezkallah(1994)

Tutu P(1982)

Hewitt& POwen (1992)

Lahey & PLee (1992)

Lahey & PLee (1992)

H adiabatic natural R-12 78 10

H adiabatic natural R-22 78 10

H adiabatic forced R-12 136 10

V-U adiabatic forced S-W 68 10.2

V-U adiabatic forced A-W 53 9.7

H adiabatic forced A-W 8 52.2

V-U adiabatic forced A-W 42 31.8

V-U adiabatic forced A-W 16 57

V-D adiabatic forced A-W 16 57

0.1

0.1

0.24

0.1

0.1

300-460

V-U — vertical upward; V-D — vertical downward; H — horizontal; S-W — steam-water; R-12Refrigerant-12; R-22 — Refrigerant-22; P — pipe.

309

Appendix XVIII

DETAILED RESULTS OF ASSESSMENT OFVOID FRACTION CORRELATIONS

The assessment was carried out by standard statistical procedure. The error (et), mean

error ( e"), mean of absolute error (|e |) , R.M.S. error (erms) and standard deviation (a) are

calculated as follows:

x 100(1)

where

the subscripts c and m refer to calculated and measured values respectively.

1 N

e =—Ve.-Ntr •

(2)

(3)

f N \ 0 5

rms

a =

(4)

N

v J

N 2\ 0.5

N-l

V J

(5)

Table XVIII.I shows the range of parameters of the data used for the assessment whichformed a part (about 3292 data points) of the TPFDB data bank. The data used for theassessment was screened by deleting those data with predicted errors exceeding ± 100% byany of the four correlations [i.e. Chexal-Lellouche, Rouhani, Modified Smith (modified byMochizuki and Ishii) and Hughmark]. Number of data points deleted is about 2.7% of the totaldata in the original data bank. It is found that the erroneous data are not concentrated in asingle dataset but present in almost all the datasets used in this data bank.

310

Parameter

Quality (%)

Mass-Flux (kg/m s)

Hydraulic Diameter (mm)

Measured Void fraction (%)

Pressure (bar)

Minimum

0.01

125

10

40

7

TABLE XVIII.I. RANGE OF PARAMETERS OF VOID FRACTION DATA USED FORASSESSMENT

Maximum

22

2950

38

90

51

From the frequency distribution given in Figures XVIII.I to XVIII.III only the ModifiedSmith correlation shows a skewness towards the negative side (Fig. XVIII.III) which indicatesan underprediction to some extent. A comparison of the measured and predicted void fractionsare given in Figures XVIII.IV to XVIII.VI which show predicted void fraction, ccc to beconsistently more than the measured void fraction ocm except in the case of modified Smithcorrelation. For the modified Smith correlation, the predictions are more or less evenlydistributed around the zero line. It may be noted that while Chexal-Lellouche and Rouhani aredrift flux models, Hughmark is a kj5 model and Modified Smith correlation is a slip ratiobased model.

Assessment of correlations for the limiting conditions:

Void fraction correlations have to satisfy the following limiting conditions:

(1) As x tends to 0, a tends to 0 (lower limiting condition)(2) As x tends to 1, a tends to 1 (upper limiting condition)(3) As P tends to Pcrit, a tends to x (critical limiting condition).

To check for the compliance of the correlations with the lower and upper limitingconditions, void fractions predicted by different correlations are studied over a wide range ofmass fluxes and pressures for x — 0 and x = 1. In order to allow for the round-off errors andapproximations made in the computation of void fractions using various correlations, thefollowing allowances are made to the limiting conditions. It is assumed that a correlationsatisfies the limiting conditions if it satisfies the following conditions:

(1) At x = 0.000001, a is less than 0.001 (approximation of lower limiting condition)(2) At x = 1, a is greater than 0.999 (approximation of upper limiting condition)(3) At P = 218.3 bar, Maximum deviation of predicted void fraction from the mass quality.

over the entire range of mass flux, i.e. 0 to 10 000 kg/m2s, is less than 1% (approximation ofcritical limiting condition).

The results of the observations are listed in Table XVIII.II.

311

TABLE XVIII.II.

Correlation

name

LIMITING CONDITIONS

G<100.(

atx = 0; at x =a= 0 a =

) kg/m2s

= 1; at1

P~Pcr>a = x

atxa

G>

= 0;= 0

100.0

atx =a =

kg/m2

-1;1

s

atP=Pcr;a = x

Chexal et al.(1996)

ModifiedSmith

yes

yes

Rouhani

Zuber-Findlay

Bankoff

yes

yes

yes

no

yes

yes

no

no

yes forG>10

yes

no

no

yes

yes

yes

yes

yes

yes

yes for G yes>140

yes

no

no

yes

yes yes for G>2050

no

yes

Bankoff-Jones

GE-Ramp

yes

yes

yes

yes forG>10

yes

no

yes

yes

yes

yes

yes

no

Bankoff-Malnes

Homogene-ous model

Martinelli-Nelson

Hughmark

Osmachkin -Borisov

Thorn

Nabizadeh

Armand

Dix

yes

yes

yes

yes

yes

yes

yes

yes

yes

yes

yes

yes

no

yes

yes

no

yes

no

no

yes

no

no

yes

no

no

no

no

yes

yes

yes

yes

yes

yes

yes

yes

yes

yes

yes

yes

no

yes

yes

no

yes

no

no

yes

no

no

yes

no

no

no

no

312

It is observed that the homogeneous model and the slip ratio based models satisfy all thethree limiting conditions for all mass fluxes. Among the top four correlations only themodified Smith correlation satisfies all the three limiting conditions. The Chexal-Lellouchecorrelation satisfies all the three limiting conditions for G > 140 kg/m2s whereas Rouhanicorrelation satisfies all the three limitting conditions only for G > 2000 kg/m2s. From theseconsiderations, the Chexal-Lellouche and the modified Smith correlations may be used incomputer codes for reactor analysis.

30 -

£

>

10 -

-100 -80 -60 -40 -20 0 20 40 60 80 100

percentage error

FIG. XVIII. I. Error distribution in predicted void fractions using Chexal-Lellouchecorrelation.

313

30 _

I . I . I . I . I . I . I . I

-100 -80 -60 -40 -20 0 20 40 60 80 100

percentage error

FIG. XVIII. II. Error distribution in predicted void fractions using Hughmark correlation.

314

IS

20 -

-100 -80 -60 -40 -20 0 20

percentage error

FIG. XVIII.III. Error distribution in predicted void fractions using modified Smithcorrelation.

315

0.4 -

0.0

0.0FIG.

XVIII.IV. Comparison of measured and predicted void fractions using Chexal-Lellouchecorrelation.

316

0.0 0.2

FIG. XVIII. V. Comparison of measured and predicted void fraction using Hughmarkcorrelation.

317

0 . 4 -

0 . 2 -

0.0

0.0

a

FIG. XVIII. VI. Comparison of measured and predicted void fractions using modified Smithcorrelation.

318

Appendix XIX

DETAILED RESULTS OF ASSESSMENT OF FLOW PATTERN DATA

The criteria proposed by Taitel et al. (1980), Mishima and Ishii (1984) and Solbrig(1986) are given in Tables XIX.I and XIX.II for bubbly-slug and slug-annular transitionsrespectively. The bubbly-slug criteria proposed by Taitel et al. consists of three criteriadesignated as Taitel et al. I, II and III. Taitel et al. Ill is an upper limit beyond which bubblyflow cannot exist whereas criterion II demarcates dispersed bubbly and slug flow.

Only Solbrig has provided a criterion for slug-annular transition. His recommendedcriterion is Solbrig I. However, Solbrig also discusses another criterion denoted as Solbrig IIin Table XIX.II. Mishima and Ishii have proposed two different criteria for the transition toannular flow. The criterion corresponding to annular flow with entrainment is considered herefor assessment. Taitel et al. proposed an upperlimit of jo beyond which only anular flow ispossible.

1. Comparison of the various transition criteria

Figure XIX.I shows a comparison of the criteria for bubbly-slug and slug-annulartransitions in JG-JL plane. Corresponding plots in CC-JR plane is shown in Fig. XIX.II. Thefollowing observations can be made from these figures:

(i) The bubbly — slug transition criteria proposed by Taitel et al. and Mishima-Ishii areclose to each other.

(ii) Both Taitel et al. and Mishima-Ishii criteria for transition to annular flow are found to beindependent of the liquid superficial velocity (Fig. XIX.I). While Mishima-Ishii suggestthat the criterion for annular flow transition should not be extended beyond the JL valuecorresponding to bubbly- slug transition, no such upper limit is specified by Taitel et al.Plotting these criteria in OC-JR plane (Fig. XIX.II) shows that at higher values of JL thevoid fraction can go below that specified for bubbly to slug transition. This suggests thatan upper limit of JL needs to be specified for this criterion although no such limit isspecified by Taitel et al. and Mishima-Ishii.

2. Data used for assessment of flow pattern maps

For assessment, a part of the flow pattern data contained in TPFDB data bank was used.Currently, this data bank consists of 811 bubbly, 818 slug and 762 annular flow points. Inaddition, it has 64 bubbly-slug and 62 slug-annular transition data points (Table XIX.III). Itconsists mainly of steam-water flow data at reasonably high pressure (>10 bar). Somerefrigerant and air-water data are also included in the data bank. The data bank includes flowpattern data for diabatic and adiabatic two-phase flow. The range of parameters of the flowpattern data for vertical upward flow are given in Table XIX.IV. Since the amount ofdispersed bubbly flow data in the present data bank are very few Taitel et al. criterion I only isconsidered for the assessment.

319

TABLE XTX.I. BUBBLY FLOW TO SLUG FLOW TRANSITION CRITERIA

Author Criteria in JG-JL plane Criteria inOC-JR plane

Taitel et al. I j L = 3jG-1.15

Taitel et al. II

Taitel et al. Ill

Mishima-Ishii

Solbrig

J L + J G = 4 '^D0429fcr / p )°°8 9

.0.072

-|0.446

j G = 1.083 j L

j L = (3.33/ Co -l)jG-(O.76/Co)(agAp/pL2)

Co = 1.2-0.2(pG/pL)1/2 for round tubes

Co = 1.35 - 0.35(po/pL)1/2for rectangular tubes

JG=1.083jL

a = 0.25

a = 0.25 - 0.52

a = 0.52

a = 0.3

a = 0.52

TABLE XDC.II. CRITERIA FOR TRANSITION TO ANNULAR FLOW

Author

Taitel-Dukler

Mishima-Ishii

Solbrig I

Solbrig II

Transition criterion

0.5

f / \ 0.251[<W?L -Po) j

r i025

N i"L

for annular flow with entrainment

a = . /4

a = 2/3

320

10

0.1

0.01

Mishima-lshii

-Taiteletal. I, l l & l

Solbrig

bubbly-slugtransition criteria

_ bubbly Transition toannular flow

0.1 10 100

FIG. XIX. I. Comparison of the various flow pattern maps for air-water flow at 25 °C in a 25.4mm id. tube.

321

10

1 o

-5

-100.0

bubbly

0.2

bubbly-slug

'transition crifefi T"

Transition to

ânnularfli

annular

Taitel et al. I, II & III

Mishima-lshii

Solbrig

0.4 0.6 0.8

a1.0

FIG. XIX. II. Comparison of the different flow pattern maps for air-water flow at 25° C and0.1 MPa in a 25.4 mm Id. tube.

322

TABLE XIX.III. FLOW PATTERN DATA

Geo- Fluidmetry

Flow Pattern

B B-S C S- A A- W- F D F B- B TA W A - - A -

B A F

tube

tube

tube

Rectangular

channel

RodBundle

AirWater

SteamWater

R-12

SteamWater

SteamWater

157

84

68

413

89

28

-

-

36

106

303

181

158

70

74 7 49 24

13 26 366 22 31 34

. 94 . . .

- 222 -

29 31 10 36

- - - 422

2 51 4 863

- - - 343

- - - 793

- - - 301

Total 811 64 818 87 62 762 32 55 70 5 2822

B: bubbly flow; B-S: bubbly to slug transition; S: slug flow; C: churn flow; S-A: slug to annular transition; A:annular; AW: annular wavy; WA: Wispy annular; F: froth; DB: dispersed bubble; F-A: froth to annular transition; B-A: bubbly to annular transition; B-F: bubbly to froth transition; T: total data points.

TABLE XIX.IV. RANGE OF PARAMETERS FOR FLOW PATTERN DATA

Serial No.

1

2

3

4

5

6

7

8

Parameter

pressure (MPa)

mass flux (kg/m2s)

hydraulic diameter (mm)

quality (fraction)

JL (m/s)

jo (m/s)

fluid used

geometry of test section

Range

0.1-14

50-5000

5-51

-0.03-0.5

0.05-11

0.0-80

water, R-12 and air-water

round tubes, rectangular channels and rod bundles

323

o bubbly flow data— Mishima-lshii— Taitel et al. I

-7

0.0

FIG. XlXJIIa. Comparison of bubbly flow data with various bubbly-slug transition criteria.

324

70

63-

56-

4 9 -

4 2 -

3 5 -

I

— 28 - I

21 -

1 4 -

7 -

slug flow dataMishima-lshiiTaiteletal. ISolbrig

0.0 0.31

0.41

a

i0.5

1 '0.6

1 1 '0.7

10.8 0.9

FIG. XlX.IIIb. Comparison of slug flow data with various bubbly-slug transition criteria.

325

6 0 -

4 0 -

2 0 -

0 - -

o annular flow dataSolbrig I slug-annular criterionSolbrig II slug-annular criterion

D

n

B

0.0 0.1 0.2 0.3 0.4 a 0.5 0.6 0.7 0.8 0.9

FIG. XIX.IIIc. Comparison of annular flow data with various slug-annular transition criteria.

326

7.0

3.5 -

0.0 - -

-3.5 -

-7.0

o

oo

1 1 1

o tube data

• rod bundle data

Taiteletal. I

Mishima-lshiiSolbrig

0.0 0.2 0.4 a 0.6 0.8 1.0

FIG. XIX.IV. Comparison of bubbly-slug transition data with various bubbly-slug transitioncriteria.

327

- - Solbrig IMishima-lshii

— Solbrigll• tube data• rod bundle data

FIG. XIX. V. Comparison of the slug-annular transition data with various transition criteria atIMP a.

328

It must be mentioned that no filtering/screening of the raw data was done for the steam-water and refrigerant two-phase flow. These data were obtained at relatively high systempressure and the errors due to specific volume change is not significant. However, most air-water data are obtained at near atmospheric pressure and errors due to specific volume changeare significant in some cases. Such data are excluded from the data bank. A large body ofavailable air-water data do not qualify for inclusion in the data bank.

3. Assessment procedure

In principle, the flow pattern transition criteria must be assessed against flow patterntransition data. However, since the amount of transition data are limited, each transitioncriterion is tested with the flow pattern data before and after the transition. For example, thebubbly-slug transition criterion is tested with bubbly and slug flow data. Such an approach isfollowed while testing the transition criteria by Taitel et al. and Mishima-Ishii. However, thisapproach is only an approximate test of the transition criteria as the flow pattern data can belocated far away from the transition point.

The flow pattern transition criteria when plotted in the JG-JL plane, will depend on thetube diameter, pressure and fluid used. Therefore, flow pattern transition criteria need to beassessed for each tube diameter, pressure and fluid. However, Khare et al. (1997) showed thatif the experimental data are plotted in GC-JR plane, then a single graph can be used for the entiredata, irrespective of the fluid, tube diameter, pressure, etc. for the assessment of the bubbly-slug transition criteria proposed by the different authors. Also, the flow pattern data showed adefinite trend when plotted in the OC-JR plane. Therefore, the OC-JR plane was chosen for theassessment of the bubbly-slug transition criteria.

For the above assessment procedure, the void fraction and relative velocity are to becalculated for each flow pattern data. In cases, where the data are available in terms of JG andJL, the JRis calculated as JR = JG-JL- For calculating the void fraction, the Zuber-Findlay (1965)correlation is made use of. It may be noted that JR is always obtained directly from measureddata whereas a is not measured but calculated. In cases, where the data are given in terms ofthe mass flux and quality, the jo and JL are estimated as jo= Gx /po and JL = G(l —X)/PL.

The results of this analysis are shown in Figs. XlX.IIIa, b and c for bubbly, slug andannular flow. The trends of the bubbly and slug flow data given in Figs. XlX.IIIa and bsuggest that an essential requirement for the bubbly to slug flow transition is a near zerorelative superficial velocity. This is further confirmed by the experimental bubbly-slugtransition data plotted in Fig. XDC.IV. The transition data also clearly shows that there is nounique value of a for bubbly to slug flow transition. The transition from bubbly flow to slugflow depends on the relative superficial velocity and void fraction. None of the criteria used inthe present assessment reproduces the trend of the transition data well.

Fig. XIX.V compares the experimental slug-annular transition data contained in the databank with various slug-annular transition criteria. Clearly, none of the proposed criteriareproduces the trend of the transition data. However, the Solbrig I criterion is closer to thepipe data whereas Solbrig II criterion is closer to the rod bundle data indicating that the slug-annular transition criterion can be geometry dependent.

329

Annex A

INTERNATIONAL NUCLEAR SAFETY CENTER DATABASE

A.l. DATABASE PURPOSE AND CONTENTS

The United States Department of Energy (USDOE) and the Russian Ministry of AtomicEnergy (MINATOM) signed a joint statement in September 1995 to establish InternationalCenters for Nuclear Safety. As a result, in October 1995 the International Nuclear SafetyCenter (INSC) was established at Argonne National Laboratory (ANL). The Russian INSCwas established in Moscow in July 1996. Initially hosted at the Research and DevelopmentInstitute of Power Engineering, the Russian INSC is currently an independent organizationwithin MINATOM.

The main goal of the International Nuclear Safety Center is to collaborate with othernations to advance the development and use of nuclear safety technology and thedissemination of nuclear safety information.

A key element for the INSC to accomplish its main goal is the development of anInternational Nuclear Safety database accessible electronically through the World Wide Web.The main purpose of the INSC database is to foster the international exchange of nuclearsafety-related information with the aim of supporting worldwide improvements in civiliannuclear safety.

The International Nuclear Safety Center Database is a comprehensive World WideWeb- based resource for safety analysis and risk evaluation of nuclear power plants and othernuclear facilities all over the world. The readily available World Wide Web technology allowseasy access to the database from anywhere in the world. Although most of the providedinformation is available to the public, mechanisms have been put in place to restrict access toproprietary information only to selected individuals or sites.

Although the scope of the database is worldwide, the current focus is on Soviet-designed nuclear power plants in Russia and Eastern Europe, and on reactor types in Chinaand India. This and the pages referenced hereon provide an outline for the database and serveas a core for further development.

The database is being implemented by the Reactor Analysis Division at ArgonneNational Laboratory using the division's Unix-based workstation network. Informationcataloging and database maintenance is performed with the Oracle® database managementsystem providing controlled access to database elements based on user identity and accesslevel authorization. The database and its content are verified and maintained in compliancewith applicable quality assurance standards and practices.

Currently, the INSC database maintained at ANL contains the following information:

— Basic information on about 600 Power Reactors in 35 countries.

— Links to the US NRC database for plant technical documentation of 113 operable USreactors.

331

— Basic Plant Parameters for other selected reactors.

— Information for 590 Research Reactors in 74 countries.

— Information for 560 Fuel Processing Facilities in 44 countries.

— Bibliography of Reports and Documents.

— Computational Tools and Input Data Sets.

— The database provides access to Material Properties to meet the needs of analysts usingcomputer codes and doing experiments for safety evaluation of nuclear reactors and otherfacilities. The focus is on LWRs, with an initial emphasis on materials unique to Sovietnuclear reactor designs. Categories are Fuel, Cladding, Absorber Materials, StructuralMaterials, Coolant, Concretes, and Severe Accident Mixtures. Part of this database hasbeen established in collaboration with the IAEA.

— Descriptions, summaries, and results of the joint projects between the US and RussianInternational Nuclear Safety Centers.

— Collaboration clipboards are implemented to serve as an electronic forum to facilitatestructured interorganizational communication among the participants of INSC relatedactivities.

— Links to other information resources and databases allow access to additional sources ofinformation interesting for the typical INSC Database user, such as the INSP Database atthe Pacific Northwest National Laboratory.

— Currently under development: thermohydraulics data provided through the IAEA'sCoordinated Research Programme (CRP) on Thermohydraulics Relationships forAdvanced Water-Cooled Reactors.

Through the collaboration between the US and Russian International Nuclear Safetycenters it has been possible to expand the resources of the INSC database, by addingadditional data sources on remote Web sites such as the Russian INSC in Moscow, or otherRussian organizations. The database architecture is such that the resources of the databases atthe US and Russian Centers can be linked together transparently, allowing for a flexible andscalable platform for future development.

There are several institutes in other countries that perform work in collaboration withthe US International Nuclear Safety Center. The database provides links to those institutes andtheir network resources and may hold additional materials regarding collaboration between theUS and other countries in the future.

— A new Lithuanian INSC Web Site was established at the Lithuanian Energy Institute inKaunas, Lithuania. This web site is under development and will provide access todetailed data on Lithuanian nuclear facilities.

— The Nuclear Safety Institute of the Russian Academy of Sciences (IBRAE) maintains aWeb Site and provides access to detailed information on the Kola nuclear power plantand especially its Reactor #4. This data was collected and installed using USDOE fundsand in collaboration with the US INSC. Other projects resulted in the establishment of amaterials properties database for high temperatures to be used for the simulation ofreactor accidents.

332

The INSC Database can be reached at:

h t t p : / / w w w . i n s c . a n l . g o v

or, by e-mail, the database manager can be contacted:

[email protected] or by Fax, at (630) 252-6690

A.2. THERMOHYDRAULICS DATA IN THE INSC DATABASE

The database on thermohydraulics data within the INSC database has been initiated as aresult of the Coordinated Research Programme (CRP) on Thermohydraulic Relationships forAdvanced Water-Cooled Reactors established under the auspices of the International AtomicEnergy Agency (IAEA).

Organizations participating in the CRP are providing their experimental data for itsstorage on the INSC database. The thermohydraulics database can be currently reached at thefollowing Web address:

http://www.insc.anl.gov:/thrmhydr/iaea

After the data providers review the contents, the database will be accessible through asubsection in the home page of the INSC database (www.insc.anl.gov).

The current contents of the database are as follows:

— Look-up table for Critical Heat Flux (CHF) in 8-mm tubes, developed by the AtomicEnergy of Canada Limited (AECL) and the Institute of Physics and Power Engineering(IPPE) in Obninsk, Russia.

Look-up tables available provide values of CHF at discrete values of pressure, quality,and mass flux. The ranges of the three parameters are from 0.1 to 20 MPa of pressure,50% to 100 % of vapor quality, and 0 to 7500 kg m~2 s"1 of mass flux.

The database contains multiple tables and graphic representations that permit finding theCHF value for any fix value of one of the three parameters, as a function of the othertwo parameters. The CHF Look-up table is also included in the TECDOC, Chapter 6.

— CHF databank for WWER reactor applications, contributed by the Nuclear ResearchInstitute (NRI), Rez, Czech Republic. This section contains experimental CHF data forWWER fuel bundles, obtained with the SKODA Large Water Loop Test facility. 166CHF data points are provided, along with a description of the facility and experimentalequipment.

— Look-up table for the post-dryout (PDO) heat transfer in tubes, provided by the Instituteof Physics and Power Engineering in Obninsk (IPPE), Russian Federation.

The look-up table was developed for PDO heat transfer in 10-mm tubes. It providesvalues of the PDO heat transfer coefficient for a range of pressures between 4 and

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20 MPa, mass flux between 250 to 2000 kg m~2 s"1, quality between -0.2 to 2.2, andheat fluxes between 0.2 and 1 Mw iincluded in the TECDOC, Chapter 5.heat fluxes between 0.2 and 1 Mw m 2 . The PDO heat transfer look-up table is also

— Look-up table for CHF in WWER rod bundles, contributed by the Institute of Physicsand Power Engineering (IPPE) in Obninsk, Russia.

The look-up table is applicable to rod bundles with triangular lattice, a heated diameterof 9.36 mm, and a pitch-to-diameter ratio of 1.4. The CHF values in the table are basedon experimental bundle CHF data and predictions based on a semi-empirical model. Therange of applicability of the look-up table is for pressures between 1.5 and 20 MPa,mass fluxes between 220 and 5040 kg m~2 s"1, and qualities between -0.52 and 0.9. Thelook-up table is also included in the TECDOC, Chapter 4.

In preparation — CHF data from low power and low flow experiments, provided by theKorea Advanced Institute of Science and Technology (KAIST).

In preparation — CHF data for high flow and low pressure conditions, provided by the ChinaInstitute of Atomic Energy (CIAE).

In preparation — PDO data for high flow and low pressure conditions, provided by the ChinaInstitute of Atomic Energy (CIAE).

Future additions — Documentation of other thermohydraulics relationships in use in nuclearreactor safety analyses.

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Annex B

PREPARED METHODOLOGY TO SELECT RANGES OFTHERMOHYDRAULIC PARAMETERS

B.I. INTRODUCTORY REMARKS

The thermalhydraulic phenomena of interest for the study of transient behaviour ofexisting water cooled reactors and for advanced concepts have been discussed in Chapter 2,respectively. An overall view of the foreseeable system behaviour has been given in thatrespect, [see also Aksan and D'Auria (1993 and 1995)].

In the present chapter the attention is addressed towards the phenomena of directinterest to the CRP, i.e. CHF, film boiling and pressure drops. These are described into detailin Chapters 3, 4 and 5, respectively, where aspects like phenomenology, experiments,modelling, and code capabilities are considered. Before such an evaluation, it is worthwhile toconsider the parameters affecting the CHF, the film boiling heat transfer and the pressuredrops together with the respective ranges of interest from a reactor design, operation andsafety analysis point of view.

The activity should be considered as a pilot study: a systematic and final evaluation,specifically including an optimized selection of relevant combinations among ranges, wouldrequire resources that are well beyond the limits of the present activity. However, theobjective can be reached in the present framework of making available ranges of parameterssuitable for evaluating the existing data base, for deriving a more objective judgement aboutcode capabilities and for planning further activities in the area.

With reference to each of the three phenomena, four groups of quantities aredistinguished: this is considered as sufficient information to characterize the phenomenon(Section B.2). Ranges of variations are identified in Section 3B, making reference to thevariables selected in the previous section and to the situations expected to be of interest towater cooled reactors (both current generation and advanced concepts).

B.2. QUANTITIES CHARACTERIZING THE PHENOMENA

Each thermalhydraulic phenomenon, specifically if it occurs during a complex transient,depends upon a large number of parameters. The "importance" on the phenomenon of thevarious parameters is clearly different among each other; a detailed ranking implies the use ofsubjective judgement; the "importance" may be a function of the range of variation of theparameter.

In this context, with the aim of characterizing as far as possible each phenomenon, anattempt is made to select a necessary/sufficient number of parameters suitable for such apurpose. Four groups of parameters are identified, connected, respectively with:

(a) geometry (local and system geometry including microscopic surface geometry);(b) thermalhydraulic boundary and initial conditions (e.g. thermal flux distribution in the

case of CHF and film boiling), including flow conditions;(c) material properties/constitutive laws;(d) transient effects (i.e. time variations of any quantity).

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B.2.1. CHF

Critical heat flux is important in different conditions of a nuclear plant and may occur indifferent locations (see also Chapter 3): typical conditions are accident (e.g. DBA),operational transient, coupled neutronic thermalhydraulic instabilities (in BWR); typicallocations are core and steam generators (in PWR). However during a LOCA, CHF may occurin the majority of the structures of the primary circuit also affecting the heat release to thefluid. In addition, the knowledge of CHF is of fundamental importance for the fuel design. Areview of the present state of the art including identification of important parameters affectingthe phenomena and predictive capabilities of the models and of associated system codes canbe found in Ninokata and Aritomi (1992) and NED Issue dedicated to the Memory of Prof. K.Becker (1996).

With reference to the four groups of parameters identified above, the considerations andthe choices below are made.

a) Geometry.

The investigation is limited to vertical rod bundles, i.e. at least a 2 x 2 configuration,though other configurations like single rod, single tube, tube bundles, plate, large unheatedcylinder, horizontal or inclined fuel bundle, etc., are of interest in the technology.

hi this assumption, the considered geometric parameters are:

gl) rod diameter;g2) channel equivalent diameter (including the effects of surface roughness, pitch/diameter

ratio, distance from unheated wall, etc.);g3) heated length.

It may be noted that parameters like array type (square or triangular), presence andconfiguration of the fuel box, configuration of the fluid entrance, presence and configurationof spacer grids, presence of oxide layer, roughness, etc., are not directly considered (see theprevious discussion). In addition, equivalent diameter is assumed to include the informationconnected with different geometry related parameters.

b) Thermalhydraulic boundary and initial conditions.

The following parameters are selected:

tl) pressure;t2) liquid temperature at channel inlet;t3) linear power (uniform/constant axial distribution);t4) power shape;t5) channel inlet flow/fluid velocity (i.e. mass flux, assumed to be single phase subcooled

liquid);t6) rod surface temperature.

It is assumed that the values of parameters like channel exit equilibrium quality, flowpattern, local void fraction, etc., can be calculated as a function of the parameters above and

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below. Rod surface temperature (item t6), has been added for completeness; it depends alsoupon heat transfer coefficient (i.e. from a number of parameters not explicitly reported here)and upon parameters directly considered here. Radial flux distribution in the bundle isassumed flat; so element flux tilt is not considered.

c) Material properties/constitutive laws.

It is assumed that only the fluid and the cladding base material affect the phenomenon.Aspects like oxide/crud formation are neglected together with the internal configuration of therod (cladding thickness, gap conductivity, etc.).

In these assumption the following parameters are considered:

ml) cladding material thermal capacity;m2) latent heat of vaporization;m3) liquid/steam density ratio;m4) surface tension.

d) Transient effects.

Most of the information (both experiments and correlations) connected with CHF isdirectly related to stationary conditions. However, in practical situations, "quasi" steady stateand unsteady conditions must be distinguished. It is assumed that "quasi" steady conditionscan be dealt with stationary conditions as characterized above. In order to stress theimportance of unsteady situations the following parameters are introduced (not exhaustive list;individual time variations of parameters like pressure, flow, etc. can be important, as well ascombinations of simultaneous transients involving flow-pressure-power, etc.; in addition, forthe sake of simplicity, conditions including oscillatory flows are not taken into account):

vl) time variations (slope and duration of the power excursion) of local linear power;v2) oscillations characteristics of local linear power.

B.2.2. Film boiling

In the case of film boiling the same quantities considered for CHF are important andshould be used for defining the Phenomenological Areas (Ph. A.— see below); an exceptionto this is represented by the parameter m3 that seems uninfluent for the film boilingphenomenon, with main reference to the groups of parameters a to d, the following quantitiesshould be added, [see also Hewitt and Delhaye (1992)].

g4) aspect ratio (geometry related parameter assumed representative for simulating radiationheat transfer phenomena);

t7) fluid temperatures inside the channel (both steam and liquid if present or applicable);t8) temperature (including spatial distribution) of the structural materials heat sink;m5) thermal radiation emissivity and absorption coefficient for the fluid;m6) thermal radiation emissivity and absorption coefficient for the structural material.

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B.2.3. Pressure drops

Pressure drops are clearly important in different (all) the parts of the nuclear powerplants, including primary and secondary loop: their characterization is of fundamental interestfor steady state and transient situations. With regard to both local pressure drop anddistributed pressure drop types, the system geometry plays a decisive role together with thecondition of "fully developed" flow. Strictly speaking, no zone of a typical water cooledreactor can be identified where the "fully developed" flow situation applies, with the possiblepartial exception represented by parts of the tubes in steam generator primary side in WesternPWR equipped with U-Tubes or with Once-Through steam generators.

A systematic and comprehensive search of all the parameters affecting the pressure dropin all the situations of interest in a Water Cooled Reactor, is again well outside the purpose ofthe present activity.

In addition, the consideration of transient situations may imply the introduction ofparameters like the flashing delay, the number of nucleation sites, etc. on the experimentalside, and the consideration of the time derivative terms on the code side.

Considering the above, the field of investigation has been dramatically restricted makingreference to the situation of steady state in a vertically heated boiling channel without internalrestrictions (i.e. spatial grids, obstructions, etc.).

Reference is made hereafter to the total pressure drop per unit length (i.e. Pa/m) in asituation where the "fully developed" flow condition is applicable. It must be noted that thewall-to-fluid friction, the gravity and the "spatial" acceleration, contribute to the consideredquantity, hi the following, parameters affecting the pressure drop per unit length are identified.

a) Geometry.

The drastic assumptions made, bring to these parameters (the "span", characterizes thedistance along the flow direction between two pressure taps that are connected to a pressuretransducer):

gl) channel equivalent diameter;g2) length of the considered span divided by the channel length;g3) bottom elevation of the span divided by the channel length.

Equivalent diameter is assumed, again, to include information connected with differentgeometry related parameters.

b) Thermalhydraulic boundary and initial conditions.

The following parameters are selected:

tl) absolute pressure (at channel inlet);t2) liquid temperature at channel inlet;t3) linear power (uniform/constant axial distribution);t4) channel inlet flow/fluid velocity (i.e. mass flux, assumed to be single phase subcooled

liquid);t5) rod surface temperature.

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It might be noted that power shape is assumed to have a second order effect if theselected span length over channel length is sufficiently small. Rod surface temperature maysignificantly affect pressure drop specifically in cases where it separates wetted from un-wetted zones. The information about parameters tl, t2, t3 and t4 allows the evaluation of localvoid fraction, local velocities and flow regimes that may have a strong impact on thecalculation of pressure drop (clearly there may be a feedback between these values and thepressure drop value).

c) Material properties!constitutive laws.

hi these assumption the following parameters are considered:

ml) liquid viscosity;m2) steam viscosity;m3) liquid/steam density ratio;m4) surface tension.

It should be noted that a number of parameters connected with the interaction betweenliquid and steam at the interface (e.g. interfacial drag, interfacial area, bubble or droplet sizes,etc., including those causing a flow regime instead of another) may largely affect the pressuredrop. Measurement difficulties suggest not to include these parameters in the list.

B.3. RANGES OF VARIATION

When a reference phenomenon is assigned in reactor safety and design technologies (i.e.one of the 67 phenomena in Chapter 2), the definition of ranges of variations may beimportant in different frameworks:

a) ranges of validity of a correlation;b) ranges of availability of experimental data;c) expected ranges of variations in nuclear power plants.

The ranges of validity of a correlation (item a), imply the knowledge of the ranges ofvariations of relevant quantities considered by the "independent" assessment of thecorrelation. If the correlation (or the model) is implemented in a system code, this also impliesthe verification of the built-up model including the possible influence from other parts of thecode. The ranges of validity also signify suitable ranges of availability (next item).

The ranges of availability (item b), imply the knowledge of the experimental researchescarried out in the scientific community all over the world; suitable data are needed, so aspectslike experimental facility design criteria, boundary conditions for the tests, sources andquantification of errors, quality of instrumentation and of recorded data, must be evaluated, hiaddition, once the ranges needed for the investigation are known (next item), preliminaryscaling studies should be carried out: this could avoid the need of systematically covering, inthe experiments, the whole ranges of selected parameters.

The expected ranges of variations in the plants (item c), imply the knowledge of planttransient scenarios and the deep understanding of phenomena; this, necessarily, also dependsupon activities leading to items a) and b). These links must be recognized, when searching for

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the ranges of variations in the plants, attentions should also be paid to the interactions amongthe ranges. For instance, in the case of CHF, hypothetical ranges for linear power, pressureand flowrate could be 0.1-50 kW/m, 0.1-20 MPa and 5-30000 kg/m2s, respectively; in thiscase a power of 50 Kw/m may not occur at low pressure; again, the occurrence of the lowflow condition (i.e. 5 kg/m2s) might have very low probability when extreme (high) values ofpressure or power are of interest. As a summary, ranges intersections should beconsidered.

hi addition, Phenomenological Areas (Ph. A.) are introduced in the present analysisconsidering relevant intersections of the parameters ranges (parameters are those defined inSection B.2).

The identification of parameter ranges and, as a consequence, of phenomenologicalareas, include engineering judgement connected with:

(1) choice of relevant parameters: e.g. steam or liquid velocities can be selected instead ofliquid velocity and slip ratio, channel inlet quantities can be selected instead of localquantities;

(2) the consideration of the mutual interactions between various phenomena: CHF may beaffected by pressure drop, so parameters relevant for pressure drop are inherentlyrelevant for CHF;

(3) level of detail of the analytical or of the experimental investigation: the bubblediameters or bubble density may be important parameters to be used in addition to (orinstead of) void fraction; 2-D or 3-D local system behaviour including cross sectionparameter distributions (e.g. velocity profiles in a cross section) may also be important.

Owing to all of the above the present one must be considered as a pilot study; as suchthe ranges of parameters and the phenomenological areas are limited to the CHF phenomenon.

Assuming that zircaloy and water are the only materials involved, in the case of CHF,the characterization of the ranges of parameters becomes simpler; in this case, materialproperties (parameters ml to m6), are implicitly identified and depend upon other parametershere considered: their ranges of variations are not reported here.

B.3.1. Ranges of parameters for CHF

The following ranges apply:

gl) 0.006-0.013g2) 0.002-0.015

g3) 1.0-4.5

tl) 0.1-20.

t2) 0-150.

t3) 0. 1-20.

mm

m

MPa

K

kW/m

(1)

(1)

(11)

(2)

(3)

(4)

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-

kg/m2s

K

kW/msSHz

(5)

(6)

(7)

(8)(9)

t4) 1-2. 5

t5) 0-15000.

t6) 0-40.

vl) 0-20.1-2.

v2) 0.1-2.5-200% - (10)

(1) this also includes advanced reactor and advanced fuel design;

(2) four sub-ranges identified (these are needed for the definition of the Phenomenologicalareas, see below):

tla) 0.1-2.5 MPa; tlb) 2.5-7.5 MPa; tic) 7.5-16. MPa; tld) 16-20 MPa;

(3) subcooling value;

(4) only the maximum values of the average linear power are considered here;absolutemaximum linear power should be obtained by multiplying this value with the value atitem t4; maximum "transient" power value (i.e. power excursion) needs consideration ofitem vl;

(5) three power shapes identified: t4a (chopped) cosine with central peak; t4b bottompeaked: chopped cosine in the bottom 1/3 of the active length and uniform power in theupper 2/3 of the active length; t4c top peaked: uniform power in the bottom 2/3 of theactive length and chopped cosine in the upper 1/3 of the active length. It is important toadd that all the above is related to a vertical bundle and is not directly applicable to theCANDU geometry;

(6) or0-15m/s;

(7) 0. and 40 K are the minimum and the maximum temperature difference expectedbetween the rod surface and the fluid, respectively;

(8) linear variation of the generated power;

(9) duration of the assumed triangular peak power trend;

(10) amplitude of the power oscillation related to the actual linear power;

(11) in the case of CANDU the upper limit must be extended to 6.0 m.

B.4. PHENOMENOLOGICAL AREAS

The definition of Phenomenological Areas (Ph. A.) constitutes the final step of theactivity and requires additional assumptions. One parameter is assumed as the leadingparameter.

B.4.1. CHF

The system pressure (parameter tl) is assumed as leading parameter and four sub-rangesare identified as given in Section B.3.1 on this basis the following Ph. A. are identified (e.g.PA.l = Phenomenological Area 1; in addition "X" means that the overall range must beconsidered as reported in Section B.3.1):

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tl t2 t3 t4 t5 t6 gl g2 g3 vl v2

PA.1 tla 0-50 0.1-2 t4a 0-2000 X X X X X X

PA.2 tlb 0-100 1-20 t4a,b,c 1000-15000 X X X X X X

PA.3 tic 0-150 1-20 t4a,b,c 1000-15000 X X X X X X

PA.4 tld 0-150 10-20 t4a 5000-15000 X X X X X X

B.5. FURTHER ACTIVITIES

The comparison between the ranges of phenomena available from experimentalprograms, [Aksan and D'Auria (1993)] and the boundaries of the phenomenological areas,might give a direct information about the need for future experiments.

The phenomenological areas can be used to define ranges of validity (or of the bestsuitability) for correlations or codes and, as a follow up of the evolution of codes/correlationdeficiencies, eventually for planning improvements or new developments.

Large amounts of resources can be envisaged for finalizing the systematic approach hereproposed in the areas of planning of new experiments, advanced correlation or new codes.

REFERENCES TO ANNEX B

AKSAN, S.N., et al., 1993, Separate Effect Test Matrix for Thermalhydraulic CodesValidation: Phenomena Characterization and Selection of Facilities and Tests — Vol. Ill,OECD/CSNI Rep. OCDE/GD(94)82, Paris (F).

AKSAN, S.N.,et al., 1994, Thermalhydraulic Phenomena in the CSNI Separate EffectValidation Matrix, Int. Conf. on New Trends in Nuclear System Thermalhydraulics, Pisa (I).

AKSAN, S.N., et al., 1995, Overview of the CSNI Separate Effects Tests Validation Matrix,NURETH-7, Saratoga Springs.

HEWITT, G.F., DELHAYE, J.M., ZUBER, N., (Eds), 1992, "Post-dryout heat transfer",Multiphase Science and Technology, CRC Press.

NINOKATA, H., ARITOMI, M., (Eds), 1992, Subchannel Analysis in Nuclear Reactors;Proc. Int. Sem. on Subchannel Analysis, Tokyo.

NED ISSUE DEDICATED TO THE MEMORY OF PROF. K. BECKER, 1996, J. Nucl. Eng.Design 163 1-2.

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CONTRIBUTORS TO DRAFTING AND REVIEW

Akimoto, H.

Baek, W.P.

Bobkov, V.P.

Cevolani, S.

Chang, S.H.

Chen, Y.Z.

Cheng, X.

Chung, M.K.

Ivashkevitch, A.A.

Leung, K.H.

Macek, J.

Pilkhwal, D.S.

Roglans-Ribas, J.

Smogalev, I.P.

Tanrikut, A.

Venkat Raj, V.

Vijayan, P.K.

Vinogradov, V.N.

Yesin. O.

Japan Atomic Energy Research Institute, Japan

Korea Advanced Institute of Science and Technology,Republic of Korea

Institute of Physics and Power Engineering, Russian Federation

ENEA, ERG/FISS, Italy

Korea Advanced Institute of Science and Technology,Republic of Korea

China Institute of Atomic Energy, China

Kernforschungzentrum Karlsruhe, Germany

Korea Atomic Energy Research Institute, Republic of Korea


Chalk River Laboratories, Canada

Nuclear Research Institute, Czech Republic

Bhabha Atomic Research Centre, India

Argonne National Laboratory, United States of America


Turkish Atomic Energy Authority, Turkey




Middle East Technical University, Turkey

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