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Investigating the Effect of Tube
Dimensions and Operating
Conditions on Heat Transfer
Performance in a Rising Film
Vertical Tube Evaporator
Omkar Prabhakar THAVAL Bachelor of Technology (Sugar Engineering)
Master of Applied Science (Research), QUT
THESIS
Submitted in fulfilment of the requirements for the degree of
Doctor of Philosophy
School of Chemistry, Physics and Mechanical Engineering
Science and Engineering Faculty
Queensland University of Technology
2019
Dedicated to the Sugar Research Institute
team who taught me the value of good and
reliable data.
“Without data you are just another person with an opinion”
– W. Edwards Deming.
Data Scientist
Investigating the Effect of Tube Dimensions and Operating Conditions on Heat Transfer Performance in a
Rising Film Vertical Tube Evaporator I
Keywords
Annular Flow, Boiling Mechanism, Boiling Patterns, Brix, Bubbly Flow, Capital
Cost Model, Calandria Retrofitting, De-entrainment of Juice, Heat Transfer
Coefficient, Heat Flux, Headspace Pressure, Juice Level, Operating Costs, Optimum
Tube Dimensions, Pressure Difference, Rising Film Evaporator, Robert Evaporator,
Sucrose Degradation, Slug Flow, Temperature Difference, Tube Diameter, Tube
Dimensions, Tube Length, Vertical Tube.
Investigating the Effect of Tube Dimensions and Operating Conditions on Heat Transfer Performance in a
Rising Film Vertical Tube Evaporator III
Abstract
This thesis reports on a study to investigate the effects of tube dimensions and
operating conditions on heat transfer performance of a vertical rising film evaporator
tube. The study is undertaken to build a foundation, on which an improved design of
the Robert-type evaporator can be developed, seeking better performance in terms of
heat transfer coefficient (HTC), and at the same time reducing the capital cost
associated with designing, fabrication and installation of the equipment. Robert
evaporators in Australian sugar factories are traditionally constructed with 44.45 mm
outside diameter stainless steel tubes of ~2 m length for all stages of evaporation.
There are a few vessels with longer tubes (up to 2.8 m) and smaller and larger
diameters (38.1 and 50.8 mm). This PhD project is undertaken to investigate the heat
transfer performance of tubes of different lengths and diameters for the whole range
of process conditions typically encountered in the evaporator set. The study was
carried out in four phases.
The first phase of the project involved the development of a capital costs model
to understand the cost implications for constructing evaporator vessels with calandrias
having tubes of different dimensions. A capital cost model was developed, which
provides a relative cost of constructing and installing Robert evaporators of the same
heating surface area (HSA) but with different tube dimensions. Evaporators of 2000,
3000, 4000 and 5000 m2 were investigated. The results showed that the conventional
evaporator, with 2 m tubes of 44.45 mm outside the diameter, is more expensive than
all the other tube arrangements, except for evaporators with 2 m tubes of 50.8 mm
outside diameter.
The second phase of the project involved the experimental investigations with a
single tube evaporator rig for different tube dimensions. The experimental program
was undertaken in two sections. Nine tubes were tested for the operating conditions of
1st, 3rd, and 5th effect positions in a quintuple evaporator set and the HTC was
determined. Tests with four of the tubes were replicated to understand the tube length
and tube diameter interaction and build confidence in the data. The results showed that
selection of tube length and tube diameter cannot be independent of each other. The
tube diameter is more important than tube length in achieving maximum HTC. The
IV
Investigating the Effect of Tube Dimensions and Operating Conditions on Heat Transfer Performance in a
Rising Film Vertical Tube Evaporator
results showed that as the brix of the juice increases, HTC decreases. An optimum
juice level exists that corresponds to maximum HTC, and brix and tube diameter are
two factors strongly affecting the optimum juice level. It was found the optimum juice
levels were lower for smaller diameter tubes and the optimum juice level was higher
for larger diameter tubes. Empirical models were developed for maximum HTC and
optimum juice level.
The third phase of the project involved investigating the boiling patterns in the
single tube evaporator for different tube dimensions and operating conditions. Six
distinct boiling patterns were identified and the relationship to the overall HTC was
analysed. The Annular Flow boiling regime was found to not exist in the test
conditions, which reflected sugar mill evaporators. The dominant regimes were
hypothesised as being Bubbly and Slug flow regimes. Boiling patterns with uniform
HTC values along the tube length and with low HTC at the bottom of the tube were
identified as occurring when good heat transfer performance was achieved.
The fourth phase of the project involved identifying the favoured tubes based on
HTC performance and the capital and operating costs. For evaporators at effect 1st to
3rd effect of a quintuple set, cost savings of ~20% could be achieved if small diameter
(38,1 mm) and long tubes (3 or 4 m) are used instead of the traditional tubes. Operating
cost savings include the reduction in sucrose degradation losses in evaporators by
installing vessels with smaller diameter and longer tubes as these vessels have smaller
diameter and juice holds up volume, thus reducing the residence time (for juice) in the
evaporator. Replacing the calandria in an existing evaporator with a calandria
comprising smaller diameter and longer tubes could be an attractive option for
increasing the HSA and capacity of the set for a much lower cost than replacing the
whole evaporator.
Investigating the Effect of Tube Dimensions and Operating Conditions on Heat Transfer Performance in a
Rising Film Vertical Tube Evaporator V
Table of Contents
Keywords ...................................................................................................................... I
Abstract ...................................................................................................................... III
Table of Contents ........................................................................................................ V
List of Figures ........................................................................................................... XV
List of Tables............................................................................................................. XX
Abbreviations & Symbols ...................................................................................... XXV
Statement of Original Authorship ....................................................................... XXVII
Acknowledgements .............................................................................................. XXIX
List of Publications .............................................................................................. XXXI
CHAPTER 1: INTRODUCTION .......................................................................... 1
1.1 Introductory Remarks ......................................................................................... 1
1.2 The Australian Sugar Industry ............................................................................ 1
1.3 Raw Sugar Production ........................................................................................ 1
1.4 The Evaporation Station ..................................................................................... 3
1.4.1 Overview ................................................................................................... 3
1.4.2 Multiple effect evaporation ....................................................................... 3
1.4.3 Evaporator design ...................................................................................... 4
1.4.4 Evaporator performance ............................................................................ 6
1.5 Scope of Research............................................................................................... 8
1.5.1 Research problem ...................................................................................... 8
1.5.2 Objectives .................................................................................................. 9
1.5.3 Individual contribution to the research team ........................................... 10
1.6 Overview of thesis ............................................................................................ 11
CHAPTER 2: LITERATURE REVIEW ............................................................ 13
2.1 Introductory Remarks ....................................................................................... 13
VI
Investigating the Effect of Tube Dimensions and Operating Conditions on Heat Transfer Performance in a
Rising Film Vertical Tube Evaporator
2.2 Condensation Heat Transfer ............................................................................. 13
2.2.1 Introductory remarks ............................................................................... 13
2.2.2 Laminar film on a vertical surface .......................................................... 13
2.2.3 Concluding remarks ................................................................................ 16
2.3 Flow Boiling ..................................................................................................... 17
2.3.1 Introductory remarks ............................................................................... 17
2.3.2 Regimes of boiling .................................................................................. 17
2.3.3 Two – phase flow .................................................................................... 18
2.3.4 Existing flow pattern maps ...................................................................... 19
2.4 Transition Mechanisms (Adiabatic Flows) ....................................................... 20
2.4.1 Introductory remarks ............................................................................... 20
2.4.2 The transition from bubble flow.............................................................. 20
2.4.3 The transition from slug flow .................................................................. 22
2.4.4 The transition to annular flow ................................................................. 24
2.4.5 Flow pattern maps ................................................................................... 25
2.4.6 Concluding remarks ................................................................................ 25
2.5 Previous Pilot Plant Investigations of Sugar Factory Evaporators ................... 26
2.5.1 Introductory remarks ............................................................................... 26
2.5.2 Kestner evaporator .................................................................................. 26
2.5.3 Guo et al. investigations .......................................................................... 27
2.5.4 Broadfoot and Dunn investigations ......................................................... 29
2.5.5 Pennisi’s investigations ........................................................................... 31
2.5.6 The SRI design of Robert evaporator ...................................................... 36
2.5.7 Selection of tube dimensions................................................................... 37
2.5.8 Concluding remarks ................................................................................ 38
2.6 Operational Investigations on Robert vessels ................................................... 39
Investigating the Effect of Tube Dimensions and Operating Conditions on Heat Transfer Performance in a
Rising Film Vertical Tube Evaporator VII
2.6.1 Introductory remarks ............................................................................... 39
2.6.2 Smith and Taylor investigations .............................................................. 39
2.6.3 Jayes’ evaporation model ........................................................................ 40
2.6.4 Watson investigation ............................................................................... 40
2.6.5 Shah and Peacock investigations............................................................. 42
2.6.6 Broadfoot and Tan investigations ........................................................... 43
2.6.7 Empirical relationships for HTC ............................................................. 43
2.6.8 Concluding remarks ................................................................................ 45
2.7 CFD Modelling ................................................................................................. 46
2.7.1 Introductory remarks ............................................................................... 46
2.7.2 CFD and heat transfer models ................................................................. 47
2.7.3 Concluding remarks ................................................................................ 48
2.8 Concluding Remarks ........................................................................................ 48
CHAPTER 3: CAPITAL COST MODEL .......................................................... 51
3.1 Introductory Remarks ....................................................................................... 51
3.2 Evaporator Designs and Costs .......................................................................... 51
3.2.1 Introductory remarks ............................................................................... 51
3.2.2 Number of tubes ...................................................................................... 51
3.2.3 Vessel internal diameter .......................................................................... 54
3.2.4 Capital costs ............................................................................................ 54
3.2.5 Installation costs ...................................................................................... 58
3.2.6 Concluding remarks ................................................................................ 59
3.3 Other Considerations in the Design of Evaporators ......................................... 60
3.3.1 Introductory remarks ............................................................................... 60
3.3.2 Sucrose degradation during juice evaporation ........................................ 60
3.3.3 Buffer volume for improved juice level and syrup brix control ............. 61
3.3.4 De-entrainment of droplets of juice from the vapour stream .................. 62
VIII
Investigating the Effect of Tube Dimensions and Operating Conditions on Heat Transfer Performance in a
Rising Film Vertical Tube Evaporator
3.3.5 Concluding remarks ................................................................................ 64
3.4 Concluding Remarks ........................................................................................ 64
CHAPTER 4: EXPERIMENTAL PROGRAM ................................................. 67
4.1 Introductory Remarks ....................................................................................... 67
4.2 Experimental Rig .............................................................................................. 67
4.3 Experimental Design ........................................................................................ 70
4.3.1 Selection of the experimental factors ...................................................... 70
4.3.2 Design of experiments ............................................................................. 73
4.4 Experimental Procedure.................................................................................... 74
4.5 Calculating HTC from Condensate Measurements .......................................... 75
4.5.1 Introductory remarks ............................................................................... 75
4.5.2 Determining condensate flow rate (kg/s) ................................................ 75
4.5.3 Determining temperature difference ....................................................... 76
4.5.4 Example showing HTC calculation......................................................... 76
4.6 Analysis of Potential Errors with Condensate Collection ................................ 80
4.6.1 Introductory remarks ............................................................................... 80
4.6.2 Collection of condensate from the base of the steam chest ..................... 80
4.6.3 Overflowing in a free-flowing scenario .................................................. 83
4.6.4 Overflowing due to blockage at the entrance to a drainage tube ............ 84
4.6.5 Concluding remarks on the collection of condensate from the four
sections of the heating tube ..................................................................... 85
4.7 Analysis of Potential Errors of Operating Conditions ...................................... 86
4.7.1 Introductory remarks ............................................................................... 86
4.7.2 Analysis of variance of the operating conditions .................................... 87
4.7.3 Concluding remarks ................................................................................ 94
4.8 The Effect of Tube Dimensions and Operating Conditions on Heat Flux and
Heat Transfer Coefficient ........................................................................................... 94
Investigating the Effect of Tube Dimensions and Operating Conditions on Heat Transfer Performance in a
Rising Film Vertical Tube Evaporator IX
4.8.1 Introductory remarks ............................................................................... 94
4.8.2 Review of the experimental data ............................................................. 95
4.8.3 Concluding remarks .............................................................................. 105
4.9 Concluding Remarks ...................................................................................... 107
CHAPTER 5: ANALYSIS OF HEAT TRANSFER COEFFICIENT
RESULTS ...................................................................................................... 109
5.1 Introductory remarks ...................................................................................... 109
5.2 Features of the Pilot Evaporator Rig that may affect HTC Results ................ 109
5.2.1 Influence of clean and new tubes .......................................................... 109
5.2.2 Effect of gutters on the tube .................................................................. 110
5.2.3 Effect of the downtake .......................................................................... 111
5.2.4 Comparison of industrial and pilot evaporator HTC values ................. 111
5.2.5 Concluding remarks .............................................................................. 113
5.3 Visual Observations of Boiling Patterns ........................................................ 113
5.3.1 Introductory remarks ............................................................................. 113
5.3.2 No visible juice head above top plate.................................................... 113
5.3.3 Visible juice head above top plate......................................................... 113
5.3.4 Substantial juice head above top plate .................................................. 114
5.4 Overview of the results ................................................................................... 114
5.5 Comparison of Original432 and Replicate128 Results for the Overall HTC 115
5.5.1 Introductory remarks ............................................................................. 115
5.5.2 HTC vs juice level results for M2 tube ................................................. 115
5.5.3 HTC vs juice level results for S2 tube................................................... 117
5.5.4 HTC vs juice level results for M3 tube ................................................. 119
5.5.5 HTC vs juice level results for S3 tube................................................... 121
5.5.6 Concluding Remarks ............................................................................. 124
5.6 Analysis of the Results of the Original432 Tests ........................................... 124
X
Investigating the Effect of Tube Dimensions and Operating Conditions on Heat Transfer Performance in a
Rising Film Vertical Tube Evaporator
5.6.1 Introductory remarks ............................................................................. 124
5.6.2 TL:TD:B:HS interaction plot .................................................................. 127
5.6.3 TD:JL interaction plot ............................................................................ 129
5.6.4 Concluding remarks .............................................................................. 131
5.7 Analysis of HTCmax Results ............................................................................ 131
5.7.1 Introductory remarks ............................................................................. 131
5.7.2 Method for HTCmax selection ................................................................ 131
5.7.3 HTCmax results ....................................................................................... 131
5.7.4 Concluding remarks .............................................................................. 134
5.8 Analysis of Optimum Juice Level .................................................................. 134
5.8.1 Introductory remarks ............................................................................. 134
5.8.2 Optimum juice level (JLopt(%)) for HTCmax ............................................ 135
5.8.3 Concluding remarks .............................................................................. 139
5.9 Developing Empirical Relationships .............................................................. 139
5.9.1 Introductory remarks ............................................................................. 139
5.9.2 Empirical relationship for HTCmax ........................................................ 140
5.9.3 Empirical relationship for optimum juice level (JLopt(mm)).................... 143
5.9.4 Concluding remarks .............................................................................. 145
5.10 Concluding Remarks ...................................................................................... 146
CHAPTER 6: BOILING PATTERNS IN THE HEATING TUBE ................ 149
6.1 Introductory Remarks ..................................................................................... 149
6.2 Comparison of Replicate Results with Original Results for the Section HTCs ...
........................................................................................................................ 150
6.2.1 Introductory remarks ............................................................................. 150
6.2.2 Comparison of the HTC results for individual tube sections for
Brix-20 tests .......................................................................................... 151
Investigating the Effect of Tube Dimensions and Operating Conditions on Heat Transfer Performance in a
Rising Film Vertical Tube Evaporator XI
6.2.3 Comparison of the HTC results for individual tube sections for
Brix-70 tests .......................................................................................... 155
6.2.4 Concluding remarks .............................................................................. 155
6.3 Identification of Boiling Patterns.................................................................... 156
6.3.1 Introductory remarks ............................................................................. 156
6.3.2 Boiling patterns ..................................................................................... 156
6.3.3 Concluding remarks .............................................................................. 158
6.4 Determination of Factors Influencing the Boiling Pattern ............................. 158
6.4.1 Introductory remarks ............................................................................. 158
6.4.2 Factors affecting the boiling patterns .................................................... 159
6.4.3 Concluding remarks .............................................................................. 161
6.5 Analysis of Variance of Individual Sections HTC ......................................... 162
6.5.1 Introductory remarks ............................................................................. 162
6.5.2 ANOVA for individual section HTC results ......................................... 162
6.5.3 Concluding remarks .............................................................................. 171
6.6 Analysis of Variance of the HTC Values for Individual Sections Corresponding
to Overall HTCmax .................................................................................................... 172
6.6.1 Introductory remarks ............................................................................. 172
6.6.2 ANOVA for individual section corresponding to HTCmax results ........ 172
6.6.3 Uniform boiling pattern for tests at HTCmax ......................................... 176
6.6.4 Non-uniform boiling pattern with low HTC at the top for tests at
HTCmax .................................................................................................. 177
6.6.5 Non-uniform boiling pattern with low HTC at the bottom for test at
HTCmax .................................................................................................. 178
6.6.6 Non-uniform boiling with low HTC at intermediate sections for
tests at HTCmax ...................................................................................... 179
6.6.7 Concluding remarks .............................................................................. 180
6.7 Boiling Mechanism ......................................................................................... 181
6.7.1 Introductory remarks ............................................................................. 181
XII
Investigating the Effect of Tube Dimensions and Operating Conditions on Heat Transfer Performance in a
Rising Film Vertical Tube Evaporator
6.7.2 Review of the literature on boiling mechanisms in a rising film tube
evaporator .............................................................................................. 181
6.7.3 Proposed boiling mechanism ................................................................ 184
6.7.4 Concluding remarks .............................................................................. 186
6.8 Boiling Patterns in the Tube that Provide Superior Heat Transfer Coefficient ....
........................................................................................................................ 186
6.8.1 Introductory remarks ............................................................................. 186
6.8.2 Uniform boiling pattern ......................................................................... 187
6.8.3 Low HTC at the bottom of the tube ...................................................... 189
6.8.4 Concluding remarks .............................................................................. 190
6.9 Concluding Remarks ...................................................................................... 190
CHAPTER 7: SELECTING OPTIMUM TUBE DIMENSIONS ................... 193
7.1 Introductory remarks ...................................................................................... 193
7.2 Methodology for Determining the Optimum Tube Dimensions .................... 193
7.2.1 Introductory remarks ............................................................................. 193
7.2.2 Favoured tubes based on HTCmax .......................................................... 193
7.2.3 Concluding remarks .............................................................................. 198
7.3 Capital Costs for Constructing and Installing Evaporators ............................ 198
7.3.1 Introductory remarks ............................................................................. 198
7.3.2 Construction costs ................................................................................. 199
7.3.3 Foundations and structural costs ........................................................... 201
7.3.4 Insulation and cladding costs ................................................................ 203
7.3.5 Design weight and design costs ............................................................ 204
7.3.6 Total costs ............................................................................................. 207
7.3.7 Concluding remarks .............................................................................. 208
7.4 Selection of the Optimum Tube Dimensions.................................................. 208
7.4.1 Introductory remarks ............................................................................. 208
Investigating the Effect of Tube Dimensions and Operating Conditions on Heat Transfer Performance in a
Rising Film Vertical Tube Evaporator XIII
7.4.2 Basis of selection ................................................................................... 208
7.4.3 Estimates of capital costs savings ......................................................... 209
7.4.4 Estimates of operating costs savings ..................................................... 210
7.4.5 Selection of the optimum tube dimension ............................................. 212
7.4.6 Concluding remarks .............................................................................. 213
7.5 Retrofitting of Calandria for Existing Evaporators ........................................ 213
7.5.1 Introductory remarks ............................................................................. 213
7.5.2 Practical considerations of retrofitting a calandria ................................ 214
7.5.3 Retrofit options ...................................................................................... 214
7.5.4 Further design considerations................................................................ 215
7.5.5 Concluding remarks .............................................................................. 215
7.6 Concluding Remarks ...................................................................................... 215
CHAPTER 8: GENERAL DISCUSSIONS AND CONCLUSIONS ............... 217
8.1 Introductory remarks ...................................................................................... 217
8.2 Aim of the Research ....................................................................................... 217
8.3 Comments on the Experimental Program ....................................................... 218
8.4 Summary of the Research Outcomes .............................................................. 219
8.4.1 Capital cost model ................................................................................. 219
8.4.2 Heat transfer performance of different tube dimensions ....................... 219
8.4.3 Understanding the boiling patterns in the single tube ........................... 221
8.4.4 Selecting the optimum tube dimensions................................................ 222
8.5 Significance of the Research .......................................................................... 223
8.5.1 Introductory remarks ............................................................................. 223
8.5.2 Increase in HTC .................................................................................... 223
8.5.3 Reducing capital costs ........................................................................... 224
8.5.4 Reducing operating costs ...................................................................... 224
8.5.5 Retrofitting of calandrias ....................................................................... 224
XIV
Investigating the Effect of Tube Dimensions and Operating Conditions on Heat Transfer Performance in a
Rising Film Vertical Tube Evaporator
8.6 Recommendations for Future Research .......................................................... 225
8.7 Concluding Remarks ...................................................................................... 226
BIBLIOGRAPHY .................................................................................................. 229
APPENDIX A: DESCRIPTION OF EXPERIMENTAL RIG .......................... 235
APPENDIX B: CFD MODEL–STEAM SIDE .................................................... 253
APPENDIX C: ORIGINAL432 DATA SET - EXPERIMENTAL DESIGN AND
RESULTS ............................................................................................................ 257
APPENDIX D: REPLICATE128 DATA SET - EXPERIMENTAL DESIGN
AND RESULTS ...................................................................................................... 279
APPENDIX E: HTCMAX AND VCCMAX RESULTS OF ORIGINAL432 AND
REPLICATE128 TESTS ........................................................................................ 289
APPENDIX F: INDIVIDUAL SECTIONS HTC RESULTS OF ORIGINAL432
EXPERIMENTS .................................................................................................... 295
APPENDIX G: INDIVIDUAL SECTIONS VCC RESULTS OF ORIGINAL432
EXPERIMENTS .................................................................................................... 307
APPENDIX H: INDIVIDUAL SECTIONS HTC RESULTS OF
REPLICATE128 EXPERIMENTS ....................................................................... 319
APPENDIX I: INDIVIDUAL SECTIONS VCC RESULTS OF REPLICATE128
EXPERIMENTS .................................................................................................... 325
APPENDIX J: REPLICATE128 ANOVA ........................................................... 331
APPENDIX K: COMPARISON OF INDIVIDUAL SECTIONS HTC FOR
TESTS WITH BRIX-70 ......................................................................................... 337
APPENDIX L: UNIFORM BOILING PATTERN RESULTS – ORIGINAL432
AND REPLICATE128 DATASETS ..................................................................... 343
APPENDIX M: RESULTS SHOWING LOW HTC AT TOP SECTION –
ORIGINAL432 AND REPLICATE128 DATASETS ......................................... 349
APPENDIX N: RESULTS SHOWING LOW HTC AT BOTTOM SECTION –
ORIGINAL432 AND REPLICATE128 DATASETS ......................................... 365
APPENDIX O: RESULTS SHOWING LOW HTC AT INTERMEDIATE
SECTIONS – ORIGINAL432 AND REPLICATE128 DATASETS ................. 373
APPENDIX P: ANALYSIS OF VARIANCE ...................................................... 377
Investigating the Effect of Tube Dimensions and Operating Conditions on Heat Transfer Performance in a
Rising Film Vertical Tube Evaporator XV
List of Figures
Figure 1.1 The process of raw sugar production .......................................................... 2
Figure 1.2 Multiple effect evaporation diagram .......................................................... 4
Figure 1.3 Typical design of Robert evaporator (Neill et al., 1996) ............................ 5
Figure 2.1 Flow regimes of the film of condensate on a cooled vertical surface
(Bejan, 1993)................................................................................................ 14
Figure 2.2 Laminar film condensation, supplied by a reservoir of stationary
saturated vapour (Bejan, 1993) .................................................................... 15
Figure 2.3 Flow regimes for forced convection boiling inside a tube (Incropera
& Dewitt, 1996) ........................................................................................... 18
Figure 2.4 Flow patterns in vertical flow (Taitel et al., 1980) ................................... 19
Figure 2.5 Model of slug flow (McQuillan & Whalley, 1985) .................................. 23
Figure 2.6 Flow pattern map for vertical tubes 51 mm diameter, air-water at
100 kPa abs (Taitel et al., 1980) .................................................................. 25
Figure 2.7 Effect of liquid level on HTC (Guo et al., 1983) ...................................... 28
Figure 2.8 Effect of ΔT on HTC at selected constant liquid levels (h) (Guo et
al., 1983) ...................................................................................................... 29
Figure 2.9 Variation of HTC with operating level of juice at 15 brix
((Broadfoot & Dunn, 2007) ......................................................................... 30
Figure 2.10 HTC data for varying ΔT, calandria pressure and brix for the total
tube (Pennisi, 2004) ..................................................................................... 33
Figure 2.11 HTC values for water solution for segments of the evaporator tube
(Pennisi, 2004) ............................................................................................. 34
Figure 2.12 HTC values for Brix-20 sucrose solution for segments of the
evaporator tube (Pennisi, 2004) ................................................................... 35
Figure 2.13 HTC values for Brix-45 sucrose solutions for segments of the
evaporator tube (Pennisi, 2004) ................................................................... 36
Figure 2.14 Variation of head of juice above the calandria with operating level
Watson (1986b) ............................................................................................ 41
Figure 2.15 Variation of HTC with operating level for a conventional Robert
evaporator with mini-downtake (Watson, 1986b) ....................................... 42
Figure 3.1 Output sheet for the tube layout program for the Robert evaporator
design ........................................................................................................... 52
XVI
Investigating the Effect of Tube Dimensions and Operating Conditions on Heat Transfer Performance in a
Rising Film Vertical Tube Evaporator
Figure 3.2 Number of tubes for 2000, 3000, 4000 and 5000 m2 vessels with
different tube dimensions ............................................................................. 53
Figure 3.3 Vessel ID for 2000, 3000, 4000 and 5000 m2 vessels with different
tube dimensions ........................................................................................... 54
Figure 3.4 Costs of materials for 2000, 3000, 4000 and 5000 m2 vessels with
different tube dimensions as fraction of cost of materials for vessels
with M2 calandrias ....................................................................................... 56
Figure 3.5 Total costs (ex-works) for 2000, 3000, 4000 and 5000 m2 vessels
with different tube dimensions as fraction of cost (ex-works) for
vessels with M2 calandrias .......................................................................... 58
Figure 3.6 Total mass on foundations for 2000, 3000, 4000, and 5000 m2
vessels with different tube dimensions as fraction of the total mass for
vessels with M2 calandrias .......................................................................... 59
Figure 3.7 Juice volume intensity for 2000, 3000, 4000 and 5000 m2 vessels
with different tube dimensions..................................................................... 61
Figure 4.1 Schematic representation of the single-tube evaporator rig ..................... 68
Figure 4.2 Pilot evaporator rig ................................................................................... 70
Figure 4.3 Condensate collection (mm) for individual sections (1 to 4) and for
section 5 ....................................................................................................... 79
Figure 4.4 Mean values of unaccounted section 5 condensate flow expressed as
percentage of total flow on tube surface ...................................................... 82
Figure 4.5 Mean values of measured brix for each level of each factor for the
Original432 tests with all results included .................................................. 89
Figure 4.6 B:HS:ΔP interaction plot with measured pressure difference as a
response factor ............................................................................................. 91
Figure 4.7 Actual average temperature differences for the three brix ....................... 93
Figure 4.8 Target temperature differences for the three brix ..................................... 93
Figure 4.9 Effect of tube dimensions and operating conditions on heat flux and
heat transfer coefficient for tests at Brix-20 ................................................ 96
Figure 4.10 Effect of tube dimensions and operating conditions on heat flux
and heat transfer coefficient for tests at Brix-35 .......................................... 97
Figure 4.11 Effect of tube dimensions and operating conditions on heat flux
and heat transfer coefficient for tests at Brix-70 .......................................... 98
Figure 4.12 Relationship between heat transfer coefficient and heat flux at the
optimum juice level at Brix-20 .................................................................. 100
Investigating the Effect of Tube Dimensions and Operating Conditions on Heat Transfer Performance in a
Rising Film Vertical Tube Evaporator XVII
Figure 4.13 Relationship between heat transfer coefficient and heat flux at the
optimum juice level at Brix-35 .................................................................. 101
Figure 4.14 Relationship between heat transfer coefficient and heat flux at the
optimum juice level at Brix-70 .................................................................. 102
Figure 5.1 Schematic representation of condensate pattern on the outside of the
heating tube for experimental and industrial arrangements ....................... 110
Figure 5.2 Comparison of industrial and pilot evaporator HTC values for the
M2 tube dimension .................................................................................... 112
Figure 5.3 Relationship between HTC and juice level for the M2 tube .................. 117
Figure 5.4 Relationship between HTC and juice level for the S2 tube .................... 119
Figure 5.5 Relationship between HTC and juice level for the M3 tube .................. 121
Figure 5.6 Relationship between HTC and juice level for the S3 tube .................... 123
Figure 5.7 Mean values of HTC for each level of each factor for the
Original432 tests with all results included ................................................ 125
Figure 5.8 TL:TD:B:HS interaction plot for the Original432 dataset ....................... 128
Figure 5.9 TL:TD:B:HS interaction plot for the Original432 dataset with
separate plots for brix and headspace pressure .......................................... 129
Figure 5.10 TD:JL interaction plot for the Original432 dataset ............................... 130
Figure 5.11 TD:JL interaction for the Original432 dataset with three separate
plots for brix ............................................................................................... 130
Figure 5.12 Mean values of HTCmax for each level of each factor from the
Original432 tests (108 data points)............................................................ 132
Figure 5.13 TD:B:HS interaction for HTCmax for the Original432 dataset .............. 134
Figure 5.14 Mean values of JLopt(%) for each level of each factor from the
Original432 tests (108 data points)............................................................ 135
Figure 5.15 TL:B:HS interaction plot for the optimum juice level in the
Original432 dataset .................................................................................... 137
Figure 5.16 TD:ΔP interaction plot for the optimum juice level in the
Original432 dataset .................................................................................... 138
Figure 5.17 TD:ΔP interaction plot for Original432 dataset for three separate
plots for brix ............................................................................................... 139
Figure 5.18 Measured and predicted HTCmax .......................................................... 141
Figure 5.19 Measured and predicted optimum juice level ....................................... 144
Figure 6.1 Number of results showing uniform boiling throughout the tube for
each level of each factor for Original432 tests .......................................... 159
XVIII
Investigating the Effect of Tube Dimensions and Operating Conditions on Heat Transfer Performance in a
Rising Film Vertical Tube Evaporator
Figure 6.2 Number of results showing non-uniform boiling with low HTC at
the top for each level of each factor for Original432 tests ........................ 160
Figure 6.3 Number of results showing non-uniform boiling with low HTC at
the bottom for each level of each factor for Original432 tests .................. 160
Figure 6.4 Number of results showing non-uniform boiling with low HTC at
intermediate sections for each level of each factor for Original432
tests ............................................................................................................ 161
Figure 6.5 TL:TD:B:HS interaction plot for HTC for section 1 ................................ 163
Figure 6.6 TL:TD:B:HS interaction plot for HTC for section 2 ................................ 163
Figure 6.7 TL:TD:B:HS interaction plot for HTC for section 3 ................................ 164
Figure 6.8 TL:TD:B:HS interaction plot for HTC for section 4 ................................ 164
Figure 6.9 TL:B:ΔP interaction plot for HTC for section 1 ...................................... 165
Figure 6.10 TL:HS:ΔP interaction plot for HTC for section 2 ................................. 166
Figure 6.11 TL:B:ΔP interaction plot for HTC for section 2 .................................... 166
Figure 6.12 TL:JL:HS interaction plot for HTC for section 3 .................................. 167
Figure 6.13 TL:JL:HS interaction plot for HTC for section 4 .................................. 168
Figure 6.14 JL:HS:ΔP interaction plot for HTC for section 4 at HS1 values .......... 169
Figure 6.15 JL:HS:ΔP interaction plot for HTC for section 4 for HS2 values ........ 169
Figure 6.16 TD:JL interaction plot for HTC for section 1 ........................................ 170
Figure 6.17 TD:JL interaction plot for HTC for section 2 ........................................ 171
Figure 6.18 TD:B:HS interaction plot for HTCmax for the four sections for
Brix- 20 ...................................................................................................... 174
Figure 6.19 TD:B:HS interaction plot for HTCmax for the four sections for
Brix- 35 ...................................................................................................... 175
Figure 6.20 TD:B:HS interaction plot for HTCmax for the four sections for
Brix- 70 ...................................................................................................... 176
Figure 6.21 Mean values of overall HTCmax with uniform boiling pattern
(O432) ........................................................................................................ 177
Figure 6.22 Mean values of overall HTCmax with non-uniform boiling pattern
and low HTC at top (O432) ....................................................................... 178
Figure 6.23 Mean values of overall HTCmax with non-uniform boiling pattern
and low HTC at intermediate section (O432) ............................................ 179
Figure 6.24 Mean values of overall HTCmax with non-uniform boiling pattern
and low HTC at intermediate sections (O432) .......................................... 180
Investigating the Effect of Tube Dimensions and Operating Conditions on Heat Transfer Performance in a
Rising Film Vertical Tube Evaporator XIX
Figure 6.25 Flow pattern map for vertical tubes 51 mm diameter, air-water at
100 kPa abs (Taitel et al., 1980) ................................................................ 183
Figure 6.26 Flow pattern map for experimental results ........................................... 184
Figure 7.1 Influence of tube length and tube diameter on HTCmax for Brix-20 ....... 195
Figure 7.2 Influence of tube length and tube diameter on HTCmax for Brix-35 ....... 196
Figure 7.3 Influence of tube length and tube diameter on HTCmax for Brix-70 ....... 197
Figure 7.4 Materials and labour costs for evaporators with favoured tubes
dimensions for 1st, 3rd and 5th effect positions ........................................... 200
Figure 7.5 Design vessel weight and design costs for evaporators with the
favoured tubes for 1st, 3rd and 5th effect positions ...................................... 206
XX
Investigating the Effect of Tube Dimensions and Operating Conditions on Heat Transfer Performance in a
Rising Film Vertical Tube Evaporator
List of Tables
Table 2.1 Maximum length of evaporator tubes for different tube diameters
(Hugot & Jenkins, 1986) .............................................................................. 38
Table 2.2 Optimal tube lengths recommended for the different effect
parameters (Hugot & Jenkins, 1986) ........................................................... 38
Table 3.1 Code for different tube dimensions ............................................................ 53
Table 3.2 Tube costing based on tube diameter ......................................................... 55
Table 3.3 Cost data for construction of an evaporator ............................................... 56
Table 3.4 Maximum specific vapour rates for acceptable up-flow vapour
velocities in the headspace of vessels comprising tubes of 38.1 mm
OD and 4 m length ....................................................................................... 63
Table 3.5 Maximum specific vapour rates for LSEA II louvres in vessels
comprising tubes of 38.1 mm OD and 4 m length ....................................... 64
Table 4.1 Factors and levels explored in the experiment ........................................... 71
Table 4.2 Experimental factors investigated for juice at Brix-20 .............................. 72
Table 4.3 Experimental factors investigated for juice at Brix-35 .............................. 72
Table 4.4 Experimental factors investigated for juice at Brix-70 ............................. 73
Table 4.5 Density of saturated liquid and latent heat of condensation for the 12
steam chest pressures ................................................................................... 78
Table 4.6 Results of analysis of variance of unaccounted section 5 condensate
flow (%) with main sources (percent of total flow on tube surface) ........... 83
Table 4.7 Maximum value, mean value and standard deviation of the
unaccounted section 5 condensate rate for all levels of each factor for
tests at Brix-20 ............................................................................................. 84
Table 4.8 Maximum values, minimum values, mean values and standard
deviation of the experimental factors ........................................................... 87
Table 4.9 Analysis of variance of measured brix ....................................................... 88
Table 4.10 Analysis of variance of measured pressure difference............................. 90
Table 4.11 Analysis of variance of calculated temperature difference ...................... 92
Table 4.12 Conversions of heat flux to VCC for different calandria pressures ......... 95
Table 4.13 List of tubes showing high and low HTC for corresponding brix and
temperature difference ............................................................................... 103
Investigating the Effect of Tube Dimensions and Operating Conditions on Heat Transfer Performance in a
Rising Film Vertical Tube Evaporator XXI
Table 4.14 Summary of the observations and comments for heat flux of three
brix ............................................................................................................. 104
Table 4.15 General observations for tube dimensions that provided higher
levels of heat transfer coefficient for the three brix levels ......................... 107
Table 5.1 Average values for overall HTC for all tube dimensions with Brix-
20, Brix-35 and Brix-70 ............................................................................. 114
Table 5.2 Comparison of data for Original432 and Replicate128 for M2 tube ....... 116
Table 5.3 Comparison of data for Original432 and Replicate128 for S2 tube ........ 118
Table 5.4 Comparison of Original432 and Replicate128 for M3 tube .................... 120
Table 5.5 Comparison of Original432 and Replicate128 for S3 tube ..................... 122
Table 5.6 Analysis of variance of HTC from Original432 tests with 4th order
interactions ................................................................................................. 126
Table 5.7 Analysis of variance of HTCmax from Original432 tests ......................... 133
Table 5.8 Analysis of variance of optimum juice level (JLopt-% tube height)
corresponding to HTCmax from the Original432 tests ............................... 136
Table 5.9 List of parameters considered for inclusion in the empirical model ........ 140
Table 5.10 Analysis of variance of regression model for HTCmax ........................... 142
Table 5.11 Typical operating conditions in factory vessels and the predicted
HTCmax from two models ........................................................................... 143
Table 5.12 Typical operating conditions in factory vessels and the predicted
optimum juice levels (absolute and % tube height) ................................... 145
Table 6.1 Categories to define differences between the individual section HTC
values and the overall HTC........................................................................ 151
Table 6.2 Individual section HTC comparison with M2 tubes for Brix-20 juice .... 152
Table 6.3 Individual section HTC comparison with S2 tubes for Brix-20 juice ...... 152
Table 6.4 Individual section HTC comparison with M3 tube for Brix-20 juice ...... 153
Table 6.5 Individual section HTC comparison with S3 tube for Brix-20 juice ....... 153
Table 6.6 Comparison of the HTC data for individual sections between
Original432 and Replicate128 datasets for the four tubes for Brix-20
tests ............................................................................................................ 154
Table 6.7 Comparison of the HTC data for individual sections between
Original432 and Replicate128 datasets for M2, S2, M3 and S3 tubes
for Brix-70 tests ......................................................................................... 155
Table 6.8 Categorisation and description of the boiling patterns............................. 157
Table 6.9 Boiling pattern allocation for Original432 and Replicate128 datasets .... 158
XXII
Investigating the Effect of Tube Dimensions and Operating Conditions on Heat Transfer Performance in a
Rising Film Vertical Tube Evaporator
Table 6.10 HTC pattern and the corresponding figure number ............................... 159
Table 6.11 Results of observations of the influence of experimental factors on
the boiling patterns ..................................................................................... 161
Table 6.12 Summary of significant factors and interactions for the individual
sections HTC values (Original432) ........................................................... 162
Table 6.13 Boiling pattern allocation for HTCmax results from Original432
dataset ........................................................................................................ 172
Table 6.14 Summary of significant factors and interactions for the individual
sections HTCmax (Original432) .................................................................. 173
Table 6.15 Factors affecting overall HTCmax for uniform boiling for three brix
levels .......................................................................................................... 177
Table 6.16 Factors affecting overall HTCmax for the boiling pattern with low
HTC at the top for the three brix values .................................................... 178
Table 6.17 Factors affecting overall HTCmax the boiling pattern with low HTC
at the bottom for the three brix values ....................................................... 179
Table 6.18 Factors affecting overall HTCmax for the boiling pattern with low
HTC at an intermediate section for the three brix values .......................... 180
Table 6.19 Proposed boiling regimes for boiling patterns ....................................... 185
Table 6.20 Average HTCmax for different boiling patterns at three brix .................. 187
Table 6.21 Tube dimensions and operating conditions for HTCmax with uniform
boiling pattern ............................................................................................ 188
Table 6.22 Observation with uniform boiling pattern for three brix values ............ 188
Table 6.23 Tube dimensions and operating conditions for HTCmax with low
HTC at bottom ........................................................................................... 189
Table 6.24 Observations with non-uniform boiling pattern (low HTC at the
bottom of the tube) for three brix values ................................................... 190
Table 7.1 Favoured tubes based on HTCmax for 1st, 3rd and 5th effect positions ...... 198
Table 7.2 Heating surface areas of the respective vessels for the favoured tubes
for 1st, 3rd and 5th effect positions .............................................................. 199
Table 7.3 Cost data for foundations and structure to support the evaporator .......... 201
Table 7.4 Foundations and structural costs for evaporators comprising the
favoured tubes for 1st, 3rd and 5th effect positions (HSA of M2
evaporator of 2000 m2) .............................................................................. 202
Investigating the Effect of Tube Dimensions and Operating Conditions on Heat Transfer Performance in a
Rising Film Vertical Tube Evaporator XXIII
Table 7.5 Foundations and structural costs for evaporators comprising the
favoured tubes for 1st, 3rd and 5th effect positions (HSA of M2
evaporator of 5000 m2) .............................................................................. 202
Table 7.6 Cost data for insulation and cladding of the evaporator .......................... 203
Table 7.7 Insulation area and costs for the favoured tubes for 1st, 3rd and 5th
effect positions (HSA of M2 evaporator of 2000 m2) ................................ 204
Table 7.8 Insulation area and costs for the favoured tubes for 1st, 3rd and 5th
effect positions (HSA of M2 evaporators of 5000 m2) .............................. 204
Table 7.9 Details of the evaporator vessels with the favoured tube dimensions
to equate to the heat transfer performance of a 2000 m2 HSA M2
evaporator .................................................................................................. 207
Table 7.10 Details of the evaporator vessels with the favoured tube dimensions
to equate to the heat transfer performance of a 5000 m2 HSA M2
evaporator .................................................................................................. 208
Table 7.11 Estimate of cost savings from using S3 and M3 tubes in Robert
evaporators at the 1st effect and 3rd effect instead of using a Robert
evaporator with M2 tubes .......................................................................... 210
Table 7.12 Sucrose degradation and operating cost savings .................................... 212
Table 7.13 Evaporator heating surface details for retrofit options........................... 215
Investigating the Effect of Tube Dimensions and Operating Conditions on Heat Transfer Performance in a
Rising Film Vertical Tube Evaporator XXV
Abbreviations & Symbols
A Heat transfer area, m2
ANOVA Analysis of variance
B Brix
BPE Boiling point elevation
DP Pressure difference, kPa
𝑔 Acceleration due to gravity, m/s2
HS Headspace pressure, kPa abs
HSA Heating surface area, m2
ℎ𝐿 Condensation heat transfer coefficient, W/m2/K
ℎ𝑓𝑔′ Latent heat of condensation (corrected with the Jakob
number), kJ/kg
JL Juice level, % tube height
𝑘 Thermal conductivity, W/m/K
𝐿 Length of the wall, m
𝑁𝑢𝐿 Nusselt number
OD Outside diameter, mm
Q Heat flux, W/m2
𝑄𝐺 Gas volumetric flowrate, m3/s
𝑄𝐿 Liquid volumetric flowrate, m3/s
𝑞′ Total heat flux per unit length, W/m
R Recirculation rate, kg/s/m
S Condensate rate, kg/s
Tj Temperature of juice, °C
Ts Temperature of steam, °C
𝑇𝑠𝑎𝑡 Saturation temperature of the liquid – vapour interface (K)
𝑇𝑤 Wall temperature, (K)
TL Tube length, m
TD Tube diameter, mm
U Heat transfer coefficient, W/m2/K
𝑈𝐺 Gas velocity, m/s
XXVI
Investigating the Effect of Tube Dimensions and Operating Conditions on Heat Transfer Performance in a
Rising Film Vertical Tube Evaporator
𝑈𝐺𝑠 Gas superficial velocity, m/s
𝑈𝐿 Liquid velocity, m/s
𝑈𝐿𝑠 Liquid superficial velocity, m/s
VCC Vapour condensation coefficient, kg/h/m2
WR Wetting rate, kg/s/m
𝛼 Void fraction
λs Latent heat of steam, J/kg
𝜇 Viscosity, Pa.s
ρl Density of liquid, kg/m3
𝜌𝐺 Density of gas, kg/m3
ρv Density of vapour, kg/m3
𝜐 Kinematic viscosity, m2/s
𝑣𝑝 Absolute velocity of the gas slug, m/s
𝜎 Surface tension of liquid, N/m
Investigating the Effect of Tube Dimensions and Operating Conditions on Heat Transfer Performance in a
Rising Film Vertical Tube Evaporator XXVII
Statement of Original Authorship
The work contained in this thesis has not been previously submitted to meet
requirements for an award at this or any other higher education institution. To the best
of my knowledge and belief, the thesis contains no material previously published or
written by another person except where due reference is made.
Signature:
Date: May 2019
QUT Verified Signature
Investigating the Effect of Tube Dimensions and Operating Conditions on Heat Transfer Performance in a
Rising Film Vertical Tube Evaporator XXIX
Acknowledgements
Firstly, I would sincerely like to thank my principal supervisor, Professor Ross
Broadfoot, for his encouragement to undertake this PhD, and for his guidance and
patience throughout the long investigation. I would like to thank my associate
supervisor, A/Prof Geoff Kent, for his guidance in designing the experiments and
analysing the data. I would also like to thank my associate supervisor, Dr Floren Plaza,
for his assistance with CFD model development.
Secondly, I would like to thank the Sugar Research Australia (SRA) and Sugar
Research Limited (SRL) for their financial support of this project. I would also like to
thank Queensland University of Technology for a tuition fee waiver scholarship.
Thirdly, I would like to thank those who assisted in the experimental
investigations of the project. Craig Cuttriss of Kaima Engineering is acknowledged for
fabricating the pilot evaporator rig. Brett Stone of Applied Project Engineering is
acknowledged for his assistance in installing the rig and the support he provided during
changing the tubes and dealing with breakdowns. The management and staff of Rocky
Point Sugar Mill (Bruce Tyson, Terry Drury, Peter Bresow, Glen McIntosh) are
sincerely acknowledged for their permission to undertake the experiments at the mill
and for their immeasurable support. I would like to thank Neil McKenzie for his
assistance in setting up the control system of the rig and the data collection system. I
would like to thank Mr David Moller and Mr Neil McKenzie for their assistance in
commissioning the pilot evaporator.
Fourthly, I would like to thank those who assisted in analysing the data and
interpreting the results. I would like to thank Dr Wim Dekkers from the School of
Chemistry, Physics and Mechanical Engineering, Science and Engineering Faculty,
QUT, for his assistance with analysing the results. I would also like to thank Dr
Anthony Mann, Dr Darryn Rackemann and Mr David Moller from the Centre for
Tropical Crops and Biocommodities (CTCB) for fruitful discussions about the results.
I would like to thank Diane Kolomeitz for professional editing and proof reading the
thesis.
XXX
Investigating the Effect of Tube Dimensions and Operating Conditions on Heat Transfer Performance in a
Rising Film Vertical Tube Evaporator
Fifthly, I would like to thank the High-Performance Computing (HPC) group at
Queensland University of Technology for their assistance in the CFD model
development.
Sixthly, I wish to thank the staff and students of the Centre for Tropical Crops
and Biocommodities (CTCB), in particularly the Bioprocessing group, for their
ongoing guidance and support throughout this investigation.
Seventhly, I wish to thank my friends Chris Henderson, David Moller, Dr Darryn
Rackemann and Dr Anthony Mann for their support and patience. I also wish to thank
my family for their support during this long investigation.
Lastly, I would like to thank my wife Priya Patankar, who for reasons best known
to her, agreed to marry me, and for her support during the final months of this
investigation.
Investigating the Effect of Tube Dimensions and Operating Conditions on Heat Transfer Performance in a
Rising Film Vertical Tube Evaporator XXXI
List of Publications
1. Thaval OP, Broadfoot, R (2014). Capital cost model for Robert
evaporators. Proceedings of the 36th Annual Conference of the Australian
Society of Sugar Cane Technologists, Gold Coast, Australia.
2. Thaval OP, Broadfoot, R, Kent GA & Rackemann, DW (2016).
Determining optimum tube dimensions for Robert evaporators.
Proceedings of the XXIX International Society of Sugar Cane
Technologists Congress, Chiang Mai, Thailand.
3. Thaval OP, Broadfoot, R & Kent GA (2017). Boiling mechanism in
rising film vertical tube evaproator. Proceedings of the Annual
Convention of Sugar Technologists Association of India, Kochi, India.
4. Thaval OP, Broadfoot, R, Kent GA & Rackemann, DW (2019).
Investigating the effects of tube dimensions and operating conditions on
HTC of rising film evaporators. Proceedings of the XXX International
Society of Sugar Cane Technologists Congress, Tucuman, Argentina.
(Accepted)
5. Thaval OP, Broadfoot, R, & Kent GA (2019). Understanding the effect
of tube dimensions and operating conditions on boiling mechanism in
rising film vertical tube evaporator. (Proposed)
XXXII
Investigating the Effect of Tube Dimensions and Operating Conditions on Heat Transfer Performance in a
Rising Film Vertical Tube Evaporator
Introduction 1
CHAPTER 1: INTRODUCTION
1.1 Introductory Remarks
The sugar industry is a process industry, comprising several unit operations to
produce raw or white plantation sugar. The evaporation of juice is one of the unit
operations and has the aim to remove most of the water from the clarified juice. For
most factories, it is important that the evaporator station is economical in the usage of
process steam. Several evaporator designs have been adopted in the industry, with each
having advantages and disadvantages, depending on the application. This thesis deals
with the development of an improved design of the Robert (rising film type) evaporator
and endeavours to achieve better performance in terms of heat transfer coefficient
(HTC), while at the same time reducing the capital cost associated with fabrication and
installation of the equipment.
This chapter provides a general overview of the Australian sugar industry, the
raw sugar manufacturing process, the evaporator station, and conventional evaporator
station terminology. The chapter also covers the scope of research, defines the research
problem and the objectives of the research. The chapter concludes with an overview
of the document.
1.2 The Australian Sugar Industry
The Australian sugar industry is one of Australia’s largest and most important
rural industries and sugarcane is Queensland’s largest agricultural crop. The
Queensland sugar industry produces about 35 million tonnes of sugarcane from
400,000 hectares annually. This sugarcane crop produces approximately 4,200,000
tonnes of raw sugar, 1 million tonnes of molasses and 10 million tonnes of bagasse
annually. Approximately 85% of the raw sugar produced is exported, generating up to
AUD 1.5 billion in export earnings for Queensland (Australian Sugar Milling
Council).
1.3 Raw Sugar Production
Figure 1.1 shows the raw sugar manufacturing process.
2 Introduction
Figure 1.1 The process of raw sugar production
The cane grown in the field is harvested using mechanical harvesters and
transported to the sugar mill. The cane billets are passed through a shredder to open
the fibrous cells and make the juice to be extracted more accessible. After exiting the
shredder, the prepared cane is passed on to the milling train. The milling process
essentially involves the removal of juice from sugarcane by squeezing the cane
between pairs of large cylindrical rolls in a series of milling units collectively called a
milling train. To aid in the extraction process, water is added to the final milling unit
and juice is recirculated in a counter-current fashion. This is commonly known as
compound imbibition. The extracted juice is sent to the clarification station to remove
the insoluble solids and some of the soluble impurities. The clarified juice is passed to
an evaporator supply juice (ESJ) tank, from which the ESJ is fed to the evaporator
station. The aim of the evaporator station is to boil off excess water contained in the
juice. Multi-stage evaporation is employed to achieve high steam economy. The syrup
leaving the final evaporator vessel is boiled in a crystallisation pan operating under
vacuum. The syrup is super-saturated and seed crystals are added to the liquid to
initiate crystal growth. The resulting mixture of crystals and liquor, called massecuite,
is sent to the centrifugal station to separate the crystals from the liquid by spinning the
massecuite at high speed in perforated baskets. The raw sugar crystals are dried in a
Introduction 3
rotary drum, through which air is passed in counter-current flow to the sugar. The raw
sugar is sent to storage to wait for shipment to refineries in Australia and overseas.
1.4 The Evaporation Station
1.4.1 Overview
The concentration of clarified juice or ESJ from 15 brix to 70 brix is undertaken
in a multiple effect evaporator set having due regard for saving of steam (energy
efficiency) and for efficiency in the use of the installed heat transfer area (capital). The
evaporator station is the single largest consumer of low pressure (LP) steam (typically
at 200-250 kPa abs) in the sugar factory. Factories have identified the need to reduce
the energy requirements of the evaporator station, so that larger quantities of energy
can be used for co-generated electricity production and for other purposes.
1.4.2 Multiple effect evaporation
Norbert Rillieux, in 1844, developed the multiple effect evaporation system for
the Louisiana sugar industry in order to achieve more efficient usage of steam. Using
the graduated pressure difference between the process steam and vacuum in the
headspace of the final vessel as a driving force for heat transfer, the vapour generated
in the first evaporator is used to evaporate water from juice in the second evaporator,
and so on, till the vapour from the final vessel is condensed in a barometric condenser.
Typically, four, five or six stages of evaporation are used.
Figure 1.2 shows the typical layout of a multiple effect evaporation set. A
temperature difference is required to transfer the heat from the steam chest (calandria)
to the boiling juice, and so the temperature of the vapour at the outlet of the vessel will
always be lower than that of the vapour used as the heating source.
The magnitude of the temperature difference is a measure of the thermal
efficiency of the vessel. Low pressure steam is used as the heat source in the first effect
and is typically at 118 °C to 125 °C in the saturated condition or very slightly
superheated, while the temperature of the vapour at the outlet of the final effect is
usually about 50 to 58 °C at saturated conditions. The saturation temperature of the
vapour at the outlet of the final effect vessel is regulated by controlling the headspace
pressure (vacuum) in the final effect. With the vapour pressure being controlled by the
4 Introduction
two extremes, at the first and the final effect of the set, the pressure of the vapour
streams in the remainder of the effects in the set are left to equilibrate naturally.
Many factors influence the equilibrium pressures and these include the
distribution of heat transfer area among the effects in the set, the heat transfer
coefficient (HTC) of the individual effects, the vapour flow rates, and rates of
withdrawal of vapour from individual vessels for other heating duties e.g. for juice
heating, pan boiling.
Figure 1.2 Multiple effect evaporation diagram
1.4.3 Evaporator design
The sugar industry uses both the plate type and tubular type evaporators, and
these can operate as either rising film or falling film mode. The rising or falling film
designation is in reference to the direction of juice flow, e.g. the juice in a rising film
type evaporator enters the vessel beneath the heating element and rises up through the
vertical heating tubes or plates, due to the boiling action of the juice inside the tubes
(Pennisi, 2004). As this study is considering the tube type evaporator, in particularly
the Robert type, which is used almost universally in the Australian sugar industry, only
the tube-type evaporator is described below.
The tube-type evaporator consists of a series of vertical tubes packed into a
heating element called a calandria. Saturated LP steam or vapour condenses on the
outside of the tubes while the juice boils on the inside. Tube-type evaporators are
available in two forms viz., falling-film and rising-film types. In falling-film tube
evaporators the juice is pumped onto a perforated plate located above the tops of the
Introduction 5
tubes and the juice flows downwards as a film on the inside of the tubes. Vapour also
passes down the tubes. In rising-film tube evaporators the juice is fed into the space
beneath the calandria, boils inside the tubes and the concentrated juice is removed from
either the top or bottom of the vessel. Vapour passes up the tubes and into the
‘headspace’ of the vessel. Figure 1.3 shows a typical design of the tube-type, rising-
film evaporator known as the Robert evaporator.
Figure 1.3 Typical design of Robert evaporator (Neill et al., 1996)
Several variations of juice entry and exit locations above and below the calandria
have been adopted in the Robert evaporator. This gave rise to the terms under and over,
when describing the location of the juice entry and outlet locations, e.g. an under-over
configuration has the juice entry below the calandria and the juice exit above the
calandria. By far the most common evaporator in the Australian industry is the tube-
type, rising-film evaporator in the under-under configuration.
The new Robert evaporators installed in the industry in the past decade have
incorporated a central downtake, which preferentially removes the juice from above
the top tube plate and passes it to the base of the vessel via the central downtake. The
tubes in the Robert-type evaporators are commonly 44.45 mm outside diameter, 2.0 m
in length and 304 stainless steel. Tubes of these dimensions have traditionally been
6 Introduction
used in the Australian industry for all stages of evaporation. There are only a relatively
few vessels with different tube lengths or diameters.
The main advantages of the Robert evaporator, compared with other designs
such as falling-film evaporators, are the low maintenance costs, good access to all
sections of the vessel for repair, the ease of cleaning including chemical and
mechanical/hydraulic cleaning and the robust control, due to the large buffer volume
of juice held in the base of these vessels. The main disadvantages are the longer
retention time for juice, which can result in sucrose inversion and increased colour
formation in the juice, and the large footprint for a given heating surface area. The
design is relatively simple and can be made by several local heavy engineering
suppliers. Robert evaporators are relatively expensive (AUD 1200 per 1 m2 of heating
surface area, fully installed) but service life is typically more than 30 years.
1.4.4 Evaporator performance
The performance and operating conditions of an evaporator can be assessed in
terms of the coefficient of evaporation, overall heat transfer coefficient and vapour
condensation coefficient (VCC).
Coefficient of evaporation
The coefficient of evaporation (COE) is commonly used for estimating the
required size of an evaporator. It is a measure of the vapour-producing performance of
an evaporator and is expressed as the mass rate of vapour passing to the headspace per
unit area of heat transfer. A maximum value for Australian evaporators is typically
40 kg/h/m2, which corresponds to a heat flux of about 25 kW/m2. Generally, the COE
is of limited value in assessing multiple-effect evaporator performance, as it measures
how hard the evaporator is being worked, which is often not the limiting factor. It is
found that the temperature difference (i.e. the driving force) is often the rate
determining factor Watson (1986a).
Overall heat transfer coefficient
A better indicator of performance when the temperature difference is restricted
is the overall heat transfer coefficient. This is defined as:
HTC =
Q
A ΔT
1.1
Introduction 7
where 𝐻𝑇𝐶 is the heat transfer coefficient (W/m2/K),
Q is the heat flux (W),
A is the heat transfer area (m2),
ΔT is the temperature difference available for heat transfer i.e. between
the vapour and the juice, K.
The heat flux Q is calculated by:
Q = S λs 1.2
where S is condensate rate (of condensed steam), kg/s
λs is the latent heat of condensation for the steam in the calandria as
determined from the measured pressure within the calandria, J/kg.
The temperature difference ΔT for heat transfer is calculated by:
ΔT = Ts − Tj 1.3
where Ts is the saturation temperature of steam in the calandria steam chest as
determined from the measured pressure within the calandria, °C.
Tj is the boiling temperature of the juice, as estimated from the saturation
temperature of the vapour in the headspace of the evaporator plus the
boiling point elevation of the juice (as determined from the saturation
temperature of the vapour and the average brix of juice within the
evaporator), °C.
The boiling point elevation (Batterham et al., 1973) is calculated by:
𝐵𝑃𝐸 =
(𝑇𝑗 + 273.2)2
((100 + 273.2)2
𝐵𝐶 + (100 − 𝑇𝑗))
1.4
𝐵𝐶 = −0.138 + 2.23
𝐵𝑥
(100 − 𝐵𝑥)+ 0.119 (
𝐵𝑥
100 − 𝐵𝑥)
2
1.5
where 𝐵𝑥 is the juice brix
In practice, the temperature of juice varies along the length of the tube. The juice
at the bottom of the tube has a higher boiling point due to the head of the juice above
8 Introduction
it. As a simplification a single value for the boiling temperature of the juice is used, as
defined above.
In practice, the values for HTC decrease with each stage farther down a multiple-
effect evaporator set, owing to the increasing viscosity of the juice, which results from
the higher brix and lower temperature in the later stages of evaporation. Larger
temperature differences exist for subsequent stages down the set to compensate for the
lower HTCs and ensure the required heat transfer for each effect is achieved.
Vapour condensation coefficient
The vapour condensation coefficient (VCC) defines the vapour rate entering the
calandria of the evaporator and is condensed. The VCC is obviously closely related
to heat flux at the surface of the heating tube. The VCC is the condensed vapour rate
per m2 of heating surface area (Broadfoot & Dunn, 2004).
VCC = 3600
S
A
1.6
Hence, HTC can be defined in terms of VCC as:
HTC =
VCC λs
3600 ΔT
1.7
For normal operating conditions, the VCC is considered to be the controlled
variable, as set by the steam rate supplied to the first stage of evaporation. Hence to
achieve this condensation rate, the ΔT is a dependent, interrelated variable. The heat
transfer coefficient of the evaporator is then set by the magnitude of Q and ΔT.
However, if there is inadequate ΔT available across the vessel, then the steam rate that
is condensed within the calandria will decrease. The ΔT for a given VCC value will
primarily depend on (Broadfoot & Dunn, 2004):
➢ Juice properties (brix, temperature, viscosity, surface tension); and
➢ Surface properties on the juice side of the tubes (nucleation sites, scale)
1.5 Scope of Research
1.5.1 Research problem
There are two main types of rising film tube evaporator viz., Kestner evaporators
of 6 to 7 m tube length and the Robert evaporator. Kestner evaporators are used in
several overseas factories but are only suited to the evaporation of low brix juice e.g.,
Introduction 9
in 1st and 2nd effects. Robert evaporators are suitable for all stages of juice evaporation.
Australia has traditionally used stainless steel tubes of 44.45 mm outside diameter;
1.9-2.2 m long in all vessels throughout the set.
New evaporation plant for Australian factories is very expensive. During the
past 10 years the Australian sugar industry has installed eight Robert evaporators with
a total surface area of 34,000 m2 and cost more than AUD 40 m (2011 dollars). The
installation of several more evaporators is likely over the next two decades, as factories
need to replace old equipment and upgrade factories for increased energy efficiency.
At present, the optimum tube dimensions (based on minimum capital cost for a defined
evaporation duty) are not known, and the selection of the tube dimensions is currently
based on historical experience and tradition. Depending on the heat transfer
coefficient that can be achieved, there may be scope for considerable cost savings if
tubes of different dimension than the traditional dimensions are used.
Some Brazilian sugar factories have installed 4 m, 3.5 m, 3.0 m and 2.5 m for 1st
effect, 2nd effect, 3rd effect and 4th effect respectively, with the tubes mostly being
38.1 mm outside diameter. Comments from Brazilian technologists suggest that the
HTC is quite poor for the 4 m Robert vessels, although no comprehensive HTC data
are available in the literature. Poor HTC values could be attributed to many factors,
including the heating surface not being fully wetted by juice or scale deposits on the
tubes as the result of ineffective chemical cleaning procedures. It would appear that
the use of longer, small-diameter tubes would allow substantial savings in the capital
cost to be realised and also result in reduced sucrose inversion. However, the effect of
tube dimensions on the heat-transfer performance at different stages of evaporation is
not known. This information must be known before a particular tube dimension could
be recommended for a specific evaporation duty.
1.5.2 Objectives
The prime objectives of the project are to develop an increased understanding of
the heat-transfer performance of rising-film evaporator tubes of different dimensions
and to have a better understanding of the influence of tube dimensions on the
mechanism of rising film evaporation. The specific aims and outcomes of the project
are to
10 Introduction
• Develop a capital cost model to determine the costs of designing, fabricating
and installing Robert vessels of the same heating surface area but different
tube dimensions.
• Determine the HTC of tubes with different lengths and diameter operating at
different conditions.
• Determine the optimum tube dimensions and operating conditions favouring
maximum heat transfer coefficient.
• Determine the HTC at different sections of the tube in order to understand
the boiling patterns.
• Postulate a theory on boiling mechanism based on the boiling patterns
• Select the optimum tube dimensions for a particular evaporation duty by
considering the heat transfer performance, the capital costs and the operating
costs collectively.
1.5.3 Individual contribution to the research team
The project was funded by Sugar Research Australia (SRA) and Sugar Research
Limited (SRL).
The design of the single tube evaporator rig was quite complex owing to the need
to be able to test tubes of different diameters and different lengths. A drafter was
contracted to work with the student and the Principal Supervisor to develop the design
of the experimental rig.
The project provided an opportunity for the PhD student to develop design,
experimental and modelling skills and to gain experience in the process area of juice
evaporation.
The experimental rig was installed at Rocky Point Sugar Mill adjacent to factory
evaporators. The Engineering and Production staff at the factory provided excellent
support to the student in installing the rig and in replacing a tube between tests. A
tradesman was also contracted to assist with the procedure of dismantling the
apparatus, installing a replacement tube of different dimension and reassembling the
apparatus in readiness for the next series of experiments.
Introduction 11
1.6 Overview of thesis
Chapter 1 provides a general overview of the Australian sugar industry and raw
sugar production. The chapter describes multiple effect evaporation, general principles
in evaporation, different evaporator designs, and assessment of evaporator
performance in terms of coefficient of evaporation, overall heat transfer coefficient
and vapour condensation coefficient. Chapter 1 also describes the scope of the
research and the objectives of the project.
Chapter 2 reviews the previous research in evaluating and increasing the heat
transfer performance of evaporators. The chapter discusses the different tubed
evaporators’ designs (climbing and rising film), boiling mechanism in rising film and
previous investigations on pilot plant and factory evaporators. The CFD models
developed for predicting the evaporator performance are also discussed. The chapter
concludes with discussions on the poor understanding of the boiling mechanism in
Robert evaporators, selection of tube dimensions for different effects, the interaction
of tube dimensions and operating conditions and their effect on heat transfer
performance.
Chapter 3 describes a capital cost model for Robert evaporators developed for
2000, 3000, 4000 and 5000 m2 vessels with 2 m, 3 m, and 4 m tube lengths and tube
outside diameters of 38.10 mm, 44.45 mm, and 50.80 mm. The results show that the
conventional evaporator with tubes of 2 m length and 44.45 mm outside diameter is
more expensive than evaporators having calandrias with the other tube dimensions,
except for evaporators with 2 m tubes of 50.8 mm outside diameter. Cost savings of
~15% are shown to be available by using tubes of 3 m length and 38.1 mm diameter.
Chapter 4 describes the experiments conducted on the single-tube evaporator
rig with tubes of different lengths and diameters. Heat transfer performance data are
obtained for all the tubes across the full range of industrial processing conditions.
Analysis of potential errors of condensate collection showed that the measured
condensate flow rates on the heating tube were reliable for determining the heat
transfer coefficient and vapour condensation coefficient. Analysis of potential errors
of operating conditions showed that the values of the operating conditions utilised
during the test program were in close agreement with the target values. This analysis
demonstrated that the experimental program was well structured, and the operating
12 Introduction
conditions were sufficiently different from each other to affect the heat transfer
performance.
Chapter 5 details the analysis of the HTC measurements. Analysis of variance
was undertaken for the HTC measurements to determine the effects of tube dimensions
and operating conditions along with interactions on HTC. The maximum HTC
(HTCmax) was determined at the optimum juice level. The effects of tube dimensions
and operating conditions along with the interactions on HTCmax and optimum juice
level were determined. Empirical models for HTCmax and the optimum juice levels
were developed.
Chapter 6 describes the boiling patterns in the heating tubes. Six different boiling
patterns were identified from the HTC data for different sections of the heating tube.
A boiling mechanism was postulated based on the boiling mechanism theory and the
measured HTC results for the different sections of the tube. The boiling patterns in the
tube corresponding to the maximum HTC values were identified and the effects of
tube dimensions and operating conditions on these boiling patterns were determined.
Chapter 7 details the selection of optimum tube dimensions based on capital cost,
operating cost and HTC. The suitability of retrofitting tubes into existing vessels is
discussed and a case is detailed.
Chapter 8 discusses the conclusions from the study and applications of the work
in industry, research and consultation. The chapter provides recommendations for
further work in understanding the boiling mechanism in rising film evaporators.
Literature Review 13
CHAPTER 2: LITERATURE REVIEW
2.1 Introductory Remarks
In the previous chapter, evaporation concepts were introduced. This chapter
discusses previous investigations of the performance and operation of factory and pilot
plant evaporators. The chapter details the condensation and boiling heat transfer theory
in the literature. The chapter concludes with a discussion of the limitations of the
previous investigations in understanding the effect of tube dimensions and operating
conditions on the heat transfer coefficient of sugar juice evaporators.
2.2 Condensation Heat Transfer
2.2.1 Introductory remarks
The overall heat transfer coefficient consists of individual heat transfer
coefficients. It is known that different flow regimes occur inside the tube and present
different resistances to heat transfer. Similarly, the condensation on the outside of the
tube has a different profile along its length. It is therefore important to understand the
resistances offered by the condensation in order to understand the influence on the
overall HTC. This section describes the condensation heat transfer theory.
2.2.2 Laminar film on a vertical surface
The simplest convection phase change process is the condensation of vapour on
a cold vertical surface as shown in Figure 2.1 (Bejan, 1993). On the left side of Figure
2.1, three distinct regions of condensation are shown. The laminar section occurs at
the top of the wall where the film of condensate is the thinnest. The condensate flows
downward and enters the wavy section as more steam condenses on the wall and the
condensate film is thicker. Finally, if the wall is long enough, the condensate film
enters and remains in the turbulent flow regime. On the right side of Figure 2.1, the
laminar film region, which is the simplest of the three regions, is shown. The flow of
the liquid film interacts with the descending boundary layer of the cooled vapour. The
temperature of the liquid – vapour interface is the saturation temperature that
corresponds to the local pressure along the wall, Tsat. The saturation temperature is
sandwiched between the temperature of the isothermal vapour reservoir, T∞ and the
14 Literature Review
wall temperature Tw. Through the shear stress at the liquid–vapour interface, the
downward flow the liquid film is instigated. The vapour in the descending jet that aids
in the downward flow of liquid is cooler than the vapour reservoir and warmer than
the liquid in the film attached to the wall.
This two–phase flow is considerably more complicated in the wavy and turbulent
sections of the wall. In some applications, where the film is sufficiently long to exhibit
all three regions, the overall heat transfer rate from the vapour reservoir to the wall is
dominated by the contributions made by the wavy and turbulent sections (Bejan,
1993).
Figure 2.1 Flow regimes of the film of condensate on a cooled vertical surface
(Bejan, 1993)
Figure 2.2 shows the two–dimensional laminar film in which the distance y
measures the downward length of the film. This flow is much simpler than that shown
in Figure 2.1, as in this case the entire reservoir of vapour is isothermal at the saturation
pressure, Tsat. The simplification focuses exclusively on the flow of the liquid film and
neglects the movement of the nearest layers of vapour.
Literature Review 15
Figure 2.2 Laminar film condensation, supplied by a reservoir of stationary
saturated vapour (Bejan, 1993)
The overall Nusselt number based on the L-averaged heat transfer coefficient is
given by:
NuL =hLL
kl= 0.943 × [
L3hfg′ g(ρl − ρv)
klvl(Tsat − Tw)]
14
2.1
where NuL is the Nusselt number,
hL is the condensation heat transfer coefficient (W/m2/K),
L is the length of the wall (m),
kl is the thermal conductivity of the condensate (W/m/K),
hfg′ is the latent heat of condensation (corrected with the Jakob number),
(kJ/kg),
g is acceleration due to gravity (m/s2),
ρl is the density of liquid (kg/m3),
ρv is the density of vapour (kg/m3),
16 Literature Review
vl is the kinematic viscosity of the liquid (m2/s),
Tsat is the saturation temperature of the liquid – vapour interface (K),
Tw is the wall temperature, (K).
The total condensation rate ΓL (kg/s/m) is proportional to the total cooling rate
provided by the vertical wall:
ΓL =
q′
hfg′
=kl
hfg′ (Tsat − Tw)NuL
2.2
where q′ is the total heat flux per unit length (W/m).
The laminar film equations discussed above were developed by Nusselt (1916)
based on the assumption that the effect of inertia is negligible in the momentum
balance (Bejan, 1993). The complete momentum equation was used by Sparrow and
Gregg (1959). Their solution for NuL is lower than that determined by Nusselt equation
(2.1) when Prandtl1 number is smaller than 0.03 and the Jakob2 number is greater than
0.01.
2.2.3 Concluding remarks
It is often assumed that the condensation of vapour presents very little resistance
to the heat transfer compared to the juice side resistance in sugar juice evaporators.
For both the laminar film regime and turbulent film regime, the length of the wall has
a negative impact on the condensation heat transfer. This seems logical as the film of
the condensate on the wall adds another barrier to heat transfer, owing to its low
thermal conductivity. This effect is more profound in laminar film regime than in
turbulent, as in the turbulent regime the film thickness is not uniform along the length
of the tube. However, Peacock (2001) concluded that condensation heat transfer was
constant up to tube length of 6 m and for tubes above 6 m, the condensation heat
transfer increased. The evaporators used in the sugar industry in recent times have
1 Prandtl number is a dimensionless number approximating the ratio of momentum
diffusivity to thermal diffusivity.
2 𝐽𝑎 =𝑐𝑝(𝑇𝑤−𝑇𝑠𝑎𝑡)
ℎ𝑓𝑔 Jakob number represents the ratio of sensible heat to latent heat
absorbed (or released) during the phase change process.
Literature Review 17
longer tubes and some claim to have high overall heat transfer coefficient. The
condensation heat transfer coefficient is not recorded.
2.3 Flow Boiling
2.3.1 Introductory remarks
In section 2.2, heat transfer theory was described for condensation that occurs
with a change of phase from vapour to liquid. Boiling heat transfer is defined as a
mode of heat transfer that occurs with a phase change from liquid to vapour. There are
two types of boiling: pool boiling and flow boiling. Pool boiling is boiling on a heating
surface submerged in a pool of initially stagnant liquid. Flow boiling is boiling in a
flowing stream of fluid, where the heating surface may be the channel wall confining
the flow. A boiling flow is composed of a mixture of liquid and vapour and usually
comprises two-phase flow. Since evaporators in the sugar industry have flow boiling
in vertical channels, the heat transfer mechanism of flow boiling is discussed below.
2.3.2 Regimes of boiling
The existence of different boiling regimes has been documented by several
authors. Figure 2.3 shows the flow regimes for forced convection boiling inside a
vertical tube. Heat transfer to the subcooled liquid that enters the tube is initially by
forced convection. Once boiling is initiated, bubbles that appear at the surface grow
and are carried into the liquid mainstream. There is an increase in the convection heat
transfer coefficient associated with this bubbly flow regime. As the volume fraction of
the vapour increases, bubbles begin to coalesce, forming slugs of vapour. The regime
is termed as slug flow, which is followed by an annular flow regime, in which the
liquid is moving as a thin film along the inner surface of the tube. The vapour moves
at a larger velocity through the core of the tube. The heat transfer coefficient increases
through the bubbly flow regime and increases further to the annular flow. It is believed
that as annular flow gives way to mist flow, the maximum heat transfer coefficient is
achieved. The transition regime is identified by the growth of dry spots, until the
surface is completely dry, and all remaining liquid is in the form of droplets appearing
in the vapour core. The convection coefficient continues to decrease through the mist
flow regime (Incropera & Dewitt, 1996).
18 Literature Review
Figure 2.3 Flow regimes for forced convection boiling inside a tube (Incropera
& Dewitt, 1996)
2.3.3 Two – phase flow
When gas-liquid mixtures flow upward in a vertical tube, the two-phase mixture
may distribute in several patterns. Each of these patterns is characterised by the radial
and/or axial distribution of liquid and gas Taitel et al. (1980). There are four basic flow
patterns for up flow as shown in Figure 2.4 as described by Taitel et al. (1980). These
patterns are:
1. Bubble flow: The gas phase is approximately uniformly distributed in the
form of discrete bubbles in a continuous liquid phase.
2. Slug flow: Most of the gas is located in large, bullet-shaped bubbles, which
have a diameter almost equal to the pipe diameter. They move uniformly
Increasing
Literature Review 19
upward and are sometimes designated as “Taylor bubbles”. Taylor bubbles
are separated by slugs of continuous liquid, which bridge the pipe and
contain small gas bubbles. The liquid flows downward in the form of a thin
falling film between the Taylor bubble and the pipe wall.
3. Churn flow: Churn flow is similar to Slug flow; however, it is more chaotic,
frothy and disordered. The bullet-shape Taylor bubbles become narrower
and their shape is distorted. The continuity of the liquid in the slug between
successive Taylor bubbles is constantly destroyed by a high local gas
concentration in the slug. The accumulating liquid forms a bridge and is
again lifted by the gas. The oscillatory or alternating direction of motion of
liquid is typical of churn flow.
4. Annular flow: Annular flow is characterised by the continuity of the gas
phase along the core of the pipe. The liquid phase moves upwards partly as
liquid film and partly in the form of droplets entrained in the gas core.
Figure 2.4 Flow patterns in vertical flow (Taitel et al., 1980)
2.3.4 Existing flow pattern maps
There are a variety of flow-pattern maps for vertical flow proposed in the
literature. These maps propose transition boundaries in a two-dimensional co-ordinate
20 Literature Review
system. The selection of co-ordinates for the published maps has been of two basic
types.
1. The first group uses dimensional co-ordinates such as superficial velocities
𝑈𝐺𝑠 and 𝑈𝐿𝑠 (Sternling, 1965; Wallis, 1969) or superficial momentum flux,
𝜌𝐺𝑈𝐺𝑠2 and 𝜌𝐿𝑈𝐿𝑠
2 (Hewitt & Roberts, 1969). For a given pipe size and set of
fluid properties, the transition of the flow patterns can be mapped.
2. The second group represents the results by dimensionless co-ordinates in an
attempt to apply the results to line sizes and fluid properties other than those
of the data used to locate the curves. Taitel et al. (1980) suggested that the
use of dimensionless co-ordinates is more general than the use of
dimensional ones, since there was no theoretical basis.
Taitel et al. (1980) compared the various maps and found differences both as to
absolute value and trend. They stated that in most cases, the transition boundaries are
empirically located and do not rest in suitable physical models. Taitel et al. (1980)
concluded that a theoretical basis under the transition relationships was required to
improve both the prediction and classification of experimentally observed flow
patterns.
2.4 Transition Mechanisms (Adiabatic Flows)
2.4.1 Introductory remarks
In order to predict the conditions under which transition between flow patterns
occurs, it is required to understand the physical mechanism of the transition. In this
section, each transition is analysed, and the physical mechanism is described. The
reported experimental and modelling work on the transition of flow patterns in most
cases is for adiabatic (no heat addition) flows. The transitions described in this section
are for adiabatic flows.
2.4.2 The transition from bubble flow
Transition from the dispersed bubble condition observed at low gas rates to slug
flow requires a process of agglomeration or coalescence. The discrete bubbles combine
into the larger vapour spaces growing in diameter to that of the tube, which are
observed at the transition to slug flow. As the gas rate increases, the bubble density
increases and the closer bubble spacing results in an increased coalescence rate.
Literature Review 21
However, as the liquid rate increases, the turbulent fluctuations associated with the
flow can destroy the larger bubbles formed from the agglomeration. If the fluctuations
are quite intense, the breakup will prevent re-coalescence and the dispersed bubble
pattern is maintained.
The gas phase is distributed into discrete bubbles when initiated at low flow rates
into a large diameter vertical pipe of liquid (flowing at low velocity). Studies of bubble
motion showed that if the bubbles are very small, they behave as rigid spheres rising
vertically in rectilinear motion. Above a critical size (about 1.5 mm for air-water at
low pressure) the bubbles begin to deform, and the upward motion of the bubbles
results in a zig-zag path with extensive randomness. The bubbles randomly collide and
coalesce forming larger individual bubbles with the spherical cap similar to that of
Taylor bubbles of slug flow. However, the bubbles have not reached the diameter of
the pipe. Hence, bubble flow is characterised by smaller bubbles moving in zig-zag
motion and the occasional appearance of large Taylor-type bubbles. With further
increase in gas flow rate, with the liquid flow still being low, the bubble density
increases and reaches a point where the dispersed bubbles become so closely packed
that collisions and agglomeration occur, leading to larger bubbles. This results in a
transition to slug flow (Taitel et al., 1980).
If the gas bubbles rise at a velocity 𝑈𝐺, this velocity is related to the superficial
gas velocity 𝑈𝐺𝑠 by
𝑈𝐺 =
𝑈𝐺𝑠
𝛼
2.3
where α is the void fraction
Similarly, the average liquid velocity 𝑈𝐿 is given in terms of liquid superficial
velocity 𝑈𝐿𝑠 as:
𝑈𝐿 =
𝑈𝐿𝑠
1 − 𝛼
2.4
Designating 𝑈𝑂 as the rise velocity of the gas bubbles relative to the average
liquid velocity, equation 2.3 and 2.4 yield
𝑈𝐿𝑠 = 𝑈𝐺𝑠
1 − 𝛼
𝛼− (1 − 𝛼)𝑈𝑂
2.5
22 Literature Review
The rise velocity of relatively large bubbles has been shown by Harmathy
(1960)to be insensitive to the bubble size and given by the relation
𝑈𝑂 = 1.53 [𝑔(𝜌𝐿 − 𝜌𝐺)𝜎
𝜌𝐿2 ]
14
2.6
where 𝜌𝐺 is the density of gas (kg/m3),
𝜎 is the surface tension of liquid (N/m),
Substituting equation 2.6 into 2.5 and considering the transition to slug flow to
occur when 𝛼 = 𝛼𝑇 = 0.25 results in equation 2.7. This equation characterises the
transition for conditions where the dispersion forces are not dominant (Taitel et al.,
1980).
𝑈𝐿𝑠 = 3.0 𝑈𝐺𝑠 − 1.15 [𝑔(𝜌𝐿 − 𝜌𝐺)𝜎
𝜌𝐿2 ]
14
2.7
For the transition from non-dispersed bubble flow to dispersed bubble flow
𝑈𝐿𝑠 − 𝑈𝐺𝑠 = 4 [
𝐷0.429𝑔0.446 𝜎0.089
𝜌𝐿0.017 µ𝐿
0.072 ] 2.8
where 𝐷 is the tube diameter (m)
µ𝐿 is the liquid viscosity (Pa.s)
McQuillan and Whalley (1985)used 𝛼 = 0.52 on the assumption that dispersed
bubble flow would become unstable if the void fraction became sufficient to indicate
a cubic lattice of bubbles. McQuillan and Whalley (1985)stated that the formation of
a closely packed lattice was assumed to limit the stability of dispersed bubble flow and
hence the transition from dispersed bubble flow occurs when 𝛼 = 0.74.
Mishima and Ishii (1984)made no distinction between dispersed bubble flow and
non-dispersed bubble flow and stated that bubble flow would become unstable at void
fraction of 𝛼 = 0.3.
2.4.3 The transition from slug flow
The bubble flow regime becomes unstable due to the formation of large vapour
spaces within the flow. As a result of this process, slug flow may be formed. In some
circumstances (at high liquid flow rates) slug flow may also be unstable and therefore
Literature Review 23
the bubble flow may change directly to churn flow or annular flow. If the conditions
are favourable for slug flow to form, the large vapour spaces will assume the
characteristic bullet shape. For further increases in gas flow rate, a transition between
slug flow and churn flow will occur (Taitel et al., 1980).
Figure 2.5 shows the model of slug flow (McQuillan & Whalley, 1985).
Consecutive gas slugs rise in a vertical tube, separated by regions of liquid flow. If the
slug flow occurs as a development of bubble flow, the regions of liquid flow will be
bubbly. The small amount of gas that flows as bubbles in the liquid slugs is neglected.
As shown in Figure 2.5, the gas slug rises at an absolute velocity 𝑣𝑝. The liquid film
adjacent to the gas slug flows downward as a free-falling film at a velocity 𝑣𝑓.
Figure 2.5 Model of slug flow (McQuillan & Whalley, 1985)
Nicklin and Davidson (1962) proposed the following equation, which may be
used to determine the rise velocity of the gas slug.
𝑣𝑝 = 1.2 (𝑄𝐺 + 𝑄𝐿
𝐴) + 0.35 [
𝑔𝐷(𝜌𝐿 − 𝜌𝐺)
𝜌𝐿]
12
2.9
where 𝐴 is the cross-sectional area (m2),
24 Literature Review
𝑣𝑝 is the absolute velocity of the gas slug (m/s),
𝑄𝐺 is the gas volumetric flowrate (m3/s),
𝑄𝐿 is the liquid volumetric flowrate (m3/s).
The second term on the r.h.s. of equation 2.9 gives the rise velocity of a large
bubble in stagnant liquid and was derived theoretically by Davis and Taylor (1950).
The first term on the r.h.s. adds the liquid velocity at the centre line, since 1.2 is the
approximate ratio of centre line to average velocity in fully developed turbulent flow.
2.4.4 The transition to annular flow
When gas flow rates are high, the liquid flows upwards adjacent to the wall and
gas flows in the centre carrying entrained liquid droplets, termed as Annular Flow. The
upward flow of liquid against gravity, results from the forces exerted by the fast-
moving gas core. The liquid film, having a wavy interface, tends to shatter and enter
the gas core as entrained droplets. The interfacial shear and the drag forces on the
waves and the droplets cause the liquid to move upwards. On the basis of the idea put
forward by Turner et al. (1969). Taitel et al. (1980) suggested that annular flow cannot
exist, unless the gas velocity in the gas core is sufficiently high to lift the entrained
droplets. When the gas rate is insufficient, the droplets fall back, accumulate, form a
bridge and churn and slug flow takes place.
Taitel et al. (1980) proposed an inequality which must be satisfied if the annular
flow is to exist. This equation balances the drag and gravity forces acting on the
droplet and assumes that the entrained droplets are gradually accelerated as they move
into the gas core.
𝑣𝐺𝑠 ≥ 3.2 [𝑔𝜎(𝜌𝐿 − 𝜌𝐺)
𝜌𝐿2 ]
14
2.10
McQuillan and Whalley (1985)disagreed with Taitel et al. (1980) and proposed
a simple inequality to predict the existence of annular flow:
𝑣𝐺𝑠∗ ≥ 1 2.11
where 𝑣𝐺𝑠∗ is the modified Froude number.
Literature Review 25
The modified Froude number represents a comparison between the inertial and
gravitational forces. The critical value of unity was observed empirically for air-water
(McQuillan & Whalley, 1985).
2.4.5 Flow pattern maps
Figure 2.6 shows the flow pattern map for vertical tubes of 51 mm diameter for
air-water at 100 kPa abs (Taitel et al., 1980). The bubbly flow, plug (slug) flow, churn
flow and annular flow regions are characterised by the gas and liquid superficial
velocities. At low gas superficial velocity (<0.08 m/s), bubbly flow regime is observed.
At gas superficial velocities in the range of 0.08 – 1 m/s and corresponding liquid
superficial velocities in the range of 0.02 – 1 m/s slug (plug) flow regime is observed.
Annular flow is only seen to exist for gas superficial velocities above 10 m/s.
Figure 2.6 Flow pattern map for vertical tubes 51 mm diameter, air-water at
100 kPa abs (Taitel et al., 1980)
2.4.6 Concluding remarks
The transition mechanism from bubbly flow, slug flow and to annular flow, was
discussed in this section. The theory used to determine the gas and liquid superficial
velocities that define each mechanism was described. The formation of large slugs
26 Literature Review
(Taylor bubbles) and the velocity of slugs were discussed. It was found that annular
flow only existed when gas superficial velocities are above 10 m/s for the case of air–
water mixture at pressure of 100 kPa abs. Although the churn flow is shown in Figure
2.6, the formation of churn flow is a subject of debate. Mao and Dukler
(1993)concluded that there is little evidence for considering churn flow to be a separate
and distinct flow pattern. Several authors have stated that churn flow is in fact a
manifestation of slug flow and no transition actually occurs.
2.5 Previous Pilot Plant Investigations of Sugar Factory Evaporators
2.5.1 Introductory remarks
Previous investigations play an important part in understanding the evaporation
process. This section explores the investigations undertaken on factory vessels and
pilot plant evaporator rigs. These investigations have been undertaken to better
understand the unit operation of juice evaporation, to develop reliable heat transfer
coefficient relationships based on the process variables, to better understand the
boiling mechanisms in different designs and to develop a new or improved design of
industrial evaporator.
2.5.2 Kestner evaporator
James et al. (1978) used a single tube pilot plant Kestner evaporator to
investigate heat transfer characteristics when simulating different evaporator effects.
Tests carried out showed that the Kestner evaporator, which is used predominantly as
a 1st effect vessel in the South African sugar industry, would operate most favourably
at the tail of the evaporator set when compared to the conventional, Robert-type
evaporator. However, these results were based on unrealistically high juice inflow
rates. Practical experience has determined that the Kestner evaporator is suitable at
the 1st and 2nd effects.
Rama and Munsamy (2008) undertook plant trials to determine the effect of tube
wetting rate (kg/min/tube) on the performance of the Kestner evaporator with respect
to specific evaporation rate (kg/h/m2) and heat transfer coefficient (W/m2/K). The
investigations were prompted by very low HTC values for an industrial Kestner
evaporator. Increasing the wetting rate by 62% increased the specific evaporation rate
by 40%.
Literature Review 27
Walthew and Whitelaw (1996) investigated the factors affecting the
performance of the Kestner evaporator. The independent variables that were studied
were:
• Average temperature difference between the steam and the juice, ΔT
• Feed rate to the base of the evaporator
• Feed temperature
• Recycle of juice from above the top tube plate to the base of the
evaporator, either open or closed
• Brix of the feed juice
It was found that the HTC increased at higher levels of ΔT, feed rate and brix.
The increase in HTC with increased feed rate and ΔT can be explained in terms of
conventional theory and previous investigations. However, an increase in HTC at
higher brix was unexpected, since higher brix values are associated with higher
viscosities. There was significant interaction between the feed temperature and
recycle, which indicated that at high feed temperature, having the recycle open, greatly
improved the HTC. This seems understandable as at higher temperature without the
recycle, the tube may be drying out and not be fully wetted.
2.5.3 Guo et al. investigations
Guo et al. (1983) undertook pilot plant investigations on a triple tube evaporator
unit at the University of Queensland. The tubes were standard stainless-steel
evaporator tubes of 44 mm OD and approximately 1.9 m length. The tubes were
mounted through glands in a 200 mm diameter steam jacket. The vapour formed was
separated from the splashing liquor in a disengagement chamber and was then
condensed in a water-cooled surface condenser. The condensate was returned to the
base of the evaporator through a flow meter. The separated liquor was returned via an
external recirculation leg. For each run, the temperature of the steam, the splashing
liquor in the disengagement space and the vapour temperature were measured. The
effects of static liquor level in the tubes, temperature difference, boiling temperature
and the brix of juice on heat transfer performance were investigated.
Tests with boiling water at 100 °C showed the following. At low levels, the water
did not circulate so the evaporator tube was not filled, and low heat transfer coefficient
28 Literature Review
values were measured. As the level increased, the coefficient rose rapidly and as
circulation started, the HTC reached a maximum value corresponding to an ‘optimum’
level. The optimum level ranged from one-quarter to one-half of the tube height.
Increasing the level above this value caused a gradual drop in the HTC, which was
attributed to the effect of hydrostatic pressure on the boiling point. Figure 2.7 shows
the effect of liquid level (as a fraction of tube height) on HTC for the tests by Guo et
al., (1983).
Figure 2.7 Effect of liquid level on HTC (Guo et al., 1983)
The HTC curves in Figure 2.8 for water at 100 °C show the same data as for
Figure 2.7 but as a function of temperature difference (ΔT). The lower the ΔT, the
higher is the optimum level corresponding to the maximum HTC value.
Literature Review 29
Figure 2.8 Effect of ΔT on HTC at selected constant liquid levels (h) (Guo et al.,
1983)
Guo et al. (1983) found that boiling temperature, Tb had no detectable effect on
the optimum liquid level in the tube. However, HTC decreased as the boiling point
decreased (increasing vacuum). The effect was not large and the drop in HTC was 10%
for a 30 °C drop in temperature.
According to Guo et al. (1983), sugar and sugar molasses solutions show similar
trends to water in the effects of level, ΔT and Tb. The brix of the solution does not
appear to affect the location of the optimum level. However, HTC was found to
decrease with increase in brix from 3000 W/m2/K for water to a value of 2000 W/m2/K
for 65 brix syrups or molasses. These data are for boiling at atmospheric pressure.
2.5.4 Broadfoot and Dunn investigations
Broadfoot and Dunn (2004) conducted a pilot plant investigation on a 20 m2
evaporator vessel with 76 tubes of standard dimensions (44.45 mm OD and 1.985 m
length) to develop an improved correlation for HTC that would provide more reliable
simulations of evaporator stations in energy efficient configurations. Figure 2.9 shows
the variation of HTC with operating juice level at 15 brix. It is observed that the
maximum HTC was achieved for juice levels about 20% of the tube height.
30 Literature Review
Figure 2.9 Variation of HTC with operating level of juice at 15 brix ((Broadfoot
& Dunn, 2007)
The observations from the pilot plant study (Broadfoot and Dunn, 2007) were as
follows:
• The optimum juice level for the maximum HTC value was lower for juice
at lower brix and higher for juice at higher brix. The optimum level for
juice at brix below 25 was 20% – 35% of the tube height, and for juice
above 40 brix, was 35% – 45% of the tube height.
• For evaporation at higher VCC, the maximum HTC value was higher and
occurred at lower juice level.
• At higher headspace pressure, the maximum HTC value was higher than
for evaporation at lower headspace pressure. The effect is attributed to
the lower viscosity of the juice at the higher temperature;
• The influence of VCC on HTC was slightly less at a lower headspace
pressure than at higher headspace pressure;
• The influence of VCC on HTC was less for juice at 70 brix than for juice
at 15 brix. As well, for juice at 70 brix, the effect of VCC on the optimum
juice level was less than for juice at 15 brix.
Literature Review 31
2.5.5 Pennisi’s investigations
Investigations on a single tube evaporator rig were conducted by Pennisi (2004).
The single tube was 2 m long and 44.45 mm OD. The condensate was collected in four
gutters, which were located equidistantly on the outside of the tube.
The experimental program was designed to determine heat transfer performance
for four process variables (ΔT, brix, temperature and juice level in the tube) at a wider
range than normal operating conditions, which typically exist in factory evaporators.
In the normal operation of factory evaporators, a small ΔT (5 °C to 8 °C) exists in the
1st effect, which typically operates at high calandria pressures and low brix. As the
calandria pressure reduces from the first to the last effect of the multiple effect
evaporator, both the brix of juice and ΔT increase. The test rig was operated so that all
three variables (ΔT, brix, juice temperature) could be manipulated independently to
cover a broad range of conditions.
Boiling within the vessel was allowed to occur for a sufficient period of time to
stabilise before the static level was measured. The condensate from each of the four
gutters was collected in separate containers. The condensate from the inner wall of the
steam jacket was also collected. The volumes of collected condensates were
determined and the condensate rates were calculated. The HTC for each segment of
tube was then calculated from equation 1.7. The HTC for the entire tube was calculated
from the summed values of the condensate values.
The condensate rates provided vapour condensation coefficient (VCC) values
ranging between 4.3 kg/h/m2 and 87.8 kg/h/m2. Typical values for VCC in factory
evaporators are between 12 and 40 kg/h/m2.
The results from the study by Pennisi (2004) are summarised below:
• The highest value of HTC was obtained for boiling water at the highest
calandria pressure (100 kPa abs) and highest temperature difference (T =
15C).
• The lowest values of HTC were for the high brix solution (Brix-45) at the
lowest calandria pressure and lowest temperature difference (T = 5C).
These observations are in agreement with data for typical factory
operations where the HTC is lowest at the final stages of the set where the
32 Literature Review
brix of juice is highest and the boiling temperature lowest (i.e. the viscosity
of the sucrose solution is highest).
• In general, the HTC values were slightly lower than are normally measured
in factory evaporators for comparable process conditions. For example, in
a factory evaporator the HTC for Brix-20 juice at a calandria pressure of
100 kPa (abs) and T = 10 °C would range from 2500 to 2800 W/m2/K.
HTC values for the test rig were ~ 2000 W/m2/K. Also, heat transfer for
Brix-45 juice at a calandria pressure of 60 kPa abs and T = 15 °C in a
factory evaporator would range from ~600 to 1000 W/m2/K. The single-
tube rig produced values of about 200 W/m2/K.
• One substantial difference between the trials with the single-tube rig and
factory evaporator was the lack of superheat in the sucrose solution that
exists in the base of the single-tube rig. The juice entering a factory
evaporator (except for the first effect) is superheated as it is boiled at a
higher temperature and pressure in the previous effect. The flashing of
vapour from the juice on entry into a factory evaporator is thought to
enhance heat transfer performance. The temperature of the sucrose
solution in the single-tube rig did not exceed the saturation temperature of
water at the headspace pressure plus the boiling point elevation as it was a
closed recirculating system.
• For the sucrose solutions of Brix-20 and Brix-45, and a given calandria
pressure, the HTC values were generally higher for T = 15 °C than for T
= 5 °C. The higher T values corresponded to trials with higher heat flux.
Similar behaviour is thought to occur in factory evaporators, although the
effect is not well defined. The higher HTC value at the higher T is
attributed to the onset of boiling being at a lower level in the tube than
would occur for low T values.
• For juice at a given brix, the value of T appeared to have a larger influence
on the HTC values for operation at higher calandria pressures. In fact, at
the calandria pressure of 60 kPa (abs) the value of T appeared to have only
minimal influence on the HTC value.
Literature Review 33
Figure 2.10 HTC data for varying ΔT, calandria pressure and brix for the total
tube (Pennisi, 2004)
Pennisi (2004) calculated HTC for the individual segments of the evaporator
tubes. Figure 2.11, Figure 2.12 and Figure 2.13 show the HTC data for segments of
the single tube for water, Brix-20 and Brix-45 solutions respectively. Section 1 of the
trials by Pennisi (2004) is at the top of the heating tube and section 4 is at the bottom
of the heating tube. The observations from the HTC plots are summarised below:
• For water in Figure 2.11, as calandria pressure increased, HTC for all
segments increased significantly. The incremental increase in HTC for
an increase in calandria pressure was greatest for ΔT of 10 °C.
• For Brix-20 juice in Figure 2.12, the data were not consistent with
increase in calandria pressure. For ΔT of 5 °C, HTC increased from 60
to 80 kPa abs calandria pressure and dropped at 100 kPa abs. For ΔT of
10 °C, 3 out of 4 segments showed a drop in HTC with increase in
calandria pressure, then all segments showed an increase in HTC at 100
kPa calandria pressure. For ΔT of 15 °C, all segments showed an increase
in HTC with increasing calandria pressure, but the incremental increase
was much higher from 60 kPa abs to 80 kPa abs than from 80 kPa abs to
100 kPa abs.
0
500
1000
1500
2000
2500
3000
3500
4000
50 60 70 80 90 100 110
HT
C (
W.m
-2K
-1)
Calandria pressure (kPa abs)
0 brix, T diff = 5
0 brix, T diff = 10
0 brix, T diff = 15
20 brix, T diff = 5
20 brix, T diff = 10
20 brix, T diff = 15
45 brix, T diff = 5
45 brix T diff = 10
45 brix, T diff = 15
34 Literature Review
• For Brix-45 juice in Figure 2.13, the data showed an increase in HTC
with increase in calandria pressure for ΔT of 8.5 °C. For Brix-45 juice,
ΔT of 3 °C the HTC decreased from segment 1 to segment 4 for the
calandria pressure change from 60 to 80 kPa abs. For the change in
calandria pressure from 80 to 100 kPa abs the HTC increased. For ΔT of
3 °C at low calandria pressure, it is likely that the juice was not rising up
the tube and the upper part of the tube was not fully wetted.
Delta T (5 oC)
Calandria pressure (kPa abs)
50 60 70 80 90 100 110
HT
C (
W/m
2/K
)
0
500
1000
1500
2000
2500
3000
3500
4000
Segment 1
Segment 2
Segment 3
Segment 4
Delta T (10 oC)
Calandria pressure (kPa abs)
50 60 70 80 90 100 110
HT
C (
W/m
2/K
)
0
500
1000
1500
2000
2500
3000
3500
4000
Segment 1
Segment 2
Segment 3
Segment 4
Delta T (15 oC)
Calandria pressure (kPa abs)
50 60 70 80 90 100 110
HT
C (
W/m
2/K
)
0
500
1000
1500
2000
2500
3000
3500
4000
Segment 1
Segment 2
Segment 3
Segment 4
Water
Figure 2.11 HTC values for water solution for segments of the evaporator tube
(Pennisi, 2004)
Literature Review 35
Delta T (5 oC)
Calandria pressure (kPa abs)
50 60 70 80 90 100 110
HT
C (
W/m
2/K
)
0
500
1000
1500
2000
2500
3000
3500
Segment 1
Segment 2
Segment 3
Segment 4
Delta T (10 oC)
Calandria pressure (kPa abs)
50 60 70 80 90 100 110
HT
C (
W/m
2/K
)
0
500
1000
1500
2000
2500
3000
3500
Segment 1
Segment 2
Segment 3
Segment 4
Delta T (15 oC)
Calandria pressure (kPa abs)
50 60 70 80 90 100 110
HT
C (
W/m
2/K
)
0
500
1000
1500
2000
2500
3000
3500
Segment 1
Segment 2
Segment 3
Segment 4
Brix-20 juice
Figure 2.12 HTC values for Brix-20 sucrose solution for segments of the
evaporator tube (Pennisi, 2004)
36 Literature Review
Delta T (3 oC)
Calandria pressure (kPa abs)
50 60 70 80 90 100 110
HT
C (
W/m
2/K
)
0
500
1000
1500
2000
2500
3000
Segment 1
Segment 2
Segment 3
Segment 4
Delta T (8.5 oC)
Calandria pressure (kPa abs)
50 60 70 80 90 100 110
HT
C (
W/m
2/K
)
0
500
1000
1500
2000
2500
3000
Segment 1
Segment 2
Segment 3
Segment 4
Brix-45 juice
Figure 2.13 HTC values for Brix-45 sucrose solutions for segments of the
evaporator tube (Pennisi, 2004)
2.5.6 The SRI design of Robert evaporator
The Sugar Research Institute (SRI) investigated the performance of the Robert
evaporator design and presented a novel design to overcome the shortcomings of the
original Robert design.
Wright et al. (2003) describe the SRI design for the installation of a 5300 m2
vessel at 1st effect position at San Antonio factory, Nicaragua. The average HTC was
3014 W/m2/K over the whole 12-day operational testing period. These results were
claimed to be 23% higher than for the typical HTC achieved in Australian evaporators
under the same juice outlet brix and temperature conditions.
The steam, condensate and incondensable gases are arranged to move uniformly
from an annulus on the outside of the vessel radially to the centre of the vessel.
According to (Quinan et al., 1985), a small number of 150 mm diameter mild steel
downcomer tubes should be dispersed around the calandria among the stainless steel
heating tubes. These downcomers act as stay bars and importantly provide a
recirculation return path for the juice from above the top tube plate to below the bottom
tube plate.
Additionally, a large central downcomer is provided in the SRI design, with a
sealed pipe outlet for the juice through the bottom cone. Arrangements are made for
Literature Review 37
the bypass of juice from the lowest point in the vessel to the outlet pipe, as this feature
assists the control of the juice level.
The general performance and heat transfer results of the SRI design have been
superior compared with the conventional Robert design.
2.5.7 Selection of tube dimensions
The effect of tube dimensions on HTC has been detailed by previous researchers
(Gerasimenko, 1968; Hugot & Jenkins, 1986; Kroll & McCutchan, 1968; Peacock,
2001). Gerasimenko (1968) concluded that at atmospheric pressure, the maximum
HTC coefficient was obtained with 25 mm OD tubes and tubes of 57 mm OD exhibited
the lowest HTC. For high concentrations of the solution, the HTC values of 25 mm
OD tubes were lower than for 57 and 38 mm OD tubes. Tubes of 38 mm OD provided
good heat transfer performance under all conditions.
Previous investigators (Gerasimenko, 1968; Hugot & Jenkins, 1986; Kroll &
McCutchan, 1968; Peacock, 2001) have postulated that tube dimensions should be
selected based on the effect position in a multiple effect set. Hugot and Jenkins (1986)
recommended that vessels should use tubes with the same diameter but with decreasing
tube length from first to final vessel. A practical benefit of this arrangement is to reuse
the tubes, when the ends close to the tube plates wear or corrode. They provided no
heat transfer considerations for the basis of this tube selection. Hugot and Jenkins
(1986) mentioned that smaller diameter tubes give theoretically a higher heat transfer
coefficient, because the mean distance of segments of juice from the heating surface
is smaller. Additionally, tubes of smaller diameter allow installation of a larger heating
surface area in a vessel for a given vessel diameter. Hugot and Jenkins (1986) claimed
that tube length and diameter are not independent of each other. Moreover, they stated
that the choice of tube diameter for multiple effects is not of prime importance.
Table 2.1 shows the maximum length of evaporator tubes for the different tube
diameters, as recommended by Hugot & Jenkins (1986). For small diameter tubes,
long tubes can be used. For 38 mm tube diameter, Table 2.2 shows the optimal tube
lengths of the multiple effect taking into account all factors, including cost (Hugot &
Jenkins, 1986).
38 Literature Review
Table 2.1 Maximum length of evaporator tubes for different tube diameters
(Hugot & Jenkins, 1986)
Tube OD
(mm)
Maximum
length
m ft
50 2.5 8
38 3.5 11
35 4.0 13
30 4.5 15
Table 2.2 Optimal tube lengths recommended for the different effect
parameters (Hugot & Jenkins, 1986)
Effect Optimal
tube length
(m)
1 4.0
2 3.5
3 3.0
4 2.5
5 2.25
2.5.8 Concluding remarks
In comprehending the investigation undertaken by James et al. (1978), the
determination of HTC seems to be an error because the measured condensate rate
included the condensate from the inside walls of the shell.
The investigations conducted by Guo et al. (1983) and Broadfoot and Dunn
(2007) found that an optimum juice level exists, which maximises the HTC. Departure
from the optimum liquid level reduces the HTC. The influence of liquid level on HTC
is greater at juice levels below the optimum than above the optimum level (Watson,
1986b). The results of Guo et al., (1983) and Broadfoot and Dunn (2007) indicated
that the optimum juice level was lower for operation at higher ΔT (or VCC). The
operating parameters investigated by Guo et al. (1983) and Broadfoot and Dunn (2007)
have been investigated in this PhD study for tubes of different diameter and length.
The pilot plant investigation on a single tube by Pennisi (2004) throws some
light on the boiling characteristics inside a tube with the calculation of HTC on
Literature Review 39
different sections of the tube. The HTC calculations of the different segments of the
tubes are shown in Figure 2.11, Figure 2.12 and Figure 2.13. The plots are not
consistent and provide little information on the boiling mechanism of the rising film
evaporator. The significance of juice level and juice return is not discussed in the
thesis. The investigations were conducted for a single tube of 2.0 m length and 44.45
mm OD.
Although the SRI design is an improved version of the Robert vessel, there
remains scope for further improvements in the design, particularly by incorporating
heating tubes with the preferred dimension to maximise HTC. Several of the features
of the SRI design are likely to be adopted in the new design for Robert vessels using
the outcomes from this study.
The investigations undertaken by Broadfoot and Dunn (2004) were on a pilot
plant evaporator with 20 tubes of the standard dimensions. The trials assisted in
understanding the effect of juice properties and operational conditions on HTC for the
standard tubes. The trials did not enhance the understanding of the boiling mechanism
in the Robert evaporator.
2.6 Operational Investigations on Robert vessels
2.6.1 Introductory remarks
Sugar factory technologists have undertaken trials to better understand the
operation of the Robert evaporator in order to increase efficiency. Many of these
investigations have been used to develop empirical correlations for HTC and to
determine the optimum liquid level in the tubes. Although some of the results
contradict each other, the literature provides an understanding of the main factors
affecting the performance of Robert evaporator. They also highlight differences in
operating Robert vessels in different sugar mills.
2.6.2 Smith and Taylor investigations
Smith and Taylor (1981) present heat transfer data in multiple effect evaporators
covering 15 Robert vessels at three mills. HTC was plotted against brix, temperature
difference (ΔT) and viscosity. It was concluded from the experiment that the influence
of ΔT on HTC could not be deduced. HTC values from second to penultimate effect
were in the range of 1800 to 3500 W/m2/C, with no pronounced dependence on effect
number. The optimum vapour saturation temperature for the final effect was
40 Literature Review
determined to be in the range of 55 to 60 °C. A heating surface area distribution,
wherein the last effect is double the size of intermediate effects, was calculated to
provide 6% greater evaporation rate than the conventional arrangement. There is some
doubt on this conclusion, as no evaporator installations are known to have adopted this
arrangement. The problem with this conclusion is that the operation of a Robert vessel
as a final evaporator with low VCC creates serious problems with poor mixing of the
juice and high propensity to develop scale on the heating tubes.
2.6.3 Jayes’ evaporation model
Jayes (2004) developed a spreadsheet model of a multiple effect evaporation
train and the optimising routines in the spreadsheet software to find the distribution of
heating surface area along the evaporator train, which gives the highest specific
evaporation rate. The model uses a mathematical relation, which states that the ratio
of the area of the effect to the temperature difference in the effect is a constant. This
model is not suitable for the majority of evaporation stations as the extraction of bleed
vapour from individual evaporators, which is commonplace, is not addressed.
2.6.4 Watson investigation
The Fairymead Sugar Company installed downcomers in the new 1st effect
vessel of 5100 m2. The tube dimensions were 2.76 m length and 38.1 mm OD. Due to
the large diameter of the vessel it was thought that one central downcomer would not
reduce the liquid level in the tubes. Hence, multiple downcomers were evenly
distributed throughout the calandria. Watson (1986b) stated that for a commercial scale
evaporator, a considerable head of liquid above the top tube plate was required before
the maximum heat transfer coefficients were obtained. This observation contradicted
with the results of Guo et al. (1983) on the pilot scale evaporator with an external leg,
which showed that the maximum HTC was obtained just as the liquid started to appear
above the top tube plate. This difference may have been due to the non-uniformity of
liquid and steam conditions across the much larger calandria in the commercial
evaporator.
The downcomers reduce the quantity of juice collecting above the tube plate by
providing a return path. Observations on the operation of the vessel without the
downcomers were obtained by blocking the downcomers during a maintenance stop.
The results are shown in Figure 2.14, where it was concluded that the use of the
Literature Review 41
downcomers reduced the head of juice. Figure 2.15 shows the HTC measurements
over a single day when downcomers were operating. Low HTC values are evident at
low juice levels as the tubes are not fully wetted. The maximum HTC was recorded
when the static juice level was about 23% of the tube height. Increasing the juice level
above this value resulted in juice being collected above the calandria with a reduction
in HTC. At an operating level of 45% the HTC was decreased by 10% from its
maximum value.
Figure 2.14 Variation of head of juice above the calandria with operating level
Watson (1986b)
42 Literature Review
Level of juice in tubes (% tube height)
0 10 20 30 40 50
HT
C (
W/m
2/K
)
0
500
1000
1500
2000
2500
3000
3500
Figure 2.15 Variation of HTC with operating level for a conventional Robert
evaporator with mini-downtake (Watson, 1986b)
2.6.5 Shah and Peacock investigations
Shah and Peacock (2013) developed a set of correlations to predict the minimum
recirculation rate and liquid level for juice of up to 65 brix, corresponding to various
temperature driving forces and the optimum heat transfer coefficient. A second set of
correlations was developed to predict the juice velocity as a function of temperature
driving force, the Reynolds number and the Grashof number. The results were
dimensionless numbers, which can be easily interpreted in terms of heat transfer
theory. Together, these correlations were used in designing a semi-sealed downtake
ensuring adequate recirculation and a sufficient liquid level within the Robert
evaporator to optimise heat transfer.
The correlations developed by Shah and Peacock (2013) are shown below:
hminimum = −0.0149 ΔT + 0.5816 2.12
where hminimum is the minimum liquid level as a fraction of the total tube height.
R = 0.008123 ΔT2 − 0.0246 ΔT + 0.4744 2.13
where R is recirculation rate, kg/min/tube.
WR = 0.001053 ΔT2 − 0.003188 ΔT + 0.0618 2.14
Literature Review 43
where WR is wetting rate, kg/s/m
Shah (2013) proposed some key principles in the design of Robert vessels and
focused on feed distribution and pipe design. The juice pressure drop associated with
the piping design alters the hydraulics within the system and results in preferential
flow, which can cause inadequate distribution of juice, the venting of incondensable
gases or condensate draining. The adequate removal of condensate and incondensable
gases maximised the area available for heat transfer and the HTC is maximised by
increased recirculation.
2.6.6 Broadfoot and Tan investigations
Broadfoot and Tan (2005) undertook juice sampling trials on a conventional
Robert evaporator and an SRI Robert evaporator. The sampling trials provided
information on brix profiles for the juice within the vessels and gave insight into the
juice flow patterns in both designs.
The juice below the calandria of the conventional Robert vessel, and the juice
entering the base of the heating tubes were within 0.5 units of the brix of the outlet
juice. For the SRI Robert vessel, the juice below the calandria was at an intermediate
brix between the brix of the juice at the inlet and the outlet. The availability of lower
brix juice at the base of the heating tubes across the calandria is beneficial to heat
transfer performance. For both the designs, the juice near the top tube plate was of
higher brix than the juice at the base of the heating tubes. As Robert evaporators
operate in rising film action, this scenario is expected. The information on juice brix
profiles and juice flow patterns within Robert vessels is useful for design
improvements.
2.6.7 Empirical relationships for HTC
Empirical relationships for heat transfer coefficients for evaporators are required
for assessing and predicting the performance of the evaporator set. Over the years,
many authors have proposed correlations for HTC. Some of these correlations are
summarised in this section.
The Dessin formula
The French engineer, Dessin, proposed a formula permitting the evaporation
coefficient to be calculated for any vessel of a multiple effect set. This formula was
44 Literature Review
modified by Hugot and Jenkins (1986) to take juice concentration as the average of the
inlet and outlet brix. A modified Dessin formula, as given by Jenkins (1966), included
a reduction in HTC (kW/m2/K) to 85% to allow for fouling:
HTC = 2.2 × 10−7 λs(100 − Bjav)(Ts − 54) 2.15
where Bjav is the average brix of the juice entering and leaving the vessel, %
Ts is the condensing temperature of the heating steam/vapour in the
calandria, °C
Sugar Engineer’s Library
Another formula for overall HTC (kW/m2/K) is provided in an online design of
Robert evaporators in the Sugar Engineers' Library (2014). It is a function of juice or
syrup temperature and brix as:
HTC = 0.465 Tj Bj−1 2.16
where Tj juice temperature (estimated as Tv + Tbpe), °C
Bj is the brix of the juice leaving the vessel.
The ‘Australian Typical’ formula
Wright (2008) recommends the use of the ‘Australian Typical’ formula to be
used for conventional Robert evaporator vessels. The formula for HTC (W/m2/K) s
shown below:
HTC = 16.94 × TJ
1.0174 × (B
86 − B)
−0.2695
2.17
The Broadfoot & Dunn correlation
Broadfoot and Dunn (2007) presented pilot plant and factory evaporator
performance results and developed a correlation for heat transfer coefficient
(kW/m2/K), which included a term for the vapour condensation coefficient (VCC).
HTC = 21.6 × 10−6 VCC0.4 λs µ−0.34 2.18
where µ is the estimated viscosity of the exit juice, Pa.s
Literature Review 45
Formulae based on regressions on the combined Australian dataset
A combined dataset was assembled to include the 67 measurements of Australian
sugar factories and 75 of the Broadfoot and Dunn (2007) measurements. With the
latter, the HTC values had to be multiplied by 0.85 to allow for the fact that they were
carried out on clean vessels, and the other data were based on factory vessels, which
were cleaned every two weeks (Wright, 2008). The combined dataset yielded the
correlation for HTC (kW/m2/K).
HTC = 0.00056 (110 − Bj)1.0025
Tj0.8294 2.19
2.6.8 Concluding remarks
The concept of recirculation rate proposed by Shah and Peacock (2013) is not
entirely clear. Several Robert vessels operating in Australian mills in under–under
configuration have no mini-downtake or central downtake but the performance is
satisfactory. For these evaporators, juice must flow from above the top tube plate to
below the bottom tube plate by flowing down the heating tubes. There is no alternative
defined recirculation path for the flow of juice.
The juice sampling undertaken by Broadfoot and Tan (2005) showed that the
juice throughout the vessel is of very uniform brix and the average brix throughout the
vessel is only a unit or two below the outlet brix. This situation occurs despite the
evaporator having no defined recirculation path. According to the hypothesis proposed
by Shah and Peacock (2013), the Australian design should not work or give very poor
performance but this is clearly not the case.
The optimum juice level proposed by Shah and Peacock (2013) is lower at the
tail end of the set, which contradicts the results shown by Broadfoot and Dunn (2007),
and practical experience that the preferred juice level is higher at the tail end where
juice at higher brix is boiled. The requirement for the higher juice level is attributed to
the higher viscosity of the juice at the tail end of the set. There is consensus that ΔT,
which is closely related to vapour rate, is important in determining the optimum juice
level. However, the influence of vapour rate on the optimum juice level in factory
evaporators is considered to be not as significant as suggested by Shah and Peacock
(2013).
46 Literature Review
Shah and Peacock (2013) stated that larger areas at the tail end are helpful in
reducing ΔT. This is logical theoretically but ignores the major concern that operating
a final vessel with a low vapour rate per unit area will result in poor mixing, reduce
the HTC and cause faster scaling. Poor mixing may even result in crystal forming due
to the wide variations in brix within the vessel.
The Robert design proposed by Shah (2013) is similar to the SRI design, with
the difference that even juice distribution is favoured in the former and the peripheral
feed is used in the latter. The central downtake in the SRI design is sealed and provides
recirculation, as compared to Shah (2013) where strong emphasis is given to having
adequate recirculation to produce sufficient wetting.
The Broadfoot and Tan (2005) investigations have given good insights into the
juice flow patterns within the Robert vessels. It is evident that the SRI design has
created a marked change in the juice flow patterns within the vessel, which results in
increased separation of the inlet and outlet juice, providing lower brix juice to the base
of the heating tubes across the whole cross-section of the calandria.
The ‘Australian Typical’ HTC correlation as described by Wright (2008) is
considered to be the most reliable relationship and is used to compare the HTC
correlations developed in this study.
Several of the Robert vessels in the Australian sugar industry operate without
mini-downtake and with the under–under juice flow arrangement. By necessity, the
juice rising up the tubes and above the top tube plate must also travel down the heating
tubes at some point. This phenomenon is observed as sections above the top tube plate
stop boiling for a short time.
2.7 CFD Modelling
2.7.1 Introductory remarks
Computational Fluid Dynamics (CFD) modelling has found a wide range of
applications in the sugar industry. Over the past two decades, CFD modelling has been
used for assessing boiler performance, designing clarifiers, evaporators and vacuum
pans (Steindl (2003); Pennisi et al. (2003); Pennisi et al. (2004); Rackemann, Plaza, et
al. (2006)). This section reviews the CFD models that have been developed for
modelling Robert evaporators. The work done in CFD modelling of boiling
Literature Review 47
massecuite in vertical calandria tubes in vacuum pans is also mentioned, due to the
similarities of the principle. The main difference in vacuum pans is the much higher
viscosity of the massecuite compared with the juice in evaporators; massecuite is
boiled under a headspace pressure of 15 kPa abs.
2.7.2 CFD and heat transfer models
Steindl (2003) developed a CFD model of the 1st vessel of the set and
investigated two alternative evaporator configurations. It was found that the optimal
flow pattern of juice inside an evaporator vessel is plug flow, with no internal
recirculation, stagnant regions or bypassing. The calculated benefits to the throughput
capacity from plug flow, range from 4% for the 1st effect to above 30% for the final
effect. CFD modelling of typical evaporators, which have three peripheral juice inlets
and a single central juice outlet (in under-under configuration), showed significant
mixing and recirculation of the juice, as well as short-circuiting of juice from the feed
inlet to the outlet. CFD modelling of the alternative evaporator configurations
indicated that the preferred configuration is a vessel with fully distributed feed and a
single central juice outlet (i.e., similar to the SRI design).
Pennisi et al. (2003) presented a numerical model for the single-phase fluid flow
inside a sugar mill evaporator. The model incorporated the effect of temperature and
sugar concentration (brix) on the fluid properties. The standard k-ε turbulence model
was used in the investigation. The governing equations for incompressible single-
phase flow with heat transfer are the unsteady Navier-Stokes equations in their
conservation form.
Atkinson et al. (2000) developed a one-dimensional mathematical model for
two-phase flow in heated calandria tubes. For a given set of geometric and thermo-
physical parameters, the model results were presented as characteristic curves,
showing the net pressure difference generated in the calandria tube as a function of
mass flow rate and applied heat.
Stephens and Harris (2002) developed an improved one-dimensional
mathematical model of two-phase flow in a calandria tube with constant wall
temperature for vacuum pans. The predicted results from the model were in agreement
with available experimental measurements. These relationships can be improved with
experimental work on heat transfer in a single tube.
48 Literature Review
Rackemann, Broadfoot, et al. (2006) detailed the development of a CFD model
to predict the circulation patterns and heat transfer occurring in natural circulation
vacuum pans. The CFD model was validated against velocity data measured in factory
pans. The predictions were in reasonable agreement with factory measurements. The
validated CFD model was then used to investigate the effects of altering the key
dimensions in batch and continuous pans.
CFD modelling investigations into the steam side operation of the calandria of
vacuum pans and evaporators was undertaken by Rackemann, Plaza, et al. (2006). The
CFD model was validated with factory measurements and was found to have
limitations in the condensation physics in that the steam cannot be fully condensed
without causing convergence issues. Two parts of the model needed improvement; the
physical part of the model to enable condensing of more than 80% of the steam and a
better correlation for heat transfer within the calandria that takes into account the
restriction caused by the resistance on the juice side.
2.7.3 Concluding remarks
The complicated physics associated with an evaporator can be understood with
the help of CFD models. The developed CFD models that have been used to predict
circulation patterns and heat transfer in evaporator and vacuum pans are described. A
complete CFD model of the evaporator with steam side and juice side (two-phase)
model is not available. The CFD model developed by Pennisi (2004) for a Robert
evaporator is the most advanced. However, complete mesh independence was not
achieved due to the memory hardware limitations of the computer used to solve the
problems. Simplifying assumptions were used to model the calandria section, which
was critical to the model’s ability to produce accurate predictions of the fluid flow
inside the evaporator vessel. The inclusion of the vapour flash from the juice on entry
to the vessel would significantly improve the accuracy of predictions.
A CFD model of an evaporator is not developed in the project although a CFD
model was developed for the vapour and gas flows in the steam chest of the pilot
evaporator (as discussed in section 4.6).
2.8 Concluding Remarks
Previous investigations in the field of evaporation have been discussed in the
chapter. The boiling mechanisms in Robert vessels, pilot plant studies and factory trials
Literature Review 49
that have been undertaken have been explored. Many interesting concepts and theories
have been reviewed in this chapter and will form the basis of comparison with the
experimental data acquired in this PhD study and analysed in Chapters 4, 5 and 6.
Capital Cost Model 51
CHAPTER 3: CAPITAL COST MODEL
3.1 Introductory Remarks
This PhD study investigates the heat transfer performance of tubes of different
lengths and diameters for the whole range of process conditions typically encountered
in the evaporator set. Incorporation of the results from the experimental investigations
into practical evaporator designs requires an understanding of the cost implications for
constructing evaporator vessels with calandrias having tubes of different dimensions.
Cost savings are expected for tubes of smaller diameter and longer length in terms of
material, labour and installation costs in the factory. These savings must be considered
in terms of the required heat transfer area for the evaporation duty, which will likely
be a function of the tube dimensions.
In this chapter, a capital cost model is described, which provides a relative cost
of constructing and installing Robert evaporators of the same heating surface area
(HSA) but with different tube dimensions. Evaporators of 2000, 3000, 4000 and
5000 m2 are investigated.
3.2 Evaporator Designs and Costs
3.2.1 Introductory remarks
The main design parameters for vessels of 2000, 3000, 4000, 5000 m2 are
calculated for calandrias comprising three tube lengths (2, 3 and 4 m) and three outside
diameters (38.1, 44.45 and 50.8 mm). All tubes have a wall thickness of 1.2 mm. The
capital cost for each design and several other parameters are calculated.
3.2.2 Number of tubes
A tube layout program developed by the Sugar Research Institute (SRI) Australia
is used to calculate the vessel internal diameter (ID) given the required HSA, tube
dimensions, pitch of tubes, number of mini-downtake, incondensable gas removal and
stay bar details. A snap shot of the output sheet for the tube layout program for the
conventional tube dimensions is shown in Figure 3.1. All designs included in this
paper include a diametric join of the calandria, mini-downtakes comprising 150 mm
diameter pipes, incondensable gas removal pipes and stay bars. The evaporator design
52 Capital Cost Model
is based on the SRI evaporator design (Moller et al., 2003; Wright et al., 2003), which
includes a central downtake, steam annulus with slots for the radial inflow of steam
into the calandria, two steam entries and central off-take of condensate.
For the designs assessed in this project, the clearances between the heating tubes
and the evaporator body components e.g., the outer tube and the wall of the calandria
are the same for all designs. Each vessel is designed to have a 5 m strake height above
the top tube plate, a gap between the bottom tube plate and the base at the outer wall
of 300 mm and a W-shaped bottom.
Figure 3.1 Output sheet for the tube layout program for the Robert evaporator
design
The specification of the HSA of the evaporator is based on the internal diameter
of the tube and the length between the outer faces of the tube plates. This specification
is different from that documented in the BSES manual (Bureau of Sugar Experiment
Stations 1984), which is based on the outside diameter (OD) of the tubes and includes
all wetted areas (mini-downtake, central downtake, tube plates). The code for the
dimensions of the tubes that are considered in this project is shown in Table 3.1.
Capital Cost Model 53
Table 3.1 Code for different tube dimensions
Tube length
(m)
Tube OD
(mm)
Code
2 38.10 S2
44.45 M2
50.80 L2
3 38.10 S3
44.45 M3
50.80 L3
4 38.10 S4
44.45 M4
50.80 L4
The number of tubes for each tube dimension is shown in Figure 3.2. It is evident
that an L4 tube dimension requires the fewest tubes. Calandrias with tube dimensions
S4 require 42 % fewer tubes than the conventional M2 calandria for the same HSA.
As a consequence, a calandria with S4 tubes will provide cost savings in drilling and
honing of the holes in the tube plates, inserting and expanding the tubes. These costs
are examined further in the chapter.
Tubes
S2 S3 S4 M2 M3 M4 L2 L3 L4
Num
ber
of
tubes
0
5000
10000
15000
20000
25000
2000
3000
4000
5000
Figure 3.2 Number of tubes for 2000, 3000, 4000 and 5000 m2 vessels with
different tube dimensions
54 Capital Cost Model
3.2.3 Vessel internal diameter
Figure 3.3 shows the vessel internal diameter (ID) for calandrias with the
different tube dimensions. The vessel ID is the factor that determines the footprint for
the vessel, the mass of steel in the vessel, the volume of juice held in the vessel at the
normal operating level, the total mass of the vessel and contents for the design of the
supporting structure and foundations, and the cross-sectional area in the vapour space
for the up flow of vapour and housing for de-entrainment louvres. Smaller vessels are
attractive on all counts, apart from a potential impact on juice level control owing to a
reduced buffer volume of juice and higher up flow vapour velocities. The diameter of
the vessel is reduced by 33% when the S4 tube dimensions are used rather than the
conventional tube dimensions, M2.
Tubes
S2 S3 S4 M2 M3 M4 L2 L3 L4
Ves
sel I
D (
m)
0
2
4
6
8
102000
3000
4000
5000
Figure 3.3 Vessel ID for 2000, 3000, 4000 and 5000 m2 vessels with different tube
dimensions
3.2.4 Capital costs
The material costs of the vessels include the costs of heating tubes and carbon
steel boiler plate. The costs of the tubes of the three diameters per linear metre are
Capital Cost Model 55
shown in Table 3.2. Also shown in Table 3.2 are the costs of the tubes per unit of HSA
(based on tube ID).
Table 3.2 Tube costing based on tube diameter
Tube OD (mm) AUD/m AUD/m2 of HSA
38.1 10.67 95.1
44.45 11.25 85.2
50.8 13.49 88.7
The cost of carbon steel boiler plate is assumed to be AUD 15000/m3 (or AUD
1910/t). Wastage in material is accounted by 3% in tubes and 25% in plate steel. The
simplifying assumption has been made that wastage is proportional to steel used i.e.,
variability in wastage due to the use of standard plate sizes is ignored. Transportation
cost for steel plate is 3% and for tubes is 5% of the material costs.
Figure 3.4 shows the costs of materials (without fabrication costs) for vessels
with calandrias of different tube dimensions. The data for each HSA are presented
relative to the material costs for a vessel of the same HSA comprising the conventional
tube dimensions, M2.
As expected, for evaporators with the same tube diameter, the material costs are
lower where calandrias of longer tubes are used as the vessel diameter is reduced. For
a fixed tube length, the calandrias comprising 44.45 mm OD tubes have the lowest
cost of materials for the vessel and heating tubes. This is partly because of the lower
cost of the 44.45 mm OD tubes per m2 of HSA than the 38.10 mm and 50.80 mm OD
tubes.
56 Capital Cost Model
Tubes
S2 S3 S4 M2 M3 M4 L2 L3 L4
Fra
ctio
n of
M2 c
ost
of
mat
eria
ls
0.90
0.95
1.00
1.05
1.10
2000
3000
4000
5000
Figure 3.4 Costs of materials for 2000, 3000, 4000 and 5000 m2 vessels with
different tube dimensions as fraction of cost of materials for vessels with M2
calandrias
Table 3.3 shows the cost data used for the assessment of the cost of the fabricated
evaporators (ex-works). Some of these data have been obtained from discussions with
sugar factory engineers, while other data are estimated by the authors as they were not
available because of commercial sensitivities.
Table 3.3 Cost data for construction of an evaporator
Description of parameter Value
Labour requirement to manufacture vessel 70 man hours per tonne of
steel
Labour cost AUD 70 per man hour
Fitting of tubes (placement and expansion at top
and bottom tube plates)
5 min per tube
Workshop overhead costs 30% of labour costs
Project management costs 10% of material, labour and
workshop costs
Profit margin 15% of total costs
Capital Cost Model 57
Figure 3.5 shows the capital costs (ex-works) for the evaporator with calandrias
of different dimensions. As for Figure 3.4, the data for each HSA are expressed
relative to the costs of vessels of the same HSA with calandrias of M2 tubes. As
expected, the material and labour costs are lower for vessels with long tubes and small
diameter and greater for vessels with short tubes and large diameter. Comparison of
the data in Figure 3.5 and Figure 3.4 shows the impact of labour costs in manufacturing
the vessels and inserting and expanding the heating tubes into the calandrias.
The data in Figure 3.5 show the length of tube has a strong impact on capital
costs. For example, increasing the tube length from 2 m to 3 m provides a 13 to 15%
cost saving. Incrementally, there is a larger cost saving in increasing the tube length
from 2 m to 3 m than from 3 m to 4 m. This finding is to be expected.
Smaller diameter tubes provide a capital cost saving, but this is of lesser
influence than the length of the tube. For the same length of tube, the cost saving in
using tubes of 38.10 mm OD is only 3 to 5% compared with tubes of 44.45 mm OD.
This result is strongly dependent on the cost of tube per m2 of HSA given in Table 3.2.
One clear observation from Figure 3.5 is that the evaporators with the
conventionally used tube dimensions M2 are more expensive than all the other tube
arrangements, except for evaporators with L2 tubes.
58 Capital Cost Model
Tubes
S2 S3 S4 M2 M3 M4 L2 L3 L4
Fra
ctio
n of
M2 c
ost
0.7
0.8
0.9
1.0
1.1
2000
3000
4000
5000
Figure 3.5 Total costs (ex-works) for 2000, 3000, 4000 and 5000 m2 vessels with
different tube dimensions as fraction of cost (ex-works) for vessels with M2
calandrias
3.2.5 Installation costs
The installation costs include the costs of the foundations and structure to
support the evaporator, insulation and cladding costs, pipework, instrumentation and
control costs. The installation costs are likely to be proportional (probably not linearly)
to the weight of the vessel used for the design of the foundations and supporting
structure (i.e., weight of the vessel and both the calandria and juice side full of
condensate and juice respectively).
Figure 3.6 shows the total mass on the foundations for the vessels with different
tube dimensions. The mass of juice is calculated for juice of 40 brix. The data for
each HSA are presented relative to the values for M2. Comparing the S4 tube design
with the conventional M2 tube design, a 40% reduction in the mass on the foundations
and structure is achieved.
Another benefit with the S4 tube design, and in general for small diameter
vessels, is the smaller footprint, which gives an additional saving on installation costs.
Capital Cost Model 59
The costs of locating a vessel within an existing factory are generally proportional to
the footprint, although these costs are very site-specific. Thus, in some situations,
considerable savings may also be obtained for the smaller footprint of vessels with
smaller body diameter.
Cranage costs for installing the vessel are affected by the mass of the vessel and
also access to the location for the vessel, which depends on the site for the new
evaporator. The data in Figure 3.4 provide a reasonable indication of the relative
masses (empty vessels) to be lifted into position.
Tubes
S2 S3 S4 M2 M3 M4 L2 L3 L4
Fra
ctio
n of
M2 m
ass
on
foun
dat
ions
0.6
0.8
1.0
1.2
2000
3000
4000
5000
Figure 3.6 Total mass on foundations for 2000, 3000, 4000, and 5000 m2 vessels
with different tube dimensions as fraction of the total mass for vessels with M2
calandrias
3.2.6 Concluding remarks
For each evaporator, the number of tubes, vessel internal diameter, cost of
materials, total costs (ex-works) and total mass on the structure and foundations are
calculated and plotted. The parameters for the different designs are compared with the
calandria, comprising 44.45 mm OD tubes 2 m long that are generally used in the
60 Capital Cost Model
Australian sugar industry. The model shows that for the cost of materials, total costs
(ex-works) and the mass on foundations, the values for M2 calandria are significantly
higher than for the calandrias with longer tubes and smaller diameter, with the effect
of tube diameter being less than the effect of tube length. Vessels comprising S4 tubes
have the smallest vessel diameter, lowest cost ex-works and smallest mass on the
foundations.
3.3 Other Considerations in the Design of Evaporators
3.3.1 Introductory remarks
The Robert-type evaporator provides larger buffer volumes, which are beneficial
for level and brix control. Additionally, the potential for sucrose degradation and
entrainment of juice droplets in the up-flow vapour have to be considered when
designing an evaporator. These topics are explored in this section.
3.3.2 Sucrose degradation during juice evaporation
The extent of sucrose degradation that occurs in the juice evaporation process is
a function of the juice conditions (pH, temperature and brix) and the residence time.
The evaporation conditions that are likely to experience higher levels of sucrose
degradation are where high levels of steam economy are sought e.g., where extensive
vapour bleeding is undertaken and where the process steam supplied to the calandria
of effect 1 is at higher pressure. For these stations, large evaporation areas are provided
in the front end of the set and the boiling temperatures are high (e.g., 118 °C). These
arrangements provide longer residence times for the juice at high temperatures, thus
providing conditions conducive to higher rates of sucrose degradation.
There is potential with the use of smaller diameter vessels associated with
calandrias comprising smaller diameter, longer tubes that the juice volume per unit
heating surface area can be reduced. Figure 3.7 shows the calculated juice volume
intensity (litres per m2 of HSA) for the different calandrias. These values are
determined for the base of the evaporator having a fixed gap between the bottom tube
plate and the base of the evaporator at the outer wall (300 mm) and angles in a W-
shaped bottom of 15 degrees (outer plate) and 30 degrees (inner plate). The juice
operating level is set at 35% of the tube height. The data show that calandrias
comprising longer tubes of smaller diameter should allow operation with a shorter
residence time for the juice and hence provide reduced potential for sucrose
Capital Cost Model 61
degradation. In this regard, the benefits of using longer tubes of smaller diameter
would be greater at the front end of the set where the rates of sucrose degradation are
faster and reductions in the residence time for juice would be very beneficial.
Of note in Figure 3.7, vessels with calandrias using the conventional tubes M2
provide the second largest juice volume intensity, second only to vessels with L2 tubes.
Vessels with S4 tubes have juice volume intensities of ~6 L/m2 compared with vessels
with M2 tubes of ~11 L/m2.
Tubes
S2 S3 S4 M2 M3 M4 L2 L3 L4
Juic
e vo
lum
e in
tens
ity (
L/m
2)
0
2
4
6
8
10
12
14 2000
3000
4000
5000
Figure 3.7 Juice volume intensity for 2000, 3000, 4000 and 5000 m2 vessels with
different tube dimensions
3.3.3 Buffer volume for improved juice level and syrup brix control
The juice volume in Robert evaporators provides a buffer volume, which is
beneficial for juice level control and the syrup brix control in the final evaporator. The
author is unaware of any study into the minimum volume (or residence time), below
which juice level control or syrup brix control would be problematic.
As stated, evaporator stations for steam-efficient operation will likely include
additional area at the front end of the set. So, at the front end of the set at least,
62 Capital Cost Model
installing vessels with low juice volume intensity should not create an issue for juice
level control as there should be adequate juice volume.
For vessels at the tail end of the set it may be more important to consider the
volume of juice held in the vessel in order to achieve effective control of juice level
and syrup brix. Burke et al. (2014) discusses the fluctuations in vapour flows through
the evaporator set resulting from the variations in pan stage vapour demand, and the
control options for juice level and syrup brix control. It is therefore considered
important that the juice volumes and residence times in these latter vessels are
considered in selecting the appropriate evaporator design. If a small-diameter, long-
tube calandria is beneficial from a heat transfer efficiency and cost perspective, it may
be that a larger juice volume than in a conventional configuration will be required
below the bottom tube plate to provide sufficient volume of juice for control purposes.
3.3.4 De-entrainment of droplets of juice from the vapour stream
In practice, the de-entrainment of droplets of juice from the vapour stream
passing to the next vessel is achieved through:
• the provision of a large distance from the boiling level of the juice to the
de-entrainment system, thus providing the opportunity for droplets to
disengage from the up flow of vapour and fall back, and
• The de-entrainment equipment itself.
Vessels of smaller diameter produce a stronger up-flow velocity for the same
vapour rate and so the intensity of droplets impinging on the de-entrainment system is
likely to be increased. For the investigations in this paper a constant strake height
above the top tube plate of 5 m is assumed. This height is reasonably common in the
current installations of Robert evaporator.
Up flow velocities in the conventional evaporator vessels comprising calandrias
of 44.45 mm OD tubes and 2 m length for specific vapour rates from the heating
surface of 40 kg/h/m2 (considered a maximum vapour rate in current operation of the
conventional evaporators) are estimated to be ~1 m/s at the 1st effect and ~9 m/s at the
final effect. These are assumed to be the maximum acceptable up-flow velocities.
The vessel configuration comprising a calandria of small diameter, long tubes
will produce the highest vapour velocities for the same specific vapour rate. It is also
Capital Cost Model 63
found that the vessels of larger HSA provide a higher heating surface area per cross-
sectional area of vessel and so will also produce a slightly higher up-flow vapour
velocity than vessels of smaller heating surface area, for the same specific vapour rate.
Table 3.4 shows the maximum specific vapour rates that produce acceptable
vapour up-flow velocities. The data are shown for calandrias comprising tubes of
38.10 mm OD and 4 m long, in evaporators of 2000 and 5000 m2, for vapour pressures
of 13, 80 and 160 kPa abs.
Table 3.4 Maximum specific vapour rates for acceptable up-flow vapour
velocities in the headspace of vessels comprising tubes of 38.1 mm OD and 4 m
length
Vapour pressure, kPa abs Maximum specific vapour rate*, kg/h/m2
Vessel of 2000 m2 Vessel of 5000 m2
13 18 16
80 18 17
160 20 19
* Based on a maximum allowable up flow velocity of 1 m/s for 160 kPa abs, 5 m/s for
80 kPa abs and 9 m/s at 13 kPa abs.
As a guide for calandrias of 38.10 mm OD but shorter tubes, the maximum
specific vapour rates that can be accommodated are 30% greater for 3 m tubes and
75% greater for 2 m tubes than shown in Table 3.4.
It is apparent from the data in Table 3.4 that the vapour velocities and potential
impact on entrainment must be considered when designing an installation of a
calandria with high heating surface area per unit cross-sectional area of vessel. Up-
flow vapour velocities are likely to be of greatest concern at the front end of the set
(vapour pressures of 160 kPa abs), where specific vapour rates of 22 to 30 kg/h/m2 are
usual. At the tail end of the set, specific vapour rates are often less than 18 kg/h/m2,
particularly for energy-efficient installations. As well, it is unlikely that calandrias
with tubes of 38.10 mm OD and 4 m length would be suitable for the final vessel from
the point-of-view of effectively producing rising film boiling.
Consideration has been given to the specific vapour rates that could be
accommodated by a de-entrainment system of LSEA II louvres (a common design
used in Australian factories) installed in the headspace of the evaporator comprising
calandrias of different dimensions. For the study, the louvre face was assumed to be
a square with the corners located 200 mm from the circular shell. A safety margin for
64 Capital Cost Model
the installed louvre area of 30% above the minimum area required for breakthrough of
the droplets in the vapour stream exiting the louvres was allowed. The results show,
as expected, the vessels of smallest diameter (viz., calandria comprising 38.10 mm OD
tubes and 4 m long) have the lowest specific vapour rate that can be accommodated.
The vessels with the capacity to process the highest vapour rate comprise calandrias
of 50.80 mm OD tubes, 2 m long.
Table 3.5 Maximum specific vapour rates for LSEA II louvres in vessels
comprising tubes of 38.1 mm OD and 4 m length
Vapour pressure
kPa (abs)
Maximum specific vapour rate
kg/h/m2
13 16
80 35
160 47
The data in Table 3.5 indicate that for almost all practical operating conditions,
sufficient LSEA II louvre area can be installed in the headspace of the vessels, without
the need for increasing the diameter of the headspace or installing an external
separator. It is only at the final effect conditions that the vapour rate may exceed the
breakthrough velocity, and, for these conditions, it is unlikely that calandrias of these
dimensions would be suitable for the final vessel.
3.3.5 Concluding remarks
Consideration is given for the different designs of evaporator vessels with
different tube dimensions for the juice hold-up volume and de-entrainment of juice
droplets carried with the vapour up- flow in the headspace of the vessels. These
matters will need to be considered in selecting the optimal tube dimensions for the
different evaporation stages.
3.4 Concluding Remarks
A capital cost model for Robert evaporator has been developed for 2000, 3000,
4000 and 5000 m2 vessels with 2 m, 3 m, and 4 m tube lengths and 38.10 mm,
44.45 mm, and 50.80 mm tube outside diameter.
Capital Cost Model 65
The results show that the conventional evaporator with 2 m tubes of 44.45 mm
outside diameter is more expensive than all the other tube arrangements except for
evaporators with 2 m tubes of 50.8 mm outside diameter.
Relative to the conventional evaporator, cost savings in the ex-works cost of
~12% are likely in using 3 m long tubes of 44.45 mm OD and ~15% if 3 m long tubes
of 38.10 mm outside diameter tubes are used. Further savings are made by the use of
4 m long tubes, but the incremental cost reduction is less than increasing the tube
length from 2 to 3 m. Longer tube vessels have smaller diameter and considerably less
mass on the structure and foundations than the conventional evaporator, and so
additional savings through reduced installation costs would be achieved.
Vessels comprising longer tubes and smaller diameter have a lower juice volume
per unit of heating surface area. This feature is likely to be important for vessels early
in the evaporator set when high process steam pressures are used.
The vapour up-flow velocities and the impact on the de-entrainment system will
need to be considered for vessels comprising small diameter, longer tubes.
The results from this analysis are used in conjunction with results for heat
transfer efficiency for calandrias of different tube dimensions, as discussed in Chapters
4 and 5. In combination, these results allow the optimum Robert evaporator vessel
design to be determined for the different evaporation duties, as discussed in Chapter
7.
Experimental Program 67
CHAPTER 4: EXPERIMENTAL
PROGRAM
4.1 Introductory Remarks
In Chapter 3, the capital costs associated with the fabrication and installation of
Robert-type evaporators were discussed. It was concluded that ~12% savings can be
achieved for the same heating surface area if evaporators having 3 m long tubes with
44.45 mm outside diameter are installed, compared with using the conventional tubes
(M2 size). The saving increases to 15% if 3 m long tubes of 38.1 mm outside diameter
are used. The HTC performances of tubes with different dimensions, other than the
standard M2 size, are not known. To understand the HTC performance and boiling
mechanism in rising-film vertical tubes of different dimensions, pilot plant
investigations were undertaken. This chapter discusses the experimental program, the
design of experiments, the experimental procedure, and the analysis of the potential
errors for both the condensate collection and the operating conditions. The effects of
tube dimensions and operating conditions on heat flux and heat transfer coefficient are
also discussed. The chapter concluded that the errors associated with the condensate
collection and the operating conditions were sufficiently small to be able to provide
reliable determinations of the HTC and VCC for each of the tests.
4.2 Experimental Rig
The schematic arrangement of the single-tube evaporator developed for this
experiment can be seen in Figure 4.1. The pilot plant evaporator rig, the accessories,
the control system, the data logging system and the commissioning are described
broadly in Appendix A.
68 Experimental Program
Figure 4.1 Schematic representation of the single-tube evaporator rig
The four main components are the juice tank located below the heating tube, the
heating tube, the steam chest around the heating tube and the headspace above the
heating tube. The juice held in the vessel fills the juice tank and partly fills the heating
tube. The level of juice inside the heating tube is known to affect the heat transfer. The
juice inside the tube boils and produces vapour that passes through the headspace of
the vessel and is condensed in a plate heat exchanger, which is supplied with cooling
water. The condensed vapour flows to a separator under vacuum or atmospheric
pressure, depending on the test conditions. The condensate from the separator is heated
with an immersion heater to the boiling temperature of the juice before returning to the
juice tank.
The single stainless steel heating tube is encased in a steam chest allowing the
steam that enters the steam chest to condense on the outside of the heating tube. The
steam was distributed inside the steam chest via two pipes, which extended the full
height of the steam chest and were located on opposite sides of it. These pipes
contained equally spaced holes to distribute the steam and direct the steam away from
Experimental Program 69
the heating tube. This arrangement was essential to ensure that the condensate on the
outside of the tube was not disturbed by the incoming steam that may influence the
boiling of the juice inside the tube. A CFD model was developed to investigate the
steam velocity within the steam chest. The CFD model is described in Appendix B.
The condensate on the outside of the heating tube was collected in four gutters,
which were located equidistantly along the length of the tube. The condensate from
each gutter was drained under gravity to its individual container located below the
vessel. A fifth container collected the condensate from the bottom tube plate. Each
container was fitted with a pressure transducer at its base to provide a continuous
measurement of the head (height) of condensate in the container.
Noxious (incondensable) gases were removed from the steam chest through two
pipes within the steam chest, which were connected to vacuum or atmosphere,
depending on the test conditions. The arrangement of the noxious gas removal pipes
was similar to that for the steam entry pipes, thus ensuring the noxious gases did not
accumulate within the steam chest and were withdrawn uniformly along the full height
of the steam chest.
Juice samples were taken at the beginning and end of each test to check that the
brix of the juice had not changed through the test. Experience showed that the brix
remained reasonably consistent through the course of a test.
The boiling juice that collected above the heating tube may fall back into the
heating tube or pass to the juice tank via an external juice return line called a downtake.
Figure 4.2 shows the pilot evaporator rig, control unit and the computer to log
the data.
70 Experimental Program
Figure 4.2 Pilot evaporator rig
4.3 Experimental Design
4.3.1 Selection of the experimental factors
The objective of the experiment was to investigate the effect of tube dimensions
and operating conditions on the HTC of a single tube in a Robert evaporator
configuration. The experimental factors selected were tube length, tube diameter, juice
brix, juice level, headspace pressure and pressure difference between the steam chest
and the headspace. Although steam rate is an important parameter in evaporator
performance, it was not a controlled variable in the experimental procedure. Instead,
the steam chest pressure and the headspace pressure were controlled to nominated set
points and the difference in pressure between the steam chest and headspace
determined the resulting steam rate.
Experimental Program 71
Table 4.1 shows the experimental factors and number of levels for each of the
factors. Three levels of tube length and three levels of tube diameter were selected.
Hence, a total of nine tubes of different lengths and diameters were tested. The tubes
that were selected are the same as those considered in the capital cost model (see Table
3.1).
Table 4.1 Factors and levels explored in the experiment
Factor Levels
Tube length (TL, m) 3
Tube diameter (TD, mm) 3
Brix, (B°) 3
Juice level, (JL,% tube height) 4
Headspace pressure (HS, kPa abs) 2
Pressure difference (ΔP, kPa) 2
The selected conditions covered the wide range of industrial operating
conditions for multiple effect evaporators in raw sugar factories. The juice level,
headspace pressure and pressure difference factors were selected to be consistent with
the brix of juice, according to where that brix is achieved in an evaporator set and to
encompass the usual parameter range achieved in Robert evaporators in Australian
sugar factories. The juice in the first effect (low brix) boils above atmospheric
pressure, and juice in the final effect (high brix) boils under vacuum. The temperature
difference in the first effect is smaller than the temperature difference in the final
effect.
Consideration was given to designing the experimental program to measure the
heat transfer performance for each tube at several brix levels under the same operating
conditions of juice level, headspace pressure and pressure difference. This approach
would include testing low brix juice at low boiling temperature and high temperature
difference and high brix juice (syrup) at high boiling temperature and low temperature
difference. This process would ensure the results were free from confounding
interactions of the operating conditions. However, the test program would have
included many tests that were not only impractical industrially, but would not have
produced a boiling regime. For example, a test using Brix-70 juice with a small
temperature difference (which is typical of industrial boiling for Brix-20 juice) would
not have initiated rising film boiling to wet the total length of tube. It was therefore
72 Experimental Program
decided to structure the test program to encompass the practical operating conditions
that are typical of industrial evaporators for the 1st effect (typically Brix-20), 3rd effect
(typically Brix-35) and 5th effect (typically Brix-70) of a quintuple evaporator set.
The experimental factors, which were investigated for Brix-20, Brix-35 and
Brix-70 juices are shown in Table 4.2, Table 4.3 and Table 4.4. It should be noted that
in subsequent tables the following terminologies are used.
• HS1 and HS2: These are the two headspace pressures and HS1is the higher
of the two.
• DP1 and DP2: These are the two pressure differences and DP1 is the lower
of the two.
• JL1, JL2, JL3 and JL4: These are the four juice levels and the order from the
lowest to the highest is JL1 to JL4.
Table 4.2 Experimental factors investigated for juice at Brix-20
Factor Level 1 Level 2 Level 3 Level 4
Tube length (TL, m) 2 3 4 –
Tube diameter (TD, mm) 38.1 44.45 50.8 –
Juice level, (JL,% tube height) 20 30 40 50
Headspace pressure (HS, kPa abs) 149 126 – –
Pressure difference (ΔP, kPa) 33 45 – –
Table 4.3 Experimental factors investigated for juice at Brix-35
Factor Level 1 Level 2 Level 3 Level 4
Tube length (TL, m) 2 3 4 –
Tube diameter (TD, mm) 38.1 44.45 50.8 –
Juice level, (JL,% tube height) 20 35 45 60
Headspace pressure (HS, kPa abs) 94 72 – –
Pressure difference (ΔP, kPa) 35 50 – –
Experimental Program 73
Table 4.4 Experimental factors investigated for juice at Brix-70
Factor Level 1 Level 2 Level 3 Level 4
Tube length (TL, m) 2 3 4 –
Tube diameter (TD, mm) 38.1 44.45 50.8 –
Juice level, (JL,% tube height) 30 45 55 70
Headspace pressure (HS, kPa abs) 29 22 – –
Pressure difference (ΔP, kPa) 42 60 – –
4.3.2 Design of experiments
Since the number of levels of each factor was not the same (as shown in Table
4.1), the experiment was conducted as a full factorial experiment, to avoid the
complexity of selecting tests for a fractional factorial design. Because of the
difficulties associated with changing the tubes of different length and diameter and, to
a lesser extent, changing the brix and juice level, the experimental program was
conducted in a split-split-plot arrangement (TIBCO Spotfire, 2010) so that the tube
dimensions, brix and juice level were changed less frequently than in a fully
randomised experimental design. The tube dimensions formed the top order of the
experiment also known as the whole plot. The brix and juice level experimental factors
formed the subplot and the headspace pressure and pressure difference formed the sub-
sub-plot of the experiment. The structure of the experimental program is shown in
Appendix C.
The nine tubes were selected for testing in a random order. For each tube, the
brix and juice level combinations were selected for testing in a random order. For each
of the brix and juice level combinations, the headspace pressure and pressure
difference combinations were selected for testing in a random order.
With six experimental factors at the chosen number of levels, the design of the
experiment included 432 tests. These 432 tests henceforth are referred to as
Original432. For an analysis of variance (ANOVA) of the whole plot consisting of a
3 x 3 factorial experiment, the tests provided information on the significance of tube
length and tube diameter factors individually, but no information was available on the
interaction between tube length and tube diameter. The eight degrees of freedom for
the 3 x 3 whole-plot experiment were consumed by the length (2), diameter (2) and
residuals (4).
74 Experimental Program
A replicated 2 × 2 whole-plot experiment was conducted to examine the tube
length and tube diameter interaction. The four tubes investigated in the replicate
experiment were M2, S2, M3 and S3. To reduce the number of tests in the replicates,
brix levels of 20 and 70 only were selected. Juice levels, headspace pressure and
pressure difference factors were kept the same as for the Original432 experiment. A
total of 128 tests were conducted in this second experiment. These 128 tests henceforth
are referred to as Replicate128.
4.4 Experimental Procedure
The Brix-20 and Brix-70 juice were sampled directly from the factory’s first and
final evaporators respectively. The Brix-35 juice was prepared manually by diluting
Brix-70 juice with hot water. Prior to each test conducted at the Brix-20 and Brix-35
levels, the evaporator rig was boiled with water at atmospheric pressure to preheat the
pilot evaporator from a cold start. For Brix-70 tests, the rig needed to be cooler and
water boiling at atmospheric pressure was not done. The test temperature is the set
point temperature calculated from the set point headspace pressure plus the boiling
point elevation, depending on the brix of the juice. The juice was transferred into the
rig using vacuum for tubes of 4 m length and was poured through the juice return line
for tubes of 2 and 3 m length. The use of vacuum was minimised since low pressure
caused the high temperature juice to flash in the vessel, increasing the brix of the juice.
Also, setting the required juice level was difficult with high vacuum. Once the juice
was transferred to the rig at the required level, this state was referred to in the
experiment as a boil. For each boil, four tests were conducted at two different
headspace pressures and two different pressure differences.
All the tests were conducted with the valve in the external downtake in the open
position. Also, for all tests, the condensed vapour return to the juice tank was heated
to the boiling temperature of the juice. The supply of juice at the boiling temperature
is, however, not usual in factory vessels. In the first vessel, the juice entering is often
5–10 °C lower than the boiling temperature of the juice and requires heating within the
evaporator to reach that temperature. This heating is often referred to as sensible
heating. From the second effect onwards in industrial evaporators, juice entering the
vessel is at a higher temperature than the boiling temperature of the vessel, causing the
juice to flash as it enters the vessel.
Experimental Program 75
When conducting the tests, steady boiling conditions were established before
logging of the data commenced. The complete data logging system is explained in
detail in Appendix A. For each test, data were logged for all the operating conditions
and for the height of condensate collected in each reservoir. The sections of the tube
were designated section 1 to 4 with section 1 being the top section and section 4 being
the bottom section. The condensate collected from the bottom tube plate was
designated section 5. Each test was conducted for approximately 20–25 minutes,
ensuring a period of steady condensate collection was obtained before moving on to
the next test. Once the four tests for each boil were completed, the rig was brought to
atmospheric pressure and the conditions established for the next boil (randomly
selected juice brix and juice level). The process was then repeated.
4.5 Calculating HTC from Condensate Measurements
4.5.1 Introductory remarks
The condensing vapour on the outside of the tube is accumulated in four
equidistant gutters along the length of the tube and drained to condensate containers
located below the steam chest. The HTC was calculated using the condensate data.
This section describes the procedure and the calculations for determining HTC from
the raw data.
4.5.2 Determining condensate flow rate (kg/s)
The height of condensate (mm) collected in each reservoir was measured using
the differential pressure transducer in the base of the reservoir, logged and plotted
against time (minutes). An example of the data for condensate collection in each
reservoir is shown in Figure 4.3. A linear regression was fitted and for most cases
𝑅2~ 1 was determined, indicating steady boiling conditions had been reached. The
equation of the form (𝑦 = 𝑚𝑥 + 𝑐) where m is the slope for each plot is shown below
the label for each of the graphs. Parameter m is the condensate collection rate and has
the unit mm/min. Parameter c has the unit mm.
The internal diameter of each of the reservoirs for collecting condensate from
the heating tube (sections 1 to 4) was 70 mm and the internal diameter of the reservoir
for section 5 was 100 mm.
76 Experimental Program
The condensate rate (kg/s) for each of the tube sections and for the collection on
the bottom tube plate was calculated from the rate of filling of the condensate reservoir,
the cross-sectional area of the reservoir and the estimated density of the condensate (as
a function of temperature). The condensate rates from the four sections are summed
to provide the total condensate rate formed on the outside of the heating tube.
4.5.3 Determining temperature difference
Using the total condensate rate for the heating tube, together with the latent heat
of condensation (function of calandria pressure–using Steam Tables) the heat flux for
the test is calculated using equation 1.2. The temperature difference between the
vapour temperature in the steam chest and the temperature of the juice is calculated
using equation 1.3. Based on the calculated heating surface area of the tube (outside
diameter and distance between the outer faces of the tube plates), the overall HTC for
the test is calculated using equation 1.1. The VCC for the test is calculated from the
total condensate rate for the four sections of the tube, divided by the heating surface
area of the tubes using equation 1.6. The temperature of the juice is determined from
the headspace pressure and boiling point elevation (from the brix) using the correlation
1.4 and 1.5 on page 7.
4.5.4 Example showing HTC calculation
To demonstrate an example of HTC calculation, a test from the experimental
investigations is selected. This test corresponds to the condensate collection results
shown in Figure 4.3.
Tube dimensions
Tube length – 2 m
Tube diameter – 44.45 mm
HSA – 0.07 m2 for each section, 0.28 m2 for the entire tube.
Operating parameters
Juice brix – 20
Juice level (%tube height) – 40
Steam chest pressure – 194 kPa abs
Headspace pressure – 149 kPa abs
Experimental Program 77
Pressure difference – 45 kPa
Temperature difference – 7.7 (taking into account boiling point elevation at 20
brix and juice temperature of 111.49 ℃ )
Condensate rate (slope in mm/min) – Section 1 – 17.76
Section 2 – 21.28
Section 3 – 21.12
Section 4 – 17.45
Tube – 77.61
Calculations
Calculating condensate volume flow rate (m3/s) in each condensate container
Section 1 – (17.76
1000
60) 𝑥 (
𝜋
4𝑥0.072) = 1.14 𝑥 10^ − 6
Section 2 – (21.28
1000
60) 𝑥 (
𝜋
4𝑥0.072) = 1.36 𝑥 10^ − 6
Section 3 – (21.12
1000
60) 𝑥 (
𝜋
4𝑥0.072) = 1.35 𝑥 10^ − 6
Section 4 – (17.45
1000
60) 𝑥 (
𝜋
4𝑥0.072) = 1.12 𝑥 10^ − 6
Entire tube – 4.98 𝑥 10−6
Calculating condensate mass flow rate (kg/s)
�̇�𝐶 = �̇�𝐶 𝑥 𝜌
Where �̇�𝐶 is the mass flow rate of condensate, (kg/s)
�̇�𝐶 is the volumetric flow rate of condensate, (m3/s)
𝜌 is the density of saturated liquid, (kg/m3)
The density of the saturated liquid and latent heat of condensation are calculated
from the properties of the steam (Steam Table). Table 4.5 below shows the density of
the saturated liquid and latent heat of condensation for the 12 steam chest pressures.
78 Experimental Program
Table 4.5 Density of saturated liquid and latent heat of condensation for the 12
steam chest pressures
Steam chest
pressure (kPa
abs)
Steam chest
temperature (℃)
Density of
saturated liquid
(kg/m3)
Latent heat of
condensation (kJ/kg)
194 119.27 943.74 2204.48
182 117.28 945.33 2210.02
171 115.35 946.85 2215.34
159 113.13 948.58 2221.44
144 110.15 950.88 2229.55
129 106.91 953.33 2238.30
122 105.29 954.53 2242.65
107 101.53 957.28 2252.63
89 96.41 960.94 2266.11
82 94.18 962.49 2271.91
71 90.33 965.11 2281.86
64 87.62 966.91 2288.82
Calculating heat flux 𝑄 from condensate flow rate and latent heat of steam using
equation 1.2.
Section 1 – 2370 W
Section 2 – 2840 W
Section 3 – 2818 W
Section 4 – 2329 W
Tube – 10356 W
Calculating heat transfer coefficient using equation 1.1.
Section 1 – 4397 W/m2/K
Section 2 – 5269 W/m2/K
Section 3 – 5228 W/m2/K
Section 4 – 4321 W/m2/K
Tube – 4803 W/m2/K
Experimental Program 79
Section 1
y=17.76x+41.21
Time (minutes)
0 2 4 6 8 10 12 14 16
Co
nd
ensa
te c
olle
ctio
n (
mm
)
0
50
100
150
200
250
300
350
Section 2
y=21.28x+2.45
Time (minutes)
0 2 4 6 8 10 12 14 16
Co
nd
ensa
te c
olle
ctio
n (
mm
)
0
50
100
150
200
250
300
350
Section 3
y=21.12x+15.57
Time (minutes)
0 2 4 6 8 10 12 14 16
Co
nd
ensa
te c
olle
ctio
n (
mm
)
0
50
100
150
200
250
300
350
Section 4
y=17.45x+29
Time (minutes)
0 2 4 6 8 10 12 14 16
Co
nd
ensa
te c
olle
ctio
n (
mm
)
0
50
100
150
200
250
300
350
Section 5
y=16.33x+10.7
Time (minutes)
0 2 4 6 8 10 12 14 16
Co
nd
ensa
te c
olle
ctio
n (
mm
)
0
50
100
150
200
250
300
350
Figure 4.3 Condensate collection (mm) for individual sections (1 to 4) and for
section 5
80 Experimental Program
4.6 Analysis of Potential Errors with Condensate Collection
4.6.1 Introductory remarks
It is important to understand the potential errors associated with the experimental
investigation before analysing the data and interpreting the results. The heating tube
was designed to allow condensate to be collected from four sections of the tube, with
the condensate formed on a tube section being transferred to its reservoir. Three
scenarios that could occur exist within the steam chest, which would adversely affect
the measurement of condensate rates for a section of the heating tube.
1. Condensate departs the outside of the tube section and so is not collected
in the reservoir for that tube section but passes to the bottom tube plate.
2. Condensate overflows a gutter and flows to the tube section below.
3. Condensate overflows the bottom gutter to the bottom tube plate.
All scenarios would cause an error in the individual section’s HTC value and
lead to misinterpretation of the boiling mechanism, causing an error in the calculation
of the overall HTC for the whole tube. This section investigates the data for evidence
that any of these scenarios was occurring.
4.6.2 Collection of condensate from the base of the steam chest
Potential sources of condensate in the reservoir for section 5 include
i. Condensed vapour on the inner wall of the steam chest due to convective
and radiation heat losses from the outer wall of the steam chest. The
evaporator rig was lagged with Rockwool insulation with 30 mm of
insulation thickness. The insulation around the flanges was loose, as the
rig was frequently disassembled to change the tube. A section of the rig
around the support structure was not lagged due to the difficulty in being
able to place insulation around the support. These sections in particular
would contribute to heat losses and condensation on the inside of the
steam chest.
ii. Condensate that may enter the steam chest with the vapour. The quantity
of condensate from this source should be small, as a condensate trap was
Experimental Program 81
placed after the steam valve to remove the condensate in the steam pipe
before the steam enters the steam chest.
iii. Condensate departing the outside of a tube section caused by the impact
of the inflowing steam.
iv. Condensate overflowing the bottom gutter.
With regard to item iii above, a CFD model of the steam side of the pilot
evaporator was developed and used to determine the velocity and flow path of the
steam entering the calandria. The steam velocity was found to be very low near the
tube surface and it was concluded that the steam entering the steam chest would not
disrupt the condensate on the tube, nor disturb the condensate pattern. The velocity
profile output from the CFD model is shown in Appendix B.
The condensate rate from the base of the steam chest was calculated for each of
the tests. The condensate rates ranged from 0.003 kg/s to 0.00012 kg/s with the low
rates being for tests at Brix-70. The highest condensate rates were for Brix-20. Heat
loss calculations were undertaken to estimate the quantity of condensate in section 5
that would be attributed to heat losses through the outer wall of the steam chest. These
rates ranged from 0.0023 kg/s (for tests with steam chest pressure of 194 kPa abs) and
0.00012 kg/s (for tests with steam chest pressure of 64 kPa abs). These estimates of
condensate rate due to heat losses were subtracted from the measured condensate rate
to provide an ‘unaccounted’ condensate rate for section 5. Unaccounted condensate
rates for section 5 ranged from 0.003 kg/s to 0.0001 kg/s.
Figure 4.4 shows the mean values of the unaccounted section 5 condensate flow
expressed as a percentage of the total flow on the tube surface, as measured from the
section 1 to section 4 condensate collections.
82 Experimental Program
Figure 4.4 Mean values of unaccounted section 5 condensate flow expressed as
percentage of total flow on tube surface
Table 4.6 shows the analysis of variance of unaccounted section 5 condensate
flow as % of the total flow on the tube surface. It was found that only pressure
difference has a significant effect on the relative magnitude of the unaccounted section
5 condensate flows. It is well known and demonstrated in section 4.8 on page 94 that
higher pressure difference results in higher VCC (kg/h/m2) on the tube surface, for all
other process conditions being the same. However, Figure 4.4 shows that higher
unaccounted section 5 condensate flow (as percentage of the condensate flow on the
tube surface) was achieved at lower pressure difference. The higher unaccounted
section 5 condensate flow for tests with the lower pressure difference provides further
evidence that the large unaccounted section 5 condensate flow is not caused by
condensate being displaced from the outside of the heating tube. An explanation is
not obvious, but it may be that at lower pressure difference and subsequently lower
vapour rates, the condensation of vapour in the supply vapour lines is a greater
proportion of the total flow and this condensate flows to the base of the steam chest on
entering the steam chest. Excess condensate entering the steam chest will have no
Experimental Program 83
influence on the measured condensate rates on the different sections of the heating
tube and hence on the measured VCC and calculated HTC values.
Table 4.6 Results of analysis of variance of unaccounted section 5 condensate
flow (%) with main sources (percent of total flow on tube surface)
Source
Degrees of
freedom
Mean
square
Variance
ratio
Significance
level
TL 2 78183 1.38 –
TD 2 106948 1.89 –
Residuals 4 56476
B 2 65823 2.02 –
JL 3 30509 0.94 –
Residuals 94 32557
HS 1 64263 2.58 –
ΔP 1 192009 7.72 0.006
Residuals 322 24872
4.6.3 Overflowing in a free-flowing scenario
The gutters, which were fabricated for condensate collection, were designed to
handle condensate flow rates well above those expected in the trials. Calculations show
the drain tubes should be able to transfer at 0.0065 kg/s per tube. Of all the tests, the
largest condensate rate collected for an individual tube section was 0.0015 kg/s, which
is well below the capacity of the drain tube to pass condensate to the reservoir in a
free-flowing situation. It is therefore concluded that if the entrance to the drain tube is
not restricted in any way, the condensate should drain readily from the gutter to the
reservoir.
Table 4.7 shows the maximum, mean and the standard deviation values of the
unaccounted section 5 condensate rate for all levels of each factor for tests at Brix-20.
The maximum value of unaccounted condensate rate viz. 0.0031 kg/s is observed for
headspace pressure of 149 kPa abs, pressure difference of 45 kPa, tube length of 4 m,
tube diameters of 38.1 and 50.8 mm and juice level of 30% tube height. The high value
of unaccounted condensate rate for headspace pressure and pressure difference is
explained, since they correspond to larger temperature difference. Longer tube lengths
would correspond to higher surface area of the tube and the steam chest. Juice level of
30% tube height would correspond to better heat transfer coefficient and higher
condensation rates. The not-so-readily explained result in Table 4.7 is tube diameter.
84 Experimental Program
Higher unaccounted condensate rate are shown for 38.1 and 50.8 mm tube diameters
but the unaccounted condensate rate for the 44.45 mm tube diameter is 40% lower than
the other two diameters. This result is not properly understood.
Table 4.7 Maximum value, mean value and standard deviation of the
unaccounted section 5 condensate rate for all levels of each factor for tests at
Brix-20
Factor Level Maximum
value, kg/s
Mean
value, kg/s
Standard
deviation, kg/s
HS pressure (kPa
abs)
149 0.0031 0.0013 0.0006
126 0.0023 0.0011 0.0005
ΔP (kPa) 33 0.0021 0.0011 0.0005
45 0.0031 0.0013 0.0006
Tube length (m) 2 0.0020 0.0011 0.0004
3 0.0018 0.0011 0.0004
4 0.0031 0.0014 0.0007
Tube diameter
(mm)
38.1 0.0031 0.0013 0.0006
44.45 0.0018 0.0010 0.0004
50.8 0.0031 0.0013 0.0006
Juice level
(%tube height)
20 0.0018 0.0010 0.0005
30 0.0031 0.0014 0.0006
40 0.0022 0.0012 0.0005
50 0.0022 0.0013 0.0006
4.6.4 Overflowing due to blockage at the entrance to a drainage tube
If an overflow did occur from a gutter, the overflowing condensate is expected
to flow to the tube section below the gutter (due to the commonly referred to ‘teapot
effect’) and cause an increase in the measured condensate rate of the section below.
The HTC values of individual sections of the Replicate128 dataset showed good
consistency with the corresponding values for the same conditions in the Original432
dataset. This comparison is provided in section 6.2. The fact that the replicate tests
were undertaken several weeks later and showed similar HTC results for the individual
sections of the heating tubes indicates that overflowing of condensate was not
occurring due to a blockage at the entrance to a drainage tube.
Experimental Program 85
4.6.5 Concluding remarks on the collection of condensate from the four sections of
the heating tube
The condensate rate from the base of the steam chest (section 5) was measured
for each of the tests and an allowance made for condensation on the inside wall of the
steam chest, due to radiation and convective heat transfer to atmosphere. After
deducting this allowance, an unaccounted condensate rate for section 5 was
determined. For several tests, the unaccounted condensate rate for section 5 (expressed
as a percentage of the total of flow on tube surface) was greater than 10%.
A comprehensive investigation has been undertaken to determine if the
measured condensate rate for any of the four sections of the heating tube may be in
error due to either condensate separating from the tube condensate and not being
drained from a gutter to the reservoir or a gutter overflowing condensate. The
investigations showed that:
• The steam velocity was found to be very low near the tube surface and
it was concluded that the steam entering the steam chest would not
disrupt the condensate on the tube or disturb the condensate pattern (see
Appendix B).
• The capacity of the drainage tube on each gutter far exceeds the
maximum condensate rate. Thus, without any physical restriction at the
entrance of the drainage tube, gutters should not overflow.
• Overflowing of a gutter could occur due to blockage of the entrance to
the drainage tube (e.g. due to a bubble or physical item lying at the
entrance). The HTC results for individual sections of tubes for the same
test conditions in the Replicate128 and Original432 series showed
similar values. Because the tests were undertaken several weeks apart
it is very unlikely a physical blockage would occur for a specific tube
section in a specific test, for both series.
As a result of these investigations it is concluded that there is no evidence of
overflowing of gutters or condensate separating from the tube.
All possible options have been explored to understand the cause of the
unaccounted quantity of condensate that collects on the base of the steam chest. There
is some indication that some condensate is entering with the steam supply and this is
86 Experimental Program
a greater percentage relative to the rate condensed on the heating tube for tests at low
steam rate. However, strategic analysis by various scenarios confirmed that the
presence of the unaccounted condensate would not affect the HTC results.
4.7 Analysis of Potential Errors of Operating Conditions
4.7.1 Introductory remarks
The operating conditions of the experimental program were selected such that
the difference between the levels of each factor is sufficiently large to cause a change
in heat transfer response.
Juice level was set to a precision of 5 mm and the juice level measured after the
run was in close agreement to within 5 to 10 mm of the initial level, corresponding to
an error of 2.5% for the shortest tube with the lowest level. The variation of headspace
pressure from the set value was negligible for each run, since headspace pressure was
well controlled. The juice was sampled from the factory evaporators and the brix of
the sample after adjustment by dilution with water (when needed) was within 1–2 units
of the required brix. The brix of the sample was measured before and after the test and
the brix reading after the test was recorded. For most tests, the required calandria
pressure was able to be controlled closely to the set point. However, for some of the
20 brix tests, the calandria pressure of 194 kPa abs (149 kPa abs headspace pressure
and 45 kPa pressure difference) was not able to be achieved since the vapour supply
used to regulate the calandria pressure was at a lower pressure.
Table 4.8 shows the maximum, minimum, mean and standard deviation values
for the experimental factors. Because factory samples of the ESJ and syrup were taken
for the tests, the brix was difficult to tightly regulate to the desired value and standard
deviations of 1.3 to 2.3 units resulted. For the tests of brix 20 and 35 this variation in
brix should have a small influence on the HTC. The brix of the juice at brix 70 was
more difficult to regulate, as of the high brix, relatively small changes in water content
have a large influence on the brix value. The high standard deviations of ΔP2 and ΔT3
for the first effect are explained in the above section by the inability to supply vapour
at 194 kPa abs for several tests. The high standard deviations of all the four ΔTs for
5th effect conditions can be attributed in part to the sensitivity of boiling point elevation
at higher brix values and the variation in juice brix among the tests. Headspace pressure
Experimental Program 87
is not included in Table 4.8, since it was well controlled, and the set point was always
achieved.
Table 4.8 Maximum values, minimum values, mean values and standard
deviation of the experimental factors
Effect Factor
Set
point
Maximum
value
Minimum
value
Mean Standard
deviation
1 B 20 21.7 14.2 18.2 1.7
ΔP1 33 33 33 33 0
ΔP2 45 45 35 40 3.2
ΔT1 5.7 5.9 5.6 5.7 0.1
ΔT2 6.5 6.7 6.4 6.5 0.1
ΔT3 7.7 7.8 6.1 7 0.5
ΔT4 8.9 8.9 8.6 8.8 0.1
3 B 35 38.5 34 36.1 1.3
ΔP1 35 35 35 35 0
ΔP2 50 50 50 50 0
ΔT1 7.9 8 7.7 7.8 0.1
ΔT2 9.8 10.8 9.6 10.2 0.2
ΔT3 11.2 11.2 11 11.1 0.1
ΔT4 13.5 13.6 13.4 13.5 0.1
5 B 70 74 65 70 2.3
ΔP1 42 42 42 42 0
ΔP2 60 60 60 60 0
ΔT1 17.2 21.7 16 18.8 1.3
ΔT2 20.9 24 19.7 21.8 1
ΔT3 23.3 24.4 22.1 23.2 0.6
ΔT4 27.4 28.5 26.3 27.4 0.6
4.7.2 Analysis of variance of the operating conditions
The following sections describe an analysis of variance of the actual operating
conditions, to identify if any other factors were inadvertently varied along with the
desired factor and could possibly have confounded the results. The analysis also helps
understand the impact that variations in operating conditions have on the calculated
values of heat transfer coefficient.
Brix
Table 4.9 presents the analysis of variance of measured brix values for the
Origianl432 tests. It is observed that brix has the most significant effect on measured
88 Experimental Program
brix values. An unexpected result is the significance of tube length on measured brix
values. Figure 4.5 shows the mean values for measured brix for all the factors. For
Brix-20 and Brix-35, the maximum deviation with tube length is 1 unit. For Brix-70,
the maximum deviation with tube length is 3 units.
Figure 5.7 on page 125 shows the mean values of HTC for each level of each
factor for the Origianl432 tests. For 15 units change in brix (Brix-20 to Brix-35), the
change in HTC is ~1500 W/m2/K. Hence, each unit change in brix corresponds to
100 W/m2/K. For tests with Brix-20, a change of 100 W/m2/K is small (< 5%) of the
mean of the HTC values for Brix-20.
Table 4.9 Analysis of variance of measured brix
Source
Degrees of
freedom
Mean
square
Variance
ratio
Significance
level
TL 2 118.6 7.34 0.045
TD 2 1.5 0.09 –
Residuals 4 16.14
B 2 97838 8646 0.000
JL 3 7.82 0.7 –
B:JL 6 18.8 1.6 –
Residuals 88 11.3 – –
HS 1 9.3E-28 0.71 –
ΔP 1 4.92E-29 0.03 –
B:HS 2 3.2E-30 0.00 –
B:ΔP 2 1.9E-28 0.15 –
JL:HS 3 8.06E-28 0.62 –
JL:ΔP 3 1.38E-27 1.06 –
HS:ΔP 1 3.5E-28 0.27 –
B:JL:HS 6 2.12E-27 1.62 –
B:JL:ΔP 6 1.18E-27 0.91 –
B:HS:ΔP 2 3.38E-29 0.02 –
JL:HS:ΔP 3 1.38E-27 1.06 –
B:JL:HS:ΔP 6 1.98E-27 1.52 –
Residuals 288 1.3E-27
For 35 units change in brix (Brix-35 to Brix-70), the change in HTC is ~1000
W/m2/K. Hence, each unit change in brix corresponds to 30 W/m2/K. For tests with
Brix-35, a change of 30 W/m2/K is small (< 5%) of HTC values for Brix-35.
Experimental Program 89
Figure 5.7 on page 125 shows the mean values of HTC for tests with Brix-70.
According to Figure 4.5, a change of 3 units of brix corresponds to a change in HTC
value of 250 W/m2/K. Hence each unit change in brix corresponds to 80 W/m2/K,
which is large (> 10%) compared to the mean of the HTC values for Brix-70.
Figure 4.5 Mean values of measured brix for each level of each factor for the
Original432 tests with all results included
Pressure difference
The pressure difference values were selected to generate a temperature
difference or driving force for heat transfer. For each brix, two pressure difference
values were selected, along with two headspace pressure values. The headspace
pressure values were always held at set point in the experimental program. This section
describes the analysis of variance for the measured pressure difference.
Table 4.10 shows the analysis of variance of measured pressure difference for
the Original432 tests. Three main effects (B, HS, ΔP), three 2nd order interaction
(B:HS, B:ΔP, HS:ΔP) and one 3rd order interaction (B:HS:ΔP) were identified with a
significance level less than 0.05.
90 Experimental Program
Figure 4.6 shows the B:HS:ΔP interaction plot with measured pressure
difference as the response factor. It is evident that for Brix-35 and Brix-70, the
measured pressure difference coincides with the set pressure difference. For Brix-20,
the measured pressure difference is lower than the set points for headspace pressure of
149 kPa (abs). The explanation for this is that the calandria set point of 194 kPa (abs)
could not always be achieved, since the vapour source from the factory itself was at
lower pressure.
Table 4.10 Analysis of variance of measured pressure difference
Source
Degrees of
freedom
Mean
square
Variance
ratio
Significance
level
TL 2 4.8 4.36 –
TD 2 0.96 0.87 –
Residuals 4 1.1
B 2 6345.5 8212.4 0.000
JL 3 1.3 1.67 –
B:JL 6 1.5 1.97 –
Residuals 88 0.77 – –
HS 1 54.67 62.37 0.000
ΔP 1 21998 25098 0.000
B:HS 2 57.5 65.6 0.000
B:ΔP 2 613.2 699.7 0.000
JL:HS 3 1.56 1.78 –
JL:ΔP 3 1.38 1.57 –
HS:ΔP 1 53.8 61.4 0.000
B:JL:HS 6 1.35 1.54 –
B:JL:ΔP 6 1.43 1.63 –
B:HS:ΔP 2 57.4 65.5 0.000
JL:HS:ΔP 3 1.19 1.36 –
B:JL:HS:ΔP 6 1.6 1.83 –
Residuals 288 0.88
Experimental Program 91
Figure 4.6 B:HS:ΔP interaction plot with measured pressure difference as a
response factor
Temperature difference
The temperature difference in the evaporator rig was a consequence of the
headspace pressure, the calandria pressure and the brix of the sample (and the boiling
point elevation). This section describes the analysis of variance for the measured
temperature differences.
Table 4.11 shows the analysis of variance of the measured temperature
difference for the Original432 tests. Three main effects (B, HS, ΔP) and three 2nd order
interactions (B:HS, B:ΔP, HS:ΔP) were identified, with a significance level less than
0.05.
92 Experimental Program
Table 4.11 Analysis of variance of calculated temperature difference
Source
Degrees of
freedom
Mean
square
Variance
ratio
Significance
level
TL 2 10.38 6.25 –
TD 2 1.24 0.74 –
Residuals 4 1.66
B 2 9139 4476.4 0.000
JL 3 0.86 0.42 –
B:JL 6 0.64 0.31 –
Residuals 88 2.04 – –
HS 1 704 478.2 0.000
ΔP 1 1485 1008.7 0.000
B:HS 2 71.3 48.4 0.000
B:ΔP 2 129 87.6 0.000
JL:HS 3 0.6 0.4 –
JL:ΔP 3 1.7 1.16 –
HS:ΔP 1 27.95 18.9 0.000
B:JL:HS 6 1.3 0.88 –
B:JL:ΔP 6 1.52 1.03 –
B:HS:ΔP 2 1.98 1.3 –
JL:HS:ΔP 3 0.77 0.52 –
B:JL:HS:ΔP 6 1.6 1.1 –
Residuals 288 1.47
Figure 4.7 shows the actual average temperature differences and Figure 4.8
shows the target temperature differences for the three brix. It is evident in most cases
the actual average temperature difference was in close agreement with the target
temperature difference.
For Brix-20, the actual temperature difference corresponding to the headspace
pressure of 149 kPa abs and pressure difference of 45 kPa was not achieved. However,
the actual average temperature difference is statistically different from the other three
temperature differences for Brix-20.
Experimental Program 93
Figure 4.7 Actual average temperature differences for the three brix
Figure 4.8 Target temperature differences for the three brix
94 Experimental Program
4.7.3 Concluding remarks
The operating conditions were selected to represent typical factory conditions
for a first, third and final effect in a quintuple evaporator set. It is concluded that the
experiment was well controlled and the few disparities between the target values and
the achieved values would not substantially influence the results. The achieved values
for the operating conditions are statistically different from each other.
4.8 The Effect of Tube Dimensions and Operating Conditions on Heat Flux
and Heat Transfer Coefficient
4.8.1 Introductory remarks
The experimental program was designed to induce a heat flux through the
imposed temperature difference between the heating steam and boiling juice for a
given brix and operating juice level. The HTC was then calculated based on the heat
flux, the heating surface area of the tube and the effective temperature difference (see
section 1.4.4). Four temperature differences were selected for each level of juice brix
as explained in section 4.3. This section describes the initial observations of the effects
of tube dimensions and operating conditions on the heat flux and the heat transfer
coefficient.
As described in section 1.4.4, the VCC and heat flux (Q/A) are closely related
as shown
Q
A=
VCC λs
3600
4.1
Thus, the only factor influencing the relationship is the change in latent heat λs
for the different steam chest pressures. Table 4.12 shows the conversion factor
between Q/A (kW/m2) and VCC (kg/h/m2).
Experimental Program 95
Table 4.12 Conversions of heat flux to VCC for different calandria pressures
Calandria
pressure, kPa abs
Latent
heat, kJ/kg
To convert heat flux (kW/m2) to VCC
(kg/h/m2) multiply heat flux by the factor
194 2204.5 1.63
182 2210.0 1.63
171 2215.3 1.63
159 2221.4 1.62
144 2229.5 1.61
129 2238.3 1.61
122 2242.6 1.61
107 2252.6 1.60
89 2266.1 1.59
82 2271.9 1.58
71 2281.9 1.58
64 2288.8 1.57
4.8.2 Review of the experimental data
Appendix C presents the detailed experimental results from the Original432 tests
and Appendix D presents the results from the Replicate128 tests.
The data from the Original432 dataset are plotted as HTC versus heat flux for
each imposed temperature difference. The plots are arranged in groups of four for
each juice brix value and are shown in Figure 4.9, Figure 4.10 and Figure 4.11. Each
plot shows the results for the nine tubes and four juice levels. These data lie on a
straight line with slope equal to 1/∆T according to equation 1.1 in section 1.4.4. As
expected, the maximum HTC occurs for a series of tests at constant ∆T when the heat
flux is greatest, and likewise the minimum HTC occurs when the heat flux is lowest.
96 Experimental Program
HS 149 kPa abs/DP 33 kPa/DeltaT 5.6
Heat flux (kW/m2)
0 10 20 30 40 50
HT
C (
W/m
2/K
)
0
1000
2000
3000
4000
5000
6000
L2L3L4M2M3M4 S2S3S4
HS 149 kPa abs/DP 45 kPa/DeltaT 7.7
Heat flux (kW/m2)
0 10 20 30 40 50
HT
C (
W/m
2/K
)
0
1000
2000
3000
4000
5000
6000
HS 126 kPa abs/DP 33 kPa/DeltaT 6.5
Heat flux (kW/m2)
0 10 20 30 40 50
HT
C (
W/m
2/K
)
0
1000
2000
3000
4000
5000
6000
HS 126 kPa abs/DP 45 kPa/DeltaT 8.7
Heat flux (kW/m2)
0 10 20 30 40 50
HT
C (
W/m
2/K
)
0
1000
2000
3000
4000
5000
6000
Figure 4.9 Effect of tube dimensions and operating conditions on heat flux and
heat transfer coefficient for tests at Brix-20
Experimental Program 97
HS-94 kPa abs/DP-35 kPa/DeltaT-7.9
Heat flux (kW/m2)
0 10 20 30 40 50
HT
C (
W/m
2/K
)
0
1000
2000
3000
4000
5000
HS-94 kPa abs/DP-50 kPa/DeltaT-11.2
Heat flux (kW/m2)
0 10 20 30 40 50
HT
C (
W/m
2/K
)
0
1000
2000
3000
4000
5000
HS-72 kPa abs/DP-35 kPa/DeltaT-9.8
Heat flux (kW/m2)
0 10 20 30 40 50
HT
C (
W/m
2/K
)
0
1000
2000
3000
4000
5000
HS-72 kPa abs/DP-50 kPa/DeltaT-13.5
Heat flux (kW/m2)
0 10 20 30 40 50
HT
C (
W/m
2/K
)
0
1000
2000
3000
4000
5000
L2
L3
L4
M2
M3
M4
S2
S3
S4
Figure 4.10 Effect of tube dimensions and operating conditions on heat flux and
heat transfer coefficient for tests at Brix-35
98 Experimental Program
HS-29 kPa abs/DP-42 kPa/DeltaT-17.2
Heat flux (kW/m2)
0 5 10 15 20 25 30
HT
C (
W/m
2/K
)
0
200
400
600
800
1000
1200
1400
HS-29 kPa abs/DP-60 kPa/DeltaT-23.3
Heat flux (kW/m2)
0 5 10 15 20 25 30
HT
C (
W/m
2/K
)
0
200
400
600
800
1000
1200
1400
HS-22 kPa abs/DP-42 kPa/DeltaT-20.9
Heat flux (kW/m2)
0 5 10 15 20 25 30
HT
C (
W/m
2/K
)
0
200
400
600
800
1000
1200
1400
HS-22 kPa abs/DP-60 kPa/DeltaT-27.4
Heat flux (kW/m2)
0 5 10 15 20 25 30
HT
C (
W/m
2/K
)
0
200
400
600
800
1000
1200
1400
L2
L3
L4
M2
M3
M4
S2
S3
S4
Figure 4.11 Effect of tube dimensions and operating conditions on heat flux and
heat transfer coefficient for tests at Brix-70
The data in Figure 4.9, Figure 4.10 and Figure 4.11 show several important findings:
• For all tests except for the test at Brix-20 with set points of 149 kPa abs
for the headspace and pressure difference of 45 kPa, the data lie very
tightly on a straight line with slope at the target 1
∆T . Thus, for all tests
except the ones mentioned above, the process variables for the tests were
at the set points for the headspace pressure and the steam chest pressure.
For the test at Brix-20 with the headspace pressure of 149 kPa abs and
pressure difference of 45 kPa, the plot is not completely linear. The
explanation for this was given in section 4.7.2 on page 87, where the
Experimental Program 99
target steam chest pressure of 194 kPa abs was not achieved for all tests
as the vapour supply pressure from the factory evaporator was often
slightly lower than 194 kPa abs;
• For tests at the same brix and headspace pressure operation with a larger
pressure difference (steam chest pressure to headspace pressure), this
results in a higher heat flux. There is one exception to this, which is for
M2 tube at Brix-70 for the lower head space pressure of 22 kPa abs. A
higher heat flux and HTC were obtained for this test at a pressure
difference of 42 kPa compared with a pressure difference of 60 kPa.
Investigations of the boiling conditions for the test at the lower pressure
difference show high VCC on the tube. A similar result is observed for
the Replicate128 data set3;
• For each juice brix, headspace pressure and pressure difference, for each
individual tube, there is an optimum juice level, which achieved the
maximum heat flux and HTC for that tube and processing conditions;
• For each set of operating conditions and for each tube operating at its
optimum juice level, each tube was able to achieve a certain peak value
of heat flux and HTC. Thus, for each set of conditions a specific tube
operating at its optimum juice level achieved the maximum heat flux and
maximum HTC for the imposed operating conditions; and
• The maximum HTC values are much greater for the tests at Brix-20
compared with Brix-35 and likewise for Brix-35 compared with Brix-70.
Figure 4.12, Figure 4.13 and Figure 4.14 show plots of HTC versus heat flux for
each of the test conditions at Brix-20, Brix-35 and Brix-70 respectively for the juice
level that provided the maximum HTC (and heat flux) for each of the nine tubes. These
figures show the maximum HTC and heat flux that was obtained for each tube at the
nominated processing conditions, and consequently show which tube provided the
highest heat flux and highest HTC for the imposed processing conditions.
3 The Original432 and Replicate128 tests for the M2 tube for Brix-70, HS pressure
22 kPa abs and pressure difference of 42 kPa showed similar results viz. low HTC
for juice levels of 30,, 55 and 70% of tube height and high HTC values for 45% juice
level. The HTC values for the Original432 and Replicate128 are shown in
Appendices C and D.
100 Experimental Program
Table 4.13 lists the tubes in the order of highest HTC first to lowest HTC last,
for the tests at the three brix values. The HTC values for the three brix values are
further divided into two categories, being for Brix-20 by HTC values above or below
4000 W/m2/K; for Brix-35 by HTC values above or below 2500 W/m2/K; for Brix-70
by HTC values above or below 500 W/m2/K.
HS-149 kPa abs/DP-33 kPa/DeltaT-5.6
Heat flux (kW/m2)
0 5 10 15 20 25 30 35
HT
C (
W/m
2/K
)
0
1000
2000
3000
4000
5000
6000
HS-149 kPa abs/DP-45 kPa/DeltaT-7.7
Heat flux (kW/m2)
0 10 20 30 40 50
HT
C (
W/m
2/K
)
0
1000
2000
3000
4000
5000
6000
HS-126 kPa abs/DP-33 kPa/DeltaT-6.5
Heat flux (kW/m2)
0 10 20 30 40 50
HT
C (
W/m
2/K
)
0
1000
2000
3000
4000
5000
6000
HS-126 kPa abs/DP-45 kPa/DeltaT-8.7
Heat flux (kW/m2)
0 10 20 30 40 50
HT
C (
W/m
2/K
)
0
1000
2000
3000
4000
5000
6000
L2
L3
L4
M2
M3
M4
S2
S3
S4
Figure 4.12 Relationship between heat transfer coefficient and heat flux at the
optimum juice level at Brix-20
Experimental Program 101
HS-94 kPa abs/DP-35 kPa/DeltaT-7.9
Heat flux (kW/m2)
0 10 20 30 40 50
HT
C (
W/m
2/K
)
0
1000
2000
3000
4000
5000
HS-94 kPa abs/DP-50 kPa/DeltaT-11.2
Heat flux (kW/m2)
0 10 20 30 40 50
HT
C (
W/m
2/K
)
0
1000
2000
3000
4000
5000
HS-72 kPa abs/DP-35 kPa/DeltaT-9.8
Heat flux (kW/m2)
0 10 20 30 40 50
HT
C (
W/m
2/K
)
0
1000
2000
3000
4000
5000
HS-72 kPa abs/DP-50 kPa/DeltaT-13.5
Heat flux (kW/m2)
0 10 20 30 40 50
HT
C (
W/m
2/K
)
0
1000
2000
3000
4000
5000
L2L3L4M2M3M4S2S3S4
Figure 4.13 Relationship between heat transfer coefficient and heat flux at the
optimum juice level at Brix-35
102 Experimental Program
HS-29 kPa abs/DP-42 kPa/DeltaT-17.2
Heat flux (kW/m2)
0 5 10 15 20 25 30
HT
C (
W/m
2/K
)
0
200
400
600
800
1000
1200
1400
HS-29 kPa abs/DP-60 kPa/DeltaT-23.3
Heat flux (kW/m2)
0 5 10 15 20 25 30
HT
C (
W/m
2/K
)
0
200
400
600
800
1000
1200
1400
HS-22 kPa abs/DP-42 kPa/DeltaT-20.9
Heat flux (kW/m2)
0 5 10 15 20 25 30
HT
C (
W/m
2/K
)
0
200
400
600
800
1000
1200
1400
HS-22 kPa abs/DP-60 kPa/DeltaT-27.4
Heat flux (kW/m2)
0 5 10 15 20 25 30
HT
C (
W/m
2/K
)
0
200
400
600
800
1000
1200
1400
L2
L3
L4
M2
M3
M4
S2
S3
S4
Figure 4.14 Relationship between heat transfer coefficient and heat flux at the
optimum juice level at Brix-70
The following general comments are made for the data in Table 4.13.
• For Brix-20, tubes of smaller diameter (38.1 mm and 44.45 mm)
provided higher HTC values. Tubes of 2, 3 and 4 m provided high HTC
values;
• For Brix-35, tubes of 3 and 4 m length provided higher HTC values.
Tubes of 44.45 mm diameter provided high HTC values;
• For Brix-70, tubes of 2 m length and larger diameter (44.45 and 50.8
mm) provided higher HTC values.
Experimental Program 103
More detailed investigation of the heat flux and HTC data shown in Figure 4.9
to Figure 4.14 was undertaken and the results of these observations are shown in Table
4.14.
Table 4.13 List of tubes showing high and low HTC for corresponding brix and
temperature difference
Brix Test conditions Tubes
demonstrating good
HTC
Tubes
demonstrating poor
HTC
(>4000 W/m2/K) (<4000 W/m2/K)
20 HS:149/ΔP:33/DeltaT:5.6 L3, M2, S2, S4, L2,
M3, S3
L4, M4
HS:149/ΔP:45/DeltaT:7.7 S2, M2, M3, S4 S3, M4, L2, L3, L4
HS:126/ΔP:33/DeltaT:6.5 S2, M2, L2, S4, S3 M3, M4, L3, L4
HS:126/ΔP:45/DeltaT:8.7 S2, M3, S3, M4, S4 M2, L2, L3, L4
(>2500 W/m2/K) (<2500 W/m2/K)
35 HS:94/ΔP:35/DeltaT:7.9 S3, M3, M4, M2 S2, S4, L2, L3, L4
HS:94/ΔP:50/DeltaT:11.2 M3, S3 M4, L2, M2 S2, S4, L3, L4
HS:72/ΔP:35/DeltaT:9.8 L2, M4, M3 S2, S3, S4, M2, L3,
L4
HS:72/ΔP:50/DeltaT:13.5 M4 L2, L3, L4, M2, M3,
S2, S3, S4
(>500 W/m2/K) (<500 W/m2/K)
70 HS:29/ΔP:42/DeltaT:17.2 L2, M2, S3 S2, S4, M3, M4, L3,
L4
HS:29/ΔP:60/DeltaT:23.3 M2, L2, L3 S2, S3, S4, M3, M4,
L4
HS:22/ΔP:42/DeltaT:20.9 M2, L2, S2 S3, S4, M3, M4, L3,
L4
HS:22/ΔP:60/DeltaT:27.4 S2, L3 S3, S4, M2, M3, M4,
L2, L4
104 Experimental Program
Table 4.14 Summary of the observations and comments for heat flux of three
brix
Juice
brix
Observation Comments
20 Largest heat flux (for the
optimum tube and juice level)
occurs at the largest imposed ∆T
–
The maximum HTC values for
the tests at the higher headspace
pressure are higher than for the
tests at the lower headspace
pressure.
The lower viscosity of the juice at
the higher boiling temperature is
most likely the cause of the
increased heat transfer.
The two series of trials at the
higher headspace pressure (149
kPa abs) produced similar
maximum values for HTC,
although these were at
substantially different heat flux
values.
It appears the juice boiling
temperature has a strong influence
in determining the HTC values.
For some tubes and test
conditions the juice level has a
strong influence on the heat flux
and the HTC.
–
35 Largest heat flux (for the
optimum tube and juice level)
occurs at the second largest
imposed ΔT and not the largest
∆T as for the tests at Brix-20.
The reason is attributed to boiling at
a higher temperature (greater
influence on juice viscosity) having
a strong influence on the heat
transfer efficiency and this effect
being greater than the effect of
larger ∆T.
The maximum HTC values for
the tests at the higher headspace
pressure are higher than for the
tests at the lower headspace
pressure.
This result is similar to that for juice
at Brix-20, and for the same
reasons.
The two series of trials at the
higher headspace pressure (94
kPa abs) produced reasonably
similar maximum values for
HTC, although the maximum
HTC at the lower ∆T was higher.
As for Brix-20 and Brix-70 it
appears the juice boiling
temperature has a strong influence
on the HTC values.
Experimental Program 105
Juice
brix
Observation Comments
70 Largest heat flux (for the
optimum tube and juice level)
occurs at the second largest
imposed ΔT.
This result is similar to that observed
for juice at Brix-35 and is attributed to
boiling at a higher temperature (greater
influence on juice viscosity) having a
strong influence on the heat transfer
efficiency and this effect being greater
than the effect of larger ∆T.
The maximum HTC values for
the tests at the higher
headspace pressure are higher
than for the tests at the lower
headspace pressure*.
This result is similar to those observed
for juice at Brix-20 and Brix-35, and
for the same reasons.
The two series of trials at the
higher headspace pressure (29
kPa abs) produced similar
maximum values for HTC,
although these were at
substantially different heat
flux values.
As for Brix-20 and Brix-35 it appears
the juice boiling temperature has a
strong influence in determining the
HTC values.
For some tubes and test
conditions the juice level has a
strong influence on the heat
flux and the HTC.
This result is similar to that for the tests
at Brix-20 and Brix-35.
For some tubes and test
conditions the juice level has a
strong influence on the heat
flux and the HTC.
This result is similar to that for the tests
at Brix-20.
*This statement is based on the bulk of the data in Figure 4.11 and excludes the apparent exceptional value for M2 at
a headspace pressure of 22 kPa abs and pressure difference of 42 kPa.
4.8.3 Concluding remarks
Examination of the raw data plotted as HTC versus heat flux at the various
processing conditions has shown the following:-
• The processing conditions for a test involve setting the headspace
pressure, the steam chest pressure and the brix of the juice. For these
conditions a specific temperature difference (∆T) exists between the
steam side of the heating tube and the average boiling temperature of the
juice. For the imposed processing conditions each test on a specific tube
at a selected juice level results in a certain heat flux, from which the HTC
is calculated.
106 Experimental Program
As expected from the calculation of HTC, a linear relationship exists
between HTC and the heat flux that is obtained for the imposed ∆T. The
slope of the plot of HTC versus heat flux is 1/∆T. Plots were prepared
for each set of processing conditions (single values of ∆T) and included
the HTC and heat flux results for the nine tubes and four juice levels. For
all tests apart from those requiring a steam chest pressure of 194 kPa abs,
the test conditions for headspace pressure and steam chest pressure were
at (or very close to) the nominated set point. For some tests at a
nominated steam chest of 194 kPa abs, only a slightly lower pressure was
able to be achieved.
• For each tube operating at a nominated processing condition an optimum
operating level for the juice in the heating tube exists, for which the HTC
and heat flux are maximised. For many tests, for the imposed ∆T, the
juice operating level has a strong effect on the achieved heat flux and
HTC.
• For tests at specific processing conditions (e.g. a certain juice brix,
headspace pressure and steam chest pressure):
o For each tube, at the imposed operating conditions an optimum
operating level for the juice in the heating tube exists, for which
the HTC and heat flux are maximised.
o Tubes of different dimensions experienced different levels of heat
flux and hence calculated HTC values for the imposed operating
conditions. Consequently, for a given set of processing
conditions, certain tubes provide a higher level of heat transfer
efficiency than other tubes. In general terms, observations on the
effects of tube dimensions on HTC are summarised in Table 4.15.
Experimental Program 107
Table 4.15 General observations for tube dimensions that provided higher levels
of heat transfer coefficient for the three brix levels
Juice brix Favoured tube length, m Favoured tube diameter, mm
20 2, 3 and 4 38.1 and 44.45
35 3 and 4 44.45
70 2 44.45 and 50.8
• For tests at Brix-20 the maximum heat flux was obtained for the test at
the highest ∆T. This corresponded to the test at the lower headspace
pressure and larger pressure difference. However, for the tests at Brix-
35 and Brix-70, the maximum heat flux was at the higher headspace
pressure and larger pressure difference. This corresponded to the second
highest ∆T. The difference in these results is attributed to the stronger
dependence of HTC on juice viscosity at higher juice brix values.
Consequently, for the tests at Brix-35 and Brix-70, the effect of juice
boiling temperature on juice viscosity has a greater effect on heat flux
and the calculated HTC than the ∆T.
• For tests at Brix-20, Brix-35 and Brix-70 the maximum HTC was
obtained for the tests at the higher headspace pressure (i.e. higher boiling
temperature).
4.9 Concluding Remarks
The experimental program was designed to investigate the effect of tube
dimensions and operating conditions on heat transfer performance of a single tube in
a rising film evaporator rig. The selection of the experimental factors, the design of the
experiments and the experimental procedure are explained in detail.
An analysis of potential errors was undertaken to ensure that the measured
condensate flow rates on the heating tube were reliable, before determining the heat
transfer coefficient and vapour condensation coefficient. A thorough investigation was
carried out to determine if there was any evidence that the high condensate flow rate
to the base of the steam chest was the result of condensate departing the heating tube
or overflowing gutters. The measured data were investigated from several approaches
to determine if such evidence existed. It was concluded that there was no evidence of
108 Experimental Program
overflowing gutters or condensate separating from the heating tube and falling to the
base of the steam chest.
The most likely explanation for the high condensate flow to the base of the steam
chest was condensate entering with the vapour supply. Vapour entering the steam chest
is dispersed away from the heating tube and the associated condensate would not pass
near the surface of the heating tube.
As well, replicate tests showed very good consistency in the results for the
individual sections of the heating tubes. Consequently, the measured data on the
individual sections of the heating tube are considered to be reliable and suitable for
determination of the overall HTC and investigations of the mechanism of heat transfer
occurring at the individual sections of the heating tube.
An analysis of potential errors in the values of the operating conditions was
conducted. This analysis found that the values of the operating conditions utilised
during the test program were in close agreement with the target values. The analysis
demonstrated that the experimental program was well structured, and the operating
conditions were sufficiently different from each other to allow each factor an
opportunity to alter the heat transfer performance.
Analysis of Heat Transfer Coefficient Results 109
CHAPTER 5: ANALYSIS OF HEAT
TRANSFER COEFFICIENT
RESULTS
5.1 Introductory remarks
This section discusses in detail the HTC results from the experiments described
in Chapter 4. The preliminary assessment of the results in Chapter 4 demonstrated the
existence of an optimum juice level, which provided the maximum HTC value for a
given tube and operating conditions. For a given set of operating conditions, particular
tubes provided better heat transfer performance. In this chapter, the Replicate128
results are firstly compared with the Original432 results, in order to increase the
confidence in the Original432 dataset. The Original432 dataset are analysed in detail.
For both datasets, analysis of variance was undertaken with the two response factors
HTC and VCC. The optimum juice level (JLopt %) corresponding to the maximum
HTC value for a given set of conditions (HTCmax) was selected and this new response
factor analysed. Empirical models for HTCmax and JLopt(mm) were developed4. The
section concludes with identifying the tube dimensions that provide the strongest heat
transfer performance for different effect positions in a quintuple set.
Appendix C presents the detailed experimental results from the Original432 tests
and Appendix D presents the results from the Replicate128 tests. Appendix E provides
the results for the optimum juice level, HTCmax and VCCmax values for the Original432
datasets.
5.2 Features of the Pilot Evaporator Rig that may affect HTC Results
5.2.1 Influence of clean and new tubes
Industry experience has shown that brand new tubes have higher heat transfer
performance than tubes that have been in service for some time, even after cleaning.
Chemical cleaning of evaporators with caustic soda solution is commonly undertaken
4 JLopt (%) is the juice level expressed as % of the tube height whereas JLopt (mm) is the juice level
expressed absolute length (mm).
110 Analysis of Heat Transfer Coefficient Results
with reasonably good results, but the tubes are never entirely clean. The tubes
purchased for the pilot evaporator were brand new tubes and after each day of testing,
the evaporator was thoroughly boiled with water. It was expected that the calculated
heat transfer coefficients for the pilot evaporator would be higher than for industrial
evaporators, because of the extremely clean tube surface.
5.2.2 Effect of gutters on the tube
The tubes fabricated for the experimental investigations had gutters between the
four sections to allow the condensate flow of each section to be collected separately.
This arrangement changes the film thickness of the condensate when compared to a
tube of the same length without the gutters, such as for an industrial tube. Figure 5.1
shows the schematic representation of condensate pattern for tubes in the experimental
configuration and for industrial tubes.
Figure 5.1 Schematic representation of condensate pattern on the outside of the
heating tube for experimental and industrial arrangements
Industrial tube
condensate
collection Experimental Rig
tube condensate
collection
L
l
Analysis of Heat Transfer Coefficient Results 111
The average film thickness on an industrial tube would be thicker than on the
tube in the experimental rig for the same vapour condensation rate. The thinner
condensate film in the experimental rig will reduce the resistance to heat transfer on
the steam side and slightly enhance the overall heat transfer efficiency. However, the
effect is likely to be relatively small, as the resistance to heat transfer for the
condensate film is much lower than the thermal resistance on the juice side (Peacock,
2001).
5.2.3 Effect of the downtake
All tests were undertaken with the downtake line open. There was no facility for
measuring the flowrate of juice returning to the juice tank through the external
downtake.
As discussed in section 2.6.4, mini-downtakes in sugar mill evaporators reduce
the liquid head above the top tube plate and increase HTC (Watson, 1986b; Wright et
al., 2003). Industrial evaporators typically have one mini-downtake for ~400 tubes and
for a calandria comprising M2 heating tubes, the average distance from a heating tube
to the edge of the downtake is ~200 mm and the ratio of downtake cross-sectional area
to total heating tube cross-sectional area is 0.034. The pilot evaporator had one
downtake for one tube. For the M2 tube in the pilot evaporator, the distance from the
edge of the heating tube to the edge of the downtake is ~55 mm and the ratio of
downtake cross-sectional area to total heating tube cross-sectional area is 0.14. As a
consequence, it is likely that, compared with an industrial evaporator, a greater
proportion of the pool of juice above the top tube plate returned to the juice tank
through the downtake line, as opposed to running down inside the heating tube. These
changes are expected to have a positive effect on the heat transfer performance.
5.2.4 Comparison of industrial and pilot evaporator HTC values
In this section, the HTC results from the single-tube evaporator rig are compared
with industrial results. The Australian industry predominantly uses M2 tube dimension
for all stages of evaporation. Hence the HTC data for other tube dimensions for
industrial vessels are not readily available.
Figure 5.2 shows the industrial and pilot evaporator HTC values for the M2 tube
dimension. The industrial evaporator HTC values are acquired from Broadfoot (2013).
112 Analysis of Heat Transfer Coefficient Results
It is to be noted that the industrial HTC values are for different evaporator sets
operating under different conditions e.g. vapour bleeding schemes.
It is evident from Figure 5.2 that the pilot evaporator HTC values are slightly
higher than for the industrial vessels, especially for 1st effect conditions. For the 3rd
and 5th effect conditions, HTC values for both the pilot evaporator and industrial
vessels are in close proximity. Most importantly, the HTC values for both the
evaporators show the same trend with brix, temperature difference and juice
temperature.
Effect number
0 1 2 3 4 5 6
HT
C (
W/m
2/K
)
0
1000
2000
3000
4000
5000
6000
Industrial
Pilot evaporator
Brix
10 20 30 40 50 60 70 80
HT
C (
W/m
2/K
)
0
1000
2000
3000
4000
5000
6000
Temperature difference (oC)
0 10 20 30 40 50 60 70
HT
C (
W/m
2/K
)
0
1000
2000
3000
4000
5000
6000
Juice temperature (oC)
20 40 60 80 100 120 140
HT
C (
W/m
2/K
)
0
1000
2000
3000
4000
5000
6000
Figure 5.2 Comparison of industrial and pilot evaporator HTC values for the
M2 tube dimension
Analysis of Heat Transfer Coefficient Results 113
5.2.5 Concluding remarks
The HTC results achieved with the single tube evaporator are expected to be
higher than those calculated in industrial evaporators owing to the positive effects on
heat transfer efficiency of using new tubes, removing condensate at four sections from
the tube, the closeness of the downtake and having a relatively larger cross-sectional
area of the downtake. Of these factors, it is likely that the closeness and larger relative
downtake area would affect the boiling mechanism inside the tube to the greatest
extent.
While the HTC and VCC results for the tube in the experimental rig are expected
to be greater than an industrial tube of the same dimensions operating under the same
processing conditions, the relative performance data of the tubes with different
dimensions are expected to be valid and transferrable to performance in industrial
evaporators.
5.3 Visual Observations of Boiling Patterns
5.3.1 Introductory remarks
The headspace of the single tube evaporator was fitted with a sight glass, which
allowed the movement of juice and froth above the top tube plate to be observed. In
industrial evaporators, the preferred boiling conditions generally show a vigorous
boiling juice and froth layer above the top plate for a height of 200 to 300 mm. The
boiling behaviours in the experimental rig were noted while conducting the
experiments and are presented in Appendix C. This section describes the three boiling
patterns observed.
5.3.2 No visible juice head above top plate
For a few tests, boiling juice was not evident above the top tube plate. This
behaviour was described as ‘no visible juice head’. Analysis of the data later confirmed
that for these tests, HTC was very low. One example where this behaviour was
observed was for Brix-70 juice in a 4 m tube with low ∆T.
5.3.3 Visible juice head above top plate
When the juice was consistently slightly above the top tube plate, this scenario
was described as ‘visible juice head’. Of the three boiling behaviours, this behaviour
114 Analysis of Heat Transfer Coefficient Results
was observed more frequently. When this behaviour was observed, good heat transfer
performance (high HTC) was generally calculated.
5.3.4 Substantial juice head above top plate
Where the juice was consistently boiling at a height of 50 mm to 250 mm above
the top tube plate, this behaviour was defined as ‘substantial juice head’. These tests
reported the highest HTC values and often included the tests at the optimum juice level
in the tube, which corresponds to maximum HTC.
5.4 Overview of the results
The results from the experimental investigation are summarised in this section.
The section provides an overview of the HTC results for all tube dimensions, for the
three brix levels, which are known to significantly affect HTC.
The average values of the overall HTC obtained for each tube for the three brix
values are shown in Table 5.1. The data show the usual trend observed in factory
evaporators, of higher HTC values at lower juice brix and much lower values at Brix-
70 (typical of the final factory evaporator). The values are of the same magnitude as
usually experienced in factory evaporators. However, it must be remembered that
these data include HTC values for operation with non-optimum juice levels and these
would depress the HTC below those normally encountered in industrial evaporators.
Table 5.1 Average values for overall HTC for all tube dimensions with Brix-20,
Brix-35 and Brix-70
Tube Brix-20
(W/m2/K)
Brix-35
(W/m2/K)
Brix-70
(W/m2/K)
S2 ~3000 ~700 ~200
S3 ~3500 ~2000 ~350
S4 ~3500 ~500 ~200
M2 ~3500 ~1700 ~400
M3 ~2500 ~1100 ~150
M4 ~3000 ~2200 ~250
L2 ~2500 ~1500 ~400
L3 ~2500 ~1000 ~200
L4 ~800 ~400 ~100
Analysis of Heat Transfer Coefficient Results 115
5.5 Comparison of Original432 and Replicate128 Results for the Overall HTC
5.5.1 Introductory remarks
As mentioned in section 4.3, the replicates were undertaken to determine if a
tube length and tube diameter interaction was significant and to check the consistency
of data from repeat tests. The replicate tests were undertaken for four tubes viz., M2,
S2, M3 and S3 at the boiling conditions for juice at Brix-20 and Brix-70. This section
compares the results from the Original432 and Replicate128 datasets.
The results for Brix-20 and Brix-70 are discussed below. For each tube, the
boiling tests were undertaken for two headspace pressures, two pressure differences
and four juice levels. For each plot shown below, these boiling conditions are shown,
as is the ∆T.
5.5.2 HTC vs juice level results for M2 tube
Figure 5.3 shows the HTC vs juice level plots for the M2 tube for the
Original432 and Replicate128 datasets for juice at Brix-20 and Brix-70. The patterns
of HTC versus juice level for each of the tests are similar.
Table 5.2 shows the comparison of the HTCmax and optimum juice level for the
Original432 and Replicate128 datasets for M2 tube. The juice levels corresponding to
the maximum HTC are similar for the two datasets. The maximum HTC values
however, are different for some tests for the two datasets. In most cases, the
Replicate128 dataset shows lower HTC than the Original432 dataset.
One item of rate in is the high HTC value of M2 tube at Brix-70 for juice level
of 45% compared with the other three juice levels for both the Original432 and
Replicate128 datasets. This high value was discussed in section 4.7.
116 Analysis of Heat Transfer Coefficient Results
Table 5.2 Comparison of data for Original432 and Replicate128 for M2 tube
Brix Headspace
Pressure
(kPa abs)
Pressure
difference
(kPa)
Temperature
difference
(°C)
Optimum juice
level (% tube
height)
HTCmax (W/m2/K)
Org432 Rep128 Org432 Rep128
20 149 33 5.6 40 40 5509 4958
149 45 7.7 40 40 5663 5097
126 33 6.5 30 30 4835 2655
126 45 8.6 30 50 2639 4506
70 29 42 17.6 45 45 625 548
29 60 23.6 30 30 557 546
22 42 22.2 45 45 934 878
22 60 28.8 70 70 478 821
Analysis of Heat Transfer Coefficient Results 117
Original (20 brix)
Juice level (%tube height)
15 20 25 30 35 40 45 50 55
HT
C (
W/m
2/K
)
0
1000
2000
3000
4000
5000
6000
HS:149/DP:33/DT:5.6 oC
HS:149/DP:45/DT:7.7 oC
HS:126/DP:33/DT:6.5 oC
HS:126/DP:45/DT:8.6 oCReplicate (70 brix)
Juice level (%tube height)
20 30 40 50 60 70 80
HT
C (
W/m
2/K
)
0
200
400
600
800
1000
Original (70 brix)
Juice level (%tube height)
20 30 40 50 60 70 80
HT
C (
W/m
2/K
)
0
200
400
600
800
1000
HS:29/DP:42/DT:17.6 oC
HS:29/DP:60/DT:23.6 oC
HS:22/DP:42/DT:22.2 oC
HS:22/DP:60/DT:28.8 oC
Replicate (20 brix)
Juice level (%tube height)
15 20 25 30 35 40 45 50 55
HT
C (
W/m
2/K
)
0
1000
2000
3000
4000
5000
6000
Figure 5.3 Relationship between HTC and juice level for the M2 tube
5.5.3 HTC vs juice level results for S2 tube
Figure 5.4 shows the HTC vs juice level plots for the S2 tube for the Original432
and Replicate128 datasets for juice at Brix-20 and Brix-70. The patterns of HTC versus
juice level for each of the tests are similar.
Table 5.3 shows the comparison of the HTCmax and optimum juice level for the
Original432 and Replicate128 datasets for S2 tube. The juice levels corresponding to
the maximum HTC are similar for the two datasets. There is good agreement between
118 Analysis of Heat Transfer Coefficient Results
the values for the HTCmax and optimum juice level values for the Original432 and
Replicate128 datasets.
Table 5.3 Comparison of data for Original432 and Replicate128 for S2 tube
Brix Headspace
Pressure
(kPa abs)
Pressure
difference
(kPa)
Temperature
difference
(°C)
Juice level (%
tube height)
HTCmax (W/m2/K)
Org432 Rep128 Org432 Rep128
20 149 33 5.6 30 30 4661 4772
149 45 7.7 30 30 4152 4270
126 33 6.5 30 30 4938 5075
126 45 8.6 40 40 5225 5142
70 29 42 17.6 70 70 453 482
29 60 23.6 70 70 444 477
22 42 22.2 55 55 535 539
22 60 28.8 70 70 546 589
Analysis of Heat Transfer Coefficient Results 119
Original (20 brix)
Juice level (%tube height)
15 20 25 30 35 40 45 50 55
HT
C (
W/m
2/K
)
0
1000
2000
3000
4000
5000
6000
HS:149/DP:33/DT:5.6 oC
HS:149/DP:45/DT:7.7 oC
HS:126/DP:33/DT:6.5 oC
HS:126/DP:45/DT:8.6 oCReplicate (70 brix)
Juice level (%tube height)
20 30 40 50 60 70 80
HT
C (
W/m
2/K
)
0
200
400
600
800
1000
Original (70 brix)
Juice level (%tube height)
20 30 40 50 60 70 80
HT
C (
W/m
2/K
)
0
200
400
600
800
1000
HS:29/DP:42/DT:17.6 oC
HS:29/DP:60/DT:23.6 oC
HS:22/DP:42/DT:22.2 oC
HS:22/DP:60/DT:28.8 oC
Replicate (20 brix)
Juice level (%tube height)
15 20 25 30 35 40 45 50 55
HT
C (
W/m
2/K
)
0
1000
2000
3000
4000
5000
6000
Figure 5.4 Relationship between HTC and juice level for the S2 tube
5.5.4 HTC vs juice level results for M3 tube
Figure 5.5 shows the HTC vs juice level plots for the M3 tube for the
Original432 and Replicate128 datasets for juice at Brix-20 and Brix-70. The patterns
of HTC versus juice level for each of the tests are similar.
Table 5.4 shows the comparison of the HTCmax and optimum juice level for the
Original432 and Replicate128 datasets for M3 tube. There is good agreement between
the values for the HTCmax and optimum juice level values for the Original432 and
Replicate128 datasets.
120 Analysis of Heat Transfer Coefficient Results
Table 5.4 Comparison of Original432 and Replicate128 for M3 tube
Brix Headspace
Pressure
(kPa abs)
Pressure
difference
(kPa)
Temperature
difference
(°C)
Juice level (%
tube height)
HTCmax (W/m2/K)
Org432 Rep128 Org432 Rep128
20 149 33 5.6 30 30 4343 4227
149 45 7.7 30 30 4084 3971
126 33 6.5 50 50 3620 3529
126 45 8.6 30 30 4459 4335
70 29 42 17.6 70 70 454 431
29 60 23.6 70 70 337 320
22 42 22.2 45 45 197 217
22 60 28.8 45 45 231 254
Analysis of Heat Transfer Coefficient Results 121
Original (20 brix)
Juice level (%tube height)
15 20 25 30 35 40 45 50 55
HT
C (
W/m
2/K
)
0
1000
2000
3000
4000
5000
6000
HS:149/DP:33/DT:5.6 oC
HS:149/DP:45/DT:7.7 oC
HS:126/DP:33/DT:6.5 oC
HS:126/DP:45/DT:8.6 oC Replicate (70 brix)
Juice level (%tube height)
20 30 40 50 60 70 80
HT
C (
W/m
2/K
)
0
200
400
600
800
1000
Original (70 brix)
Juice level (%tube height)
20 30 40 50 60 70 80
HT
C (
W/m
2/K
)
0
200
400
600
800
1000
HS:29/DP:42/DT:17.6 oC
HS:29/DP:60/DT:23.6 oC
HS:22/DP:42/DT:22.2 oC
HS:22/DP:60/DT:28.8 oC
Replicate (20 brix)
Juice level (%tube height)
15 20 25 30 35 40 45 50 55
HT
C (
W/m
2/K
)
0
1000
2000
3000
4000
5000
6000
Figure 5.5 Relationship between HTC and juice level for the M3 tube
5.5.5 HTC vs juice level results for S3 tube
Figure 5.6 shows the HTC vs juice level plots for the S3 tube for the Original432
and Replicate128 datasets for juice at Brix-20 and Brix-70. The patterns of HTC versus
juice level for each of the tests are similar.
Table 5.5 shows the comparison of the HTCmax and optimum juice level for the
Original432 and Replicate128 datasets for S3 tube. There is good agreement between
the values for the HTCmax and optimum juice level values for the Original432 and
Replicate128 datasets.
122 Analysis of Heat Transfer Coefficient Results
Table 5.5 Comparison of Original432 and Replicate128 for S3 tube
Brix Headspace
Pressure
(kPa abs)
Pressure
difference
(kPa)
Temperature
difference
(°C)
Juice level (%
tube height)
HTCmax (W/m2/K)
Org432 Rep128 Org432 Rep128
20 149 33 5.6 40 40 4221 4010
149 45 7.7 40 40 3749 3561
126 33 6.5 20 20 4133 3846
126 45 8.6 20 20 3867 3598
70 29 42 17.6 70 70 539 593
29 60 23.6 55 55 427 448
22 42 22.2 45 45 466 443
22 60 28.8 55 55 385 404
Analysis of Heat Transfer Coefficient Results 123
Original (20 brix)
Juice level (%tube height)
15 20 25 30 35 40 45 50 55
HT
C (
W/m
2/K
)
0
1000
2000
3000
4000
5000
6000
HS:149/DP:33/DT:5.6 oC
HS:149/DP:45/DT:7.7 oC
HS:126/DP:33/DT:6.5 oC
HS:126/DP:45/DT:8.6 oCReplicate (70 brix)
Juice level (%tube height)
20 30 40 50 60 70 80
HT
C (
W/m
2/K
)
0
200
400
600
800
1000
Original (70 brix)
Juice level (%tube height)
20 30 40 50 60 70 80
HT
C (
W/m
2/K
)
0
200
400
600
800
1000
HS:29/DP:42/DT:17.6 oC
HS:29/DP:60/DT:23.6 oC
HS:22/DP:42/DT:22.2 oC
HS:22/DP:60/DT:28.8 oC
Replicate (20 brix)
Juice level (%tube height)
15 20 25 30 35 40 45 50 55
HT
C (
W/m
2/K
)
0
1000
2000
3000
4000
5000
6000
Figure 5.6 Relationship between HTC and juice level for the S3 tube
Figure 5.3 to Figure 5.6 shows very strong replication of the profiles of HTC
versus juice level in the two datasets.
For many tests, the variation of HTC with juice level was not a consistent,
gradually changing variation, but often quite discontinuous. This result is unexpected
but interestingly, is replicated closely in the two datasets.
124 Analysis of Heat Transfer Coefficient Results
Two interesting observations are made:
• Brix-20 and M2 tubes: The general pattern is a faster decline in HTC at
juice levels below the optimum compared with juice levels above the
optimum. This pattern agrees with the observations of Broadfoot and
Dunn (2007) for their work on M2 tubes.
• Brix-20 and S2 tubes: The general pattern is a faster decline in HTC at
juice levels above the optimum compared with juice levels below the
optimum i.e. opposite behaviour than for the M2 tubes at Brix-20.
5.5.6 Concluding Remarks
Comparisons of the HTC versus juice level patterns for the Original432 and
Replicate128 datasets show very similar patterns for the four tables and test conditions
at Brix-20 and Brix-70.
The juice levels corresponding to the maximum HTC are the same for the two
datasets for the S2, M3 and S3 tubes and for all except one set of conditions for the
M2 tube. There is good agreement for the values of HTCmax between the two datasets
for S2, M3 and S3 tubes. For some unknown reasons, the HTCmax value for the M2
tube is more variable than for the S2, M3 and S3 tubes.
The good repeatability of the HTC patterns shown in replicate datasets increases
the confidence in the results obtained. The consistency of the results between the two
datasets suggests that juice properties, such as surface tension variation, were not
influencing the heat transfer performance and the boiling juice pattern to a large extent.
It is noted from the HTC versus juice level patterns that headspace pressure and
pressure difference (and corresponding ∆T) also affect the optimum juice level and the
maximum HTC. The effects of operating conditions on HTCmax and optimum juice
level are investigated further in the chapter.
5.6 Analysis of the Results of the Original432 Tests
5.6.1 Introductory remarks
This section describes the analysis of variance for the Original432 tests for HTC.
The section details the main effects and interactions affecting the HTC for the nine
tubes.
Analysis of Heat Transfer Coefficient Results 125
Figure 5.7 shows the mean values of HTC for each of the experimental factors
at each level. It was found that tube length and tube diameter alone do not affect the
HTC significantly. The most important factor affecting HTC was brix of the juice. As
expected from industrial experience, higher HTC was achieved at lower brix and HTC
was lower at higher brix.
Figure 5.7 Mean values of HTC for each level of each factor for the Original432
tests with all results included
Table 5.6 presents the analysis of variance of HTC. The ANOVA is undertaken
for split-split-plot design, with whole plot for tube dimensions, sub-plot for brix and
juice level and sub-sub-plot for headspace pressure and pressure difference. The same
procedure is applied for all ANOVA for all datasets. Significant interactions were
achieved up to 4th order. Two main factors (B, HS), three 2nd order interactions (B:HS,
TD:B, TD:JL), two 3rd order interaction (TL:TD:B, TL:TD:HS) and one 4th order
interaction (TL:TD:B:HS) were identified with a level of significance less than 0.05.
The lower order interaction identified as significant is included in the higher order
interaction.
126 Analysis of Heat Transfer Coefficient Results
Table 5.6 Analysis of variance of HTC from Original432 tests with 4th order
interactions
Source
Degrees of
freedom
Mean
square
Variance
ratio
Significance
level
TL 2 6562399 0.69 –
TD 2 21762038 2.28 –
Residuals 4 9548502
B 2 230647154 245.15 0.000
JL 3 2569618 2.73 –
TL:B 4 1868540 1.99 –
TL:JL 6 890671 0.95 –
TD:B 4 9562815 10.16 0.000
TD:JL 6 3354494 3.57 0.011
B:JL 6 2106656 2.24 –
TL:TD:B 8 3278353 3.48 0.008
TL:TD:JL 12 1005306 1.07 –
TL:B:JL 12 789134 0.84 –
TD:B:JL 12 1666036 1.77 –
Residuals 24 940844
HS 1 5271514 15.17 0.000
ΔP 1 264281 0.76 –
TL:HS 2 947255 2.73 –
TL:ΔP 2 65834 0.19 –
TD:HS 2 96601 0.28 –
TD:ΔP 2 96802 0.28 –
B:HS 2 3138628 9.03 0.000
B:ΔP 2 858313 2.47 –
JL:HS 3 273703 0.79 –
JL:ΔP 3 46677 0.13 –
HS:ΔP 1 46190 0.13 –
TL:TD:HS 4 1389868 4.00 0.004
TL:TD:ΔP 4 179391 0.52 –
TL:B:HS 4 564882 1.63 –
TL:B:ΔP 4 1091752 3.14 –
TL:JL:HS 6 748109 2.15 –
TL:JL:ΔP 6 166142 0.48 –
TL:HS:ΔP 2 832428 2.40 –
TD:B:HS 4 1148956 3.31 –
TD:B:ΔP 4 383181 1.10 –
TD:JL:HS 6 467756 1.35 –
Analysis of Heat Transfer Coefficient Results 127
Source
Degrees of
freedom
Mean
square
Variance
ratio
Significance
level
TD:JL:ΔP 6 187437 0.54 –
TD:HS:ΔP 2 281050 0.81 –
B:JL:HS 6 404672 1.16 –
B:JL:ΔP 6 74783 0.22 –
B:HS:ΔP 2 76723 0.22 –
JL:HS:ΔP 3 565762 1.63 –
TL:TD:B:HS 8 1172778 3.38 0.002
TL:TD:B:ΔP 8 298091 0.86 –
TL:TD:JL:HS 12 360754 1.04 –
TL:TD:JL:ΔP 12 164010 0.47 –
TL:TD:HS:ΔP 4 286797 0.83 –
TL:B:JL:HS 12 244066 0.70 –
TL:B:JL:ΔP 12 242668 0.70 –
TL:B:HS:ΔP 4 384196 1.11 –
TL:JL:HS:ΔP 6 96163 0.28 –
TD:B:JL:HS 12 320568 0.92 –
TD:B:JL:ΔP 12 258218 0.74 –
TD:B:HS:ΔP 4 455442 1.31 –
TD:JL:HS:ΔP 6 497655 1.43 –
B:JL:HS:ΔP 6 613441 1.77 –
Residuals 116 347431
5.6.2 TL:TD:B:HS interaction plot
Figure 5.8 presents the TL:TD:B:HS interaction plot. The headspace pressure
“HS1” represents boiling at higher headspace pressure and “HS2” represents boiling
at lower headspace pressure. The headspace pressures corresponding to the brix are
presented in Table 4.2, Table 4.3 and Table 4.4.
128 Analysis of Heat Transfer Coefficient Results
Figure 5.8 TL:TD:B:HS interaction plot for the Original432 dataset
It is observed from Figure 5.8 that higher brix results in lower HTC. It is known
that higher boiling temperature (higher headspace pressure) results in higher HTC
(Broadfoot & Dunn, 2007). The results from the Original432 dataset show that there
is an effect of headspace pressure on HTC, but the effect is not consistent through the
full dataset. The choice of headspace pressure values for the three brix values could be
the possible cause for the inconsistency.
Figure 5.9 shows TL:TD:B:HS interaction with the dataset split in brix values and
headspace pressure. The rows show the three brix values and the columns show the
two headspace pressure. The following conclusions are drawn from Figure 5.9:
• 2 m tube length, higher HTC was achieved at 44.45 mm OD
• 3 m tube length, higher HTC was achieved at 38.1 mm OD
• 4 m tube length, higher HTC was achieved at 44.45 mm OD
Analysis of Heat Transfer Coefficient Results 129
Figure 5.9 TL:TD:B:HS interaction plot for the Original432 dataset with
separate plots for brix and headspace pressure
5.6.3 TD:JL interaction plot
Figure 5.10 shows the TD:JL interaction plot. The four juice levels for the three
brix values were different. Given the inconsistency in the effect of headspace pressure,
it makes sense to look at the juice level effects for different brix.
Figure 5.11 shows the TD:JL interaction plot for each of the three brix values on
separate plots. It is observed that for Brix-20, the highest HTC is achieved at 30% juice
level for 38.1 and 44.45 mm tube diameter tubes. For 50.8 mm tube diameter, the
highest HTC is achieved at juice level of 40% tube height (10% higher than for 38.1
and 44.45 mm).
For Brix-35, juice level does not show a strong effect on HTC for 38.1 mm tube
diameter up to 45% juice level. There is drop in HTC for juice level higher than 45%.
The data for the 50.8 mm tube diameter tube show the highest HTC occurs at 35%
juice level. The 44.45 mm tube diameter shows the highest HTC at juice level of 60%
tube height.
130 Analysis of Heat Transfer Coefficient Results
For Brix-70, highest HTC is achieved at a juice level of 70% tube height for all
the tube diameters.
Figure 5.10 TD:JL interaction plot for the Original432 dataset
Figure 5.11 TD:JL interaction for the Original432 dataset with three separate
plots for brix
Analysis of Heat Transfer Coefficient Results 131
5.6.4 Concluding remarks
The analysis of variance of HTC for the Original432 dataset has been discussed
in this section. It was found that brix is the most dominating factor affecting HTC.
Tube length and tube diameter interaction was found to be significant. It was
concluded that for 2, 3 and 4 m tube length, 44.45, 38.1 and 44.45 mm tube diameters
respectively showed higher HTC than the other tube dimensions. The effects of juice
level and headspace pressure on HTC were not consistent amongst the dataset.
5.7 Analysis of HTCmax Results
5.7.1 Introductory remarks
For each brix, HTC was calculated at four juice levels, of which one juice level
was found to be the optimum juice level. This optimum juice level corresponds to
HTCmax. Two methods were used in determining the HTCmax. This section details the
methods used for determining HTCmax, the ANOVA and the significant interactions
for HTCmax for the Original432 and Replicate128 datasets.
5.7.2 Method for HTCmax selection
With Method 1, the HTCmax was selected by identifying the maximum HTC
value on the graphs. With Method 2, polynomial regressions were plotted with the
HTC and VCC against the juice level to identify the curve of the regression. The
polynomial regression was used to determine the HTC at juice level values not tested
(below 20% and above 70%). The results between both methods were similar. An
analysis of variance was undertaken to test the differences, and this showed the same
conclusion. Hence, Method 1 was selected in determining the HTCmax results.
5.7.3 HTCmax results
The HTCmax results are presented for the Original432 dataset. The Original432
dataset contains 108 HTCmax results. Figure 5.12 shows the mean values of HTCmax
for all the experimental factors at each level. It is evident from Figure 5.12 that brix
has the most significant effect on HTCmax.
132 Analysis of Heat Transfer Coefficient Results
Figure 5.12 Mean values of HTCmax for each level of each factor from the
Original432 tests (108 data points)
Table 5.7 shows the analysis of variance of HTCmax for the Original432 dataset.
Two main effects (B, HS) and one 3rd order interaction (TD:B:HS) were identified with
significance level less than 0.05.
Analysis of Heat Transfer Coefficient Results 133
Table 5.7 Analysis of variance of HTCmax from Original432 tests
Source
Degrees of
freedom
Mean
square
Variance
ratio
Significance
level
TL 2 7605799 4.31 –
TD 2 9027073 5.12 –
Residuals 4 1763889
B 2 96679890 62.58 0.000
TL:B 4 1356587 0.88 –
TD:B 4 3724704 2.41 –
Residuals 8 1544845 – –
HS 1 1284893 4.38 0.043
ΔP 1 794988 2.71 –
TL:HS 2 471666 1.61 –
TL:ΔP 2 132652 0.45 –
TD:HS 2 735357 2.51 –
TD:ΔP 2 29695 0.10 –
B:HS 2 774050 2.64 –
B:ΔP 2 442284 1.51 –
HS:ΔP 1 16133 0.05 –
TL:TD:HS 4 509971 1.74 –
TL:TD:ΔP 4 169562 0.58 –
TL:B:HS 4 222860 0.76 –
TL:B:ΔP 4 356036 1.21 –
TL:HS:ΔP 2 947662 3.23 –
TD:B:HS 4 1087098 3.70 0.013
TD:B:ΔP 4 263404 0.90 –
TD:HS:ΔP 2 31442 0.11 –
B:HS:ΔP 2 24413 0.08 –
Residuals 36 293421
Figure 5.13 presents the TD:B:HS interaction plot. For Brix-20 higher HTC is
achieved for tubes of 38.1 and 44.45 mm diameter. For Brix-35 and Brix-70, higher
HTCmax is achieved for tubes of 44.45 mm diameter.
For tubes of 38.1 mm OD, the headspace pressure has negligible influence on
the HTCmax whereas for the tubes of 44.45 mm and 50.8 mm OD, the higher headspace
pressure provides substantially higher values of HTCmax. The one exception to this is
the tube of 50.8 mm OD at 35 brix.
134 Analysis of Heat Transfer Coefficient Results
In the ANOVA for HTC with the Original432 dataset, TL;TD:B:HS interaction
was found to be significant. However, for the HTCmax tube diameter is identified to be
significant. This concludes that tube diameter is a more important dimension than tube
length in influencing HTCmax.
Figure 5.13 TD:B:HS interaction for HTCmax for the Original432 dataset
5.7.4 Concluding remarks
The HTCmax results are presented and the interactions of operating conditions on
HTCmax are discussed. It was concluded that higher brix results in lower HTCmax. Tube
diameter is more important than tube length in influencing HTCmax. For tubes of
38.1 mm diameter, headspace pressure has little influence on HTCmax. For tubes of
44.45 and 50.8 mm diameter, higher headspace pressure generally provides
substantially higher values of HTCmax.
5.8 Analysis of Optimum Juice Level
5.8.1 Introductory remarks
The operation of the evaporator with optimum juice level is imperative in order
to achieve maximum heat transfer performance. Sugar factory staff usually operates
Analysis of Heat Transfer Coefficient Results 135
the vessel with a certain dynamic head (juice level above the top tube plate) to ensure
that the tube is fully wetted. This does not necessarily mean that HTCmax is being
achieved. In setting this level, the actual optimum juice level may not be set, but it
ensures that the minimum requirement to fully wet the top of the tube is achieved.
This section describes the interaction of optimum juice level with tube
dimensions, headspace pressure and pressure difference.
5.8.2 Optimum juice level (JLopt(%)) for HTCmax
The optimum juice level corresponding to HTCmax is presented in Appendix E.
Figure 5.14 shows the mean values of the optimum juice level (% tube height) results
for the Original432 tests. It is observed that optimum juice level is lower for lower
brix and increases with increase in brix. This observation agrees closely with practical
experience with industrial Robert evaporators.
Figure 5.14 Mean values of JLopt(%) for each level of each factor from the
Original432 tests (108 data points)
Table 5.8 shows the analysis of variance of optimum juice levels corresponding
to HTCmax from the Original432 dataset. One main source (B), one 2nd order
136 Analysis of Heat Transfer Coefficient Results
interaction (TD:ΔP) and one 3rd order interaction (TL:B:HS) were identified with
significance level than 0.05.
Table 5.8 Analysis of variance of optimum juice level (JLopt-% tube height)
corresponding to HTCmax from the Original432 tests
Source
Degrees of
freedom
Mean
square
Variance
ratio
Significance
level
TL 2 41.89 0.26 –
TD 2 46.06 0.28 –
Residuals 4 163.77
B 2 5381.48 18.27 0.001
TL:B 4 110.65 0.38 –
TD:B 4 587.73 2.00 –
Residuals 8 294.5 – –
HS 1 75 0.84 –
ΔP 1 237.03 2.66 –
TL:HS 2 4.86 0.05 –
TL:ΔP 2 100.23 1.13 –
TD:HS 2 0.69 0.01 –
TD:ΔP 2 321.06 3.60 0.037
B:HS 2 202.77 2.28 –
B:ΔP 2 195.37 2.19 –
HS:ΔP 1 0.92 0.01 –
TL:TD:HS 4 173.26 1.95 –
TL:TD:ΔP 4 24.88 0.28 –
TL:B:HS 4 284.72 3.20 0.024
TL:B:ΔP 4 46.06 0.52 –
TL:HS:ΔP 2 264.12 2.97 –
TD:B:HS 4 190.97 2.14 –
TD:B:ΔP 4 52.31 0.59 –
TD:HS:ΔP 2 143.28 1.61 –
B:HS:ΔP 2 250.92 2.82 –
Residuals 36 89.07
Figure 5.15 shows the TL:B:HS interaction plot for optimum juice level. It is
observed that tube length and headspace pressure do not show consistency in the
results. Hence the effect of tube length and headspace pressure on optimum juice level
is not completely clear.
Analysis of Heat Transfer Coefficient Results 137
Figure 5.15 TL:B:HS interaction plot for the optimum juice level in the
Original432 dataset
Figure 5.16 shows the TD:ΔP interaction plot. At higher pressure differences,
optimum juice level was higher for 38.1 and 50.8 mm tube diameters. However, for
44.45 mm tube diameter, higher pressure difference resulted in lower optimum juice
level. This result is in agreement with factory experience with calandrias of 44.45 mm
tube diameter.
Figure 5.17 shows the TD:ΔP interaction plot with three separate plots for brix. The
data in Figure 5.17 show the following:
For 38.1 mm tube diameter;
• Pressure difference has no effect on optimum juice level at Brix-20
• Optimum juice level increases with increase in pressure difference at Brix-
35 and Brix-70
For 44.45 mm tube diameter;
• Optimum juice level decreases with increase in pressure difference for Brix-
20 and Brix-70
138 Analysis of Heat Transfer Coefficient Results
• Optimum juice increases slightly with increase in pressure difference for
Brix-35
For 50.8 mm tube diameter;
• For all three brix values, optimum juice level increases with increase in
pressure difference.
The reason for the variability in the effect of pressure difference for the different
tube diameters and different juice brix values is not known. However, the effect of
juice level when nominated in terms of the absolute level (in mm) shows a more
consistent pattern of lower optimum juice level for higher pressure difference.
Figure 5.16 TD:ΔP interaction plot for the optimum juice level in the
Original432 dataset
Analysis of Heat Transfer Coefficient Results 139
Figure 5.17 TD:ΔP interaction plot for Original432 dataset for three separate
plots for brix
5.8.3 Concluding remarks
The optimum juice level (as % of tube height) corresponding to maximum HTC
was analysed. It was found that juice at higher brix required higher optimum juice
levels. The effect of tube length and headspace pressure on optimum juice level was
not consistent across the full dataset. It was found that in general, for tubes of 38.1 and
50.8 mm diameter, the optimum juice level increases with increases in pressure
difference while for 44.45 mm tube diameter, optimum juice level decreases with
increase in pressure difference. Among these results there was some variability in the
effect for the different brix values.
5.9 Developing Empirical Relationships
5.9.1 Introductory remarks
Empirical relationships for HTC and optimum juice level were developed by
previous investigators. The relationships have been discussed in section 2.6. This
section describes the empirical relationships developed for HTCmax and optimum juice
level from the Original432 dataset.
140 Analysis of Heat Transfer Coefficient Results
5.9.2 Empirical relationship for HTCmax
An empirical relationship for HTCmax was developed that takes into account
different processing conditions, allowing more reliable simulations of evaporator
stations for energy efficient scenarios to be undertaken. It is to be noted that some
HTCmax results were omitted from the data to develop a regression model valid over a
wide range of operating conditions. For example, HTCmax results of L4 tube were
below average (very poor) for Brix-20 tests. Inclusion of these results would result in
poor regression and lessen the applicability of the regression to industrial scenarios.
Hence these results were not included in the regression model. Table 5.9 shows the list
of parameters considered in the step-wise regression of the model.
Table 5.9 List of parameters considered for inclusion in the empirical model
List of parameters Symbol
Tube length (mm) TL
Tube diameter (mm) TD
Brix B
Headspace pressure (kPa abs) HS
Pressure difference (kPa) ΔP
Tube length × Tube diameter TL:TD
Tube length × Brix TL:B
Tube length × Headspace pressure TL:HS
Tube length × Pressure difference TL:ΔP
Tube diameter × Brix TD:B
Tube diameter × Headspace pressure TD:HS
Tube diameter × Pressure difference TD:ΔP
Brix × Headspace pressure B:HS
Brix × Pressure difference B:ΔP
Headspace pressure × Pressure difference HS:ΔP
Latent heat of steam (kJ/kg) 𝜆𝑆
Temperature of steam (°C) TS
Temperature of juice (°C) TJ
Viscosity of juice (Pa.s) 𝜇
Temperature difference (°C) ΔT
Vapour condensation coefficient (kg/h/m2) VCC
Analysis of Heat Transfer Coefficient Results 141
Step-wise regression was undertaken to determine the parameters in the
empirical model. The best empirical relationship for HTCmax was found to be:
𝐻𝑇𝐶𝑚𝑎𝑥 = 𝐵−0.4901 𝑇𝑗1.3582 𝑉𝐶𝐶0.8877 5.1
where 𝐵 is the brix of the juice,
𝑇𝑗 is the temperature of the juice, °C
𝑉𝐶𝐶 is the vapour condensation coefficient, kg/h/m2
It is important to understand the significance of each of the parameters in the
equation when developing an empirical relationship. As mentioned in section 5.7.3,
brix is the most dominating factor affecting HTCmax followed by headspace pressure.
The temperature of the juice is a function of the headspace pressure in the vessel. As
vapour bleeding changes, VCC values of the effects change and the developed
equation takes this into account when predicting the HTC of the effect. The analysis
of variance of the regression model is shown in Table 5.10.
Figure 5.18 shows the measured and predicted HTCmax. The predictions from the
empirical model provide a good match with measured HTCmax (R2 = 0.94) and are in
agreement with industry values.
Measured HTCmax
(W/m2/K)
0 2000 4000 6000
Pre
dic
ted H
TC
max
(W
/m2/K
)
0
2000
4000
6000
Figure 5.18 Measured and predicted HTCmax
142 Analysis of Heat Transfer Coefficient Results
Table 5.10 Analysis of variance of regression model for HTCmax
Source
Degrees of
freedom
Mean
square
Variance
ratio
Significance
level
B 1 869 109278 0.000
Tj 1 71.26 8959 0.000
VCC 1 2.66 334 0.000
Residuals 89 0.008
It is evident from equation 5.1 that as brix increases, HTCmax decreases and as
temperature of juice and VCC increase, HTCmax increases. Table 5.11 shows examples
of the typical operating conditions in factory vessels and the predicted empirical
HTCmax from two models viz. (Equation 5.1 and Australian Typ as discussed in section
2.6.7 on page 43). The ‘AusTyp’ formula is extensively used for predicting HTC when
undertaking evaporator simulations. The ‘AusTyp’ does not contain the VCC
parameter and shows higher HTC than ‘Equation 5.1’ correlation.
The incorporation of VCC into equation 5.1 is an important inclusion in the
correlation to allow improved simulations of evaporator stations, which incorporate
extensive bleeding of vapour (i.e. for stations that often experience very low VCC
values).
Analysis of Heat Transfer Coefficient Results 143
Table 5.11 Typical operating conditions in factory vessels and the predicted
HTCmax from two models
Brix Temperature of
juice (°C)
VCC (kg/h/m2) HTCmax (W/m2/K)
Equation
5.1
AusTyp
17 115 25 2734 3086
20 115 25 2524 2918
25 115 25 2263 2690
17 110 20 2111 2949
17 110 25 2574 2949
17 110 35 3469 2949
17 110 40 3906 2949
35 105 25 1696 2134
35 100 25 1587 2031
35 95 25 1480 1928
35 100 15 1008 2031
35 100 20 1302 2031
35 100 25 1587 2031
70 60 10 250 733
70 60 15 359 733
70 60 20 463 733
65 60 15 372 805
70 65 15 400 795
70 75 15 486 920
5.9.3 Empirical relationship for optimum juice level (JLopt(mm))
As expected from the assessments of the factors influencing the optimum juice
level (section 5.8.2), the development of a satisfactory empirical relationship for
optimum juice level was difficult. Developing an empirical relationship for juice level
(% tube height) did not give a robust correlation and the model either over-predicted
or under-predicted optimum juice level. However, the empirical relationship
developed with absolute juice level (mm) resulted in a better correlation. The list of
parameters shown in Table 5.9 was considered for inclusion in the model.
Step-wise regression was undertaken to determine the parameters in the
empirical model. The best empirical relationship for optimum juice level (𝐽𝐿𝑜𝑝𝑡 mm)
is given by:
𝐽𝐿𝑜𝑝𝑡 (𝑚𝑚) = 𝑇𝐿0.7253 𝐵0.4544 ΔT−0.1122 5.2
144 Analysis of Heat Transfer Coefficient Results
where 𝑇𝐿 is the tube length, mm
𝐵 is the brix of the juice,
ΔT is the temperature difference between the steam and juice, °C
Figure 5.19 shows the predicted and measured values of JLopt (mm). The data
are differentiated for tubes of 2, 3 and 4 m lengths. The correlation coefficient R2 for
the match of the predicted values is 0.61. The R2 values for 2, 3 and 4 m tube length
are 0.31, 0.36 and 0.39 respectively.
Measured optimum juice level (mm)
0 500 1000 1500 2000 2500 3000
Pre
dic
ted o
ptim
um j
uice
leve
l (m
m)
0
500
1000
1500
2000
2500
3000
Tube length - 2 m
Tube length - 3 m
Tube length - 4 m
Figure 5.19 Measured and predicted optimum juice level
Table 5.12 shows the typical operating conditions in factory vessels and the
predicted optimum juice levels (absolute and %tube height). The predictions for tube
length of 2 m are above the accepted values in the Australian industry but are still in
range. The predictions are in agreement with observations in industrial evaporators.
For example, operation at a higher juice brix given a higher juice level and operation
at a higher temperature difference gives a slightly lower optimum juice level.
Analysis of Heat Transfer Coefficient Results 145
It is noted that the correlation incorporates a tube length term, such that for
longer tubes the optimum juice level (mm) is higher. This result is logical.
Table 5.12 Typical operating conditions in factory vessels and the predicted
optimum juice levels (absolute and % tube height)
Tube
length (m)
Brix ΔT
(°C)
Optimum juice
level (mm)
Optimum juice level (%
tube height)
2000 20 5 807 40
2000 35 6 1020 51
2000 20 7 777 39
2000 35 7 1002 50
2000 70 20 1221 61
2000 70 12 1293 65
3000 70 20 1638 55
3000 70 12 1735 58
3000 15 5 950 32
3000 20 6 1061 35
3000 20 7 1043 35
3000 35 8 1325 44
4000 15 5 1171 29
4000 35 8 1633 41
Despite the confounding results from the analysis for optimum juice level (mm)
in section 5.8.2, the correlation for optimum juice level (mm) has provided
dependencies for brix and ΔT that are in general agreement with the expression in
industrial evaporators with M2 tubes.
5.9.4 Concluding remarks
The empirical equation developed for HTCmax is valid for different tube
dimensions (S2, S3, S4, M2, M3, M4, L2 and L3) over a wide range of operating
conditions. The HTCmax correlation is shown to be a function of brix, juice temperature
and VCC. The predicted HTCmax values are in close agreement to the measured
HTCmax values. The predicted HTCmax values for M2 tubes are in general agreement
with HTCmax values for industrial evaporators with M2 tubes.
An empirical model for optimum juice level (mm) was developed. The optimum
juice level is a function of tube length, brix and temperature difference. The optimum
juice level increases with increase in tube length and brix and decreases with increase
146 Analysis of Heat Transfer Coefficient Results
in temperature difference. The predictions for optimum juice level are also in general
agreement with the experience with industrial evaporators with M2 tubes.
5.10 Concluding Remarks
In this study, an experimental investigation was undertaken to determine the
HTC of different tube lengths and diameters (nine tubes) for different operating
conditions corresponding to those typically experienced at the 1st, 3rd and 5theffects.
Replicates were undertaken for four tubes to understand the tube length and tube
diameter interaction and to determine the consistency in the results.
The replicate HTC results showed very good agreement with the original results,
thus providing confidence in the data for which replicates were not undertaken.
Analysis of the HTC results from the Original432 dataset showed the tube length
and tube diameter interaction to be significant. In other words, the selection of tube
length and tube diameter is not independent of each other in relation to achieving good
heat transfer performance. This result confirms the conclusion made by Hugot and
Jenkins (1986). The replicate analysis confirmed the result. It was concluded that as
brix increases, HTC decreases. For 2, 3 and 4 m tube lengths, tube diameters of 44.45,
38.1 and 44.45 mm respectively gave higher HTC values. The effects of juice level,
headspace pressure and pressure difference on HTC were not consistent through the
complete dataset, although the results indicate that juice level and headspace pressure
influence the HTC.
For many tests, the variation of HTC with juice level was not a consistent,
gradually changing variation, but often quite discontinuous. This result is unexpected
but interestingly replicated closely in the two datasets.
Two interesting observations are made:
• Brix-20 and M2 tubes: The general pattern is a faster decline in HTC at juice
levels below the optimum compared with juice levels above the optimum;
• Brix-20 and S2 tubes: The general pattern is a faster decline in HTC at juice
levels above the optimum compared with juice levels below the optimum i.e.
opposite behaviour than for the M2 tubes at Brix-20.
HTCmax results were determined from the Originla432 dataset. It was concluded
that tube diameter is more important than tube length in affecting HTCmax. This result
Analysis of Heat Transfer Coefficient Results 147
contradicts the statement by Hugot and Jenkins (1986). As brix increases, HTCmax
decreases. For Brix-20, higher HTCmax is achieved for tubes of 38.1 and 44.45 mm
diameter. For Brix-35 and Brix-70, higher HTCmax is achieved for tubes of 44.45 mm
tube diameter. For tubes of 38.1 mm diameter, headspace pressure has little influence
on HTCmax. For tubes of 44.45 and 50.8 mm diameter, higher headspace pressure
generally results in substantially higher values of HTCmax.
Analysis of optimum juice level corresponding to HTCmax showed that as brix
increases, optimum juice level increases. The effect of tube length and headspace
pressure on optimum juice level was not completely clear. There was also large
variability in the effect of pressure difference on the optimum juice level for the
different tube diameters and the different juice brix.
Empirical relationships were developed for HTCmax and optimum juice level
(mm). The empirical relationship for HTCmax showed good agreement with measured
result and industry values for M2 evaporators. The empirical relationship for optimum
juice level showed satisfactory agreement with measured results and the trend of the
predictions from the model was in agreement with industry practice for M2
evaporators.
The analysis of HTCmax assisted in understanding the effect of tube dimensions
and operating conditions on HTCmax. The selection of optimum tube dimensions for
maximum heat transfer coefficient is detailed in Chapter 7. However, it is interesting
enough to state here that the traditional tube dimension M2 was determined to provide
good heat transfer performance for the three effect positions.
Boiling Patterns in the Heating Tube 149
CHAPTER 6: BOILING PATTERNS IN
THE HEATING TUBE
6.1 Introductory Remarks
In Chapter 5, the heat transfer coefficients of the tubes of different lengths and
diameter were analysed. The effects of tube length, tube diameter, juice brix, juice
level, headspace pressure and pressure difference, along with the interaction of these
parameters on HTC, were discussed. It was determined that an optimum juice level
exists, which corresponds to the maximum HTC for each set of test conditions.
The HTCmax results differ with tube length, tube diameter, headspace pressure
and pressure difference for a given juice brix. In order to understand the influence of
operating conditions on the HTCmax results, the HTC values of the individual sections
of the heating tube were investigated in this chapter. This chapter describes the
different patterns of HTC values for the individual sections of the heating tubes and
proposes different boiling mechanisms that may be associated with those HTC
patterns. For example, a test may show low HTC at the bottom section of the tube
while the rest of the tube was boiling with a higher HTC, say close to the overall HTC.
The HTC pattern may provide an insight into the boiling pattern inside the tube.
The variations of the HTC results for the different tube sections and the possible
boiling patterns were examined through a staged process:-
1. The consistency of the HTC patterns was examined by analysing the
results for the corresponding tests in the Original432 and Replicate128
datasets.
2. Identification of the HTC patterns that existed and determination of
which patterns were more common, and under which test conditions.
3. Qualitative determination of the factors influencing the boiling patterns.
4. Analysis of variance of the HTC and HTCmax for the individual sections
of the tubes.
150 Boiling Patterns in the Heating Tube
5. Determination of the predominant boiling pattern when HTCmax values
were achieved and the influence that the various factors have at these
conditions.
6. Postulation of the boiling mechanism in the tube corresponding to the
different HTC patterns.
7. Determination of the boiling patterns in the tube that provides superior
heat transfer performance.
Appendix F presents the HTC results and Appendix G the VCC results for the
individual sections of the tubes for the Original432 dataset. Corresponding results for
the Replicate128 dataset are given in Appendix H and I.
6.2 Comparison of Replicate Results with Original Results for the Section
HTCs
6.2.1 Introductory remarks
In section 5.5, the Replicate128 test results were compared with the Original432
test results. It was found that the overall HTC vs juice level trends for both datasets
were similar. These results very likely indicate that the boiling behaviour inside the
tube was similar for the two datasets at the same test conditions. However, this
assumption needs to be checked by comparing the HTC values for the individual
sections of tubes in the Original432 and Replicate128 datasets.
For each test, the difference between the overall HTC for the whole tube and the
HTC value for each individual section was calculated and allocated to one of three
categories, as shown in Table 6.1. A colour code and number code were assigned to
each category to facilitate the analyses of the data. The 15% variation from the overall
HTC value, which was chosen to define the category, was selected based on the
average error of HTC for 20 Brix, 35 Brix and 70 Brix juice tests. The error was
calculated from the square root of the mean square of the residuals in Table 5.6 and
the highest average HTC from Table 5.1. Section 1 is the top part of the heating tube
and Section 4 is the bottom part of the heating tube.
Boiling Patterns in the Heating Tube 151
Table 6.1 Categories to define differences between the individual section HTC
values and the overall HTC
Factor Higher (>15%
above overall
HTC)
Lower (>15%
below overall
HTC)
Within (15% of
overall HTC)
Colour
Number +1 -1 0
6.2.2 Comparison of the HTC results for individual tube sections for Brix-20 tests
The individual HTC results for tests of four different tubes (M2, S2, M3, S3)
from the Original432 and Replicate128 datasets were assigned to the categories of
Table 6.1. These results are shown in Table 6.2, Table 6.3, Table 6.4 and Table 6.5 for
M2, S2, M3 and S3 tubes respectively for the Brix-20 juice tests. The operating
conditions for each test number shown in the tables are detailed in Appendix C and
Appendix D.
Comparison of the HTC patterns for the Original432 and Replicate128 data for
the same test conditions allows the consistency of the boiling behaviour for each test
to be determined. In each table, the percentages of results lying in each of the three
categories are shown.
For each test at the same operating conditions, the HTC values for each tube
section for the Original432 and Replicate128 datasets were assigned to one of the
categories defined in Table 6.1. If the individual section of the tube had the same
boiling category for the Original432 and Replicate128 datasets, then consistency was
good. If the individual section had boiling category one level apart (either from 0 to 1,
1 to 0, 0 to -1 and -1 to 0), consistency was assumed to be satisfactory. If the individual
section had boiling category two levels apart (either from -1 to 1 or 1 to -1) consistency
was assumed to be poor.
This analysis allowed the consistency of the individual HTC values, relative to
the overall HTC values, to be compared.
Table 6.6 summarises the results from the Brix-20 juice tests for M2, S2, M3,
and S3 tubes (based on the data in Table 6.2, Table 6.3, Table 6.4 and Table 6.5).
152 Boiling Patterns in the Heating Tube
Table 6.2 Individual section HTC comparison with M2 tubes for Brix-20 juice
Test Original432 Replicate128 Test Section
1
Section
2
Section
3
Section
4
Section
1
Section
2
Section
3
Section
4
241 -1 0 1 0 -1 0 1 0 5
242 -1 -1 1 1 -1 -1 1 1 7
243 0 0 1 0 0 0 1 0 6
244 0 -1 0 1 0 -1 0 1 8
277 1 -1 -1 -1 1 -1 -1 -1 25
279 0 0 0 0 0 0 0 0 27
278 0 1 0 -1 0 1 0 -1 26
280 -1 0 0 1 -1 0 0 1 28
260 0 0 0 0 0 0 0 0 9
259 0 0 0 0 0 0 0 0 10
258 0 0 0 0 0 0 0 0 11
257 -1 -1 1 1 -1 -1 1 1 12
284 0 0 0 0 -1 -1 0 1 1
281 0 0 0 0 -1 0 0 1 3
283 -1 0 1 0 -1 0 1 1 2
282 -1 0 0 1 -1 -1 0 1 4 Category Comparison of results (%)
Individual section HTC in same zone 89 Individual section HTC one zone apart 11
Individual section HTC two zones apart 0
Table 6.3 Individual section HTC comparison with S2 tubes for Brix-20 juice
Test Original432 Replicate128 Test Section
1
Section
2
Section
3
Section
4
Section
1
Section
2
Section
3
Section
4
230 -1 -1 -1 1 -1 -1 -1 1 37
231 -1 -1 0 1 -1 -1 0 1 38
232 -1 1 -1 0 -1 1 -1 0 40
219 0 -1 0 1 0 -1 0 1 39
218 0 1 -1 0 0 1 -1 0 57
217 0 1 -1 0 0 1 -1 0 59
220 0 1 -1 0 0 1 -1 0 58
215 -1 0 0 1 -1 0 0 1 60
213 1 0 -1 1 1 0 -1 1 33
214 -1 0 -1 1 -1 0 -1 1 35
216 0 1 -1 0 0 1 -1 0 34
194 0 0 0 0 0 0 0 0 36
193 -1 0 0 1 -1 0 0 1 63
196 -1 -1 -1 1 -1 -1 -1 1 62
195 -1 1 0 0 -1 1 0 0 64
239 -1 -1 0 1 -1 -1 0 1 61 Category Comparison of results (%)
Individual section HTC in same zone 100 Individual section HTC one zone apart 0
Individual section HTC two zones apart 0
Boiling Patterns in the Heating Tube 153
Table 6.4 Individual section HTC comparison with M3 tube for Brix-20 juice
Test Original432 Replicate128 Test Section
1
Section
2
Section
3
Section
4
Section
1
Section
2
Section
3
Section
4
121 -1 1 -1 1 -1 1 -1 1 69
122 -1 -1 -1 1 -1 -1 -1 1 70
124 -1 -1 1 1 -1 -1 1 1 72
123 -1 -1 1 1 -1 -1 1 1 71
102 1 1 0 -1 1 1 0 -1 89
104 0 0 0 -1 0 0 0 -1 91
101 0 1 0 -1 0 1 0 -1 90
103 0 0 0 -1 0 0 0 -1 92
118 -1 0 1 1 -1 0 1 1 65
120 -1 0 -1 1 -1 0 -1 1 67
117 -1 -1 1 1 -1 -1 1 1 66
119 -1 -1 0 1 -1 -1 0 1 68
100 1 1 -1 -1 1 1 -1 -1 95
98 1 1 0 -1 1 1 0 -1 94
97 0 1 0 -1 0 1 0 -1 96
99 0 0 0 -1 0 0 0 -1 93 Category Comparison of results (%)
Individual section HTC in same zone 100 Individual section HTC one zone apart 0
Individual section HTC two zones apart 0
Table 6.5 Individual section HTC comparison with S3 tube for Brix-20 juice
154 Boiling Patterns in the Heating Tube
Test Original432 Replicate128 Test Section
1
Section
2
Section
3
Section
4
Section
1
Section
2
Section
3
Section
4
80 1 0 -1 0 1 0 -1 0 101
79 1 0 -1 0 1 0 -1 0 102
77 0 1 0 -1 0 1 0 -1 104
78 0 0 0 -1 0 0 0 -1 103
93 0 1 -1 0 0 1 -1 0 121
96 0 1 -1 0 0 1 -1 0 123
95 1 1 -1 -1 1 1 -1 -1 122
94 1 1 -1 -1 1 1 -1 -1 124
74 0 1 -1 0 0 1 -1 0 97
73 1 1 -1 -1 1 1 -1 -1 99
76 1 1 -1 -1 1 1 -1 -1 98
75 1 1 0 -1 1 1 0 -1 100
51 1 1 0 -1 1 1 0 -1 127
52 1 1 -1 -1 1 1 -1 -1 126
49 1 1 -1 -1 1 1 -1 -1 128
50 0 0 1 -1 0 0 1 -1 125 Category Comparison of results (%)
Individual section HTC in same zone 100 Individual section HTC one zone apart 0
Individual section HTC two zones apart 0
Table 6.6 Comparison of the HTC data for individual sections between
Original432 and Replicate128 datasets for the four tubes for Brix-20 tests
Tube Percentage of data for individual section HTC values
In the same
category
One category
apart
Two categories
apart
M2 89 11 0
S2 100 0 0
M3 100 0 0
S3 100 0 0
Average across all
tubes
97 3 0
Analysis of the two datasets showed that 97% of the results had similar
individual section HTC values relative to the overall HTC. Only 3% of results were
found to have individual section HTC values at categories one level apart and no tests
showed a section of the tube that was two categories apart.
Overall it was concluded for the trials with these four tubes with Brix-20 juice
that the HTC patterns along the length of the tubes were very similar. This result most
Boiling Patterns in the Heating Tube 155
likely indicates that the boiling behaviour in the tubes was also consistent between the
Original432 and Replicate128 datasets for tests at the same operating conditions.
6.2.3 Comparison of the HTC results for individual tube sections for Brix-70 tests
Appendix K contains tables that compare the HTC patterns for M2, S2, M3 and
S3 tubes for tests with Brix-70 juice. Table 6.7 summarises the results to compare the
HTC values for the individual tube sections for the Brix-70 juice tests for M2, S2, M3
and S3 tubes. Analysis of the two datasets showed that 57% of the individual section
HTC values belonged to the same category. Of the remainder, 28% of the individual
HTC values were found at categories one level apart and 15% of the dataset two levels
apart.
Obviously, the HTC patterns for the tests on the four tubes with Brix-70 juice
were not as consistent between the Original432 and Replicate128 datasets as for the
tests with Brix-20 juice.
Table 6.7 Comparison of the HTC data for individual sections between
Original432 and Replicate128 datasets for M2, S2, M3 and S3 tubes for Brix-70
tests
Tube Percentage of data for individual section HTC values
In the same
category
One category
apart
Two categories
apart
M2 58 34 8
S2 63 28 9
M3 61 20 19
S3 47 28 25
Average across all
tubes
57 28 15
The data in Table 6.7 with Brix-70 juice do not show that any of the four tubes
provided a markedly greater level of consistency or inconsistency.
6.2.4 Concluding remarks
The HTC of the individual sections of the four tubes in the replicate dataset were
compared to the HTC of the individual sections from the corresponding original
dataset.
Tests with Brix-20 juice demonstrated a high level of consistency in the results
for the two series of tests. The results showed 97% of the individual section HTC
156 Boiling Patterns in the Heating Tube
values in the two datasets were within 15% of each other. No test conditions produced
HTC values for an individual section of tube, two categories apart.
Tests with Brix-70 juice showed a much lower level of consistency; only 56%
of the individual sections HTC values were within 15% of each other. Of the
remainder of the tests, 15% of the individual sections of tube produced HTC values
two categories apart.
The reason for the Brix-70 tests demonstrating a much lower level of consistency
in HTC for the individual sections between the Original432 and Replicate128 datasets
is not known. The conclusions in section 5.5.6 on page 124, demonstrate that the juice
properties, such as surface tension, were not affecting the overall HTC values for the
whole tube. It may be that variations in juice properties such as surface tension had a
greater influence on the boiling behaviour in industrial sections for juice at Brix-70
than for juice at Brix-20. Also, as shown in the test data (see section 4.7.2), the
variation in brix among the Brix-70 juice tests was greater than the variation in brix
among the Brix-20 juice tests. The effect of the variation in brix on HTC was
proportionally much greater for the Brix-70 juice tests than for the Brix-70 juice tests.
6.3 Identification of Boiling Patterns
6.3.1 Introductory remarks
It is evident from Table 6.2 to Table 6.5 and the tables in Appendix K that the
patterns defining the variation of HTC among the individual sections of the tubes are
different for the different operating conditions. The different HTC for the different
tube sections indicates that different boiling patterns were present for the different test
conditions. This section categorises the boiling patterns observed for the Original432
and Replicate128 datasets.
6.3.2 Boiling patterns
Six boiling patterns were identified in the Original432 and Replicate128 datasets
and these patterns are presented in Table 6.8. Of the six boiling patterns, one has HTC
values for all four sections of the tube within 15% of the overall HTC value–designated
Uniform Boiling. For the other five boiling patterns, a low HTC region exists at some
part of the tube while the rest of the tube is boiling within or higher than 15% of the
overall HTC. Appendices L, M, N and O present the data for the two datasets for
Uniform boiling, Non-uniform boiling–low HTC at top; Non-uniform boiling–low
Boiling Patterns in the Heating Tube 157
HTC at bottom; Non-uniform boiling–low HTC at an intermediate section
respectively. Table 6.9 shows the percentage of the tests in the Original432 and
Replicate128 datasets that aligned with the different boiling patterns.
As shown in Table 6.9, four of the boiling patterns represent more than 10% of
the data.
Table 6.8 Categorisation and description of the boiling patterns
Category of HTC pattern Description of category
Uniform boiling along the
tube
HTC of all the four sections of the tube are
within 15% of the overall HTC
Non-uniform boiling; low
HTC at the top section
HTC at top section >15% below the overall
HTC; HTC for other tube sections within 15%
or >15% above overall HTC
Non-uniform boiling; low
HTC at the bottom section
HTC at bottom section >15% below the overall
HTC; HTC for other tube sections within 15%
or >15% above overall HTC
Non-uniform boiling; low
HTC at the top and bottom
section
HTC at top and bottom section >15% below the
overall HTC; HTC for other tube sections
within 15% or >15% above overall HTC
Non-uniform boiling; low
HTC at an intermediate
section (i.e. section 2 and/or 3)
HTC at intermediate section (section 2 and/or
3) >15% below the overall HTC; HTC for other
tube sections within 15% or >15% above
overall HTC
Non-uniform boiling; low
HTC at top and intermediate
section (i.e. section 1 and 2 or
3)
HTC at top and intermediate section (section 1
and 2 or 3) >15% below the overall HTC; HTC
for other tube sections within 15% or >15%
above overall HTC
The same percentage of tests demonstrating the same boiling pattern would not
be expected in Table 6.9 for the Original432 and Replicate128 datasets. One factor
contributing to this difference is that the Original432 dataset incorporated nine tubes
and the Replicate128 dataset incorporated only four tubes.
It is evident from Table 6.9, that Non-uniform boiling–low HTC at the top of the
heating tube is the most common of all the boiling patterns followed by Non-uniform
boiling–low HTC at bottom, for both the Original432 and Replicate128 datasets.
158 Boiling Patterns in the Heating Tube
Table 6.9 Boiling pattern allocation for Original432 and Replicate128 datasets
Boiling pattern Location of
data
Percentage of data in this
category
Original432
dataset
Replicate128
dataset
Uniform Appendix L 9.5 5.5
Non-uniform; low HTC at
top
Appendix M 49.5 43.7
Non-uniform; low HTC at
bottom
Appendix N 19.9 27.3
Non-uniform; low HTC at
intermediate section
Appendix O 10.2 18
Non-uniform; low HTC at
top and bottom
– 1.9 1.6
Non-uniform; low HTC at
top and intermediate
– 4.4 1.6
No particular pattern – 4.6 2.3
6.3.3 Concluding remarks
The analysis of the individual section HTC results identified that several
different boiling patterns were experienced in the single-tube pilot evaporator during
the experiments. Six distinct boiling patterns were identified, which included uniform
boiling and non-uniform boiling throughout the tube. The non-uniform boiling–low
HTC at the top of the heating tube was found to be the most common boiling pattern
for both the Original432 and Replicate128 datasets. Non-uniform boiling with low
HTC at the bottom section was found to be the next most common pattern. It is
hypothesised that each of these HTC patterns is associated with a different boiling
mechanism occurring in the tube.
6.4 Determination of Factors Influencing the Boiling Pattern
6.4.1 Introductory remarks
This section provides a qualitative analysis to understand the influence that tube
dimensions and operating conditions have on the formation of the different boiling
patterns. For each pattern of HTC values, the number of tests with that pattern was
divided among the different levels of each factor. The Original432 dataset was
analysed to determine which factors are most influential in establishing each HTC
pattern.
Boiling Patterns in the Heating Tube 159
6.4.2 Factors affecting the boiling patterns
Figure 6.1, Figure 6.2, Figure 6.3 and Figure 6.4 show the distribution of the
number of tests for each level of each factor for the Original432 dataset for the four
dominant HTC patterns, as summarised in Table 6.10. The non-uniform boiling with
low HTC at both the top and bottom simultaneously and with low HTC at the top and
intermediate sections, are not shown due to their low prevalence.
Table 6.10 HTC pattern and the corresponding figure number
Figure number HTC pattern
Figure 6.1 Uniform
Figure 6.2 Non uniform; low HTC at top
Figure 6.3 Non uniform; low HTC at bottom
Figure 6.4 Non uniform; low HTC at intermediate section
Figure 6.1 to Figure 6.4 provide information on which levels of specific factors
are most prevalent for each pattern of boiling. Also, it is clear that variations in the
levels of some factors have minimal influence on the boiling patterns. The results of
these observations are summarised in Table 6.11.
Experimental factors
TL TD B JL HS DP
Num
ber
of
resu
lts
0
5
10
15
20
25
30
TL-2 m
TL-3 m
TL-4 m
TD-38.1 mm
TD-44.45 mm
TD-50.8 mm
Brix-20
Brix-35
Brix-70
JL1
JL2
JL3
JL4
HS1
HS2
DP1
DP2
Figure 6.1 Number of results showing uniform boiling throughout the tube for
each level of each factor for Original432 tests
160 Boiling Patterns in the Heating Tube
Experimental factors
TL TD B JL HS DP
Num
ber
of
resu
lts
0
20
40
60
80
100
120
TL-2 m
TL-3 m
TL-4 m
TD-38.1 mm
TD-44.45 mm
TD-50.8 mm
Brix-20
Brix-35
Brix-70
JL1
JL2
JL3
JL4
HS1
HS2
DP1
DP2
Figure 6.2 Number of results showing non-uniform boiling with low HTC at the
top for each level of each factor for Original432 tests
Experimental factors
TL TD B JL HS DP
Num
ber
of
resu
lts
0
10
20
30
40
50
60
TL-2 m
TL-3 m
TL-4 m
TD-38.1 mm
TD-44.45 mm
TD-50.8 mm
Brix-20
Brix-35
Brix-70
JL1
JL2
JL3
JL4
HS1
HS2
DP1
DP2
Figure 6.3 Number of results showing non-uniform boiling with low HTC at the
bottom for each level of each factor for Original432 tests
Boiling Patterns in the Heating Tube 161
Experimental factors
TL TD B JL HS DP
Num
ber
of
resu
lts
0
5
10
15
20
25
30
TL-2 m
TL-3 m
TL-4 m
TD-38.1 mm
TD-44.45 mm
TD-50.8 mm
Brix-20
Brix-35
Brix-70
JL1
JL2
JL3
JL4
HS1
HS2
DP1
DP2
Figure 6.4 Number of results showing non-uniform boiling with low HTC at
intermediate sections for each level of each factor for Original432 tests
Table 6.11 Results of observations of the influence of experimental factors on
the boiling patterns
HTC patterns Factors which have a strong influence on
the HTC pattern
Uniform 2 m tube length
Brix-20
Higher juice levels
Higher headspace pressure
Non uniform; low HTC at top Brix-35 and Brix-70
Lower juice levels
Non uniform; low HTC at bottom 4 m tube length
44.45 mm tube diameter
Brix-20 and Brix-70
Higher juice levels
Non uniform; low HTC at
intermediate section
2 m tube length
38.1 mm tube diameter
Lower headspace pressure
6.4.3 Concluding remarks
The factors affecting the boiling patterns are discussed in this section. It was
concluded that different tube dimensions and different operating conditions affect the
HTC patterns.
162 Boiling Patterns in the Heating Tube
6.5 Analysis of Variance of Individual Sections HTC
6.5.1 Introductory remarks
This section details the analysis of variance of individual section HTC values.
6.5.2 ANOVA for individual section HTC results
Analysis of variance was undertaken for the individual section HTC values to
determine the experimental factors affecting the HTC values of the individual sections.
The ANOVA tables are shown in Appendix P (Tables P.1 to Table P.4). Table 6.12
shows the single parameters and interactions that were found to have a significant
effect on the HTCs for the four sections. The 4th order interaction (TL:TD:B:HS) was
found to be significant for all four sections.
Table 6.12 Summary of significant factors and interactions for the individual
sections HTC values (Original432)
Tube
section
Factor identified with significance level less than 0.05
Single
parameter
2nd order
interaction
3rd order
interaction
4th order
interaction
Section 1 B, HS TD:B, TD:JL,
TD:HS
TL:TD:B
TL:TD:HS
TL:B: ΔP
TL:TD:B:HS
Section 2 B, JL,HS, ΔP TD:B, TD:JL,
B:JL, B:HS,
B:ΔP
TL:TD:B
TL:TD:HS
TL:B:ΔP
TL:HS:ΔP
TL:TD:B:HS
Section 3 B, HS TD:B, TD:JL TL:TD:B
TL:TD:HS
TL:JL:HS
TD:B:HS
TL:TD:B:HS
Section 4 B, HS TL:B, TD:B,
TL:HS, B:HS,
B: ΔP
TL:TD:B
TL:TD:HS
TL:JL:HS
TD:B:HS
TL:B:HS
JL:HS:ΔP
TL:TD:B:HS
Figure 6.5 to Figure 6.8 show the TL:TD:B:HS interaction plot for sections 1 to
4. It is observed that as brix increases, HTC of the individual sections decreases.
Although there are a few anomalies, S3, M4 and L4 tubes show higher HTC for Brix-
35 than for Brix-20 for sections 3 and 4. The reason for this is not clear.
Boiling Patterns in the Heating Tube 163
Figure 6.5 TL:TD:B:HS interaction plot for HTC for section 1
Figure 6.6 TL:TD:B:HS interaction plot for HTC for section 2
164 Boiling Patterns in the Heating Tube
Figure 6.7 TL:TD:B:HS interaction plot for HTC for section 3
Figure 6.8 TL:TD:B:HS interaction plot for HTC for section 4
Boiling Patterns in the Heating Tube 165
Figure 6.9 shows the TL:B:ΔP interaction plot for section 1. It is evident that
there is no consistency in the behaviour for the three brix values. The effect of tube
length and pressure difference on section 1 HTC is not clear.
Figure 6.9 TL:B:ΔP interaction plot for HTC for section 1
Figure 6.10 shows the TL:HS:ΔP interaction plot for section 2. It is observed that
HTC is generally higher for the HS1 and DP1 combination for all tube lengths. HTC
reduces from HS1 to HS2 with one exceptions viz. for 4 m tube length and higher
pressure difference.
Figure 6.11 shows the TL:B:ΔP interaction plot for section 2. There is no
consistency in the results. The effects of tube length and pressure difference on section
2 HTC values are not clear.
166 Boiling Patterns in the Heating Tube
Figure 6.10 TL:HS:ΔP interaction plot for HTC for section 2
Figure 6.11 TL:B:ΔP interaction plot for HTC for section 2
Boiling Patterns in the Heating Tube 167
Figure 6.12 and Figure 6.13 show the TL:JL:HS interaction plot for sections 3
and 4 respectively. For section 4 it is observed that an increase in tube length results
in a decrease in HTC for all the juice levels at both the headspace pressures. This can
be explained by the increased hydrostatic head at the bottom of the longer tube
increasing the saturation temperature and suppressing the formation of vapour bubbles.
However, for section 3, no consistency is observed in the results.
Figure 6.12 TL:JL:HS interaction plot for HTC for section 3
168 Boiling Patterns in the Heating Tube
Figure 6.13 TL:JL:HS interaction plot for HTC for section 4
Figure 6.14 shows the JL:HS:ΔP interaction plot for HTC for section 4 for HS1
values. Pressure difference has an effect on section 4 at lower juice levels (JL1 and
JL2). Similarly, the JL:HS:ΔP interaction plot for HTC for section 4 at HS2 values is
shown in Figure 6.15. Pressure difference has an effect on HTC at lower juice level
(JL1).
Boiling Patterns in the Heating Tube 169
Figure 6.14 JL:HS:ΔP interaction plot for HTC for section 4 at HS1 values
Figure 6.15 JL:HS:ΔP interaction plot for HTC for section 4 for HS2 values
170 Boiling Patterns in the Heating Tube
Figure 6.16 and Figure 6.17 show the TD:JL interaction plot for sections 1 and
2. For 44.45 and 50.8 mm tube diameter, the sections 1 and 2 show similar trends.
However, for 38.1 mm tube diameter, juice level corresponding to the highest HTC
has shifted from JL3 for section 2 to JL2 for section 1.
Figure 6.16 TD:JL interaction plot for HTC for section 1
Boiling Patterns in the Heating Tube 171
Figure 6.17 TD:JL interaction plot for HTC for section 2
6.5.3 Concluding remarks
The ANOVA for the individual section HTC was analysed. The ANOVA shows
that tube length, tube diameter, brix and headspace pressure have significant effects
on the HTC of the individual sections.
As a general trend, headspace pressure seems to have little influence on section
1 and 3 HTC for all the three brix for S2, M2, M4 and L4 tube dimensions. For section
2 HTC, headspace pressure has little influence for all three brix for S2 and L4 tube
dimensions. For section 4, headspace pressure has little influence for all three brix for
S2, M3 and L4 tube dimensions. The findings show that a decrease in headspace
pressure for these tube dimensions would be less likely to cause a drop in overall HTC.
As a general trend regarding brix, it is observed that as brix increases, HTC
decreases. The S3, M4 and L4 tubes show higher HTC for Brix-35 than for Brix-20
for sections 3 and 4.
172 Boiling Patterns in the Heating Tube
6.6 Analysis of Variance of the HTC Values for Individual Sections
Corresponding to Overall HTCmax
6.6.1 Introductory remarks
Of great interest is to understand the patterns of HTC for the individual sections
for operation at the optimal juice levels, that is, for the HTCmax results for the nine
tubes and test conditions of juice brix, headspace pressure and pressure difference.
The boiling patterns discussed in section 6.3.2 were identified for the HTC
results. Table 6.13 shows the boiling pattern allocations for the HTCmax results from
the Original432 dataset. The same four common boiling patterns, which were
identified as being most prevalent in the Original432 results for HTC, were also
common for HTCmax. However, for the conditions providing HTCmax there is a greater
percentage showing uniform boiling pattern and non-uniform boiling pattern–low
HTC at bottom. There are fewer results in the non-uniform boiling pattern–low HTC
at top section category, indicating that selection of the optimal juice level reduces the
likelihood of this particular boiling pattern.
Table 6.13 Boiling pattern allocation for HTCmax results from Original432
dataset
Boiling pattern Percentage of data in this
category
Uniform 18.5
Non-uniform; low HTC at top 30.6
Non-uniform; low HTC at bottom 28.7
Non-uniform; low HTC at intermediate
section
11.1
Non-uniform; low HTC at top and bottom 1.9
Non-uniform; low HTC at top and
intermediate
5.6
No particular pattern 3.7
6.6.2 ANOVA for individual section corresponding to HTCmax results
Analysis of variance was undertaken for individual section HTC values
corresponding to the overall HTCmax to determine the experimental factors affecting
the HTC values of individual sections of the tube at these conditions. The ANOVA
tables are shown in Appendix P (Tables P.5 to P.8). In order to simplify the
descriptions, these section HTC values will be referred to as section HTCmax.
Boiling Patterns in the Heating Tube 173
Table 6.14 presents a summary of the factors and interactions for the individual
section HTCmax that were found to be significant. Brix is identified as a significant
factor for all the sections. TD:B:HS is identified as significant for sections 1, 2 and 3.
Table 6.14 Summary of significant factors and interactions for the individual
sections HTCmax (Original432)
Tube section Factor identified with significance level less than 0.05
Single parameter 2nd order
interaction
3rd order
interaction
Section 1 B, HS TD:B, TD:HS TD:B:HS, TL:HS: ΔP
Section 2 B, HS, ΔP TD:B TL:HS:ΔP, TD:B:HS
Section 3 B - TD:B:HS
Section 4 TL, B -
The HTCmax results for the whole tube are discussed in section 5.7.3 on page
131. The TD:B:HS interaction was found to be significant for HTCmax. The individual
section HTCmax values show TD:B:HS as significant for three-out-of-four sections,
implying that tube diameter affects the HTC of the individual sections. Since the effect
of brix on HTCmax is known, tube diameter and headspace pressure are for the four
sections for each of the three brix values. Figure 6.18, Figure 6.19 and Figure 6.20
show the TD:B:HS interaction plots for Brix-20, Brix-35 and Brix-70 respectively.
For Brix-20, Brix-35 and Brix-70, the results show that headspace pressure has
close-to-no effect on section 1, 2 and 4 HTC for 38.1 mm tube diameter. Headspace
pressure has a slight effect on section 3 HTC, for all the three tubes’ diameter.
For the four sections of the tube, the individual section HTCmax value was higher
for the higher headspace pressure. The only notable exception was for section 3 in the
38.1 mm diameter tube.
Also, the effect of tube diameter for the individual section HTCmax values is
similar for sections 1 to 3 viz. HTC values similar for the 38.1 and 44.45 mm diameter
tubes but low HTC values exist for the 50.8 mm diameter tube. For section 4 of the
tube, higher HTC values are achieved for the 38.1 mm diameter than compared with
the two larger diameter tubes.
174 Boiling Patterns in the Heating Tube
Figure 6.18 TD:B:HS interaction plot for HTCmax for the four sections for
Brix- 20
Figure 6.19 shows that for Brix-35, the tubes with 44.45 mm diameter showed
higher individual section HTCmax values than for the tubes of the other diameters. As
well, the individual section HTCmax values for the tubes of 44.45 mm are substantially
higher for the higher headspace pressure for sections 1 to 3, while for section 4 there
is little influence of headspace pressure.
Boiling Patterns in the Heating Tube 175
Figure 6.19 TD:B:HS interaction plot for HTCmax for the four sections for
Brix- 35
For Brix-70 (Figure 6.20), no consistent pattern for the effects of tube diameters
or headspace pressure on individual section HTCmax values was obvious.
176 Boiling Patterns in the Heating Tube
Figure 6.20 TD:B:HS interaction plot for HTCmax for the four sections for
Brix- 70
6.6.3 Uniform boiling pattern for tests at HTCmax
In section 6.4, the apparent influence of each level of each factor from the
experimental design for the Original432 dataset was investigated for the four
predominant boiling patterns. This section investigates the effect of each level of each
factor on the overall HTCmax where a uniform boiling pattern existed. A quantitative
analysis was undertaken for uniform boiling pattern for Brix-20, Brix-35 and Brix-70.
The classification of the boiling pattern is based on brix, since brix is known to be the
most dominant factor affecting HTCmax.
Figure 6.21 shows the mean values of overall HTCmax for tests when the uniform
boiling pattern existed. Table 6.15 details the factors affecting the overall HTCmax for
uniform boiling. Juice level is shown to be a factor in Table 6.15 and Figure 6.22.
These juice levels are optimum juice levels corresponding to maximum HTC for
different tube dimensions.
Boiling Patterns in the Heating Tube 177
Table 6.15 Factors affecting overall HTCmax for uniform boiling for three brix
levels
Brix Factors which have a strong influence on the overall HTCmax
20 Tube diameter, juice level
35 Tube diameter, headspace pressure
70 Tube length, tube diameter, juice level, headspace pressure
Figure 6.21 Mean values of overall HTCmax with uniform boiling pattern (O432)
6.6.4 Non-uniform boiling pattern with low HTC at the top for tests at HTCmax
The non-uniform boiling pattern showing low HTC at the top section of the tube
formed the largest dataset containing 34 tests. Figure 6.22 shows the mean values of
overall HTCmax for tests when a non-uniform boiling pattern showing low HTC at the
top section existed. Table 6.16 shows the factors affecting the overall HTCmax for a
non-uniform boiling pattern with low HTC at the top section.
178 Boiling Patterns in the Heating Tube
Table 6.16 Factors affecting overall HTCmax for the boiling pattern with low
HTC at the top for the three brix values
Brix Factors which have a strong influence on the overall HTCmax
20 Tube length, tube diameter, juice level, pressure difference
35 Tube length, tube diameter, juice level
70 Tube length, tube diameter, juice level, headspace pressure
Figure 6.22 Mean values of overall HTCmax with non-uniform boiling pattern
and low HTC at top (O432)
6.6.5 Non-uniform boiling pattern with low HTC at the bottom for test at HTCmax
The non-uniform boiling pattern showing low HTC at the bottom section of the
tube contained 31 tests. Figure 6.23 shows the mean values of overall HTCmax for tests
when a non-uniform boiling pattern showing low HTC at the bottom section existed.
Table 6.17 shows the factors affecting the overall HTCmax for a non-uniform boiling
pattern with low HTC at the bottom section.
Boiling Patterns in the Heating Tube 179
Table 6.17 Factors affecting overall HTCmax the boiling pattern with low HTC
at the bottom for the three brix values
Brix Factors which have a strong influence on the overall HTCmax
20 Tube length, juice level
35 Tube length, tube diameter, juice level, headspace pressure
70 Tube length, juice level, pressure difference
Figure 6.23 Mean values of overall HTCmax with non-uniform boiling pattern
and low HTC at intermediate section (O432)
6.6.6 Non-uniform boiling with low HTC at intermediate sections for tests at HTCmax
The non-uniform boiling pattern showing low HTC at intermediate sections of
the tube contained 12 tests. Figure 6.24 shows the mean values of overall HTCmax for
tests when a non-uniform boiling pattern with low HTC at an intermediate section
existed. Table 6.17 shows the factors affecting the overall HTCmax: a non-uniform
boiling pattern with low HTC at an intermediate section.
180 Boiling Patterns in the Heating Tube
Table 6.18 Factors affecting overall HTCmax for the boiling pattern with low
HTC at an intermediate section for the three brix values
Brix Factors which have a strong influence on the overall HTCmax
20 Tube diameter, juice level, pressure difference
35 Headspace pressure
70 Tube diameter
sin
Figure 6.24 Mean values of overall HTCmax with non-uniform boiling pattern
and low HTC at intermediate sections (O432)
6.6.7 Concluding remarks
The ANOVA of the individual section HTC values producing the HTCmax were
analysed. It was found that brix is the most significant factor affecting the HTC values
for all individual sections at the HTCmax conditions. Both tube diameter and tube length
were found to affect the individual HTC values for conditions corresponding to the
overall HTCmax. For specific conditions, headspace pressure and pressure difference
are also important factors affecting the HTC values of the individual sections for the
tests corresponding to the HTCmax values. A third order interaction (TD:B:HS) was
found to be significant for sections 1, 2 and 3.
Boiling Patterns in the Heating Tube 181
The influence of each factor on the four most common boiling patterns was
analysed. The factors having strong influence on the HTCmax for the different boiling
patterns are summarised in Table 6.15, Table 6.16, Table 6.17 and Table 6.18. Both
tube diameter and tube length were found to affect the HTCmax value for the various
conditions. For specific conditions, headspace pressure and pressure difference were
also important factors affecting the HTCmax values.
6.7 Boiling Mechanism
6.7.1 Introductory remarks
The various patterns of HTC values for the individual sections of the heating
tube are attributed to variations in the boiling patterns for the juice within the tube. In
this section, possible boiling mechanisms are proposed, which relate to the observed
effects of tube dimensions and operating conditions on the HTC values. While the
proposed boiling mechanisms relate to the single heating tube used in the experimental
rig, the proposed boiling mechanisms are likely to provide a reasonable description of
the boiling mechanisms in industrial vertical-tube rising-film evaporators. One cause
of any differences, if they exist, between the boiling patterns for the single tube and
the tubes in an industrial evaporator, is the influence of juice flow from adjacent tubes
pooling above the tube plate affecting the juice flow rising in an individual tube.
It is to be noted that the effect of gutters on the outside of the tube, although
ignored for calculation of the overall HTC, may influence the boiling patterns.
Consequently, the boiling patterns of industrial tubes when a thicker condensate layer
would exist at the base of the tube may show a slightly different boiling pattern,
resulting from a slightly lower HTC at the bottom of the tube.
6.7.2 Review of the literature on boiling mechanisms in a rising film tube evaporator
In section 2.3 on page 17, the flow regimes in vertical channels were described.
It is accepted that the different flow regimes inside the vertical tube possess different
resistances to heat transfer. Hence, in order to maximise the heat transfer for a
particular set of operating conditions, it is logical to seek to achieve a flow regime
which imposes the least resistance to heat transfer on the juice side for the maximum
length of the vertical tube. According to theory, HTC increases from bubbly flow to
slug flow to annular flow, with the latter having the least resistance to heat transfer
with a liquid film along the tube wall and vapour core. However, when the annular
182 Boiling Patterns in the Heating Tube
flow regime gives way to the mist flow regime there is a drop in HTC in the region
with single phase vapour (Bejan, 1993).
In tests that showed a uniform boiling pattern, it would be reasonable to assume
that the annular flow regime was not reached. This assumption is based on the fact that
part of the tube is filled with liquid (dynamic liquid level5), some of which would only
have single-phase saturated liquid convective heat transfer, and/or a section of nucleate
boiling exists. The occurrence of the annular flow regime for the entire length of the
tube would be impossible.
In tests that showed a non-uniform boiling pattern with low HTC at the bottom
the conventional flow regime, as shown in Figure 2.3 on page 18, would explain the
boiling mechanism. If, for these results, annular flow exists in the top section, the HTC
of the top section would have to be higher than the HTC for the uniform boiling pattern
results, which was determined to not have an annular flow regime. The HTC results of
Section 1 (top section) for the uniform boiling pattern and the non-uniform boiling
pattern with low HTC at bottom are shown in Appendix L and N respectively. The
HTC values of the two boiling patterns at the top section of the tube are similar.
5 Dynamic liquid level is used to represent the liquid level inside the tube when the
liquid is under saturated boiling. This level is higher than the set static liquid level
owing to the presence of vapour bubbles.
Boiling Patterns in the Heating Tube 183
Figure 6.25 Flow pattern map for vertical tubes 51 mm diameter, air-water at
100 kPa abs (Taitel et al., 1980)
Chen et al. (2006) identified seven typical flow patterns in vertical two-phase
flow for tubes ranging in diameter from 1.1 to 4.26 mm. Chen et al. (2006) concluded
that the flow patterns for the large diameter tubes (2.88 and 4.06 mm) strongly
resemble flow pattern characteristics found in normal size (above 2.88 mm) tubes.
Mishima and Ishii (1984)presented flow pattern maps for tubes of 12 mm diameter
and 1.0 m length operating at 100 kPa pressure. Their flow pattern maps clearly
indicate the existence of annular flow when gas velocities were above 10 m/s. Watson
(1987) stated that slug flow and not annular flow is expected to occur in Australian
design evaporators; although Watson (1987) did not provide any supporting results or
reference to the conclusion.
The gas and liquid superficial velocities were determined using equations 2.7
and 2.8 on page 22, and shown on the graph in Figure 6.25. Values for superficial gas
velocities have been calculated for the range of tests in the experimental program.
These values are plotted in Figure 6.26, together with the superficial liquid velocity. It
is evident from the range of values in Figure 6.26 and comparison to the locations of
the flow regimes in Figure 6.26, that all the results lie in the churn flow regime.
However, the formation of churn flow is a subject of debate. Mao and Dukler
184 Boiling Patterns in the Heating Tube
(1993)concluded that there is little evidence for considering churn flow to be a separate
and distinct flow pattern. Several authors have stated that churn flow is in fact a
manifestation of slug flow and no transition actually occurs. Hence, it is hypothesised
that for the test conditions, bubbly and slug flow regimes (gas velocity <10 m/s) are
dominant. It is postulated that annular flow does not exist in the single tube evaporator.
Superficial gas velocity (m/s)
0.01 0.1 1 10 100
Sup
erfic
ial l
iqui
d v
eloci
ty (
m/s
)
0.01
0.1
1
10
100
TD-38.1 mm
TD-44.45 mm
TD-50.8 mm
Figure 6.26 Flow pattern map for experimental results
6.7.3 Proposed boiling mechanism
As discussed in the previous section, it was postulated that for the test conditions
that are typical of industrial Robert evaporators, annular flow did not exist in the single
tube. Hence, the presence of bubbly and slug flow is dominant in the single tube
evaporator. The presence of a sub-cooled liquid region could also be dismissed, since
the juice entering the base of the heating tube should be close to the temperature for
boiling at the headspace pressure (See Experimental Procedure - section 4.4 on page
74).
Boiling Patterns in the Heating Tube 185
Table 6.19 presents the proposed boiling phases for the various boiling patterns
that have been identified. The term “dry out” is proposed here to describe the situation
where the tube surface is not fully wetted by liquid. This mechanism should not be
confused with mist flow, which occurs post annular flow. Descriptions and
justifications for the proposed boiling patterns are given below.
Table 6.19 Proposed boiling regimes for boiling patterns
Boiling pattern Section 1 Section 2 Section 3 Section 4
Uniform boiling Bubble/slug Bubble/slug Bubble/slug Bubble/slug
Low HTC at top Dry out Dry out Bubble Bubble
Low HTC at bottom Bubble/slug Bubble/slug Bubble Bubble
Low HTC at
intermediate
Bubble/Slug Not know Not known Bubble/slug
stated that, during the transition from bubble flow to slug flow, bubble flow is
characterised by small bubbles moving in zig-zag motion and the occasional
appearance of large, Taylor-type bubbles. With further increase in gas flow rate, the
liquid flow still being low, the bubble density increases and reaches a point where the
dispersed bubbles become so closely packed that a high frequency of collisions and
agglomeration occurs, leading to larger bubbles. Hence, the occurrence of bubble and
slug flow together could explain the uniform boiling throughout the tube.
With higher brix and lower headspace pressure (higher viscosities), the ability
of the juice to rise up the tube for a given heat flux is dampened, compared with
operation with lower brix juice at higher headspace pressure (lower viscosities). The
effects of brix and headspace pressure are found to be substantial, to the extent where
low HTC at the top section occurred even for tubes of small length (2 m). The bottom
sections of the tube showed relatively acceptable HTC and hence resemble bubbly
flow. The top section is proposed to be drying out and a steep decrease in overall HTC
is recorded.
With longer tubes and higher operating juice levels, the HTC of the bottom
section is reduced (refer to Figure 6.3). A possible explanation for this reduction is the
increased pressure on the juice at the bottom section and reduced temperature
difference between the vapour in the steam chest and the saturation temperature at the
bottom of the tube. It is postulated that the bottom sections could be under a bubble
186 Boiling Patterns in the Heating Tube
flow (saturated nucleate boiling) regime and the top sections could be under a slug
flow regime. The interesting part is the effect of tube diameter of 44.45 mm (OD) and
brix of 20 and 70 on this boiling pattern (Figure 6.3). This effect was not entirely
understood.
The reduction of HTC at the intermediate section was the most confounding
pattern observed in the single tube evaporator. The reduction of HTC at the
intermediate section has been termed in the literature as Boiling crisis or Critical heat
flux (Hong Chae Kim et al., 2000). However, this phenomenon is normally present for
conditions of very high ΔT (e.g. >100 °C) in boilers. It is possible that a form of vapour
blanketing is occurring in these intermediate sections.
6.7.4 Concluding remarks
A boiling mechanism is proposed, wherein the boiling patterns identified are
related to the HTC patterns on the tubes. A boiling mechanism is proposed, wherein
Annular flow does not exist in tubes of sugar mill evaporators and Bubbly and Slug
flow regimes are dominant. The four boiling patterns, which accounted for more than
90% of the results, have been described by a possible boiling regime.
6.8 Boiling Patterns in the Tube that Provide Superior Heat Transfer
Coefficient
6.8.1 Introductory remarks
As discussed earlier, the preferred boiling pattern in the tube would present the
least resistance to heat transfer on the juice side. The boiling patterns identified and
related to the boiling flows are explained in the above sections. This section determines
the boiling patterns in the tube that provide superior heat transfer performance. The
tube dimensions and the operating conditions, which are most likely to provide the
proposed boiling pattern, are investigated.
Table 6.20 presents the average overall HTCmax values for the different boiling
patterns for Brix-20 (1st effect), Brix-35 (3rd effect) and Brix-70 (5th effect). The
uniform boiling pattern shows the highest HTCmax for all the three brix values. Low
HTC at the bottom and low HTC at intermediate position show similar HTCmax values
and these are lower than for the uniform boiling pattern. Of the two patterns, low HTC
at the bottom was the higher at all the three brix values. The boiling pattern with low
Boiling Patterns in the Heating Tube 187
HTC at the top shows the lowest HTCmax values for all the three brix values. Thus,
boiling conditions that result in a low HTC at the top section are the least favoured.
Table 6.20 Average HTCmax for different boiling patterns at three brix
Boiling pattern % of
results
Brix-20 Brix-35 Brix-70
Uniform boiling 18 4593 2899 512
Low HTC at top 31 2431 1701 370
Low HTC at bottom 29 3939 2616 468
Low HTC at intermediate 10 3733 2443 475
Low HTC at top and
intermediate 4
- - -
Low HTC at top and bottom 4 - - -
No pattern 4 - - -
Further discussion of the results is undertaken for the two proposed boiling
pattern of uniform boiling and low HTC at the bottom, to determine which tubes and
operating conditions promote boiling with these two patterns.
6.8.2 Uniform boiling pattern
Table 6.21 shows the tube dimensions and operating conditions for HTCmax with
a uniform boiling pattern. The observations are summarised in Table 6.22.
188 Boiling Patterns in the Heating Tube
Table 6.21 Tube dimensions and operating conditions for HTCmax with uniform
boiling pattern
Tube Brix JL
(mm)
HS
(kPa
abs)
ΔP
(kPa)
Achieved
ΔT (°C)
Set
ΔT
(°C)
HTC
(W/m2/K)
S2 20 800 126 45 8.8 8.8 5225
S4 20 1600 149 33 5.8 5.8 4504
S4 20 1200 149 45 7.7 7.7 4039
S4 20 800 126 33 6.5 6.5 4214
S4 20 800 126 45 8.8 8.8 3795
M2 20 800 149 33 5.7 5.7 5509
M2 20 800 149 38 6.5 7.7 5663
L2 20 800 149 33 5.7 5.7 4378
L2 20 400 149 35 6.1 7.7 3784
L2 20 800 126 33 6.5 6.5 4557
L3 20 1200 149 33 5.7 5.7 5668
L3 20 1200 149 35 6.1 7.7 3778
S3 35 1800 72 35 9.6 9.8 2161
M2 35 1200 94 35 7.9 7.9 3020
M3 35 1800 94 35 7.8 7.9 3632
M3 35 1800 94 50 11.1 11.2 3550
M3 35 1800 72 50 13.5 13.5 2134
M3 70 1350 22 60 27.8 27.4 231
L2 70 1400 29 60 23.5 23.3 797
L3 70 1650 29 60 23.0 23.3 508
Table 6.22 Observation with uniform boiling pattern for three brix values
Brix Observations
Brix-20
The S4 tube shows a uniform boiling pattern irrespective of operating
conditions (headspace pressure and pressure difference)
The M2, L2 and L3 tubes shows a uniform boiling pattern occurs more
commonly at the higher headspace pressure (149 kPa abs)
Brix-35 The M3 tube shows a uniform boiling pattern more often than the other
tubes. No operating conditions are dominant
Brix-70 Only three tubes at Brix-70 showed uniform boiling for the HTCmax
condition
No single tube nor operating condition dominates
Boiling Patterns in the Heating Tube 189
6.8.3 Low HTC at the bottom of the tube
Table 6.23 shows the tube dimensions and operating conditions for HTCmax with
low HTC at the bottom of the tube. The observations are summarised in Table 6.24.
Table 6.23 Tube dimensions and operating conditions for HTCmax with low
HTC at bottom
Tube Brix JL
(mm)
HS
(kPa
abs)
ΔP
(kPa)
Achieved
ΔT (°C)
Set
ΔT
(°C)
HTC
(W/m2/K)
S3 20 600 126 33 6.5 6.5 4133
S3 20 600 126 45 8.8 8.7 3867
S3 20 1200 149 41 7.0 7.0 3749
M2 20 600 126 33 6.5 6.5 4835
M3 20 900 149 33 5.7 5.7 4343
M3 20 900 149 45 7.7 7.6 4084
M3 20 1500 126 33 6.5 6.5 3589
M3 20 900 126 45 8.7 8.7 4459
M4 20 1600 149 45 7.8 7.6 3725
M4 20 2000 126 33 6.6 6.5 3134
M4 20 1600 126 45 8.8 8.7 3806
M4 20 1200 149 33 5.7 5.7 3542
S2 35 400 72 35 9.7 9.8 2294
M2 35 900 72 50 13.5 13.5 2267
M4 35 1400 94 35 8.0 7.9 3530
M4 35 2400 94 50 11.2 11.2 2989
L3 35 1800 72 50 13.5 13.5 2002
S3 70 2100 29 42 17.5 17.2 539
M2 70 600 29 60 22.7 23.3 557
M2 70 600 22 60 26.9 27.4 478
M2 70 900 22 42 20.4 20.9 934
M3 70 2100 29 60 23.7 23.3 337
M3 70 2100 29 42 17.6 17.2 454
M4 70 1800 29 60 23.4 23.3 412
M4 70 2800 22 42 21.7 20.9 249
M4 70 2200 22 60 28.5 27.4 441
L2 70 1400 29 42 17.5 17.2 769
L2 70 1400 22 42 21.1 20.9 589
L3 70 2100 22 60 26.5 27.4 623
L4 70 2800 29 60 23.3 23.3 91
L4 70 2200 22 60 28.5 27.4 75
190 Boiling Patterns in the Heating Tube
Table 6.24 Observations with non-uniform boiling pattern (low HTC at the
bottom of the tube) for three brix values
Brix Observations
Brix-20
S3, M3 and M4 tubes are the tubes that more commonly show low HTC
in the bottom section
For the M3 and M4 tubes no operating condition is dominant
Brix-35 Only five tubes showed low HTC at the bottom section and no single
tube or operating condition dominates
Brix-70 Seven of the nine tubes showed low HTC at the bottom section. Tubes
M2 and M4 were the more common. For both tubes, the higher pressure
difference dominates
Comparison of the data in Table 6.21 and Table 6.23 shows that for
Brix-70, many more of the HTCmax test conditions showed lower HTC
at the bottom than uniform boiling
6.8.4 Concluding remarks
The two boiling patterns in the tube, which provided superior heat transfer
performance, were identified as uniform boiling and low HTC at the bottom. Those
tube dimensions and operating conditions that are likely to promote these boiling
patterns were determined. Although it is well understood that the formation of the
boiling patterns is not directly controlled, setting the operating conditions for the
evaporator close to the optimum conditions will ensure good heat transfer performance
is achieved.
6.9 Concluding Remarks
The HTC of the individual sections of the four tubes in the Replicate128 dataset
were compared with the HTC of the individual sections from the corresponding
Original432 dataset. A high level of consistency in the results of the two series of tests
was obtained for the Brix-20 tests. The consistency was not as good for the Brix-70
tests.
The HTC of the individual sections of the Original432 dataset were analysed.
Six boiling patterns were identified, of which four boiling patterns accounted for more
than 90% of the results. The four boiling patterns were
• Uniform boiling pattern
• Low HTC at the top section of the tube
Boiling Patterns in the Heating Tube 191
• Low HTC at the bottom section of the tube
• Low HTC at the intermediate sections of the tube
These four boiling patterns were qualitatively and quantitatively analysed to
understand the occurrence of these boiling patterns and their effect on the overall HTC
of the tube.
Juice brix is identified as a significant factor affecting the HTC values for all
four sections of the tube, for the conditions corresponding to the overall HTCmax.
A boiling theory was proposed, wherein it was concluded that Annular Flow did
not exist in the single tube evaporator. The two dominant flow regimes in the single
evaporator tube and most likely in the industrial rising-film tube evaporator are bubbly
and slug flows. Low HTC at the bottom section is boiling associated with high
hydrostatic head (e.g. long tube), while low HTC at the top of the tube most likely
indicates drying out of the tube surface (i.e. insufficient wetting). No mechanism has
been proposed to describe the circumstances with low HTC at the intermediate sections
of the tube.
After examining the HTC patterns for those tests that provided the overall
HTCmax results, it was determined that Uniform boiling and Low HTC at bottom were
the boiling patterns in the tube that provided superior heat transfer performance.
Of the two boiling patterns, uniform boiling pattern provided the higher HTC.
However, the formation of boiling patterns is not essentially a matter of control.
Operating the evaporator close to the optimum conditions might result in formation of
these boiling patterns and good heat transfer performance can be achieved.
In general terms, uniform boiling conditions are more likely to be established for
boiling at Brix-20 with headspace pressure. Uniform boiling appears to form in the
tubes of all three diameters. For tubes of 38.1 mm diameter, tubes of 4 m length
produced uniform boiling, whereas for tubes of 44.45 mm and 50.8 mm diameter,
uniform boiling was more likely to be achieved with the shorter tubes.
The second favoured boiling pattern with low HTC at the bottom was likely to
be established for all three brix values, and particularly for Brix-20 and Brix-70. Tubes
S3, M3 and M4 were shown to be more likely to produce this boiling pattern at Brix-
20. For Brix-70, tubes with diameter 44.45 mm and 50.8 mm appeared more likely to
192 Boiling Patterns in the Heating Tube
produce this boiling pattern than the 38.1 mm tube. A higher pressure difference also
enhanced the formation of this boiling pattern.
.
Selecting Optimum Tube Dimensions 193
CHAPTER 7: SELECTING OPTIMUM
TUBE DIMENSIONS
7.1 Introductory remarks
In Chapter 3, the costs associated with designing, fabricating and installing a
Robert evaporator with different tube dimensions were calculated. The heat transfer
performances of the tubes of different dimensions for the typical range of operating
conditions were analysed in Chapter 5.
Chapter 7 provides the selection of the tube dimensions that provide good heat
transfer performance for different effect positions in a quintuple effect set, taking into
account the heat transfer performance (HTCmax) in addition to the capital and
installation costs and the operating costs for the 1st, 3rd and 5th effects in a quintuple
set.
7.2 Methodology for Determining the Optimum Tube Dimensions
7.2.1 Introductory remarks
Chapter 5 details the HTCmax results for the nine tube dimensions for the 1st, 3rd
and 5th stages of evaporation in a multiple effect set. Although capital cost is an
important criterion when procuring a new vessel, higher heat transfer coefficients
allow reductions in the HSA required to achieve the same rate of evaporation, achieve
higher juice processing rates for the installed areas, or extend the period of operation
between cleans. In addition, an important benefit of increased HTCs is the ability to
achieve the required rate of evaporation with a smaller temperature difference. This
benefit is of particular interest to factories seeking to reduce their process steam
consumption and fuel usage (Moller et al., 2003; Rose et al., 2009).
7.2.2 Favoured tubes based on HTCmax
The analysis undertaken in section 5.8 on page 134 determined the tubes that
provided good heat transfer performance for the typical operating conditions in the 1st
effect, 3rd effect and 5th effect of a quintuple evaporator set.
194 Selecting Optimum Tube Dimensions
In order to determine which tubes are most suitable for a particular evaporation
duty, three aspects need to be considered. These three aspects include:
• The HTC data for the tubes;
• The capital costs to construct and install an evaporator with these tubes; and
• The operating costs of using an evaporator with a particular tube. Operating
costs are associated with sucrose loss through hydrolysis and potential for
juice entrainment into the discharged vapour.
These matters are considered in the following sections, to determine the most
suitable tubes (optimum tubes) for each effect position.
Figure 7.1, Figure 7.2 and Figure 7.3 show the HTCmax results for the nine tube
dimensions for Brix-20, Brix-35 and Brix-70 respectively. Each data value shown in
Figure 7.1 to Figure 7.3 is the average of the HTCmax values for two headspace
pressures and two pressure differences, i.e., the average of the four ∆T values for the
tests at the nominated juice brix. These figures therefore show which tubes provide
good and poor heat transfer performance for the typical conditions for the 1st, 3rd and
5th effect positions in a quintuple set.
It is evident from Figure 7.1, that tubes of small and medium diameter (38.1 and
44.45 mm) show high HTCmax values and tubes M2, S2, M3, S3 and S4 provide
HTCmax values close to or above 4000 W/m2/K). It is seen that tubes with large
diameter (50.8 mm) provide consistently lower HTCmax values than tubes with 38.1
and 44.45 mm tube diameter, for all the tube lengths. The lowest HTCmax value is for
the L4 tube size.
Selecting Optimum Tube Dimensions 195
Figure 7.1 Influence of tube length and tube diameter on HTCmax for Brix-20
Figure 7.2 shows the HTCmax results for Brix-35. This result is an interesting and
unexpected finding from the study. The reason for the variable data for the tubes of
38.1 mm diameter with different length is not known. Compared to the M2 tube
dimensions (traditional), M3, S3, and M4 tube dimensions show higher HTCmax.
Tubes S4 and L4 show very poor heat transfer performance.
196 Selecting Optimum Tube Dimensions
Figure 7.2 Influence of tube length and tube diameter on HTCmax for Brix-35
Figure 7.3 shows that for Brix-70, tube dimensions giving the highest HTCmax
are M2 and L2. Tube lengths of 3 and 4 m result in very low HTCmax. Tube L4
provides very poor heat transfer performance for juice at Brix-70.
Selecting Optimum Tube Dimensions 197
Figure 7.3 Influence of tube length and tube diameter on HTCmax for Brix-70
Table 7.1 shows those tube dimensions that provided good heat transfer
performance for each effect position. The average HTCmax value for each case is also
shown in Table 7.1, as is the ratio of HTCmax to the HTCmax value for M2.
Examination of the data in Table 7.1 shows that for the 1st effect, M2 and S2
have the highest HTCmax, for the 3rd effect M3 and M4 have the highest HTCmax and
for the 5th effect, M2 and L2 have similar HTCmax values. Each of the tubes shown in
Table 7.1 is considered appropriate to achieve good heat transfer performance at the
nominated processing conditions.
198 Selecting Optimum Tube Dimensions
Table 7.1 Favoured tubes based on HTCmax for 1st, 3rd and 5th effect positions
Effect
number
Tube with good heat
transfer performance
Average HTCmax
value (W/m2/K)
Ratio of HTCmax
to HTCmax for
M2
1 M2 4660 1.00
S2 4740 1.02
M3 4240 0.91
S3 3990 0.86
S4 4140 0.81
3 M2 2620 1.00
M3 3030 1.16
S3 2800 1.07
M4 2950 1.13
5 M2 650 1.00
L2 640 0.98
7.2.3 Concluding remarks
The favoured tube dimensions based on the HTCmax results are presented in this
section. It was found that for the 1st effect position, five different tube dimensions had
good heat transfer performance, including the traditional M2 dimensions. For the 3rd
effect position, three tube dimensions were identified with heat transfer performance
better than M2. It was concluded that for the final effect position, M2 and L2 tube
dimensions had the highest (and similar) heat transfer performance, while tubes of
other dimensions had substantially worse heat transfer performance.
7.3 Capital Costs for Constructing and Installing Evaporators
7.3.1 Introductory remarks
The capital costs of the vessels comprising the favoured tube dimensions are
described in this section. The cost model (Chapter 3) was used to determine the
construction and installation costs of each of the evaporators in Table 7.1. In order to
account for the differences in heat transfer performance as defined by HTCmax, the
areas of the vessels was selected so that HTCmax x heating surface area (HSA) is
constant for a nominated HSA for an M2 evaporator. Thus, the evaporators with the
different tube dimensions would have the same evaporation capacity, for a given ∆T.
The cost analysis was undertaken for evaporators of 2000 m2 and 5000 m2
comprising M2 tubes. The areas of the respective vessels for the favoured tubes,
Selecting Optimum Tube Dimensions 199
having the same HTCmax x HSA as for the M2 evaporator, are shown in Table 7.2 for
M2 evaporators of 2000 and 5000 m2.
Table 7.2 Heating surface areas of the respective vessels for the favoured tubes
for 1st, 3rd and 5th effect positions
Effect
number
Tube with good heat transfer
performance
HSA for
2000 (m2)
HSA for
5000 (m2)
1 M2 2000 5000
S2 1960 4900
M3 2200 5490
S3 2330 5810
S4 2250 5620
3 M2 2000 5000
M3 1720 4310
S3 1870 4670
M4 1770 4420
5 M2 2000 5000
L2 2040 5100
The basis of costs for labour, materials, designs etc. are given in Chapter 3.
7.3.2 Construction costs
In this section, the construction costs of evaporators comprising the favoured
tube dimensions for the 1st, 3rd, and 5th effect positions are discussed.
Figure 7.4 shows the materials and labour costs for evaporators with the favoured
tubes for the 1st, 3rd and 5th effect positions relative to the M2 evaporator at these effect
positions. The material costs for the 1st effect position are higher for small diameter
and long tubes. This result is due to the increased heating surface areas of the vessels
with small diameter and long tubes, compared with the M2 tube dimensions. However,
the labour costs are reduced up to 20% for vessels comprising small diameter and long
tubes, due to the smaller vessel diameter and fewer tubes to be installed.
For the 3rd effect position, the materials and labour costs both show a reduction
of ~20% for vessels with medium diameter and long tubes. For the 5th effect position,
the M2 tube dimensions show lower materials and labour costs than for an evaporator
with the L2 tube dimensions.
200 Selecting Optimum Tube Dimensions
Tubes
M2 S2 M3 S3 S4
Mat
eria
ls c
ost
s (f
ract
ion
of
M2)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1st
effect position
Tubes
M2 S2 M3 S3 S4
Lab
ou
r co
sts
(fra
ctio
n o
f M
2)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Area-2000
Area-5000
1st
effect position
3rd
effect position
Tubes
M2 M3 S3 M4
Mat
eria
ls c
ost
s (f
ract
ion
of
M2)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
3rd
effect position
Tubes
M2 M3 S3 M4
Lab
ou
r co
sts
(fra
ctio
n o
f M
2)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
5th
effect position
Tubes
M2 L2
Mat
eria
ls c
ost
s (f
ract
ion
of
M2)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
5th
effect position
Tubes
M2 L2
Lab
ou
r co
sts
(fra
ctio
n o
f M
2)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Figure 7.4 Materials and labour costs for evaporators with favoured tubes
dimensions for 1st, 3rd and 5th effect positions
Selecting Optimum Tube Dimensions 201
7.3.3 Foundations and structural costs
The foundations for the vessels were assumed to comprise a square pad of N32
concrete, with sides equal in length to the diameter of the vessel plus one metre and a
depth of 0.5 m. The reinforced steel mesh in the pad was set at three levels, with
spacing in each direction of 200 mm. The vessels are supported on universal beam
pillars of dimensions 200 mm by 200 mm (weight 41 kg/m of length). The number of
pillars required was based on each pillar being capable of supporting 96 t. The vessel
weight used to calculate the number of supporting pillars was the mass on the
foundations when the juice side is full of 40 brix juice and the calandria is full of
condensate (see section 3.2.5). The minimum number of pillars used was six,
irrespective of weight of the vessel. For heavier vessels, the number of pillars was
increased according to the calculation method above. The design weights for
evaporators with the favoured tubes are provided in section 7.3.5.
Table 7.3 shows the cost data for foundations and structure to support the
evaporators. It was assumed that wastage of concrete, reinforced steel and pillars
would be 6%. The labour requirement for preparation of the foundations, laying
reinforced steel and filling with concrete, was taken to be three man hours/tonne of
steel.
Table 7.3 Cost data for foundations and structure to support the evaporator
Description of
parameter
Value
N32 concrete for
foundation
AUD 250 per m3
Reinforced steel AUD 4 per m
Universal beam pillar AUD 240 per m
Wastage 6%
Labour requirement 3 man hours/tonne steel (preparation, laying reinforced
steel and filling)
Labour cost AUD 70 per man hour
Table 7.4 and Table 7.5 show the foundations and structural costs (materials and
labour) for evaporators with the favoured tubes for the 1st, 3rd and 5th effect positions
with equivalent evaporation performance to evaporators with M2 tubes for HSA of
2000 and 5000 m2 respectively.
202 Selecting Optimum Tube Dimensions
Table 7.4 Foundations and structural costs for evaporators comprising the
favoured tubes for 1st, 3rd and 5th effect positions (HSA of M2 evaporator of
2000 m2)
Effect
number
Tubes N32 concrete
for
foundation
cost (AUD)
Reinforced
steel cost
(AUD)
Steel
pillars
cost
(AUD)
Total
foundation &
structural
costs (AUD)
1 M2 6043 5882 7560 19485
S2 5275 5145 7560 17980
M3 4757 4642 7560 16959
S3 4423 4316 7560 16299
S4 3481 3414 7560 14455
3 M2 6043 5882 7560 19485
M3 3956 3873 7560 15389
S3 3757 3680 7560 14997
M4 3301 3235 7560 14096
5 M2 6043 5882 7560 19485
L2 6804 6622 7560 20986
Table 7.5 Foundations and structural costs for evaporators comprising the
favoured tubes for 1st, 3rd and 5th effect positions (HSA of M2 evaporator of
5000 m2)
Effect
number
Tubes N32 concrete
for
foundation
cost (AUD)
Reinforced
steel cost
(AUD)
Steel
pillars
cost
(AUD)
Total
foundation &
structural
costs (AUD)
1 M2 12851 12468 10080 35399
S2 11109 10780 10080 31969
M3 9866 9592 10080 29538
S3 9096 8833 10080 28009
S4 7014 6834 7560 21408
3 M2 12851 12468 10080 35399
M3 8088 7873 7560 23521
S3 7621 7412 7560 22593
M4 6551 6374 7560 20485
5 M2 12851 12468 10080 35399
L2 14609 14171 12600 41380
For 2000 m2 HSA, there is a reduction in N32 concrete and reinforced steel costs
of 20, 30 and 40% with M3, S3 and S4 tube dimensions respectively as compared to
Selecting Optimum Tube Dimensions 203
M2 tube dimensions. The cost savings are higher, with 5000 m2 HSA. For 2000 m2
HSA, there is no reduction in the costs for the steel pillars when using tubes of smaller
diameter or longer. As mentioned earlier, the minimum number of pillars is taken to
be six; hence vessels with longer tubes than M2 have the same number of pillars,
despite having lower vessel diameter and foundation weight. For the 5000 m2 HSA,
the number of pillars varies among the vessels between 6 and 10, depending on the
mass on the foundations.
7.3.4 Insulation and cladding costs
The vessel is insulated and clad at the top cone, the strake and the steam annulus.
Table 7.6 shows the cost data for insulation and cladding of the evaporator. The
scaffolding costs include the labour and materials and increase with the height of the
vessel (Bundaberg Walkers Engineering Ltd, 2015).
Table 7.6 Cost data for insulation and cladding of the evaporator
Description of parameter Value
Insulation and cladding costs AUD 340 per m2
Scaffolding (including labour and materials) AUD 30000 for 2 m calandria
AUD 35000 for 3 m calandria
AUD 40000 for 4 m calandria
Table 7.7 and Table 7.8 show the insulation and cladding costs of the favoured
tubes for the 1st, 3rd and 5th effect positions to equate to the M2 HSA of 2000 and
5000 m2 respectively. It was observed that although there is a 15–20% reduction in
the area for insulation with S3 and S4 tube dimensions, the overall insulation and
cladding cost savings are negligible. This effect is due to the increased scaffolding
costs for taller vessels.
204 Selecting Optimum Tube Dimensions
Table 7.7 Insulation area and costs for the favoured tubes for 1st, 3rd and 5th
effect positions (HSA of M2 evaporator of 2000 m2)
Effect
number
Tubes Area for insulation
(m2)
Insulation and cladding costs
(AUD)
1 M2 189 100584
S2 171 93774
M3 176 100872
S3 167 97450
S4 155 98024
3 M2 189 100584
M3 154 92535
S3 148 90387
M4 149 100584
5 M2 189 100584
L2 206 107142
Table 7.8 Insulation area and costs for the favoured tubes for 1st, 3rd and 5th
effect positions (HSA of M2 evaporators of 5000 m2)
Effect
number
Tubes Area for insulation
(m2)
Insulation and cladding costs
(AUD)
1 M2 333 154602
S2 298 141555
M3 301 147454
S3 283 140927
S4 257 136143
3 M2 333 154602
M3 260 132168
S3 249 128021
M4 245 154602
5 M2 333 154602
L2 367 167411
7.3.5 Design weight and design costs
The design weight was calculated when the entire juice side of the vessel is filled
with juice (density–1.2 kg/m3) and the steam side is entirely filled with condensate.
This weight, plus the weight of the empty vessel, is the total weight on the foundations.
The juice side volume includes all tubes, mini-downtakes, central downtake, vapour
space and one-third of the top cone. These considerations are essential to ensure the
Selecting Optimum Tube Dimensions 205
support columns can withstand the weight of the vessel if the condensate pump or the
juice valve fails, and the vessel fills with juice and/or condensate. Figure 7.5 shows
the design weight for the evaporators, with the favoured tubes for the 1st, 3rd and 5th
effect positions relative to the M2 evaporator at these effect positions.
The design costs include the project management costs and profit margin. The
calculation methodology for determining the project management costs and profit
margin are detailed in Table 3.3 on page 56. As shown in Figure 7.5, there is a
substantial reduction in design costs for small and medium diameters and long tubes
for the 3rd effect positions.
206 Selecting Optimum Tube Dimensions
Tubes
M2 S2 M3 S3 S4
Des
ign
ves
sel w
eig
ht
(t)
(fra
ctio
n o
f M
2)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1st
effect position
Tubes
M2 S2 M3 S3 S4
Des
ign
co
sts
(fra
ctio
n o
f M
2)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Area-2000
Area-5000
1st
effect position
3rd
effect position
Tubes
M2 M3 S3 M4
Des
ign
ves
sel w
eig
ht
(t)
(fra
ctio
n o
f M
2)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
3rd
effect position
Tubes
M2 M3 S3 M4
Des
ign
co
sts
(fra
ctio
n o
f M
2)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
5th
effect position
Tubes
M2 L2
Des
ign
ves
sel w
eig
ht
(t)
(fra
ctio
n o
f M
2)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
5th
effect position
Tubes
M2 L2
Des
ign
co
sts
(fra
ctio
n o
f M
2)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Figure 7.5 Design vessel weight and design costs for evaporators with the
favoured tubes for 1st, 3rd and 5th effect positions
Selecting Optimum Tube Dimensions 207
7.3.6 Total costs
Table 7.9 and Table 7.10 provide details of the evaporators with the favoured
tube dimensions, which provide equivalent heat transfer performance to 2000 m2 and
5000 m2 evaporators with M2 tubes. The juice level in the tubes is the optimum level
determined from the experimental investigations (section 5.8). The optimum juice
level affects the juice level intensity (juice volume per m2 of HSA).
The data in Table 7.9 and Table 7.10 show that, at the 1st and 3rd effect positions,
the diameter of the vessel is reduced by ~18% and the mass on foundations reduced
by ~20% when S3 tube dimensions are used, compared to the conventional M2 tube
dimensions. The juice level intensity is reduced by ~40% with S3 tube dimensions.
These reductions are even greater when S4 tube dimensions are used.
For the 1st effect position, cost savings of between 4 and 10% are indicated by
suing the favoured tube dimensions compared with the M2 tube. Larger cost savings
(of 18 to 20%) are indicated for the favoured tubes at the 3rd effect position, because
of the superior HTCmax values of these tubes relative to the M2 tubes. For the 5th effect
position, the M2 evaporator is the lower cost option.
Table 7.9 Details of the evaporator vessels with the favoured tube dimensions to
equate to the heat transfer performance of a 2000 m2 HSA M2 evaporator
Effect Code Area
(m2)
No.
of
tubes
Vessel
ID (m)
Optimum
juice level
in tubes
Design
vessel
weight
(t)
Juice
intensity,
(L/m2)
Total
cost
(M
AUD)
1 M2 2000 7590 5.78 35% 322 9.27 1.28
S2 1960 8770 5.34 33% 278 7.56 1.21
M3 2200 5574 5.02 35% 279 7.34 1.21
S3 2330 6986 4.80 30% 259 5.76 1.23
S4 2250 5024 4.15 28% 221 4.71 1.14
3 M2 2000 7590 5.78 56% 322 11.65 1.28
M3 1720 4354 4.49 60% 225 10.07 1.03
S3 1870 5578 4.35 50% 214 7.58 1.05
M4 1770 3374 4.01 47% 205 7.72 1.01
5 M2 2000 7590 5.78 40% 322 9.83 1.28
L2 2040 6718 6.20 70% 366 15.24 1.37
208 Selecting Optimum Tube Dimensions
Table 7.10 Details of the evaporator vessels with the favoured tube dimensions
to equate to the heat transfer performance of a 5000 m2 HSA M2 evaporator
Effect Code Area
(m2) No. of
tubes Vessel
ID (m) Optimum
juice
level in
tubes
Design
vessel
weight
(t)
Juice
intensity,
(L/m2)
Total
cost
(M
AUD)
1 M2 5000 18986 8.89 35% 762 10.35 2.58
S2 4900 21900 8.20 33% 652 8.40 2.46
M3 5490 13890 7.67 35% 642 7.91 2.39
S3 5810 17304 7.32 30% 593 6.20 2.44
S4 5620 12576 6.31 28% 496 4.99 2.22
3 M2 5000 18986 8.89 56% 762 12.73 2.58
M3 4310 10920 6.85 60% 512 10.53 1.99
S3 4670 13924 6.62 50% 485 7.98 2.06
M4 4420 8432 6.06 47% 453 7.96 1.89
5 M2 5000 18986 8.89 40% 762 10.91 2.58
L2 5100 16814 9.55 70% 874 16.59 2.80
7.3.7 Concluding remarks
The various costs associated with the design, fabrication and installation of the
evaporator vessels with the favoured tube dimensions for the 1st, 3rd, and 5th effect
positions were determined. Estimates of the total costs for the evaporator installations
with the favoured tube dimensions are provided.
The total cost was calculated from the materials, labour, freight of material,
wastage, workshop costs, support structure and foundations, insulation and cladding,
project management costs and profit margins.
7.4 Selection of the Optimum Tube Dimensions
7.4.1 Introductory remarks
This section discusses the selection of optimum tube dimensions based on
HTCmax measurements, calculated costs for an installation and operating costs.
7.4.2 Basis of selection
Many factors are considered by factory management in selecting the appropriate
tube dimensions including heat transfer performance, installed cost, access to site for
installing the evaporator (crane hire etc.), availability of replacement tubes, potential
Selecting Optimum Tube Dimensions 209
sucrose degradation, potential entrainment of juice in the vapour flow and perceived
risk in departing from previously used tube dimensions. If the assessment is based
largely on installed cost, given appropriate heat transfer is achieved and the other
factors are acceptable, then the data in Table 7.9 and Table 7.10 indicate that
evaporators with S4, M4 and M2 tubes are preferred for the 1st effect, 3rd effect and 5th
effect respectively. This result applies to both the 2000 m2 and 5000 m2 vessels.
Discussions with Australian factory staff indicate that there is stronger interest
in using 3 m long tubes rather than 4 m long tubes in future installations of Robert
evaporators. There are two main reasons for this, viz., (1) use of 4 m long tubes would
be a major departure from the traditional 2 m long tubes, and (2) the up-flow vapour
velocity for the same VCC will be more than double compared with that for the M2
tube, which is likely to cause overloading of the juice de-entrainment louvres within
the vessel, as discussed in section 3.3.4 The industry already has a few Robert
evaporators with 38 mm diameter tubes after 1st effect position (Watson, 1986b) and
at Millaquin and Rocky Point mills (Broadfoot, 2017) and so the use of smaller
diameter tubes at the 1st effect and 3rd effect positions is likely to be perceived as low
risk.
It is for these reasons that the interest from the industry for future installations
into Robert evaporators will be in comparing S3 and M3 tubes with the traditional M2
tubes.
7.4.3 Estimates of capital costs savings
Table 7.11 shows the cost savings in using S3 and M3 tubes in the 1st and 3rd
effect positions relative to using evaporators with M2 tubes. For the 5th effect, the M2
tube dimensions are preferred, based on both the HTC and capital costs.
210 Selecting Optimum Tube Dimensions
Table 7.11 Estimate of cost savings from using S3 and M3 tubes in Robert
evaporators at the 1st effect and 3rd effect instead of using a Robert evaporator
with M2 tubes
Tube
dimensions
Saving in installed cost relative to cost of M2 evaporator
(AUD)
1st effect 3rd effect
2000 m2 HSA
S3 48,000 222,000
M3 61,000 245,000
5000 m2 HSA
S3 139,000 519,000
M3 188,000 591,000
The cost savings for the S3 and M3 tubes, relative to the M2 tubes, are
substantially greater for the 3rd effect than for the 1st effect because the heat transfer
performance of S3 and M3 tubes in the 3rd effect is superior to that for the M2 tubes.
For the 1st effect, the S3 and M3 tubes provide slightly inferior heat transfer
performance than the M2 tubes, but overall the savings on installation costs of the S3
and M3 tubes outweigh the influence of slightly inferior heat transfer performance.
The cost savings from using S3 tubes instead of M2 tubes are ~5% for the 1st effect
and ~20% for the 3rd effect. The cost savings are greater for the M3 tubes than for the
S3 tubes at both the 1st and 3rd effect positions. As expected, the cost savings are greater
for the evaporator of larger HSA.
7.4.4 Estimates of operating costs savings
For the use of S3 and M3 tubes at the 1st and 3rd effects, de-entrainment of juice
from the up-flow vapour should be able to be effectively achieved using conventional
louvre systems located within the head space of the evaporator. Hence, for most
practical applications, the de-entrainment of juice should be managed adequately for
similar costs compared to the M2 evaporator.
Under certain circumstances, sucrose degradation during juice evaporation can
be a major operational cost, resulting in a loss of revenue for the factory.
The extent of sucrose degradation that occurs in the juice evaporation process is
a function of the juice conditions (pH, temperature and brix) and the residence time
(Vukov, 1965). The evaporation conditions that are likely to experience large sucrose
Selecting Optimum Tube Dimensions 211
losses are where high levels of steam economy are sought, e.g., where extensive
vapour bleeding is undertaken and where the process steam pressure is high. Several
studies have shown that under these conditions, the majority of sucrose degradation
that occurs during evaporation is in the first evaporation stage (Purchase et al., 1987;
Schaffler et al., 1985). Sucrose losses should be low (<0.1% of sucrose in clarified
juice) when minimal vapour bleeding is undertaken and the process steam pressure is
200 kPa abs or lower (Rackemann & Broadfoot, 2016).
As noted in Table 7.9 and Table 7.10, Robert evaporators with different tube
dimensions have markedly different juice hold-up volumes per m2 of HSA (juice
intensity as described in section 3.3.2 on page 60). Evaporator vessels with lower juice
volume intensities will provide shorter residence times for the juice and hence
experience reduced sucrose loss through hydrolysis.
Using the correlation developed by Vukov (1965), the sucrose losses in a 1st
effect evaporator have been calculated for evaporators with the favoured tube
dimensions, based on the evaporation capacity being equivalent to that of a 5000 m2
M2 evaporator. The results and the assumed processing conditions are shown in Table
7.12. For the assumed conditions, the vapour loading would be 24 kg/h per m2 of
HSA. The average juice residence time in each evaporator is calculated for operation
at the optimum juice level (see Table 7.10). In all cases, due to the smaller juice holdup
volume than for an M2 evaporator, the calculated sucrose loss is less than for the M2
evaporator.
Table 7.12 also shows the estimated increase in annual revenue that would be
expected for an Australian factory utilising a 5000 m2 evaporator at the 1st effect in an
energy efficient plant. It was assumed that the cane/sugar mass ratio is 7 (typical of
Australian factories), the annual crop is 1.3 million t of cane, sugar price is AUD 400
per t, molasses price is AUD 120 per t, and final molasses is of 45 purity and 78 dry
substance. The values of the discounted increases in revenues (using a discount rate
of 15% for a 10 year period), from reduced sucrose losses relative to using a M2
evaporator, are also shown in Table 7.12.
These results demonstrate that for a factory intending to use Robert evaporators
at the 1st effect in a situation where a large HSA is required to suit vapour bleeding
arrangements and a high boiling temperature will be used, serious consideration should
be given to using smaller diameter and longer tubes than M2, e.g., S3 or S4.
212 Selecting Optimum Tube Dimensions
Table 7.12 Sucrose degradation and operating cost savings
Process conditions for 1st effect:
Juice inflow: 425 m3/h, 90 purity, 16 brix
Conditions in vessel: 22 brix, 119 °C and pH 6.8 at 20 °C
Parameter M2 S2 M3 S3 S4
Residence time, min 10.1 8.0 8.4 7.0 5.4
Predicted sucrose degradation
(%)
0.40 0.32 0.34 0.28 0.22
Annual saving in reduced sucrose
loss relative to the loss for a M2
evaporator (AUD)
75,000 56,000 112,000 168,000
Discounted value* over 10 years
of increased revenue due to
reduced sucrose loss relative to
the loss for an M2 evaporator
(M AUD)
0.45 0.34 0.67 1.01
* Discount rate of 15% per annum
7.4.5 Selection of the optimum tube dimension
New Robert evaporator vessels, comprising S3 and M3 tubes, provide
installation costs savings of 5 to 7% at the 1st effect and 20 to 22% at the 3rd effect
compared with an M2 Robert evaporator, for the same evaporation capacity. While
S4 tubes at the 1st effect and M4 tubes at the 3rd effect are well suited to these
applications, providing good heat transfer performance and would provide greater cost
savings, Australian mills are unlikely to utilise a 4 m long tube in a Robert evaporator.
Thus, S3 and M3 tubes are the favoured tubes for the 1st and 3rd effects from a cost and
heat transfer point-of-view.
For the installation of a Robert evaporator at the 1st effect in a factory seeking to
reduce the process steam consumption to a low level, major operational cost savings
are achieved for evaporators with S3 and M3 tubes compared to an evaporator with
M2 tubes, owing to the lower juice volume intensity of the evaporators with the S3
and M3 tubes. Reduced sucrose degradation would occur in the 1st effect vessel as a
result of the shorter residence time for the juice at the high boiling temperature. Use
of an evaporator with S3 tubes provides a larger increase in revenue compared with
the use of the M3 tubes, because of the lower juice volume intensity of the S3 tube.
For the 5th effect, a Robert evaporator with the traditional M2 tube is favoured.
Selecting Optimum Tube Dimensions 213
7.4.6 Concluding remarks
The selection of optimum tube dimensions is discussed in this section. Robert
evaporators comprising calandrias of S3 and M3 tubes are recommended for the 1st
and 3rd effect positions, compared with using the traditional M2 tube. This assessment
is based on the heat transfer performance of the different tubes, cost analysis for
fabricating and installing the evaporators, operating costs associated with sucrose
losses through hydrolysis and reduced risk compared with installing 4 m long tubes.
The S3 and M3 tubes are also recommended for the 2nd effect on the basis that
the operating conditions for the 2nd effect are intermediate between the conditions for
the 1st and 3rd effects.
At the 1st effect in a factory, which operates to reduce the process steam
consumption to a low level (typically requiring a large area allocation and high boiling
temperature at the 1st effect), a Robert evaporator comprising S3 tubes is
recommended. An evaporator with S3 tubes has a much lower juice volume intensity
than the M2 evaporator and would experience a large reduction in the extent of sucrose
hydrolysis. The evaporator with the S3 tubes also has a lower juice volume intensity
than the M3 evaporator.
The heat transfer investigations and cost analysis determined that for the 5th
effect, a Robert evaporator with the traditional M2 tube is favoured. The M2 tube is
also recommended for the 4th effect as for many evaporator stations, particularly for
the steam efficient configurations, the brix of juice in the 4th effect is quite high (e.g.
60 brix) and so the processing conditions are not markedly different from those for the
5th effect.
7.5 Retrofitting of Calandria for Existing Evaporators
7.5.1 Introductory remarks
When an evaporator station requires the installation of additional area, the usual
procedure is to install another evaporator at the appropriate position or to replace an
existing evaporator with a new vessel of larger HSA to debottleneck the capacity.
However, consideration should be given to whether it may be feasible to replace the
calandria comprising M2 tubes of an existing evaporator with a favoured tube being
longer, or of smaller diameter. The experimental investigations have shown that this
214 Selecting Optimum Tube Dimensions
change could be feasible at the 1st to 3rd effect positions. Obviously, retrofitting a new
calandria is only feasible if the remainder of the vessel body has adequate service life.
7.5.2 Practical considerations of retrofitting a calandria
When factories are upgrading the evaporator station to increase the capacity
and/or changing the configuration to suit increased steam efficiency, larger heating
surface areas are required. When increased steam efficiency is being sought, the
additional area will likely be placed in the effects upstream of the effect from which
maximum vapour bleeding is undertaken. In most scenarios, the additional area is
required in one, or perhaps two, of the first three effects in a quintuple set. In these
circumstances, retrofitting of a new calandria into an existing vessel may be feasible.
If a calandria is to be replaced with one of larger area, smaller diameter and/or
longer tubes would be used. Some additional practical matters have to be considered.
When the calandria is replaced with a new calandria comprising longer tubes,
the height of the vessel will most likely be increased in order to retain de-entrainment
efficiency. It is preferable to retain the base of the vessel at its current position, and
consequently the top cone and vapour offtake pipe will be raised. These costs must be
taken into account in the financial assessment to determine the viability of the retrofit.
If the top of the headspace cannot be lifted due to height limitations, lowering the
bottom remains the only option. In most cases, this option will be feasible if the
evaporators are located at a sufficient elevation above the ground floor level.
Consideration will need to be given to the transfer of the juice from one vessel to the
next, due to the different elevation of the base of the retrofitted evaporator.
7.5.3 Retrofit options
Design calculations have been undertaken for typical 2000 m2 and 5000 m2
Robert evaporators comprising M2 tubes (internal diameters of vessels being 5.78 and
8.89 m respectively) being replaced with calandrias using S3 and M3 tube dimensions,
with the pitch of tubes set at the minimum according to Australian Standards for a
pressure vessel. For this retrofit, the top of the vessel would be 1 m higher, assuming
the strake height is unchanged. The HSAs for the retrofitted evaporators are shown in
Table 7.13.
Selecting Optimum Tube Dimensions 215
Table 7.13 Evaporator heating surface details for retrofit options
Original HSA of M2
evaporator
Details of evaporator with
S3 tubes
Details of evaporator with
M3 tubes
Number of
tubes
HSA
(m2)
Number of
tubes
HSA
(m2)
2000 10430 3500 7590 3000
5000 26034 8740 18986 7500
The data in Table 7.13 show that using S3 tubes, the HSA is increased by 75%
and using M3 tubes the HSA is increased by 50%. These are large increases in area
and would be sufficient to suit most applications for a retrofit. If a smaller increase in
area is required, then it would be feasible to increase the pitch of the tubes (resulting
in fewer tubes being installed) or reducing the height of the tubes (e.g. use 2.8 m tubes).
7.5.4 Further design considerations
The large increases in area that can be achieved by retrofitting S3 or M3 tubes
will increase the vapour rate from the vessel substantially. Retrofitting a calandria at
the 3rd effect position with S3 tube dimensions (previous one being M2 tube) would
result in higher HTC with an enhanced area. In such cases, increasing the strake height
may be necessary to avoid entrainment of juice. If increasing the strake height is not
an option, efficient louvre designs must be installed.
7.5.5 Concluding remarks
Replacing a calandria of M2 tubes in an existing evaporator with a new calandria
comprising S3 or M3 tubes provides a large increase in heating surface area (up to
75% increase). This retrofitting option may be a much cheaper option than installing
a new evaporator of the larger required area. However, there are several practical
matters including the maintenance of de-entrainment efficiency that must be
considered for the retrofit options.
7.6 Concluding Remarks
The experimental program determined that the traditional tube M2 provided
good heat transfer performance across the full set of processing conditions that are
typically found in a quintuple evaporation station. The experimental program also
showed that tubes of 38.1 mm outside diameter and/or longer tubes (3 or 4 m length)
216 Selecting Optimum Tube Dimensions
provided comparable heat transfer performance to the traditional tube at the 1st effect
position, and superior heat transfer performance at the 3rd effect position. Australian
mills are unlikely to utilise 4 m long tubes in Robert evaporators and so the favoured
tubes for the 1st to 3rd effects positions are S3 and M3. For the 5th effect position, the
traditional tube is favoured.
A cost analysis determined that evaporator vessels with the traditional tube are
more expensive than evaporator vessels comprising tubes of smaller diameter and/or
greater length. Thus, cost savings of ~20% should be possible by using tubes such as
38.1 mm outside diameter and 3 m length at the 3rd effect position.
An important benefit from using smaller diameter and longer tubes is that the
juice volume is smaller than in an evaporator with the traditional tube dimensions. For
a 1st effect evaporator operating in a high steam efficiency scenario (typically at high
boiling temperature and with large HSA), the smaller juice volume and shorter
residence time would provide for reduced sucrose losses and increased revenue for the
factory.
When an increase in HSA in the 1st to 3rd effects is required in order to increase
the juice processing capacity of the set and/or to suit an upgrade for a more steam-
efficient configuration, a financially attractive option may be to replace the calandria
of M2 tubes in an existing evaporator body with a calandria comprising smaller
diameter and longer tubes. This option should be much less expensive than installing
a new evaporator. Again, tubes S3 and M3 would be recommended for the replacement
calandrias.
General Discussions and Conclusions 217
CHAPTER 8: GENERAL DISCUSSIONS
AND CONCLUSIONS
8.1 Introductory remarks
This chapter summarises the research of this thesis and highlights the main
conclusions from the research. The knowledge gained during this research, along with
the significance and benefits to the Australian raw sugar industry are described.
Recommendations are made for further work, based on the foundation of this research.
8.2 Aim of the Research
The research project aimed to investigate the effect of tube dimensions and
operating conditions on the HTC of a rising film vertical tube evaporator. The research
aims are summarised in six parts:
• Developing a capital cost model to determine the costs of designing,
fabricating and installing Robert vessels of the same heating surface area but
comprising tubes of different dimensions.
• Determining the HTC of tubes with different lengths and diameters operating
through the full range of operating conditions experienced in industrial raw
sugar factory evaporators.
• Determining the optimum tube dimensions and operating conditions that
provide the maximum heat transfer coefficient (HTCmax) at the typical
conditions for the 1st effect, 3rd effect and 5th effect positions.
• Determining the HTC at different sections of the tube, in order to understand
the boiling patterns for the juice within the tube.
• Postulating a theory on boiling mechanisms based on the variation of HTC
along the length of the tube.
• Selecting the optimum tube dimensions for industrial evaporators based on
HTCmax, capital costs and operational costs.
218 General Discussions and Conclusions
8.3 Comments on the Experimental Program
Heat transfer measurements were undertaken for nine stainless steel tubes
comprising three different diameters and three different lengths for the following range
of operating conditions, corresponding to the conditions at the 1st, 3rd and 5th effects:
three brix values, two headspace pressures, two pressure differences and four juice
levels within the heating tube. In addition, replicate tests were undertaken for four
tubes (two different diameters and two different lengths) for the operating conditions
corresponding to the 1st and 5th effects.
The designation for the diameters of the tubes was S, M and L being for
38.1 mm, 44.45 mm and 50.8 mm outside diameters respectively. The tube lengths
were 2, 3 and 4 m. Thus, a code M2 was for the tube of 2 m length and 44.45 mm
outside diameter. This M2 tube is the tube traditionally used in evaporators in
Australian factories.
Each of the heating tubes was fitted with gutters on the outside of the tube, to
collect and drain condensate to an external container. Four gutters, which were spaced
equidistantly along the length of the tube, were installed on each tube. Thus, HTC
values could be calculated from the condensate collected for the four individual
sections on the tube and overall HTC values calculated from the total condensate rate
on the tube.
The test program was undertaken at typical industrial conditions, but a few
characteristics of the rig meant that the heat transfer performance might be slightly
different from that experienced in industrial evaporators. These factors included
• the drainage of condensate on the outside of the tube being from four
positions, whereas condensate in industrial evaporators drains to the
bottom plate;
• the single tube was combined with an adjacent downtake for juice flow
to the base of the evaporator, which would likely have reduced to some
extent the flow of juice down into the top of the heating tube. In
industrial evaporators, downtakes are provided but are located slightly
more distant from the heating tube on average than in the experimental
rig; and
General Discussions and Conclusions 219
• the tubes being new and clean for the tests (i.e. without any scale
deposits). Industrial evaporator tubes, even after a clean, would
generally have a slight deposit of scale, which would reduce the heat
transfer.
The replicate tests with the four tubes demonstrated a high level of consistency
with the heat transfer results of the original test program with the nine tubes. This
consistency provided confidence in the determinations of the heat transfer performance
for the nine tubes at the different operating conditions.
8.4 Summary of the Research Outcomes
8.4.1 Capital cost model
A capital cost model for the Robert evaporator was developed for 2000, 3000,
4000 and 5000 m2 vessels with 2 m, 3 m, and 4 m tube lengths and 38.10 mm,
44.45 mm, and 50.80 mm tube outside diameter.
The results showed that the conventional evaporator, for which Australian
factories almost universally use 2 m tubes of 44.45 mm outside diameter, is more
expensive than using all the other tubes, except for evaporators with 2 m tubes of 50.8
mm outside diameter.
Relative to the conventional evaporator, cost savings in the ex-works cost of
~12% are likely in using 3 m long tubes of 44.45 mm outside diameter and ~15% if 3
m long tubes of 38.10 mm outside diameter are used. Further savings are made by the
use of 4 m long tubes, but the incremental cost reduction is less than increasing the
tube length from 2 to 3 m. Longer tube vessels have smaller diameter and considerably
less mass on the structure and foundations than the conventional evaporator, and so
additional savings through reduced installation costs would be achieved.
8.4.2 Heat transfer performance of different tube dimensions
The experimental investigations were undertaken to determine the HTC of
different tube lengths and diameters (nine tubes) for different operating conditions,
corresponding to the typical conditions in the 1st, 3rd and 5th effects (the Original432
dataset). Replicate tests were undertaken for the M2, S2, M3 and S3 tubes, to
understand the tube length and tube diameter interaction and to determine the
consistency in the results. These replicate tests were designated Replicate128.
220 General Discussions and Conclusions
The selection of two headspace pressures and two pressure differences for each
set of test conditions provided heat transfer data (heat flux and HTC) for four
temperature differences between the vapour in the steam chest and the boiling juice.
Analysis of the HTC results showed tube length and tube diameter interaction to
be significant. In other words, the choice of tube length and diameter cannot be
independent of each other in selecting a high level of heat transfer performance. The
trends observed from the results of the experimental program show that for tube
lengths of 3 m and higher, small diameter tubes are preferred. The replicate analysis
confirmed the result. It was concluded that as brix increases, HTC decreases. Also, at
higher headspace pressure the HTC values were generally higher. The effect of
headspace pressure is attributed to the lower viscosity of the juice at the higher boiling
temperature when the headspace pressure is higher. For 2 and 3 m tube lengths, 44.45
and 38.1 mm tube diameters gave higher HTC. For 4 m tube length, both 44.45 and
38.1 mm tube diameters gave higher HTC.
For each tube at each set of processing conditions (juice brix, headspace pressure
and pressure difference), HTC measurements were undertaken at four juice levels. In
all cases, a particular juice level provided a maximum HTC value (HTCmax) for those
conditions.
HTCmax results were determined from the Originla432 dataset. Analysis of
variance determined that tube diameter is more important than tube length in affecting
HTCmax. As brix increases, HTCmax decreases. For Brix-20, higher HTCmax values are
achieved at 38.1 and 44.45 mm tube diameter. For Brix-35 and Brix-70, higher HTCmax
values are achieved at 44.45 mm tube diameter. For Brix-35, the tube of 38.1 mm
diameter and 3 m length (S3) also provided good heat transfer performance.
Analysis of the optimum juice levels corresponding to HTCmax showed that as
brix increases, optimum juice level increases. The effect of tube length and headspace
pressure on optimum juice level was not clear. It was found that for tubes of 38.1 and
50.8 mm diameters, the optimum juice level increases with increase in pressure
difference, while for 44.45 mm tube diameter, the optimum juice level decreases with
increase in pressure difference.
General Discussions and Conclusions 221
Empirical relationships were developed for HTCmax and optimum juice level
(expressed as the actual level in the tube in mm). The empirical relationship for
HTCmax was
𝐻𝑇𝐶 = 𝐵−0.4901 𝑇𝑗1.3582 𝑉𝐶𝐶0.8877 8.1
where 𝐵 is the brix of the juice,
𝑇𝑗 is the temperature of the juice, °C
𝑉𝐶𝐶 is the vapour condensation coefficient, kg/h/m2
This relationship showed good agreement with the measured results (R2 = 0.94)
and with industry values, although the experimental data are slightly higher than
typical industry values at Brix-20.
The empirical relationship for optimum juice level (mm) was
𝐽𝐿𝑜𝑝𝑡 = 𝑇𝐿0.7253 𝐵0.4544 ΔT−0.1122 8.2
where 𝑇𝐿 is the tube length, mm
ΔT is the temperature difference between the steam and juice, °C.
8.4.3 Understanding the boiling patterns in the single tube
The HTC values for the individual sections of the tube of the Original432 dataset
were analysed to determine the variations relative to the overall HTC values. Six HTC
patterns were identified, of which four patterns accounted for more than 90% of the
results. The test conditions for each of these four HTC patterns were qualitatively and
quantitatively analysed to determine which tube dimensions and operating conditions
were most common for each of these boiling patterns. The relationship between these
HTC patterns and the magnitude of the overall HTC of the tube was also investigated.
The uniform boiling pattern was determined to be bubbly/slug flow boiling for the
whole length, while the low HTC at the bottom was of similar boiling behaviour but
bubbly flow at the bottom section. The boiling pattern that provided the second highest
overall heat transfer performance was Low HTC at bottom, for which the bottom
section of the tube had HTC value more than 15% below the overall HTC value. The
other two HTC patterns were Low HTC at top and Low HTC at intermediate section.
Both these patterns resulted in a lower overall HTC than the other two patterns.
222 General Discussions and Conclusions
A boiling mechanism was proposed for each of the four dominant HTC patterns.
It was concluded that Annular Flow did not exist in the single tube evaporator.
A new mechanism termed as “dry out” was identified to occur in the tube for the
low HTC at the top pattern. This mechanism was observed to be more likely to occur
for long tubes and low operating juice levels, wherein insufficient juice is able to rise
to the top of the tube and boiling is restricted to the bottom section of the tube. For the
boiling pattern with Low HTC at the intermediate section, no boiling pattern was
identified. The literature suggests that a Boiling Crisis or Critical Heat Flux can exist,
whereby bubbles adhere on the inner surface of the tube and as an insulating blanket
to heat transfer. However, the behaviour is only expected for very large temperature
differences between vapour and liquid and would not be expected in an evaporator.
The formation of a specific boiling pattern cannot be independently set.
However, setting the operating conditions for the evaporator, close to the optimum
conditions, will likely ensure that boiling patterns are formed, and good heat transfer
performance is achieved.
8.4.4 Selecting the optimum tube dimensions
The traditional 44.45 mm diameter, 2 m tube provides good heat transfer
performance across the full set of processing conditions typically found in a quintuple
evaporation station. It has been found that tubes of 38.1 mm outside diameter and/or
longer tubes (3 or 4 m length) provide comparable (or perhaps slightly inferior) heat
transfer performance to the traditional tube at the 1st effect position, and superior heat
transfer performance at the 3rd effect position.
Evaporator vessels with the traditional tube are more expensive than evaporator
vessels comprising tubes of smaller diameter and/or greater length. Thus, cost savings
of ~20% should be possible by using tubes such as 38.1 mm outside diameter and 3 m
length at the 3rd effect position. Even larger savings are achieved with 4 m long tubes.
However, Australian Mills are unlikely to utilise 4 m long tubes in Robert evaporators
and so the favoured tubes for the 1st to 3rd effects positions are S3 and M3. For the 4th
and 5th effect positions the traditional tube (M2) is favoured
An important benefit from using smaller diameter and longer tubes is that the
juice volume is smaller than in an evaporator with traditional tube dimensions. For a
1st effect evaporator operating in a high steam efficiency scenario (typically at high
General Discussions and Conclusions 223
boiling temperature and with large heating surface area), the smaller juice volume and
shorter residence time would provide for reduced sucrose losses and increased revenue
for the factory. This aspect reinforces the benefit of using S3 or M3 tubes at the 1st
effect position.
When an increase in heating surface area in the 1st to 3rd effects is required in
order to increase the juice processing capacity of the set and/or to suit an upgrade for
a more steam-efficient configuration, a financially attractive option may be to replace
the existing calandria of 44.45 mm and 2 m tubes with a calandria comprising smaller
diameter and longer tubes. Tubes of 38.1 mm or 44.45 mm diameter and 3 m length
(S3 and M3) are recommended for the replacement calandrias. Increases in heating
surface area of 75% and 50% respectively are achievable. This option should be much
less expensive than installing a new evaporator.
8.5 Significance of the Research
8.5.1 Introductory remarks
For practical application within the Australian sugar industry, this PhD study
• provided the cost implications for installing new Robert evaporators with
calandrias comprising tubes of different dimensions,
• determined the tube dimensions and juice level in the tube, which
provided the best heat transfer performance for the typical operating
conditions at the different effect positions,
• provided an understanding of the boiling mechanism in the rising film
vertical tube evaporator, and
• determined, through consideration of the heat transfer performance and
the capital and operating costs of the evaporators, the optimum tube
dimensions for use at the different effect positions.
8.5.2 Increase in HTC
An increase in HTC as a result of selecting the optimum tube dimensions for the
different effect positions would
1. allow reductions in the heating surface area required to achieve the same
rate of evaporation, or
224 General Discussions and Conclusions
2. achieve higher juice processing rates for the installed areas, or
3. extend the period of operation between cleans, compared with the use of
tubes of the traditional dimensions.
An important benefit of increased HTCs is the ability to achieve the required rate
of evaporation with a smaller temperature difference. This benefit is of particular
interest to factories seeking to reduce their process steam consumption and fuel usage.
8.5.3 Reducing capital costs
Selecting tube dimensions with smaller diameter and longer tubes would reduce
the vessel diameter, weight of the vessel, labour costs, foundations and structural costs,
and insulation costs. The potential savings from using S3 or M3 tubes for the same
heating surface area are ~15% for S3 tubes and ~12% for M3 tubes, compared with
using the M2 tubes.
8.5.4 Reducing operating costs
Vessels with smaller vessel diameter have lower juice volume intensities, which
results in lower juice residence times in the vessels. Sucrose degradation is primarily
a function of juice residence time and juice temperature. Reducing the juice residence
time in the early effects of the set would decrease the potential sucrose degradation
and increase the revenue of the factory.
For a Robert evaporator at the 1st effect in a factory seeking to reduce the process
steam consumption to a low level (usually operating at a high juice boiling
temperature), S3 and M3 tubes are favoured compared to an evaporator with M2 tubes,
owing to the lower juice volume intensity of these evaporators leading to reduced
sucrose losses. An evaporator with 38.1 mm diameter and 3 m long tubes provides a
larger increase in revenue compared with an evaporator with M3 tubes because of the
lower juice volume intensity of the evaporator with S3 tubes.
8.5.5 Retrofitting of calandrias
For situations where additional area is required at the 1st to 3rd effect positions
and the body of an existing evaporator with calandria of 44.45 mm diameter and 2 m
long tubes is in good condition, it may be feasible to retrofit a calandria with 38.1 mm
or 44.45 mm diameter and 3 m long tubes. Increases in area up to 75% and 50%
respectively can be achieved using 38.1 mm or 44.45 mm diameter and 3 m long tubes.
General Discussions and Conclusions 225
The retrofit option is likely to be much cheaper than installing a new evaporator of the
required area.
8.6 Recommendations for Future Research
While the research undertaken in this PhD study is considered comprehensive,
there remain tasks to understand the following:
• Why, at Brix-35, S2 tubes produced substantially inferior HTC values
compared with S3 tubes but at Brix-20 S2 and S3 tubes produced similar
and good HTC values?
• Would tubes of 25 mm diameter provide sufficiently good heat transfer
performance at the 1st effect position (and perhaps even the 2nd and 3rd
effect positions) to be feasible? Substantial cost savings are likely with
the use of 25 mm diameter tubes, compared with the longer diameter
tubes.
• To what extent has the removal of condensate at gutters on the tubes
affected the overall HTC values?
• What further information can be obtained to better understand the boiling
mechanism in vertical rising-film evaporators?
The CFD model development was only undertaken on the steam side of the
experimental rig. Further work is required to:
• Develop a CFD model of a single rising-film vertical tube to incorporate
two-phase flow. This model may use the HTC relationship and boiling
pattern information determined in this PhD study for validation.
• Develop a CFD model of a wedge of a Robert evaporator incorporating
the CFD model of the single tube. This CFD model would specifically
need to examine the effects of juice rising from individual tubes passing
across the top tube plate and flowing down adjacent tubes. This
behaviour is known to occur in industrial Robert evaporators.
The experimental setup, although quite sophisticated could be modified for
future investigations. Few of the modifications are listed here to assist future
investigators in this area of research:
226 General Discussions and Conclusions
• Include a stirrer in the juice tank to ensure good mixing of condensate
return into the juice.
• Include a small flowmeter in the juice downtake line to measure rate.
The author is not sure whether a suitable and very small flowmeter is
available.
• Undertake replicate trials on juice of 35 brix. In hindsight data at 35 brix
are more important than data at 70 brix, especially with the industrial
application of long tubes (>3 m length).
• No changes to the method of measuring HTC are proposed but some
trials on tubes with only a large bottom gutter would be worthwhile to
determine the influence of condensate on the outside of the tube on HTC
performance and to align this with theory.
8.7 Concluding Remarks
In conclusion, the study has contributed to the knowledge of rising film vertical
tube evaporators through the following determinations:
• Tube length and tube diameter interaction is significant in affecting HTC of
the tube. In other words, the selection of tube length and tube diameter cannot
be independent of each other in seeking to maximise the HTC performance.
• At higher brix, the HTC is lower. Also, at a higher headspace pressure the
HTC is higher. This latter effect is attributed to the lower viscosity of the
juice at the higher boiling temperature.
• Juice level and tube diameter interaction is significant in affecting the HTC
of the tube. Tube diameter should be considered when selecting the juice level
in the evaporator. Higher juice levels for small diameter tubes and lower juice
levels for large diameter tubes have a detrimental effect on HTC.
• For a given tube and boiling at certain operating conditions, an optimum juice
level in the tube exists, which provides a maximum HTC (HTCmax). The
optimum juice level and HTCmax values are functions of juice brix, tube
diameter, tube length, headspace pressure and pressure difference.
• Tube diameter is more important than tube length in affecting HTCmax.
General Discussions and Conclusions 227
• Empirical models were developed for HTCmax and optimum juice level.
• Six different boiling patterns were identified to exist for the nine tubes and
operating conditions of the experimental program. Among these boiling
patterns, it was postulated that the bubbly and slug flow regime are dominant,
and an annular flow regime does not exist in the heating tube for typical
conditions in sugar mill evaporators. Boiling patterns with uniform HTC
values along the tube length and with low HTC at the bottom of the tube were
identified when good heat transfer performance is achieved.
• Favoured tube dimensions were selected, based on HTCmax. For the typical
operating conditions at the 1st effect, the traditional tube M2 and tubes S2,
M3, S3 and S4 provided high values of HTCmax. At the typical 3rd effect
boiling conditions, the traditional tube M2 and tubes M3, S3 and M4 provided
high values of HTCmax. For the typical 5th effect boiling conditions, the
traditional tube M2 and tube L2 provided high values of HTCmax.
• A cost model was developed, which showed that the fabrication and
installation costs for evaporators with smaller diameter and/or longer tubes
were substantially lower than for evaporators with the traditional M2 tube.
• For evaporators at the 1st effect in a steam efficient configuration (typically
high juice boiling temperature and large heating surface areas), tubes of
smaller diameter and/or longer tubes than the traditional M2 tube have
smaller juice hold-up volumes. Consequently, the extent of sucrose
hydrolysis would be less in these evaporators than for the M2 tube evaporator
owing to the shorter juice residence time.
• Based on considerations of the HTC performance, capital costs for an
installation, operating costs (particularly related to the potential sucrose
degradation at the 1st effect) and also practical considerations, the favoured
tubes in a quintuple evaporator set are:-
• For the 1st to 3rd effects, tubes S3 and M3
• For the 4th and 5th effects, the traditional M2 tube.
• Retrofitting of a calandria comprising S3 or M3 tubes into an existing
evaporator with M2 tubes may be a financially attractive alternative to
228 General Discussions and Conclusions
installing a new evaporator, in circumstances where additional heating
surface area is required. The retrofitting of the S3 or M3 tubes is only
recommended for evaporators at the 1st to 3rd effect positions, owing to their
good heat transfer performance at these positions.
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Appendix A: Description of Experimental Rig 235
APPENDIX A: DESCRIPTION OF
EXPERIMENTAL RIG
In Chapter 2, heat transfer results from previous pilot plant investigations and
factory trials of Robert evaporators were discussed. A major part of this study included
the assessment of the heat transfer performance of a single evaporator tube operating
in rising-film mode. The pilot evaporator rig was constructed so as to accommodate
the installation of tubes with different lengths and diameters. The heat-transfer
performance for each tube was evaluated for the full range of process conditions
normally experienced in factory vessels. The design, construction and commissioning
of the rig were completed in 2013 and are broadly described in this Appendix. The full
experimental program was conducted during the 2014 crushing season at Rocky Point
Mill between July and November.
Appendix A: Description of Experimental Rig 237
A.1. Designing of the single tube evaporator rig
A.1.1. Design and construction of single tube
The single tube evaporator, which was used in the PhD study by Steven Pennisi
(at James Cook University), was used as a starting point for designing the experimental
rig (Pennisi, 2004). The rig at JCU was designed with a single stainless steel tube of 2
m length and 44.45 mm OD (i.e. M2 dimension).
The scope of this PhD study was extended to investigate the single-tube
evaporator rig with tubes of different dimensions as shown in Table 3.1. For future
references to the tube dimensions, the code shown in Table 3.1 on page 53 for each
tube is used. Since the evaporator rig from JCU was used for only the M2 dimension,
the rig had to be modified significantly. A draftsman was contracted to prepare the
manufacturing drawings.
The heating sources used in the evaporator rig were vapours from the factory
vessels at the 1st, 2nd, 3rd and 4th effects. Since Rocky Point mill has cogeneration, the
exhaust steam pressure is 250 kPa (abs) and the exhaust steam connection was located
distant from the rig installation. Hence, it was decided to use vapour from the 1st effect
as the heating source when operating the rig as a 1st effect. This arrangement is logical,
as the pressure of the 1st effect vapour is ~200 kPa (abs) (120 °C), which is typical of
the exhaust steam pressure in factories without cogeneration.
The vapour rate is not a controlled parameter in the experimental setup. Based
on the run, the pressure inside the calandria is controlled by an automatic control valve
through a PID controller. This is discussed in detail in section A.2. The maximum and
minimum values of vapour condensation coefficient for Australian vessels are 40
kg/h/m2 and 12 kg/h/m2 respectively (Watson, 1986a).
When designing the single tube rig, the anticipated maximum and minimum
vapour rates were used. The vapour rates for the nine tubes are described in A.1. These
data show that the maximum condensation rate on the tube is calculated at 25.5 kg/h
and the minimum condensation rate at 2.9 kg/h.
238 Appendix A: Description of Experimental Rig
Table A.1 Highest and lowest vapour rate for tubes
Tube Vapour rate (kg/h)
VCC–12 kg/h/m2 VCC–40 kg/h/m2
S2 2.9 9.6
M2 3.4 11.2
L2 3.8 12.8
S3 4.3 14.4
M3 5.0 16.8
L3 5.7 19.2
L2 5.7 19.2
L3 6.7 22.3
L4 7.7 25.5
Each tube has four gutters attached to the outside of the tubes, which are placed
equidistantly along the heating tube to drain the condensate to separate collection
chambers. This arrangement allows the determination of the heat transfer coefficient
at the different sections of the tube and for the entire tube length. The gutters were
designed to drain the condensed vapour for the highest vapour rate, without
overflowing and causing an error in the HTC calculations. The length and area of each
section is shown in Table A.2.
Table A.2 Section length and area for all tubes
Tube Section
length (m)
Section area (m2)
Section 1 Section 2 Section 3 Section 4
S2 0.50 0.06 0.06 0.06 0.06
M2 0.50 0.07 0.07 0.07 0.07
L2 0.50 0.08 0.08 0.08 0.08
S3 0.75 0.09 0.09 0.09 0.09
M3 0.75 0.10 0.10 0.10 0.10
L3 0.75 0.12 0.12 0.12 0.12
S4 1.00 0.12 0.12 0.12 0.12
M4 1.00 0.14 0.14 0.14 0.14
L4 1.00 0.16 0.16 0.16 0.16
In designing the gutter and the pipe to drain the condensate, a check needs to be
made on the pressure losses through the pipe to the collection chamber. The longest
tube in the experimental program is L4 and this would provide the greatest frictional
loss as it has the highest condensation flow and longest drain tube from the uppermost
gutter to the container.
Appendix A: Description of Experimental Rig 239
Figure A.1. shows a photograph of the gutters and condensate drain pipes. The
pipe used for draining the condensate from the gutters is 9.53 mm diameter pipe (1
mm thickness).
Figure A.1 View of the gutters and drain pipes on two of the heating tubes
To determine the pressure drop in the pipe, the K-Hooper equation (Hooper,
1981) was used. Frictional losses were calculated, and the resulting pressure drop is
shown below in kPa and mm of fluid, based on the conditions for L4 tube (see Table
A.1).
Fluid flow (t/h)–6.4 × 10-3
Pipe ID–7.53 mm
Pipe length–5 m
240 Appendix A: Description of Experimental Rig
Two 45 degree bends
One entrance and one exit
Viscosity of condensate at 20 °C
Pressure drop–0.1212 kPa (12.34 mm of fluid)
This pressure loss is equivalent to 2.4 mm per metre of length of the drain pipe,
which indicates that, even for a condensation rate several times the expected maximum
condensation rate, the drain tubes should readily drain the condensate from the gutter
to the condensate container. Overflowing of the gutters due to frictional losses in the
drain pipes should not occur.
A.1.2 Fabrication of vapour lines
As mentioned earlier, the heating sources in the evaporator rig were the vapours
from factory vessels. Vapour pipes from the 1st, 2nd, 3rd and 4th effect vapour lines were
connected to a single manifold near the rig installation. A condensate reservoir was
fabricated and installed on the vapour manifold after the steam control valve, to drain
the condensate that is present with the vapour stream before the vapour enters the
steam chest of the experimental rig.
A.1.3 Headspace and sight glass arrangement
As the liquid inside the tube boils, the vapour is passed through the headspace
of the rig. The headspace was made up of two sections. The first section, which was
just above the steam chest, was 600 mm long, 200 NB SCH 40 SS pipe with a sight
glass. The second section was 450 mm long, 400 NB SCH 40 SS pipe. This section
was added to reduce the entrainment of juice in the vapour when operating at high
evaporation conditions. The headspace equipment is shown in Figure A.2.
The vapour is withdrawn from the headspace through a trap to remove entrained
liquid. The trap was a 250 NB polycarbonate container (Figure A.2), which provided
a flow reversal designed to disengage the liquid. The separated liquid is collected in
the trap and the vapour passes through to the heat exchanger.
A.1.4 Heat exchanger, condenser and vacuum arrangement
The plate-type heat exchanger condensed the vapour by heat exchange with
cooling water. By necessity, in order to ensure that the total vapour flow is condensed,
the condensate is slightly sub-cooled (by up to 10 °C).
Appendix A: Description of Experimental Rig 241
The condensed vapour from the heat exchanger passes to a separator pot where
incondensable gases are removed. The separator pot vents the incondensable gases to
vacuum (for trials with the headspace below atmospheric pressure) and to atmosphere
(for trials with the headspace above the atmospheric pressure).
The vacuum connection is procured from the factory’s vacuum pump via a
control valve. The control system for regulating the pressure (vacuum or above
atmospheric pressure) is discussed in section A.2.
The sub-cooled condensate from the separator pot is heated using an immersion
heater located in the pipe, transferring the condensate back to the juice tank. The
amount of sub-cooling is regulated so that the heating load does not overload the
immersion heater. The control systems for regulating the temperature of the cooled
condensate and the heated condensate are discussed in section A.2.
242 Appendix A: Description of Experimental Rig
Figure A.2 Steam chest and headspace arrangement
Headspace
Sight glass
Steam
chest Steam pipe
Headspace
pressure
transmitter
Steam
chest
pressure
transmitter
External
juice return
line
Vapour
trap
Nox gases
pipe to
vacuum
Appendix A: Description of Experimental Rig 243
A.1.5 Condensate collection for the heating tube and condensate level measurement
The condensate from each gutter and the base of the steam chest (flowing in 10
mm pipe) passed through a cooling jacket (32 NB SS pipe with sealed ends) before
entering the respective condensate container.
The cooled condensate was collected in polycarbonate containers of 76 mm OD
and 700 mm height for each of the four gutters and in a 100 mm OD 700 mm high
container for condensate from the base of the steam chest. The base of each container
had connections for a differential pressure transmitter (ΔP cell) and a drain valve.
The measurement setup for the ΔP cell is shown in Figure A.3. The low pressure
side of the ΔP cell was connected to the polycarbonate container and the high pressure
side was connected to a stand pipe (15 NB stainless steel pipe) holding a column of
water with a constant height of 700 mm. A manifold was located level with the top of
the polycarbonate container to equalise the pressure in the headspace of the container
to that of the steam chest. Thus, condensate collected in the gutter flowed by gravity
(via the cooling jacket) to the polycarbonate container. Before the start of each run,
condensate was drained from the reservoir.
The ΔP cell on the base of each container has a constant head of 700 mm water
on its high pressure side with the pressure on the low pressure side being the head of
condensate in the container, which varied from zero (empty container) to 700 mm (full
container). Thus, the differential pressure ranges between 700 mm and 0 mm. The ΔP
cells were calibrated from 0 to 700 mm.
244 Appendix A: Description of Experimental Rig
Figure A.3 Arrangement for measuring the pressure head of condensate in the
container
The high performance Yokogawa differential pressure transmitters EJX110A
were selected to measure the condensate level in the containers. These transmitters
feature a single crystal silicon resonant sensor with output of 4 to 20 mA DC signal
corresponding to the measured differential pressure. The EJX110A- M capsule was
selected, as its range and accuracy suited the duty. The ambient temperature limits for
the EJX110A are -30 to 80 °C. In order to suit the temperature conditions, the
condensate was cooled prior to entering the containers. Cooling water was passed
through jackets that surrounded the drain tubes.
Figure A.4 shows a photograph of the polycarbonate containers, the cooling
jackets and the DP transmitters under the experimental rig.
Appendix A: Description of Experimental Rig 245
Figure A.4 Arrangement of the DP transmitters and polycarbonate containers
A.1.6 Juice return and take off arrangement
A juice return line was provided to transfer juice from the top tube plate to the
juice tank below the steam chest. This setup replicates a mini downtake, which is often
provided in factory evaporators.
A.1.7 Assembly of the evaporator rig
Figure 4.1 on page 68 shows the layout of the evaporator rig assembly. The juice
tank was mounted on the support frame and the 2 m steam chest was placed on top.
The tube was then inserted from the top of the steam chest and using a spirit level, the
DP cell Support
frame
Polycarbonate
container
Manifold for
pressure
equalisation
Condensate
reservoir
Condensed
vapour
Cooling
water jackets
246 Appendix A: Description of Experimental Rig
tube was aligned vertically, and all the bolts were tightened. Anti-Seize was used on
all the bolts to avoid cramming due to high temperature in the calandria and juice tank.
As described in section 4.3 on page 70, experiments were undertaken for nine
tubes. The procedure that was followed when changing a tube is explained below:
1. Isolate all utilities from the evaporator; turn off the immersion heater and
drain all the juice from the juice tank.
2. Uncouple all the unions on pipes on the rig.
3. Disconnect the condensate drainage pipes from the containers.
4. Remove the headspace vessel and unbolt the steam chest from the juice
tank.
5. Lift the steam chest with the chain block and unbolt the top flange on the
steam chest.
6. Lift the heating tube out of the steam chest and place it safely in storage.
7. As an example, if the existing set up is for a 2 m tube and a 3 m tube is
to be installed, install the 1 m steam chest above the 2 m steam chest. [If
the tube is of 4 m length, install the two 1 m steam chests above the 2 m
steam chest.]
8. Insert the selected heating tube inside the steam chest and reinstall the
top flange
9. Place the headspace vessel back in position and reinstall all connections.
10. Ensure all the unions on the pipework are connected correctly.
11. Connect the condensate drainage pipes into the cooling jackets and
connect each drain pipe to the condensate container.
12. Fill the steam chest with water and hydro test the vessel for any leaks.
Recheck all connections if any leaks are found.
A.2 Instrumentation and Control System of the Rig
A.2.1. Introductory remarks
This section describes the instrumentation and the control systems required to
operate the rig. There are four control loops in the evaporator rig and each one is
Appendix A: Description of Experimental Rig 247
described in detail. Figure A.6 shows the arrangement for the instrumentation and
control system for the evaporator rig.
A.2.2 Headspace pressure control system
The arrangement for the headspace pressure control is shown in Figure A.6. The
pressure within the headspace of the evaporator rig was measured by the absolute
pressure transmitter (PT1), which sends an input signal to the proportional-integral-
derivative (PID 1) controller. The output signal from the controller regulates the valve
to the vacuum source or to atmosphere. The controller is set to forward-acting when
operating above atmospheric pressure and reverse-acting when operating below
atmospheric pressure. The operator enters a pressure set point for the headspace based
on the required boiling conditions for the run.
248 Appendix A: Description of Experimental Rig
Figure A.6 Experimental rig control system
Appendix A: Description of Experimental Rig 249
A.2.3 Vapour pressure control
The arrangement for the pressure control of vapour within the steam chest is
shown in Figure A.6. The pressure within the calandria of the evaporator rig is
measured by the absolute pressure transmitter (PT2), which sends an input signal to
the PID 2 controller. The output signal from the controller modulates the position of
the control valve (MSV) to allow/restrict vapour flow in the manifold. The steam
valves (SV1, SV2, and SV3) valves are manual valves for different tube heights. The
operator enters a pressure set point for the steam chest, based on the required boiling
conditions of the run.
A.2.5 Temperature control of the condensed vapour leaving the heat exchanger
In order to ensure the heating duty of the immersion heater is within its power
rating, the temperature of the condensed vapour is controlled to be ~10 °C below the
headspace saturation temperature. The PID 4 controller uses the temperature reading
from RTD2 (PV) and modulates the position of the valve to allow/restrict the flow of
cooling water to the heat exchanger.
A.2.4 Temperature control of return condensed vapour
The condensed vapour needs to be reheated to the boiling temperature of the
juice before adding it back to the juice tank. The juice temperature set point is
determined from RTD1. The RTD3 measures the temperature after the immersion
heater. The PID 3 controller regulates the power input to the immersion heater to the
heat the condensate until the RTD3 signal is at the set point. An auto switch is
implemented in the immersion heater to turn off the heater when the return leg has no
fluid. The switch had to be turned on manually before the start of each run.
A.2.6 Juice level monitoring
The juice level within the heating tube of the evaporator rig was measured by
the differential pressure transmitter (PT3) mounted on the juice tank. The low pressure
side of the transmitter was connected to the headspace of the rig. A glass tube
connected to the juice tank and to the headspace was installed to provide a visual check
on the level of juice and assist in setting the conditions for a run.
The instrumentation requirements are listed in Table A.4
250 Appendix A: Description of Experimental Rig
Table A.4 List of instruments for the control of the evaporator rig
Tag Duty Type Control system Controller
PT1 Saturated
steam/vapour
Absolute
pressure
transmitter
Headspace
pressure
PID 1
PT2 Saturated
steam/vapour
Absolute
pressure
transmitter
Steam chest
pressure
PID 2
PT3 Level
monitoring
Differential
pressure
transmitter
Juice level
monitoring
RTD1 Juice/water Resistance
temperature
detectors
Juice tank
temperature
RTD2 Condensate Resistance
temperature
detectors
Condensate
temperature
before
immersion heater
PID 4
RTD3 Condensate Resistance
temperature
detectors
Condensate
temperature after
immersion heater
PID 3
Cartridge
heater, ½” D
×10” L
A.3 Data Logging
A.3.1 Introductory remarks
The pilot plant evaporator rig contained individual PID controllers to control the
operating parameters, as described in section A.2. The process variable signals from
these controllers along with the measurements of the condensate level in the
polycarbonate containers were routed through an Automation Direct Programmable
Logic Controller (PLC). This section describes the data logging system for the pilot
plant rig.
A.3.2 Programmable logic controller (PLC)
The process variable signals were wired into the analogue input modules of the
PLC. The Automation Direct Logic PLC utilises DirectSOFT32, a proprietary
software interface program suite to allow programming of the PLC and data access.
A part of this suite is the DSData Server. DSData Server is an application that
allows the third party software applications to read and write data to the PLC. DSData
supports two different mechanisms for undertaking this:
Appendix A: Description of Experimental Rig 251
• Dynamic Data Exchange (DEE)
• Object Linking and Embedding for process control (OLE).
The project data was logged in Microsoft Excel with a simple visual basic macro
accessing and storing data with DEE via the DSData interface.
A.3.3 Process data logging
The process data that was logged for each run included juice level, juice
temperature, calandria pressure, headspace pressure and the condensate level in the
five polycarbonate containers. All the operating values were displayed on the excel
spreadsheet on the computer screen, which was placed next to the control box. The
computer screen was checked often to make sure data was being logged.
A.4 Commissioning of the Rig
The evaporator rig was commissioned during a two week period in mid-
November 2013, prior to the factory ceasing crushing operations for the 2013 season.
Overall the evaporator rig operated and functioned well. The instrumentation
and control system in particular worked well. The main changes needed to prepare the
rig for the experimental program were:-
• Insulation of the rig needed to be completed
• Spare polycarbonate containers were required to be constructed in
readiness for failures
• The manual valves for draining the condensate from the polycarbonate
containers needed to be replaced by solenoid valves so they could be
operated remotely
• The control valve for regulating the cooling water flow to the heat
exchanger needed to be replaced with a larger valve.
For the commissioning, only the M2 tube was tested; hence the possible
problems associated with changing tubes were still unknown. It was expected that,
even with the assistance of Rocky Point tradesmen, a full day might be taken to change
a tube.
252 Appendix A: Description of Experimental Rig
A.5 Experimental trials in 2014
The experimental trials were undertaken in the period July to November 2014 at
Rocky Point sugar factory. The trials included the Original432 and Replicate128
experiments. A total of 13 tubes were changed during the trials. Table A.5 presents the
test order for the Original432 and Replicate128 experiments.
Table A.5 Test order for the tubes for the Original432 and Replicate128
experiments
The procedure for changing a tube took approximately 7 hours. A contractor
tradesman assisted with replacing the tube and preparing the rig for the next series of
experimental trials.
A.5 Concluding Remarks
The design, construction and installation of the evaporator rig have been
described in this Appendix. The control system has also been described.
Commissioning was undertaken late in the 2013 crushing season. The modifications
that were required have been listed. These modifications were completed prior to
undertaking the experimental trials in the 2014 season.
Order Tube
Original432
1 M4
2 S3
3 M3
4 L4
5 S2
6 M2
7 L2
8 L3
9 S4
Replicate128
1 M2
2 S2
3 M3
4 S3
Appendix B: CFD Model–Steam Side 253
APPENDIX B: CFD MODEL–STEAM
SIDE
B.1 Introductory Remarks
This appendix presents the CFD model simulations on the steam side of the pilot
evaporator. The modelling demonstrates that the velocity of vapour in the vicinity of
the outer wall of the heating tube is very low. The likelihood of the vapour flow
disturbing the condensate film on the outside of the tube is negligible.
Appendix B: CFD Model–Steam Side 255
Figure B.1 CFD model showing the steam velocity profile for a 0.5 m section of
the pilot evaporator
Appendix C: Original432 Data Set - Experimental Design and Results 257
APPENDIX C: ORIGINAL432 DATA SET -
EXPERIMENTAL DESIGN AND
RESULTS
C.1 Introductory remarks
This appendix presents the results of the Original432 experiments conducted
with the evaporator rig. Nine tubes were tested with a wide range of operating
conditions. Table C.1 presents the experimental design. The HTC and VCC results of
the Original432 experiments are shown in Table C.2. Visual observations of the
boiling pattern were discussed in section 5.3 on page 113. Three boiling patterns were
identified:
• No visible juice above top plate (NV)
• Visible juice above top plate (VJ)
• Substantial juice above top plate (SJ)
Table C.2 presents the visual observations for each test. The code shown above
is used to describe the visual observations of the test.
Appendix C: Original432 Data Set - Experimental Design and Results 259
Table C.1 Order of tests for the Original432 experiment
Test TL
(m)
TD
(mm)
Brix JL (% tube
height)
JL (abs in
mm)
HS (kPa
abs)
ΔP
(kPa)
36 4 44.45 20 20 800 149 33
33 4 44.45 20 20 800 149 45
35 4 44.45 20 20 800 126 33
34 4 44.45 20 20 800 126 45
8 4 44.45 20 30 1200 149 33
6 4 44.45 20 30 1200 149 45
5 4 44.45 20 30 1200 126 33
7 4 44.45 20 30 1200 126 45
32 4 44.45 20 40 1600 149 33
30 4 44.45 20 40 1600 149 45
31 4 44.45 20 40 1600 126 33
29 4 44.45 20 40 1600 126 45
1 4 44.45 20 50 2000 149 33
4 4 44.45 20 50 2000 149 45
3 4 44.45 20 50 2000 126 33
2 4 44.45 20 50 2000 126 45
13 4 44.45 35 20 800 94 35
16 4 44.45 35 20 800 94 50
15 4 44.45 35 20 800 72 35
14 4 44.45 35 20 800 72 50
9 4 44.45 35 35 1400 94 35
12 4 44.45 35 35 1400 94 50
11 4 44.45 35 35 1400 72 35
10 4 44.45 35 35 1400 72 50
45 4 44.45 35 45 1800 94 35
48 4 44.45 35 45 1800 94 50
47 4 44.45 35 45 1800 72 35
46 4 44.45 35 45 1800 72 50
26 4 44.45 35 60 2400 94 35
27 4 44.45 35 60 2400 94 50
25 4 44.45 35 60 2400 72 35
28 4 44.45 35 60 2400 72 50
42 4 44.45 70 30 1200 29 42
44 4 44.45 70 30 1200 29 60
43 4 44.45 70 30 1200 22 42
41 4 44.45 70 30 1200 22 60
39 4 44.45 70 45 1800 29 42
37 4 44.45 70 45 1800 29 60
38 4 44.45 70 45 1800 22 42
40 4 44.45 70 45 1800 22 60
23 4 44.45 70 55 2200 29 42
24 4 44.45 70 55 2200 29 60
21 4 44.45 70 55 2200 22 42
22 4 44.45 70 55 2200 22 60
19 4 44.45 70 70 2800 29 42
260 Appendix C: Original432 Data Set - Experimental Design and Results
Test TL
(m)
TD
(mm)
Brix JL (% tube
height)
JL (abs in
mm)
HS (kPa
abs)
ΔP
(kPa)
18 4 44.45 70 70 2800 29 60
20 4 44.45 70 70 2800 22 42
17 4 44.45 70 70 2800 22 60
80 3 38.1 20 20 600 149 33
79 3 38.1 20 20 600 149 45
77 3 38.1 20 20 600 126 33
78 3 38.1 20 20 600 126 45
93 3 38.1 20 30 900 149 33
96 3 38.1 20 30 900 149 45
95 3 38.1 20 30 900 126 33
94 3 38.1 20 30 900 126 45
74 3 38.1 20 40 1200 149 33
73 3 38.1 20 40 1200 149 45
76 3 38.1 20 40 1200 126 33
75 3 38.1 20 40 1200 126 45
51 3 38.1 20 50 1500 149 33
52 3 38.1 20 50 1500 149 45
49 3 38.1 20 50 1500 126 33
50 3 38.1 20 50 1500 126 45
86 3 38.1 35 20 600 94 35
85 3 38.1 35 20 600 94 50
88 3 38.1 35 20 600 72 35
87 3 38.1 35 20 600 72 50
70 3 38.1 35 35 1050 94 35
69 3 38.1 35 35 1050 94 50
72 3 38.1 35 35 1050 72 35
71 3 38.1 35 35 1050 72 50
81 3 38.1 35 45 1350 94 35
82 3 38.1 35 45 1350 94 50
84 3 38.1 35 45 1350 72 35
83 3 38.1 35 45 1350 72 50
68 3 38.1 35 60 1800 94 35
65 3 38.1 35 60 1800 94 50
66 3 38.1 35 60 1800 72 35
67 3 38.1 35 60 1800 72 50
62 3 38.1 70 30 900 29 42
64 3 38.1 70 30 900 29 60
63 3 38.1 70 30 900 22 42
61 3 38.1 70 30 900 22 60
59 3 38.1 70 45 1350 29 42
58 3 38.1 70 45 1350 29 60
57 3 38.1 70 45 1350 22 42
60 3 38.1 70 45 1350 22 60
91 3 38.1 70 55 1650 29 42
92 3 38.1 70 55 1650 29 60
90 3 38.1 70 55 1650 22 42
89 3 38.1 70 55 1650 22 60
Appendix C: Original432 Data Set - Experimental Design and Results 261
Test TL
(m)
TD
(mm)
Brix JL (% tube
height)
JL (abs in
mm)
HS (kPa
abs)
ΔP
(kPa)
53 3 38.1 70 70 2100 29 42
54 3 38.1 70 70 2100 29 60
56 3 38.1 70 70 2100 22 42
55 3 38.1 70 70 2100 22 60
121 3 44.45 20 20 600 149 33
122 3 44.45 20 20 600 149 45
124 3 44.45 20 20 600 126 33
123 3 44.45 20 20 600 126 45
102 3 44.45 20 30 900 149 33
104 3 44.45 20 30 900 149 45
101 3 44.45 20 30 900 126 33
103 3 44.45 20 30 900 126 45
118 3 44.45 20 40 1200 149 33
120 3 44.45 20 40 1200 149 45
117 3 44.45 20 40 1200 126 33
119 3 44.45 20 40 1200 126 45
100 3 44.45 20 50 1500 149 33
98 3 44.45 20 50 1500 149 45
97 3 44.45 20 50 1500 126 33
99 3 44.45 20 50 1500 126 45
139 3 44.45 35 20 600 94 35
138 3 44.45 35 20 600 94 50
137 3 44.45 35 20 600 72 35
140 3 44.45 35 20 600 72 50
130 3 44.45 35 35 1050 94 35
129 3 44.45 35 35 1050 94 50
132 3 44.45 35 35 1050 72 35
131 3 44.45 35 35 1050 72 50
128 3 44.45 35 45 1350 94 35
127 3 44.45 35 45 1350 94 50
125 3 44.45 35 45 1350 72 35
126 3 44.45 35 45 1350 72 50
107 3 44.45 35 60 1800 94 35
106 3 44.45 35 60 1800 94 50
108 3 44.45 35 60 1800 72 35
105 3 44.45 35 60 1800 72 50
142 3 44.45 70 30 900 29 42
141 3 44.45 70 30 900 29 60
143 3 44.45 70 30 900 22 42
144 3 44.45 70 30 900 22 60
115 3 44.45 70 45 1350 29 42
116 3 44.45 70 45 1350 29 60
113 3 44.45 70 45 1350 22 42
114 3 44.45 70 45 1350 22 60
136 3 44.45 70 55 1650 29 42
133 3 44.45 70 55 1650 29 60
134 3 44.45 70 55 1650 22 42
262 Appendix C: Original432 Data Set - Experimental Design and Results
Test TL
(m)
TD
(mm)
Brix JL (% tube
height)
JL (abs in
mm)
HS (kPa
abs)
ΔP
(kPa)
135 3 44.45 70 55 1650 22 60
109 3 44.45 70 70 2100 29 42
110 3 44.45 70 70 2100 29 60
112 3 44.45 70 70 2100 22 42
111 3 44.45 70 70 2100 22 60
181 4 50.8 20 20 800 149 33
183 4 50.8 20 20 800 149 45
182 4 50.8 20 20 800 126 33
184 4 50.8 20 20 800 126 45
177 4 50.8 20 30 1200 149 33
178 4 50.8 20 30 1200 149 45
179 4 50.8 20 30 1200 126 33
180 4 50.8 20 30 1200 126 45
169 4 50.8 20 40 1600 149 33
170 4 50.8 20 40 1600 149 45
171 4 50.8 20 40 1600 126 33
172 4 50.8 20 40 1600 126 45
146 4 50.8 20 50 2000 149 33
145 4 50.8 20 50 2000 149 45
148 4 50.8 20 50 2000 126 33
147 4 50.8 20 50 2000 126 45
186 4 50.8 35 20 800 94 35
185 4 50.8 35 20 800 94 50
188 4 50.8 35 20 800 72 35
187 4 50.8 35 20 800 72 50
176 4 50.8 35 35 1400 94 35
173 4 50.8 35 35 1400 94 50
175 4 50.8 35 35 1400 72 35
174 4 50.8 35 35 1400 72 50
167 4 50.8 35 45 1800 94 35
168 4 50.8 35 45 1800 94 50
166 4 50.8 35 45 1800 72 35
165 4 50.8 35 45 1800 72 50
163 4 50.8 35 60 2400 94 35
164 4 50.8 35 60 2400 94 50
161 4 50.8 35 60 2400 72 35
162 4 50.8 35 60 2400 72 50
158 4 50.8 70 30 1200 29 42
157 4 50.8 70 30 1200 29 60
159 4 50.8 70 30 1200 22 42
160 4 50.8 70 30 1200 22 60
156 4 50.8 70 45 1800 29 42
155 4 50.8 70 45 1800 29 60
153 4 50.8 70 45 1800 22 42
154 4 50.8 70 45 1800 22 60
189 4 50.8 70 55 2200 29 42
190 4 50.8 70 55 2200 29 60
Appendix C: Original432 Data Set - Experimental Design and Results 263
Test TL
(m)
TD
(mm)
Brix JL (% tube
height)
JL (abs in
mm)
HS (kPa
abs)
ΔP
(kPa)
191 4 50.8 70 55 2200 22 42
192 4 50.8 70 55 2200 22 60
150 4 50.8 70 70 2800 29 42
149 4 50.8 70 70 2800 29 60
152 4 50.8 70 70 2800 22 42
151 4 50.8 70 70 2800 22 60
229 2 38.1 20 20 400 149 33
230 2 38.1 20 20 400 149 45
231 2 38.1 20 20 400 126 33
232 2 38.1 20 20 400 126 45
219 2 38.1 20 30 600 149 33
218 2 38.1 20 30 600 149 45
217 2 38.1 20 30 600 126 33
220 2 38.1 20 30 600 126 45
215 2 38.1 20 40 800 149 33
213 2 38.1 20 40 800 149 45
214 2 38.1 20 40 800 126 33
216 2 38.1 20 40 800 126 45
194 2 38.1 20 50 1000 149 33
193 2 38.1 20 50 1000 149 45
196 2 38.1 20 50 1000 126 33
195 2 38.1 20 50 1000 126 45
226 2 38.1 35 20 400 94 35
225 2 38.1 35 20 400 94 50
227 2 38.1 35 20 400 72 35
228 2 38.1 35 20 400 72 50
224 2 38.1 35 35 700 94 35
223 2 38.1 35 35 700 94 50
222 2 38.1 35 35 700 72 35
221 2 38.1 35 35 700 72 50
204 2 38.1 35 45 900 94 35
203 2 38.1 35 45 900 94 50
202 2 38.1 35 45 900 72 35
201 2 38.1 35 45 900 72 50
200 2 38.1 35 60 1200 94 35
199 2 38.1 35 60 1200 94 50
198 2 38.1 35 60 1200 72 35
197 2 38.1 35 60 1200 72 50
239 2 38.1 70 30 600 29 42
237 2 38.1 70 30 600 29 60
240 2 38.1 70 30 600 22 42
238 2 38.1 70 30 600 22 60
210 2 38.1 70 45 900 29 42
212 2 38.1 70 45 900 29 60
211 2 38.1 70 45 900 22 42
209 2 38.1 70 45 900 22 60
264 Appendix C: Original432 Data Set - Experimental Design and Results
Test TL
(m)
TD
(mm)
Brix JL (% tube
height)
JL (abs in
mm)
HS (kPa
abs)
ΔP
(kPa)
235 2 38.1 70 55 1100 29 42
236 2 38.1 70 55 1100 29 60
233 2 38.1 70 55 1100 22 42
234 2 38.1 70 55 1100 22 60
206 2 38.1 70 70 1400 29 42
208 2 38.1 70 70 1400 29 60
207 2 38.1 70 70 1400 22 42
205 2 38.1 70 70 1400 22 60
241 2 44.45 20 20 400 149 33
242 2 44.45 20 20 400 149 45
243 2 44.45 20 20 400 126 33
244 2 44.45 20 20 400 126 45
277 2 44.45 20 30 600 149 33
279 2 44.45 20 30 600 149 45
278 2 44.45 20 30 600 126 33
280 2 44.45 20 30 600 126 45
260 2 44.45 20 40 800 149 33
259 2 44.45 20 40 800 149 45
258 2 44.45 20 40 800 126 33
257 2 44.45 20 40 800 126 45
284 2 44.45 20 50 1000 149 33
281 2 44.45 20 50 1000 149 45
283 2 44.45 20 50 1000 126 33
282 2 44.45 20 50 1000 126 45
245 2 44.45 35 20 400 94 35
246 2 44.45 35 20 400 94 50
247 2 44.45 35 20 400 72 35
248 2 44.45 35 20 400 72 50
268 2 44.45 35 35 700 94 35
267 2 44.45 35 35 700 94 50
266 2 44.45 35 35 700 72 35
265 2 44.45 35 35 700 72 50
263 2 44.45 35 45 900 94 35
264 2 44.45 35 45 900 94 50
262 2 44.45 35 45 900 72 35
261 2 44.45 35 45 900 72 50
286 2 44.45 35 60 1200 94 35
285 2 44.45 35 60 1200 94 50
288 2 44.45 35 60 1200 72 35
287 2 44.45 35 60 1200 72 50
251 2 44.45 70 30 600 29 42
252 2 44.45 70 30 600 29 60
250 2 44.45 70 30 600 22 42
249 2 44.45 70 30 600 22 60
269 2 44.45 70 45 900 29 42
272 2 44.45 70 45 900 29 60
271 2 44.45 70 45 900 22 42
Appendix C: Original432 Data Set - Experimental Design and Results 265
Test TL
(m)
TD
(mm)
Brix JL (% tube
height)
JL (abs in
mm)
HS (kPa
abs)
ΔP
(kPa)
270 2 44.45 70 45 900 22 60
256 2 44.45 70 55 1100 29 42
253 2 44.45 70 55 1100 29 60
255 2 44.45 70 55 1100 22 42
254 2 44.45 70 55 1100 22 60
275 2 44.45 70 70 1400 29 42
276 2 44.45 70 70 1400 29 60
274 2 44.45 70 70 1400 22 42
273 2 44.45 70 70 1400 22 60
314 2 50.8 20 20 400 149 33
315 2 50.8 20 20 400 149 45
313 2 50.8 20 20 400 126 33
316 2 50.8 20 20 400 126 45
295 2 50.8 20 30 600 149 33
296 2 50.8 20 30 600 149 45
294 2 50.8 20 30 600 126 33
293 2 50.8 20 30 600 126 45
310 2 50.8 20 40 800 149 33
311 2 50.8 20 40 800 149 45
312 2 50.8 20 40 800 126 33
309 2 50.8 20 40 800 126 45
292 2 50.8 20 50 1000 149 33
290 2 50.8 20 50 1000 149 45
291 2 50.8 20 50 1000 126 33
289 2 50.8 20 50 1000 126 45
324 2 50.8 35 20 400 94 35
323 2 50.8 35 20 400 94 50
321 2 50.8 35 20 400 72 35
322 2 50.8 35 20 400 72 50
304 2 50.8 35 35 700 94 35
303 2 50.8 35 35 700 94 50
302 2 50.8 35 35 700 72 35
301 2 50.8 35 35 700 72 50
320 2 50.8 35 45 900 94 35
319 2 50.8 35 45 900 94 50
318 2 50.8 35 45 900 72 35
317 2 50.8 35 45 900 72 50
299 2 50.8 35 60 1200 94 35
300 2 50.8 35 60 1200 94 50
297 2 50.8 35 60 1200 72 35
298 2 50.8 35 60 1200 72 50
332 2 50.8 70 30 600 29 42
329 2 50.8 70 30 600 29 60
330 2 50.8 70 30 600 22 42
331 2 50.8 70 30 600 22 60
333 2 50.8 70 45 900 29 42
336 2 50.8 70 45 900 29 60
266 Appendix C: Original432 Data Set - Experimental Design and Results
Test TL
(m)
TD
(mm)
Brix JL (% tube
height)
JL (abs in
mm)
HS (kPa
abs)
ΔP
(kPa)
334 2 50.8 70 45 900 22 42
335 2 50.8 70 45 900 22 60
328 2 50.8 70 55 1100 29 42
325 2 50.8 70 55 1100 29 60
326 2 50.8 70 55 1100 22 42
327 2 50.8 70 55 1100 22 60
308 2 50.8 70 70 1400 29 42
305 2 50.8 70 70 1400 29 60
307 2 50.8 70 70 1400 22 42
306 2 50.8 70 70 1400 22 60
379 3 50.8 20 20 600 149 33
377 3 50.8 20 20 600 149 45
380 3 50.8 20 20 600 126 33
378 3 50.8 20 20 600 126 45
347 3 50.8 20 30 900 149 33
346 3 50.8 20 30 900 149 45
348 3 50.8 20 30 900 126 33
345 3 50.8 20 30 900 126 45
373 3 50.8 20 40 1200 149 33
376 3 50.8 20 40 1200 149 45
374 3 50.8 20 40 1200 126 33
375 3 50.8 20 40 1200 126 45
351 3 50.8 20 50 1500 149 33
350 3 50.8 20 50 1500 149 45
352 3 50.8 20 50 1500 126 33
349 3 50.8 20 50 1500 126 45
364 3 50.8 35 20 600 94 35
362 3 50.8 35 20 600 94 50
363 3 50.8 35 20 600 72 35
361 3 50.8 35 20 600 72 50
384 3 50.8 35 35 1050 94 35
382 3 50.8 35 35 1050 94 50
383 3 50.8 35 35 1050 72 35
381 3 50.8 35 35 1050 72 50
356 3 50.8 35 45 1350 94 35
355 3 50.8 35 45 1350 94 50
354 3 50.8 35 45 1350 72 35
353 3 50.8 35 45 1350 72 50
357 3 50.8 35 60 1800 94 35
360 3 50.8 35 60 1800 94 50
359 3 50.8 35 60 1800 72 35
358 3 50.8 35 60 1800 72 50
344 3 50.8 70 30 900 29 42
343 3 50.8 70 30 900 29 60
342 3 50.8 70 30 900 22 42
341 3 50.8 70 30 900 22 60
340 3 50.8 70 45 1350 29 42
Appendix C: Original432 Data Set - Experimental Design and Results 267
Test TL
(m)
TD
(mm)
Brix JL (% tube
height)
JL (abs in
mm)
HS (kPa
abs)
ΔP
(kPa)
339 3 50.8 70 45 1350 29 60
338 3 50.8 70 45 1350 22 42
337 3 50.8 70 45 1350 22 60
371 3 50.8 70 55 1650 29 42
370 3 50.8 70 55 1650 29 60
369 3 50.8 70 55 1650 22 42
372 3 50.8 70 55 1650 22 60
368 3 50.8 70 70 2100 29 42
367 3 50.8 70 70 2100 29 60
366 3 50.8 70 70 2100 22 42
365 3 50.8 70 70 2100 22 60
403 4 38.1 20 20 800 149 33
401 4 38.1 20 20 800 149 45
402 4 38.1 20 20 800 126 33
404 4 38.1 20 20 800 126 45
400 4 38.1 20 30 1200 149 33
398 4 38.1 20 30 1200 149 45
397 4 38.1 20 30 1200 126 33
399 4 38.1 20 30 1200 126 45
390 4 38.1 20 40 1600 149 33
391 4 38.1 20 40 1600 149 45
392 4 38.1 20 40 1600 126 33
389 4 38.1 20 40 1600 126 45
385 4 38.1 20 50 2000 149 33
387 4 38.1 20 50 2000 149 45
388 4 38.1 20 50 2000 126 33
386 4 38.1 20 50 2000 126 45
425 4 38.1 35 20 800 94 35
427 4 38.1 35 20 800 94 50
426 4 38.1 35 20 800 72 35
428 4 38.1 35 20 800 72 50
429 4 38.1 35 35 1400 94 35
432 4 38.1 35 35 1400 94 50
431 4 38.1 35 35 1400 72 35
430 4 38.1 35 35 1400 72 50
422 4 38.1 35 45 1800 94 35
421 4 38.1 35 45 1800 94 50
424 4 38.1 35 45 1800 72 35
423 4 38.1 35 45 1800 72 50
420 4 38.1 35 60 2400 94 35
418 4 38.1 35 60 2400 94 50
417 4 38.1 35 60 2400 72 35
419 4 38.1 35 60 2400 72 50
414 4 38.1 70 30 1200 29 42
416 4 38.1 70 30 1200 29 60
415 4 38.1 70 30 1200 22 42
413 4 38.1 70 30 1200 22 60
268 Appendix C: Original432 Data Set - Experimental Design and Results
Test TL
(m)
TD
(mm)
Brix JL (% tube
height)
JL (abs in
mm)
HS (kPa
abs)
ΔP
(kPa)
411 4 38.1 70 45 1800 29 42
412 4 38.1 70 45 1800 29 60
410 4 38.1 70 45 1800 22 42
409 4 38.1 70 45 1800 22 60
395 4 38.1 70 55 2200 29 42
393 4 38.1 70 55 2200 29 60
394 4 38.1 70 55 2200 22 42
396 4 38.1 70 55 2200 22 60
408 4 38.1 70 70 2800 29 42
405 4 38.1 70 70 2800 29 60
407 4 38.1 70 70 2800 22 42
406 4 38.1 70 70 2800 22 60
Appendix C: Original432 Data Set - Experimental Design and Results 269
Table C.2 Results from the Original432 experiment
Test Brix ΔP (kPa) ΔT (°C) HTC
(W/m2/K)
VCC
(kg/h/m2)
Observations on
boiling pattern
36 17.9 33 5.73 2826 26.37 VJ
33 17.9 40 6.91 2802 31.57 VJ
35 17.9 33 6.54 2969 31.48 VJ
34 17.9 45 8.76 3474 49.47 VJ
8 17.8 33 5.73 3542 33.08 SJ
6 17.8 45 7.73 3269 41.25 SJ
5 17.8 33 6.55 1751 18.58 NV
7 17.8 45 8.77 3453 49.20 SJ
32 17 33 5.76 2975 27.92 VJ
30 17 45 7.76 3725 47.19 VJ
31 17 33 6.57 3118 33.22 VJ
29 17 45 8.79 3806 54.39 VJ
1 15 33 5.83 1441 13.68 VJ
4 15 40 7.01 3596 41.10 SJ
3 15 33 6.64 3134 33.73 SJ
2 15 45 8.86 3097 44.59 VJ
13 36 35 7.86 898 11.35 NV
16 36 50 11.10 1374 24.64 NV
15 36 35 9.74 2308 35.91 VJ
14 36 50 13.49 2159 46.75 VJ
9 34 35 7.97 3530 45.24 SJ
12 34 50 11.21 2007 36.33 VJ
11 34 35 9.84 2494 39.23 VJ
10 34 50 13.59 2435 53.14 SJ
45 36.2 35 7.85 3328 42.00 VJ
48 36.2 50 11.09 1132 20.27 VJ
47 36.2 35 9.73 2628 40.85 VJ
46 36.2 50 13.48 2651 57.35 VJ
26 34.7 35 7.93 2651 33.82 NV
27 34.7 50 11.17 2989 53.93 SJ
25 34.7 35 9.81 2510 39.34 VJ
28 34.7 50 13.56 2319 50.47 VJ
42 68 42 17.70 145 4.05 NV
44 68 60 23.77 252 9.50 NV
43 68 42 21.32 146 4.90 NV
41 68 60 27.88 187 8.26 NV
39 69.5 42 17.34 186 5.08 NV
37 69.5 60 23.42 412 15.32 NV
38 69.5 42 20.98 118 3.88 NV
40 69.5 60 27.54 200 8.72 NV
23 65 42 18.30 261 7.54 NV
24 65 60 24.38 308 11.93 NV
21 65 42 21.90 71 2.44 NV
22 65 60 28.46 441 19.90 VJ
19 66 42 18.11 149 4.26 NV
270 Appendix C: Original432 Data Set - Experimental Design and Results
Test Brix ΔP (kPa) ΔT (°C) HTC
(W/m2/K)
VCC
(kg/h/m2)
Observations on
boiling pattern
18 66 60 24.19 386 14.81 VJ
20 66 42 21.72 249 8.50 NV
17 66 60 28.28 409 18.35 VJ
80 17.9 33 5.73 3886 36.27 SJ
79 17.9 40 6.91 3737 42.11 SJ
77 17.9 33 6.54 4133 43.83 SJ
78 17.9 45 8.76 3867 55.08 SJ
93 21.7 33 5.59 3389 30.84 VJ
96 21.7 40 6.76 3521 38.84 VJ
95 21.7 33 6.40 2917 30.27 VJ
94 21.7 45 8.62 2978 41.74 VJ
74 20 33 5.65 4221 38.86 SJ
73 20 41 6.99 3749 42.78 SJ
76 20 33 6.47 3457 36.24 VJ
75 20 45 8.69 3445 48.64 VJ
51 16.3 33 5.79 2616 24.66 NV
52 16.3 36 6.29 2177 22.33 NV
49 16.3 33 6.60 2166 23.16 NV
50 16.3 45 8.82 3114 44.62 VJ
86 37.7 35 7.76 2020 25.20 NV
85 37.7 50 11.00 2735 48.59 VJ
88 37.7 35 9.64 296 4.56 NV
87 37.7 50 13.39 800 17.20 NV
70 38 35 7.74 3998 49.77 SJ
69 38 50 10.98 2964 52.58 SJ
72 38 35 9.62 1144 17.60 NV
71 38 50 13.38 1006 21.60 NV
81 38 35 7.74 3763 46.84 VJ
82 38 50 10.98 3231 57.30 SJ
84 38 35 9.62 1532 23.56 NV
83 38 50 13.38 1000 21.48 NV
68 38 35 7.74 840 10.46 NV
65 38 50 10.98 2041 36.20 NV
66 38 35 9.62 2161 33.24 NV
67 38 50 13.38 1806 38.78 NV
62 66.8 42 17.95 258 7.32 NV
64 66.8 60 24.03 350 13.35 NV
63 66.8 42 21.57 271 9.20 NV
61 66.8 60 28.13 325 14.48 NV
59 67 42 17.91 272 7.68 NV
58 67 60 23.99 376 14.31 NV
57 67 42 21.53 466 15.79 NV
60 67 60 28.09 246 10.94 NV
91 67.6 42 17.78 427 11.97 NV
92 67.6 60 23.86 427 16.19 NV
90 67.6 42 21.41 404 13.61 NV
89 67.6 60 27.97 385 17.05 NV
Appendix C: Original432 Data Set - Experimental Design and Results 271
Test Brix ΔP (kPa) ΔT (°C) HTC
(W/m2/K)
VCC
(kg/h/m2)
Observations on
boiling pattern
53 69 42 17.47 539 14.84 NV
54 69 60 23.54 347 12.97 NV
56 69 42 21.10 346 11.48 NV
55 69 60 27.66 103 4.51 NV
121 17.9 33 5.73 1964 18.33 NV
122 17.9 40 6.91 1193 13.44 NV
124 17.9 33 6.54 1223 12.97 NV
123 17.9 45 8.76 909 12.95 NV
102 20 33 5.65 4343 39.98 VJ
104 20 45 7.65 4084 51.00 SJ
101 20 33 6.47 2016 21.13 SJ
103 20 45 8.69 4459 62.96 SJ
118 20 33 5.65 2922 26.90 VJ
120 20 45 7.65 2105 26.29 NV
117 20 33 6.47 2288 23.99 NV
119 20 45 8.69 1079 15.24 NV
100 18 33 5.73 3288 30.67 VJ
98 18 45 7.72 3530 44.51 VJ
97 18 33 6.54 3620 38.37 VJ
99 18 45 8.76 4057 57.75 SJ
139 35.9 35 7.86 126 1.59 NV
138 35.9 50 11.11 206 3.69 NV
137 35.9 35 9.74 169 2.64 NV
140 35.9 50 13.49 194 4.20 NV
130 38.5 35 7.71 548 6.79 NV
129 38.5 50 10.95 337 5.97 NV
132 38.5 35 9.59 485 7.43 NV
131 38.5 50 13.35 838 17.94 NV
128 37.5 35 7.77 900 11.24 NV
127 37.5 50 11.01 775 13.79 NV
125 37.5 35 9.65 633 9.77 NV
126 37.5 50 13.40 698 15.03 NV
107 36.5 35 7.83 3632 45.74 SJ
106 36.5 50 11.07 3550 63.48 SJ
108 36.5 35 9.71 2794 43.36 SJ
105 36.5 50 13.46 2134 46.11 SJ
142 70 42 17.22 71 1.93 NV
141 70 60 23.29 226 8.37 NV
143 70 42 20.86 104 3.42 NV
144 70 60 27.42 52 2.27 NV
115 68.5 42 17.58 138 3.84 NV
116 68.5 60 23.66 25 0.93 NV
113 68.5 42 21.21 197 6.57 NV
114 68.5 60 27.77 231 10.18 NV
136 70 42 17.22 20 0.54 NV
133 70 60 23.29 248 9.16 NV
134 70 42 20.86 91 2.97 NV
272 Appendix C: Original432 Data Set - Experimental Design and Results
Test Brix ΔP (kPa) ΔT (°C) HTC
(W/m2/K)
VCC
(kg/h/m2)
Observations on
boiling pattern
135 70 60 27.42 89 3.87 NV
109 68.5 42 17.58 454 12.59 NV
110 68.5 60 23.66 337 12.67 NV
112 68.5 42 21.21 64 2.12 NV
111 68.5 60 27.77 58 2.57 NV
181 17.9 33 5.73 831 7.75 NV
183 17.9 40 6.91 508 5.72 NV
182 17.9 33 6.54 896 9.50 NV
184 17.9 45 8.76 457 6.51 NV
177 17 33 5.76 714 6.50 NV
178 17 40 6.94 684 7.75 NV
179 17 33 6.57 540 5.75 NV
180 17 45 8.79 664 9.48 NV
169 17.2 33 5.75 611 5.73 NV
170 17.2 41 7.10 817 9.46 NV
171 17.2 33 6.57 731 7.78 NV
172 17.2 45 8.79 456 6.51 NV
146 21.9 33 5.58 802 7.56 NV
145 21.9 39 6.59 587 6.51 NV
148 21.9 33 6.40 684 7.32 NV
147 21.9 45 8.62 654 9.15 NV
186 36 35 7.86 125 1.58 NV
185 36 50 11.10 103 1.85 NV
188 36 35 9.74 283 4.40 NV
187 36 50 13.49 206 4.46 NV
176 34 35 7.97 523 6.70 NV
173 34 50 11.21 190 3.43 NV
175 34 35 9.84 780 12.27 NV
174 34 50 13.59 843 18.39 NV
167 36.2 35 7.85 353 4.45 NV
168 36.2 50 11.09 244 4.37 NV
166 36.2 35 9.73 120 1.86 NV
165 36.2 50 13.48 492 10.65 NV
163 34.7 35 7.93 124 1.58 NV
164 34.7 50 11.17 288 5.19 NV
161 34.7 35 9.81 740 11.59 NV
162 34.7 50 13.56 386 8.40 NV
158 68 42 17.70 28 0.77 NV
157 68 60 23.77 28 1.07 NV
159 68 42 21.32 11 0.38 NV
160 68 60 27.88 23 1.01 NV
156 69.5 42 17.34 123 3.37 NV
155 69.5 60 23.42 48 1.80 NV
153 69.5 42 20.98 94 3.09 NV
154 69.5 60 27.54 48 2.09 NV
189 65 42 18.30 117 3.37 NV
190 65 60 24.38 46 1.77 NV
Appendix C: Original432 Data Set - Experimental Design and Results 273
Test Brix ΔP (kPa) ΔT (°C) HTC
(W/m2/K)
VCC
(kg/h/m2)
Observations on
boiling pattern
191 65 42 21.90 152 5.22 NV
192 65 60 28.46 75 3.36 NV
150 70 42 17.22 192 5.21 NV
149 70 60 23.29 91 3.36 NV
152 70 42 20.86 54 1.79 NV
151 70 60 27.42 52 2.26 NV
229 17.5 33 5.74 2515 23.54 NV
230 17.5 35 6.08 2831 28.06 NV
231 17.5 33 6.56 4618 49.07 VJ
232 17.5 45 8.78 3074 43.84 VJ
219 20 33 5.65 4661 42.91 SJ
218 20 40 6.83 4152 46.26 SJ
217 20 33 6.47 4938 51.76 SJ
220 20 45 8.69 3804 53.71 SJ
215 18 33 5.73 4358 40.65 VJ
213 18 41 7.07 3688 42.53 SJ
214 18 33 6.54 2092 22.17 NV
216 18 45 8.76 5225 74.39 SJ
194 18 33 5.73 1987 18.54 NV
193 18 44 7.56 1077 13.29 NV
196 18 33 6.54 1475 15.63 NV
195 18 45 8.76 935 13.31 NV
226 36.5 35 7.83 170 2.14 NV
225 36.5 50 11.07 1350 24.14 NV
227 36.5 35 9.71 2294 35.60 VJ
228 36.5 50 13.46 721 15.58 NV
224 37 35 7.80 424 5.32 NV
223 37 50 11.04 397 7.07 NV
222 37 35 9.68 395 6.11 NV
221 37 50 13.43 2130 45.94 VJ
204 37 35 7.80 823 10.32 NV
203 37 50 11.04 647 11.53 NV
202 37 35 9.68 75 1.16 NV
201 37 50 13.43 1413 30.48 VJ
200 37.2 35 7.79 764 9.57 NV
199 37.2 50 11.03 276 4.91 NV
198 37.2 35 9.67 26 0.40 NV
197 37.2 50 13.42 99 2.14 NV
239 70 42 17.22 22 0.60 NV
237 70 60 23.29 286 10.59 NV
240 70 42 20.86 42 1.39 NV
238 70 60 27.42 290 12.59 NV
210 70.5 42 17.09 17 0.47 NV
212 70.5 60 23.16 130 4.77 NV
211 70.5 42 20.73 19 0.63 NV
209 70.5 60 27.29 25 1.08 NV
235 71.5 42 16.81 5 0.14 NV
274 Appendix C: Original432 Data Set - Experimental Design and Results
Test Brix ΔP (kPa) ΔT (°C) HTC
(W/m2/K)
VCC
(kg/h/m2)
Observations on
boiling pattern
236 71.5 60 22.88 35 1.29 NV
233 71.5 42 20.47 535 17.21 VJ
234 71.5 60 27.03 168 7.20 NV
206 72 42 16.66 453 11.90 NV
208 72 60 22.73 444 16.05 VJ
207 72 42 20.32 492 15.72 VJ
205 72 60 26.88 546 23.27 VJ
241 18.2 33 5.72 3638 33.89 VJ
242 18.2 37 6.40 3124 32.57 NV
243 18.2 33 6.53 2255 23.87 NV
244 18.2 45 8.75 1651 23.49 NV
277 19.5 33 5.67 3033 28.02 VJ
279 19.5 40 6.85 5133 57.34 SJ
278 19.5 33 6.49 4835 50.83 SJ
280 19.5 45 8.71 2639 37.34 VJ
260 20 33 5.65 5509 50.72 SJ
259 20 38 6.50 5663 59.99 SJ
258 20 33 6.47 4784 50.15 SJ
257 20 45 8.69 2636 37.22 VJ
284 20 33 5.65 5051 46.50 SJ
281 20 37 6.33 4792 49.44 SJ
283 20 33 6.47 3550 37.21 VJ
282 20 45 8.69 2521 35.59 VJ
245 37 35 7.80 2272 28.50 VJ
246 37 50 11.04 1795 32.00 VJ
247 37 35 9.68 844 13.06 NV
248 37 50 13.43 1287 27.76 NV
268 38 35 7.74 1357 16.89 NV
267 38 50 10.98 1689 29.96 NV
266 38 35 9.62 803 12.34 NV
265 38 50 13.38 2218 47.62 VJ
263 35 35 7.91 1639 20.86 NV
264 35 50 11.16 1843 33.20 NV
262 35 35 9.79 1133 17.73 NV
261 35 50 13.54 2267 49.28 NV
286 35 35 7.91 3020 38.44 VJ
285 35 50 11.16 2970 53.51 VJ
288 35 35 9.79 2228 34.86 VJ
287 35 50 13.54 1884 40.96 NV
251 72 42 16.66 262 6.89 NV
252 72 60 22.73 557 20.13 NV
250 72 42 20.32 34 1.09 NV
249 72 60 26.88 478 20.35 NV
269 71.9 42 16.69 625 16.46 VJ
272 71.9 60 22.76 437 15.80 NV
271 71.9 42 20.35 934 29.89 VJ
270 71.9 60 26.91 385 16.42 NV
256 69.8 42 17.27 417 11.35 VJ
Appendix C: Original432 Data Set - Experimental Design and Results 275
Test Brix ΔP (kPa) ΔT (°C) HTC
(W/m2/K)
VCC
(kg/h/m2)
Observations on
boiling pattern
253 69.8 60 23.34 150 5.56 NV
255 69.8 42 20.91 346 11.37 NV
254 69.8 60 27.47 28 1.20 NV
275 74 42 16.00 501 12.65 VJ
276 74 60 22.08 376 13.17 VJ
274 74 42 19.69 367 11.37 NV
273 74 60 26.25 474 19.73 VJ
314 18 33 5.73 3433 32.02 VJ
315 18 35 6.07 3784 37.40 VJ
313 18 33 6.54 1708 18.10 NV
316 18 45 8.76 43 0.61 NV
295 16.9 33 5.77 2912 27.35 NV
296 16.9 37 6.44 1555 16.33 NV
294 16.9 33 6.58 2644 28.19 NV
293 16.9 45 8.80 1327 18.97 NV
310 20 33 5.65 4378 40.31 VJ
311 20 41 6.99 3446 39.33 VJ
312 20 33 6.47 4557 47.77 VJ
309 20 45 8.69 1684 23.78 NV
292 18.5 33 5.71 3227 30.00 VJ
290 18.5 37 6.38 2580 26.86 VJ
291 18.5 33 6.52 1788 18.90 NV
289 18.5 45 8.74 1794 25.49 NV
324 36 35 7.86 510 6.45 NV
323 36 50 11.10 819 14.68 NV
321 36 35 9.74 561 8.72 NV
322 36 50 13.49 702 15.21 NV
304 37 35 7.80 1472 18.47 NV
303 37 50 11.04 2256 40.23 VJ
302 37 35 9.68 2966 45.89 VJ
301 37 50 13.43 2215 47.76 NV
320 35 35 7.91 187 2.38 NV
319 35 50 11.16 1058 19.07 NV
318 35 35 9.79 1376 21.52 NV
317 35 50 13.54 2268 49.31 NV
299 35 35 7.91 1421 18.08 NV
300 35 50 11.16 2802 50.48 VJ
297 35 35 9.79 1510 23.63 NV
298 35 50 13.54 789 17.15 NV
332 70 42 17.22 4 0.10 NV
329 70 60 23.29 616 22.80 VJ
330 70 42 20.86 214 7.01 NV
331 70 60 27.42 103 4.49 NV
333 67 42 17.91 588 16.63 VJ
336 67 60 23.99 157 5.97 NV
334 67 42 21.53 256 8.68 NV
335 67 60 28.09 110 4.87 NV
328 73 42 16.34 10 0.25 NV
276 Appendix C: Original432 Data Set - Experimental Design and Results
Test Brix ΔP (kPa) ΔT (°C) HTC
(W/m2/K)
VCC
(kg/h/m2)
Observations on
boiling pattern
325 73 60 22.42 729 25.95 VJ
326 73 42 20.02 337 10.60 NV
327 73 60 26.58 151 6.38 NV
308 69 42 17.47 769 21.18 SJ
305 69 60 23.54 797 29.80 SJ
307 69 42 21.10 589 19.54 VJ
306 69 60 27.66 413 18.11 VJ
379 18.2 33 5.72 29 0.27 NV
377 18.2 40 6.90 2205 24.80 NV
380 18.2 33 6.53 1895 20.06 NV
378 18.2 45 8.75 610 8.67 NV
347 17.5 33 5.74 2631 24.62 NV
346 17.5 40 6.92 2586 29.20 NV
348 17.5 33 6.56 2217 23.56 NV
345 17.5 45 8.78 1467 20.92 NV
373 18.2 33 5.72 5668 52.80 SJ
376 18.2 35 6.06 3778 37.30 VJ
374 18.2 33 6.53 2224 23.54 VJ
375 18.2 45 8.75 2629 37.40 VJ
351 14.2 33 5.86 4063 38.75 VJ
350 14.2 40 7.03 1945 22.31 VJ
352 14.2 33 6.67 621 6.71 NV
349 14.2 45 8.89 2106 30.42 NV
364 34.1 35 7.96 753 9.64 NV
362 34.1 50 11.21 521 9.42 NV
363 34.1 35 9.84 1096 17.22 NV
361 34.1 50 13.59 1077 23.50 NV
384 34 35 7.97 615 7.89 NV
382 34 50 11.21 498 9.01 NV
383 34 35 9.84 1195 18.80 NV
381 34 50 13.59 883 19.27 NV
356 34.9 35 7.92 742 9.44 NV
355 34.9 50 11.16 543 9.79 NV
354 34.9 35 9.80 1596 24.99 NV
353 34.9 50 13.55 1431 31.11 NV
357 35.2 35 7.90 689 8.75 NV
360 35.2 50 11.15 523 9.42 NV
359 35.2 35 9.78 411 6.42 NV
358 35.2 50 13.53 2002 43.49 VJ
344 73 42 16.34 57 1.48 NV
343 73 60 22.42 154 5.48 NV
342 73 42 20.02 252 7.94 NV
341 73 60 26.58 301 12.69 NV
340 72.9 42 16.38 127 3.28 NV
339 72.9 60 22.45 155 5.52 NV
338 72.9 42 20.05 56 1.76 NV
337 72.9 60 26.61 149 6.29 NV
371 71.2 42 16.89 136 3.62 NV
Appendix C: Original432 Data Set - Experimental Design and Results 277
Test Brix ΔP (kPa) ΔT (°C) HTC
(W/m2/K)
VCC
(kg/h/m2)
Observations on
boiling pattern
370 71.2 60 22.97 508 18.54 VJ
369 71.2 42 20.55 47 1.53 NV
372 71.2 60 27.11 261 11.23 NV
368 73.2 42 16.28 313 8.04 NV
367 73.2 60 22.35 347 12.32 NV
366 73.2 42 19.96 114 3.59 NV
365 73.2 60 26.52 623 26.18 VJ
403 17.9 33 5.73 3938 36.76 SJ
401 17.9 45 7.72 3514 44.33 SJ
402 17.9 33 6.54 4214 44.69 SJ
404 17.9 45 8.76 3795 54.05 SJ
400 17.5 33 5.74 4212 39.41 SJ
398 17.5 45 7.74 4039 51.04 SJ
397 17.5 33 6.56 4108 43.65 VJ
399 17.5 45 8.78 2559 36.51 VJ
390 15 33 5.83 4504 42.77 VJ
391 15 45 7.82 3387 43.28 VJ
392 15 33 6.64 1065 11.46 NV
389 15 45 8.86 1654 23.82 NV
385 16 33 5.80 4121 38.90 VJ
387 16 40 6.97 1529 17.39 NV
388 16 33 6.61 1631 17.47 NV
386 16 45 8.83 3692 52.97 VJ
425 37 35 7.80 712 8.94 NV
427 37 50 11.04 400 7.14 NV
426 37 35 9.68 796 12.32 NV
428 37 50 13.43 761 16.40 NV
429 35 35 7.91 42 0.54 NV
432 35 50 11.16 32 0.58 NV
431 35 35 9.79 29 0.45 NV
430 35 50 13.54 32 0.69 NV
422 35 35 7.91 710 9.03 NV
421 35 50 11.16 332 5.98 NV
424 35 35 9.79 652 10.20 NV
423 35 50 13.54 734 15.95 NV
420 35 35 7.91 663 8.44 NV
418 35 50 11.16 550 9.90 NV
417 35 35 9.79 1250 19.57 NV
419 35 50 13.54 889 19.33 NV
414 70 42 17.22 182 4.94 NV
416 70 60 23.29 333 12.33 NV
415 70 42 20.86 71 2.32 NV
413 70 60 27.42 180 7.80 NV
411 67 42 17.91 168 4.75 NV
412 67 60 23.99 347 13.21 NV
410 67 42 21.53 47 1.58 NV
409 67 60 28.09 253 11.26 NV
395 67.6 42 17.78 255 7.16 NV
278 Appendix C: Original432 Data Set - Experimental Design and Results
Test Brix ΔP (kPa) ΔT (°C) HTC
(W/m2/K)
VCC
(kg/h/m2)
Observations on
boiling pattern
393 67.6 60 23.86 327 12.40 NV
394 67.6 42 21.41 129 4.34 NV
396 67.6 60 27.97 52 2.32 NV
408 69 42 17.47 224 6.16 NV
405 69 60 23.54 371 13.89 NV
407 69 42 21.10 110 3.66 NV
406 69 60 27.66 398 17.45 NV
Appendix D: Replicate128 Data Set - Experimental Design and Results 279
APPENDIX D: REPLICATE128 DATA
SET - EXPERIMENTAL DESIGN AND
RESULTS
D.1 Introductory Remarks
This appendix presents the results of the Replicates128 experiments conducted
with the evaporator rig. Four tubes were tested with a range of operating conditions.
Brix of 20 and 70 were selected to keep the experiment in manageable size. Table D.1
presents the experimental design. The HTC and VCC results of the Replicate128
experiments are shown in Table D.2. Table D.2 includes the visual observations for
each test.
Appendix D: Replicate128 Data Set - Experimental Design and Results 281
Table D.1 Order of tests for the Replicate128 experiment
Test TL
(m)
TD
(mm)
Brix JL (% tube
height)
JL (abs in
mm)
HS (kPa
abs)
ΔP
(kPa)
5 2 44.45 20 20 400 149 33
7 2 44.45 20 20 400 149 45
6 2 44.45 20 20 400 126 33
8 2 44.45 20 20 400 126 45
25 2 44.45 20 30 600 149 33
27 2 44.45 20 30 600 149 45
26 2 44.45 20 30 600 126 33
28 2 44.45 20 30 600 126 45
9 2 44.45 20 40 800 149 33
10 2 44.45 20 40 800 149 45
11 2 44.45 20 40 800 126 33
12 2 44.45 20 40 800 126 45
1 2 44.45 20 50 1000 149 33
3 2 44.45 20 50 1000 149 45
2 2 44.45 20 50 1000 126 33
4 2 44.45 20 50 1000 126 45
21 2 44.45 70 30 600 29 42
22 2 44.45 70 30 600 29 60
23 2 44.45 70 30 600 22 42
24 2 44.45 70 30 600 22 60
30 2 44.45 70 45 900 29 42
29 2 44.45 70 45 900 29 60
32 2 44.45 70 45 900 22 42
31 2 44.45 70 45 900 22 60
14 2 44.45 70 55 1100 29 42
13 2 44.45 70 55 1100 29 60
15 2 44.45 70 55 1100 22 42
16 2 44.45 70 55 1100 22 60
18 2 44.45 70 70 1400 29 42
17 2 44.45 70 70 1400 29 60
20 2 44.45 70 70 1400 22 42
19 2 44.45 70 70 1400 22 60
69 3 44.45 20 20 400 149 33
70 3 44.45 20 20 400 149 45
72 3 44.45 20 20 400 126 33
71 3 44.45 20 20 400 126 45
89 3 44.45 20 30 600 149 33
91 3 44.45 20 30 600 149 45
90 3 44.45 20 30 600 126 33
92 3 44.45 20 30 600 126 45
65 3 44.45 20 40 800 149 33
67 3 44.45 20 40 800 149 45
66 3 44.45 20 40 800 126 33
68 3 44.45 20 40 800 126 45
95 3 44.45 20 50 1000 149 33
94 3 44.45 20 50 1000 149 45
282 Appendix D: Replicate128 Data Set - Experimental Design and Results
Test TL
(m)
TD
(mm)
Brix JL (% tube
height)
JL (abs in
mm)
HS (kPa
abs)
ΔP
(kPa)
96 3 44.45 20 50 1000 126 33
93 3 44.45 20 50 1000 126 45
81 3 44.45 70 30 600 29 42
83 3 44.45 70 30 600 29 60
82 3 44.45 70 30 600 22 42
84 3 44.45 70 30 600 22 60
74 3 44.45 70 45 900 29 42
73 3 44.45 70 45 900 29 60
75 3 44.45 70 45 900 22 42
76 3 44.45 70 45 900 22 60
86 3 44.45 70 55 1100 29 42
85 3 44.45 70 55 1100 29 60
87 3 44.45 70 55 1100 22 42
88 3 44.45 70 55 1100 22 60
77 3 44.45 70 70 1400 29 42
79 3 44.45 70 70 1400 29 60
78 3 44.45 70 70 1400 22 42
80 3 44.45 70 70 1400 22 60
37 2 38.1 20 20 600 149 33
38 2 38.1 20 20 600 149 45
40 2 38.1 20 20 600 126 33
39 2 38.1 20 20 600 126 45
57 2 38.1 20 30 900 149 33
59 2 38.1 20 30 900 149 45
58 2 38.1 20 30 900 126 33
60 2 38.1 20 30 900 126 45
33 2 38.1 20 40 1200 149 33
35 2 38.1 20 40 1200 149 45
34 2 38.1 20 40 1200 126 33
36 2 38.1 20 40 1200 126 45
63 2 38.1 20 50 1500 149 33
62 2 38.1 20 50 1500 149 45
64 2 38.1 20 50 1500 126 33
61 2 38.1 20 50 1500 126 45
49 2 38.1 70 30 900 29 42
51 2 38.1 70 30 900 29 60
50 2 38.1 70 30 900 22 42
52 2 38.1 70 30 900 22 60
42 2 38.1 70 45 1350 29 42
41 2 38.1 70 45 1350 29 60
43 2 38.1 70 45 1350 22 42
44 2 38.1 70 45 1350 22 60
54 2 38.1 70 55 1650 29 42
53 2 38.1 70 55 1650 29 60
55 2 38.1 70 55 1650 22 42
56 2 38.1 70 55 1650 22 60
45 2 38.1 70 70 2100 29 42
47 2 38.1 70 70 2100 29 60
Appendix D: Replicate128 Data Set - Experimental Design and Results 283
Test TL
(m)
TD
(mm)
Brix JL (% tube
height)
JL (abs in
mm)
HS (kPa
abs)
ΔP
(kPa)
46 2 38.1 70 70 2100 22 42
48 2 38.1 70 70 2100 22 60
101 3 38.1 20 20 600 149 33
102 3 38.1 20 20 600 149 45
104 3 38.1 20 20 600 126 33
103 3 38.1 20 20 600 126 45
121 3 38.1 20 30 900 149 33
123 3 38.1 20 30 900 149 45
122 3 38.1 20 30 900 126 33
124 3 38.1 20 30 900 126 45
97 3 38.1 20 40 1200 149 33
99 3 38.1 20 40 1200 149 45
98 3 38.1 20 40 1200 126 33
100 3 38.1 20 40 1200 126 45
127 3 38.1 20 50 1500 149 33
126 3 38.1 20 50 1500 149 45
128 3 38.1 20 50 1500 126 33
125 3 38.1 20 50 1500 126 45
113 3 38.1 70 30 900 29 42
115 3 38.1 70 30 900 29 60
114 3 38.1 70 30 900 22 42
116 3 38.1 70 30 900 22 60
106 3 38.1 70 45 1350 29 42
105 3 38.1 70 45 1350 29 60
107 3 38.1 70 45 1350 22 42
108 3 38.1 70 45 1350 22 60
118 3 38.1 70 55 1650 29 42
117 3 38.1 70 55 1650 29 60
119 3 38.1 70 55 1650 22 42
120 3 38.1 70 55 1650 22 60
109 3 38.1 70 70 2100 29 42
111 3 38.1 70 70 2100 29 60
110 3 38.1 70 70 2100 22 42
112 3 38.1 70 70 2100 22 60
Appendix D: Replicate128 Data Set - Experimental Design and Results 285
Table D.2 Results from the Replicate128 experiment
Test Brix ΔP (kPa) ΔT (°C) HTC
(W/m2/K)
VCC
(kg/h//m2)
5 17.9 33 5.73 3449 32.19
7 17.9 37 6.41 2963 30.94
6 17.9 33 6.54 2139 22.68
8 17.9 45 8.76 1567 22.32
25 21.7 33 5.59 2832 25.77
27 21.7 40 6.76 4782 52.76
26 21.7 33 6.40 4506 46.76
28 21.7 45 8.62 2451 34.35
9 20.0 33 5.65 4958 45.65
10 20.0 38 6.50 5097 53.99
11 20.0 33 6.47 4306 45.13
12 20.0 45 8.69 2372 33.50
1 16.3 33 5.79 3364 31.71
3 16.3 37 6.46 3539 37.29
2 16.3 33 6.60 3845 41.12
4 16.3 45 8.69 2655 37.48
21 70.0 42 16.66 257 6.75
22 70.0 60 22.73 546 19.73
23 70.0 42 20.86 33 1.07
24 70.0 60 27.42 459 19.94
30 67.0 42 17.91 548 15.47
29 67.0 60 23.99 390 14.85
32 67.0 42 20.35 878 28.10
31 67.0 60 26.91 362 15.43
14 67.6 42 17.78 372 10.45
13 67.6 60 23.86 7 0.28
15 67.6 42 21.41 311 10.46
16 67.6 60 27.97 25 1.11
18 69.0 42 17.47 436 12.02
17 69.0 60 23.54 335 12.51
20 69.0 42 21.10 326 10.81
19 69.0 60 27.66 821 35.98
69 18.9 33 5.69 1878 17.41
70 18.9 40 6.87 1139 12.77
72 18.9 33 6.51 1168 12.32
71 18.9 45 8.73 867 12.30
89 20.5 33 5.63 4227 38.78
91 20.5 45 7.63 3971 49.47
90 20.5 33 6.45 1961 20.50
92 20.5 45 8.67 4335 61.07
65 16.0 33 5.80 2707 25.56
67 16.0 45 7.79 1963 24.97
66 16.0 33 6.61 2128 22.79
68 16.0 45 8.83 1009 14.47
95 17.0 33 5.76 3203 30.06
94 17.0 45 7.76 3443 43.62
286 Appendix D: Replicate128 Data Set - Experimental Design and Results
Test Brix ΔP (kPa) ΔT (°C) HTC
(W/m2/K)
VCC
(kg/h//m2)
96 17.0 33 6.57 3529 37.60
93 17.0 45 8.79 3960 56.60
81 70.0 42 17.22 75 2.03
83 70.0 60 23.29 237 8.79
82 70.0 42 20.86 109 3.59
84 70.0 60 27.42 55 2.38
74 67.0 42 17.91 149 4.22
73 67.0 60 23.99 27 1.02
75 67.0 42 21.21 217 7.23
76 67.0 60 27.77 254 11.20
86 67.6 42 17.78 20 0.57
85 67.6 60 23.86 254 9.62
87 67.6 42 21.41 93 3.12
88 67.6 60 27.97 92 4.07
77 68.5 42 17.58 431 11.96
79 68.5 60 23.66 320 12.04
78 68.5 42 21.21 60 2.02
80 68.5 60 27.77 56 2.45
37 20.00 33 5.65 2633 24.24
38 20.00 35 5.99 2960 28.91
40 20.00 33 6.47 4822 50.54
39 20.00 45 8.69 3199 45.16
57 16.00 33 5.80 4772 45.06
59 16.00 40 6.97 4270 48.57
58 16.00 33 6.61 5075 54.35
60 16.00 45 8.83 3931 56.40
33 19.00 33 5.69 4298 39.84
35 19.00 41 7.03 3633 41.68
34 19.00 33 6.50 2061 21.72
36 19.00 45 8.72 5142 72.90
63 20.00 33 5.65 1913 17.61
62 20.00 44 7.49 1033 12.62
64 20.00 33 6.47 1417 14.85
61 20.00 45 8.69 895 12.64
49 72.00 42 17.22 23 0.62
51 72.00 60 23.29 429 15.88
50 72.00 42 20.32 65 2.09
52 72.00 60 26.88 443 18.89
42 69.70 42 17.29 20 0.56
41 69.70 60 23.37 154 5.73
43 69.70 42 20.73 23 0.76
44 69.70 60 27.29 30 1.29
54 68.00 42 17.70 5 0.14
53 68.00 60 23.77 36 1.35
55 68.00 42 21.32 539 18.07
56 68.00 60 27.88 171 7.56
45 70.00 42 17.22 482 13.09
47 70.00 60 23.29 477 17.65
Appendix D: Replicate128 Data Set - Experimental Design and Results 287
Test Brix ΔP (kPa) ΔT (°C) HTC
(W/m2/K)
VCC
(kg/h//m2)
46 70.00 42 20.86 527 17.30
48 70.00 60 27.42 589 25.60
101 18.00 33 5.73 3617 33.73
102 18.00 40 6.90 3478 39.16
104 18.00 33 6.54 3846 40.76
103 18.00 45 8.76 3598 51.22
121 16.90 33 5.77 3186 29.91
123 16.90 40 6.94 3327 37.68
122 16.90 33 6.58 2754 29.36
124 16.90 45 8.80 2832 40.49
97 20.00 33 5.65 4010 36.92
99 20.00 41 6.99 3561 40.64
98 20.00 33 6.47 3284 34.42
100 20.00 45 8.69 3273 46.21
127 18.50 33 5.71 2705 25.15
126 18.50 36 6.22 2248 22.78
128 18.50 33 6.52 2235 23.62
125 18.50 45 8.74 3204 45.52
113 66.80 42 17.95 251 7.10
115 66.80 60 24.03 339 12.95
114 66.80 42 21.57 263 8.93
116 66.80 60 28.13 315 14.05
106 67.00 42 17.91 258 7.29
105 67.00 60 23.99 357 13.60
107 67.00 42 21.53 443 15.00
108 67.00 60 28.09 233 10.39
118 67.60 42 17.78 448 12.57
117 67.60 60 23.86 448 17.00
119 67.60 42 21.41 424 14.29
120 67.60 60 27.97 404 17.90
109 69.00 42 17.47 593 16.33
111 69.00 60 23.54 381 14.26
110 69.00 42 21.10 381 12.63
112 69.00 60 27.66 113 4.96
Appendix E: HTCmax and VCCmax Results of Original432 and Replicate128 Tests 289
APPENDIX E: HTCmax AND VCCmax
RESULTS OF ORIGINAL432 AND
REPLICATE128 TESTS
E.1 Introductory Remarks
This appendix presents the HTCmax results of the Original432 and Replicates128
experiments. The selection of HTCmax results is detailed in section 5.7.2 on page 131.
Tests were undertaken at four juice levels and an optimum juice level was determined,
which corresponded to the maximum heat transfer coefficient. The HTCmax and
VCCmax results are presented along with the corresponding operating conditions during
the test. For the target operating conditions, refer to Table C.1 and D.1 using the test
number for Original432 and Replicate128 tests respectively.
Appendix E: HTCmax and VCCmax Results of Original432 and Replicate128 Tests 291
Table E.1 HTCmax and VCCmax results from the Original432 experiment
Test TL
(m)
TD
(mm)
Brix JL (%
tube
height)
JL
(mm)
HS
(kPa
abs)
ΔP
(kPa)
ΔT
(°C)
HTCmax
(W/m2/K)
VCCmax
(kg/h/m2)
8 4 44.45 17.8 30 1200 149 33 5.73 3542 33.08
30 4 44.45 17 40 1600 149 45 7.76 3725 47.19
3 4 44.45 15 50 2000 126 33 6.64 3134 33.73
29 4 44.45 17 40 1600 126 45 8.79 3806 54.39
9 4 44.45 34 35 1400 94 35 7.97 3530 45.24
27 4 44.45 34.7 60 2400 94 50 11.17 2989 53.93
47 4 44.45 36.2 45 1800 72 35 9.73 2628 40.85
46 4 44.45 36.2 45 1800 72 50 13.48 2651 57.35
23 4 44.45 65 55 2200 29 42 18.3 261 7.54
37 4 44.45 69.5 45 1800 29 60 23.42 412 15.32
20 4 44.45 66 70 2800 22 42 21.72 249 8.5
22 4 44.45 65 55 2200 22 60 28.46 441 19.9
74 3 38.1 20 40 1200 149 33 5.65 4221 38.86
73 3 38.1 20 40 1200 149 41 6.99 3749 42.78
77 3 38.1 17.9 20 600 126 33 6.54 4133 43.83
78 3 38.1 17.9 20 600 126 45 8.76 3867 55.08
70 3 38.1 38 35 1050 94 35 7.74 3998 49.77
82 3 38.1 38 45 1350 94 50 10.98 3231 57.3
66 3 38.1 38 60 1800 72 35 9.62 2161 33.24
67 3 38.1 38 60 1800 72 50 13.38 1806 38.78
53 3 38.1 69 70 2100 29 42 17.47 539 14.84
92 3 38.1 67.6 55 1650 29 60 23.86 427 16.19
57 3 38.1 67 45 1350 22 42 21.53 466 15.79
89 3 38.1 67.6 55 1650 22 60 27.97 385 17.05
102 3 44.45 20 30 900 149 33 5.65 4343 39.98
104 3 44.45 20 30 900 149 45 7.65 4084 51
97 3 44.45 18 50 1500 126 33 6.54 3620 38.37
103 3 44.45 20 30 900 126 45 8.69 4459 62.96
107 3 44.45 36.5 60 1800 94 35 7.83 3632 45.74
106 3 44.45 36.5 60 1800 94 50 11.07 3550 63.48
108 3 44.45 36.5 60 1800 72 35 9.71 2794 43.36
105 3 44.45 36.5 60 1800 72 50 13.46 2134 46.11
109 3 44.45 68.5 70 2100 29 42 17.58 454 12.59
110 3 44.45 68.5 70 2100 29 60 23.66 337 12.67
113 3 44.45 68.5 45 1350 22 42 21.21 197 6.57
114 3 44.45 68.5 45 1350 22 60 27.77 231 10.18
181 4 50.8 17.9 20 800 149 33 5.73 831 7.75
170 4 50.8 17.2 40 1600 149 41 7.1 817 9.46
182 4 50.8 17.9 20 800 126 33 6.54 896 9.5
180 4 50.8 17 30 1200 126 45 8.79 664 9.48
176 4 50.8 34 35 1400 94 35 7.97 523 6.7
164 4 50.8 34.7 60 2400 94 50 11.17 288 5.19
175 4 50.8 34 35 1400 72 35 9.84 780 12.27
174 4 50.8 34 35 1400 72 50 13.59 843 18.39
150 4 50.8 70 70 2800 29 42 17.22 192 5.21
149 4 50.8 70 70 2800 29 60 23.29 91 3.36
191 4 50.8 65 55 2200 22 42 21.9 152 5.22
192 4 50.8 65 55 2200 22 60 28.46 75 3.36
219 2 38.1 20 30 600 149 33 5.65 4661 42.91
218 2 38.1 20 30 600 149 40 6.83 4152 46.26
292 Appendix E: HTCmax and VCCmax Results of Original432 and Replicate128 Tests
Test TL
(m)
TD
(mm)
Brix JL (%
tube
height)
JL
(mm)
HS
(kPa
abs)
ΔP
(kPa)
ΔT
(°C)
HTCmax
(W/m2/K)
VCCmax
(kg/h/m2)
217 2 38.1 20 30 600 126 33 6.47 4938 51.76
216 2 38.1 18 40 800 126 45 8.76 5225 74.39
204 2 38.1 37 45 900 94 35 7.8 823 10.32
225 2 38.1 36.5 20 400 94 50 11.07 1350 24.14
227 2 38.1 36.5 20 400 72 35 9.71 2294 35.6
221 2 38.1 37 35 700 72 50 13.43 2130 45.94
206 2 38.1 72 70 1400 29 42 16.66 453 11.9
208 2 38.1 72 70 1400 29 60 22.73 444 16.05
233 2 38.1 71.5 55 1100 22 42 20.47 535 17.21
205 2 38.1 72 70 1400 22 60 26.88 546 23.27
260 2 44.45 20 40 800 149 33 5.65 5509 50.72
259 2 44.45 20 40 800 149 38 6.5 5663 59.99
278 2 44.45 19.5 30 600 126 33 6.49 4835 50.83
280 2 44.45 19.5 30 600 126 45 8.71 2639 37.34
286 2 44.45 35 60 1200 94 35 7.91 3020 38.44
285 2 44.45 35 60 1200 94 50 11.16 2970 53.51
288 2 44.45 35 60 1200 72 35 9.79 2228 34.86
261 2 44.45 35 45 900 72 50 13.54 2267 49.28
269 2 44.45 71.9 45 900 29 42 16.69 625 16.46
252 2 44.45 72 30 600 29 60 22.73 557 20.13
271 2 44.45 71.9 45 900 22 42 20.35 934 29.89
249 2 44.45 72 30 600 22 60 26.88 478 20.35
310 2 50.8 20 40 800 149 33 5.65 4378 40.31
315 2 50.8 18 20 400 149 35 6.07 3784 37.4
312 2 50.8 20 40 800 126 33 6.47 4557 47.77
289 2 50.8 18.5 50 1000 126 45 8.74 1794 25.49
304 2 50.8 37 35 700 94 35 7.8 1472 18.47
300 2 50.8 35 60 1200 94 50 11.16 2802 50.48
302 2 50.8 37 35 700 72 35 9.68 2966 45.89
317 2 50.8 35 45 900 72 50 13.54 2268 49.31
308 2 50.8 69 70 1400 29 42 17.47 769 21.18
305 2 50.8 69 70 1400 29 60 23.54 797 29.8
307 2 50.8 69 70 1400 22 42 21.1 589 19.54
306 2 50.8 69 70 1400 22 60 27.66 413 18.11
373 3 50.8 18.2 40 1200 149 33 5.72 5668 52.8
376 3 50.8 18.2 40 1200 149 35 6.06 3778 37.3
374 3 50.8 18.2 40 1200 126 33 6.53 2224 23.54
375 3 50.8 18.2 40 1200 126 45 8.75 2629 37.4
364 3 50.8 34.1 20 600 94 35 7.96 753 9.64
355 3 50.8 34.9 45 1350 94 50 11.16 543 9.79
354 3 50.8 34.9 45 1350 72 35 9.8 1596 24.99
358 3 50.8 35.2 60 1800 72 50 13.53 2002 43.49
368 3 50.8 73.2 70 2100 29 42 16.28 313 8.04
370 3 50.8 71.2 55 1650 29 60 22.97 508 18.54
342 3 50.8 73 30 900 22 42 20.02 252 7.94
365 3 50.8 73.2 70 2100 22 60 26.52 623 26.18
390 4 38.1 15 40 1600 149 33 5.83 4504 42.77
398 4 38.1 17.5 30 1200 149 45 7.74 4039 51.04
402 4 38.1 17.9 20 800 126 33 6.54 4214 44.69
404 4 38.1 17.9 20 800 126 45 8.76 3795 54.05
425 4 38.1 37 20 800 94 35 7.8 712 8.94
418 4 38.1 35 60 2400 94 50 11.16 550 9.9
Appendix E: HTCmax and VCCmax Results of Original432 and Replicate128 Tests 293
Table E.2 HTCmax and VCCmax results from the Replicate128 experiment
Test TL
(m)
TD
(mm)
Brix JL (%
tube
height)
JL
(mm)
HS
(kPa
abs)
ΔP
(kPa)
ΔT
(°C)
HTCmax
(W/m2/K)
VCCmax
(kg/h/m2)
9 2 44.45 20 40 800 149 33 5.65 4958 45.65
10 2 44.45 20 40 800 149 38 6.5 5097 53.99
26 2 44.45 21.7 30 600 126 33 6.4 4506 46.76
4 2 44.45 16.3 50 1000 126 45 8.69 2655 37.48
30 2 44.45 67 45 900 29 42 17.91 548 15.47
22 2 44.45 70 30 600 29 60 22.73 546 19.73
32 2 44.45 67 45 900 22 42 20.35 878 28.1
19 2 44.45 69 70 1400 22 60 27.66 821 35.98
89 3 44.45 20.5 30 600 149 33 5.63 4227 38.78
91 3 44.45 20.5 30 600 149 45 7.63 3971 49.47
96 3 44.45 17 50 1000 126 33 6.57 3529 37.6
92 3 44.45 20.5 30 600 126 45 8.67 4335 61.07
77 3 44.45 68.5 70 1400 29 42 17.58 431 11.96
79 3 44.45 68.5 70 1400 29 60 23.66 320 12.04
75 3 44.45 67 45 900 22 42 21.21 217 7.23
76 3 44.45 67 45 900 22 60 27.77 254 11.2
97 3 38.1 20 40 1200 149 33 5.65 4010 36.92
99 3 38.1 20 40 1200 149 41 6.99 3561 40.64
104 3 38.1 18 20 600 126 33 6.54 3846 40.76
103 3 38.1 18 20 600 126 45 8.76 3598 51.22
109 3 38.1 69 70 2100 29 42 17.47 593 16.33
117 3 38.1 67.6 55 1650 29 60 23.86 448 17
107 3 38.1 67 45 1350 22 42 21.53 443 15
120 3 38.1 67.6 55 1650 22 60 27.97 404 17.9
57 2 38.1 16 30 900 149 33 5.8 4772 45.06
59 2 38.1 16 30 900 149 40 6.97 4270 48.57
58 2 38.1 16 30 900 126 33 6.61 5075 54.35
36 2 38.1 19 40 1200 126 45 8.72 5142 72.9
45 2 38.1 70 70 2100 29 42 17.22 482 13.09
47 2 38.1 70 70 2100 29 60 23.29 477 17.65
55 2 38.1 68 55 1650 22 42 21.32 539 18.07
48 2 38.1 70 70 2100 22 60 27.42 589 25.6
Appendix F: Individual sections HTC Results of Original432 experiments 295
APPENDIX F: INDIVIDUAL SECTIONS
HTC RESULTS OF ORIGINAL432
EXPERIMENTS
F.1 Introductory Remarks
This appendix presents the HTC results of the individual sections from the
Original432 experiments. Section 1 is the top-most section of the tube and section 4
is the bottom-most section of the tube. The tube dimensions and operating conditions
of the HTC results are presented in Table C.1 and C.2 in Appendix C.
Appendix F: Individual sections HTC Results of Original432 experiments 297
Table F Individual section HTC results for the Original432 experiment
Test Section 1 HTC
(W/m2/K)
Section 2 HTC
(W/m2/K)
Section 3 HTC
(W/m2/K)
Section 4 HTC
(W/m2/K)
36 4512 2579 1950 2261
33 4618 2641 1700 2248
35 5010 3311 1619 1935
34 5496 4570 2009 1820
8 4484 4627 2784 2273
6 4949 3450 3355 1319
5 2378 2456 1658 511
7 4691 4557 3631 933
32 4679 3318 2040 1864
30 5415 4574 3298 1614
31 4824 4198 2006 1444
29 4953 5019 3948 1303
1 2769 1874 628 493
4 5002 4543 3115 1723
3 4415 4282 2741 1099
2 4451 4135 3107 693
13 787 1085 1161 561
16 391 1022 1666 2420
15 1147 2059 3044 2981
14 1444 2054 2567 2570
9 5034 4833 3281 973
12 623 1373 2689 3344
11 1172 2206 3243 3355
10 2181 2505 2508 2546
45 2669 3665 4504 2476
48 360 589 1353 2227
47 1908 2671 3060 2873
46 2005 2579 3106 2912
26 3429 3569 2389 1218
27 3698 4004 3117 1135
25 3485 3255 2384 917
28 2018 2294 2635 2330
42 10 108 323 139
44 72 279 372 284
43 14 133 304 133
41 4 235 306 203
39 0 219 348 175
37 535 497 360 255
38 19 73 257 121
40 26 265 306 202
23 142 426 316 160
24 406 278 299 250
21 29 106 107 42
22 479 535 471 279
19 206 203 124 63
298 Appendix F: Individual sections HTC Results of Original432 experiments
Test Section 1 HTC
(W/m2/K)
Section 2 HTC
(W/m2/K)
Section 3 HTC
(W/m2/K)
Section 4 HTC
(W/m2/K)
18 382 491 425 244
20 249 333 309 104
17 460 527 427 224
80 4838 3995 3018 3695
79 4737 4132 2812 3269
77 4415 5042 3890 3185
78 4198 4244 3963 3065
93 3394 4966 2109 3087
96 3747 4829 2389 3118
95 3469 4123 2221 1853
94 3688 3792 2433 1999
74 4708 5327 3114 3736
73 4492 4677 2957 2869
76 4332 4067 2560 2869
75 4277 4197 3054 2252
51 3155 3413 2475 1423
52 3137 3284 1105 1181
49 3126 3169 1659 710
50 3444 3414 3856 1741
86 753 1080 2500 3747
85 1712 2845 3069 3315
88 257 225 257 446
87 498 661 940 1101
70 3386 4082 4485 4039
69 1097 2463 3672 4626
72 397 1101 1460 1619
71 412 894 1263 1455
81 2935 3827 4709 3580
82 2306 3064 3934 3620
84 1112 1559 1677 1780
83 861 936 1182 1023
68 213 980 1048 1120
65 1894 1951 2173 2146
66 1940 2033 2293 2378
67 1230 1571 2025 2399
62 62 50 508 414
64 80 76 571 672
63 184 110 359 432
61 302 61 311 626
59 63 326 370 327
58 204 78 482 738
57 721 275 453 416
60 123 53 268 539
91 503 466 417 320
92 319 238 470 682
90 506 419 300 392
89 294 156 550 538
Appendix F: Individual sections HTC Results of Original432 experiments 299
Test Section 1 HTC
(W/m2/K)
Section 2 HTC
(W/m2/K)
Section 3 HTC
(W/m2/K)
Section 4 HTC
(W/m2/K)
53 970 466 404 315
54 262 321 434 369
56 988 176 67 154
55 86 100 155 70
121 1459 2587 514 3295
122 785 575 209 3203
124 388 516 1662 2326
123 288 384 1235 1729
102 5111 5036 4629 2594
104 4684 4487 4550 2614
101 2195 2360 2070 1438
103 4624 4544 5067 3602
118 900 2537 3959 4291
120 449 2406 1553 4012
117 761 1384 3661 3348
119 349 622 1158 2188
100 4637 4274 2735 1508
98 4379 4195 3722 1823
97 4036 4232 3691 2523
99 4431 4372 4581 2843
139 44 35 17 408
138 32 20 6 765
137 0 0 0 677
140 0 0 0 776
130 269 644 240 1038
129 42 301 302 705
132 81 207 501 1151
131 78 138 1254 1880
128 404 528 1122 1545
127 482 445 972 1203
125 50 455 912 1116
126 110 457 907 1321
107 3175 3569 4133 3652
106 3569 3547 3803 3281
108 1913 2355 3544 3365
105 2197 1956 2257 2126
142 0 0 57 228
141 0 0 422 482
143 0 0 101 316
144 0 0 34 175
115 0 92 340 121
116 0 28 54 17
113 0 258 350 180
114 199 220 261 246
136 0 0 0 79
133 41 78 484 388
134 0 0 78 284
300 Appendix F: Individual sections HTC Results of Original432 experiments
Test Section 1 HTC
(W/m2/K)
Section 2 HTC
(W/m2/K)
Section 3 HTC
(W/m2/K)
Section 4 HTC
(W/m2/K)
135 0 1 19 337
109 685 564 303 263
110 431 365 303 249
112 63 112 48 31
111 67 83 47 37
181 428 970 461 1463
183 135 563 260 1074
182 233 782 415 2154
184 155 329 319 1026
177 242 513 499 1603
178 362 820 389 1237
179 148 614 283 1171
180 176 590 314 1627
169 166 690 318 1315
170 215 723 384 1993
171 383 867 412 1308
172 156 331 322 1035
146 312 707 673 1516
145 103 393 477 1374
148 317 502 498 1419
147 449 315 447 1344
186 10 128 206 155
185 25 42 72 274
188 288 257 131 454
187 192 304 206 121
176 233 498 262 1097
173 11 64 79 605
175 63 306 1407 1344
174 206 157 1209 1800
167 330 521 353 207
168 249 222 113 392
166 29 49 84 318
165 16 700 609 644
163 10 127 204 154
164 50 433 291 377
161 39 686 1050 1184
162 111 85 384 964
158 0 0 69 41
157 33 16 51 15
159 0 0 16 29
160 22 12 32 25
156 174 200 90 29
155 0 19 123 52
153 0 111 195 68
154 0 0 64 128
189 165 189 85 28
190 30 36 81 37
Appendix F: Individual sections HTC Results of Original432 experiments 301
Test Section 1 HTC
(W/m2/K)
Section 2 HTC
(W/m2/K)
Section 3 HTC
(W/m2/K)
Section 4 HTC
(W/m2/K)
191 95 286 116 109
192 105 121 54 18
150 120 362 147 138
149 128 147 66 22
152 36 42 96 43
151 41 66 71 30
229 1016 1993 1573 5480
230 1259 2156 2975 4932
231 3836 5532 3828 5275
232 2958 2265 3149 3924
219 4602 5961 3051 5028
218 4652 5227 2479 4253
217 4447 6803 2997 5505
220 3221 3917 3396 4684
215 5403 4294 2525 5210
213 2484 3736 2359 6174
214 1959 2563 1664 2181
216 4990 5706 4485 5719
194 760 2205 1756 3229
193 713 726 665 2203
196 958 2216 1286 1440
195 526 778 1046 1388
226 32 121 210 316
225 765 1105 1553 1977
227 2798 2385 2202 1793
228 674 470 710 1029
224 294 346 498 558
223 567 239 249 531
222 266 369 535 408
221 1825 1578 2317 2801
204 667 513 1040 1072
203 593 388 699 907
202 67 57 42 133
201 1354 1206 1296 1798
200 510 740 961 846
199 84 233 488 298
198 22 13 25 41
197 105 58 44 189
239 0 0 5 83
237 59 220 66 800
240 0 0 0 170
238 23 16 224 896
210 0 0 0 69
212 0 105 221 193
211 0 0 0 77
209 0 0 32 68
302 Appendix F: Individual sections HTC Results of Original432 experiments
Test Section 1 HTC
(W/m2/K)
Section 2 HTC
(W/m2/K)
Section 3 HTC
(W/m2/K)
Section 4 HTC
(W/m2/K)
235 0 0 0 21
236 32 36 43 31
233 321 611 626 580
234 124 119 337 93
206 357 461 532 462
208 172 158 950 498
207 528 517 394 528
205 535 138 608 904
241 2645 3621 4560 3726
242 2602 1078 4612 4204
243 2100 2098 2594 2227
244 1420 1250 1815 2121
277 5012 2506 2398 2214
279 5050 5813 5250 4420
278 4711 6014 4836 3779
280 1562 2254 2851 3888
260 5294 5909 5740 5093
259 5217 6179 6151 5105
258 4561 5098 5122 4355
257 885 2020 3271 4368
284 4738 5632 5384 4448
281 4571 5360 5024 4212
283 2140 3416 4875 3767
282 1910 2180 2400 3592
245 515 2618 3119 2834
246 465 899 2076 3739
247 916 597 1036 827
248 628 514 1384 2624
268 1368 1497 1278 1284
267 1220 1080 1374 3083
266 552 521 900 1237
265 3222 1757 1666 2226
263 1667 1643 1988 1260
264 1440 1369 1563 3001
262 723 920 1381 1508
261 3067 2159 1972 1870
286 2899 2811 2999 3372
285 3558 3039 2440 2844
288 2623 1781 1991 2517
287 2921 2010 1463 1143
251 348 280 242 177
252 602 619 547 462
250 61 42 16 17
249 543 512 457 399
269 440 725 692 643
272 217 369 590 571
271 1551 868 751 564
Appendix F: Individual sections HTC Results of Original432 experiments 303
Test Section 1 HTC
(W/m2/K)
Section 2 HTC
(W/m2/K)
Section 3 HTC
(W/m2/K)
Section 4 HTC
(W/m2/K)
270 271 447 426 396
256 568 465 354 281
253 0 0 171 428
255 471 386 293 233
254 43 25 17 25
275 654 544 435 372
276 422 399 355 327
274 500 409 312 248
273 598 415 493 392
314 3391 3262 3681 3396
315 3706 3791 3747 3892
313 913 2324 898 2695
316 48 49 43 30
295 3131 2693 2746 3080
296 1431 1365 1538 1884
294 2793 2832 2175 2776
293 1284 1413 1171 1440
310 4246 4484 4497 4283
311 3026 3572 3564 3623
312 4252 4539 4676 4762
309 823 1309 1642 2962
292 3328 2645 2849 4084
290 2544 2364 2107 3306
291 1791 1635 1530 2197
289 1764 1726 1262 2425
324 371 491 544 635
323 774 708 773 1021
321 385 336 297 1224
322 462 562 547 1239
304 871 997 1192 2828
303 1380 1240 2399 4005
302 2419 2602 2841 4002
301 1368 1583 2231 3677
320 114 129 220 285
319 1328 953 862 1091
318 1269 1020 1378 1835
317 2190 2028 2231 2625
299 864 1255 1392 2172
300 2123 2466 2720 3897
297 1298 1286 1432 2024
298 353 499 744 1559
332 0 1 2 11
329 198 563 845 858
330 0 23 81 750
331 0 37 16 361
333 510 246 769 828
336 0 0 0 627
304 Appendix F: Individual sections HTC Results of Original432 experiments
Test Section 1 HTC
(W/m2/K)
Section 2 HTC
(W/m2/K)
Section 3 HTC
(W/m2/K)
Section 4 HTC
(W/m2/K)
334 0 0 242 784
335 0 0 0 438
328 0 0 17 21
325 717 773 692 732
326 0 222 541 583
327 0 0 29 577
308 1729 785 193 366
305 824 805 776 782
307 891 568 479 418
306 692 62 341 558
379 23 22 35 36
377 1142 854 2824 4001
380 364 879 2418 3919
378 235 23 627 1553
347 1270 2198 3176 3879
346 2177 2076 2691 3401
348 1280 1438 2584 3564
345 654 868 1344 3000
373 5600 5900 5480 5693
376 3686 3594 4014 3818
374 1286 1436 2635 3537
375 3242 2833 2116 2326
351 4283 4041 3938 3989
350 994 1159 2117 3508
352 48 289 655 1491
349 1012 1255 2397 3762
364 315 666 879 1152
362 248 337 643 856
363 226 301 1240 2615
361 169 414 1055 2672
384 255 285 815 1106
382 221 417 638 715
383 74 586 1782 2339
381 134 434 1037 1928
356 237 634 940 1155
355 235 432 698 808
354 354 1085 2104 2843
353 2288 716 789 1929
357 316 587 840 1012
360 264 463 604 762
359 89 301 483 771
358 2189 2136 2073 1612
344 0 37 44 148
343 0 33 213 370
342 0 66 342 600
341 0 86 571 548
340 0 165 195 148
Appendix F: Individual sections HTC Results of Original432 experiments 305
Test Section 1 HTC
(W/m2/K)
Section 2 HTC
(W/m2/K)
Section 3 HTC
(W/m2/K)
Section 4 HTC
(W/m2/K)
339 41 199 208 172
338 0 78 88 57
337 37 219 205 136
371 157 128 144 115
370 571 537 473 451
369 73 54 39 23
372 295 302 249 200
368 297 393 281 281
367 185 443 392 368
366 259 81 34 83
365 806 645 520 521
403 4147 3730 4360 3517
401 4177 3447 3965 2468
402 4248 3933 4515 4161
404 3816 3722 4317 3325
400 4376 4291 4518 3663
398 3674 3818 4373 4290
397 3701 4137 4689 3903
399 2027 2394 3112 2704
390 4312 5078 4605 4020
391 3380 3517 3865 2787
392 167 1552 1123 1416
389 762 1272 1237 3346
385 4308 4156 4734 3285
387 1416 1562 1705 1433
388 1510 1667 1819 1528
386 3795 3774 3865 3335
425 137 703 594 1415
427 167 289 424 721
426 264 295 725 1902
428 458 226 806 1554
429 64 54 39 12
432 12 21 37 57
431 15 22 37 41
430 27 27 37 36
422 399 867 587 986
421 148 155 391 633
424 157 77 520 1853
423 0 604 637 1694
420 285 557 764 1047
418 304 418 539 938
417 388 854 1399 2361
419 253 423 840 2042
414 52 176 266 234
416 252 286 425 370
415 70 56 94 64
413 152 204 208 154
306 Appendix F: Individual sections HTC Results of Original432 experiments
Test Section 1 HTC
(W/m2/K)
Section 2 HTC
(W/m2/K)
Section 3 HTC
(W/m2/K)
Section 4 HTC
(W/m2/K)
411 9 184 261 219
412 286 340 399 362
410 0 56 76 54
409 210 271 315 216
395 142 238 283 357
393 376 208 331 394
394 86 124 132 175
396 47 46 47 70
408 67 240 322 265
405 258 358 466 403
407 59 130 143 108
406 329 470 455 338
Appendix G: Individual sections VCC Results of Original432 experiments 307
APPENDIX G: INDIVIDUAL SECTIONS
VCC RESULTS OF ORIGINAL432
EXPERIMENTS
G.1 Introductory Remarks
This appendix presents the VCC results of the individual sections of the heating
tube from the Original432 experiments. Section 1 is the top-most section of the tube
and section 4 is the bottom-most section of the tube. The tube dimensions and
operating conditions of the experiments are presented in Table C.1 and C.2 in
Appendix C.
Appendix G: Individual sections VCC Results of Original432 experiments 309
Table G Individual section VCC results for the Original432 experiment
Test Section 1 VCC
(kg/m2/h)
Section 2 VCC
(kg/m2/h)
Section 3 VCC
(kg/m2/h)
Section 4 VCC
(kg/m2/h)
36 42.11 24.07 18.20 21.11
33 52.03 29.75 19.16 25.33
35 53.13 35.11 17.17 20.52
34 78.27 65.08 28.61 25.92
8 41.87 43.21 26.00 21.23
6 62.47 43.55 42.34 16.65
5 25.24 26.05 17.59 5.42
7 66.84 64.92 51.73 13.29
32 43.91 31.14 19.15 17.49
30 68.59 57.94 41.77 20.44
31 51.40 44.72 21.38 15.38
29 70.79 71.74 56.42 18.62
1 26.29 17.79 5.96 4.68
4 57.17 51.92 35.60 19.69
3 47.52 46.09 29.50 11.83
2 64.10 59.54 44.75 9.98
13 9.94 13.71 14.68 7.09
16 7.00 18.31 29.86 43.37
15 17.85 32.03 47.36 46.38
14 31.27 44.48 55.59 55.65
9 64.51 61.94 42.05 12.46
12 11.27 24.85 48.68 60.54
11 18.43 34.70 51.02 52.77
10 47.60 54.67 54.73 55.55
45 33.68 46.25 56.83 31.24
48 6.44 10.54 24.22 39.87
47 29.66 41.51 47.56 44.66
46 43.37 55.79 67.21 63.01
26 43.73 45.52 30.48 15.53
27 66.72 72.25 56.25 20.48
25 54.62 51.01 37.36 14.38
28 43.93 49.92 57.34 50.71
42 0.27 3.01 9.03 3.89
44 2.71 10.53 14.05 10.71
43 0.47 4.47 10.20 4.46
41 0.19 10.39 13.50 8.98
39 0.00 5.99 9.53 4.80
37 19.91 18.50 13.38 9.49
38 0.61 2.42 8.49 3.99
40 1.14 11.55 13.37 8.83
23 4.10 12.29 9.13 4.62
24 15.72 10.76 11.56 9.68
21 0.99 3.67 3.68 1.43
22 21.62 24.15 21.22 12.59
19 5.88 5.80 3.55 1.79
310 Appendix G: Individual sections VCC Results of Original432 experiments
Test Section 1 VCC
(kg/m2/h)
Section 2 VCC
(kg/m2/h)
Section 3 VCC
(kg/m2/h)
Section 4 VCC
(kg/m2/h)
18 14.67 18.87 16.35 9.36
20 8.52 11.37 10.57 3.55
17 20.61 23.63 19.15 10.02
80 45.15 37.29 28.16 34.49
79 53.37 46.55 31.68 36.83
77 46.81 53.47 41.25 33.77
78 59.78 60.45 56.44 43.64
93 30.88 45.19 19.19 28.09
96 41.34 53.27 26.35 34.40
95 36.00 42.79 23.05 19.23
94 51.69 53.14 34.10 28.02
74 43.34 49.05 28.67 34.39
73 51.26 53.38 33.75 32.75
76 45.41 42.64 26.83 30.07
75 60.39 59.26 43.12 31.80
51 29.73 32.16 23.33 13.41
52 32.18 33.69 11.33 12.12
49 33.42 33.88 17.74 7.59
50 49.36 48.93 55.26 24.95
86 9.40 13.47 31.19 46.75
85 30.41 50.54 54.53 58.89
88 3.95 3.47 3.96 6.87
87 10.71 14.21 20.20 23.68
70 42.15 50.81 55.83 50.28
69 19.46 43.68 65.13 82.05
72 6.11 16.93 22.46 24.91
71 8.86 19.20 27.11 31.25
81 36.53 47.64 58.62 44.56
82 40.89 54.34 69.77 64.21
84 17.10 23.97 25.79 27.37
83 18.48 20.10 25.37 21.96
68 2.65 12.20 13.04 13.94
65 33.60 34.60 38.54 38.07
66 29.84 31.26 35.27 36.58
67 26.41 33.73 43.48 51.51
62 1.75 1.40 14.38 11.74
64 3.06 2.92 21.78 25.66
63 6.23 3.74 12.18 14.66
61 13.47 2.71 13.86 27.89
59 1.79 9.22 10.44 9.25
58 7.78 2.99 18.35 28.13
57 24.41 9.31 15.35 14.10
60 5.46 2.36 11.94 23.98
91 14.11 13.07 11.70 8.99
92 12.11 9.01 17.80 25.83
90 17.04 14.10 10.11 13.19
89 13.05 6.90 24.39 23.86
Appendix G: Individual sections VCC Results of Original432 experiments 311
Test Section 1 VCC
(kg/m2/h)
Section 2 VCC
(kg/m2/h)
Section 3 VCC
(kg/m2/h)
Section 4 VCC
(kg/m2/h)
53 26.73 12.84 11.13 8.67
54 9.81 12.01 16.23 13.82
56 32.78 5.83 2.21 5.11
55 3.77 4.37 6.81 3.09
121 13.62 24.15 4.80 30.76
122 8.84 6.48 2.35 36.09
124 4.12 5.47 17.63 24.67
123 4.11 5.46 17.59 24.62
102 47.06 46.37 42.62 23.88
104 58.49 56.04 56.82 32.64
101 23.01 24.73 21.70 15.08
103 65.29 64.15 71.55 50.86
118 8.29 23.36 36.45 39.51
120 5.61 30.05 19.40 50.10
117 7.98 14.51 38.38 35.09
119 4.92 8.79 16.35 30.89
100 43.25 39.86 25.51 14.07
98 55.22 52.90 46.92 22.99
97 42.78 44.85 39.11 26.74
99 63.07 62.24 65.22 40.47
139 0.56 0.44 0.21 5.15
138 0.57 0.35 0.10 13.72
137 0.00 0.00 0.00 10.54
140 0.00 0.00 0.00 16.82
130 3.34 7.98 2.97 12.88
129 0.74 5.33 5.34 12.46
132 1.24 3.17 7.68 17.64
131 1.68 2.96 26.86 40.28
128 5.05 6.60 14.02 19.31
127 8.58 7.91 17.28 21.39
125 0.77 7.02 14.07 17.21
126 2.36 9.83 19.52 28.41
107 39.97 44.94 52.05 45.98
106 63.81 63.42 68.01 58.67
108 29.68 36.54 54.99 52.22
105 47.47 42.26 48.77 45.95
142 0.00 0.00 1.55 6.19
141 0.00 0.00 15.63 17.85
143 0.00 0.00 3.31 10.37
144 0.00 0.00 1.48 7.59
115 0.00 2.56 9.43 3.36
116 0.00 1.05 2.03 0.63
113 0.00 8.60 11.69 6.01
114 8.74 9.67 11.47 10.84
136 0.00 0.00 0.00 2.16
133 1.52 2.87 17.89 14.36
134 0.00 0.00 2.55 9.32
312 Appendix G: Individual sections VCC Results of Original432 experiments
Test Section 1 VCC
(kg/m2/h)
Section 2 VCC
(kg/m2/h)
Section 3 VCC
(kg/m2/h)
Section 4 VCC
(kg/m2/h)
135 0.00 0.04 0.81 14.64
109 19.02 15.66 8.40 7.29
110 16.21 13.72 11.39 9.36
112 2.11 3.74 1.60 1.05
111 2.94 3.65 2.07 1.64
181 4.00 9.05 4.30 13.66
183 1.52 6.35 2.92 12.10
182 2.47 8.29 4.41 22.84
184 2.21 4.68 4.55 14.61
177 2.20 4.67 4.54 14.59
178 4.00 9.05 4.30 13.65
179 1.53 6.38 2.94 12.15
180 2.46 8.27 4.40 22.80
169 1.53 6.35 2.93 12.11
170 2.46 8.25 4.39 22.74
171 4.01 9.09 4.31 13.71
172 2.21 4.68 4.55 14.61
146 2.94 6.66 6.34 14.29
145 1.15 4.36 5.29 15.23
148 3.39 5.37 5.33 15.17
147 6.44 4.51 6.41 19.25
186 0.13 1.62 2.61 1.96
185 0.45 0.75 1.29 4.90
188 4.49 4.01 2.04 7.07
187 4.17 6.59 4.46 2.61
176 2.98 6.39 3.36 14.06
173 0.19 1.15 1.43 10.96
175 0.98 4.81 22.13 21.14
174 4.50 3.42 26.38 39.28
167 4.16 6.58 4.46 2.61
168 4.46 3.98 2.03 7.02
166 0.45 0.76 1.30 4.94
165 0.34 15.15 13.18 13.92
163 0.13 1.62 2.61 1.96
164 0.90 7.81 5.25 6.80
161 0.60 10.75 16.46 18.55
162 2.42 1.86 8.36 20.97
158 0.00 0.00 1.93 1.15
157 1.23 0.59 1.91 0.55
159 0.00 0.00 0.52 0.98
160 0.97 0.52 1.43 1.10
156 4.77 5.46 2.46 0.80
155 0.00 0.70 4.58 1.93
153 0.00 3.67 6.44 2.25
154 0.00 0.00 2.79 5.57
189 4.77 5.46 2.46 0.80
190 1.17 1.38 3.13 1.42
Appendix G: Individual sections VCC Results of Original432 experiments 313
Test Section 1 VCC
(kg/m2/h)
Section 2 VCC
(kg/m2/h)
Section 3 VCC
(kg/m2/h)
Section 4 VCC
(kg/m2/h)
191 3.28 9.84 4.01 3.76
192 4.76 5.45 2.45 0.80
150 3.27 9.82 4.00 3.75
149 4.75 5.44 2.45 0.80
152 1.18 1.38 3.15 1.43
151 1.79 2.86 3.06 1.30
229 9.51 18.65 14.71 51.27
230 12.48 21.38 29.50 48.89
231 40.76 58.79 40.68 56.05
232 42.20 32.30 44.91 55.97
219 42.37 54.89 28.09 46.30
218 51.82 58.23 27.61 47.38
217 46.62 71.31 31.41 57.71
220 45.48 55.30 47.95 66.13
215 50.40 40.05 23.55 48.60
213 28.65 43.08 27.20 71.20
214 20.77 27.16 17.63 23.11
216 71.03 81.24 63.85 81.42
194 7.09 20.56 16.38 30.12
193 8.80 8.96 8.20 27.19
196 10.16 23.48 13.63 15.27
195 7.49 11.08 14.89 19.76
226 0.40 1.53 2.65 3.98
225 13.67 19.76 27.77 35.35
227 43.42 37.01 34.16 27.83
228 14.56 10.16 15.33 22.24
224 3.69 4.34 6.25 7.00
223 10.12 4.26 4.44 9.48
222 4.11 5.71 8.28 6.32
221 39.36 34.04 49.96 60.40
204 8.36 6.44 13.05 13.44
203 10.58 6.92 12.46 16.18
202 1.03 0.89 0.65 2.05
201 29.20 26.00 27.95 38.77
200 6.39 9.27 12.03 10.60
199 1.49 4.14 8.69 5.31
198 0.35 0.20 0.39 0.64
197 2.26 1.26 0.96 4.07
239 0.00 0.00 0.15 2.25
237 2.19 8.14 2.43 29.59
240 0.00 0.00 0.00 5.57
238 1.00 0.71 9.73 38.93
210 0.00 0.00 0.00 1.86
212 0.00 3.85 8.15 7.09
211 0.00 0.00 0.00 2.53
209 0.00 0.00 1.37 2.94
314 Appendix G: Individual sections VCC Results of Original432 experiments
Test Section 1 VCC
(kg/m2/h)
Section 2 VCC
(kg/m2/h)
Section 3 VCC
(kg/m2/h)
Section 4 VCC
(kg/m2/h)
235 0.00 0.00 0.00 0.55
236 1.16 1.30 1.57 1.12
233 10.35 19.67 20.14 18.66
234 5.30 5.09 14.43 4.00
206 9.39 12.11 13.98 12.14
208 6.21 5.71 34.29 17.97
207 16.89 16.53 12.59 16.88
205 22.80 5.89 25.89 38.51
241 24.64 33.73 42.48 34.71
242 27.13 11.24 48.09 43.83
243 22.24 22.21 27.47 23.58
244 20.19 17.78 25.82 30.18
277 46.30 23.15 22.16 20.46
279 56.42 64.94 58.65 49.38
278 49.53 63.22 50.84 39.72
280 22.11 31.90 40.34 55.01
260 48.74 54.41 52.85 46.89
259 55.27 65.46 65.16 54.08
258 47.81 53.44 53.69 45.65
257 12.50 28.52 46.19 61.67
284 43.63 51.86 49.57 40.96
281 47.16 55.31 51.84 43.46
283 22.44 35.80 51.10 39.48
282 26.97 30.78 33.89 50.71
245 6.47 32.85 39.13 35.55
246 8.29 16.03 37.02 66.68
247 14.17 9.24 16.03 12.80
248 13.54 11.09 29.84 56.58
268 17.03 18.63 15.91 15.99
267 21.63 19.16 24.36 54.68
266 8.49 8.02 13.84 19.03
265 69.19 37.72 35.77 47.79
263 21.22 20.91 25.30 16.03
264 25.94 24.66 28.16 54.06
262 11.31 14.40 21.61 23.59
261 66.67 46.93 42.87 40.65
286 36.90 35.78 38.17 42.92
285 64.11 54.75 43.96 51.23
288 41.04 27.87 31.15 39.39
287 63.50 43.69 31.80 24.85
251 9.16 7.37 6.36 4.66
252 21.76 22.34 19.74 16.68
250 1.95 1.35 0.50 0.56
249 23.13 21.82 19.48 16.98
269 11.60 19.09 18.23 16.93
272 7.86 13.35 21.33 20.65
271 49.66 27.80 24.04 18.06
Appendix G: Individual sections VCC Results of Original432 experiments 315
Test Section 1 VCC
(kg/m2/h)
Section 2 VCC
(kg/m2/h)
Section 3 VCC
(kg/m2/h)
Section 4 VCC
(kg/m2/h)
270 11.57 19.04 18.18 16.88
256 15.46 12.66 9.63 7.66
253 0.00 0.00 6.35 15.87
255 15.49 12.68 9.65 7.68
254 1.89 1.07 0.76 1.10
275 16.52 13.73 10.97 9.39
276 14.80 13.98 12.45 11.46
274 15.49 12.68 9.65 7.68
273 24.89 17.24 20.49 16.30
314 31.63 30.42 34.34 31.68
315 36.63 37.47 37.04 38.47
313 9.68 24.63 9.52 28.56
316 0.68 0.70 0.61 0.43
295 29.40 25.29 25.79 28.92
296 15.03 14.34 16.15 19.79
294 29.78 30.19 23.19 29.59
293 18.35 20.20 16.74 20.59
310 39.10 41.29 41.40 39.43
311 34.54 40.76 40.67 41.34
312 44.57 47.57 49.02 49.92
309 11.61 18.48 23.19 41.82
292 30.94 24.59 26.49 37.98
290 26.48 24.61 21.93 34.41
291 18.93 17.28 16.17 23.22
289 25.07 24.52 17.92 34.46
324 4.69 6.20 6.88 8.03
323 13.88 12.69 13.87 18.30
321 5.99 5.23 4.63 19.04
322 10.00 12.16 11.85 26.82
304 10.93 12.50 14.95 35.48
303 24.60 22.12 42.78 71.43
302 37.43 40.26 43.95 61.91
301 29.50 34.14 48.11 79.29
320 1.45 1.65 2.80 3.63
319 23.92 17.16 15.54 19.65
318 19.86 15.96 21.57 28.72
317 47.60 44.08 48.49 57.07
299 10.99 15.97 17.72 27.64
300 38.26 44.43 49.01 70.21
297 20.31 20.12 22.41 31.67
298 7.67 10.86 16.18 33.90
332 0.00 0.03 0.06 0.31
329 7.34 20.84 31.27 31.76
330 0.00 0.76 2.67 24.60
331 0.00 1.61 0.69 15.68
333 14.41 6.97 21.73 23.40
336 0.00 0.00 0.00 23.88
316 Appendix G: Individual sections VCC Results of Original432 experiments
Test Section 1 VCC
(kg/m2/h)
Section 2 VCC
(kg/m2/h)
Section 3 VCC
(kg/m2/h)
Section 4 VCC
(kg/m2/h)
334 0.00 0.00 8.20 26.54
335 0.00 0.00 0.00 19.50
328 0.00 0.00 0.43 0.55
325 25.53 27.53 24.65 26.09
326 0.00 7.00 17.04 18.37
327 0.00 0.00 1.23 24.28
308 47.65 21.64 5.33 10.09
305 30.81 30.12 29.00 29.26
307 29.56 18.84 15.88 13.89
306 30.32 2.73 14.95 24.45
379 0.22 0.21 0.33 0.34
377 12.84 9.60 31.77 45.01
380 3.86 9.30 25.60 41.49
378 3.35 0.33 8.92 22.09
347 11.88 20.57 29.71 36.30
346 24.58 23.44 30.38 38.39
348 13.61 15.28 27.46 37.88
345 9.33 12.38 19.18 42.80
373 52.17 54.96 51.05 53.03
376 36.40 35.48 39.63 37.70
374 13.62 15.20 27.90 37.45
375 46.11 40.30 30.10 33.09
351 40.86 38.55 37.56 38.05
350 11.40 13.30 24.29 40.25
352 0.52 3.12 7.08 16.11
349 14.62 18.13 34.61 54.32
364 4.04 8.53 11.25 14.75
362 4.48 6.10 11.63 15.48
363 3.55 4.73 19.50 41.11
361 3.68 9.03 23.02 58.29
384 3.26 3.66 10.44 14.18
382 4.01 7.55 11.54 12.94
383 1.16 9.22 28.02 36.79
381 2.93 9.47 22.62 42.07
356 3.01 8.07 11.98 14.72
355 4.24 7.79 12.59 14.56
354 5.53 16.98 32.95 44.50
353 49.76 15.57 17.16 41.96
357 4.02 7.46 10.68 12.86
360 4.75 8.34 10.86 13.71
359 1.39 4.71 7.55 12.06
358 47.54 46.39 45.02 35.02
344 0.00 0.96 1.14 3.82
343 0.00 1.17 7.60 13.16
342 0.00 2.08 10.76 18.90
341 0.00 3.64 24.05 23.09
340 0.00 4.27 5.05 3.81
Appendix G: Individual sections VCC Results of Original432 experiments 317
Test Section 1 VCC
(kg/m2/h)
Section 2 VCC
(kg/m2/h)
Section 3 VCC
(kg/m2/h)
Section 4 VCC
(kg/m2/h)
339 1.45 7.09 7.40 6.13
338 0.00 2.46 2.77 1.79
337 1.54 9.25 8.63 5.74
371 4.18 3.40 3.84 3.06
370 20.84 19.59 17.25 16.47
369 2.36 1.76 1.25 0.75
372 12.67 12.95 10.70 8.58
368 7.63 10.10 7.21 7.21
367 6.58 15.73 13.93 13.05
366 8.13 2.54 1.08 2.62
365 33.88 27.10 21.84 21.88
403 38.70 34.81 40.69 32.83
401 52.70 43.48 50.01 31.14
402 45.05 41.70 47.88 44.13
404 54.35 53.01 61.48 47.35
400 40.94 40.15 42.27 34.28
398 46.43 48.25 55.27 54.22
397 39.33 43.96 49.83 41.48
399 28.91 34.15 44.39 38.57
390 40.95 48.22 43.73 38.17
391 43.19 44.94 49.39 35.61
392 1.80 16.71 12.09 15.24
389 10.97 18.32 17.81 48.18
385 40.68 39.23 44.69 31.01
387 16.10 17.77 19.39 16.30
388 16.17 17.85 19.48 16.37
386 54.45 54.15 55.45 47.84
425 1.72 8.82 7.45 17.75
427 2.98 5.15 7.56 12.86
426 4.08 4.56 11.21 29.44
428 9.87 4.87 17.37 33.50
429 0.81 0.68 0.50 0.15
432 0.22 0.38 0.67 1.03
431 0.23 0.35 0.58 0.64
430 0.58 0.59 0.81 0.78
422 5.07 11.03 7.47 12.55
421 2.66 2.79 7.05 11.41
424 2.45 1.21 8.13 29.00
423 0.00 13.13 13.84 36.83
420 3.63 7.08 9.73 13.33
418 5.47 7.53 9.70 16.90
417 6.06 13.36 21.89 36.95
419 5.49 9.20 18.25 44.39
414 1.40 4.77 7.22 6.37
416 9.32 10.59 15.73 13.70
415 2.28 1.82 3.08 2.11
413 6.59 8.85 9.06 6.71
318 Appendix G: Individual sections VCC Results of Original432 experiments
Test Section 1 VCC
(kg/m2/h)
Section 2 VCC
(kg/m2/h)
Section 3 VCC
(kg/m2/h)
Section 4 VCC
(kg/m2/h)
411 0.25 5.20 7.37 6.19
412 10.91 12.97 15.20 13.78
410 0.00 1.88 2.58 1.84
409 9.35 12.06 14.03 9.61
395 4.00 6.69 7.93 10.02
393 14.24 7.89 12.54 14.92
394 2.88 4.16 4.45 5.89
396 2.08 2.02 2.06 3.10
408 1.86 6.61 8.86 7.31
405 9.64 13.39 17.43 15.08
407 1.96 4.33 4.76 3.59
406 14.43 20.58 19.96 14.82
Appendix H: Individual sections HTC Results of Replicate128 experiments 319
APPENDIX H: INDIVIDUAL SECTIONS
HTC RESULTS OF REPLICATE128
EXPERIMENTS
H.1 Introductory Remarks
This appendix presents the HTC results of the individual sections of the heating
tube from the Replicate128 experiments. Section 1 is the top-most section of the tube
and section 4 is the bottom-most section of the tube. The tube dimensions and
operating conditions of the experiments are presented in Table D.1 and D.2 in
Appendix D.
Appendix H: Individual sections HTC Results of Replicate128 experiments 321
Table H Individual section HTC results for the Replicate128 experiment
Test Section 1 HTC
(W/m2/K)
Section 2 HTC
(W/m2/K)
Section 3 HTC
(W/m2/K)
Section 4 HTC
(W/m2/K)
5 2508 3433 4324 3533
7 2467 1022 4374 3987
6 1992 1990 2461 2113
8 1347 1186 1722 2013
25 4681 2340 2240 2068
27 4705 5415 4891 4117
26 4390 5604 4506 3521
28 1451 2094 2648 3611
9 4765 5318 5166 4583
10 4695 5561 5536 4594
11 4105 4588 4610 3920
12 797 1818 2944 3931
1 2485 2322 3422 5228
3 2666 3039 3311 5141
2 2099 3490 5082 4710
4 1548 1746 2496 4828
21 342 275 237 174
22 590 606 536 453
23 58 40 15 17
24 522 492 439 383
30 386 635 606 563
29 194 329 526 509
32 1458 816 706 530
31 255 420 401 372
14 507 415 316 251
13 0 0 13 16
15 423 346 264 210
16 39 22 16 23
18 569 473 378 324
17 376 355 316 291
20 443 363 276 220
19 1027 663 804 789
69 1395 2474 491 3151
70 749 549 199 3059
72 371 493 1588 2222
71 275 366 1178 1649
89 4975 4902 4505 2524
91 4555 4364 4424 2542
90 2136 2295 2014 1399
92 4495 4417 4926 3501
65 834 2350 3668 3975
67 419 2244 1448 3741
66 708 1287 3404 3113
68 326 582 1082 2045
95 4516 4162 2663 1469
94 4272 4093 3630 1779
322 Appendix H: Individual sections HTC Results of Replicate128 experiments
Test Section 1 HTC
(W/m2/K)
Section 2 HTC
(W/m2/K)
Section 3 HTC
(W/m2/K)
Section 4 HTC
(W/m2/K)
96 3935 4125 3598 2460
93 4325 4268 4472 2775
81 0 0 60 239
83 0 0 443 506
82 0 0 106 332
84 0 0 36 183
74 0 100 367 131
73 0 30 59 18
75 0 283 385 198
76 218 242 287 271
86 0 0 0 81
85 42 80 496 398
87 0 0 80 291
88 0 1 19 347
77 651 536 288 250
79 410 347 288 236
78 60 107 45 30
80 63 79 45 35
37 1064 2086 1646 5736
38 1317 2255 3111 5157
40 4006 5777 3998 5508
39 3078 2356 3276 4083
57 4713 6104 3124 5149
59 4784 5375 2549 4373
58 4571 6992 3080 5658
60 3328 4047 3509 4840
33 5329 4235 2490 5139
35 2447 3680 2323 6082
34 1931 2525 1639 2149
36 4910 5615 4414 5628
63 732 2122 1690 3108
62 684 696 638 2114
64 920 2128 1235 1384
61 504 746 1002 1330
49 0 0 8 83
51 89 330 99 1200
50 0 0 0 261
52 35 25 343 1371
42 0 0 0 82
41 0 125 263 229
43 0 0 0 93
44 0 0 38 82
54 0 0 0 21
53 32 36 44 31
55 324 616 630 584
56 126 121 343 95
45 380 490 566 492
47 185 170 1019 534
Appendix H: Individual sections HTC Results of Replicate128 experiments 323
Test Section 1 HTC
(W/m2/K)
Section 2 HTC
(W/m2/K)
Section 3 HTC
(W/m2/K)
Section 4 HTC
(W/m2/K)
46 566 554 422 566
48 577 149 655 975
101 4502 3718 2808 3439
102 4408 3845 2617 3042
104 4108 4692 3619 2963
103 3906 3949 3687 2851
121 3190 4668 1983 2902
123 3541 4563 2257 2947
122 3276 3894 2098 1750
124 3507 3605 2313 1901
97 4472 5061 2958 3549
99 4267 4444 2809 2726
98 4115 3864 2432 2725
100 4063 3987 2901 2139
127 3262 3528 2559 1472
126 3240 3392 1141 1220
128 3225 3270 1712 733
125 3544 3513 3968 1791
113 60 48 492 402
115 78 74 554 652
114 178 107 348 419
116 293 59 302 607
106 60 310 351 311
105 194 75 457 701
107 685 261 430 396
108 117 50 255 512
118 528 489 438 336
117 335 250 493 716
119 531 440 315 411
120 309 164 578 565
109 1067 513 444 346
111 289 353 477 406
110 1087 193 73 169
112 95 110 171 77
Appendix I: Individual sections VCC Results of Replicate128 experiments 325
APPENDIX I: INDIVIDUAL SECTIONS
VCC RESULTS OF REPLICATE128
EXPERIMENTS
I.1 Introductory Remarks
This appendix presents the VCC results of the individual sections of the heating
tube from the Replicate128 experiments. Section 1 is the top-most section of the tube
and section 4 is the bottom-most section of the tube. The tube dimensions and
operating conditions of the experiments are presented in Table D.1 and D.2 in
Appendix D.
Appendix I: Individual sections VCC Results of Replicate128 experiments 327
Table I Individual section VCC results from the 2 × 2 factorial experiment
Test Section 1 VCC
(kg/m2/h)
Section 2 VCC
(kg/m2/h)
Section 3 VCC
(kg/m2/h)
Section 4 VCC
(kg/m2/h)
5 23.40 32.05 40.36 32.97
7 25.77 10.67 45.68 41.64
6 21.12 21.10 26.09 22.40
8 19.18 16.89 24.53 28.67
25 42.60 21.29 20.38 18.82
27 51.90 59.74 53.96 45.43
26 45.56 58.16 46.77 36.55
28 20.34 29.35 37.11 50.61
9 43.87 48.97 47.57 42.20
10 49.74 58.91 58.64 48.67
11 43.03 48.09 48.32 41.09
12 11.25 25.67 41.57 55.50
1 23.42 21.88 32.25 49.27
3 28.09 32.02 34.88 54.16
2 22.44 37.32 54.34 50.37
4 21.86 24.65 35.24 68.17
21 8.98 7.22 6.23 4.56
22 21.32 21.90 19.34 16.35
23 1.91 1.33 0.49 0.55
24 22.67 21.38 19.09 16.64
30 10.90 17.95 17.14 15.91
29 7.39 12.55 20.05 19.41
32 46.68 26.13 22.60 16.98
31 10.87 17.90 17.09 15.87
14 14.23 11.64 8.86 7.05
13 0.00 0.00 0.50 0.60
15 14.25 11.67 8.88 7.06
16 1.73 0.98 0.70 1.01
18 15.69 13.04 10.42 8.92
17 14.06 13.28 11.83 10.89
20 14.72 12.05 9.17 7.29
19 45.02 29.07 35.24 34.60
69 12.94 22.94 4.56 29.22
70 8.40 6.16 2.23 34.29
72 3.91 5.20 16.74 23.44
71 3.90 5.19 16.71 23.39
89 45.65 44.98 41.34 23.16
91 56.74 54.36 55.11 31.66
90 22.32 23.99 21.05 14.62
92 63.33 62.23 69.40 49.33
65 7.87 22.19 34.63 37.53
67 5.33 28.55 18.43 47.59
66 7.58 13.78 36.46 33.34
68 4.68 8.35 15.53 29.34
95 42.39 39.06 25.00 13.79
94 54.12 51.84 45.99 22.53
328 Appendix I: Individual sections VCC Results of Replicate128 experiments
Test Section 1 VCC
(kg/m2/h)
Section 2 VCC
(kg/m2/h)
Section 3 VCC
(kg/m2/h)
Section 4 VCC
(kg/m2/h)
96 41.93 43.95 38.33 26.21
93 61.81 61.00 63.91 39.66
81 0.00 0.00 1.62 6.50
83 0.00 0.00 16.41 18.74
82 0.00 0.00 3.47 10.88
84 0.00 0.00 1.56 7.97
74 0.00 2.82 10.38 3.69
73 0.00 1.16 2.24 0.70
75 0.00 9.46 12.85 6.61
76 9.61 10.64 12.61 11.92
86 0.00 0.00 0.00 2.26
85 1.60 3.02 18.79 15.08
87 0.00 0.00 2.68 9.79
88 0.00 0.05 0.85 15.37
77 18.07 14.87 7.98 6.93
79 15.40 13.04 10.82 8.89
78 2.00 3.56 1.52 0.99
80 2.79 3.47 1.97 1.56
37 9.79 19.20 15.15 52.81
38 12.86 22.02 30.38 50.36
40 41.99 60.55 41.90 57.74
39 43.46 33.27 46.26 57.65
57 44.49 57.63 29.49 48.61
59 54.41 61.14 28.99 49.74
58 48.95 74.88 32.98 60.59
60 47.75 58.06 50.35 69.44
33 49.39 39.25 23.08 47.63
35 28.07 42.22 26.66 69.78
34 20.35 26.62 17.28 22.65
36 69.61 79.61 62.58 79.79
63 6.74 19.54 15.56 28.61
62 8.36 8.51 7.79 25.83
64 9.65 22.31 12.94 14.50
61 7.12 10.53 14.14 18.78
49 0.00 0.00 0.22 2.25
51 3.28 12.21 3.65 44.39
50 0.00 0.00 0.00 8.35
52 1.50 1.07 14.59 58.39
42 0.00 0.00 0.00 2.23
41 0.00 4.62 9.77 8.51
43 0.00 0.00 0.00 3.03
44 0.00 0.00 1.64 3.52
54 0.00 0.00 0.00 0.57
53 1.21 1.37 1.65 1.18
55 10.87 20.66 21.14 19.60
56 5.56 5.34 15.16 4.20
45 10.33 13.32 15.38 13.35
47 6.84 6.28 37.72 19.77
Appendix I: Individual sections VCC Results of Replicate128 experiments 329
Test Section 1 VCC
(kg/m2/h)
Section 2 VCC
(kg/m2/h)
Section 3 VCC
(kg/m2/h)
Section 4 VCC
(kg/m2/h)
46 18.58 18.19 13.85 18.57
48 25.08 6.48 28.48 42.36
101 41.99 34.68 26.19 32.07
102 49.63 43.29 29.46 34.25
104 43.54 49.73 38.36 31.41
103 55.60 56.21 52.49 40.59
121 29.96 43.83 18.62 27.25
123 40.10 51.67 25.56 33.37
122 34.92 41.51 22.36 18.66
124 50.14 51.55 33.08 27.18
97 41.18 46.60 27.24 32.67
99 48.69 50.71 32.06 31.11
98 43.14 40.50 25.49 28.57
100 57.37 56.29 40.97 30.21
127 30.33 32.81 23.79 13.68
126 32.83 34.37 11.56 12.36
128 34.09 34.56 18.09 7.74
125 50.34 49.91 56.37 25.45
113 1.70 1.36 13.95 11.39
115 2.97 2.83 21.13 24.89
114 6.04 3.63 11.81 14.22
116 13.06 2.62 13.45 27.06
106 1.70 8.76 9.92 8.78
105 7.39 2.84 17.43 26.73
107 23.19 8.85 14.58 13.40
108 5.19 2.24 11.34 22.78
118 14.82 13.72 12.28 9.44
117 12.71 9.46 18.69 27.12
119 17.89 14.81 10.62 13.85
120 13.70 7.25 25.61 25.06
109 29.41 14.13 12.24 9.54
111 10.79 13.21 17.85 15.20
110 36.06 6.42 2.43 5.62
112 4.14 4.81 7.49 3.40
Appendix J: Replicate128 ANOVA 331
APPENDIX J: REPLICATE128 ANOVA
J.1 Introductory Remarks
This appendix presents analysis of variance for Replicate128 dataset. Six-order
interactions were identified to be significant. The replicate tests were undertaken to
investigate the tube length and tube diameter interaction, which was found to be
significant. The repeatability of the results might have caused the higher order
interactions to be significant. Hence the interactions with small effects could have been
enhanced with the replicate dataset.
Appendix J: Replicate128 ANOVA 333
Table J.1 Analysis of variance of HTC from Replicates128 tests
Source
Degrees of
freedom
Mean
square
Variance
ratio
Significance
level
TL 1 2972755 59.4 0.004
TD 1 8878 0.18 –
TL:TD 1 90300 1.8 –
Rep. block 1 67392 1.34 –
Residuals 3 50000
B 1 540897084 13211.7 0.000
JL 3 3837648 93.7 0.000
TL:B 1 2523627 61.6 0.000
TL:JL 3 1719539 42 0.000
TD:B 1 168255 421 –
TD:JL 3 7370316 180 0.000
B:JL 3 4562838 111.4 0.000
TL:TD:B 1 1662573 40.6 0.000
TL:TD:JL 3 1837374 44.9 0.000
TL:B:JL 3 3047831 74.4 0.000
TD:B:JL 3 7768684 189.7 0.000
TL:TD:B:JL 3 3107923 75.9 0.000
Residuals 28 40941
HS 1 2991066 42.3 0.000
ΔP 1 1222742 17.3 0.000
TL:HS 1 21903 0.3 –
TL:ΔP 1 170075 2.4 –
TD:HS 1 2996850 42.3 0.000
TD:ΔP 1 368220 5.2 0.02
B:HS 1 2701716 38.2 0.000
B:ΔP 1 1130956 16 0.000
JL:HS 3 238895 3.3 0.02
JL:ΔP 3 1133 0.01 –
HS:ΔP 1 310652 4.4 0.04
TL:TD:HS 1 962319 13.6 0.000
TL:TD:ΔP 1 44783 0.6 –
TL:B:HS 1 353375 4.9 0.027
TL:B:ΔP 1 235904 3.3 –
TL:JL:HS 3 331440 4.68 0.004
TL:JL:ΔP 3 370581 5.24 0.002
TL:HS:ΔP 1 928468 13.1 0.000
TD:B:HS 1 2294969 32.4 0.000
334 Appendix J: Replicate128 ANOVA
Source
Degrees of
freedom
Mean
square
Variance
ratio
Significance
level
TD:JL:HS 3 483572 6.8 0.000
TD:JL:ΔP 3 534105 7.5 0.000
TD:HS:ΔP 1 1331837 18.8 0.000
B:JL:HS 3 812727 11.5 0.000
B:JL:ΔP 3 271251 3.8 0.012
B:HS:ΔP 1 107684 1.5 –
JL:HS:ΔP 3 559847 7.9 0.000
TL:TD:B:HS 1 660345 9.3 0.003
TL:TD:B:ΔP 1 30926 0.4 –
TL:TD:JL:HS 3 305339 4.3 0.006
TL:TD:JL:ΔP 3 219707 3.1 0.03
TL:TD:HS:ΔP 1 882603 12.5 0.000
TL:B:JL:HS 3 726525 10.2 0.000
TL:B:JL:ΔP 3 722577 10.2 0.000
TL:B:HS:ΔP 1 1131436 16 0.000
TL:JL:HS:ΔP 3 467698 6.6 0.000
TD:B:JL:HS 3 287100 4.1 0.009
TD:B:JL:ΔP 3 779639 11.02 0.000
TD:B:HS:ΔP 1 1927592 27.2 0.000
TD:JL:HS:ΔP 3 836470 11.8 0.000
B:JL:HS:ΔP 3 425708 6 0.001
TL:TD:B:JL:HS 3 148790 2.1 –
TL:TD:B:JL:ΔP 3 289268 4.1 0.01
TL:TD:B:HS:ΔP 1 1134543 16 0.000
TL:TD:JL:HS:ΔP 3 617297 8.7 0.000
TL:B:JL:HS:ΔP 3 450794 6.4 0.006
TD:B:JL:HS:ΔP 3 928153 13.1 0.000
TL:TD:B:JL:HS:ΔP 3 543758 7.7 0.000
Residuals 96 70725
Appendix J: Replicate128 ANOVA 335
Table J.2 Analysis of variance of HTCmax from Replicate128 tests
Source
Degrees of
freedom
Mean
square
Variance
ratio
Significance
level
TL 1 2972755 59.4 0.004
TD 1 8878 0.18 –
TL:TD 1 90300 1.8 –
Rep. block 1 67392 1.34 –
Residuals 3 50000
B 1 234649442 2938.5 0.000
TL:B 1 726293 9.1 0.04
TD:B 1 8081 0.1 –
TL:TD:B 1 846369 10.6 0.03
Residuals 4 79852
HS 1 486583 32.2 0.000
ΔP 1 768900 50.9 0.000
TL:HS 1 44403 2.9 –
TL:ΔP 1 253808 16.8 0.000
TD:HS 1 1633123 108.1 0.000
TD:ΔP 1 56357 3.73 –
B:HS 1 420344 27.8 0.000
B:ΔP 1 248413 16.44 0.000
HS:ΔP 1 28301 1.8 –
TL:TD:HS 1 987705 65.4 0.000
TL:TD:ΔP 1 588238 38.9 0.000
TL:B:HS 1 358152 23.7 0.000
TL:B:ΔP 1 121264 8.03 0.01
TL:HS:ΔP 1 416645 27.6 0.000
TD:B:HS 1 1449987 95.9 0.000
TD:B:ΔP 1 1010 0.07 –
TD:HS:ΔP 1 421039 27.8 0.000
B:HS:ΔP 1 33539 2.22 0.000
TL:TD:B:HS 1 1097005 72.6 0.000
TL:TD:B:ΔP 1 165025 10.9 0.003
TL:TD:HS:ΔP 1 730890 48.4 0.000
TL:B:HS:ΔP 1 220068 14.6 0.001
TD:B:HS:ΔP 1 314605 20.8 0.000
TL:TD:B:HS:ΔP 1 506313 33.5 0.000
Residuals 24 15109
Appendix K: Comparison of individual sections HTC for Tests with Brix-70 337
APPENDIX K: COMPARISON OF
INDIVIDUAL SECTIONS HTC FOR
TESTS WITH BRIX-70
K.1 Introductory Remarks
This appendix presents the uniform boiling pattern results from the Original432
and Replicate128 experiments in Table L.1 and Table L.2 respectively. This boiling
pattern shows that the HTC of the four individual sections was within 15% of the
overall HTC.
Appendix K: Comparison of individual sections HTC for Tests with Brix-70 339
Table K.1 Individual section HTC comparison with M2 tube with Brix-70
results
Test Original432 Replicate128 Test
Section 1 Section 2 Section 3 Section 4 Section 1 Section 2 Section 3 Section 4
251 1 0 0 -1 1 0 0 -1 21
252 -1 1 0 0 0 0 0 -1 22
250 1 0 -1 -1 1 1 -1 -1 23
249 1 0 0 -1 0 0 0 -1 24
269 0 0 0 -1 -1 1 0 0 30
272 -1 -1 1 1 -1 -1 1 1 29
271 -1 -1 0 1 1 0 -1 -1 32
270 0 0 0 0 -1 1 0 0 31
256 1 1 -1 -1 1 0 -1 -1 14
253 1 0 -1 -1 -1 -1 1 1 13
255 1 0 -1 -1 1 0 -1 -1 15
254 1 0 0 -1 1 0 -1 0 16
275 0 0 0 -1 1 0 0 -1 18
276 -1 1 0 0 0 0 0 0 17
274 1 0 -1 0 1 0 -1 -1 20
273 1 0 0 -1 1 -1 0 0 19
Category Comparison of results (%)
Individual section HTC in same zone 58
Individual section HTC one zone apart 34
Individual section HTC two zones apart 8
340 Appendix K: Comparison of individual sections HTC for Tests with Brix-70
Table K.2 Individual section HTC comparison with S2 tube with Brix-70 results
Test Original432 Replicate128 Test
Section 1 Section 2 Section 3 Section 4 Section 1 Section 2 Section 3 Section 4
237 -1 -1 -1 1 -1 -1 -1 1 49
240 -1 -1 -1 1 -1 -1 -1 1 51
238 -1 -1 -1 1 -1 -1 -1 1 50
210 -1 0 1 0 -1 -1 -1 1 52
212 -1 -1 -1 1 -1 -1 -1 1 42
211 -1 -1 1 1 -1 -1 1 1 41
209 0 0 1 0 -1 -1 -1 1 43
235 -1 -1 1 0 -1 -1 1 1 44
236 -1 -1 -1 1 -1 -1 -1 1 54
233 -1 -1 -1 1 0 0 1 0 53
234 -1 0 1 0 -1 0 1 0 55
206 0 0 -1 0 -1 -1 1 -1 56
208 -1 -1 -1 1 -1 0 1 0 45
207 -1 -1 1 1 -1 -1 1 0 47
205 -1 -1 1 -1 0 0 -1 0 46
239 0 -1 0 1 0 -1 0 1 48
Category Comparison of results (%)
Individual section HTC in same zone 63
Individual section HTC one zone apart 28
Individual section HTC two zones apart 9
Appendix K: Comparison of individual sections HTC for Tests with Brix-70 341
Table K.3 Individual section HTC comparison with M3 tube with Brix-70
results
Test Original432 Replicate128 Test
Section 1 Section 2 Section 3 Section 4 Section 1 Section 2 Section 3 Section 4
142 -1 -1 -1 1 -1 -1 -1 1 81
141 -1 -1 1 0 -1 -1 1 1 83
143 -1 -1 -1 1 -1 -1 0 1 82
144 1 1 -1 -1 -1 -1 -1 1 84
115 -1 -1 1 1 -1 -1 1 0 74
116 -1 0 1 -1 -1 0 1 -1 73
113 -1 -1 1 1 -1 1 1 0 75
114 1 0 0 -1 0 0 0 0 76
136 -1 -1 0 1 -1 -1 -1 1 86
133 -1 1 1 0 -1 -1 1 1 85
134 -1 -1 0 1 -1 -1 0 1 87
135 0 1 -1 -1 -1 -1 -1 1 88
109 -1 -1 -1 1 1 1 -1 -1 77
110 0 0 0 0 1 0 0 -1 79
112 -1 -1 -1 1 0 1 -1 -1 78
111 1 1 -1 -1 0 1 -1 -1 80
Category Comparison of results (%)
Individual section HTC in same zone 61
Individual section HTC one zone apart 20
Individual section HTC two zones apart 19
342 Appendix K: Comparison of individual sections HTC for Tests with Brix-70
Table K.4 Individual section HTC comparison with S3 tube with Brix-70 results
Test Original432 Replicate128 Test
Section 1 Section 2 Section 3 Section 4 Section 1 Section 2 Section 3 Section 4
86 -1 -1 1 1 -1 -1 1 1 113
85 -1 1 1 1 -1 -1 1 1 115
88 1 0 0 -1 -1 -1 1 1 114
87 1 0 -1 -1 0 -1 0 1 116
70 -1 -1 1 1 -1 1 1 1 106
69 -1 -1 1 1 -1 -1 1 1 105
72 -1 -1 0 1 1 -1 0 0 107
71 -1 0 1 0 -1 -1 0 1 108
81 -1 -1 1 1 1 0 0 -1 118
82 1 -1 0 0 -1 -1 0 1 117
84 1 0 -1 0 1 0 -1 0 119
83 1 -1 -1 -1 -1 -1 1 1 120
68 0 -1 0 1 1 0 -1 -1 109
65 -1 -1 0 1 -1 0 1 0 111
66 -1 -1 1 1 1 -1 -1 -1 110
67 -1 0 1 -1 -1 0 1 -1 112
Category Comparison of results (%)
Individual section HTC in same zone 47
Individual section HTC one zone apart 28
Individual section HTC two zones apart 25
Appendix L: Uniform boiling pattern results – Original432 and Replicate128 datasets 343
APPENDIX L: UNIFORM BOILING
PATTERN RESULTS – ORIGINAL432 AND
REPLICATE128 DATASETS
L.1 Introductory Remarks
This appendix presents the uniform boiling pattern results from the Original432 and
Replicate128 experiments in Table M.1 and Table M.2 respectively. This boiling pattern shows
that the HTC of the top section (section 1) was lower than 15% of the overall HTC.
Appendix L: Uniform boiling pattern results – Original432 and Replicate128 datasets 345
Table L.1 Results from Original432 tests demonstrating uniform boiling pattern
TL
(m)
TD
(mm)
Brix JL (%
tube
height)
JL
(mm)
HS
(kPa
abs)
ΔP
(kPa)
ΔT
(°C)
Section 1
(W/m2/K)
Section 2
(W/m2/K)
Section 3
(W/m2/K)
Section 4
(W/m2/K)
Overall
(W/m2/K)
4 44.45 34 35 1400 72 50 13.59 2181 2505 2508 2546 2435
4 44.45 34.7 60 2400 72 50 13.56 2018 2294 2635 2330 2319
3 38.1 38 60 1800 94 50 10.98 1894 1951 2173 2146 2041
3 38.1 38 60 1800 72 35 9.62 1940 2033 2293 2378 2161
3 44.45 36.5 60 1800 94 35 7.83 3175 3569 4133 3652 3632
3 44.45 36.5 60 1800 94 50 11.07 3569 3547 3803 3281 3550
3 44.45 36.5 60 1800 72 50 13.46 2197 1956 2257 2126 2134
3 44.45 68.5 45 1350 22 60 27.77 199 220 261 246 231
2 38.1 18 40 800 126 45 8.76 4990 5706 4485 5719 5225
2 44.45 19.5 30 600 149 40 6.85 5050 5813 5250 4420 5133
2 44.45 20 40 800 149 33 5.65 5294 5909 5740 5093 5509
2 44.45 20 40 800 149 38 6.5 5217 6179 6151 5105 5663
2 44.45 20 40 800 126 33 6.47 4561 5098 5122 4355 4784
2 44.45 20 50 1000 149 33 5.65 4738 5632 5384 4448 5051
2 44.45 20 50 1000 149 37 6.33 4571 5360 5024 4212 4792
2 44.45 38 35 700 94 35 7.74 1368 1497 1278 1284 1357
2 44.45 35 60 1200 94 35 7.91 2899 2811 2999 3372 3020
2 44.45 74 70 1400 29 60 22.08 422 399 355 327 376
2 50.8 18 20 400 149 33 5.73 3391 3262 3681 3396 3433
2 50.8 18 20 400 149 35 6.07 3706 3791 3747 3892 3784
2 50.8 16.9 30 600 149 33 5.77 3131 2693 2746 3080 2912
2 50.8 16.9 30 600 126 45 8.8 1284 1413 1171 1440 1327
2 50.8 20 40 800 149 33 5.65 4246 4484 4497 4283 4378
2 50.8 20 40 800 149 41 6.99 3026 3572 3564 3623 3446
346 Appendix L: Uniform boiling pattern results – Original432 and Replicate128 datasets
TL
(m)
TD
(mm)
Brix JL (%
tube
height)
JL
(mm)
HS
(kPa
abs)
ΔP
(kPa)
ΔT
(°C)
Section 1
(W/m2/K)
Section 2
(W/m2/K)
Section 3
(W/m2/K)
Section 4
(W/m2/K)
Overall
(W/m2/K)
4 44.45 34 35 1400 72 50 13.59 2181 2505 2508 2546 2435
4 44.45 34.7 60 2400 72 50 13.56 2018 2294 2635 2330 2319
3 38.1 38 60 1800 94 50 10.98 1894 1951 2173 2146 2041
3 38.1 38 60 1800 72 35 9.62 1940 2033 2293 2378 2161
3 44.45 36.5 60 1800 94 35 7.83 3175 3569 4133 3652 3632
3 44.45 36.5 60 1800 94 50 11.07 3569 3547 3803 3281 3550
3 44.45 36.5 60 1800 72 50 13.46 2197 1956 2257 2126 2134
3 44.45 68.5 45 1350 22 60 27.77 199 220 261 246 231
2 38.1 18 40 800 126 45 8.76 4990 5706 4485 5719 5225
2 44.45 19.5 30 600 149 40 6.85 5050 5813 5250 4420 5133
2 44.45 20 40 800 149 33 5.65 5294 5909 5740 5093 5509
2 44.45 20 40 800 149 38 6.5 5217 6179 6151 5105 5663
2 44.45 20 40 800 126 33 6.47 4561 5098 5122 4355 4784
2 44.45 20 50 1000 149 33 5.65 4738 5632 5384 4448 5051
2 44.45 20 50 1000 149 37 6.33 4571 5360 5024 4212 4792
2 44.45 38 35 700 94 35 7.74 1368 1497 1278 1284 1357
2 44.45 35 60 1200 94 35 7.91 2899 2811 2999 3372 3020
2 44.45 74 70 1400 29 60 22.08 422 399 355 327 376
Appendix L: Uniform boiling pattern results – Original432 and Replicate128 datasets 347
Table L.2 Results from Replicate128 tests demonstrating uniform boiling pattern
TL
(m)
TD
(mm)
Brix JL (%
tube
height)
JL
(mm)
HS
(kPa
abs)
ΔP
(kPa)
ΔT
(°C)
Section 1
(W/m2/K)
Section 2
(W/m2/K)
Section 3
(W/m2/K)
Section 4
(W/m2/K)
Overall
(W/m2/K)
2 44.45 21.7 30 600 149 40 6.76 4705 5415 4891 4117 4782
2 44.45 20 40 800 149 33 5.65 4765 5318 5166 4583 4958
2 44.45 20 40 800 149 38 6.5 4695 5561 5536 4594 5097
2 44.45 20 40 800 126 33 6.47 4105 4588 4610 3920 4306
2 44.45 69 70 1400 29 60 23.54 376 355 316 291 335
3 44.45 67 45 900 22 60 27.77 218 242 287 271 255
2 38.1 19 40 1200 126 45 8.72 4910 5615 4414 5628 5142
Appendix M: Results showing low HTC at top section – Original432 and Replicate128 datasets 349
APPENDIX M: RESULTS SHOWING
LOW HTC AT TOP SECTION –
ORIGINAL432 AND REPLICATE128
DATASETS
M.1 Introductory remarks
This appendix presents the non-uniform boiling pattern showing low HTC at top
section results from the Original432 and Replicate128 experiments in Table M.1 and
Table M.2 respectively. This boiling pattern shows that the HTC of the top section
(section 1) was lower than 15% of the overall HTC.
Appendix M: Results showing low HTC at top section – Original432 and Replicate128 datasets 351
Table M.1 Results from Original432 tests demonstrating low HTC at the top section
TL
(m)
TD
(mm)
Brix JL (%
tube
height)
JL
(mm)
HS
(kPa
abs)
ΔP
(kPa)
ΔT
(°C)
Section 1
(W/m2/K)
Section 2
(W/m2/K)
Section 3
(W/m2/K)
Section 4
(W/m2/K)
Overall
(W/m2/K)
4 44.45 36 20 800 94 50 11.1 391 1022 1666 2420 1374
4 44.45 36 20 800 72 35 9.74 1147 2059 3044 2981 2308
4 44.45 36 20 800 72 50 13.49 1444 2054 2567 2570 2159
4 44.45 34 35 1400 94 50 11.21 623 1373 2689 3344 2007
4 44.45 34 35 1400 72 35 9.84 1172 2206 3243 3355 2494
4 44.45 36.2 45 1800 94 35 7.85 2669 3665 4504 2476 3328
4 44.45 36.2 45 1800 94 50 11.09 360 589 1353 2227 1132
4 44.45 36.2 45 1800 72 35 9.73 1908 2671 3060 2873 2628
4 44.45 36.2 45 1800 72 50 13.48 2005 2579 3106 2912 2651
4 44.45 68 30 1200 29 42 17.7 10 108 323 139 145
4 44.45 68 30 1200 29 60 23.77 72 279 372 284 252
4 44.45 68 30 1200 22 42 21.32 14 133 304 133 146
4 44.45 68 30 1200 22 60 27.88 4 235 306 203 187
4 44.45 69.5 45 1800 29 42 17.34 0 219 348 175 186
4 44.45 69.5 45 1800 22 42 20.98 19 73 257 121 118
4 44.45 69.5 45 1800 22 60 27.54 26 265 306 202 200
4 44.45 65 55 2200 29 42 18.3 142 426 316 160 261
4 44.45 65 55 2200 22 42 21.9 29 106 107 42 71
3 38.1 37.7 20 600 94 35 7.76 753 1080 2500 3747 2020
3 38.1 37.7 20 600 94 50 11 1712 2845 3069 3315 2735
3 38.1 37.7 20 600 72 50 13.39 498 661 940 1101 800
3 38.1 38 35 1050 94 35 7.74 3386 4082 4485 4039 3998
3 38.1 38 35 1050 94 50 10.98 1097 2463 3672 4626 2964
3 38.1 38 35 1050 72 35 9.62 397 1101 1460 1619 1144
3 38.1 38 35 1050 72 50 13.38 412 894 1263 1455 1006
3 38.1 38 45 1350 94 35 7.74 2935 3827 4709 3580 3763
3 38.1 38 45 1350 94 50 10.98 2306 3064 3934 3620 3231
352 Appendix M: Results showing low HTC at top section – Original432 and Replicate128 datasets
TL
(m)
TD
(mm)
Brix JL (%
tube
height)
JL
(mm)
HS
(kPa
abs)
ΔP
(kPa)
ΔT
(°C)
Section 1
(W/m2/K)
Section 2
(W/m2/K)
Section 3
(W/m2/K)
Section 4
(W/m2/K)
Overall
(W/m2/K)
3 38.1 38 45 1350 72 35 9.62 1112 1559 1677 1780 1532
3 38.1 38 60 1800 94 35 7.74 213 980 1048 1120 840
3 38.1 38 60 1800 72 50 13.38 1230 1571 2025 2399 1806
3 38.1 66.8 30 900 29 42 17.95 62 50 508 414 258
3 38.1 66.8 30 900 29 60 24.03 80 76 571 672 350
3 38.1 66.8 30 900 22 42 21.57 184 110 359 432 271
3 38.1 67 45 1350 29 42 17.91 63 326 370 327 272
3 38.1 67 45 1350 29 60 23.99 204 78 482 738 376
3 38.1 67 45 1350 22 60 28.09 123 53 268 539 246
3 38.1 67.6 55 1650 29 60 23.86 319 238 470 682 427
3 38.1 67.6 55 1650 22 60 27.97 294 156 550 538 385
3 38.1 69 70 2100 29 60 23.54 262 321 434 369 347
3 38.1 69 70 2100 22 60 27.66 86 100 155 70 103
3 44.45 17.9 20 600 149 33 5.73 1459 2587 514 3295 1964
3 44.45 17.9 20 600 149 40 6.91 785 575 209 3203 1193
3 44.45 17.9 20 600 126 33 6.54 388 516 1662 2326 1223
3 44.45 17.9 20 600 126 45 8.76 288 384 1235 1729 909
3 44.45 20 40 1200 149 33 5.65 900 2537 3959 4291 2922
3 44.45 20 40 1200 149 45 7.65 449 2406 1553 4012 2105
3 44.45 20 40 1200 126 33 6.47 761 1384 3661 3348 2288
3 44.45 20 40 1200 126 45 8.69 349 622 1158 2188 1079
3 44.45 35.9 20 600 94 35 7.86 44 35 17 408 126
3 44.45 35.9 20 600 94 50 11.11 32 20 6 765 206
3 44.45 35.9 20 600 72 35 9.74 0 0 0 677 169
3 44.45 35.9 20 600 72 50 13.49 0 0 0 776 194
3 44.45 38.5 35 1050 94 35 7.71 269 644 240 1038 548
3 44.45 38.5 35 1050 94 50 10.95 42 301 302 705 337
3 44.45 38.5 35 1050 72 35 9.59 81 207 501 1151 485
3 44.45 38.5 35 1050 72 50 13.35 78 138 1254 1880 838
Appendix M: Results showing low HTC at top section – Original432 and Replicate128 datasets 353
TL
(m)
TD
(mm)
Brix JL (%
tube
height)
JL
(mm)
HS
(kPa
abs)
ΔP
(kPa)
ΔT
(°C)
Section 1
(W/m2/K)
Section 2
(W/m2/K)
Section 3
(W/m2/K)
Section 4
(W/m2/K)
Overall
(W/m2/K)
3 44.45 37.5 45 1350 94 35 7.77 404 528 1122 1545 900
3 44.45 37.5 45 1350 94 50 11.01 482 445 972 1203 775
3 44.45 37.5 45 1350 72 35 9.65 50 455 912 1116 633
3 44.45 37.5 45 1350 72 50 13.4 110 457 907 1321 698
3 44.45 36.5 60 1800 72 35 9.71 1913 2355 3544 3365 2794
3 44.45 70 30 900 29 42 17.22 0 0 57 228 71
3 44.45 70 30 900 29 60 23.29 0 0 422 482 226
3 44.45 70 30 900 22 42 20.86 0 0 101 316 104
3 44.45 70 30 900 22 60 27.42 0 0 34 175 52
3 44.45 68.5 45 1350 29 42 17.58 0 92 340 121 138
3 44.45 68.5 45 1350 29 60 23.66 0 28 54 17 25
3 44.45 68.5 45 1350 22 42 21.21 0 258 350 180 197
3 44.45 70 55 1650 29 42 17.22 0 0 0 79 20
3 44.45 70 55 1650 29 60 23.29 41 78 484 388 248
3 44.45 70 55 1650 22 42 20.86 0 0 78 284 91
3 44.45 70 55 1650 22 60 27.42 0 1 19 337 89
4 50.8 17.9 20 800 149 33 5.73 428 970 461 1463 831
4 50.8 17.9 20 800 149 40 6.91 135 563 260 1074 508
4 50.8 17.9 20 800 126 33 6.54 233 782 415 2154 896
4 50.8 17.9 20 800 126 45 8.76 155 329 319 1026 457
4 50.8 17 30 1200 149 33 5.76 242 513 499 1603 714
4 50.8 17 30 1200 149 40 6.94 362 820 389 1237 684
4 50.8 17 30 1200 126 33 6.57 148 614 283 1171 540
4 50.8 17 30 1200 126 45 8.79 176 590 314 1627 664
4 50.8 17.2 40 1600 149 33 5.75 166 690 318 1315 611
4 50.8 17.2 40 1600 149 41 7.1 215 723 384 1993 817
4 50.8 17.2 40 1600 126 33 6.57 383 867 412 1308 731
4 50.8 17.2 40 1600 126 45 8.79 156 331 322 1035 456
4 50.8 21.9 50 2000 149 33 5.58 312 707 673 1516 802
354 Appendix M: Results showing low HTC at top section – Original432 and Replicate128 datasets
TL
(m)
TD
(mm)
Brix JL (%
tube
height)
JL
(mm)
HS
(kPa
abs)
ΔP
(kPa)
ΔT
(°C)
Section 1
(W/m2/K)
Section 2
(W/m2/K)
Section 3
(W/m2/K)
Section 4
(W/m2/K)
Overall
(W/m2/K)
4 50.8 21.9 50 2000 149 39 6.59 103 393 477 1374 587
4 50.8 21.9 50 2000 126 33 6.4 317 502 498 1419 684
4 50.8 21.9 50 2000 126 45 8.62 449 315 447 1344 654
4 50.8 36 20 800 94 35 7.86 10 128 206 155 125
4 50.8 36 20 800 94 50 11.1 25 42 72 274 103
4 50.8 34 35 1400 94 35 7.97 233 498 262 1097 523
4 50.8 34 35 1400 94 50 11.21 11 64 79 605 190
4 50.8 34 35 1400 72 35 9.84 63 306 1407 1344 780
4 50.8 34 35 1400 72 50 13.59 206 157 1209 1800 843
4 50.8 36.2 45 1800 72 35 9.73 29 49 84 318 120
4 50.8 36.2 45 1800 72 50 13.48 16 700 609 644 492
4 50.8 34.7 60 2400 94 35 7.93 10 127 204 154 124
4 50.8 34.7 60 2400 94 50 11.17 50 433 291 377 288
4 50.8 34.7 60 2400 72 35 9.81 39 686 1050 1184 740
4 50.8 34.7 60 2400 72 50 13.56 111 85 384 964 386
4 50.8 68 30 1200 29 42 17.7 0 0 69 41 28
4 50.8 68 30 1200 22 42 21.32 0 0 16 29 11
4 50.8 69.5 45 1800 29 60 23.42 0 19 123 52 48
4 50.8 69.5 45 1800 22 42 20.98 0 111 195 68 94
4 50.8 69.5 45 1800 22 60 27.54 0 0 64 128 48
4 50.8 65 55 2200 29 60 24.38 30 36 81 37 46
4 50.8 65 55 2200 22 42 21.9 95 286 116 109 152
4 50.8 70 70 2800 29 42 17.22 120 362 147 138 192
4 50.8 70 70 2800 22 42 20.86 36 42 96 43 54
4 50.8 70 70 2800 22 60 27.42 41 66 71 30 52
2 38.1 17.5 20 400 149 33 5.74 1016 1993 1573 5480 2515
2 38.1 17.5 20 400 149 35 6.08 1259 2156 2975 4932 2831
2 38.1 17.5 20 400 126 33 6.56 3836 5532 3828 5275 4618
2 38.1 20 30 600 126 45 8.69 3221 3917 3396 4684 3804
Appendix M: Results showing low HTC at top section – Original432 and Replicate128 datasets 355
TL
(m)
TD
(mm)
Brix JL (%
tube
height)
JL
(mm)
HS
(kPa
abs)
ΔP
(kPa)
ΔT
(°C)
Section 1
(W/m2/K)
Section 2
(W/m2/K)
Section 3
(W/m2/K)
Section 4
(W/m2/K)
Overall
(W/m2/K)
2 38.1 18 40 800 149 41 7.07 2484 3736 2359 6174 3688
2 38.1 18 50 1000 149 33 5.73 760 2205 1756 3229 1987
2 38.1 18 50 1000 149 44 7.56 713 726 665 2203 1077
2 38.1 18 50 1000 126 33 6.54 958 2216 1286 1440 1475
2 38.1 18 50 1000 126 45 8.76 526 778 1046 1388 935
2 38.1 36.5 20 400 94 35 7.83 32 121 210 316 170
2 38.1 36.5 20 400 94 50 11.07 765 1105 1553 1977 1350
2 38.1 37 35 700 94 35 7.8 294 346 498 558 424
2 38.1 37 35 700 72 35 9.68 266 369 535 408 395
2 38.1 37 45 900 94 35 7.8 667 513 1040 1072 823
2 38.1 37.2 60 1200 94 35 7.79 510 740 961 846 764
2 38.1 37.2 60 1200 94 50 11.03 84 233 488 298 276
2 38.1 37.2 60 1200 72 35 9.67 22 13 25 41 26
2 38.1 70 30 600 29 42 17.22 0 0 5 83 22
2 38.1 70 30 600 29 60 23.29 59 220 66 800 286
2 38.1 70 30 600 22 42 20.86 0 0 0 170 42
2 38.1 70 30 600 22 60 27.42 23 16 224 896 290
2 38.1 70.5 45 900 29 42 17.09 0 0 0 69 17
2 38.1 70.5 45 900 29 60 23.16 0 105 221 193 130
2 38.1 70.5 45 900 22 42 20.73 0 0 0 77 19
2 38.1 70.5 45 900 22 60 27.29 0 0 32 68 25
2 38.1 71.5 55 1100 29 42 16.81 0 0 0 21 5
2 38.1 71.5 55 1100 22 42 20.47 321 611 626 580 535
2 38.1 71.5 55 1100 22 60 27.03 124 119 337 93 168
2 38.1 72 70 1400 29 42 16.66 357 461 532 462 453
2 38.1 72 70 1400 29 60 22.73 172 158 950 498 444
2 44.45 18.2 20 400 149 33 5.72 2645 3621 4560 3726 3638
2 44.45 18.2 20 400 149 37 6.4 2602 1078 4612 4204 3124
2 44.45 19.5 30 600 126 45 8.71 1562 2254 2851 3888 2639
356 Appendix M: Results showing low HTC at top section – Original432 and Replicate128 datasets
TL
(m)
TD
(mm)
Brix JL (%
tube
height)
JL
(mm)
HS
(kPa
abs)
ΔP
(kPa)
ΔT
(°C)
Section 1
(W/m2/K)
Section 2
(W/m2/K)
Section 3
(W/m2/K)
Section 4
(W/m2/K)
Overall
(W/m2/K)
2 44.45 20 40 800 126 45 8.69 885 2020 3271 4368 2636
2 44.45 20 50 1000 126 33 6.47 2140 3416 4875 3767 3550
2 44.45 20 50 1000 126 45 8.69 1910 2180 2400 3592 2521
2 44.45 37 20 400 94 35 7.8 515 2618 3119 2834 2272
2 44.45 37 20 400 94 50 11.04 465 899 2076 3739 1795
2 44.45 37 20 400 72 50 13.43 628 514 1384 2624 1287
2 44.45 38 35 700 94 50 10.98 1220 1080 1374 3083 1689
2 44.45 38 35 700 72 35 9.62 552 521 900 1237 803
2 44.45 35 45 900 94 50 11.16 1440 1369 1563 3001 1843
2 44.45 35 45 900 72 35 9.79 723 920 1381 1508 1133
2 44.45 71.9 45 900 29 42 16.69 440 725 692 643 625
2 44.45 71.9 45 900 29 60 22.76 217 369 590 571 437
2 44.45 71.9 45 900 22 60 26.91 271 447 426 396 385
2 44.45 69.8 55 1100 29 60 23.34 0 0 171 428 150
2 50.8 18 20 400 126 33 6.54 913 2324 898 2695 1708
2 50.8 20 40 800 126 45 8.69 823 1309 1642 2962 1684
2 50.8 36 20 400 94 35 7.86 371 491 544 635 510
2 50.8 36 20 400 72 35 9.74 385 336 297 1224 561
2 50.8 36 20 400 72 50 13.49 462 562 547 1239 702
2 50.8 37 35 700 94 35 7.8 871 997 1192 2828 1472
2 50.8 37 35 700 94 50 11.04 1380 1240 2399 4005 2256
2 50.8 37 35 700 72 35 9.68 2419 2602 2841 4002 2966
2 50.8 37 35 700 72 50 13.43 1368 1583 2231 3677 2215
2 50.8 35 45 900 94 35 7.91 114 129 220 285 187
2 50.8 35 60 1200 94 35 7.91 864 1255 1392 2172 1421
2 50.8 35 60 1200 94 50 11.16 2123 2466 2720 3897 2802
2 50.8 35 60 1200 72 50 13.54 353 499 744 1559 789
2 50.8 70 30 600 29 42 17.22 0 1 2 11 4
2 50.8 70 30 600 29 60 23.29 198 563 845 858 616
Appendix M: Results showing low HTC at top section – Original432 and Replicate128 datasets 357
TL
(m)
TD
(mm)
Brix JL (%
tube
height)
JL
(mm)
HS
(kPa
abs)
ΔP
(kPa)
ΔT
(°C)
Section 1
(W/m2/K)
Section 2
(W/m2/K)
Section 3
(W/m2/K)
Section 4
(W/m2/K)
Overall
(W/m2/K)
2 50.8 70 30 600 22 42 20.86 0 23 81 750 214
2 50.8 70 30 600 22 60 27.42 0 37 16 361 103
2 50.8 67 45 900 29 60 23.99 0 0 0 627 157
2 50.8 67 45 900 22 42 21.53 0 0 242 784 256
2 50.8 67 45 900 22 60 28.09 0 0 0 438 110
2 50.8 73 55 1100 29 42 16.34 0 0 17 21 10
2 50.8 73 55 1100 22 42 20.02 0 222 541 583 337
2 50.8 73 55 1100 22 60 26.58 0 0 29 577 151
3 50.8 18.2 20 600 149 33 5.72 23 22 35 36 29
3 50.8 18.2 20 600 149 40 6.9 1142 854 2824 4001 2205
3 50.8 18.2 20 600 126 33 6.53 364 879 2418 3919 1895
3 50.8 18.2 20 600 126 45 8.75 235 23 627 1553 610
3 50.8 17.5 30 900 149 33 5.74 1270 2198 3176 3879 2631
3 50.8 17.5 30 900 149 40 6.92 2177 2076 2691 3401 2586
3 50.8 17.5 30 900 126 33 6.56 1280 1438 2584 3564 2217
3 50.8 17.5 30 900 126 45 8.78 654 868 1344 3000 1467
3 50.8 18.2 40 1200 126 33 6.53 1286 1436 2635 3537 2224
3 50.8 14.2 50 1500 149 40 7.03 994 1159 2117 3508 1945
3 50.8 14.2 50 1500 126 33 6.67 48 289 655 1491 621
3 50.8 14.2 50 1500 126 45 8.89 1012 1255 2397 3762 2106
3 50.8 34.1 20 600 94 35 7.96 315 666 879 1152 753
3 50.8 34.1 20 600 94 50 11.21 248 337 643 856 521
3 50.8 34.1 20 600 72 35 9.84 226 301 1240 2615 1096
3 50.8 34.1 20 600 72 50 13.59 169 414 1055 2672 1077
3 50.8 34 35 1050 94 35 7.97 255 285 815 1106 615
3 50.8 34 35 1050 94 50 11.21 221 417 638 715 498
3 50.8 34 35 1050 72 35 9.84 74 586 1782 2339 1195
3 50.8 34 35 1050 72 50 13.59 134 434 1037 1928 883
3 50.8 34.9 45 1350 94 35 7.92 237 634 940 1155 742
358 Appendix M: Results showing low HTC at top section – Original432 and Replicate128 datasets
TL
(m)
TD
(mm)
Brix JL (%
tube
height)
JL
(mm)
HS
(kPa
abs)
ΔP
(kPa)
ΔT
(°C)
Section 1
(W/m2/K)
Section 2
(W/m2/K)
Section 3
(W/m2/K)
Section 4
(W/m2/K)
Overall
(W/m2/K)
3 50.8 34.9 45 1350 94 50 11.16 235 432 698 808 543
3 50.8 34.9 45 1350 72 35 9.8 354 1085 2104 2843 1596
3 50.8 35.2 60 1800 94 35 7.9 316 587 840 1012 689
3 50.8 35.2 60 1800 94 50 11.15 264 463 604 762 523
3 50.8 35.2 60 1800 72 35 9.78 89 301 483 771 411
3 50.8 73 30 900 29 42 16.34 0 37 44 148 57
3 50.8 73 30 900 29 60 22.42 0 33 213 370 154
3 50.8 73 30 900 22 42 20.02 0 66 342 600 252
3 50.8 73 30 900 22 60 26.58 0 86 571 548 301
3 50.8 72.9 45 1350 29 42 16.38 0 165 195 148 127
3 50.8 72.9 45 1350 29 60 22.45 41 199 208 172 155
3 50.8 72.9 45 1350 22 42 20.05 0 78 88 57 56
3 50.8 72.9 45 1350 22 60 26.61 37 219 205 136 149
3 50.8 73.2 70 2100 29 60 22.35 185 443 392 368 347
4 38.1 17.5 30 1200 126 45 8.78 2027 2394 3112 2704 2559
4 38.1 15 40 1600 126 33 6.64 167 1552 1123 1416 1065
4 38.1 15 40 1600 126 45 8.86 762 1272 1237 3346 1654
4 38.1 37 20 800 94 35 7.8 137 703 594 1415 712
4 38.1 37 20 800 94 50 11.04 167 289 424 721 400
4 38.1 37 20 800 72 35 9.68 264 295 725 1902 796
4 38.1 37 20 800 72 50 13.43 458 226 806 1554 761
4 38.1 35 35 1400 94 50 11.16 12 21 37 57 32
4 38.1 35 35 1400 72 35 9.79 15 22 37 41 29
4 38.1 35 35 1400 72 50 13.54 27 27 37 36 32
4 38.1 35 45 1800 94 35 7.91 399 867 587 986 710
4 38.1 35 45 1800 94 50 11.16 148 155 391 633 332
4 38.1 35 45 1800 72 35 9.79 157 77 520 1853 652
4 38.1 35 45 1800 72 50 13.54 0 604 637 1694 734
4 38.1 35 60 2400 94 35 7.91 285 557 764 1047 663
Appendix M: Results showing low HTC at top section – Original432 and Replicate128 datasets 359
TL
(m)
TD
(mm)
Brix JL (%
tube
height)
JL
(mm)
HS
(kPa
abs)
ΔP
(kPa)
ΔT
(°C)
Section 1
(W/m2/K)
Section 2
(W/m2/K)
Section 3
(W/m2/K)
Section 4
(W/m2/K)
Overall
(W/m2/K)
4 38.1 35 60 2400 94 50 11.16 304 418 539 938 550
4 38.1 35 60 2400 72 35 9.79 388 854 1399 2361 1250
4 38.1 35 60 2400 72 50 13.54 253 423 840 2042 889
4 38.1 70 30 1200 29 42 17.22 52 176 266 234 182
4 38.1 70 30 1200 29 60 23.29 252 286 425 370 333
4 38.1 70 30 1200 22 60 27.42 152 204 208 154 180
4 38.1 67 45 1800 29 42 17.91 9 184 261 219 168
4 38.1 67 45 1800 29 60 23.99 286 340 399 362 347
4 38.1 67 45 1800 22 42 21.53 0 56 76 54 47
4 38.1 67 45 1800 22 60 28.09 210 271 315 216 253
4 38.1 67.6 55 2200 29 42 17.78 142 238 283 357 255
4 38.1 67.6 55 2200 22 42 21.41 86 124 132 175 129
4 38.1 69 70 2800 29 42 17.47 67 240 322 265 224
4 38.1 69 70 2800 29 60 23.54 258 358 466 403 371
4 38.1 69 70 2800 22 42 21.1 59 130 143 108 110
4 38.1 69 70 2800 22 60 27.66 329 470 455 338 398
Appendix M: Results showing low HTC at top section – Original432 and Replicate128 datasets 361
Table M.2 Results from Replicate128 tests demonstrating low HTC at the top section
TL
(m)
TD
(mm)
Brix JL (%
tube
height)
JL
(mm)
HS
(kPa
abs)
ΔP
(kPa)
ΔT
(°C)
Section 1
(W/m2/K)
Section 2
(W/m2/K)
Section 3
(W/m2/K)
Section 4
(W/m2/K)
Overall
(W/m2/K)
2 44.45 17.9 20 400 149 33 5.73 2508 3433 4324 3533 3450
2 44.45 17.9 20 400 149 37 6.41 2467 1022 4374 3987 2963
2 44.45 21.7 30 600 126 45 8.62 1451 2094 2648 3611 2451
2 44.45 20 40 800 126 45 8.69 797 1818 2944 3931 2373
2 44.45 16.3 50 1000 149 33 5.79 2485 2322 3422 5228 3364
2 44.45 16.3 50 1000 149 37 6.46 2666 3039 3311 5141 3539
2 44.45 16.3 50 1000 126 33 6.6 2099 3490 5082 4710 3845
2 44.45 16.3 50 1000 126 45 8.69 1548 1746 2496 4828 2655
2 44.45 67 45 900 29 42 17.91 386 635 606 563 548
2 44.45 67 45 900 29 60 23.99 194 329 526 509 390
2 44.45 67 45 900 22 60 26.91 255 420 401 372 362
2 44.45 67.6 55 1100 29 60 23.86 0 0 13 16 7
3 44.45 18.9 20 400 149 33 5.69 1395 2474 491 3151 1878
3 44.45 18.9 20 400 149 40 6.87 749 549 199 3059 1139
3 44.45 18.9 20 400 126 33 6.51 371 493 1588 2222 1169
3 44.45 18.9 20 400 126 45 8.73 275 366 1178 1649 867
3 44.45 16 40 800 149 33 5.8 834 2350 3668 3975 2707
3 44.45 16 40 800 149 45 7.79 419 2244 1448 3741 1963
3 44.45 16 40 800 126 33 6.61 708 1287 3404 3113 2128
3 44.45 16 40 800 126 45 8.83 326 582 1082 2045 1009
3 44.45 70 30 600 29 42 17.22 0 0 60 239 75
3 44.45 70 30 600 29 60 23.29 0 0 443 506 237
3 44.45 70 30 600 22 42 20.86 0 0 106 332 110
3 44.45 70 30 600 22 60 27.42 0 0 36 183 55
3 44.45 67 45 900 29 42 17.91 0 100 367 131 150
3 44.45 67 45 900 29 60 23.99 0 30 59 18 27
3 44.45 67 45 900 22 42 21.21 0 283 385 198 217
362 Appendix M: Results showing low HTC at top section – Original432 and Replicate128 datasets
TL
(m)
TD
(mm)
Brix JL (%
tube
height)
JL
(mm)
HS
(kPa
abs)
ΔP
(kPa)
ΔT
(°C)
Section 1
(W/m2/K)
Section 2
(W/m2/K)
Section 3
(W/m2/K)
Section 4
(W/m2/K)
Overall
(W/m2/K)
3 44.45 67.6 55 1100 29 42 17.78 0 0 0 81 20
3 44.45 67.6 55 1100 29 60 23.86 42 80 496 398 254
3 44.45 67.6 55 1100 22 42 21.41 0 0 80 291 93
3 44.45 67.6 55 1100 22 60 27.97 0 1 19 347 92
2 38.1 20 20 600 149 33 5.65 1064 2086 1646 5736 2633
2 38.1 20 20 600 149 35 5.99 1317 2255 3111 5157 2960
2 38.1 20 20 600 126 33 6.47 4006 5777 3998 5508 4822
2 38.1 16 30 900 126 45 8.83 3328 4047 3509 4840 3931
2 38.1 19 40 1200 149 41 7.03 2447 3680 2323 6082 3633
2 38.1 20 50 1500 149 33 5.65 732 2122 1690 3108 1913
2 38.1 20 50 1500 149 44 7.49 684 696 638 2114 1033
2 38.1 20 50 1500 126 33 6.47 920 2128 1235 1384 1417
2 38.1 20 50 1500 126 45 8.69 504 746 1002 1330 896
2 38.1 72 30 900 29 42 17.22 0 0 8 83 23
2 38.1 72 30 900 29 60 23.29 89 330 99 1200 430
2 38.1 72 30 900 22 42 20.32 0 0 0 261 65
2 38.1 72 30 900 22 60 26.88 35 25 343 1371 444
2 38.1 69.7 45 1350 29 42 17.29 0 0 0 82 21
2 38.1 69.7 45 1350 29 60 23.37 0 125 263 229 154
2 38.1 69.7 45 1350 22 42 20.73 0 0 0 93 23
2 38.1 69.7 45 1350 22 60 27.29 0 0 38 82 30
2 38.1 68 55 1650 29 42 17.7 0 0 0 21 5
2 38.1 68 55 1650 22 42 21.32 324 616 630 584 539
2 38.1 68 55 1650 22 60 27.88 126 121 343 95 171
2 38.1 70 70 2100 29 42 17.22 380 490 566 492 482
2 38.1 70 70 2100 29 60 23.29 185 170 1019 534 477
3 38.1 66.8 30 900 29 42 17.95 60 48 492 402 251
3 38.1 66.8 30 900 29 60 24.03 78 74 554 652 340
3 38.1 66.8 30 900 22 42 21.57 178 107 348 419 263
Appendix M: Results showing low HTC at top section – Original432 and Replicate128 datasets 363
TL
(m)
TD
(mm)
Brix JL (%
tube
height)
JL
(mm)
HS
(kPa
abs)
ΔP
(kPa)
ΔT
(°C)
Section 1
(W/m2/K)
Section 2
(W/m2/K)
Section 3
(W/m2/K)
Section 4
(W/m2/K)
Overall
(W/m2/K)
3 38.1 67 45 1350 29 42 17.91 60 310 351 311 258
3 38.1 67 45 1350 29 60 23.99 194 75 457 701 357
3 38.1 67 45 1350 22 60 28.09 117 50 255 512 234
3 38.1 67.6 55 1650 29 60 23.86 335 250 493 716 449
3 38.1 67.6 55 1650 22 60 27.97 309 164 578 565 404
3 38.1 69 70 2100 29 60 23.54 289 353 477 406 381
3 38.1 69 70 2100 22 60 27.66 95 110 171 77 113
Appendix N: Results showing low HTC at bottom section – Original432 and Replicate128 datasets 365
APPENDIX N: RESULTS SHOWING
LOW HTC AT BOTTOM SECTION –
ORIGINAL432 AND REPLICATE128
DATASETS
N.1 Introductory Remarks
This appendix presents the non-uniform boiling pattern showing low HTC at
bottom section results from the Original432 and Replicate128 experiments in Table
N.1 and Table N.2 respectively. This boiling pattern shows that the HTC of the bottom
section (section 4) was lower than 15% of the overall HTC.
Appendix N: Results showing low HTC at bottom section – Original432 and Replicate128 datasets 367
Table N.1 Results from Original432 tests demonstrating low HTC at the bottom section
TL
(m)
TD
(mm)
Brix JL (%
tube
height)
JL
(mm)
HS
(kPa
abs)
ΔP
(kPa)
ΔT
(°C)
Section 1
(W/m2/K)
Section 2
(W/m2/K)
Section 3
(W/m2/K)
Section 4
(W/m2/K)
Overall
(W/m2/K)
4 44.45 17.9 20 800 149 33 5.73 4512 2579 1950 2261 2826
4 44.45 17.9 20 800 149 40 6.91 4618 2641 1700 2248 2802
4 44.45 17.9 20 800 126 33 6.54 5010 3311 1619 1935 2969
4 44.45 17.9 20 800 126 45 8.76 5496 4570 2009 1820 3474
4 44.45 17.8 30 1200 149 33 5.73 4484 4627 2784 2273 3542
4 44.45 17.8 30 1200 149 45 7.73 4949 3450 3355 1319 3269
4 44.45 17.8 30 1200 126 33 6.55 2378 2456 1658 511 1751
4 44.45 17.8 30 1200 126 45 8.77 4691 4557 3631 933 3453
4 44.45 17 40 1600 149 33 5.76 4679 3318 2040 1864 2975
4 44.45 17 40 1600 149 45 7.76 5415 4574 3298 1614 3725
4 44.45 17 40 1600 126 33 6.57 4824 4198 2006 1444 3118
4 44.45 17 40 1600 126 45 8.79 4953 5019 3948 1303 3806
4 44.45 15 50 2000 149 33 5.83 2769 1874 628 493 1441
4 44.45 15 50 2000 149 40 7.01 5002 4543 3115 1723 3596
4 44.45 15 50 2000 126 33 6.64 4415 4282 2741 1099 3134
4 44.45 15 50 2000 126 45 8.86 4451 4135 3107 693 3097
4 44.45 36 20 800 94 35 7.86 787 1085 1161 561 898
4 44.45 34 35 1400 94 35 7.97 5034 4833 3281 973 3530
4 44.45 36.2 45 1800 94 35 7.85 2669 3665 4504 2476 3328
4 44.45 34.7 60 2400 94 35 7.93 3429 3569 2389 1218 2651
4 44.45 34.7 60 2400 94 50 11.17 3698 4004 3117 1135 2989
4 44.45 34.7 60 2400 72 35 9.81 3485 3255 2384 917 2510
4 44.45 69.5 45 1800 29 60 23.42 535 497 360 255 412
4 44.45 65 55 2200 29 42 18.3 142 426 316 160 261
4 44.45 65 55 2200 29 60 24.38 406 278 299 250 308
4 44.45 65 55 2200 22 42 21.9 29 106 107 42 71
4 44.45 65 55 2200 22 60 28.46 479 535 471 279 441
368 Appendix N: Results showing low HTC at bottom section – Original432 and Replicate128 datasets
TL
(m)
TD
(mm)
Brix JL (%
tube
height)
JL
(mm)
HS
(kPa
abs)
ΔP
(kPa)
ΔT
(°C)
Section 1
(W/m2/K)
Section 2
(W/m2/K)
Section 3
(W/m2/K)
Section 4
(W/m2/K)
Overall
(W/m2/K)
4 44.45 66 70 2800 29 42 18.11 206 203 124 63 149
4 44.45 66 70 2800 29 60 24.19 382 491 425 244 386
4 44.45 66 70 2800 22 42 21.72 249 333 309 104 249
4 44.45 66 70 2800 22 60 28.28 460 527 427 224 409
3 38.1 17.9 20 600 126 33 6.54 4415 5042 3890 3185 4133
3 38.1 17.9 20 600 126 45 8.76 4198 4244 3963 3065 3867
3 38.1 21.7 30 900 126 33 6.4 3469 4123 2221 1853 2917
3 38.1 21.7 30 900 126 45 8.62 3688 3792 2433 1999 2978
3 38.1 20 40 1200 149 41 6.99 4492 4677 2957 2869 3749
3 38.1 20 40 1200 126 33 6.47 4332 4067 2560 2869 3457
3 38.1 20 40 1200 126 45 8.69 4277 4197 3054 2252 3445
3 38.1 16.3 50 1500 149 33 5.79 3155 3413 2475 1423 2616
3 38.1 16.3 50 1500 149 36 6.29 3137 3284 1105 1181 2177
3 38.1 16.3 50 1500 126 33 6.6 3126 3169 1659 710 2166
3 38.1 16.3 50 1500 126 45 8.82 3444 3414 3856 1741 3114
3 38.1 67.6 55 1650 29 42 17.78 503 466 417 320 427
3 38.1 69 70 2100 29 42 17.47 970 466 404 315 539
3 38.1 69 70 2100 22 42 21.1 988 176 67 154 346
3 38.1 69 70 2100 22 60 27.66 86 100 155 70 103
3 44.45 20 30 900 149 33 5.65 5111 5036 4629 2594 4343
3 44.45 20 30 900 149 45 7.65 4684 4487 4550 2614 4084
3 44.45 20 30 900 126 33 6.47 2195 2360 2070 1438 2016
3 44.45 20 30 900 126 45 8.69 4624 4544 5067 3602 4459
3 44.45 18 50 1500 149 33 5.73 4637 4274 2735 1508 3288
3 44.45 18 50 1500 149 45 7.72 4379 4195 3722 1823 3530
3 44.45 18 50 1500 126 33 6.54 4036 4232 3691 2523 3620
3 44.45 18 50 1500 126 45 8.76 4431 4372 4581 2843 4057
3 44.45 68.5 45 1350 29 60 23.66 0 28 54 17 25
3 44.45 68.5 70 2100 29 42 17.58 685 564 303 263 454
Appendix N: Results showing low HTC at bottom section – Original432 and Replicate128 datasets 369
TL
(m)
TD
(mm)
Brix JL (%
tube
height)
JL
(mm)
HS
(kPa
abs)
ΔP
(kPa)
ΔT
(°C)
Section 1
(W/m2/K)
Section 2
(W/m2/K)
Section 3
(W/m2/K)
Section 4
(W/m2/K)
Overall
(W/m2/K)
3 44.45 68.5 70 2100 29 60 23.66 431 365 303 249 337
3 44.45 68.5 70 2100 22 42 21.21 63 112 48 31 64
3 44.45 68.5 70 2100 22 60 27.77 67 83 47 37 58
4 50.8 36 20 800 72 50 13.49 192 304 206 121 206
4 50.8 36.2 45 1800 94 35 7.85 330 521 353 207 353
4 50.8 68 30 1200 29 60 23.77 33 16 51 15 28
4 50.8 69.5 45 1800 29 42 17.34 174 200 90 29 123
4 50.8 69.5 45 1800 22 42 20.98 0 111 195 68 94
4 50.8 65 55 2200 29 42 18.3 165 189 85 28 117
4 50.8 65 55 2200 29 60 24.38 30 36 81 37 46
4 50.8 65 55 2200 22 42 21.9 95 286 116 109 152
4 50.8 65 55 2200 22 60 28.46 105 121 54 18 75
4 50.8 70 70 2800 29 42 17.22 120 362 147 138 192
4 50.8 70 70 2800 29 60 23.29 128 147 66 22 91
4 50.8 70 70 2800 22 42 20.86 36 42 96 43 54
4 50.8 70 70 2800 22 60 27.42 41 66 71 30 52
2 38.1 36.5 20 400 72 35 9.71 2798 2385 2202 1793 2294
2 38.1 71.5 55 1100 22 60 27.03 124 119 337 93 168
2 44.45 19.5 30 600 149 33 5.67 5012 2506 2398 2214 3033
2 44.45 19.5 30 600 126 33 6.49 4711 6014 4836 3779 4835
2 44.45 35 45 900 94 35 7.91 1667 1643 1988 1260 1639
2 44.45 35 45 900 72 50 13.54 3067 2159 1972 1870 2267
2 44.45 35 60 1200 72 50 13.54 2921 2010 1463 1143 1884
2 44.45 72 30 600 29 42 16.66 348 280 242 177 262
2 44.45 72 30 600 29 60 22.73 602 619 547 462 557
2 44.45 72 30 600 22 42 20.32 61 42 16 17 34
2 44.45 72 30 600 22 60 26.88 543 512 457 399 478
2 44.45 71.9 45 900 22 42 20.35 1551 868 751 564 934
2 44.45 69.8 55 1100 29 42 17.27 568 465 354 281 417
370 Appendix N: Results showing low HTC at bottom section – Original432 and Replicate128 datasets
TL
(m)
TD
(mm)
Brix JL (%
tube
height)
JL
(mm)
HS
(kPa
abs)
ΔP
(kPa)
ΔT
(°C)
Section 1
(W/m2/K)
Section 2
(W/m2/K)
Section 3
(W/m2/K)
Section 4
(W/m2/K)
Overall
(W/m2/K)
2 44.45 69.8 55 1100 22 42 20.91 471 386 293 233 346
2 44.45 74 70 1400 29 42 16 654 544 435 372 501
2 44.45 74 70 1400 22 42 19.69 500 409 312 248 367
2 44.45 74 70 1400 22 60 26.25 598 415 493 392 474
2 50.8 18 20 400 126 45 8.76 48 49 43 30 43
2 50.8 69 70 1400 29 42 17.47 1729 785 193 366 769
2 50.8 69 70 1400 22 42 21.1 891 568 479 418 589
3 50.8 35.2 60 1800 72 50 13.53 2189 2136 2073 1612 2002
3 50.8 71.2 55 1650 29 42 16.89 157 128 144 115 136
3 50.8 71.2 55 1650 22 42 20.55 73 54 39 23 47
3 50.8 71.2 55 1650 22 60 27.11 295 302 249 200 261
3 50.8 73.2 70 2100 22 42 19.96 259 81 34 83 114
3 50.8 73.2 70 2100 22 60 26.52 806 645 520 521 623
4 38.1 17.9 20 800 149 45 7.72 4177 3447 3965 2468 3514
4 38.1 15 40 1600 149 45 7.82 3380 3517 3865 2787 3387
4 38.1 16 50 2000 149 33 5.8 4308 4156 4734 3285 4121
4 38.1 35 35 1400 94 35 7.91 64 54 39 12 42
4 38.1 69 70 2800 22 60 27.66 329 470 455 338 398
Appendix N: Results showing low HTC at bottom section – Original432 and Replicate128 datasets 371
Table N.2 Results from Replicate128 tests demonstrating low HTC at the bottom section
TL
(m)
TD
(mm)
Brix JL (%
tube
height)
JL
(mm)
HS
(kPa
abs)
ΔP
(kPa)
ΔT
(°C)
Section 1
(W/m2/K)
Section 2
(W/m2/K)
Section 3
(W/m2/K)
Section 4
(W/m2/K)
Overall
(W/m2/K)
2 44.45 21.7 30 600 149 33 5.59 4681 2340 2240 2068 2832
2 44.45 21.7 30 600 126 33 6.4 4390 5604 4506 3521 4505
2 44.45 70 30 600 29 42 16.66 342 275 237 174 257
2 44.45 70 30 600 29 60 22.73 590 606 536 453 546
2 44.45 70 30 600 22 42 20.86 58 40 15 17 33
2 44.45 70 30 600 22 60 27.42 522 492 439 383 459
2 44.45 67 45 900 22 42 20.35 1458 816 706 530 878
2 44.45 67.6 55 1100 29 42 17.78 507 415 316 251 372
2 44.45 67.6 55 1100 22 42 21.41 423 346 264 210 311
2 44.45 69 70 1400 29 42 17.47 569 473 378 324 436
2 44.45 69 70 1400 22 42 21.1 443 363 276 220 326
3 44.45 20.5 30 600 149 33 5.63 4975 4902 4505 2524 4227
3 44.45 20.5 30 600 149 45 7.63 4555 4364 4424 2542 3971
3 44.45 20.5 30 600 126 33 6.45 2136 2295 2014 1399 1961
3 44.45 20.5 30 600 126 45 8.67 4495 4417 4926 3501 4335
3 44.45 17 50 1000 149 33 5.76 4516 4162 2663 1469 3203
3 44.45 17 50 1000 149 45 7.76 4272 4093 3630 1779 3444
3 44.45 17 50 1000 126 33 6.57 3935 4125 3598 2460 3530
3 44.45 17 50 1000 126 45 8.79 4325 4268 4472 2775 3960
3 44.45 67 45 900 29 60 23.99 0 30 59 18 27
3 44.45 68.5 70 1400 29 42 17.58 651 536 288 250 431
3 44.45 68.5 70 1400 29 60 23.66 410 347 288 236 320
3 44.45 68.5 70 1400 22 42 21.21 60 107 45 30 61
3 44.45 68.5 70 1400 22 60 27.77 63 79 45 35 56
2 38.1 68 55 1650 22 60 27.88 126 121 343 95 171
3 38.1 18 20 600 126 33 6.54 4108 4692 3619 2963 3846
3 38.1 18 20 600 126 45 8.76 3906 3949 3687 2851 3598
372 Appendix N: Results showing low HTC at bottom section – Original432 and Replicate128 datasets
TL
(m)
TD
(mm)
Brix JL (%
tube
height)
JL
(mm)
HS
(kPa
abs)
ΔP
(kPa)
ΔT
(°C)
Section 1
(W/m2/K)
Section 2
(W/m2/K)
Section 3
(W/m2/K)
Section 4
(W/m2/K)
Overall
(W/m2/K)
3 38.1 16.9 30 900 126 33 6.58 3276 3894 2098 1750 2755
3 38.1 16.9 30 900 126 45 8.8 3507 3605 2313 1901 2832
3 38.1 20 40 1200 149 41 6.99 4267 4444 2809 2726 3562
3 38.1 20 40 1200 126 33 6.47 4115 3864 2432 2725 3284
3 38.1 20 40 1200 126 45 8.69 4063 3987 2901 2139 3273
3 38.1 18.5 50 1500 149 33 5.71 3262 3528 2559 1472 2705
3 38.1 18.5 50 1500 149 36 6.22 3240 3392 1141 1220 2248
3 38.1 18.5 50 1500 126 33 6.52 3225 3270 1712 733 2235
3 38.1 18.5 50 1500 126 45 8.74 3544 3513 3968 1791 3204
3 38.1 67.6 55 1650 29 42 17.78 528 489 438 336 448
3 38.1 69 70 2100 29 42 17.47 1067 513 444 346 593
3 38.1 69 70 2100 22 42 21.1 1087 193 73 169 381
3 38.1 69 70 2100 22 60 27.66 95 110 171 77 113
Appendix O: Results showing low HTC at intermediate sections – Original432 and Replicate128 datasets
373
APPENDIX O: RESULTS SHOWING
LOW HTC AT INTERMEDIATE
SECTIONS – ORIGINAL432 AND
REPLICATE128 DATASETS
O.1 Introductory Remarks
This appendix presents the non-uniform boiling pattern showing low HTC at
intermediate section (section 2 and/or 3) results from the Original432 and
Replicate128 experiments in Table O.1 and Table O.2 respectively. This boiling
pattern shows that the HTC of the intermediate sections (section 2 and/or 3) were lower
than 15% of the overall HTC while the HTC of the top and bottom sections being
within or higher than 15% of the overall HTC.
Appendix O: Results showing low HTC at intermediate sections – Original432 and Replicate128 datasets 375
Table O.1 Results from Original432 tests demonstrating low HTC at an intermediate section
TL
(m)
TD
(mm)
Brix JL (%
tube
height)
JL
(mm)
HS
(kPa
abs)
ΔP
(kPa)
ΔT
(°C)
Section 1
(W/m2/K)
Section 2
(W/m2/K)
Section 3
(W/m2/K)
Section 4
(W/m2/K)
Overall
(W/m2/K)
3 38.1 17.9 20 600 149 33 5.73 4838 3995 3018 3695 3886
3 38.1 17.9 20 600 149 40 6.91 4737 4132 2812 3269 3737
3 38.1 21.7 30 900 149 33 5.59 3394 4966 2109 3087 3389
3 38.1 21.7 30 900 149 40 6.76 3747 4829 2389 3118 3521
3 38.1 20 40 1200 149 33 5.65 4708 5327 3114 3736 4221
3 38.1 67 45 1350 22 42 21.53 721 275 453 416 466
3 38.1 67.6 55 1650 22 42 21.41 506 419 300 392 404
3 38.1 69 70 2100 22 42 21.1 988 176 67 154 346
4 50.8 68 30 1200 22 60 27.88 22 12 32 25 23
2 38.1 20 30 600 149 33 5.65 4602 5961 3051 5028 4661
2 38.1 20 30 600 149 40 6.83 4652 5227 2479 4253 4152
2 38.1 20 30 600 126 33 6.47 4447 6803 2997 5505 4938
2 38.1 18 40 800 126 33 6.54 1959 2563 1664 2181 2092
2 38.1 72 70 1400 22 42 20.32 528 517 394 528 492
2 44.45 19.5 30 600 149 33 5.67 5012 2506 2398 2214 3033
2 44.45 37 20 400 72 35 9.68 916 597 1036 827 844
2 44.45 38 35 700 72 50 13.38 3222 1757 1666 2226 2218
2 44.45 35 60 1200 94 50 11.16 3558 3039 2440 2844 2970
2 44.45 35 60 1200 72 35 9.79 2623 1781 1991 2517 2228
2 44.45 69.8 55 1100 22 60 27.47 43 25 17 25 28
2 50.8 16.9 30 600 126 33 6.58 2793 2832 2175 2776 2644
2 50.8 35 45 900 94 50 11.16 1328 953 862 1091 1058
3 50.8 18.2 40 1200 126 45 8.75 3242 2833 2116 2326 2629
3 50.8 73.2 70 2100 22 42 19.96 259 81 34 83 114
4 38.1 70 30 1200 22 42 20.86 70 56 94 64 71
376 Appendix O: Results showing low HTC at intermediate sections – Original432 and Replicate128 datasets
Table O.2 Results from Replicate128 tests demonstrating low HTC at an intermediate section
TL
(m)
TD
(mm)
Brix JL (%
tube
height)
JL
(mm)
HS
(kPa
abs)
ΔP
(kPa)
ΔT
(°C)
Section 1
(W/m2/K)
Section 2
(W/m2/K)
Section 3
(W/m2/K)
Section 4
(W/m2/K)
Overall
(W/m2/K)
2 44.45 17.9 20 400 126 45 8.76 1347 1186 1722 2013 1567
2 44.45 69 70 1400 22 60 27.66 1027 663 804 789 821
2 38.1 20 20 600 126 45 8.69 3078 2356 3276 4083 3198
2 38.1 16 30 900 149 33 5.8 4713 6104 3124 5149 4773
2 38.1 16 30 900 149 40 6.97 4784 5375 2549 4373 4270
2 38.1 16 30 900 126 33 6.61 4571 6992 3080 5658 5075
2 38.1 19 40 1200 149 33 5.69 5329 4235 2490 5139 4298
2 38.1 19 40 1200 126 33 6.5 1931 2525 1639 2149 2061
2 38.1 70 70 2100 22 42 20.86 566 554 422 566 527
2 38.1 70 70 2100 22 60 27.42 577 149 655 975 589
3 38.1 18 20 600 149 33 5.73 4502 3718 2808 3439 3617
3 38.1 18 20 600 149 40 6.9 4408 3845 2617 3042 3478
3 38.1 16.9 30 900 149 33 5.77 3190 4668 1983 2902 3186
3 38.1 16.9 30 900 149 40 6.94 3541 4563 2257 2947 3327
3 38.1 20 40 1200 149 33 5.65 4472 5061 2958 3549 4010
3 38.1 67 45 1350 22 42 21.53 685 261 430 396 443
Appendix P: Analysis of Variance 377
APPENDIX P: ANALYSIS OF VARIANCE
P.1 Introductory Remarks
This appendix presents the analysis of variance for individual section HTCmax
from the Original432 dataset. The significant interactions are analysed in section 6.5.2.
Appendix P: Analysis of Variance 379
Table P.1 Analysis of variance of HTC of section 1 from Original432 tests with
3rd order interactions
Source
Degrees of
freedom
Mean
square
Variance
ratio
Significance
level
TL 2 2604453 0.14 –
TD 2 37594189 2.01 –
Residuals 4 18669978
B 2 240942219 141.94 0.000
JL 3 4517936 2.66 –
TL:B 4 195755 0.12 –
TL:JL 6 2091768 1.23 –
TD:B 4 16901863 9.96 0.000
TD:JL 6 5808118 3.42 0.014
B:JL 6 2390898 1.41 –
TL:TD:B 8 4899175 2.89 0.021
TL:TD:JL 12 1800409 1.06 –
TL:B:JL 12 1438937 0.85 –
TD:B:JL 12 2239058 1.32 –
Residuals 24 1697487
HS 1 7420366 15.06 0.000
ΔP 1 414099 0.84 –
TL:HS 2 268549 0.55 –
TL:ΔP 2 437831 0.89 –
TD:HS 2 329020 0.67 –
TD:ΔP 2 36412 0.07 –
B:HS 2 5883033 11.94 0.000
B:ΔP 2 919474 1.87 –
JL:HS 3 588920 1.20 –
JL:ΔP 3 104759 0.21 –
HS:ΔP 1 848451 1.72 –
TL:TD:HS 4 1411947 2.87 0.026
TL:TD:ΔP 4 259696 0.53 –
TL:B:HS 4 1035779 2.10 –
TL:B:ΔP 4 2060539 4.18 0.003
TL:JL:HS 6 442951 0.90 –
TL:JL:ΔP 6 22534 0.05 –
TL:HS:ΔP 2 828208 1.68 –
TD:B:HS 4 727702 1.48 –
TD:B:ΔP 4 394429 0.80 –
TD:JL:HS 6 852412 1.73 –
380 Appendix P: Analysis of Variance
Source
Degrees of
freedom
Mean
square
Variance
ratio
Significance
level
TD:JL:ΔP 6 126252 0.26 –
TD:HS:ΔP 2 21839 0.04 –
B:JL:HS 6 447021 0.91 –
B:JL:ΔP 6 252769 0.51 –
B:HS:ΔP 2 279976 0.57 –
JL:HS:ΔP 3 640105 1.30 –
TL:TD:B:HS 8 1637427 3.32 0.002
TL:TD:B:ΔP 8 792984 1.61 –
TL:TD:JL:HS 12 479053 0.97 –
TL:TD:JL:ΔP 12 189417 0.38 –
TL:TD:HS:ΔP 4 644665 1.31 –
TL:B:JL:HS 12 228510 0.46 –
TL:B:JL:ΔP 12 619137 1.26 –
TL:B:HS:ΔP 4 445405 0.90 –
TL:JL:HS:ΔP 6 134491 0.27 –
TD:B:JL:HS 12 396152 0.80 –
TD:B:JL:ΔP 12 183922 0.37 –
TD:B:HS:ΔP 4 887954 1.80 –
TD:JL:HS:ΔP 6 757523 1.54 –
B:JL:HS:ΔP 6 1071255 2.17 –
Residuals 116 492587
Appendix P: Analysis of Variance 381
Table P.2 Analysis of variance of HTC of section 2 from Original432 tests with
3rd order interactions
Source
Degrees of
freedom
Mean
square
Variance
ratio
Significance
level
TL 2 2944228 0.21 –
TD 2 36326252 2.63 –
Residuals 4 13826518
B 2 270365235 225.35 0.000
JL 3 6011506 5.01 0.008
TL:B 4 1753123 1.46 –
TL:JL 6 1313665 1.09 –
TD:B 4 17277802 14.40 0.000
TD:JL 6 5212019 4.34 0.004
B:JL 6 3592189 2.99 0.025
TL:TD:B 8 3224738 2.69 0.029
TL:TD:JL 12 1204478 1.00 –
TL:B:JL 12 934821 0.78 –
TD:B:JL 12 2091457 1.74 –
Residuals 24 1199734
HS 1 8233992 15.52 0.000
ΔP 1 2993187 5.64 0.019
TL:HS 2 1570721 2.96 –
TL:ΔP 2 551977 1.04 –
TD:HS 2 106519 0.20 –
TD:ΔP 2 72817 0.14 –
B:HS 2 2434233 4.59 0.012
B:ΔP 2 1794202 3.38 0.037
JL:HS 3 582780 1.10 –
JL:ΔP 3 117523 0.22 –
HS:ΔP 1 128171 0.24 –
TL:TD:HS 4 1875343 3.53 0.009
TL:TD:ΔP 4 109680 0.21 –
TL:B:HS 4 613484 1.16 –
TL:B:ΔP 4 1772718 3.34 0.013
TL:JL:HS 6 813745 1.53 –
TL:JL:ΔP 6 217394 0.41 –
TL:HS:ΔP 2 1945960 3.67 0.029
TD:B:HS 4 1099621 2.07 –
TD:B:ΔP 4 664627 1.25 –
TD:JL:HS 6 625522 1.18 –
382 Appendix P: Analysis of Variance
Source
Degrees of
freedom
Mean
square
Variance
ratio
Significance
level
TD:JL:ΔP 6 165139 0.31 –
TD:HS:ΔP 2 129015 0.24 –
B:JL:HS 6 831381 1.57 –
B:JL:ΔP 6 142575 0.27 –
B:HS:ΔP 2 288089 0.54 –
JL:HS:ΔP 3 377618 0.71 –
TL:TD:B:HS 8 1316409 2.48 0.016
TL:TD:B:ΔP 8 488272 0.92 –
TL:TD:JL:HS 12 410278 0.77 –
TL:TD:JL:ΔP 12 360950 0.68 –
TL:TD:HS:ΔP 4 453564 0.85 –
TL:B:JL:HS 12 232740 0.44 –
TL:B:JL:ΔP 12 258963 0.49 –
TL:B:HS:ΔP 4 1198271 2.26 –
TL:JL:HS:ΔP 6 226203 0.43 –
TD:B:JL:HS 12 338076 0.64 –
TD:B:JL:ΔP 12 282008 0.53 –
TD:B:HS:ΔP 4 457428 0.86 –
TD:JL:HS:ΔP 6 1023934 1.93 –
B:JL:HS:ΔP 6 739208 1.39 –
Residuals 116 530686
Appendix P: Analysis of Variance 383
Table P.3 Analysis of variance of HTC of section 3 from Original432 tests with
3rd order interactions
Source
Degrees of
freedom
Mean
square
Variance
ratio
Significance
level
TL 2 5238741 0.48 –
TD 2 24368868 2.24 –
Residuals 4 10869243
B 2 195834632 192.40 0.000
JL 3 2487131 2.44 –
TL:B 4 2583420 2.54 –
TL:JL 6 1001641 0.98 –
TD:B 4 7354507 7.23 0.001
TD:JL 6 3183947 3.13 0.021
B:JL 6 1451101 1.43 –
TL:TD:B 8 8666000 8.51 0.000
TL:TD:JL 12 1184585 1.16 –
TL:B:JL 12 929436 0.91 –
TD:B:JL 12 2103079 2.07 –
Residuals 24 1017847
HS 1 3671847 8.41 0.004
ΔP 1 90232 0.21 –
TL:HS 2 951134 2.18 –
TL:ΔP 2 50905 0.12 –
TD:HS 2 1884 0.00 –
TD:ΔP 2 241653 0.55 –
B:HS 2 1262975 2.89 –
B:ΔP 2 319674 0.73 –
JL:HS 3 308350 0.71 –
JL:ΔP 3 231172 0.53 –
HS:ΔP 1 6518 0.01 –
TL:TD:HS 4 2271100 5.20 0.001
TL:TD:ΔP 4 521496 1.19 –
TL:B:HS 4 1021409 2.34 –
TL:B:ΔP 4 770458 1.76 –
TL:JL:HS 6 1217942 2.79 0.014
TL:JL:ΔP 6 382103 0.87 –
TL:HS:ΔP 2 783002 1.79 –
TD:B:HS 4 2449519 5.61 0.000
TD:B:ΔP 4 653670 1.50 –
TD:JL:HS 6 467145 1.07 –
384 Appendix P: Analysis of Variance
Source
Degrees of
freedom
Mean
square
Variance
ratio
Significance
level
TD:JL:ΔP 6 426961 0.98 –
TD:HS:ΔP 2 777742 1.78 –
B:JL:HS 6 383282 0.88 –
B:JL:ΔP 6 117219 0.27 –
B:HS:ΔP 2 70671 0.16 –
JL:HS:ΔP 3 530396 1.21 –
TL:TD:B:HS 8 1829232 4.19 0.000
TL:TD:B:ΔP 8 611433 1.40 –
TL:TD:JL:HS 12 494240 1.13 –
TL:TD:JL:ΔP 12 213654 0.49 –
TL:TD:HS:ΔP 4 136662 0.31 –
TL:B:JL:HS 12 489947 1.12 –
TL:B:JL:ΔP 12 392197 0.90 –
TL:B:HS:ΔP 4 494315 1.13 –
TL:JL:HS:ΔP 6 244354 0.56 –
TD:B:JL:HS 12 428737 0.98 –
TD:B:JL:ΔP 12 343756 0.79 –
TD:B:HS:ΔP 4 775777 1.78 –
TD:JL:HS:ΔP 6 515891 1.18 –
B:JL:HS:ΔP 6 679222 1.55 –
Residuals 116 436830
Appendix P: Analysis of Variance 385
Table P.4 Analysis of variance of HTC of section 4 from Original432 tests with
3rd order interactions
Source
Degrees of
freedom
Mean
square
Variance
ratio
Significance
level
TL 2 23005300 6.46 –
TD 2 3029998 0.85 –
Residuals 4 3561657
B 2 228926494 164.08 0.000
JL 3 1646634 1.18 –
TL:B 4 7395276 5.30 0.003
TL:JL 6 262645 0.19 –
TD:B 4 4404220 3.16 0.032
TD:JL 6 2101835 1.51 –
B:JL 6 2508045 1.80 –
TL:TD:B 8 6782373 4.86 0.001
TL:TD:JL 12 1025176 0.73 –
TL:B:JL 12 801337 0.57 –
TD:B:JL 12 1595094 1.14 –
Residuals 24 1395236
HS 1 2759219 7.99 0.006
ΔP 1 404000 1.17 –
TL:HS 2 1910367 5.53 0.005
TL:ΔP 2 286007 0.83 –
TD:HS 2 920855 2.67 –
TD:ΔP 2 587660 1.70 –
B:HS 2 4181468 12.10 0.000
B:ΔP 2 1133612 3.28 0.041
JL:HS 3 159447 0.46 –
JL:ΔP 3 54178 0.16 –
HS:ΔP 1 256235 0.74 –
TL:TD:HS 4 1333719 3.86 0.006
TL:TD:ΔP 4 233408 0.68 –
TL:B:HS 4 890520 2.58 0.041
TL:B:ΔP 4 615935 1.78 –
TL:JL:HS 6 979781 2.84 0.013
TL:JL:ΔP 6 544900 1.58 –
TL:HS:ΔP 2 222621 0.64 –
TD:B:HS 4 880790 2.55 0.043
TD:B:ΔP 4 250105 0.72 –
TD:JL:HS 6 557469 1.61 –
386 Appendix P: Analysis of Variance
Source
Degrees of
freedom
Mean
square
Variance
ratio
Significance
level
TD:JL:ΔP 6 481403 1.39 –
TD:HS:ΔP 2 1003789 2.91 –
B:JL:HS 6 308585 0.89 –
B:JL:ΔP 6 318169 0.92 –
B:HS:ΔP 2 99847 0.29 –
JL:HS:ΔP 3 934017 2.70 0.049
TL:TD:B:HS 8 1405498 4.07 0.000
TL:TD:B:ΔP 8 268047 0.78 –
TL:TD:JL:HS 12 580347 1.68 –
TL:TD:JL:ΔP 12 283201 0.82 –
TL:TD:HS:ΔP 4 347121 1.00 –
TL:B:JL:HS 12 451839 1.31 –
TL:B:JL:ΔP 12 380459 1.10 –
TL:B:HS:ΔP 4 96748 0.28 –
TL:JL:HS:ΔP 6 117894 0.34 –
TD:B:JL:HS 12 438159 1.27 –
TD:B:JL:ΔP 12 394936 1.14 –
TD:B:HS:ΔP 4 426997 1.24 –
TD:JL:HS:ΔP 6 338920 0.98 –
B:JL:HS:ΔP 6 596374 1.73 –
Residuals 116 345442
Appendix P: Analysis of Variance 387
Table P.5 Analysis of variance of HTCmax of section 1 from Original432 tests
with 3rd order interactions
Source
Degrees of
freedom
Mean
square
Variance
ratio
Significance
level
TL 2 7397941 1.88 –
TD 2 17219568 4.37 –
Residuals 4 3943846 –
B 2 100189005 59.65 0.000
TL:B 4 697330 0.42 –
TD:B 4 6970377 4.15 0.041
Residuals 8 1679629
HS 1 2892285 6.95 0.012
ΔP 1 328451 0.79 –
TL:HS 2 622307 1.50 –
TL:ΔP 2 394636 0.95 –
TD:HS 2 1529004 3.67 0.035
TD:ΔP 2 110523 0.27 –
B:HS 2 1139347 2.74 –
B:ΔP 2 294905 0.71 –
HS:ΔP 1 46050 0.11 –
TL:TD:HS 4 303932 0.73 –
TL:TD:ΔP 4 490645 1.18 –
TL:B:HS 4 1067305 2.57 –
TL:B:ΔP 4 414015 1.00 –
TL:HS:ΔP 2 1709616 4.11 0.025
TD:B:HS 4 1367720 3.29 0.021
TD:B:ΔP 4 309287 0.74 –
TD:HS:ΔP 2 265289 0.64 –
B:HS:ΔP 2 5395 0.01 –
Residuals 36 416058
Appendix P: Analysis of Variance 389
Table P.6 Analysis of variance of HTCmax of section 2 from Original432 tests
Source
Degrees of
freedom
Mean
square
Variance
ratio
Significance
level
TL 2 6324521 2.16 –
TD 2 17020978 5.80 –
Residuals 4 2934040 –
B 2 125156668 81.04 0.000
TL:B 4 2316491 1.50 –
TD:B 4 7177250 4.65 0.031
Residuals 8 1544436
HS 1 4037071 9.81 0.003
ΔP 1 2158471 5.24 0.028
TL:HS 2 524878 1.27 –
TL:ΔP 2 370180 0.90 –
TD:HS 2 939946 2.28 –
TD:ΔP 2 160539 0.39 –
B:HS 2 779351 1.89 –
B:ΔP 2 1112463 2.70 –
HS:ΔP 1 22473 0.05 –
TL:TD:HS 4 594776 1.44 –
TL:TD:ΔP 4 116680 0.28 –
TL:B:HS 4 510687 1.24 –
TL:B:ΔP 4 694956 1.69 –
TL:HS:ΔP 2 2295074 5.57 0.008
TD:B:HS 4 1341997 3.26 0.022
TD:B:ΔP 4 122488 0.30 –
TD:HS:ΔP 2 38065 0.09 –
B:HS:ΔP 2 15643 0.04 –
Residuals 36 411687
Appendix P: Analysis of Variance 391
Table P.7 Analysis of variance of HTCmax of section 3 from Original432 tests
Source
Degrees
of freedom
Mean
square
Variance
ratio
Significance
level
TL 2 6579628 3.01 –
TD 2 10700357 4.89 –
Residuals 4 2189556 –
B 2 85051627 25.85 0.000
TL:B 4 1398117 0.42 –
TD:B 4 2635829 0.80 –
Residuals 8 3290632
HS 1 485522 1.28 –
ΔP 1 317775 0.84 –
TL:HS 2 679622 1.79 –
TL:ΔP 2 130499 0.34 –
TD:HS 2 713698 1.88 –
TD:ΔP 2 265858 0.70 –
B:HS 2 629141 1.66 –
B:ΔP 2 267951 0.71 –
HS:ΔP 1 116040 0.31 –
TL:TD:HS 4 572017 1.51 –
TL:TD:ΔP 4 273890 0.72 –
TL:B:HS 4 414545 1.09 –
TL:B:ΔP 4 429535 1.13 –
TL:HS:ΔP 2 559623 1.48 –
TD:B:HS 4 1998697 5.28 0.002
TD:B:ΔP 4 769559 2.03 –
TD:HS:ΔP 2 248426 0.66 –
B:HS:ΔP 2 92440 0.24 –
Residuals 36 378714
Appendix P: Analysis of Variance 393
Table P.8 Analysis of variance of HTCmax of section 4 from Original432 tests
Source
Degrees of
freedom
Mean square Variance
ratio
Significance
level
TL 2 11810395 14.26 0.015
TD 2 1706308 2.06 –
Residuals 4 828349 –
B 2 84167518 40.25 0.000
TL:B 4 2582220 1.23 –
TD:B 4 1848260 0.88 –
Residuals 8 2091126
HS 1 19115 0.06 –
ΔP 1 897736 2.69 –
TL:HS 2 682222 2.05 –
TL:ΔP 2 144119 0.43 –
TD:HS 2 154443 0.46 –
TD:ΔP 2 419801 1.26 –
B:HS 2 1002893 3.01 –
B:ΔP 2 546795 1.64 –
HS:ΔP 1 48607 0.15 –
TL:TD:HS 4 800473 2.40 –
TL:TD:ΔP 4 215572 0.65 –
TL:B:HS 4 714230 2.14 –
TL:B:ΔP 4 153447 0.46 –
TL:HS:ΔP 2 135278 0.41 –
TD:B:HS 4 401190 1.20 –
TD:B:ΔP 4 417037 1.25 –
TD:HS:ΔP 2 355596 1.07 –
B:HS:ΔP 2 70135 0.21 –
Residuals 36 333262
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