Two-phase Flow Structure

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Two-phase ow structure in large diameter pipes

T.R. Smith, J.P. Schlegel, T. Hibiki, M. IshiiSchool of Nuclear Engineering, Purdue University, 400 Central Dr, West Lafayette, IN 47907-2017, United States

a r t i c l e i n f o

Article history:Received 24 May 2011Received in revised form 8 September 2011Accepted 22 October 2011Available online 15 December 2011

Keywords:Large pipeInterfacial areaVoid fractionFlow regime

a b s t r a c t

Flow in large pipes is important in a wide variety of applications. In the nuclear industry in particular,understanding of ow in large diameter pipes is essential in predicting the behavior of reactor systems.

This is especially true of natural circulation Boiling Water Reactor (BWR) designs, where a large-diameterchimney above the core provides the gravity head to drive circulation of the coolant through the reactor.The behavior of such reactors during transients and during normal operation will be predicted usingadvanced thermalhydraulics analysis codes utilizing the two-uid model. Essential to accurate two-uid model calculations is reliable and accurate computation of the interfacial transfer terms. Theseinterfacial transfer terms can be expressed as the product of one term describing the potential drivingthe transfer and a second term describing the available surface area for transfer, or interfacial area con-centration. Currently, the interfacial area is predicted using ow regime dependent empirical correla-tions; however the interfacial area concentration is best computed through the use of the one-dimensional interfacial area transport equation (IATE). To facilitate the development of IATE sourceand sink term models in large-diameter pipes a fundamental understanding of the structure of thetwo-phase ow is essential. This understanding is improved through measurement of the local void frac-tion, interfacial area concentration and gas velocity proles in pipes with diameters of 0.102 m and0.152 m under a wide variety of ow conditions. Additionally, ow regime identication has been per-formed to evaluate the existing ow regime transition criteria for large pipes. This has provided a moreextensive database for the development and evaluation of IATE source and sink models. The data showsthe expected trends with some distortion in the transition region between cap-bubbly and churn-turbu-lent ow. The ow regime map for the 0.102 m and 0.152 m diameter test sections agree with the exist-ing ow regime transition criteria. It may be necessary to perform further experiments in larger pipes andat higher gas ow rates to expand the range of conditions for which models can be developed and tested.

2011 Elsevier Inc. All rights reserved.

1. Introduction

Two-phase ows occur in a wide variety of common industrialapplications. Many of these applications involve large diameterpipes. This is especially true of the chemical and petroleum indus-tries, where bubble column chemical reactors and large pipe

pumping systems are quite common. In the nuclear industry, twophase ows often occur in large channels. For this reason a lackof fundamental knowledge in this area can have signicant rami-cations for nuclear safety. In next-generation BWR systems, forexample, the ow through the reactor is driven by natural circula-tion. This requires a large diameter chimney section above the coreto provide the necessary gravity head ( Ishii et al., 1998 ). Thisregion is very sensitive to variations in the two-phase ow, espe-cially during reactor startup. Flow in large pipes has several signif-icant differences from ow in small pipes. Once the ow channel

diameter is larger than the maximum cap bubble size, which isdened by Kataoka and Ishii (1987) as

DH DH

ffiffiffiffiffiffir g D qq 30 1

a variety of fundamental changes to the ow occur. Here, DH is thehydraulic diameter, r is the surface tension, g is gravitational accel-eration, and D q is the density difference between the liquid and gasphases. First slug bubbles bridging the entire pipe cross-section canno longer be sustained due to Taylor instability, which causes theupper surface of larger bubbles to distort and collapse, breakingthe large bubble into two or more daughter bubbles. This resultsin signicant three-dimensional recirculatory behavior as the liquidows around the cap bubbles rather than being forced out of theway, as is the case with slug bubbles. This causes signicantchanges to the void fraction and velocity proles and can result invery different behavior from ow in smaller pipes, where slug bub-bles can be sustained. For reactor safety it is vitally important that

0142-727X/$ - see front matter 2011 Elsevier Inc. All rights reserved.doi: 10.1016/j.ijheatuidow.2011.10.008

Corresponding author. Tel.: +1 765 494 5759; fax: +1 765 494 9570.E-mail address: [email protected] (M. Ishii).

International Journal of Heat and Fluid Flow 33 (2012) 156167

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the capability to accurately model and predict two-phase ows insuch systems be developed.

These models will be integrated into existing thermalhydrau-lic analysis codes for use in predicting system behavior. The mostaccurate way of predicting system behavior is full-scale testing,however in the nuclear industry full-scale tests are expensiveand often impractical. In place of full-scale tests, a variety of scaled,separate effect, and local phenomena studies are used to developmathematical models for the prediction of ow behavior under awide variety of conditions. These models are then solved numeri-cally using a computer. For this approach, reliable models withappropriate constitutive relations are essential for accurate predic-tions of the behavior of two-phase ow systems.

Most of these analysis codes make use of the two-uid model,which is currently the most practical model for two-phase ow be-cause it is more detailed than other models while using fewer re-sources than DNS or LES. This two-uid model is the mostdetailed two-phase ow model currently used in system analysiscodes. This model treats each phase separately, resulting in twosets of balance equations for mass, momentum and energy. Theone drawback to this model is its complexity, which is largelyintroduced by the terms representing the transfer of mass,momentum and energy across the gasliquid interface. Mathemat-ically, the one-dimensional version of the two-uid model is givenas ( Ishii and Hibiki, 2010 ):

@ ha kiq k@ t

@ @ z ha kiq khh

v zkii hCki 2

@ ha kiq khhv kii@ t

@ @ z

C v k hakiq khhv zkii2

h a ki@ hh pkii

@ z

@ @ z

ha kihhskzz sT kzz ii 4 a kwskw

D ha kiq k g z

hhv kiiihCki h M ik r ak s ii z pki pk@ a k@ z 3

@ ha kiq khhhkii@ t

@ @ z

C hk ha kiq khhv kz iihhhkii

hakiDkDt

hh pkii @ @ z

ha kihhqk qT k ii nh A

akw q00kw hhhkiiihCki

hq00ka ii h Uiki 4

Xk hCki 0 5

Xk hM ik r a k s ii z 0 6

Xk hCkihhhkiii h q00ka ii 0 : 7 Here, C k, M ik, si, q00ki, and u k are the mass generation, generalizedinterfacial drag, interfacial shear stress and interfacial heat ux,which are key parameters in the interfacial transfer of mass,

momentum and energy. Denitions of other quantities can be foundin the nomenclature.

Nomenclature

Latin Charactersa i interfacial area concentration (1/m)C constantD diameter (m)d diameter (m)F fraction of eddies causing breakup () g gravitational acceleration (m/s 2); breakup frequency

(s 1)h enthalpy (J/kg)K g constant ()L length (m)M interfacial momentum transfer (kg/m 2 s2)N l f viscosity number ()n concentration (m 3) p pressure (kPa)q heat transfer (W/m 2)r radial location of measurement (m)R pipe radius (m)r radius (m)S collision cross-sectional area (m 2)t correlated time (s)t b breakup time (s)u velocity (m/s)V volume (m 3)v velocity (m/s)We Weber number ()

Greek Charactersa void fraction ()b PDF of daughter particle size ()e turbulent dissipation rate (m 2/s 3)h collision frequency (s 1)

C interfacial mass transfer (kg/m 3 s)k coalescence efciency ()l viscosity (Pa s)U energy source due to turbulent dissipation (W/m 3)u source or sink term for IATE (1/ms)D q density difference between phases (kg/m 3)D T time interval (s)s characteristic time (s)q density (kg/m 3)r surface tension (N/m)r v 2 variances shear force (N/m 3)

Superscripts and Subscripts non-dimensional valueb bubblec critical valueh hydraulici interfacial value; bubble index j bubble indexk value for phase kT value due to turbulencet turbulent uctuationted value for turbulent Eddyv value for velocityw value at the wall z denotes axial directionOperators P

summationhi area-averaged quantityhhii void-weighted area-averaged quantity

time-averaged quantity

T.R. Smith et al. / International Journal of Heat and Fluid Flow 33 (2012) 156167 157


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The interfacial transfer terms can be thought of as being com-posed of two components, one being the amount of interface avail-able for transfer, or interfacial area concentration, and the otherbeing the driving potential for the transfer, with the form being

Interfacial l Transfer Terms a1 Driv ing Force 8

Therefore in order to close the two-uid model accurate constitu-

tive relations must be developed for the driving forces and theinterfacial area concentration.Traditionally the interfacial area concentration has been speci-

ed using static, ow-regime dependent criteria. This approachhas some shortcomings however, as they are limited by the accu-racy of the ow regime transition criteria and the experimentalrange for which they have been validated. This static nature limitsthe ability of the models to predict truly dynamic features of two-phase ow during transient events and in developing ow, espe-cially in the transition regions between ow regimes. This methodcan also lead to numerical instabilities and bifurcations that can re-sult in degraded convergence or prevent convergence altogether.Further, the majority of these models have been developed forsmall pipes rather than for large-diameter channels.

For these reasons a more dynamic approach to the prediction of interfacial area concentration has been proposed by developing atransport equation for the uid particle number density. Integrat-ing such an equation over the entire range of bubble sizes resultedin a number density transport equation. Multiplying the numberdensity transport equation by the average surface area of a bubblean interfacial area transport equation (IATE) was developed whichwas later rened and is given by Ishii and Hibiki (2010) as,

@ a i@ t

r a i~v i 2

3a ia @ a@ t r a~v g g ph

1

3 waa i

2

X j R j pD2

bc R ph 9

where a i is the average interfacial area per unit volume of uid and

~v i is the interfacial velocity. On the right side of Eq. (9) R j representsthe source and sink reaction rates of interfacial area due to theinteraction of uid particles by breakup and coalescence processes,while R ph represents the source and sink reaction rate of interfacialarea concentration due to evaporation or condensation.

This was followed by the development of the two-group IATE, inwhich the bubble number density equation was averaged twice,once for small spherical and distorted Group 1 bubbles and oncefor cap-shaped Group 2 bubbles with diameter larger thanDb 4= ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r = g Dqp based on the bubble drag properties and the workof Ishii and Zuber (1979). Additional details regarding this model-ing effort can be found in Ishii and Hibiki (2010) . This renement of the IATE is shown in Eqs. (10) and (11) for a one-dimensional, stea-dy-state system with no phase change. In the equations, C is a con-

stant and Dc 1 is the ratio of the Group 1 Sauter mean diameter tothe maximum distorted bubble size. This allowed improved accu-racy in the slug and churn-turbulent ow regimes, however bothof these models were developed for small pipes.

ddz

ha i1 ihhv i1 ii 2

3 C Dc 1

2 ha i1 iha 1 i ddz ha 1 ihhv g 1 ii X j hu j1 i 10 ddz

ha i2 ihhv i2 ii 2 ha i2 i3 ha 2 i

ddz

ha 2 ihhv g 2 ii

C Dc 1 2 ha i1 i

ha 1 iddz

ha 1 ihhv g 1 ii X j h/ j2 i ; 11 In order to complete the transport equation, these source and sink

processes must be modeled mechanistically with the effect of thehydrodynamic differences between small diameter and large

diameter channels kept in mind. To validate and benchmark thesemodels it is necessary to have a fundamental understanding of the ow structure, which requires a signicant database of interfa-cial area concentration data covering a wide range of ow condi-tions and pipe diameters. To expand the existing database anexperiment has been undertaken to make measurements of theinterfacial area concentration and void fraction proles in roundpipes with diameters of 0.102 m and 0.152 m.

2. Previous studies of interfacial area concentration in largepipes

An early experiment measuring interfacial area concentrationfor large pipes was reported by Sun et al. (2002) . This experimentreported data collected in a 0.102 m diameter test section for thepurposes of evaluating one-group IATE models. As the data wasto be used for the one-group model, which performs well only inbubbly ows, the data for this experiment was limited to void frac-tions less than 0.3.

In 2003 , Sun et al. reported additional data including void frac-tion and interfacial area concentration proles as well as bubble

number frequency data. The detailed structure of the two-phaseow was investigated to determine the development of the inter-facial structure along the ow direction and provide a limited data-base for the future development of the two-group IATE. Voidfractions for this data were as high as 0.45 and included severalconditions in the cap bubbly ow regime as well as the bubbly owregime.

Later Shoukri et al. (2003) studied the structure of two-phaseow in a test section with 0.2 m diameter. The radial distributionsof void fraction, bubble velocity, bubble size and interfacial areaconcentration were measured using dual-sensor optical probes.Experimental conditions were limited to void fractions smallerthan 0.04 as the experiment was intended to measure the hydrody-namics at low void fractions. The authors noted that wall-peak

void proles occur only when the void fraction was very smalland that the bubble sizes for ows in large pipes were smaller thanthe bubble sizes reported in the literature for ow in small pipes.This results in a somewhat higher interfacial area concentrationfor ows in large pipes under similar ow conditions.

Shen et al. (2006) also studied two-phase ows in a 0.2 m diam-eter facility using dual-sensor optical probes. Void fractions for thisstudy were as high as 0.4, however interfacial area concentrationdata was only reported for some ow conditions as dual-sensorprobes cannot accurately measure interfacial area when cap-shaped Taylor bubbles are present, at void fractions higher thanabout 0.25.

Additionally Prasser (2007) performed experiments using airand water in a 0.195 m diameter test facility. A double wire-meshsensor was used to calculate the void fraction and bubble veloci-ties. The use of the wire-mesh sensor allowed direct reconstructionof the three-dimensional structure of the two-phase ow so thatthe total interfacial area concentration could be calculated directlyfrom the measured bubble shapes. This allows rapid calculation of the two-phase ow parameters, however the resolution of thewire-mesh sensors is only about 3 mm.

3. Experimental facility

3.1. Experimental loop

A schematic of the experimental loop used in this study isshown in Fig. 1. The system pressure can be as high as 500 kPa,

with liquid supercial velocities up to 10 m/s and gas supercialvelocities up to 20 m/s in the 0.102 m diameter test section and

158 T.R. Smith et al. / International Journal of Heat and Fluid Flow 33 (2012) 156167


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4 m/s liquid velocity and 9 m/s gas velocity in the 0.152 m diame-ter test section. Water is stored in a stainless steel reservoir. A cen-trifugal pump establishes the liquid ow rate, while compressedair is supplied by a compressor system. The water ow rate is mea-sured using a magnetic ow meter with an accuracy of 1% whilethe air ow rate is measured by rotameters or Venturi mass owmeters, also with an accuracy of 1%. The air and water mix in amixing chamber at the base of the test section before owingthrough the test section and returning to the reservoir, which alsoserves as a separator. The mixing chamber consists of three stain-less steel porous tubes, with pore sizes of 10 l m. Rotameters areused to maintain a constant liquid ow velocity over the poroustubes so that the size distribution of the bubbles sheared off thetubes remains relatively constant for all experiments. This also en-sures that the inlet ow condition remains as bubbly ow for allpossible test conditions.

Two vertical test sections, one with diameter of 0.102 m andone with diameter of 0.152 m, are used. Each is tted with a varietyof instrumentation including differential pressure transmitters andthree mounting anges for conductivity probes and impedancemeters, which are located at z/DH = 5.0, 20 and 30 for the0.102 m section and z /D

H = 4.0, 11 and 18 for the 0.152 m section.

The differential pressure cell measures the pressure drop along thetest section. For ow visualization, a high-speed movie camera(Kodak Motioncorder Analyzer model 1000/SR) with frame ratesup to 10,000 frames per second is used to capture images for thestudy of particle motions. These images were also used to verifythe classication of ow conditions in ow regime identication.

The experimental conditions for the measurement of interfacialarea concentration are given in Fig. 2 with the ow regime bound-aries modeled by Schlegel et al. (2009) for large diameter pipes. Asthe gures show, the tests cover a wide range of ow conditions

Fig. 1. Experimental loop.

Fig. 2. Test conditions with ow regime transitions proposed by Schlegel et al. (2009) , (a) 0.102 m test section, and (b) 0.152 m test section.



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from bubbly ow to churn ow, so that the resulting data will berepresentative of ows encountered in many typical industrialsettings.

3.2. Conductivity probes

The electrical conductivity probe is the key instrument in thisstudy. First proposed by Neal and Bankoff (1963) it has been oneof the most widely used instruments for local measurements ingasliquid two-phase ow experiments. A diagram of a conductiv-ity probe used in this study is shown in Fig. 3 (Kim et al., 2000 ).Variation in the impedance between the sensors, measured as achange in voltage, shows when the sensor tips are surrounded byliquid or by gas. A multi-sensor conductivity probe is capable of measuring the local interfacial velocity of individual bubbles andthereby determine the local time-averaged interfacial area concen-tration. The development of the miniaturized probe used in thisstudy is found in the work of Kim et al. (2000) . The cross-sectionalarea of the four sensor probe is about 0.5 mm 2.

The uncertainty of the conductivity probe can be generally di-vided into two sources. The rst source is that due to the probestructure itself, which is related to the interface velocity, probegeometry, and measurement rate. This uncertainty gives theuncertainty in the velocity of a single bubble interface based onthe uncertainty in measuring the time taken for the interface totravel between sensors. For this experiment fteen separate probeswere used. The same fteen probes were used for all of the exper-iments, and the maximum uncertainty from this source is 9.8%using a measurement frequency of 20 kHz. Based on the work of Kim et al. (2000) , who compared the results of probe measure-ments to the results of image processing techniques, there is a sec-

ond uncertainty due to the deformation of the interfaces of largebubbles on contact with the probe. Based on the measurementuncertainty of the probes and the reported disagreement betweenthe two measurement techniques, the additional uncertainty dueto this source is approximately 6%. Using error propagation tech-niques gives a total experimental uncertainty of 11.5%. This uncer-tainty applies to interfacial area concentration measurements aswell as the individual group void fraction measurements, as thebubble group is determined by the bubble chord length. The errorin the total void fraction, however, is governed by statisticalparameters and measurement duration and in this experiment isapproximately 5%. This uncertainty is based on the uncertainty inwhen a bubble interface crosses the sensor due to the discreetmeasurement method, and is computed based on the total number

of bubble signals, measurement frequency, and time-averaged voidfraction.

These experimental uncertainties can be evaluated using otherone-dimensional approaches. The void fraction measurementsmade by conductivity probes is converted into an area-averaged

value using a weighted sum, then compared to the void fractioncomputed from differential pressure measurements. Using the 5%uncertainty in the conductivity probe measurement and the 1%uncertainty in the differential pressure measurement gives an ex-pected difference of 5.5%. Analysis of the differential pressure datashows an average difference of 5.26%, within the expected discrep-ancy. The interfacial area concentration is computed from the mea-sured interfacial velocity, so this measure can be validated againstthe gas ow rate measurement by computing the area-averagedgas ux from the local data. The gas ow rate measurement hasa 3% uncertainty, meaning that the expected discrepancy betweenthe two measurement methods should be less than 14.5%. Compar-ison of the two measurement methods shows an average differ-ence of 13.6%, which is less than the expected value.

3.3. Flow regime identication

Several experiments were also performed using the electricalimpedance void meter. The electrical impedance void meter con-sists of two conducting electrodes on opposing sides of the testsection. A high-frequency alternating current is passed throughthe two-phase mixture. As water conducts electricity rather readilybut air does not, the variation in the impedance of the mixture asthe ow passes through the measurement volume allows the voidfraction to be measured. This impedance is converted into a volt-age output and measured by a computer. This provides a measure-ment of the time-dependent area-averaged void fraction. Thepattern of variations in the void fraction signal is characteristic of

the ow structure, or ow regime.To determine the ow regime from the impedance meter signal,

a neural network classication system is used. A neural network isa simulated group of interconnected articial neurons intended tosimulate the function of the human brain on a limited scale. In theself-organized approach, the neural network is given a number of sample data sets and told to group them into several categories.The network then trains itself using these sample sets to recognizethe most signicant features of the data sets and correctly catego-rize the inputs. This training is accomplished by altering the weightvalues of the inputs for each of the various neurons.

The inputs to the neural network are the mean and standarddeviation of the void fraction signal from the electrical impedancemeter. The neural network system used for ow regime identica-

tion in this study is a committee of three neural networks. Eachneural network is trained using one-third of the experimental data.

Fig. 3. Current design for four-sensor conductivity probe ( Kim et al., 2000 ).



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Each network then is used to categorize the remaining data intobubbly, slug, churn and annular ow. In this way, each data pointis classied twice to conrm the categorization. The result of theneural network ow regime identication process is a numberassociated with each input that corresponds to the category num-ber which that data point was assigned to. These numbers are thenassociated with the ow conditions for each experiment to create

the ow regime map ( Mi et al., 1998 ).

4. Results and discussion

4.1. Proles of local data

Local proles of void fraction and interfacial area concentrationcan provide a great deal of insight into the behavior and structureof two phase ows. For this reason, the proles for several sets of conditions have been measured and are shown in Figs. 47 . Fig. 4shows the proles for all tests with liquid velocity of 1.0 m/s inthe 0.102 m diameter test section. This data was collected at axiallocation z /DH = 20. Each data set represents a different gas super-cial velocity, allowing evaluation of the effect of the gas velocity onthe void and interfacial area concentration proles. When consid-ering the void fraction proles, it is interesting to note that for low-er Group 1 void fractions, a wall peak in the Group 1 void proleexists even for higher gas velocity conditions while the prole isnearly at for higher Group 1 void fractions. This behavior is rea-sonable based on the expected bubble behavior given the behaviorof the lift force at lower void fractions and due to Group 1 bubblesbeing crowded out of the center of the pipe by larger Group 2 bub-bles at higher gas ow rates ( Hibiki and Ishii, 2007 ). As expected,the Group 2 void fraction shows distinct center peaking for all owconditions. The total void fraction plot shows that the transitionfrom wall peaking to center peaking occurs at area-averaged void

fraction of about 15%, where the void prole is nearly at. Thiscorresponds roughly to the void fraction at which Group 2 bubblesbegin to be seen.

The local proles show signicant differences from those insmaller pipe ows. Typically small pipe data is either center-peaked or wall-peaked depending on the ow conditions or devel-opment length ( Hibiki et al., 2001 ). In large pipes however the

available development length is much shorter, with L/D of 30 forthe 0.102 m diameter pipe and 18 for the 0.152 m diameter pipe.These types of ows are thus generally developing ows. The tur-bulence in two-phase ows plays an important role in determiningthe proles and wall-peaking phenomenon. In particular, the tur-bulence intensity may be attenuated at high liquid volumetricuxes or for very small bubble sizes ( Elgholbashi and Abou-Arab,1983; Kataoka et al., 1992 ). Large particles such as Group 2 bub-bles, however, can enhance the turbulence in the ow. Using sim-ple models, Kataoka and Serizawa (1995) demonstrated thatinterfacial transfer of turbulence to small-scale bubbles decreasesturbulence due to the energy required to move the interface, whiledrag on large bubbles results in a source of turbulence due to inter-facial drag. Turbulent mixing near the wall region especially is en-hanced by these larger bubbles, resulting in minimization of thewall-peaking phenomenon. The experimental data indicates thatwall-peaking in large pipes is over-predicted when using small-pipe models ( Ohnuki and Akimoto, 1998 ), which means that eitherthe lift force is smaller or turbulent dispersion forces near the wallare larger in large pipe ows. The newly acquired data for the0.102 m diameter test loop conrms this data.

The interfacial area concentration proles also show interestingbehavior. Unsurprisingly the magnitude of the interfacial area con-centration follows the void fraction magnitude rather closely, withthe average value peaking under similar ow conditions. Wallpeaking is even more prevalent for the interfacial area concentra-tion, however. This indicates a denite change in bubble size across

Fig. 4. Effect of changing gas velocity on void fraction and interfacial area concentration.



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the pipe with bubbles near the pipe wall having a much smalleraverage size than Group 1 bubbles near the center of the pipe. As expected, the total interfacial area concentration peaks at voidfractions between 50% and 60%. At higher void fractions, the in-

Fig. 5. Effect of changing liquid velocity on void fraction and interfacial area concentration.

Fig. 6. Effect of pipe diameter on void fraction and interfacial area concentration.



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creased Group 2 void fraction and increased bubble size results inreduced interfacial area concentrations.

Fig. 5 shows similar data, but for varying liquid supercialvelocities and approximately constant gas velocities in the0.102 m diameter test section. As the gure shows, the effect of changing the liquid velocity on the total void fraction prole is verysmall and the effect on the shape of the Groups 1 and 2 void frac-tion proles is small. The largest effect of liquid velocity is that athigher liquid velocity the increased turbulence results in a greaterproportion of Group 1 bubbles. This leads to a higher Group 1 voidfraction and higher total interfacial area concentration at higherliquid velocities.

The void and interfacial are concentration proles for similarow conditions in the 0.102 m and 0.152 m diameter test sectionsare shown in Fig. 6. The similarly shaded lines indicate that theow conditions are similar, and the two different symbols for thatshade indicate the pipe diameter for that test condition. The datafor the 0.102 m diameter test section was collected at axial loca-tion z/DH = 20, while the data for the 0.152 m test section was col-lected at axial location z/DH = 18. The gure shows several things.First, that the transition from wall peak to center peak void proleoccurs at lower void fraction in the 0.152 m diameter pipe. Second,the data from the larger test section shows signicantly increasedvoid fraction in both bubble groups and greatly increased interfa-

Fig. 7. Gas velocity and bubble size for varied ow conditions and pipe diameters.

Fig. 8. Axial development of void prole in 0.102 m diameter test facility.



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cial area concentration for Group 1 bubbles. This is likely due to in-creased turbulence as the pipe diameter increases, resulting in anincrease in the rate of bubble breakup. It should be noted thatthe Group 2 interfacial area concentration remains relativelyconstant between pipe sizes, which indicates that the increasedturbulence has much smaller effect on larger bubbles. The excep-

tion to this at the lowest gas velocity condition, where Group 2bubbles exist for the 0.152 m test section but not for the 0.102 mtest section. Based on the interfacial area concentration prolesthese Group 2 bubbles are relatively small. This difference is likelydue to slight differences in the experimental conditions.

Fig. 7 shows the gas velocity and Sauter mean diameter for eachbubble group for the same ow conditions as shown in Fig. 6. Asexpected, the bubble diameter tends to decrease near the pipewalls. The larger test section shows a trend for larger bubbles thanthe 0.102 m test section at low gas velocities, but smaller bubblesat higher velocities. Also, the bubble velocities tend to be smaller inthe larger test section, explaining the increase in the void fractionseen in Fig. 6. The velocity proles all show that the gas velocity isrelatively constant across the pipe, though for higher gas velocities

there is a slight decrease in the gas velocity as one moves awayfrom the pipe center.Figs. 8 and 9 show the axial development of the Groups 1 and 2

void fraction proles for the 0.102 m and 0.152 m diameter testfacilities for selected ow conditions. Each gure shows identicalow conditions to allow comparison of the ow development ineach test section. As both gures show, little ow development oc-curs for L/D greater than 45. In this case, ow development ismeant to refer to changes in the shape of the phase distribution.Some increase in the void fraction occurs over the length of bothtest sections, however this has very little effect on the void distri-bution, as evidenced by the gures, or on the velocity distribution.Of note in the two gures are the distinct differences in the prolesfor the two pipe diameters, as has been noted for previous gures.The Group 1 void fraction tends to be signicantly higher while theGroup 2 void fraction is signicantly lower for the larger diameter

test facility, and the Group 2 void prole in the 0.152 m diameterfacility is much more linear from pipe center to pipe wall thanthe prole in the 0.102 m facility.

4.2. Area-averaged data and ow development

As most thermalhydraulic analysis codes are one-dimensional,the area-averaged data is of specic interest here due to its appli-cability to code testing and evaluation. Fig. 10 shows a selection of the area-averaged void fraction data. The void fraction data is plot-ted with the void fraction prediction using the model developed byHibiki and Ishii (2007) for liquid velocities of 0 m/s and 1.0 m/s.The data for high liquid velocity is predicted well, however thereis some scatter in the data for lower liquid velocities. This maybe the result of the increased recirculation seen in large diameterpipe ows at higher void fractions. As the liquid ow directionoscillates due to the presence of large bubbles, some bubbles movedownward. These bubbles cannot be measured accurately usingexisting conductivity probe methods. This may result in void frac-tion measurements which are less than the actual void fraction for

low liquid velocities and void fractions over about 0.2.Additionally, Fig. 11 shows the measured change in interfacialarea concentration as compared to the predicted change if onlygas expansion contributed, n = ha ii meas /ha ii pred . To calculate theexpansion contribution to the interfacial area concentration, theexpansion term from the interfacial area transport equation wasused. Accordingly, the change in interfacial area concentrationcan be described as

ddz h

a i1 ihhv g 1 ii 2

3 CDc 1 ha i1 iha 1 i ha 1 ihhv g 1 iiP dP dz 13

ddz

ha i2 ihhv g 2 ii 2

3ha i2 iha 2 i ha 2 ihhv g 2 iiP dP dz

CDc 1ha i1 iha 1 i

ha 1 ihhv g 1 iiP

dP dz 14

Fig. 9. Axial development of void prole in 0.152 m diameter test facility.



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for Groups 1 and 2 respectively, where P is the system pressure.This then provides the change in interfacial area concentrationper unit length of the test section at each of the three measurementlocations. To approximate the total change due to expansion, this isthen multiplied by the total length between one measurement loca-tion and the next, giving expected values at the second and third

location. The data in the gure is then the ratio of this value tothe measured interfacial area concentration, with values less than

unity indicating that interfacial area concentration sinks are domi-nant and values greater than unity indicating that interfacial areaconcentration sources are dominant. As the gure shows, for the0.102 m diameter test section bubble coalescence is dominant atnearly all of the conditions except for those at very low gas owrates, where the bubbles are too dispersed for many coalescence

interactions to occur. The trend is similar for the 0.152 m diametertest section, however in this case coalescence is dominant even at

Fig. 10. Area-averaged void fraction data.

Fig. 11. Comparison of measured change in interfacial area concentration with predicted change due to bubble expansion.



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lower gas ow rates. Overall, much of the data is quite far fromunity. This emphasizes the need for mechanistic bubble interactionmodels for the IATE to accurately predict the behavior of two-phaseows.

4.3. Flow regime identication

Currently the interfacial area concentration is calculated byusing static, ow-regime dependent correlations based on existingexperimental data. For this reason it is important that, until thedevelopment of the IATE is complete and has been incorporatedinto the most recent thermalhydraulic analysis codes, the ow re-gime transitions be accurately determined in order to improve theaccuracy and applicability of the correlations. Therefore the resultsof the ow regime identication as described in Section 3.3 havebeen presented in Fig. 12. The ow regime transitions are thosepredicted by Schlegel et al. (2009) . As the map for the 0.102 m testsection shows, the existing ow regime transition criteria perform

reasonably well with the ow regime transitions as given by theneural network agreeing well with those given by the model. Themap for the 0.152 m diameter test section also shows very goodagreement with the model. The map generated by the neural net-work shows that the transition from bubbly to cap-bubbly ow oc-curs at slightly lower void fraction than in the 0.102 m test section,however this is likely due to the injection method. The increasedgas velocity required to achieve a given ow condition in the largertest section requires signicantly increased gas ow rates, whichmay result in larger cap bubbles being formed at the test sectioninlet for some conditions where this would not be the case in thesmaller test section. This would articially decrease the void frac-tion at which the transition is seen for the 0.152 m test section andwould account for the trend seen in the gure.

5. Conclusions

Flow in large pipes is signicant in many industries from phar-maceuticals to nuclear energy. In the nuclear industry, an under-standing of ow in large pipes is essential for predictions of reactor safety and performance. These predictions will be devel-oped using thermalhydraulics analysis codes, all of which usethe two-uid model to calculate the behavior of two-phase uidows. The two-uid model is the most practical model for two-phase ow available, however it is also quite complex. The mostsignicant source of complexity is the interfacial transfer terms,which can be decomposed into two components: one deningthe available surface area for transfer and another dening the po-

tential driving the transfer. For the two-uid model to be accurateboth of these components must be correctly modeled. The most

advanced model for the interfacial area concentration is the inter-facial area transport equation (IATE), however this model has notbeen well-developed in large pipes. To facilitate the developmentof IATE models, experiments have been performed in large pipes

of diameters 0.102 m and 0.152 m, with liquid supercial velocitiesup to 2 m/s and gas supercial velocities up to 8 m/s in the 0.102 mdiameter pipe. Measurements of local void fraction, interfacial areaconcentration, and interface velocity were made at three axiallocations along the test section using electrical conductivity probeswith cross sections of 0.2 mm 2. The resulting local proles havebeen presented along with the axial development of the area-aver-aged quantities and the results of ow regime identication per-formed using electrical impedance void probes.

This has resulted in the development of a more extensive data-base for the development of interfacial area source and sink termsfor the two-group IATE. The trends shown by the data are as ex-pected. At low void fractions, the void prole displays a wall peak.This transitions to a center peak near the transition from bubbly

ow to cap-bubbly ow. The data in the larger test section showssimilar total void fraction values to the smaller test section buthigher Group 1 void fraction and therefore a higher interfacial areaconcentration. These effects are likely due to increased turbulentmixing in the larger test section, as the smaller test section is nearthe boundary of the transition to large pipe behavior and maytherefore still exhibit some of the stabilizing effects of the pipewall on the ow. The area-averaged data also shows the expectedtrends. Further, the data indicates that the inlet conditions mayhave strong effects on the ow pattern. The ow regime mapdeveloped for the 0.102 m diameter test section conrms the exist-ing ow regime transition criteria for large pipes as does the mapdeveloped for the 0.152 m test section, but the map for the 0.152 mtest section shows that the inlet conditions can result in inducedchanges to the ow pattern.

To improve the database of interfacial area concentration datain large pipes it may be necessary to perform experiments in largertest sections and at signicantly higher gas ow rates so that theperformance of IATE models can be validated for the entire rangeof ow conditions that may be seen in reactor systems.

Acknowledgments

This work was performed at Purdue University under the aus-pices of the US Nuclear Regulatory Commission, Ofce of NuclearRegulatory Research, through the Institute of Thermal Hydraulics.

References

Elgholbashi, S., Abou-Arab, T., 1983. Two-equation turbulence model for two-phaseows. Phys. Fluids 26, 931938.

Fig. 12. Flow regime maps with ow regime transitions proposed by Schlegel et al. (2009) .



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Hibiki, T., Ishii, M., Xiao, Z., 2001. Axial interfacial area transport of vertical upwardtwo-phase ow. Int. J. Heat Mass Transfer 44, 18691888.

Hibiki, T., Ishii, M., 2007. Lift force in bubbly ow systems. Chem. Eng. Sci. 62, 64576476.

Ishii, M., Zuber, N., 1979. Drag coefcient and relative velocity in bubbly, droplet orparticulate ows. AIChE Journal 25, 843855.

Ishii, M., Revankar, S.T., Leonardi, T., Dowlati, R., Bertodano, M.L., Babelli, I., Wang,W., Pokharna, H., Ransom, V.H., Viskanta, R., Han, J.T., 1998. The three-levelscaling approach with application to the Purdue University Multi-DimensionalIntegral Test Assembly (PUMA). Nucl. Eng. Des. 186, 177211.

Ishii, M., Hibiki, T., 2010. Thermo-uid dynamics of two-phase ow, second ed.Springer, New York.

Kataoka, I., Ishii, M., 1987. Drift-ux model for large diameter pipe and newcorrelation for pool void fraction. Int. J. Heat Mass Transfer 30, 19271939.

Kataoka, I., Besnard, D., Serizawa, A., 1992. Basic equation of turbulence andmodeling of interfacial transfer terms in gasliquid two-phase ow. Chem. Eng.Commun., 221236.

Kataoka, I., Serizawa, A., 1995. Modeling and prediction of turbulence in bubblytwo-phase ow. In: Proc. 2nd Int. Conference on Multiphase Flow. April 37, pp.1116.

Kim, S., Fu, X.Y., Wang, X., Ishii, M., 2000. Development of the miniaturized foursensor conductivity probe and the signal processing scheme. Int. J. Heat MassTransfer 43 (22), 41014118.

Mi, Y., Ishii, M., Tsoukalas, L.H., 1998. Vertical two-phase ow identication usingadvanced instrumentation and neural networks. Nucl. Eng. Des. 184, 409420.

Neal, L.G., Bankoff, S.G., 1963. A high resolution resistivity probe for determinationof local void properties in gasliquid ow. AIChE J. 9, 490494.

Ohnuki, A., Akimoto, H., 1998. Prediction of phase distribution under bubbly ow ina large vertical pipe by multidimensional two-uid model. In: Third Int.Conference on Multiphase Flow, ICMF 98, Lyon, France. June 812, 1998.

Prasser, H.M., 2007. Evolution of interfacial area concentration in a vertical airwater ow measured by wire-mesh sensors. Nucl. Eng. Des. 237, 16081617.

Schlegel, J.P., Sawant, P., Paranjape, S., Ozar, B., Hibiki, T., Ishii, M., 2009. Voidfraction and ow regime in adiabatic upward two-phase ow in large diameterpipes. Nucl. Eng. Des. 238, 28642874.

Shen, X., Saito, Y., Mishima, K., Nakamura, H., 2006. A study on the characteristics of upward airwater two-phase ow in a large diameter pipe. Exp. Therm. FluidSci. 31, 2136.

Shoukri, M., Hassan, I., Gerges, I., 2003. Two-phase bubbly ow structure in large-diameter vertical pipes. Can. J. Chem. Eng. 81, 205211.

Sun, X., Smith, T.R., Kim, S., Ishii, M., Uhle, J., 2002. Interfacial area of bubbly ow ina relatively large diameter pipe. Exp. Therm. Fluid Sci. 27, 97109.

Sun, X., Smith, T.R., Kim, S., Ishii, M., Uhle, J., 2003. Interfacial structure of airwatertwo-phase ow in a relatively large pipe. Exp. Fluids 34, 206219.


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