PREDICTION OF POLYDISPERSE STEAM BUBBLE CONDENSATION IN SUB-COOLED WATER USING THE INHOMOGENEOUS MUSIG MODEL

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1 PREDICTION OF POLYDISPERSE STEAM BUBBLE CONDENSATION IN SUB-COOLED WATER USING THE INHOMOGENEOUS MUSIG MODEL C. Lfante *, T. Frank *, A.D. Burns, D. Lucas and E. Krepper * ANSYS Germany GmbH, Staudenfeldweg 2, Otterfng, D-83624, Germany School of Process Materal and Envronmental Engneerng, CFD Centre, Unversty of Leeds, LS2 9JT, UK Insttute of Safety Research, Forschungszentrum Dresden-Rossendorf, POB 50 9, Dresden, D-034, Germany Abstract The am of ths paper s to present the valdaton of a new methodology mplemented n ANSYS CFX (ANSYS, 2009), that extends the standard capabltes of the nhomogeneous MUltple-SIze Group model (MUSIG) by addtonally accountng for bubble sze changes due to heat and mass transfer. Bubble condensaton plays an mportant role n sub-cooled bolng or steam njecton nto pools among many other applcatons of nterest n the Nuclear Reactor Safety (NRS) area and other engneerng areas. Snce the mass transfer rate between phases s proportonal to the nterfacal area densty, a polydsperse modellng approach consderng dfferent bubble szes s of man mportance, because an accurate predcton of the bubble dameter dstrbuton s requred. The standard MUSIG approach s an nhomogeneous one wth respect to bubble veloctes, whch combnes the sze classes nto dfferent so-called velocty groups to precsely capture the dfferent behavour of the bubbles dependng on ther sze. In the framework of collaboraton between ANSYS and the Forschungszentrum Dresden-Rossendorf (FZD) an extenson of the MUSIG model was developed, whch allows to take nto account the effect of mass transfer due to evaporaton and condensaton on the bubble sze dstrbuton changes n addton to breakup and coalescence effects. After the successful verfcaton of the model, the next step was the valdaton of the new developed model aganst expermental data. For ths purpose an experment was chosen, whch was nvestgated n detal at the TOPFLOW test faclty at FZD. It conssts of a steam bubble condensaton case at 2MPa pressure n 3.9K sub-cooled water at a large dameter (DN200) vertcal ppe. Sub-cooled water flows nto the 95.3 mm wde and 8 m heght ppe, were steam s njected at z=0.0 m and s recondensng. The expermental results are publshed n (Lucas, et al., 2007). Usng a wre-mesh sensor technque the man characterstcs of the two-phase flow were measured,.e. radal steam volume fracton dstrbuton and bubble dameter dstrbuton at dfferent heghts and cross-sectons. ANSYS CFX 2.0 was used for the numercal predcton. A 60 degrees ppe sector was modelled n order to save computatonal tme, dscretzed nto a mesh contanng about elements refned towards the ppe wall and towards the locaton of the steam njecton nozzles. Interfacal forces due to drag, lft, turbulent dsperson and wall lubrcaton force were consdered. The numercal results were compared to the expermental data. The agreement s hghly satsfactory, provng the capablty of the new MUSIG model extenson to accurately predct such complex two-phase flow.

2 Introducton Computatonal Flud Dynamcs (CFD) smulatons are ncreasngly used for analyses of potental accdent scenaros n Nuclear Reactor Safety (NRS) analyss. Typcal examples for the relevance of bubble condensaton n NRS are sub-cooled bolng n core coolng channels or emergency coolng systems, steam njecton nto pools or steam bubble entranment nto sub-cooled lquds by mpngng jets, e.g. n case of Emergency Core Coolng Injecton (ECC) nto a partally uncovered cold leg (Lucas et al., 2009). All these cases are connected wth pronounced 3-dmensonal flow characterstcs, thus adequate smulatons requre the applcaton of CFD codes. Many actvtes were conducted n the last years to mprove the modellng of adabatc bubbly flows n the frame of CFD. In ths case models for momentum transfer between the phases are most mportant. Usually they are expressed as bubble forces for nterphase momentum transfer. Expermental nvestgatons as well as Drect Numercal Smulatons (DNS) showed that these bubble forces strongly depend on the bubble sze. In addton to the well known drag force, also vrtual mass, lft, turbulent dsperson and wall forces have to be consdered (Lucas, et al., 2007). The lft force even changes ts sgn n dependence of the bubble sze (Tomyama, 998) and Eötvos number. In consequence large bubbles are pushed to the opposte drecton than small bubbles f a gradent of the lqud velocty perpendcular to the relatve bubble velocty exsts (Lucas, et al., 200) (Prasser, et al., 2007). To smulate the separaton of small and large bubbles, more than one momentum equaton s requred (Krepper, et al., 2005) For ths reason the so-called Inhomogeneous MUSIG (MUlt SIze Group) model was mplemented nto the ANSYS CFX code (Frank, 2005)(Frank, et al., 2006) (Krepper, et al., 2005) (Frank, et al., 2008). It allows consderng a number of bubble szes ndependently for the mass and momentum balance, also called bubble classes. For a proper modellng of bubble coalescence and breakup, a large number of bubble classes (e.g. 5-25) s requred. Dfferent ndependent groups of bubble classes can be consdered for the momentum balance as well. They are called velocty groups. Fewer number of velocty groups (e.g. 2-3) are usually consdered due to the hgh computatonal effort n solvng ndvdual sets of momentum transport equatons. A common crteron for the classfcaton can be derved from the dependency of the bubble forces on the bubble sze, e.g. the change of the sgn of the lft force. In the conventonal verson of the Inhomogeneous MUSIG model, only mass transfer between the bubble classes due to bubble coalescence and breakup can be modelled. In case of flows wth phase change, addtonal transfers between the sngle classes and the lqud, and transfers between bubble classes caused by growth or shrnkng of bubbles due to evaporaton and condensaton processes have to be consdered. The addtonal terms for the extenson of the MUSIG model are descrbed later n the paper, and were mplemented nto a customzed solver based on ANSYS CFX 2. These extensons of the Inhomogeneous MUSIG model permt the smulaton of flows wth phase change. For a smulaton based on physcs, proper closure models for evaporaton and condensaton rates are further requred. Usually these phase transfer rates are assumed to be proportonal to the nterfacal area densty and the overheatng or sub-coolng. For ths reason detaled nformaton on the evoluton of local bubbles sze dstrbutons and local temperature profles s needed. In the past, wre-mesh sensors were successfully used to measure local bubble sze dstrbutons n ar-water (Lucas, et al., 2008) and adabatc steam-water (Prasser, et al., 2007) flows n a vertcal ppe. These data were used to valdate models for bubble forces and to extent also models for bubble coalescence and breakup. Experments usng the wre-mesh sensor technology were done to nvestgate bubble condensaton n an upwards drected vertcal ppe. They clearly showed the effect of nterfacal area densty by comparson of expermental results for whch only the ntal bubble sze dstrbuton was modfed by usng dfferent orfce szes for bubble njecton, but keepng the gas and lqud flow rates constant (Prasser, et al., 2007). The goal of ths paper s to valdate the extenson of the Inhomogeneous MUSIG model aganst one of these condensaton test case confguratons. 2

3 Governng equatons The nhomogeneous MUltple SIze Group model (MUSIG) s based on the Euleran multphase flow modelng approach (ANSYS, 2009)(Frank, et al., 2006)(Frank, et al., 2006). It s based on ensemble mass and momentum transport equatons for all phases. Therefore, the contnuty equatons read as N r r P (r ρ ) + (r ρ U ) = S + Γ t α α α α α MSα αβ β= r where r α s the phase volume fracton, ρ α the phase densty, N p the number of phases, U α the r phase velocty, SMS α specfed mass sources and Γ αβ s the mass flow rate per unt volume from phase β to phase α. The phase- momentum equatons read as: r r r ρ + ρ = t r r r r µ U + U r p + r ρ g + NP β= ( rα αuα ) ( rα αuα Uα ) T α α ( α ( α ) ) α ( ) r r r r + + ( Γ U Γ U ) + S + M, αβ β βα α Mα α α α where µ α represents the phase vscosty, p the pressure, the gravtatonal acceleraton, Γ Γ descrbes the momentum transfer nduced by mass transfer and S r Mα refers to momentum sources due to external body forces and user defned momentum sources. r M α descrbes the nterfacal forces actng on phase α due to the presence of other phases (drag, lft, wall lubrcaton, turbulent dsperson and vrtual mass force): r r r r r r M = F + F + F + F + F α α,d α,l α,wl α,td α,vm Snce the sum of all phases must occupy the whole doman volume, the followng constrant must be satsfed N P rα = α= Extenson of the Inhomogeneous MUSIG model The nhomogeneous MUltple SIze Group model (MUSIG) assumes that the dsperse phase s polydsperse,.e. t s composed of dfferent sze partcles (classes). Ths methodology can be appled both to bubbles and to droplets, although the work here presented s focussed on bubbly flows. The user selects a set of ntal bubble dameters (d ) and defnes a reference densty π 3 ( ), and the correspondng masses of the bubble classes are then computed m = ρref d 6. Ths s the value whch s gong to characterze the class and reman constant durng the smulaton. 3

4 The dfferent knds of bubbles are then splt nto the so-called velocty groups, and all bubble classes n the same velocty group share the velocty feld and other man varables. As mentoned, t s well-known that small and large bubbles behave n a sgnfcant dfferent manner. Small bubbles flow wth the flud phase, large bubbles are more nfluenced by buoyancy. On the other hand sde the lft coeffcent changes ts sgn at a crtcal bubble dameter, whch depends on the Eötvos number and hence on pressure and temperature. These are just some examples of the dfferences n the movement of bubbles of dfferent sze. In order to get an accurate predcton of the flow pattern, all these partculartes must be solved. Defnng dfferent velocty groups for dfferently behavng groups of bubble sze classes, these bubbble sze effects can be taken nto account. Nevertheless, the standard formulaton of the nhomogeneous MUSIG model allows only mass transfer between velocty groups due to break up and coalescence of bubbles. The extenson of the method presented here consders mass transfer due to condensaton or evaporaton as well,.e. the growth and shrnk of the bubbles or even the appearance/dsappearance of bubbles due to phase change are also consdered. For ths purpose the formulaton of the MUSIG model has been modfed, and one more term whch accounts for the mass transfer due to phase change has been ncluded. The MUSIG model s a populaton balance approach,.e. an equaton for the bubble number densty can be wrtten. In ts standard form the MUSIG model reads: r r r n(m, r, t) + r ( U(m, r, t)n(m, r, t) ) + t = B D + B D B B C C where n s the number of bubbles of mass m per cubc meter at poston r r and tme t. The four terms on the RHS of Eq. correspond to the brth and death of bubbles due break up and coalescence, and can be wrtten as: B B = g( ε;m)n( ε, t)dε m m DB = n(m, t) 0 g( ε;m)dε m BC = Q(m ; )n(m, t)n(m, t)d 2 ε ε ε ε 0 DC = n(m, t) Q(m; ε)n( ε, t)dt, 0 beng g(m;ε) the specfc breakup rate (the rate at whch partcles of mass m break nto partcles of mass ε and m ε) and Q(m;ε) the specfc coalescence rate (the rate at whch partcles of mass m coalesce wth partcles of mass ε to form partcles of mass m+ε). In order to extend the capabltes of the model n order to consder phase change effects, the followng term was ncluded nto the LHS of Eq. : r r n(m, r, t) m(r, t) m t The bubble number densty equaton (Eq. + Eq. ) can now be dscretzed nto sze classes by ntegratng t between the lmts of each bubble class. A bubble number densty for each bubble class can then be defned as follows: 4

5 m + /2 N (t) = n(m, t)dm m /2 Snce mn = ρ dfrd, beng ρ d the densty of the dsperse phase, r d the volume fracton of the dsperse phase, and f the sze fracton of -class bubbles, the extended equaton can be re-wrtten n terms of a sze fracton equaton as j ( ρ rd f ) + ( ρ r j duf ) = BB D B + B C D C + S t x fc beng,,, the result of the mathematcal manpulaton of the correspondng break up and coalescence terms (B B, D B, B C and D C ), and S fc the transformaton of the term n Eq.. The frst four are: BB = ρ drd g(m j;m )f j j> DB = ρ drd f g(m ;m j) j> 2 m j + m k B C = ( ρ dr d) Q(m j;m )X jkf jf k 2 j k m jm k 2 D C = ( ρ dr d) Q(m ;m j)ff j j m j where (m j + m k ) m m < m + m < m m m m (m + m ) X m m m m 0 otherwse j k + j k jk = < j + k < + m+ m s the fracton of mass due to coalescence between class j and k at tme t whch goes nto class. Fnally the last term reads as: S m m Γ Γ m m m+ m fc = m m Γ Γ+ m m m+ m (evaporaton) (condensaton) where m s the mass of bubbles n class, and Γ the drect mass transfer per unt volume and tme between the contnuous lqud phase and the bubble sze class. These source terms reflect the effect of mass transfer between lqud and bubble sze class, as well as the transfer between MUSIG groups due to bubble growth or shrnkng. Ths can be checked by consderng the net transfer at the group boundary. In case of condensaton, bubble szes shrnk,.e. bubbles are shfted to smaller mass classes. Consderng the net transfer at the lower boundary of bubble 5

6 sze group there s a snk n bubble sze group accordng to the Eq. equal to m Γ. m m m On the other hand the related source n bubble sze group - s equal to m m m Summaton of gan and loss results n m Γ = Γ. m m Assumng sphercal bubbles, the Sauter mean dameter for the velocty group j s obtaned accordng to: Γ. j s, j = ( j) r d r d The sum runs over all MUSIG classes whch belong to the velocty group j. The mass transfer for the MUSIG groups s evaluated based on the Sauter mean dameter, the nterfacal area densty, and the mass transfer per unt volume and tme for velocty group j (Γ j ): a 6r d s, j Γ = Γ j = Γ j = Γ j a 6r j j rj d d S, j r d where a represents the nterfacal area densty. The mass transfer per unt volume and tme for velocty group j (Γ j ) can be computed from the volume related heat flux to the nterface and heat of evaporaton a Γ = ( h (T T ) h (T T )) j j G, j G s L, j L S H LG Heren T G, T L and T S are the gas, lqud and saturaton temperatures, H LG the heat of evaporaton, and h G,j and h L,j the heat transfer coeffcents from gas and lqud sde to the nterface. Valdaton case descrpton After the dervaton of the model, and ts mplementaton n a customzed solver based on ANSYS CFX 2, a verfcaton process was carred out. A collecton of smplfed test cases wth gven condensaton or evaporaton rates were analyzed and compared to ther analytcal soluton. Several confguratons regardng boundary condtons, bubble class and velocty group defntons were nvestgated, provdng n all cases the same result as the analytcal soluton. Detals of the verfcaton are not ncluded here and can be obtaned from (Lfante, et al., 2009a) and (Lfante, et al., 2009b). Once the new mplementaton was completed, a complex valdaton case was chosen to test the adequateness of the model for applcatons where break up, coalescence and phase change take place smultaneously. The present work was performed n collaboraton wth the Forschungszentrum Dresden-Rossendorf,and a condensaton case expermentally nvestgated at the TOPFLOW test faclty was selected for the model valdaton. 6

7 Fgure : Geometry detals of the TOPFLOW test faclty at FZD (DN200 vertcal ppe) The TOPFLOW faclty (see Fgure ) conssts of a large vertcal DN200 ppe (8 m heght, 95mm ppe dameter). By means of njecton chambers lke the one n Fgure 2 (left),gas can be njected nto the flud flowng through the ppe at dfferent heght of the test secton. In the nvestgated case sub cooled water was flowng upwards and steam was njected through 72 small njecton nozzles of mm dameter. Usng a wre mesh sensor technque (Fgure 2, rght) (Prasser, et al., 2007) and placng t at a constant poston at the end of the test secton n varyng dstance to the used njecton chamber, the expermentalsts at FZD measured radal steam volume fracton dstrbutons and radal bubble sze dstrbutons for dfferent length of flow development n the ppe. These values were determned for the dfferent elevatons of the steam njecton named wth letters, beng A the njecton level closest to the sensors (22cm above t), and R the furthest (7.8 m below the wre-mesh sensors). Fgure 2: Left: Injecton chamber at the TOPFLOW faclty. Rght: Wre mesh devce. Expermental results of the chosen confguraton, n addton to many others, are compled n (Prasser, et al., 2007). From the dfferent arrangements nvestgated n that paper, the so-called

8 run #3 s the one whch s nvestgated n ths paper by means of CFD smulaton. The man physcal propertes defnng ths case are summarzed n Table : Pres. [MPa] J W [m/s] J S [m/s] T W [ C] T S [ C] T L [ C] D nj [mm] Table : Man physcal characterstcs of the selected valdaton test case from TOPFLOW measurements. Fgure 3 shows the expermental results regardng the radal steam volume fracton dstrbutons at the mentoned dstances between steam njecton and measurement cross-secton. For level A a local maxmum of about 30% can be observed, as expected from the rato between the water and the steam superfcal veloctes n ths partcular test case. Ths large value evdences the complexty of the applcaton. It can be notced that substantal steam condensaton s takng place along the ppe, and the larger s the njecton-measurement dstance, the lower amount of steam s present n the ppe. Fgure 3: Expermental radal steam volume fracton dstrbuton at dfferent elevatons (levels A to R) 8

9 Fgure 4: Radal bubble sze dstrbuton ( drg dd B ) at dfferent elevatons of steam njecton (levels A to R) In addton, Fgure 4Error! Reference source not found. shows the radal bubble sze (dameter) dstrbuton at the same elevatons, represented by the quantty dr g dd B. In ths manner the cross-sectonal average of the steam volume fracton can be computed by evaluatng the ntegral area under each profle. The condensaton effect s vsble here as well snce the enclosed area under the curves decreases along the ppe. Beng ths a condensaton case, one would expect that the maxmum of the mentoned curves (representng the most common bubble class at each elevaton) s shfted towards smaller bubble dameters along the ppe. However, except for the upmost elevatons, ths value remans almost constant close to 9 mm. Ths ndcates that not only condensaton s playng a role n the applcaton but coalescence as well. Ths was a further reason for choosng ths case for the valdaton of the extenson of the MUSIG model. CFD Model valdaton CFD Setup defnton A three-dmensonal model contanng one sxth of the geometry was consdered for the numercal smulatons. In ths way the three-dmensonal effects due to the steam njecton through dscrete nozzles can be reproduced, and computatonal tme can be saved n comparson wth the smulaton of the whole doman. Symmetry boundary condtons were appled to the two sde planes of the symmetry sector An nlet boundary condton based on the water superfcal velocty, outlet boundary condton based on averaged statc pressure and adabatc ppe wall were consdered for the smulaton. Snce no expermental nformaton about water velocty dstrbuton or turbulence quanttes at the ppe nlet was avalable, the computatonal doman was enlarged by two meters n front of the steam njecton n order to ensure that the flow s completely developed when t reaches the steam njecton locatons. A numercal grd contanng elements was employed. It was refned towards the wall 9

10 and near the njecton locatons. No grd-ndependency analyss was performed because prevous numercal studes for adabatc ar/water flow through the TOPFLOW test faclty (Frank, 2006) carred out for several dfferent superfcal velocty ratos had proven the adequateness of ths grd resoluton. The njecton nozzles were modelled by means of source ponts located close to the wall. The orgnal nozzle dameter n the experments was mm. Due to the large steam superfcal velocty, ths leads to an extreme large steam njecton velocty / / 0.00/2 In ntal nvestgatons ths had strongly deterorated the convergence of the numercal smulatons. Therefore, for part of the computatons, a larger nozzle dameter was consdered (4 mm), keepng the steam mass flow rate constant, but provdng a lower njecton velocty. The turbulence of the contnuous phase was modelled by the SST turbulence model (Menter, 994). As n all multphase applcatons, the consderaton of the nterfacal momentum, heat and mass transfer s crucal for the accuracy of the numercal results. In the present case Grace drag, Tomyama lft and FAD turbulent dsperson force were consdered, as well as the Tomyama wall lubrcaton force (ANSYS, 2009). Break up and coalescence were modelled followng the standard approach n ANSYS CFX usng the Luo & Svendensen and Prnce & Blanch models respectvely (Luo, et al., 996) (Prnce, et al., 990). The correspondng break up factor (0.025) and coalescence factor (0.05) were chosen from prevous nvestgatons (Krepper, 2008). The gaseous phase was assumed to be at saturaton temperature and to be composed of 25 dfferent bubble classes, dstrbuted nto three velocty groups, whose lmts were Frst group [0 mm, 3 mm] Second group [3 mm, 6 mm] Thrd group [6 mm, 30 mm] The selecton of the velocty group boundares was chosen dependng on the Eötvos number, whch allows predctng the crtcal dameter at whch the sgn of the lft coeffcent n the lft force formulaton of Tomyama changes. Usng ths value the dfferent bubble classes were arranged nto velocty groups where the coeffcent s clearly postve, transtonal or close to zero, or clearly negatve. Results and dscusson The frst smple test performed was a comparson of the new mplementaton aganst a smulaton where the dameter of the bubbles s assumed to be locally constant. It s a locally monodsperse approach. For the computaton of ths local dameter t was assumed that the number densty of bubbles nsde the doman was constant. The nlet bubble dameter was taken from the experments. The most frequent bubble dameter at level A was consdered as a representatve value for the njected bubbles. In ths way the local bubble dameter s evaluated n terms of the total number of bubbles and the nlet bubble dameter d = f ( d, N ) B Bnlet Bnlet Fgure 5 shows a comparson of the cross sectonal averaged steam volume fracton at dfferent elevatons between the results obtaned by means of the monodsperse approach and the frst smulatons applyng the extenson of the MUSIG model consderng phase change effects. The monodsperse approach s strongly under predctng the amount of vapour n the doman observed n the experments. And even the results obtaned wth the new mplementaton are over predctng t, they are sgnfcantly closer to the expermental values. 0

11 Fgure 5: Cross-sectonal averaged steam volume fracton at dfferent elevatons wth respect to the njecton level and compared for the monodsperse approach and the extended MUSIG approach (Confg ). Fgure 6 shows the radal steam volume fracton at level C (33 cm above the steam njecton) for the dfferent smulatons conducted and the correspondng expermental values (crosses). Results correspondng to the frst smulaton (green dashed profle) show an over predcton of the local maxmum amount of steam (55% aganst 30%), and addtonally ts locaton s shfted towards the wall n comparson wth the experments. Ths smulaton allowed us to get detaled knowledge and to optmze the numercal parameters to reach convergence (lke the necessary tegraton tme step among others). However, results were stll far from the experments. Therefore some changes/mprovements n the setup were carred out. The frst modfcaton conssted of dsplacng the poston of the source ponts (SP) from the wall to 75 mm away from the centre of the ppe. Ths was the locaton where the expermentalsts at FZD observed the maxmum concentraton of steam at steam njecton to measurement dstance of level A. By applyng ths change, a reducton of the local maxmum of steam and a dsplacement of t towards the centre of the ppe could be observed (brown dashed profle). Next step was the consderaton of the wall lubrcaton force, whch was not taken nto account n the prevous two smulatons.

12 Fgure 6: Radal steam volume fracton dstrbuton at level C (33 cm above the njecton level) for dfferent setup confguratons. As expected the steam was thereby eby further kept away from the wall and for the steam volume fracton drectly at the wall a more physcal behavor could be observed. Further, the nfluence of the turbulent dsperson force was ncreased by enlargng the turbulent dsperson coeffcent from.0 to.5 (dash dotted lght green), whch corresponds to the level of uncertanty regardng ths model parameter n accordance to the model dervaton by dfferent authors n lterature. A slght mprovement could be observed. The parameter whch had the largest nfluence n the numercal results was the correlaton used for the heat transfer. Frst results were obtaned usng the Ranz-M Marshall correlaton. It was proven n ths applcaton, as well as n the lterature, that ths correlaton under predcts the heat transfer and therefore the condensaton rate n applcatons wth large amount of steam and wth bubble damters larger than mm. Instead, a new correlaton suggested by Prof. Tomyama (Tomyama, 2009) was mplemented (blue profle), provdng a satsfactory agreement wth the expermental results regardng both the value of the local amount of steam volume fracton and the radal poston of ts maxmum value. Only at the centre of the ppe the steam volume fracton s stll under predcted. The last test of ths frst nvestgaton conssted of usng the mproved setup (shft of source ponts locaton, consderaton of the wall lubrcaton force, ncrease of the turbulent dsperson coeffcent and use of the Tomyama heat transfer correlaton) and the orgnal njecton nozzle dameter n order to evaluate the mportance of the radal momentum of steam njecton, whch was not consdered when a larger nozzle dameter was appled n the CFD smulatons. The computatonal al tme requred due to the larger njecton velocty was sgnfcantly ncreased. The effect ect of ths modfcaton can be observed n Fgure 5 (red sold profle) snce the predcted steam volume fracton maxmum s thereby moved towards the centre of the ppe. Detaled results for three of the presented smulatons wll be shown next. They wll be named Confguraton (basc setup results - green curve), Confguraton 2 (mproved setup - blue curve) and Confguraton 3 (mproved setup and orgnal nozzle dameter red curve). Man characterstcs n setup of these smulatons are summarzed n Table 2.

13 Confg. Confg. 2 Confg. 3 SP 97[mm] 97[mm] 75[mm] F WL - C TD Nu ReP Pr ReP Pr ReP Pr D nj [mm] [mm] 4[mm] Table 2: Man CFD setup dfferences between selected confguratons: Locaton of the source ponts; consderaton of the wall lubrcaton force; turbulent dsperson coeffcent; heat transfer correlaton for Nusselt number; njecton nozzle dameter. The cross-sectonal averaged steam volume fracton at dfferent steam njecton elevatons and for the three selected CFD setup confguratons are plotted n Fgure 7. The horzontal axs corresponds to the dstance between steam njecton and the measurement plane, beng zero at the njecton locaton, and 8m for the largest dstance n the TOPFLOW experment. The results correspondng to the frst confguraton are able to reproduce the accumulaton of steam rght after the njecton and the trends of the expermental results. However, after L>0.5m the steam volume fracton s strongly over predcted. The second and thrd confguraton behave n a smlar way durng the frst two meters of the ppe after the steam njecton. Fnally, the predcton usng the thrd CFD confguraton shows a good quanttatve agreement to the expermental values as well. Fgure 7: Cross-sectonal averaged steam volume fracton at dfferent elevatons wth respect to the njecton level and compared for the three selected CFD confguratons. Fgure 8 shows the total steam volume fracton at steady state at a vertcal plane between two adjacent njecton nozzles for the three dfferent CFD confguratons. As already observed n Fgure 6 for level C, t can be seen that for the frst confguraton the steam remans all along the ppe near to the wall. Ths s n contradcton wth what was observed durng the experments, 3

14 where the steam was formng a knd of rng shaped pattern n the measurements. Ths radal steam dstrbuton s however present at the pctures correspondng to the second and thrd confguraton. Both results are qualtatvely analogous. Nevertheless the nfluence of the nozzle dameter s evdent from ths comparson, snce the steam s slghtly shfted towards the centre of the ppe n the thrd case and a hgher amount of steam volume fracton (less recondensaton) s predcted along the ppe as well. Detaled results correspondng to the three selected confguratons are presented n Fgure 9 and Fgure 0. Fgure 9 shows the radal steam volume fracton dstrbuton at the elevatons A, C, F, I, L and O (.e. measurement at 22, 33, 60, 55, 259 and 45cm above the steam njecton locaton). At elevatons A, C and F t can be seen that the frst confguraton s predctng the steam to reman close to the wall whle the dstrbuton of the steam for the second and thrd confguraton approaches reasonably the expermental results. The larger radal momentum of steam njecton n the thrd CFD confguraton causes the steam to move n the drecton of the centre of the ppe n comparson wth the second confguraton. For the upper elevatons (I, L and O) less steam s predcted. The second and thrd confguraton results show sgnfcant better agreement to the experments n comparson wth the frst smulaton, and as already observed n Fgure 7 the thrd confguraton predcts slghtly more steam as the second one. For the same dstances between steam njecton and measurement cross secton the radal bubble sze dstrbutons can be analyzed. For all elevatons the frst confguraton s only able to reproduce the locaton of the maxmum of the drg dd B profle, but due to the strong over predcton of the steam volume fracton n the doman ths profle s strongly over predcted as well. The second and thrd confguraton are n much better concordance wth the experments and are able to reproduce reasonably good the expermental values for all nvestgated steam njecton elevatons. Fgure 8: Steady state steam volume fracton at a vertcal plane between two adjacent njecton nozzles. Left: Confguraton ; Mddle: Confguraton 2; Rght: Confguraton 3. 4

15 Fgure 9: Predcted and expermental radal steam volume fracton dstrbutons at elevatons A, C, F, I, L and O (22 cm, 33 cm, 60 cm, 55, 259 and 45 cm respectvely above the njecton) 5

16 Fgure 0: Predcted and expermental radal bubble sze dstrbutons ( g B dr dd ) at elevatons A, C, F, I, L and O (22 cm, 33 cm, 60 cm, 55, 259 and 45 cm respectvely above the njecton).. 6

17 Conclusons A new methodology to extend the capabltes of the Multple-sze group model (MUSIG) has been presented n ths paper. The mplemented MUSIG model extenson allows smulatng two-phase flow applcatons where not only coalescence and break up of bubbles take place, but where bubble sze dstrbuton changes under the nfluence of mass transfer due to phase change. The new model s able to predct the shrnk or growth of bubbles when evaporaton or condensaton takes place. The new extended nhomogeneous MUSIG model was developed n collaboraton of ANSYS wth FZD and has been mplemented nto a customzed solver based on ANSYS CFX 2. In order to valdate the extended populaton balance model for polydsperse bubbly flows a complex water/steam experment has been chosen. It conssts of sub cooled water flowng upwards through the DN200 vertcal ppe of TOPFLOW (FZD), nto whch large amount of steam has been njected. The valdaton case shows locally values up to 30% of steam volume fracton, where condensaton and steam bubble coalescence are the man phenomena takng place. Thanks to the detaled measurements performed at FZD the evoluton of the flow along the whole ppe s known, and correspondng measurement data have been used to carry out an extensve analyss of the numercal results obtaned by applyng the proposed new MUSIG model formulaton. Several confguratons of the numercal setup have been nvestgated.. For three of them a detaled comparson aganst expermental data has been presented. Frst obtaned CFD results (confguraton ) have been mproved by modfyng some of the numercal parameters and physcal submodels. For the so-called confguratons 2 and 3, a satsfactory agreement to the expermental data has been obtaned. Both smulatons are able to reasonably predct the radal steam volume fracton at all elevatons along the ppe. The bubble sze dstrbuton at the same postons, n terms of the varable drg dd has been also nvestgated, B beng lkewse satsfactorly estmated n the numercal smulatons. Results correspondng to the thrd confguraton approach slghtly more accurately the expermental nvestgatons than the second one. However, t s also more computatonal tme demandng due to the hgh steam njecton veloctyes.. Acknowledgements Ths research has been supported by the German Mnstry of Economy (BMW) under the contract number n the framework of the German CFD Network on Nuclear Reactor Safety Research and Allance for Competence n Nuclear Technology, Germany. References ANSYS Inc ANSYS CFX 2 Users Manual Frank, T Entwcklung von CFD-Software zur Smulaton mehrdmensonaler Strömungen m Reaktorkühlsystem. Otterfng : Germany, ANSYS TR Frank, T Progress n the numercal smulaton (CFD) of 3-dmensonal gas-lqud multphase flows. Nedernhausen be Wesbaden : Germany, Aprl 2005, 2. NAFEMS CFD-Semnar "Smulaton komplexer Strömungsvorgänge (CFD) - Anwendungen und Entwcklungstendenzen", pp. -8. Frank, T, et al Valdaton of CFD models for mono- and polydsperse ar-water two-phase flows n ppe. 3, 2008, Nuclear Engneerng and Desgn (NED), Vol. 238, pp Frank, T, et al Valdaton of CFD models for mono and polydsperse ar-water two-phase flows n ppes. Garchng : Germany, 2006, CFD4NRS Workshop on Benchmarkng of CFD Codes for Applcaton to Nuclear Reactor Safety. Krepper, E The nhomogenous MUSIG model for the smulaton of polydspersed flows. 2008, 7

18 Nuclear Engneerng and Desgn, Vol. 238, p. polydspersed flows. Krepper, E, Lucas, D and Prasser, H-M On the modellng of bubbly flow n vertcal ppes. 2005, Nuclear Engneerng and Desgn, Vol. 235, pp Lfante, C, et al. 2009b. Entwcklung von CFD-Software zur Smulaton mehrdmensonaler Strömungen n Reaktor-kühlsystemen. Otterfng : Germany, 2009b. ANSYS/TR Lfante, C, et al. 2009a. Extenson of the Multple-Sze Group (MUSIG) Model to Phase Change Effects. Dresden : Germany, 2009a, Workshop on Multphase Flows, Smulaton, Experment and Applcaton. Lucas, D and Prasser, H-M Steam bubble condensaton n sub-cooled water n case of co-current vertcal ppe flow. Steam bubble condensaton n sub-cooled water n case of co-current vertcal ppe flow. Nuclear Engneerng and Desgn. 2007, Vol. 237, 5, pp Lucas, D, et al Benchmark database on the evoluton of two-phase flows n a vertcal ppe. Grenoble : France, 2008, XCFD4NRD, Experments and CFD Code Applcatons to Nuclear Reactor Safety. Lucas, D, Krepper, E and Prasser, H-M Predcton of radal gas profles n vertcal ppe flow on bass of the bubble sze dstrbuton. 200, Internatonal Journal of Thermal Scences, Vol. 40, pp Lucas, D, Krepper, E and Prasser, H-M Use of models for lft, wall and turbulent dsperson forces actng on bubbles for poly-dsperse flows. 2007, Chemcal Scence and Engneerng, Vol. 62, pp Luo, S.M. and Svedensen, H Theoretcal Model for Drop and Bubble Breakup n Turbulent Dspersons. 996, AIChE Journal, Vol. 42, pp Menter, F Two-equaton eddy-vscosty turbulence models for engneerng. 994, AIAA-Journal, Vol. 8. Prasser, H-M, et al Evoluton of the structure of a gas-lqud two-phase flow n a large vertcal ppe. 2007, Nuclear Engneerng and Desgn, Vol. 237, pp Prnce, M and Blanch, H Bubble Coalescence and Break-Up n Ar-Sparged Bubble Columns. 990, AIChE Journal, Vol. 36. Tomyama, A Progress n Computatonal Bubble Dynamcs. Dresden : Germany, 2009, Workshop on Multphase Flows. Smulaton, Experment and Applcaton. Tomyama, A Struggle wth computatonal bubble dynamcs. Lyon : France, 998, 3rd Internatonal Conference on Multphase Flow. 8