VALIDATION OF EULERIAN MULTIPHASE FLOW MODELS FOR NUCLEAR SAFETY APPLICATIONS

Transcription

1 r International Symposium on Two-Phase Flow Moelling an Experimentation Pisa, -4 September 4 VAIDATION OF EUERIAN MUTIPHASE FO MODES FOR NUCEAR SAFETY APPICATIONS Thomas Frank*, Junmei Shi, Alan D. Burns** *ANSYS ermany, Stauenfelweg, D-864 Otterfing, ermany, Thomas.Frank@ansys.com, FZR, Institute of Safety Research, Bautzener anstr. 8, D-8 Dresen, ermany, J.Shi@fz-rossenorf.e, **ANSYS CFX, The emini Blg., Fermi Avenue, Dicot, OX QR, UK, Alan.Burns@ansys.com ABSTRACT The CFD package CFX-5 has been use to preict the evelopment of upwar irecte gas-liqui flows in a vertical pipe. Uner the assumption of monoisperse bubbles the ilute gas-liqui flow has been preicte using the Eulerian framework of multiphase flow moeling. The capabilities of the CFX-5 flow solver have been extene by taking into account aitional non-rag forces like lift, turbulent ispersion an wall lubrication forces. Range of applicability an accuracy of the numerical moel have been valiate against measure gas voi fraction profiles obtaine at the MT-oop test facility of the Forschungszentrum Rossenorf (FZR in the bubbly flow regime. Best agreement of numerical results with experimental ata coul be obtaine for a wie range of experimental conitions, if Menter s k-ω Shear Stress Transport (SST turbulence moel has been use in combination with the Favre average rag (FAD turbulent ispersion force moel as erive by Burns et al. []. Furthermore results of extensive numerical experiments [] for the examination an comparison of ifferent moel formulations for the wall lubrication an turbulent ispersion forces are presente in this paper. INTRODUCTION Preiction of multiphase flows in the fiel of esign, optimization an safety analysis of chemical an nuclear plants requires etaile knowlege of the ifferent flow regimes in gas-liqui multiphase flows an the mechanisms of mass, momentum an heat transfer between the gaseous an liqui phases. So the evelopment of gas voi fraction istributions in isperse bubbly flows epens not only on the bubble rag, but also on transverse lift, turbulent ispersion, bubble-wall interation an bubble inuce turbulence. For higher gas volume flow rates the mathematical escription of bubble size istribution, bubble breakup an coalescence in epenence on the local flow properties becomes of crucial importance for the escription of the main flow phenomena. The emphasis of this paper is the further evelopment of the multiphase flow moels for isperse bubbly flows in the commercial CFD package CFX-5. Due to the necessity to moel many of the unresolve etails of technical flows in an Eulerian framework of moeling, it is further necessary to assess the accuracy of the CFD metho with the help of experimental ata. Results for gas voi fraction istribution from wiremesh sensor measurements in a vertical pipe bubbly flow at the MT oop test facility at the Forschungszentrum Rossenorf (FZR are use to valiate the range of applicability an the accuracy of the implemente moels. OUTINE OF THE PHYSICA MODE overning equations an CFX-5 two-flui moel The numerical simulations presente in this work are base on the CFX-5.6 two-flui (or multiflui Euler-Euler approach. The Eulerian moeling framework is base on ensemble-average mass an momentum transport equations for all phases. Regaring the liqui phase as continuum (= an the gaseous phase (bubbles as isperse phase (= with a constant bubble iameter P these equations without mass transfer between phases rea: t t ( r ρ +. ( r ρ U = ( r ρu +. ( r ρu U T.( µ ( ( = r U + U r p + r ρ g + F + M D where M represents the sum of interfacial forces besies the rag force F D, like lift force F, wall lubrication force F an turbulent ispersion force F TD. For the steay state investigations within the scope of this paper it ha been proven that the virtual mass force F VM is small in comparison with the other non-rag forces an therefore it can be safely neglecte. Turbulence of the liqui phase has been moele using either a stanar k-ε moel or Menter s k-ω Shear Stress Transport (SST moel [5]. The turbulence of the isperse bubbly phase was moele using a zero equation turbulence moel an bubble inuce turbulence has been taken into account accoring to Sato [6]. The rag force between the bubbles an the flui was consiere in the istorte bubble regime accoring to the race rag moel buil into CFX-5 [7]. Moeling of non-rag forces The lift force. The voi fraction istribution in gas-liqui two-phase flows is not only etermine by the rag force but ( (

2 is mainly influence by the so-calle non-rag forces. In vertical pipe flows the main contribution of the non-rag forces is irecte perpenicular to the flow irection or pipe axis. So the transversal lift force acting on a spherical particle ue to flui velocity shear can be expresse as: F = C r ( U U U ρ ( For soli spherical particles the lift force coefficient C is usually positive an can be etermine in epenency on the particle Reynols number an a imensionless shear rate parameter. Corresponing correlations ha been publishe by Saffman (965/68, Mcaughlin (99/9, Dany & Dwyer (99, Mei, Arian & Klausner (99/9/94, egenre & Magnauet (998 an Tomiyama (998 (see [, ]. In the works of Tomiyama (998 an Moraga et al. (999 negative values for the lift force coefficient for bubbles an spherical soli particles were reporte. The correlation given by Moraga et al. was base on experimental ata of Alajbegovic et al. (994 an was explaine by superposition of invisci aeroynamic an vortex-sheing inuce lift forces resulting in a sign change of the lift force with increasing particle Reynols number an shear rate. Similarly for bubbles with a larger bubble iameter, bubble eformation an asymmetric wake effects become of importance, so that the lift force coefficient C becomes negative. A correlation for C as a function of the bubble Eötvös number was publishe by Tomiyama (998 [8]. This correlation has been use here in a slightly moifie form, where the value of C for Eo > has been change to C =-.7 to ensure a steay epenency of C = C (Eo : C with: min = f ( Eo,.7, f ( Eo [.88tanh(.Re, f ( Eo ], =.5Eo.4Eo P.59Eo Eo 4 Eo Eo < 4 > where Eo is the Eötvös number base on the long axis H of a eformable bubble, i.e.: Eo = g ( ρ ρ Eo = g H, ( ρ ρ H = P P ( +.6Eo / The wall lubrication force. Antal et al. (99 [9] propose an aitional wall lubrication force to moel the repulsive force of a wall on a bubble, which is cause by the asymmetric flui flow aroun bubbles in the vicinity of the wall ue to the flui bounary layer: F rel rel (4 (5 (6 = C r ρ U ( U n n n (7 with: C C C =, + P y max (8 The authors recommene coefficient values of C =-. an C =.5. However the coefficients etermine by Krepper et al. [] for the investigate test geometry were C =-.64 an C =.5. Tomiyama [8] has moifie the wall lubrication force formulation of Antal base on experiments with air bubbles in glycerin: y ( D y C (9 P = C where the coefficient C is epenent on the Eötvös number for eformable bubbles. Again ue to the assumption of a steay epenency of C = C (Eo we use a slightly change expression for this wall lubrication coefficient: C.9Eo+.79 e =.599Eo Eo 5 5 < Eo ( < Eo The turbulent ispersion force. Initially a simple formulation of the turbulent ispersion force was propose by opez e Bertoano et al. [] from the Rensselaer Polytechnic Institute (RPI: F = C ρ k r TD TD ( where ifferent constant values for the turbulent ispersion force coefficient of C TD =.,,.5 have been use by many authors. This moel will be further reference to as the RPI TD moel. Several other moels ha appeare in the literature (see [], notably those of Carrica [4] an osman & Issa [5,6], which ha shown that the turbulent ispersion coefficient C TD is in fact a function of the Stokes number an other flow properties. Recently Burns et al. [] publishe a mathematical erivation for the turbulent ispersion force base on a secon time averaging process applie to the rag term in the momentum transport equations of Eulerian multiphase flow moeling, since the physical mechanism responsible for turbulent ispersion is the action of turbulent eies via interphase rag. F = D A ( U U D, β β β F = D ( A ( U U + a ( u u D, β β β β β ( Here the interphase rag is expresse via interfacial area ensity A β an a coefficient D β. If the time average rag term is expresse in terms of so-calle Favre or massweighte average velocities: U r u = U + r ( we obtain from eq. (:

3 ( F = D A U U D, β β β r u r u a ( u β β β β u + Dβ Aβ + r rβ A β (4 Regaring the first term as the rag term expresse in Favre average variables we obtain an expression for the turbulent ispersion force from the aitional correlation terms in eq. (4. In case of ilute isperse multi-phase flow, the turbulent ispersion force term can be further simplifie using the following expression for interfacial area ensity an ey iffusivity hypothesis: 6rβ νt Aβ =, r u = r (5 β where r is a turbulent Schmit number for volume fraction ispersion, expecte to be in the orer of unity. In that case we finally obtain for the turbulent ispersion force in Favre average momentum transport equations: F D A ν r r r t β TD, = β β r rβ r (6 istribute over the pipe cross section. A large number of tests with ifferent ratios of air an water superficial velocities resulting in a slightly varying bubble iameter were performe (Tab.. In the tests use for the current valiation the loop was operate with air at atmospheric pressure an o C temperature. Stationary conitions were settle for each experiment. as voi fraction profiles were measure at a height of.8m above the air injection using a fast wiremesh sensor evelope at FZR [] with 4x4 electroes. Aitionally bubble size an voi fraction istributions are available for ifferent measurement cross sections at ifferent /D=.6,...,59.. Tab. : Test conitions for experimental investigations at the MT-oop test facility FZR Test No. P [mm] U m / ] m / ] [, sup s U [, sup s This moel will be further reference to as the Favre Average Drag (FAD TD moel. Comparing expression from eq. (6 for isperse two-phase flows with the expression for F TD from the RPI TD moel in eq. (, we see that the two moels are equivalent if the turbulent ispersion force coefficient C TD of the RPI TD moel is set to: C TD C D A k µ β β = + r ρ ε r r β ν U t U = CD 4 k r r P (7 It will be shown from the numerical simulations, that the variation in the value of the turbulent ispersion force coefficient C TD in the FAD TD moel is large in comparison with the assume constant values for C TD from the RPI TD moel in eq. ( an that it can not be neglecte for isperse bubbly flows. CFX-5 NUMERICA SIMUATIONS AND COMPA- RISON ITH EXPERIMENTA DATA Experiments an voi fraction profile ata Numerical simulation ata has been valiate against extensive experimental results for air-water bubbly flows available from a FZR atabase [, 4]. The measurements at the MT-oop test facility (Fig. were carrie out at a vertical test section of 4m height an 5.mm inner iameter. Air bubbles were injecte into an upwar water flow at normal conitions using a sparger with 9 capillaries equally Fig. : MT-oop test facility for vertical pipe flow investigations Setup of the numerical simulation Extensive numerical simulations for the ifferent test cases from Tab. ha been carrie out in orer to valiate the previously iscusse non-rag force moels. Therefore the lift, wall lubrication an turbulent ispersion forces in accorance to the eq. (, (4, (7, (8, (9, (6 an (7 were implemente into CFX-5.6 using User Fortran routines or CC comman language expressions. The numerical simulations ha been carrie out in accorance with the Best Practice uielines for CFD coe valiation [7]. For the vertical pipe flow geometry shown in

4 Fig. raial symmetry has been assume, so that the numerical simulations coul be performe on a 6 o raial sector of the pipe with symmetry bounary conitions at both sies. Inlet conitions were assume to be homogeneous in terms of superficial liqui an gas velocities an volume fractions for both phases in accorance with the experimental setup conitions from Tab.. For the isperse bubbly phase a mean bubble iameter was specifie, which was etermine from the test case wiremesh sensor ata. At the outlet cross section of the.8m long pipe section an average static pressure outlet bounary conition was use. Tab. : Hierarchy of numerical meshes ri level No. of CV s in pipe cross section No. of CV s along pipe axis No. of CV s A hierarchy of 5 numerical gris was constructe, where the number of gri elements has been increase by a factor of from a coarser to a finer mesh (scaling factor of / in each coorinate irection, see Tab.. The numerical meshes use local refinement towars the outer pipe wall, while min/max cell size an cell aspect ratios were kept almost constant for all ifferent numerical gris. Dimensionless y + values varie between y + =9. on the coarsest mesh an y + =.5 on the finest mesh. For investigation of flow solver convergence the gas holup an the global mass balances for both phases in the vertical pipe were efine as monitore target variables. Reliable converge solutions coul be obtaine on all gri levels for a satisfie convergence criterion base on the maximum resiuals of.e-5 an for a physical time scale of the fully implicit solution metho of t=.5s. Numerical simulation vs. Experiment For the comparison of the numerically preicte an measure gas volume fraction profiles at the uppermost measurement cross section at z=.m (/D=59. all ata have been normalize: r ( x = * 8 D r ( x D / r ( x x x (8 where x is the coorinate in raial irection. In a first series of numerical simulations the epenency of the gas voi fraction istribution on the flui phase turbulence moel (stanar k-ε vs. SST moel an the turbulent ispersion force moel (RPI vs. FAD TD moel has been investigate for test case FZR-74. Aitionally the Tomiyama lift an wall lubrication forces have been taken into account. Fig. shows the comparison of the gas voi fraction profiles for the n gri level with the experimental result. It can be observe, that the Tomiyama lift an wall lubrication forces are well balance an give a pronounce wall peak in the gas voi fraction profile, which is the expecte voi fraction istribution for the given bubble iameter in this test case. On the other han this wall peak is much too pronounce in comparison with the experimental Normalize Air Volume ri evel : k-eps + RPI TD (.5 ri evel : k-eps + FAD TD ri evel : SST + RPI TD (.5 ri evel : SST + FAD TD Fig. : Comparison of voi fraction profiles for test case FZR-74 Normalize Air Volume ri evel : k-eps + RPI TD (.5 ri evel : k-eps + FAD TD ri evel : SST + RPI TD (.5 ri evel : SST + FAD TD Fig. : Voi fraction profiles using reuce Tomiyama s lift an wall lubrication forces (FZR-74 ata for the simulations using the stanar k-ε turbulence moel. Furthermore the turbulent ispersion of the isperse phase is unerpreicte with the RPI TD moel also resulting in too high gas voi fraction values in the wall peak. Best results coul be obtaine with the combination of the SST turbulence moel for the continuous phase using automatic wall function treatment [5, 7] an the FAD TD moel for the isperse phase. The higher turbulent ispersion of the FAD TD moel leas not only to better agreement of voi fraction ata within the region of the wall peak but leas also to a substantial improvement of the voi fraction istribution near the pipe axis. Normalize Air Volume ri evel : RPI TD (.5 ri evel : RPI TD (.5 ri evel : FAD TD ri evel : FAD TD Fig. 4: Comparison of RPI vs. FAD TD moel for test case FZR-74 with Tomiyama lift an Antal s wall lubrication forces an Sato moel Since in Fig. the numerically preicte level of the voi fraction profile in the pipe core is still less than the experimentally measure value it coul be suggeste, that the

5 Tomiyama lift force preicts too high positive values, which are not well balance with the turbulent ispersion force in that core region. Therefore an analogous numerical experiment has been carrie out by reucing the amplitue of the Tomiyama lift an wall lubrication forces by a factor of.5. Results for the raial gas voi fraction istribution in Fig. show the same trens as iscusse for the previous series of numerical simulations. Again the combination of the SST turbulence moel with the FAD moel for the turbulent ispersion force elivers the best agreement with the experimental result. ith the reuce lift an wall lubrication forces the agreement in the pipe core region is very goo, while the maximum amplitue of the wall peak in the gas volume fraction is slightly below the measure value. A similar numerical investigation ha been carrie out using the Tomiyama lift an Antal s wall lubrication forces with the SST turbulence an Sato moels on two ifferent gri levels of refinement. Fig. 4 shows, that again the RPI TD moel unerpreicts the turbulent ispersion in the pipe core leaing to higher amplitue of the peak in the gas volume fraction istribution near the wall. Aitionally with Antal s wall lubrication force the raial location of the wall peak is preicte to close to the wall in comparison with experimental results. Normalize Air Volume Normalize Air Volume ri evel ri evel ri evel ri evel Fig. 5: ri inepenence of numerical results: FZR-74 with Tomiyama lift an Tomiyama wall lubrication forces, FAD TD an Sato moel ri evel ri evel ri evel ri evel Fig. 6: ri inepenence of numerical results: FZR-74 with Tomiyama lift an Antal s wall lubrication forces, FAD TD an Sato moel It has further to be mentione, that the graient of the gas voi fraction in the turbulent ispersion force term can lea to numerical noe-to-noe oscillations, if central ifferences are use for the iscretization of this term. These oscillations can be avoie by inclusion of the turbulent ispersion force in a coupling algorithm similar to the algorithm evelope by Rhie & Chow for suppression of pressure fluctuations on colocate gris. Furthermore, the gri epenence of the numerical results has been stuie. Figs. 5 an 6 show the corresponing gas voi fraction profiles in comparison with the experimental ata for gri levels to 4 using either Tomiyama s or Antal s wall lubrication force formulation. In Fig. 5 numerical simulations give almost gri inepenent results for gri resolutions finer then the n gri level, when Tomiyama s wall lubrication force formulation has been use. For the case whith Antal s wall lubrication (Fig. 6, gri inepenent results coul not be obtaine even on the 4 th gri level. On gris with finer gri resolution the misbalance between Antal s wall lubrication force an Tomiyama s lift force leas to increasing amplitue of the wall peak in the gas volume fraction istribution, while the raial location of the voi fraction maximum remains unchange. Again the raial shift of the voi fraction peak towars the wall can be observe in Fig. 5 in comparison with the obtaine voi fraction istributions from Figs. - an 5. This inicates, that the wall lubrication force erive from Antal s formulation seems too weak in orer to balance Tomiyama s lift force at the correct raial location, so that the isperse phase is too much accumulate within a certain number of gri cells near the wall. Nevertheless Figs. 4-6 show again, that the use of the FAD TD moel leas to a significant improvement in the agreement of the numerical results with the experimental voi fraction ata, especially regaring the higher gas voi fraction values in the pipe core an the maximum amplitue of the wall peak in the gas voi fraction profiles. ith the constant coefficient RPI TD moel the near-wall voi fraction peak in the gas volume fraction istribution is overpreicte in all cases ue to a reuce turbulent ispersion force. Consequently high concentration of the isperse phase near the wall leas to large errors in the gas voi fraction level in the pipe core by using the RPI TD moel. Further Figs. 7- show the istribution of the lift an wall lubrication forces in the cross section at z=.m (/D=59. for the following four ifferent simulations an for the gri levels -4: (a Tomiyama lift (., Antal s wall lubrication an RPI turbulent ispersion forces (C TD =.5; (b Tomiyama lift (., Antal s wall lubrication an FAD turbulent ispersion forces; (c Tomiyama lift (., Tomiyama wall lubrication (. an FAD turbulent ispersion forces; ( reuce Tomiyama lift (.5, reuce Tomiyama wall lubrication (.5 an FAD turbulent ispersion forces. It can be observe, that for the cases (a an (b the lift an wall lubrication forces reach their highest values very close to the wall, on st r gri levels even within the wall nearest gri cell. Otherwise in cases (c an ( a force balance between the Tomiyama lift an wall lubrication forces can be establishe at a certain gri inepenent wall istance. In the simulations where Antal s wall lubrication force was use, a similar balance of the non-rag forces is not establishe up to the gri cell closest to the wall. In combination with the RPI TD moel this ha le even to numerical instabilities in the numerical solutions on gri levels an 4.

6 5 Force term [kg m - s - ] ift force: Case (a ift force: Case (b -5-5 ift force: Case (c ift force: Case ( all lubr. force: Case (a all lubr. force: Case (b all lubr. force: Case (c all lubr. force: Case ( Force term [kg m - s - ] ift force: Case (b - ift force: Case (c ift force: Case ( all lubr. force: Case (b - all lubr. force: Case (c all lubr. force: Case ( - Fig. 7: Distribution of non-rag force terms on st gri level (FZR-74 Force term [kg m - s - ] ift force: Case (a -5-5 ift force: Case (b ift force: Case (c ift force: Case ( all lubr. force: Case (a all lubr. force: Case (b all lubr. force: Case (c all lubr. force: Case ( Fig. 8: Distribution of non-rag force terms on n gri level (FZR-74 Force term [kg m - s - ] ift force: Case (b -5-5 ift force: Case (c ift force: Case ( all lubr. force: Case (b all lubr. force: Case (c all lubr. force: Case ( Fig. 9: Distribution of non-rag force terms on r gri level (FZR-74 Fig. : Distribution of non-rag force terms on 4 th gri level (FZR-74 Finally the physical setup with the implementation of the Tomiyama lift an wall lubrication forces an the FAD TD force moel was applie to ifferent flow conitions efine by the experimental setup given in Tab. for the test cases FZR-8 to FZR-4. For computational efficiency these simulations were carrie out using two-imensional gris consiering the axi-symmetrical geometry. Again careful gri epenence stuies were carrie out. The final gri inepenent results were obtaine on gris with 5x6 control volumes an with raial near wall refinement of gri cells. Normalize Air Volume Normalize Air Volume FZR-8: RPI TD (.5 FZR-8: FAD TD FZR-8: Experiment Fig. : Comparison of numerical simulation vs. experimental results for FZR FZR-9: RPI TD (.5 FZR-9: FAD TD FZR-9: Experiment Fig. : Comparison of numerical simulation vs. experimental results for FZR-9

7 Normalize Air Volume FZR-4: RPI TD (.5 FZR-4: FAD TD FZR-4: Experiment Fig. : Comparison of numerical simulation vs. experimental results for FZR-4 the isperse bubbly phase in a pronounce wall peak of the voi fraction (FZR-4. This change in gas voi fraction istribution with increase superficial water velocity an ecrease ratio of air to water volume flow rate can be well preicte with the implemente physical moels. In the intermeiate range (FZR-4/4 both the RPI an the FAD TD moels still unerpreict the near wall turbulent ispersion resulting in an overpreiction of near wall gas volume fractions. Furthermore the Tomiyama wall lubrication moel leas to a thin bubble free region near the wall, while measurement ata still etect a significant level of air voi fraction in this region. Nevertheless, the reuce accuracy of the wire mesh sensor measurement close to the pipe wall is also at least partially responsible for this iscrepancy. Normalize Air Volume FZR-4: RPI TD (.5 FZR-4: FAD TD FZR-4: Experiment Fig. 4: Comparison of numerical simulation vs. experimental results for FZR-4 C TD [-] FZR-8 FZR-9 FZR-4 FZR-4 FZR-4 FZR-7 FZR-9 FZR-74 RPI-TD-Moel Normalize Air Volume FZR-4: RPI TD (.5 FZR-4: FAD TD FZR-4: Experiment Fig. 5: Comparison of numerical simulation vs. experimental results for FZR-4 For comparison, the simulations were also carrie out with the RPI TD moel an CTD=.5. Results of these test case preictions are presente in Figs. -5 an compare with the experimentally measure gas voi fraction profiles. It can be observe that the agreement between numerical simulation an experimental results are fairly goo, if the several sources of uncertainties are taken into account. These uncertainties inclue temperature, phase change (certain amount of evaporation an compressible effects (hyrostatic bubble expansion on voi fraction, breakup an coalescence phenomena, which ha not yet been taken into account in the numerical simulations, the constants of experimental conitions an possible measurement accuracy. Figs. -5 show the change in gas volume fraction profiles from a nearly uniform voi fraction istribution with only a weak wall peak (FZR-8 to a strong concentration of Fig. 6: Turbulent ispersion force coefficient C TD vs. pipe raius If for the above numerical simulations the turbulent ispersion force coefficient C TD from eq. (7 is plotte over the pipe raius an compare with the recommene constant value of C TD =.5 for the RPI TD moel, we can see the strong ifference in the preicte turbulent ispersion force of the FAD TD moel (see Fig. 6. Especially in the core of the gas-liqui bubbly pipe flow the turbulent ispersion force coefficient C TD in the FAD TD moel shows a strong increase in comparison with the value commonly use with the RPI TD moel. Furthermore it can be observe, that the overall values of the C TD coefficient ecrease with increasing superficial liqui velocity U,sup or Reynols number. SUMMARY & CONCUSIONS Consieration of the lift, wall lubrication an turbulent ispersion forces in the multiphase momentum equations is essential for the moeling of gas-liqui bubbly pipe flows or of even greater importance in more complex flow situations. The multiphase flow capabilities of the CFX-5 flow solver have been enhance by implementation of some of the most wiely use moels for the aitional non-rag force terms. Aitionally the Favre Average Drag (FAD turbulent ispersion moel in its formulation erive by Burns [] has been implemente an successfully valiate against experimental ata for the raial gas volume fraction istribution from the MT-oop test facility at Forschungszentrum Rossenorf (FZR. Valiation tests have shown, that ilute gas-liqui bubbly flows with a monoisperse bubble

8 size istribution can successfully be preicte with the multiphase moels of CFX-5. In epenence on the bubble iameter either a near wall peak or a core peak in the gas voi fraction profiles of vertically upwar irecte pipe flow has been etermine in accorance with the experimental results. Best agreement with the experimental ata has been establishe using the SST turbulence moel with automatic wall treatment for the liqui phase turbulence moeling, the Tomiyama lift an wall lubrication force moels together with the FAD turbulent ispersion force moel for the isperse phase. Further evelopment is necessary for bubbly flows of higher gas voi fraction taking into account bubble breakup an coalescence together with the ifferent velocities of isperse phases with ifferent bubble sizes in a framework of multi-flui Eulerian moeling. ACKNOEDEMENT This research was carrie out in strong cooperation between ANSYS an the Forschungszentrum Rossenorf (FZR, ermany. Further this research was supporte by the erman Ministry of Economy an abour (BMA in the framework of the RS-BMA network project CFD-Verbunvorhaben Entwicklung von CFD-Software zur Simulation mehrimensionaler Strömungen in er Reaktorsicherheit an in the project TOPFO - Transient Two Phase Flow Test Facility for gemeric investigation of Two Phase Flows an further Development an Valiation of CFD Coes. NOMENCATURE A β [/m] - interfacial area ensity C [-] - lift force coefficient C TD [-] - turbulent ispersion force coefficient C [-] - wall lubrication force coefficient C µ [-] - turbulence moel constant H [m] - long axis of a eformable bubble P [m] - bubble iameter D [m] - pipe iameter g( ρ ρ Eo P = [-] - Eötvös number k [m /s ] - turbulence kinetic energy [m] - pipe length n [-] - wall normal vector p [Pa] - pressure r [-] - voi fraction ρ U U P ReP = [-] µ - particle Reynols number U [m/s] - velocity U rel =U -U [m/s] - slip velocity y [m] - wall istance y + [-] - imensionless wall istance CFD network project Development of CFD coes for multiimensional flows in reactor safety applications reek symbols ε [m /s ] - turbulence ey issipation ρ [kg/m ] - ensity ν [m /s] - kinematic viscosity ν t [m /s] - turbulent viscosity µ [kg/m s] - viscosity r [-] - Schmit number [N/m] - surface tension Subscripts an superscripts - fluctuation - gaseous phase - liqui phase sup - superficial t - turbulent, β - inices for continuous an isperse phase in a phase pair REFERENCES. A.D. Burns, Th. Frank, I. Hamill, J.-M. Shi, The Favre Average Drag Moel for Turbulence Dispersion in Eulerian Multi-Phase Flows, ICMF 4, 5th Int. Conf. Multiphase Flow, Yokohama, Japan, 4.. Th. Frank, F.R. Menter, Bubble flow in vertical pipes Investigation of the test case VD-/ for the valiation of CFD coes, ANSYS CFX ermany, Technical Report No. TR--9, pp. 4, October.. H.-M. Prasser, D. ucas, E. Krepper, D. Balauf, A. Böttger, U. Rohe et.al, Strömungskarten un Moelle für transiente Zweiphasenströmungen, Forschungszentrum Rossenorf, ermany, Report No. FZR-79, pp. 8, June. 4. D. ucas, E. Krepper, H.-M. Prasser, Development of bubble size istributions in vertical pipe flow by consieration of raial gas fraction profiles, ICMF, 4th Int. Conf. Multiphase Flow, New Orleans, A, USA, pp. -, June. 5. F.R. Menter, Two-equation ey-viscosity turbulence moels for engineering applications, AIAA-Journal, Vol., No. 8, Y. Sato, K. Sekoguchi, iqui velocity istribution in two phase bubble flow, Int. J. Multiphase Flow, Vol., pp. 79, CFX-5.6 Users Manual, ANSYS,. 8. A. Tomiyama, Struggle with computational bubble ynamics, ICMF 98, r Int. Conf. Multiphase Flow, yon, France, pp. -8, June S.P. Antal, R.T. ahey, J.E. Flaherty, Analysis of phase istribution in fully evelope laminar bubbly two-phase flow, Int. J. Multiphase Flow, Vol. 7, pp , 99.. E. Krepper, H.M. Prasser, Measurements an CFX- Simulations of a bubbly flow in a vertical pipe, AMIF- ESF orkshop "Computing Methos for Two-Phase Flow", Aussois, France, pp. 8, -4 January.

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