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CT&F Ciencia, Tecnología y FuturoISSN: 0122-5383ctyf@ecopetrol.com.coECOPETROL S.A.ColombiaGuerrero, Esteban; Muñoz, Felipe; Ratkovich, NicolásCOMPARISON BETWEEN EULERIAN AND VOF MODELS FOR TWO-PHASE FLOWASSESSMENT IN VERTICAL PIPESCT&F Ciencia, Tecnología y Futuro, vol. 7, núm. 1, diciembre, 2017, pp. 73-83ECOPETROL S.A.Bucaramanga, ColombiaAvailable in: http://www.redalyc.org/articulo.oa?id 46553766005How to citeComplete issueMore information about this articleJournal's homepage in redalyc.orgScientific Information SystemNetwork of Scientific Journals from Latin America, the Caribbean, Spain and PortugalNon-profit academic project, developed under the open access initiative

CT&F - Ciencia, Tecnologíay FuturoBETWEEN- Vol. 7 Num.1 Dec.AND2017VOFPag.MODELS7 COMPARISONEULERIANFOR TWO-PHASE FLOW ASSESSMENT IN VERTICAL PIPESISSN Print 0122ISSN Online 2 2-1Journal of oil, gas and alternative energy sourcesCOMPARISON BETWEEN EULERIAN AND VOFMODELS FOR TWO-PHASE FLOW ASSESSMENTIN VERTICAL PIPESCOMPARACIÓN DE LOS MODELOS EULERIANO Y VOF PARA EVALUACIÓNDE FLUJO BIFÁSICO EN TUBERÍAS VERTICALESCOMPARAÇÃO DOS MODELOS EULERIANO E VOF PARA AVALIAÇÃO DE ESCOAMENTOBIFÁSICO EM TUBULAÇÕES VERTICAISEsteban Guerrero1*, Felipe Muñoz1 and Nicolás Ratkovich1.1Uni er i ae lo An e , Bogot D.C., Colom iae-mail e.guerrero 11unian e .e u.co(Received: Apr. 04, 2016; Accepted: Aug. 24, 2017)ABSTRACTTe a ro riate c aracteri ation o t e t o- a e loa een recently con i ere a a to ic ointere t at in u trial le el. T e Com utational Flui Dynamic CFD i one o t e tec ni ue u e ort i analy i . Commonly, t e Volume O Flui VOF mo el an t e Eulerian mo el are u e to mo elt e t o- a e lo . T e mat ematical ormulation o t e e mo el cau e i erence in t eir con ergence,com utational time an accuracy. T i article e cri e t e i erence et een t e e t o mo el or a licationin t e t o- a e u ar - lo . In or er to accom li t i o ecti e, t e CFD mo el ere ali ateite erimental re ult . T i tu y mo ele i e eriment it an ort ogonal utter ly gri . A a re ult, t eEulerian mo el o mean uare error 1 .lo er t an t e VOF mo el 1 .0or lo oi ractionlo0.2 . Furt ermore, it a emon trate t at Eulerian mo el er ormance i in e en ent rom gri ,en ing le com utational time t an t e VOF mo el. Finally, it a etermine t at only t e VOF mo elre ict t e attern lo .Keywords: CFD, Two-phase flow, Void fraction, Flow patternsHow to cite:uerrero, E te an., Mu o , Feli e., Rat o ic , Nicola . 2017 . Com ari on et een Eulerian an VOFmo el or t o- a e lo a e ment in ertical i e . CT&F - Ciencia, Tecnología y Futuro, 7 1 , 7 - .*To whom correspondence should be addressedCT&F - Ciencia, Tecnología y Futuro - Vol. 7 Num. 1Dec. 201773

ESTEBANUERRERO et al.RESUMENLa correcta caracteri aci n el lu o i ico e a uelto un tema e inter a ni el in u trial. Lamec nica e lui o com utacional CFD, or u igla en ingl e una e la t cnica utili a aara e to an li i . Com nmente e utili a en e ta erramienta el mo elo e olumen e lui o VOF,or u igla en ingl y mo elo Euleriano. La ormulaci n matem tica e e to mo elo genera i erenciaen u con ergencia, e actitu y e em e o com utacional. E te tra a o one en e i encia la i erenciae e to o mo elo ara a licacione e lu o i ico en irecci n ertical. Con el in e lle ar a ca oe te o eti o e e e ali ar e to mo elo con re ulta o e erimentale . En e te royecto e reali lamo elaci n e ei e erimento acien o u o e un malla o ti o ortogonal mari o a . Como re ulta o elmo elo Euleriano re enta un error cua r tico me io 1 .in erior al mo elo VOF 1 .0ara lu ocon a a racci n e acío0.2 . Por otro la o, e e i enci ue el mo elo Euleriano e in e en ientee la malla ermitien o un tiem o e imulaci n menor al el mo elo VOF. Finalmente, e etermin ueel mo elo VOF ermite re ecir el atr n e lu o a i erencia el mo elo Euleriano.Palabras clave: CFD, Flu o iico, Fracci n e acío, Patronee lu o.RESUMOAcaracteri a o a e ua a o e coamento i ico tem e torna o um a unto e intere e nom ito in u trial. A mec nica o lui o com utacional CFD, or ua igla em inglumaa t cnica ara e a an li e . Ne ta erramenta utili a- e normalmente o mo elo e olume elui o VOF, or igla em ingle o mo elo Euleriano. A ormula o matem tica e te mo elo gerai eren a na ua con erg ncia, e ati o e e em en o com utacional. E te tra al o e taca a i eren ae te oi mo elo ara a lica e e e coamento i ico em ire o ertical. Para atingir e e o eti oreci o ali ar e te mo elo com re ulta o e erimentai . Ne te ro eto reali ou- e a mo elagem eei e erimento em regan o uma mal a ortogonal. Como re ulta o, o mo elo Euleriano a re enta umerro ua r tico m io 1 .in erior ao mo elo VOF 1 .0ara lu o com ai a ra o e a io0.2 . Por ua e , e i enciou- e ue o mo elo Euleriano in e en ente a mal a, o i ilitan o umerío o e imula o menor ao o mo elo VOF. Por im, eterminou- e ue o mo elo VOF er e arare er o a r o e e coamento ao contr rio o mo elo Euleriano.Palavras-chave: CFD, E coamento i74ico, Fra o e a io, Pa r ee lu o.CT&F - Ciencia, Tecnología y Futuro - Vol. 7 Num. 1Dec. 2017

COMPARISON BETWEEN EULERIAN AND VOF MODELS FOR TWO-PHASE FLOW ASSESSMENT IN VERTICAL PIPES1. INTRODUCTIONThe multiphase ow, speci cally the gas-liquid twophase ow, is an operating condition found in differenttypes of industries. It appears in systems of energygeneration, mass transportation, heat transfer, equipmentfor separation and reaction processes, and equipment forenvironmental control (Ishii & Hibiki, 2011).The nuclear and petroleum industries mainly workwith the gas-liquid two-phase ow in their processes.The former, works with this phenomenon in the boilingwater or pressurized water nuclear reactors used forthe generation of electrical power. The latter, confrontsthe multiphase ow during oil and gas production invertical, horizontal and inclined pipes. Furthermore,the two-phase ow appears when well production isenhanced by steam, water or gas injection (Zhang, Wang,Sarica & Brill, 2003). As a consequence, the correctlyoperation of these processes is xed to the variables thatdescribe the gas-liquid two-phase ow. The variation inthe volume fractions of the two-phase ow varies froma discontinuous production to a shutdown of the process(Abdulkadir, 2011). For that reason, characterizationof the gas-liquid two-phase ow is essential to avoidoperating problems.Different techniques are used to determine thegas-liquid two-phase flow. Experimental methodsmeasure important parameters like local void fraction,bubble size and phase velocities. However, everyinstrument has advantages and disadvantages in theircost, intrusiveness and resolution (Da Silva, 2008).There is no a cheap non-intrusive multiphase measuringinstrument giving the best resolution (Sharaf et al.,2011). Other predictive methods are the empiricaland semi-empirical correlations. Woldesemayat andGhajar (2008) listed and compared 68 void fractioncorrelations. Nevertheless, all these correlations wereformulated for speci c ow patterns, inclinations andoperating conditions. As a consequence, the two-phaseow models present incorrect predictions when theyare extrapolated. Finally, Computational Fluid Dynamic(CFD) is a useful technique to predict the two-phaseow behavior under any condition.The CFD (model) is capable of simulating thetwo-phase ow by using different physical models.CT&F - Ciencia, Tecnología y Futuro - Vol. 7 Num. 1Dec. 2017Wachem & Almstedt (2003) conducted a review of themathematical formulation for CFD models to predictthe behavior of the fluid-fluid flow and solid-fluidow. For the liquid-gas two-phase ow, researchesmainly used the Eulerian model (Krishna, Urseanu, vanBaten & Ellenberger, 1999; Ahmai & Al-Makky, 2014;Shang, 2015) or the Volume of Fluid (VOF) modelwhich is an Eulerian approach (Anglart & Podowski,2001; Fang, David, Rogacs & Goodson, 2010;Abdulkadir, 2011). Additionally, vertical ows havebeen analyzed using both CFD models (Abdulkadir,2011; Shang, 2015). Nevertheless, these researchesdid not stablish a selection criterion for both models.This study demonstrates the differences between theEulerian model and the VOF model for the two-phaseow assessment in vertical pipes. Models comparisonwill analyze accuracy, distinguishable phases andcomputational performance. Finally, it proposes aninnovative criteria for the selection of the multiphaseow model on CFD simulations.2. THEORETICAL FRAMEThe analyses of the CFD results take into accountthe hydrodynamic of the two-phase ow. The previousbehavior is called the flow patterns. This sectionexplains the possible ow patterns that are acquired in avertical pipe con guration at different phase velocities.Furthermore, the analysis is easier if Eulerian and VOFmodels differences are understood, as shown in themathematical formulation for each model.Flow patternsThe phase con gurations in vertical pipes are: bubblyow, slug ow, churn ow, annular ow and mist ow.Previously these are listed from low velocity to highvelocity. Moreover, an increase in the gas ow is oneof the ways that transitions between patterns occur. Byincreasing gas velocity in a bubbly ow, small bubblescoalesce to form the Taylor bubbles in slug ow. Churnow is an instable slug ow resulting from raisingthe gas velocity. Annular ow appears when gas owincreases, creating an interface stress larger than theeffects of gravity. As a consequence, liquid phase isthrown out of the center of the pipe (Thome, 2004).The ow pattern appearances are shown in Figure 1. Amist ow has the same con guration as a bubbly owexcept that their phases are inverted (Abdulkadir, 2011).75

ESTEBANUERRERO et al.constant and uniform in the whole pipe. Hence, Eulerianand VOF models only consider mass and momentumtransfers. The mathematical formulation for both physicmodels are detailed in this section.Eulerian modelThis method analyzes each phase using one equationfor each transport phenomenon. Equations (1) and (2)show the conservation of mass and momentum for phasei (Siemens, 2014).aca BuFigure 1. Flo attern in ertical i e .ly & mi t lo . Slug lo . c C urn lo . Annular lo .Source Bratlan , 2010 .Transport mechanisms are different in pipes withdiameters longer than 50 mm. Consequently, differentflow regimes appear (Sharaf & Luna-Ortiz, 2014).Hence, the pipe diameters modeled in this study areabout 50 mm. Furthermore, a ow pattern map forupward ow in a 50 mm diameter tube is used to predictow patterns (Hewitt, Delhaye & Zuber, 1986). Figure2 shows the map mentioned before.Bu10ul m/s1.0IlycaSlug or c urnIII0.1SlugIIe0.011000.1 (α ρ t i i l.(αi ρi l l1αi P αi ρi gαi (τi τit Mi2Additionally, the equation (3) must be achieved. MiFor the previous equations α is the void fraction,u is the super cial velocity, g is the gravity, P is thepressure, τ is the molecular stress, τt is the turbulentstress, ρ is the density and Mi represents the momentumtransfer in the interface. Furthermore, Eulerian modelrequires specifying the bubble s gas size. Therefore, thediscontinuous phase solution is an agglomerate of thesebubbles (Siemens, 2014).D0As a difference, this method analyzes all phasesusing a unique equation for each transport phenomenon.Equations (4) and (5) show the conservation of mass andmomentum respectively (Abdulkadir, 2011). t00.(ρ 42001.0ug m/s10.0100Figure 2. E erimental con ition lotte on He itt et al.1lo attern ma .Mathematical modelsThe gas-liquid two-phase ow involves transport ofmomentum, mass and heat. Nevertheless, heat transferis omitted, setting the assumption that temperature is76.(αi ρi lVOF modelAnnularIVE (α ρi i t (ρ t.(ρ P ρg (τ τtDensity and viscosity are calculated as a function ofthe volume fraction, as shown in the Equations (6) and(7), respectively.ρ i ρiαiμ i μiαiCT&F - Ciencia, Tecnología y Futuro - Vol. 7 Num. 1Dec. 2017

COMPARISON BETWEEN EULERIAN AND VOF MODELS FOR TWO-PHASE FLOW ASSESSMENT IN VERTICAL PIPESThe VOF model adds an additional equation solvingthe interfaces. It uses a continuity equation as a functionof the volume fractions as shown in the Equation (8).Consequently, this method does not require specifyingthe bubble gas size (Abdulkadir, 2011). αi t3. METHODOLOGYThis section describes the modeling study procedure.First, the test matrix and facilities geometries arepresented. Second, it explains the mesh generation andselection criterion. Finally, the time-step is selected bythe Courant-Friedrich-Lévy condition (CFL criterion). (αiDifferences between both models enable simulationswith different accuracy, distinguishable phases andcomputational performance. Therefore, a methodologyis established to study this problem.Test matrixThe CFD models performance in the two-phaseflow assessment were validated by experimentalresults. Data was obtained by different authors: Sunet al. (2004), Krepper, Lucas & Prasser (2005) andWestende (2008). Experiments were replicated usingthe CFD software STAR-CCM v9.02 from Siemens.Operating conditions and facilities geometries aredescribed in Table 1, where ui is the super cial velocityof phase i, z is the pipe height and z/D describes themeasurement tool location in the pipe. Each studiedcase was developed at atmospheric pressure.Turbulence modelThe gas-liquid two-phase flow has a turbulentdynamic which has to be taking account in the CFDmodels. In this research, the k-ε turbulence modelwas used to close the consecutive equations for bothmodels. Equations (9) and (10) show the PDE equationsdescribing this model (Ratkovich, Majumder & Bentzen,2013).(ρuj k j kt k j σk jρuj ε j t ε j σε j(t( uj ui xi xjFigure 2 shows the experimental conditions plottedon Hewitt et al. (1986) ow pattern map. The study caseslocation on Figure 2 predicted that the experimentaldata is the bubbly ow and the annular ow. Therefore,this project studied the two-phase ow with low andhigh void fractions. The CFD prediction is used as thevariable average, as the solution obtains a steady signal. uj -ρε xi( uC1 t ε j k j ij εC2 ρεkjj1The new two variables correspond to the turbulentkinetic energy (k) and the dissipation rate (ε). Theconstants values of σε, σk, C1 and C2 are 1.2, 1.0, 1.44and 1.9, respectively. Finally, the turbulence effect on theviscosity (turbulent viscosity, μt ) has to be involved inthe conservative equations using the effective viscosity(μe f f ) as shown in the equation (11).ueffuut11Table 1.aeulA0. 1 0BMesh generationThe CFD solution method requires a grid to solvethe partial differential equations of both models. Meshdimensions and arrangement may create a variety ofgrids for the same geometry. However, the solutionconvergence, accuracy and velocity depend upon themesh quality. Hernandez, Abdulkadir & Azzopardi.ug0eometrie an o erating con itioner0.010. 11C1.00000.2200D1.00000.0E0.012.200F0.0 1121.200CT&F - Ciencia, Tecnología y Futuro - Vol. 7 Num. 10Dec. 2017100uria e ere gSun et al.2000.0 0. 1re0.0 12.000.0 00.00er et al.200We ten e20077

ESTEBAN(2010) determined that the best mesh distribution forpipes is the orthogonal grid (also known as butter yshape gird). Figure 3 illustrates the grid distributionmentioned before.The grid presented in Figure 3 was associated withUERRERO et al.the CFL criterion which uses the Courant number. Themathematical representation of this number is describedin Equation (12).Where C is the Courant number ( 0.25), Δt is theuG t xC12time-step and Δx is the mesh cell size in direction of themaximum uid velocity component. The velocity uG iscalculated by the Drift-Flux model (Ujang et al., 2008)described in Equation (13).Where g is gravity, Res is the Reynolds number for0.0 12 mDMT modelFa 2 Ra1( 1.uG.1 1 e Re2.s(uM.35 gD1the liquid phase and D is the pipe diameter. Based onthe previous equations and the experiments description,a correct time-step is calculated to achieve a stablesimulation.three boundary conditions. The inlet and outlet facewere modeled with a velocity inlet and outlet pressureconditions, respectively. The surrounding face useda wall boundary condition. In addition, the meshdistribution was tested using a grid independence testto remove any mesh dependency in the system solution.Two selection criteria were established in the gridindependence test: resulting in accuracy and simulationtime. The experiment case D was simulated with fourgrids that contained 43 400, 228 780, 312 800 and 415140 mesh cells. As Eulerian and VOF models havea different mathematical formulation, previous testswere carried for each model to have the correct griddistribution for both models.Stability criterionUnsteady simulation was used to model the twophase ow dynamics. Consequently, the model stabilitydepends strongly upon the time-step established.Convergence problems are present when the time-stepis larger than velocity magnitude. The previous situationprovokes the ow going through a large quantity of cellswithout solving intermediate points. As a consequencethe CFD software brings up values to the intermediatepoints without solving the next interactions, in most ofcases creating a diverge system (Abdulkadir, 2011). Dueto the previous problem, the time-step is selected by784. RESULTS AND ANALYSISThis section describes the results in two parts.The rst section exposes the mesh independence testsresults and describes the grid selected. The second partdescribes the two CFD models performance.Geometry meshingThe simulation of the case D experiment was usedto carry out the mesh independence test. Krepper etal. (2005) measured the void fraction using a sensorplaced at z/D 60 with a ow inlet of ug 0.34 m/s andul 1.00 m/s. The average void fraction was 0.2618 with astandard deviation of 10%. Results obtained by the VOFmodel and the Eulerian model are shown in Figure 4The VOF model in Figure 4 establishes that increasing000ErrorFigure 3. Ort ogonal Butter ly gri0201000022 7 0MeEulerFigure 4. Me12 001 1 0CellVOFin e en ence te t E erimental an CFD re ultcom ari onCT&F - Ciencia, Tecnología y Futuro - Vol. 7 Num. 1Dec. 2017

COMPARISON BETWEEN EULERIAN AND VOF MODELS FOR TWO-PHASE FLOW ASSESSMENT IN VERTICAL PIPESthe Eulerian model is capable to predict the variablevalues in 40 000 inner interactions. However, this newmagnitude of interactions also requires more simulationtime than the VOF model.Case studies1 01 01201000Timethe mesh cells number in the grid will decrease the errorbetween the simulation and the experimental results.When considering the first selection criterion thatstandard deviation is 10 % for the experimental result,only the grid with 415 140 mesh cells could modelthe system correctly. On the other hand, the Eulerianmodel results demonstrate that resulted accuracy is notmodi ed by the number of mesh cells. Furthermore,these results show that simulations with Eulerian modelobtain an error equal to the standard deviation of theexperimental results.The second selection criterion for the grid is thesimulation time. This parameter was analyzed using aone-node of the processor of an Intel core-i5 computerwith 6 GB of memory ram. The study s results are shownin Figure 5. It is evident that both models require morecomputer time if the number of mesh cells increase.Considering the previous results, the grid selected forthe Eulerian model is the mesh with 43 400 cells, asit reduces the simulation time without any effect inthe accuracy of the results. On the contrary, the gridselected for the VOF model is the mesh with 41 5140cells guaranteeing the accuracy of good results despitehigher simulation time.The simulation time spent by the Eulerian model andthe VOF model is compared in Figure 5. The simulationstudied requires 62 000 inner interactions to completethe physical time established by the problem. This testproved that the Eulerian model always requires moresimulation time than the VOF model. The reason forthe previous result is that Eulerian model has moreequations to solve than the VOF model. Furthermore,002000022 7 0MeEuler 2000 iterFigure 5. Me12 001 1 0CellVOF 2000 iterEuler 0000 iterin e en ence te t Simulation timeThe two-phase ow experiments described in Table1 were simulated using the Eulerian model and the VOFmodel. Table 2 shows the results for cases A, B, C, andD in which the variable analyzed is the void fraction.The cases E and F analyzed the total gas velocityand their results are shown in Table 2. Additionally,these tables show the experiment results obtainedby the authors and the standard deviation of theirexperimentation. The simulation results demonstratethat the Eulerian model and the VOF model can describecorrectly the two-phase ow with low void fractions.Table 2. Re ult o ca e A, B, C an D u ing Eulerian mo el an VOF mo elaeαeeri e alaaruleriae ia iαrr rF0.00.012. 10.11.770.0 220.10.10111. 2C0.1. 20.11 . 10.11.D0.2 20.210. 70.2 012.0uG,CFDrr ruG,CFDrr rαeeri e alaare ia i.2αB2.70.0rr rAae2 . 1FFE17.0.7212.202 .12.222 .2F2 .0 1.21.201 .7021.1 .10CT&F - Ciencia, Tecnología y Futuro - Vol. 7 Num. 1Dec. 2017079

ESTEBANUERRERO et al.This fact is corroborated by the CFD results of casesA, B, C and D which are inside of the experimentedstandard deviations. On the contrary, both modelsshowed errors higher than the standard deviation whensimulating ows with higher void fractions.0.0.0.0.Figure 6 shows the void fractions prediction ofEulerian and VOF models for cases A, B, C and D. Thecase C result for the VOF model shows an error higherthan 30%. Considering void fraction magnitude, theprevious error is strongly signi cant. Therefore, thetwo-phase ow dynamics affects the accuracy of theVOF model. The best model selection criterion is therelative error which is calculated by the Equation (14).By modeling the low void fraction ow, the Eulerianmodel shows an error (13.86 %) smaller than the VOFmodel (19.04 %). Additionally, both models obtainthe same error ( 23 %) in the prediction of high voidfraction ow.Total Error1 NN i1CFDie erimentalie erimentali114 CFD0.0.20.20.10.10.00.000.00.1Eulerian0.10.2 eVOF0.200.0.- 0Figure 6. VOF mo el an Eulerian mo el re iction orca e A, B, C an DThe physical models differ in their mathematicalformulation as it was explained in the theoreticalbackground. This difference causes a distinct solutionappearance for both models in spite of the similar variable1.00000. 00000. 00000. 00000.200000.00000ace80ceEulerian Mo elVOF Mo elFigure 7. Voiaraction or t e ca e tu iey VOF mo el an Eulerian mo el 1.7 m oi eCT&F - Ciencia, Tecnología y Futuro - Vol. 7 Num. 1Dec. 2017

COMPARISON BETWEEN EULERIAN AND VOF MODELS FOR TWO-PHASE FLOW ASSESSMENT IN VERTICAL PIPESvalues that they obtained in the system s solution. TheVOF model details better the bubbles in the two-phaseow than the Eulerian model, as shown in Figure 7. Asan explanation, the VOF model solves the interface bythe continuity of the equation as a function of the volumefraction, Equation (9), differentiating phase variables asnone of the other equations distinguish phases. On thecontrary, the Eulerian model does not solve the interfacebetween liquid and gas phases. As a consequence, eachcell has an average value for each variable. Hence, theEulerian model solutions have a uniform color for thevoid fraction parameter. Moreover, Figure 7 shows thatthe VOF model is the correct physical model predictingthe ow pattern.The simulation results have a correct physicalmeaning considering that the case studies are organized inan ascendant manner according to the void fraction. Theprevious fact is corroborated in Figure 7. Additionally,as it was predicted in Figure 2, Figure 9 shows that casesA, B, C, and D have a bubbly ow as the ow pattern,and cases E and F an annular pattern. However, the VOFmodel shows problems when modelling the liquid lmbetween the wall and gas ows as caused by the meshdistribution. It is required to develop a more nenessmesh near the pipe wall to obtain this phenomenon.5. CONCLUSIONS CFD is a method capable to predict the dynamics ofthe gas-liquid two-phase ow. This project conducteda comparison between two CFD models in an upwardow. The methods studied are the Eulerian and VOFmodels. The first part evaluated the grid-modelrelations. The results demonstrated that the Eulerianmodel performance to predict the void fraction isirrelevant to the number of mesh cells in the grid.Moreover, the results exposed that Eulerian modelrequires more simulation time than the VOF modelusing the same grid. Nonetheless, the Eulerian modelwould spent less time if a grid with a low number ofmesh cells is used, due to the mesh independency.The second part assessed the model prediction of thetwo-phase ow properties. In the bubbly ow, theEulerian model is more accurate than VOF model bya difference of 5% in the void fraction prediction. Onthe other hand, both models showed problems whensimulating the annular ow. Models accuracy may beCT&F - Ciencia, Tecnología y Futuro - Vol. 7 Num. 1Dec. 2017increased by coupling new the CFD models. Oppositeto the Eulerian model, the VOF model is capableof distinguishing the discontinuous and continuousphases in the solution appearance.ACKNOWLEDGEMENTSWe would like to express our sincere gratitude toSiemens for all questions solved that supported therelated research.REFERENCESAbdulkadir, M. (2011). Experimental and computational uiddynamics (CFD) studies of gas-liquid ow in bends. PhDThesis. University of Nottingham, Nottingham, England.Ahmai, S. & Al-Makky A. (2014). Simulation of two phaseow in elbow with problem solving. International Journalof Modern Physics C.Anglart, H. & Podowski, M. (2001). Mechanisticmultidimensional modeling of slug ow- 4th InternationalConference on Multiphase Flow.Bratland, O. (2010). Pipe ow 2. Multi-phase ow assurance.Chonburi, Tailandia: Dr. Ove Bratland Flow AssuranceConsulting.Siemens. (2014). Documentation for STAR-CCM . Siemens.Da Silva, M. (2008). Impedance sensors for fast multiphaseow measurement and imaging. PhD Thesis. TechnischenUniversität Dresden.Fang, C., David, M., Rogacs, A. & Goodson, K. (2010). Volumeof uid simulation of the boiling two-phase ow in a vaporventing microchannel. Frontiers in Heat and Mass Transfer.Hernandez, V., Abdulkadir, M. & Azzopardi, B.J. (2010). Gridgeneration issues in the CFD modeling of the two-phaseow in a pipe. Journal of Computational Multiphase Flows,3(1), 13-26.Hewitt, G.F., Delhaye, J.M. & Zuber, N. (1986). Multiphasescience and technology (Volume 2). Springer-Verlag,Germany: Berlin.81

ESTEBANIshii, M. & Hibiki, T. (2011). Thermo- uid dynamics of twophase ow (2nd Ed.). West Lafayette, U.S.A.: Springer.Krepper, E., Lucas, D. & Prasser, H. (2005). On the modelingof bubbly ow in vertical pipes. Nuclear engineering anddesign, 235, 597-611.Krishna, R., Urseanu, M., van Baten, J. & Ellenberger, J. (1999).In uence of scale on the hydrodynamics of bubble columnsoperating in the churn-turbulent regime: experiments vs.Eulerian simulations. Chemical Engineering Science. 54,4903-4911.Ratkovich, N., Majumder, S.K. and Bentzen, T.R. (2013).Empirical correlations and CFD siulations of vertical twophase gas-liquid (Newtonian and non-Newtonian) slugow compared against experimental data of void fraction.Chemical Engineering Research and Design. 91, 988-998.Shang, Z. (2015). A novel drag force coef cient model forgas-water two-phase ows under different ow patterns.Nuclear and Engineering and Design. 288, 208-219Sharaf, S., Da Silva, M., Hampel, U., Zippe, C., Beyer, M. &Azzopardi, BJ. (2011). Comparison between wire meshsensor and gamma densitometry void measurements in twophase ows. Meas. Sci. Technol. 22(10).UERRERO et al.Van Der Meulen, G.P. (2012). Churn-annular gas-liquid owsin large diameter vertical pipes. PhD Thesis. University ofNottingham, Nottingham, England.Wachem, B.G.M. & Almstedt, A.E. (2003). Methods ormultiphase computational fluid dynamics. ChemicalEngineering Journal. 96, 81-98.Westende, J.M.C. (2008). Droplets in annular-dispersedgas-liquid pipe- ows. PhD Thesis. Delft University oftechnology, Netherlands.Woldesemayat, M. & Ghajar, A. (2007). Comparison of voidfraction correlations for different ow patterns in horizontaland upward inclined pipes. International Journal ofMultiphase Flow, 33, 347-370.Zhang, H.Q., Wang, Q., Sarica, C. & Brill, J. (2003). Uni edmodel for the gas-liquid pipe ow via slug dynamics-Part1: Model development. Journal of Energy ResourcesTechnology, 125, 266-273.AUTHORSEsteban GuerreroAf liation: Universidad de los Andes, Bogotá D.C., Colombiae-mail: e.guerrero911@uniandes.edu.coSharaf, S. & Luna-Ortiz, E. (2014). Comparison between thetwo-phase models and wire mesh sensor measurementsin medium and large diameter pipes. 14th AIChE SpringMeeting. New Orleans, U.S.A.Felipe MuñozAf liation: Universidad de los Andes, Bogotá D.C., Colombiae-mail: fmunoz@uniandes.edu.coSun, X., Paranjape, S., Kim, S., Ozar, B. & Ishii, M. (2004).Liquid velocity in upward and downward air-water ows.Annals of Nuclear Energy, 31, 357-373.Nicolás RatkovichAf liation: Universidad de los Andes, Bogotá D.C., Colombia.e-mail: n.rios262@uniandes.edu.coThome, J.R. (2004). Engineering Data book III. LausanneSwitzerland: Wolverine Tube, Inc.Tkaczyk, P. (2011). CFD simulation of annular ows throughbends. PhD Thesis. University of Nottingham, Nottingham,England.Ujang, P.M., Pan, L., Man eld, P.D., Lawrence, C.J. & Hewitt,G.F. (2008). Prediction of the translational velocity ofliquid slugs in gas-liquid slug ow using computationaluid dynamics. Multiphase Science and Technology, 20(1),25-79.82CT&F - Ciencia, Tecnología y Futuro - Vol. 7 Num. 1Dec. 2017

COMPARISON BETWEEN EULERIAN AND VOF MODELS FOR TWO-PHASE FLOW ASSESSMENT IN VERTICAL PIPESNOMENCLATURECT&F - Ciencia, Tecnología y Futuro - Vol. 7 Num. 1CCourant Number [-]DPipe diameter [m]gGravity [ 9.81 m/s2]i,jPhases index [-]PPressure [Pa]ReReynolds number [-]tTime [s]uMMixture velocity [m/s]uSuper cial velocity [m/s]uGTotal gas velocity [m/s]αVoid fraction [-]ρDensity [kg/m3]τMolecular stress [Pa]τtTurbulent stress [Pa]Dec. 201783

(CFD) is a useful technique to predict the two-phase ow behavior under any condition. The CFD (model) is capable of simulating the two-phase Àow by using different physical models. Wachem & Almstedt (2003) conducted a review of the mathematical formulation for CFD models to predict the behavior of the fluid-fluid flow and solid-fluid Àow.

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