Bothe, D.

Falconi, C.

Lehrenfeld, C.

Marschall, H.

Meyer, C.

Reusken, A.

Schlüter, M.

Wörner, M.

Wörner, Martin

KITopen

KIT – Universität des Landes Baden-Württemberg undnationales Forschungszentrum in der Helmholtz-GemeinschaftJahrestreffen der ProcessNet Fachausschüsse CFD und Mehrphasenströmungen Lüneburg 2015 www.kit.eduAnalyse und Verständnis lokaler drei-dimensionaler Effekte bei der Taylor-Strömung in einem quadratischen Mini-KanalC. Falconi1#, C. Lehrenfeld2&, H. Marschall3, C. Meyer4, D. Bothe3, A. Reusken2, M. Schlüter4, M. Wörner1ProcessNet Fachausschusssitzung CFD und Mehrphasenströmungen19.-20. März 2015, Lüneburg1Karlsruher Institut für Technologie, 2RWTH Aachen, 3TU Darmstadt, 4TU Hamburg-Harburgaktuelle Adressen: # Automotive Simulation Center, Stuttgart; &Technische Universität WienJahrestreffen der ProcessNet Fachausschüsse CFD und Mehrphasenströmungen Lüneburg 20152OutlineIntroductionExperimentNumerical simulationsResultsDiscussionConclusions20.03.2015Jahrestreffen der ProcessNet Fachausschüsse CFD und Mehrphasenströmungen Lüneburg 20153Guiding measure Taylor flowTaylor flow in millimeter size channels is of practical technical relevance and of fundamental physical interestGoal: Provide detailed experimental data under well controlled conditions which allow for a quantitative validation of numerical methods and computer codesThree cases from two experimental groupsTBCC = Taylor Bubble Circular ChannelBoden et al. Exp Fluids 55 (2014) 1Aland et al. Int J Num Meth Fluids 73 (2013) 344 TBSC = Taylor Bubble Square ChannelBoden et al. Exp Fluids 55 (2014) 1Marschall et al. Comp Fluids 102 (2014) 336TFSC = Taylor Flow Square ChannelMeyer et al. Int J Multiph Flow 67 (2014) 140Falconi et al. Phys Fluids submitted20.03.2015Taylor bubble      Taylor flowHZDR(group Hampel)TUHH(group Schlüter)Jahrestreffen der ProcessNet Fachausschüsse CFD und Mehrphasenströmungen Lüneburg 20154Taylor flow experimentGeometry Square vertical mini-channel (2.1 mm side length)Flow direction Co-current upwardGas phase AirLiquid phase Water/glycerol mixtureGas volume fraction 0.370.02Bubble length 3.260.18 mmLiquid slug length 1.330.09 mmUnit cell length 4.590.27 mmBubble velocity 135.91.9 mm/sCapillary number 0.1                            Ca = UBµL/Reynolds number 7.0                            Re = LDhUB/µLMeasurements Velocity field in liquid slug and liquid film (µPIV)Estimation of bubble shape from µPIV observations20.03.2015This very regular Taylor flow is realized by a special injection valve combined with a compensation pipe for eliminating pressure fluctuationsMeyer, Hoffmann, Schlüter, Int J Multiph Flow 67 (2014) 140148Jahrestreffen der ProcessNet Fachausschüsse CFD und Mehrphasenströmungen Lüneburg 20155Experiment20.03.2015Meyer, Hoffmann, Schlüter, Int J Multiph Flow 67 (2014) 140148Refractive index matchingJahrestreffen der ProcessNet Fachausschüsse CFD und Mehrphasenströmungen Lüneburg 20156Equations and computer codes Single-field formulation for two immiscible Newtonian fluids with constant density, viscosity and surface tension (sharp interface limit)Three academic in-house codes for 3D interface capturing FS3D (ITLR Stuttgart, TU Darmstadt) Volume-of-Fluid method (PLIC geometrical reconstruction, split advection) Finite volume discretization on fixed staggered Cartesian gridAdvanced surface tension force model (balanced CSF)TURBIT-VOF (KIT) Similar to FS3D but un-split advection and less advanced surface tension model DROPS (RWTH Aachen)Level-set method with reinitializationFinite element method with adaptive multilevel mesh hierarchyLaplace Beltrami technique for surface tension, discontinuous pressure field20.03.2015Marschall et al. Computers & Fluids 102 (2014) 336352 T0, ( ) ( ) ( )t p                   fu u uu u u g nJahrestreffen der ProcessNet Fachausschüsse CFD und Mehrphasenströmungen Lüneburg 20157 20.03.2015Computational set-upFrom experimentSide length Dh = 2.076 mmUnit cell length LUC= 4.59 mmGas volume fraction  = 0.375Target value for simulationsExperimental bubble velocitySimulations are transient but only quasi-steady results are analyzed here Physical properties Liquid GasDensity [kg/m3] 1197.2 1.3Viscosity [kg/ms] 0.0481 210-5Surface tension [N/m] 0.0624Jahrestreffen der ProcessNet Fachausschüsse CFD und Mehrphasenströmungen Lüneburg 20158Grid and integral simulation resultsFS3D TUV DROPS DevC [%] Exp. DevE [%]Domain VUC / 4 VUC VUC / 8Grid* (for VUC) 6464128 100100220 6464128UB [mm/s] 135.9 135.9 135.0 0.4 135.91.9 0.2LB [mm] 3.355 3.328 3.329 0.5 3.260.18 2.4LS [mm] 1.235 1.262 1.261 1.4 1.330.09 5.8p/LUC [Pa] 117.8 119.2 121.2 1.5J [mm3/s] 377.2 391.6 382.6 2.020.03.2015J = total superficial velocity (volumetric flow rate of the two-phase flow) *Grid resolution corresponds to about 3 mesh cells per lateral film width (smallest length scale of the flow)1 3 mean meanC EmeanMaxDev , Devi iCFD CFD Exp CFDCFD Exp    Jahrestreffen der ProcessNet Fachausschüsse CFD und Mehrphasenströmungen Lüneburg 20159 20.03.2015Bubble shapeB B BS S S//z z Lz z LJahrestreffen der ProcessNet Fachausschüsse CFD und Mehrphasenströmungen Lüneburg 201510Cut zB/LB [-] FS3D TUV DROPS DevC [%] Exp. DevE [%]Bubble radius [µm] L 0.25 952 961 960 0.6 9468 1.20.5 918 925 922 0.4 9408 2.00.75 824 825 824 0.1 8478 2.7D 0.25 983 991 993 0.60.5 949 953 954 0.30.75 839 845 839 0.5Film thickness [µm] L 0.25 86 77 78 7.1 928 12.70.5 120 113 116 3.2 988 18.70.75 214 213 214 0.3 1919 11.9D 0.25 485 477 475 1.30.5 519 515 514 0.60.75 629 623 629 0.6Extreme value L zB/LB 0.198 0.173 0.194 1.5RB,max-L 959 973 967 0.8F,min-L 79 65 71 10.3D zB/LB 0.273 0.270 0.275 0.3RB,max-D 985 991 994 0.5F,min-D 483 477 474 1.120.03.2015Quantitative comparison of bubble shapeJahrestreffen der ProcessNet Fachausschüsse CFD und Mehrphasenströmungen Lüneburg 201511 20.03.2015Velocity profiles in liquid slugJahrestreffen der ProcessNet Fachausschüsse CFD und Mehrphasenströmungen Lüneburg 201512 20.03.2015Velocity profiles in bubble and film Jahrestreffen der ProcessNet Fachausschüsse CFD und Mehrphasenströmungen Lüneburg 201513 20.03.2015Quantitative comparison of velocity profileszS/LS [-] FS3D TUV DROPS DevC [%] Exp. DevE [%]Liquid slug [mm/s] 0.9 146.4 152.7 146.1 2.9 141.3 5.00.5 169.0 174.8 171.2 1.8 178.3 3.70.1 148.9 144.9 149.0 1.8 151.2 2.4zB/LB [-]Bubble [mm/s] 0.75 199.0 192.8 211.46 5.20.5 270.9 264.0 284.7 4.20.25 250.6 245.0 250.6 1.5Centerline axial velocityJahrestreffen der ProcessNet Fachausschüsse CFD und Mehrphasenströmungen Lüneburg 201514 20.03.2015Flow fieldStreamlines (moving ref. frame)Gas phaseOne main vortexTwo counter-rotating vortices at bubble nose and rearPositions of center of main vortex is different in lateral and diagonal cut  flow in bubble is three-dimensionalLiquid phaseRegion with circulation flow (channel center) and bypass flow (near wall) are separated by the dividing streamlineVertical velocity uz (fixed frame)Regions with negative velocity in rear part of the liquid film  local backflow(Results of FS3D)Jahrestreffen der ProcessNet Fachausschüsse CFD und Mehrphasenströmungen Lüneburg 201515 20.03.2015Local backflow in liquid filmIsosurface uz = - 0.016 m/s(FS3D) (TURBIT-VOF)Jahrestreffen der ProcessNet Fachausschüsse CFD und Mehrphasenströmungen Lüneburg 201516Local backflow in co-current flowLocal backflow results in a temporal inversion of the wall shear stress at a fixed position during passage of a Taylor bubbleImportant for various applications with Taylor flowHeat and mass transferCleaning of membranes for ultrafiltrationSynthesis of nanoparticlesBiological and medical applications with living cellsLiterature statusThe phenomenon of possible shear stress reversal is known for some time Local backflow in co-current Taylor flow has not been measured beforeIt has been found in computations for circular tubesS.P. Quan, Co-current flow effects on a rising Taylor bubble, IJMF 37 (2011) 888 Questions related to present results for square channelWhy differ axial locations with backflow in lateral film and corner region? Can we give criteria when this newly discovered phenomenon occurs?20.03.2015Jahrestreffen der ProcessNet Fachausschüsse CFD und Mehrphasenströmungen Lüneburg 201517Sufficient condition for backflowLiquid mass balance in moving frame of reference yields20.03.2015 L,mfr B F B B F B( ) ( ) ( )V J U A U z U A z   BzAF B B B( ) ( )A z A A z F B( )U zJBUJ  = total superficial velocity of the Taylor flowUF = mean axial velocityin liquid film at position zBB( )J U AF B F( )U U AJahrestreffen der ProcessNet Fachausschüsse CFD und Mehrphasenströmungen Lüneburg 201518Sufficient condition for backflowFrom liquid mass balance it follows For an axisymmetric bubble it isThis relation can be used to compute the mean velocity in the liquid film, UF, from the axial profile of the bubble diameter20.03.20152B BBhF B 2B B2h( )4( )( )14D zJ UDU zD zDB B BF BB B( )1( )( )1U A zU z J AA zJAB B B( ) 1U A zJ A backflow occurs whereJahrestreffen der ProcessNet Fachausschüsse CFD und Mehrphasenströmungen Lüneburg 201519 20.03.2015Evaluation from L/D bubble profilesL/D2B,F,Bh2B,2L/LhD/D414DJ UDDUDPredicted backflow regionsPredicted regions with backflow differ as observed L/D profiles differ bubble is not axisymmetric. Why?Jahrestreffen der ProcessNet Fachausschüsse CFD und Mehrphasenströmungen Lüneburg 201520Bubble aspect ratio20.03.2015B B/ 0.27z L B B/ 0.17z L Minimum diagonal film thicknessMinimum lateral film thicknessJahrestreffen der ProcessNet Fachausschüsse CFD und Mehrphasenströmungen Lüneburg 201521Pressure field20.03.2015(Results of TURBIT-VOF)Non-dimensional (periodic) pressure field in two horizontal cross-sections In front part of the bubble the pressure is higher in the lateral film than in the corner filmIn the rear part of the film it is oppositeJahrestreffen der ProcessNet Fachausschüsse CFD und Mehrphasenströmungen Lüneburg 201522Force balance normal to the interfaceLocal force balance normal to the interface in a horizontal cross-sectionNeglecting normal viscous stresses the pressure jump is locally balanced by capillary forcesFor the given azimuthal variation of pL this can only be achieved by a change of the local interface curvature This causes the deviation of the bubble shape from rotational symmetry20.03.2015     T T ˆ ˆ: 2L G L L L G G G L Lp p H            v v v v n n2G Lp p H  .const min max1 1 12 2B Lp pHR R       B .Gp p const Jahrestreffen der ProcessNet Fachausschüsse CFD und Mehrphasenströmungen Lüneburg 201523Refined liquid mass balance analysisSplitting the liquid flux into two parts through lateral and diagonal film We are interest in the position where the axial velocity in L/D film is minimal  derivative with respect to zB gives20.03.2015B F,L B B F,L B F,D B B F,D B( ) ( ) ( ) ( ) ( )J U A U z U A z U z U A z          B BF,L F,D F,D F,LF,L F,D B F,D B B F,L BB B B B( ) ( )U UU U A AA A U U z U U zz z z z                  F,D F,LFF,D B F,LB B BU UAA U Az z z    F F,L F,DA A A Jahrestreffen der ProcessNet Fachausschüsse CFD und Mehrphasenströmungen Lüneburg 201524 20.03.2015Refined liquid mass balance analysisThinnest lateral filmThinnest diagonal film  F,D F,LFF,D B F,LB B B00 0U UAA U Az z z     Region I >0 >0 >0Region II>0=0 <0>0>0>0?<0<0Region III <0 <0 <0FBAzF,LBUzF,DBUzIn the lower part of region II the derivatives have opposite signs so that the position of velocity minimum in the  L and D film differ  cf. local profiles of uzJahrestreffen der ProcessNet Fachausschüsse CFD und Mehrphasenströmungen Lüneburg 201525Approximate criteria for backflowBackflow occurs forCircular channelsCorrelation of Liu et al. (2005) or Abiev (2013) for UB/JCorrelation of Aussilious & Quere (2000) for F  AB/A Square channelsCorrelation of Liu et al. (2005) for UB/JCorrelation of Kreutzer et al. (2005) for DB, DL  AB/AIf the Taylor bubble is not axisymmetric then the local backflows in the lateral and diagonal film occur in different axial regionsTransition occurs at Ca  0.04 - 0.1 (for larger values bubble is axisymm.)20.03.2015B B111U AJ A Both ratios depend on the capillary numberB BU ACaJ A  Jahrestreffen der ProcessNet Fachausschüsse CFD und Mehrphasenströmungen Lüneburg 201526Conclusions and outlook20.03.2015Quantification of relative deviations between codesBubble diameter 0.6% Minimum liquid film thickness 10% (model for surface tension force )Centerline velocity liquid slug 3% ()Centerline velocity within bubble 5% Analysis of local backflow in rear part of the liquid filmTemporal reversal of wall shear stress during passage of a Taylor bubbleLocation of backflow region in lateral and diagonal film (square channel)For non-axisymmetric bubbles, the local backflow occurs at different axial positions in the lateral and corner filmReason: a cross-over of the diagonal/lateral bubble aspect ratioVariation of bubble aspect ratio has strong implications on local flow in rear filmApproximate criteria when phenomena may occur in practice OutlookInfluence of Ca and Re on size of backflow regionTrapezoidal and triangular channelsJahrestreffen der ProcessNet Fachausschüsse CFD und Mehrphasenströmungen Lüneburg 201527 20.03.2015Thank you for your attention!We gratefully acknowledge the funding by the DFG

Analyse und Verständnis lokaler drei-dimensionaler Effekte bei der Taylor-Strömung in einem quadratischen Mini-Kanal

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Analyse und Verständnis lokaler drei-dimensionaler Effekte bei der Taylor-Strömung in einem quadratischen Mini-Kanal

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