Cai, X.

Deutschmann, O.

Marschall, H.

Wörner, Martin

English

KITopen

KIT – University of the State of Baden-Wuerttemberg and National Research Center of the Helmholtz Association2nd International Symposium on Multiscale Multiphase Process Engineering, 24 – 27 Sept. 2014, Hamburg, Germanywww.kit.eduA Phase Field Method with Adaptive Mesh Refinement for Numerical Simulation of 3D Wetting Processes with OpenFOAM®X. Cai1, H. Marschall2, M. Wörner1, O. Deutschmann11 Karlsruhe Institute of Technology, Institute of Catalysis Research and Technology, Germany2 Technische Universität Darmstadt, Center of Smart Interfaces, Germany2AgendaMotivation Numerical method Phase field method coupled with Navier-StokesImplementation in OpenFOAM®Test-cases Droplet spreading on flat surfaceDroplet sliding on inclined surfaceAnisotropic wetting on chemically-heterogeneous surfaceTwo phase flows in sponge structureOngoing work and outlook X. Cai, H. Marschall, M. Wörner, O. Deutschmann, 2nd International Symposium on Multiscale Multiphase Process Engineering (MMPE)26. Sept. 20143Motivationoil recovery from porous structureinsecticides sprayink-jet printingcoatinglubricationsolid sponge chemical reactor   droplet wetting / spreadingX. Cai, H. Marschall, M. Wörner, O. Deutschmann, MMPE226. Sept. 20144Cahn-Hilliard eq. coupled to momentum eq.surface tension termlinear momentum, viscous stress and buoyancy terms mixture properties: density and viscosityPhase Field Methods (only Cahn-Hilliard)Phase field (C ) as phase indictordifference of volumetric phase fractionsCahn-Hilliard eq. for phase field advectionresolve paradox at moving contact line C23 2 21CCtC CPeC Cnu2 2,3ULPeLCnκ : mobility parameterε : mean-field thicknessλ : mixing energy parameterL : reference lengthU : reference velocity2( )CCtu22( 1)( 1)C C C C• Non-dimensional form:X. Cai, H. Marschall, M. Wörner, O. Deutschmann, 2nd International Symposium on Multiscale Multiphase Process Engineering (MMPE)26. Sept. 2014SolidGas (C =-1)Liquid (C =1)2s2 cosˆ ( 1)2eC CCnn• Boundary condition:5Implementation in OpenFOAM®interDyMFoam as starting pointPhase field advection equationCahn-Hilliard: mobility term is a 4th order derivative (for now treated in segregated manner with time-step sub-cycling)Allen-Cahn: Lagrange multiplier to enforce phase volume conservation Relative density flux term in momentum eq. due to diffusion of components   (Ding et al. 2007, Abels et al. 2012)                                                                          Consistent use of conservative volumetric fluxes and central for volume conservationSurface tension in energy formulation As surface tension energy densityExplicit source term transferred to pressure equation (Rhie-Chow interpolation practice)1. Solve transport equation for phase field advection2. Update chemical potential3. Calculate surface tension, buoyancy & mixture ρ, μ4. Solve N-S eqs. for velocitywhile (runTime.run()){}Pseudo code:X. Cai, H. Marschall, M. Wörner, O. Deutschmann, 2nd International Symposium on Multiscale Multiphase Process Engineering (MMPE)26. Sept. 201462D Simulation of Droplet SpreadingEötvös number (Eo):• Eo << 1capillarity-driven regime• Eo >> 1gravity-driven regime• Eo ≈ 1transitional regimeAnalytical capillarity reg. (*)Analytical gravity reg.(**)Simulation resultsEo = 0.1 Eo = 1 Eo = 10Eo = 0.01EoH’(***)(*)Chen et al. 2009  (**)Dupont et al. 2007     (***) H’ : normalized height of droplet θe = 60°26. Sept. 20142( )a bgDEoX. Cai, H. Marschall, M. Wörner, O. Deutschmann, 2nd International Symposium on Multiscale Multiphase Process Engineering (MMPE)7Droplet Spreading on Flat Surfacee = 45°X. Cai, H. Marschall, M. Wörner, O. Deutschmann, 2nd International Symposium on Multiscale Multiphase Process Engineering (MMPE)26. Sept. 2014Experiment by Zosel 1993droplet of PIB solutionon smooth flat PTFE surfaceStatic contact angle θe  = 58°R0 = 1.2 ~ 1.5 mm Simulation setupEötvös no. = 0density ratio = 1viscosity ratio = 0.05Quarter symmetryAdaptive Mesh Refinementtwo level refinementat each time-step 8Droplet Spreading on Flat SurfaceX. Cai, H. Marschall, M. Wörner, O. Deutschmann, 2nd International Symposium on Multiscale Multiphase Process Engineering (MMPE)26. Sept. 2014Zosel, A., Studies of the Wetting Kinetics of Liquid-Drops on Solid-Surfaces. Colloid Polym Sci, 1993. 271(7): p. 680-687.2 23LUPe9Droplet Sliding on Inclined Surfacee = 45°X. Cai, H. Marschall, M. Wörner, O. Deutschmann, 2nd International Symposium on Multiscale Multiphase Process Engineering (MMPE)26. Sept. 2014Experiment by Le Grand et al. 2005droplet of silicon oilinclined surface (7° < α < 52° )θe  = 52°Droplet volume = 6 mm3Half symmetryAdaptive Mesh Refinementtwo level refinementat each time-step N. Le Grand, A. Daerr, L. Limat, Shape and motion of drops sliding down an inclined plane, J. Fluid Mech. 541 (1) (2005) 293.10Droplet Sliding on Inclined Surfacee = 45°X. Cai, H. Marschall, M. Wörner, O. Deutschmann, 2nd International Symposium on Multiscale Multiphase Process Engineering (MMPE)26. Sept. 2014Dimensionless parameters• U : sliding velocity• α :  inclination angleMismatch btw. physical interface thickness and one used in simulation   → simulated U*  >> exp. U2/3( )sinU gCa Bo V11Droplet Sliding on Inclined Surfacee = 45°X. Cai, H. Marschall, M. Wörner, O. Deutschmann, 2nd International Symposium on Multiscale Multiphase Process Engineering (MMPE)26. Sept. 2014Dimensionless parameters• U : sliding velocity• α :  inclination angleMismatch btw. physical interface thickness and one used in simulation   → simulated U*  >> exp. UCombining Kim et al. 2002 and Yue et al. 2010, we derive:2/3( )sinU gCa Bo Vln( / *)(0.3,0.4)* ln( / )bbRUSU R• Rb : droplet radius• λ : physical slip length• λ* : numerical slip length12Droplet Sliding on Inclined Surfacee = 45°X. Cai, H. Marschall, M. Wörner, O. Deutschmann, 2nd International Symposium on Multiscale Multiphase Process Engineering (MMPE)26. Sept. 2014Dimensionless parameters• U : sliding velocity• α :  inclination angleMismatch btw. physical interface thickness and one used in simulation   → simulated U*  >> exp. UCombining Kim et al. 2002 and Yue et al. 2010, we derive:2/3( )sinU gCa Bo Vln( / *)(0.3,0.4)* ln( / )bbRUSU R• Validation of our derived S• Currently the code has not considered the pinning effect (i.e. contact angle hysteresis) • Rb : droplet radius• λ : physical slip length• λ* : numerical slip length13Droplet Sliding on Inclined Surfacee = 45°X. Cai, H. Marschall, M. Wörner, O. Deutschmann, 2nd International Symposium on Multiscale Multiphase Process Engineering (MMPE)26. Sept. 2014Dimensionless parameters• U : sliding velocity• α :  inclination angleMismatch btw. physical interface thickness and one used in simulation   → simulated U*  >> exp. UCombining Kim et al. 2002 and Yue et al. 2010, we derive:2/3( )sinU gCa Bo Vln( / *)(0.3,0.4)* ln( / )bbRUSU R• Rb : droplet radius• λ : physical slip length• λ* : numerical slip length• Boc  is constant for pining effect• αc is critical inclination angle 2/3( )sinc cgBo V14Droplet Sliding on Inclined Surfacee = 45°X. Cai, H. Marschall, M. Wörner, O. Deutschmann, 2nd International Symposium on Multiscale Multiphase Process Engineering (MMPE)26. Sept. 2014Scaling factor S  is related to mobility factor κSimulation results using different S (resp. different κ ) collapse into a single curveVia S,  numerical results are independent of κProvided physical slip length is known, phase field simulation is a predictive tool!15Spreading on Chemically Heterogeneous Surfacee = 45°X. Cai, H. Marschall, M. Wörner, O. Deutschmann, 2nd International Symposium on Multiscale Multiphase Process Engineering (MMPE)26. Sept. 2014Experiment by Jansen et al. 2013Alternating strips made of:SiO2, hydrophilic,                       θe  = 40° (red) PFDTS, hydrophobic,                θe  = 106° (yellow) Anisotropic wettingdroplet elongated in direction parallel to stripsStick-slip motionH.P. Jansen et al., Lattice Boltzmann modeling of directional wetting: comparing simulations to experiments, Phys. Rev. E 88 (2013) 013008–013017.16Bottom Viewe = 45°X. Cai, H. Marschall, M. Wörner, O. Deutschmann, 2nd International Symposium on Multiscale Multiphase Process Engineering (MMPE)26. Sept. 2014ExperimentJansen et al. 2013Lattice-Boltzmann simulation Jansen et al. 2013Our simulation(four cells per strip)T = 20 T = 40 T = 100 T = 900Time17Wetting in Solid Sponge Structure e = 45°X. Cai, H. Marschall, M. Wörner, O. Deutschmann, 2nd International Symposium on Multiscale Multiphase Process Engineering (MMPE)26. Sept. 2014S. Meinicke (Institut für Thermische Verfahrenstechnik, KIT) provides the sponge geometrycalculations on exemplary sponge sample type: Al2O3porosity = 80%20 pores per inch (ppi)→ investigations on further sponge types planned/projected/ongoingbased on MRI and (µ)CT scannings reconstruction of sponge structure in MATLAB produces STL file blockMesh + snappyHexMeshsolid sponge chemical reactor   geometry for CFD simulation   18First Results e = 45°X. Cai, H. Marschall, M. Wörner, O. Deutschmann, 2nd International Symposium on Multiscale Multiphase Process Engineering (MMPE)26. Sept. 2014Blue iso-surface     → interface btw. liquid and gas Pressure-driven (from left to right) 19First Results e = 45°X. Cai, H. Marschall, M. Wörner, O. Deutschmann, 2nd International Symposium on Multiscale Multiphase Process Engineering (MMPE)26. Sept. 2014Blue iso-surface     → interface btw. liquid and gas Pressure-driven (from left to right) 20Ongoing work – Numerical Method DevelopmentCurrent state: Novel top-level solver: phaseFieldFoam, supporting foam-typical algorithmic flexibility, e.g.rhoPhi = phaseField.correct(C, Phi);3 new model libraries(following common strategy design pattern; run-time selection via factory method)• diffuseInterfaceModelsAbstract base class for diffuse interface models.• diffuseInterfacePropertiesDiffuse interface mixture properties from phase transport properties.• phaseContactAngle (generalization of alphaContactAngle)Abstract base class for phaseContactAngle boundary conditions for both the volume-of-fluid and the phase-field approach.Static and dynamic contact angle models, e.g. FAM-based impl. of wall energy relaxation.Bunch of utilities for pre- and post processing, e.g. generic smoothField utility.Further steps: Implementation of so-called compensation scheme for wall energy relaxation model.Implementation of block-coupled solution approach to phase field transport(simultaneous solution of decomposed Cahn-Hilliard equation).X. Cai, H. Marschall, M. Wörner, O. Deutschmann, 2nd International Symposium on Multiscale Multiphase Process Engineering (MMPE)26. Sept. 201421Pinning effect of droplet on inclined surfaceDroplet wetting on topologically heterogeneous (rough) surfaceTwo-phase flows in sponge structureProvide closure for macroscopic modelCoupling hydrodynamics with mass transfer and chemical kinetics Next Steps towards ApplicationX. Cai, H. Marschall, M. Wörner, O. Deutschmann, 2nd International Symposium on Multiscale Multiphase Process Engineering (MMPE)26. Sept. 201422Further OutlooksRelease of the solver phaseFieldFoam to OpenFOAM-extend under GNU General Public LicensephaseFieldFoam advantageously applied for a wide range of multi-scale multi-phase flows:Droplet/bubble breakup/coalescenceViscoelastic two-phase flow… …Phase field simulation in sponge structure can also be applied in:Fuel cellsOil recoveryHeat exchanger… …X. Cai, H. Marschall, M. Wörner, O. Deutschmann, 2nd International Symposium on Multiscale Multiphase Process Engineering (MMPE)26. Sept. 201423(*) Website: https://www.hzdr.de/db/Cms?pNid=2972AcknowledgementFunded by Helmholtz Energy Alliance “Energy-efficient chemical multiphase processes” (HA-E-0004)(*)Partners:X. Cai, H. Marschall, M. Wörner, O. Deutschmann, 2nd International Symposium on Multiscale Multiphase Process Engineering (MMPE)26. Sept. 2014

A phase field method with adaptive mesh refinement for numerical simulation of 3D wetting processes with OpenFoam

https://publikationen.bibliothek.kit.edu/230096925/150923737

A phase field method with adaptive mesh refinement for numerical simulation of 3D wetting processes with OpenFoam

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