A sharp surface tension modeling method for two‐phase incompressible interfacial flows

A surface tension implementation algorithm for two-phase incompressible interfacial flows is presented in this study. The surface tension effect is treated as a jump condition at the interface and incorporated into the Navier-Stokes equation via a capillary pressure gradient. The interface is tracked by a coupled level set and volume-of-fluid (CLSVOF) method based on the finite-volume formulation on a fixed Eulerian grid. It has been shown in a stationary benchmark test the spurious currents are greatly reduced and the sharp pressure jump across the interface is well preserved. Numerical instabilities caused by the sharp treatment on a fixed grid are avoided. Several dynamic tests are performed to further validate the accuracy and versatility of the present method, the results of which are in good agreement with data reported in the literature.

[1]  W. Shyy,et al.  Assessment of volume of fluid and immersed boundary methods for droplet computations , 2004 .

[2]  R. Fedkiw,et al.  A Boundary Condition Capturing Method for Poisson's Equation on Irregular Domains , 2000 .

[3]  Ronald Fedkiw,et al.  A Boundary Condition Capturing Method for Multiphase Incompressible Flow , 2000, J. Sci. Comput..

[4]  D. J. Torres,et al.  On the theory and computation of surface tension: the elimination of parasitic currents through energy conservation in the second-gradient method , 2002 .

[5]  Brian T. Helenbrook,et al.  A Numerical Method for Solving Incompressible Flow Problems with a Surface of Discontinuity , 1999 .

[6]  S. Osher,et al.  A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method) , 1999 .

[7]  P. Colella,et al.  Non-convex profile evolution in two dimensions using volume of fluids , 1997 .

[8]  Matthew W. Williams,et al.  A balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework , 2006, J. Comput. Phys..

[9]  S. Cummins,et al.  Estimating curvature from volume fractions , 2005 .

[10]  Gian Piero Celata,et al.  Terminal velocity of single bubbles in surface tension force dominant regime , 2002 .

[11]  Said I. Abdel-Khalik,et al.  Accurate representation of surface tension using the level contour reconstruction method , 2005 .

[12]  Zhaoyuan Wang.  Numerical Study On Capillarity- Dominant Free Surface And Interfacial Flows , 2007 .

[13]  M. Sussman,et al.  A Coupled Level Set and Volume-of-Fluid Method for Computing 3D and Axisymmetric Incompressible Two-Phase Flows , 2000 .

[14]  Andrea Prosperetti,et al.  Motion of two superposed viscous fluids , 1981 .

[15]  Stéphane Popinet,et al.  A front-tracking algorithm for accurate representation of surface tension , 1999 .

[16]  F. Durst,et al.  Comparison of volume-of-fluid methods for surface tension-dominant two-phase flows , 2006 .

[17]  M. Sussman.  A second order coupled level set and volume-of-fluid method for computing growth and collapse of vapor bubbles , 2003 .

[18]  C. W. Hirt,et al.  Volume of fluid (VOF) method for the dynamics of free boundaries , 1981 .

[19]  M. Rudman.  A Volume-Tracking Method for Incompressible Multifluid Flows with Large Density Variations , 1998 .

[20]  E. Shirani,et al.  Interface pressure calculation based on conservation of momentum for front capturing methods , 2005 .

[21]  D. B. Kothe,et al.  RIPPLE: A Computer Program for Incompressible Flows with Free Surfaces , 1991 .

[22]  Mark Sussman,et al.  A sharp interface method for incompressible two-phase flows , 2007, J. Comput. Phys..

[23]  Nahmkeon Hur,et al.  A COUPLED LEVEL SET AND VOLUME-OF-FLUID METHOD FOR THE BUOYANCY-DRIVEN MOTION OF FLUID PARTICLES , 2002 .

[24]  Zhaoyuan Wang,et al.  A numerical method for capillarity-dominant free surface flows , 2007, J. Comput. Phys..

[25]  Brian L. Smith,et al.  A novel technique for including surface tension in PLIC-VOF methods , 2002 .

[26]  Cheng-Feng Tai,et al.  Assessment of sharp- and continuous-interface methods for drop in static equilibrium , 2004 .

[27]  J. Brackbill,et al.  A continuum method for modeling surface tension , 1992 .

[28]  John S. Lowengrub,et al.  An improved geometry-aware curvature discretization for level set methods: Application to tumor growth , 2006, J. Comput. Phys..

[29]  S. Zaleski,et al.  DIRECT NUMERICAL SIMULATION OF FREE-SURFACE AND INTERFACIAL FLOW , 1999 .

[30]  M. Renardy,et al.  PROST: a parabolic reconstruction of surface tension for the volume-of-fluid method , 2002 .

[31]  Gihun Son,et al.  EFFICIENT IMPLEMENTATION OF A COUPLED LEVEL-SET AND VOLUME-OF-FLUID METHOD FOR THREE-DIMENSIONAL INCOMPRESSIBLE TWO-PHASE FLOWS , 2003 .

[32]  S. Osher,et al.  A level set approach for computing solutions to incompressible two-phase flow , 1994 .

[33]  David J. Torres,et al.  The point-set method: front-tracking without connectivity , 2000 .