A Coupled Level Set and Volume of Fluid method for automotive exterior water management applications

Abstract Motivated by the need for practical, high fidelity, simulation of water over surface features of road vehicles a Coupled Level Set Volume of Fluid (CLSVOF) method has been implemented into a general purpose CFD code. It has been implemented such that it can be used with unstructured and non-orthogonal meshes. The interface reconstruction step needed for CLSVOF has been implemented using an iterative ‘clipping and capping’ algorithm for arbitrary cell shapes and a re-initialisation algorithm suitable for unstructured meshes is also presented. Successful verification tests of interface capturing on orthogonal and tetrahedral meshes are presented. Two macroscopic contact angle models have been implemented and the method is seen to give very good agreement with experimental data for a droplet impinging on a flat plate for both orthogonal and non-orthogonal meshes. Finally the flow of a droplet over a round edged channel is simulated in order to demonstrate the ability of the method developed to simulate surface flows over the sort of curved geometry that makes the use of a non-orthogonal grid desirable.

[1]  M. Griebel,et al.  Simulation of Droplet Impact with Dynamic Contact Angle Boundary Conditions , 2014 .

[2]  S. Jakirlic,et al.  Dynamic contact angle of spreading droplets: Experiments and simulations , 2005 .

[3]  M. Arienti,et al.  An embedded level set method for sharp-interface multiphase simulations of Diesel injectors , 2014 .

[4]  Hang Ding,et al.  Numerical Simulations of Flows with Moving Contact Lines , 2014 .

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

[6]  F. Xiao Large Eddy Simulation of liquid jet primary breakup , 2012 .

[7]  R. G. Cox Inertial and viscous effects on dynamic contact angles , 1998, Journal of Fluid Mechanics.

[8]  I. Hutchings,et al.  Numerical studies of the influence of the dynamic contact angle on a droplet impacting on a dry surface , 2009 .

[9]  Rs Cant,et al.  Robust Conservative Level Set Method for 3D Mixed-Element Meshes — Application to LES of Primary Liquid-Sheet Breakup , 2014 .

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

[11]  F. Xiao,et al.  LARGE EDDY SIMULATION OF SINGLE DROPLET AND LIQUID JET PRIMARY BREAKUP USING A COUPLED LEVEL SET/VOLUME OF FLUID METHOD , 2014 .

[12]  Sadik Dost,et al.  Validation of the S‐CLSVOF method with the density‐scaled balanced continuum surface force model in multiphase systems coupled with thermocapillary flows , 2017 .

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

[14]  Ieuan Owen,et al.  THE FLOW OF THIN LIQUID FILMS AROUND CORNERS , 1985 .

[15]  D. Juric,et al.  A front-tracking method for the computations of multiphase flow , 2001 .

[16]  H. Marschall,et al.  voFoam - A geometrical Volume of Fluid algorithm on arbitrary unstructured meshes with local dynamic adaptive mesh refinement using OpenFOAM , 2013, 1305.3417.

[17]  Kensuke Yokoi,et al.  A practical numerical framework for free surface flows based on CLSVOF method, multi-moment methods and density-scaled CSF model: Numerical simulations of droplet splashing , 2013, J. Comput. Phys..

[18]  Dominique Thévenin,et al.  Practice of vehicle soiling investigations: A review , 2011 .

[19]  Santiago Márquez Damián,et al.  An extended mixture model for the simultaneous treatment of short and long scale interfaces , 2013 .

[20]  Hyung Taek Ahn,et al.  Geometric Algorithms for 3D Interface Reconstruction , 2007, IMR.

[21]  Y. Shikhmurzaev Capillary Flows with Forming Interfaces , 2007 .

[22]  F. Stern,et al.  A coupled level set and volume-of-fluid method for sharp interface simulation of plunging breaking waves , 2009 .

[23]  O. Voinov Hydrodynamics of wetting , 1976 .

[24]  F. Xiao,et al.  Large Eddy Simulation of Liquid-Jet Primary Breakup in Air Crossflow , 2013 .

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

[26]  L. Tanner,et al.  The spreading of silicone oil drops on horizontal surfaces , 1979 .

[27]  R. G. Cox The dynamics of the spreading of liquids on a solid surface. Part 2. Surfactants , 1986, Journal of Fluid Mechanics.

[28]  Dieter Bothe,et al.  lentFoam – A hybrid Level Set/Front Tracking method on unstructured meshes , 2015 .

[29]  D. Legendre,et al.  Numerical simulation of spreading drops , 2013 .

[30]  R. Hoffman A study of the advancing interface. I. Interface shape in liquid—gas systems , 1975 .

[31]  Julio Hernández,et al.  Analytical and geometrical tools for 3D volume of fluid methods in general grids , 2008, J. Comput. Phys..

[32]  M. Trujillo,et al.  Evaluating the performance of the two-phase flow solver interFoam , 2012 .

[33]  E. B. Dussan,et al.  LIQUIDS ON SOLID SURFACES: STATIC AND DYNAMIC CONTACT LINES , 1979 .

[34]  E. Hopfinger,et al.  Motion of drops on inclined surfaces in the inertial regime , 2013, Journal of Fluid Mechanics.

[35]  D. Legendre,et al.  Numerical Simulation of Sliding Drops on an Inclined Solid Surface , 2014 .

[36]  Marianne M. Francois,et al.  An interface reconstruction method based on an analytical formula for 3D arbitrary convex cells , 2016, J. Comput. Phys..

[37]  R. G. Cox The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow , 1986, Journal of Fluid Mechanics.

[38]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme. II. Monotonicity and conservation combined in a second-order scheme , 1974 .

[39]  Chohong Min,et al.  On reinitializing level set functions , 2010, J. Comput. Phys..

[40]  F. Xiao,et al.  LES of turbulent liquid jet primary breakup in turbulent coaxial air flow , 2014 .

[41]  Jaap de Vries,et al.  A comprehensive model for simulating the interaction of water with solid surfaces in fire suppression environments , 2013 .

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

[43]  T. Ménard,et al.  Coupling level set/VOF/ghost fluid methods: Validation and application to 3D simulation of the primary break-up of a liquid jet , 2007 .

[44]  Jochen Wiedemann,et al.  Advances in Modelling A-Pillar Water Overflow , 2015 .

[45]  R. LeVeque High-resolution conservative algorithms for advection in incompressible flow , 1996 .

[46]  Dominique Legendre,et al.  Numerical simulation of static and sliding drop with contact angle hysteresis , 2010, J. Comput. Phys..

[47]  Joaquin Gargoloff,et al.  Modelling A-Pillar Water Overflow: Developing CFD and Experimental Methods , 2012 .

[48]  Stéphane Zaleski,et al.  A mesh-dependent model for applying dynamic contact angles to VOF simulations , 2008, J. Comput. Phys..

[49]  Anthony J. Robinson,et al.  Influence of surface tension implementation in Volume of Fluid and coupled Volume of Fluid with Level Set methods for bubble growth and detachment , 2013 .