A VOSET method combined with IDEAL algorithm for 3D two-phase flows with large density and viscosity ratio

Abstract In order to accurately, robustly and efficiently simulate the three-dimensional (3D) interfacial flow problems with large density and viscosity ratio, we should, on the one hand, adopt the accurate and robust interface capturing method, on the other hand, use the efficient solution algorithm for coupling the velocity and pressure. In this paper, a coupled volume-of-fluid and level set (VOSET) method is applied to capture the two-phase interface, while an inner doubly iterative efficient algorithm for linked equations (IDEAL) is used to couple the velocity and pressure. Both of the VOSET method and the IDEAL algorithm were first proposed by the present author and further extended by other authors. Finally, the superiority of the VOSET method combined with the IDEAL algorithm (VOSET + IDEAL) is verified by three interfacial flow problems with large density and viscosity ratio.

[1]  Suhas V. Patankar,et al.  A Calculation Procedure for Two-Dimensional Elliptic Situations , 1981 .

[2]  Ng Niels Deen,et al.  Numerical simulation of gas bubbles behaviour using a three-dimensional volume of fluid method , 2005 .

[3]  W. Q. Tao,et al.  A coupled volume-of-fluid and level set (VOSET) method for computing incompressible two-phase flows , 2010 .

[4]  Numerical simulation of bubble dynamics in the gravitational and uniform electric fields , 2017 .

[5]  Bo Yu,et al.  Performance analyses of the IDEAL algorithm combined with the fuzzy control method for 3D incompressible fluid flow and heat transfer problems , 2016 .

[6]  Xiao-dong Wang,et al.  A Critical Review of Dynamic Wetting by Complex Fluids: From Newtonian Fluids to Non-Newtonian Fluids and Nanofluids. , 2016, Advances in colloid and interface science.

[7]  S. Zaleski,et al.  Volume-of-Fluid Interface Tracking with Smoothed Surface Stress Methods for Three-Dimensional Flows , 1999 .

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

[9]  W. Tao,et al.  Phase Change Heat Transfer Simulation for Boiling Bubbles Arising from a Vapor Film by the VOSET Method , 2011 .

[10]  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 .

[11]  D. Spalding,et al.  A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows , 1972 .

[12]  David F. Fletcher,et al.  Implementation of a height function method to alleviate spurious currents in CFD modelling of annular flow in microchannels , 2015 .

[13]  Dmitri Kuzmin,et al.  An optimization-based approach to enforcing mass conservation in level set methods , 2014, J. Comput. Appl. Math..

[14]  R. Scardovelli,et al.  Height function based Volume of Fluid code for simulations of multiphase magnetic fluids , 2015 .

[15]  Henk A. van der Vorst,et al.  Efficient and reliable iterative methods for linear systems , 2002 .

[16]  J. P. V. Doormaal,et al.  ENHANCEMENTS OF THE SIMPLE METHOD FOR PREDICTING INCOMPRESSIBLE FLUID FLOWS , 1984 .

[17]  S. Na,et al.  Three-dimensional thermal simulation of nanosecond laser ablation for semitransparent material , 2013 .

[18]  G. Yeoh,et al.  An algorithm to calculate interfacial area for multiphase mass transfer through the volume-of-fluid method , 2016 .

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

[20]  Jie Ouyang,et al.  Development of new finite volume schemes on unstructured triangular grid for simulating the gas–liquid two‐phase flow , 2016 .

[21]  Bo Yu,et al.  Development of a VOF+LS+SPP method based on FLUENT for simulating bubble behaviors in the electric field , 2017 .

[22]  Wen-Quan Tao,et al.  A Direct Numerical Simulation for Nucleate Boiling by the VOSET Method , 2014 .

[23]  Thomas Y. Hou,et al.  Boundary integral methods for multicomponent fluids and multiphase materials , 2001 .

[24]  Dongliang Sun,et al.  A three-dimensional volume of fluid & level set (VOSET) method for incompressible two-phase flow , 2015 .

[25]  Zhiguo Qu,et al.  An Efficient Segregated Algorithm for Incompressible Fluid Flow and Heat Transfer Problems—IDEAL (Inner Doubly Iterative Efficient Algorithm for Linked Equations) Part I: Mathematical Formulation and Solution Procedure , 2008 .

[26]  Fabian Denner,et al.  Comparative study of mass-conserving interface capturing frameworks for two-phase flows with surface tension , 2014 .

[27]  A. Sharma,et al.  Numerical modelling of bubble growth in microchannel using Level Set Method , 2016 .

[28]  Qiang Li Numerical simulation of melt filling process in complex mold cavity with insets using IB-CLSVOF method , 2016 .

[29]  Olivier Desjardins,et al.  A mesh-decoupled height function method for computing interface curvature , 2015, J. Comput. Phys..

[30]  Toshiyuki Hayase,et al.  A consistently formulated QUICK scheme for fast and stable convergence using finite-volume iterative calculation procedures , 1992 .

[31]  Dongxiao Shi,et al.  Numerical Simulation of Bubble Dynamics in a Uniform Electric Field by the Adaptive 3D-VOSET Method , 2015 .

[32]  Guy Lauriat,et al.  Natural convection and wall condensation or evaporation in humid air-filled cavities subjected to wall temperature variations , 2011 .

[33]  J. A. Sethian,et al.  Fast Marching Methods , 1999, SIAM Rev..

[34]  Tai Wang,et al.  A coupled volume-of-fluid and level set (VOSET) method on dynamically adaptive quadtree grids , 2013 .

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

[36]  C. K. Thornhill,et al.  Part IV. An experimental study of the collapse of liquid columns on a rigid horizontal plane , 1952, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[37]  F. Faura,et al.  An improved height function technique for computing interface curvature from volume fractions , 2009 .

[38]  Xiaofeng Yang,et al.  An adaptive coupled level-set/volume-of-fluid interface capturing method for unstructured triangular grids , 2006, J. Comput. Phys..

[39]  Huijin Xu,et al.  Modeling metal foam enhanced phase change heat transfer in thermal energy storage by using phase field method , 2016 .

[40]  Dongxiao Shi,et al.  Numerical Simulation of a Falling Ferrofluid Droplet in a Uniform Magnetic Field by the VOSET Method , 2014 .

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

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

[43]  A. Gosman,et al.  Solution of the implicitly discretised reacting flow equations by operator-splitting , 1986 .

[44]  H. E. Bailey,et al.  Newton's method applied to finite-difference approximations for the steady-state compressible Navier-Stokes equations , 1991 .

[45]  C. H. Yu,et al.  An improved interface preserving level set method for simulating three dimensional rising bubble , 2016 .

[46]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method , 1979 .

[47]  Bo Yu,et al.  A coupled volume-of-fluid and level set (VOSET) method based on remapping algorithm for unstructured triangular grids , 2017 .

[48]  Mehdi Raessi,et al.  A three-dimensional volume-of-fluid method for reconstructing and advecting three-material interfaces forming contact lines , 2016, J. Comput. Phys..

[49]  Lijun Liu,et al.  CONTROL OF OXYGEN TRANSPORT IN THE MELT OF A CZOCHRALSKI-SILICON CRYSTAL GROWTH , 2012 .

[50]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[51]  W. Tao,et al.  Performance Analysis of IDEAL Algorithm Combined with Bi-CGSTAB Method , 2010 .

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

[53]  M. Ansari,et al.  Capturing of interface topological changes in two-phase gas–liquid flows using a coupled volume-of-fluid and level-set method (VOSET) , 2016 .

[54]  Jianren Fan,et al.  A mass conserving level set method for detailed numerical simulation of liquid atomization , 2015, J. Comput. Phys..

[55]  Ya-Ling He,et al.  Performance analysis of IDEAL algorithm for three‐dimensional incompressible fluid flow and heat transfer problems , 2009 .

[56]  Ya-Ling He,et al.  An Efficient Segregated Algorithm for Incompressible Fluid Flow and Heat Transfer Problems—IDEAL (Inner Doubly Iterative Efficient Algorithm for Linked Equations) Part II: Application Examples , 2008 .