An Improved Coupled Level Set and Continuous Moment-of-Fluid Method for Simulating Multiphase Flows with Phase Change

doi:10.1007/s42967-023-00286-6

Abstract

Abstract: An improved algorithm for computing multiphase flows is presented in which the multimaterial Moment-of-Fluid (MOF) algorithm for multiphase flows, initially described by Li et al. (2015), is enhanced addressing existing MOF difficulties in computing solutions to problems in which surface tension forces are crucial for understanding salient flow mechanisms. The Continuous MOF (CMOF) method is motivated in this article. The CMOF reconstruction method inherently removes the “checkerboard instability” that persists when using the MOF method on surface tension driven multiphase (multimaterial) flows. The CMOF reconstruction algorithm is accelerated by coupling the CMOF method to the level set method and coupling the CMOF method to a decision tree machine learning (ML) algorithm. Multiphase flow examples are shown in the two-dimensional (2D), three-dimensional (3D) axisymmetric “RZ”, and 3D coordinate systems. Examples include two material and three material multiphase flows: bubble formation, the impingement of a liquid jet on a gas bubble in a cryogenic fuel tank, freezing, and liquid lens dynamics.

Key words: Moment-of-Fluid(MOF), Surface tension, Two phase flow, Phase change, Deforming boundaries with change(s) in topology, Two-dimensional(2D), Three-dimensional(3D) axisymmetric, 3D

Zhouteng Ye, Cody Estebe, Yang Liu, Mehdi Vahab, Zeyu Huang, Mark Sussman, Alireza Moradikazerouni, Kourosh Shoele, Yongsheng Lian, Mitsuhiro Ohta, M. Yousuff Hussaini. An Improved Coupled Level Set and Continuous Moment-of-Fluid Method for Simulating Multiphase Flows with Phase Change[J]. Communications on Applied Mathematics and Computation, 2024, 6(2): 1034-1069.

TrendMD

References

[1] Ahn, H.T., Shashkov, M.: Multi-material interface reconstruction on generalized polyhedral meshes. J. Comput. Phys. 226(2), 2096-2132 (2007)
[2] Ahn, H.T., Shashkov, M.: Adaptive moment-of-fluid method. J. Comput. Phys. 228(8), 2792-2821 (2009)
[3] Ancellin, M., Després, B., Jaouen, S.: Extension of generic two-component VOF interface advection schemes to an arbitrary number of components. J Comput. Phys. 473, 111721 (2022)
[4] Arienti, M., Sussman, M.: An embedded level set method for sharp-interface multiphase simulations of diesel injectors. Int. J. Multiph. Flow 59, 1-14 (2014)
[5] Asuri Mukundan, A., Ménard, T., Brändle de Motta, J.C., Berlemont, A.: A hybrid moment of fluid-level set framework for simulating primary atomization. J. Comput. Phys. 451, 110864 (2022)
[6] Bentz, M., Knoll, R., Hasan, M., Lin, C. Low-g fluid mixing: further results from the tank pressure control experiment. In: 29th Joint Propulsion Conference and Exhibit, AIAA-93-2423. AIAA (1993)
[7] Bentz, M., Meserole, J., Knoll, R.: Jet mixing in low gravity-results of the tank pressure control experiment. In: 28th Joint Propulsion Conference and Exhibit, p. 3060 (1992)
[8] Bonhomme, R., Magnaudet, J., Duval, F., Piar, B.: Inertial dynamics of air bubbles crossing a horizontal fluid-fluid interface. J. Fluid Mech. 707, 405-443 (2012)
[9] Brackbill, J.U., Kothe, D.B., Zemach, C.: A continuum method for modeling surface tension. J. Comput. Phys. 100(2), 335-354 (1992)
[10] Breiman, L., Friedman, J., Olshen, R., Stone, C.: Classification and Regression Trees. Wadsworth & Brooks/Cole Advanced Books & Software, Monterey, CA (1984)
[11] Caboussat, A., Francois, M.M., Glowinski, R., Kothe, D.B., Sicilian, J.M.: A numerical method for interface reconstruction of triple points within a volume tracking algorithm. Math. Comput. Model. 48(11), 1957-1971 (2008)
[12] Colella, P., Woodward, P.R.: The piecewise parabolic method (ppm) for gas-dynamical simulations. J. Comput. Phys. 54(1), 174-201 (1984)
[13] Cummins, S.J., Francois, M.M., Kothe, D.B.: Estimating curvature from volume fractions. Comput. Struct. 83(6/7), 425-434 (2005)
[14] De Gennes, P.-G., Brochard-Wyart, F., Quéré, D.: Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves. Springer Science & Business Media, New York (2013)
[15] Dyadechko, V., Shashkov, M.: Moment-of-fluid interface reconstruction. Los Alamos report LA-UR-05-7571 (2005)
[16] Dyadechko, V., Shashkov, M.: Reconstruction of multi-material interfaces from moment data. J. Comput. Phys. 227(11), 5361-5384 (2008)
[17] Enright, D., Fedkiw, R., Ferziger, J., Mitchell, I.: A hybrid particle level set method for improved interface capturing. J. Comput. Phys. 183(1), 83-116 (2002)
[18] Francois, M.M., Cummins, S.J., Dendy, E.D., Kothe, D.B., Sicilian, J.M., Williams, M.W.: A balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework. J. Comput. Phys. 213(1), 141-173 (2006)
[19] Gibou, F., Fedkiw, R.P., Cheng, L.-T., Kang, M.: A second-order-accurate symmetric discretization of the Poisson equation on irregular domains. J. Comput. Phys. 176(1), 205-227 (2002)
[20] Glimm, J., Isaacson, E., Marchesin, D., McBryan, O.: Front tracking for hyperbolic systems. Adv. Appl. Math. 2(1), 91-119 (1981)
[21] Godunov, S.: Different methods for shock waves. PhD Dissertation. Moscow State University (1954)
[22] Godunov, S., Bohachevsky, I.: Finite difference method for numerical computation of discontinuous solutions of the equations of fluid dynamics. Matematičeskij sbornik 47(3), 271-306 (1959)
[23] Harten, A.: High resolution schemes for hyperbolic conservation laws. J. Comput. Phys. 135(2), 260-278 (1997)
[24] Helsby, F., Tuson, K.: Behaviour of air bubbles in aqueous solutions. Research 8, 270-275 (1955)
[25] Hirt, C.W., Nichols, B.D.: Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39(1), 201-225 (1981)
[26] Hu, H., Jin, Z.: An icing physics study by using lifetime-based molecular tagging thermometry technique. Int. J. Multiph. Flow 36(8), 672-681 (2010)
[27] Huang, Z., Lin, G., Ardekani, A.M.: Consistent, essentially conservative and balanced-force phase-field method to model incompressible two-phase flows. J. Comput. Phys. 406, 109192 (2020)
[28] Huang, Z., Lin, G., Ardekani, A.M.: A consistent and conservative phase-field model for thermo-gas-liquid-solid flows including liquid-solid phase change. J. Comput. Phys. 449, 110795 (2022)
[29] Jemison, M., Loch, E., Sussman, M., Shashkov, M., Arienti, M., Ohta, M., Wang, Y.: A coupled level set-moment of fluid method for incompressible two-phase flows. J. Sci. Comput. 54(2/3), 454-491 (2013)
[30] Jemison, M., Sussman, M., Arienti, M.: Compressible, multiphase semi-implicit method with moment of fluid interface representation. J. Comput. Phys. 279, 182-217 (2014)
[31] Kim, J.: Phase field computations for ternary fluid flows. Comput. Methods Appl. Mech. Engrg. 196(45), 4779-4788 (2007)
[32] Kucharik, M., Garimella, R.V., Schofield, S.P., Shashkov, M.J.: A comparative study of interface reconstruction methods for multi-material ALE simulations. J. Comput. Phys. 229(7), 2432-2452 (2010)
[33] Li, G., Lian, Y., Guo, Y., Jemison, M., Sussman, M., Helms, T., Arienti, M.: Incompressible multiphase flow and encapsulation simulations using the moment-of-fluid method. Int. J. Numer. Meth. Fluids 79(9), 456-490 (2015)
[34] Liu, Y., Sussman, M., Lian, Y., Hussaini, M.Y., Vahab, M., Shoele, K.: A novel supermesh method for computing solutions to the multi-material Stefan problem with complex deforming interfaces and microstructure. J. Sci. Comput. 91(1), 1-40 (2022)
[35] Lyu, S., Wang, K., Zhang, Z., Pedrono, A., Sun, C., Legendre, D.: A hybrid VOF-IBM method for the simulation of freezing liquid films and freezing drops. J. Comput. Phys. 432, 110160 (2021)
[36] Markstein, G.: Interaction of flow pulsations and flame propagation. J. Aeronaut. Sci. 18(6), 428-429 (1951)
[37] Miao, F., Wu, B., Sun, Z., Peng, C.: Calibration method of the laser beam based on liquid lens for 3D precise measurement. Measurement 178, 109358 (2021)
[38] Milcent, T., Lemoine, A.: Moment-of-fluid analytic reconstruction on 3D rectangular hexahedrons. J. Comput. Phys. 409, 109346 (2020)
[39] Ohta, M., Kikuchi, D., Yoshida, Y., Sussman, M.: Robust numerical analysis of the dynamic bubble formation process in a viscous liquid. Int. J. Multiph. Flow 37(9), 1059-1071 (2011)
[40] Olsson, E., Kreiss, G.: A conservative level set method for two phase flow. J. Comput. Phys. 210(1), 225-246 (2005)
[41] Osher, S., Sethian, J.A.: Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79(1), 12-49 (1988)
[42] Pathak, A., Raessi, M.: A three-dimensional volume-of-fluid method for reconstructing and advecting three-material interfaces forming contact lines. J. Comput. Phys. 307, 550-573 (2016)
[43] Pei, C., Vahab, M., Sussman, M., Hussaini, M.Y.: A hierarchical space-time spectral element and moment-of-fluid method for improved capturing of vortical structures in incompressible multi-phase/multi-material flows. J. Sci. Comput. 81(3), 1527-1566 (2019)
[44] Qiu, R., Huang, R., Xiao, Y., Wang, J., Zhang, Z., Yue, J., Zeng, Z., Wang, Y.: Physics-informed neural networks for phase-field method in two-phase flow. Phys. Fluids 34(5), 052109 (2022)
[45] Remmerswaal, R.A., Veldman, A.E.: Parabolic interface reconstruction for 2D volume of fluid methods. J. Comput. Phys. 469, 111473 (2022)
[46] Salas, M.D.: Shock fitting method for complicated two-dimensional supersonic flows. AIAA J. 14(5), 583-588 (1976)
[47] Saurel, R., Abgrall, R.: A multiphase Godunov method for compressible multifluid and multiphase flows. J. Comput. Phys. 150(2), 425-467 (1999)
[48] Schofield, S.P., Garimella, R.V., Francois, M.M., Loubère, R.: Material order-independent interface reconstruction using power diagrams. Int. J. Numer. Meth. Fluids 56(6), 643 (2008)
[49] Schofield, S.P., Garimella, R.V., Francois, M.M., Loubère, R.: A second-order accurate material-order-independent interface reconstruction technique for multi-material flow simulations. J. Comput. Phys. 228(3), 731-745 (2009)
[50] Shetabivash, H., Dolatabadi, A., Paraschivoiu, M.: A multiple level-set approach for modelling containerless freezing process. J. Comput. Phys. 415, 109527 (2020)
[51] Shin, S., Juric, D.: A hybrid interface method for three-dimensional multiphase flows based on front tracking and level set techniques. Int. J. Numer. Meth. Fluids 60(7), 753-778 (2009)
[52] Shu, C.-W., Osher, S.: Efficient implementation of essentially non-oscillatory shock-capturing schemes. J. Comput. Phys. 77(2), 439-471 (1988)
[53] Sijoy, C., Chaturvedi, S.: Volume-of-fluid algorithm with different modified dynamic material ordering methods and their comparisons. J. Comput. Phys. 229(10), 3848-3863 (2010)
[54] Smith, K.A., Solis, F.J., Chopp, D.: A projection method for motion of triple junctions by level sets. Interfac Free Bound 4(3), 263-276 (2002)
[55] Starinshak, D.P., Karni, S., Roe, P.L.: A new level set model for multimaterial flows. J. Comput. Phys. 262, 1-16 (2014)
[56] Sussman, M.: A second order coupled level set and volume-of-fluid method for computing growth and collapse of vapor bubbles. J. Comput. Phys. 187(1), 110-136 (2003)
[57] Sussman, M., Ohta, M.: A stable and efficient method for treating surface tension in incompressible two-phase flow. SIAM J. Sci. Comput. 31(4), 2447-2471 (2009)
[58] Sussman, M., Puckett, E.G.: A coupled level set and volume-of-fluid method for computing 3D and axisymmetric incompressible two-phase flows. J. Comput. Phys. 162(2), 301-337 (2000)
[59] Sussman, M., Smereka, P., Osher, S.: A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys. 114(1), 146-159 (1994)
[60] Tatebe, O.: The multigrid preconditioned conjugate gradient method. In: the Sixth Copper Mountain Conference on Multigrid Methods, Part 2. NASA, Copper Mountain (1993)
[61] Unverdi, S.O., Tryggvason, G.: A front-tracking method for viscous, incompressible, multi-fluid flows. J. Comput. Phys. 100(1), 25-37 (1992)
[62] Vahab, M., Pei, C., Hussaini, M.Y., Sussman, M., Lian, Y.: An adaptive coupled level set and moment-of-fluid method for simulating droplet impact and solidification on solid surfaces with application to aircraft icing. In: 54th AIAA Aerospace Sciences Meeting, p. 1340 (2016)
[63] Vahab, M., Sussman, M., Shoele, K.: Fluid-structure interaction of thin flexible bodies in multi-material multi-phase systems. J. Comput. Phys. 429, 110008 (2021)
[64] Van Leer, B.: Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov’s method. J. Comput. Phys. 32, 101-136 (1979)
[65] Vu, T.V., Tryggvason, G., Homma, S., Wells, J.C.: Numerical investigations of drop solidification on a cold plate in the presence of volume change. Int. J. Multiph. Flow 76, 73-85 (2015)
[66] Welch, S.W., Wilson, J.: A volume of fluid based method for fluid flows with phase change. J. Comput. Phys. 160(2), 662-682 (2000)
[67] Zalesak, S.T.: Fully multidimensional flux-corrected transport algorithms for fluids. J. Comput. Phys. 31(3), 335-362 (1979)