شبیه سازی عددی دو بعدی اندرکنش شاک و حباب در جریان های دو فازی تراکم پذیر

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانش آموخته دکتری دانشکده فنی مهندسی دانشگاه تربیت مدرس

2 دانشیار دانشکده فنی مهندسی دانشگاه تربیت مدرس

چکیده


در این مقاله تاکید اصلی بر تسخیر دقیق فصل مشترک و مطالعه اندرکنش شاک و حباب در جریان‌های دو فازی گاز-گاز و گاز – مایع است.  بدین منظور برای اولین بار از حلگر ریمان HLLC و روش حل عددی گودونوف برای معادلات دو سیالی 5 معادله‌ای کاپیلا استفاده شد و کد نویسی به صورت دوبعدی و با دقت مرتبه دو انجام شد. مسائل اندرکنش شاک و حباب هلیم در هوا و حباب هوا در آب شبیه­سازی شد.  نتایج عددی بدست آمده برابری عالی با نتایج تجربی و نتایج قبلی بدست آمده توسط محققین با روش‌های عددی و معادلات دیگر دارد. این روش در عین سادگی،  قادر است موج شاک گذرا و ناپیوستگی­های مواد و ناپایداری‌های فصول مشترک را به دقت و بدون نوسان و پخش عددی اضافی تسخیر نماید. 

کلیدواژه‌ها


عنوان مقاله [English]

Two-dimensional numerical simulation of shock-bubble interaction in compressible two-phase flows

نویسندگان [English]

  • Abdolhosein Daremi Zadeh 1
  • Mohammad Reza Ansari 2
چکیده [English]

The main objective of this paper is the accurate interface capturing and study on the shock-bubble interaction in gas-gas and gas-liquid two-phase flows. For this aim, the HLLC Riemann solver and Godunov numerical method were used for the first time for the 5-equation Kapila model. Transient shock wave interaction with Helium-Air and Air-Water bubbles were simulated. Numerical results were compared with available experimental results. The results have excellent agreement with experimental and previous published numerical results obtained by methods that are more sophisticated. Results show that the present method is able to capture transient shock waves and materials discontinuities and interfaces instabilities accurately and without any diffusion and oscillation.

کلیدواژه‌ها [English]

  • Two-Phase Flows
  • Compressible
  • Shock Wave
  • Godunov Numerical Method
  • Interface
[1] D. Scheffler and J. Zukas، “Practical aspects of numerical simulations of dynamic events:Material interfaces”، Int. J. Impact Eng. 24(8), pp: 821–842، 2000.
[2] J. Pilliod and E. Puckett، “Second-order accurate Volume-of-Fluid algorithms for tracking material interfaces”، J. Comput.Phys. 199, pp: 465–502، 2004.
[3] J. A. Sethian. “Level Set Methods: Evolving Interfaces in Geometry، Fluid. Mechanics، Computer Vision and Material Science”.Cambridge University Press، 1996.
[4] S. Osher and R. Fedkiw. “Level set methods:An overview and some recent results”.J.Comput. Phys. 169(2) , pp: 463–502، 2001.
[5] S. Unverdi and G. Tryggvason. “A front tracking method for viscous incompressible flows”. J. Comput. Phys. 100, pp:25–37،1992.
[6] H. Terashima، G. Tryggvason. “A fronttracking/ ghost-fluid method for fluid interfaces in compressible flows”. J. Comput.Phys. 228, pp: 4012-4037, 2009.
[7] H. Terashima، G. Tryggvason. “A fronttracking method with projected interface conditions for compressible multi-fluid flows”. Computers & Fluids 39,pp:1804–1814,2010.
[8] J. Doneal، A. Huerta، J.P. Ponthot، and A.Rodriguez-Ferran. “Arbitrary Lagrangian- Eulerian Methods”. In E. Stein، R. de Borst، and T. J. Hughes، editors، Encyclopedia of Computational Mechanics، chapter 14. John Wiley & Sons،2004.
[9] H.R. Anbarlooei، K. Mazaheri. “Moment of fluid interface reconstruction method in multi-material arbitrary Lagrangian Eulerian (MMALE) algorithms”. Comput. Methods Appl. Mech. Engrg. 198, pp: 3782–3794, 2009.
[10] R. Saurel and O. Le Metayer. “A multiphase model for interfaces، shocks، detonation waves and cavitation”. J. Fluid Mech. 431, pp: 239–271، 2001.
[11] E. Johnsen، T. Colonius.” Implementation of WENO schemes in compressible multicomponent flow problems”. J. Comput. Phys. 219,pp:715–732,2006.
[12] S. Kawai. H. Terashima. “A high-resolution scheme for compressible multicomponent flows With shock waves”. Int. J. Numer. Meth. Fluids, 66(10), pp: 1207-1225, 2010.
[13] E.Johnsen. “Spurious oscillations and conservation errors in interface-capturing schemes”. Annual Research Briefs 2008،Center for Turbulence Research، NASA Ames and Stanford University; 115–126،
2008.
[14] C.-H. Chang، M.-S. Liou. “A robust and accurate approach to computing compressible multiphase flow: Stratified flow model and AUSM +-up scheme”. J. Comput. Phys. 225, pp: 840–873, 2007.
[15] R.Abgrall. “How to prevent pressure oscillations in multicomponent flow calculations: A quasi-conservative approach” . J. Comput. Phys. 125(1) , pp: 150–160،
1996.
[16] K.-M. Shyue. “An efficient shock-capturing algorithm for compressible multi- component problems”. J. Comp. Phys. 142, pp: 208–242،
1998.
[17] K.-M. Shyue. “A high-resolution mapped grid algorithm for compressible multiphase flow problems”. J. Comput. Phys. 229,pp: 8780–8801,2010.
[18] R. Saurel. R.Abgrall. “A multiphase Godunov method for compressbile multifluid and multiphase flows”. J. Comput. Phys. 150(2) , pp: 425–467، 1999.
[19] C.E.Castro ,E.F.Toro. “A Riemann solver and upwind methods for a two-phase flow model non-conservative form”، Int. J. Numer. Meth. Fluids, 50, pp: 275–307, 2006.
[20] S.T.Munkejord.” Comparison of Roe-type methods for solving the two-fluid model with and without pressure relaxation”، Computers & Fluids 36, pp: 1061–1080, 2007.
[21] S.T.Munkejord. “A Numerical Study of Two-Fluid Models with Pressure and Velocity Relaxation”، Adv. Appl. Math. Mech. 2, pp. 131-159, 2010.
[22] S.A.Tokareva,E.F.Toro . “HLLC-type Riemann solver for the Baer–Nunziato equations of compressible two-phase flow”،
Journal of Computational Physics 229, pp: 3573–3604, 2010.
[23] M.Dumbser,E.F. Toro, “A Simple Extension of the Osher Riemann Solver to Non-conservative Hyperbolic Systems”، J. Sci. Comput. DOI 10.1007/s10915-010-9400-3 ،
2010.
[24] R.Kapila، R. Menikoff، J. Bdzil، S. Son، and D. Stewart. “Two-phase modeling of DDT in granular materials: Reduced equations”. Phys. Fluid، 13, pp: 3002–3024، 2001.
[25] R. Saurel، F. Petitpas، and R. A. Berry. “Simple and efficient relaxation methods for interfaces separating compressible fluids، cavitating flows and shocks in multiphase mixtures”. J. Comput. Phys. 228(5), pp: 1678–1712، 2009.
[26] G. Allaire، S. Clerc، and S. Kokh. “A five-equation model for the simulation of interfaces between compressible fluids”. J. Comput. Phys. 181, pp: 577–616، 2002.
[27] Murrone and H. Guillard. “A five-equation reduced model for compressible two- phase flow problems”. J. Comput. Phys. 202(2), pp: 664–698، 2005.
[28] J.J. Kreeft، B. Koren. “A new formulation of Kapila’s five-equation model for compressible two-fluid flow، and its numerical treatment”. J. Comput. Phys. 229, pp: 6220–6242, 2010.
[29] S. Qamar، M. Ahmed. “A high order kinetic flux-vector splitting method for the reduced five-equation model of compressible two-fluid flows”. J. Comput. Phys.228, pp: 9059-9078, 2009.
[30] S. Koch، F. Lagoutière. “An anti-diffusive numerical scheme for the simulation of interfaces between compressible fluids by means of a five-equation model”. 229, pp: 2773-2809, 2010.
[31] M. Baer and J. Nunziato. “A two-phase mixture theory for the deflagration-to-detonation transition (DDT) in reactive granular materials.” Int. J. Multiphase Flows،12,pp:861–889، 1986.
[32] E. F. Toro. “Riemann Solvers and Numerical Methods for Fluid Dynamics”. Springer، Berlin، 1999.
[33] S. F. Davis. “Simplified second-order Godunov-type methods”. SIAM J. Sci. Statist.Comput. 9, pp: 445–473، 1998.
[34] J.F.Haas، B.Sturtevant، “Interaction of weak shock waves with cylindrical and spherical gas in homogeneities”، Journal of Fluid Mechanics 181, pp: 41-76, 1987.
[35] Marquina، P. Mulet. “A flux-split algorithm applied to conservative models for multicomponent compressible flows”. J. Comput. Phys. 185 120-138, 2003.
[36] J.J. Quirk، S. Karni، "On the dynamics of a shock-bubble interaction"، Journal of Fluid Mechanics 318, pp: 129–163, 1996.
[37] C. Wang، C.-W. Shu. “An interface treating technique for compressible multi-medium flow with Runge–Kutta discontinuous Galerkin method”. J. Comput. Phys. 229, pp: 8823–8843, 2010.
[38] J.W. Banks et al. “A high-resolution Godunov method for compressible multi-material flow on overlapping grids”. J. Comput. Phys. 223,pp: 262–297,2007.
[39] R.R. Nourgaliev، T.N. Dinh، T.G. Theofanous.”Adaptive characteristics-based matching for compressible multifluid dynamics”. J. Comput. Phys. 213, pp: 500–529, 2006.
[40] S.K. Sambasivan، H.S. UdayKumar. “Sharp interface simulations with Local Mesh Refinement for multi-material dynamics in strongly shocked flows”. Computers & Fluids 39, pp: 1456–1479, 2010.