The Interaction of the Shock Wave with the Bubble and the Effect of Computational Grid Size on the Problem Simulation with A Fully Coupled Pressure-Based Algorithm

Document Type : Research Article

Authors

1 Energy Conversion / Faculty of Mechanical Engineering / Tarbiat Modares University / Tehran / Iran

2 tarbia modares university

3 tarbiat modares university

Abstract

When a shock wave propagates through a flow field that has nonlinear thermodynamic properties, different processes occur simultaneously. Wave compression, wave refraction, and vortex generation are examples of these processes that cause the waveform and thermodynamic properties of the fluid to change. The interaction of a shock wave with a cylindrical bubble is an example of a wave-bubble collision problem in which all of the above processes are observed. Due to the high computational cost of density-based algorithms in solving compressible interfacial flow problems such as shock wave interaction with the two-phase flow, using a fully coupled pressure-based algorithm is a good solution that will solve the problem with proper accuracy while reducing computation time. In this paper, using this algorithm, the interaction of the shock wave with the bubble is investigated; while validating the results, the effect of the computational grid size and the method of discretization of the governing equations are determined. It was observed that by increasing the number of computational grids according to the first-order upwind method, the simulation results become more accurate, and the numerical diffusion amount decreases. Also, by changing the discretization method to second-order upwind, the instabilities on the interface of the two phases increase due to spurious fluctuations, and the shape of the interface obtained from the numerical solution moves away from the experimental results.

Keywords

Main Subjects

References

[1] D. Ranjan, J. Oakley, R. Bonazza, Shock-bubble interactions, Annual Review of Fluid Mechanics, 43 (2011) 117-140.
[2] N.J. Zabusky, Vortex paradigm for accelerated inhomogeneous flows: Visiometrics for the Rayleigh-Taylor and Richtmyer-Meshkov environments, Annual review of fluid mechanics, 31(1) (1999) 495-536.
[3] F. MARBLE, E. ZUKOSKI, J. Jacobs, G. Hendricks, Shock enhancement and control of hypersonic mixing and combustion, in:  26th Joint Propulsion Conference, 1990, pp. 1981.
[4] J. Yang, T. Kubota, E.E. Zukoski, A model for characterization of a vortex pair formed by shock passage over a light-gas inhomogeneity, Journal of Fluid Mechanics, 258 (1994) 217-244.
[5] M. Delius, F. Ueberle, W. Eisenmenger, Extracorporeal shock waves act by shock wave-gas bubble interaction, Ultrasound in medicine & biology, 24(7) (1998) 1055-1059.
[6] W. Eisenmenger, The mechanisms of stone fragmentation in ESWL, Ultrasound in medicine & biology, 27(5) (2001) 683-693.
[7] U. Hwang, K.A. Flanagan, R. Petre, CHANDRA X-ray observation of a mature cloud-shock interaction in the bright eastern knot region of Puppis A, The Astrophysical Journal, 635(1) (2005) 355.
[8] J. Lindl, Development of the indirect‐drive approach to inertial confinement fusion and the target physics basis for ignition and gain, Physics of plasmas, 2(11) (1995) 3933-4024.
[9] F. Denner, C.-N. Xiao, B.G. van Wachem, Pressure-based algorithm for compressible interfacial flows with acoustically-conservative interface discretisation, Journal of Computational Physics, 367 (2018) 192-234.
[10] V. Coralic, T. Colonius, Finite-volume WENO scheme for viscous compressible multicomponent flows, Journal of computational physics, 274 (2014) 95-121.
[11] R. Abgrall, How to prevent pressure oscillations in multicomponent flow calculations: a quasi conservative approach, Journal of Computational Physics, 125(1) (1996) 150-160.
[12] K.-M. Shyue, An efficient shock-capturing algorithm for compressible multicomponent problems, Journal of Computational Physics, 142(1) (1998) 208-242.
[13] G. Allaire, S. Clerc, S. Kokh, A five-equation model for the simulation of interfaces between compressible fluids, Journal of Computational Physics, 181(2) (2002) 577-616.
[14] A. Marquina, P. Mulet, A flux-split algorithm applied to conservative models for multicomponent compressible flows, Journal of Computational Physics, 185(1) (2003) 120-138.
[15] M. Ansari, A. Daramizadeh, Numerical simulation of compressible two-phase flow using a diffuse interface method, International journal of heat and fluid flow, 42 (2013) 209-223.
[16] X.Y. Hu, B. Khoo, N.A. Adams, F. Huang, A conservative interface method for compressible flows, Journal of Computational Physics, 219(2) (2006) 553-578.
[17] G. Perigaud, R. Saurel, A compressible flow model with capillary effects, Journal of Computational Physics, 209(1) (2005) 139-178.
[18] M.R. Baer, J.W. Nunziato, A two-phase mixture theory for the deflagration-to-detonation transition (DDT) in reactive granular materials, International journal of multiphase flow, 12(6) (1986) 861-889.
[19] A. Murrone, H. Guillard, A five equation reduced model for compressible two phase flow problems, Journal of Computational Physics, 202(2) (2005) 664-698.
[20] G. Allaire, S. Clerc, S. Kokh, A five-equation model for the numerical simulation of interfaces in two-phase flows, Comptes Rendus de l'Académie des Sciences-Series I-Mathematics, 331(12) (2000) 1017-1022.
[21] E.F. Toro, M. Spruce, W. Speares, Restoration of the contact surface in the HLL-Riemann solver, Shock waves, 4(1) (1994) 25-34.
[22] E.F. Toro, The Riemann problem for the Euler equations, in:  Riemann Solvers and Numerical Methods for Fluid Dynamics, Springer, 2009, pp. 115-162.
[23] K.-M. Shyue, A volume-fraction based algorithm for hybrid barotropic and non-barotropic two-fluid flow problems, Shock Waves, 15(6) (2006) 407-423.
[24] D.R. van der Heul, C. Vuik, P. Wesseling, A conservative pressure-correction method for flow at all speeds, Computers & Fluids, 32(8) (2003) 1113-1132.
[25] P. Wesseling, Principles of computational fluid dynamics, Springer Science & Business Media, 2009.
[26] F. Moukalled, L. Mangani, M. Darwish, The finite volume method, in:  The finite volume method in computational fluid dynamics, Springer, 2016, pp. 103-135.
[27] F.H. Harlow, A.A. Amsden, A numerical fluid dynamics calculation method for all flow speeds, Journal of Computational Physics, 8(2) (1971) 197-213.
[28] J. Van Doormaal, G. Raithby, B. McDonald, The segregated approach to predicting viscous compressible fluid flows,  (1987).
[29] R.R. Nourgaliev, T.-N. Dinh, T.G. Theofanous, Adaptive characteristics-based matching for compressible multifluid dynamics, Journal of Computational Physics, 213(2) (2006) 500-529.
[30] R. Saurel, R. Abgrall, A multiphase Godunov method for compressible multifluid and multiphase flows, Journal of Computational Physics, 150(2) (1999) 425-467.
[31] L. Michael, N. Nikiforakis, The evolution of the temperature field during cavity collapse in liquid nitromethane. Part I: inert case, Shock Waves, 29(1) (2019) 153-172.
[32] S.-W. Ohl, C.-D. Ohl, Acoustic Cavitation in a Microchannel, in:  Handbook of Ultrasonics and Sonochemistry, Springer Singapore, Singapore, 2016, pp. 99-135.
[33] S. Pan, S. Adami, X. Hu, N.A. Adams, Phenomenology of bubble-collapse-driven penetration of biomaterial-surrogate liquid-liquid interfaces, Physical Review Fluids, 3(11) (2018) 114005.
[34] J.-F. Haas, B. Sturtevant, Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities, Journal of Fluid Mechanics, 181 (1987) 41-76.
[35] G. Rudinger, L.M. Somers, Behaviour of small regions of different gases carried in accelerated gas flows, Journal of Fluid Mechanics, 7(2) (1960) 161-176.
[36] D. Ranjan, J. Niederhaus, B. Motl, M. Anderson, J. Oakley, R. Bonazza, Experimental investigation of primary and secondary features in high-Mach-number shock-bubble interaction, Physical review letters, 98(2) (2007) 024502.
[37] R.K.A.N, K.Mazaheri, Two-dimensional numerical study of shock collision with non-reactive bubble, Tarbiat Modares University Thesis, Tarbiat Modares University, 2012.(In Persian)
[38] X. Bai, M. Li, Simulating compressible two-phase flows with sharp-interface discontinuous Galerkin methods based on ghost fluid method and cut cell scheme, Journal of Computational Physics, 459 (2022) 111107.
[39] J.H. Niederhaus, J. Greenough, J. Oakley, D. Ranjan, M. Anderson, R. Bonazza, A computational parameter study for the three-dimensional shock–bubble interaction, Journal of Fluid Mechanics, 594 (2008) 85-124.
[40] J.W. Banks, D.W. Schwendeman, A.K. Kapila, W.D. Henshaw, A high-resolution Godunov method for compressible multi-material flow on overlapping grids, Journal of Computational Physics, 223(1) (2007) 262-297.
[41] B. Reimann, V. Hannemann, K. Hannemann, Computations of shock wave propagation with local mesh adaptation, in:  Shock Waves, Springer, 2009, pp. 1383-1388.
Amirkabir Journal of Mechanical Engineering
Volume 54, Issue 9
December 2022
Pages 2041-2060

Files

Share

How to cite

Statistics