Numerical Investigation of a Shock Accelerated Heavy Gas Cylinder in the Self-Similar Regime

Show more

References

[1] Richtmyer, R.D. (1960) Taylor Instability in a Shock Acceleration of Compressible Fluids. Communications on Pure and Applied Mathematics, 13, 297-319.

http://dx.doi.org/10.1002/cpa.3160130207

[2] Meshkov, E.E. (1968) Instability of the Interface of Two Gases Accelerated by a Shock Wave. Soviet Fluid Dynamics, 4, 101-104.

http://dx.doi.org/10.1007/BF01015969

[3] Lindl, J.D., McCropy, R.L. and Campbell, E.M. (1992) Progress toward Ignition and Propagating Burn in Inertial Confinement Fusion. Physics Today, 45, 32-40.

http://dx.doi.org/10.1063/1.881318

[4] Yang, J., Kubota, T. and Zukoski, E.E. (1994) A Model for Characterization of a Vortex Pair Formed by Shock Passage over a Light-Gas Inhomogeneity. Journal of Fluid Mechanics, 258, 217-244.

http://dx.doi.org/10.1017/S0022112094003307

[5] Arnett, D. (2000) The Role of Mixing in Astrophysics. The Astrophysical Journal Supplement Series, 127, 213-217.

http://dx.doi.org/10.1086/313364

[6] Kumar, S., Orlicz, G., Tomkins, C., Goodenough, C., Prestridge, K., Vorobieff, P. and Benjamin, R. (2005) Stretching of Material Lines in Shock-Accelerated Gaseous Flows. Physics of Fluids, 17, Article ID: 082107.

http://dx.doi.org/10.1063/1.2031347

[7] Moore, D.W. (1975) The Rolling Up of a Semi-Infinite Vortex Sheet. Proceedings of the Royal Society of London A, 345, 417-430.

http://dx.doi.org/10.1098/rspa.1975.0147

[8] Pullin, D.I. (1978) The Large-Scale Structure of Unsteady Self-Similar Rolled-Up Vortex Sheets. Journal of Fluid Mechanics, 88, 401-430.

http://dx.doi.org/10.1017/S0022112078002189

[9] Krasny, R. (1986) A Study of Singularity Formation in a Vortex Sheet by the Point-Vortex Approximation. Journal of Fluid Mechanics, 167, 65-93.

http://dx.doi.org/10.1017/S0022112086002732

[10] Klein, R.I., McKee, C.F. and Colella, P. (1994) On the Hydrodynamic Interaction of Shock Waves with Interstellar Clouds. 1: Nonradiative Shocks in Small Clouds. The Astrophysical Journal, 420, 213-236.

http://dx.doi.org/10.1086/173554

[11] Hwang, U., Flanagan, K.A. and Petre, R. (2005) Chandra X-Ray Observation of a Mature Cloud-Shock Interaction in the Bright Eastern Knot Region of Puppis A. Astrophysical Journal, 635, 355-364.

http://dx.doi.org/10.1086/497298

[12] Haas, J.F. and Sturtevant, B. (1987) Interaction of Weak Shock Waves with Cylindrical and Spherical Gas Inhomogeneities. Journal of Fluid Mechanics, 181, 41-76.

http://dx.doi.org/10.1017/S0022112087002003

[13] Jacobs, J.W. (1993) The Dynamics of Shock Accelerated Light and Heavy Gas Cylinders. Physics of Fluids A, 5, 2239-2247.

http://dx.doi.org/10.1063/1.858562

[14] Tomkins, C.D., Kumar, S., Orlicz, G. and Prestridge, K.P. (2008) An Experimental Investigation of Mixing Mechanisms in Shock-Accelerated Flow. Journal of Fluid Mechanics, 611, 131-150.

http://dx.doi.org/10.1017/S0022112008002723

[15] Picone, J.M. and Boris, J.P. (1983) Vorticity Generation by Asymmetric Energy Deposition in a Gaseous Medium. Physics of Fluids, 26, 365-382.

http://dx.doi.org/10.1063/1.864173

[16] Quirk, J.J. and Karni, S. (1994) On the Dynamics of a Shock-Bubble Interaction. NASA CR 194978, ICASE Report No. 94-75.

[17] Weirs, V.G., Dupont, T. and Plewa, T. (2008) Three-Dimensional Effects in Shock-Cylinder Interactions. Physics of Fluids, 20, Article ID: 044102.

http://dx.doi.org/10.1063/1.2884787

[18] Shankar, S.K., Kawai, S. and Lele, S.K. (2011) Two-Dimensional Viscous Flow Simulation of a Shock Accelerated Heavy Gas Cylinder. Physics of Fluids, 23, Article ID: 024102.

http://dx.doi.org/10.1063/1.3553282

[19] Dimonte, G. and Schneider, M. (2000) Density Ratio Dependence of Rayleigh-Taylor Mixing for Sustained and Impulsive Acceleration Histories. Physics of Fluids, 12, 304-321.

http://dx.doi.org/10.1063/1.870309

[20] Alon, U., Hecht, J., Ofer, D. and Shvarts, D. (1995) Power Laws and Similarity of Rayleigh-Taylor and Richtmyer-Meshkov Mixing Fronts at All Density Ratios. Physical Review Letters, 74, 534-537.

http://dx.doi.org/10.1103/PhysRevLett.74.534

[21] Sohn, S.-I. (2008) Quantitative Modeling of Bubble Competition in Richtmyer-Meshkov Instability. Physical Review E, 78, Article ID: 017302.

http://dx.doi.org/10.1103/PhysRevE.78.017302

[22] Bai, J.S., Wang, T., Li, P., Zou, L.Y, and Liu, C.L. (2009) Numerical Simulation of the Hydrodynamic Instability Experiments and Flow Mixing. Science in China Series G, 52, 2017-2040.

http://dx.doi.org/10.1007/s11433-009-0277-9

[23] Colella, P. and Woodward, P.R., (1984) The Piecewise Parabolic Method (PPM) for Gas-Dynamical Simulations. Journal of Computational Physics, 54, 174-201.

http://dx.doi.org/10.1016/0021-9991(84)90143-8

[24] Vreman, W. (2004) An Eddy-Viscosity Subgrid-Scale Model for Turbulent Shear Flow: Algebraic Theory and Applications. Physics of Fluids, 16, 3670-3681.

http://dx.doi.org/10.1063/1.1785131

[25] Miles, J.W. (1958) On the Disturbed Motion of a Plane Vortex Sheet. Journal of Fluid Mechanics, 4, 538-552.

http://dx.doi.org/10.1017/S0022112058000653

[26] Samtaney, R. and Pullin, D.I. (1996) On Initial-Value and Self-Similar Solutions of the Compressible Euler Equations. Physics of Fluids, 8, 2650-2655.

http://dx.doi.org/10.1063/1.869050

[27] Jones, B.D. and Jacobs, J.W. (1997) A Membraneless Experimental for the Study of Richtmyer-Meshkov Instability of a Shock-Accelerated Gas Interface. Physics of Fluids, 9, 3078-3085.

http://dx.doi.org/10.1063/1.869416

[28] Zhang, S., Zabusky, N.J., Peng, G. and Gupta, S. (2004) Shock Gaseous Cylinder Interactions: Dynamically Validated Initial Conditions Provide Excellent Agreement between Experiments and Numerical Simulations to Late-Intermediate Time. Physics of Fluids, 16, 1203-1216.

http://dx.doi.org/10.1063/1.1651483

[29] Picone, J.M. and Boris, J.P. (1988) Vorticity Generation by Shock Propagation through Bubbles in a Gas. Journal of Fluid Mechanics, 189, 23-51.

http://dx.doi.org/10.1017/S0022112088000904

[30] Tong, B.G., Yin, X.Y. and Zhu, K.Q. (2009) Theory of Vortex Motion. 2nd Edition, University of Science and Technology of China Press, Hefei.