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On the refraction of shock waves

Published online by Cambridge University Press:  21 April 2006

L. F. Henderson
L. F. Henderson
Affiliation:
Department of Mechanical Engineering, University of Sydney, Sydney, NSW 2006. Australia
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Abstract

This paper discusses the refraction of plane shock waves in media with arbitrary equations of state. Previous work is reviewed briefly, then a rigorous definition of wave impedance is formulated. Earlier definitions are shown to be unsatisfactory. The impedance is combined with the boundary conditions at the media interface to study both head-on and oblique shock incidence. The impedance determines the nature of the reflected and transmitted waves, their intensities, and the fractions of energy and power that are reflected and transmitted. The refractive index is also defined and determines whether or not a wave will be refracted, and also helps determine whether the wave system will be regular or irregular. The fundamental law of refraction is derived and shown to be a consequence of the fact that an arbitrary point on a shock or an expansion wave follows a ray path of minimum time between any two points on the path. This is a generalization of Fermat's Principle to media that are deformed and convected by the waves propagating through them.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 198 , January 1989 , pp. 365 - 386
Copyright
1989 Cambridge University Press

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References

Abdel-Fattah, A. M., Henderson, L. F. & Lozzi, A., 1976 Precursor shock waves at a slow-fast gas interface. J. Fluid Mech. 76, 157–176.Google Scholar
Abdel-Fattah, A. M. & Henderson, L. F.1978a Shock waves at a fast-slow interface. J. Fluid Mech. 86, 15–32.Google Scholar
Abdel-Fattah, A. M. & Henderson, L. F.1978b Shock waves at a slow-fast gas interface. J. Fluid Mech. 89, 79–95.Google Scholar
Ames Research Staff1953 Equations, tables and charts for compressible flow. NACA Rep. 1135.Google Scholar
Bethe, H. A.: 1942 The theory of shock waves for an arbitrary equation of state. OSRD Rep. 545.Google Scholar
Cathersoo, C. J. & Sturtevant, B., 1983 Shock dynamics in non-uniform media. J. Fluid Mech. 127, 539–561.Google Scholar
Courant, R. & Friedrichs, K. O., 1948 Supersonic Flow and Shock Waves. Interscience.
Dewey, J. M.: 1965 Precursor shocks produced by a large-yield chemical explosion. Nature 205, 1306.Google Scholar
Flores, J. & Holt, M., 1982 Shock wave interactions with the ocean surface. Phys. Fluids 25, 238–246.Google Scholar
Fry, M. A. & Book, D. L., 1986 Shock dynamics in heated layers. In Proc. 15th Intl Symp. on Shock Waves and Shock Tubes (ed. D. Bershader & R. Hanson), pp. 517–522. Stanford University Press.
Glowacki, W. J., Kuhl, A. L., Glaz, H. M. & Ferguson, R. E., 1986 In Proc. 15th Intl Symp. on Shock Waves and Shock Tubes (ed. D. Bershader & R. Hanson), pp. 187–194. Stanford University Press.
Gvozdeava, L. G., Faresov, Yu, M., Brossard, J. & Charpentier, N., 1986 Normal shock wave reflexion on porous compressible material. Prog. Astron. Aeron. 106, 155–165.Google Scholar
Haas, J. F. & Sturtevant, B., 1987 Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities. J. Fluid Mech. 181, 41–76.Google Scholar
Henderson, L. F.: 1966 The refraction of a plane shock wave at a gas interface. J. Fluid Mech. 26, 607–637.Google Scholar
Henderson, L. F.: 1970 On shock impedance. J. Fluid Mech. 40, 719–735.Google Scholar
Henderson, L. F.: 1988 On the thermodynamic stability of steady-state adiabatic systems. J. Fluid Mech. 189, 509–529.Google Scholar
Jahn, R. G.: 1956 The refraction of shock waves at a gaseous interface. J. Fluid Mech. 1, 457–489.Google Scholar
Kinsler, L. E., Frey, A. R., Coppens, A. B. & Sanders, J. V., 1982 Fundamentals of Acoustics. Wiley.
Markstein, G. H.: 1964 Experimental studies of flame-front instability. Nonsteady Flame Propagation, AGARDograph 75, pp. 75–100. Pergamon.
von Neumann, J.: 1943 Oblique reflexion of shock waves. In Collected Works, vol. 6, pp. 238–299. Pergamon.
Picone, J. M., Boris, J. P., Oran, E. S. & Ahearne, R., 1986 Rotational motion generated by shock propagation through a non-uniform gas. In Proc. 15th Intl Symp. on Shock Waves and Shock Tubes (ed. D. Bershader & R. Hanson), pp. 523–529. Stanford University Press.
Picone, J. M., Oran, E. S., Boris, J. P. & Young, T. R., 1984 Theory of vorticity generation by shock wave and flame interactions. Prog. Astron. Aeron. 94, 429–448.Google Scholar
Polachek, H. & Seeger, R. J., 1951 On shock wave phenomena; refraction of shock waves at a gaseous interface. Phys. Rev. 84, 922–929.Google Scholar
Reichenbach, H.: 1985 Roughness and heated layer effects on shock wave propagation and reflection-experimental results. E-Mach-Inst. Rep. E24/85. Frieberg: Fraunhofer-Gesellschaft.
Sommerfeld, M.: 1985 The unsteadiness of shock waves propagating through gas-particle mixtures. Expts Fluids 3, 197–206Google Scholar
Sugimura, T., Tokita, K. & Fujiwara, T., 1984 Nonsteady shock wave propagating in a bubble-liquid system. Prog. Astron. Aeron. 94, 320–331.Google Scholar
Taub, A. H.: 1947 Refraction of plane shock waves. Phys. Rev. 72, 51–60.Google Scholar