Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-19T04:53:36.077Z Has data issue: false hasContentIssue false
  • English
  • Français

Shock dynamics in non-uniform media

Published online by Cambridge University Press:  20 April 2006

C. J. Catherasoo  and
B. Sturtevant
C. J. Catherasoo
Affiliation:
Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, CA 91125
B. Sturtevant
Affiliation:
Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, CA 91125
Get access Rights & Permissions [Opens in a new window]

Abstract

The theory of shock dynamics in two dimensions is reformulated to treat shock propagation in a non-uniform medium. The analysis yields a system of hyperbolic equations with source terms representing the generation of disturbances on the shock wave as it propagates into the fluid non-uniformities. The theory is applied to problems involving the refraction of a plane shock wave at a free plane gaseous interface. The ‘slow–fast’ interface is investigated in detail, while the ‘fast–slow’ interface is treated only briefly. Intrinsic to the theory is a relationship analogous to Snell's law of refraction at an interface. The theory predicts both regular and irregular (Mach) refraction, and a criterion is developed for the transition from one to the other. Quantitative results for several different shock strengths, angles of incidence and sound-speed ratios are presented. An analogy between shock refraction and the motion of a force field in unsteady one-dimensional gasdynamics is pointed out. Also discussed is the limiting case for a shock front to be continuous at the interface. Comparison of results is made with existing experimental data, with transition calculations based on three-shock theory, and with the simple case of normal interaction.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 127 , February 1983 , pp. 539 - 561
Copyright
© 1983 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abd-El-Fattah, A. M. & Henderson, L. F. 1978 Shock waves at a slow–fast gas interface J. Fluid Mech. 89, 79–95.Google Scholar
Abd-El-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
Chester, W. 1954 The quasi-cylindrical shock tube. Phil. Mag. 45 (7), 1293–1301.
Chisnell, R. F. 1955 The normal motion of a shock wave through a non-uniform one-dimensional medium Proc. R. Soc. Lond. A232, 350–370.Google Scholar
Chisnell, R. F. 1957 The motion of a shock wave in a channel, with applications to cylindrical and spherical shock waves J. Fluid Mech. 2, 286–298.Google Scholar
Collins, R. & Chen, H. T. 1970 Propagation of a shock wave of arbitrary strength in two half planes containing a free surface J. Comp. Phys. 5, 415–422.Google Scholar
Collins, R. & Chen, H. T. 1971 Motion of a shock wave through a non-uniform fluid. In Proc. 2nd Int. Conf. on Numerical Methods in Fluid Dynamics (ed. M. Holt). Lecture Notes in Physics, vol. 8, pp. 264–269. Springer.
Henderson, L. F. 1966 The refraction of a plane shock wave at a gas interface J. Fluid Mech. 26, 607–637.Google Scholar
Hoffman, A. L. 1967 A single-fluid model for shock formation in MHD shock tubes J. Plasma Phys. 1, 193–207.Google Scholar
Hornung, H. G., Oertel, H. & Sandeman, R. J. 1979 Transition to Mach reflection of shock waves in steady and pseudosteady flow with and without relaxation J. Fluid Mech. 90, 541–560.Google Scholar
Jahn, R. G. 1956 The refraction of shock waves at a gaseous interface J. Fluid Mech. 1, 457–489.Google Scholar
Kutler, P. & Shankar, V. 1977 Diffraction of a shock wave by a compression corner: part II – single Mach reflection. A.I.A.A. J. 15, 197–203.
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
Shankar, V., Kutler, P. & Anderson, D. 1978 Diffraction of a shock wave by a compression corner: part I – regular refraction. A.I.A.A. J. 16, 4–5.
Taub, A. H. 1947 Refraction of plane shock waves Phys. Rev. 72, 51–60.Google Scholar
Whitham, G. B. 1957 A new approach to problems of shock dynamics. Part 1. Two-dimensional problems J. Fluid Mech. 2, 145–171.Google Scholar
Whitham, G. B. 1958 On the propagation of shock waves through regions of non-uniform area or flow J. Fluid Mech. 4, 337–360.Google Scholar
Whitham, G. B. 1959 A new approach to problems of shock dynamics. Part 2. Three-dimensional problems J. Fluid Mech. 5, 369–386.Google Scholar