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On the gas dynamics of an intense explosion with an expanding contact surface

Published online by Cambridge University Press:  29 March 2006

H. K. Cheng  and
J. W. Kirsch
H. K. Cheng
Affiliation:
University of Southern California, Los Angeles, California
J. W. Kirsch
Affiliation:
University of Southern California, Los Angeles, California Present address: Systems, Science and Software, La Jolla, California.
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Abstract

The structure of a strong blast wave under the influence of an expanding inner contact surface is studied asymptotically in the Newtonian limit: $\epsilon \equiv (\gamma - 1)/2\gamma \ll 1, \epsilon \dot{y}^2_s \gg a^2_{\infty}$. The theory treats the interaction of a shock layer and an inner flow region (the entropy wake) and reduces the problem to an ordinary differential equation for the shock radius. The pressure–volume relation of Cheng et al. (1961) is recovered and extended to a higher order of ε.

It is shown that, depending on the rate of growth of the contact surface, the shock layer may ‘reattach’ to the surface at large time. In a number of cases, the reattachment is approached in an oscillatory manner which leads to a period of non-uniformity. The associated problem of multiple time scales (treated in sequels to this paper) is identified.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 39 , Issue 2 , 10 November 1969 , pp. 289 - 305
Copyright
© 1969 Cambridge University Press

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References

Busemann, A. 1933 Flüssigkeits-und-Gasbewegung. Handwörterbuch der Naturwissenschaften, vol. 4, 2nd edition. Jena: Gustav Fischer.
Chapkis, R. L. 1965 Newtonian hypersonic flow theory for power-law shock waves. Stanford University, Ph.D. Dissertation.
Cheng, H. K. & Pallone, A. J. 1956 Inviscid leading-edge effect in hypersonic flow J. Aero. Sci. 23, 700–702.Google Scholar
Cheng, H. K., Hall, J. G., Gollan, T. C. & Hertzberg, A. 1961 Boundary layer displacement and leading-edge bluntness effects in high temperature hypersonic flow. J. Aero. Sci. 28, 353–381, 410.Google Scholar
Chernyi, G. G. 1959 Introduction to Hypersonic Flow. English translation 1961. New York: Academic.
Cleary, J. W. 1965 An experiment and theoretical investigation of the press distribution and flow fields of blunted cones at hypersonic Mach numbers. NASA TND-2969.Google Scholar
Cleary, J. W. & Axelson, J. A. 1964 Theoretical aerodynamics characteristics of sharp and circularly blunt-wedge airfoils. NASA TR-202.Google Scholar
Cole, J. D. 1957 Newtonian flow theory for slender bodies J. Aero. Sci. 24, 448–455.Google Scholar
Cole, J. D. 1968 Perturbation Methods in Applied Mathematics. New York: Ginn/Blaisdell.
Diaber, J. W., Hertzberg, A. & Wittliff, C. E. 1966 Laser generated implosions Phys. Fluids, 9, 617–619.Google Scholar
Freeman, N. C. 1956 On the theory of hypersonic flow past plane and axially-symmetric bluff bodies J. Fluid Mech. 1, 366–386.Google Scholar
Freeman, N. C. 1960 A note on the explosion solution of Sedov with application to the Newtonian theory of unsteady hypersonic flow. J. Aero. Sci. 27, 77–78, 956.Google Scholar
Freeman, N. C., Cash, R. F. & Bedder, D. 1964 An experimental investigation of asymptotic hypersonic flows J. Fluid Mech. 18, 379–384.Google Scholar
Guiraud, J. P., Vallee, D. & Zolver, R. 1965 Bluntness effects in hypersonic small disturbance theory. Basic Developments in Fluid Dynamics, vol. 1, ed. M. Holt. New York: Academic. pp. 127–247.
Hayes, W. D. & Probstein, R. F. 1966 Hypersonic Flow Theory, vol. 1, Inviscid Flows. Now York: Academic. Pp. 74–103, 355–366.
Kirsch, J. W. 1969 The unsteady flow field created by an arbitrary expansion of a piston following an energetic, impulsive start. University of Southern California, Ph.D. Thesis.
Ladyzhenskii, M. D. 1961 The hypersonic area rule. English translation, 1963 AIAA J. 1, 2696–2698.Google Scholar
Latter, R. 1955 Similarity solution for a spherical shock wave J. Appl. Phys. 26, 954–960.Google Scholar
Lees, L. & Kubota, T. 1957 Inviscid hypersonic flow over blunt-nosed slender bodies J. Aero. Sci. 24, 195–202.Google Scholar
Lin, S. C. 1954 Cylindrical shock wave produced by instantaneous energy release J. Appl. Phys. 25, 54–57.Google Scholar
Mirels, H. 1962 Hypersonic flow over slender bodies associated with power-law shocks. Advances in Applied Mechanics vol. 7. New York: Academic.
Parker, E. N. 1963 Interplanetary Dynamical Processes. New York: Interscience.
Schneider, W. A. 1968 Asymptotic behaviour of hypersonic flow over blunted slender wedges AIAA J. 6, 2235–2236.Google Scholar
Sedov, L. I. 1959 Similarity and Dimensional Methods in Mechanics. English translation 1959. New York: Academic.
Taylor, G. I. 1950 The formation of a blast wave by a very intense explosion. Proc. Roy. Soc. London, A 201, 159–186.Google Scholar
Van Dyke, M. D. 1964 Perturbation Methods in Fluid Mechanics. New York: Academic.