Shock Dynamics in Non-Uniform Media

Author: Catherasoo, Christopher Jeyaparan

Year: 1982

Degree: Dissertation (Ph.D.)

Advisor: Sturtevant, Bradford

Committee Members: Sturtevant, Bradford; Housner, George W.; Kubota, Toshi; Roshko, Anatol; Saffman, Philip G.

Option: Aeronautics

DOI: 10.7907/7knb-5s50

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.

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