Journal of Fluid Mechanics



Oblique shock reflection from an axis of symmetry: shock dynamics and relation to the Guderley singularity


H. G. HORNUNG a1 and D. W. SCHWENDEMAN a2
a1 Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, CA 91125, USA
a2 Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, USA

Abstract

Oblique shock reflection from an axis of symmetry is studied using Whitham's theory of geometrical shock dynamics, and the results are compared with previous numerical simulations of the phenomenon by Hornung (2000). The shock shapes (for strong and weak shocks), and the location of the shock-shock (for strong shocks), are in good agreement with the numerical results, though the detail of the shock reflection structure is, of course, not resolved by shock dynamics. A guess at a mathematical form of the shock shape based on an analogy with the Guderley singularity in cylindrical shock implosion, in the form of a generalized hyperbola, fits the shock shape very well. The smooth variation of the exponent in this equation with initial shock angle from the Guderley value at zero to 0.5 at 90° supports the analogy. Finally, steady-flow shock reflection from a symmetry axis is related to the self-similar flow.

(Received July 31 2000)
(Revised December 5 2000)



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