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

Hornung, H. G. and Schwendeman, D. W. (2001) Oblique shock reflection from an axis of symmetry: shock dynamics and relation to the Guderley singularity. Journal of Fluid Mechanics, 438 . pp. 231-245. ISSN 0022-1120. doi:10.1017/S0022112001004360.

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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.

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Hornung, H. G.0000-0002-4903-8419
Additional Information:Copyright © 2001 Cambridge University Press. (Received 31 July 2000 and in revised form 5 December 2000) We wish to thank Dale Pullin and Gerry Whitham for valuable discussions.
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ID Code:12590
Deposited By: Archive Administrator
Deposited On:13 Dec 2008 05:07
Last Modified:08 Nov 2021 22:29

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