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On generation and convergence of polygonal-shaped shock waves

Published online by Cambridge University Press:  26 April 2006

N. Apazidis  and
M. B. Lesser
N. Apazidis
Affiliation:
Department of Mechanics, Royal Institute of Technology, 100 44 Stockholm, Sweden
M. B. Lesser
Affiliation:
Department of Mechanics, Royal Institute of Technology, 100 44 Stockholm, Sweden
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Abstract

A process of generation and convergence of shock waves of arbitrary form and strength in a confined chamber is investigated theoretically. The chamber is a cylinder with a specifically chosen form of boundary. Numerical calculations of reflection and convergence of cylindrical shock waves in such a chamber filled with fluid are performed. The numerical scheme is similar to the numerical procedure introduced by Henshaw et al. (1986) and is based on a modified form of Whitham's theory of geometrical shock dynamics (1957, 1959). The technique used in Whitham (1968) for treating a shock advancing into a uniform flow is modified to account for non-uniform conditions ahead of the advancing wave front. A new result, that shocks of arbitrary polygonal shapes may be generated by reflection of cylindrical shocks off a suitably chosen reflecting boundary, is shown. A study is performed showing the evolution of the shock front's shape and Mach number distribution. Comparisons are made with a theory which does not account for the non-uniform conditions in front of the shock. The calculations provide details of both the reflection process and the shock focusing.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 309 , 25 February 1996 , pp. 301 - 319
Copyright
© 1996 Cambridge University Press

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