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On imploding cylindrical and spherical shock waves in a perfect gas

Ponchaut, N. F. and Hornung, H. G. and Pullin, D. I. and Mouton, C. A. (2006) On imploding cylindrical and spherical shock waves in a perfect gas. Journal of Fluid Mechanics, 560 . pp. 130-122. ISSN 0022-1120.

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The problem of a cylindrically or spherically imploding and reflecting shock wave in a flow initially at rest is studied without the use of the strong-shock approximation. Dimensional arguments are first used to show that this flow admits a general solution where an infinitesimally weak shock from infinity strengthens as it converges towards the origin. For a perfect-gas equation of state, this solution depends only on the dimensionality of the flow and on the ratio of specific heats. The Guderley power-law result can then be interpreted as the leading-order, strong-shock approximation, valid near the origin at the implosion centre. We improve the Guderley solution by adding two further terms in the series expansion solution for both the incoming and the reflected shock waves. A series expansion, valid where the shock is still weak and very far from the origin, is also constructed. With an appropriate change of variables and using the exact shock-jump conditions, a numerical, characteristics-based solution is obtained describing the general shock motion from almost infinity to very close to the reflection point. Comparisons are made between the series expansions, the characteristics solution, and the results obtained using an Euler solver. These show that the addition of two terms to the Guderley solution significantly extends the range of validity of the strong-shock series expansion.

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Hornung, H. G.0000-0002-4903-8419
Additional Information:Copyright © 2006 Cambridge University Press. Reprinted with permission. (Received 4 July 2005 and in revised form 6 January 2006) Published online 20 July 2006 N.P. and D.P. were partially supported by the Academic Strategic Alliances Program of the Accelerated Strategic Computing Initiative (ASCI/ASAP) under subcontract no. B341492 of DOE contract W-7405-ENG-48.
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ID Code:4820
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Deposited On:08 Sep 2006
Last Modified:22 Nov 2019 09:58

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