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A model for the axial decay of a shock wave in a large abrupt area change

Published online by Cambridge University Press:  29 March 2006

S. A. Sloan  and
M. A. Nettleton
S. A. Sloan
Affiliation:
Central Electricity Research Laboratories, Kelvin Avenue, Leatherhead, Surrey, England
M. A. Nettleton
Affiliation:
Central Electricity Research Laboratories, Kelvin Avenue, Leatherhead, Surrey, England
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Abstract

A shock-dynamic model based on the symmetrical expansion of the critical shock is used to analyse the progressive decay of an originally planar shock wave through a large and abrupt area change. This is tested against measurements of shock strength made along the axes of area changes where the shock waves are free to expand in two or three dimensions.

The critical shock is defined as the configuration when the decaying shock wave at the axis first becomes curved. The axial shock begins to decay less than one diameter from the entrance of the area change. Differences between the experimental onset of decay and the theoretical position of the critical shock are accounted for by the non-ideal behaviour of a practical pressure transducer.

The model predicts that, when the shock wave is decaying symmetrically, there is a linear relationship between a derived function ε of the decaying shock strength and the distance from the area change. This is confirmed experimentally for all the shocks studied. The quantitative application of the results in three dimensions up to 400 mm enables accurate predictions of experimental results at 1 m for M < 2·0. Also, the model may be applied to three-dimensional results to predict accurately equivalent results in two dimensions.

The numerical values of ε are based on the equivalence of the ratio of the shock areas and the ratio of their Chisnell (1957) functions. Hence correlations between experimental results and predictions of the model are evidence that Chisnell's theory can be extended to include large and abrupt area changes.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 71 , Issue 4 , 28 October 1975 , pp. 769 - 784
Copyright
© 1975 Cambridge University Press

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