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

Published online by Cambridge University Press:  19 April 2006

S. A. Sloan  and
M. A. Nettleton
S. A. Sloan
Affiliation:
Central Electricity Research Laboratories, Kelvin Avenue, Leatherhead, Surrey KT22 7SE, England
M. A. Nettleton
Affiliation:
Central Electricity Research Laboratories, Kelvin Avenue, Leatherhead, Surrey KT22 7SE, England
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Abstract

A series of initially planar shock waves was allowed to expand from a shock tube into a near half-space. The strength of the wall shock was measured at two positions on the slightly concave front wall. These measurements are compared with shock strengths predicted by a shock-dynamic model based on the cylindrical expansion of a critical shock. Chisnell's (1957) theory is used to account for the effect of the increasing surface area of the expanding wall shock, and Whitham's (1957) treatment to correct for the curvature of the wall. The critical shock strength is obtained from Skews’ (1967) experimental measurements of the Mach number of the self-similar wall shock following two-dimensional diffraction at a 90° edge.

The model predicts the relatively small degree of attenuation observed between the measuring stations, but overestimates the absolute shock strength. The most likely cause is that, in the early stages of expansion, the wall shock experiences further attenuation owing to its interaction with the expanding flow. These effects are shown to be short range and of negligible importance at the first measuring station, 1·86 tube diameters from the axis. Thus, using the experimental results at this station as the starting point, the model predicts accurately the shock strength at 3·76 diameters. It is concluded that Chisnell's theory can be applied to the weakening of the wall shock in ducts with large abrupt changes in cross-section only when the wall shock is some distance from the entrance to the area change.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 88 , Issue 2 , 27 September 1978 , pp. 259 - 272
Copyright
© 1978 Cambridge University Press

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