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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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References

Chester, W. 1953 The propagation of shock waves in a channel of non-uniform width. Quart. J. Mech. Appl. Math. 6, 440.Google Scholar
Chester, W. 1954 The quasi-cylindrical shock tube. Phil. Mag. Ser. 7, 45, 1293.Google Scholar
Chisnell, R. F. 1957 The motion of a shock wave in a channel with applications to cylindrical and spherical shock waves. J. Fluid Mech. 2, 286.Google Scholar
Davies, P. O. A. L. & Guy, T. B. 1971 Shock wave propagation in ducts with abrupt area expansions. Symp. Internal Flows, Univ. Salford, paper 30, p. D46.Google Scholar
Deckker, B. E. L. & Gururaja, J. 1970 An investigation of shock wave behaviour in ducts with a gradual or sudden enlargement in cross-sectional area. Fluid Mech. Conv., Univ. Glasgow, paper 4, p. 27. (See also Proc. Inst. Mech. Engrs 184, 3G.)Google Scholar
Nettleton, M. A. 1973 Shock attenuation in a gradual area change. J. Fluid Mech. 60, 209.Google Scholar
Skews, B. W. 1967 The shape of a diffracting shock wave. J. Fluid Mech. 29, 297.Google Scholar
Sloan, S. A. & Nettleton, M. A. 1975 A model for the axial decay of a shock wave in a large abrupt area change. J. Fluid Mech. 71, 769.Google Scholar
Smith, C. E. 1966 The starting process of a hypersonic nozzle. J. Fluid Mech. 24, 625.Google Scholar
Whitham, G. B. 1957 A new approach to the problems of shock dynamics. Part 1. Two-dimensional problems. J. Fluid Mech. 2, 145.Google Scholar
Whitham, G. B. 1959 A new approach to the problems of shock dynamics. Part 2. Three-dimensional problems. J. Fluid Mech. 5, 369.Google Scholar