Journal of Fluid Mechanics

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Proximal bodies in hypersonic flow

STUART J. LAURENCEa1, R. DEITERDINGa2 and G. HORNUNGa1

a1 Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, CA 91125, USA

a2 Oak Ridge National Laboratory, PO Box 2008 MS6367, Oak Ridge, TN 37831, USA

Abstract

Hypersonic flows involving two or more bodies travelling in close proximity to one another are encountered in several important situations. The present work seeks to explore one aspect of the resulting flow problem by investigating the forces experienced by a secondary body when it is within the domain of influence of a primary body travelling at hypersonic speeds.

An analytical methodology based on the blast wave analogy is developed and used to predict the secondary force coefficients for simple geometries in both two and three dimensions. When the secondary body is entirely inside the primary shocked region, the nature of the lateral force coefficient is found to depend strongly on the relative size of the two bodies. For two spheres, the methodology predicts that the secondary body will experience an exclusively attractive lateral force if the secondary diameter is larger than one-sixth of the primary diameter. The analytical results are compared with those from numerical simulations and reasonable agreement is observed if an appropriate normalization for the relative lateral displacement of the two bodies is used.

Results from a series of experiments in the T5 hypervelocity shock tunnel are also presented and compared with perfect-gas numerical simulations, with good agreement. A new force-measurement technique for short-duration hypersonic facilities, enabling the experimental simulation of the proximal bodies problem, is described. This technique provides two independent means of measurement, and the agreement observed between the two gives a further degree of confidence in the results obtained.

(Received February 09 2007)

(Revised June 13 2007)

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