Impulsive Motion of a Sphere at Supersonic Speeds

[+] Author and Article Information
Stephen S. H. Chang

Lockheed Missiles and Space Company, Sunnyvale, Calif. 94088

J. Fluids Eng 102(1), 41-46 (Mar 01, 1980) (6 pages) doi:10.1115/1.3240622 History: Received January 01, 1979; Online October 26, 2009


This paper presents an analytical transient solution to the subsonic flow near the stagnation region of a sphere which starts impulsively at a constant supersonic speed. The analysis is based upon a series expansion in time of the flow variables and of the shape of the moving shock. The coefficients of the series are determined analytically by substituting the series into the differential equations of motion and the standard Rankine-Hugoniot jump conditions. The series is extended over 30 terms at stagnation point and up to nine terms near the sonic point. The first four terms are in agreement with the known solutions. By recasting them in Euler’s transformation, the series is analytical beyond their natural region of convergence. The results match the experiments and are in agreement with the known steady-state numerical solutions.

Copyright © 1980 by ASME
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