Similarity Solution for Transonic Flow Past a Cone

Author: Shen, Yung-chung

Year: 1956

Degree: Dissertation (Ph.D.)

Advisor: Cole, Julian D.

Committee Member: Unknown, Unknown

Option: Aeronautics; Mathematics

DOI: 10.7907/74PX-HS89

Abstract

By applying a transonic expansion procedure to a conical flow field, a system of approximate transonic equations, boundary conditions, and shock relations is derived. A similarity law for the pressure coefficient on the surface of slender cones is established. The surface pressure is computed by solving the approximate equations.

By use of similarity, the second order differential equations of the first two steps of the approximation scheme are reduced to first order equations. The solution of the first step is carried out numerically in great detail for different transonic parameters; the procedure for solving the latter is explained in the Appendix.

The results are compared with the exact solution, and a highly satisfactory agreement is reached.

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