Mathematical Problems in Engineering
Volume 3 (1997), Issue 3, Pages 217-241

Nonlinear unsteady supersonic flow analysis for slender bodies of revolution: Theory

D. E. Panayotounakos and M. Markakis

Department of Engineering Science, Section of Mechanics, National Technical University of Athens, Athens GR-157 73, Hellas, Greece

Received 7 March 1996

Copyright © 1997 D. E. Panayotounakos and M. Markakis. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We construct analytical solutions for the problem of nonlinear supersonic flow past slender bodies of revolution due to small amplitude oscillations. The method employed is based on the splitting of the time dependent small perturbation equation to a nonlinear time independent partial differential equation (P.D.E.) concerning the steady flow, and a linear time dependent one, concerning the unsteady flow. Solutions in the form of three parameters family of surfaces for the first equation are constructed, while solutions including one arbitrary function for the second equation are extracted. As an application the evaluation of the small perturbation velocity resultants for a flow past a right circular cone is obtained making use of convenient boundary and initial conditions in accordance with the physical problem.