Mathematical Problems in Engineering
Volume 3 (1998), Issue 6, Pages 481-501

Nonlinear unsteady supersonic flow analysis for slender bodies of revolution: Series solutions, convergence and results

M. Markakis and D. E. Panayotounakos

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

Received 7 March 1996

Copyright © 1998 M. Markakis and D. E. Panayotounakos. 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.


In Ref. [6] the authors constructed analytical solutions including one arbitrary function for the problem of nonlinear, unsteady, supersonic flow analysis concerning slender bodies of revolution due to small amplitude oscillations. An application describing a flow past a right circular cone was presented and the constructed solutions were given in the form of infinite series through a set of convenient boundary and initial conditions in accordance with the physical problem. In the present paper we develop an appropriate convergence analysis concerning the before mentioned series solutions for the specific geometry of a rigid right circular cone. We succeed in estimating the limiting values of the series producing velocity and acceleration resultants of the problem under consideration. Several graphics for the velocity and acceleration flow fields are presented. We must underline here that the proposed convergence technique is unique and can be applied to any other geometry of the considered body of revolution.