A rapidly convergent procedure for solving the equations of subsonic potential flow. II. Analytic solutions

Abstract

This is a continuation of a previous paper (Tayler 1960) which obtained a second approximation to the subsonic potential flow equations. Results were obtained numerically for a circular cylinder and were shown to have an error of less than 1 % in the velocity distribu­tion at free-stream Mach numbers near the lower critical. In this paper by making a further approximation an analytic solution of these second approximation equations is obtained, valid for all two-dimensional bodies for which the conformal transformation of their cross-section into a circle is known. Results are obtained for a circular cylinder and compared with those obtained numerically. The two sets of results are not significantly different. Results are also obtained for Kaplan’s aerofoil and a circular cylinder with circulation. A detailed comparison is made with existing methods of solution, together with a discussion of the advantages of both the analytic and numerical methods of these two papers. Solutions are obtained in the lower transonic region, but no attempt has been made to prove the convergence of the method.