A transonic hodograph theory for aerofoil design

Abstract

An introductory description of a hodograph method for the Computation of advanced shock-free aerofoils is presented. The method is based on the approximate solution of Tricomi boundary value problems for the hodograph equations. The approximate solution is a sum of a basic solution having the required singularity on the hodograph surface corresponding to free-stream conditions and a finite linear combination of regular additional solutions. The basic and additional solutions are constructed with function-theoretic methods developed by Lighthill, Goldstein, Nieuwland and others. The coefficients in the finite linear combination of solutions are determined in such a way that approximate solutions of Tricomi boundary value problems are obtained. A special error functional is introduced and minimized in the process of determining aerodynamically acceptable approximate solutions. A few computational results give an idea of the performance of the method.