Inverse method of designing two-dimensional transonic airfoil sections.

Abstract

The approximate compressible theory of two-dimensional airfoil sections at transonic speeds is obtained by means of the method of integral relations and quasi-linearization. The theory is an inverse method in which airfoil sections are obtained from prescribed velocity distributions which are assumed to be shock free at design Mach numbers. In order to decrease the number of strips necessary to keep the accuracy of results, the singularity of equations at stagnation points is removed analytically and the remaining regular parts of equations are transformed into a two-point boundary value problem of a system of nonlinear ordinary differential equations by means of the method of integral relations; and these equations are integrated through using quasi-linearization and the Runge-Kutta-Gill numerical method. Application of quasi-linearization admits the use of as many strips as one wishes and the accuracy of results can be improved without limit. An iterative cycle is set up to make the resulting profiles close when the pressure distributions are arbitrarily prescribed. Examples of airfoil sections designed with a four strip method and an experimental pressure distribution are presented. The rate of convergence of quasi-linearization is shown to be high.