Supercritical flow past symmetrical airfoils

Abstract

A numerical method is developed for computing steady supercritical flow about an ellipse at zero angle of attack. The flow is assumed to be two-dimensional, inviscid, isentropic and irrotational. The free-stream Mach number lies in the high subsonic range so that a shock wave occurs locally near the body. The full potential equations are solved by Telenin's method and the ‘method of lines’. Smooth interpolating functions are assumed for the unknown flow variables in selected co-ordinate directions. The resulting set of ordinary differential equations is then integrated away from or along the body depending upon whether the flow is smooth or discontinuous. Jump conditions of the governing equations are applied across the shock wave so that it is perfectly sharp. A doublet solution for flow past a closed body is used as the farfield boundary condition. Supercritical flow calculations have been performed for ellipses with thickness ratio of 0·2 and 0·4 at various free-stream Mach numbers. The present results are compared with the shock-capturing method, and good agreement is obtained.