High Subsonic Flow with Normal Shock Wave at Nearly Critical Mach Number

Abstract

High subsonic flow past a biconvex circular arc aerofoil with a pair of normal shock waves at nearly critical Mach number is discussed by a very simple approximation procedure. The shock waves are assumed to be the normal shock waves which start from the surface of the aerofoil and stand perpendicularly to the direction of the uniform flow. The locations of the sonic line and the shock waves are treated as unknown parameters to be determined in the course of analysis. The results show that these parameters have real physical meaning only when the Mach number exceeds the usual critical Mach number calculated by means of Prandtl-Glauert approximation. The results also suggest that the curvature of the profile must change discontinuously at its intersection with the shock wave. This fact is also confirmed by applying Lin's exact consideration. Thus, it is concluded that there can exist no high subsonic flow of ideal fluid with normal shock waves starting form the surface past a profile having continuous curv...