Effect of three-dimensional flow on limiting pressure differential for interaction of boundary layer with shock waves

Abstract

In the interaction of shock waves with a boundary layer there is a limiting value of the shock wave intensity which may be sustained by the boundary layer without separation. If the intensity of the shock wave is greater than the limiting value, a boundary layer separation zone is formed, and the flow rearranges itself so that the intensity of the shock wave 2 ahead of the separation zone (Fig. 1) is equal to the limiting value. In the study of the separation of the two-dimensional boundary layer the relations $$Cp = \frac{{p_2 - p_1 }}{{{\raise0.5ex\hbox{$\scriptstyle 1$}\kern-0.1em/\kern-0.15em\lower0.25ex\hbox{$\scriptstyle 2$}}\rho _1 u_1 ^2 }} = /\left( {R, M} \right)$$ are obtained for the laminar and turbulent boundary layers. Here p1 and p2 are the static pressures ahead of and behind the shock, ρ1 and u1 are the density and velocity in the approaching flow, M is the Mach number, R is the Reynolds number. In the present paper we consider the effect of flow three-dimensionality on the value of Cp. We shall limit ourselves to consideration of three-dimensional flow on lines of convergence and lines of divergence, although the conclusions are qualitatively valid in the more general case.