Once again on the supersonic flow separation near a corner

Abstract

Laminar boundary-layer separation in the supersonic flow past a corner point on a rigid body contour, also termed the compression ramp, is considered based on the viscous–inviscid interaction concept. The ‘triple-deck model’ is used to describe the interaction process. The governing equations of the interaction may be formally derived from the Navier–Stokes equations if the ramp angle θ is represented as θ = θ0Re−1/4, where θ0 is an order-one quantity and Re is the Reynolds number, assumed large. To solve the interaction problem two numerical methods have been used. The first method employs a finite-difference approximation of the governing equations with respect to both the streamwise and wall-normal coordinates. The resulting algebraic equations are linearized using a Newton–Raphson strategy and then solved with the Thomas-matrix technique. The second method uses finite differences in the streamwise direction in combination with Chebychev collocation in the normal direction and Newton–Raphson linearization.Our main concern is with the flow behaviour at large values of θ0. The calculations show that as the ramp angle θ0 increases, additional eddies form near the corner point inside the separation region. The behaviour of the solution does not give any indication that there exists a critical value θ*0 of the ramp angle θ0, as suggested by Smith & Khorrami (1991) who claimed that as θ0 approaches θ*0, a singularity develops near the reattachment point, preventing the continuation of the solution beyond θ*0. Instead we find that the numerical solution agrees with Neiland's (1970) theory of reattachment, which does not involve any restriction upon the ramp angle.