Numerical and asymptotic solutions for the supersonic flow near the trailing edge of a flat plate at incidence

Abstract

The equations which govern the flow at high Reynolds number in the vicinity of the trailing edge of a finite flat plate at incidence to a uniform supersonic stream are solved numerically using a finite-difference procedure. The critical order of magnitude of the angle of incidence α* for the occurrence of separation on one side of the plate is α* = O(R−¼) (Brown & Stewartson 1970), where R is a representative Reynolds number for the flow, and results are computed for three such values of α* which characterize the possible behaviour of the flow above the plate. The final set of computations leads to a numerical value for the trailing-edge stall angle α*_s, the angle of incidence which just causes the flow to separate at the trailing edge of the plate. Analytic solutions are available in the form of asymptotic expansions near the trailing edge in terms of the scaled variable of order R^−⅜. A multi-layer-type of expansion which occurs in the case α* = α_s* is presented in detail for comparison with the computed solution.