Second-order asymptotic solution for laminar separation

Abstract

The method of matched asymptotic expansions is used to obtain a second-order triple-deck solution for the case of constant wall temperature. It includes the problem of an adiabatic wall as a special case. The theory is applied to the case of a supersonic flow over a compression ramp with laminar separation. A numerical procedure is presented for solving the lower_deck equations by using the Crank-Nicolson finite-difference scheme. A modification of the boundary conditions for an adiabatic wall made it possible to solve for the total second-order solution instead of solving for the different orders in succession. Sample results and comparisons with other solutions are presented. The region of separation predicted by the second-order theory is larger than that predicted by the first_order theory. Moreover, for the case of cooled walls, the second-order theory predicts negative temperatures and densities, depending on the Reynolds number and the degree of cooling, thus indicating a breakdown of the theory.