The numerical solution of the asymptotic equations of trailing edge flow

Abstract

Abstract According to Stewartson (1969, 1974) and to Messiter (1970), the flow near the trailing edge of a flat plate has a limit structure for Reynolds number Re→∞ consisting of three layers over a distance O(Re-3/8) from the trailing edge: the inner layer of thickness O(Re-5/8) in which the usual boundary layer equations apply; an intermediate layer of thickness O(Re-1/2) in which simplified inviscid equations hold, and the outer layer of thickness O(Re-3/8) in which the full inviscid equations hold. These asymptotic equations have been solved numerically by means of a Cauchy-integral algorithm for the outer layer and a modified Crank-Nicholson boundary layer program for the displacement-thickness interaction between the layers. Results of the computation compare well with experimental data of Janour and with numerical solutions of the Navier-Stokes equations by Dennis & Chang (1969) and Dennis & Dunwoody (1966).