Iterative computation of transonic shock-free profile flow at zero incidence

Abstract

An approximate form of the transonic integral equation of Oswatitsch for steady inviscid flow past a thin symmetric profile at zero incidence has been studied iteratively. A direct iteration scheme has been presented, which converges to the same shock-free supercritical flow for four different starting solutions. Another square-root iteration scheme, which converges in subcritical flow, has been discussed. Also, the computational results delivered by the Schubert-Schleiff series [2] are presented briefly. Computational results show that, for a parabolic arc profile, shock-free supercritical flow exists for values of the reduced thickness ratio τ in the range 0.596<τ<0.64.