Prandtl–Meyer flows with homogeneous condensation. Part 1. Subcritical flows

Abstract

Prandtl–Meyer flows with heat addition from homogeneous condensation not exceeding a critical value (subcritical flows) are investigated by an asymptotic method in the double limit of a large nucleation time followed by a small droplet growth time. The physically distinct condensation zones, with detailed analytical structure, are displayed along streamlines and the flow field in each zone is determined utilizing the asymptotic solution of the rate equation along streamlines. In particular the nucleation wave front, which corresponds to states of maximum nucleation along streamlines, is accurately located independently of the particular condensation model employed. Results obtained using the classical nucleation equation together with the Hertz–Knudsen droplet growth law show, despite qualitative agreement, considerable differences between the nucleation wave fronts and measured onset conditions for the experiments of Smith (1971), because of intersecting characteristics in the heat addition zones. This shows the necessity of including an embedded oblique shock wave in the expansion fan of corner expansion flows for the cases investigated.