Prandtl–Meyer flows with homogeneous condensation. Part 2. Supercritical flows

Abstract

Prandtl–Meyer flows with embedded oblique shock waves due to excessive heat release from condensation (supercritical flows) are considered by extending the subcritical asymptotic solution of Delale & Crighton (1998). The embedded shock origin is located by the construction of the envelope of the family of characteristics emanating either from the corner or from the deflected wall in the parabolic approximation. A shock fitting technique for embedded oblique shock waves is introduced in the small deflection angle approximation and the law of deflection of a streamline through an embedded oblique shock wave is established within the same approximation. The network of characteristics downstream of the embedded shock front is constructed and the solution for the flow field therein is evaluated by utilizing the asymptotic solution of the rate equation along streamlines downstream of the shock front together with the equations of motion in characteristic form. Results obtained by employing the classical nucleation equation and the Hertz–Knudsen droplet growth law, compared with the supercritical experiments of Smith (1971) for moist air expansions, show that supercritical Prandtl–Meyer flows can only be realized locally when the embedded shock lies sufficiently far downstream of the throat, where the corner is located.