Asymptotic solution of transonic nozzle flows with homogeneous condensation. II. Supercritical flows

A detailed analysis of supercritical transonic nozzle flows with stationary normal shock waves is presented. A classification scheme based on the normal shock location is obtained using asymptotic methods, and four distinct supercritical flow regimes are distinguished. A simple shock fitting technique that determines the shock location within any desired precision is introduced. Consequently, an algorithm that exhibits the asymptotic solution in each supercritical flow regime is developed for the expansion of moist air in nozzles with atmospheric supply conditions by utilizing the classical nucleation theory and the Hertz-Knudsen droplet growth law. Good agreement with the recent static pressure measurements and visualized shock locations is achieved in relatively slender nozzles when the condensed phase is assumed to consist purely of water drops.