Asymptotic solution of transonic nozzle flows with homogeneous condensation. I. Subcritical flows

The one-dimensional (1-D) asymptotic solution of subcritical transonic nozzle flows with nonequilibrium homogeneous condensation is presented. An algorithm based on a local iterative scheme that exhibits the asymptotic solution in distinct condensation zones is developed for transonic moist air expansions under atmospheric supply conditions. Two models that characterize the state of the condensed phase as water drops or ice crystals are employed, together with the classical nucleation theory and Hertz-Knudsen droplet growth law. It is shown that the 1-D asymptotic predictions are in good agreement with the recent static pressure measurements of moist air expansions in relatively slender nozzles when the condensed phase is assumed to consist purely of water drops. © 1993 American Institute of Physics

The mathematical theory of thermal choking in nozzle flows

The mathematical theory of sub- and supercritical nozzle flows is presented by a unified description of integro-algebraic and differential formulations of the flow equations. The critical amount of heat necessary for a thermally choked flow is defined and models which approximate this critical amount of heat are constructed for nozzle flows with both given internal heat source distributions and nonequilibrium condensation. In particular a cubic equation for an estimate of the limiting condensate mass fraction for shock free condensing flows is derived and a criterion for the existence of supercritical condensing flows based on this estimate is established. The necessary and sufficient conditions for thermal choking are then stated. It is shown that the commonly accepted view, which asserts that the flow Mach number reaches unity at thermal choking (known to be not always true in condensing flows), only exhibits a necessary condition for a thermally choked flow. © 1993 Birkhäuser Verlag