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.