Thermal Choking Due to Nonequilibrium Condensation

Abstract

A theory of thermal choking due to nonequilibrium condensation in a nozzle is presented. An explicit equation for the critical quantity of heat in condensing flow has been derived. The equation is of general validity and applies to vapor-droplet flow with or without a carrier gas. It has been usually assumed in the literature that the classical gas dynamics result for the critical quantity of heat applies in condensing flow as well. The classical result is, however, obtained by considering external heat addition to an ideal gas in a constant area duct. In this paper it is shown that the area variation across the condensation zone (although small) and the depletion in the mass of vapor as a result of condensation have profound effects on the critical quantity of heat. The present equation (derived from an integral, control-volume approach) agrees very well with results from full time-marching solution of the nonequilibrium, differential gas dynamic equations. The classical gas dynamics result, on the other hand, seriously underpredicts the critical heat for condensing flow in nozzles (by a factor of three in the example calculation presented).