Two-fluid theory of the condensation and evaporation effects in fluid flow

A two-fluid theory for the effects of condensation and evaporation in the fluid flow has been formulated. Attention is given to a mixture of two fluids of which fluid 1 is a perfect gas while fluid 2 may exist in its liquid, vapor or a mixture of a liquid and its own vapor state. A dryness fraction lambda is introduced. When lambda = 1, fluid 2 is in gaseous state; when lambda = 0, fluid 2 is in liquid state and when lambda is greater than 0 and less than 1, fluid 2 is a mixture of a liquid and its own vapor. A relaxation time t-lambda characterizes the relaxation process of evaporation or condensation. With this formulation an investigation may be conducted of the relaxation zone in the condensation shock in a supersonic wind tunnel as well as the unsteady flow region due to condensation and evaporation when the mass concentration of water in moist air is very high. The general fundamental equations of this two-fluid theory are given. A special case of one-dimensional unsteady nozzle flow with condensation and evaporation is discussed in details. Finally, the sound speed of fluid 2 is briefly analyzed.