Transonic flow of moist air around thin airfoils

A new small-disturbance model for two-dimensional, steady, and diabatic transonic flow of moist air around a thin airfoil is presented. The study is based on theoretical analyses and numerical simulations. The condensation processes include the nonequilibrium and homogeneous condensation for purified supersaturated moist air and the equilibrium and heterogeneous condensation for moist air with foreign nuclei. The model explores the nonlinear interactions between the near-sonic speed of the flow, the small thickness ratio and angle of attack of the airfoil, and the small amount of water vapor in the air. The flow field is governed by a nonhomogeneous (extended) transonic small-disturbance (TSD) equation for the solution of the velocity perturbation potential coupled with the condensation equations. In the case where the nonequilibrium and homogeneous condensation occurs, the classical nucleation and condensation equations are reduced to a set of four ordinary differential equations for the calculation of the condensate (or sublimate) mass fraction. In the case where the equilibrium and heterogeneous condensation occurs, the condensate mass fraction can be expressed in terms of the velocity potential. The asymptotic analysis gives the similarity parameters that govern the flow problem in each case. An iterative numerical method which combines the type-sensitive difference scheme of Murman and Cole [14] for the solution of TSD equation with Simpson's integration rule for the estimation of condensate mass production is developed. The numerical scheme is studied for mesh convergence and also shows agreement of the pressure coefficient distribution, of the condensate mass fraction distribution, and of the water vapor pressure as a function of temperature with available results [23] from simulations using the Euler equations. The present work provides the theoretical understanding of two-dimensional transonic flows of moist air around thin airfoils with energy supply by the condensation.