A Small Disturbance Model for Transonic Flow of Pure Steam With Condensation

Abstract

A small-disturbance model to study transonic steady condensing flow of pure steam around a thin airfoil is developed. Water vapor thermodynamics is described by the perfect gas model and its dynamics by the compressible inviscid flow equations. Classical nucleation and droplet growth theory for homogeneous and nonequilibrium condensation is used to compute the condensate mass fraction. The model is derived from an asymptotic analysis of the flow and condensation equations in terms of the proximity of upstream flow Mach number to 1, the small thickness ratio of airfoil, the small quantity of condensate, and the small angle-of-attack. The flow field may be described by a nonhomogeneous and nonlinear partial differential equation along with a set of four ordinary differential equations for calculating condensate mass fraction. The analysis provides a list of similarity parameters that describe the flow physics. A numerical scheme, which is composed of Murman and Cole's algorithm for the computation of flow parameters and Simpson's integration method for calculation of condensate mass fraction, is applied. The model is used to analyze the effects of heat release due to condensation on the aerodynamic performance of airfoils operating in steam at high temperatures and pressures near the vapor–liquid saturation dome.