Drag and lift in nonadiabatic transonic flow

Transonic flows with heat addition over airfoils have been calculated for different angles of attack. The fluid is a mixture of an inert carrier gas and a small amount of a condensible vapor. For the phase change process coupled to the flow, two limiting cases are investigated: nonequilibrium condensation after significant supersaturation and homogeneous nucleation and equilibrium condensation. Numerical calculations based on the Euler equations are linked with either the classical nucleation theory coupled with microscopic or macroscopic droplet growth laws or an equilibrium process. An improved explicit time-dependent diabatic finite volume method is developed and applied to calculate stationary flows. Reservoir conditions of pressure, temperature, and vapor content are varied to simulate internal flows in transonic wind tunnels, turbomachinery, and atmospheric flight at low altitudes. The pressure drag and the lift may increase or decrease. Homogeneous condensation in internal flows produces a maximum decrease of the pressure drag of about 60% and a maximum lift decrease of 35%. Nonequilibrium phase transition of the vapor content in atmospheric flight decreases the lift about 10%, whereas the drag remains nearly constant. With the assumption of the more realistic equilibrium condensation process in atmospheric flight, the lift changes inversely; it increases about 30%, but the pressure drag increases more than 200%. Nonequilibrium and equilibrium condensation in transonic flow are quite easy to distinguish by the position and the extension of the normal shock. The equilibrium process enlarges the supersonic area remarkably, whereas it reduces in size when the vapor condenses not in equilibrium, i.e., gasdynamic phenomena may be used as a tool for the identification of the nature of the actual phase transition process.