The effect of multiply reflected molecules in free molecule flow over a general body

Abstract

A method was devised and calculations were performed to determine the effects of reflected molecules on the aerodynamic force and moment coefficients for a body in free molecule flow. A procedure was developed for determining the velocity and temperature distributions of molecules reflected from a surface of arbitrary momentum and energy accommodation. A system of equations, based on momentum and energy balances for the surface, incident, and reflected molecules, was solved by a numerical optimization technique. The minimization of a "cost" function, developed from the set of equations, resulted in the determination of the defining properties of the flow reflected from the arbitrary surface. The properties used to define both the incident and reflected flows were: average temperature of the molecules in the flow, angle of the flow with respect to a vector normal to the surface, and the molecular speed ratio. The properties of the reflected flow were used to calculate the contribution of multiply reflected molecules to the force and moments on a test body in the flow. The test configuration consisted of two flat plates joined along one edge at a right angle to each other. When force and moment coefficients of this 90' concave wedge were compared to results that did not include multiple reflections, it was found that multiple reflections could nearly double lift and drag coefficients, with nearly a 50% increase in pitching moment for cases with specular or nearly specular accommodation. The cases of diffuse or nearly diffuse accommodation often had minor reductions in axial and normal forces when multiple reflections were included. There were several cases of intermediate accommodation where the addition of multiple reflection effects more than tripled the lift coefficient over the convex technique.