Development of the Distribution Function on the Centerline of a Free Jet Expansion

Abstract

Spherical source flow which closely approximates the flow on the centerline of an axisymmetric free jet expansion, is used as a theoretical model. The ellipsoidal statistical model is used to describe the intermolecular collisions. Three partial moments of the distribution function, and the value of the distribution function for a zero perpendicular component of molecular velocity, are calculated as functions of distance and molecular velocity for two values of the Prandtl number (23 and 1), and for two gross collision rates such that the viscosity would be proportional to T1/2 and T, where T is the temperature. The quantities calculated correspond to idealized experimental measurements. It is found that the distribution function is, to a good approximation, ellipsoidal in velocity space for (Tr − Tp)/T≲1, where Tr and Tp are the parallel and perpendicular temperatures, respectively. It is also found that the deduction of Tp and Tr from the experimental quantities by fitting with an assumed Gaussian velocity dependence can lead to serious errors as the flow becomes frozen. There is a significant effect of the Prandtl number upon some of the results.