Kinetic Theory of Source Flow Expansion with Application to the Free Jet

Abstract

A systematic approximation has been constructed for the moment equations of kinetic theory which describe source flow expansion. For small source Knudsen number, the moments are expanded and solutions are obtained near the source. These solutions are nonuniformly valid far from the source, breaking down when transition flow is encountered. To analyze the rarefied regime, the equations are rescaled taking account that the flow is hypersonic in the transition regime. This allows us to apply a hypersonic approximation to the moment equations in the rarefied regime and subsequently match this to the inviscid solution. For spherical expansion we resolve the problem to a relaxation process with two translation temperatures, one along streamlines T∥, and the other transverse to streamlines T⊥. We obtain expressions for the terminal Mach number in terms of source Knudsen number and intermolecular force law, and a simple rarefaction criteria is found which states that transition flow is encountered when T∥ − T⊥ ≅ Tisentropic.