Spherical Source Flow with a Finite Back Pressure

The interaction of a hypersonic spherical source flow with a rarefied background is investigated using the Boltzmann equation with model collision terms. Employing multifluid descriptions of the flow, it is found that two length scales, Rp and R∞, are important in describing the interaction as the background becomes increasingly rarefied. Background scattering occurs on the scale of Rp and jet scattering on the scale of R∞. Matched asymptotic expansions of the variables in the two regions are developed in terms of the parameter ε = Rp/R∞→0, and first-order composite solutions constructed. These solutions describe the transition away from the perfect vacuum limit of the expanding flow.