Supersonic collisions of non-uniform gaseous bodies

Abstract

The collision of uniform gas streams is analysed by the Rankine–Hugoniot equations, which gives a precise description of its behaviour, and also by the computational von Neumann–Richtmeyer (VNR) method. The latter gives large spurious entropy generation at the collision interface, but comparison of the two sets of results indicates how a reasonable estimate of temperature in the collision interface could be obtained from the VNR results. The VNR method is then applied to the collision of identical gas streams in which the variations of density and temperature are similar to those along the diameter of a gaseous planet. Estimated true peak temperatures are found by discounting spurious entropy generation as indicated by the uniform stream system. Estimated peak temperatures increase with time and after 800 s a temperature greater than 4 × 106 K is indicated. The effect of going from a non-gravitational one-dimensional model to a gravitational three-dimensional planetary model is considered. The lateral spread of material in three dimensions would result in lower temperatures. However, this is offset by increases of temperature due to the release of gravitational energy and also energy released by D–D reactions that would be triggered at a temperature around 2–3 × 106 K.