Description of the Thermal Spike Resulting from the Expansion of a Perfect Gas from an infinite Reservoir into a Void Main

摘要

The one-dimensional, inviscid equations of motion are applied to the problem of describing the shock and rarefaction wave which form when the flow of a perfect gas from an infinite reservoir into a vacuous main is initiated. Characteristic theory is applied to show that the rarefaction wave is a centered, simple, backward-facing expansion wave. It is further shown that the stagnation temperature is a strict function of the local sound speed in the domain of this wave, and that the sound speed has a fixed, distinct value on each of the straight characteristics of the wave. The Rankine-Hugoniot Relations are used to show that the shock coincides with the greatest lower bound of characteristics. The local sound speed monotonically decreases to zero as the limit of characteristics in the wave domain is approached, resulting in the stagnation temperature monotonically approaching its maximum value there. It is deduced that the stagnation temperature function described in this report represents the thermal spike observed during the establishment of flow in a short-duration test facility. It is concluded that the thermal spike is the artifact of the flow work done to form the shock at the initiation of the blow-down process in such a facility.