Supersonic Flow With Variable Specific Heat

Abstract Formulas are developed for stagnation conditions and one-dimensional flow through shock waves, including Rankine-Hugoniot values, taking into account the variation of the specific heat of air with temperature by means of the concept of mean specific heats. These formulas are reduced to correction factors that may be applied to the widely used constant specific-heat formulas up to a Mach number of 7. The corrections involved are appreciable in the case of the density change through a shock wave and for the total pressure ratio across a shock wave, as well as for stagnation pressures and temperatures. The limitations imposed by the deviation of a gas at high pressure from the ideal equation of state, relaxation time, and dissociation are discussed.