Effect of Heat-capacity Lag on the Flow Through Oblique Shock Waves

An analysis is made of the effects of variable heat capacity on the flow parameters for oblique shock waves at high supersonic speeds at sea level. Two sets of results are obtained: one corresponding to conditions immediately behind the shock wave where only the active degrees of freedom of the molecules are in equilibrium; and another representing the asymptotic conditions far behind the shock wave where all the degrees of freedom are in equilibrium. The flow characteristics behind strong oblique shock waves are shown to depend upon the distance downstream of the wave as well as the Mach number and flow deflection. The density distribution at high speeds is many times as sensitive to beat-capacity changes as the pressure distribution. The effect of heat-capacity variation is expected to be of increasing significance at higher altitudes. The study of heat-capacity effects was used as background information to derive a very simple expression for predicting pressures due to shock waves and expansion waves at Mach numbers from 1.3 to infinity. The pressure equation is applied to several problems and is shown to be surprisingly accurate.