Oblique Shock Relations for Air at Mach 7.8 and 7200 R Stagnation Temperature

Abstract

Oblique shock relations for dissociated air in thermodynamic equilibrium have been calculated for a free stream flow Mach number of 7.8 in the test section with an equilibrium stagnation temperature of 7200 R in the reservoir. The results for the density, pressure and temperature ratios, and flow deflection across the shock wave are presented as functions of the shock wave angle. Complete equilibrium has been assumed in the calculations, utilizing the best available thermodynamic properties of air for the region considered. The real gas oblique shock relations have been experimentally verified by testing an adjustable two-dimensional wedge model in a hypersonic shock tunnel. Correlations of the calculated and experimental pressure ratios and shock wave angles are presented as functions of flow deflection angle. When allowance was made for the boundary layer displacement effect, the correlation was seen to be good. The reservoir conditions were selected to insure that the flow in the shock tunnel would be close to equilibrium.T HE ADVENT of missiles and space vehicles traveling at hypersonic flight speeds has recently stimulated much interest in the shock waves produced by such bodies. In particular, there has been considerable discussion of the "real gas effects" in the air immediately behind high Mach number shock waves. By "real gas effects" is meant the departure of the thermodynamic properties of the medium from a perfect gas with a constant specific heat ratio of 1.4. Although air departs from this perfect gas model at temperatures as low as 540 R, this concept has been used with considerable success in the past for analyzing low Mach number shock properties. However, at any flow condition even approaching that under consideration here, this model must be abandoned and, instead, the actual thermodynamic properties of air used.As soon as shock waves strong enough to excite vibration, dissociation or ionization and strong enough to produce chemical reactions are considered, the reaction rate question immediately comes to the forefront. In dealing with shock processes wherein a gas is required to absorb large quantities of kinetic energy as internal energy virtually instantaneously, one must be concerned not only with the final thermodynamic properties, but also with the time needed.to achieve thermodynamic equilibrium. A rigorous analytical method for treating the shock problem w r ould be to set up a careful kinetic theory model of the gas molecules with reaction rates, and then to analyze exactly what happens as the flow proceeds through the momentum and energy readjustments at the shock region. Unfortunately, there is insufficient knowledge of the properties and reaction rates of air at the present time to employ such a method. It is conceivable also that even if all of the rate constants and interaction parameters were known, the complexity of the calculation would prevent a practical solution.Recently (1,2) 5 shock relations for air under the assumption of instantaneous thermodynamic equilibrium downstrea...

Hypersonic Shock Wave-Boundary Layer Interaction and Leading Edge Slip

“…The free stream Mach number and the ratio of specific heats 7 = 1.4 were used to calculate the pressure ratio across the shock wave from an oblique shock relationship. Since the free stream temperature in the test section is 810 R for a reflected stagnation temperature of 7200 R, the ratio of specific heats of 1.4 is valid as long as the shock wave angle is not large (28).…”

“…By measuring the shock wave angle from the Schlieren photograph as a function of the distance from the leading edge, the pressure ratio across the shock can be calculated by using the oblique shock wave relationship for perfect gas, as well as for real gas with thermodynamic equilibrium (28). From the leading edge the pressure ratio across the shock wave increased with X up to "a peak value corresponding to the maximum shock wave angle.…”