Real-gas extensions to tangent-wedge and tangent-cone analysis methods
DOI: 10.2514/1.28521 Engineering codes are powerful tools for the conceptual design stage. Use of these codes in early design stages enables higher fidelity computational fluid dynamics calculations or wind-tunnel tests to be performed on more mature configurations. Two widely used engineering tools for conceptual level supersonic/hypersonic aerodynamic prediction are tangent-wedge and tangent-cone methods. Unfortunately, these analysis tools lack the ability to systematically account for effects of real-gas flow across the oblique shock wave. This paper derives an extension to the classical oblique shock wave equations where the effects of real-gas flow changes are modeled using theoretical models borrowed from statistical mechanics. Using an enthalpy balance across the shock wave, the Einstein model for a diatomic gas is analytically integrated to give a relationship of temperature, ratio of specific heats, and velocity on the downstream side of the shock wave. This relationship replaces the energy equation used in the ideal-gas obliqueshockanalysis.Thismethodisadaptedtoconical flowfieldassuminganinitialshockangle,andusingthenew oblique shock algorithm to compute properties immediately behind the conical shock. The resulting model is compared to equilibrium real-gas calculations and shown to give accurate results well into the hypersonic flow regime, approximately Mach 20.