Hypersonic flow over spherically blunted cone capsules for atmospheric entry, Part 2: Vibrational non-equilibrium effects

Abstract

Atmospheric entry capsules shaped as spherically blunted, large apex-angle cones are widely used in space missions. In Part 1 of this study (Hornung et al. (2019)) we explored flows over the two elements of the capsule shape, the sphere and the sharp cone with detached shock, theoretically and computationally. Using a large number of inviscid, perfect-gas computations, analytical functions of two independent variables, the normal-shock density ratio and a cone-angle parameter were found for the dimensionless shock wave stand-off distance and the drag coefficient of a sharp cone. An analytical description was found for the shock stand-off distance in the transition from the 90 degree cone (flat-faced cylinder) to the sphere. In Part 1 it was speculated that the perfect-gas results have relevance to non-equilibrium situations if the normal-shock density ratio is replaced by the density ratio based on the average density along the stagnation streamline. In Part 2 the investigation is extended to blunted-cone capsule shapes. High-precision force measurements and schlieren image analysis are performed in the High-Enthalpy Shock Tunnel Göttingen (HEG) of the German Aerospace Centre using air as test gas, at conditions where vibrational non-equilibrium effects are significant. Accordingly, results are compared to viscous numerical predictions using different physico-chemical models. A theoretical model is constructed for the density profile along the stagnation streamline that is determined by the free-stream conditions and gives the average density. Comparisons of the experimental and numerical results for the dimensionless shock stand-off distance and the drag coefficient, with the extension of the analytical functions of Part 1 to vibrationally relaxing flow exhibit very good agreement in all of a range of geometries.