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, Martinez Schramm & Hannemann, J. Fluid Mech., vol. 871, 2019, pp. 1097–1116) 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 $\varepsilon$ and a cone-angle parameter $\eta$ (which is a function of $\varepsilon$ and the cone half-angle $\theta$ ) 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 $^\circ$ 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 the test gas, at conditions where vibrational non-equilibrium effects are significant. Accordingly, results are compared with 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.

Numerical study on the non-equilibrium characteristics of high-speed atmospheric re-entry flow and radiation of aircraft based on fully coupled model

“…At present there are many thermochemical non-equilibrium simulations on the aerothermodynamics of hypersonic re-entry vehicles (Sanderson et al 2004;Kim, Kang & Park 2020;Li et al 2021;Miró Miró et al 2021;Passiatore et al 2022;Wu et al 2022;Schramm, Hannemann & Hornung 2023). In these numerical studies, the thermal non-equilibrium effect was described by the multi-temperature energy equations (Zheng et al 2021).…”

“…Therefore, compared with the conventional thermochemical non-equilibrium models, the collisional-radiative model can more reasonably predict the energy relaxation processes, chemical non-equilibrium and excited energy levels non-equilibrium phenomena. At present, the collisional-radiative model is usually implemented in zero-dimensional (0-D) (Teulet, Sarrette & Gomes 2001;Bultel et al 2006;Capitelli et al 2007;Annaloro & Bultel 2014) and one-dimensional (1-D) models (Panesi et al 2009;Campoli et al 2020;Du et al 2022), but has not been used in multi-dimensional flow calculations so far due to its intensive computational cost, and some simplification methods, such as the multi-group maximum entropy method, were proposed for simplifying the CR model for future coupling to multi-dimensional computational fluid dynamics (CFD) simulation (Liu et al 2015;Munafo, Liu & Panesi 2015;Munafo, Mansour & Panesi 2017;Sahai et al 2017Sahai et al , 2019Sahai et al , 2020Sharma, Liu & Panesi 2020). The 0-D calculations of the air collisional-radiative model for typical re-entry conditions indicated that the distributions of chemical species exhibit large differences from the results obtained by the global air chemical models (Bultel et al 2006;Annaloro & Bultel 2014).…”

“…2022; Wu et al. 2022; Schramm, Hannemann & Hornung 2023). In these numerical studies, the thermal non-equilibrium effect was described by the multi-temperature energy equations (Zheng et al.…”