Impact of fundamental molecular kinetics on macroscopic properties of high-enthalpy flows: The case of hypersonic atmospheric entry

Thermochemical nonequilibrium is one of the most challenging issues when dealing with hypersonic flows experienced by objects (space vehicles, meteoroids, space debris) at atmospheric entry. The case of a hypersonic flow past a sphere is considered as a test model for systems in strong chemical and thermal nonequilibrium conditions, mimicking the extreme environment experienced by objects entering a planetary atmosphere. The problem has been studied using the state-to-state approach, calculating directly the distribution of vibrational levels of ${\mathrm{O}}_2$ and ${\mathrm{N}}_2$, together with the flow field, including also viscous effects. Nonequilibrium distributions are observed and the results have been compared with macroscopic experimental data, showing that the state-to-state model is able to provide better capabilities for predicting experimental results than the traditional multitemperature approach. The use of graphics processing units allowed us to obtain these results in a two-dimensional configuration, opening additional perspectives in the investigation of reacting flows.

Figure 1

Case 1: Numerical and experimental [74, Fig. 10] shock shape (supposing that the experimental error is equal to that provided for the results along the stagnation line, see Table 1, the bow shock error bar would fall inside the symbol dimension): (a) StS model and (b) Park model.

Figure 2

Case 1: Stagnation line profiles: (a) closeup of the Mach number profiles at the shock position along with the experimental stand-off distance ($X/R=-0.1129\pm 1.33\%$) [74, row 18, Table 1] and (b) density profiles.

Figure 3

Closeup of the Mach number stagnation line profiles at the shock position along with the experimental stand-off distance [74, Table 1]: (a) case 2; (b) case 3; (c) case 4; and (d) case 5.

Figure 4

Case 1: Stagnation line profiles: (a) translational and vibrational temperature profiles. Points 1, 2, and 3 show the location along the stagnation line where vibrational distributions have been evaluated (see Fig. 5); (b) oxygen atom reaction rate: the inset shows the mass fractions of O (${\mathrm{Y}}_O$).

Figure 5

Case 1: stagnation line populations with actual to Boltzmann ratio in the inset: (a) ${\mathrm{N}}_2$ and (b) ${\mathrm{O}}_2$. Populations have been evaluated along the stagnation streamline and downstream of the shock wave at probes 1, 2, and 3 whose locations are given in Fig. 4.

Figure 6

Case 1: wall surface populations with the actual to Boltzmann ratio in the inset: (a) ${\mathrm{N}}_2$ and (b) ${\mathrm{O}}_2$. The azimuthal angle $\theta$ is defined in Fig. 1.

Figure 7

Case 1: actual to Boltzmann ratio for the highest vibrational level: (a) ${\mathrm{N}}_2$ and (b) ${\mathrm{O}}_2$.

Figure 8

Case 1: grid convergence study performed with the Park model: Mach number (a) and temperature profiles (b) along the stagnation line for both the BASE and FINE grid.

Figure 9

Case 1: grid convergence study performed with the Park model: contour plot and isolines of the Mach number computed on the BASE and on the FINE grid, respectively. The bow-shock experimental position is also shown.

Figure 10

Case 1: (a) Temperature, (b) density, and (c) pressure contour plots: (left) Park and (right) StS.

Figure 11

Comparison between GPU and CPU performance in terms of time per iteration (s) and energy consumption per iteration (J) by considering the BASE grid ($152\times 392$ fluid cells) and the setup of case 1.