Effect of finite-rate catalysis on wall heat flux prediction in hypersonic flow

This work deals with the simulation of hypersonic flows past a copper sphere by using a finite-rate catalysis model coupled with either a state-to-state (StS) or a multitemperature thermochemical nonequilibrium approach. Without detailed state-specific data for copper catalytic recombination, molecules formed on the surface are described with three different statistics: one reproducing the incoming distribution, one considering a uniform distribution, and the third populating only the highest vibrational level. Following recent experimental and theoretical results, very high enthalpy and very low pressure conditions have been considered. The finite-rate partial catalysis model provides results that are closer to the experimental ones than those obtained by a fully catalytic approach. The multitemperature model shows better agreement with experiments, whereas among the StS catalytic approaches the outcomes have shown that the surface recombination on only the highest energy level gives more accurate results.

Figure 1

Nozzle flow: gas rototranslational temperature contour plot obtained by using both the Park (top) and the StS (bottom) models.

Figure 2

Nozzle flow: rototranslational temperature, vibrational temperature, and Mach number profiles along the nozzle axis.

Figure 3

Nozzle flow distributions at $x=3.5\mathrm{m}$ along the axis: (a) ${\mathrm{N}}_2$ and ${\mathrm{O}}_2$ populations; (b) actual to Boltzmann ratio.

Figure 4

Nozzle flow: species mass fractions along the axis: (a) linear scale, (b) log scale.

Figure 5

Flow past a sphere: pressure contour plot: (a) Park and StS-1; (b) StS-1 and StS-3.

Figure 6

Flow past a sphere: stagnation line temperature profiles. Points 1, 2, 3, and 4 show the location along the stagnation line where vibrational distributions have been evaluated (see Figs. 9 and 10).

Figure 7

Flow past a sphere: stagnation line mass fractions: (a) comparison with Park; (b) comparison among StS models.

Figure 8

Flow past a sphere: wall recombination coefficients as a function of the azimuthal angle $\theta$ [deg].

Figure 9

Flow past a sphere: StS-1 approach: 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. 6.

Figure 10

Flow past a sphere: (a) ${\mathrm{N}}_2$ and (b) ${\mathrm{O}}_2$ vibrational distribution. Populations have been evaluated along the stagnation streamline and downstream of the shock wave at probes 2, 3, and 4, whose locations are given in Fig. 6.