## 3 Results and Discussions
### Species  
Table 3 lists the shock standoff distance and parametric ratio across the shock along the stagnation line for each model combination. It can be found that the effects of different chemical kinetic models with the same number of gas species on the shock standoff distance, the ratios of pressure and density across the shock are extremely small and negligible. Meanwhile, it can be found that at higher Mach numbers and altitudes, the models with different numbers of gas species have much greater influence on the thickness and density of the shock layer, and the lower number of species leads to a thicker shock layer. The thickness of the shock layer is positively correlated with the density ratio ahead of and behind the shock wave, that is, the lower the density behind the shock, the thicker the shock layer. The shock standoff distance of perfect gas is much higher than that of chemically reacting gas mixture. Figure 4 shows the pressure distributions along the stagnation lines computed by the 5-, 7-, and 11-species models of Dunn-Kang, Gupta, and Park combined with the two different temperature models for the three freestream conditions, respectively. It is found that the pressure distributions along the stagnation lines obtained by different models are nearly the same as that of a perfect gas under the same freestream condition. This is because the pressure behind the shock is a \"mechanical\" parameter that depends mainly on the freestream speed and density. The pressure is uneasily affected by thermochemical nonequilibrium. The pressure behind the shock remains almost constant and its value can be approximated by the relation of pressure ratio across the normal shock. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{\(\mathrm{Ma}=29.05\)} & \multicolumn{3}{c}{Dunn-Kang (1T/2T)} & \multicolumn{3}{c}{Gupta (1T/2T)} & \multicolumn{3}{c}{Park (1T/2T)} & \multicolumn{3}{c}{Perfect Gas} \\ Species & SS & 7S & 11S & 5S & 7S & 11S & 5S & 7S & 11S & \(\backslash\) \\ \hline \(\delta\) (mm) & 1T & 141 & 141 & 140 & 141 & 141 & 140 & 143 & 143 & 141 & 380 \\  & 2T & 145 & 145 & 144 & 145 & 145 & 143 & 147 & 147 & 145 & 380 \\ \(\rho/\rho_{\infty}\) & 1T & 14.17 & 14.19 & 14.62 & 14.17 & 14.22 & 14.62 & 14.08 & 14.11 & 14.52 & 5.92 \\  & 2T & 13.10 & 13.26 & 14.09 & 13.01 & 13.29 & 14.09 & 13.15 & 13.23 & 13.96 & \\  & 1T & 1015 & 1013 & 1016 & 1015 & 1016 & 1017 & 1015 & 1016 & 1017 & 974 \\  & 2T & 1012 & 1013 & 1016 & 1012 & 1013 & 1017 & 1013 & 1014 & 1016 & 974 \\ \hline \multicolumn{2}{c}{\(\mathrm{Ma}=34.34\)} & \multicolumn{3}{c}{Dunn-Kang (1T/2T)} & \multicolumn{3}{c}{Gupta (1T/2T)} & \multicolumn{3}{c}{Park (1T/2T)} & \multicolumn{3}{c}{Perfect Gas} \\ Species & SS & 7S & 11S & 5S & 7S & 11S & 5S & 7S & 11S & \(\backslash\) \\ \hline \(\delta\) (mm) & 1T & 173 & 173 & 146 & 173 & 172 & 145 & 174 & 173 & 149 & 377 \\  & 2T & 203 & 192 & 151 & 203 & 191 & 151 & 200 & 193 & 155 & \\  & 1T & 9 Figure 2 suggests that the chemical reaction models with different numbers of gas species not only have a significant effect on the shock standoff distance but also the temperature distribution behind the shock. The different numbers of species determine the composition of the gas in the flow field and the number of chemical processes. Figures 5 and 6 show the trend of species number density along the stagnation line predicted by different gas species models. The species number density mainly changes dramatically just behind the shock and near the wall. The curves of N and e\({}^{-}\) show the same patterns for both the one- and two-temperature models. The 5-species model contains no ionization reactions, and the diatomic molecules dissociate completely within a small distance behind the shock, while NO is generated. Both the 7-species model and the 11-species model contain ionization reactions.