## 3 Results and Discussions
### Species
The electrons in the 7-species model are mainly provided by the ionization of a small portion of NO, while the 11-species model contains more ionization reactions, and thus the electron density in the flow field of the 11-species model is significantly higher than that of the 7-species model. Ionization and dissociation reactions are both endothermic processes. Compared to 5- and 7-species models, the 11-species model contains more endothermic reactions, possibly resulting in most conversion of the internal energy of air into the zero-point energy of the reaction products, thus lowest temperature is achieved in the flow field. Under the three freestream conditions, the descending order of translational-rotational temperature for the three models is 5-species > 7-species > 11-species. For all models, because the pressures are almost the same in the shock layer. Therefore, as the temperature of the shock layer increases, the density decreases. Consequently, the order of the shock standoff distance for the three models is 5-species > 7-species>11-species. Figure 4: Pressure distribution along the stagnation line under different conditions. Figure 5: Number density of atom nitrogen along the stagnation line for one temperature model with different chemical kinetic model. Figure 6: Number density of electron along the stagnation line for two temperature model with different chemical kinetic model. To investigate the differences caused by the chemical models with different number of species in detail. The stable values of mass fractions of all species behind the shock wave along the stagnation lines of two cases (\(Ma\) = 29.05 and \(Ma\) = 38.94) are compared in Table 4. It can be found that at \(Ma\) = 29.05, the proportions of N and O dominate and the total proportion of other species is very little, which means that the 5-, 7- and 11-species models can lead to the similar effects of chemical reactions on the flow simulation. However, at \(Ma\) = 38.94, the ionization reactions become significant and generate considerable quantities of NO\({}^{+}\), N\({}^{+}\) and O\({}^{+}\). In fact, the ionization reactions are endothermic and can lower the temperature level in the shock layer as shown in Figure 3. Therefore, compared to the case of \(Ma\) = 29.05, the shock layer temperatures obtained by the 5-, 7- and 11-species models decrease in turn more significantly for the case of \(Ma\) = 38.94. As above-mentioned discussion, the chosen number of species in air reaction models has a more significant impact on the shock stand-off distance as the Mach number and altitude grow higher. Figure 5 shows that the number densities of nitrogen atom reach almost the same level in the shock layer for all model combinations, so is the case of oxygen atom. Therefore, the thermochemical models have no obvious impact on the results of dissociation reactions of O\({}_{2}\) and N\({}_{2}\). However, this situation is not applicable for all species. Figure 6 demonstrates that, no matter what chemical reaction models are used, there are significant differences in the electron concentration and the shock standoff distance between the two temperature models, which indicates that thermodynamic processes of high temperature air are no longer reliably governed by a single temperature.