**4. Validation of numerical models**

### **4.1 Validation of Lobb sphere blunt body**

By comparing our result of **Figure 7** with that of Tristan [30] which shows the variation of the temperature along with the relaxation range, one notices a good agreement between the two results in terms of pace and the quantitative terms. The slight difference is because Tristan considered a flow out of vibrational equilibrium. The study was simulated under the flowing free stream conditions (**Table 3**).

**Figure 7.** *Temperature along the stagnation ling.*


### **Table 3.**

*Lobb sphere free stream boundary condition [30].*


**Table 4.**

*Position of the shock of the Lobb sphere [30].*

**Table 4** illustrates that this result agrees well with the experimentally determined value with an error of 2.89% [32] and the numerical values obtained in the literature [33, 34].
