**3.2 Mesh independence**

An appropriate grid appears to be the key to numerical prediction accuracy, particularly in the case of aerodynamic heating prediction. A grid independence investigation was undertaken over multiple grid densities before initiating the CFD simulations. Because the heat transfer between the surrounding air and the vehicle wall was so important in this research, attention has been devoted to the near-wall mesh quality.

In the Lobb sphere blunt body, five-level grids are employed, and the details of these grids are shown in **Table 1**. The region located near the wall has meshed with a gradient structured mesh. The flow temperature for different grids is shown in **Figure 5**, we notice that the more the grid is refined more the temperature is stable where the result starts to be independent of the mesh. As computational time depends on the size of the grid. Thus the grid of case 4 is used in the following simulations with considering the calculation efficiency.


**Table 1.** *Lobb sphere grid independency.*

**Figure 5.** *Lobb sphere grid independency.*


#### **Table 2.**

*Blunt spike configuration grid independency.*

*Aero Heating Optimization of a Hypersonic Thermochemical Non-Equilibrium Flow… DOI: http://dx.doi.org/10.5772/intechopen.101659*

**Figure 6.** *Blunt spike grid independency.*

Always by the same refinement method, the sensitivity test for the spike mesh was performed for three different mesh densities (**Table 2**). We notice that the result become independent of mesh from adapt 2 because the variation of temperature is no longer observed during the refinement in **Figure 6**, from adapt 2 with a temperature of 11123 k to adapt 3 with temperature 11232 k so we can consider that the "adapted 2 mesh" is the optimum mesh.
