**3. Numerical modeling**

For aerodynamic flow, Reynolds-Average Navier-Stokes (RANS) equations are adopted as the governing equations. The convective terms are approximated by the AUSM-DV scheme [28] with a MUSCL approach to increase the numerical accuracy. The turbulence model is required for several shear layers including the boundary layer, The k-*ω* model (SST) [29] model in the region close to the wall was used.

### **3.1 Computational model**

The structures of a Lobb sphere blunt body are shown in **Figure 1**. The diameter of the body is 6.35 mm with a length of 1.3 mm [30]. The geometry in **Figure 1** was created in a way that the simulation will be run using the axisymmetric Navier-Stock's equations, therefore, a two-dimensional symmetric geometry is created, with an axis defined at the radial centre of the studied body. This technique makes it possible to reduce the computational domain used and consequently reduce the calculation time.

Then we set up an opposing jet in the same Lobb sphere with a radius of 0.5 mm as shown in **Figure 2**.

**Figure 1.** *Lobb sphere mesh and geometry.*

**Figure 2.** *Lobb sphere with opposing jet mesh and geometry.*

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

**Figure 3.** *Blunt spike mesh and geometry.*

**Figure 4.** *Configuration of the spiked blunt body for simulation [31].*

Next, we install the second heat reduction configuration, the blunt Spike in front of the same Lobb sphere body profile to reconfigure the flow field and reduce the overheating in a re-entry hypersonic flight as shown in **Figure 3**. **Figure 4** shows the configuration and dimensions of the spiked (4) [31].

• The characteristic dimensional are d/D = 0.1, L/D = 0.9 and Rt/D = 0.2 where:

D: is the diameter of the spherical head profile, d: is the diameter of the spike,

L: is the spike length and Rt: is the transition part radius at the spike root.
