# An Effective Simulation Scheme for Predicting the Aerodynamic Heat of a Scramjet-Propelled Vehicle
## 3 Validation Tests
### Hypersonic Stage
#### 3.4.3 Simulation Parameters  
Based on the SST k-omega and Spalart-Allmaras turbulence models, combined with two flux types, we adopted three different cell Reynolds numbers to carry out multiple groups of simulations, and the simulation tests showed that a cell Reynolds number of 40 was the appropriate value for the wedge section. \(S\) is the distance to the original point of the wedge along the wedge surface and \(Y\) is the normal distance to the wedge surface. \(T_{INF}\) is the freestream's static temperature ahead of interaction, which was 81.2 K. \(U_{INF}\) is the freestream's velocity ahead of interaction, which was 1274 m/s. \(T\) and \(U\) are the local freestream temperature and velocity, respectively. Figure 20 shows distribution diagrams of \(T/T_{INF}\) and \(U/U_{INF}\) versus \(Y\) from the experiment and the simulation, respectively, at \(S\) = 0.055 m. The identical distribution diagrams at \(S\) = 0.105 m and \(S\) = 0.155 m are depicted in Figures 21 and 22, respectively. The overall distribution trend of the simulation data matched well with the experiment data. The results based on the Spalart-Allmaras turbulence model, the cell Reynolds number of 40 and AUSM+ flux type were the closest to the experimental data, and the average error ratio of \(T/T_{INF}\) and \(U/U_{INF}\) were about (7.41% 3.1%), (5.46% 2.14%), and (6.32% 2.22%), respectively. Further, another four simulations with different aspect ratios based on Spalart-Allmaras, a cell Reynolds number of 40 and an AUSM+ flux type were performed. The aspect ratios 80, 40, 10, and 2 were adopted, and Figures 23-25 represent the distribution diagrams of the error ratios of \(T\) and \(U\). As depicted in Figure 23, at S = 0.055 m, the mean errors of \(T\) and \(U\) corresponding to the four aspect ratio conditions were (7.41%, 3.1%), (6.04%, 2.07%), (5.97%, 2.05%), and (5.43%, 1.93%), and the optimal simulation results were obtained when the aspect ratio was 2. In Figures 24 and 25, we can observe the same consequences. At \(S\) = 0.105 m, the mean errors of \(T\) and \(U\) corresponding to the four aspect ratio conditions were (5.46%, 2.18%), (4.96%, 2.17%), (4.96%, 2.17%), and (4.89%, 2.16%). At \(S\) = 0.155 m, the mean errors of \(T\) and \(U\) corresponding to the four aspect ratio conditions were (6.32%, 2.59%), (6.04%, 2.56%), (6.03%, 2.56%), and (6.01%, 2.54%). When the aspect ratio decreased from 80 to 40, the error ratios of T and U were reduced to a certain extent. However, with the further reduction of the aspect ratio, the optimization effect of the numerical calculation decreased. At S equals 0.055 m, the maximum changes of error ratio of \(T\) and \(U\) were 0.54% and 0.12%, respectively; at \(S\) equals \begin{table}
\begin{tabular}{c c c} \hline \hline
**Validation Parameters** & **SST k-omega** & **Spalart-Allmaras** \\ \hline \multirow{2}{*}{Solver} & Density-based & Density-based \\  & Flux: AUSM+/ROE & Flux: AUSM+/ROE \\ \hline \multirow{3}{*}{Materials} & Density: Ideal-gas & Density: Ideal-gas \\  & Viscosity: Sutherland law & Viscosity: Sutherland law \\  & C\({}_{p}\) (\(\beta\)/kg-k): 1006.43 & C\({}_{p}\) (\(\beta\)/kg-k): 1006.43 \\ \hline \multirow{3}{*}{Initial conditions} & Mach number: 7.05 & Mach number: 7.05 \\  & Static pressure: 576 Pa & Static pressure: 576 Pa \\  & Static Temperature: 81.2 K & Static Temperature: 81.2 K \\ \hline \multirow{3}{*}{Boundary conditions} & INPUT: pressure far field & INPUT: pressure far field \\  & FARFIELD: pressure far field & FARFIELD: pressure far field \\ \cline{1-1}  & OUTPUT: pressure outlet & OUTPUT: pressure outlet \\ \cline{1-1}  & WALL: no slip, isothermal wall, 311 K & WALL: no slip, isothermal wall, 311 K \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Validation parameters of convergence results at the hypersonic stage. In conclusion, the performance of the Spalart-Allmaras model was better than that of the SST k-omega model for the wedge section at the hypersonic stage.