# An Effective Simulation Scheme for Predicting the Aerodynamic Heat of a Scramjet-Propelled Vehicle
## 3 Validation Tests
### High Supersonic Stage
#### 3.3.3 Simulation Parameters
When the aspect ratio was equal to 100, the optimal simulation results could be obtained, and the mean error, error variance, and mean error ratio were 0.022, 5.47 \(\times\) 10\({}^{-5}\), and 9.1%, respectively. Subsequently, as the aspect ratio decreased, the error ratio increased. Figure 13b is a comparison of the wall pressure coefficient distribution from the experiment and the simulation adopting the Spalart-Allmaras model at \(T_{W}=100\) K. The overall distribution trend of the simulation data matched well with the experiment data and the simulation results were very close to the experiment data at the upper stream of the wedge section. The error ratio distribution of the numerical data with the experiment data at the wedge section is displayed in Figure 14a. The results based on a cell Reynolds number of 8 and the AUSM+ flux type were the closest to the experimental data and the average error ratio was about 11.18%. The aspect ratios 400, 200, 100, and 50 were adopted; Figure 14b shows the distribution diagram of the error ratio of the pressure coefficient. As the aspect ratio decreased, the error ratio decreased. When the aspect ratio was equal to 200, the optimal simulation results could be obtained, and the mean error, error variance, and mean error ratio were 0.027, 8.95 \(\times\) 10\({}^{-5}\), and 10.9%, respectively. Subsequently, as the aspect ratio decreased, the error ratio increased. To sum up, at \(T_{W}=100\) K, a grid strategy with a cell Reynolds number of 16 and aspect ratio of 100, combined with a numerical method, adopting the SST k-omega turbulence model, the density-based solver, and the AUSM+ flux type, obtained an optimal simulation. Similarly, other multiple groups of simulation were performed at \(T_{W}=290\) K. The overall distribution trend of the simulation data adopting the SST k-omega model matched well with the experiment data, as can be seen in Figure 15a. Figure 15b describes the error ratio distribution of numerical data with the experiment data at the wedge section. The results based on a cell Reynolds number of 16 and an AUSM+ flux type were the closest to the experimental data and the average error ratio was about 8.27%. Further, using the same number of cells, another four simulations with different aspect ratios based on a cell Reynolds number of 16 and an AUSM+ flux type were performed. The aspect ratios 400, 200, 100, and 50 were adopted; Figure 16a demonstrates the distribution diagram of the error ratio of the pressure coefficient. As the aspect ratio decreased, the error ratio decreased. When the aspect ratio was equal to 200, the optimal simulation results could be obtained, and the mean error, error variance and mean error ratio were 0.018, \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{2}{c}{**Validation Parameters**} \\ \hline Solver & Density-based & Density-based \\  & Flux: AUSM+/ROE & Flux: AUSM+/ROE \\ \hline Models & SST k-omega & Spalart-Allmaras \\ \hline Materials & Density: Ideal-gas & Density: Ideal-gas \\  & Viscosity: Sutherland law & Viscosity: Sutherland law \\  & C\({}_{\text{P}}\) (\(\hat{\text{J}}\)/kg-\(\hat{\text{k}}\)): 1006.43 & C\({}_{\text{P}}\) (\(\hat{\text{J}}\)/kg-\(\hat{\text{k}}\)): 1006.43 \\ \hline Initial conditions & Mach number: 5 & Mach number: 5 \\  & Static pressure: 850.5173 Pa & Static pressure: 850.5173 Pa \\  & Static Temperature: 79.17 K & Static Temperature: 79.17 K \\ \hline Boundary conditions & INPUT: pressure far field & INPUT: pressure far field \\  & FARIFIELD: pressure far field & FARIFIELD: pressure far field \\  & OUTPUT: pressure outlet & OUTPUT: pressure outlet \\  & WALL: no-slip, isothermal, & WALL: no-slip, isothermal, \\  & 100 K/290 K & 100 K/290 K \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Validation parameters of convergence results at the high supersonic stage. 8.16 \(\times\) 10\({}^{-5}\), and 7.45%, respectively. Subsequently, as the aspect ratio decreased, the error ratio increased.