# 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  
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 simulation at \(T_{W}=\) 100 K. Figure 12 presents the wall pressure coefficient distributions from the experiment and the simulation adopting the SST k-omega model, where \(X\)-axis is the ratio between the location of \(x\) and \(L\), and the \(Y\)-axis is the wall pressure coefficient. The overall distribution trend of the simulation data matches well with the experiment data and the simulation results are very close to the experiment data at the upper stream of the wedge section, where \(x\)/\(L\) is between 0 and 1. At the wedge section of interest, where \(x\)/\(L\) is greater than 1, the error ratio distribution of numerical data with the experimental data is illustrated in Figure 12. The results based on cell Reynolds number of \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Computational** \\ **Domains** \\ \end{tabular} } & \multicolumn{8}{c}{**x/L**} \\ \cline{2-13}  & \multicolumn{2}{c}{**1.1**} & \multicolumn{2}{c}{**1.15**} & \multicolumn{2}{c}{**1.175**} & \multicolumn{2}{c}{**1.19**} & \multicolumn{2}{c}{**1.21**} & \multicolumn{2}{c}{**1.23**} \\ \hline \multirow{2}{*}{6c} & 0.2193 & 0.001419 & 0.2286 & 0.001370 & 0.2201 & 0.001338 & 0.2216 & 0.001279 & 0.2230 & 0.001247 & 0.2229 & 0.001233 \\  & 5.96\% & 6.75\% & 7.10\% & 8.30\% & 9.01\% & 10.03\% & 13.75\% & 14.23\% & 15.03\% & 15.99\% & 15.07\% & 16.34\% \\ \hline \multirow{2}{*}{8c} & 0.2173 & 0.001437 & 0.2261 & 0.001386 & 0.2226 & 0.001352 & 0.2246 & 0.001295 & 0.2254 & 0.001259 & 0.2253 & 0.001248 \\  & 4.99\% & 5.56\% & 5.93\% & 7.23\% & 7.98\% & 9.09\% & 12.58\% & 13.15\% & 14.12\% & 15.18\% & 14.16\% & 15.32\% \\ \hline \multirow{2}{*}{12c} & 0.2178 & 0.001431 & 0.2266 & 0.001381 & 0.2221 & 0.001347 & 0.2244 & 0.001290 & 0.2248 & 0.001255 & 0.2245 & 0.001245 \\  & 5.24\% & 5.96\% & 6.17\% & 7.56\% & 8.18\% & 9.43\% & 12.66\% & 13.49\% & 14.35\% & 15.54\% & 14.46\% & 15.53\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Computational domain independency study of three levels of sizes with error ratios. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{ \begin{tabular}{c} **Mesh** \\ **(Cells)** \\ \end{tabular}  } & \multicolumn{8}{c}{**x/L**} \\ \cline{2-13}  & \multicolumn{2}{c}{**1.1**} & \multicolumn{2}{c}{**1.15**} & \multicolumn{2}{c}{**1.175**} & \multicolumn{2}{c}{**1.19**} & \multicolumn{2}{c}{**1.21**} & \multicolumn{2}{c}{**1.23**} \\ \hline \multirow{2}{*}{280,000} & 0.2173 & 0.001437 & 0.2261 & 0.001386 & 0.2226 & 0.001352 & 0.2246 & 0.001295 & 0.2254 & 0.001259 & 0.2253 & 0.001248 \\  & 4.99\% & 5.56\% & 5.93\% & 7.23\% & 7.98\% & 9.09\% & 12.58\% & 13.15\% & 14.12\% & 15.18\% & 14.16\% & 15.32\% \\ \hline \multirow{2}{*}{540,000} & 0.2151 & 0.001453 & 0.2243 & 0.001401 & 0.2251 & 0.001372 & 0.2275 & 0.001313 & 0.2280 & 0.001277 & 0.2279 & 0.001277 \\  & 3.94\% & 4.51\% & 5.80\% & 6.22\% & 6.95\% & 7.74\% & 11.45\% & 11.95\% & 13.11\% & 13.96\% & 13.13\% & 14.17\% \\ \hline \multirow{2}{*}{740,000} & 0.2154 & 0.001448 & 0.2242 & 0.001406 & 0.2253 & 0.001368 & 0.2277 & 0.001315 & 0.2276 & 0.001274 & 0.2277 & 0.001263 \\  & 4.08\% & 4.84\% & 5.04\% & 5.89\% & 6.86\% & 8.01\% & 11.37\% & 11.81\% & 13.28\%16 and the AUSM+ flux type were the closest to the experimental data and the average error ratio was about 10.73%. Further, another four simulations with different aspect ratios based on a cell Reynolds number of 16 and the AUSM+ flux type were performed. The aspect ratios 400, 200, 100, and 50 were adopted; Figure 13a reveals the distribution diagram of the error ratio of the pressure coefficient. As the aspect ratio decreased, the error ratio decreased.