# An Effective Simulation Scheme for Predicting the Aerodynamic Heat of a Scramjet-Propelled Vehicle
## 3 Validation Tests
### Supersonic Stage
#### 3.2.3 Simulation Parameters  
Figure 8 shows the wall surface pressure distributions from the experiment and the simulation, where the \(X\)-axis \(x\) is the distance to the original point of the wedge section and the \(Y\)-axis is the ratio between the wall surface pressure and the total pressure of the freestream. The overall tracking effect of the simulation data on the experiment data was acceptable. The simulation errors of the two models were very close at the upper stream of the wedge section. At the wedge section, where \(x\) was bigger than 0, the mean error rate of SST k-omega data was 4.76%, and that of Spalart-Allmaras was 5.19%. The variance of SST k-omega simulation error was 0.001043, and that of Spalart-Allmaras was 0.003091. Figure 9 indicates the density profiles at x = 0 from the experiment and the simulation, the \(X\)-axis is the ratio between local density and the freestream density, and the \(Y\)-axis is the y location. The average error rate of the SST k-omega data was 7.92%, and that of Spalart-Allmaras was 10.04%. The variance of the SST k-omega simulation error was 0.00307, and that of Spalart-Allmaras was 0.003417. In general, the trend of the simulation results was in good agreement with the experimental data, and the SST k-omega simulation results were better than those of Spalart-Allmaras at the supersonic stage.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{2}{c}{**Validation Parameters**} \\ \hline \hline \multirow{2}{*}{Solver} & Pressure-based with coupled & Pressure-based with coupled \\  & algorithm & algorithm \\ \hline Models & SST k-omega & Spalart-Allmaras \\ \hline \multirow{4}{*}{Materials} & Density: Ideal-gas & Density: Ideal-gas \\  & Viscosity: Sutherland law & Viscosity: Sutherland law \\  & C\({}_{\text{p}}\) (j/kg-k): 1006.43 & C\({}_{\text{p}}\) (j/kg-k): 1006.43 \\ \hline \multirow{4}{*}{Initial conditions} & Mach number: 2.85 & Mach number: 2.85 \\  & Static pressure: 5881 Pa & Static pressure: 5881 Pa \\  & Static Temperature: 102.88 K & Static Temperature: 102.88 K \\ \hline \multirow{4}{*}{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, 300 K & WALL: no-slip, isothermal, 300 K \\ \hline \hline \end{tabular}
\end{table}
Table 6: Validation parameters of convergence results at the supersonic stage.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Mesh (Cells)**} & \multicolumn{8}{c}{**x (m)**} \\ \cline{2-10}  & \multicolumn{4}{c}{**(p/p\({}_{\text{u}}\), Temperature and Error Ratio)**} \\ \cline{2-10}  & \multicolumn{2}{c}{**0**} & \multicolumn{2}{c}{**0.02**} & \multicolumn{2}{c}{**0.04**} & \multicolumn{2}{c}{**0.06**} & \multicolumn{2}{c}{**0.08**} \\ \hline \multirow{2}{*}{270,000} & 0.0861 & 252.149 & 0.1103 & 252.941 & 0.1396 & 253.461 & 0.0443 & 254.013 & 0.0353 & 254.314 \\  & 8.81\% & / & 9.55\% & / & 8.10\% & / & 10.11\% & / & 9.98\% & / \\ \hline \multirow{2}{*}{520,000} & 0.0850 & 262.052 & 0.1118 & 262.631 & 0.1412 & 263.803 & 0.0439 & 264.211 & 0.0358 & 264.702 \\  & 7.44\% & / & 8.28\% & / & 7.08\% & / & 9.33\% & / & 8.83\% & / \\ \hline \multirow{2}{*}{720,000} & 0.0853 & 264.043 & 0.1117 & 260.574 & 0.1405 & 264.887 & 0.0441 & 262.059 & 0.0356 & 265.413 \\  & 7.80\% & / & 8.40\% & / & 7.51\% & / & 9.61\% & / & 9.22\% & / \\ \hline \hline \end{tabular}
\end{table}
Table 5: Grid independency study of three levels of different mesh with error ratios.