# An Effective Simulation Scheme for Predicting the Aerodynamic Heat of a Scramjet-Propelled Vehicle
## 4 Simulation Scheme and Aerothermal Prediction  
Regardless of the influence of fuel and engine performance, it was assumed that the climbing phase would be uniformly accelerated and that the acceleration process would be completed instantly. According to the flight path of the RBCC vehicle in Figure 1b, the climbing phase was divided into 34 sub-phases in seconds. Each sub-phase remained at a constant speed and the acceleration of the next sub-phase occurred instantly. Every sub-stage was classified into the corresponding stage described in Section 2, based on Mach number. An effective simulation scheme for predicting the aerodynamic heat of a scramjet-propelled vehicle is shown in Table 13. The external flow field model for the simulation was established based on a wedge-shaped head and the wedge angle \(\alpha\) was 20\({}^{\circ}\), as shown in Figure 26.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Phase** & **Initial Conditions (Altitude, Velocity, Pressure, Temperature, Wall Temperature)** & **Simulation Parameters** \\ \hline \hline \multicolumn{3}{c}{Transonic stage} \\  & & Mesh with value of \(y^{+}\) is 1, \\  & & turbulence model applying \\  & & Spalart-Allmaras and \\  & & pressure-based solver adopting \\  & & coupled algorithm \\ \hline \hline \multicolumn{3}{c}{Transonic stage} \\  & & Mesh with value of \(y^{+}\) is 1, \\  & & turbulence model applying \\  & & Spalart-Allmaras and \\  & & pressure-based solver adopting \\  & & coupled algorithm \\ \hline \hline \multicolumn{3}{c}{Cruising phase} \\  & & & \\ \end{tabular}
\end{table}
Table 13: Simulation scheme for aerodynamic heat prediction of RBCC scramjet-propelled vehicle in the flight path.  
Figure 27 presents the aerodynamic heat of the RBCC scramjet-propelled vehicle in the flight path, as shown in Figure 1b. During the ejection phase, which lasted for about 10 s, the vehicle rose from 11 km to 16 km in altitude, the velocity accelerated from 0.8 Ma to 3 Ma, and the aerodynamic heat increased from an initial temperature of 216.65 K (\(-\)56.35 \({}^{\circ}\)C) to 543 K (270 \({}^{\circ}\)C), with a temperature change of 326.35 \({}^{\circ}\)C and an average temperature change rate of 326.635 \({}^{\circ}\)C/s. During the sub-combustion stamping stage, which lasted for about 20 s, the vehicle rose from 16 km to 26 km in altitude, the velocity accelerated from 3 Ma to 6 Ma, and the aerodynamic heat increased from a temperature of 543 K (270 \({}^{\circ}\)C) to 1550 K (1277 \({}^{\circ}\)C), with a temperature change of 1007 \({}^{\circ}\)C and an average temperature change rate of 50.35 \({}^{\circ}\)C/s. During the super-combustion stamping stage, which lasted for about 4 s, the vehicle rose from 26 km to 30 km in altitude, the velocity accelerated from 6 Ma to 6.5 Ma, and the aerodynamics heat increased from a temperature of 1550 K (1277 \({}^{\circ}\)C) to 2010 K (1737 \({}^{\circ}\)C), with a temperature change of 460 \({}^{\circ}\)C and an average temperature change rate of 115 \({}^{\circ}\)C/s. During the cruising phase, the vehicle maintained a constant speed and altitude of 6.5 Ma and 30 km, and the aerodynamic heat finally increased to 2130 K (1857 \({}^{\circ}\)C). With the increase of velocity, the average temperature change rate also increased. During a flight time of about 34 s, the aerodynamic heat increased from 216.65 K to 2130 K, and the temperature change reached about 1913.35 \({}^{\circ}\)C, which was consistent with the descriptions in Refs. [33; 34; 35], and the maximum average temperature change rate reached 115 \({}^{\circ}\)C/s. The RBCC hypersonic vehicle experienced severe aerodynamic thermal problems during the flight.  
Figure 27: The aerodynamic heat prediction for RBCC scramjet-propelled vehicle in the flight path.