# An Effective Simulation Scheme for Predicting the Aerodynamic Heat of a Scramjet-Propelled Vehicle
## 2 Flight Path of Scramjet-Propelled Vehicle and Numerical Procedures  
Rocket-based combined cycle (RBCC) is the ideal power system for future scramjet-propelled vehicles and single-stage re-use vehicles. To minimize wave resistance during flight, RBCC vehicles tend to have a pointed head with a slender fuselage, and the typical part of RBCC vehicles is a wedge-shaped section. The X51A vehicle and its flight path are as shown in Figure 1a,b [18]. The flight path consists of a climbing phase, cruising phase, and attack phase, and the climbing phase also includes an ejection phase, a sub-combustion stamping phase, and a super-combustion stamping phase. During the climbing phase, the flight speed of the vehicle rapidly increases, and it is a phase of complex temperature changes. In the cruising phase, the vehicle keeps a constant altitude and speed and the flight distance accounts for about 90% of the total range; it could be viewed as a steady-state phase. These two phases are the main phases of the flight path, and the simulation scheme for aerodynamic heat prediction is proposed covering these two phases in this paper. After arriving at the target airspace, the vehicle enters the attack phase, in which it shifts down and attacks the target accurately.  
According to the different Mach numbers, the vehicle is in different external flow field environments [7; 19]. At the transonic speed stage (when the Mach number is between 0.6 and 1), compressibility effects such as flow choking becoming important. At the supersonic speed stage (Mach number between 1 and 3), depending on the specific shape of the aircraft, a shock wave may be produced in the airflow. At the high supersonic (when the Mach number is between 3 and 5) and hypersonic speed stage (when the Mach number is bigger than 5), aerodynamic heating becomes very important. The flight path of the RBCC scramjet-propelled vehicle spans all of the above stages; therefore, a specific piecewise analysis is needed. According to the Mach number of the flight path, the simulation scheme is divided into four stages. To ensure the reliability of the prediction results, the simulation parameters should be confirmed by validation tests at each stage.  
For flows involving compressibility and heat transfer, three conservation equations for mass, momentum, and energy need to be solved. When the flow is turbulent, additional transport equations are also solved, adopting the one-equation RANS Spalart-Allmaras model, which is the most widely applied [20], and the two-equation RANS SST k-omega turbulence model [21]. The control-volume-based technique is used to discretize the above equations. Firstly, the external flow field model is divided into discrete control volumes using a computational grid. Secondly, the integration of equations on the individual control volumes to algebraic equations for the discrete dependent variables and conserved scalars is accomplished using an upwind scheme. Next, the above-discretized equations are linearized, and the resultant linear equation system is solved to yield variables. Two numerical solvers, a pressure-based solver and a density-based solver, were applied in this study. More details about these equations and the finite volume method could be found in Ref. [22].