# An Effective Simulation Scheme for Predicting the Aerodynamic Heat of a Scramjet-Propelled Vehicle
## 1 Introduction  
Aerodynamic heat prediction plays an important role in the design and optimization of hypersonic vehicles [1, 2]. In general, there are three technical approaches to aerodynamic heat prediction: the engineering estimation [3], the wind tunnel experiment [4], and computational fluid dynamics (CFD) [5, 6]. With the development of computer technology, CFD has made great progress; its results offer higher accuracy than engineering estimation, and, unlike the wind tunnel experiment, its simulation ability can cover the entire flight trajectory. The CFD technology has become an indispensable means in the study of aerothermal predictions. Its results are influenced by many factors, such as Mach number, gird strategy, and numerical methods, which include turbulence models, upwind scheme, limiter, and so on. Domestic and foreign scholars have carried out research into these factors. The aerodynamic characteristics of different Mach numbers are different, and the corresponding grid strategy and numerical method are also different [7]. In terms of grid strategy, the height of the first layer of wall cells has a great influence on the numerical calculation results, and the mesh needs to be adjusted several times according to the CFD results, which is a time-consuming part of the CFD process. Ref. [8] discusses the effect of the grid on aerothermal prediction by taking an external flow field simulation model based on a blunt body as an example. The results show that the deviation of the results could reach more than 20% when the Reynolds number of the wall grid is doubled while other conditions are unchanged. Ref. [9] considers the effect of cell Reynolds numbers on aerothermal prediction by applying a cylinder as an example. The results show that it is necessary to keep the cell Reynolds number less than 10 in the aerothermal calculation, and Refs. [10, 11] presents similar research cases. Ref. [12] shows that the property of shock stability influences the accuracy of heating prediction. Ref. [13] reveals that the aspect ratioof wall cells near the shock is a major factor and Ref. [14] suggests that the aspect ratio of wall cells near the shock should be larger than six for predicting hypersonic heating, taking a blunt body and a blunt cone as examples. The experimental data of X33, which is a reusable reentry hypersonic vehicle, are used to validate the above conclusions. In terms of the numerical method, turbulence is a difficult problem in flows and the current simulation equations for turbulence include Reynolds Averaged Navier-Stokes (RANS), Large Eddy, Separated Eddy, and Direct Numerical Simulation (DNS), etc. Considering the limitations of robustness and computational efficiency, RANS is still the main turbulence simulation method adopted at present [15]. When there are discontinuities in flows, the artificial viscosity, which can affect the calculation accuracy, is usually added to the central scheme to suppress oscillations. Therefore, varieties of upwind schemes have gradually become the mainstream approach to numerical calculation. In addition, the limiter is applied to limit the difference gradient to avoid oscillations. Ref. [16] discusses the calculation accuracy of AUSM+, Roe's FDS, and FVS by taking the flow around a cylinder and a blunt as examples. The results show that the calculation accuracy of these three upwind schemes is better than that of the central difference scheme, and the numerical results of AUSM+ and Roe's FDS are closer to the experimental data. Ref. [17] adopts Minmod, van leer, and osher-c limiters to simulate the external flow field of a blunt. The results indicate that the maximum heat flow value and heat distribution characteristics obtained by the Minmod limiter are better than the other two limiters. In current research, the reusable reentry vehicle is the main research object of aerothermal prediction.