## 2 Model and Experimental/Numerical Methods
### Computational Fluid Dynamics (CFDs) Method  
Based on the experimental model shown in Figure 1a, due to its vertical symmetric shape, only half of the model was used for the analysis to save computing costs. Surrounding the model with a half cylinder whose diameter was variable, a computational domain integrating internal and external flow was formed between the symmetry plane, the model, and the half cylinder, as shown in Figure 4a. An unstructured hybrid grid was chosen as the pattern of the computational grid. The wall was composed of triangular grids. In the external flow region, the overall size of the wall grids was not greater than 1.2 mm, and in the internal flow region, the overall size was not greater than 0.8 mm. Prisms covered the whole aerodynamic surface. The height of the first layer of the prisms was 0.005 mm, and the height of each layer increased proportionally, with an increase ratio of 1.35. The total thickness of the prisms in the external flow region was 4.26 mm, while in the internal flow region, the total thickness was 2.33 mm. The remaining computational domain was filled with tetrahedral grids. Figure 4 shows the detailed characteristics of the CFD grid; the number of the grid reached 24 million. The far-field pressure inlet boundary condition was set on the green surface of the half cylinder. The pressure outlet condition was set on the the yellow surface of the half cylinder. The symmetry boundary condition was set on the symmetry plane, and the adiabatic wall boundary condition was set on the aerodynamic surface of the model. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Order Number** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** \\ \hline
**x/l** & 0.406 & 0.451 & 0.5 & 0.543 & 0.584 & 0.607 & 0.659 & 0.597 & 0.617 & 0.637 \\
**Side** & B & B & B & B & B & B & B & L & L & L \\ \hline
**Order Number** & **11** & **12** & **13** & **14** & **Sensor 1** & **Sensor 2** & **Sensor 3** \\ \hline
**x/l** & 0.657 & 0.677 & 0.697 & 0.714 & 0.706 & 0.633 & 0.684 \\
**Side** & L & L & L & L & L & B & B \\ \hline \hline \end{tabular} B: Body side; L: Lip side.  
\end{table} 
Table 1: Details of pressure-measuring points and their location distribution. Figure 3: Wind tunnel system of this experiment. The calculation results were obtained using the finite volume method (FVM) and Reynolds-averaged Navier-Stokes equations. Equation (1) is the conservation form of compressible Navier-Stokes equations. The calculation object was perfect gas (air) [9; 13; 15; 48], and the fluid's viscosity was computed using the Sutherland equation. Since the calculation problem concerned compressible flow, and in order to address to the calculation accuracy and efficiency, a density-based solver conducted via an implicit time integration method and second-order upwind ROE difference scheme was chosen to solve the complex problem. Considering that the flow separation caused by the shock boundary-layer interaction is widespread in hypersonic inlets, the Ku-SST mode (which has good simulation ability for separated flow) was selected for the turbulence model. Effectiveness was validated for this turbulence model via an extensive application in solving the shock boundary-layer interaction problems and flow mechanism problems in air inlets [49; 50; 51]. \[\frac{\partial\overline{U}}{\partial t}+\frac{\partial\overline{F}}{\partial x }+\frac{\partial\overline{C}}{\partial y}+\frac{\partial\overline{H}}{ \partial z}=\frac{\partial\overline{S}_{x}}{\partial x}+\frac{\partial \overline{S}_{y}}{\partial y}+\frac{\partial\overline{S}_{z}}{\partial z} \tag{1}\]  
Based on the above grid and CFD method, wall Y-plus could be controlled near to or less than one, as shown in Figure 5. More than that, as described in Section 5, the flow field structure and pressure distribution obtained from the CFD calculation and experiments were compared, and the results showed a high degree of agreement. Figure 4: Computational domain, CFD grid, and boundary condition.