## 3 Results and Discussion  
### Design and Performance Evaluation Methods  
Firstly, the parametric design methodology for the simplified, integrated model is shown in Figure 4. Drawing from practical experience, enhancing the two-dimensional characteristics of the under-surface of the hypersonic aircraft can contribute to improving its wide speed adaptability. It is noteworthy that this paper primarily focuses on the inlet performance and does not delve into the overall aerodynamic forces and load analysis of the vehicle. In the case of a hypersonic vehicle equipped with a ventral inlet, the impact of its leeward surface is deemed negligible. The forebody can be treated as a flat plate with a specific length L\({}_{1}\) and half-width W\({}_{1}\). The length L\({}_{1}\) of the forebody is a key indicator of the install location of the inlet. In order to prevent the detached shock waves at the tip of the forebody, the model head is sharpened, and a specific angle \(\theta\) is given. Figure 3: Comparison of flat plate centerline pressure [18]. Figure 2: Schematic diagram of computational grid and boundary conditions for the model. In the design of the inlet, a mixed-compress 2D inlet and an isostraight isolator was selected. This design incorporates various key parameters, including the external compression angle \(\alpha\), inlet height H, width W\({}_{2}\), inlet length L\({}_{2}\), and throat height h. The isolator is configured as an isostraight shape, aligned with the inlet exit, with a designated length L\({}_{3}\). The external compression angle \(\alpha\) significantly impacts the compression strength of the inlet. The shock-on-lip condition and reflected shock-on-shoulder are adopted to achieve a better total pressure recovery. An oblique excitation relationship is utilized to derive the intrinsic connection among the design Mach number Ma, inlet compression angle \(\alpha\), inlet height H, inlet length L\({}_{2}\), isolator length L\({}_{3}\), and throat height h, as depicted in Equation (1). \[\left\{ \begin{array}{l}\tan(\alpha-\beta_{1})=\frac{1}{M\alpha^{2}}\cdot \frac{\sin(2\beta_{1})}{\cos^{2}(\beta_{1})-\frac{1}{M\alpha^{2}}}\\ ma_{2}=\sqrt{\frac{2+(\gamma-1)Ma^{2}}{2\gamma M^{2}}\sin^{2}\beta_{1}-(\gamma -1)}\cdot\frac{1}{\cos(\beta_{1}-\theta)}\\ \tan(\alpha-\beta_{2})=\frac{1}{ma_{2}\cdot}\frac{\sin(2\beta_{1})}{\cos^{2}( \beta_{1})-\frac{1}{ma_{2}^{2}}}\\ \frac{H}{\tan\beta_{1}}+\frac{h}{\tan(\beta_{2}-\alpha)}=\frac{H-h}{\tan\alpha} \\ L_{2}=\frac{H-h}{\tan a}\\ L_{3}=6\cdot h\end{array} \right. \tag{1}\]  
where \(\beta_{1}\) and \(\beta_{2}\) represent the incident excitation wave and throat excitation wave excitation angles, respectively, \(\gamma\) is the specific heat ratio, and \(ma_{2}\) represents the post-incident shock wave Mach number. To evaluate the overall performance of the inlet, a 3D unstructured mesh was established for numerical simulation. The boundary conditions and grid configuration are illustrated in Figure 5. The height of the first-layer near-wall grid was set to 0.1 mm. Figure 4: Parameterized method of the integrated model. Figure 5: Schematic diagram of boundary conditions and 3D mesh CFD model. The mass flow coefficient \(\phi\) is introduced as an important parameter to evaluate the airflow capture capability of the inlet. This parameter has a direct impact on the engine thrust. The computing formula of the mass flow coefficient is established as Equation (2). Specifically, where \(\overset{\bullet}{\mathfrak{m}}_{air}\) is the actual captured mass flow rate of the inlet, \(\rho\) is the incoming flow density, u is the incoming flow velocity, and \(A_{FCT}\) is the maximum captured area of the inlet discussed above. \[\phi=\overset{\bullet}{\mathfrak{m}}_{air}/\rho uA_{FCT} \tag{2}\]  
In order to quantify the energy loss in the airflow compression process, the total pressure recovery coefficient \(\sigma_{inlet}\) is introduced.