# Experimental and Numerical Research on End-Wall Flow Mechanism of High-Loading Tandem Stators
## 2 Research Object and Method
### Research Methodology
#### 2.2.2 Numerical Methods and Grid Settings  
In this study, the numerical simulations were executed using ANSYS CFX 18.0 software. The calculations were performed using a steady-state formulation. For time discretization, a fourth-order Runge-Kutta method was employed, while spatial discretization utilized high-resolution schemes available in CFX. A series of experimental data was obtained by [PERSON] and [PERSON] et al. [28; 29] on the LSLSAC test facility, and a comparative analysis was conducted between the computational results from k-\(\varepsilon\), RNG k-\(\varepsilon\), k-\(\omega\), BSL k-\(\omega\), and SST k-\(\omega\) turbulence models within CFX, as shown in Figure 4. The results indicated that the calculated characteristic curves by the k-\(\omega\) turbulence model matched well with the  
Figure 3: Measurement points arrangement at the rotor and stator outlet [25]. experimental results across the entire flow range, thereby demonstrating its reliability and accuracy. Therefore, the k-\(\omega\) turbulence model was used in this paper. Convergence was determined when the residuals fell below \(10^{-5}\) and did not decrease further, and the variation in mass flow rate did not exceed 0.1%. Figure 5 shows the computational domain of the tandem blades and the stator grids. Two blade rows (R1 + S1) were used in the calculation of tandem blades. The inlet section of the computational domain was 0.5 times the chord length of the tandem rotor to eliminate the non-convergence caused by the interference of rotor potential on the inlet boundary. The outlet section of the computational domain was twice the chord of the tandem stator. The computational mesh was generated by Numeca Autogrid5 9.0 software, with a structured mesh being employed. An O4H topology structure was adopted, and an incomplete matching mesh strategy was applied to both FB and RB sections in order to guarantee high-quality meshing in the critical region between FB and RB. Additionally, the meshes were densified at the circumferential interface to capture intricate flow details. To verify the grid independence of the tandem blade calculations, three computational domain meshes were set up: Mesh1, Mesh2, and Mesh3, where the number of grid points was 4.9 million, 8.9 million, and 11.7 million, respectively. The distribution of mesh elements in the rotor and stator domains is shown in Table 2. Figure 6 shows the comparison of compressor stage efficiency of different meshes. It could be seen that the efficiency between Mesh2 and Mesh3 was minimal, indicating that Mesh2 has achieved grid independence. It was finally determined that the axial, circumferential, and spanwise grid points of the tandem stator were 201, 110, and 57, respectively, and the axial grid points of the stator exit  
Figure 4: Comparison of the pressure rise coefficient obtained from different turbulence models with experimental results [28]. Figure 5: (**a**) Calculated model of tandem-blade compressor; (**b**) detailed mesh of tandem stators. domain were 101. The tandem stator was calculated by a single channel, with the number of the stator domain grid points of about 2.5 million. And the tandem rotor was calculated by dual channels, with the number of the rotor domain grid points of about 6.3 million. The grid height of the first layer of each end-wall was set as 0.005 mm, ensuring that the y+ value was less than 1. The inlet boundary conditions are specified with total temperature, total pressure, and flow angle, where the specified total pressure and flow angle are based on the spanwise distribution of the rotor inlet parameters measured experimentally, and the total temperature was 288.15 K. The calculation setup eliminated the cumulative error from the IGV and S0 in the simulation of the five blade rows (IGV + S0 + R1 + S1 + OGV). The comparison results also showed that the calculation setup of two blade rows was closer to the experimental data. The interface between the rotor and stator was handled using a mixed-plane method.