## 2 Methodology
### Model Simulation and Experimental Verification  
Due to the intricate structure of the multi-blade centrifugal fan, the computational domain must be simplified to reduce computation time. As illustrated in Figure 4a, the Multi-Reference Frame (MRF) is employed to define the dynamic and static regions. Specifically, the impeller flow area is deemed dynamic, and its rotation axis and angular velocity are specified. Meanwhile, the other flow areas are designated static. To ensure proper fluid exchange, the interface between the two regions must be redefined to achieve one-to-one correspondence. The boundary conditions are set to velocity-inlet and outflow, whereas the remaining surfaces are defined as walls. The pressure-velocity coupling adopts the SIMPLE algorithm, and the second-order upwind scheme is used for discretization. The hybrid grid is used to improve the grid quality. As shown in Figure 4a, a structured grid is used because of the simple structure of the outlet domain and the small number of grids. It can be seen from Figure 4b,c that the volute and impeller domain structures are complex, so they need to be encrypted to ensure the quality of the computational grid. To ensure that the simulation results are no longer dependent on the level of grid refinement, it is necessary to verify the grid independence of the fan model. As shown in Table 2, in this study, total grid numbers of 4.2 million, 7.7 million, and 9.8 million were used to simulate the steady state of the centrifugal fan. By comparing the y+ values for the impeller, volute, and outlet with three different grid numbers, it was analyzed that both 7 million and 9 million grids were reasonable choices. Considering the principles of saving time and cost, the number of grids for option 2 was ultimately selected. The corresponding grid counts for the impeller flow field, volute flow field, and outlet extension section were 3.75 million, 3.27 million, and 0.6 million, respectively. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Number of Grids** & **Impeller Region** & **Volute Region** & **Outlet Region** \\ \hline Grid 1 & \(4.2\times 10^{6}\) & 20.52 & 41.51 & 82.47 \\ \hline Grid 2 & \(7.7\times 10^{6}\) & 14.7 & 35.4 & 75.5 \\ \hline Grid 3 & \(9.8\times 10^{6}\) & 13.5 & 33.5 & 73.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The number of grids and the y+ values. Figure 3: Schematic diagram of partial flow effect in impeller channel. As shown in Figure 5, it presents the y+ values of different positions of the wind turbine under different grids. When the grid number is 7.7 \(\times\) 10\({}^{6}\) and 9.8 \(\times\) 10\({}^{6}\), there is little difference in the y+ values. In this case, it is a reasonable choice to select 7.7 \(\times\) 10\({}^{6}\). According to the fan test standards [35], an experimental platform was established and a fan performance test was conducted. Figure 6 is the photo of the experimental setup. As shown, the core device mainly includes a test fan, an air chamber, a nozzle, a rectification, and an auxiliary fan. This study employed ANSYS Fluent 2021 R2 [36] as the primary Computational Fluid Dynamics (CFD) simulation tool. Fluent 2021 R2 is a widely used advanced CFD software  
Figure 4: (a) Calculation domain and boundary conditions, (b) rid of volute and impeller, and (c) grid of impeller cross-section. Figure 5: The y+ values of each part of the wind turbine under different grid numbers. Figure 6: The photo of the experimental setup. package in the engineering field, capable of simulating and analyzing various complex fluid flow phenomena, including laminar flow, turbulent flow, multiphase flow, and heat transfer problems. It also offers a rich library of physical models to meet the needs of different application scenarios. Under different working conditions, the air volume is changed by adjusting the load pressure at the fan outlet.