## 5 Sample Database Establishment for RBF Model: Numerical Simulation and Experimental Verification
### Verification of Numerical Model and Sample Calculation  
Figure 11a displays the simplified diagram of the computing domain, which was divided into the impeller fluid domain, solute fluid domain, inlet fluid domain and outlet fluid domain. The inlet and outlet watersheds were extended appropriately for accurately simulating the flow conditions at the inlet and outlet of the fan. The inlet channel was a hemispherical inlet. The outlet flow area was extended to five times the radius of the solute inlet, and a rectifying plate was set in the outlet extension section so as to eliminate the vortex structure caused by separation and reduce the influence of the outlet airflow on the internal flow of the fan. In order to accurately simulate the complex flow, the wind turbine was discretized by structural grids. Unstructured grids were adopted for complex motors and support structures. The overall grid is depicted in Figure 11b,c presents the impeller structure grids.  
The internal flow field of the multi-blade centrifugal fan was solved by FLUENT 19.1. The simulation medium was 25 \({}^{\circ}\)C dry air. The multiple reference frame model (MRF) was applied to the simulation of the impeller rotation. All the walls were assumed to be fixed walls except that the blade was set as a moving wall relative to the impeller flow field. The inlet and outlet boundary conditions were set as pressure inlet and pressure outlet. The pressure-based implicit solver was specified.  
The shear stress transport model (SST \(k\)-\(\omega\)) was used to close the turbulence term to solve the three-dimensional Reynolds averaged Navier-Stokes equation for its high calculation accuracy in the area with a large velocity gradient near the vortex. The velocity and pressure coupling model was selected using the versatile SIMPLE algorithm. The momentum equation, dissipation rate equation and turbulent kinetic energy equation were discretized with a second-order upwind scheme. The residual root means square (RMS) value of the governing equation was specified to be less than \(10^{-5}\) to ensure the accuracy and convergence of numerical calculations [31].  
For the SST \(k\)-\(\omega\) turbulence model used in this study, the treatment of wall shear stress has a great influence on the accuracy of numerical scheme. The dimensionless distance (\(y\)+) must be limited to obtain accurate data from the SST model. The first mesh node should be placed in the viscous region at the bottom when dividing the grid. It is generally considered that the \(y\)+ value is less than 5. The empirical formula of y+ is:  
\[Y_{nufl}=6\bigg{(}\frac{V_{ref}}{v}\bigg{)}^{-\frac{2}{3}}\bigg{(}\frac{L_{ref }}{2}\bigg{)}^{\frac{1}{3}}y^{+} \tag{9}\]  
where \(Y_{nufl}\) is the height of the first layer of the boundary layer grid, in mm; \(V_{ref}\) is the reference speed, in m/s; \(L_{ref}\) is the reference length, in m; \(v\) is the fluid kinematic viscosity, in m\({}^{2}\)/s; and \(y^{+}\) is a dimensionless parameter indicating the boundary point between the  
Figure 11: Calculation domains and grid model (**a**) Calculation domains (**b**) Fan grid (**c**) Mesh in blade passage.  
viscous bottom and logarithmic layers. The height of the first layer of the boundary layer grid should be <0.44 mm.  
When the girl of the whole fluid domains reaches more than 2.6 million meshes, the total pressure and the flow rate in this model varies within 1% (Figure 12). Thus, comprehensively considering the accuracy of the calculation and the time cost of the optimization project, the calculated grid number was determined to be 2,675,823.  
The numerical and experimental performance curves obtained in this study are in agreement with the large flow area (Figure 13). In the small flow rate region, however, there is some significant error due to the difficulty of numerically simulating turbulence and boundary layer separation. The design flow condition error is 2%, which is within an acceptable range.