# Optimization Design of Centrifugal Fan Blades Based on Bezier Curve Method
## 2 The Experiment and Numerical Methodology of the Fan
### Boundary Condition and Mesh Validation  
The internal flow within a voluteless centrifugal fan is approximately adiabatic during operation. Therefore, it can be simplified as a viscous incompressible flow. In this study the commercial software ANSYS Fluent 2023R1 was used to study the three-dimensional voluteless centrifugal fan. The turbulence model used was the realizable k-\(\epsilon\) model. The enhanced wall treatment was applied for near wall treatment. This treatment is suitable for both coarse meshes as well as fine meshes. Other solid wall boundary conditions were set as viscous, no-slip, adiabatic solid walls. The SIMPLE algorithm was applied for the pressure-velocity coupling, and the second-order upwind scheme was applied for the  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Design flow rate/kg\(\cdot\)s\({}^{-1}\) & 0.964 \\ Design rotational speed/r\(\cdot\)min\({}^{-1}\) & 3100 \\ Number of blades & 6 \\ Outer diameter of impeller/mm & 360 \\ Inner diameter of impeller/mm & 213 \\ Blade inlet angle/\({}^{\circ}\) & 20 \\ Blade outlet angle/\({}^{\circ}\) & 30.9 \\ Thickness of blades/mm & 2 \\ Width of the impeller/mm & 94 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The main design parameters of the voluteless centrifugal fan.  
Figure 1: Schematic of the fan model: (**a**) the voluteless centrifugal fan and (**b**) the computational domain of the fan.  
momentum equation, energy equation, and turbulence dissipation equation. A mass flow rate of 0.964 kg\(\cdot\)s\({}^{-1}\) was given for the inlet, and the gauge pressure of outlet boundary condition was set to 0 Pa. During the calculation, a multi-reference frame model was used, with the impeller domain set as the rotating domain and the inlet and outlet domain as the stationary domains and the rotational speed was set to 3100 r\(\cdot\)min\({}^{-1}\). The interface between the dynamic and static interfaces was used to transmit data. According to the mesh quantity and accuracy requirements, the convergence residual was set to \(10^{-5}\), and the inlet and outlet static pressure difference and impeller torque were monitored. When the convergence residual met the design requirements or the monitoring value remained basically unchanged, it was considered that the calculation has converged.  
The meshes of the impeller surface, middle section, and boundary layers are given in Figure 2a. Five layers of boundary, with the height of the first layer of 0.03 mm, were used to capture the complex flow-field information near the impeller. And the y+ of the impeller meshes was close to 2, as shown in Figure 2b.  
Static pressure is a fundamental parameter for the operation of a voltteless centrifugal fan, so the static pressure at the maximum efficiency condition was selected as the evaluation index for mesh independence verification. Considering the computational resources and time costs, the mesh size settings corresponding to the 9.77 million mesh model was selected for the numerical calculation after mesh independence verification, as shown in Figure 3.