## 5 Validation of the Redesigned Axial-Flow Fan
### Numerical Validation  
To validate the improved performance of the redesigned fan, a three-dimensional CFD analysis is conducted, with the results summarized in Tables 2 and 3. The analysis reveals several noteworthy findings. First, the redesigned fan exhibits a notable increase in the volume flow rate, with a gain of approximately 2.3% compared to the original design. Second, the aerodynamic performance of the redesigned fan demonstrates a substantial enhancement, focusing on calculating the averaged force distribution along the spanwise direction of the blade. As illustrated in Figure 13a, it is observed that there is a slight increase in the thrust of the optimized fan, which leads to an increase in the output power of 7%. Also, a substantial reduction in the torque is evident within the designated target radial range for the optimized fan. This reduction in the torque is instrumental in decreasing the input power by 9% and subsequently elevating the overall efficiency of the optimized fan, which outperforms the original fan by a significant margin. Notably, the efficiency of the optimized fan is increased by 17%, particularly prominent in the regions corresponding to \(0.4<\) r/R \(<0.9\), which aligns with the target radial regions identified in the two-dimensional cascade analysis. These findings underscore the successful optimization of the fan's performance, with the most substantial gains realized in the specified radial regions of interest. Third, in addition to its improved performance metrics, the redesigned fan also yields a reduction in the overall sound pressure level, registering a decrease of approximately 10.8 dBA compared to the original fan. These findings collectively underscore the successful application of the present design procedure in optimizing the fan's flow performance, efficiency, and acoustic characteristics. Further analysis is performed to study the detailed flow structure, resulting in the improved flow and noise performance of the optimized fan. To verify if the angle of attack considered for the airfoil cascade simulations matches the application in the redesigned three-dimensional fan, Figure 14a compares the angle of attack distribution between the two models. An apparent discrepancy between the two outcomes is noted; however, the overall trajectory of the angle of attack for the optimized fan closely resembles that of the original fan. The complex three-dimensional flow features that were overlooked in the two-dimensional cascade study are the cause of this difference. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & **Volume Flow Rate [CMM]** & **OSPL [dBA]** \\ \hline Original model & A & B \\ Optimized model & 1.02 A & B–10.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of the volume flow fan, and the overall sound pressure level computed for the two fan models. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Total Input Power [W]** & **Total Output Power [W]** & **Efficiency** \\ \hline Original model & \(W_{input}\) & \(W_{output}\) & \(\eta\) \\ Optimized model & 0.91 \(W_{input}\) & 1.07 \(W_{output}\) & 1.17 \(\eta\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of the input power, output power, and efficiency computed for the two fan models. Figure 13: Area-weighted averaged force distribution along the spanwise direction of the blade: (a) thrust coefficient, (b) torque coefficient, and (c) efficiency. Figure 14b displays the time-averaged streamline, which accurately illustrates the distribution of the wall shear stress. It precisely identifies the location of separation and transition in the laminar-turbulence boundary layer [26; 27]. It is confirmed by comparing the two fan designs that the original fan had many eddy currents close to the leading edge and that a separation point could be seen rather far from the leading edge. Moreover, the flow through the leading edge and along the camber line directed itself toward the tip of the blade, intensifying the tip vortex.