# Performance Optimization Design of Diagonal Flow Fan Based on Ensemble of Surrogates Model
## 5 Numerical Simulation Analysis and Experimental Verification  
### Energy Loss Analysis  
In the process of the fan working on the fluid through the blade, due to the viscosity of the fluid medium and the existence of Reynolds stress, the irreversible process of the conversion of mechanical energy to internal energy occurs. So, there must be irreversible loss. Entropy generation theory [19; 20] is introduced here to study the energy loss caused by viscous dissipation and turbulent dissipation in the fan before and after optimization from the perspective of thermodynamics. The viscous dissipative entropy generation and turbulent dissipative entropy generation can be obtained from the following equation. Figure 13 shows the specific definition of different blade height sections of the fan, and Figure 14 shows the entropy generation cloud diagram of different blade heights of the fan.  
Figure 12: Optimization objective Pareto frontier.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Design Parameter** & \(v_{0}\) & \(v_{1}\) & \(v_{2}\) & \(v_{3}\) \\ \hline Original & 0.417 & 3.074 & 1.779 & 0.551 \\ Optimized & 0.317 & 1.878 & 1.152 & 0.488 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Parameters before and after arc optimization of diagonal flow fan blade.  
Viscous dissipation entropy generation is:  
\[\dot{S}_{\overline{D}}^{\prime\prime}=\frac{\mu}{T_{\rm t}}\Bigg{[}\bigg{(} \frac{\partial\overline{u}}{\partial y}+\frac{\partial\overline{v}}{\partial x} \bigg{)}^{2}+\bigg{(}\frac{\partial\overline{u}}{\partial z}+\frac{\partial \overline{w}}{\partial x}\bigg{)}^{2}+\bigg{(}\frac{\partial\overline{v}}{ \partial z}+\frac{\partial\overline{w}}{\partial y}\bigg{)}^{2}\Bigg{]}+\frac{2 \mu}{T_{\rm t}}\Bigg{[}\bigg{(}\frac{\partial\overline{u}}{\partial x}\bigg{)}^ {2}+\bigg{(}\frac{\partial\overline{v}}{\partial y}\bigg{)}^{2}+\bigg{(}\frac{ \partial\overline{w}}{\partial z}\bigg{)}^{2}\Bigg{]} \tag{14}\]  
Turbulent dissipation entropy generation is:  
\[\dot{S}_{D^{\prime}}^{\prime\prime}=\frac{\mu}{T_{\rm t}}\Bigg{[}\bigg{(}\frac {\partial u^{\prime}}{\partial y}+\frac{\partial v^{\prime}}{\partial x} \bigg{)}^{2}+\bigg{(}\frac{\partial u^{\prime}}{\partial z}+\frac{\partial w^ {\prime}}{\partial x}\bigg{)}^{2}+\bigg{(}\frac{\partial v^{\prime}}{\partial z }+\frac{\partial w^{\prime}}{\partial y}\bigg{)}^{2}\Bigg{]}+\frac{2\mu}{T_{ \rm t}}\Bigg{[}\bigg{(}\frac{\partial u^{\prime}}{\partial x}\bigg{)}^{2}+ \bigg{(}\frac{\partial v^{\prime}}{\partial y}\bigg{)}^{2}+\bigg{(}\frac{ \partial w^{\prime}}{\partial z}\bigg{)}^{2}\Bigg{]} \tag{15}\]  
where \(\overline{u},\overline{v},\) and \(\overline{w}\) are the components of average velocity in \(x,y,\) and \(z\) directions, m/s; \(u^{\prime},\)\(v^{\prime},\) and \(w^{\prime}\) are the components of pulsating velocity in \(x,y,\) and \(z\) directions, m/s; \(T_{\rm t}\) is the temperature, K; and \(\mu\) is hydrodynamic viscosity, Pa-s.  
It can be seen from Figure 14 that the entropy generation of the blade part at the low blade height section (such as Span0.05, Span0.2, and Span0.4) mainly comes from the wake shedding, which will produce large unstable pressure pulsation, resulting in energy loss. At the high section of the middle blade (such as Span0.6 and Span0.8), blade loss caused by  
Figure 14: Cross-section entropy cloud diagram of different fan blade heights before and after optimization. (**a**) Original. (**b**) Optimized.  
Figure 13: Different leaf height sections.  
the incoming flow impact is gradually highlighted. The impact loss of the original impeller is more obvious, mainly in the leading edge area of the blade. The optimized impeller is due to the viscous effect of the airflow and the turbulent additional shear stress. At the high blade section (such as Span0.95), the tip leakage of the impeller is dominant, and there is no significant difference before and after optimization.