# Simulation of the Influence of Wing Angle Blades on the Performance of Counter-Rotating Axial Fan
## 4 Analysis of Optimization Results
### Q Isosurface Analysis  
Due to the relatively complex flow field in the fan wheel area, there are a large number of vortices near the blades, and the vortices will reduce the efficiency of the fan and increase the noise. Therefore, this paper uses the \(Q\) isosurface method to discriminate the flow  
Figure 6: Total pressure distribution on blade surface. (**a**) Total pressure distribution of the first-stage blade; and (**b**) total pressure distribution of the second-stage blades. field in the two-stage impeller area of the fan, and observe the distribution of the vortex core position. The research on vortices is in the process of continuous exploration, and a variety of vortex identification technologies have been developed. At present, the \(Q\) criterion and the Lambda2 criterion are commonly used. Indeed, lambda2 is a very powerful tool in the comparison between the different configurations in terms of vortical structures as done, e.g., in [PERSON] et al. [17], [PERSON] et al. [18], and [PERSON] et al. [19]. I think \(Q\) criterion is more suitable for the analysis of fan impeller flow field in this paper. The definition of \(Q\) isosurface is:  
\[Q=\frac{1}{2}(\Omega_{ij}\Omega_{ij}-\sigma_{ij}\sigma_{ij}) \tag{1}\]  
\(\Omega_{ij}\) represents the vorticity tensor; \(\sigma_{ij}\) represents the strain rate tensor, and the expressions are as follows:  
\[\Omega_{ij}=\frac{1}{2}(\frac{\partial u_{i}}{\partial x_{j}}-\frac{\partial u _{j}}{\partial x_{i}}) \tag{2}\]  
\[\sigma_{ij}=\frac{1}{2}(\frac{\partial u_{i}}{\partial x_{j}}+\frac{\partial u _{j}}{\partial x_{i}}) \tag{3}\]  
The equation that reduces Equation (1) to 3D Cartesian coordinates is:  
\[ \begin{array}{l}Q=-\frac{1}{2}[\left(\frac{\partial u}{\partial x}\right)^{ 2}+\left(\frac{\partial v}{\partial y}\right)^{2}+\left(\frac{\partial u}{ \partial z}\right)^{2}]\\ -\frac{\partial u}{\partial y}\cdot\frac{\partial v}{\partial x}-\frac{ \partial u}{\partial z}\cdot\frac{\partial u}{\partial x}-\frac{\partial v}{ \partial z}\cdot\frac{\partial w}{\partial y}\end{array}  \tag{4}\]  
In Formula (4): \(u,v,w\) are the velocity components of the velocity \(v\) in the \(x,y,\) and \(z\) directions, m/s. When \(Q>0\), it means that the rotation of the fluid mass is dominant. Figure 7 shows the \(Q\) isosurface distribution of the blade angle blade fan and the prototype fan in the first-stage and second-stage impeller regions. The \(Q\) isosurface of the first-stage and second-stage impellers are about \(2.5\times 10^{5}\) s\({}^{-2}\) and \(8.5\times 10^{4}\) s\({}^{-2}\), respectively. It can be seen from the figure that the vortices near the blade are mainly divided into the tip leakage vortex, the tip separation vortex and the blade shedding vortex. From the comparison between the prototype fan and the blade angle blade fan, it is found that compared with the prototype fan blade, although the blade angle structure has no obvious effect on the improvement of the vortex core distribution of the tip separation vortex and the tip leakage vortex, it improves the core distribution of the vortex at the trailing edge of the blade. The generation mechanism of the blade shedding vortex is the same as that of the Karman vortex street [20]. The formation of the Karman vortex street is due to the interaction of the inertia and viscosity of the fluid on the back of the cylinder after the fluid contacts the solid surface. A periodic vortex is formed, and the vortex will periodically fall off behind the solid with the flow of the airflow. The size of the period is related to the Reynolds number Re of the fluid and the shape of the solid. The blade shedding vortex will also produce periodic vortices in the area of the trailing edge and pressure surface of the blade. When the frequency of the shedding vortex coincides with the natural frequency of the blade rotation, resonance will occur, causing the blade to vibrate violently, which will lead to damage or failure of the blade.