# Effects of \"S\"-Type Bowed Guide Vanes on Unsteady Flow in 1.5-Stage Axial Compressors
## 3 Results and Discussion  
### Unsteady Aerodynamic Results under the Design Condition  
Table 3 shows the pressure ratio and total efficiency of different guide vane bending coefficients under the design condition. It can be seen that the guide vane bending coefficient has little effect on the overall aerodynamic performance. The pressure ratio decreases with the increase of \(a\). The pressure ratio of the \(a\) = 10 mm model decreases by 0.18% compared with the \(a\) = 0 mm model. The total efficiency of the \"S\"-type bowed models is reduced. The total efficiency of the structure with the \(a\) = \(-\)10 mm decreases the most, which is 0.57%. Figure 7 shows the turbulent kinetic energy distribution of models with different bending coefficients at different axial positions under the design condition at the time \(t\) = 0 T. The left figure is the front 2 mm position of the moving vane, which is the inflow of the moving vane. The middle figure is the middle position of the moving vane passage. The right figure is the back 2 mm position of the moving vane, which is downstream of the moving vane. It can be seen that, although the flow channels are geometrically symmetrical, the turbulent kinetic energy distribution of different flow channels is different, which is caused by the inherent unsteadiness of turbulence. At the inflow of the moving vane, the distribution of the high turbulent kinetic energy region is the same as the guide vane shape. This is because as the fluid flows downstream, the guide vane surface boundary layer changes to the turbulent boundary layer. The flow in the turbulent boundary layer is disordered. The turbulent boundary layers on both sides fall off and converge at the guide vane trailing edge, forming a wake area with higher turbulence intensity and more vortices. In addition, there are also regions with higher turbulent kinetic energy near the endwall, where the turbulent kinetic energy intensity near the hub is higher than that near the shroud. The area with higher turbulence kinetic energy regions near the shroud of the \(a\) = \(-\)5 mm model is very small while that of the other models is large. Figure 6: Time step verification. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Bending Coefficient \(a\)/mm** & \(-\)**10** & \(-\)**5** & **0** & **5** & **10** \\ \hline pressure ratio & 1.1908 & 1.1904 & 1.1903 & 1.1901 & 1.1882 \\ total efficiency/\% & 82.39 & 82.66 & 82.93 & 82.64 & 82.51 \\ \hline \end{tabular}
\end{table} 
Table 3: Overall aerodynamic performance under the design condition. In the moving vane channel, the turbulent kinetic energy of the main flow area is low, and the areas with high turbulent kinetic energy are mainly concentrated on the moving vane surface and endwall, which is caused by the boundary layer. Among them, the turbulent kinetic energy near the hub is significantly higher. This is because the fluid domain of the moving vane is a rotating domain. Under the effect of centrifugal forces, the fluid in the moving vane channel tends to move in the radial direction, so the fluid near the hub is easier to perform flow separation. Among them, the turbulent kinetic energy of the \(a=-5\) mm model is the smallest near the hub. With the increase of \(a\), the turbulent kinetic energy near the hub shows an increasing trend. In addition, the intensity of turbulent kinetic energy near the suction surface of the moving vane is also significantly higher than that near the pressure surface. This is depended by the shape of the vane. The pressure surface is concave while the suction surface is convex. Fluid flow separation is more likely to occur when flowing through a convex surface. Turbulent kinetic energy distribution downstream of the moving vane is also uneven in the circumferential direction according to the shape of the moving vane. The turbulent kinetic energy intensity is high in the wake area near the moving vane trailing edge, and low in the mainstream area near the middle of the moving vane channel.