# 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
For the \"S\"-type bowed guide vanes, 0.25 H and 0.75 H blade-height sections are the locations where the guide vane deviates most from the original model. Figure 12 shows the Mach number distribution of different positions at different times of the model with a guide vane bending coefficient \(a=0\) mm under the design condition. The moving vane with a black outline is the moving vane monitored in the unsteady aerodynamic calculation. The fluid forms a boundary layer on the guide vane surface. When the fluid flows out of the guide vane passage, the boundary layers on both sides fall off and converge at the trailing edge, forming a vortex zone with low velocity behind. The velocity of the mainstream near the middle of the guide vane channel is high, which results in uneven velocity distribution at the guide vanes outlet. The moving vanes will be alternately impacted by the high-speed fluid in the mainstream area and the low-speed fluid in the vortex area, so they will be subject to the periodic unsteady aerodynamic exciting force. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Bending Coefficient \(a/\)mm** & \(-\mathbf{10}\) & \(-\mathbf{5}\) & \(\mathbf{0}\) & \(\mathbf{5}\) & \(\mathbf{10}\) \\ \hline tangential exciting force mean value/N & 131.2 & 132.8 & 131.9 & 131.4 & 132.2 \\ axial exciting force mean value/N & 181.1 & 182.3 & 182.2 & 181.6 & 180.7 \\ tangential exciting force amplitude value/N & 0.448 & 3.033 & 4.882 & 5.609 & 4.460 \\ axial exciting force amplitude value/N & 0.578 & 3.722 & 6.013 & 6.876 & 5.423 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Exciting force under design conditions. Figure 10: Frequency domain distribution of aerodynamic exciting force under design conditions. (**a**) Tangential aerodynamic exciting force; (**b**) Axial aerodynamic exciting force. and a vortex zone with a lower flow velocity is formed behind the stator vanes trailing edge. The Mach number at the stator outlet is also relatively low, even lower than that at the guide vane inlet. At the \(h=0.5\) H position, the flow field distribution in the guide vane and moving vane passage is similar to that at the position of \(h=0.25\) H, but the maximum Mach number appears at the stator vanes suction surface. The Mach number at the stator outlet is lower than that in the moving vane passage, but slightly higher than that at the guide vane inlet. At the \(h=0.75\) H position, the Mach number in the stator passage is further increased, a large area of the high Mach number appears on the pressure stator surface side, and the Mach number at the stator outlet is also significantly increased compared with that at the inlet of the guide vane. In summary, the Mach number tends to increase with the increase of the blade height. The increase at the downstream position is more obvious. The red dotted line marks the relative position of the moving vane leading edge and the guide vane. For the \(a=0\) mm model, although the guide vane is straight, the moving vane is designed to be twisted, so the relative position at different blade heights is slightly different. At \(t=0.25\) T, the moving vane leading edge is roughly at the position just passing the guide vane trailing edge, although relative positions of different blade heights are slightly different. We analyze the influence of the guide vane wake on the exciting force of the moving vane at this time. If there is no guide vane in this compressor stage, the moving vane incoming flow is uniform along the tangential direction. The flow force acting on the moving vane should be constant. The direction of the force is indicated by the black arrows in the figure. When the guide vane exists, the moving vane incoming flow is uneven. At the time \(t=0.25\) T, the low-speed fluid from the guide vane wake impacts the suction surface of the moving vane as shown in the blue circle, while the high-speed fluid from the main flow area of the guide vane impacts the pressure surface of the moving vane as shown in the red circle.