## 3 Results and Discussion  
### Comprehensive Performance under Stationary Condition  
The \(Re=10,000\) condition is selected as the instance to illustrate the comprehensive performance of the serpentine channel with various thickness turning vane in this section. Figure 4 shows the streamlines of case1, case3, and case5. It can be observed that the streamlines in the pass1 of the channels are roughly parallel to the surface. The working fluid is accelerated due to the effect of the section contraction. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Variable**} & **Grid1** & **Grid2** & **Grid3** & **Grid4** \\ \hline \multicolumn{2}{c}{Number of grids (\(10^{6}\))} & 0.79 & 1.44 & 2.33 & 4.40 \\ \hline \multirow{3}{*}{Stationary \(Re=10,000\)} & \(Nu_{\text{up}}\) & 104.1 & 101.1 & 99.1 & 98.7 \\  & Relative deviation (\%) & 5.5 & 2.4 & 0.4 & - \\  & \(\Delta p\) [Pa] & 1557 & 1507 & 1484 & 1471 \\  & Relative deviation (\%) & 5.8 & 2.4 & 0.9 & - \\ \hline \multirow{3}{*}{Rotating \(Re=10,000\)} & \(Nu_{\text{up}}\) & 105.8 & 103.2 & 100.7 & 100.4 \\  & Relative deviation (\%) & 5.4 & 2.8 & 0.3 & - \\ \cline{1-1}  & \(\Delta p\) [Pa] & 1144 & 1093 & 1080 & 1075 \\ \cline{1-1}  & Relative deviation (\%) & 6.4 & 1.7 & 0.5 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The mesh independence verification based on case4 model. Figure 3: Grid of the case4 channel. For case1, the cooling medium impinges the upstream side wall of pass2 under the action of turning, forming a flow acceleration region downstream of the impact. The other side of the wall presents the characteristics of flow separation, forming a swirling vortex. The vortex is large in scale and has a wide range of influence, and it does not dissipate until the middle reaches of pass2. The whole second turning region presents spiral flow state under the influence of channel profile. There is also a flow separation phenomenon in the upstream of pass3. However, the fluid quickly reattaches and eventually accelerates from pass3 under the effect of section contraction. For case3 and case5, the fluid is formed into inner and outer streams by the diversion of the turning vane. The inner fluid impacts the turning vane wall surface and changes the direction of flow at an accelerated rate. There is also a swirling vortex near the outlet of the inner basin. However, its scale and influence range are significantly weakened compared to case1, and the flow separation is significantly improved. The outer fluid is accelerated because of the reduction of circulation area. Due to the rectification effect of the turning vane, the characteristics of impingement first and then acceleration on the wall upstream of pass2 is attenuated. With the increase of the thickness of the turning vane, the scale and influence range of the swirling vortex decrease gradually. The acceleration effect of the outer fluid is stronger. It is worth noting that the spiral flow state only appears in the inner basin of the second turning region. The outer streamline is roughly parallel to the surface, and the flow separation phenomenon upstream of pass3 is also improved. Figure 5 shows the vorticity based on Q criterion and streamline counter in the middle and outlet section of the first turning region. It can be observed that there are two wall vortexes cling to the suction side in the middle cross section of case1. A secondary corner vortex evoked by the wall vortex generates near the outer side of the channel. The overall vorticity intensity near inside of pass2 on the outlet cross section is higher, indicating that the flow condition of this area is more disordered. This is related to the flow separation phenomenon in the upstream of pass2 described above. For case3 and case5, the turning vane divides the turning region into inner and outer flow basins. In the middle cross section, the wall vortex and the secondary corner vortex only appear in the inner basin.