## 3 Results and Discussion
### Comprehensive Performance under Stationary Condition
The end-wall vortex is produced near the end face of the turning vane in the outer basin and develops gradually along the flow direction. In the outlet cross section, the end-wall vortex has separated from the turning vane wall with larger scope and stronger intensity. The high vorticity intensity region is situated at the inner basin of the outlet cross section, with area markedly smaller than case1. With the increase of turning blade thickness, the fluid flow region is further compressed. The influence range and intensity of the end-wall vortex gradually increase and the high-vorticity intensity area is gradually squeezed, which is mutually confirmed with the improvement of flow separation by the turning vane described above. Figure 4: Streamlines of channels, \(Re\) = 10,000. Figure 5: The vorticity based on Q criterion and streamline counters of the first turning region, \(Re=10,000\). The \(Nu\) distribution counters in PS and SS of the channel are shown in Figure 6. Since the working medium in pass1 is in a flat flow state, the boundary layer develops well so that the heat transfer capacity is low, and the \(Nu\) is low in pass1. Due to the outward migration and shock of the fluid during the flow direction transition, the heat exchange is stronger on the side of pass2 near pass3. The fluid impinges the PS, and the wall \(Nu\) upstream of pass2 presents 'PS > SS'. The disordered flow state destroys the flow boundary layer in the upstream of pass2, which enhances the heat exchange. The swirling vortex is exhausted near the midstream. The flow velocity at the downstream is low and there is no disturbance near the side of pass1, which causes poor heat transfer conditions. Therefore, the low \(Nu\) zone is distributed there. In case3 and case5, the fluid enters pass2 in a uniform state due to the influence of the diversion and rectification of the turning vane. The nonuniformity between PS and SS is reduced. The fluid in the outer basin accelerates and impacts the side wall because of the cross-section contraction, which enhances the heat exchange in the first turning region. The inside wall of the turning vane is struck by the fluid to form a high \(Nu\) region. Then, the inner and outer fluids converge at the outlet of the first turning vane. Two high \(Nu\) zones  
Figure 6: The \(Nu\) counters, \(Re\) = 10,000: (**a**) case1; (**b**) case3; (**c**) case5. are presented at the first protrusion structure near the outlet of the first turning region. With the increase of turning blade thickness, the acceleration of the outer fluid and the impact effect of the inner fluid are enhanced. In consequence, the \(Nu\) increases significantly. In the second turning region, there is also an impact-enhanced phenomenon in both the inner and outer basin. However, the difference is that the outer side of the second turning region is an arc. The fluid flows uniformly, and the \(Nu\) of the outer basin wall decreases. At the outlet of the second turning region, the flow state of the fluid is improved. The fluid disturbance weakens upstream of pass3 so that the \(Nu\) decreases. Nevertheless, with the increase of the vane thickness, this phenomenon has been improved. It is worth noting that the inlet of the turning vane is directly impinged by the working medium, and there is also a high \(Nu\) region. The influence range increases with the enlargement of the vane thickness. For analyzing the impact of the turning vane on the heat exchange of the serpentine channel more intuitively, the surface is segmented into 28 zones shown in Figure 7. To reduce the influence of the inlet and outlet effects, only the wall average \(Nu\)/\(Nu_{0}\) in the region 1-26 is counted, as shown in Figures 8 and 9. It can be obtained from figure that the \(Nu\) of pass1 and pass3 increases along the flow direction, while pass2 decreases. This is mainly because the fluid accelerates/decelerates as the channel contracts/expands. The maximum and minimum values are obtained near the first and second turning region, respectively.