## 3 Results and Discussion
### Wake Propagation in the AITD  
Figure 4 compares the turbulence intensity (\(T_{u}\)) distribution at the midspan of Section B1-B6. The initial shape of the wakes (as shown in Section B1 of Figure 4) is very similar under conditions with different reduced frequencies, and the peak value of the turbulence intensity is almost the same. When propagation is downstream, the wakes also move clockwise (as following the flow direction) due to the tangential velocity induced by the rotation of the rods. As shown in Figure 4, the approximate migration of the wakes is identified by the red and black arrows for the cases of \(f\) = 0.71 and 1.61, respectively. The tangential velocity of the wakes increases with \(f\), and their travel distance in the AITD passage also increases. As shown in Figure 4, with the journey from Section B1 to B6, the sweeping wake (red arrow) travels one more pitch of the sweeping rods in the circumferential direction in the case of \(f\) = 1.61 than in the case of \(f\) = 0.71 (black arrow). The increasing travel distance of the wakes inevitably affects their shape and dissipation in the cases with high reduced frequencies: in Section B5, the adjacent wakes have already diffused to the contact position in the cases with high \(f\) (such as \(f\) = 1.61), while there is an obvious freestream region with low \(T_{u}\) in the case of \(f\) = 0.71; in Section B6, by comparison with the \(f\) = 0.71 case, the range of the high \(T_{u}\) region increases by 10% span, and its peak turbulence intensity decreases by 0.73% in the case of \(f\) = 1.61. These results indicate that  
Figure 3: AITD model and results for validation (SA: saddle point; S3 and S4: horseshoe vortices). the increasing reduced frequency of the sweeping wakes is beneficial to the acceleration of wake diffusion, interaction, and dissipation. Figure 5 compares the time mean streamwise vorticity (\(C_{\text{ms}}\)) contours of Sections B1-B6 for the various \(f\) cases. In Section B1, the initial wake shape is radial, while in Section B3-B6, the wakes gradually become inclined and the inclination increases with the increasing \(f\). This is because the tangential velocity induced by the sweeping rods decreases with the lifting of the AITD channel, but the reduction near the hub is less than that near the casing due to the conservation of angular momentum, resulting in the tangential velocity difference in the radial direction and the circumferential inclination of the wakes, as shown with the red dashed line. Under the coupling effect between the circumferential motion of the wakes and the radial movement of the low-energy fluid along the wakes from the hub to the casing [29], the wake vortices near the hub are stretched in Section B3 (as shown by \"Str\" in Figure 5). This stretching effect becomes more obvious in Section B4-B6, resulting in the enhanced dissipation of the wakes in the corresponding regions. Figure 4: The \(T_{u}\) distribution at the midspan of Sections B1–B6 (black arrow: the \(T_{u}\) peak (wake center) trace in the \(f\) = 0.71 case; red arrow: the \(T_{u}\) peak (wake center) trace in the \(f\) = 1.61 case). Figure 5: Time mean streamwise vorticity contours of Sections B1-B6. Comparing the cases with different \(f\), the residual vortices near the hub in Sections B5 and B6 decrease with the increasing \(f\): the wake vortices near the hub are almost dissipated in Section B5 for the \(f=1.61\) case, while there are still a certain number of residual wake vortices in Section B6 for the \(f=0.71\) and \(0.90\) cases. This means that the increasing \(f\) of the sweeping rod is conducive to accelerating the wake dissipation near the hub, because it enhances the circumferential motion and stretching effects of the wakes. Along with increasing \(f\), the promoted circumferential inclination of the wakes increases the spacing between the adjacent wake vortices and the radial travel path of the low-energy fluid, thus delaying the wake vortex squeezing and exhaustion in the middle-upper AITD passage.