# Effect of Lateral End Plates on Flow Crossing a Yawed Circular Cylinder
## 4 Conclusions  
The flow crossing a yawed circular cylinder at a subcritical Reynolds number of 3900 is numerically investigated using large eddy simulation (LES) at three yaw angles of 15\({}^{\circ}\), 30\({}^{\circ}\), and 45\({}^{\circ}\). The effect of the end-plate wall boundary condition on the vortex structure in the wake is investigated. Two boundary conditions of two end-plate walls are explored, respectively, viz. nonslip and periodic. The vortex structure in the wake and fore-and-aft streamline development are qualitatively examined. Moreover, the pressure profile on the cylinder wall and lift coefficient spectra of the segmental cylinder are quantitatively analyzed. The numerical simulation results reveal that the boundary condition on the wall of two lateral end-plates is a decisive factor influencing the flow characteristics in the wake. Under the periodic boundary condition, the numerical simulations demonstrate that even at larger yaw angles (up to 45\({}^{\circ}\)), the flow characteristics in the wake still hold a similar flow structure as flow normally crossing a circular cylinder. However, when the nonslip boundary condition is imposed on the two lateral end-plate walls, the flow behaviors in the wake become complicated and the vortex structure in the wake drastically deviates from regular Strouhal vortex shedding. The flow behaviors in the wake under the nonslip boundary condition can be concluded as follows. 1. Vortex structure: No organized Strouhal vortex is shed in the wake; the vortex structure in the wake exhibits a tapering shape towards the tip end. At a large yaw angle, such as 45\({}^{\circ}\), it even becomes a wedge shape lying on the tip end. 2. Streamline: The incoming streamlines undergo several changes in direction when passing a yawed cylinder. In the wake, they are pushed towards the tip side and eventually separated away from the wall of the cylinder. The flow pattern is formed in the wake as the streamlines on the tip side are becoming denser while the streamlines on the base end are becoming sparser. Moreover, at a large yaw angle such as 30\({}^{\circ}\) and 45\({}^{\circ}\), a secondary wall-attached axial flow, besides the incoming streamlines, is originated at the trailing edge from the base end, which is also separated from the wall and finally coalesces with the primary incoming flow. Figure 17: Power spectra of segmental lift coefficient at yaw angles of 30\({}^{\circ}\) and 45\({}^{\circ}\). 3. Pressure distribution: On most portions of the rear wall of the cylinder except the region around the trailing edge, a positive axial pressure gradient is formed from the base side to the tip side, which contributes to the separation of the above axial flow attached on the rear surface of the cylinder. In the region around the trailing edge, a convex pressure spike at the base end initiates the secondary axial flow around the trailing edge. 4. Spectral power of local lift force: The power spectra analysis of the local lift coefficient shows that the frequency distribution is broadband in the base side while there are two peak frequencies in the tip side, where the larger one corresponds to the value predicted by the independent principle, and the smaller one is generated by the secondary axial flow separation from the rear wall of the cylinder. The authors should discuss the results and how they can be interpreted in the perspective of previous studies and the working hypotheses. The findings and their implications should be discussed in the broadest context possible. Future research directions may also be highlighted. Conceptualization, writing--review and editing, supervision, project administration, and funding acquisition are done by R.-Q.D. Methodology, software, validation, formal analysis, investigation, resources, data curation, writing--original draft preparation and visualization were done by [PERSON]. This research was funded by the National Natural Science Foundation of China (Grant No. 51779126). The authors declare no conflict of interest.