# Effect of Lateral End Plates on Flow Crossing a Yawed Circular Cylinder
## 1 Introduction  
Flow crossing a yawed circular cylinder is a significant issue, not only in academia but also from a practical point of view. In mechanical engineering, the induced vibration caused by crossing flow over heat transfer tubes has a severe impact on the mechanical integrity and life span of heat exchangers. In engineering applications, the so-called \"independence principle\" (proposed by [PERSON] [1], hereinafter IP) is commonly used to evaluate the vortex shedding frequency of a uniform incoming flow crossing a yawed cylinder, assuming independence between the normal component and the axial component of the incoming flow velocity. In the IP hypothesis, a uniform flow passing a yawed cylinder is postulated as being quasi-two-dimensional, and the characteristics of the vortex wakes behind a circular cylinder are barely controlled by the normal component of the incoming flow velocity, such as organized Strouhal vortices shedding and vortex structure in the wake. However, a literature review reveals that the validity of the IP is still in question. Conflicting conclusions on the IP validity for uniform flows crossing yawed circular cylinders have been made in previous reports. Earlier in 1982, [PERSON] [2] experimentally investigated the applicability of the IP to subsonic turbulent flow over a swept rearward-facing step. It was shown that the validity of the IP is strongly dependent on the yaw angle, which is valid up to a yaw angle of 38 degrees. [PERSON] et al. [3] measured in a wind tunnel the pressure distribution on the surface of a yawed circular cylinder andinvestigated the wake size behind the yawed cylinder by a visualization technique. He concluded that a flow around a yawed circular cylinder is three-dimensional and nonuniform along the axis of the cylinder so that the IP is absolutely prevented. Moreover, they attributed the failure of the IP to the aspect ratio of the circular cylinder, which was very important for the flow characteristics related to vortex shedding. [PERSON] et al. [4] investigated three-dimensional flow past a yawed circular cylinder of infinite length using direct numerical simulation, in which the yaw angle changes from 0 to 60 degrees. It was concluded that the Strouhal number and mean drag coefficient agree well with the IP at different yaw angles. [PERSON] et al. [5] investigated the spanwise dependence of vortex-shedding from yawed circular cylinders. They concluded that the IP was shown to predict the vortex-shedding frequency reasonably well along the entire cylinder span for smaller yaw angles (less than 20 degrees), while the vortex-shedding in the wake becomes more disorderly. [PERSON] et al. [6] experimentally investigated the validity of the IP for cross-flow passing a yawed cylinder. It was reported that the IP is to some degree valid at low inclination angles, but the peak lift force was noticeably different from the prediction of the IP. They ascribed the inconsistence to the neglect of the effects of the axial component of the flow in the IP hypothesis. [PERSON] et al. [7] numerically explored the flow past a yawed cylinder of finite length using the finite volume/fictitious domain method. They argued that the IP is inaccurate in the flow regime. Therefore, there is significant uncertainty in basic characteristics such as vortex shedding in the wake as a flow crosses a yawed circular cylinder. Theoretically, the IP is based on the assumption that the Reynolds stress terms in the streamwise and spanwise equations are independent, which are only established for a yawed cylinder with an infinite length; otherwise, the IP solution is precluded. Therefore, the end conditions of a yawed cylinder are decisive factors for the vortex-shedding behavior in the wake as a flow sweeps it. The Ramberg experiments [8] have shown that the characteristics of the vortex wake behind yawed cylinders are very sensitive to the end conditions. [PERSON] [9] reviewed the various types of vortex generation and the related response characteristics of yawed cylinders.