Flow around a circular cylinder with a free end
Heseltine, Jonathan Lucas
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A circular cylinder with a free end is one of the simplest possible three dimensional structures, yet flow around such a body is complex and not well understood. Numerous previous studies have examined this flow situation; however there is disagreement within the literature about the exact nature of the flow behaviour. The primary dispute is whether a pair of counter-rotating trailing vortices exists near the free end or whether the Kármán vortices are inclined near the cylinder free end and attach onto the body. There is a distinct lack of quantitative wake velocity results from previous work. Therefore, the focus of this study is to obtain such results in order to determine the structure of the wake. Velocity measurements were made in the wake of various circular cylinders mounted vertically perpendicular to a horizontal ground plane. Experiments were conducted in the subcritical Reynolds number regime at ReD = 6x104 using a seven-hole pressure probe capable of determining the time-averaged velocity vector. From the literature, there is evidence that the flow pattern is sensitive to the cylinder aspect ratio and boundary layer thickness relative to the cylinder height. Therefore, the aspect ratio was varied from 3 to 9 by changing the cylinder height while keeping the boundary layer height to cylinder diameter ratio constant at 2.5. For the higher aspect ratio cylinders, results indicate that there are streamwise vortical structures near both ends of the circular cylinder with the vortex pair near the tip of the cylinder much stronger than near the base. As well, thermal anemometry measurements show that the periodicity of the wake weakens near the cylinder ends, with the peak of the power spectrum of the velocity fluctuations being more broadbanded. This suggests that there is indeed a complicated streamwise vortex structure near the free end that is likely composed of inclined Kármán vortices interacting with a strong downwash flow. The strong downwash flow toward the ground plane in this region would act to increase the vorticity of the inclined Kármán vortices while moving the vortices toward the ground plane as they travel downstream. The circulation of the vortex structures becomes weaker downstream and the structures grow in size as additional fluid is entrained. There is also a slight spreading of the tip structures as they travel downstream. When the cylinder aspect ratio is reduced to 3, the lower vortical structures disappear while the strong tip vortex structures remain and a vortex shedding peak is still present in the power spectrum of velocity fluctuations very near the ground plane.