Parallel vortex shedding at Re $\;{=}{\bm {O(10^4)}$ – a transverse control cylinder technique approach

Abstract

In the present studies, the effects of the end conditions of a circular cylinder on its wake at a fairly high Reynolds number of $Re = 1.57\times 10^4$ were studied. The transverse control cylinder technique (TCCT) was previously reported to be able to induce parallel vortex shedding at $Re = O(10^2)$. In the present work, experimental results showed that the TCCT is still effective in inducing parallel vortex shedding at $Re = O(10^4)$. Initially, before the inclusion of the control cylinders, vortices shed by the main cylinder were curved (all shapes referred to are time-averaged shapes) owing to the influence of the cylinder end conditions. Later, two larger control cylinders of diameter D were included and were located normal and upstream of the main cylinder near its ends to change its end conditions. By manipulating the control distance (the gap between the control cylinders and the main cylinder), different vortex-shedding patterns could be induced. With both control cylinders fixed at the optimum control distance of $L_1 = L_2 = L_0 = 1.26D$, the main cylinder was induced to shed parallel vortices. For the cases of curved vortex shedding (without control cylinders) and parallel vortex shedding (with control cylinders at the optimum distance of $L_1 = L_2 = L_0 = 1.26D)$, various aerodynamic parameters of the main cylinder were measured and compared. Results showed that the inclusion of the control cylinders speeded up the flow velocity at the ends of the main cylinder and led to a more uniform pressure distribution over the central span of the main cylinder, which finally resulted in parallel vortex shedding. Aerodynamic parameters such as drag coefficient and Strouhal number associated with parallel vortex shedding were found to be larger than their curved shedding counterparts. However, extra caution should be exercised in interpreting their implications as these data were under the influence of additional wind-tunnel blockage caused by the presence of the control cylinders. Preliminary and approximate calculations had shown that blockage effects were likely to be responsible for a significant part in the change in the aerodynamic parameters such as the drag coefficient and Strouhal number when the control cylinders were installed. When the control cylinders were symmetrically placed, but not at the optimum distance $(L_1 = L_2\ne L_0)$, the vortex-shedding pattern became curved, and was concave or convex downstream at $L_1 = L_2 < L_0$ or $L_1 = L_2 > L_0$, respectively. When the control cylinders were asymmetrically placed $(L_1\ne L_2)$, oblique vortex shedding was induced, with the oblique vortex slanting in the same way as the straight line joining the centres of the control cylinders. The relation between the Strouhal numbers for parallel and oblique vortex shedding was found to still follow the cosine law. The present work confirms earlier finding by other workers that a non-uniform spanwise base pressure distribution was the cause of spanwise base flow, which led to curved or oblique vortex shedding.