Passive control of rotational response of a square cylinder with small circular rods

This work proposed a passive method by arranging several small circular rods to control the rotational dynamics of a square cylinder. Two-dimensional numerical investigations were conducted at a low Reynolds number of 120 and in a wide reduced velocity range of Ur = 2–20. Effects of the rod number and arrangement as well as the gap distance between the small rods and square cylinder were examined. For a single square cylinder, a critical reduced velocity of Ur = 6.5 is identified. Rotary angles remain near zero in Ur = 2–6, while a sharp rise occurs at Ur = 6.5, reaching a peak of 38.05° at Ur = 8, after which it slightly declines. The frequencies follow two different growth rates before and after the critical reduced velocity. When eight small rods are evenly arranged around the square cylinder, rotary angles of the structure do not exceed 5° and 90% reductions are achieved as compared with the single square cylinder, showing the most effective suppression. However, the associated drag coefficients are significantly increased due to the increased projected area in the in-line direction as well as the frequent separation and reattachment behaviors. Optimal drag reductions are achieved when two rods are placed at the windward and leeward position, which are helpful to reduce the local high pressure and recover base pressure, respectively. Bifurcation, which is characterized by a non-zero time-averaged rotary angle, appears at high reduced velocity when two side-by-side rods are arranged at the windward position. After bifurcation, these two rods stay below the square cylinder, causing an asymmetrical configuration and thus asymmetrical flow distributions. A recommended gap distance between the small rods and square cylinder is half length of the edge of the square cylinder, under which rotary angles remain zero across the entire Ur range, indicating perfectly excellent rotation suppression. At this configuration, no vortex shedding occurs and flow field is stable and symmetry.