Flow over a circular cylinder with a flexible splitter plate

Abstract

In the present work, we study the flow field around, and forces acting on, a circular cylinder with an attached flexible splitter plate/flap. Two cases of flap length ( $L/D$ ), namely, $L/D = 5$ and $L/D = 2$ have been investigated focusing on the effect of variations in flap flexural rigidity, $EI$ . We find that for a range of $EI$ and Reynolds numbers $Re = UD/\nu$ , a non-dimensional bending stiffness $K^{\ast }=EI/((1/2)\rho U^2 L^3)$ collapses flap motion and forces on the system well, as long as $Re>5000$ . In the $L/D = 5$ flap case, two periodic flap deformation regimes in the form of travelling waves are identified (modes I and II), with mode I occurring at $K^{\ast } \approx 1.5\times 10^{-3}$ and mode II at lower $K^{\ast }$ values ( $K^{\ast }<3\times 10^{-5}$ ). In the $L/D = 2$ flap case, we find a richer set of flapping modes (modes A, B, C and D) that are differentiated by their flapping characteristics (symmetric/asymmetric and amplitude). Force measurements show that the largest drag reduction occurs in mode I ( $L/D = 5$ ) and mode C ( $L/D = 2$ ), which also correspond to the lowest lift and wake fluctuations, with the mode C wake fluctuations being lower than even the rigid splitter plate case. In contrast, the highest fluctuating lift, in both $L/D$ cases, occurs at higher $K^{\ast }$ , when the wake frequency is close to the first structural bending mode frequency of the flap. The observed rich range of flap/splitter plate dynamics could be useful for applications such as drag reduction, vibration suppression, reduction of wake fluctuations and energy harvesting.