Fluid–structure interaction of a square cylinder at different angles of attack

Abstract

Abstract This study investigates the free transverse flow-induced vibration (FIV) of an elastically mounted low-mass-ratio square cylinder in a free stream, at three different incidence angles: ${{\alpha }}=0^\circ $ , $20^\circ $ and $45^\circ $ . This geometric setup presents a body with an angle of attack, sharp corners and some afterbody, and therefore is a generic body that can be used to investigate a wide range of FIV phenomena. A recent study by Nemes et al. ( J. Fluid Mech. , vol. 710, 2012, pp. 102–130) provided a broad overview of the flow regimes present as a function of both the angle of attack ${{\alpha }}$ and reduced flow velocity ${U^{*}}$ . Here, the focus is on the three aforementioned representative angles of attack: ${{\alpha }}=0^\circ $ , where the FIV is dominated by transverse galloping; ${{\alpha }}=45^\circ $ , where the FIV is dominated by vortex-induced vibration (VIV); and an intermediate value of ${{\alpha }}=20^\circ $ , where the underlying FIV phenomenon has previously been difficult to determine. For the ${{\alpha }}=0^\circ $ case, the amplitude of oscillation increases linearly with the flow speed except for a series of regimes that occur when the vortex shedding frequency is in the vicinity of an odd-integer multiple of the galloping oscillation frequency, and the vortex shedding synchronizes to this multiple of the oscillation frequency. It is shown that only odd-integer multiple synchronizations should occur. These synchronizations explain the ‘kinks’ in the galloping amplitude response for light bodies first observed by Bearman et al. ( J. Fluids Struct. , vol. 1, 1987, pp. 19–34). For the ${{\alpha }}=45^\circ $ case, the VIV response consists of a number of subtle, but distinctly different regimes, with five regimes of high-amplitude oscillations, compared to two found in the classic VIV studies of a circular cylinder. For the intermediate ${{\alpha }}=20^\circ $ case, a typical VIV ‘upper branch’ occurs followed by a ‘higher branch’ of very large-amplitude response. The higher branch is caused by a subharmonic synchronization between the vortex shedding and the body oscillation frequency, where two cycles of vortex shedding occur over one cycle of oscillation. It appears that this subharmonic synchronization is a direct result of the asymmetric body. Overall, the FIV of the square cylinder is shown to be very rich, with a number of distinct regimes, controlled by both ${{\alpha }}$ and ${U^{*}}$ . Importantly, ${{\alpha }}$ controls the underlying FIV phenomenon, as well as controlling the types of possible synchronization between the oscillation and vortex shedding.