Vortex-induced vibrations of a diamond cross-section: Sensitivity to corner sharpness

This paper studies the fluid–structure interaction of an elastically mounted square cross-section cylinder immersed in a free stream. The cross-section is mounted such that its sides are at 45° to the free stream direction, in a “diamond” configuration, and its motion is constrained to the transverse direction relative to the flow direction. Apart from the cross-section, this setup is the same as the majority of single-degree-of-freedom vortex-induced vibration studies of cylinders. Two-dimensional direct numerical simulations of this system have been performed. The Reynolds number based on the point-to-point distance of the cross-section has been fixed at Re=200). Simulations at this Reynolds number allow a direct comparison with previous results from circular cylinders, and therefore focus directly on the impact of the geometry. The sensitivity of the flow, and therefore the motion of the cylinder, to geometrical effects is considered. This is done by rounding the two side corners (those pointing across the flow) at a given radius. For well-rounded corners, the flow behaviour resembles that of a circular cylinder undergoing vortex-induced vibration. However, below a critical radius, the dynamics are considerably altered. Highly disordered and irregular wakes and body motions are observed, as well as a synchronized, periodic P+S wake mode (Williamson and Roshko, 1988), which consists of a pair of vortices on one side, and a single vortex on the other side, shed per oscillation cycle, which results in a non-zero mean lift force. A period-doubled version of this P+S wake is also presented. The spatial structure, and the spatio-temporal symmetries of each of these modes is reported. The results show that even though the spatio-temporal symmetry of the flow is unaffected by the geometry when the body is rigidly mounted (the flow always saturating to a Kármán vortex street) geometric features such as sharp corners can induce a number of spontaneous symmetry breaking bifurcations when the body is elastically mounted. Which of these various modes is observed is shown to be a function of both the corner radius and the spring stiffness, expressed through the reduced velocity.