Numerical study on two-degree-of-freedom vortex induced vibrations suppression of a circular cylinder via synthetic jets at different excitation frequencies

In this work, a pair of synthetic jets are investigated for control of vortex induced vibration (VIV) of a circular cylinder in uniform flow in the low Reynolds number regime. In particular, the study focuses on three representative phase differences (0, pi/2, and pi p) between the pair of synthetic jets to study the influence of synthetic jet excitation frequency ratio f(sj)* (f(sj)* = f(sj)/f(n,water)) on 2DOF VIVs control by two-dimensional numerical simulation. The Reynolds number is fixed at 150, the mass ratio m* (m* = m(osc)/m(d)) of the circular cylinder is 2.0, and the natural oscillation frequencies in the in-flow and cross-flow directions are equal. The amplitude response, frequency response, hydrodynamic forces, and wake patterns are analyzed. The results show that both in-flow and cross-flow oscillations of the circular cylinder can be significantly suppressed by synthetic jets with various phase differences, and the wake becomes symmetric when f(sj)* >= 4.0. When f(sj)* < 4.0, many fluctuations can be observed from the changing curves of in-flow and cross-flow oscillation amplitudes, and the oscillation may be enhanced by the occurrence of lock-in between the oscillation frequencies and the synthetic jet excitation frequencies. Besides, vortex shedding modes of the controlled cases are significantly different in blowing and suction phases of the synthetic jet, when the excitation frequency is very low, such as f(sj)* = 0.2.