Forced Oscillation Of A Square Cylinder With 8-shaped Trajectory

Flow around oscillating bluff-bodies is a common phenomenon involved in many engineering applications such as suspension bridges,offshore structures,and high-rise buildings etc.The present numerical study which focuses on the flow around forced oscillating square cylinder can provide a better understanding of the complicated flow physics associated with the vibrating structures.Therefore,the present study has great significance in both academic research and engineering applications.Flow around square cylinder undergoing the figure-8 trajectories with different phase angles at Reynolds number Re=100 is investigated numerically.The frequency ratio f^*(=f_y/f₀)is in the range from 0.7 to 1.3,where f_y is the oscillation frequency in y direction,f₀ is the vortex shedding frequency of the fixed square cylinder.Four different phase angles?between transverse and inline cylinder motions are investigated,namely0°,-15°,-30°and-45°,which determines the inclination of the figure-8 path.The effect of the anticlockwise(ACLW)and clockwise(CLW)orientations of the cylinder motion is also investigated in the present study.Based on the flow structures,vortex shedding frequencies and the time histories of lift,two vortex maps are classified for each direction of cylinder orbit.Furthermore,there are three flow regimes identified in each vortex map,viz.,2S flow,beating flow,and coalescence beating flow.In the beating and coalescence beating flow regimes,the time history of C_L endures a beat-like change,and the mode is periodic over the beating period T_B instead of the oscillation period T_y.However,the vortex amalgamation phenomenon appears only in the coalescence beating flow.On the other hand,the transition between two flow regimes corresponds to a variation in the relationship between the vortex shedding frequency f_s and oscillation frequency f_y.In the beating regime,f_s>f_y,while f_s=f_y in the 2S regime,which indicates that the 2S flow is in the lock-in range.In the coalescence beating regime,f_s<f_y.A numerical study on the flow around square cylinder following figure-8 trajectories with different amplitudes is also conducted.The Reynolds number is constant and equals to 100.The f^*is in the range from 0.6 to 1.2.The amplitude ratio?(=A_x^*/A_y^*,where A_x^*and A_y^*are the normalized amplitudes in x and y directions respectively)is fixed at 0.1,0.2,0.3,0.4 and 0.5,which can make different amplitudes of the figure-8path.All the cases are tested at?=0°,and only ACLW oscillating direction is adopted.Detailed analysis has been carried out to extract the vortex shedding dynamics and flow structures.Four distinct flow regimes are determined,viz.,2S flow,P+S flow,beating flow and coalescence beating flow.The P+S flow and the 2S flow appears at?=0.1 and?=0.2,0.3,0.4,0.5 respectively.The beating flow and coalescence beating flow present at all test values of?.