Flow Induced Stability Diagram Of A Square Cylinder At A Low Reynolds Number

With the increasing wide range of applications of bluff bodies in many engineering fields including offshore oil drilling platform,high-rise buildings and the transmission line etc.,the study of flow-induced vibration of these structures has attracted great attention.Vortex-induced vibration?VIV?and galloping are the two well-known phenomena in the problems of fluid-structure interaction.Galloping is associated with the high-amplitude and low-frequency oscillation of the bodies,and it happens to the long elastic non-circular cylinders.In this work,the phenomena of the transverse oscillation of an elastically mounted square cylinder is numerically examined.Mainly,the effect of damping ratio and mass ratio on the critical reduced velocity marking the onset of galloping and other corresponding related parameters at a low Reynolds number?Re=170,based on the free stream velocity and the diameter of the cylinder?is numerically investigated by changing dimensionless reduced velocity.The damping ratio?is varied from 0 to 1 for different mass ratio m^*?5?m^*?30?in the range of reduced velocity U_r=3⁸0.Finite volume method is adopted in this paper.First,the influence of the reduced velocity on the response of the square cylinder is studied by changing the natural frequency of the system under the condition of fixed damping ratio and mass ratio.Later,the critical reduced velocities U_rcc marking the occurrence of galloping are investigated for different combinations of damping and mass ratios.The numerical results indicate that for high?,U_rcis proportional to m^*.For each fixed m^*,the value of U_rcincreases with the increase of?.The results also suggest that the m^*?parameter cannot characterize the system response adequately alone,but to a certain extent it can predict the occurrence of galloping.In addition,the intrinsic mechanism of galloping phenomenon is further revealed by analyzing the phase angle relationship between lift coefficient and displacement,the instantaneous vorticity diagram,the vibration frequency and some related dynamic parameters.