Dependence On Mass Ratio Of Critical Reynolds Number For Galloping Of Square Prism

Flow-induced vibration(FIV)can be observed in aerodynamics,hydrodynamics and other related engineering fields.The mechanical energy from vibration can be captured and applied to generate electricity by a bladeless wind turbine in wind power engineering.However,large-amplitude vibration might cause huge destructive damage on structures.The study of galloping of square prism is of great significance for structural protection and energy utilization in civil and energy engineering.Dependence on mass ratio of critical Reynolds number for galloping is investigated in the present study.The responses of the vibration,i.e.amplitude,flow structure,forces,frequencies and added mass ratio,are discussed as well.The square prism(side width D)with various mass ratio(m^*=1-20)undergoes a transverse vibration.The reduced velocity(U_r=U?/f_nD,where U?is the free-stream velocity and f_n is the natural frequency)is changed from 2 to 60 at Re=140-162.As U_r gradually increases,the flow responses of square prism are classified into four branches,i.e.,initial branch(IB),lower branch(LB),desynchronization branch(DB)and galloping branch(GB).The critical Reynolds number(Re_cg)of GB decreases with the increase of m^*.Re_cg decreases dramatically from 162 to 140 with m^*increasing from1 to 20.Moreover,the U_r corresponding to onset of GB is smaller at a larger m^*.The variations of added mass ratio(m_a^*)in different flow branches are well investigated.In general,m_a^*drops rapidly in IB,then declines gently in LB and DB but jumps from negative to positive at the onset of galloping.The total lift force can be decomposed into potential force and vortex force.The vortex force coefficient and potential force coefficient both reach their peaks at the onset of LB,while total lift force falls to its minima.