Vortex-induced Vibration Characteristics Of A Rotating Circular Cylinder With Two Degrees Of Freedom Under Different Inflow Conditions

Vortex-induced vibration(VIV)of bluff body structures is a ubiquitous phenomenon in nature and many engineering fields.Vortex-induced vibration of structures is an important safety-related issue in fluid machinery and power engineering equipment.The rotation of bluff body is one of the simplest vortex-induced vibration control methods.As the most common bluff body structure in marine engineering,the rotation of the circular cylinder can enhance or suppress the vibration response of the cylinder,so the rotation can be applied to vortex-induced vibration energy harvesting and vibration control.In engineering fields such as ocean engineering and deep-sea drilling,two-degree-of-freedom vortex-induced vibration of the rotating circular cylinder can be observed in slender rotating structures exposed to seawater erosion.This paper comprehensively considers four inflow conditions:uniform flow,linear shear flow,fitted ocean currents,and parabolic flow.The vortex-induced vibration response of a two-degree-of-freedom rotating circular cylinder is numerically investigated within the range of the reduced velocity 3.0≤U~*≤14.A rigid cylinder of diameter D rotates counterclockwise around its axis and the range of rotating rates is0≤α≤1.5.Under the affection of incoming flow,the rotating cylinder can vibrate freely in streamwise and cross-flow directions.The amplitude response,frequency response,offset,and lift-drag coefficient of the rotating cylinder were obtained by numerical study,and the X-Y movement trajectories and near-wake structures of the rotating cylinder were captured.The vortex shedding patterns of the rotating cylinders under different inflow conditions are summarized.In this paper,the effects of parameters such as inflow conditions,rotating rates,and reduced velocity on the amplitude-frequency response,force characteristics,movement trajectories,wake structure,and vortex shedding patterns of the rotating cylinder are analyzed.For the uniform inflow,the maximum amplitudes of the rotating cylinder in the streamwise and cross-flow directions are 0.363D and 0.611D,respectively.For the linear shear flow,the maximum amplitudes in the streamwise and cross-flow directions are 0.414D and 0.820D,respectively.For the fitted ocean currents,the maximum amplitudes in the streamwise and cross-flow directions are 0.409D and 0.738D,respectively.For the parabolic flow,the maximum amplitudes in the streamwise and cross-flow directions are 0.419D and 0.738D,respectively.The rotation enhanced the vibration amplitude of the streamwise direction of the cylinder and suppresses the vibration amplitude of the cross-flow direction.For the non-rotating cylinder,the trajectories of uniform flow,fitted ocean currents,and parabolic flow present a symmetrical"8"-shaped,and the"droplet"-shaped trajectory can be observed under shear flow.For the rotating cylinder,the trajectories under the four inflow conditions all present a single closed-loop ellipse.The"8"-shaped movement trajectory indicates that the vibration frequency of the cylinder in the streamwise direction is twice that of the cross-flow direction.The movement trajectories of single closed-loop such as droplet-shaped and ellipse shows that the vibration frequency of the cylinder is always consistent in streamwise and cross-flow directions.The Magnus effect caused by rotation offsets the equilibrium position of the cylinder downward from its initial position.The rotation of the cylinder can stretch the vortex shedding from the surface of the cylinder,and this phenomenon is more pronounced at high rotational speeds.The Magnus effect caused by rotation results in the asymmetry in the counterclockwise and clockwise vortex intensity and an upward offset of the near-wake structure.The hydrodynamic force acting on a cylinder is closely related to the separation of the shear layer on the cylinder surface and wake vortex shedding.Six vortex shedding patterns(2S,S+P,P+S,2P,P+T,and U-shaped)and three wake vortex transition modes(2S~*,S+P~*,and P~*+S)are observed in the two-degree-of-freedom vortex-induced vibration of the rotating cylinder.