The mechanism investigation of two-degree-of-freedom vortex-induced vibration with electro-magnetic forces

Abstract

The electro-magnetic forces generated by electromagnetic field take control of the flow in the electrolyte solution. In this paper, the mechanism of two-degree-of-freedom vortex-induced vibration controlled by electro-magnetic forces is investigated numerically. With the coordinate at the moving cylinder, the stream function-vorticity equations, the initial and boundary conditions and distribution of hydrodynamic force are deduced in the exponential-polar coordinate. The equation of vorticity transport is solved by the alternative-direction implicit algorithm. The equation of stream function is integrated by means of a fast Fourier transform algorithm. The cylinder motion is calculated by the Runge-Kutta method. The flow field, pressure, lift/drag and cylinder displacement are interacted along the transverse and streamwise direction, where the instantaneous variations are discussed. The derivation shows that the vibration displacement in one direction, whose effects on the flow field influence the vortex-induced forces in both directions, affects the inertial force only in the corresponding direction and is independent of that in the other direction. The numerical calculations show that the vortex-induced vibration is affected by two factors, i.e., the vortex shedding and the cylinder shift. Both of the two factors have influences on the shear layers in the transverse direction and the secondary vortex in the streamwise direction, which further leads to the variations of lift/drag and the cylinder motion. Along the transverse direction, the strength of shear layer on one side is increased by the vortex shedding while the strength of shear layer on the other side is increased by the cylinder shift. Along the streamwise direction, the pressure of cylinder tail is varied with the effect of shedding vortex on the secondary vortex while the effect of cylinder shift on the secondary vortex is also opposite to that of shedding vortex. Notably, the effect of cylinder shift prevails over the effect of shedding vortex so that the former is dominated in the total effects. The flow separation and vortex shedding are suppressed as the fluid of boundary layer is accelerated under the action of electro-magnetic forces. Meanwhile, the vibration displacements decrease gradually along both the transverse and streamwise directions, which also suppresses the effects of pressure/suction sides. Therefore, the vibration is suppressed and the cylinder turns steady rapidly. In addition, the thrust generated by the wall electro-magnetic force counteracts the drag generated by the fluid electro-magnetic force, which means that the final position is at the upstream of the initial position. The experimental results show that the vortexes on the cylinder are suppressed fully and the flow field is steady under the action of electro-magnetic force, which agrees well with the numerical results.