Exponential-polar coordinates attached to a moving cylinder are used to deduce the stream function-vorticity equations for two-degree-of-freedom vortex-induced vibration, the initial and boundary conditions, and the distribution of the hydrodynamic force, which consists of the vortex-induced force, inertial force, and viscous damping force. The fluid-structure interactions occurring from the motionless cylinder to the steady vibration are investigated numerically, and the variations of the flow field, pressure, lift/drag, and cylinder displacement are discussed. Both the dominant vortex and the cylinder shift, whose effects are opposite, affect the shear layer along the transverse direction and the secondary vortex along the streamwise direction. However, the effect of the cylinder shift is larger than that of the dominant vortices. Therefore, the former dominates the total effects of the flow field. Moreover, the symmetry of the flow field is broken with the increasing shear rate. With the effect of the background vortex, the upper vortices are strengthened, and the lower vortices are weakened; thus, the shear layer and the secondary vortices induced by the upper shedding vortices are strengthened, while the shear layer and the secondary vortices induced by the lower shedding vortices are weakened. Therefore, the amplitudes of the displacement and drag/lift dominated by the upper vortex are larger than those of the displacement and drag/lift dominated by the lower vortex.
Abstract:The control of vortex-induced vibration (VIV) in shear flow with different distributions of Lorentz force is numerically investigated based on the stream function-vorticity equations in the exponential-polar coordinates exerted on moving cylinder for Re = 150. The cylinder motion equation coupled with the fluid, including the mathematical expressions of the lift force coefficient C l , is derived. The initial and boundary conditions as well as the hydrodynamic forces on the surface of cylinder are also formulated. The Lorentz force applied to suppress the VIV has no relationship with the flow field, and involves two categories, i.e., the field Lorentz force and the wall Lorentz force. With the application of symmetrical Lorentz forces, the symmetric field Lorentz force can amplify the drag, suppress the flow separation, decrease the lift fluctuation, and then suppress the VIV while the wall Lorentz force decreases the drag only. With the application of asymmetrical Lorentz forces, besides the above-mentioned effects, the field Lorentz force can increase additional lift induced by shear flow, whereas the wall Lorentz force can counteract the additional lift, which is dominated on the total effect.
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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.