The electro-magnetic control of vortex-induced vibration (VIV) of a circular cylinder is investigated numerically in the exponential-polar coordinates attached on the moving cylinder for Re=150 in the paper. Compared with the fixed cylinder, the vibration of cylinder leads to the shift of stagnation point, the shear layer strength and the inertial force, which affects the hydrodynamic forces on the cylinder. The effects of the instantaneous wake geometries and the corresponding cylinder motion on the hydrodynamic forces for one entire period of vortex shed are discussed in the drag-lift phase diagram. The Lorentz force for controlling the vibration cylinder is classified into the field Lorentz force and the wall Lorentz force. The field Lorentz force decreases the lift oscillation, and in turn, suppresses the VIV, whereas the wall Lorentz force has no effect on the lift.
The characteristics of a uniform-shear flow over a circular cylinder are in- vestigated numerically by using the alternative-direction implicit （ADI） algorithm and a fast Fourier transform （FFT） one in the exponential-polar coordinates for Re = 150 and 0 ≤ K ≤ 0.46. The diagram of lift-drag phase, implying the detail information about the fluctuations of drag and lift as well as the flow patterns in the wake and fluctuating pres- sure on the cylinder surface, is used to describe the effects of the shear rate on the flow. Results show that the upper （or lower） closed curve of a phase diagram corresponds to the first （or second） half shedding cycle. The lift-drag phase diagram will move down-left with the increase of shear rate K such that the lift is exerted from the upper side to the lower side, and the drag on the first half shedding cycle is smaller than that on the second half.
The flow of the weak electrolyte solution can be controlled by Lorentz force achieved with the suitable magnetic and electric fields, and it has the advantages of vortex street suppression, drag reduction, lift enhancement and oscillatory suppression for the flow over a bluff body. The electro-magnetic control of vortex-induced vibration (VIV) of a circular cylinder in the shear flow was investigated numerically in the exponential-polar coordinates attached on the moving cylinder for Re=150. With the effect of background vorticity, the vortex street of VIV cylinder was composed of two parallel rows with an opposite sign of the vortices which inclines toward the lower side and the strength of upper vortex is larger than that of lower vortex. The lift force vibrated periodically with the effect of vortex shedding and the mean value was negative due to the background vorticity. The Lorentz force for controlling the VIV cylinder was classified into the field Lorentz force and the wall Lorentz force. The field Lorentz force suppresses the lift oscillation, and in turn, suppresses the VIV, whereas the wall Lorentz force increases the lift.
In this paper, the electro-magnetic control of a cylinder wake in shear flow is investigated numerically. The effects of the shear rate and Lorentz force on the cylinder wake, the distribution of hydrodynamic force, and the drag/lift phase diagram are discussed in detail. It is revealed that Lorentz force can be classified into the field Lorentz force and the wall Lorentz force and they affect the drag and lift forces independently. The drag/lift phase diagram with a shape of ＂8＂ consists of two closed curves, which correspond to the halves of the shedding cycle dominated by the upper and lower vortices respectively. The free stream shear （K 〉 0） induces the diagram to move downward and leftward, so that the average lift force directs toward the downside. With the upper Lorentz force, the diagram moves downwards and to the right by the field Lorentz force, thus resulting in the drag increase and the lift reduction, whereas it moves upward and to the left by the wall Lorentz force, leading to the drag reduction and the lift increase. Finally the diagram is dominated by the wall Lorentz force, thus moving upward and leftward. Therefore the upper Lorentz force, which enhances the lift force, can be used to overcome the lift loss due to the free stream shear, which is also obtained in the experiment.
