Suppression mechanism of two-degree-of-freedom vortex-induced vibration by Lorentz forces in the uniform flow

In this paper, the control of 2DOF VIV (two-degree-of-freedom vortex-induced vibration) by Lorentz force has been investigated numerically based on the derivation of stream function-vorticity equations together with the initial and boundary conditions in exponential-polar coordinates attached on a moving cylinder, hydrodynamics forces and the cylinder motion equation. From the derivations of force components, the lift/drag induced by the inertial force only depend on the motion along the corresponding direction, while the lift/drag induced by flow field is affected by the cylinder motion along the two directions. Based on the calculation results, the displacement variation of 2DOF VIV along the transverse direction is similar with that of 1DOF VIV (one-degree-of-freedom vortex-induced vibration). However, the secondary vortex is strengthened with the effect of the pressure side and weakened with the effect of the suction side. With the application of symmetrical Lorentz force, the effects of the pressure/suction side and vortex shedding are weakened, which lead to the suppression of 2DOF VIV. Moreover, the cylinder vibration is fully suppressed and the drag is negative due to the net thrust generated if Lorentz force is large enough, which means the final position of cylinder is at the upstream of the initial position. Furthermore, the fluid-structure interactions from the quiescent cylinder to the steady vibration and then vibration control by Lorentz force are investigated. The shear layers and secondary vortexes grow with the increase of cylinder amplitude and decay with the decrease of cylinder amplitude due to the suppression of cylinder vibration controlled by Lorentz force in the whole process.