Nonlinear characteristics of vortex-induced vibration at low Reynolds number

Numerical simulations of vortex-induced vibration of a two-dimensional elastic circular cylinder under the uniform flow are calculated when Reynolds number is 200. In order to achieve the vortex-induced vibration, two-dimensional incompressible Navier–Stokes equations are solved with the space–time finite element method, the equations of the cylinder motion are solved with the new explicit integral method and the emeshing is achieved by the spring analogy technology. Considering vortex-induced vibration with the low reduced damping parameters, the variety trends of the lift coefficient, the drag coefficient, the displacement of cylinder are analyzed under different oscillating frequencies of cylinder. The nonlinear phenomena of locked-in, beat and phaseswith are captured successfully. The limit cycle and bifurcation of lift coefficient and displacement are analyzed. Besides, the Poincare sections of the lift coefficient are used for discussing the bifurcation of periodic solution. There are some differences in nonlinear characteristics between the results of the one degree of freedom cylinder model and those of the two degrees of freedom cylinder model. The streamwise vibration has a certain effect on the lateral vibration.

Research highlights
► The present study proposes to discuss in detail the vortex-induced vibration of an elastic cylinder with both one degree of freedom and two degree of freedom under the uniform flow.
► The 2D incompressible Navier–Stokes equations are solved with the space–time finite element method, the equation of the cylinder motion is solved with the new explicit integral method and the mesh renew is achieved by the spring moving mesh technology.
► Considering the situation of low mass-damping and low Reynolds, the locked in, beat and phaseswith are captured. The nonlinear phenomena, such as the limit cycle and bifurcation of lift coefficient and displacement, are analyzed by the cases with one degree of freedom and two degrees of freedom.
► Finally, the comparisons of the two cases are discussed and it is shown that the streamwise vibration has a certain effect on the lateral vibration.