Numerical Simulation of Vortex-Induced Vibration with Three-Step Finite Element Method and Arbitrary Lagrangian-Eulerian Formulation

Abstract

Numerical simulations were performed in this paper to investigate an elastically mounted circular cylinder subjected to vortex-induced vibration (VIV). A three-step finite element method (FEM) is introduced for solving the incompressible fluid flow equations in two dimensions. The computational procedure is coupled with a mesh movement scheme by use of the arbitrary Lagrangian-Eulerian (ALE) formulation on account of the body motion in the flow field. On running the numerical simulations, the Reynolds number was kept constant of Re = 100 and the reduced velocity [Formula: see text] = U/([Formula: see text] D) was varied from 3.0 to 10.2 by changing the natural frequency [Formula: see text] of the cylinder. The mass ratio m* = 4m/ρπD2 and damping ratio ξ are set to be 10.0 and 0.01, respectively, where U is free-stream velocity, D the diameter of the circular cylinder, m the mass of the cylinder per unit length, and ρ the density of the fluid. Numerical results are examined for the response amplitude of transverse direction as well as the phase angle, φ, between the lift force and the transverse displacement of the cylinder. The numerical results reveal that the transverse amplitudes present only two branches, namely, initial branch and lower branch, rather than three branches as the results obtained from high-Re experiments with low m∗ξ. On the other hand, the phase angles present almost linear increase with the reduced velocity in the synchronization region. However, experiments concerned with high Re exhibit a sudden jump in phase angle of approximate [Formula: see text]. The difference between the present study and the high-Re experiment is attributed to no substantial vortex shedding mode transition at the present numerical results of laminar flow.