Vortex-Induced Vibration (Viv) Around A Cylinder At Low Reynolds Numbers: The Lock-In Phenomenon

Abstract

In this paper some numerical results for vortex-induced vibrations (VIVs) of a cylinder at
low Reynolds number are presented. The main goal of these preliminary results is the capturing of
synchronization/lock-in phenomenon when Reynolds number is swept for low dimensionless mass ratio
(m ' 153.3524). This fluid-structure interaction problem (FSI) contains three main problems to
be solved, the computational fluid dynamics (CFD), the computational mesh dynamics (CMD) and the
multi-body dynamics (MBD). In this work this last problem is oversimplified to a single body dynamics,
the cylinder. A stabilized ALE (Arbitrary Lagrangian-Eulerian) formulation is used to solve the incompressible
laminar Navier Stokes equations. The cylinder is considered as a rigid body and it is free to
vibrate along the vertical (transverse) direction and it is fixed to move in the horizontal one. The mesh
dynamics may be solved in general by a global optimization strategy, however, in some special cases, a
simple ad-hoc procedure may be adopted. For each sub-problem a second order accurate in time scheme
is adopted. The fluid-structure interaction problem is solved with a strong coupling using a fixed point
iteration strategy. It consists of an additional loop over the three problems forcing the convergence inside
each time step. Hysteretic and vortex-shedding modes are two additional topics that deserve special
attention and they are going to be included in a future work.