NUMERICAL STUDY OF THE FLOW PAST A CYLINDER EXCITED TRANSVERSELY TO THE INCIDENT STREAM. PART 1: LOCK-IN ZONE, HYDRODYNAMIC FORCES AND WAKE GEOMETRY

Abstract The numerical study of the flow past a circular cylinder forced to oscillate transversely to the incident stream is presented herein, at a fixed Reynolds number equal to 106. The finite element technique was favoured for the solution of the Navier–Stokes equations, in the formulation where the stream function and the vorticity are the field variables. The cylinder oscillation frequency ranged between 0·80 and 1·20 of the natural vortex-shedding frequency, and the oscillation amplitude extended up to 50% of the cylinder diameter. Since the resolution of the characteristics of synchronized wakes is the focus of the study, the first task is the determination of the boundary of the lock-in region. The computation revealed that, when the cylinder oscillation frequency exceeds the frequency of the natural shedding of vortices, the flow is not absolutely periodic at subsequent cycles but a quasiperiodic flow pattern occurs, which creates difficulty in the determination of the lock-in boundary. The time histories of the drag and lift forces for various oscillation parameters are presented, while the vorticity contours were favoured for the numerical flow visualization. The hydrodynamic forces, the phase angle between the lift force and the cylinder displacement, and the parameters of the wake geometry when steady state was reached, are presented in cumulative diagrams. These diagrams indicate the effect of the oscillation parameters on the hydrodynamic forces and on the wake geometry.