Numerical study of the flow past a cylinder excited transversely to the incident stream. Part 1: Lock-in zone, hydrodynamic forces and wake geometry

The numerical study of the how past a circular cylinder forced to oscillate transversely to the incident stream is presented herein, at a fixed Reynol ds number equal to 106. The finite element technique was favoured for the s olution of the Navier-Stokes equations, in the formulation where the stream function and the vorticity are the field variables. The cylinder oscillati on frequency ranged between 0.80 and 1.20 of the natural vortex-shedding fr equency, and the oscillation amplitude extended up to 50% of the cylinder d iameter. Since the resolution of the characteristics of synchronized wakes is the focus of the study, the first task is the determination of the bound ary of the lock-in region. The computation revealed that, when the cylinder oscillation frequency exceeds the frequency of the natural shedding of vor tices, the flow is not absolutely periodic at subsequent cycles but a quasi periodic flow pattern occurs, which creates difficulty in the determination of the lock-in boundary. The time histories of the drag and lift forces fo r various oscillation parameters are presented, while the vorticity contour s were favoured for the numerical flow visualization. The hydrodynamic forc es, the phase angle between the lift force and the cylinder displacement, a nd the parameters of the wake geometry when steady state was reached, are p resented in cumulative diagrams. These diagrams indicate the effect of the oscillation parameters on the hydrodynamic forces and on the wake geometry. (C) 2000 Academic Press.