Hydrodynamics of a Contracting Cylinder in Translation*

The present study examines the effects of body contraction on the hydrodynamics of a circular cylinder shortly after it is subjected to an impulsive start. Results for the development of the fluid vorticity, hydrodynamic impulse and drag were obtained using computational fluid dynamics and a transient re-meshing scheme that allowed accurate computation of the viscous layers in the vicinity of the cylinder surface. Computational results were obtained for Re = (Ua/$\nu )$ = 9500, and a constant cylinder diameter, up to t* = tU/a = 6; U is the cross flow velocity and ``a'' is the cylinder radius. In this case the drag force increased with time and exhibited undulations that were correlated with vortex shedding events. Computations for a contracting cylinder were initiated at t* = 3.6 using average contraction rates of r = (da/dt)/U = -0.38 and -0.50. These revealed a symmetric but very complex vortex shedding pattern. The drag force on the gradually contracting cylinder decreased initially and then oscillated about zero. For the more rapid contraction the cylinder experienced a strong thrust, due to the hydrodynamic impulse of the shed vorticity, before tapering off.