Viscous oscillatory flow around a circular cylinder at low Keulegan-Carpenter numbers and frequency parameters

The results of a numerical study of the viscous oscillating flow around a circular cylinder at low Keulegan-Carpenter numbers (KC) and frequency parameters (beta) are presented in this paper. The finite element method was used for the solution of the Navier-Stokes equations in the formulation where the streamfunction and vorticity are the field variables. The computation was conducted at Keulegan-Carpenter numbers extending up to KC=15 and frequency parameters ranging between beta=6 and 100. At low values of the Keulegan-Carpenter number the flow remains symmetrical. As the Keulegan-Carpenter number is increased over a certain value which depends also on the frequency parameter, asymmetries appear in the Bow which are eventually amplified and lead finally to complex vortex-shedding patterns, some of which are markedly different from those observed at higher frequency parameters. The solution revealed that although for certain values of KC and beta the shedding of vortices is periodic, there also exists a complicated flow regime in which the how is not periodic but switches between different modes in consecutive cycles of flow oscillation. For the various how cases examined, the traces of the hydrodynamic forces are presented and the hydrodynamic coefficients and RMS values of the in-line force are compared with experimental evidence. (C) 1998 John Wiley & Sons, Ltd.