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 aroun d a circular cylinder at low Keulegan-Carpenter numbers (KC) and frequ ency parameters (beta) are presented in this paper. The finite element method was used for the solution of the Navier-Stokes equations in th e formulation where the streamfunction and vorticity are the field var iables. The computation was conducted at Keulegan-Carpenter numbers ex tending up to KC=15 and frequency parameters ranging between beta=6 an d 100. At low values of the Keulegan-Carpenter number the flow remains symmetrical. As the Keulegan-Carpenter number is increased over a cer tain value which depends also on the frequency parameter, asymmetries appear in the Bow which are eventually amplified and lead finally to c omplex vortex-shedding patterns, some of which are markedly different from those observed at higher frequency parameters. The solution revea led that although for certain values of KC and beta the shedding of vo rtices is periodic, there also exists a complicated flow regime in whi ch the how is not periodic but switches between different modes in con secutive cycles of flow oscillation. For the various how cases examine d, the traces of the hydrodynamic forces are presented and the hydrody namic coefficients and RMS values of the in-line force are compared wi th experimental evidence. (C) 1998 John Wiley & Sons, Ltd.