Numerical Study of Oscillatory Flow Past a Pair of Cylinders at Low Reynolds and Keulegan-Carpenter Numbers

Abstract

The results of a numerical study of the viscous oscillating flow around a pair of circular cylinders are presented herein, for a constant frequency parameter, β, equal to 50, and Keulegan-Carpenter numbers, KC, ranging between 0.2 and 10. The cylinders were placed side-by-side to the oncoming flow, for a pitch to diameter ratio, P/D, equal to 1.2. The finite-element method was employed for the solution of the Navier-Stokes equations, in the formulation where the stream function and the vorticity are the field variables. The streamlines and vorticity contours generated from the solution were used for the flow visualization. At low values of the Keulegan-Carpenter number the flow remains symmetrical with respect to the horizontal axis of symmetry of the domain. As the Keulegan-Carpenter number is increased asymmetries appear in the flow, which are eventually amplified and lead finally to more complicated vortex-shedding patterns. These asymmetries generate an aperiodic flow configuration at consecutive cycles, which becomes almost chaotic as KC grows larger. For the various Keulegan-Carpenter numbers examined the traces of the hydrodynamic forces are presented, and the r.m.s. values of the hydrodynamic forces and the coefficients of the in-line force were evaluated.