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The results of a numerical study of the viscous oscillating flow around four 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 on the vertices of a square, whose two sides were perpendicular and two parallel to the oncoming flow, for a pitch ratio, P/D, equal to 4. 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 the vorticity contours generated from the solution were used for the flow visualization. When the Keulegan-Carpenter number is lower than 4, the flow remains symmetrical with respect to the horizontal axis of symmetry of the solution domain and periodic at consecutive cycles. As KC increases to 4 the flow becomes aperiodic in different cycles, although symmetry with respect to the horizontal central line of the domain is preserved. For KC equal to 5 asymmetries appear intermittently in the flow, which are eventually amplified as KC increases still further. These asymmetries, in association with the aperiodicity at different cycles, lead to an almost chaotic configuration, as KC grows larger. For characteristic cases the flow pattern and the traces of the hydrodynamic forces are presented. In addition, the mean and r.m.s. values of the in-line and transverse forces and the hydrodynamic coefficients of the inline force were evaluated for the entire range of Keulegan-Carpenter numbers examined.

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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 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 vorticity contours generated from the solution were used mainly for the flow visualization, whereas the stream-lines and isobars are shown in some cases. At low values of the Keulegan-Carpenter number the flow remains symmetrical with respect to the horizontal axis of symmetry of the solution 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 time-histories 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.