Numerical Study of Oscillatory Flow Past Four Cylinders in Square Arrangement for Pitch Ratio Equal to 4

Abstract

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.