The vortex shedding around four circular cylinders in an in-line square configuration

Abstract

This paper presents a numerical study of three-dimensional (3D) vortex shedding flow in the wake of four circular cylinders in a square configuration with a constant space-to-diameter ratio of 2. Numerical tests are carried out for Reynolds number (Re) in the range from 100 to 500. Four wake flow regimes are identified at this spacing ratio. Regime 1 ($100 \le {\mathop{\rm Re}\nolimits} \le 220$100≤ Re ≤220) is characterized by the inclination of weak spanwise vortices and weak streamwise vortices, where the wake behind four cylinder array shares similar features to that behind a single cylinder with a large equivalent diameter. It is observed that the onset of three-dimensionality in the wake behind four cylinder array occurs at lower Re than that behind a single cylinder. Regime 2 ($240 \le {\mathop{\rm Re}\nolimits} \le 300$240≤ Re ≤300) is characterized by the appearance of the regular wavy spanwise vortices and rib-shaped streamwise vortices. The wavelength of the spanwise vortices is about 1.2 and the wake flow is similar to the transition mode B of a single cylinder. Regime 3 ($320 \le {\mathop{\rm Re}\nolimits} \le 380$320≤ Re ≤380) is characterized by severe vortex dislocations in the wake of the cylinders and regime 4 ($400 \le {\mathop{\rm Re}\nolimits} \le 500$400≤ Re ≤500) is characterized by the absence of vortex dislocations and the strong streamwise vortices. The flow between the upstream and the downstream cylinders is predominantly two-dimensional in regimes 1, 2, and 3 and becomes 3D in regime 4. Physical mechanisms responsible for different flow regimes are proposed and discussed in details. Significant changes in the root-mean-square force coefficients, wake formation length, and phase angle of the lift coefficients on the downstream cylinders are observed when the flow transits from one regime to another.