Simulation of three-dimensional flow around a square cylinder at moderate Reynolds numbers

TLDR

Direct numerical simulations of 2‑D and 3‑D unsteady flow around a square cylinder at Re 150–500 were performed using an implicit fractional‑step finite‑volume method with second‑order accuracy, and the influence of spanwise aspect ratio, grid refinement, and time step was examined under periodic boundary conditions. The simulations show that flow transitions from 2‑D to 3‑D shedding between Re 150–200, with both spanwise instability modes A and B present, and exhibit low‑frequency force pulsations at Re 200–300; Strouhal numbers and mean drag coefficients agree with experiments, while spanwise force coupling increases between Re 300–500.

Abstract

Direct numerical simulations of two-dimensional (2D) and 3-D unsteady flow around a square cylinder for moderate Reynolds numbers (Re=150–500) are performed, employing an implicit fractional step method finite-volume code with second-order accuracy in space and time. The simulations, which are carried out with a blockage ratio of 5.6%, indicate a transition from 2-D to 3-D shedding flow between Re=150 and Re=200. Both spanwise instability modes, A and B, are present in the wake transitional process, similar to the flow around a circular cylinder. However, seemingly in contrast to a circular cylinder, the transitional flow around a square cylinder exhibits a phenomenon of distinct low-frequency force pulsations (Re=200–300). For 3-D simulations, the Strouhal number and the mean drag coefficient are in general agreement with existing experiments. Between Re=300 and 500, an increase in the spanwise coupling of fluctuating forces is indicated. The influence of the spanwise aspect ratio using periodic boundary conditions, a finer grid, and a finer time step is also investigated.