Numerical investigation of the onset of three-dimensional characteristics in flow past a pair of square cylinders at various arrangements

Abstract

An incompressible Navier-Stokes solver has been developed to analyze the three-dimensional viscous flow around a pair of square cylinders at a low Reynolds number (Re = 100) at various arrangements. A semi-implicit finite difference scheme was employed on a staggered grid, which facilitated the easier application of boundary conditions while achieving satisfactory accuracy and stability. A third-order upwind (Kawamura-Kuwahara) scheme was applied to discretize the convective terms and a second-order central difference scheme to discretize the diffusive terms. Time integration was performed using a second-order accurate Adams-Bashforth scheme. An iterative pressure-velocity correction was used to obtain a divergence-free velocity field. Aspects of the flow such as vorticity profiles, the time evolution of lift and drag coefficients, and three-dimensionality appearance were studied. Three-dimensional characteristics ceased to appear in a tandem arrangement, irrespective of the gap ratio. In contrast, the side by side arrangement showed a clear three-dimensional transition in the flow when analyzing the vortex structures. Further investigations carried out for staggered arrangement keeping the center to center distance constant and varying the stagger angle (alpha) reveal that the three-dimensional behavior starts at alpha = 30 degrees and keeps progressing with the angle increase.