New insights into numerical simulations of flow around two tandem square cylinders

Flows around tandem square cylinders at Re = 100 are numerically studied using a characteristic-based penalty operator splitting finite element method based on a multistep algorithm. The validation of the code and numerical method is performed for flows around single square cylinders. L/D effects (with L being the center-to-center distance and D being the square cylinder width) on the flow structures and parameters are investigated for 1.5 ≤ L/D ≤ 9.0. The flow structures, especially far downstream of the square cylinder, indicate six distinct flow regimes. The two-layered vortex formation (TVF) and secondary vortices formation (SVF) modes are defined, and their mechanisms are analyzed. The evolution of TVF into SVF proceeds through the combination of single and binary vortex formations. Variations in the physical flow parameters, including the coefficients of fluctuating lift (CL′), time-averaged drag (C̄D), and amplitude lift (CLA), as well as the Strouhal number and phase lag (ϕ), are analyzed for various L/D values. Obvious jumps in the flow parameters occur at both square cylinders for L/D = 4.4–4.5 because of vortex impingement. Finally, insight into the physics underlying the relationship between CL−upA, CL−up′, and ϕ is derived from the simulation results. The local maximum and minimum of CL−upA and CL−up′ occur at ϕ = 2π and 3π, respectively, corresponding to in-phase and anti-phase vortex shedding by the cylinders. The pressures on the upper and lower sides of the upstream square cylinder decrease and increase, respectively, leading to reductions in CL−upA and CL−up′ as the flow pattern changes from in-phase to anti-phase.