This article presents a two-dimensional numerical study of the unsteady laminar flow from a square cylinder in presence of multiple small control cylinders. The cylinders are placed in an unconfined medium at low Reynolds numbers (Re = 100 and 160). Different flow phenomena are captured for the gap spacings (g = s/D, where s is the surface-to-surface distance between the main cylinder and small control cylinders and D is the size of the main cylinder) between 0.25 – 3 and angle of attack (θ) ranging from 30⁰ to 180⁰. Numerical calculations are performed by using a lattice Boltzmann method. In this paper, the important flow physics of different observed flow patterns in terms of instantaneous vorticity contours visualization, time-trace analysis of drag and lift coefficients and power spectra analysis of lift coefficient are presented and discussed. Drag reduction and suppression of vortex shedding is also discussed in detail and compared with the available experimental and numerical results qualitatively as well as quantitatively. In addition, the mean drag coefficient, Strouhal number, root-mean-square values of the drag and lift coefficients are determined and compared with a single square cylinder without small control cylinders. We found that the drag is reduced 99.8% and 97.6% for (θ, g) = (30⁰, 3) at Re = 100 and 160, respectively.

Flow patterns and aerodynamic characteristics behind three side-by-side square cylinders has been found depending upon the unequal gap spacing (g₁ = s₁/d and g₂ = s₂/d) between the three cylinders and the Reynolds number (Re) using the Lattice Boltzmann method. The effect of Reynolds numbers on the flow behind three cylinders are numerically studied for 75 ≤ Re ≤ 175 and chosen unequal gap spacings such as (g₁, g₂) = (1.5, 1), (3, 4) and (7, 6). We also investigate the effect of g₂ while keeping g₁ fixed for Re = 150. It is found that a Reynolds number have a strong effect on the flow at small unequal gap spacing (g₁, g₂) = (1.5, 1.0). It is also found that the secondary cylinder interaction frequency significantly contributes for unequal gap spacing for all chosen Reynolds numbers. It is observed that at intermediate unequal gap spacing (g₁, g₂) = (3, 4) the primary vortex shedding frequency plays a major role and the effect of secondary cylinder interaction frequencies almost disappear. Some vortices merge near the exit and as a result small modulation found in drag and lift coefficients. This means that with the increase in the Reynolds numbers and unequal gap spacing shows weakens wakes interaction between the cylinders. At large unequal gap spacing (g₁, g₂) = (7, 6) the flow is fully periodic and no small modulation found in drag and lift coefficients signals. It is found that the jet flows for unequal gap spacing strongly influenced the wake interaction by varying the Reynolds number. These unequal gap spacing separate wake patterns for different Reynolds numbers: flip-flopping, in-phase and anti-phase modulation synchronized, in-phase and anti-phase synchronized. It is also observed that in case of equal gap spacing between the cylinders the effect of gap spacing is stronger than the Reynolds number. On the other hand, in case of unequal gap spacing between the cylinders the wake patterns strongly depends on both unequal gap spacing and Reynolds number. The vorticity contour visualization, time history analysis of drag and lift coefficients, power spectrum analysis of lift coefficient and force statistics are systematically discussed for all chosen unequal gap spacings and Reynolds numbers to fully understand this valuable and practical problem.