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.

A two-dimensional numerical study of flow across rows of identical square cylinders arranged in staggered fashion is carried out. This study will unreveal complex flow physics depending upon the Reynolds number (Re) and gap spacing (g) between the cylinders. The combined effect of Reynolds number and gap spacing on the flow physics around staggered rows of cylinders are numerically studied for 20 ≤ Re ≤ 140 and 1 ≤ g ≤ 6. We use the lattice Boltzmann method for numerical computations. It is found that with increase in gap spacing between the cylinders the critical Reynolds number for the onset of vortex shedding also increases. We observed a strong effect of Reynolds number at g = 2 and 4. Secondary cylinder interaction frequency disappears for large Reynolds number at g = 6 and 5 and the flow around cylinders are fully dominated by the primary vortex shedding frequency. This ensures that at large gap spacing with an increase in the Reynolds number the wakes interaction between and behind the cylinders is weaken. Furthermore, it also ensures that the wake interaction behind the cylinders is strongly influenced by the jets in the gap spacing between the cylinders. We also found that g = 2 is the critical gap spacing for flow across rows of staggered square cylinders for the considered range of Reynolds number. Depending on the Reynolds number we observed; synchronous, quasi-periodic-I, quasi-periodic-II, and chaotic flow patterns. In synchronous flow pattern, an in-phase and anti-phase characteristics of consecutive cylinders has been observed. The important physical parameters are also analyzed and discussed in detail.

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The equation of radiative transfer in non-conservative case for diffuse reflection in a plane-parallel semi-infinite atmosphere with axial symmetry has been solved by Laplace transform and Wiener-Hopf technique. We have determined the emergent intensity in terms of Chandrasekhar's H-function and the intensity at any optical depth by inversion.

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