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Two-dimensional incompressible fluid flows around square cylinders at different arrangements have been numerically analyzed in the present work. The calculations are carried out for several values of Reynolds number (Re) ranging from 20 to 180. The results are presented in the form of vorticity contours and temporal histories of drag and lift coefficients. Besides, the physical parameters, namely, the average drag and lift coefficients and Strouhal number, are evaluated as a function of Re. Two different states of flow are predicted in the current investigation by systematically varying Re for steady and unsteady regimes. Vortex shedding is studied at different arrangements of the square cylinders allowing the investigation of three possible configurations. Special attention is paid to compute the drag and lift forces acting on the different obstacles, which allowed determining the optimal configuration in terms of both drags and lifts. The unsteady periodic wake is characterized by the Strouhal number, which varies with the Reynolds number and the obstacle geometry. The values of vortex shedding frequencies are consequently calculated in this study.

The fluid flow over three staggered square cylinders at two symmetrical arrangements has been numerically investigated in this study. The numerical calculations are carried out for several values of the Reynolds number (Re) ranging from 1 to 180. The results are presented in the form of vorticity contours and temporal histories of drag and lift coefficients. Furthermore, the physical parameters, namely, the average drag and lift coefficients and Strouhal number are presented as a function of Re. Two different states of flow are found in this work by systematically varying Re: steady and unsteady states. The transition to unsteady state regime is exhibited via Hopf bifurcation first in the second configuration followed consequently by the first one with critical Reynolds number of Re${}_{\mathrm{\text{c}}}=22.37$ and Re${}_{\mathrm{\text{c}}}=22.45$, respectively. It is observed that the bifurcation point of the steady regime to the unsteady one is very much influenced by the change in the geometry of the obstacle. The unsteady periodic wake is characterized by the Strouhal number, which varies with the Reynolds number and the obstacle geometry. Hence, the values of vortex shedding frequencies are estimated for both the considered configurations. Computations obtained also reveal that the spacing in the wake leads to reducing the pressure and enhancing the fluid flow velocity for both arrangements by monotonically strengthening the Reynolds number value. Furthermore, the drag and lift coefficients are determined, which allowed determining; the best configuration in terms of both lift and drag. It is observed that the drag force is dependent on the obstacle geometry and strengthens while lowering the Reynolds number. On the other hand, an opposite trend of the lift drag evolutions is observed for both configurations and considerably affected by the arrangements shape.

This study focuses on the characteristics of flow past three side-by-side rectangular cylinders under the effect of aspect ratios (AR) and Reynolds numbers (Re) at two different gap ratios ($g$) using the lattice Boltzmann method. For this purpose, AR is varied in the range of 0.25–4, the Re values are 100, 140 and 180 and the two different values of $g$ taken into account are $g=0.5$ and 3. The results are presented in the form of vorticity contours, temporal histories of drag and lift coefficients and power spectrum of lift coefficients. Also, the variation of physical parameters like mean drag coefficient, Strouhal number and the root-mean-square values of drag and lift coefficients with Re and AR is presented for $g=0.5$ and 3. The current numerical computations yield that for both gap ratios and all Re, there exist four different flow regimes depending on AR: (a) steady flow, (b) modulated flow, (c) symmetric flow and (d) periodic flow. At narrow gap ratios, the jet flow emerging within the gaps of cylinders altered the flow structures and fluid forces abruptly. The aspect ratio is found to have more influence on the flow characteristics of cylinders as compared to the Reynolds numbers at large gap ratios.

This study aims to numerically investigate the optimal conditions for fluid flow control around a single square cylinder with the help of a pair of attached flat plates. It is comparatively a new approach for controlling fluid flows as compared to the traditional solo plate flow control devices. The plates are attached adjacent to the both rear corners of the cylinder and their length (l) is varied from $0.1$ to 4 times size of main cylinder while fixing the height (h) at $0.2$. By varying the length, the plates manage to control the flow gradually. This study discusses how a steady wake can be achieved through control plates. Results indicate that the flow regime changes from unsteady to transitional at $l=2.7$ while for $l>3.1$ the steady flow appears. The streamlines visualizations reveal different flow structures termed as the oval-eye vortex, chain necklace vortex, sphere vortex, hair pin vortex and wooden eyes vortex-like structures. Among these the oval-eye vortex structure is found to have higher flow induced forces and shedding frequencies while the wooden eyes vortex structure is found to have minimal flow induced forces and shedding frequencies. After $l=3.2$, the plates’ efficacy is proven by a 100$\%$ reduction in Strouhal number, root-mean-square values of lift coefficient and amplitudes of lift and drag coefficients. This study reveals that $l=3.2$ is the best optimal value of plates length for complete wake and fluid forces control.

A two-dimensional model for toxic contaminants was developed and incorporated into a laterally integrated hydrodynamics and transport model to investigate the effect of reservoir flow regime on contamination level in a reservoir after a toxic spill. The model describes the physical, chemical, and biological processes and predicts unsteady vertical and longitudinal distributions of a toxic chemical. Simulation results suggested that the persistence of a contaminant was significantly influenced by different flow regimes. It was found that the toxicant plume was more persistent in an interflow than in an overflow which moved more slowly and experienced greater volatilization and dissipation. This analysis can assist in spill control and reservoir management.