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Numerical investigations are carried out for the flow around two inline square cylinders with a flat plate, placed in the wake, using the lattice Boltzmann method. Main emphasis of this work is to find the optimum values of the gap ratio (L/d) between cylinders and plate for maximum vortex shedding control and suppression of flow induced forces. The gap ratio between both cylinders as well as between second cylinder and plate is varied in the range 0.5 to 10 by fixing Reynolds number at 150. Three different flow structures are observed by systematically increasing the gap ratio: solo body (L/d = 0.5), reattachment flow (1 ≤ L/d 2.5. An interesting fact revealed through this study is that the control plate, with dimensions chosen in present study, does not always suppress the fluid forces and controls vortex shedding process. In some cases, its presence in the wake may be critical in terms of fluid forces and vortex shedding.

This work presents a numerical simulation performed to study the effect of Reynolds number (Re = 80–200) on fluid flow over a square rod attached to two small controlling rods using the Lattice Boltzmann method. For this reason, the spacing ratio between the control rods and main rod varies systematically from g = 0.5–5. Flow has been subdivided into three flow regimes based on spacing ratios. The first flow regime is considered at a small gap (g = 0.5, 1, and 1.5), the second flow regime is obtained at a moderate gap (g = 2, 2.5, and 3), and the third flow regime is considered a at large gap (g = 4–5). Five different types of flow modes were noticed in the given flow regimes. The values Re = 200 and g = 5 were found to be critical due to a sudden change in flow characteristics. The maximum value of Cdmean is 0.869 and the largest percent reduction (65.15%) in the mean drag coefficient was found at Re = 200 and g = 2.

In this work, numerical simulations are performed in order to study the effects of aspect ratio (AR) and Reynolds number (Re) on flow characteristics of three side-by-side rectangular cylinders for fixed spacing ratio ( g ), using the lattice Boltzmann method (LBM). The Reynolds number varies within the range 60 ≤ Re ≤ 180, aspect ratio is between 0.25 and 4, and spacing ratio is fixed at g = 1.5. The flow structure mechanism behind the cylinders is analyzed in terms of vorticity contour visualization, time-trace analysis of drag and lift coefficients, power spectrum analysis of lift coefficient and variations of mean drag coefficient, and Strouhal number. For different combinations of AR and Re, the flow is characterized into regular, irregular, and symmetric vortex shedding. In regular and symmetric vortex shedding the drag and lift coefficients vary smoothly while reverse trend occurs in irregular vortex shedding. At small AR, each cylinder experiences higher magnitude drag force as compared to intermediate and large aspect ratios. The vortex shedding frequency was found to be smaller at smaller AR and increased with increment in AR.

This study focuses on the transitions in flow states around two-, three- and four-inline square cylinders under the effect of Reynolds numbers at two different gap spacing values using the lattice Boltzmann method. For this purpose, Reynolds number is varied in the range 1–130 while two different values of spacing taken into account are gap spacing = 2 and 5. Before going to actual problem, the code is tested for flow around a single square cylinder by comparing the results with experimental and numerical results of other researchers, and good agreement is found. The current numerical computations yield that for both spacing values and all combinations of cylinders there exist three different sates of flow depending on Reynolds numbers: steady state, transitional state and unsteady state. It is found that the range of Reynolds numbers for these flow states is different for both spacing values. At gap spacing = 2 the range of Reynolds numbers for each flow state decreases by increasing the number of cylinders while at gap spacing = 5 opposite trend is observed. The results also show that at gap spacing = 2 the reduction in drag force is greater than the corresponding reduction at gap spacing = 5. The maximum reduction in drag force is observed at Reynolds numbers = 1 at both spacing values. Similarly, at both spacing values and all Reynolds numbers, the maximum reduction in drag force is observed for the case of four-inline square cylinders. Keywords: Drag reduction, Flow states, Gap spacing, Inline cylinders, Reynolds number

Numerical simulations are carried out to study the effect of aspect ratio (AR) and gap spacing (g) for flow past a row of rectangular cylinders using lattice Boltzmann method (LBM). The Reynolds number (Re) is fixed at 150, gap spacing is taken in the range from 0.25 to 4 while the aspect ratio varies from 0.5 to 2. Depending on AR and g, the flow is classified in to three major classes; (i) modulated (ii) symmetric and (iii) synchronized. In each class different flow patterns are observed. In modulated class, the flow behind cylinders shows merging and distortion while the force coefficients are modulated. The observed flow patterns for this class are:nearly-bistable, deflected, flip-flopping and chaotic. The flow behind middle cylinder in symmetric class is either steady or nearly steady. In this class symmetric and nearly-symmetric flow patterns are observed. In synchronized class, the flow behind each cylinder is fully developed with alternate negative and positive vortices. The flow pattern observed for this class are: quasi-synchronized, synchronized and non-synchronized. Fluid forces acting on each cylinder, flow structure mechanism, time signal analysis of drag and lift coefficients and vortex shedding frequencies are investigated systematically for different AR and g. The results show that at small g and AR, flow is complex and is more affected by AR as compared to g. At large g and AR the flow is synchronized throughout the computational domain. The results further show that the mean drag coefficients of all cylinders increase with corresponding decrease in g for fixed AR. While at fixed values of g the mean drag coefficients show variation for all AR. At large g and fixed AR the mean drag coefficient of all cylinders approaches to single cylinder and all cylinders experience same drag. It has been observed that the smaller spacing values have more influence on Strouhal number as compared to higher spacing values.

In this paper numerical investigations are performed to examine the effect of Reynolds numbers (Re) and spacing ratios (g) on flow around a row of five side-by-side square cylinders using the lattice Boltzmann method. The Reynolds number is varied in the range 75 ≤ Re ≤ 175, while spacing ratio is varied between 0.5 and 5. The flow structure mechanism around a row of five side-by-side square cylinders is studied in terms of vorticity contours visualization, time trace analysis of drag and lifts coefficients, and power spectrum analysis of lift coefficient. The effect of Re on force statistics like mean drag coefficient and Strouhal number is also analyzed. The present data are compared with the data of single square cylinder and good agreement is observed for large spacing ratio (g = 5). The flow behind five side-by-side square cylinders is classified into three different flow regimes and these regimes are further subdivided into seven different regimes. The observed flow regimes are compared with those of the other researchers published studies and found good agreement.

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 ([Formula: see text]) 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 [Formula: see text] taken into account are [Formula: see text] 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 [Formula: see text] 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 work focuses on the analysis of flow structure mechanism behind three rectangular bodies arranged side-by-side. Such type of arrangement can be seen in various applications of practical significance. Lattice Boltzmann method is adopted as a numerical technique for the current study. The simulations are performed for the unsteady, Newtonian and the incompressible flow past three rectangular bodies to investigate the behavior of flow at different aspect ratios, gap ratios and fixed Reynolds number. The numerical results obtained from the proposed study are compared with the results available in the literature. The observed findings of the current study line up well with the existing findings of other researchers.

This work presents the numerical investigations performed to study the proximity effects on fluid flow characteristics around three inline square cylinders using the lattice Boltzmann method. For this purpose the gap spacing (g) is systematically varied in the range 0.5 to 16 diameters of cylinder by keeping Reynolds number fixed at 200. Five different flow patterns are observed at different values of spacing: bluff body flow, gap trapped flow, irregular flow, alternate shedding, and modulated shedding. These patterns have a significant effect on flow induced forces and vortex shedding frequency. The spacing value g = 2 is found to be critical due to sudden changes in fluid flow characteristics. The flow parameters of first cylinder are found to be closer to single cylinder values but for middle and third cylinder the differences confirm the wake interference effect even at large values of spacing.

Numerical simulations are performed, in the range of 0.5 ≤ g ≤ 5, where g is the separation ratio between the cylinders at fixed Reynolds number 150 and aspect ratio 2, for flow past five side-by-side rectangular cylinders. A two-dimensional code is developed using the lattice Boltzmann method. The effect of separation ratio on the vortex shedding frequency, time-trace analysis of drag and lift coefficients, power spectra analysis of lift coefficients and force statistics exerted on the cylinders is quantified together with the observed flow structure. Five different flow structures were found and named as nearly symmetric (g = 0.5), flip-flopping (g = 1), modulated (g = 1.5), strongly interactive (g = 2, 2.5 and 3) and weakly interactive (g = 4 and 5) flow structures. It is found that the vortices are generated on the surfaces of the cylinders as width of the cylinder is 2h (h is the width of the rectangular cylinders) and due to this there is modulation in time-history analysis of drag and lift coefficients for all chosen cases except at g = 0.5. The Strouhal number is also calculated using Welch’s method for comparison, and correlation of lift coefficients for different combinations is also given.

The research presents a numerical investigation of flow past three side-by-side square cylinders using the multi-relaxation-time lattice Boltzmann method. A comparison is made between equal and unequal gap spacings behind the three cylinders. Fluid forces acting on the cylinders, wake structure mechanism, time-trace analysis of drag and lift coefficients and vortex shedding frequencies are investigated systematically for different equal and unequal gap spacings. The Reynolds number is kept at 150 and unequal gap spacings (g 1, g 2) = (0.5, 0.6), (0.6, 0.5), (1.5, 1.6), (1.6, 1.5), (2.5, 2.6), (2.6, 2.5), (4, 4.1) and (4.1, 4) are selected for the investigation. For comparison we have also investigated the effect of equal gap spacings varied from 0.5 to 4. The results show that the wake structure and fluid forces are responsible for a slight change in gap spacing between any two cylinders. It is observed that the effects of unequal gap spacings on force statistics such as drag and lift coefficients, Strouhal number and the vortex shedding mechanism are notable at (g 1, g 2) = (0.5, 0.6), (0.6, 0.5), (1.5, 1.6) and (1.6, 1.5) and are completely different from those at equal gap spacings (g = 0.5 and 1.5). The results further show that at (g 1, g 2) = (4, 4.1) and (4.1, 4) the unequal gap spacing effect almost diminishes and only the primary vortex shedding frequency is observed. The bistable, asymmetric, inphase–antiphase and modulated synchronized flow patterns observed in this study.

A numerical study for flow past a square cylinder in a two-dimensional channel with a detached flat plate is investigated in this paper. A flat plate is detached downstream in order to control the flow around and behind the square cylinder. Fluid forces acting on the square cylinder, wake structure mechanism and vortex shedding frequency are presented systematically for different Reynolds numbers and spacing ratios. Effects of Reynolds numbers upon physical parameters are also studied. Variation of Reynolds number is from 75 to 200, based on the incoming flow velocity and width of cylinder. The lattice Boltzmann method is used for this numerical investigation. In this study, we choose three different spacing ratios namely closely, moderately and widely. Numerical studies show that some physical parameters significantly reduced by the detached flat plate for closely spacing ratio. The results which we obtained in this investigation are authentic in the sense that some other experimental observations by different authors can be deduced from our results.

In this paper, the effect of gap spacing on the flow past three square cylinders in tandem arrangement is studied numerically using a 2-D multi-relaxation-time lattice Boltzmann method (MRT-LBM). The Reynolds number is fixed at 75 and variation of the gap spacing is from 0.5 to 17. The results are compared to some earlier published results and found to be in good agreement. Five different wake modes are observed by the increment in the gap spacing. To understand the effect of different gap spacings on the flow-induced forces; a detailed analysis of mean drag coefficient, time signal analysis of drag and lift coefficients, Strouhal number, root mean square values of drag and lift coefficients is presented in this article. In this study, it is observed that the critical gap spacing is 3, its existence and effects on the flow characteristics are also studied.

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.