Search results for: Reynolds number to Froude number

Authors: Shams-Ul-Islam, Hamid Rahman, Waqas Sarwar Abbasi

Abstract:

Numerical calculations of flow around a square cylinder are presented using the multi-relaxation-time lattice Boltzmann method at Reynolds number 150. The effects of upstream locations, downstream locations and blockage are investigated systematically. A detail analysis are given in terms of time-trace analysis of drag and lift coefficients, power spectra analysis of lift coefficient, vorticity contours visualizations and phase diagrams. A number of physical quantities mean drag coefficient, drag coefficient, Strouhal number and root-mean-square values of drag and lift coefficients are calculated and compared with the well resolved experimental data and numerical results available in open literature. The results had shown that the upstream, downstream and height of the computational domain are at least 7.5, 37.5 and 12 diameters of the cylinder, respectively.

Keywords: Grid independence, Multi-relaxation-time lattice Boltzmann method, Physical quantities, Square cylinder, Vorticity contours visualizations.

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Authors: T. Damak, O. Kriaa, A. Baccar, M. A. Ben Ayed, N. Masmoudi

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In the last few years, Automatic Number Plate Recognition (ANPR) systems have become widely used in the safety, the security, and the commercial aspects. Forethought, several methods and techniques are computing to achieve the better levels in terms of accuracy and real time execution. This paper proposed a computer vision algorithm of Number Plate Localization (NPL) and Characters Segmentation (CS). In addition, it proposed an improved method in Optical Character Recognition (OCR) based on Deep Learning (DL) techniques. In order to identify the number of detected plate after NPL and CS steps, the Convolutional Neural Network (CNN) algorithm is proposed. A DL model is developed using four convolution layers, two layers of Maxpooling, and six layers of fully connected. The model was trained by number image database on the Jetson TX2 NVIDIA target. The accuracy result has achieved 95.84%.

Keywords: Automatic number plate recognition, character segmentation, convolutional neural network, CNN, deep learning, number plate localization.

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Authors: Arash Mir Abdolah Lavasani, Meghdad Ebrahimi Sabet

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In this paper, the 2-D unsteady viscous flow around two cam shaped cylinders in tandem arrangement is numerically simulated in order to study the characteristics of the flow in turbulent regimes. The investigation covers the effects of high subcritical and supercritical Reynolds numbers and L/D ratio on total drag coefficient. The equivalent diameter of cylinders is 27.6 mm The space between center to center of two cam shaped cylinders is define as longitudinal pitch ratio and it varies in range of 1.5< L/D<6. Reynolds number base on equivalent circular cylinder varies in range of 27×103< Re <166×103 Results show that drag coefficient of both cylinders depends on pitch ratio. However, drag coefficient of downstream cylinder is more dependent on the pitch ratio.

Keywords: Cam shaped, tandem, numerical, drag coefficient, turbulent.

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Authors: Prateek Kishore, T. M. Muruganandam

Abstract:

Supersonic wind tunnel nozzles are generally capable of producing a constant Mach number flow in the test section of the wind tunnel. As a result, most of the supersonic vehicles are widely designed using steady state flow characteristics which may have errors while facing unsteady situations. This study aims to explore the possibility of varying the Mach number of the flow during wind tunnel operation. The nozzle walls are restricted to be inflexible for cooling near the throat due to high stagnation temperature requirement of the flow to simulate the conditions as experienced by the vehicle. Two simple independent mechanisms, rotation and translation of nozzle walls have been analyzed and the nozzle ranges have been optimized to vary the Mach number from Mach 2 to Mach 5 using minimum number of nozzles in the wind tunnel.

Keywords: Method of characteristics, Nozzle, supersonic wind tunnel, variable Mach number.

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Authors: Zeinab Sayed Abdel-Rehim

Abstract:

A computational fluid dynamic (CFD-Fluent 6.2) for two-dimensional fluid flow is applied to predict the pressure drop and heat transfer characteristics of laminar and turbulent flow past staggered flat-tube bank. Effect of aspect ratio ((H/D)/(L/D)) on pressure drop, temperature, and velocity contour for laminar and turbulent flow over staggered flat-tube bank is studied. The theoretical results of the present models are compared with previously published experimental data of different authors. Satisfactory agreement is demonstrated. Also, the comparison between the present study and others analytical methods for the Re number with Nu number is done. The results show as the Reynolds number increases the maximum velocity in the passage between the upper and lower tubes increases. The comparisons show a fair agreement especially in the turbulent flow region. The good agreement of the data of this work with these recommended analytical methods validates the current study.

Keywords: Aspect ratio ((H/D)/(L/D)), CFD, fluid flow, heat transfer, staggered arrangement, tube bank, and turbulent flow.

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Authors: Ahmet Tekcan

Abstract:

Let p be a prime number, Fp be a finite field, and let k ∈ F*p. In this paper, we consider the number of rational points onconics Cp,k: x2 − ky2 = 1 over Fp. We proved that the order of Cp,k over Fp is p-1 if k is a quadratic residue mod p and is p + 1 if k is not a quadratic residue mod p. Later we derive some resultsconcerning the sums ΣC[x]p,k(Fp) and ΣC[y]p,k(Fp), the sum of x- and y-coordinates of all points (x, y) on Cp,k, respectively.

Keywords: Elliptic curve, conic, rational points.

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Authors: M. I. Youssef, A. E. Emam, M. Abd Elghany

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In this paper, a residue number arithmetic is used in direct sequence spread spectrum system, this system is evaluated and the bit error probability of this system is compared to that of non residue number system. The effect of channel bandwidth, PN sequences, multipath effect and modulation scheme are studied. A Matlab program is developed to measure the signal-to-noise ratio (SNR), and the bit error probability for the various schemes.

Keywords: Spread Spectrum, Direct sequence, Bit errorprobability and Residue number system.

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Authors: Shatha A. Yousif, Hatem Jasim, Ali R. Abas, Dheya P. Yousef

Abstract:

To study the effect of the cross direction in bead wheat, three hybrid combinations (Babyle 113, Iratome), (Sawa, Tamose2) and (Al Hashymya, Al Iraq) were tested for plant height, spike and awn length, number of grains per spike, 1000-grain weight, number of tillers/m and grain yield. The results revealed that the direction of the crosses significantly effect on the number of grains/spike, number of tillers/m and grain yields. Grain yield was positively and significantly correlated with 1000-grain weight, number of grains per spike and tillers. Depend on the results of heritability and genetic advance it was suggested that 1000-grain weight, number of grains per spike and tillers should be given emphasis for future wheat yield improvement programs.

Keywords: Correlation, Genetic Advance, Heritability, Wheat, Yield Traits.

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Authors: Jahanfar Daneshian, P. Jonoubi, D. Barari Tari

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In order to investigate water deficit stress on 24 of soybean (Glycine Max. L) cultivars and lines in temperate climate, an experiment was conducted in Iran Seed and Plant Improvement Institute. Stress levels were irrigation after evaporation of 50, 100, 150 mm water from pan, class A. Randomized Completely Block Design was arranged for each stress levels. Some traits such as, node number, plant height, pod number per area, grain number per pod, grain number per area, 1000 grains weight, grain yield and harvest index were measured. Results showed that water deficit stress had significant effect on node number, plant height, pod number per area, grain number per pod, grain number per area, 1000 grains weight and harvest index. Also all of agronomic traits except harvest index influenced significantly by cultivars and lines. The least and most grain yield was belonged to Ronak X Williams and M41 x Clark respectively.

Keywords: Soybean, water deficit stress, Agronomic traits, Yield

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Authors: Muhammad Amjad Sohail, Rizwan Ullah

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This research paper presents the CFD analysis of oscillating airfoil during pitch cycle. Unsteady subsonic flow is simulated for pitching airfoil at Mach number 0.283 and Reynolds number 3.45 millions. Turbulent effects are also considered for this study by using K-ω SST turbulent model. Two-dimensional unsteady compressible Navier-Stokes code including two-equation turbulence model and PISO pressure velocity coupling is used. Pressure based implicit solver with first order implicit unsteady formulation is used. The simulated pitch cycle results are compared with the available experimental data. The results have a good agreement with the experimental data. Aerodynamic characteristics during pitch cycles have been studied and validated.

Keywords: Angle of attack, Centre of pressure, subsonic flow, pitching moment coefficient, turbulence mode

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Authors: F. Ayça Varol Saraçoğlu, Hayrullah Ağaçcıoğlu

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Experimental studies to investigate the depth of the scour conducted at a side-weir intersection located at the 1800 curved flume which located Hydraulic Laboratory of Yıldız Technical University, Istanbul, Turkey. Side weirs were located at the middle of the straight part of the main channel. Three different lengths (25, 40 and 50 cm) and three different weir crest height (7, 10 and 12 cm) of the side weir placed on the side weir station. There is no scour when the material is only kaolin. Therefore, the cohesive bed was prepared by properly mixing clay material (kaolin) with 31% sand in all experiments. Following 24h consolidation time, in order to observe the effect of flow intensity on the scour depth, experiments were carried out for five different upstream Froude numbers in the range of 0.33-0.81. As a result of this study the relation between scour depth and upstream flow intensity as a function of time have been established. The longitudinal velocities decreased along the side weir; towards the downstream due to overflow over the side-weirs. At the beginning, the scour depth increases rapidly with time and then asymptotically approached constant values in all experiments for all side weir dimensions as in non-cohesive sediment. Thus, the scour depth reached equilibrium conditions. Time to equilibrium depends on the approach flow intensity and the dimensions of side weirs. For different heights of the weir crest, dimensionless scour depths increased with increasing upstream Froude number. Equilibrium scour depths which formed 7 cm side-weir crest height were obtained higher than that of the 12 cm side-weir crest height. This means when side-weir crest height increased equilibrium scour depths decreased. Although the upstream side of the scour hole is almost vertical, the downstream side of the hole is inclined.

Keywords: Clay-sand mixed sediments, scour, side weir.

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Authors: Hari Mohan Kushwaha, Santosh K. Sahu

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In the present study, analysis of heat transfer is carried out in the slip flow region for the fluid flowing between two parallel plates by employing the asymmetric heat fluxes at surface of the plates. The flow is assumed to be hydrodynamically and thermally fully developed for the analysis. The second order velocity slip and viscous dissipation effects are considered for the analysis. Closed form expressions are obtained for the Nusselt number as a function of Knudsen number and modified Brinkman number. The limiting condition of the present prediction for Kn = 0, Kn2 = 0, and Brq1 = 0 is considered and found to agree well with other analytical results.

Keywords: Knudsen Number, Modified Brinkman Number, Slip Flow, Velocity Slip.

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Authors: H. Bayat, M. Majidi, M. Bolhasani, A. Karbalaie Alilou, A. Mirabdolah Lavasani

Abstract:

Unsteady flow and heat transfer from a circular cylinder in cross-flow is studied numerically. The governing equations are solved by using finite volume method. Reynolds number varies in range of 50 to 200; in this range flow is considered to be laminar and unsteady. Al2O3 nanoparticle with volume fraction in range of 5% to 20% is added to pure water. Effects of adding nanoparticle to pure water on lift and drag coefficient and Nusselt number is presented. Addition of Al2O3 has inconsiderable effect on the value of drags and lift coefficient. However, it has significant effect on heat transfer; results show that heat transfer of Al2O3 nanofluid is about 9% to 36% higher than pure water.

Keywords: Nanofluid, heat transfer, unsteady flow, forced convection, cross-flow.

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Authors: Sumit Gandhi

Abstract:

The effect of an abruptly expanding channel on the main characteristics of hydraulic jump is considered experimentally. The present study was made for supercritical flow of Froude number varying between 2 to 9 and approach to expanded channel width ratios 0.4, 0.5, 0.6 and 0.8. Physical explanations of the variation of these characteristics under varying flow conditions are discussed based on the observation drawn from experimental results. The analytical equation for the sequent depth ratio in an abruptly expanding channel as given by eminent hydraulic engineers are verified well with the experimental data for all expansion ratios, and the empirical relation was also verified with the present experimental data.

Keywords: Abruptly Expanding Channel, Hydraulic Jump, Efficiency, Sequent Depth Ratio.

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Authors: Boualem Chetti

Abstract:

In this paper, the dynamic characteristics of a threelobe journal bearing lubricated with micropolar fluids are determined by the linear stability theory. Lubricating oil containing additives and contaminants is modelled as micropolar fluid. The modified Reynolds equation is obtained using the micropolar lubrication theory .The finite difference technique has been used to determine the solution of the modified Reynolds equation. The dynamic characteristics in terms of stiffness, damping coefficients, the critical mass and whirl ratio are determined for various values of size of material characteristic length and the coupling number. The computed results show that the three-lobe bearing lubricated with micropolar fluid exhibits better stability compared with that lubricated with Newtonian fluid. According to the results obtained, the effect of the parameter micropolar fluid is remarkable on the dynamic characteristics and stability of the three-lobe bearing.

Keywords: Three-lobe bearings, Micropolar fluid, Dynamic characteristics, Stability analysis.

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Authors: Nyah C. Temaneh, F. A. Phiri, E. Ruhunga

Abstract:

Most of the well known methods for generating Gaussian variables require at least one standard uniform distributed value, for each Gaussian variable generated. The length of the random number generator therefore, limits the number of independent Gaussian distributed variables that can be generated meanwhile the statistical solution of complex systems requires a large number of random numbers for their statistical analysis. We propose an alternative simple method of generating almost infinite number of Gaussian distributed variables using a limited number of standard uniform distributed random numbers.

Keywords: Gaussian variable, statistical analysis, simulation ofCommunication Network, Random numbers.

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Authors: Shatha A. Yousif, Qasim M. Zamil, Hasan Y. Al Muhi, Jamal A. Al Shammari

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Potato (Solanum tuberosum L.) is one of the major vegetable crops that are grown world –wide because of its economic importance. This experiment investigated the effect of local sands (River Base, Al-Ekader and Karbala) on number and total weight of minitubers. Statistical analysis revealed that there were no significant differences among sand cultures in number of stem/plant, chlorophyll index and tubers dry weight. River Base sand had the highest plant height (74.9 cm), leaf number/plant number (39.3), leaf area (84.4 dcm2⁄plant), dry weight/plant (26.31), tubers number/plant (8.5), tubers weight/plant (635.53 gm) and potato tuber yields/trove (28.60 kg), whereas the Karbala sand had lower performance. All the characters had positive and significant correlation with yields except the traits number of stem and tuber dry weight.

Keywords: Correlation, Potato, Sand Culture, Yield.

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Authors: S. GhaffariTooran, H. Abolghasemi, H. Bahmanyar, M. Esmaeili, A. Safari

Abstract:

Using plug flow model in conjunction with experimental solute concentration profiles, overall volumetric mass transfer coefficient based on continuous phase (Koca), in a packed liquid-liquid extraction column has been optimized. Number of 12 experiments has been done using standard system of water/acid acetic/toluene in a 6 cm diameter, 120 cm height column. Thorough consideration of influencing parameters we intended to correlate dimensionless parameters in term of overall Sherwood number which has an acceptable average error of about 15.8%.

Keywords: Packed column, mass transfer coefficient, solvent extraction, Sherwood number.

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Authors: Kamel Allaw, Jocelyne Adjizian Gerard, Makram Chehayeb, Nada Badaro Saliba

Abstract:

In developing countries, such as Lebanon, the demographic data are hardly available due to the absence of the mechanization of population system. The aim of this study is to evaluate, using only remote sensing data, the correlations between the number of population and the characteristics of roads network (length of primary roads, length of secondary roads, total length of roads, density and percentage of roads and the number of intersections). In order to find the influence of the different factors on the demographic data, we studied the degree of correlation between each factor and the number of population. The results of this study have shown a strong correlation between the number of population and the density of roads and the number of intersections.

Keywords: Population, road network, statistical correlations, remote sensing.

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Authors: Hossein Shokouhmand , Koohyar Vahidkhah, Mohammad A. Esmaeili

Abstract:

A numerical investigation of surface heat transfer characteristics of turbulent air flows in different parallel plate grooved channels is performed using CFD code. The results are obtained for Reynolds number ranging from 10,000 to 30,000 and for arc-shaped and rectangular grooved channels. The influence of different geometric parameters of dimples as well as the number of them and the geometric and thermophysical properties of channel walls are studied. It is found that there exists an optimum value for depth of dimples in which the largest wall heat flux can be achieved. Also, the results show a critical value for the ratio of wall thermal conductivity to the one of fluid in which the dependence of wall heat flux to this ratio almost vanishes. In most cases examined, heat transfer enhancement is larger for arc-shaped grooved channels than rectangular ones.

Keywords: dimple, heat transfer enhancement, Numerical, optimum value, turbulent air flow.

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Authors: Betül Gezer, Ahmet Tekcan, Osman Bizim

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In elliptic curve theory, number of rational points on elliptic curves and determination of these points is a fairly important problem. Let p be a prime and Fp be a finite field and k ∈ Fp. It is well known that which points the curve y2 = x3 + kx has and the number of rational points of on Fp. Consider the circle family x2 + y2 = r2. It can be interesting to determine common points of these two curve families and to find the number of these common points. In this work we study this problem.

Keywords: Elliptic curves over finite fields, rational points on elliptic curves and circles.

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Authors: Cheng-Chung Yang, Jr-Ming Miao, Fuh-Lin Lih, Tsung-Lung Liu, Ming-Hui Ho

Abstract:

The operation performance of a valveless micro-pump is strongly dependent on the shape of connected nozzle/diffuser and Reynolds number. The aims of present work are to compare the performance curves of micropump with the original straight nozzle/diffuser and contoured nozzle/diffuser under different back pressure conditions. The tested valveless micropumps are assembled of five pieces of patterned PMMA plates with hot-embracing technique. The structures of central chamber, the inlet/outlet reservoirs and the connected nozzle/diffuser are fabricated with laser cutting machine. The micropump is actuated with circular-type PZT film embraced on the bottom of central chamber. The deformation of PZT membrane with various input voltages is measured with a displacement laser probe. A simple testing facility is also constructed to evaluate the performance curves for comparison. In order to observe the evaluation of low Reynolds number multiple vortex flow patterns within the micropump during suction and pumping modes, the unsteady, incompressible laminar three-dimensional Reynolds-averaged Navier-Stokes equations are solved. The working fluid is DI water with constant thermo-physical properties. The oscillating behavior of PZT film is modeled with the moving boundary wall in way of UDF program. With the dynamic mesh method, the instants pressure and velocity fields are obtained and discussed.Results indicated that the volume flow rate is not monotony increased with the oscillating frequency of PZT film, regardless of the shapes of nozzle/diffuser. The present micropump can generate the maximum volume flow rate of 13.53 ml/min when the operation frequency is 64Hz and the input voltage is 140 volts. The micropump with contoured nozzle/diffuser can provide 7ml/min flow rate even when the back pressure is up to 400 mm-H2O. CFD results revealed that the flow central chamber was occupied with multiple pairs of counter-rotating vortices during suction and pumping modes. The net volume flow rate over a complete oscillating periodic of PZT

Keywords: valveless micropump、PZT diagraph、contoured nozzle/diffuser、vortex flow.

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Authors: Ahmad Salehi

Abstract:

An acyclic coloring of a graph G is a coloring of its vertices such that:(i) no two neighbors in G are assigned the same color and (ii) no bicolored cycle can exist in G. The acyclic chromatic number of G is the least number of colors necessary to acyclically color G. Recently it has been proved that any graph of maximum degree 5 has an acyclic chromatic number at most 8. In this paper we present another proof for this result.

Keywords: Acyclic Coloring, Vertex coloring.

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Authors: Daniela I. Borissova, Ivan C. Mustakerov

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The paper addresses a problem of optimal staffing in open shop environment. The problem is to determine the optimal number of operators serving a given number of machines to fulfill the number of independent operations while minimizing staff idle. Using a Gantt chart presentation of the problem it is modeled as twodimensional cutting stock problem. A mixed-integer programming model is used to get minimal job processing time (makespan) for fixed number of machines' operators. An algorithm for optimal openshop staffing is developed based on iterative solving of the formulated optimization task. The execution of the developed algorithm provides optimal number of machines' operators in the sense of minimum staff idle and optimal makespan for that number of operators. The proposed algorithm is tested numerically for a real life staffing problem. The testing results show the practical applicability for similar open shop staffing problems.

Keywords: Integer programming, open shop problem, optimal staffing.

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Authors: Radouane Elbahjaoui, Hamid El Qarnia

Abstract:

Melting of Paraffin Wax (P116) dispersed with Al₂O₃ nanoparticles in a rectangular latent heat storage unit (LHSU) is numerically investigated. The storage unit consists of a number of vertical and identical plates of nano-enhanced phase change material (NEPCM) separated by rectangular channels in which heat transfer fluid flows (HTF: Water). A two dimensional mathematical model is considered to investigate numerically the heat and flow characteristics of the LHSU. The melting problem was formulated using the enthalpy porosity method. The finite volume approach was used for solving equations. The effects of nanoparticles’ volumetric fraction and the Reynolds number on the thermal performance of the storage unit were investigated.

Keywords: Nano-enhanced phase change material, phase change material, nanoparticles, latent heat storage unit, melting.

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Authors: Phavanee Narataruksa, Karn Pana-Suppamassadu, Sabaithip TungkamaniRungrote Kokoo, Prayut Jiamrittiwong

Abstract:

The major focus of this work was to characterize hydrodynamics in a packed-bed with and without static mixer by using Computational Fluid Dynamic (CFD). The commercial software: COMSOL MULTIPHYSICSTM Version 3.3 was used to simulate flow fields of mixed-gas reactants i.e. CO and H2. The packed-bed was a single tube with the inside diameter of 0.8 cm and the length of 1.2 cm. The static mixer was inserted inside the tube. The number of twisting elements was 1 with 0.8 cm in diameter and 1.2 cm in length. The packed-bed with and without static mixer were both packed with approximately 700 spherical structures representing catalyst pellets. Incompressible Navier-Stokes equations were used to model the gas flow inside the beds at steady state condition, in which the inlet Reynolds Number (Re) was 2.31. The results revealed that, with the insertion of static mixer, the gas was forced to flow radially inward and outward between the central portion of the tube and the tube wall. This could help improving the overall performance of the packed-bed, which could be utilized for heterogeneous catalytic reaction such as reforming and Fischer- Tropsch reactions.

Keywords: Packed Bed, Static Mixer, Computational Fluid Dynamic (CFD).

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Authors: B. Manshoor, M. Jaat, Amir Khalid

Abstract:

Circle grid space filling plate is a flow conditioner with a fractal pattern and used to eliminate turbulence originating from pipe fittings in experimental fluid flow applications. In this paper, steady state, incompressible, swirling turbulent flow through circle grid space filling plate has been studied. The solution and the analysis were carried out using finite volume CFD solver FLUENT 6.2. Three turbulence models were used in the numerical investigation and their results were compared with the pressure drop correlation of BS EN ISO 5167-2:2003. The turbulence models investigated here are the standard k-ε, realizable k-ε, and the Reynolds Stress Model (RSM). The results showed that the RSM model gave the best agreement with the ISO pressure drop correlation. The effects of circle grids space filling plate thickness and Reynolds number on the flow characteristics have been investigated as well.

Keywords: Flow conditioning, turbulent flow, turbulent modeling, CFD.

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Authors: M. Yousaf, S. Usman

Abstract:

The present study focused on the investigation of the effects of roughness elements on heat transfer during natural convection in a rectangular cavity using numerical technique. Roughness elements were introduced on the bottom hot wall with a normalized amplitude (A*/H) of 0.1. Thermal and hydrodynamic behaviors were studied using computational method based on Lattice Boltzmann method (LBM). Numerical studies were performed for a laminar flow in the range of Rayleigh number (Ra) from 103 to 106 for a rectangular cavity of aspect ratio (L/H) 2.0 with a fluid of Prandtl number (Pr) 1.0. The presence of the sinusoidal roughness elements caused a minimum to maximum decrease in the heat transfer as 7% to 17% respectively compared to smooth enclosure. The results are presented for mean Nusselt number (Nu), isotherms and streamlines.

Keywords: Natural convection, Rayleigh number, surface roughness, Nusselt number, Lattice Boltzmann Method.

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Authors: Hossein Khademolhosseini, Mehdi Hosseinzadeh

Abstract:

The residue number system (RNS), due to its properties, is used in applications in which high performance computation is needed. The carry free nature, which makes the arithmetic, carry bounded as well as the paralleling facility is the reason of its capability of high speed rendering. Since carry is not propagated between the moduli in this system, the performance is only restricted by the speed of the operations in each modulus. In this paper a novel method of number representation by use of redundancy is suggested in which {rn- 2,rn-1,rn} is the reference moduli set where r=2k+1 and k =1, 2,3,.. This method achieves fast computations and conversions and makes the circuits of them much simpler.

Keywords: Binary to RNS converter, Carry save adder, Computer arithmetic, Residue number system.

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Authors: S. Ul. Islam, H. Rahman, W. S. Abbasi, N. Rathore

Abstract:

In this research numerical simulations are performed, using the multi-relaxation-time lattice Boltzmann method, in the range 3 ≤ β = w[d] ≤ 30 at Re = 100, 200 and 300, where β the blockage ratio, w is the equispaced distance between centers of cylinders, d is the diameter of the cylinder and Re is the Reynolds number, respectively. Special attention is paid to the effect of the equispaced distance between centers of cylinders. Visualization of the vorticity contour visualization are presented for some simulation showing the flow dynamics and patterns for blockage effect. Results show that the drag and mean drag coefficients, and Strouhal number, in general, decrease with the increase of β for fixed Re. It is found that the decreasing rate of drag and mean drag coefficients and Strouhal number is more distinct in the range 3 ≤ β ≤ 15. We found that when β > 15, the blockage effect almost diminishes. Our results further indicate that the drag and mean drag coefficients, peak value of the lift coefficient, root-mean-square value of the lift and drag coefficients and the ratio between lift and drag coefficients decrease with the increase of Re. The results indicate that symmetry boundary condition have more blockage effect as compared to periodic boundary condition.

Keywords: Blockage ratio, Multi-relaxation-time lattice Boltzmann method, Square cylinder, Vortex formation.

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