Periodic Array Of Cylinders Research Articles

Particle capture efficiency in a multi-wire model for high gradient magnetic separation

High gradient magnetic separation (HGMS) is an efficient way to remove magnetic and paramagnetic particles, such as heavy metals, from waste water. As the suspension flows through a magnetized filter mesh, high magnetic gradients around the wires attract and capture the particles removing them from the fluid. We model such a system by considering the motion of a paramagnetic tracer particle through a periodic array of magnetized cylinders. We show that there is a critical Mason number (ratio of viscous to magnetic forces) below which the particle is captured irrespective of its initial position in the array. Above this threshold, particle capture is only partially successful and depends on the particle's entry position. We determine the relationship between the critical Mason number and the system geometry using numerical and asymptotic calculations. If a capture efficiency below 100% is sufficient, our results demonstrate how operating the HGMS system above the critical Mason number but with multiple separation cycles may increase efficiency.

Experimental study of free-surface fluctuations in open-channel flow in the presence of periodic cylinder arrays

ABSTRACTThe presence of periodic cylinder arrays in a laboratory-scale open-channel flow may induce significant fluctuations in the free-surface elevation. Experimental observations show four types of free-surface patterns, which include plane surface, transversely oscillating surface, longitudinally oscillating surface, and locally disturbed surface. The transversely oscillating surface appears to be standing waves confined between the two sidewalls in the flume and is well described by velocity potential equations. By considering the effect of the cylinder density, a modified dispersion equation is used to compute the frequency of the standing waves. The computed results agree well with the measured dominant frequency especially for cases with higher cylinder density, in comparison with those calculated using the equation without considering the effect of cylinder density. The data analysis also shows that the fluctuation in the free-surface elevation varies with flow conditions, and the maximum fluctuation occurs when the cylinder-diameter-based Reynolds number varies in the range of 600–800 or the cylinder-diameter-based Froude number varies in the range of 0.24–0.32.

Permeability of fluid flow through a periodic array of cylinders

The three-dimensional model of an incompressible Newtonian viscous fluid slowly flowing through a periodic array of cylinders is considered. We use homogenization to determine a system of equations that are then solved numerically to calculate the permeability. We determine the permeability as a function of the angle the cylinders make with the bottom surface. Numerical results are obtained using a Taylor–Hood mixed finite element method. The numerical approach is validated by comparing the results with computed results of Rocha and Cruz, for a simple cubic array of spheres, with good agreement. Results are presented for different cylindrical densities and angles. When the flow aligns and is perpendicular to an array of cylinders, the results are validated with experimental data. The spherical part of the permeability is compared with the Kozeny–Carman equation. Applications of these results include modeling fluid flow through biological hairlike structures such as animal hair, glass rods, fiberglass, filter pads, polymer gel, collagen, nylon fibers and natural rice field or trees.

Numerical modeling of turbulent flow through isotropic porous media

Turbulent flow through porous media is of considerable theoretical and practical interest in various engineering disciplines such as chemical, mechanical, nuclear, geological, environmental, petroleum, etc. In the present work, a numerical study of turbulent flow through porous media was carried out. The porous media was considered to be made of a spatially periodic array of infinite square cylinders. The low Re–k–ε–Lam–Bremhorst (LB) turbulent model was employed for the description of the turbulent flow in the porous media. The transport equations were solved only through the flow domains having different porosities. The porosity of the medium (ϕ) and the Reynolds number (ReD), were taken in the range of 0.3⩽ϕ⩽0.84, and 100⩽ReD⩽40,000, respectively. The influence of ϕ and ReD on normalized turbulent kinetic energy, 〈k〉f and dissipation rate, 〈ε〉f was investigated and the simulated data were compared with two different turbulent flow models, namely, large eddy simulation (LES), and v2f model. The predictions of turbulent parameters using low Re k–ε–LB turbulent model were found to be in good agreement with the LES than that with v2f model. The macroscopic pressure variation across the flow domain was also investigated and the predictions of the pressure gradient were found to be in good agreement with the Forchheimer-extended Darcy law. At low ReD (ReD=100) the low Re–k–ε–LB predictions were deviating from the DNS, LES and v2f predictions. This means that the proposed low Re–k–ε–LB model will hold valid only for flows having ReD>300. A correlation for macroscopic pressure gradient as a function of porosity is also proposed for high ReD.

Experimental and numerical study of two-phase flows in arrays of cylinders

In this paper we study the spreading of a liquid jet in a periodic array of cylinders with a characteristic size of the passages between solid obstacles equal to 1.5mm, close to the capillary length. An important outcome of our study is to show that this configuration allows most of the two-phase flow regimes described in the literature about trickle beds to be observed, even with no gas injection. Different aspects of the flow phenomenology have been studied, such as bubble creation and transport. As direct numerical methods for tracking interfaces would require too much computation time, especially in three-dimensional cases, we propose to simulate the two-phase flows observed experimentally with two-dimensional simulations corresponding to the spreading of a liquid jet in an array of disks. We show that this numerical approach allows the phenomenology observed experimentally to be reproduced satisfactorily. Hence, numerical simulations can be used subsequently to study the effects of specific parameters without setting up a new experimental procedure. As an example, the stabilizing effect of gas injection on the flow pattern is studied numerically.

Effective complex permittivity tensor of a periodic array of cylinders

We determine the effective complex permittivity of a two-dimensional composite, consisting of an arbitrary doubly periodic array of identical circular cylinders in a homogeneous matrix, and whose dielectric properties are complex-valued. Efficient formulas are provided to determine the effective complex permittivity tensor which are in excellent agreement with numerical calculations. We also show that in contrast to the real-valued case, the real and imaginary parts of the effective complex-valued tensor can exhibit non-monotonic behavior as functions of volume fraction of cylinders, and can be either greater or less than that of the constituents.

Acoustic wave diffraction at the upper edge of a two-dimensional periodic array of finite rigid cylinders. A comprehensive design model of periodicity-based devices

Diffraction at the upper edge of a two-dimensional periodic array of finite rigid cylinders immersed in air as well as the effect on its wave propagation properties are numerically and experimentally reported in this work. The diffraction and the band gap effects, due to the finite length of the cylinders and the periodicity of the array, are the two phenomena that must be taken into account in the design of real devices based on periodicity to control the propagation of waves. We also present a model which allows the separate analysis of each of these two phenomena and provides a comprehensive procedure for designing more efficient devices based on arrays of scatterers, following the concept of tunability developed by some authors.

SPECTRAL-DOMAIN FORMULATION OF PILLAR-TYPE PHOTONIC CRYSTAL WAVEGUIDE DEVICES OF INFINITE EXTENT

This paper presents a novel formulation for the modeling of electromagnetic wave propagation in pillar-type photonic crystal waveguide devices. The structure under consideration is formed in an infinitely extended pillar-type photonic crystal and the wave propagation is controlled by removing some cylinders from the original periodic structure. The structure is considered as cascade connections of straight waveguides, and the input/output properties of the devices are obtained using an analysis method of multilayer structure. Each layer includes periodic circular cylinder array with defects, and the transfer-matrix is obtained by using a spectral-domain approach based on the recursive transition-matrix algorithm with the lattice sums technique and the pseudo-periodic Fourier transform.

Multi-resonant plasmonic nanodome arrays for label-free biosensing applications

The characteristics and utility of plasmonic nanodome arrays capable of supporting multiple resonance modes are described. A low-cost, large-area replica molding process is used to produce, on flexible plastic substrates, two-dimensional periodic arrays of cylinders that are subsequently coated with SiO2 and Ag thin films to form dome-shaped structures, with 14 nm spacing between the features, in a precise and reproducible fashion. Three distinct optical resonance modes, a grating diffraction mode and two localized surface plasmon resonance (LSPR) modes, are observed experimentally and confirmed by finite-difference-time-domain (FDTD) modeling which is used to calculate the electromagnetic field distribution of each resonance around the nanodome array structure. Each optical mode is characterized by measuring sensitivity to bulk refractive index changes and to surface effects, which are examined using stacked polyelectrolyte layers. The utility of the plasmonic nanodome array as a functional interface for biosensing applications is demonstrated by performing a bioassay to measure the binding affinity constant between protein A and human immunoglobulin G (IgG) as a model system. The nanoreplica molding process presented in this work allows for simple, inexpensive, high-throughput fabrication of nanoscale plasmonic structures over a large surface area (120 × 120 mm(2)) without the requirement for high resolution lithography or additional processes such as etching or liftoff. The availability of multiple resonant modes, each with different optical properties, allows the nanodome array surface to address a wide range of biosensing problems with various target analytes of different sizes and configurations.

On the spectral accuracy of a fictitious domain method for elliptic operators in multi-dimensions

This work is a continuation of the authors efforts to develop high-order numerical methods for solving elliptic problems with complex boundaries using a fictitious domain approach. In a previous paper, a new method was proposed, based on the use of smooth forcing functions with identical shapes, mutually disjoint supports inside the fictitious domain and whose amplitudes play the role of Lagrange multipliers in relation to a discrete set of boundary constraints. For one-dimensional elliptic problems, this method shows spectral accuracy but its implementation in two dimensions seems to be limited to a fourth-order algebraic convergence rate. In this paper, a spectrally accurate formulation is presented for multi-dimensional applications. Instead of being specified locally, the forcing function is defined as a convolution of a mollifier (smooth bump function) and a Lagrange multiplier function (the amplitude of the bump). The multiplier function is then approximated by Fourier series. Using a Fourier Galerkin approximation, the spectral accuracy is demonstrated on a two-dimensional Laplacian problem and on a Stokes flow around a periodic array of cylinders. In the latter, the numerical solution achieves the same high-order accuracy as a Stokes eigenfunction expansion and is much more accurate than the solution obtained with a classical third order finite element approximation using the same number of degrees of freedom.

Quantitative characterization of the microstructure and transport properties of biopolymer networks

Biopolymer networks are of fundamental importance to many biological processes in normal and tumorous tissues. In this paper, we employ the panoply of theoretical and simulation techniques developed for characterizing heterogeneous materials to quantify the microstructure and effective diffusive transport properties (diffusion coefficient De and mean survival time τ) of collagen type I networks at various collagen concentrations. In particular, we compute the pore-size probability density function P(δ) for the networks and present a variety of analytical estimates of the effective diffusion coefficient De for finite-sized diffusing particles, including the low-density approximation, the Ogston approximation and the Torquato approximation. The Hashin–Strikman upper bound on the effective diffusion coefficient De and the pore-size lower bound on the mean survival time τ are used as benchmarks to test our analytical approximations and numerical results. Moreover, we generalize the efficient first-passage-time techniques for Brownian-motion simulations in suspensions of spheres to the case of fiber networks and compute the associated effective diffusion coefficient De as well as the mean survival time τ, which is related to nuclear magnetic resonance relaxation times. Our numerical results for De are in excellent agreement with analytical results for simple network microstructures, such as periodic arrays of parallel cylinders. Specifically, the Torquato approximation provides the most accurate estimates of De for all collagen concentrations among all of the analytical approximations we consider. We formulate a universal curve for τ for the networks at different collagen concentrations, extending the work of Torquato and Yeong (1997 J. Chem. Phys. 106 8814). We apply rigorous cross-property relations to estimate the effective bulk modulus of collagen networks from a knowledge of the effective diffusion coefficient computed here. The use of cross-property relations to link other physical properties to the transport properties of collagen networks is also discussed.

Accurate analysis of electromagnetic scattering from periodic circular cylinder array with defects

This paper considers the two-dimensional electromagnetic scattering from periodic array of circular cylinders in which some cylinders are removed, and presents a formulation based on the recursive transition-matrix algorithm (RTMA). The RTMA was originally developed as an accurate approach to the scattering problem of a finite number of cylinders, and an approach to the problem of periodic cylinder array was then developed with the help of the lattice sums technique. This paper introduces the concept of the pseudo-periodic Fourier transform to the RTMA with the lattice sums technique, and proposes a spectral-domain approach to the problem of periodic cylinder array with defects.

SPH simulations of a viscoelastic flow around a periodic array of cylinders confined in a channel

In this paper a numerical study on the performance of the Smoothed Particle Hydrodynamics method (SPH) in the case of a flow of a viscoelastic liquid around a linear array of cylinders confined in a channel is presented. Numerical convergence in the case of a low Reynolds number Newtonian flow was demonstrated by Ellero et al. in [Int. J. Numer. Methods Eng. 86 (2011) 1027]. Here viscoelastic effects are incorporated in the SPH scheme according to the Oldroyd-B model presented in [Phys. Rev. E 79 (2009) 056707]. Good agreement of the dimensionless drag force acting on the cylinder with literature data is observed for a wide range of Weissenberg numbers We. The case of closely spaced cylinders is also investigated and the impact of We on the solution discussed. It turns out that in this case the Newtonian solution exhibits a stable secondary flow represented by two counter-rotating vortices. When elasticity is considered, above a critical Weissenberg number We c these vortices become unstable, breaking the plane symmetry and producing a quasi-periodic flow of mass in and out of the gap region between cylinders. Correspondingly, the flow becomes increasingly unsteady and a dramatic increase in the cylinder’s drag is observed. The results are in qualitative agreement with experimental observations made on Boger liquids under similar flow conditions.

Solution of flow around complex‐shaped surfaces by an immersed boundary‐body conformal enrichment method

SUMMARYSolving the flow around objects with complex shapes may involve extensive meshing work that has to be repeated each time a change in the geometry is needed. Time consuming meshing can be avoided when the solution algorithm can tackle grids that do not fit the shape of immersed objects. This work presents applications of a recently proposed immersed boundary—body conformal enrichment method to the solution of the flow around complex shaped surfaces such as those of a metallic foam matrix. The method produces solutions of the flow satisfying accurately Dirichlet boundary conditions imposed on the immersed fluid/solid interface. The boundary of immersed objects is defined using a level‐set function, and the finite element discretization of interface elements is enriched with additional degrees of freedom, which are eliminated at element level. The method is first validated in the case of flow problems for which reference solutions on body‐conformal grids can be obtained: flow around an array of spheres and flow around periodic arrays of cylinders. Then, solutions are shown for the more complex flow inside a metallic foam matrix. A multiscale approach combining the solution at the pore level by the immersed boundary method and the macro‐scale solution with simulated permeability is used to solve actual experimental configurations. The computed pressure drop as a function of the flow rate on the macro scale configuration replicating two experimental setups is compared with the experimental data for various foam thicknesses. Copyright © 2011 National Research Council Canada

Propagation of elastic waves through a lattice of cylindrical cavities

We consider wave propagation through a doubly periodic array of cavity cylinders in an isotropic elastic medium using the method of matched asymptotic expansions based on the assumptions that the scatterer size is much smaller than both the wavelength and the array periodicity. There is no restriction on the wavelength relative to the periodicity, and hence the method yields explicit approximations that describe the phenomena associated with periodic media. This is illustrated with square and hexagonal lattices.

SPECTRAL-DOMAIN FORMULATION OF ELECTROMAGNETIC SCATTERING FROM CIRCULAR CYLINDERS LOCATED NEAR PERIODIC CYLINDER ARRAY

This paper considers a periodic circular cylinder array with additional cylinders and formulates the electromagnetic scattering problem of this imperfectly periodic structure. Generally, the flelds in imperfectly periodic structures have continuous spectra, and the spectral-domain approaches require appropriate discretization schemes in many cases. The present formulation is based on the pseudo-periodic Fourier transform and the discretization scheme can be considered only inside the Brillouin zone.

SPH simulations of flow around a periodic array of cylinders confined in a channel

AbstractIn this paper, we present a numerical study on the performance of SPH in the case of a very viscous flow of a Newtonian liquid around a linear array of cylinders confined in a channel. This specific flow problem, being characterized by a complex mixing of both shear and extensional behaviour, allows to quantify systematically the accuracy of the standard SPH in, up to now, rarely considered complex geometries. Global accuracy tests based on the estimation of the dimensionless drag force acting on the cylinder as well as the inspection of the local velocity profiles are considered and compared with reference solutions. In agreement with previous findings, the impact of two numerical parameters, namely the smoothing length h and particle spacing Δx, is discussed and found to be crucial for the overall order of convergence of the method. In particular, accurate results can be obtained which are in very good agreement with standard mesh‐based methods provided that the number of neighbours is chosen properly.The present results, being based on a detailed convergence analysis in a complex flow problem, justify the applicability of the SPH method to more complex wall‐bounded flows upon critical choice of the model parameters and at the same time can serve as a useful benchmark test for further modelling improvement in the field. Copyright © 2010 John Wiley & Sons, Ltd.

Volumetric diffusers: Pseudorandom cylinder arrays on a periodic lattice

Most conventional diffusers take the form of a surface based treatment, and as a result can only operate in hemispherical space. Placing a diffuser in the volume of a room might provide greater efficiency by allowing scattering into the whole space. A periodic cylinder array (or sonic crystal) produces periodicity lobes and uneven scattering. Introducing defects into an array, by removing or varying the size of some of the cylinders, can enhance their diffusing abilities. This paper applies number theoretic concepts to create cylinder arrays that have more even scattering. Predictions using a boundary element method are compared to measurements to verify the model, and suitable metrics are adopted to evaluate performance. Arrangements with good aperiodic autocorrelation properties tend to produce the best results. At low frequency power is controlled by object size and at high frequency diffusion is dominated by lattice spacing and structural similarity. Consequently the operational bandwidth is rather small. By using sparse arrays and varying cylinder sizes, a wider bandwidth can be achieved.

Electromagnetic bound states in the radiation continuum for periodic double arrays of subwavelength dielectric cylinders

Electromagnetic bound states in the radiation continuum are studied for periodic double arrays of subwavelength dielectric cylinders in TM polarization. They are similar to localized waveguide mode solutions of Maxwell’s equations for metal cavities or defects of photonic crystals, but, in contrast to the latter, their spectrum lies in the radiation continuum. The phenomenon is identical to the existence of bound states in the radiation continuum in quantum mechanics, discovered by von Neumann and Wigner. In the formal scattering theory, these states appear as resonances with the vanishing width. For the system studied, the bound states are shown to exist at specific distances between the arrays in the spectral region where one or two diffraction channels are open. Analytic solutions are obtained for all bound states (below the radiation continuum and in it) in the limit of thin cylinders (the cylinder radius is much smaller than the wavelength). The existence of bound states is also established in the spectral region where three and more diffraction channels are open, provided the dielectric constant and radius of the cylinders are fine-tuned. The near field and scattering resonances of the structure are investigated when the distance between the arrays varies in a neighborhood of its critical values at which the bound states are formed. In particular, it is shown that the near field in the scattering process becomes significantly amplified in specific regions of the array as the distance approaches its critical values. The effect may be used to control optical nonlinear effects by varying the distance between the arrays near its critical values.

Surface-enhanced Raman nanodomes

We demonstrate a surface-enhanced Raman scattering (SERS) substrateconsisting of a closely spaced metal nanodome array fabricated on flexible plasticfilm. We used a low-cost, large-area replica molding process to produce atwo-dimensional periodic array of cylinders that is subsequently overcoated withSiO2 and silver thin films to form dome-shaped structures. Finite element modeling was used toinvestigate the electromagnetic field distribution of the nanodome array structureand the effect of the nanodome separation distance on the electromagnetic fieldenhancement. The SERS enhancement from the nanodome array substrates wasexperimentally verified using rhodamine 6G as the analyte. With a separationdistance of 17 nm achieved between adjacent domes using a process that is preciselycontrolled during thin film deposition, a reproducible SERS enhancement factor of1.37 × 108 was demonstrated. The nanoreplica molding process presented in this work allowsfor simple, low-cost, high-throughput fabrication of uniform nanoscale SERSsubstrates over large surface areas without the requirement for high resolutionlithography or defect-free deposition of spherical microparticle monolayer templates.