Permeability of periodic arrays of spheres

Kadaksham, A.; Pillapakkam, Shriram; Singh, Pushpendra

doi:10.1016/j.mechrescom.2005.01.005

Cited by 5 publications

(3 citation statements)

References 9 publications

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“…The case of a flow through networks of spheres has been studied by Sangani and Acrivos [2], Kadaksham et al [18], Chapman and Higdon [19]. For reasons of clarity, our numerical solutions are compared only with the ones provided by Chapman and Higdon [19].…”

Section: Flow Through Regular Arrays Of Spheresmentioning

confidence: 99%

Fast Fourier Transformation method for computing the permeability of periodic porous media

Kiên

Hùng

2017

Vietnam J. Mech.

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A Fourier-based method is adopted to determine the permeability of periodic porous media made up of a rigid skeleton saturated by viscous fluid. The flow, induced by a prescribed macroscopic gradient of pressure, adopts the Stokes equations with incorporating a condition of adherence at the surface of the solid. The permeability is determined by solving a linear problem on a unit cell for which we determine the local velocity fields due to a prescribed gradient of pressure. The method uses the Fourier Transformation and exact expressions of the periodic Green tensor in the Fourier space. It is shown that the resolution of the problem requires an introducing of undetermined forces acting within the solid phase.

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Section: Flow Through Regular Arrays Of Spheresmentioning

confidence: 99%

Fast Fourier Transformation method for computing the permeability of periodic porous media

Kiên

Hùng

2017

Vietnam J. Mech.

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“…For instance, the permeability of porous media with cylinders has been investigated by Sparrow and Loeffler [37], Banerjee and Hadaller [38], Sangani and Acrivos [6], Drummond and Tahir [39], Larson and Higdon [40,41], Wang [9] and Idris [42]. The numerical implementation of the Stokes problem through an array of rigid spheres has been provided by Sangani and Acrivos [7], Barrere et al [10], Chapman and Higdon [43], Kadaksham et al [44]. Note that some works deal with the extension of the self-consistent in the field of periodic homogenization method to derive analytic expressions for the permeability [45,46] but the formula are restricted to some particular microstructures corresponding to porous media with rigid cylinders or spheres.…”

Section: Benchmark Problemsmentioning

confidence: 99%

Computation of permeability with Fast Fourier Transform from 3-D digital images of porous microstructures

Monchiet

Grande

2016

International Journal of Numerical Methods for Heat &Amp; Fluid Flow

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Purpose – The purpose of this paper is to present a fully automated numerical tool for computing the effective permeability of porous media from digital images which come from the modern imagery technique. Design/methodology/approach – The permeability is obtained by the homogenization process applied to a periodic rigid solid in which the fluid flow is described by the Stokes equations. The unit cell problem is solved by using the Fast Fourier Transform (FFT) algorithm, well adapted for the microstructures defined by voxels. Findings – Various 3-D examples are considered to show the capacity of the method. First, the case of flow through regular arrays of aligned cylinders or spheres are considered as benchmark problems. Next, the method is applied to some more complex and realistic porous solids obtained with assemblies of overlapping spherical pores having identical or different radii, regularly or randomly distributed within the unit cell. Originality/value – The use of FFT allows the resolution of high-dimension problems and open various possibilities for computing the permeability of porous microstructures coming from X-ray microtomography.

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“…µ is the dynamic viscosity and k ij the components of the permeability tensor of the considered medium. The determination of the permeability of a periodic porous medium knowing the geometry of the microstructure has been studied by many authors, see for instance [1], [2], [3], [4]. The methods to obtain a solution of the problem at the microscopic scale include expansion into series of eigenfunctions, finite element methods, etc.…”

Section: Introductionmentioning

confidence: 99%

A FFT-based method to compute the permeability induced by a Stokes slip flow through a porous medium

Monchiet

Bonnet

Lauriat

2009

Comptes Rendus. Mécanique

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The paper presents a FFT based-method for obtaining the permeability of a periodic micro-porous medium. The periodic medium is constituted of a rigid solid matrix saturated by a viscous fluid. The flow obeys the Stokes equations and a slip condition at the surface of the rigid skeleton is considered. The permeability is obtained from the homogenization of periodic media and an extension of the FFT method used for composite elastic media. The incorporation of the slip condition is made trough the introduction of an interphase between the fluid and the solid. The method of solution uses the classical expansion along Neumann series of the velocity field of the periodic problem and Green's tensor in Fourier space. To cite this article : Résumé Cet article présente une méthode basée sur la FFT pour la détermination de la perméabilité d'un milieu poreux périodique. Le milieu poreux est constitué d'une matrice solide indéformable saturée par un fluide visqueux. L'écoulement obéit aux equations de Stokes et une condition de glissement sur la surface du squelette solide estégalement considérée. La perméabilité est alors obtenue en résolvant leś equations issues de l'homogénéisation de milieux périodiques et par une extension de la méthode FFT utilisée pour les matériaux compositesélastiques périodiques. La prise en compte de la condition de glissement est effectuée en introduisant une interphase entre le fluide visqueux et le solide. La méthode repose sur une représentation du champ de vitesses en séries de Fourier et sur l'expression explicite du tenseur de Green dans l'espace de Fourier. Pour citer cet article :

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Permeability of periodic arrays of spheres

Cited by 5 publications

References 9 publications

Fast Fourier Transformation method for computing the permeability of periodic porous media

Fast Fourier Transformation method for computing the permeability of periodic porous media

Computation of permeability with Fast Fourier Transform from 3-D digital images of porous microstructures

A FFT-based method to compute the permeability induced by a Stokes slip flow through a porous medium

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