Creeping flows of power-law fluids through periodic arrays of elliptical cylinders

Woods, J.K.; Spelt, Peter D. M.; Lee, Peter; Selerland, T.; Lawrence, C.J.

doi:10.1016/s0377-0257(03)00056-9

Cited by 37 publications

(37 citation statements)

References 18 publications

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“…In a companion paper [14], we present results for the corresponding flows with finite inertia and show that simple scaling arguments can be used for the correction to the drag coefficient due to finite Reynolds numbers. In [34] we show that results for creeping flows of power-law fluids through arrays of elliptical cylinders follow similar trends to those presented here.…”

Section: Discussionsupporting

confidence: 82%

“…with φ max = π/4, the maximum possible solid area fraction [34]. The result for hexagonal arrays is essentially the same as (15), but with an additional factor of 3 (n+1)/2 /2 n on the righthand side and with φ max = π/(2 √ 3).…”

Section: Lubrication Theory For Concentrated Arraysmentioning

confidence: 56%

“…The lubrication theory shows that the pressure drop through each gap in the array is proportional to the local flux Q to the power n, so that, for square arrays, F i ∼ V n i , where F i is the i-component of the force on a cylinder in the array [34]. Denoting the angle between the force and the x 1 -axis (an axis of the array) by θ F , and the angle between the averaged velocity and the x 1 -axis by θ,…”

Section: Lubrication Theory For Off-axis Flowsmentioning

confidence: 99%

“…We found that X is not much affected by a difference between shear and extensional viscosities, so we have used (34) here as the total local viscosity. X is seen to be smaller than unity only for a narrow band around the plane of symmetry and a ring around the centre of the domain.…”

Section: Extensional Viscositymentioning

confidence: 99%

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Flows of inelastic non-Newtonian fluids through arrays of aligned cylinders. Part 1. Creeping flows

et al. 2005

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Numerical simulations are presented for flows of inelastic non-Newtonian fluids through periodic arrays of aligned cylinders, for cases in which fluid inertia can be neglected. The truncated power-law fluid model is used to define the relationship between the viscous stress and the rate-of-strain tensor. The flow is shown to be dominated by shear effects, not extension. Numerical simulation results are presented for the drag coefficient of the cylinders and the velocity variance components, and are compared against asymptotically valid analytical results. Square and hexagonal arrays are considered, both for crossflow in the plane perpendicular to the alignment vector of the cylinders (flows along the axes of the array as well as off-axis flows), and for flow along the cylinders. It is shown that the observed strong dependence of the drag coefficient on the power-law index (through which the stress tensor is related to the rate-of-strain tensor) can be described at all solid area fractions by scaling the drag on a cylinder with appropriate velocity and length scales. The velocity variance components show only a weak dependence on the power-law index. The results for steady-state drag and velocity variances are used in an approximate theory for flows accelerated from rest. The numerical simulation data for unsteady flows agree very well with the approximate theory.

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Section: Discussionsupporting

confidence: 82%

Section: Lubrication Theory For Concentrated Arraysmentioning

confidence: 56%

Section: Lubrication Theory For Off-axis Flowsmentioning

confidence: 99%

Section: Extensional Viscositymentioning

confidence: 99%

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Flows of inelastic non-Newtonian fluids through arrays of aligned cylinders. Part 1. Creeping flows

et al. 2005

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“…The physics behind the phenomenon of obtaining non-zero β angle can be explained as follows (Idris et al 2004;Orgeas et al 2006;Woods et al 2003); First, since the flow equations are non-linear, the apparent permeability coefficients depend on the flow angle. Second, for the non-Newtonian flows that are not aligned with one of the axes of symmetry, the apparent permeability coefficients of the matrix varies in different directions.…”

Section: The Power-law Fluid Flow Through Anisotropic Fibrous Mediamentioning

confidence: 99%

Modelling of Power-law Fluid Flow Through Porous Media Using Smoothed Particle Hydrodynamics

Vakilha

Manzari

2008

Transp Porous Med

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The flow of non-Newtonian fluids through two-dimensional porous media is analyzed at the pore scale using the smoothed particle hydrodynamics (SPH) method. A fully explicit projection method is used to simulate incompressible flow. This study focuses on a shear-thinning power-law model (n < 1), though the method is sufficiently general to include other stress-shear rate relationships. The capabilities of the proposed method are demonstrated by analyzing a Poiseuille problem at low Reynolds numbers. Two test cases are also solved to evaluate validity of Darcy's law for power-law fluids and to investigate the effect of anisotropy at the pore scale. Results show that the proposed algorithm can accurately simulate non-Newtonian fluid flows in porous media.

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Steady Flow of Power Law Fluids across a Circular Cylinder

2006

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gammes de conditions, soit 5 ≤ Re ≤ 40 et 0,6 ≤ n ≤ 2. Le comportement rhéofl uidifi ant (n < 1) du fl uide réduit la taille de la zone de recirculation et accroît également la séparation; d'autre part, les fl uides rhéoépaississants (n > 1) montrent un comportement opposé. En outre, alors que la taille du sillage varie de manière non monotone avec l'indice de loi de puissance, elle ne semble pas infl uencer les valeurs du coeffi cient de traînée. Le coeffi cient de pression de stagnation et le coeffi cient de traînée montrent aussi une dépendance complexe envers l'indice de loi de puissance et le nombre de Reynolds. Les distributions des coeffi cients de pression, de la vorticité et de la viscosité sur la surface du cylindre sont également présentées afi n de mieux comprendre les cinématiques d'écoulement détaillées.

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Creeping flows of power-law fluids through periodic arrays of elliptical cylinders

Cited by 37 publications

References 18 publications

Flows of inelastic non-Newtonian fluids through arrays of aligned cylinders. Part 1. Creeping flows

Flows of inelastic non-Newtonian fluids through arrays of aligned cylinders. Part 1. Creeping flows

Modelling of Power-law Fluid Flow Through Porous Media Using Smoothed Particle Hydrodynamics

Steady Flow of Power Law Fluids across a Circular Cylinder

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