CFD modeling of porous membranes

Pak, Afshin; Mohammadi, Toraj; Hosseinalipour, Seyed Mostafa; Allahdini, Vida

doi:10.1016/j.desal.2007.01.152

Cited by 83 publications

(52 citation statements)

References 14 publications

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“…The classic Beavers-Joseph slip condition [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42] was originally phrased in terms of the normal derivative of the tangential velocity (i.e., only the first term in square brackets, above), whereas we add the transposed gradient term to make the slip velocity proportional to the wall shear stress-as appears in [27] and [30]. The difference is negligible at macroscopic lengthscales, but becomes significant when the problem is scaled to resolve the (weakly singular) fine structure at the origin.…”

Section: Statement Of the Problemmentioning

confidence: 99%

Stokes flow singularity at a corner joining solid and porous walls at arbitrary angle

Nitsche

2017

J Eng Math

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Motivated by the internal flow geometry of spiral-wound membrane modules with ladder-type spacers, we consider the Stokes flow singularity at a corner that joins porous and solid walls at arbitrary wedge angle Θ. Seepage flux through the porous wall is coupled to the pressure field by Darcy's law; slip is described by a variant of the Beavers-Joseph boundary condition. On a macroscopic, outer length scale, the singularity appears like a jump discontinuity in the normal velocity, characterized by a non-integrable 1/r divergence of the pressure. For arbitrary Θ, we develop an algebraic criterion to determine the admissible radial exponent(s) in a leading, inner similarity solution-which represents a weaker, integrable singularity in the pressure. A complete map of exponent versus Θ is provided for 0 < Θ < 2π : this has an intricate structure with infinitely many solution branches clustering around Θ = π and Θ = 2π . By generalizing the similarity form with a (ln r ) term and iterating on the slip and seepage conditions, we can carry the outer and inner power series to arbitrarily high order. Nevertheless, a numerical splice is required in between. For this purpose, we apply an iterative, numerical-asymptotic patching scheme described by Nitsche and Parthasarathi (J Fluid Mech 713:183-215, 2012). Detailed velocity and pressure profiles are calculated for three wedge angles (Θ = 3π/4, π/2, π/4) and two dimensionless slip lengths (σ = 20, 40). The general trends for decreasing wedge angle are (i) weakening of the pressure singularity, (ii) increasing magnitude of the radial component of velocity, and (iii) movement of the inner-outer transition farther from the corner. Wedges with Θ < π are seen to differ fundamentally from the flat wedge (Θ = π ) previously considered by Nitsche and Parthasarathi (2012).Keywords Low-Reynolds-number flow · Porous walls · Generalized similarity solutions · Boundary integral method Electronic Supplementary material The online version of this article

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Section: Statement Of the Problemmentioning

confidence: 99%

Stokes flow singularity at a corner joining solid and porous walls at arbitrary angle

Nitsche

2017

J Eng Math

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“…According to Damak et al [5][6][7] and Pak et al [8], as the fluid is forced to pass under the membrane in crossflow, the solvent is forced to flow through the membrane due to the action of a pressure difference across the permeable membrane. The decrease in permeate flow rate is closely related to the decrease in driving force and increased resistance to permeation.…”

Section: Advances In Mechanical Engineeringmentioning

confidence: 99%

“…The local permeation velocity is given by Darcy's law, written as the resistance-in-series model [4][5][6][7][8]…”

Section: Advances In Mechanical Engineeringmentioning

confidence: 99%

Separation Process by Porous Membranes: A Numerical Investigation

Cunha

Souza

Neto

et al. 2014

Advances in Mechanical Engineering

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A major problem associated with the membrane separation processes is the permeate flux drop, limiting the widespread of industrial application of this process. This occurs due to the accumulation of solute concentration near the membrane surface. An exact quantification of the concentration polarization as a function of process conditions is essential to estimate the system performance satisfactorily. In this sense, this work aims to predict the behavior of the concentration polarization boundary layer along the length of a permeable tubular membrane, over various operation conditions. The numerical solution of the Navier-Stokes equation, coupled to Darcy's and mass transfer equations, is obtained by the commercial software ANSYS CFX 12, considering a twodimensional computational domain. The study evaluates the effects of axial Reynolds and Schmidt numbers on the concentration polarization boundary layer thickness during the cross-flow filtration process. Numerical results have shown that the mathematical model is able to predict the formation and growth of the concentration polarization boundary layer along the length of the tubular membrane.

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“…The goal is to explain the concentration polarization layer which is responsible for the permeate flux limitation. For example, Darcovich et al 9 and Geraldes et al 10 have used membrane with the shape of a flat plate; Serra et al 11 and Serra and Wiesner 12 used circular membranes; and Bellhouse et al, 13 Pak et al, 14 and Alves et al 15 used tubular membranes. Souza 1 used a separation module equipped with tubular ceramic membrane, where the contaminated water is introduced into the device through a rectangular inlet at the module bottom and perpendicular to the membrane surface.…”

Section: Introductionmentioning

confidence: 99%

Produced water treatment by ceramic membrane: A numerical investigation by computational fluid dynamics

Magalhães

Lima

Neto

et al. 2017

Advances in Mechanical Engineering

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The disposal of industrial effluents into the environment is an issue that has attracted attention of researchers and engineers with particular reference for produced water originating from the petroleum industry. Separation process using ceramic membranes has been an alternative used to obey requirements of environmental agencies in Brazil related to disposal of oil and grease. Accordingly, we have studied numerically the fluid flow into a separation module with tubular membrane. The conservation equations for mass, linear momentum, and mass transport in conjunction with the renormalization group k-e turbulence model were resolved with aid of the ANSYS CFX 12 commercial package. Results of the streamlines, vector velocity, pressure, velocity, and concentration fields are presented and analyzed. It was concluded that the proposed mathematical model predicts the behavior of the flow within the separation module and that increasing the level of turbulence and putting an impermeable section into the inlet region of the membrane reduce the effect of the polarization layer.

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CFD modeling of porous membranes

Cited by 83 publications

References 14 publications

Stokes flow singularity at a corner joining solid and porous walls at arbitrary angle

Stokes flow singularity at a corner joining solid and porous walls at arbitrary angle

Separation Process by Porous Membranes: A Numerical Investigation

Produced water treatment by ceramic membrane: A numerical investigation by computational fluid dynamics

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