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A non-Darcy model for recirculating flow through a fluid-sediment interface in a cylindrical container

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Summary

A numerical investigation has been undertaken to characterize the axisymmetric laminar flow generated by a rotating disk inside a cylinder with an open top, containing a viscous fluid above as layer of fluid-saturated porous medium. The mathematical model is based on a continuum approach for both fluid and porous regions. Attention is focussed on conditions favouring steady, stable, axisymmetric solutions of the Darcy-Brinkman-Lapwood equation. The accuracy of the method is verified by solving some vortex flow problems in disk-cylinder geometries and comparing the results with: (a) existing numerical solutions and, (b) experimental pressure measurements in a similar geometry. Calculations are performed to investigate the fluid exchange between the porous region (porewater) and the overlying water. Results indicate that flow through composite (fluid-sediment) systems can be handled with good accuracy by the method presented here. With our approach the magnitude of advective porewater transport in sediments may be predicted. This finding is important for improved designs of flux chambers and also for understanding advective transport phenomena.

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Abbreviations

B :

binary parameter (0 or 1)

Da:

Darcy number

K :

permeability of the porous medium

H :

Height

L :

reference length

p :

pressure

R :

radius

Re:

Reynolds number

t :

time

u :

radial velocity component

U :

reference velocity

v :

azimuthal velocity component

v :

seepage velocity

V :

intrinsic velocity

w :

axial velocity component

ɛ:

porosity (fluid volume/total volume)

ν:

azimuthal component of vorticity

μ:

dynamic viscosity

\(\tilde \mu \) :

effective viscosity

Ω:

angular velocity

ψ:

streamfunction

ϱ:

fluid density

d :

disk

i, j :

coordinates of the grid points inr−z plane

p :

porous medium

dp :

disk to porous medium

*:

non-dimensional parameters

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Author notes

  1. A. Khalili & M. Huettel

    Present address: Max-Planck-Institute for Marine Microbiology, Celsiusstr. 1, D-28359, Bremen, Germany

  2. A. J. Basu

    Present address: Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur Campus, 560064, Bangalore, India

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    1. A. Khalili
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    3. M. Huettel
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    Khalili, A., Basu, A.J. & Huettel, M. A non-Darcy model for recirculating flow through a fluid-sediment interface in a cylindrical container. Acta Mechanica 123, 75–87 (1997). https://doi.org/10.1007/BF01178402

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