Finite Element Modelling of Flow Through a Porous Medium Between Two Parallel Plates Using The Brinkman Equation |
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Authors: | M Parvazinia V Nassehi R J Wakeman M H R Ghoreishy |
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Institution: | (1) Chemical Engineering Department, Loughborough University, Loughborough, Leicestershire, LE11 3TU, U.K.;(2) Iran Polymer and Petrochemical Institute, PO Box 14185/458, Tehran, Iran |
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Abstract: | Despite the widespread use of the Darcy equation to model porous flow, it is well known that this equation is inconsistent
with commonly prescribed no slip conditions at flow domain walls or interfaces between different sections. Therefore, in cases
where the wall effects on the flow regime are expected to be significant, the Darcy equation which is only consistent with
perfect slip at solid boundaries, cannot predict velocity and pressure profiles properly and alternative models such as the
Brinkman equation need to be considered. This paper is devoted to the study of the flow of a Newtonian fluid in a porous medium
between two impermeable parallel walls at different Darcy parameters (Da). The flow regime is considered to be isothermal and steady. Three different flow regimes can be considered using the Brinkman
equation: free flow (Da > 1), porous flow (high permeability, 1 > Da > 10−6) and porous flow (low permeability Da < 10−6). In the present work the described bench mark problem is used to study the effects of solid walls for a range of low to
high Darcy parameters. Both no-slip and slip conditions are considered and the results of these two cases are compared. The
range of the applicability of the Brinkman equation and simulated results for different cases are shown. |
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Keywords: | porous flow Brinkman equation wall boundary conditions Darcy parameter |
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