Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-28T22:29:50.054Z Has data issue: false hasContentIssue false
  • English
  • Français

A determination of the effective viscosity for the Brinkman–Forchheimer flow model

Published online by Cambridge University Press:  26 April 2006

R. C. Givler  and
S. A. Altobelli
R. C. Givler
Affiliation:
Engineering Sciences Center, Sandia National Laboratories, Albuquerque, NM 87185, USA
S. A. Altobelli
Affiliation:
Lovelace Medical Foundation, Albuquerque, NM 87108, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The effective viscosity μe for the Brinkman–Forchheimer flow (BFF) model has been determined experimentally for steady flow through a wall-bounded porous medium. Nuclear magnetic resonance (NMR) techniques were used to measure non-invasively the ensemble-average velocity profile of water flowing through a tube filled with an open-cell rigid foam of high porosity (ϕ = 0.972). By comparing these data with the BFF model, for which all remaining parameters were measured independently, it was determined that μe = (7.5+3.4−2.4)μf, where μf was the viscosity of the fluid. The Reynolds number, based upon the square root of the permeability, was 17.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 258 , 10 January 1994 , pp. 355 - 370
Copyright
© 1994 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Caprihan, A. & Fukushima, E. 1990 Flow measurements by NMR. Phys. Rep. 198, 195–235.Google Scholar
Chen, F. & Chen, C. F. 1992 Convection in superposed fluid and porous layers. J. Fluid Mech. 234, 97–119.Google Scholar
Durlofsky, L. & Brady, J. F. 1987 Analysis of the Brinkman equation as a model for flow in porous media. Phys. Fluids 30, 3329–3341.Google Scholar
Haacke, E. M. & Patrick, J. L. 1986 Reducing motion artifacts in two-dimensional Fourier transform imaging. Magn. Reson. Imaging 4, 359–376.Google Scholar
Hsu, C. T. & Cheng, P. 1990 Thermal dispersion in a porous medium. Intl. J. Heat Mass Transfer 33, 1587–1597.Google Scholar
Irvine, T. F. & Hartnett, J. P. 1978 Advances in Heat Transfer, Vol. 4, Academic.
Kladias, N. & Prasad, V. 1991 Experimental verification of Darcy–Brinkman–Forchheimer flow model for natural convection in porous media. J. Thermophys. 5, 560–576.Google Scholar
Kolodziej, J. A. 1988 Influence of the porosity of a porous medium on the effective viscosity in Brinkman's filtration equation. Acta Mechanica 75, 241–254.Google Scholar
Larson, R. E. & Higdon, J. J. L. 1986 Microscopic flow near the surface of two-dimensional porous media. Part I. Axial flow. J. Fluid Mech. 166, 449–472.Google Scholar
Lundgren, T. S. 1972 Slow flow through stationary random beds and suspensions of spheres. J. Fluid Mech. 51, 273–299.Google Scholar
Nield, D. A. 1991 The limitations of the Brinkman–Forchheimer equation in modeling flow in a saturated porous medium and at an interface. Intl J. Heat Fluid Flow 12, 269–272.Google Scholar
Shoemaker, D. P., Garland, C. W. & Steinfeld, J. I. 1974 Experiments in Physical Chemistry, 3rd edn. McGraw-Hill.
Vafai, K. & Kim, S. J. 1990 Fluid mechanics of the interface region between a porous medium and a fluid layer–an exact solution. Intl J. Heat Fluid Flow 11, 254–256.Google Scholar
Watkins, J. C. & Fukushima, E. 1988 High-pass, birdcage coil for nuclear magnetic resonance. Rev. Sci. Instrum. 59, 926–929.Google Scholar