Summary
We investigate the flow through a porous medium both numerically and experimentally. The computer simulation solves a generalized non-linear extension to Darcy's law, known as Darcy-Brinkman-Lapwood-Forchheimer (DBLF) equation in a way that allows us to estimate the significance of each term in this equation. The numerical results have been validated against tracer transport data obtained using positron emission tomography (PET), a novel, non-invasive technique for flow-visualization. The results indicate that viscous diffusion is of significance over a narrow region, “the Brinkman-layer”, below the fluid-sediment interface, and that the Darcy equation alone is not sufficient to estimate the advective transport correctly.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Thibodeaux, L. J., Boyle, J. D.: Bedform-generated convective transport in bottom sediment. Nature325, 341–343 (1987).
Savant, S. A., Reible, D. D., Thibodeaux, L. J.: Convective transport within stable river sediments. Water Resour. Res.23, 1763–1768 (1987).
Vafai, K., Kim, S. J.: Analysis of surface enhancement by a porous substrate. ASME J. Heat Transfer112, 700–706 (1990).
Eriksson, L., Dahlbom, M., Widen, L.: Positron emission tomography — a new technique for studies of the central nervous system. J. Microsc.157, 305–333 (1989).
Darcy, H. P. G.: Les fontanes publiques de la villa de Dijon. Paris: Viktor Dalmont 1856.
Forchheimer, Ph.: Wasserbewegung durch Boden. Z. Ver. Deutsch. Ing.49, 1782–1788 (1901).
Brinkman, H. C.: A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Appl. Sci. Res.A1, 27–34 (1947).
Wooding, R. A.: Steady state free convection of liquid in a saturated permeable medium. J. Fluid Mech.2, 273–285 (1957).
Nield, D. A., Bejan, A.: Convection in porous media. Berlin Heidelberg New York Tokyo: Springer 1992.
Beavers, G. S., Joseph, D. D.: Boundary condition at a naturally permeable wall. J. Fluid Mech.30, 197–207 (1967).
Khalili, A., Basu, A. J., Huettel, M.: A non-Darcy model for recirculating flow through a fluid-sediment interface in a cylindrical container. Acta Mech123, 75–87 (1997).
Lerman, A.: Chemical processes-water and sediment environments. New York: Wiley 1979.
Berner, R. A.: Early diagenesis. Princeton: Princeton University Press 1980.
Landau, L. D., Lifshitz, E. M.: Fluid mechanics. Oxford: Pergamon Press 1993.
Chorin, A. J.: Numerical solution of the Navier-Stokes equations. Math. Comp.22, 745–762 (1968).
Khalili, A., Basu, A. J., Mathew, J.: A simpler implicit scheme for computing unsteady incompressible flows. Comput. Fluid Dyn. J.6, 385–398 (1997).
Sørensen, N. S., Christiansen, E. A.: Direct numerical simulation of rotating fluid flow in a closed cylinder. Phys. Fluids7, 764–778 (1995).
Baveye, P., Sposito, G.: Water movement through soils and aquifers. Water Resour Res.20, 521–530 (1984).
Verruijt, A., Barends, F. B. J.: Mechanics of fluids in layered soils. In: Advances in transport phenomena in porous media (Bear, J., Corapcioglu, M. Y., eds.). Dordrecht: Martinus Nijhoff 1987.
Huang, Y. B., Gryte, C. G.: Gamma camera imaging of oil displacement in thin slabs of porous media. Soc. Pet. Eng. Paper No. 16476 (1987).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Khalili, A., Basu, A.J., Pietrzyk, U. et al. Advective transport through permeable sediments: A new numerical and experimental approach. Acta Mechanica 132, 221–227 (1999). https://doi.org/10.1007/BF01186969
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01186969