Pattern Formation at the Onset of Convection in Porous Media

Details Pattern Formation at the Onset of Convection in Porous Media Pattern Formation at the Onset of Convection in Porous Media

Jan 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993phdt........56h&link_type=abstract

Thesis (PH.D.)--DUKE UNIVERSITY, 1993.Source: Dissertation Abstracts International, Volume: 54-12, Section: B, page: 6419.

Statistics

Computation

Shadowgraphy

Scientific paper

This work presents a modified shadowgraphic technique which is used to visualize wavepattern formation in convecting fluid-saturated porous media. Two porous media types are studied. This first is a stacked grid of bars which is saturated with water. The heat transfer curve, represented by a plot of the Rayleigh number vs. the Nusselt number, shows a sharp bifurcation to convection. The orientation of the convection rolls is determined by grid geometry in the upper and lower bar layers. This stable, two-dimensional convective state exists from the critical temperature difference up to approximately three times the critical difference. Above the stable two-dimensional state, three-dimensional wavepatterns appear. These patterns, which are temporally steady, are accompanied by a slight decrease in the slope of the heat transfer curve. A further increase in temperature difference drives the system into an unsteady regime. The second medium type studied is a porous matrix created by stacking randomly-drilled disks. In this system, a rounded primary bifurcation is observed in the heat transfer curve. The rounded bifurcation is a manifestation of localized modes of convection. The wavepattern, which has a complicated, three-dimensional structure, is different with each cycling through the onset of convection. The cause for both the rounded bifurcation and for the appearance of the complicated patterns is spatial fluctuations in thermo-physical properties. The final section of this work explores the role of horizontal permeability variation on convection initiation by a reduced Galerkin computational method. Three permeability variations are considered. The first variation, which is also the simplest, is a linear ramp in permeability. Rounding of the heat transfer curve is noted at convection onset. The second permeability variation studied is a single mode cosine function in an aspect ratio = 2 system. In this case, little rounding in noted. The critical value of the Rayleigh number is observed to be a strong function of the permeability variation. The final permeability variation simulated is a variation derived from the random medium which is used in the experimental section. (Abstract shortened by UMI.).

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