Convection and flow in porous media. Part 1. Visualization by magnetic resonance imaging

Abstract

We describe an experimental study of porous media convection (PMC) from onset to 8Rac. The goal of this work is to provide non-invasive imaging and high-precision heat transport measurements to test theories of convection in PMC. We obtain velocity information and visualize the convection patterns using magnetic resonance imaging (MRI). We study both ordered and disordered packings of mono-disperse spheres of diameter d = 3.204 ± 0.029 mm, in circular, rectangular, and hexagonal planforms. In general, the structure of the medium plays a role which is not predicted by theories which assume a homogeneous system. Disordered media are prepared by pouring mono-disperse spheres into the container. Large ordered regions of close packing for the spheres, with grain boundaries and isolated defects, characterize these media. The defects and grain boundaries play an important role in pattern formation in disordered media. Any deviation from close packing produces a region of larger porosity, hence locally larger permeability. The result is spatial variations in the Rayleigh number, Ra. We define the critical Ra, Rac, as the Rayleigh number at the onset of convection in the ordered regions. We find that stable localized convective regions exist around grain boundaries and defects at Ra < Rac. These remain as pinning sites for the convection patterns in the ordered regions as Ra increases above Rac up to 5Rac, the highest Ra studied in the disordered media. In ordered media, spheres are packed such that the only deviations from close packing occur within a thin (<d) region near the vertical walls. Stable localized convection begins at 0.5Rac in the wall regions but appears to play only a weak role in the pattern formation of the interior regions (bulk), since different stable patterns are observed in the bulk at the same Ra after each cycling of Ra below Rac, even for similar patterns of small rolls in the wall regions. The experiments provide a test of the following predictions for PMC: (i) that straight parallel rolls should be linearly stable for Rac < Ra < 5Rac; (ii) that at onset, the rolls should have a dimensionless wavevector qc = π; (iii) that at the upper end of this range rolls should lose stability to cross-rolls; (iv) that the initial slope of the Nusselt curve should be 2; (v) that there should be a rapid decay of vertical vorticity - hence no complex flows, such as those which occur for Rayleigh- Benard convection (RBC) within the nominal regime of stable parallel rolls. These predictions are in partial agreement with our findings for the bulk convection in the ordered media. We observe roll-like structures which relax rapidly to stable patterns between Rac and 5Rac. However we find a wavenumber which is 0.7π compared to π derived from linear stability theory. We find an asymmetry between the size of the upfiowing regions and downfiowing regions as Ra grows above Rac. The ratio of the volume of the upfiowing to the volume of the downfiowing regions decreases as Ra increases and leads to a novel time-dependent state, which does not consist of cross-rolls. This time-dependent state begins at 6Rac and is observed up to 8Rac, the largest Ra which we studied. It seems likely that the occurrence of this state is linked to departures from the Boussinesq approximation at higher Ra. We also find that the slope of the Nusselt curve is 0.7, which does not agree with the predicted value of 2.