CONVECTION AND FLOW IN POROUS-MEDIA .1. VISUALIZATION BY MAGNETIC-RESONANCE-IMAGING

We describe an experimental study of porous media convection (PMC) fro m onset to 8Ra(c). The goal of this work is to provide non-invasive im aging 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 diame ter d = 3.204 +/- 0.029 mm, in circular, rectangular, and hexagonal pl anforms. In general, the structure of the medium plays a role which is not predicted by theories which assume a homogeneous system. Disorder ed media are prepared by pouring mono-disperse spheres into the contai ner. Large ordered regions of close packing for the spheres, with grai n boundaries and isolated defects, characterize these media. The defec ts 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 s patial variations in the Rayleigh number, Ra. We define the critical R a, Ra-c, as the Rayleigh number at the onset of convection in the orde red regions. We find that stable localized convective regions exist ar ound grain boundaries and defects at Ra < Ra-c. These remain as pinnin g sites for the convection patterns in the ordered regions as Ra incre ases above Ra-c up to 5Ra(c), the highest Ra studied in the disordered media. In ordered media, spheres are packed such that the only deviat ions from close packing occur within a thin (< d) region near the vert ical walls. Stable localized convection begins at 0.5 Ra-c 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 o bserved in the bulk at the same Ra after each cycling of Ra below Ra-c , even for similar patterns of small rolls in the wall regions. The ex periments provide a test of the following predictions for PMC: (i) tha t straight parallel rolls should be linearly stable for Ra-c < Ra < 5R a(c); (ii) that at onset, the rolls should have a dimensionless waveve ctor q(c) = pi; (iii) that at the upper end of this range rolls should lose stability to cross-rolls; (iv) that the initial slope of the Nus selt curve should be 2; (v) that there should be a rapid decay of vert ical 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 fi ndings for the bulk convection in the ordered media. We observe roll-l ike structures which relax rapidly to stable patterns between Ra-c and 5Ra(c). However we find a wavenumber which is 0.7 pi compared to pi d erived from linear stability theory. We find an asymmetry between the size of the upflowing regions and downflowing regions as Ra grows abov e Ra-c. The ratio of the volume of the upflowing to the volume of the downflowing regions decreases as Ra increases and leads to a novel tim e-dependent state, which does not consist of cross-rolls. This time-de pendent state begins at 6Ra(c) and is observed up to 8Ra(c), the large st Ra which we studied. It seems likely that the occurrence of this st ate is linked to departures from the Boussinesq approximation at highe r Ra. We also find that the slope of the Nusselt curve is 0.7, which d oes not agree with the predicted value of 2.