Rayleigh–Bénard Convection in a Gas-Saturated Porous Medium at Low Darcy Numbers

Abstract

Natural convection heat transfer is measured in a horizontal enclosure filled with a gas-saturated porous medium composed of glass spheres. The height-to-pore scale ratio (H/d) is in the range of 25–150, yielding a low Darcy number (5.87×10−8≤Da≤1.94×10−6), which satisfies the porous medium assumption more rigorously. The maximum values attained for the modified Rayleigh numbers (Ra* up to 6150) and fluid Rayleigh numbers (Raf up to 2.5×1011) at these low Darcy numbers enable access to both the Darcy and Forchheimer flow regimes. The heat transfer relationship just beyond the onset of convection is in good accordance with theory and previous experiments, varying linearly with the modified Rayleigh number. For higher modified Rayleigh numbers, the data diverge as a function of the Darcy number, depending on both Da and the modified Rayleigh number. Transition points between the Darcy and Forchheimer regimes are estimated. At the highest fluid Rayleigh numbers, the data with the largest pore scales show some evidence of moving toward a regime similar to that of Rayleigh–Bénard convection, where boundary layer and plume length scales are small enough that the details of the porous medium cease to matter. It is argued that even in this regime, the boundary layer length scales are not diminished enough to make the contribution of Brinkman drag significant.