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Gravity-driven convection of fluid at parameters near its thermodynamiccritical point inside a porous layer heated from below (Rayleigh-Darcyconvection) is studied. The fluid having the temperature slightly above thecritical one is one-component. The hydrodynamic model describing a highcompressible fluid phase at variable physical properties inside a solid matrixat a uniform porosity is analyzed. A near-critical fluid is assumed to be thevan der Waals gas. In the limit of small variations in the density andthermodynamic coefficients where the Oberbeck-Boussinesq approximation isapplicable, the correlation relations for the key criteria of similarity underthe stratification effect are obtained. These relations connect the modelparameters (the Rayleigh-Darcy and Prandtl numbers appearing in thedimensionless governing equations) with the criteria of similarity (the realRayleigh-Darcy and Prandtl numbers characterizing convection actually).Steady-state Rayleigh-Darcy convection near the stability threshold inconditions of the Oberbeck-Boussinesq approximation to be valid is simulatednumerically. A set of solutions is analyzed with the use of the correlationrelations resulting in a universal dependency of the corrected Nusselt numberon the real Rayleigh-Darcy number described by a single curve. Convection ofnear-critical fluid is compared with that of normal fluid. The temperaturedifference at boundaries corresponding to the convection onset and depending onthe Schwarzschild and Rayleigh criteria is analyzed analytically. As obtained,near the critical point, the threshold temperature difference at boundariesbecomes independent of solid matrix and is determined solely by the criticaladiabatic temperature gradient of fluid phase.

Rayleigh-Darcy convection in a porous layer: A comparison of near-critical and normal fluid phases