  Gravity-driven convection of fluid at parameters near its thermodynamic
critical point inside a porous layer heated from below (Rayleigh-Darcy
convection) is studied. The fluid having the temperature slightly above the
critical one is one-component. The hydrodynamic model describing a high
compressible fluid phase at variable physical properties inside a solid matrix
at a uniform porosity is analyzed. A near-critical fluid is assumed to be the
van der Waals gas. In the limit of small variations in the density and
thermodynamic coefficients where the Oberbeck-Boussinesq approximation is
applicable, the correlation relations for the key criteria of similarity under
the stratification effect are obtained. These relations connect the model
parameters (the Rayleigh-Darcy and Prandtl numbers appearing in the
dimensionless governing equations) with the criteria of similarity (the real
Rayleigh-Darcy and Prandtl numbers characterizing convection actually).
Steady-state Rayleigh-Darcy convection near the stability threshold in
conditions of the Oberbeck-Boussinesq approximation to be valid is simulated
numerically. A set of solutions is analyzed with the use of the correlation
relations resulting in a universal dependency of the corrected Nusselt number
on the real Rayleigh-Darcy number described by a single curve. Convection of
near-critical fluid is compared with that of normal fluid. The temperature
difference at boundaries corresponding to the convection onset and depending on
the Schwarzschild and Rayleigh criteria is analyzed analytically. As obtained,
near the critical point, the threshold temperature difference at boundaries
becomes independent of solid matrix and is determined solely by the critical
adiabatic temperature gradient of fluid phase.
