Numerical simulation of two- and threedimensional free convection flows in a horizontal porous annulus using a pressure and temperature formulation.

Abstract

Abstract--A numerical investigation of two-dimensional and three-dimensional free convection flows in a saturated porous horizontal annulus heated from the inner surface is carried out, using a Fourier-Galerkin approximation for the periodic azimuthal and axial directions and a coUocation-Chebyshev approximation in the confined radial direction. The numerical algorithm integrates the Darcy-Boussinesq's equations formulated in terms of pressure and temperature. This method gives an accurate description of the 2-D multicellular structures for a large range of Rayleigh number and radii ratio. Some considerations about the existence of the various 2-D solutions previously described in the literature are reported. The 3-13 spiral flows are described in the vicinity of the transition from the 2-D unicellular flows. Bifurcation points between 2-D unicellular flows and either 2-D multicellular or 3-D flows are also determined numerically.