Transition from laminar to chaotic natural convection of air saturating a porous square enclosure

Abstract

An unsteady natural convection in a square cavity filled with a saturated air porous medium have been investigated numerically. The lower half of vertical walls are hot and the upper half walls are cold while the horizontal walls are adiabatic. The Darcy-Brinkman and the energy equations are solved numerically using the finite volume method and the TDMA algorithm. Results are analyzed in terms of streamlines, isotherms, averaged Nusselt number, phase portrait, attractors, spectra amplitude, Lyapunov exponents for a Darcy number and a Prandtl number respectively equal to 10–3 and 0.71 and a wide range of Rayleigh number (4 × 106 to 4 × 107). It has been found that, as Rayleigh number increases, the natural convection change from steady state to periodic oscillation state to non-periodic-oscillatory state. The phase portrait and the Lyapunov exponents show that the natural convection evolves to a deterministic chaos following the scenario of that of Ruelle–Takens.