Subcritical oscillatory instability in porous beds

Abstract

This paper presents a study of the stability of gas flow subject to an adverse temperature and concentration gradient. The onset and the development of convection were studied using a numerical technique and the analytical linear and nonlinear stability theories. The range covered, for a unity aspect ratio and Ω=ε/σ, was R C Le=20 and 40 with Le=0.5−10. The thermal Rayleigh number was chosen as the bifurcation parameter and the range covered was from 0 to 150. Numerical solutions of the set of governing equations show a symmetrical steady and oscillating mode in subcritical flows. A bifurcation phenomenon was found, which showed the existence of two symmetrical branches. Steady state convection can be developed below the critical value R T c predicted by the linear theory. This study has demonstrated that the presence of two diffusing components (heat and mass) with different diffusivities can lead to the development of subcritical oscillating instabilities in the range 4 π+ ξ≤ R T ≤ R T c− ξ′.