ROUTE TO CHAOS IN CHEMICALLY ENHANCED THERMAL-CONVECTION IN POROUS-MEDIA

Exothermic chemical reactions can influence natural convection effects in a porous medium. Such phenomena may occur in tubular reactors, oxidation of solid materials in large containers, chemical vapor deposition systems, liquid explosives, and others. Experimental evidence indicates that the influence of natural convection in many chemically reacting systems cannot be neglected. In the present work, transient effects of a two-dimensional convection generated and sustained by an exothermic chemical reaction and a constant boundary wall temperature are studied. The Darcy-Boussinesq equations are used to describe fluid flow through porous media with a zero-order chemical reaction. A recently developed method is used to compute the singular points (such as limit and symmetry breaking bifurcation points) precisely as a function of Rayleigh (Ra) and Frank-Kamenetskii (Fk) numbers. Fold curves are drawn as a function of Ra, and Fk. Flow behavior is governed by two natural parameters, namely, Ra and Fk. Multiple stationary solutions arise over an intermediate range of Ra. The solution structure, i.e., the interconnections between the various branches appear quite complicated. Determination of linear stability on the these solution branches reveal that all two-dimensional, stationary solutions develop some form of instability at higher values of Ra. Transient simulations reveal the emergence of time periodic solutions at higher Ra. The nature and frequency of these periodic solutions depend on the route followed in the parameter space Fk and Ra. The various routes to chaos are identified in this parameter space.