Mixing intensification by natural convection with application to a chemical reactor design

The current work is focused on the numerical study of mass transport inside a cubical reactor agitated by natural convection. The inner face of the bottom wall is covered with a catalytic layer, where a first order chemical reaction takes place with negligible internal resistance to mass transfer. The reactor operates discontinuously and its time evolution is simulated until a 90% reactant conversion is reached. A Galerkin spectral method is used for the spatial discretization of the differential conservation equations of momentum, internal energy and concentration of the reactant species. The solute concentration is advanced in time by means of a 7-8th order Runge-Kutta-Fehlberg method with automatic adjustment of the time-step. The bifurcation diagram of the natural convection flow is established for Rayleigh numbers up to Ra=1.5×10⁵ and a Prandtl number of Pr=6. Amongst the several branches of steady solutions that coexist within this range of Ra, the flow pattern that has the widest stability domain and maximizes the heat transfer rate is selected. The spatial structure and the mixing capabilities of the selected flow pattern are analyzed. The competitiveness of the present reactor is assessed for Pr=6 and different values of the Rayleigh and Schmidt numbers (in the respective ranges 7.5×10⁴≤Ra≤1.5×10⁵ and 6≤Sc≤2000) and the Damkohler number (1≤φ≤100). It is found that, after a short transient, the values of the reactor efficiency, η, become time-independent. The external mass transfer rates can be therefore characterized in terms of η and thickness of the concentration boundary layer, δ_c. The dependence of both η and δ_c on the problem parameters (Ra, Sc and φ) is analysed. The effectiveness of the natural convection-driven catalytic reactor is at least as high as that typically found in previous studies, where mass transfer was promoted by forced convection.