The Rayleigh--Benard convection in gas with chemical reactions

I. B. Palymskiy ; P. A. Fomin ; H. Hieronymus

Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 10 (2007) no. 4, pp. 371-383

Résumé

The problem of the Rayleigh–Benard convection for a chemical equilibrium gas is solved numerically. The gas is assumed to be incompressible, and the layer boundaries are assumed to be flat, isothermal, and free from the shear stress. The Boussinesq model with the coefficient at the buoyancy term depending on the transverse coordinate is used. The resultant nonlinear system of equations is solved by a previously developed numerical method based on the spectral representation of vorticity and temperature fields. Convection in incompressible gas is impossible. But, as is shown here, in an incompressible gas with chemical reactions, convection is possible owing to the anomalous dependence of the thermal expansion coefficient on temperature. Linear analysis shows that the critical Rayleigh number is essentially decreasing at a low pressure. The instability domain spreads toward higher temperatures as the pressure increases. By the numerical method, various convection nonlinear modes are obtained: stationary, periodic, quasi-periodic, and stochastic convection. The proposed model of convection of a chemical equilibrium gas can be useful for the understanding of the transition of a cellular combustion of surface systems into an explosion (initiation of the surface detonation) and for the calculation of operating modes of chemical reactors.