The onset of Rayleigh–Bénard instability in molecular radiating gases

Abstract

Radiation effect on the onset of Rayleigh–Bénard instability is studied theoretically in the case of real molecular emitting and absorbing gases. Radiative transfer is treated using the full integro-differential formulation without recourse to the differential approximation or to the asymptotic optically thin or optically thick limiting cases. The marginal stability is determined using a combined Galerkin-collocation method based on Chebyshev polynomials. A modified correlated-k (CK) model is developed for NH3, H2O and CO2 in order to take into account the fine spectral structure of the absorption coefficient and of its derivative with respect to temperature. No restrictions are made concerning the nature of the bounding surfaces and their radiative properties. The study of gray media allows us to discuss first the limitations of the differential approximation and the validity range of the optically thin and thick limits. The principle of exchange of stability is found to hold for all the studied cases. For real radiating gases, a reasonable agreement with the few available experimental data which are related to NH3 is first shown and then a parametric study for H2O and CO2 is reported. It is shown that neither radiation effect on the static temperature profile nor the radiative damping of thermal disturbances can be neglected. Radiation effects on the delay of instability onset increase with temperature, layer depth, and decrease with boundary emissivities. Pressure effects depend on the level of saturation of gas active absorption bands.