The transverse instability in a differentially heated vertical cavity filled with molecular radiating gases. I. Linear stability analysis

Radiation effects on the onset of the transverse instability in a different ially heated vertical cavity containing molecular emitting and absorbing ga ses in the so-called conduction regime is studied theoretically. Radiative transfer is treated using the full integro-differential formulation. The ne utral stability curves are determined using a combined Galerkin-collocation method based on Chebyshev polynomials. A modified correlated-k model and t he absorption distribution function model are used in order to take into ac count the spectral structure of the absorption coefficient for radiating mo lecules such as H2O and CO2. For transparent media, perfect agreement is fo und with the available data reported in the literature and, particularly, t he principle of exchange of stability is found to hold for Prandtl number v alues less than 12.46. The study of gray media allows us to examine the bas ic mechanisms that yield to the onset of transverse instability as travelin g waves. For real radiating gases, a parametric study for H2O and CO2 is re ported. It is shown that the radiative transfer delays the onset of the tra nsverse instability and this delay increases with temperature and decreases with boundary emissivities, while layer depth effects depend on the level of saturation of the gas active absorption bands. Whatever the gas consider ed, it is found that neither radiation effect on the basic flow nor the rad iative power disturbances can be neglected. (C) 2001 American Institute of Physics.