Premixed flame stability under flow-induced anisotropic diffusion and heat loss #

Aiden Kelly, Joel Daou, Julien Landel

15:30 Monday in 4Q08.

Part of the Boundary layer flows and stability session.

Abstract #

Taylor dispersion, which refers to shear-flow enhanced diffusion, has been an ubiquitous investigation topic in areas involving transport phenomena since the early papers by Taylor in the 1950s. Despite its popularity, the topic has not been addressed in combustion until recently. The current presentation is dedicated to studying the effect of Taylor dispersion on the thermo-diffusive instabilities of premixed flames, transverse to the direction of a shear flow. The study also accounts for the effect of heat losses. A linear stability analysis is carried out analytically in the limit of infinite Zeldovich number β, leading to a dispersion relation that generalises classical relations in the literature. This dispersion relation involves three parameters, l (the reduced Lewis number), p (the Taylor-dispersion coefficient which is proportional to the Peclet number), and κ (the heat loss coefficient). Diagrams are produced indicating the regions of flame stability and their implications on the cellular and oscillatory instabilities are discussed. An evolution equation describing the flame dynamics is derived in the weakly non-linear regime near the onset of the cellular instability. The analysis indicates that both Taylor dispersion and heat loss play a destabilising role when considering the cellular instability. The size of the cells produced by the cellular instability is predicted to be a decreasing function of p. On the other hand, it is found that the oscillatory instability is promoted by larger values of κ, while it is suppressed by an increase in the value of p. Numerical simulations are carried out complementing the results of the analytical study, focusing in particular on the effect of adopting a finite value of β. It is found that the effect of β is opposite to that of p, with decreases in β or increases in p promoting the cellular instability, while inhibiting the oscillatory instability. Increases in β promote both instabilities.