The effect of gravity and thermal expansion on the propagation of a triple flame in a horizontal channel

We investigate the effect of thermal expansion and gravity on the propagation of a triple flame in a horizontal channel with porous walls, where the fuel and oxidiser concentrations are prescribed. The triple flame therefore propagates in a direction perpendicular to the direction of gravity, a configuration that does not seem to have received any dedicated investigation in the literature. In particular, we examine the effect of the non-dimensional flame-front thickness ∊ on the propagation speed of the triple flame for different values of the thermal expansion coefficient α and the Rayleigh number Ra. When gravity is not accounted for (Ra = 0), and for small values of ∊, the numerically calculated propagation speed is found to agree with predictions made in previous studies based on scaling laws [1]. We show that the well known monotonic relationship between U and ∊, which exists in the constant density case when the Lewis numbers are of order unity or larger, persists for triple flames undergoing thermal expansion. Under strong enough gravitational effects (Ra ≫ 1), however, the relationship is no longer found to be monotonic. For a fixed value of ∊, the relationship between the Rayleigh number and the propagation speed is shown to vary qualitatively depending on the value of ∊ chosen, exhibiting hysteresis if ∊ is small enough and displaying local maxima, local minima or monotonic behaviour for other values of ∊. All of the steady solutions presented in the paper have been found to be stable, except for those on the middle branches of the hysteresis curves.