Modelling of premixed laminar flame propagating in channels

Abstract

The dynamics of the intrinsically unstable premixed flames propagating in channels is studied by means of numerical modelling in this work. Critical conditions of extinction and the influence of the thermal-diffusive effect on the dynamics of flame propagating in planar channels with cold sidewalls under gravity is investigated. For the horizontally propagating flames, the appearance of inversion influences the effect of thermal-diffusion on the asymmetry of flame fronts. For upwards propagating flames, the convex shape of the flame imposed by the mode of ignition combined with buoyancy can suppress
the thermal-diffusive effects; in contrast, the buoyancy alone cannot damp the thermal diffusive effects even for quite large Froud numbers in regard to the appearance of inversion. The variation of Lewis number has no essential effect on the planar flame shape formation when flame propagates downward. Lowering Lewis number can significantly decrease the critical conditions of extinction. However, if Lewis number is smaller than some limit, its further effect on the critical extinction conditions is unsignificant.
In the two-step consecutive reaction, the effects of the ratio of Damkohler numbers, heat release rates, activation energy and Lewis number on the separation and fragmentation of flames are considered. The inversion is more pronounced in combustion with separated flame fronts than for single-step reactions. However, the inversion is obvious only when the two flame fronts are close enough to each other. Thus, the details of combusiiition chemistry may have a strong effect on the stability of the flame front. The thermal diffusive effect of the first flame is, in certain way, dominant and has influence on the
second flame. The presence of the first reaction suppresses the thermal-diffusive effect of the second reaction in regard to the appearance of inversion.
The propagation of flames at a variety of Reynolds number ranging from 70 to 1000 are explored. For longer channels or a flat initial flame front, the inversion of the flame is apparent for Reynolds number higher than 200. For large &, the computational grids should be very fine because of the small thickness of preheat zone. The Generalized Curvilinear
Coordinate Gridding method is introduced and an elliptic grid generator based on the variational approach is employed to construct the solution-adaptive grids. However, we found out that the global structure of the algorithm required by the adaptive grid approach might be not as efficient as simplified non-adaptive grids for prospective use of massively parallel computers.