Acceleration of Non-Equidiffusive Flames in Channels: Computational Simulations and Analytical Studies.

摘要

When a premixed flame front spreads in a narrow pipe, wall friction continuously distorts the flame shape. As a result, the flame front acquires a larger surface area, consumes more fuel per unit time and, thereby, propagates faster. While this mechanism of flame acceleration due to wall friction has widely been studied, especially within the last decade, the analytical and computational studies were mostly devoted to equidiffusive flames, where the Lewis number, defined as the thermal to mass diffusivity ratio, is unity, Le = 1. However, in reality thermal and mass diffusion are typically not balanced, especially in rich and lean mixtures. Hence, the micro-scale, diffusional-thermal effects may appear comparable with macro-scale phenomena such as wall friction. The present work sheds the light on the dynamics and morphology of Le ≠ 1 flames in channels. Specifically, it studies, by means of computational and analytical endeavors, how the interplay of finite flame thickness, stretch effect and the thermal-molecular diffusion influence the overall flame acceleration scenario. It is shown that Le > 1 flames accelerate slower, due to an effective thickening of the flame front. In contrast, Le < 1 flames exhibit faster acceleration due to effective flame channeling and other morphological deformations resembling the diffusional-thermal (DT) instability. The analysis also incorporates the internal transport flame properties into the theory of flame acceleration due to wall friction, by means of the Markstein number, Mk, that characterizes the flame response to curvature and stretch. Being a positive or negative function of thermal-chemical combustion parameters, such as the thermal expansion ratio and the Lewis and Zel'dovich numbers, the Markstein number either restrains or promotes the flame acceleration. While Mk may substantially facilitate the flame acceleration in narrow channels, this effects diminishes with the increase in the channel width. The analysis is accompanied by extensive numerical simulations of the Navier-Stokes and combustion equations, which clarify the impact of the Lewis number on the flame acceleration. It is obtained that, for Le lower than a certain critical value, at the initial stage of flame acceleration, globally-convex flame fronts split into two or more "fingers", accompanied by a drastic increase in the flame surface area and associated enhancement of the flame acceleration. Later, however, the flame fingers meet, promptly consuming the troughs, which rapidly diminishes the flame surface area and moderates the acceleration. Eventually, this results in a single, globally-convex flame front that keeps accelerating. Overall, the thermal-diffusive effects facilitate the flame acceleration scenario, thereby advancing a potential deflagration-to-detonation transition.