Critical role of blockage ratio for flame acceleration in channels with tightly spaced obstacles

Abstract

A conceptually laminar mechanism of extremely fast flame acceleration in obstructed channels, identified by Bychkov et al. [“Physical mechanism of ultrafast flame acceleration,” Phys. Rev. Lett. 101, 164501 (2008)], is further studied by means of analytical endeavors and computational simulations of compressible hydrodynamic and combustion equations. Specifically, it is shown how the obstacles length, distance between the obstacles, channel width, and thermal boundary conditions at the walls modify flame propagation through a comb-shaped array of parallel thin obstacles. Adiabatic and isothermal (cold and preheated) side walls are considered, obtaining minor difference between these cases, which opposes the unobstructed channel case, where adiabatic and isothermal walls provide qualitatively different regimes of flame propagation. Variations of the obstructed channel width also provide a minor influence on flame propagation, justifying a scale-invariant nature of this acceleration mechanism. In contrast, the spacing between obstacles has a significant role, although it is weaker than that of the blockage ratio (defined as the fraction of the channel blocked by obstacles), which is the key parameter of the problem. Evolution of the burning velocity and the dependence of the flame acceleration rate on the blockage ratio are quantified. The critical blockage ratio, providing the limitations for the acceleration mechanism in channels with comb-shaped obstacles array, is found analytically and numerically, with good agreement between both approaches. Additionally, this comb-shaped obstacles-driven acceleration is compared to finger flame acceleration and to that produced by wall friction.

Influence of kinetics on DDT simulations

“…Gas explosions have been studied experimentally [1,5] , theoretically [4,[6][7][8][9][10][11] and numerically [1,[12][13][14] . They occur when a reactive mixture is subjected to an external source of energy from which a combustion wave emerges.…”

“…Deflagrations are intrinsically unstable and tend to accelerate continuously after ignition [16] . This Flame Acceleration (FA) process is well understood thanks to extensive experimental (summarized in the Ciccarelli and Dorofeev review paper [5] ), theoretical [6][7][8] and numerical [12,13] works and depends on the degree of confinement and obstruction encountered by the flame during its propagation. FA can either result in fast deflagrations or create the appropriate conditions for the Deflagration-to-Detonation Transition (DDT).…”

Effect of Non-Equidiffusivity on Premixed Flame Propagation in Obstructed Channels

“…It is seen from Figures 4.15-4.17 that the α-dependence of FA is significant. This is however not the original result but known from the previous studies [7][8][9]. A novel outcome here is a fact that Le-variations do modify the α-dependence substantially.…”

“…While semi-open channels have proven to be a primary focus for several studies of ultrafast FA [7][8][9], channels with both open ends have also been studied. In particular, the experimental measurement and computational simulations by Yanez et al [10] does not accelerate right after the ignition; in contrast, it experiences a delay prior to sudden acceleration, presumably, followed by DDT.…”

“…However, it is recalled that Refs. [7][8][9] were limited to equidiffusive flames. Consequently, there is a fundamental interest to clarify if the Le-variations may influence the α-dependence of FA and how.…”