Analysis of flame acceleration in open or vented obstructed pipes

While flame propagation through obstacles is often associated with turbulence and/or shocks, Bychkov et al. [V. Bychkov et al., Phys. Rev. Lett. 101, 164501 (2008)10.1103/PhysRevLett.101.164501] have revealed a shockless, conceptually laminar mechanism of extremely fast flame acceleration in semiopen obstructed pipes (one end of a pipe is closed; a flame is ignited at the closed end and propagates towards the open one). The acceleration is devoted to a powerful jet flow produced by delayed combustion in the spaces between the obstacles, with turbulence playing only a supplementary role in this process. In the present work, this formulation is extended to pipes with both ends open in order to describe the recent experiments and modeling by Yanez et al. [J. Yanez et al., arXiv:1208.6453] as well as the simulations by Middha and Hansen [P. Middha and O. R. Hansen, Process Safety Prog. 27, 192 (2008)10.1002/prs.10242]. It is demonstrated that flames accelerate strongly in open or vented obstructed pipes and the acceleration mechanism is similar to that in semiopen ones (shockless and laminar), although acceleration is weaker in open pipes. Starting with an inviscid approximation, we subsequently incorporate hydraulic resistance (viscous forces) into the analysis for the sake of comparing its role to that of a jet flow driving acceleration. It is shown that hydraulic resistance is actually not required to drive flame acceleration. In contrast, this is a supplementary effect, which moderates acceleration. On the other hand, viscous forces are nevertheless an important effect because they are responsible for the initial delay occurring before the flame acceleration onset, which is observed in the experiments and simulations. Accounting for this effect provides good agreement between the experiments, modeling, and the present theory.