Analytical study in the mechanism of flame movement in horizontal tubes. II. Flame acceleration in smooth open tubes

TL;DR

This study analyzes the mechanisms behind spontaneous flame acceleration in long, smooth horizontal tubes, deriving equations and identifying two distinct regimes with different acceleration behaviors, supported by numerical solutions and experimental comparisons.

Contribution

It introduces a quasi-steady model for flame acceleration in long tubes and classifies two regimes of flame propagation with detailed numerical and experimental analysis.

Findings

Type I flames have low speed and acceleration.

Type II flames exhibit rapid acceleration.

Transitions occur between regimes in transient mixtures.

Abstract

The problem of spontaneous acceleration of premixed flames propagating in open horizontal tubes with smooth walls is revisited. It is proved that in long tubes, this process can be considered quasi-steady, and an equation for the flame front position is derived using the on-shell description. Numerical solutions of this equation are found which show that as in the case of uniform flame movement, there are two essentially different regimes of flame propagation. In the type I regime, the flame speed and its acceleration are comparatively low, whereas the type II regime is characterized by significant flame acceleration that rapidly increases as the flame travels along the tube. A detailed comparison of the obtained results with the experimental data on flame acceleration in methane-air mixtures is given. In particular, it is confirmed that flames propagating in near-stoichiometric mixtures and mixtures near the limits of inflammability belong to the types II and I, respectively, whereas flames in transient mixtures undergo transitions between the two regimes during their travel.