Premixed flame propagation in vertical tubes

TL;DR

This paper develops a theoretical framework for understanding premixed flame propagation in vertical tubes, highlighting gravity effects, finite front-thickness, and mechanisms of flame acceleration, supported by numerical solutions and experimental comparisons.

Contribution

It introduces a new analytical model for quasi-steady flame propagation considering finite front thickness and gravity effects, explaining complex flame behaviors and acceleration mechanisms.

Findings

Gravity reverses burnt gas velocity profiles.

Partial flame propagation depends on domain size and gravity.

Flame acceleration results from pressure differences and metastability.

Abstract

Analytical treatment of premixed flame propagation in vertical tubes with smooth walls is given. Using the on-shell flame description, equations describing quasi-steady flame with a small but finite front thickness are obtained and solved numerically. It is found that near the limits of inflammability, solutions describing upward flame propagation come in pairs having close propagation speeds, and that the effect of gravity is to reverse the burnt gas velocity profile generated by the flame. On the basis of these results, a theory of partial flame propagation driven by the gravitational field is developed. A complete explanation is given of the intricate observed behavior of limit flames, including dependence of the inflammability range on the size of the combustion domain, the large distances of partial flame propagation, and the progression of flame extinction. The role of the finite front-thickness effects is discussed in detail. Also, various mechanisms governing flame acceleration in smooth tubes are identified. Acceleration of methane-air flames in open tubes is shown to be a combined effect of the hydrostatic pressure difference produced by the ambient cold air and the difference of dynamic gas pressure at the tube ends. On the other hand, a strong spontaneous acceleration of the fast methane-oxygen flames at the initial stage of their evolution in open-closed tubes is conditioned by metastability of the quasi-steady propagation regimes. An extensive comparison of the obtained results with the experimental data is made.