Analytical study in the mechanism of flame movement in horizontal tubes

TL;DR

This study analyzes the mechanisms of flame movement in horizontal tubes, deriving a differential equation to describe steady flame fronts, revealing two regimes of laminar flame propagation influenced by gas expansion and comparing findings with experimental data.

Contribution

It introduces a nonlinear differential equation for steady flame fronts in horizontal tubes, highlighting two distinct propagation regimes influenced by gas expansion effects.

Findings

Two regimes of laminar flame propagation identified

Flame speed varies with gas mixture composition

Comparison with experiments supports theoretical predictions

Abstract

The problem of premixed flame propagation in wide horizontal tubes is revisited. Employing the on-shell description of flames with arbitrary gas expansion, a nonlinear second-order differential equation for the front position of steady flame is derived. Solutions to this equation, obtained numerically, reveal two distinct physical regimes of laminar flame propagation controlled by the strong baroclinic effect. They differ by the front shape and flame speed, the ratio of the total consumption rates in the two regimes being 1.4 to 1.8, depending on the value of the gas expansion coefficient. Comparison with the existing experimental data on methane-air flames is made, and explanation of the main trends in the observed flame behavior is given. It is shown, in particular, that the faster (slower) regime of combustion is realized in mixtures close to (far from) the stoichiometric composition, with pronounced changeover in between.