Potential-flow models for channelled two-dimensional premixed flames around near-circular obstacles

TL;DR

This paper develops potential-flow models for two-dimensional premixed flames in channels with obstacles, capturing complex phenomena like steady fronts, wrinkles, flash-backs, and pulsating flows through numerical solutions of integro-differential equations.

Contribution

It introduces a regularised generalisation of Frankel's equation using conformal maps and Green's functions for flames near obstacles, advancing modeling capabilities.

Findings

Numerical solutions show steady, wrinkled, and pulsating flame fronts.

The model captures noise-induced phenomena and flash-back events.

New mathematical formulations enable detailed physical insights.

Abstract

The dynamics of two-dimensional thin premixed flames is addressed in the framework of mathematical models where the flow field on either side of the front is piecewise incompressible and vorticity-free. Flames confined in channels with asymptotically-straight impenetrable walls are considered. Beside a few free propagations along straight channels, attention is focused on flames propagating against high-speed flows and positioned near a round central obstacle, or near two symmetric bumps protruding inward. Combining conformal maps and Green's functions, a regularised generalisation of Frankel's integro-differential equation for the instantaneous front shape in each configuration is derived, and solved numerically. This produces a variety of real looking phenomena: steady fronts (symmetric or not), noise-induced sub-wrinkles, flash-back events and breathing fronts in pulsating flows. Perspectives and open mathematical/physical problems are finally evoked.