Synchronized Front Propagation and Delayed Flame Quenching in Strain G-equation and Time-Periodic Cellular Flows

TL;DR

This paper investigates how strain effects influence flame front propagation in time-periodic cellular flows, revealing phenomena like synchronized front propagation, flame quenching at high flow intensities, and unique speed patterns not seen in steady flows.

Contribution

It introduces a finite difference method for G-equations with strain, analyzing flame behavior in time-periodic flows and uncovering novel propagation and quenching phenomena.

Findings

Flow enhances front propagation in strain G-equation.

Flame quenching occurs at high flow intensities.

Turbulent flame speed becomes piecewise constant with flow intensity.

Abstract

G-equations are level-set type Hamilton-Jacobi partial differential equations modeling propagation of flame front along a flow velocity and a laminar velocity. In consideration of flame stretching, strain rate may be added into the laminar speed. We perform finite difference computation of G-equations with the discretized strain term being monotone with respect to one-sided spatial derivatives. Let the flow velocity be the time-periodic cellular flow (modeling Rayleigh-B\'enard advection), we compute the turbulent flame speeds as the asymptotic propagation speeds from a planar initial flame front. In strain G-equation model, front propagation is enhanced by the cellular flow, and flame quenching occurs if the flow intensity is large enough. In contrast to the results in steady cellular flow, front propagation in time periodic cellular flow may be locked into certain spatial-temporal periodicity pattern, and turbulent flame speed becomes a piecewise constant function of flow intensity. Also the disturbed flame front does not cease propagating until much larger flow intensity.