Lagrangian formulation of turbulent premixed combustion

TL;DR

This paper develops a Lagrangian framework for turbulent premixed combustion, linking particle motion, flame front velocity, and curvature, and extends the Zimont equation to all times with experimental validation.

Contribution

It introduces a Lagrangian formulation that unifies turbulent dispersion and flame front dynamics, extending the Zimont equation for comprehensive analysis.

Findings

The model aligns well with experimental data.

Derived an exact solution revealing different combustion regimes.

Extended the Zimont equation to all elapsed times.

Abstract

The Lagrangian point of view is adopted to study turbulent premixed combustion. The evolution of the volume fraction of combustion products is established by the Reynolds transport theorem. It emerges that the burned-mass fraction is led by the turbulent particle motion, by the flame front velocity, and by the mean curvature of the flame front. A physical requirement connecting particle turbulent dispersion and flame front velocity is obtained from equating the expansion rates of the flame front progression and of the unburned particles spread. The resulting description compares favorably with experimental data. In the case of a zero-curvature flame, with a non-Markovian parabolic model for turbulent dispersion, the formulation yields the Zimont equation extended to all elapsed times and fully determined by turbulence characteristics. The exact solution of the extended Zimont equation is calculated and analyzed to bring out different regimes.