On the theory of turbulent flame velocity

TL;DR

This paper develops an analytical theory for turbulent flame velocity considering large thermal expansion and intrinsic flame instability, showing large-scale effects dominate velocity increases over small-scale turbulence.

Contribution

It introduces a new analytical model incorporating flame instability and large-scale effects, advancing understanding of turbulent flame propagation with significant thermal expansion.

Findings

Large-scale effects like flame instability significantly increase flame velocity.

Most experimental velocity increases are due to large-scale effects, not small-scale turbulence.

The theory aligns well with recent experimental data on turbulent flames.

Abstract

The renormalization ideas of self-similar dynamics of a strongly turbulent flame front are applied to the case of a flame with realistically large thermal expansion of the burning matter. In that case a flame front is corrugated both by external turbulence and the intrinsic flame instability. The analytical formulas for the velocity of flame propagation are obtained. It is demonstrated that the flame instability is of principal importance when the integral turbulent length scale is much larger than the cut off wavelength of the instability. The developed theory is used to analyse recent experiments on turbulent flames propagating in tubes. It is demonstrated that most of the flame velocity increase measured experimentally is provided by the large scale effects like the flame instability, and not by the small-scale external turbulence.