Turbulent flame speed based on the mass flow rate: theory and DNS

TL;DR

This paper develops a theoretical scaling for turbulent flame speed based on mass flow rate, validated through DNS data, introducing a new length scale for isotherm fluctuations in turbulent premixed flames.

Contribution

It presents a novel theoretical framework for turbulent flame speed derived from mass flow rate without Damköhler's hypotheses, validated with DNS data and introduces a new fluctuation length scale.

Findings

Validation with DNS data confirms the scaling.

Introduction of a new length scale for isotherm fluctuations.

Theoretical framework applicable to high Karlovitz number flames.

Abstract

Starting with an integral formulation of mass flow rate through an ensemble of isotherms constituting a statistically planar, turbulent premixed flame, a scaling for the corresponding turbulent flame speed is derived without invoking Damk{\"o}hler's hypotheses. Major approximations and interim results are validated using a large Karlovitz number, unity Lewis number, Direct Numerical Simulation (DNS) dataset of n-heptane/air mixture, computed with reduced chemistry. A new length scale quantifying the fluctuation distance of the isotherms within the premixed flame structure is introduced.