# Fractal scaling of turbulent premixed flame fronts: application to LES

## TL;DR

This paper investigates the fractal properties of turbulent premixed flame fronts and applies these findings to improve sub-grid scale modeling in Large-Eddy Simulations, demonstrating good agreement with experiments and DNS.

## Contribution

It introduces a fractal-based model for unresolved flame surface area in LES, validated against DNS and experimental data across different turbulent regimes.

## Key findings

- Fractal dimension remains relatively constant and below passive scalar fronts.
- Inner cut-off length scales with Kolmogorov dissipative scale.
- LES results show good agreement with DNS and experimental data.

## Abstract

The fractal scaling properties of turbulent premixed flame fronts have been investigated and considered for modelling sub-grid scales in the Large-Eddy-Simulation framework. Since the width of such thin reaction fronts cannot be resolved into the coarse mesh of LES, the extent of wrinkled flame surface contained in a volume is taken into account. The amount of unresolved flame front is estimated via the "wrinkling facto" that depends on the definition of a suitable fractal dimension and the scale at which the fractal scaling is lost, the inner cut-off length {\epsilon}i. In this context, the present study considers laboratory experiments and one-step reaction DNS of turbulent premixed jet flames in different regimes of turbulent premixed flames. Fractal dimension is found to be substantially constant and well below that typical of passive scalar fronts. The inner cut-off length shows a clear scaling with the dissipative scale of Kolmogorov for the regimes here considered. These features have been exploited performing Large Eddy Simulations. Good model performance has been found comparing the LES against a corresponding DNS at moderate Reynolds number and experimental data at higher Reynolds numbers.