Analysis of Thermo-Diffusive Cellular Instabilities in Continuum Combustion Fronts

TL;DR

This paper numerically investigates thermo-diffusive cellular instabilities in combustion fronts, generalizing existing models to include heterogeneity and kinetics, and explores pattern formation across different Lewis numbers with advanced computational techniques.

Contribution

It introduces a generalized model for thermo-diffusive instabilities, validated analytically and numerically, and employs adaptive mesh refinement to study large-scale cellular patterns in combustion.

Findings

Cellular and dendritic instabilities occur at low Lewis numbers.

Adaptive mesh refinement enables large domain simulations, revealing system-size effects.

Dynamics near the critical Lewis number include steady cells, tip-splitting, and merging.

Abstract

We explore numerically the morphological patterns of thermo-diffusive instabilities in combustion fronts with a continuum fuel source, within a range of Lewis numbers and ignition temperatures, focusing on the cellular regime. For this purpose, we generalize the model of Brailovsky et al. to include distinct process kinetics and reactant heterogeneity. The generalized model is derived analytically and validated with other established models in the limit of infinite Lewis number for zero-order and first-order kinetics. Cellular and dendritic instabilities are found at low Lewis numbers thanks to a dynamic adaptive mesh refinement technique that reduces finite size effects, which can affect or even preclude the emergence of these patterns. This technique also allows achieving very large computational domains, enabling the study of system-size effects. Our numerical linear stability analysis is consistent with the analytical results of Brailovsky et al. The distinct types of dynamics found in the vicinity of the critical Lewis number, ranging from steady-state cells to continued tip-splitting and cell-merging, are well described within the framework of thermo-diffusive instabilities and are consistent with previous numerical studies. These types of dynamics are classified as "quasi-linear" and characterized by low amplitude cells and may follow the mode selection mechanism and growth prescribed by the linear theory. Below this range of Lewis number, highly non-linear effects become prominent and large amplitude, complex cellular and {\it{seaweed}} dendritic morphologies emerge.