Eigenvalue-based Linear Stability Analysis of Intrinsic Instabilities in Laminar Flames

TL;DR

This paper introduces a generalized eigenvalue problem-based linear stability analysis framework that efficiently predicts intrinsic flame instabilities directly from governing equations, validated against classical and DNS results.

Contribution

It develops a scalable, accurate method for analyzing flame instabilities that significantly reduces computational cost compared to traditional DNS approaches.

Findings

The framework accurately reproduces analytical dispersion relations for classical configurations.

It achieves excellent agreement with DNS results for finite-thickness flames.

Computational effort is reduced by a factor of 10^8, enabling efficient stability analysis.

Abstract

Intrinsic instabilities of laminar premixed flames play an important role in the dynamics of hydrogen combustion and in the development of predictive models for reacting flows. However, determining their dispersion relations typically relies either on simplified analytical descriptions of the flame front or on computationally expensive direct numerical simulations (DNS). This work develops a generalized eigenvalue problem-based linear stability analysis (GEVP-LSA) framework that predicts the growth rates and spatial structure of intrinsic flame instabilities directly from the linearized governing equations of a 1D base flame. The approach is first validated using the classical Darrieus-Landau configuration, where the numerical results reproduce the analytical dispersion relation and eigenmode structure. The framework is then applied to a model flame of finite thickness governed by the reactive Navier-Stokes equations. The resulting dispersion relations and perturbation fields show excellent agreement with corresponding DNS results while reducing the computational effort by a factor of 1e8. The proposed method therefore provides an efficient and accurate tool for studying intrinsic flame instabilities and offers a scalable foundation for future stability analyses of more complex reacting-flow configurations relevant to combustion modeling and large-eddy simulations.