Modal, non-modal and sensitivity analysis of planar deflagrations with low molecular diffusivity and branching kinetics

Abstract

The dynamics of a planar premixed flame is analyzed using the Zel’dovich-Liñán-Dold two-step chemical–kinetic mechanism. The chemistry model involves an initial autocatalytic reaction with large activation energy converts the premixed fuel into intermediate radical species without heat release, followed by a temperature-independent recombination reaction that releases heat and produces the final combustion products. Focusing on low-diffusivity conditions, we revisit the modal stability of planar deflagrations and compare the results with asymptotic predictions obtained in the high-activation-energy limit. To characterize transient amplification mechanisms at finite activation energies, the stability analysis is further extended through pseudospectral and endogeneity analyses, which quantify the intrinsic sensitivity of the system to perturbations and identify the regions that most strongly influence its dynamical behavior. The adjoint-based analysis reveals transient-growth dynamics closely consistent with the optimal-response predictions. In particular, significant transient growth is observed even when the flame is linearly stable for modal disturbances, suggesting the possibility of triggering nonlinear dynamics that may ultimately lead to flame extinction. These findings are further supported by nonlinear time-dependent simulations, which reveal distinct regimes of transient flame evolution, including stable propagation, global instability, and extinction events associated with transient growth phenomena.