Computational Flame Diagnostics with Bifurcation Analysis and Chemical Explosive Mode Analysis

Limit flame phenomena, such as flame ignition, extinction and onset of instabilities, are important for fire safety, engine efficiency and pollutant emissions. Systematic identification of such limit phenomena and understanding of the underlying physicochemical processes are critical to develop a predictive capability for practical combustion systems. In the present study, systematic approaches for computational flame diagnostics are developed based on eigen-analysis of the governing equations of combustion systems to systematically extract information of the controlling processes for the limit phenomena. Specifically, a bifurcation analysis is developed based on the full Jacobian of the governing equations including both chemical and non-chemical source terms. The bifurcation analysis identifies bifurcation points of steady state combustion systems, across which the stability of the system changes, as demonstrated with perfectly stirred reactors (PSRs) as representative steady state combustion systems featuring the “S”-curve behaviors. It was shown that flame extinction may occur either at the upper turning point on the “S”-curve, which is widely accepted as the extinction state of strongly burning flames, or at a Hopf bifurcation point on the upper branch of the “S”-curve, particularly when the negative temperature coefficient (NTC) behaviors are involved. A bifurcation index is further defined to quantify the contribution of each reaction to the bifurcation points, such that the physicochemical processes controlling the limit phenomena can be identified. The bifurcation analysis is further exploited to obtain highly reduced mechanisms and to understand jet fuel combustion at high-temperature conditions. Chemical explosive mode analysis (CEMA) as another approach for computational flame diagnostics, defined based on the Jacobian of the chemical source term, is further investigated to extract salient flame features, e.g. local ignition, extinction and flame fronts, from a variety of combustion systems, including 0-D auto-ignition, PSRs, 1-D laminar premixed flames, and a turbulent flame simulated with direct numerical simulation (DNS) under the homogeneous charge compression ignition (HCCI) condition for n-heptane-air mixtures featuring NTC behaviors.