Degree centrality of combustion reaction networks for analysing and modelling combustion processes

Independent technical summary

The study applies graph-theoretic degree centrality to detailed combustion reaction networks in order to identify principal species during a combustion process.

A principal or central species is defined through its connectivity within the reaction network at a particular simulation time step or computational cell. Species with larger degree-centrality values are more highly connected within the chosen network representation under the local thermochemical conditions. This is a topological statement; it does not by itself establish reaction-rate dominance, flux dominance, sensitivity, causal control or importance to a selected combustion observable.

The degree-centrality criterion is incorporated into an adjusted dynamic adaptive chemistry workflow. Principal species are identified locally and dynamically, and the resulting network information is used together with a directed-relation-graph mechanism-reduction approach. The centrality measure therefore complements, rather than replaces, kinetics-based and reduction-error information.

The study also shows that a species classified as highly connected in a combustion reaction network is not necessarily identical to a species that must be retained for accurate predictive simulation. Network connectivity, kinetic activity, sensitivity and predictive importance therefore need to be distinguished explicitly.

Technical contribution

The work introduces a network-based diagnostic for analysing large combustion mechanisms and for supporting locally adaptive chemistry reduction. Its principal contribution is the explicit use of time- or cell-dependent reaction-network structure rather than a single globally fixed species ranking. The diagnostic describes structural connectivity; it does not constitute a complete surrogate for reaction rates, reaction fluxes, sensitivity analysis or target-observable error control.

This approach is relevant to detailed-chemistry simulations in which the thermochemical state and active reaction pathways change across time, space or operating conditions. Its usefulness depends on the network definition, local state, reduction objective and validation criterion used in the application.

Scope and application boundary

Degree centrality is a structural network measure. A large centrality value does not by itself prove that a species controls a target observable such as ignition delay, flame speed, pollutant formation or heat release, nor that it carries the largest reaction rate or flux or has the largest sensitivity coefficient.

Use of the method for a new fuel, mechanism, reactor or CFD problem requires assessment against the intended operating domain and target quantities. The selected network definition, edge weighting, threshold criteria, reduction method, retained-species logic and error controls can materially affect the resulting reduced chemistry. Validation should therefore be performed against the quantities that matter for the intended application rather than against network centrality itself.

Evidence interpretation

Degree centrality provides descriptive information about graph structure under a defined network construction and thermochemical state. Reaction-rate, flux, sensitivity and target-error measures answer different questions. Agreement of a reduced mechanism with a selected detailed-mechanism result supports that comparison and operating domain; it does not make degree centrality a universally validated species-importance metric.

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Citation

Saylam, A., Hadj Ali, K., & Fikri, M. (2020). Degree centrality of combustion reaction networks for analysing and modelling combustion processes. Combustion Theory and Modelling, 24(3), 442–459. https://doi.org/10.1080/13647830.2019.1699167

Methodological context

Degree centrality is one analytical layer within a broader combustion- kinetics toolbox. Directed-relation methods, reaction-rate and flux analysis, sensitivity analysis, mechanism reduction, adaptive chemistry and state-dependent transfer each use different information and should not be collapsed into a single importance measure.

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