Directed Relation Graph-Based Species Rank (DRGSR): An efficient mechanism reduction algorithm

While kinetic mechanisms play a pivotal role in simulating complex combustion problems, their extended scale often results in prohibitive computational cost, particularly when integrated with computational fluid dynamics simulations. This paper introduces the Directed Relation Graph Species Rank (DRGSR) algorithm, an efficient mechanism reduction technique designed to retain the essential species and reaction pathways while minimizing computational demands. Specifically, it incorporates a two-step approach: the first utilizes a directed relation graph to map species interactions and transform the kinetic information into a graph structure, and the second employs the PageRank algorithm and directed interaction coefficients to rank species based on their importance within the network. The DRGSR algorithm is validated through case studies involving both large- and small-scale, high-temperature and low-temperature mechanisms, specifically focusing on the ignition delay times for ethylene (C₂H₄) and n-heptane (C₇H₁₆). The algorithm demonstrates superior performance in reducing the number of species significantly while maintaining accuracy; for ethylene, it retains only 31 species with an error under 8 %, while for n-heptane, it achieves comparable precision with fewer species compared to existing methods. The validation is extended to predicting the laminar flame speeds, and further affirms the algorithm's reliability and generalizability. A comparative analysis of the computational cost reveals that the DRGSR algorithm not only is less time-consuming, but it also simplifies the reduction process by eliminating the iterative threshold adjustments required by methods such as Directed Relation Graph (DRG), Directed Relation Graph with Error Propagation (DRGEP) and Directed Relation Graph with Error Propagation and Sensitivity Analysis (DRGEPSA). These findings indicate that the DRGSR algorithm offers a robust, efficient and reliable approach for kinetic mechanism reduction, suitable for wide ranges of engineering applications.