High-dimensional, unsupervised cell clustering for computationally efficient engine simulations with detailed combustion chemistry

Abstract

A novel approach for computationally efficient clustering of chemically reacting environments with similar reactive conditions is presented, and applied to internal combustion engine simulations. The methodology relies on a high-dimensional representation of the chemical state space, where the independent variables (i.e. temperature and species mass fractions) are normalized over the whole dataset space. An efficient bounding-box-constrained k-means algorithm has been developed and used for obtaining optimal clustering of the dataset points in the high-dimensional domain box with maximum computational accuracy, and with no need to iterate the algorithm in order to identify the desired number of clusters. The procedure has been applied to diesel engine simulations carried out with a custom version the KIVA4 code, provided with detailed chemistry capability. Here, the cells of the computational grid are clustered at each time step, in order to reduce the computational time needed by the integration of the chemistry ODE system. After the integration, the changes in species mass fractions of the clusters are redistributed to the cells accordingly. The numerical results, tested over a variety of engine conditions featuring both single- and multiple-pulse injection operation with fuel being injected at 50° BTDC allowed significant computational time savings of the order of 3–4 times, showing the accuracy of the high-dimensional clustering approach in catching the variety of reactive conditions within the combustion chamber.