The need for more efficient and environmentally sustainable internal combustion engines is driving research towards the need to consider more realistic models for both fuel physics and chemistry. As far as compression ignition engines are concerned, phenomenological or lumped fuel models are unreliable to capture spray and combustion strategies outside of their validation domains — typically, high-pressure injection and high-temperature combustion. Furthermore, the development of variable-reactivity combustion strategies also creates the need to model comprehensively different hydrocarbon families even in single fuel surrogates. From the computational point of view, challenges to achieving practical simulation times arise from the dimensions of the reaction mechanism, that can be of hundreds species even if hydrocarbon families are lumped into representative compounds, and thus modeled with non-elementary, skeletal reaction pathways. In this case, it is also impossible to pursue further mechanism reductions to lower dimensions. CPU times for integrating chemical kinetics in internal combustion engine simulations ultimately scale with the number of cells in the grid, and with the cube number of species in the reaction mechanism. In the present work, two approaches to reduce the demands of engine simulations with detailed chemistry are presented. The first one addresses the demands due to the solution of the chemistry ODE system, and features the adoption of SpeedCHEM, a newly developed chemistry package that solves chemical kinetics using sparse analytical Jacobians. The second one aims to reduce the number of chemistry calculations by binning the CFD cells of the engine grid into a subset of clusters, where chemistry is solved and then mapped back to the original domain. In particular, a high-dimensional representation of the chemical state space is adopted for keeping track of the different fuel components, and a newly developed bounding-box-constrained k-means algorithm is used to subdivide the cells into reactively homogeneous clusters. The approaches have been tested on a number of simulations featuring multi-component diesel fuel surrogates, and different engine grids. The results show that significant CPU time reductions, of about one order of magnitude, can be achieved without loss of accuracy in both engine performance and emissions predictions, prompting for their applicability to more refined or full-sized engine grids.
On Polynomial Solutions of Pell’s Equation
