Mathematical modelling of flow and combustion in internal combustion engines
The research work reported herein addresses the problem of mathematical modelling of fluid flow and combustion in internal combustion engines. In particular, the investigation of three topics that constitute prime sources of uncertainty, in current numerical models, namely turbulence modelling, inaccuracies in the solution procedure specific to moving grids, and combustion modelling. Two and three-dimensional computations of the in-cylinder turbulent flow in a diesel engine are described first, with emphasis on the modifications made to the standard k- model of turbulence to account for rapid compression/expansion, and on the k-W model also used in the computations. It is concluded that the standard k- model may lead to poor predictions when used for internal combustion engine simulations, and that the modified model leads to more reasonable length-scale distributions, improving significantly the overall agreement of velocity predictions with experiment. It is also demonstrated that the k-W model provides better turbulence predictions than the unmodified k- model for the cases considered. The moving boundary within a reciprocating engine poses the problem that as it moves toward the cylinder head it compresses the computational grid cells, creating large aspect ratios that can adversely affect the numerical accuracy and convergence. A conservative scheme has therefore been devised that allows for the removal or addition of grid cells during the simulation, so as to maintain reasonable aspect ratios. It is concluded that with the proposed scheme convergence is obtained within fewer iterations, computational cost is therefore reduced, and that the results are generally in better agreement with experimental data. The third part of this study investigates and compares the performance of the two most commonly used combustion models (the eddy-break-up and the Arrhenius models) and proposes a new formulation of a flame-front model. Calculations have been performed for a one-dimensional test case and for a representative spark-ignition engine in order to determine the grid and time step requirements for numerical accuracy, the sensitivity of results to empirical input and the physical realism of the predictions by comparison with experimental data. It has been found for the cases considered that neither the eddy-break-up nor the Arrhenius models are appropriate for predicting engine combustion. The Arrhenius model does not represent well the combustion process for the cases considered. The eddy-break-up model is not capable of predicting the observed flame front, and the empirical constants in the model require extensive tuning to obtain predictions that match experiments. The flame-front model however, in spite of many simplifications, produces much more realistic flame-front propagation and the empirical input of the model, i.e. the flame speed, can in principle be obtained by other means other than ad-hoc tuning. It is concluded that the flame-front model requires refinement, but for the cases considered, it provides the basis of a very promising combustion model for predicting premixed combustion in engines.