Doran, E., Pitsch, H., and Cook, D., "Multi-Dimensional Flamelet Modeling of Multiple Injection Diesel Engines," SAE Technical Paper 2012-01-0133, 2012, doi:10.4271/2012-01-0133.
To enable the modeling of modern diesel engines, this work furthers the development of multi-dimensional flamelet models for application to designs that employ multiple injection strategies. First, the flamelet equations are extended to two dimensions following the work of Hasse and Peters  and Doran et al.  and a method of coupling the resulting equations interactively to a turbulent flow simulation for use in unsteady calculations is described. The external parameters required to solve the flamelet equations are the scalar dissipation rates. In previous studies, the dissipation rates of each mixture fraction have been scaled according to their realizable bounds and the cross-dissipation rate between mixture fractions has been neglected. In this work, new models for the scalar dissipation rate of each mixture fraction in a two-dimensional space are introduced along with a method for obtaining the cross-dissipation rate, the role of which in obtaining a general representation of three stream mixing is further discussed. The model framework is then applied to a split-injection diesel engine over a range of operating conditions and exhaust gas recirculation (EGR) rates, as well as for two different injection timing strategies. Comparisons of the computed results with experimental data show that the ignition delay of each injection is accurately captured for both injection strategies and the overall characteristics of combustion are well represented. The effect of engine of engine load and EGR is also captured well by the model.