Modeling combustion under engine combustion network Spray A conditions with multiple injections using the transported probability density function method

Abstract

In this study, numerical simulations of an n-dodecane spray flame—known as Spray A—with multiple injections (0.5 ms injection/0.5 ms dwell/0.5 ms injection) have been carried out using the transported probability density function method in the Reynolds-averaged Navier–Stokes framework. In terms of the methodology employed, the transported probability density function method can handle the multiple-injections case without any modification because the model does not assume that thermodynamical states lie on a low-dimensional manifold such as the mixture fraction manifold, as is the case for many other turbulent combustion models, for example, the representative interactive flamelet model and the conditional moment closure model. Simulation results have been compared with recent experimental data in terms of inert and reactive jet tip penetration and vapor boundary (from schlieren imaging), ignition delay and flame base location of the first and second fuel injection, spatial distribution of formaldehyde (CH₂O) and polyaromatic hydrocarbon (from 355-nm planar-laser-induced fluorescence). Particular attention has been paid to the ignition behavior of the second fuel injection. The timing and progression of the first- and second-stage ignition events are qualitatively well reproduced by the model. Simulation results have been further analyzed to assess the validity of the beta-function as the presumed shape of the mixture fraction probability density function, which is typically employed in mixture fraction–based models. The beta-function probability density function was found to provide a good approximation throughout the jet region apart from a brief period of around 100 µs when the second fuel stream encounters the pre-existing fuel–air mixture from the first fuel injection. Overall, it is shown that the transported probability density function model is able to capture the main features related to auto-ignition involved with multiple injections, and simulation results can be used to assess some of the underlying assumptions invoked by other models.