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Partially premixed combustion (PPC) can be applied to decrease emissions and increase fuel efficiency in direct injection, compression ignition (DICI) combustion engines. PPC is strongly influenced by the mixing of fuel and oxidizer, which for a given fuel is controlled mainly by (a) the fuel injection, (b) the in-cylinder flow, and (c) the geometry and dynamics of the engine. As the injection timings can vary over a wide range in PPC combustion, detailed knowledge of the in-cylinder flow over the whole intake and compression strokes can improve our understanding of PPC combustion. In computational fluid dynamics (CFD) the in-cylinder flow is sometimes simplified and modeled as a solid-body rotation profile at some time prior to injection to produce a realistic flow field at the moment of injection. In real engines, the in-cylinder flow motion is governed by the intake manifold, the valve motion, and the engine geometry.

Detailed chemistry and turbulence-chemistry interaction need to be properly taken into account for a realistic combustion simulation of IC engines where advanced combustion modes, multiple injections and stratified combustion involve a wide range of combustion regimes and require a proper description of several phenomena such as auto-ignition, flame stabilization, diffusive combustion and lean premixed flame propagation. To this end, different approaches are applied and the most used ones rely on the well-stirred reactor or flamelet assumption. However, well-mixed models do not describe correctly flame structure, while unsteady flamelet models cannot easily predict premixed flame propagation and triple flames. A possible alternative for them is represented by transported probability density functions (PDF) methods, which have been applied widely and effectively for modeling turbulent reacting flows under a wide range of combustion regimes.