Development of a Quasi-Dimensional K-k Turbulence Model for Direct Injection Spark Ignition (DISI) Engines Based on the Formal Reduction of a 3D CFD Approach

Combustion in SI engines strongly depends on in-cylinder turbulence characteristics. Turbulence by definition presents three-dimensional (3D) features; accordingly, 3D approaches are mainly used to investigate the in-cylinder flow and assist the engine design. However, SI engine architectures are becoming more and more complex and the generalization of technologies such as Variable Valve Timing (VVT) and Direct Injection (DI) considerably increases the number of degrees of freedom to deal with. In this context, the computing resources demanded by 3D CFD codes hugely increase and car manufacturers privilege system simulation approaches in the first phases of the design process. Accordingly, it is essential that the employed 0D/1D models well capture the main physics of the system and reproduce the impact that engine control parameters have on it. This paper deals with the development of a new predictive 0D turbulence model, formally derived from 3D transport equations of turbulence, based on the K-k formalism. Starting from the model state of the art, new equation term closures of the turbulence model are proposed based on the understanding given by the 3D models and validated against 3D CFD results. The new turbulence model is then coupled to the CFM1D combustion model developed at IFP Energies nouvelles (IFPEN) to account for the impact of turbulence on combustion. The validation of this coupling is done by comparing simulated and experimental complete engine cycles over a complete engine operating map. The ability of the new model to reproduce experimental data with good accuracy, without changing its parameterization, and its capability to compute turbulence and combustion features prove the quality and the consistency of the approach.