A Refined 0D Turbulence Model to Predict Tumble and Turbulence in SI Engines

In this work, the refinement of a phenomenological turbulence model developed in recent years by the authors is presented in detail. As known, reliable information about the underlying turbulence intensity is a mandatory prerequisite to predict the burning rate in phenomenological combustion models. The model is embedded under the form of “user routine” in the GT-Power™ software. The main advance of the proposed approach is the potential to describe the effects on the in-cylinder turbulence of some geometrical parameters, such as the intake runner orientation, the compression ratio, the bore-to-stroke ratio, and the valve number. The model is based on three balance equations, referring to the mean flow kinetic energy, the tumble vortex momentum, and the turbulent kinetic energy (3-eq. concept). An extended formulation is also proposed, which includes a fourth equation for the dissipation rate, allowing to forecast also the integral length scale (4-eq. concept). The model consistency is verified against 3D results under motored operations for various operating conditions and engine geometrical architectures. The temporal evolutions of the 0D-derived mean flow velocity, turbulence intensity, and tumble velocity present very good agreement with the 3D outcomes. The model exhibits the capability to accurately predict the tumble trends by varying some engine geometrical parameters. The proposed 0D model proves to correctly estimate the in-cylinder turbulence characteristics, without requiring any tuning adjustment with the engine speed and the valve strategy. In addition, it demonstrates the capability to properly take into account the intake duct orientation and the compression ratio without any case-dependent tuning. Some minor tunings are required to predict the effects of the bore-to-stroke ratio. The model also shows an adequate accuracy for a two-valve per cylinder engine and for two different high-performance engines.