As known, reliable information about underlying turbulence intensity is a mandatory pre-requisite to predict the burning rate in quasi-dimensional combustion models. Based on 3D results reported in the companion part I paper, a quasi-dimensional turbulence model, embedded under the form of “user routine” in the GT-Power™ software, is here presented in detail. A deep discussion on the model concept is reported, compared to the alternative approaches available in the current literature. The model has the potential to estimate the impact of some geometrical parameters, such as the intake runner orientation, the compression ratio, or the bore-to-stroke ratio, thus opening the possibility to relate the burning rate to the engine architecture.
Preliminarily, a well-assessed approach, embedded in GT-Power commercial software v.2016, is utilized to reproduce turbulence characteristics of a VVA engine. This test showed that the model fails to predict tumble intensity for particular valve strategies, such LIVC, thus justifying the need for additional refinements.
The model proposed in this work is conceived to solve 3 balance equations, for mean flow kinetic energy, tumble vortex momentum, and turbulent kinetic energy (3-eq. concept). An extended formulation is also proposed, which includes a fourth equation for the dissipation rate, allowing to forecast the integral length scale (4-eq. concept).
The impact of the model constants is parametrically analyzed in a first step, and a tuning procedure is advised. Then, a comparison between the 3- and the 4-eq. concepts is performed, highlighting the advantages of the 3-eq. version, in terms of prediction accuracy of turbulence speed-up at the end of the compression stroke. An extensive 3-eq. model validation is then realized according to different valve strategies and engine speeds.
The user-model is then utilized to foresee the effects of main geometrical parameters analyzed in part I, namely the intake runner orientation, the compression ratio, and the bore-to-stroke ratio. A two-valve per cylinder engine is also considered. Temporal evolutions of 0D- and 3D-derived mean flow velocity, turbulent intensity, and tumble velocity present very good agreements for each investigated engine geometry and operating condition. The model, particularly, exhibits the capability to accurately predict the tumble trends by varying some geometrical parameter of the engine, which is helpful to estimate the related impact on the burning rate.
Summarizing, the developed 0D model well estimates the in-cylinder turbulence characteristics, without requiring any tuning constants adjustment with engine speed and valve strategy. In addition, it demonstrates the capability to properly take into account the intake duct orientation and the compression ratio without tuning adjustments. Some minor tuning variation allows predicting the effects of bore-to-stroke ratio, as well. Finally, the model is verified to furnish good agreements also for a two-valve per cylinder engine, and with reference to two different high-performance engines.