Improving fuel efficiency and emission characteristics are significant issues in engine research. Because the engine has complex systems and various operating parameters, the experimental research is limited by cost and time. One-dimensional (1D) simulation has attracted the attention of researchers because of its effectiveness and relatively high accuracy. In a 1D simulation, the applied model must be accurate for the reliability of the simulation results. Because in-cylinder turbulence mainly determines the combustion characteristics, and mean flow velocity affects the in-cylinder heat transfer and efficiency in a spark-ignited (SI) engine, a number of sophisticated models have been developed to predict in-cylinder turbulence and mean flow velocity.
In particular, tumble is a significant factor of in-cylinder turbulence in SI engine. The existing models introduced an angular momentum for the energy input and output of the cylinder and a decay function for geometric effects of the tumble change. However, this function cannot cover different engines, which have different tumble ratios; as a result, it should be re-calculated according to the engine. In this study, the developed quasi-dimensional (QD) turbulence model also adopts an angular momentum and decay function. The correlations of a decay function are found, and the function can be utilized for different engines with the minimum tuning constant. The coefficients of the function are related to the tumble ratio and the stroke-to-bore (SB) ratio.
The model was validated with the results of mean flow velocity, turbulence intensity, and tumble ratio from three-dimensional computational fluid dynamics (3D CFD). The accuracy of the results was confirmed during the period from near the end of the compression stroke to the beginning of the expansion stroke that primarily affects combustion and heat transfer characteristics. In addition, the overall profiles of mean flow velocity, turbulence intensity, and tumble ratio are similar to 3D CFD results. This study shows that the model can be applied to engines with different tumble intensities over a range of engine speeds.