Volumetric Efficiency Model for Variable Cam-Phasing and Variable Valve Lift Applications

This paper outlines the derivation of an analytical volumetric efficiency model that can be used in mean-value engine models or in air estimation algorithms for variable cam phasing and two step valve lift applications. The model is the product of a physics-based modeling approach. It accounts for the most prominent effects that occur during the gas exchange phase of a four cycle combustion process. Variable valve lift and valve timing are intrinsically modeled in terms of their geometric nature. The gas pressure trajectory, which has a crucial impact on the volumetric efficiency, is modeled via piece-wise linear approximation functions. The proposed model has a total of 16 regression parameters that need to be adjusted on the basis of experimental data.

The model validation is based on four sets of engine mapping data, each set pertaining to one particular valve lift mode but otherwise spanning the entire engine operating envelope in terms of speed, load and cam-phasing positions. The engine mapping data used for validation purposes has been generated using an accurate simulation model for the target engine, thus alleviating the burden of procuring experimental data. The validation results suggest that the model, once properly tuned, can be expected to assess the volumetric efficiency for any given engine and for most operating conditions to within an error margin of 10% or less.