“Crank-Angle” Engine Model
For the purpose of this work the engine model described in Gambarotta et al. (2011) and Gambarotta and Lucchetti (2013) has been used, considering a turbocharged engine with EGR. In-cylinder and gas exchange processes were described using a QSF approach for intake and exhaust valves and a F&E method for manifolds and cylinders. Combustion is considered defining a proper Heat Release Rate (HRR) and pollutant formation is estimated through black-box sub-models. An original algorithm has been developed for the integration of conservation equations in the cylinder with a suitable time step (tuned to keep an angular step of ~1° CA for any engine speed n), while keeping a larger overall time step for intake and exhaust systems. Fuel system model takes account of the fuel rail dynamics (through its bulk modulus), of injectors flow characteristics and of leakages and allows to calculate injected fuel flow rate from rail pressure prail and Energizing Time ET. Black-box map-based models have been used for compressor C and variable geometry turbine (VGT).
Cycle averaged value of equivalence ratio φ is calculated from total intake air mass (obtained by integrating air mass flow rate over each cycle) and the total fuel mass injected per cycle (estimated from injected fuel flow rate). Mass flow rates of considered pollutants (CO, HC, and PM), required to calculate pollutant concentrations Xmi in the exhaust gases and then heat generated by the oxidation reactions inside the catalyst (see Catalyst Model), are estimated as a function of equivalence ratio φ and of engine speed n through experimental maps, arranged in look-up tables in the following form:
m˙i=f(n,φ)
The model and its causality scheme are described in Gambarotta et al. (2011) and Gambarotta and Lucchetti (2013). It has been used for the simulation of several automotive engines (both SI and Diesel) calibrated and validated comparing model output with experimental data, as reported in detail in Gambarotta and Lucchetti (2011, 2013) and Gambarotta (2017). The proposed model has been also used in an original PC-based Hardware-in-the-Loop (HiL) system developed by the authors (Gambarotta et al., 2012) showing good ability to predict the behavior and performance of the engine and related sub-systems both in steady and transient operating conditions.
Exhaust System and Catalyst Model
Heat transfer processes in the exhaust system have a key role in the simulation of ICEs due to the significant influence of exhaust gas temperature on after-treatment systems efficiency. Therefore, a careful description of heat exchange processes is fundamental especially during critical transients (e.g., catalyst “light-off,” particulate trap regeneration, etc.). Other emission critical phases of engine operation are long time operation at low load, when the after-treatment system is significantly cooled down, as well as at highest load, when temperatures are high enough but exhaust mass flow rates force the catalyst to operate under mass transfer deficiency. For this reason, although within the limitations imposed by a 0D approach, particular attention has been dedicated to the simulation of thermal behavior of the exhaust system.
Working fluid has been considered as a mixture of perfect gases defined through a vector of mass concentrations Xmi referred to 7 chemical species, i.e., N2, O2, CO2, H2O, CO, H2, and NO. Extensive properties ρ and cp are calculated as a weighted average taking into account mixture composition, and k = cp/cv is known from cp and gas mixture constant R. Intensive properties μ, Pr, and λ cannot be calculated that way. Dynamic viscosity μ is calculated as a function of equivalence ratio φ through an experimental correlation (Heywood, 1988):