Zero Dimensional Models for EGR Mass-Rate and EGR Unbalance Estimation in Diesel Engines

A precise estimation of the recirculated exhaust gas rate and oxygen concentration as well as a predictive evaluation of the possible EGR unbalance among cylinders are of paramount importance, especially if non-conventional combustion modes, which require high EGR flow-rates, are implemented. In the present paper, starting from the equation related to convergent nozzles, the EGR mass flow-rate is modeled considering the pressure and the temperature upstream of the EGR control valve, as well as the pressure downstream of it. The restricted flow-area at the valve-seat passage and the discharge coefficient are carefully assessed as functions of the valve lift. Other models were fitted using parameters describing the engine working conditions as inputs, following a semi-physical and a purely statistical approach. The resulting models are then applied to estimate EGR rates to both conventional and non-conventional combustion conditions. In a following step, a correlation was proposed between EGR rate and combustion metrics. This function was then applied to check the possibility of estimating the EGR unbalance, which can negatively affect combustion stability, in particular at high EGR rates. EGR unbalance was also evaluated considering the measurements of the temperature of the charge entering each cylinder. These two methods to evaluate EGR unbalance were then compared to CFD calculations.