A dynamic nucleate-boiling model for CO₂ reduction in internal combustion engines

Highlights: • A 0-D model of nucleate boiling regime for ICE was developed. • Occurrence and extent of nucleate boiling, coolant and metal temperatures predicted. • Model predictions assessed by comparison with experimental data. • Model useful for optimal coolant flow-rate set-up and for quicker engine warm-up. - Abstract: Improvements in cooling system efficiency are required in modern internal combustion engines (ICE). Optimal thermal management presents several advantages in terms of lower pump mechanical power, reduced friction losses and shorter warm-up time, which result in reduced fuel consumptions and CO₂ emissions. These goals can be achieved by adopting lower coolant flow rates, which give rise to nucleate boiling regime. The key requirement for a precision cooling strategy is the capability of developing a reliable, model-based control of the cooling regime. However, there is no model of the cooling system of an SI engine, which identifies precisely the onset of the nucleate boiling. This work fills this void. This paper presents an original zero-dimensional model of the cooling system of an ICE that predicts dynamically the onset of the nucleate boiling phenomenon and calculates the spatial-averaged metal temperature, the engine-out coolant temperature and the fraction of wall metal area subjected to nucleate boiling. Owing to the little computational effort required, the model is particularly suitable for the development of control algorithms, which can be used to optimize the thermal management strategies in real time and can be easily implemented in the ECU of a modern engine. The model has been validated by means of experimental tests under several operating conditions, involving variations in coolant flow rate, engine speed and fuel flow rate. The comparison with experimental data shows a very good agreement. Maximum and average deviation in engine-out coolant temperature are 0.61% and 0.44% respectively under steady-state conditions. The coolant flow rate, which determines the on-set of nuclear boiling computed by the proposed model, is well within the uncertainty range of the experimental evidence