A non-equilibrium evaporation model for a droplet and spray under diesel engine-relevant conditions

Most continuum-based models are constructed based on thermodynamic equilibrium assumption. Nevertheless, the time scale in high-pressure injection is extremely short, and whether there is sufficient time to reach the equilibrium state has not been confirmed. In this study, a non-equilibrium evaporation model is proposed to investigate the non-equilibrium effect on spray evolutions. First, a non-equilibrium isobaric-isothermal flash is established based on the molecular dynamic simulations and Peng-Robinson equation of state. Then, a non-equilibrium evaporation model incorporating the non-equilibrium isobaric-isothermal flash model is implemented into the Eulerian-Lagrangian spray model. Good agreements with the measured penetration lengths of sprays have been achieved. The results reveal that the evaporation time of a single droplet and the liquid penetration length of spray are underestimated by 7.3 % and 8 %, respectively, due to an overestimation in the interfacial vapor molar fraction under the equilibrium assumption at 800 K and 2.0 K. Besides, the non-equilibrium effect is found to significantly alter the formation of lean and moderately fuel-rich mixture, while it only has a slight influence on the fuel-rich mixtures. Finally, the thermodynamic non-equilibrium effect in sprays is suggested to be considered when the ambient pressure exceeds 3.0 MPa or the ambient temperature surpasses 800 K.