Analytical model for liquid film evaporation on fuel injector tip for the mitigation of injector tip wetting and the resulting particulate emissions in gasoline direct-injection engines

Unevaporated fuel films forming on the fuel injector tip of gasoline direct-injection engines burn in a diffusion flame at the time of spark, producing particulates and at some operating conditions, these films have been identified as the dominating source of particulate emissions. This work developed an analytical model for liquid film evaporation on the injector tip, that is, injector tip drying, for the mitigation of injector tip wetting and the resulting particulate emissions. The model explains theoretically how fuel films on the injector tip evaporate with time from the end of injection to the spark. The model takes into consideration engine operating conditions, including engine load and speed, tip and fuel temperatures, gas temperature and pressure, and fuel properties. The model explains the observed trends in particulate number (PN) emissions due to injector tip wetting. Engine experiments were used to validate the model by correlating the predicted film mass at the time of spark to measurements of PN emissions at different conditions. A tip drying time constant was also defined and was found to correlate well with the measured PN for all conditions tested. This time constant is a deterministic factor for mitigating tip wetting. In general, the results indicate that the liquid film evaporation on the injector tip follows a first order, asymptotic behavior. Furthermore, the tip drying physics causes the observed increasing and decreasing non-linear trends in PN emissions with the engine load and the available time for tip drying, respectively. Additionally, the liquid film evaporation on the injector tip is highly sensitive to most of the injector initial and boundary conditions, including the initial film mass after the end of injection, the wetted surface area, the available time for tip drying and the injector tip temperature. The initial film temperature has the least effect on film mass evaporation.