Tetrault, P., Plamondon, E., Breuze, M., Hespel, C. et al., "Fuel Spray Tip Penetration Model for Double Injection Strategy," SAE Technical Paper 2015-01-0934, 2015, doi:10.4271/2015-01-0934.
In this paper, a semi-empiric fuel spray tip penetration model is proposed. It is applied to single and double injection strategies taking into account the early and far field penetration. The model is based on the momentum flux as initially proposed by  for single injection but it is derived from mean mass flow rate herein. Fuel spray interaction with entrainment air is taken into account for the second injection. The proposed model is calibrated and validated using data from 9 experiments conducted with an indirect piezoelectric diesel injector under various injection strategies. The experiments included 1) injection rate measurements using the Bosch method to determine mean mass flow rate during injector opening as well as obtaining injection duration which are both entry parameters to the model; 2) Fuel spray tip penetrations were measured in a pressure vessel using high speed photography for single and double injection strategies. The experimental results were used to calibrate the model's constants and to verify the model's ability to predict spray behavior. Finally, the experimental results for some fuel injection strategies have shown that there is an interaction between the first and second spray and the paper shortly discusses these cases.