Development of a simplified dynamic model for a piezoelectric injector using multiple injection strategies with biodiesel/diesel-fuel blends

Using biodiesel/diesel fuel blends and multiple injection strategies in diesel engines have shown promising results in improving the trade-off relationship between nitrous oxides and particulate matters. In order to explain the effect of both technologies on exhaust emissions and to develop adequate control strategies, the behavior of the injection process needs to be thoroughly understood. This paper proposes a simplified model of an indirect-acting piezoelectric diesel injector. The objective was to build a model that can predict the highly transient effect of short injection events and the impact of biodiesel with sufficient precision while being sufficiently fast to be implemented in an engine control unit (ECU) for real-time closed-loop flow-rate monitoring. The model was validated against experimental results for different injection pressures as well as different energizing times (ETs) and dwell times (DTs). When comparing the use of biodiesel against diesel, simulation of the needle lift showed that there was a critical ET for which both fuels yielded the same injection duration. For shorter energizing times, the biodiesel injection duration was shorter than for diesel, while longer energizing times presented the opposite behavior. The injection duration for the different blends falls between the pure-fuel situations. The use of constant properties (density, viscosity) and constant discharge coefficient (Cd) showed no major loss in the precision of the flow-rate estimation, but revealed a great gain in calculus time while the use of pressure dependent bulk modulus proved to be essential in order to have no drastic changes in the final predictions. Finally, the model presented in this study showed that it could estimate with sufficient precision the opening and closing delay of different biodiesel/diesel blends for multiple injection strategies while yielding a calculus time enabling implementation in an ECU.