Modeling of Dynamic Responses of Injectors for an Automotive Fuel Rail System

This paper presents a computer model for simulating dynamic responses inside an injector of an automotive fuel rail system. The injector contains a filter at the top, a coil spring in the middle, and a needle and orifices at the bottom. The equations of motion for unsteady one-dimensional flow are derived for the fluid flowing through the injector. The needle motion is described by a second order ordinary differential equation. The forces exerted on the needle include the magnetic force that controls the opening and closing of the injector and the coil spring force. To account for the loss of kinetic energy, we define two loss factors K_a and K_b. The former describes the loss of kinetic energy as fluid enters the injector through the filter at the top, and the latter depicts that as fluid is ejected into a large chamber through the passage between the needle and the needle seat and across four orifices at the bottom of the injector. In particular, the loss factor K_b is defined as a function of the displacement of the needle motion. Further, we require the pressure fluctuations inside the injector to satisfy a damped wave equation. The responses of the injector are then obtained by solving a set of seven equations simultaneously, and the pressure fluctuations at any section inside the injector can be determined uniquely. The predicted pressure fluctuations inside the injector are compared with the measured data with various pulse widths and speeds. Good agreement is obtained in each case.