Modeling of fuel line wave propagation induced by injector operation

Wave propagation in a fuel line bounded on one end by a pressure regulator creating a constant head and on the other by a single fuel injector creating a time dependent flow rate is studied. It is found that a model consisting of a linearized wave equation and a linearized injector/fuel line boundary condition (including lumped damping) is convenient for analytical work. A general closed form solution of the pertinent equations can be found in terms of a recursion relation which holds for any injection history. Representative solutions are reported for sinusoidal and step function (sudden injector opening or closing) injection histories. Solutions for step function histories are superimposed to create predictions for a variety of periodic (but nonsinusoidal) injection histories. It is found to be possible to extract limiting steady state solutions from these general transient results. Predictions are compared to experimental data taken on a system consisting of a fuel line bounded at one end by a pressure regulator and on the other by a single fuel injector. The comparisons are shown to verify the behavior predicted by the model. It is concluded that the model is a useful tool for the analysis of fuel line wave propagation phenomena. It can be easily extended to more complex geometries.