### Analysis of pressure wave dynamics in fuel rail system

B Alzahabi, K Schulz

#### Abstract

A model of an amplified common rail fuel system is simulated in Matlab toanalyze the wave mechanics in the rail. The injectors are modeled as asystem of linear and non-linear ODE’s consisting of masses, a helical spring,compressibility effects from fluid volumes, and hydraulic flow throughorifices. The injector simulation then predicts the rate of oil consumption,which is then input into the rail model.The rail is modeled in three sections which are coupled together. The pointswhere the coupling occurs are the locations where the current firinginjector and the pump supply are connected to the rail. This allows themodel to control the pressure and velocity (as boundary conditions) atthese points. The rail model is based on the 1D, undamped wave equation,in a non-dimensional form [1] (in the position variable, x.) The Reduction ofOrder method was used to solve the wave equation with the Matlabfunction PDEPE.The model was run with two different sets of initial conditions - nominal(constant pressure and zero velocity,) and worst case using a simplifiedrepresentation of the pressure and velocity distribution at start of injection.This was done to determine the effect of rail waves at the start of injection,on the output of the model. The variation in fuel delivery, due to the variationin rail pressure, was then evaluated at three operating conditions - Idle,Peak Torque (PT) and High Speed Light Load (HSLL.) The simulation outputis then compared to analytical solutions of two forms of simplifiedgeometry, using the product method to solve the system [1.]

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#### References

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L. Zhong, et al., “Effect of Cycle to Cycle Variation in the Injection Pressure in a Common Rail Diesel Injection System on Engine Performance”, SAE paper 2003-01-0699. CrossRef

Qiang Hu, et al., “Prediction of Pressure Fluctuations Inside an Automotive Fuel Rail System”, SAE paper 1999-01-0561. CrossRef

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DOI: http://dx.doi.org/10.1260/175095408786927444

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