Modelling of pressure waves in the Common Rail Diesel Injection System
The aim  is to describe the behaviour of the pressure in the Common Rail Diesel Injection System mathematically. In order to understand the wave phenomena that may occur in the system, a physical model is desired. The model will be used for examining the cause of problems in the Common Rail Diesel Injection Engine that arise at certain critical working conditions. Another object of a model of the system is to use it together with a model of the injector for diagnosis purposes.
  Two different modelling methods are used and both models are based on well known physical relations. The first approach implies that the pressure waves are approximated with mechanical waves in a mass spring system. The model developed by this method does not describe the measured data very well, which mainly depend on too inaccurate estimations of physical parameters. The second method is developed from the general wave equation. This model describes the system more strictly and presents accordingly much better results than the first model. For the above explained purposes the latter model is recommended. Simulations show satisfactory results but improvements are naturally possible.
Since the models are developed for a certain working point they cannot be expected to be valid for all working conditions.
  Key words: Common Rail Diesel Injection System, physical modelling, superposition of waves, wave equation, partial differential equation
  Symbols used in the wave equation model
Abbreviations
CR Common Rail CDI Common Rail Diesel Injection ECU Engine Control Unit DI Direct Injection IDI Indirect Injection
Background
 The Common Rail Diesel Injection System (CR System) is a relative new injection system for passenger cars and Trucks. The main advantage of this injection system compared to others is that due to the high pressure in the system and the electromagnetically controlled injectors it is possible to inject the correct amounts of fuel at exactly the right moment. This implies lower fuel consumption and less emissions.
 However at certain working conditions (i.e. different combinations of engine speed and pressure) the OM613 Common Rail Diesel Injection (CDI) Engine does not run smoothly. The reason may be that there is a significant difference in the injected fuel quantities among the injectors. Measurements show that the pressure at the injectors differ in behaviour, which may explain the varying injected amounts. The system can be described by superposition of many different pressure waves and a wave phenomenon may be present. If it is known how the total pressure wave along the common rail (which from now on will be named rail only) behaves, it may be possible to avoid the varying injected amount by either controlling the injectors separately or by moving the injector pipes to more favourable locations.
  The Common Rail Diesel Injection System
The CR System  is an accumulator injection system used in Dodge Cummins CR. It provides more flexibility than any previously used injection system, but it also needs to handle much higher pressure. A brief introduction to this system follows, but further information about this system can be found in
      The Common Rail Diesel Injection System.
Injection systems
 The CR System is an injection system used in direct-injection engines. It is common to differentiate between direct-injection (DI) engines and indirect-injection (IDI) engines. In IDI engines the fuel is injected into a prechamber in which the combustion is initiated  In the DI engines the fuel is injected directly into the cylinder’s combustion chamber. DI engines feature fuel savings of up to 20 percent compared with IDI engines, but the latter,The high pressure circuit    Generates less noise than the former. The advantage of the CR System is the high pressure in the rail, which makes it possible to use precise and highly flexible injection processes. Other injection systems are the VP44 radial-piston distributor pump and the PE in-line injection pump. The first system is an electronic diesel control (EDC) injection system in which the injections are controlled by a solenoid valve. Both the duration of the injection and the injected amount of fuel depend upon the time the valve is open and the system is accordingly named time-controlled injection system. In this system fuel supply, high pressure generation and fuel distribution are all combined in one component. The PE inline injection pump creates high pressure for each cylinder in its own high-pressure chamber. The system is called a helix-controlled injection system, since the duration of injections and the injected fuel quantity are functions of the position of the so-called helix with reference to a spill port. This system is suitable for providing large injected fuel amounts, which makes it commonly used in heavy truck engines.
    The CR System system can be divided into three different functional groups
• The high pressure circuit
• The low pressure circuit
• The ECU (Engine Control Unit) with sensors
      The high pressure circuit
The high pressure circuit contains a high-pressure pump, a pressure-control valve, a high pressure accumulator (the rail) with a rail-pressure sensor, high pressure connection lines and the injectors . This part of the CR System is responsible for generating a stable high pressure level in the rail and for injecting the fuel into the engine’s combustion chambers. The high-pressure pump forces the fuel into the rail and generates a maximum pressure of (oem) bar. There is one injector for each cylinder and the injectors contain a solenoid valve which receives a current signal as an ’open’ command from the ECU at the time for injection. Every time an injection occurs, fuel is taken from the rail. The pressure control valve attempts to keep the pressure at the desired level. This control is based on measurements from the rail pressure sensor       The low pressure circuit
The low pressure circuit provides the high pressure part with fuel. The fuel is drawn out of the tank by a pre-supply pump and forced through the lines and through a fuel filter to the high-pressure pump in the high pressure circuit. Uninjected fuel from the rail is led back to the tank through the pressure control valve.
    The ECU with sensors
  The ECU evaluates signals from different sensors and supervises the correct functioning of the injection system as a whole. The main tasks for the ECU in the CR System are to keep the pressure in the rail at a desired level by controlling the pressure control valve, and to start and terminate the actual injection processes. Some of the quantities that the ECU calculates from the sensor measurements (e.g. rail pressure, engine speed, accelerator-pedal position and air temperature) are the correct quantities for fuel injections and the optimal start and duration of the injections.
The Common Rail Diesel Injection System from a modelling point of view
The CR System has already been modelled by using neural networks [3]. For this method a huge number of data-sets is needed to get reliable results. The idea of modeling the system physically was brought up in order to develop a method to estimate the injected fuel quantities as well as to find out more about the wave phenomena in the rail.
In this chapter, the physical behaviour of the different parts of the system will be described. The desired properties of the model are also stated here.
  The aim of the model and the desired properties
The main aim of the model is to explain the behaviour of the pressure waves in the high pressure accumulator of the system. The desired information is pressure signals from points along the rail. By comparing these signals it may be possible to understand why the measured pressure signals at the injectors differ. If a standing wave phenomenon is present, it would be shown in the model as well.
Since points along the rail are most interesting, the waves in the system are approximated to only propagate in one dimension. The model is developed for the working point with an engine speed of 2300 rpm, a pressure level in the rail of ( ) bar and a temperature of 40.5􁪽, and then an analysis is made to examine the domain of validity. The flow of the fuel in the rail is neglected in comparison with the speed of a pressure wave in the fuel. This can be done since the speed of the pressure wave is so high (i.e. between 1350-1480 m/s depending on the working conditions).
    Measured signals used in the model
A general description of the model with input and output signals is given in figure 3.1. The pump signal is a pressure signal measured at the end of the rail where the pipe from the pump is connected, when the system is running normally except that there are no injections. This signal is used as an input to the system at this point. The injection signals are measured at the valve ends of the injection pipes. The signal from one injector pipe (the sixth) is used as input at all the 6 points where the injection pipes are connected to the main rail. The reason for this is that, apart from a time delay, these signals are supposed to be equal. The result of the difference in the signals is not of interest in this study. The aim is to find out what happens in the
Rail signal
               when everything works properly. The rail signal is measured by the same sensor as the pump signal but with injections. This signal is the only available validation signal. The pressure at points along the rail are outputs from the model. It is interesting to compare these outputs with the injection signals to see that the general shape of the signals are the same. Frequencies above ( ) are considered as noice and all the measured data sets are lowpass filtered with this cut-off frequency before they are used.
   The pump
The high pressure pump, shown in figure, is connected to the camshaft and therefore driven with half the engine speed. It contains three pump plungers which are pumping fuel into the high pressure pipe that leads to the main rail. In an ideal situation the pressure signal from the pump would have been a constant signal. In reality the signal contains mainly three sinus-waves with different phase. The main frequency of this signal is therefore three times the frequency of the pump (i.e. the frequency of half the engine speed), which means around ( ) at an engine speed of 2300 rpm  . The sinus waves derive from the motions of the pump plungers in the pump.
.
CP3

The high pressure pump.: The pump signal. The pressure control valve
The pressure control valve at the end of the rail is electromagnetic and it is controlled by a rectangular pulse signal from the ECU. The frequency of the signal is always around (M), but the duty cycle, the relative width of the pulses, depends on the mean pressure at each working point. The ECU gets information about the pressure level from the sensor in the rail and calculates an adequate pulse width. The current pulse from the ECU controls a ball that is located in the middle of the opening.
shows. For a certain pressure level the ball is expected to stand still since the frequency of the pulses is quite high. Nevertheless a ( ) frequency component is found when frequency analyses of the pump signal and the rail signal are made. It can be assumed that this derives from the current pulse.
  The injectors
The injectors are responsible for injecting fuel into the combustion chamber. The amount of injected fuel and the time for injections are determined by the ECU and control signals are sent to the electromagnet in the injector
     The pressure control valve.
Measured signals used in the model
The opening and closing of the valve in the injector are then controlled by the electromagnet. First there is a pilot injection and
  then a main injection. Since the valve in the injector is closed very quickly, a so-called water hammer is formed in the injector pipe.
The water hammer is created when a valve is closed quickly in a pipe. To be able to describe the phenomenon the flow of the fluid can not be neglected. Consider the valve in the injector to be open and a flow in the injector pipe. There is an initial pressure p0 and an initial velocity v in the pipe as shown in . Suddenly the valve is closed, which creates a pressure wave that travels toward the main rail. The fluid between the wave and the valve will be at rest but the fluid between the wave and the rail will still have the initial velocity. When the wave reaches the main rail the whole pipe will have the pressure, but the pressure in the rail will still be ( ). This imbalance of pressure makes the fuel flow from the pipe back to the rail with the velocity v and a new pressure wave is created and it travels toward the valve end of the pipe . When the wave reaches the end, the fluid is still flowing. The pressure at this point will be less than the initial value, ( ). This leads to a rarefied wave of pressure in the other direction When this wave reaches the injectors which get more powerful with injections than without, since the amplitudes of the frequencies are higher

 

 3.1

 

  A DFT of the rail signal is produced in the same way as the DFT of the pump signal and it is shown in. Besides the frequencies from the pump described above, there is a series of multiple frequencies coming from the injections. For this working point (engine speed 2300 rpm) there are 6 injections each cycle ( ), which leads to a main frequency at ( )for the injections. Since this is also a multiple of the main frequency from the pump, the amplitude of this frequency becomes high. , the multiples of the main frequency from the injections are marked. The damped oscillations in the injection signals result in many frequencies between ( ) There are different frequencies in all the injection signals and the signals affect each other, which makes it difficult to determine the source of a certain frequency.
  Other working points
frequency spectra for different working points . Both spectra are developed from data sets with injections.  the engine speed is fixed at around 2300 rpm and the pressure level is varied. As the mean pressure increases the amplitudes of the frequencies belonging to the pump and the injections increase as well. The reason is that the amplitude of the pump signal (in the time domain) rises with the pressure. The frequencies around ( ), from the damped oscillations in the injection signals, show a pattern of interest. The amplitude of this frequency region is varying a lot along the pressure axis. It is natural that the working points with lower pressure also get lower frequency amplitudes, but the behaviour around ( ) bar is difficult to explain. In this spectrum  a movement along the frequency axis for the frequencies around ( ) is visible. It seems to be a peak that increases in frequency with increasing pressure. This phenomena does not appear , which derives from data sets measured with mean pressure around ( ) bar and with varied engine speed. This means that the cause of this frequency depends on pressure but not on the engine speed.