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Dual fuel injector modeling by finite difference method Lim, Clement 2000

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DUAL FUEL INJECTOR MODELING BY FINITE DIFFERENCE METHOD by CLEMENT LEVI B.A.Sc, The University of British Columbia, 1997 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF MECHANICAL ENGINEERING We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA NOVEMBER 2000 © Clement Lim, 2000 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia Vancouver, Canada DE-6 (2/88) ABSTRACT The development of natural gas fueling for diesel engines is a new solution to reducing diesel engine pollutants. To convert existing diesel engines to support the use of natural gas, a new type of injector must be designed. A model to predict the hydraulic and mechanical operation of injectors that introduce the natural gas into the combustion process for diesel engines will significantly lower design times and development costs. The developed injector model couples the physical kinematics of the mechanical components with the fluid mechanics of the diesel fuel and the compressed natural gas. Development of the injector model began with the modeling and validation of the diesel injector, followed by modeling and validation of the more complex gas injector. The final version of the injector simulation uses a finite difference method, where specific reservoirs at important regions in the injector are connected by passages separated into volumes of finite length. The models are validated using experimental means with the use of an Injector Test Rig. Both a diesel injector and gas injector was modified to allow the capture of hydraulic pressure data within the injector. Comparisons of model results and experimental results of this hydraulic pressure show excellent agreement for both injectors. A device was also designed for the gas injector to measure the relative timing of the individual diesel and gas jets. Comparison of the diesel and gas needle lifts from the gas injector model with the experimental data obtained from this device shows good agreement. The final version of the injector model accurately represents both the diesel and dual fuel injectors within an acceptable amount of error associated with experimental conditions. A Lax-Wendroff velocity diffusion algorithm is used to eliminate the instabilities associated with the numerical model. The accuracy of the injector models primarily depends on the precise geometrical representation of the injectors with a secondary effect coming from - effect of discharge coefficients or leakage tolerances. A study of the cycle to cycle variability for the experimental data was performed but was identified as being insufficient to establish complete confidence in the consistency of the experiment. iv TABLE OF CONTENTS ABSTRACT ii TABLE OF CONTENTS iv LIST OF FIGURES vii LIST OF TABLES x ACKNOWLEDGEMENTS xii 1.0 INTRODUCTION 1 1.1 Motivation for Research and Desired Results 2 1.2 Methodology 3 2.0 THE INJECTORS 5 2.1 Diesel Injector Geometry and Nomenclature 5 2.1.1 The Poppet Control Valve 9 2.1.2 The Cam and Plunger 10 2.1.3 Check Valve 15 2.1.4 Needle and Spring Geometry 16 2.2 Gas Injector Geometry and Nomenclature 19 2.2.1 Gas Injector Mechanics 21 2.2.2 Diesel Intensifier 22 2.2.3 Dual Needle Interaction 23 3.0 PREVIOUS WORK 28 4.0 THE EXPERIMENTAL INVESTIGATION 34 4.1 Experimental Apparatus 34 4.1.1 Injector Modifications 35 4.1.2 Injector Test Rig 36 4.1.3 6V92 Engine 39 4.1.4 Instrumentation 39 4.2 Diesel Injector Typical Results 43 4.3 Gas Injector Typical Results 45 4.4 Experimental Consistency 48 4.5 RBOIdata 51 5.0 FINITE DIFFERENCE NUMERICAL SIMULATION 53 V 5.1 Physical Assumptions 53 5.1.1 Diesel Liquid Properties 53 5.1.2 Gas (CNG) Properties 56 5.1.3 Poppet Open and Close Time 57 5.1.4 Discharge Coefficients 59 5.1.5 Pressure Losses 60 5.2 Equations 61 5.2.1 Liquid Reservoir Equation 61 5.2.2 Gas Reservoir Equation 63 5.2.3 Finite Difference Equations 64 5.2.4 Choking of Gas Flow 69 5.2.5 Boundary Conditions 70 5.2.6 Cylinder Pressure 72 5.3 General Model Layout 73 5.4 Time Reference 76 5.5 Model Numerics 80 5.5.1 Equation Specifics 80 5.5.2 Time Step Considerations 82 5.5.3 Numerical Stability 83 5.5.3.1 Causes of Instability 83 5.5.3.2 Solutions to Instabilities 84 5.5.3.3 Successive Over-Relaxation 88 6.0 RESULTS 89 6.1 Experimental-Model Comparisons 89 6.1.1 Diesel Injector Results 89 6.1.2 Gas Injector Results 91 6.1.3 Relative BOI Results 93 6.2 Sensitivity Analysis 96 6.2.1 Change in Discharge Coefficients 97 6.2.2 Change in Poppet Lift and Close Time 99 6.2.3 Effect of Leakage 101 vi 6.2.4 Effect of Transducer Modification . 103 7.0 CONCLUSIONS 105 7.1 Research Accomplishments 107 7.2 Recommendations for Future Work 108 REFERENCES 110 APPENDIX A - DIESEL INJECTOR DRAWINGS 111 APPENDIX B - EFFECT OF WALL EXPANSION ON SPEED OF SOUND AND FLUID BULK MODULUS 119 APPENDIX C - SINGLE CHANNEL SIMULATION 124 APPENDIX D - SUPPLEMENTARY DATA FROM ITR EXPERIMENT 128 APPENDIX E - SUPPLEMENTARY 6V92 DATA A 141 APPENDIX F - SUPPLEMENTARY 6V92 DATA B 154 APPENDIX G - GAS INJECTOR CODE 162 vii L I S T O F F I G U R E S Chapter 2 Figure 2.1 - Diesel Injector Assembly 6 Figure 2.2- Nomenclature Diagram 7 Figure 2.3-Poppet Valve Schematic 9 Figure 2.4 - Cam-Plunger Arrangement 10 Figure 2.5- Cam Crank Convention Diagram ' 11 Figure 2.6- Plunger Lift vs. Cam Angle Degrees for ITR 12 Figure 2.7 - Plunger Clearance 14 Figure 2.8- Check Valve Operation 15 Figure 2.9- Diesel Needle Free Body Diagram 17 Figure 2.10- Gas Injector Stack Assembly 20 Figure 2.11 - Dual Needle Orientations 24 Figure 2.12 - Diesel and Gas Needle Free Body Diagram • 25 Chapter 4 Figure 4.1 - Pressure Transducer Passage 35 Figure 4.2- ITR Schematic 37 Figure 4:3 -Injector Test Rig 38 Figure 4.4- RBOI Measurement Rig 41 Figure 4.5- RBOI Measurement Device Mounting 42 Figure 4.6- 6V92 Experimental Pressure Traces 44 Figure 4.7 - Poppet Pressure vs. CA Rel TDC - Gas Injector 47 Figure 4.8- 6V92 Diesel Injector Experimental Consistency 48 Figure 4.9- Gas Injector Experimental Consistency 6V92 Tests 49 Figure 4.10- Gas Injector Experimental Consistency ITR 50 Figure 4.11 - Typical RBOI curve ITR Tests 51 viii Chapter 5 Figure 5.1 - Effect of Pressure on Bulk Modulus _ _ _ 54 Figure 5.2 - Poppet Position vs. Crank Angle 58 Figure 5.3- Finite Difference Subdivision 64 Figure 5.4- Crank Shaft Schematic 72 Figure 5.5- General Model Layout Flowchart _ _ 74 Figure 5.6- Experimental Injector Pulse Voltage vs. Time . 77 Figure 5.7- Cam Reference to TDC of Piston 79 Figure 5.8- Cell Velocity Distribution (Passage 4) 86 Figure 5.9- Diffusion Coefficient Comparison (Cell Velocity Passage 4) 87 Chapter 6 Figure 6.1 - Poppet Pressure Traces - Diesel Experimental-Model Comparisons 90 Figure 6.2- Poppet Pressure Traces - Gas Experimental-Model Comparisons 92 Figure 6.3 - RBOI Experimental-Model Comparisons ' ' 94 Figure 6.4- Transducer Pressure Profiles for Sensitivity Analysis 98 Figure 6.5- Transducer Pressure Profile for Poppet Open/Close Sensitivity 100 Figure 6.6- Transducer Pressure Profile for Leakage Tolerance Sensitivity 102 Figure 6.7 - Effect of Transducer Passage on Injector Pressure 103 Figure 6.8- Effect of Transducer Passage on Needle Lifts 104 Appendix A Figure A.l - Diesel Injector Assembly Figure A.2- Diesel Injector Body Figure A.3- Diesel Injector Stack Figure A.4- Diesel Injector Check Valve Figure A.5- Diesel Injector Spring Holder Figure A.6- Diesel Injector Tip Figure A.7 - Diesel Injector Needle 112 113 114 115 116 117 118 ix Appendix B Figure B.l - Pressure Wave Control Volume 120 Figure B.2 - Thick Wall Nomenclature 122 Appendix C Figure C.l - Single Channel Geometry and Initial Conditions 125 Figure C.2- Pressure Output from Single Channel Simulation 126 Figure C.3- Maximum Error between Non-Diffused and Diffused Solution • 127 X LIST OF TABLES Chapter 4 Table 4.1 - 6V92 Experimental Conditions 43 Table 4.2-Gas Injector ITR Test Conditions 46 Chapter 5 Table 5.1- Gas Injector Reservoir Values . 81 Table 5.2- Passage Information 82 Chapter 6 Table 6.1 - Diesel Injector Experimental-Model Comparison Loads 90 Table 6.2- Gas Injector Experimental - Model Comparison Loads 91 Table 6.3- RBOI Numerical Comparison 95 Table 6.4 - Discharge Coefficient Sensitivity Conditions 97 Table 6.5-Poppet Open/Close Sensitivity 100 Table 6.6-Leakage Tolerance Sensitivity 102 Appendix D Table D. 1 - 800 RPM-12 °BOI 9 °PW 129 Table D.2 - 800RPM-12°BOI 12.4°PW_ 130 Table D. 3 - 1000 RPM-12 °B019 °PW 131 Table D. 4-1000 RPM -12 °BOI 13.1 °PW 132 Table D.5 - 1200 RPM-12 °BOI 9 °PW 133 Table D. 6 - 1200 RPM-12 °BOI 13.3 °PW 134 Table D. 7 - 1400 RPM-12 °BOI 9 °PW 135 Table D.8 - 1400 RPM-9.8°BOI 13.5° PW 136 Table D.9 - 1400 RPM-9.5 °BOI 3.9° PW (No Gas Injection) ' 137 Table D. 10 - 1600 RPM-8.7 BOI9.6 PW 138 Table D.H - 1800RPM-9.3°BOI 15.4°PW 139 xi Table D. 12 - 1800 RPM-12 °BOI 18.6 °PW . 140 Appendix E Table E. 1 - 600 RPM-2.75 BOI 5.4 PW 142 Table E2 - 600 RPM-2.5 BOI5.7 PW - 143 Table E.3 - 600 RPM-1.5 BOI 5.8 PW 144 Table E. 4 -1200 RPM-11 BOI 8.1 PW 145 Table E.5 - 1200 RPM-10 BOI 8.3 PW 146 Table E6-1200 RPM-10.5 BOI 20.1 PW 147 Table E 7 -1500 RPM -9 BOI 20.8 PW 148 Table E.8 - 1800 RPM-11 BOI 8 PW 149 Table E.9 - 1800 RPM-8.75 BOI 20.5 PW 150 Table E. 10 - 2100 RPM-11 BOI 8.1 PW 151 Table Ell- 2100 RPM -9 BOI 20.4 PW 153 Table E. 12 - 2100RPM-9.5BOI 20.4PW 154 Appendix F Table F. 1 - 600 RPM-3 BOI 6.5 PW 156 Table F.2 - 600 RPM-2.75 BOI 5.7 PW 157 Table F. 3 -1200 RPM -8 BOI 20.1 PW 158 Table F. 4 - 1200 RPM-11 BOI 9.1 PW 159 Table F.5 -1500 RPM-8 BOI20.9 PW 160 Table F. 6 - 1800 RPM -9.75 BOI 7.2 PW 161 Table F. 7-2100 RPM -12.75 BOI 8.1 PW 162 ACKNOWLEDGEMENTS The bulk of the experimental work performed and the associated results included in this thesis could not have been done without the help of Radu Oprea and Jeff Kohne, part df the Westport Research team at the time. Their help was invaluable in the experimental setup and testing, as well as the vast amounts of troubleshooting involved. I also thank David Mumford at Westport Research for his help in the collection of data vital to the modeling process, and for all his help coming from his modeling expertise. The amount of camaraderie and intellectual stimulation provided by my colleagues has also been of great importance to me. I am fortunate to have been able to share experiences and ideas over the past few years with, among others, Al Reid, Petro Lappas, Anne-Marie Baribeau, Gord Mctaggart-Cowan and Conor Reynolds. I thank Dr. Philip Hill, my supervisor, for presenting me with the opportunity to conduct this research, and for his guidance as each problem was overcome. The amount of confidence that he placed in me and the corresponding freedom to shape my research as I desired was not taken for granted. Finally, I owe thanks to my family for their support and encouragement. 1 Chapter 1 Introduction Within the last few years, environmental issues have become increasingly apparent as people are made aware of the problems surrounding the ecological aspects of the planet. This awareness has spread into the political community as well, forcing politicians to initiate more stringent pollutant restrictions on the industrial sector and the automotive sector. While spark ignition passenger vehicles are becoming more efficient and more environmentally sound, transport vehicles such as buses, semi-trailer trucks and trains that operate on diesel fuel have not fundamentally changed in the past twenty years. Although diesel operated vehicles make up a relatively small percentage of the total amount of vehicles on the road, the pollutants emitted by this small percentage is excessive. New emissions standards put in place by North American governments have placed the entire diesel industry under immense pressure to reduce these emissions. An idea was developed to replace the main fuel in diesel engines with an alternative, more environmentally friendly fuel, namely compressed natural gas (CNG). In general, natural gas burns cleaner, producing less nitrogen oxides (NOx) and particulate matter. However, because diesel engines rely on the auto-ignition of the fuel due to piston compression rather than a localized spark for combustion, problems will occur when replacing the fuel in a diesel engine with natural gas. Diesel fuel auto ignites at approximately 800 K, whereas CNG will auto-ignite at about 1200 K. The compression ratio in a diesel engine is set to provide a temperature of 800 K to ignite the diesel fuel, presenting engineers with a design problem. One possible solution to this problem is to redesign the engine to provide a substantial increase in compression ratio, effectively increasing the temperature in the combustion 2 cylinder to 1200 K at which point the CNG will auto-ignite. However, this solution is very expensive since it would force potential customers to purchase an entirely new engine. In addition, an increase in compression ratio may not be mechanically feasible for stress and heat transfer reasons. A more cost-effective solution to this problem is to use a small amount of diesel fuel as the ignition source. This diesel pilot will ignite under standard, operating conditions and, by a chain reaction, begin the combustion of the secondary CNG fuel. Using a small amount of diesel fuel as the ignition source provides uniform combustion of the CNG with no modifications required to the engine itself. Only a replacement of the existing diesel injectors with new dual fuel injectors is needed. The design of a new injector to supply both diesel and CNG, with strict design conditions on the relative timing, fuel ratios and injection properties of both the diesel and natural gas jets is then required. The design of a new injector to supply the injection mass, momentum and timing needs to be implemented. The difficulties in designing an injector that fits the criteria required for a successful and optimal injection show the need for mathematical simulation of the internal injector dynamics to facilitate injector design. Injector modeling has been done in the past for several diesel injector designs, with different numerical methods. However, the gas injector, with its increased mechanical and geometrical complexity and its accommodation of two fuels, has never been modeled, and will be done for the first time in this thesis. 1.1 Motivation for Research and Desired Results The motivation for the creation of a numerical injector model is for a tool to assist with the design of injectors. A numerical model will help the design of injectors by being able to predict injection timing, internal hydraulic pressures and injection fuel quantity. Coupling this hydraulic model with a finite element analysis can show regions of stress concentration due to movements and pressures, to be used for failure prediction. The hydraulic model can also be used to troubleshoot existing injectors or new injector 3 designs. The underlying need to develop an injector model is to save time and money. If we can predict problems before they occur, we can save time in the development of a new injector, as well as money because we will not be manufacturing faulty injectors. The desired result from this research is to provide a working model that is able to predict the operation of a dual fuel injector. The model should also have the flexibility to predict the operation of multiple types of injectors, with different geometry and input parameters. The model should be very accurate, with verification done by experimental means, and easy to modify for any future user. 1.2 Methodology A gradual progression in developing an injector model will make it easier to debug program errors, will help in the understanding of the injector mechanics and will establish a baseline for accuracy comparisons. The injector that we will model first is the standard diesel unit injector. The gas injector model will then be built upon the code from the diesel injector with the addition of the increased geometrical complexity and the addition of the natural gas. Verification of the accuracy of each model will be performed at distinct intervals. In chronological order, the stages to be accomplished in the project to develop a computer injector model for the gas injector are: 1. Model the diesel injector In this stage we decide upon a modeling scheme, the equations involved in the scheme that is utilized and the numerical method. The decision on a modeling scheme refers to how we will separate the geometry of the injector to accommodate ah easy implementation of differential equations. The development of the equations requires knowledge of fluid mechanics and the theory involved in this particular hydraulic simulation. The choice of numerical method to be used deals with how we will solve 4 these equations computationally. This stage also includes learning the basics of numerical simulations, research on background materials and also learning the general mechanics of the diesel engine itself. The geometry of the diesel injector is the main data required in this stage. 2. Experimentally verify the diesel injector model To confirm the accuracy of our model, we will compare the results obtained from the model with experimental data. The comparisons between model and experiment will be done using the hydraulic pressure within one region of the injector. This stage will allow us to become familiar with the experimental apparatus and the injector operation. The main experimental apparatus in this stage is the Detroit Diesel 6V92 engine. 3. Model the gas injector This part will build upon the existing code developed in part 1. The existing theory for the diesel fuel can be copied for the diesel pilot, but new equations need to be implemented for the CNG. Additionally, the new injector brings a more complex geometry, the most predominant being the addition of another needle and extra fuel delivery mechanisms. 4. Experimentally verify the dual fuel injector The verification of the dual fuel injector by experimentation is performed once more to verify the accuracy of the new model. Again, experimental hydraulic pressure from a region inside the injector will be compared to the model. Supplementary information in the form of the relative beginning of injection (RBOI) will further prove or disprove the accuracy of the model. The main apparatus used to experimentally verify the dual fuel injector is the injector test rig (ITR). 5 Chapter 2 The Injectors While there is only one mechanical motion acting on the injector itself, there are many factors that contribute to the overall timing and performance of the injector. These factors include the geometry of the inner passages, the poppet timing, the cam profile, the needle dimensions and the spring properties. Once these factors are set, the entire operation of the injector depends only on rpm, beginning of injection (BOI), and the pulsewidth (PW). The BOI and PW are controlled by the Detroit Diesel Electronic Control (DDEC) that represents these two values as electrical signals sent to the injector. The injectors that are modeled in this thesis are electronically controlled unit injectors. The timing and length of pressurization is controlled electronically rather than mechanically and fuel compression takes place within the injector body. 2.1 Diesel Injector Geometry and Nomenclature The diagram in Fig. 2.1 shows an assembly drawing of the diesel injector. This drawing shows only the relevant regions of the diesel injector as they relate to our model. 6 B O D Y PLUNGER NEEDLE SPRING NEEDLE VALVE NOZZLE HOLES CAM ACTUATED FOLLOWER SOLENOID FUEL INLET/OUTLET CHECK VALVE SPRING HOLDER INJECTOR TIP POPPET VALVE Figure 2.1 - Diesel Injector Assembly The diesel injector can be separated into two main pieces: the injector body and the injector stack assembly. The injector body is comprised of the poppet valve and plunger regions, while the injector stack assembly includes the injector stack, check valve, spring holder and injector tip. An outer casing that connects to the body surrounding the injector stack assembly allows only the very end of the injector tip to protrude. The main passage in the injector stack has a diameter of 1.60 mm. At the check valve, this passage splits into three separate passages of 1.09 mm diameter each. These passages flow around the spring and recombine in the injector tip in a volume that serves to lift the needle and begin the injector. The cam actuated follower is connected to the plunger. This plunger 7 provides the primary compression for the entire injection process. More detailed drawings of the diesel injector are located in Appendix A. Figure 2 . 2 shows the main regions required for simulation of the injector. These passage and volume names will be used throughout the rest of this document. NEEDLE ENTRY PASSAGE PRIMARY NEEDLE VOLUME NEEDLE LENGTH PASSAGE SAC VOLUME-POPPET VOLUME POPPET-PLUNGER PASSAGE PLUNGER PLUNGER VOLUME STACK PASSAGE CHECK VALVE VOLUME CHECK-HOLDER PASSAGE - INJECTION ORIFICE Figure 2.2 - Nomenclature Diagram In reference to Fig. 2 . 2 , a cam initially displaces the plunger. In the plunger volume, the diesel fuel undergoes a change in volume and a corresponding pressure increase. If the poppet valve is not closed, any pressure increase in the plunger volume is immediately relieved through the poppet-plunger passage and is sent back to the return line. However, if the poppet valve is closed, the pressure is then forced down through the injector stack passage. The check valve remains normally closed until the total pressure upstream becomes larger than the downstream pressure past the valve. If the check valve is open, the pressure increase propagates down three separate lines, and recombines at the primary needle volume where it attempts to lift the needle. When the pressure force is large 8 enough to overcome the spring pre-load force, the needle valve will open and injection will occur. It is evident that the dynamics of the fluid pressures are directly a function of the geometry and motion of the mechanical components within the injector. The size of the passages and the small volumes that comprise the inside of the injector control the mass flow and pressure increase within the injector, while the shape and geometry of the needle controls the required pressure increase for injection to occur. The motion of the components in the injector such as the poppet control valve or the plunger can be controlled extremely accurately with computer hardware and accurately machined parts. These passages and volumes are given specific abbreviations in the coding for the model, to reduce the length of the equations. Each of these regions is assigned a specific value, be it length, volume or diameter, measured experimentally from a diesel injector. The injection of the diesel fuel into the combustion cylinder occurs after a series of events have taken place. The flow of events begins with the poppet control valve and ends with the injection of the fuel into the cylinder by the nozzle holes. An investigation of the mechanical components and their role in the injection process is vital to the understanding of the workings of the injector. The main components that control the operation of the diesel injector are the poppet control valve, the cam and plunger, the check valve, and the needle and spring geometry. 9 2.1.1 The Poppet Control Valve A schematic of the poppet valve is shown in Fig. 2.3 below. A more detailed drawing can be found in Appendix A: S E A L I N G S U R F A C E S -• F L O W E N T R Y T R A P P E D V O L U M E ( W H E N C L O S E D ) F L O W E X I T Figure 2.3 - Poppet Valve Schematic P O P P E T CLOSED INFLOW/OUTFLOW TO PLUNGER V O L U M E The first object the diesel fuel entering the injector encounters is the poppet control valve. This valve controls the entire injection process by closing and allowing pressurization to occur downstream of the injector stack, or by opening and allowing the pressure to be relieved through a return line. The poppet is actuated by a solenoid that is attached to the top of the valve. The solenoid is controlled by the DDEC, which supplies current to the solenoid based on the BOI and PW calculated by the load on the engine. Flow enters through a small circular hole at the top of the poppet valve and then flows through the hollow center. When the poppet is open, two situations occur. If the plunger is on its upstroke or refueling cycle, a pressure lower than the fuel supply pressure is created at the plunger volume causing the fuel to flow into the plunger volume and refuel the remaining areas of the injector. An increase in pressure that occurs due to a plunger down stroke is relieved when the poppet opens by forcing excess fuel from the plunger 10 volume, through the poppet-plunger passage to the poppet volume and through the bottom of the poppet. This excess fuel then exits through the circular hole at the top of the valve and exits through the return line. The poppet closes only during the downstroke of the plunger, and when this occurs, any increase in pressure due to plunger movement is now forced down the injector stack and is relieved by the needle valve through injection. 2.1.2 The Cam and Plunger The plunger movement is governed by the rotation of a cam. A schematic of the cam-plunger arrangement is shown below in Fig 2.4. Figure 2.4 - Cam-Plunger Arrangement As shown, the cam does not displace the plunger directly, but pushes down on a rocker arm. This rocker arm then pushes down on the follower connected to the plunger. The contact point of the cam along the length of the rocker arm is not the same for both of our 11 experimental apparatus, the 6V92 engine and the ITR, resulting in different rates of pressure increase for each experiment. To obtain an accurate rate of pressurization due to the plunger for the computer model, measurements are made involving only the plunger movement rather than the cam profile itself. The crank convention for the cam that was used is shown below in Fig. 2.5: 0* D I R E C T I O N O F R O T A T I O N Figure 2.5 - Cam Crank Convention Diagram After attaching a dial gauge to a fixed position on the ITR, the plunger travel was recorded as the cam was rotated by one-degree intervals. The 82° angle represents the first point at which there is a discernible vertical plunger movement. The experimental data measurements are shown in Fig. 2.6 for both the 6V92 and ITR cams. 12 Plunger Travel vs. Cam Angle Degrees 0.012 — Poly. (ITR Plunger Data) | —Poly. (6V92 Plunger Data) Figure 2.6 - Plunger Lift vs. Cam Angle Degrees for ITR The ITR cam has been analyzed mathematically for use in the computer model and is shown. The development of the equations for the 6V92 cam is similar. A regression analysis is applied to the ITR profile to obtain a plunger velocity as a function of local cam angle degrees. The polynomial equation generated by the regression analysis is then used as an input to the model to begin the compression in the plunger volume. Since the injection period is always finished before the cam has reached its maximum lift, and because the refueling of the injector is not considered in this thesis, only the downward stroke of the plunger is needed. The regression fit for the experimental data is superimposed upon the experimental data above. The regression equation that is used is one of a third order polynomial. The equation is: h{0) = -4.5xl(T8 03 -5.479xlO_602 -1.8618x1 (T50+0.010705 (2.1) 13 In the above equation, 0 is the cam angle, in degrees. This angle will be referenced to the crank angle of the combustion cylinder as will be shown later. The coefficient of determination for this regression (R2) is equal to 0.99994. Regression analyses of polynomials greater than that of the third order were also calculated, but only attained an increase in the R 2 value by 0.002%. Thus, a third order polynomial is deemed to have sufficient accuracy and simplicity for our model. In the model, we want the plunger movement as a function of time so first we need to take the derivative with respect to 0. The derivative of the relationship in Eq. (2.1) is: dh , „ . . — = -1.35x10 7a2 - l.O958xlO~50- 1.8618xl0-5 de Since there is a 1:1 ratio between the cam angle and the engine crank angle, we can write: ^ = 6- RPM dt Where RPM is the engine speed in revolutions per minute. We can then modify the derivative as follows. ^L.^l^ = 6.RPM\U5xl0^ey _i.o958xlO-5(0)-1.8618xlO-5l (2.2) dO dt dt L J Equation (2.2) represents the plunger velocity as a function of local cam angle and RPM for the down stroke only. The plunger travel for the Detroit Diesel 6V92 engine differs from that of the ITR in several ways. Firstly the cam is not symmetrical around the 0° mark, but is steeper in one direction. Secondly, the cam rotates in the opposite direction to that of the ITR, causing the motion to be significantly different due to the change in contact point on the rocker 14 arm. Thirdly, the cam is not the same shape as that on the ITR and shows a different maximum stroke at its peak. A higher degree polynomial is required to obtain suitable accuracy for the regression analysis. For the 6V92 plunger, the regression equation equivalent to Eq. (2.1) is: h(0) = 3.894lxl(T1O(0)4 - 3.8392xlO_9(0)3 + 4.0206x1(T6(0)2 + 1.9894x10"5(0) + 1.0402xl0~2 This equation has an R 2 value of 0.99771 The plunger itself has a diameter of 7.5 mm and sits in a hole of side 7.9 mm. A closer view of the plunger arrangement is shown below. 0.2 m m C L E A R A N C E — v Figure 2.7 - Plunger Clearance The 0.02 mm clearance on either side of the plunger allows the fuel to escape through the poppet-plunger passage when the poppet valve is open. Any frictional effects on the fluid motion through this clearance are neglected in our calculations. The clearance farther up is small enough so that the fluid is effectively sealed from the cam follower region. 15 2.1.3 Check Valve The check valve in the injector stack is an important part of the injector assembly. The check valve is there to prevent reverse flow and possible cavitation between the injector tip and the plunger-poppet area. The check valve operation is shown in Fig. 2.8: INJECTOR STACK CHECK VALVE CHECK DISC CHECK VALVE OPEN Figure 2.8 - Check Valve Operation CHECK VALVE CLOSED The differential area between the bottom of the injector stack and the check valve volume allows a disc to be used to prevent reverse flow. When upstream pressure is greater than downstream pressure, the valve is open and a passage is created between the disc and the outer diameter of the recess in the check valve. When downstream pressure is greater than upstream pressure, the disc shifts from the bottom of the check valve to cover the area at the bottom of the injector stack preventing flow of fuel back to the plunger volume. The relevant dimensions near the check valve are as follows: 16 Stack flow passage area: 4(1.6)2 =2.01 mm2 4 Check valve flow area: |[(10.9)2-(10.53)2] = 6.23 mm2 The flow area when the valve is open is comparable to the area of the passage of the injector stack, so flow restriction is negligible when the check valve is open. The initial conditions at the injector tip of the diesel injector are not equal to supply pressure due to the check valve. Initially before the injector is run, the pressure downstream of the check valve will be equal to the pump pressure of the supply diesel fuel. However, after one full rotation of the cam, the region downstream of the check valve will be maintained at a pressure slightly lower than that of the needle lift pressure. This pressure will remain the same until the pressure upstream of the check valve exceeds this at which point the valve will switch to open and provide increased pressurization downstream. 2.1.4 Needle and Spring Geometry The needle geometry and the spring properties determine the injection timing and duration, the most important aspects affecting the combustion process. A free body diagram of the diesel needle forces is shown in Fig. 2.9: 17 S P R I N G F O R C E i P R E S S U R E F O R C E F R O M F L U I D IN S P R I N G CAVITY F R I C T I O N F O R C E ( D I R E C T I O N C H A N G E S WITH N E E D L E M O T I O N ) P R E S S U R E F O R C E F R O M P R I M A R Y N E E D L E V O L U M E P R E S S U R E F O R C E F R O M S A C V O L U M E Figure 2.9 - Diesel Needle Free Body Diagram The plunger compression will cause an increase in pressure upon a differential area of the needle. In addition, the pressure in the combustion cylinder will also act on the bottom of the needle area. These pressure forces will exert a distributed force that pushes against the spring. When the total upward force exceeds the spring pre-load, pressure force from the spring cavity and factional force, the needle will move, opening the passage to the diesel sac, at which point the fuel is injected into the cylinder. As shown in Fig. 2.9, the friction force is imposed upon the upper needle wall. The tolerance between the upper needle and the corresponding wall is small, providing a sealing surface between the primary needle volume and the spring holder. A physical comparison of the forces from the spring and this friction force show that the spring force dominates and thus the factional force can be neglected. A typical needle spring pre-load for the diesel injector is 175 N, and the frictional force is unlikely to exceed 1 N, as observed by manual needle actuation. A typical spring constant for a standard diesel unit injector is 175 kN/m and the maximum lift for a diesel needle is 0.25 mm. The pressure 18 force from the sac volume changes as the needle opens, due to an increase in pressure as fluid flows into the sac volume. In the spring cavity, fluid at pump pressure helps to keep the needle closed. This pressure force is slightly larger than atmospheric pressure and is small compared to the primary needle pressure force. The equation governing the motion of the diesel injector needle is as follows: dUneedle {PpNV A<xf + PsacAsac Pcm^cav ^preload ^ spring^1 needle ^springU needle ^friction) d t mneedle and dh needle =14 (2.3 and 2.4) "needle v ' dt In the above equation, uneedie is the needle velocity and hneedie is the needle lift. Pp-, is the pressure at the primary needle volume acting upon the needle differential area Adif. PsaC is the sac volume pressure acting on the needle area Asac and Pcav is the spring cavity pressure acting on the spring cavity area AcaV. Fpreioad is the pre-load force of 175 N , kspring is the spring constant of 175 kN/m and dspring is the damping coefficient of the spring, taken as 5 Ns/m. Faction is taken as 1 N and can change sign depending on the direction of motion of the needle, and mn e edi e is the needle mass of the diesel needle, measured at 20 mg. Due to the large magnitude of the pressure forces and the spring force, the needle inertia may be negligible since the needle mass is small and the resulting acceleration is a small difference between two large forces. In our calculation however, we will not neglect the effect of needle inertia on the needle lifts in both injectors and in the intensifier motion for the gas injector. 19 There is a relationship between the properties of the spring and the geometry of the needle. The larger the differential area on the needle, the larger the spring force must be to obtain the same injection timing. If we wish to change the injection timing, it is easier to modify the choice of springs rather than to change the geometry of the needle. 2.2 Gas Injector Geometry and Nomenclature In addition to the accommodation of natural gas, the gas injector must control the individual timing and duration of each of the fuels. Externally, the diesel and gas injectors are identical, the exception being a new fuel manifold to introduce natural gas into the gas injector. Internally however, the gas injector body contains several additional passages for supply of the gaseous fuel, and the injector stack is composed of completely different components. The gas injector modeled in this project is the Westport 6F4 injector, designed for use in commercial bus engines, and driven by the 6V92 engine. A schematic assembly drawing of the gas injector is shown in Fig. 2.10. 20 MAIN CONTROL DIESEL SUPPLY DIESEL INTENSIFIER VOLUME 3 (PLUNGER VOLUME) GAS SPRING PASSAGE 3 VOLUME 5 PASSAGE 4 VOLUME 6 DIESEL NEEDLE PASSAGE 5 VOLUME 7 VOLUME 8 SEAUNG DIESEL SUPPLY CNG SUPPLY (2X) CAGE BLOCK CHECK BLOCK DIESEL SPRING PASSAGE 6 CHECK VALVE VENT BLOCK VOLUME + GAS NEEDLE VOLUME 9 INJECTOR TIP PASSAGE 7 VOLUME 10 VOLUME 11 Figure 2.10 - Gas Injector Stack Assembly The plunger volume is connected to the diesel intensifier and to the main control diesel supply. An external pump supplies the sealing diesel at 19.7 MPa, introduced into the injector to force any leakage to flow from liquid to gas. The sealing diesel is introduced at the check valve and directly supplies volume 5. The CNG supply is connected to a specific on-vehicle compressor and is supplied at 19.3 MPa. The gas injector has two concentric needles. The inner one is for pilot liquid diesel injection, while the outer one is for the injection of the gaseous fuel. The injector stack itself is comprised of four separate parts, all of which are combined and covered with an injector casing when the injector is assembled. Unlike the diesel injector, where the components in the injector stack are free to rotate, the stack components in the dual fuel injector are rigidly assembled. The top most piece is called the cage block, the second piece below the cage block is the check block, the third piece is the vent block and finally the bottom most piece is the injector tip. The nomenclature relating to the model is also shown in Fig. 2.10, outlining the multitude of passages and volumes that need to be taken into question when modeling this injector. Physical measurements of the passages and volumes in the gas injector are outlined in section 5.5.1. 2.2.1 Gas Injector Mechanics The gas injector mechanism is complex, due to the number of volumes and passages that pressurize and the number of components that move at the same time. The diesel fuel actually injected into the cylinder for combustion is provided in the vent block and below, and is supplied solely by the sealing diesel supply line. The diesel fuel entering through the poppet valve and compressed by the plunger only serves to move the diesel intensifier and to act as the primary control for the gas needle lift. The diesel intensifier will further compress the sealing diesel and controls the diesel needle actuation. The control fuel for the gas needle is relieved through a vent line located in the vent block just above volume 4. This vent line will open only when the gas needle lifts and is not shown in Fig. 2.10. The sealing diesel, and CNG supply are independent processes that are externally pressurized and enter the injector from separate reservoirs. This design allows the gas needle to lift without the diesel needle opening at all. The main mechanical differences between the gas injector and the diesel injector are the diesel intensifier and the double needle valve design. 22 2.2.2 Diesel Intensifier There are two main reasons for the introduction of the diesel intensifier to the gas injector. Firstly, due to the location of the sealing diesel, compression must be transferred from the cam and plunger to increase the pressure of the sealing diesel to lift the diesel needle. The design of the intensifier controls the relative timing of the diesel injection; a larger area ratio will cause a greater increase in pressure and a subsequent faster pilot injection. The plunger side of the intensifier has a diameter of 3.3mm while the smaller, downstream side has a diameter of 2.5mm. This corresponds to an area ratio of 1.7. The other function of the diesel intensifier is to accurately meter the amount of diesel pilot injected into the combustion cylinder. The intensifier has a maximum movement, and compression will cease at the point when the intensifier reaches this maximum lift. The maximum movement of the intensifier from its top most position to the bottom most position is 1.24mm. Combining this with the area of the small side of the intensifier, we see that the maximum amount of pilot released is of the order: y(2.5 mm)2(l.24 m m ) « 6 mm3 This amount of pilot would be injected if the diesel fuel were incompressible. However, because the diesel fuel has a finite compressibility, the exact amount of diesel pilot released into the cylinder will be slightly less than this. The pressure forces on either side of the intensifier govern the motion of the intensifier. The equation governing the intensifier motion is as follows. 23 dumt (P3A,-P4A2 ) and dh„ int (2.5 and 2.6) dt int In the above equations, Uint is the intensifier velocity and hirt is the intensifier position. P3 and P4 are the pressures in volumes 3 and 4 as shown in Fig. 2.10. The large side area of the intensifier is A i and the corresponding small side is A2 and the total mass of the intensifier is m^. Due to the location and motion of the diesel intensifier, leakage can occur on either side of the intensifier. This leakage is proportional to the tolerances between the intensifier and the cavity in which it sits. Standard tolerance for each side is approximately 2 um on the diameter. 2.2.3 Dual Needle Interaction The parameters that need to be controlled for the gas injector process are the injection timing and duration. The addition of a second fuel to the injector requires control of the timing of the individual injections of each fuel. The relative timing between the fuels can strongly affect combustion. Improper injection timing can lead to increased emissions or a lack of sufficient power generation. A dual needle assembly, including separate springs that accompany each needle, accomplishes the timing within the gas injector. The geometry of each needle and the pressure increase at the associated needle shoulders are precisely designed to control the injection timing. A schematic of the needle assembly is shown in Fig. 2.11. 24 SPRING PIN DIESEL NEEDLE-GAS N E E D L E -I '/A 48 BOTH NEEDLES CLOSED DIESEL NEEDLE OPEN GAS NEEDLE CLOSED BOTH NEEDLES OPEN GAS NEEDLE OPEN DIESEL NEEDLE CLOSED Figure 2.11 - Dual Needle Orientations Figure 2.11 shows the four possible needle orientations during the injection cycle. The maximum lift of the diesel needle is governed by the spacing between the top of the needle and the cap above it. The maximum lift for the gas needle is governed by the spring pin spacing between the top of the pin and the casing above it. The length of this spring pin can be modified to alter the maximum lift of the gas needle. The gas and diesel springs are similar. The diesel spring has a constant of 40.8 kN/m and the gas spring has a constant of 41.1 kN/m, both significantly smaller than the constant for a diesel injector of 175 kN/m. The spring pre-loads are also similar, with the diesel spring having a pre-load of 107 N and the gas spring having a pre-load of 111 N. The diesel needle lift is opposed by only one spring. However, both springs act on the gas needle. Therefore, for the gas needle to open without the diesel needle opening, the pressure forces acting on the gas needle must be large enough to overcome both springs. A free body diagram of both needles is shown in Fig. 2.12. 25 SPRING FORCE ^ AND CAVITY PRESSURE FORCE HEAD FORCE (DIESEL NEEDLE FULLY OPEN) PRESSURE FORCE VOLUME 6 SEAT FORCE• (DIESEL NEEDLE FULLY CLOSED) PRESSURE FORCE DIESEL SAC m SPRING FORCE AND CAVITY PRESSURE FORCE HEAD FORCE PRESSURE FORCE VOLUME 4 PRESSURE FORCE VOLUME 9 PRESSURE FORCE VOLUME 7 SEAT FORCE PRESSURE FORCE DIESEL SAC PRESSURE FORCE GAS SAC CYLINDER PRESSURE FORCE Figure 2.12 - Diesel and Gas Needle Free Body Diagram The equations governing the motion of both the diesel and gas needle are as follows, where the subscripts d and g represent the diesel and gas needle respectively: Pressure and spring forces acting on the diesel needle: Fdiesel _ force — dd{lid Ug ) ^dnd Fpred + ^ 6^6 + ^sacd ^ sacd ^ caV^cavd (2.7) Pressure and spring forces acting on the gas needle: FgaS_force = ~dg{Ug ~ Ud)~ * A " FPreg + P 4 A 4 + + PsacgAacg + PcylAp Pcav^cavg Pj-^l P*acdA sacd (2.8) 26 In Eq. (2.7) and (2.8), d is the damping coefficient, k is the spring constant and Fp-. is the spring pre-load. The friction forces for both needles are considered negligible compared to the magnitude of the other forces and are excluded from consideration. The diesel needle pressure forces include the primary needle force in volume 6 and the pressure force from the sac volume. Helping to keep the needle closed is the cavity pressure denoted by Pcav acting on Acavd. The pressure forces-for the gas needle include the primary control diesel force from volume 4, the gas pressure force from volume 9 and the gas sac pressure force. In addition, the cylinder pressure acts directly on the gas needle and is denoted by P c y i , and the cavity pressure helps to keep the gas needle closed but acts on a different area denoted by Acavg. The pressure force that helps lift the diesel needle in volume 6 pushes down on the gas needle in volume 7. The sac pressure from the diesel needle also pushes down on the gas needle. When the diesel needle is closed, it imparts an additional force to the gas needle at the gas seat. Conversely, when the diesel needle is open, it helps to lift the gas needle by imparting a force at the needle head. The value of the imparted forces at the seat and head are found by equating the acceleration of both needles when the diesel needle is fully closed or fully open. When the diesel needle is fully closed, the seat force is negative when applied to the gas needle force balance. a g F F £j_ _ _g_ F •+- F F — F diesel force 'rseat * gas force seat f m \ -*F„ \mgJ F -F gas_force diesel _force 1 + -3L (2.9) 27 The force at the needle head can be found in the same way, the head force now being a positive force on the gas needle. f \ MA ,- — — F -F dieselforce gas _force V "«„ J = — ~ C2-10> The force F s e a t is non-zero when the diesel needle is fully closed, and the force Fhead is non-zero when the diesel needle is fully open. The equations governing the motion for both needles is then: dllj Pdiesel _force Pseat Phead (2.11) dt md dhd dt = ud du F — F + F g _ gas_force * seal ' •* head dt m CH <212> g In Eq. (2.11) and (2.12), u is the needle velocity, h is the needle position, ma is the mass of the diesel needle and mg is the mass of the gas needle. 28 Chapter 3 Previous Work This chapter will outline previous work, and provide a summary of the literature that was reviewed as the research progressed. The field of injector modeling has been around for many years. Even before the advent of computers, injection modeling was performed manually for diesel injectors by using tables and simplifying assumptions. Burman and DeLuca [1] show manual injector modeling for a common rail type diesel injector, where the compression takes place in a separate pump at a distance away from the combustion cylinder, and is transported by long piping to the injector itself. Even though the calculations are tedious, few assumptions were made so a large number of equations are required to fully simulate the injector. Fuel compressibility and tubing expansion equations in addition to the pressure wave and pump plunger compression equations are included in the overall simulation. The only approximation made in this manual simulation is the crank angle interval. For computer simulations, the time or crank angle interval can be made increasingly small, but the manual simulation requires a much larger advance to reduce the number of calculations. This paper suggests the use of a two-degree crank angle advance and an interpolation between points. This document provides a good basis on which to build up a computer model by providing an idea of the fluid characteristics that need to be considered when simulating an injector, as well as a good explanation of the overall physics of the hydraulics in the injector. In addition, the paper provides a brief overview of the Method of Characteristics (MOC), which is used to track the pressure waves through the piping between the compression and injection components. 29 Computer simulation of injectors began to appear in the late 1970's with models simplified due to the lack of computing power. Scullen and Hames [2] provide a very simple model to simulate the diesel injector. The model assumes that the pressure everywhere in the injector is the same, and that any pressure increase at one end of the injector is instantly propagated to the other end. Therefore, only one differential equation is used to calculate the pressure in the injector and this, surprisingly, leads to fairly good results. However, the model does show a fair amount of inaccuracy, as it does not model the oscillatory motion of the pressure rise. Although the paper uses a fairly simple model, it provides a good idea of how to approach injector simulation, and the validation of the model through experimental-model comparisons. In the early 1990's computer simulation of injectors built upon the more simplistic models by introducing multiple volumes within the injectors with pressure wave propagation between the volumes. Two papers of note by Kegl et al. [3] and by Marcic [4], use similar processes to simulate the 'common rail' type injector. These papers are very closely related to the work in this thesis, and are reviewed in more detail. The papers noted above use the Method of Characteristics (MOC) to track the pressure waves within passages connecting the pump to the injection nozzle, or passages of significance, such as along the needle length of the injection nozzle itself. The MOC is a graphical method that uses a state diagram to keep track of the fluid properties; namely the local particle velocity and the speed of sound, and a position diagram that tracks pressure waves in a passage as a function of position and time. A more in depth discussion on MOC is shown by Benson et al. [5]. While the simulations involving MOC are studied, a new method of tracking pressure distribution in a passage was developed and MOC will not be discussed further. Possible future work will include a comparison in accuracy between MOC and the model shown in this thesis. 30 In the paper by Kegl et al. [3], the development of a mathematical model to simulate the Fuel Injection Equipment (FIE) of a conventional 'common rail' type diesel injector is performed. The main assumptions used in formulating the relevant equations required to simulate the injector include: • Temperature is constant • Fuel flow is one-dimensional and viscous resistance is proportional to the velocity of the fuel • Vapor pressure of the fuel is small compared to the pressures in the system and that cavitation will occur when the pressure drops below 35 kPa • The system is free of leakage • Ambient pressure is a constant at 100 kPa • Inlet diesel liquid pressure is 150 kPa In addition, this simulation allows for two-phase fluid. The density (p),bulk modulus (E) and speed of sound (a) are not only a function of pressure but also change if any vapor is formed in the system. The model is separated into the pump side equations, the injector side equations and the transport equations for the high-pressure tube. Generally, the equations of motion provide a pressure increase with respect to time for each relevant volume within the pump or injector. The MOC is used to keep track of the pressure wave formation and reflection in the high-pressure tube connecting the pump to the injector nozzle only. Included in the equations is compensation for flow resistance. This resistance is controlled by a resistance factor and can be found using an empirical relation. To consider cavitation effects, a residual pressure calculation is made and if the residual pressure is less than the assumed vapor pressure of the fuel, vapor bubbles are formed within the liquid fuel. These vapor bubbles, assumed to be evenly distributed throughout each volume of the injector, cause a change in properties (E, p and a) as well as a change 31 of volume in the injector cavities. This volume change leads to an additional term that needs to be included in the differential equations to account for this cavitation effect. The solution of the differential equations was performed using a fifth-order Runge-Kutta method using variable steps. Experimental tests were performed and verification with the numerical model was completed for a range of load conditions. Graphically, the pressure values from the model seem to agree with the experimental results, although there is no mention of how the experimental pressure was determined. The paper by Marcic [4] again deals with the simulation of a diesel 'common rail' type injector. This paper focuses on the injector nozzle itself, rather than the valve delivery system. Similarly to Ref. [3], the equations are almost identical and cavitation is considered. However, cavitation effects are now only influencing the constant parameters (E, p and a) and not the volumes in the injector cavities, and is reasoned to be unimportant during the cycle. The major assumptions in this model include: • Fluid inertia is ignored • Experiments to determine flow discharge coefficients were conducted at steady pressure and steady flow conditions • Leakage is ignored Again, the event of a two-phase fluid is considered and accounted for in the model. The solution method of this injector simulation is similar to that of Ref. [3], with one increased complexity. The pressure wave interaction is now represented along the length of the needle, a significantly shorter length passage than that of the high-pressure tube. Again the method of characteristics was used to keep track of the pressure wave interaction and propagation. 32 The experimental testing of the injection system provided multiple pieces of data used to verify the model. The pressure at the exit of the pump, the pressure in front of the nozzle, the needle lift and the injection rate were all measured experimentally and checked to verify the model. Pressures were measured using piezoelectric transducers, needle lift measured using displacement transducers and injection rate by several methods not discussed in detail. Computer simulation was conducted using a fourth order Runge-Kutta method with variable time step. The variable step was based on permissible errors and allows for ten times halving of the time step. Experimental-model comparisons show a good correlation with all data and shows that at some points the sac pressure can even exceed the needle lift pressure at high loads. References [3] and [4] mention that cavitation effects are minimal and affect only a very small portion of the injection process. The experimental-model comparisons of both papers verify the increased accuracy of the multiple chamber pressure calculation compared to the single pressure assumption by Scullen and Hames [2]. The finite difference method of tracking pressure waves was used to track gas flow through an engine manifold in the paper by Liu et al. [6]. While mainly a comparison between MOC and finite difference methods and not specifically tailored for injectors, this paper does provide insight into problems with the finite difference method, specifically in the realm of overshoots and numerical instability. The main solution to problems of numerical overshoots is addressed by flux corrected transport with diffusion (FCT), where the velocity in a passage is diffused to the outlying passages. Along with FCT, an anti-diffusion stage is suggested, to remove excessive diffusion that can occur by using this method. The non-physical overshoot is effectively eliminated through use of this method, and will be used for the same effect in this thesis. Simulation by straight mathematical programming is not the only way to simulate the injector Third party programs that can simulate hydraulic processes are another way to 33 effectively model the injection process. One simulation package of note, SABRE, has been shown to be able to effectively model hydraulic processes. While SABRE is not used in this research because it is limited to liquid processes, it is an alternate type of simulation to consider for the most efficient and accurate means of injector modeling in the future. A comparison of the results and efficiency obtained from modeling the injector with SABRE, by MOC or by finite difference methods will be considered in future work. 34 Chapter 4 The Experimental Investigation Data from the experiment is compared with the model to troubleshoot and verify the model. This chapter will review the apparatus and the technique used to allow the collection of data. If will also show some typical results and" data manipulation required to accurately compare the results between the model and the experimental data. 4.1 Experimental Apparatus Two methods were used to run the injector. The first method is using the engine that the injector is designed for, a Detroit Diesel 6V92 engine, and second, is using the ITR. The ITR is primarily used for fatigue testing of the injector, but with simple modifications, can be instrumented to allow collection of useful data for our purposes. Each apparatus has differences that will affect the injector mechanics and change the injection properties. These differences are identified and taken into account when comparing the model to the data from each of these experiments. To obtain data from the experiment, an injector is modified so that we can obtain a pressure value from the fluid inside the injector. This modified injector is then run on both the 6V92 engine and the ITR, for various loads, the values of which can be recorded from the DDEC controller. The data is then saved on the data acquisition (DAQ), and imported to an Excel file for comparison with the model by graphical means. All model and experimental results are referenced to the crank angle of the combustion cylinder, as is convention when referring to internal combustion engines. The data from the DAQ cannot be directly imported and compared with the model, but needs to be computed from knowledge of the calibration of the instrumentation. After this is done, accurate experimental-model comparisons can be performed. 35 4.1.1 Injector Modifications Data on the pressure of the fuel inside the injector is the easiest piece of data to obtain for comparison with model results. To do this, a modification needs to be made to existing injectors so that a pressure transducer has access to the diesel fuel within the injector. An identical modification was performed on both the diesel and dual fuel injectors and involves the addition of a passage at the poppet valve connecting to a mounting that holds the pressure transducer. The passage that connects to the poppet valve volume is shown in Fig. 4.1. Figure 4.1 - Pressure Transducer Passage The pressure transducer sits in a small fitting linked to a short tube connected to the bored hole in the body of the injector. The transducer is connected to the poppet volume instead of any other volume for a variety of reasons. The main reason is that most of the injector fits in a cylindrical hole in the engine body, so that neither the injector body nor the 36 injector stack assembly has enough room to allow the introduction of a transducer passage. In addition, most of the diesel injector parts are free to move, and the gas injector has many passages where the fluid sealing would be affected by drilling a hole to the inside of the injector. The relevant dimensions of the transducer passage are: Passage Length: 22.3 mm Passage Area: 1.93 mm2 Volume at Bottom of Transducer: 197 mm3 The volume at the bottom of the transducer is estimated given the overall volume of the fitting and the approximate dimensions of the tip of the transducer. This volume is small but larger than the sac volume in the injector. In introducing an extra volume to an injector, we could be changing the injection properties and injection timing of the fuel. While this passage and volume is small compared to the overall fuel volume inside the injector, the effect of the transducer passage on the hydraulic properties of the injector needs to be addressed. This is shown in section 6.2.4. 4.1.2 Injector Test Rig The injector test rig (ITR) is a single injector fatigue-testing device. It was designed to operate a single injector for a large amount of time to test the wear resistance on the mechanical components within the injector, but was used here for short duration performance testing. A schematic of the test rig setup is shown in Fig. 4.2. 37 Injector HPDI/Diesel 1 Diesel Supply/Return 2 Sealing Diesel Supply 3 Injection Diesel Return 4 Cam Position Input 5 Optical Sensor 6 Pressun: Transducer Laptop/Wavebook DAQ Gas Supply Diesel Supply Figure 4.2 - I T R Schematic The injection timing on the ITR is simulated to mimic the 6V92 engine. The injector begins pressurization and injects the fuel a few degrees before top dead center in the engine. An onboard computer called the Detroit Diesel Electronic Control (DDEC) provides an electrical signal to the solenoid controlling the motion of the poppet valve. The RPM of the engine and the load sensed by the Throttle Position Sensor (TPS) located on the control panel govern the timing and length of this electronic signal. On a real engine onboard a vehicle, this sensor relays to the DDEC the position of the throttle as the operator pushes down on the accelerator. However, on the ITR, this sensor is a knob that we can turn to adjust the load that we wish to simulate. An optical sensor and a disc connected to the camshaft control the cam position and when the injection signal is triggered. Studs located at 60° intervals on the disc need to be calibrated with a single cam position before the experiment begins. The optical sensor sends a signal to the DDEC at regular intervals as to the angular position of the cam. The DDEC, knowing the rpm of the camshaft, can then interpolate between points to 38 accurately time the electrical pulse that controls the movement of the poppet valve in the injector. A canister at constant pressure supplies C N G at 14 MPa. As the injector is operated, the pressure in this canister will slowly decrease. However, because the tests were done in a short amount of time and because the single injector injects only small amounts of gas relative to the amount in the cylinder, no significant pressure losses were observed. The injected fuel is released into the atmosphere, rather than into a combustion cylinder in an engine. This lack of cylinder pressure will influence the injection properties and will be taken into account when the model attempts to simulate its operation. A picture of the ITR is shown in Fig. 4.3. Figure 4.3 - Injector Test Rig Also located on the ITR are oil lines that lubricate the camshaft. This oil reduces the amount of wear on the rocker arm during operation. The ITR motor can safely run at 39 speeds up to 1800 rpm. Two separate onboard pumps supply control diesel fuel and sealing diesel fuel to the injector. 4.1.3 6V92 Engine The other apparatus used for experimental comparison is the Detroit Diesel 6V92 engine. The engine was set up for experimental purposes and was located in the thermodynamics laboratory at the University of British Columbia. The pre-combustion pressurization and the actual combustion of the fuel in the 6V92 engine leads to an increase in pressure that acts directly upon the injector tip to help lift the needles. The experiments performed on the 6V92 engine will include aspects that we will be neglecting in our simulation, such as temperature and vibration effects. As with the ITR, a simulated TPS is used to vary the load on the engine. Along with the standard transducer from the injectors, we also now have a pressure trace from a transducer located within each cylinder. This transducer will give us the cylinder pressure as a function of crank angle. In addition, a piston TDC sensor was added that would give us the point at which the piston reaches TDC. The 6V92 engine experiments are the main source of experimental verification that will be used to verify the diesel injector model and will provide a good source of alternative verification to the ITR for the dual fuel injector experimental model comparison. The maximum speed that the engine can attain is 2100 rpm. 4.1.4 Instrumentation The main instrumentation used includes the pressure transducer used at the poppet valve, the data acquisition system (DAQ) and the RBOI test rig, all indicated in Fig. 4.2. Data from the experiments needs to be modified from knowledge of the calibration of the instrumentation to give accurate data for experimental-model comparisons. 40 The pressure transducer is a PCB Piezotronics model 108A02. This quartz pressure transducer is suited to measure rapidly changing pressure fluctuations over a wide range of frequencies and amplitudes. The transducer is calibrated to 0.0747 mV/kPa, and this number is used to convert the output from the transducer from voltage to pressure. The maximum allowable static pressure for this transducer is 350 MPa, well above the maximum pressure in our experiments of 150 MPa. The DAQ is composed of an IBM notebook computer and a Wavebook model 512, which includes the associated software. The Wavebook is a high-speed multi channel portable data acquisition system that essentially allows signal measurements to be recorded on a computer. The associated software is Waveview, and is where the signals are processed, modified and saved. The RBOI measurement rig is a device designed by Westport staff to measure the relative timing of the injection of both the diesel and the CNG jets from the dual fuel injector. The rig is comprised of two main components: the pressure film transducers, and the baffles to separate the jets to each transducer. The internal baffle to stop the diesel jet is located in the middle and the gas jet baffle is a plate located at the top of the rig. A drawing of the RBOI measurement rig is shown in Fig 4.4. 41 Pressure Film Gas Jet Transducers Diesel Jet Baffle Baffle Figure 4.4 - RBOI Measurement Rig The rig takes advantage of the different heights of the injection nozzles to separate the jets and collect two distinct signals on each transducer. The diesel is injected through a hollow gas needle at a lower level than the CNG, and this needle is free to rotate effectively changing the location of the diesel impingement. This needle rotation will sometimes cause no signal to be visible as the jet misses the diesel film transducer. Therefore, manual rotation of the gas needle is required to obtain a direct hit on the diesel film transducer. This is accomplished manually by abruptly increasing or decreasing the load and generating increased vibrations to rotate the gas needle. 42 The C N G is injected at a much higher momentum than the diesel jet, so separation of the C N G from the diesel film transducer is critical to obtaining a clear signal of the diesel impingement. The gas jet baffle does this effectively by surrounding the diesel injection tip below the gas injection nozzle. The mounting of this RBOI rig is shown in Fig. 4.5. Figure 4.5 - RBOI Measurement Device Mounting The injector tip protrudes through the bottom of the engine block and sits just inside the RBOI device. Four bolts attach the RBOI device to the engine block. The film transducers are piezo film sensors manufactured by AMP, model number LDT0-028K. The laminated piezo film sensors are essentially strain gauges that can produce voltage changes by impact or bending of the film. While, if accurately configured, these films can measure the absolute strain under which it is placed, it is not required for the RBOI experiments. We are only interested in the initial spike when the jets impact the film. 43 The films cannot withstand high temperatures, and can be damaged fairly easily. In addition, the diesel fuel also wears down the lamination and can destroy the film. Thus, replacement of the films is required after a few hours of experimentation time. 4.2 Diesel Injector Typical Results The diesel injector results for the 6V92 experiments will be summarized here. The same load conditions were used for both the diesel and gas injectors, as they were both in operation at the same time in different cylinders. Tests performed on the 6V92 engine will focus on the diesel injector results, with the gas injector results being used for supplemental verification for the ITR experiment. The results are all referenced to the relative crank angle of the piston in the combustion cylinder. The 6V92 experiment was performed on January 5, 1999 and data was recorded under the following conditions in Table 4.1. Table 4.1 - 6V92 Experimental Conditions RPM PW Load Description 600 5.4 Warm Idle 600 5.7 Cold Idle 600 5.8 Hot Idle 1200 20.1 , Maximum Torque 1200 8.3 30% Maximum Torque 1200 8.1 48% TPS 1500 20.8 Maximum TPS 1800 20.5 Maximum TPS 1800 8.0 30% Maximum Load 2100 8.1 30% Maximum Power 2100 20.4 Maximum Power 2100 20.4 Maximum Power 44 The load description is the status of the engine at the selected RPM and PW. TPS is independent of power or torque and is a measure of the throttle position at a set RPM. The numerical data for a single injection cycle from the 6V92 experiment is shown in Appendix E and Appendix F. Both the diesel and gas injector data is recorded but only the diesel injector data is used from the 6V92 experiment. The relationship between the RPM, load, PW and BOI is complex, and is entirely determined by the DDEC controller. It is useful to observe the general trends in the variation of these parameters to gain a good understanding of the injection process. Graphical analyses of the 6V92 test data referenced to the crank angle relative to TDC of the combustion piston for 3 types of loads are shown in Fig 4.6. 120 100 Experimental Pressure Traces vs. CA rel. TDC 2100 rpm 80 1? 0. C 60 3 If) lfl V 40 20 / -12 BOI 20.4 PW 1200 rpm jv' \ A ' \ -12 BOI 8.3 PWv > \ ' \ t 1 » \ 600 rpm \ -1.5 BOI 5.8 PW Mi * -20 -10 10 CArel. TDC 20 30 40 Figure 4.6 - 6V92 Experimental Pressure Traces The plots correspond to the loads of hot idle, 30% maximum torque and maximum power respectively. 45 From the curves above, some trends are very apparent. Firstly, and most notable, the increase in pulsewidth shows large differences in each of the traces in Fig. 4.6. With a longer pulsewidth, we observe a longer the injection period and a larger peak pressure. This is because the decrease in volume of the plunger is greater than the output of volume by the injection nozzles. Secondly, an increase in RPM changes the slope of the curve in a pressure vs. time plot, since the rate of pressure increase versus time is much higher. However, since the plots in Fig. 4.6 are referenced vs. crank angle, this rate of pressure increase is not shown. The increase in RPM also causes larger fluctuations in pressure, as the injector mechanism needs time to balance out the pressure increase and mass flow. In addition, higher RPM provides more injection cycles within a fixed time, not shown on a graph versus relative crank angle. The previous graph does not clearly show the effect of BOI on the shape of the curve, although by inspection the slope of the curve seems similar with a difference of 10° in BOI. The BOI is mainly set to control the timing of the fuel injection in the combustion cylinder, rather than to influence the shape of the curve. The increase in load leads to larger peak injection pressures and pushes the BOI back so that more fuel can be injected into the cylinder before the combustion begins. 4.3 Gas Injector Typical Results The gas injector, also known as the Westport 6F4 injector, was tested under the 6V92 and ITR apparatus. One difference between the experiments on the 6V92 and the ITR is that additional tests were performed on the dual fuel injector with varying maximum lifts in the gas needle on the 6V92. This provides multiple pressure traces to compare with our model. In addition to the 6V92 testing, additional tests were done on the ITR again on a variety of loads. The ITR load conditions as tested are outlined in Table 4.2. 46 RPM BOI PW 800 -12 9 800 -12 12.4 1000 -12 9 1000 -12 13.1 1200 -12 9 1200 -12 13.3 1400 -12 9 1400 -9.8 13.5 1400 -9.5 3.9 1600 -8.7 9.6 1800 -9.3 15.4 1800 -12 18.6 Table 4.2 - Gas Injector ITR Test Conditions These tests were performed on November 30, 1999. Experimental data from the ITR experiment is shown in Appendix D. Experimental data obtained for the gas injector from the 6V92 experiment is also shown in Appendix E for a maximum gas needle lift of 0.030" and in Appendix F for a maximum gas needle lift of 0.020". Each of these appendices shows only a single injection cycle. The supplementary results for the gas injector from the 6V92 experiment have not been used for experimental-model comparisons. The gas injection mechanism differs from that of the diesel injector. The pressurized diesel fuel used to lift the gas needle and to displace the intensifier is no longer injected into the cylinder. Instead, this fuel is relieved through a vent line as the CNG needle opens. The fuel injected into the cylinder is supplied by the sealing diesel, which is always at a pressure higher than the inflow CNG. Because of this difference in mechanisms, we cannot compare the pressure profiles of the diesel and gas injectors, and we do not expect that the profile will behave the same way as the diesel injector under variation of loads and pulsewidth. Some typical injector plots obtained from the gas injector are shown in Fig. 4.7. 47 Poppet Pressure vs CA Rel TDC Experimental - 6F4 Injector i < ° Q-3 (A (A O -20 -15 -10 0 5 10 CA Rel TDC 15 \ r V — 4 3 —f\ \A V 20 X ---•1.6V92-600 rpm-1.5 BOI 5.8 PW 2. 6V92 - 1200 rpm -12 BOI 8.3 PW 3. RTR - 800 rpm -12 BOI 9 PW 4. RTR - 1400 rpm -9.8 BO113.5 PW Figure 4.7 - Poppet Pressure vs. C A Rel T D C - Gas Injector Each curve represents a specific load condition and the RPM, BOI and PW are calculated by the DDEC to provide the required power for these loads. From this plot we see some differences in the gas injector plots for the same experimental apparatus, as well as some differences in pressure plots between experiments. Generally, the pressure traces on the ITR experiments have a higher peak pressure than the experiments on the 6V92. This is evident when comparing traces two and three, where the ITR experiment, with a lower RPM and similar pulsewidth to the 6V92 trace, has a higher peak pressure. In addition, comparison of plots two and four show large 48 differences even though load conditions are roughly similar. The cause of this difference in peak pressure is the steeper slope evident on the ITR curves. This slope change is due to the lack of cylinder pressure to aid the needle lift, forcing a larger increase in pressure before any relief by injection. A consistent aspect between the experiments is the increase in oscillation of the pressure trace as the RPM increases. Lower RPM shows lower fluctuations in the pressure trace. 4.4 Experimental Consistency Confidence in the comparison of the experiment with the model for the injection process is obtained through an investigation of the consistency between experimental cycles. Superimposed pressure traces for multiple injection cycles are shown in Fig. 4.8 for the 6V92 engine tests involving the diesel injector. 120 100 0. 60 40 20 6V92 Diesel Injector Consistency - Maximum Power 2100 rpm -12 BOI 20.4 PW -15 - — 3 A i 2 v ~ . J I (IMT 1 1 1 1 * " " , , | f r > i 5 10 CA Rel TDC 15 20 25 30 Figure 4.8 - 6V92 Diesel Injector Experimental Consistency 4 9 There are four relatively invariable aspects to the consistency graph that are observed in each of the seven curves. The first two 'bumps' denoted by points one and two are shown in every instance. Point three, the maximum pressure, remains approximately the same in each case. The end of the pulsewidth is also very close as shown by point four, although there is a definite variation of two to three degrees. The region between points two and three has a consistent slope, but the profile is erratic and shows significant discrepancy between cycles. To compare the model to this experimental data, we should compare points one, two, three and four, and the slope between points two and three. For the gas injector, it is again useful to identify the regions on the pressure trace that are repeatable during an experiment. These consistent regions can then be modeled by numerical simulation, and can be used to verify the mathematical model. Multiple superimposed curves for a single experimental injection period are shown in Fig. 4.9. Figure 4.9 - Gas Injector Experimental Consistency 6V92 Tests 50 The gas injector shows an extremely repeatable pressure trace. There does exist a little fluctuation between cycles, but the overall shape of each curve remains the same. The only property that does change is the decrease in pressure of the traces as the pulsewidth ends. The related curves from the ITR experiments are shown in Fig. 4.10. 70 60 50 0. lfl 30 w 20 10 -12 Consistency - 6F4 ITR • 1400 RPM -12 BOI 9 PW I * / \ I \ V -10 • 6 - 4 - 2 CARel TDC Figure 4.10 - Gas Injector Experimental Consistency ITR Again, the shape of the curve remains fairly consistent as the cycle progresses. There are a few fluctuations between curves, but they are very minor. Unfortunately, there are not enough cycles per load to verify if this discrepancy changes even more. In comparing the ITR curves to those of the 6V92, we see that there is much more of an oscillatory profile in the 6V92 testing, likely due to increased vibration, and cylindrical pressure. The experimental pressure traces from the 6F4 injector are much more consistent than that of the diesel injector. This is likely because the components in the 6F4 injector stack assembly are rigidly secured while those in the diesel injector are free to rotate. 51 Another test of the experimental consistency that could have been performed is to compare two separate pressure traces under the same load. That is, to run the same load at separate instances, ideally with a different load between runs. This would provide more of an idea of the experimental variance between runs rather than a reliance of multiple traces in a single set of data in a single load cycle. Unfortunately, this supplementary test was not performed and we are left to speculate as to its results. 4.5 RBOI data In addition to the pressure trace for the ITR experiment, the relative true BOI was determined between the diesel pilot and gas injection. In addition, with other timing calculations, the absolute true BOI of the initial pilot diesel injection can be determined as well. The relative BOI can be used in conjunction with the needle lift on the model as another verification to the accuracy of the numerical simulation. A typical RBOI curve in conjunction with a pressure trace is shown in Fig. 4.11. Pressure and BOI traces vs Time 1000rpm -12 BOI 9 PW o. E o 3 (0 (0 0 80 70 60 50 40 30 20 10 0 -10 - * - Transducer Pressure ~*~ Diesel BOI * CNG BOI Gas Diesel Pilot f*^\ / Injection / . Injection \ / Y f V S^v 1 w \i / V j \ 5 -10 -5 I 5 1 0.60 0.20 + 0.00 « 5--0.20 -0.60 CA Rel TDC Figure 4.11 - Typical RBOI curve ITR Tests 52 The diesel pilot and gas injection is taken at the point where the transducer voltage shows significant change with respect to the amount of noise in the system. As shown, the gas injects approximately five degrees after that of the diesel pilot for 1000 rpm. The width of the voltage signal does not necessarily denote the length at which the diesel or gas needle remains open because there is uncertainty in the elasticity of the transducer film, as well as possible adhesion to the backing surface. The gas injection BOI is cut off at -5V because of the settings on the data acquisition. The production of a diesel pilot signal strong enough to detect on the data acquisition system was also a problem. Originally, the presence of the diesel jets signal was small or non-existent. It was thought that this occurred because the diesel pilot jet is injected at a significantly lower pressure than the gas jet and that some sort of separate amplification for this signal was required. However, it was discovered that the diesel jets were moving due to needle rotation as injection cycles progressed. Since the films were placed in a fixed location, there was a point where the jets would strike on either side but not on the film itself. The solution was to force a needle rotation with erratic changes in TPS, to regain the diesel jet impingement upon the film, and to record the data when impact occurred. 53 Chapter 5 Finite Difference Numerical Simulation This chapter will outline the simulation involving the finite difference method. The simulation utilizes the finite difference approximation to accurately track pressure waves in the long passages located within the injector. The decision to use finite difference over other numerical methods was based on various reasons. Some of these reasons include increased accuracy, computer hardware restraints and time constraints. While this chapter will only deal with the finite difference mathematical process, several topics that will be discussed are common among the other types of simulations. 5.1 Physical Assumptions Some assumptions are made to variables that do not change by an appreciable amount throughout the system process. These assumptions help the overall modeling process not only in simplifying the equations involved but also in reducing the overall computation time. The effect of these assumptions on the model output will be verified by experimental-model comparisons and sensitivity analysis in Chapter 6. 5.1.1 Diesel Liquid Properties The liquid used in both injectors is diesel fuel. The properties of this liquid greatly influence the mechanics of the injection, specifically, the rate of compression and injection. The main attributes of diesel fuel that are used in our simulation are the density (p) and the bulk modulus (E). Assumptions on various conditions can simplify how we treat these properties. 54 The working fluid is compressible and a common assumption for compressible flow is the reversible adiabatic or isentropic assumption. This assumption leads to the development of the bulk modulus of the fluid and is defined as: (5.1) This relationship is required to relate the change in density to the change in pressure when developing the finite difference equations, as we will see later. To do this, we must assume that E is a constant or can be related to the absolute pressure of our system. Reference [2] shows a graphical representation of the change in E as a function of pressure in Fig.5.1. Range of Pressures in Injection Process io3 104 PM io5 106 Fuel Pressure, psi Figure 5.1 - Effect of Pressure on Bulk Modulus As shown, for 150°F or 65°C, the fuel bulk modulus undergoes a large change as the fuel pressure increases from 1000 to 10000 psi. However, the vertical line shown approximates the maximum pressure involved in the simulation of our injector at 55 maximum loads, 150 MPa. The fuel bulk modulus from atmospheric pressure to this maximum pressure changes by approximately 5%. To simplify calculations, the bulk modulus is assumed to be constant throughout the experiment since it does not change appreciably over the range of injector pressures. The bulk modulus at atmospheric pressure is used and is equal to 2 GPa. The relationship for the liquid compressibility in Fig. 5.1 is strictly only valid for an isothermal case. There is little evidence of heat transfer from the fuel and little effect of friction, so a constant temperature is a reasonable first assumption. While 65°C is high for both the ITR and 6V92 experiments, the change in bulk modulus for a 50°C change in temperature is assumed to be small relative to the absolute value of the bulk modulus. With the compressibility of the fluid now set as a constant, we can modify Eq. (5.1) to obtain the density as a function of pressure and the assumed constant compressibility. IT ^ 1 * 1 E = p—->-dp = — cT dp p E Pi =Prexp|^ E (5.2) Here, the subscript denoted by 1 is the property of the diesel fuel at atmospheric conditions and the subscript 2 represents the value at the point we wish to obtain. In addition, the walls of the injector are assumed to be rigid so that no volume expansion in the passages takes place. If the walls were not rigid, the effective bulk modulus would decrease. The walls of the injector are thick compared to the size of the passages, so it is assumed that they will not expand much, if at all. A calculation showing the effect of wall expansion on the fluid bulk modulus and the speed of sound is shown in Appendix B. 56 5.1.2 Gas (CNG) Properties The gas properties follow the same assumptions as that of the diesel fuel, specifically the isentropic assumption. In addition, a perfect gas assumption is used in conjunction with this isentropic condition and leads to the pressure-density relationship as follows: - T = C (5.3) P The perfect gas assumption is only valid at pressures well below the critical pressure or at temperatures well above the critical temperature. The critical pressure and temperature for methane, the primary component in CNG, are 4.6 MPa and 190.4 K respectively. At 19.3 MPa, the supply pressure of the inlet CNG is well above the critical pressure. However, the working temperature of the inlet CNG is about 298K, well above the critical temperature. At a pressure of 10 MPa and a temperature of 300 K, the experimental specific volume of methane is 0.0133 m3/kg. The specific volume determined from the perfect gas law is 0.0156 m3/kg. The difference between the two corresponds to a 17% error. Even though there is an error associated with using the perfect gas assumption in our calculations, the simplifications to our equations and to the numerical simulation are numerous, prompting us to use of the ideal gas law with recognition of the errors involved. In addition to the assumptions made on the gas properties, the inlet gas pressures to the 6F4 injector are also assumed to remain constant even though they are supplied by external compressors that need to maintain the pressure of the fuel as the supply depletes. This pressure can fluctuate due to pressure waves or compressor adjustments during the operation of the 6V92. The gas pressure for the ITR experiments is not externally compressed but comes from a bottle reservoir. Observations show that this pressure does not decrease significantly over the operation period. The inlet CNG is set at 19.3 MPa for the 6V92 experiments, the target pressure that the external compressor is set to attain. For the ITR experiments, the gas pressure is set at approximately 14 MPa, the pressure in the bottle at the start of the experiment. 57 5.1.3 Poppet Open and Close Time The rate of compression within the injector once the signal is sent to the solenoid is governed by the poppet closure time. Initially, an instantaneous poppet closure was assumed for the injector model, but later found to be incorrect due to the large discrepancy between the timing of the experimental and model results. Instead, the open and close time of the poppet in the model is assumed to occur in a finite amount of time. However, the actual closure time cannot be easily determined experimentally, so a closure profile is assumed. Additionally, the individual open and close times of the valve are not necessarily identical, and need to be determined either empirically or by model-experimental comparison. The poppet movement is identical for both the diesel and the 6F4 injector. The linear relationship that is used to model the closure of the poppet valve is as follows: The maximum poppet lift is equal to 0.1 mm, tboi is the absolute time at which BOI begins, and tci0Se is the closing time of the poppet determined by us. Of course, this is only valid from the point at which electronic BOI begins to the point at which the pulsewidth is over and the poppet valve begins to open again. At the end of the pulsewidth, the relationship used to model the opening of the valve is similar and is equal to: Poppet position - Maximum poppet lift- {?••>) Poppet position = Maximum poppet (5.4) open 58 Here t p w is the absolute time at which the pulsewidth is over, and topen is the opening time of the poppet, not necessarily the same as the tciose- This equation is only valid after the pulsewidth ends. An example of the poppet position is shown in Fig. 5.2. Poppet Position vs. Crank Angle 1000 rpm -12 BOI 9 PW 0.00012 0.0001 0.00008 c o '£ 8 0.00006 Q. 4-1 s o. a. o.oooM o a. 0.00002 0 -20 -15 -10 -5 0 5 10 15 20 CA Rel TDC Figure 5.2 - Poppet Position vs. Crank Angle The graph in Fig. 5.2 shows the poppet position using the closure Eq. (5.4) and the associated opening Eq. (5.5). In the case above, the time is tciose is equal to 0.5 ms and the time is topen equal to 0.8 ms. Several relationships were used to mimic the motion of the poppet valve. While a linear relationship is the easiest, a parabolic closure profile was also attempted. A comparison of the effect linear profile versus the parabolic profile reveals very little change, so the linear profile is used in the model simulation. 59 5.1.4 Discharge Coefficients One of the main injector attributes that control the injector timing is the discharge coefficient on the various orifices. The governing orifice equation is given by: The volumetric flow rate (Q) is governed by the area (A) of the orifice, the discharge coefficient (Cd), the density of the fluid in question (p) and the pressure difference across the orifice (P2-P1). The volumetric flow rate is directly proportional to the discharge coefficient that can have values within the range of 0-1. A discharge coefficient of unity suggests a non-restrictive flow, while a coefficient of 0 is a completely blocked orifice. The determination of the discharge coefficient is difficult due to the amount of experimentation required to obtain an accurate value. In addition, the amount of variability between the value obtained from one injector may not necessarily be the same for another injector due to tolerances involved. The values of the discharge coefficients are uncertain and are adjusted after comparison between model and experiment. Sensitivity analyses are performed later in this thesis to study the effect of discharge coefficients on the model behavior. Previous work performed on a mechanically controlled unit injector support the use of a discharge coefficient of 0.78 at the injection nozzle for alternate but similar injectors. In our model simulation, we will use a discharge coefficient of 0.6 at the diesel injection nozzle since this value gives a good relationship between the model and experiment for the standard diesel injector as will be seen later. Some other general model assumed discharge coefficients have the needle seat for both the gas and diesel and the CNG nozzle with a discharge coefficient of 0.8. The poppet valve will have a discharge coefficient of 0.6, and a coefficient of 0.4 will be used for the control diesel discharge vent. (5.6) 60 5.1.5 Pressure Losses Pressure losses due to entrance or frictional effects through the passages in the injector are assumed to be negligible compared to other terms in the momentum equation. The pressure loss due to entrance effects is calculated using the following equation: A P - K ^ (3.7) 2 In the Eq. (5.7), K is the loss coefficient, a function of the ratio between the diameters of the reservoir and adjacent passage. A graphical representation of the loss coefficient versus the ratio of diameters is shown in Ref [8]. Since the diameters in the reservoir and adjacent passages are similar, a loss coefficient of 0.3 was used. A comparison of the pressure drop due to entrance effects and the pressure difference between the reservoirs show that the entrance effects are excessively small, except when the pressure differences between reservoirs is small, which occurs during stages when the flow is in the process of reversing direction. Over the length of the cycle, the magnitude of the pressure drop due to entrance effects is nominally about 1% of the pressure difference between the reservoirs. The small effect of the entry losses allows us to neglect entrance effects in our simulation. Pressure losses due to frictional effects in a passage is calculated using a similar equation, and is compared to the other terms in the momentum equation in Section 5.2.2: 1*^*1 ' (5.8) p 3c D 2 In the Eq. (5.8), f is the Darcy friction factor. For laminar flow, this friction factor is equal to: J Re Re is the Reynolds number of the fluid inside the passage. 61 Comparison of the term in Eq. (5.8) with the other terms in the momentum equation show that the frictional term has a magnitude of approximately 0.2% that of the other pressure term in the momentum equation. Since both the pressure loss due to entrance effects and the pressure loss due to frictional effects are very small, our assumption to neglect these losses is acceptable. 5.2 Equations The equations defined here form the basis of the model simulation. The final model approximates the system by using reservoirs and passages. The reservoirs can contain volumetric changes such as with the plunger or needle valve movement, and the passages are used to track the pressure propagation between these volumes. The passage equations represent the main differences with simulations done in previous work, as well as the applications of these equations to the unique 6F4 injector. For brevity, only the final system equations will be presented. 5.2.1 Liquid Reservoir Equation The reservoir equations are based on the definition of the isentropic bulk modulus of the fluid: The isentropic assumption is used from now on and is dropped from the final version of Eq. (5.9). The symbol u is the specific volume of the fluid in question. Again, the bulk modulus (E) is a function of pressure and temperature as before, but is assumed to remain constant throughout the model. s E _ d u v d t (5.9) 62 Knowing that: v = m (5.10) We can then do a substitution and obtain the following relationship using the quotient rule: dP dt Em f dV dm\ m—-V — dt dt m2 _E(dV _ V drn V\dt mdt. (5.11) The first term in the parentheses on the right represents the physical change in volume of the reservoir. This is used for injector functions such as plunger movement, needle shoulder movement or intensifier motion that physically change the volume of a reservoir. The second term on the right represents the change in inflow or outflow of mass to or from the reservoir. This term can be simplified as follows: V dm 1 • 1 ( - \ • 1 < n --T = -m = -\pQ)=Q <5-12> m dt p / A J Hence, the second term becomes equal to the rate of change of volumetric flow rate to and from the reservoir. Substitution into Eq. (5.11) will obtain: dP E(* • dV\ E( dV\ Where A i n and Aout represent the inflow and outflow passages to and from the reservoir, and Win and Wo ut represent the fluid velocity through their respective passages. In some cases, where there is an orifice as the exit passage such as the diesel sac volume, the Q term can be replaced by Eq. (5.6). 63 5.2.2 Gas Reservoir Equation The gas reservoir equations are based on the first law of thermodynamics. Begin with the first law rate equation, where h is the enthalpy of the gas: • • dE * * Q- w = + w » * h»u< - m* K (5-14> at Then, neglecting heat transfer, we obtain: dV d i \ • ~P~dt= dt^pVu'+ mm"k<m ~m'nkin (5-15) In the above equation, u is the internal energy of the gas. Using the following isentropic perfect gas relations for the gas: R u = CvT = -T y-\ TR h = CJ = J — T p y _ i (5.16 and 5.17) Upon substitution of Eq. (5.16) and Eq. (5.17) into Eq. (5.15), the first law can be written as: dP_(yR) dt~\VJ /Win Tt„ — ntout T„ out lout yPdV_ V dt (5.18) In Eq. (5.18), the first term on the right is the inflow and outflow of enthalpy from the gas reservoir and the second term is the change in pressure due to an external change in volume. The inlet and outlet temperature are determined by Eq. (5.19) or Eq. (5.20): 64 In Eq. (5.19), M is the Mach number, determined by the velocity at the inlet or outlet of the adjacent passage to the reservoir. If the velocity is not known, we can use the isentropic perfect gas relationship in Eq. (5.20) to determine the temperature since we know the stagnation conditions of the gas. 5.2.2 Finite Difference Equations The final version of the injector numerical simulations uses the finite volume method to track the pressure increase within each passage. The equations are based on the subdivision of each passage into multiple volumes of the same length. A schematic representation of the multiple volume subdivision is shown in Fig. 5.3. PI P(l) P<2) P(3) 1 P(N-l) P<N) P2 V<1> V<2> W<3) V(4) W(N-l) VCN+D Figure 5.3 - Finite Difference Subdivision This schematic shows a general interior passage bordered on either side by a reservoir denoted by PI and P2. The passage is then subdivided into n cells, with the pressure in each cell defined in the center of the cell. The boundary of each cell is located a distance of dx/2 from the center and is where the velocity entering or exiting each cell is defined. The development of the equations is done for a single slug or cell within the passage. The resulting equations are then discretized appropriately for the schematic as shown above. We first begin with the continuity equation: cipAW) dp dx, ot (5.21) 65 The first term is the rate of change of mass and the second term is the rate of increase of mass in the control volume or cell. Simplifying, knowing that the area is constant along one passage, and differentiating: dx. dt ^ dx dx dt Using the compressibility relation in Eq. (5.1): 8P = p - i E, again, is the bulk modulus of the diesel fuel. Substitution of Eq. (5.1) into the continuity equation leads to the following relationship: dW pW dP + p dP P dx + E dx E dt ~ dP dW dP dt dx dx This relationship gives us the change in pressure with respect to time in one cell as a function of the velocity and pressure change across the cell and the velocity of the fluid within the cell itself. As with the reservoir equations, the velocity is still required on either side of the cell. These can be obtained by using the momentum equation and solving both the continuity and momentum equations concurrently. The momentum equation can be developed in the same way or by a F and can be expressed as: = ma relationship 66 *L = S*-.W™- (5.23) dt p dx dx Since the compressibility equation used in both the continuity and momentum equations above is only valid for a liquid, the above equations can only be used for passages containing diesel fuel. Any passages containing natural gas must use the perfect gas law instead of the compressibility relation. The method of equation development for the gas passages is similar to that of the liquid passages but uses the isentropic perfect gas relation in place of the compressibility relation: 4 = c Pr ]nP = hiCpr ^ l n F = lnC + /lnp 1 Y P -> —dP = -dp -+dp = -^-cT P p H . yP -*6p = 'yhdP (5-24) The last step involves the substitution of the perfect gas law into the equation. The symbol y is the ratio of specific heats, in this case, for methane. The use of this relationship leads to the following continuity and momentum equations: dP dW dP — = - P r — - W — dt ax ox ^ = _L^_W^L (5.25 and 5.26) dt p dx dc 67 This continuity equation is similar to that for the diesel fuel with a substitution of the bulk modulus E with the term Py. The momentum equation is identical to that of the diesel fuel. These equations by themselves cannot be used in a code because they have yet to be discretized properly for the passage. To find the value of the pressure or velocity at the center of a cell, the values of the corresponding pressures and velocities at the edges of this cell must be set from the previous time step. The discretization used follows the nomenclature used in Fig. 5.3, with the pressures defined in the middle of the cell and the velocities on the boundaries. Since both the continuity and momentum equations require a change in pressure and velocity across the cell, averaging must take place depending on which value is required. The continuity and momentum equations can be written as follows, where i is an integer representing the cell in question. dP dlV dP — = -E — — - W— dt dx cx a = -E f \ W\ -W ! • ' + 2 '-l' dx P - P l dx This is the discretization to be used if all values were defined at the center of each cell. However, since our notation is different and our velocities are already defined on the boundaries, we need to modify the above equation to fit the nomenclature in Fig. 5.3 resulting in: 68 (*) _ E(w^~w>) (W+w<+M p^  + p<)-(p<  + p<->) \a), cx I 2 ) lex a CX J lex (5.27) Equation (5.27) is what is used in the coding for the model. The discretization for the continuity equation for the gas passage is exactly the same as above with the bulk modulus being replaced by the product of Py. The momentum equation discretization is done the same way as the continuity equation and is the same for both the gas and diesel passage as follows: ffl 1 dP wcW a p cx dx — » (ffl CX -W f \ w x-w l cx ffl 11P' ' P M ) _ w w)-(wi+ w(_x) cx 2cx ffly a; 1 p , - p i - l . _ w w M + w f l cx 2cx (5.28) The total change in velocity or pressure at the new time step will be found by multiplying the flux term found from the discretization equations by the time step in our model. Because the dx terms for each passage differ according to passage length and subdivision, the discretized continuity and momentum equations are located in separate subroutines in the model with the value dx as an input variable along with the density, pressures and velocities. 69 5.2.3 Choking of Gas Flow Over the course of the injection period, the gas becomes choked when the needle opens. Initially, the gas is choked between the needle seat and the gas sac, and once the pressure in the sac rises sufficiently, the gas is choked between the gas sac and the combustion cylinder in the case of the 6V92 or the atmosphere in the case of the ITR experiment. For the ITR, when the gas needle just begins to open, the pressure ratio between the gas supply pressure and the atmospheric pressure of the gas sac is approximately equal to 0.02. The critical pressure ratio for choking to occur on the gas side is equal to: Po (5.29) \y + V This critical pressure ratio is equal to 0.546 for a specific heat ratio of CNG equal to 1.3. Choking of the gas flow will occur as long as the pressure ratio between the gas sac and the gas seat is less than 0.546. Choking of the gas flow between the atmosphere and the gas sac will occur if the pressure ratio between the two is also less than 0.546. The maximum mass flow rate that we use in the reservoir equation, Eq. (5.18), when the gas flow is choked is then: m max \y + V K) For a specific heat ratio of 1.3, this reduces to: P mmax= 0.6673A* °— (5.30) (Mo)1 The stagnation conditions are defined at the reservoir of each gas volume. 70 If the pressure ratio is small enough so that choking does not occur, the mass flow rate is determined by the following equations: ' ^ AKA 1 - » / w = , AM Where M is the Mach number of the gas at the inlet or the outlet of the reservoir. The Mach number is calculated by: M = y-l y-\ \P) (5.32) The choking occurs at the gas needle seat when the needle just begins to open. The mass flow will cease choking as the pressure at the needle seat and the gas sac begins to equalize. The mass flow between the gas sac and the atmosphere is not choked when the needle just begins to lift, and only begins to choke when the pressure in the gas sac increases due to mass flow from the seat and attains the required critical pressure for choking. 5.2.3 Boundary Conditions The boundary conditions are specified to complete the Eq. (5.27) and (5.28) for the first and last cell of each passage. For the pressure boundary condition, the pressures at the reservoirs at each end of a passage are calculated separately from Eq. (5.13) for the liquid diesel and Eq. (5.18) for the CNG. These pressures are then used as boundary equations for the passage, and are directly used to calculate the velocity and pressure in cell 1. The velocity boundary conditions also need to be specified to complete the passage equations. At an end where the velocity is entering the passage, the velocity at the 71 boundary is set to 0. This ignores any entrance effects and assumes that we are within a large reservoir and far enough away from the inlet to that reservoir. At an end where the fluid is leaving the passage, the velocity boundary condition is set to the same velocity as the last cell of the passage. This assumes that the location of our boundary condition is close to the last cell of our passage so that the velocity has little distance with which to decrease. For cell 1, assuming the flow of the fluid is going into cell 1, the equation for this cell would be as follows: = -E dt i dx V 2 J R\ K 2dx dW 1 ^ - ^ , . _ ^ ^ + 0 dt i p dx 2dx In the above equations, the subscript Rl refers to the reservoir pressure bordering cell 1. These equations are similar for the boundary condition for cell N. If the fluid were exiting cell 1 due to reverse flow, the velocity in cell 1 would replace the 0 in the momentum equation above. Due to the nature of the equations and the physics of the fluid flow, it is possible that at some point during the injection process, fluid can either be entering or leaving at both ends of a passage. This usually occurs during transitional stages when the direction of flow is in the process of changing direction, and does not last for a long period of time. 72 5.2.4 Cylinder Pressure Cylinder pressure directly affects the forces on the needle valves in the injector. The absence of cylinder pressure in the ITR experiment will cause the needle valves to lift later and remain open for a shorter period of time, decreasing the fuel mass injected. The addition of cylinder pressure in the 6V92 experiment will cause the needle valves to lift earlier and remain open for a longer period of time. The isentropic perfect gas law is used to simulate the compression of the air in the combustion cylinder as the piston moves. A schematic of the crankshaft-piston arrangement is shown in Fig. S.4. Figure 5.4 - Crank Shaft Schematic The data supplied for the 6V92 engine includes the compression ratio, the bore diameter of the piston, the connecting rod length and the total displaced volume. Knowing all these values, the calculation of the volume in the combustion cylinder can be done, since the volume at any crank angle depends on length 1, length 2 and the clearance. These values 73 are in turn a function of the stroke, the crank angle, the connecting rod length and the total displaced volume. The total volume in the cylinder at any crank angle 6 is: V = B • ^MaxDisplacement) - (Lengthl) - (Length!^ {(si si\ (si \ r 1 ~ = B- -C -1 + C r + — ~ — CO (5.33) Where B is the piston bore area, S is the stroke, Q is the compression ratio, CL is the connecting rod length and 0 is the crank angle. The compression of the fluid in the combustion cylinder is assumed to be isentropic and follows the perfect gas laws. The equation used to find the cylinder pressure at any crank angle is: PV7 = C (5.34) Pcyi and Vcyi are calculated at -120° before TDC, the point at which the exhaust valve to the combustion chamber closes. The pressure P c yi is assumed to be equal to the turbocharger pressure and Vcyi can be calculated from Eq. (5.33). Vi is calculated at the crank angle we want from Eq. (5.33) and then the pressure in the cylinder Pi can be calculated at that same crank angle from Eq. (5.34). 5.3 General Model Layout The model is laid out to simplify the organization of the various numerical processes. The entire injection coding process is separated into eight separate subroutines. Each subroutine represents individual numerical processes linked by calls from the time 74 advance procedure or the differential equation subroutine. A graphical representation of the organization of the individual processes is shown in Fig. 5.5, and the actual model code is shown in Appendix G. MAIN PROCESS CALL RPM BOI PW POPPET LIFT/CLOSE OUTPUT FILES PRESSURES VELOCITIES FLUID PROPERTIES PASSAGE SUBDIVISION RATES OF PRESSURIZATION NEEDLE A C C E L E R A T I O N NEEDLE VELOCITIES PLUNGER VELOCITY PLUNGER VOLUME RPM BOI PW POPPET LIFT/CLOSE PRESSURES VELOCITIES TIME RATES OF PRESSURIZATON FLUID ACCELERATION CHANNELUQ CHANNELGAS DERIVS PLUNGER VOLUME DISPLACEMENT! PLUNGER VELOCITY CRANK ANGLE CYLINDER VOLUME CYLINDER V O L U M E CALC TIME (REFERENCED] PLUNGER VELOCITY Figure 5.5 - General Model Layout Flowchart 1. Main Process Call As the first subroutine in the program, this procedure calls the injection simulation for various boundary conditions. The injector operating conditions modified here are the rpm, BOI, pulsewidth (PW) and the poppet lift and close time. Generally, knowing the operating conditions of the various experimental data sets, the model is run with the same conditions and then compared to the experimental plots. This subroutine simplifies 75 running the simulation for various cycles at once, as separate calls to the main process can be made here. 2. Initial Conditions and Time Process Advance This subroutine provides all the initial conditions in the passages and volumes, pump pressures and fluid characteristics. In addition, this subroutine sets the subdivision of each passage and the time step beginning, end, and size. In short, this procedure controls the entire simulation as it calls the appropriate subroutines, keeps track of the variables, controls the time advance and outputs the data files. 3. 'Derivs' Subroutine This subroutine contains all the injector geometry and the differential equations for each volume. In addition, the differential equations for the mechanical components such as the individual needles and the diesel intensifier are located here. Also, the poppet closure and open equations are located here in addition to the spring properties for needle movement. This subroutine requires a large amount of input data, including all the boundary conditions from the main process call, the velocities at the beginning and end of each passage given by the time process advance subroutine as well as any fluid properties. The outputs from this procedure are all in the form of rates of change, of either reservoir pressure or of mechanical motion. All of these derivatives are passed back to the time process advance subroutine, multiplied by the appropriate time steps and are added to the previous value of the variable. 4. 'Channelliq' and 'Channelgas' subroutines These subroutines contain only the discretized differential equations outlined in section 5.2.2 for the diesel and gas passages respectively. The required inputs for these subroutines include the pressure and velocity boundary conditions in the volumes adjacent to the passage, the pressures and velocities in the passage at the previous time 76 step, the fluid properties that change with pressure and the passage subdivision. All of these values are located in the time advance subroutine and are passed when the subroutines are called. Again the output is in the form of the rate of change of velocity or pressure with respect to time, and is sent to the time advance subroutine where it is processed. 5. Plunger Velocity and Displaced Volume Calculation The plunger velocity subroutine is called by the 'Derivs' subroutine and calculates the velocity of the plunger based on the equations given in section 2.2.2. The input to this subroutine is the crank angle relative TDC of the combustion piston and the output is the velocity of the plunger at that crank angle. The outputs from this subroutine are the rate of change of volume due td the motion of the plunger and the total volume calculated by the total displacement of the plunger. 6. Cylinder Volume Calculation The cylinder volume is calculated here using equations derived in section 5.2.4. This subroutine takes crank angle input and outputs the volume. This volume is then used in an isentropic compression calculation to find the pressure in the combustion cylinder. S.4 Time Reference To accurately correlate the model and experimental results, the timing of the pressure traces is required. For the ITR, we need to rely on two pieces of information to correctly position the pressure trace relative to a piston position, while for the 6V92 engine, we only have one point of reference and need to extrapolate for accurate timing. A piece of information that is included in the data acquisition on the ITR is the voltage sent to the solenoid by the DDEC to control the actuation of the poppet valve. This signal has a very distinctive profile, and a sample one from the experiment is shown in Fig. 5.6. 77 Experimental Injector Pulse Voltage vs Time 1000 rpm -12 BOI 9 PW 1.00 T 0.50 -0.00 • -0.50 -2 (A £ -1.00 -O > -1.50 --2.00 --2.50 --3.00 -0.003 0.004 0.005 0.006 0.007 v 0.Q08 Time (s) Figure 5.6 - Experimental Injector Pulse Voltage vs. Time The point at which the solenoid begins to close the poppet valve is defined as the electronic BOI. This is different from the actual BOI, which is the point at which the needle valve lifts and fuel is injected into the combustion cylinder. The electronic BOI is located at a specific point on the injector pulse curve, after a significant response time, as the current charges up the solenoid. This response time, or solenoid charge time, is approximately 1ms, as compared with the graphs provided by Hames et al. [7]. While the exact electronic BOI is not easily discernible from a comparison of Fig. 5.6 and the definition given from [7], the point at which the solenoid discharges and the poppet valve begins to open again is easily identified as the large downward spike. The rapid current and voltage decay by the solenoid coil signifying the end of the pulsewidth and injection cycle is common in every injector voltage graph. 78 The method used to determine correct location of the data in reference to the crank angle of the piston is to rely on two pieces of information. One, the large downward spike at the 0.002s mark in Fig. 5.6 that signifies the end of the pulsewidth, and second is the RPM, BOI and PW data recorded from the DDEC handset. The DDEC handset provides both the BOI and PW data in crank angle degrees. Knowing these two pieces of information, we can reference our data so that the rapid voltage decay lies directly on the point at which the pulsewidth ends. This will place our data in a correct location with respect to the piston position in the combustion cylinder. For Fig. 5.6, with a -12° BOI and 9° PW, the large downward voltage spike would be placed at -3° relative to TDC since this point is where the pulsewidth ends. All the data is then adjusted from this point knowing the RPM of the engine, in this case, 1000 RPM, and the sampling rate of the DAQ. The timing of the system for the 6V92 becomes more difficult because the injector pulse was not determined and because the BOI could not be recorded due to a malfunction in the DDEC handset. To offset the lack of injector pulse data, the addition of a positional transducer to give us the point where the piston reaches TDC was recorded. The resulting locating of the data for both the model and the experiment can then be set at a static point, namely 0° crank angle relative to TDC. The PW was still available from the handset but the BOI now needs to be estimated for model purposes, based on the point at which the pressure in the poppet volume begins to climb relative to the TDC of the piston. The estimation of the BOI is likely insignificant in the mathematics of the model since the region on the cam where the poppet valve closes has a constant slope. However, the comparison of any model versus experimental results, needs to be carefully scrutinized for the 6V92 data due to this problem. The time referencing in the code is set to allow flexibility in starting time for pre-pressurizatioh purposes. Everything is referenced to the crank angle of the combustion cylinder, although the cam has its own referenced angle that needs to be modified to fit with this crank reference. 79 The cam regression equation is set to its own angle reference, but knowing the offset of the cam to the combustion cylinder, we can modify this so that the cam outputs the correct lift at the correct angle. Some important angles that show the relationship of the cam with the piston for the ITR are shown in Fig. 5 . 7 . TDC START OF CAM LIFT LOCAL CAM ANGLE - 8 2 66:3' MAXIMUM CAM LIFT LOCAL CAM ANGLE 0* 28.3" EXHAUST VALVE CLOSURE Figure 5.7 - Cam Reference to TDC of Piston The maximum lift of the cam is locally set at 0°. This maximum lift occurs at an angle relative to the combustion cylinder of 28.3° after TDC. Our starting point for the model is when the cam begins to move the plunger and pressurization begins to occur inside the injector. This represents our time start of t = 0. The beginning of plunger movement occurs at -82° on the local cam reference angle corresponding to 28.3° - 82° = -53.7° referenced to the combustion cylinder TDC. Since the plunger calculation uses the local cam angle rather than the relative crank angle, the local cam angle must be calculated and before being applied to the calculation to determine the plunger movement. This is done by sending the crank angle relative to TDC to the plunger movement subroutine and subtracting by 28.3° to obtain the local 80 cam crank angle. At any angle before -53.7°, the plunger lift is equal to 0 and any angle after 28.3° is not supported by the regression calculation and is also equal to 0. The offset from the maximum cam lift to TDC of the combustion cylinder for the 6V92 engine is 43° rather than 28.3° for the ITR, and the cam begins to lift at a local cam angle of-71° rather than -82°. This corresponds to a start point of 43°-71° = -28° before TDC. The exact location of the exhaust valve closure for the 6V92 engine is not precisely known, and is taken as 66.3° before the start of the plunger movement as with the ITR. 5.5 Model Numerics The coding and mathematics of the injector simulation is only part of the total modeling process. The time advance scheme can lead to mathematical instabilities due to the large rates of pressure increase or decrease within a very short amount of time. Physically, pressure forces instantly compensate for any overshoots due to steep discontinuities but in a mathematical simulation, this compensation takes place over a finite length of time. The numerical overshoots are functions of the physical geometry of the injector, the choice of subdivision in the passages (dx) and the choice of time step size and of time step advance. 5.5.1 Equation Specifics The system of equations in the model is solved by calculating the derivative for each reservoir, using the geometrical values of the passage areas adjacent to that reservoir and the velocities determined from the passage equations. The actual numerical values associated with each reservoir are outlined below. The general reservoir equation (5.13) is again: dV\ E dt) V dV_ dt. 81 Table 5.1 shows the numerical values for each reservoir in the gas injector. The reservoir volume represents the value V, passage areas 1 and 2 represent Au, and Ao* and the volume changes 1 and 2 represent the value of dV/dt in Eq. (5.13). Table 5.1 - Gas Injector Reservoir Values Reservoir # Initial Reservoir Volume (m3) Passage Area 1 (m2) Passage Area 2 (m2) Volume Change 1 (m3/s) Volume Change 2 (m3/s) Reservoir Description 1 1.93xl0-7 1.95X10"6 - - - Transducer 2 9.51xl0-8 1.95x10* 4.91X10"6 - - Poppet * 3 7.48x10"7 4.91X10"6 2.01X10"6 4.42x10° x Uplunger 8.30X10"6 X Uintensifier Plunger 4 2.78xl0"8 2.01X10"6 4.87xl0"7 (Vent line) SxlO^XUgas Control Diesel 5 1.19xl0"8 2.01x10"* 5.07x10"* X Uintensifier Post Intensifier* 6 3.23xl0"y 2.01x10-*' 1.69X10"" 1.68x10"6 x (Udiesel'Ugas) Diesel Needle 7 1.69x10"* 1.69X10"6 1.9xl0"3x (hdiesel— hgas) Diesel Seat 8 5.76x10* 0.01195 x hdiesel 1.27xl0"8x 6 nozzle holes Diesel Sac 9 2.76X10"7 3X10-6 3X1C6 XUgas CNG Shoulder* 10 1.75x10'* 3x10* 7.54x10"3 x CNG Seat 11 1.15x10"" 7.54xl0"3 x hgfls 2.03xl0"7 x 6 nozzle holes CNG Sac * Volume also has a supply line at constant pressure 82 Using the numerical values from Table 5.1, and the velocities from the associated passages, the rate of change of pressure in each reservoir can be calculated at each time step. The lengths of the passages that connect each reservoir are shown in the Table 5.2 below. Table 5.2 - Passage Information Passage # Passage Length (m) Reservoirs Connected 1 0.0223 1-2 2 0.0418 2-3 3 0.0364 3-4 4 0.0194 5-6 5 0.0388 6-7 6 0.0485 CNG supply - 9 7 0.0198 9-10 The value of dx required for Eq. (5.27) and (5.28) are found by dividing the passage lengths shown in Table 5.2 by a cell division coefficient determined by the user. 5.5.2 Time Step Considerations The amount of time it takes for the simulation to run is directly proportional to the time step used. In addition, the time step size also affects the accuracy of the injector simulation. Both of the numerical models average around lxlO - 5 ms time step over a 10ms period with passage subdivisions of five cells. This time step seems to provide good accuracy and a relatively fast computation time. A decrease in cell size will require a decrease in time step to compensate for the increase in pressure and velocity fluxes. Generally, doubling the number of cells in a passage will require doubling the amount of time steps in the simulation. Unfortunately, this modification will increase the computation time substantially, by almost a factor of four. For computation efficiency, a passage subdivision of five cells with a lxlO - 5 ms time step shows sufficient accuracy and is used for each model result shown in this thesis. 83 5.5.3 Numerical Stability The stability of the model depends on the time steps and meshing used in the simulation as well as some of the physical properties of the injector itself. Using the passage subdivision and time step previous will produce extreme numerical instability after the injection cycle has ended. A very small time step would likely produce a fully stable and accurate solution; however, this change in time step will result in unacceptably large computation times. An alternative solution must be found to offset the instabilities acquired from the injector physics and the increase in time step and mesh size for computational purposes. r 5.5.3.1 Causes of Instability If our model is developed without any instability compensation, the output will be unstable. A time step that is too large, a mesh size that is too large, a combination of the two or sharp discontinuities in the numerical simulation are the main causes of instability in numerical processes. Generally, the ratio of Ax/At has a minimum value for stability for a given passage, but this ratio does not take into account physical effects that can cause discontinuities in the solution. The ratio of Ax/At does not have an effect on our solution since decreasing the time step to extremely small values does not eliminate instabilities. Physically, it is known that there are several discontinuities in both the diesel and the dual fuel injector. The problems were isolated to two specific areas within each injector. The diesel injector contains a check valve that prevents back flow through to the injector stack and the plunger region. Theoretically, the numerical representation of this check valve is not difficult; the pressure forces on either side of the valve govern its movement. When the side with the higher pressure shifts, the check valve will either open or close instantaneously. Realistically, the check valve will open or close in a finite amount of time, but this amount of time is comparable to the time step in our program allowing us to assume instantaneous closure. This instantaneous closure causes discontinuities because 84 the boundary conditions at the end and start of the passages enclosing the check valve must also instantaneously change. This sudden change in boundary conditions causes the velocities and pressures within the passage to begin to fluctuate chaotically, resulting in large numerical instabilities. The gas injector uses a diesel intensifier to increase the rate of diesel fuel compression to force the diesel pilot to inject first, as well as to accurately control the amount of diesel pilot used. Diesel pilot injection occurs before the intensifier has reached its maximum lift, and at the point just before the intensifier fully lifts, there is a large amount of diesel mass flow towards the needle valve as the fuel is being injected. This large mass flow combined with the small size of the injector passages, results in large velocities through the diesel passages. As shown in Fig. 2.10, the intensifier is the only source of pressure increase in the pilot injection process. When the intensifier reaches its maximum lift, a sudden discontinuity is reached, as pressurization no longer supports the large outflow of fuel from that reservoir. The final result in the model is, again, a chaotic fluctuation of pressures and velocities within that adjacent passage which will propagate to the other regions of the pilot injection passages. Of less importance, the convergence of the final solution can also be increased by a successive over-relaxation coefficient as will be discussed later. 5.5.3.2 Solutions to Instabilities Many different possible solutions were used in an attempt to stabilize the output of the model. Initially, an attempt to discern whether an excessively small passage cell size or time step would stabilize the solution. Preliminary results showed that these modifications would only delay the large oscillations that begin to occur as the model destabilizes. Attempts to add leakage or friction factors also resulted in limited improvement, at best, by reducing the rate the solution becomes unstable. 85 The method of Liu et al. was used to obtain a converged solution from our model. This method modifies the discontinuous velocity profile by making it smoother. Velocity diffusion is accomplished by swapping a fraction of the velocity value in a cell with that of its adjacent cells. After the new values of the velocities are found at time k+1, a swap is performed at the boundary of two adjacent cells and a flux parameter, Fl, is defined. Fl \Wk*) = \(Wi+r-Wr) (5.35) The diffusion operator defined as DW, is then the difference in the flux parameters above between the boundaries for each cell: DWjk+1=Fl x{jVk+')-Fl x(Wk+1) (5 36) Then the new value of each cell is defined as follows: *Wk+x = Wk+x +DWik+x (5.37) The value of 1/8 shown in Eq. (5.35) is the diffusion coefficient. A smaller number suggests a decreased amount of diffusion while a larger number will increase the amount of diffusion to other cells. Effectively l/8th of the value from the cell to be diffused is sent to each of the adjacent cells, which in turn sends l/8th of their value back to the diffused cell. The cells at the end of each passage must also be diffused. While each end cell is adjacent to a reservoir, it is incorrect to allow diffusion into the reservoir where there is a boundary condition for inflow to a passage of zero velocity. Allowing this to occur will turn each reservoir into a sink, and velocities in the passage will approach zero. So, at the end cells of each passage we impose only a one sided diffusion as follows: DWk+x = Fl3(wk+l) DWNk+l=Fl (5.38 and 5.39) 2. N~2 86 This one sided diffusion also supports outflow velocity boundary conditions. The effect of this velocity diffusion operation is very noticeable as shown in the velocity cell distribution shown in Fig 5.8, for cases with diffusion and without. SOq RPM -12 BOI 9 PW (DHTuelon) 2000000 time step* Intensifier Maximum Lift -6.B -S.7 Crw* Angla R«L TDC 800 f\PM -12 BOI 9 PW (No Diffusion) 2000000 time steps - A S *a -S.7 Crank Angle Rel. TDC a) With Diffusion b) No Diffusion Figure 5.8 - Cell Velocity Distribution (Passage 4) As shown, the velocity distribution is much more controlled and smooth in the profile with diffusion. In the profile without diffusion, the velocity distribution becomes very chaotic after the intensifier reaches maximum lift, seen as approximately the point where the velocity in the first cell decreases rapidly. The magnitudes in velocities do not match due to the inaccurate solution as the instabilities begin to take effect in the non-diffusive case. However, the question arises as to whether the amount of diffusion is excessive and decreases the accuracy of the solution. Liu et al. introduces an anti-diffusion stage to remove excessive diffusion and to increase accuracy particularly around sharp discontinuities. The use of this stage may or may not be required unless excessive diffusion is observed. A comparison of a decrease of the diffusion magnitude is shown in Fig. 5.9. 87 800 RPM -12 BOI 9 PW 1/16 Diffusion Coefficient (2 million time steps) > o -5 -10 JV / i K IN,. i \ o -a -e BP—- ' nr-w—— -4 -2| 0 7 4 . Crank Angle Rel. TDC 800 RPM-12 BOI 9 PW 1/8 Diffusion Coefficient (2 million time steps) 4| 10 0 -6 t-8 -4 -2f ! ' 0 2 4 Crank Angle Rel. TDC a) 1/16 D.C. 2 million time steps b) 1/8 D.C. 2 million time steps 800 RPM -12 BOI 9 PW 1/16 Diffusion Coefficient (8 million time steps) 20 16 i| 10 £ • g 0 •10 Crank Angle Rel. TDC c) 1716 D.C. 8 million time steps Figure 5.9 - Diffusion Coefficient Comparison (Cell Velocity Passage 4) The main difference between the change in diffusion coefficient holding the time step constant, as shown by Figs. 5.9a and 5.9b, is the oscillatory convergence as the velocity decreases to zero. We conclude that the extra diffusion introduced by the higher diffusion coefficient reduces the time step required for a stable and converged solution by comparing Figs. 5.9b and 5.9c where there is less difference in this oscillatory convergence. While it is odd that the solution becomes less smooth with more diffusion we can conclude that the less smooth solution is the converged one because an increase in the number time steps with a constant diffusion coefficient produces this increase in oscillation. From this, it can be extrapolated that a non-diffused solution would approach the diffused solution with a large enough number of time steps. We can then conclude 88 that the diffusion is not excessive and that usage of the anti-diffusion stage is not required. Manually introducing numerical diffusion into the injector simulation will affect the accuracy of our output. A study of the decrease in accuracy for a simple two-reservoir simulation shows that this decrease in accuracy is small. This single channel simulation is shown in Appendix D. 5.5.3.3 Successive Over-Relaxation In conjunction with the velocity distribution function, successive over relaxation (SOR) was applied to further force the numerical solution to converge to a steady state value. While adding this factor does not change the accuracy or computational time of the model, it does help to increase the physical-theoretical relationship of the model by quickly reaching the steady state value: SOR is applied by multiplying the flux term by a factor and then adding it to the previous value at the time step advance. In equation form, this is accomplished as follows: dP Pk+X =Pk +(SOR)—dt (5.40) dt For the solution to be stable, the SOR factor must be less than 2, and must be used in conjunction with the velocity diffusion function. The SOR factor will not stabilize an already unstable solution but will help a stable solution converge quickly. 89 Chapter 6 Results This chapter will summarize the results from the model and compare them with the results from the experimental data. As shown in the description of the injectors, values related to the numerical simulation are assumed in the absence of direct experimental measurement for the discharge coefficients for each orifice, poppet opening and closing times or leakage factors. Estimated values were chosen and modified within an acceptable range to fit the experimental data. The resulting sensitivity analysis is also discussed in this chapter. 6.1 Experimental-Model Comparisons Establishing how accurately the model represents the experiment is based on some qualitative measures such as shape and timing, as well as quantitative measures such as peak pressure and slope. The amount of confidence we can apply to each of these criteria is directly related to the experimental cycle to cycle variation. An erratic profile, in the cycle variation will allow a larger margin of error in the simulation. Generally, the peak pressure from the experiments is very consistent and needs to be considered with more scrutiny than the shape of the slope profile since this changes between cycles in the experiment. 6.1.1 Diesel Injector Results Diesel injector experimental-model comparisons were performed for four different operating conditions. The loads chosen are outlined in Table 6.1 and are shown in Fig. 6.1. 90 Table 6.1 - Diesel Injector Experimental-Model Comparison Loads Chart RPM BOI (Rel. TDC) Pulsewidth a 600 -1.5 5.8 b 1200 -12.5 8.3 c 1200 -11.5 20.1 d 2100 -8.15 20.4 •j» -12 -10 -8 « -4 -2 0 2 4 S B 10 12 14 16 16 $ c) d) — Experimental Model Figure 6.1 - Poppet Pressure Traces - Diesel Experimental-Model Comparisons Upon inspection of the experimental vs. model pressure data, we notice that the model represents the actual diesel injector well. The overall shape and pressure peaks are within 91 estimated experimental error, and the timing of the start and end of the trace is reasonably accurate. Experimentally, as the BOI is reached, we see that a short rise and fall of the pressure trace before the pressure rises steadily towards the peak value. This 'bump' in the pressure trace is common to all loads but does not appear in the model output. Physically, if the injector is functioning perfectly, these 'bumps' should not occur. Efforts to deduce the cause of this repeatable characteristic of the experiment from injector properties have failed, thus shifting the cause to external experimental conditions. Effects such as mechanical vibrations due to the engine, excessive temperature effects that were not considered in the simulation or even problems with parts of the data collection apparatus are possible causes to these experimental characteristics. 6.1.2 Gas Injector Results The experimental-model comparisons for the dual fuel injector were performed for five different operating conditions, chosen over the range of loads performed in the experiment. The main comparison performed in this section is that of the pressure trace at the poppet valve, but additional data of the RBOI was also obtained and will be compared in the following section (6.1.3). The experimental conditions used in this comparison are shown in Table 6.2, and the corresponding experimental-model comparisons are shown in Fig. 6.2. Table 6.2 - Gas Injector Experimental - Model Comparison Loads Chart RPM BOI (Rel. TDC) Pulsewidth a 800 -12 9 b 1000 -12 9 c 1200 -12 9 d 1400 -9.8 13.5 e 1600 -8.7 9.6 92 Figure 6.2 - Poppet Pressure Traces - Gas Experimental-Model Comparisons 93 Upon inspection of the graphs in Fig. 6.2, we can conclude that the model provides an accurate representation of the shape of the pressure trace during the injection cycle. However, there are a few problems in the pressure traces that can be identified either as problems in the model or in the experiment. Figures 6.2a and 6.2b are virtually identical, the model pressure trace having a larger slope and peak pressure than the experiment. Figure 6.2c shows an almost perfect match between the model and the experiment, showing an almost identical peak pressure and slope. The only slight discrepancy is in the pressure loss after pulsewidth has ended, which can be attributed to a slightly incorrect vent discharge coefficient that will be discussed in section 6.2. Figures 6.2d and 6.2e show the experimental-model comparison at higher loads. Figure 6.2d shows a very good agreement until the pressure decrease, where the experimental pressure decreases and a much slower rate than that of the model. This decrease in pressure is the first sign that the experiment may not be completely repeatable since the other four graphs show a similar pressure loss while that in Fig. 6.2d is not the same. While there is only one model plot, namely Fig. 6.2c, that accurately fits the experimental data, the other model plots are quite close to that of the experiment within an expected amount of experimental error. Each model trace has a slightly higher peak pressure, likely due to the fact that leakage is not considered at several places in the injector. An investigation of physical leakage in the injector and consequent implementation of this leakage in the model could increase the experimental-model accuracy. In addition, more experimental data is needed to assess the repeatability and to obtain a larger amount of confidence in the ITR experiments. 6.1.3 Relative BOI Results Since the ITR does not have an actual combustion cylinder, we can measure the timing between the diesel and gas injection jets by attaching a RBOI sensor underneath the injector nozzle. The timing of the jets can provide us with another source of data to further verify the accuracy of the model. We will compare the initial injection pulses on 94 the RBOI sensor data with the individual needle lifts of the model. The comparisons are done for the same loads and conditions in Table 6.2 and are shown in Fig. 6.3. 1 \ I / n / - i — i — ' CA Rel TDC a) aaa* E ._5 f w ••\y l \ s I j u CA Rd TDC b) 0.9U E - - Diesel BOI -CNG BOI — Diesel Needle Lift (Model) —CNG Needle Lift (Model) Figure 6.3 - RBOI Experimental-Model Comparisons 95 A numerical comparison summarizing the results obtained from a graphical analysis of the graphs in Fig. 6.3 are shown below in Table 6.3 (in crank angle relative to TDC): Table 6.3 - RBOI Numerical Comparison Diesel BOI (Exp) Diesel BOI (Model) CNG BOI (Exp) CNG BOI (Model) a -6.6 -7.32 -2.72 -4.04 b -6.3 -6.96 -2.1 -3.80 c -6.6 -6.56 -3.2 -3.36 d -5.12 -4.00 -1.76 -1.16 e -0.54 -2.48 2.52 0.75 The experimental RBOI data does not completely agree with the needle lift output from the model. However, this is to be expected given the associated amount of discrepancy between the pressure traces of the same loads shown in Fig. 6.2. While comparison of the experimental injection times and the model needle lifts do not completely agree with each other, they do not seriously disagree. The largest difference for the diesel jet occurs at 1600 rpm with a difference of 1.94°. For the gas jet, the largest difference occurs at the same load, with a difference of 1.77°. Since we are comparing the diesel jet impingement on the transducers a small distance away to the model needle lifts, there is some expected error between the pulses. This time discrepancy is small, but comparable to the difference in the RBOI differences above. This however, cannot be the only possibility since some of the needle lifts from the model appear later than those of the first impact of the diesel fuel spike on the RBOI plots. Generally, in all the plots in Fig. 6.3, either the diesel needle lift or the CNG needle lift is approximately equal to the pulse of the associated jet on the RBOI device. However, the other needle lift is offset from the experimental by an average of one crank angle degree. At 800 rpm, one crank angle degree is roughly equal to 0.2 ms, and can be attributed to the transport time if the velocity of the fUel exiting the nozzle is approximately 250 m/s. This velocity is not unrealistic given the pressures in the injector and the nozzle diameter at the exit. At higher rpm, the required velocity is even larger. 96 Other than fuel transport, differences between the experimental RBOI and the model needle lift can be attributed to discharge coefficients, poppet lift or close times, leakage or experimental error. It is likely that any discrepancies associated with the RBOI and the model needle lift are the same experimental problems that are associated with the differences in the pressure traces at the transducer of the injector. Differences in pressure forces, needle forces or geometric tolerances that are slightly inaccurate can cause large errors in the model output. In addition, a strong possibility of the error between the experiment and the model could be the variability of the experimental injector operation. While the main focus of the comparisons between the model and experimental data has been on the errors involved, the results are indeed very close to each other, and the model provides a good simulation of the experiment. 6.2 Sensitivity Analysis Several conditions and discharge coefficients are assumed to mathematically model the injectors. These discharge coefficients rely primarily on the geometry of the orifices through which the fuel flows, but cannot be accurately determined based on theory alone. These coefficients cannot be easily determined experimentally either, because of the miniscule size of these orifices and the low mass flow through them. Assumptions are also made on experimental conditions such as poppet valve lift and close time, tolerances between connecting pieces or physical properties that can vary from injector to injector because of the difficulty to make an accurate experimental measurement of these values. For conciseness, the sensitivity analysis will only be performed for the gas injector. Any results ascertained from the perturbations in values for the gas injector can also be accomplished with more ease for the diesel injector. All of the sensitivity analyses are performed at 800 rpm, -12° BOI and 9° PW. 97 6.2.1 Change in Discharge Coefficients There are six orifices at which a discharge coefficient is warranted. The injection nozzles for both the gas and diesel sides, the needle seat for both the gas and diesel needles, the vent line from the gas needle shoulder and the orifice to the return line at the poppet valve. Figure 6.4 represents the modifications in discharge coefficient from Table 6.4. The baseline value is default and is the second series plot in each graph. Table 6.4 - Discharge Coefficient Sensitivity Conditions Chart Discharge Coefficient Lower Value Baseline Value Upper Value a Diesel Nozzle 0.4 0.6 0.8 b CNG Nozzle 0.6 0.8 1.0 c Diesel Seat 0.6 0.8 1.0 d CNG Seat 0.6 0.8 1.0 e CNG Shoulder Vent 0.2 0.4 0.6 f Poppet Return 0.4 0.6 0.8 98 CA Rel TDC a) Diesel Nozzle -Nozzle Cd=0.4 - Cd=0.6 Cd=0.8 CA Rel TDC c) Diesel Seat -Diesel Seat Cd=0.6 -Cd=0.8 Cd=1.0 CA Rel TDC e) CNG Vent -Vent Cd = 0.2 -Cd = 0.4 •Cd = 0.6 b) CNG Nozzle -CNGCd=0.6| -Cd=0.8 -Cd=1.0 CA Rel TDC d) CNG Seat -CNG Seat Cd=0.6 -Cd=0.8 Cd=1.0 CA Rtl TDC f) Poppet Return - Poppet Cd = 0.4 •Cd = 0.6 •Cd = 0.8 Figure 6.4 - Transducer Pressure Profiles for Sensitivity Analysis 99 For the same operating conditions, the discharge coefficients have little effect on the overall shape of the pressure profiles at the pressure transducer. Changes in the discharge coefficient at the diesel injection nozzle changes the peak pressure by approximately S MPa over a 40% change in discharge coefficient. A change in the nozzle discharge coefficient does not follow the same pattern as the rise in peak pressure. This is not unexpected since the injection region is completely separate from the transducer area save for the diesel multiplier. A change in discharge coefficient on the gas side of the injection nozzle slightly increases the peak pressure, but does not have any effect on the rise in pressure, as shown in Fig. 6.4b. Changes in discharge coefficient at the diesel seat produces a small spike in peak pressure, while the gas needle seat produces only a minor change in peak transducer pressure. Changes in the CNG shoulder vent coefficient primarily modify the decrease in pressure. This occurs when the gas needle reaches a specific lift, where the control diesel fuel begins to vent and return to the diesel supply. As the discharge coefficient changes for the poppet return, an overall pressure change is observed as the poppet initially closes. The poppet discharge coefficient also causes a small change in the rise of the pressure as is expected, but this change is very minor as shown in Fig. 6.4f. Since the changes in discharge coefficients by 0.2 in either direction does not appear to produce any significant changes in the pressure profiles, the assumed baseline values for each discharge coefficient is acceptable. Changes in discharge coefficient can increase the overall accuracy of the experimental-model comparison by a small degree, but should not be relied upon to do so. 6.2.2 Change in Poppet Lift and Close Time As with the discharge coefficients, it is difficult to experimentally determine the poppet lift or close time with accuracy. While experimentally possible, it is not feasible within time and financial constraints. The baseline poppet open and close time are chosen so that experimental-model comparisons are most accurate. The baseline open and close times 100 are 0.5 ms and 0.8 ms respectively. Changes in these times are performed for sensitivity purposes and are illustrated in Fig. 6.5 for the changes outlined in Table 6.5. Table 6.5 - Poppet Open/Close Sensitivity Series Poppet Close Time (s) Poppet Open Time (s) A (Baseline) 0.0005 0.0008 B 0.0005 0.0005 C 0;0008 0.0008 Sensitivity of Poppet Open/Close Time 100 T ; (0 0. 3 cn w £ Q. CA Rel TDC Figure 6.5 - Transducer Pressure Profile for Poppet Open/Close Sensitivity The baseline values were determined from a comparison between the diesel injector model and the corresponding experimental data. The values of 0.5ms closure and 0.8ms open showed a very good fit for the diesel injector data. As shown, changing the open time does not significantly change the decrease in pressure at the end of the pulsewidth as shown between the first two series. The decrease in 101 pressure first begins at the vent line at the CNG needle, and the poppet opening only changes the pressure after it has already significantly decreased. The poppet closure time however, essentially increases the BOI and changes the point at which the pressure begins to increase. While the change in BOI will change the region on the cam that pressurizes the injector, the slope of the pressure profile remains approximately the same since the slope of the cam is approximately constant through the injection cycle. Changing the BOI will also effectively decrease the total pulsewidth as well, resulting in a lower peak pressure. While increasing the poppet closure time fits the shape of the experimental curve better overall, it does show discrepancies at the point where the pressure first begins to rise. The experimental pressure rise begins much earlier than the model with the increased closure time, indicating that the poppet closure time of 0.8ms is too large. The baseline values are used since they represent the experimental data fairly well and because of the accurate results from the diesel injector experimental-model comparisons. The poppet open and close times are assumed to be independent of the injector used. 6.2.3 Effect of Leakage Leakage is an important factor in injector operation, since it governs the pressurization and the amount of fuel needed for successful injection. As discussed earlier, the only source of possible leakage that will be considered is the leakage above and below the intensifier. The base tolerance used for leakage purposes is 0.00008" equating to approximately 2 p.m above the intensifier and 0.00004" equating to 1 um below the intensifier. Sensitivity analysis for the leakage is outlined in Table 6.6, and the corresponding results are shown in Fig. 6.6. 102 Table 6.6 - Leakage Tolerance Sensitivity Series Above Intensifier Tolerance Below Intensifier Tolerance A (Baseline) 0.00008" 0.00004" B 0.00008" 0.00008" C 0.00004" 0.00004" Sensitivity of Leakage Tolerances 100 T CA Rel TDC Figure 6.6 - Transducer Pressure Profile for Leakage Tolerance Sensitivity As shown, doubling the leakage tolerance in either direction does not significantly change the peak pressure in the transducer profile. Also, it is seen that changes in the leakage tolerance above the diesel multiplier has more of an effect on the transducer profile than changes in leakage tolerance below the diesel multiplier. This is because the sealing diesel acts to re-supply any fuel lost to leakage underneath the intensifier, while above the multiplier there is no source to replenish lost fuel once the poppet valve has closed. 103 6.2.4 Effect of Transducer Modification The addition of the transducer passage to determine the hydraulic pressure of the diesel fuel inside the injector will have an effect on the overall injection process. Experimentally, we cannot observe changes in the hydraulic pressure without the transducer passage, since it is required to collect the data itself, so the effect of the modification is not known. However, the model can predict the effect of this transducer passage easily, by removing the single volume and passage associated with the transducer. A comparison of the pressure traces at the poppet valve, for a standard gas injector with no transducer modification, and for a gas injector with a transducer modification is shown in Fig. 6.7. Effect of Transducer Passage 1000 rpm -12 BOI 9 PW CA Rel. TDC Figure 6.7 - Effect of Transducer Passage on Injector Pressure As shown, the unmodified injector shows a higher rate of pressure increase and a corresponding higher peak pressure than the modified injector does. The cause of this pressure change is the decrease of the effective volume inside the injector with the 104 elimination of the transducer passage and transducer volume. This increased pressure rise also leads to earlier needle lifts, as shown in Fig 6.8. 0.0007 0.0006 0.0005 0.0004 ( 0.0003 0.0002 0.0001 0 -0.0001 10 Effect of Transducer Passage on Needle Lifts 1000 rpm -12 BOI 9 PW T -4 CA ReL TDC Unmodified Diesel Lift Unmodified Gas Lift Modified Diesel Lift Modified Gas Lift Figure 6.8 - Effect of Transducer Passage on Needle Lifts The transducer modification decreases the pressure rise thus delaying the needle lift. However, this delay in needle lift is small, approximately 0.5° for both the diesel needle and the gas needle. The lower rate of pressure rise also decreases length of time that the needle remains open. 105 Chapter 7 Conclusions The model that was developed simulates the injection process of both injectors well. While experimental-model comparisons were not 100% accurate, model outputs show good results within expected experimental error. Attempts to increase precision by modification of coefficients that could not feasibly be determined experimentally were also performed, but could not increase the accuracy of the simulation by an appreciable amount. A finite difference method successfully models the injection process. Unlike the method of characteristics (MOC) where each pressure wave is tracked, and unlike the third party simulation program, SABRE, that does not noticeably track any pressure waves, the finite difference method finds a medium between the two by tracking pressure waves at discrete points in a passage. The finite difference method cannot be used by itself, due to physical discontinuities in the injection mechanism that causes instabilities in the numerical solution. A Lax-Wendroff velocity diffusion algorithm corrects these instabilities by averaging out the velocities in a passage. Successive over-relaxation is also used to help the numerical result to reach a steady state value faster, and while this has no bearing on the accuracy of the solution during the injection period, it will provide a better physical representation of the experimental data after the injection period is over. The diesel injector is much easier to model, and mainly depends on accurate geometry measurements and the plunger displacement profile. The development of the diesel injector, and the resulting accuracy between experiment and model show that the finite difference method is feasible and accurate. The development of the diesel injector model also provided useful information on the discharge coefficients and poppet open and close times. 106 The gas injector is more difficult to model because of the introduction of sealing diesel and the addition of compressed natural gas (CNG). In addition, the added mechanical elements of the diesel intensifier and the dual needle arrangement also complicate things. Experimental-model comparisons of the pressure traces for the gas injector show that the model successfully simulates the injector operation. The additional RBOI test provides an additional source of data with which to compare our gas model. These tests show that there are some inaccuracies between the individual needle lifts in the gas injector and the impact of the separate fuels on the pressure transducers. Both the pressure and RBOI from the model are comparable with the experimental output within expected error. The data used in the latest version of the gas injector model uses values for the discharge coefficients of 0.6 for the diesel nozzle and poppet return, 0.8 for the CNG nozzle and both the CNG and diesel seats, and 0.4 for the CNG shoulder vent. The assumed poppet closure and open times are 0.5ms and 0.8ms respectively, and leakage tolerances of 2pjn and lu.m above and below the diesel intensifier were used. Sensitivity analyses performed on each discharge coefficient shows that they all have a minimal effect on the peak pressure of the system. The discharge coefficient for the CNG shoulder vent affects the pressure decay of the gas injector more than the discharge coefficient for the poppet return. The poppet close time changes the pressure trace significantly, by effectively changing the BOI and decreasing the PW of the injection. The poppet open time does not have any significant effect on the pressure decrease of the system. The leakage tolerances assumed at the diesel intensifier do not change the pressure output by a significant amount. Larger values of the leakage tolerance are possible for different injectors, but these tolerances must be extremely large to have a significant impact on the pressure trace at the transducer. The accuracy that we can attribute to the model is directly related to the consistency of the experiments and the experimental conditions. A lack of confidence exists in the experimental results because of the unexpected variability between data of different loads. The pressure data retrieved from experiments running at different loads was expected to behave in a consistent pattern related to RPM, BOI and PW, but show 107 irregularities that can only be attributed to experimental error. The cycle to cycle variation shows a very small amount of change between cycles of the same injection load, but is not enough to conclude a lack of experimental variability. The data between injection cycles varies slightly for the diesel injector on the 6V92 engine, but does not change at all for the dual fuel injector on the test rig experiments. A day to day variation of loads, rather than a cycle to cycle variation, is required so that we can attribute a larger amount of confidence in our experimental data. This day to day variation would consist of running the experimental apparatus at the same loads on different days, so that a completely new set of data can be obtained and compared. In addition to variation of the experimental conditions, a variation of the injector used for the experiments would also provide more confidence in our experimental output. The tolerances involved in manufacturing injectors are relatively large compared to the dimensions of the injector itself, so different injectors will have different geometry, which will affect model output. 7.1 Research Accomplishments A model was developed to simulate the hydraulics and physical dynamics of the diesel injector and the 6F4 version of Westport's dual fuel injector. While this model is specifically oriented for these two injectors, the simulation can be adapted to fit any injector design. Most, if not all of the components in future injector designs are already created in the coding of this model, and only need inputs with injector specific data for new injector simulations. The coupling of several theoretical equations involving fluid and mechanical processes with a numerical simulation was coded. Assumptions in fluid or mechanical properties were identified and reasoned. Numerical instabilities were identified and solved using a velocity diffusion algorithm. 108 A large amount of experimentation was performed with the help of Westport staff. Successful modification of the experimental injectors, setup and calibration of the data acquisition, design of the RBOI sensing apparatus, operation and design of the injector test rig was all performed to obtain results with which to compare the model. Extensive experimental-model comparisons were performed, not only to identify problems in the numerical code, but also to increase the overall accuracy of the simulation. The evolution of the model over the past two years: how the injectors were to be modeled or the equations were solved, was largely due to experimental-model comparisons. The development of this model for the injectors also provided valuable information on the values of various factors that would be otherwise very costly to determine experimentally. Values for the poppet opening and closure times, discharge coefficients and leakage tolerances were attained by a combination of sensitivity analysis and model-experimental comparisons. These factors were determined within an acceptable amount of error. 7.2 Recommendations for Future Work In addition to the experimental work done in this thesis, a further test of the experimental variability should be done to provide more or less confidence in the experimental data. These tests would involve experimentation with different injectors and non-successive testing on various loads, an example of which would be to record the data under a hot idle condition, change the load to a maximum power load, change it back to the hot idle condition and record again. Comparison of the data traces from these non-successive runs would provide more insight into the experimental variability, and in turn provide more faith in the accuracy of the model. Additional testing by simulating and experimenting with newer injector designs or hydraulic equipment would help confirm the accuracy of the model. Data points in 109 addition to the pressure transducer and RBOI data would further serve to validate model accuracy. A measurement of the fuel mass delivered per cycle would help to verify our model, and would not be too difficult to implement on our experimental apparatus. A closer investigation of the leakage present in the injectors and the implementation of this leakage into the computer model may show better agreement between the model output and the experimental data. At present, leakage is only considered at one specific region in the injector, namely the diesel intensifier, but is known to exist to varying degrees at other areas in the injector. While a finite difference simulation is shown to perform well, it may not be the best method of injector simulation. A comparison of the three main simulation methods: MOC, Sabre and finite difference should be done to determine the most accurate and efficient means of injector simulation. 110 References 1. Burman P.G., and DeLuca F.: "Fuel Injection and Controls for Internal Combustion Engines," Simmons-Boardman Publishing Corporation, pp. 35-52, 1962. 2. Scullen R.S., and Hames R.J.: "Computer Simulation of the GM Unit Injector," SAE paper 780161, 1978. 3. Kegl B., Zambare V.V., Cernej A., and Dobovisek Z.: "A Parametric Study of Fuel Injection Performance by Calculation," Mechanical Engineering Publications Ltd., pp. 65-74, 1992. 4. Marcic M.: "Computer Simulation of the Diesel Fuel Injection Nozzle," SAE paper 930925, 1993. 5. Benson R.S., Horlock J.H., and Winterborne D.E.: "The Thermodynamics and Gas Dynamics of Internal Combustion Engines," Oxford University Press, Volume 1, pp. 73-143,1982. 6. Liu J., Schorn N., Schernus C , and Peng L.: "Comparison Studies on the Method of Characteristics and Finite Difference Methods for One-Dimensional Gas Flow through IC Engine Manifold," SAE paper 960078, 1996. 7. Hames R.J., Hart D.L., Gillham G.V., Weisman S.M. and Peitsch B.E.: "DDECII - Advanced Electronic Diesel Control," SAE paper 861049, 1986. 8. White F.M.: "Fluid Mechanics," McGraw-Hill, 2n d Edition, pp. 336,1986. 9. Baumeister T., Avallone E., Baumeister III T.: "Marks Standard Handbook for Mechanical Engineers," McGraw-Hill, 8th edition, Chapter 5, pp. 51, 1978. Appendix A Diesel Injector Drawings Scale 1:1 Figure A, .1 - Diesel Injector Assembly 113 T O P M O S T POSITION All dimensions in mm unless stated otherwise Only relevant dimensions shown Scale 1:1 Figure A.2 - Diesel Injector Body 114 All dimensions in mm unless stated otherwise Only relevant dimensions shown Scale 2:1 Figure A.3 - Diesel Injector Stack 115 Check valve disc not shown Disc is 10.53mm 0 and fits in center of valve All dimensions in mm unless stated otherwise Only relevant dimensions shown Scale 4:1 Figure A.4 - Diesel Injector Check Valve 116 All dimensions in mm unless stated otherwise Only relevant dimensions shown Scale 4:1 Figure A.5 - Diesel Injector Spring Holder 117 01-8 .54 (51.3 25,45 0.55-f 10 HOLES @O.1524mm0 — (0.006") All dimensions in mm unless stated otherwise Only relevant dimensions shown NEEDLE END (CLOSED) Scale 4:1 Figure A.6 - Diesel Injector Tip 118 0 2 . 2 0 0 . 8 4 . 1 3 2 . 6 0 c •2.50 6.31 8 . 8 6 2 5 l 2 0 2 4 . 2 8 7 1 6 3 . 3 5 * 4 5 . 5 0 ' X~7 All dimensions in mm unless stated otherwise Only relevant dimensions shown Scale 4:1 Figure A.7 - Diesel Injector Needle 119 Appendix B Effect of Wall Expansion on Speed of Sound and Fluid Bulk Modulus 120 The expansion of the passages in the injector due to pressure waves will change the speed of sound and the compressibility of the fuel within. We have neglected the change in fluid properties due to the expansion of the tubing, but will prove that these changes are negligible here. A control volume analysis around the pressure wave as it travels through the tube is shown in Fig. B.l , where a is the speed of sound of the fluid: a a - d u D D+dD P P + d P Figure B.l - Pressure Wave Control Volume Beginning with the momentum equation: dPA = pAa(a -du-a) —> <iP = -padu (B.l) The continuity equation is then: pAu = const dp dA du _ + — + — p A a 0 -> dp 2dD du — + — — + — p D a = 0 (B.2) The definition of the isentropic speed of sound is: (B.3) 121 Combining (B.2) and (B.3) obtains: dP 2dD du —+—— + — = 0 EL D a (B.4) For a thin walled pipe, where the stress is evenly distributed over the thickness of the pipe, the definition of the stress in that pipe is: a - — — = Ewe It w dPD -T> —r— - Ewde It dP = E, 2t_dD_ w D D (B.S) Combining (B.5) with (B.4) will obtain: dP dP D du — + — + — = 0 EL Ew t a (B.6) Combining (B.6) with (B. 1): dP = -du a EL+EW t = -padu • a 1 E^D + ^ t) When considering the change in the compressibility of the fluid due to the expansion of the tubing due to pressure waves, we see a new factor introduced that is a function of the elasticity of the fluid and wall, as well as the diameter and thickness of the tube. 122 For a standard tube in the gas injector, this factor is equal to: 1 1 _1 1 + !±L_D~ 2sl09Pa 0.0016m ~ 1.039 ~ 0 9 6 3 + Ew t 1 +165xl0 9Pa 0.005m So the expansion of the tube decreases the compressibility of the fluid by about 4%. For a thick walled pipe, the relationship between the strain and the change in pressure is calculated using the nomenclature in Fig B.2: Figure B.2 - Thick Wall Nomenclature The following tangential stress and radial stress for thick walled cylinders are shown in Ref. [9]. Tangential stress: R ^ P , - R ^ P 2 ^ - P 2 ) ^ a, = 5 5 r— (B.7) 2^ 123 Radial stress: R?PX-VP2-(PX-P2)££ -Rx2 (B.8) For an extremely thick walled pipe, R2 -»oo, and if PI » P2, then P2->0. The tangential and radial stresses become: R?PX or = — RX2PX (B.9andB.10) The tangential strain at the inner wall can be calculated knowing both the tangential and radial stresses as well as Poisson's ratio, u,: r2 E, w r=R, E, (B. l l ) w and det=dP £ dP = det = Ew dD w (B.12) Combination of this equation with Eq. (B.4) leads to the thick wall equivalent for the speed of sound: a = ! f \ 1 P , , 2EL(l + M) (B.13) Using the same values for the liquid and wall bulk modulus and assuming a Poisson's ratio of 0.3, the compressibility of the liquid changes by a factor of 0.969, similar to that of the thin walled tube. Appendix C Single Channel Simulation 125 A single channel numerical simulation is performed to estimate the effect of velocity diffusion on an already stable solution. A graphical representation of the single channel and its initial conditions is shown in Fig. C. 1: PUMP PRESSURE PUMP PRESSURE PUMP PRESSURE + 5 MPa Figure C.l - Single Channel Geometry and Initial Conditions Two reservoirs of equal volume are connected with a passage of constant area. The example performed has initial conditions of pump pressure, 344 kPa, in one reservoir and in each cell in the passage, but with an additional 5 MPa added on to the pump pressure in one reservoir. The system is then allowed to reach steady state, and should wind up with a single pressure value throughout the passage and in each reservoir. The volume of each reservoir is 0.0001 m3, the area of the connecting passage is lxlO - 7 m2 and the length of the connecting passage is 0.25 m. Five cells are used in the passage. The simulation is performed with and without smoothing. The pressure distribution in the reservoirs and the cells in the channel are shown in Fig. C.2. 126 3.6 3.4 3.2 n CL 2.8 2.6 2.4 2.2 Single Channel Example (No Diffusion) 0.5 1.5 Time (s) Figure C.2 - Pressure Output from Single Channel Simulation For no diffusion, we obtain a stable solution with the pressures converging to a steady state value of about 2.85 MPa. The solution is almost fully converged after about two seconds, although very small oscillations still occur due to the lack of any frictional effects in the system. Upon examination of the pressure trace in the single channel with diffusion, there is virtually no visible difference. An error analysis of the difference between the numerical values of both solutions provides a clearer picture of the error involved when introducing diffusion. 127 Maximum Error Between Non-Diffused and Diffused Single Channel Example 0.4 0.35 0.3 0.25 2 k_ u i 0.2 0.15 0.1 0.05 0 \ I I I 0.5 1 1.5 Time (s) 2.5 Figure C.3 - Maximum Error between Non-Diffused and Diffused Solution The maximum error is calculated by dividing the maximum difference in pressure between the non-diffused and the diffused case for each cell or reservoir, over the pressure in the same cell or reservoir from the non-diffused case. As shown in the figure above, we obtain a maximum error of 0.35% at the start of the simulation. The error involved is extremely small, allowing confident use of numerical diffusion in the injector simulation. 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T 1 t ? < ? ^ ^ ' 9 9 0 0 - N N n " » n » i o s s e o a ^ o i d b - C N c b c b v 5 i b u >cb *~ V- T - ^ ^ T>- V Appendix E Supplementary 6V92 Data Single Injection Cycle Gas Needle Maximum Lift 0.030" 142 ggggggggggggSSSSSSSSS § S § 8 S 8 8 § 8 i S S S 8 8 S 8 8 8 8 8 9999999 9999999999999'? 8 3 8 8 0 8 0 0 8 8 8 0 8 8 8 8 8 8 § 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 999999999999999999 o ID in ui 1 - m 10 in N u) in T - N 0 ^ - - N - N > - N ( J O T - O * - * - T- CM <r-wcominm -^tnmmin CM n n T-O N n v i n i D o s N u i n n f i M j ^ j N i n S C h m ^ O ^ C O C N I C M C M I ^ V C O C O C O O J ' c r O ) ! * -K " O O I- CO <P CO CO CM O O CD • CM CM CM CM CM < =9999999999999 .IO>0>inCDCMCMCMI S Si ° S! a 1 W u i u l r u i UJ u i w HI »- u i u i i y ^ w 111 i u T- UM ! § C S S g S S S E S S S 8 S S il»88$88cl»888§88 : O) (O 00 CM 1 T V) 1-H o ca tu 3 H ininincMioioinr-ininiooinuiin^ininintNininincoininin r - r ; c M ' i « - T ; c M , r - 0 - C M CM Q 1— CM ^ r- CM _| r» CM r o C M - i r - . c M ^ r - . 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CNCNCNCMCMCNCNCNCNCN I O O O O O O 8 8 S 3 S S o S S S S S 8 S S 8 S 3 3 S S S S S 8 S 3 S S o S S S S 8 S S S S 11-8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 r |99999999999'9 9 9999999 9.9 999999 9999 a a. •5 •• i n i n i n c N i n i n i n ^ u ) U ) u ) o u ) i o i n o > u ) i n t n c Q t n i A i n ^ f M ^ V h ~ : T ^ < s ( T r ~ : d ^ ' 7 r ^ o i r i ' r ~ : c b ( v ! r " : t - l ' M ' ^ cb ^  ^ t r i ^ ' r - . _ : c N 1 r - CM ' C M T j - c N T - ^ - T - o ^ o a i i c r i 9 ' 9 r T ' r T ' 9 9 9 9 <7<7 144 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 v v v 9 9 9 9 9 , 9 9 9 9 < ? 9 9 9 9 O i n i O L O ^ I A I A L O N I A I O I A I O I O U l l A ^ I O I O I A I A O ' T - O T- T-' CM o i cd cd - r -P S 3 o io o> co p _ o n T r e o * - r * o ^ „ _ 0 9 9 i o N d d » » n d j N M n » o ^ I N O N IO U) U) N l r * - * - ^ - T - c j ) C Q C n c N C N c N r ^ o o o i •<r <J> & ~*f T- r * - co (» io v T- i T - S * » C N i f C N c 2 c i 5 c f l ^ c o i p i CN CN CN CO CN I _ cn co co csj CM • CO Jjj 0) O CM V CO CM ^  « - O O O 9 9 9 9 9 9 O C N C M C M C M S ' » l O 0 1 V C 0 ^ , C O » - e O ^ ' t N c o c o c o c o o o c n o i s c n t n c N c o ~ ~ N S N N f - T - f f - O U J O C O C I . - - . . . . . . . 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' ^ •» CN C*; —j CM f Q W r » n v P ) N r N r i - r O r ' O C J ' C p 00 ~ 00 hp ' hp CO ' CO UJ ' IO T T 9 V O 5 153 » S 3 3 3 K c o ^ 8 3 8 c o , 2 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 * oi *T ai 9 O l p 0 ) S N ( 0 t a ) N N 0 0 0 ) N N N i N N N N N N N N ( *~ ' ' ~~ " I Q Q O O O O O O O O O O l 8 8 5 8 8 8 8 8 8 8 8 8 8 8 8 ^ T - d d d d d o o o d d o o o o d o o CM CO CM co in CM in CO CM to r~ CM r~ CO CM CO O) CM cn C M C M C M f M C M C M C M C M C M C M C M C M C M C M C M C O C M ^ O O f O ^ ^ O O O O ^ ^ C M ^ C f t ^ C O C O C M -? co o in CM in cocoi^^cocor^Scbdh - r -< i n c o o c M r o c o c o i o c o ^ c o o T - c M ^ o c o i n 1 S c n t ^ c o f f 8 S * S c o ? t S S i ~ 8 ! o ioo>?88^88inS8^co38cp8 ( S'r^ cMcdcocococor^ cnocpcn cocncno>cno>cno>o>cno) o o o o o • C O S C D N ^ r ^ C O N C O « l O h - l O ^ O > C N ^ r t C O C O * r h -i t o g i o n c o L n q N n r O T - N o j i a t N p n s i o c O T - T - ^ ' r n S « n 3 N S r r S A 8 n c ; 3 S S ! l&r?88Se5s5§§sl§sls?le9sse icjicjiedios'coddda'csri » co a ca co oi 2 r- r- to in in * •* co co co CM CM *• r-N O N CM IO 8 ^ 8 8 8 8 ? 8 8 8 c t 8 8 c M S 8 S & 8 & ? 8 S 8 3 S » 8 8 ^ ? ? c M S S S S 8 ^ ^ ? 8 S 8 S M : i n i ^ r - r ~ c o c o ^ S ^ o c M c O T - c M c b v > v > a i ^ r a i A t - r ~ r ^ | c q y ^ ^ c M p i ^ c o ^ ^ c M —cocor^  O O T-m CM in in m co in in in •* in m in in in in m co in in in T - ^ CM CM CO CM iri ^  * - CM CD h-T— CM T - CN rt cd «» * - • » iri «- in I D *— tO O CM O T - CM I 8 ( 8 3 CO h- »- "<r CO in CM a> T- in in in in r; 5 8 CM 8 3 CM co r» P CM 5 CM ^ O ) CO CO CO 8 co r-CM CM CM CM CM 8 c o h - i A c » r ^ c o f l Q i ^ c o ( p r ^ ~ N i o c i s s o c o o c g c o r M ^ ^ C M O S o S f O C D l O C O O J ^ - C M C f t O ^ S e o n o > p ) < o c M ( 0 ~ 3 3 8 8 o r g v i 8 8 § 5 i »- in B51~- < in S S c o c M C M c g m c g c o c o e o i o c M O C M c o c M T - r ^ c o o r - Q i n U > t 0 C O t t ^ ? ^ U ) t 0 t D t 0 t O t D C O r ^ r ^ C D C D r ^ r ~ O J coco n ui « n n n I I D co <$ Q 5 £ I CM, y-i in CO CM CO cS co s s s s s PH I C O C O T O S C O C O t f J C O C O C M S S T - C O C D S f . • co*voinincno>inoooT-i>.cococo -gnu} I rt co co : rt in in CN — : , i b * f * f * £ CM co c i rt rt rt rt rt 3 3 j: .5261 .3427 CO .5261 .3427 35 5 i ^ v ^ T - v ^- (« w r« rj r i «i u IN ^ « M N ^ !9?8a88 ' O T 8S8'8'88' K 8'S8ScSS8P iAinincNioinin*-inioinou>inin^ininincNU)ininnininin7inininintntntntoinininr^tntnina I— ^ CM 1 N Q [N *i" ' *i* 9 9 O T - T -^ cd ' - . CO rt CM: CO ^ CO CO o • r» CM UJ CO CO •« CO i co o o rt T- i - ? 5 * 8 8 8 8 8 8 8 8 8 8 8 8 8 . 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 ! • i 5 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 M m t K 8 ! 2 , " m S S 8 5 ? S £ ? > 8 _cu s es H (9 0. a a. «8 i n i o u ) U ) ^ u ) i n i n c i i n u ) t f ) c N i i o u > u ) r * u > i n u ) o u ) U ) i n o ) i f ) U ) V ) V ^ T t ^ ' 7 ' v c o r S ' : , ^ N l s ! T ^ ' ; ^ T ^ d r H ' ; ^ c » ^ ^ - T - TJ- n o C N ^ - C N o t - * o c n ' c n ' . co >-! 9^9 c o i o i o i o s i f l i o i o c o i n u i i A i a i A i o u i t i A u t i o n 9 : 0 ?9 9 1 7 9 Appendix F Supplementary 6V92 Data Single Injection Cycle Gas Needle Maximum Lift 0.020" 155 § 8 8 8 § 8 8 § 8 8 8 S 8 S 8 8 8 8 8 S S o o o ' o o o o o o o o o o 9 0 9 0 9 9 9 9 8 8 c l i 8 8 S § 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 ° 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 O LO in m d T- in in in CM in in f i c M in ro in in in •« CM CM r-- T- ^ ro' 6 5= 0 «~ CM *~ CM ro y-cb 88 o ' o ' d d o v T O O c o < c r o c N i o o * - m 9 9 0 9 9 9 0 9 9 9 o I hH o ffl 7 so I 1-H 3 es H U) If) U) CM (O U> lO ' S f j N ' I*- ^ CM CM ' CM T - ' *~ • i n i n i n o i o i n i n ^ i n i n w c M i n t n u ^ r o i n i n i n N Q CN tN Q s CM ^  CM ^  r- CMfvjr-; CM ^ ; CM ^  CM ^  h* CM I^^  CM 00 " oS ^ WCMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCM Q . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 i | 8 8 8 § § 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 # ^ 9 9 9 9 9 ^ 9 9 ^ 9 ^ 9 ^ 9 9 ^ 9 ^ 9 9 9 9 9 ^ 9 9 9 ^ 9 9 9 9 9 9 9 ^ 9 ^ 9 9 9 ^ 9 9 9 9 9 9 9 <F* co (9 Q. — - 0 0 0 0 0 0 1 1 I 8 8 8 8 8 8 8 8 8 8 S 8 8 8 8 8 S 8 S 8 8 8 8 8 8 8 8 S 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 1 "S9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 co Li Q n inininin^ rminincoin ™ — — t ( Ir f ) CM It inincMcninint-inininoLoinLnoiininincoinininr^ininLncpininininin ^ C M T - r » ^ N T - l ^ 0 C M T - r - _ J C M ' ^ co CM ~ r~ CM ' ^ (b CM T 1^ l - CM ' r ^ ^ C M ' 1 - , - C M ' \ « ? V ° 9 ' 9 9 ^ 9 T ."r 9 ^ 9 9 * 9 t T 9 '<? 156 o o r - o o o o o o o o o o o o o i 8 S C N S S 8 8 8 8 § S 8 8 § 8 8 8 8 8 8 8 o o d 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 8 8 3 5 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 0 0 9 9 0 9 9 9 9 9 9 9 9 9 9 9 9 9 9 O T- O CM CM CO CO ^ T - c o c o o » < o o 0 ^ T - r ^ ^ * ^ u 3 c p ^ h - U } * f C f t O T - r t c N r ^ o o g a ^ g p F c o r o g c N ^ r- co rsj co 1/1' . - J CN A if) r ! | S 7 8 8 8 c 8 8 8 8 8 | 8 3 2 8 8 8 8 8 8 8 8 8 8 9 9 9 0 0 9 9 9 0 9 T - ^ i n N t - W ^ V t - T - W L T ) l B r * T - T W V r - 0 ) l 1 ) T - l C N i p ^ * - O C O i n c p C N C N ^ ^ C N ^ O > r * - T - * * - Q ^ r , e f ' ' Q c o c o c N L O ^ c o i o Q Q c o ^ i ^ e N c o ^ o © 2 f , T * - r ; 1 . . JCqconinosNi i i o r ) i n N N T- T- 1 I CN n CN N/ i") u . _ 8 c o c 6 c i r ) r ~ n i n d c c ) ^ . o o t - c n ^ t - N q O N q o i i o ^ N ^ c q q ^ c q c o i n n 9' o ' d d d - r ^ i n ^ p ' p d o > c > i o D r ^ c b c b » CN »- CN in ~ ~ T- T- r- T- CN CN CN CN CN CN C N i n 0 > C 0 V f 0 C N O ) T - T - C N » - T - ' c r C O r - » - V C O C p ^ n 5 r C O g ^ C N N I » C N C N C O C N C N C N » -v N O t j f n o o a a o M CN CD CO C J " = CN Ui f ' CN • > o o at ; 8 8 2 8 o 8 $ 8 8 B : i h T ; T - ; e N 9 9 ^ 9 9 ' 6 b 9 9 d i n i n i n c N i n i n i n ^ i n i n i n o i n i n i n r - i n i n i n c N i n i n i n c o i n i n i n v i o i n i o i n i n i n i n c o in 10 in at in 10 u> r - . p j C N ' l - i ^ C N ' r ^ Q - C N N g S ; C N ^ r - CN t - CN p j 1- CN, ^  » ; CN ifj I-; CN. » ; CN. ^  r~ CN, ,3 r - CN g j C^ ( j i ' l j r ' r o"(J " " ~~ ' _ _ _ _ O r- r-o PQ r> i v© i f N • fe cu s es H § -^ L n c o c N i n c o c o c o i n t n 5 1 3 C N T - 5 C N C N C N 3 3 C D o e-tjjj g N g g g g C . | | d d d d d d d d 0 0 9 0 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 § 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 . 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8.8 8 8 8 o a. 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' ^ - o r <N ' r - . p j CN ' at • at o p ~ eo T 1 9 9 9 ' 9 9 ' 9 157 ssssssssss 8 8 8 8 8 8 § 8 8 8 9 9 9 9 9 9 9 9 9 9 ' 8888888888 9 9 9 9 9 9 9 9 9 9 IO CO IO IO IO IO IO IO IO r-; CM CM CO r- CM CM r- CM CM CO CM cd CM CM CM CM CM CM u> CQ co in r*- •««• O CO CN M- ro CN n « v j at co to>(p^ -CNCOCDCNr*>-r«»co' » T - W ^ t D C N r O f O C N C O ' T - < » (O M t - <t- T- (p T - Q I i C D C O ^ r r ^ C N C O C M T - O J C O C M ' § ; 0 £ 5 § I 3 s ^ 8 i & p ^ , co U J t O T - T - C O A C O g g g l g g C O i c o c M C M T - a c o c o r ^ c p ^ c n e M c o c M i o c o i o c o s s c M i o i o ^ c ^ >CN^CoScM8cM3ffr i8§$S^8£8?!ctCN » 8 8 5 K 8 5 5> S < iinSco^t^QcoSQr • CDCMCM^-COCOCNICOr*. t O T- Q Q T- T- t 58SSSSSSSSS § § t § 8 § § 8 § § 8 § T V ' t i B i d v ^ d d ^ ^ c j o o ' c j o ' o ' c } ^ ^ o i o i o i O T - i o i o i o c M i o i o i n c o i n i n i n v i n i n i o i o i o i o i o c o i o i o i n i ^ i n i o i p a T - C M o l ^ ^ C M ^ r ^ T - C M - J l ^ i - C N m r ^ T - C N W r ^ T - C M u j r ^ T - C N r i b «- b T - • * ~ T ~ CM -^ CM ro Y - ro T - to i - io to T - to T - r>- co * - co d a> O CM O ^ CM ^ CM CM CM888V8*-COCMCMT -38>»88COCM3CSS3 S C O Q T - C O r - T - T f T - W Q i n N Q t O r ^ t O n O C O T - t O 9 c Q C O ^ N C O C Q I A S f f i Q L O O a S V T - O n N CMiA?5^h-c»*^pcJrtKc»^i^O'^ioCMcOeo tsonpaNipyrcoolpNOcpN T - ^ S V N I O C O N Q I C O t O C O N O ' S T - n T - g N t o f t o o N g i - i s n T - o i o a a c i N n i A i o a , ; T at CM io o io co c cs)CM1cqr-.^Bieopi~ : CO O CO O O) CM CO ^  CO O CO CM O CG[ CM 0> Ol f"; CM If) Ot at p CO N . 1^  CO p in CO CO CM, H"j n V* u* w CM, CM, w r"^  ^ M u r"; U ) ^ ' c A ^ C M C O c d ^ c d « l o ' c d ^ l ^ W c O O S c M C M C A O r f D O O O O M C O C O C M C O C O C O C O * 9 * * 9 * V I O l O I O C O C d i n O O O O T - r O i - i -~" — SNS^^^^w8SS8^5c^c5 S 5 » « « ' f t S 8 S S ° « » ' S S " § 8 SS*SS838SB3833838888 ^ i n i o i o c M i n i o i o ^ i o i o i o o i n i o i n T - i o i o i o c M i o i o i o i o i n i n i o v i n i o i o i o i o i n i n i o i o ^ ^ i - p g c M ' r - ^ C M ' p - Q C M CM o r- C M ^ r - . CM ^ r-^  CM N- CM. ^ i r - ; CM I^-; CM ^ t-; CM ^ r-; CM r- r , . o i r ' . A . CM 'CM T ^ ' T - ^ O'CJJ o a *- CM CM co co *r m ui to to r-- f- co ea at at fS hH o CQ oo I •cvcQunr-T-*-*-a>vt^tDnatat*-<QiDt+-c* \^^^U^^^^^^^^^^2^a]^^^^ — — — — — — — — — — — — — — — ~ " ~ ~ ^ s i f i S S o s s t - r ^ I 1 8 8888888888888888888888^ . S L ^ b b b b b b b b b b b b b b b b b b b p b b b c d c M ' b b b b c M C O ^ i - C O ^ T - ^ C N C O l O c d ^ c d ^ b b ^ l d i -O a. i 2 CO H ^ O O O O O O O O O O O O O O O O O O O O O O O O O O O O O l O N g r t l f i N O O O ^ © N Q ( 1 ^ 8 8 8 8 8 8 8 § 8 § 8 8 8 8 8 8 8 8 8 8 8 8 8 8 £ § 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 ' 9 9 ' 9 ' 9 ' o o ^ m ' 9 ' 9 9 co cd " 01' oi oi CM t- CM CO' 11 h a . 3 » T ^ - » ^ V ^ c o r ~ i T r , ^ C M c ^ " 7 ' ^ ' - r i T ' ^ d ' ^ T r ~ : c > i r ^ ^ co ^  r-.' CM 1 ^ m OJ T N ™ PJ ' — CM ' >~: ro CM < «3 ctt n J \ j co Tp co CM Y CM j ; * 7 ^ ° 7 ° 9 ' 9 9 9 ' T 9 9 9 9 T T 9 9 O h 158 S S S S S S S S S S 3 S S S 8 8 8 S S 8 S 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 ? 9 d d 9 9 9 9 9 9 9 9 9 9 9 s s s s s s s s s s s s s s a s s s s s s 888888888888888888888 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 o *- o Y— T— i I*: *" CM. r i l*t * " CM • - ' n t g n g g N g g o o i f l ~~ i g c f t t o m d r t N l o o N S • CD co co I CO CM ^ K CM r-• T* CM T- p in CM • cn o MT to io to I C M r ^ C D C O T - T - C M L n C D C M L D ' , ' i n O S C » g 5 ^ N f f l N N N » * « N M N I ' t N O N S n Y N o b o o t t i f l O o o b i r M D C M ' ^ r m o o t n i o c N i i r- -j co r-•CT 0> CM O) T-T-CO3CMCMC0C0pC»COC0'-CM0)COCOO>< r ^ S 5 c o ^ c o M f c n K x r t o c M C N ^ , ' - ^ ' r - - r - - c CO T- CO CO * CO 8 ~ o c o ^~ ^ ~ n 1 r>; ^ q „i iri c C W O l T - C N C O c b r ^ c O ' C b C N T - ' T- i - CM CO CO CO CMCMCMi i V N N n Q N i s g n « N ^ v A o g n N g O t o S 8 s i A O S i T - c o T - n o n o T - n N ^ M N ^ v c o K c n o ^ s o w n s p i i f l ! l O r ~ r j > c O l O C D T - T - T - T - T - T -i S r t S S S S S S j C ^ j r ^ C M 5 a c M U > 5 ; 0 " C f ^ - in v co CM co in 8899888888 C O C M T - C M C M T - C 3 C 3 C 3 C 3 C 3 C 3 in inincMinioinr- ioioiooioioiOT-iAioiorMioioioninioiOMrioioi^ t-: CM • r~ ^ CM. ' r~ Q-CM N Q S CM. ^ r~ CM, pj r- CM. pj CM. TT ^ CN uj r-; CM. „• r-: CM. ^  t-; cvj <d r^  CM «r-^ T ' 7 9 ^ 9 o i - T-o PQ i K T - r - T - T - ^ T - T - T - T - ^ T - T - ^ T - t - T - T - T - T - C D N l O S N ^ N l O C l i n ^ l D C O C O l O C O ^ C O f f l ' C f V S J C N C N C N C M C N C N C N C N C N C N C N C N C N C N C N C N C N C N C N C » C O U » n ^ Q > 0 } C N O r * * r ~ 0 : q o q o o o o o o o p q g o o o o o o c o v j ^ K i g r ^ S S c N i n Q C M S i g i n S I C M C » 0 1 C O V * C ) ) r ~ O C O T - C O C I > c \ j l O C » 1 0 ^ . ^ ^ C O C p p C p c p C p C D C p C D C p C p C p C p C p c p c p c p c p c p O O C M ' ^ D . 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