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Visualization of transient single- and two-phase jets created by diesel engine injectors Chepakovich, Alexander C. 1993

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VISUALIZATION OF TRANSIENT SINGLE- AND TWO-PHASE JETS CREATED BY DIESEL ENGINE INJECTORS by ALEXANDER C. CHEPAKOVICH Dipl. Eng., The Belorussian Polytechnic Institute, 1985  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES Mechanical Engineering Department  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA April 1993 © Alexander C. Chepakovich, 1993  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.  (Signature)  Department of Mechanical Engineering ^ The University of British Columbia Vancouver, Canada  Date  ^  DE-6 (2/88)  7 / /793  II  ABSTRACT Propagation of single- and two-phase transient jets for direct injection of natural gas and natural gas with pilot (liquid) into diesel engines has been investigated experimentally by optical methods. The jets created by three (diesel, gas, and gas-diesel) electronically controlled injectors, were observed in a constant-volume chamber charged with air, the pressure of which varied from atmospheric to 3.5 MPa. The injection (gas-to-chamber) pressure ratio varied from 1.5 to 8 for gas injection. The liquid-gas mass ratio of the injected mixture for the dual-fuel injection varied from 0 to 0.9. The liquid injected with the gas was finely atomized by the gas due to the acceleration of the gas within the nozzle.  Schlieren and laser sheet systems were used for flow visualization. A single-shot video camera was used for image acquisition. Series of pictures of a jet at different time intervals from the beginning of injection were taken to determine the jet penetration rate.  The jet penetration rate was observed to be independent of the chamber pressure as long as the injection pressure ratio was constant and was proportional to the square root of time from the virtual.beginning of the jet (defined as the beginning of an equivalent impulsively started jet ) for continuous injection. The jet penetration rate was found to depend weakly on the liquid-gas mass ratio of injected two-phase mixture. The experimentally observed penetration rate of a methane jet was compared with that of a carbon dioxide jet, and no significant difference was detected.  The jet penetration rate was compared with calculations done using an integral model of the jet. The model proved to be fairly accurate in predicting the round jet propagation rate if the experimental data was plotted relative to the virtual beginning of the jet. The model was not as accurate in predicting the conical sheet jet propagation.  in  TABLE OF CONTENTS ABSTRACT LIST OF SYMBOLS^  vi  LIST OF TABLES^  ix  LIST OF FIGURES ACKNOWLEDGMENTS^ 1 INTRODUCTION^  xv 1  2 EXPERIMENTAL APPARATUS AND PROCEDURE^ 8 2.1 INTRODUCTION^  8  2.2 EXPERIMENTAL APPARATUS^  10  2.3 IMAGE ACQUISITION AND PROCESSING ^17 2.4 ERROR ANALYSIS^  22  3 EXPERIMENTAL RESULTS^  24  3.1 INTRODUCTION^  24  3.2 ROUND NOZZLE GAS INJECTOR^  24  3.2.1' EFFECT OF CHAMBER PRESSURE ^31 3.2.2 EFFECT OF PRESSURE RATIO^  32  3.2.3 VIRTUAL BEGINNING OF THE JET ^33 3.2.4 COMPARISON BETWEEN METHANE AND CARBON DIOXIDE JETS^  36  3.3 POPPET GAS-DIESEL INJECTOR^  37  3.3.1 EFFECT OF CHAMBER PRESSURE AND PRESSURE RATIO^  44  3.3.2 EFFECT OF INJECTION DURATION ^45  iv 3.3.3 EFFECT OF DIESEL-GAS MASS RATIO^46 3.3.4 EFFECT OF INJECTOR POPPET ANGLE ^48 3.3.5 COMPARISON BETWEEN METHANE AND CARBON DIOXIDE JETS^ 3.4 ROUND NOZZLE DIESEL INJECTOR^  48 50  3.4.1 EFFECT OF CHAMBER PRESSURE ^54 3.4.2 CALCULATED JET PENETRATION ^55 3.4.3 COMPARISON WITH GAS-DIESEL INJECTORS^56 3.5 SUMMARY OF EXPERIMENTAL OBSERVATIONS ^57 4 INTEGRAL MODEL OF A TRANSIENT TWO-PHASE JET ^59 4.1 INTRODUCTION^  59  4.2 STEADY-STATE CIRCULAR JET^  61  4.3 STEADY-STATE CONICAL SHEET JET ^  70  4.4 TRANSIENT CIRCULAR JET^  71  4.5 TRANSIENT CONICAL SHEET JET ^  75  4.6 SAMPLE CALCULATIONS^  77  4.7 COMPARISONS OF CALCULATIONS WITH MEASUREMENTS^  80  4.7.1 ROUND JET^  80  4.7.2 CONICAL SHEET JET^  84  5 CONCLUSIONS AND RECOMMENDATIONS ^ 6 REFERENCES  ^  ^ Appendix A. APPARATUS DRAWINGS ^ Appendix B. APPARATUS DETAILS  88 91 94 110  Appendix C. SCHLIEREN SYSTEM ^  113  Appendix D. LASER SHEET SYSTEM^  117  Appendix E. FLOW VISUALIZATION CONTROLLER ^ 120 Appendix F. PSEUDO-RADIUS FOR UNDEREXPANSION^123 Appendix F. COMPUTER CODE OF A TRANSIENT CIRCULAR JET ^129 Appendix G. TIME-DEPENDENCE OF A TRANSIENT JET PENETRATION^  133  vi  LIST OF SYMBOLS Specfic heat of two-phase mixture at constant pressure. cv^Specfic heat of two-phase mixture at constant volume.  cps^Specfic heat of gaseous phase at constant pressure. vg^Specfic  heat of gaseous phase at constant volume.  c 1^Specific heat of liquid phase. CD^Drag coefficient of vortex. Cd^Nozzle discharge coefficient. FSF^  Change of momentum due to acceleration of surrounding fluid.  FD^Drag force.  k^Specific heat ratio. k. ^n=1,2,3,...  Various constants.  1^Poppet lift. is^Effective lift. leg^Equivalent  lift.  Pseudo-lift for underexpansion. m y^Mass of air within vortex. mg^Mass of gaseous phase. mf,^Mass of injected fluid within vortex. my^Mass of vortex. M^Mach number.  M, Momentum of vortex. M^Equivalent molecular weight.  Mg^Molecular weight of the gaseous phase.  •  Ambient to jet (inside the chamber) pressure.  Pch Pressure in the chamber.  vii P.^Upstream pressure of injected gas. r^Position from axis of jet in radial direction. ro^Radius of inviscid core. Radius where steady-state jet velocity is equal to vortex velocity. ro^Radius of nozzle. rc,^Pseudo-radius of nozzle for underexpansion. r L^Radial position where jet velocity is half axial velocity. „  R^Radius of outer boundary of a jet section. R^Gas constant. R^Universal gas constant. R,^Poppet seat radius. R,^Radius of vortex. S^Jet penetration. t^Time. Ta^Temperature of ambient to jet (in the chamber) air.. T o^Static temperature of fluid leaving nozzle. T.  Upstream temperature of injected fluid.  U^Velocity of at a point in jet. U m^Maximum velocity of steady-state jet in a cross section. U.  Velocity of jet at nozzle exit.  U t^Tip velocity of vortex. U,  Velocity of vortex at its back plane.  V,  Volume of vortex.  z^Distance from nozzle exit in axial direction. Length of initial (potential core) region of jet. z o^Distance between virtual origin of jet and nozzle exit. z t^Position of jet tip (jet penetration).  viii 71,^  Position of the back of vortex.  GREEK LETTERS a^Volume concentration (volume fraction) of injected fluid. Poppet seat angle. X^Concentration by mass (mass fraction) of injected fluid at a point in jet. x.^Axial concentration by mass (mass fraction) of injected fluid. X,,^Concentration by mass (mass fraction) of vortex. Mass fraction of liquid phase in gas-liquid mixture. 11^Liquid-gas  mass ratio in gas-liquid mixture.  p^Density at a piont in jet. P.^Density of air at chamber conditions. P g^Density of injected gaseous phase at chamber conditions. Pf^Density of injected fluid at chamber conditions. P0^Density of injected fluid in nozzle. Vorticity. Non-dimensional radius of jet (dr y).  ABBREVIATIONS BOI^Beginning of Injection. BOJ^Beginning of Jet. BOJN Virtual Beginning of Jet. CNG Compressed Natural Gas. DDC Detroit Diesel Corporation. DDEC Detroit Deisel Electronic Control system. PR^Pressure Ratio. PW^Pulse Width.  ix  LIST OF TABLES Table 3.1 Round nozzle gas injector. Difference between BOJ and BOJN. Table 3.2 DDC gas injector injection delay. Table 3.3 Poppet diesel-gas injector. Difference between BOJ and BOJN.  LIST OF FIGURES Figure 1.1  An example of visualization of a jet created by a diesel engine injector.  2  Figure 2.1  General view of the experimental apparatus. (Drawing.)  10  Figure 2.2  General view of the experimental apparatus. (Photograph.)  11  Figure 2.3  Cam follower and rocker arm assembly.  12  Figure 2.4  Front view of the chamber.  13  Figure 2.5  Cross section of the chamber.  13  Figure 2.6  Commercial DDC diesel fuel electronic unit injector schematic.  14  Figure 2.7  Experimental DDC gas injector schematic.  15  Figure 2.8  UBC dual-fuel poppet injector schematic.  16  Figure 2.9  General arrangement of the image acquisition system.  18  Figure 2.10  Typical schlieren background picture.  19  Figure 2.11  Typical laser sheet background picture.  20  Figure 2.12  Definition of the jet penetration.  21  Figure 3.1  DDC gas injector jet propagation. Pch=3550 kPa, PR=1.5 (first of a sequence of 3 figures).  Figure 3.2  DDC gas injector jet propagation. Pch=3550 kPa, PR=1.5 (second of a sequence of 3 figures).  Figure 3.3  Figure 3.6  28  DDC gas injector jet propagation. Pch=2170 kPa, PR=5.0 (first of a sequence of 2 figures).  Figure 3.5  27  DDC gas injector jet propagation. Pch=3550 kPa, PR=1.5 (third of a sequence of 3 figures).  Figure 3.4  26  29  DDC gas injector jet propagation. Pch=2170 kPa, PR=5.0 (second of a sequence of 2 figures).  30  DDC gas injector penetration at the pressure ratio of 2.0.  31  xi Figure 3.7  DDC gas injector penetration at the pressure ratio of 3.0.  32  Figure 3.8  DDC gas injector penetration for different pressure ratios.  32  Figure 3.9  DDC gas injector jet penetration for different pressure ratios. Square-root-of-time dependence.  Figure 3.10  DDC gas injector observed and calculated jet penetration at PR=5.0.  Figure 3.11  41  Poppet injector jet propagation. Pch=3550 kPa, PR=3.0 (first of a sequence of 2 figures).  Figure 3.18  40  Poppet injector jet propagation. Pch=3550 kPa, PR=15 (second of a sequence of 2 figures).  Figure 3.17  38  Poppet injector jet propagation. Pch=3550 kPa, PR=1.5. (first of a sequence of 2 figures).  Figure 3.16  38  Laser sheet picture of the poppet gas-diesel injector jet. PR=2.0, Pch=3550 kPa. 4.6 ms after BOI.  Figure 3.15  37  Schlieren picture of the poppet gas-diesel injector jet. PR=2.0 ,Pch=3550 kPa. 4.6 ms after BOI.  Figure 3.14  36  DDC gas injector. Comparison between methane and carbon dioxide jets penetrations. PR=3, Pch=2170 kPa  Figure 3.13  34  DDC gas injector. Comparison between methane and carbon dioxide jets penetrations. PR=2.  Figure 3.12  33  42  Poppet injector jet propagation. Pch=3550 kPa, PR=3.0 (second of a sequence of 2 figures).  43  Figure 3.19  Poppet gas-diesel injector jet penetration. PW=2.33 ms.  44  Figure 3.20  Poppet gas-diesel injector jet penetration for different  Figure 3.21  durations of injection. PR=3.0.  45  Diesel-gas mass ratio for 20 ° poppet injector (PR > 2).  46  xii Figure 3.22  Poppet injector jet penetration at different diesel-gas mass ratios. PR-1.5, Pch=3550 kPa. ^  Figure 3.23  Poppet injector jet penetration at different diesel-gas mass ratios. PR=3.0, Pch=3549 kPa.^  Figure 3.24  47  47  Comparison of jet penetration of 20 ° and 10° poppet injectors. Pch=3550 kPa, PR=2.0, PW=2.33 ms. ^ 48  Figure 3.25  Poppet gas-diesel injector. Comparison between methane and carbon dioxide jet's penetrations. PR=2, Pch=2170 kPa. ^49  Figure 3.26  DDC diesel injector jet propagation. Pch=3550 kPa (first of a sequence of 2 figures).^  Figure 3.27  51  DDC diesel injector jet propagation. Pch=3550 kPa (second of a sequence of 2 figures).^  52  Figure 3.28  DDC diesel injector jet propagation. Pch=3550 kPa. PW=1.16 ms. ^53  Figure 3.29  DDC diesel injector jet penetration for different pressures in the chamber. PW=1.67 ms. ^  Figure 3.30  DDC diesel injector. Comparison between experimental and calculated spray penetrations. Pch=3550 kPa. ^  Figure 3.31  55  DDC,diesel injector. Comparison between experimental and calculated spray penetrations. Pch=1820 kPa. ^  Figure 3.32  54  56  Comparison of penetration of jets from different injectors. Pch=3550 kPa, PR=3.0, PW continuous. ^  57  Figure 4.1  An example of a spherical vortex at the front of a transient jet. ^60  Figure 4.2  Diagram of an axisymmetrical submerged jet.^  61  Figure 4.3  Underexpanded jet. ^  68  Figure 4.4  DDC gas injector. Normalized jet penetration. ^  69  Figure 4.5  Conical sheet jet.^  70  Figure 4.6  Characteristic structure of a circular transient jet. ^ 71  Figure 4.7  Characteristic structure of a transient conical sheet jet.  Figure 4.8  Dependence of the round jet penetration on the nozzle discharge coefficient.  Figure 4.9  83  Round methane jet. Comparison between experimentally observed and calculated penetrations. PR=5.0.  Figure 4.17  82  Round methane jet. Comparison between experimentally observed and calculated penetrations. PR=3.0.  Figure 4.16  82  Round methane jet. Comparison between experimentally observed and calculated penetrations. PR=2.0.  Figure 4.15  81  Round methane jet. Comparison between experimentally observed and calculated penetrations. PR=1.5.  Figure 4.14  80  Calculated penetration of the round jet of methane for different pressure ratios. Square-root-of-time dependence.  Figure 4.13  78  Calculated penetration of the round jet of methane for different pressure ratios.  Figure 4.12  78  Dependence of the round jet penetration on the turbulent Reynolds number.  Figure 4.11  77  Dependence of the round jet penetration on the sphere drag coefficient.  Figure 4.10  75  83  Round methane jet. Comparison between experimentally observed and calculated penetrations. PR=8.0.  84  Figure 4.18  Poppet injector calculated jet penetration^.  85  Figure 4.19  Conical sheet jet. Comparison between experimentally observed and calculated penetrations. PR=1.5.  Figure 4.20  85  Conical sheet jet. Comparison between experimentally observed and calculated penetrations. PR=2.0.  86  xiv Figure 4.21  Conical sheet jet. Comparison between experimentally observed and calculated penetrations. PR-3.0.  86  Figure A.1  Apparatus upper part assembly drawing. Figure 1 of 2.  95  Figure A.2  Apparatus upper part assembly drawing. Figure 2 of 2.  96  Figure A.3  Apparatus mounting plate.  97  Figure A.4  Bearing support 1.  98  Figure A.5  Bearing supports 2 and 3.  99  Figure A.6  Bearing support 4.  100  Figure A.7  Cam follower plate.  101  Figure A.8  Cam follower guide.  102  Figure A.9  Rocker arm assembly.  103  Figure A.10  Chamber assembly drawing.  104  Figure A.11  Chamber side 1.  105  Figure A.12  Chamber sides 2 and 4.  106  Figure A.13  Chamber side 3.  107  Figure A.14  Chamber cover plate.  108  Figure A.15  Chamber lid.  109  Figure B.1  DDC diesel injector lift as a function of the crank angle.  110  Figure C.1  General arrangement of the schlieren system.  113  Figure D.1  General arrangement of the laser sheet system.  118  Figure E.1  Front panel of the controller.  120  Figure F.1  Underexpansion coefficient.  128  xv  ACKNOWLEDGMENTS I am very grateful to Dr. Philip G. Hill for having an opportunity to work and study under his supervision. His guidance and moral support are invaluable to me. I am indebted to Patric Ouellette for his help in setting up the schlieren system and always having time to answer my questions regarding the jet model. Special thanks to Bruce Hodgins for acquiring all those numerous parts and pieces of the experimental apparatus and friendly advice and criticism. I am grateful to Dale Nagata for designing and constructing the flow visualization controller. I am thankful to the personnel of the Machine Shop, who did an excellent job of building the experimental apparatus. I am also grateful to everybody who made my studentship at the Mechanical Engineering Department to be useful and enjoyable experience. I am thankful to the Detroit Diesel Corporation for kindly providing hardware and technical assistance in fulfillment of the project.  1  1 INTRODUCTION With the introduction of new emission regulations for urban buses and trucks, the automotive industry tries to find ways to drastically reduce pollution from diesel engines. One of the directions in this quest is the use of alternative fuels, especially natural gas, which has been successfully used as an engine fuel since the advent of the internal combustion engine.  There are different methods of using gaseous fuels for powering a diesel engine which were summarized by Beck et al. (1989). They concluded that the system, in which a small amount of diesel fuel (pilot) is injected into the engine cylinder to facilitate combustion of natural gas, is the most preferable for trucks and buses. Among the major advantages of the system they listed the following: it uses the basic diesel cycle with compression ignition of pilot fuel; does not require air throttling; there is no detonation limit if gas injection is simultaneous with liquid fuel pilot injection; it allows lean burn and requires no mixture ratio control; it has diesel cycle efficiency and negligible unburned fuel in exhaust. Converted to natural gas engine performance data given at the previously mentioned paper showed that even with over 90 % (on the energy basis) displacement of diesel fuel, its power and fuel economy were the same as those of the base diesel engine.  Works by Einang et al. (1983), Miyake et al. (1983), and Wakenell et al. (1987) showed low emissions, high reliability, fuel efficiency and power of engines with direct gas injection into the engine cylinder with up to 95% displacement of diesel fuel. However, there is no commercially available system for the diesel engine conversion and research continues in various directions.  2 Conversion of the diesel engine to natural gas using direct injection method requires, among other things, changing the primary element of the fuel system - the injector. New types of injectors, as any piece of new equipment, need to be tested to determine their actual characteristics. For gas injection the jet propagation is especially important because it determines the quality of combustion. The present work investigates propagation of jets created by gas and gas-diesel injectors. This is done with the aid of flow visualization. INJECTOR  elk JET  AREA OF VIEW IN THE PICTURE BELOW  Figure 1.1 An example of visualization of a jet created by a diesel engine injector. (Magnification factor is about 3.2.)  Flow visualization techniques allow one to actually see the jet structure and fuel distribution inside the jet. For example, Figure 1.1 shows a conical sheet two-phase jet  3 1.63 ms after beginning of injection. The dimensions of the jet in the picture are approximately 3.2 times larger than those of the actual jet (for reference: the diameter of the modeled engine cylinder is 123 mm, the injector is located in the center with the injector tip protruding several millimeters below the cylinder head).  The picture was taken with the use of laser sheet flow visualization method. With this method light in the laser sheet is reflected by droplets of liquid fuel mixed with gas and the image is captured by a high shutter-speed video camera). The case represented is not a typical one (the injection was done in a non-pressurized chamber with the gas pressure equal to 3.5 MPa), and is shown here only as an example of versatility of a flow visualization technique, which allows one to clearly see the jet boundaries and structure. Some notable features of this picture are that it shows a vortex at the head of the jet and rather large droplets of liquid fuel in the middle. The presence of big droplets indicates that the process of combustion in this case would be unsatisfactory.  The flow of fuel created in the process of injection is in essence a transient turbulent jet. In the case when a mixture of gas and diesel fuel is injected, it is a two-phase jet. One of the most important characteristics of injection is the rate of the jet penetration. It influences the speed and quality of combustion, which, in turn, determines the formation of pollutants. The present work deals mainly with experimental investigation of penetration of jets created by different injectors at different conditions of injection.  Soem of the earliest experimental investigations of transient jets are mentioned by Henqrussamee (1975). He refers to two works as mostly qualitative study of the flow patterns resulting from the mixing of isothermal homogeneous fluid. The first one was done by Rizk, who around 1955 carried out a flow visualization test for the development of axi-symmetric starting water jet. The second one was done by Meyer, who around 1960  4 used smoke-traces to follow the mixing of low-velocity air jets with stagnant surroundings. Henqrussamee also mentioned a work by Ma and Ong, who around 1971 used hot-wire probes to measure the development of streamwise velocity of twodimensional, air into air, turbulent starting jet at various stations downstream of the nozzle outlet, as the first quantitative detailed study of a transient jet.  Among the first frequently cited experiments in the area were those done by Abramovich and Solan (1973) who studied initial development of a submerged laminar jet. In their experiments the jet fluid (either air or a water-glycerol mixture) was the same as the fluid in which the jet propagated. They used hot-wire probes to determine the rate of jet penetration and measure the steady-state velocity on the jet axis. The arrival time of the jet at a specified location was defined as the time between beginning of injection and the time when the average jet velocity reached 70 percent of its steady-state value. The experimental arrival times differed from the averaged values by as much as about 12 percent. The experiments showed that the speed of propagation of the jet front was approximately one half of the steady-state speed of a fluid element at the same point on the jet axis. The experimental results of the jet penetration rate were correlated by a formula expressing penetration as a function of time through a quadratic equation. This correlation shows the penetration to be approximately proportional to the square root of time.  Another fundamental experimental work was done by Witze (1980) who investigated propagation of an impulsively-started incompressible turbulent jet of air in air. He used hot-film anemometer measurements to determine the center-line velocity of the jet and its penetration. The latter was determined using the same definition of arrival time as that used by Abramovich and Solan (1973). The jet penetration was found to be proportional to the square root of time.  5 There are many similarities between transient jets and sprays. Among many works on liquid fuel spray propagation, one of the most recent was done by Minami et al. (1990) who investigated spray characteristics and combustion phenomena in high pressure fuel injection. High-speed photography combined with flow visualization techniques was used for investigation of non-evaporating fuel sprays. The paper describing their work contains very good pictures of sprays.  In the present project high pressure jets of methane have been analyzed. Fundamental research in this field has been done by Birch et al. (1978) and (1984). The earlier work presents measurements of turbulent concentration parameters in a round free steady-state methane jet. In the later work gas chromatography was used to investigate the effect of underexpansion on high pressure (2 to 70 bar) natural gas injected into air at atmospheric conditions through a 12.65 mm diameter tube with the length to diameter ratio of 50. The methane content of the gas was around 92 percent. The effect of jet fluid density in concentration decay in such underexpanded steady-state jets was shown to be similar to that of subcritical-release free jets provided that a scale factor proportional to the square root of gas-to-ambient pressure ratio is employed to describe the effective size of the jet source.  Other work on underexpanded sonic steady-state jets was done by Ewan and Moodie (1986) who did experiments with air and helium jets. They used shadowgraphy and laser Doppler anemometry to determine the near field jet structure and the axial velocity distribution in the jet. The analysis of experimental results for the underexpanded jets showed that they are similar to the incompressible jets if the actual diameter of the jet source is multiplied by a factor to account for underexpansion. This factor was shown to be equal to the square root of exit-to-ambient pressure ratio.  6 One of the most recent experimental studies in the area was done by Ouellette (1992) who used schlieren photography to investigate propagation of a transient methane conical sheet jet created by a poppet injector. In his experiments, methane was injected in air at atmospheric conditions or in a slightly pressurized chamber (up to 375 kPa (abs.)). The penetration of the jet was shown to be proportional to the square root of time except for a short time right after beginning of the jet, during which the penetration was considerably less than predicted. The penetration was also found to be proportional to the 1/4 power of the product of the gas-to-air molecular weight ratio and upstream-to-ambient pressure ratio.  To summarize the previous experimental work on transient jets, the following can be said: single-phase round jets in non-pressurized environments have been studied in sufficient detail with determination of penetration rate, velocity and concentration distributions. The area waiting to be explored is that of turbulent transient single- and two-phase jets in pressurized environments.  On the basis of the foregoing the objectives of the present work have been formulated as follows:  1.  To find the effect of gas-to-chamber pressure ratio and absolute chamber pressure on propagation of jets created by gas and gas-liquid diesel injectors.  2.  To evaluate validity of an integral transient jet model, which represents the jet as a a vortex interacting with a steady-state jet and environment, by comparison of predicted jet penetration rates with experimentally observed ones.  7 3.  To find the effect of different liquid-to-gas mass ratios on the two-phase jet penetration rate.  4.  To find the effect of injection duration (period when the valve admitting fuel into the chamber is open) on transient jet propagation.  To achieve these objectives, an experimental jet visualization apparatus was constructed to simulate the dynamics of liquid and gas injection in a Detroit Diesel 6V-92 diesel engine. This engine is the prime mover of urban buses and is targeted for conversion to natural gas fueling by research currently under way in the Mechanical Engineering Department of the UBC.  In this work the jet propagation is investigated using schlieren and laser sheet flow visualization techniques. A model of the transient jet, describing it as quasi-steady-state jet feeding a vortex structure, has been used to calculate jet penetration rate for comparison with experimental values. The primary emphasis of this work is on obtaining experimental data and high quality pictures of the jet propagation (some of them can be found in Chapter 3). It is also interesting to compare the results predicted by the analytical model modified to represent the transient two-phase jet (whose description is given in Chapter 4) with those obtained experimentally. The new experimental apparatus proved to be a versatile and reliable tool of investigation. Description of the apparatus is given in the following chapter.  8  2 EXPERIMENTAL APPARATUS AND PROCEDURE 2.1 INTRODUCTION This chapter describes the experimental apparatus and the procedure of image acquisition used in the present work. Visualization of injection of natural gas, diesel fuel, and their combinations by diesel engine injectors has been done with a specially built experimental apparatus, and with schlieren and laser sheet systems of flow visualization. The acquisition of images was made using a high-shutter-speed, single-shot video camera. Computer software was used for picture processing and measurements. The accuracy of the measurements is discussed at the end of the chapter.  There were four major objectives in setting up the experimental rig:  1.  To simulate the process of fuel injection in a Detroit Diesel 6V-92 diesel engine as far as the fuel supply, injector lift, and injection timing are concerned. This allowed use of the same injectors as those which are employed in performance testing in the engine. This is important because the present work is a part of a bigger project aimed at designing and testing of a gas-diesel dual-fuel diesel injector.  2.  To achieve the same gas-to-chamber (supply-to-chamber) pressure ratios and absolute chamber pressures as those in the engine cylinder.  3.^To be able to use both schlieren and laser sheet flow visualization techniques. It is usually impossible to use a laser sheet for gas injection visualization without adding a light-dispersing agent in the gas which would effect the jet propagation and compatibility of the flow visualization results with results obtained in the  9 engine testing. Therefore the schlieren method was used for gas injection visualization. As far as the laser sheet method is concerned, we hoped (and later it was shown to be the case) that this method of visualization would be superior in cases of dual fuel and diesel injection, as it reveals the structure of the jet in a cutting plane.  4.^To satisfy the requirements of safety, reliability, repeatability, and ease of operation.  The present work is a continuation of flow visualization investigation of diesel engine injection at the Mechanical Engineering Department of the UBC started by Ouellette (1992). He used schlieren photography to examine propagation of a transient methane conical sheet jet created by a poppet injector in atmospheric or a slightly pressurized chamber (up to 375 kPa (abs.)).  The apparatus does not simulate the piston movement, swirl, liquid fuel evaporation and combustion present in the actual engine cylinder during the injection. The engine cylinder is replaced in the apparatus with a square chamber. The lengths of the chamber sides are equal to the cylinder diameter. Also, the engine piston shape has not been modeled, and air in the chamber is at ambient temperature. These factors have a significant effect on the fuel jet propagation and should be investigated when the simpler cases of the present work are fully understood.  10  2.2 EXPERIMENTAL APPARATUS Figures 2.1 and 2.2 show general views of the experimental apparatus; the detailed design drawings are given in Appendix A. The apparatus reproduces the main features of fuel injection in Detroit Diesel 6V-92 diesel engine. The design incorporates the following originally manufactured parts of the engine: engine cylinder head, cam shaft with its bearings and follower.  FLYWHEEL CAM SHAFT CAM FOLLOWER^INJECTOR  MOUNTING PLATE CYLINDER HEAD CHAMBER BELT TRANSMISSION ELECTRICAL MOTOR  Figure 2.1 General view of the experimental apparatus. (Drawing.)  11  Figure 2.2 General view of the experimental apparatus. (Photograph.)  The engine cylinder head is used as the base for mounting other parts of the apparatus. The construction above it, which is shown in part in Figure 2.3, provides mechanical actuation of the injector plunger necessary for the fuel injection. The movement of the cam  12 is transmitted into the movement of the injector plunger through the cam follower and rocker arm assembly.  CAM SHAFT  CAM FOLLOWER  ROCKER ARM  INJECTOR  Figure 23 Cam follower and rocker arm assembly. A chamber for flow visualization (see Figures 2.4 and 2.5) is attached to the bottom part of the cylinder head. The chamber is used for both schlieren and laser sheet methods of flow visualization, and can be pressurized up to 5.5 MPa. The chamber has two large windows (113 by 38 mm), through which light beam passes in schlieren method of flow visualization. A small window (38 by 5 mm) admits light sheet into the chamber in laser  13 sheet method of flow visualization. A detailed description of the experimental apparatus is given in Appendix B.  Figure 2.4 Front view of the chamber. (The tip of injector is seen in the center.)  CYLINDER HEAD  INJECTOR  111.111111r .■^&h.^ /  ^*  ■■... Nli WINDOW SIDE 1  ^  .  1^ •^r 4..\  t/^// p  WINDOW SIDE 2  1\s„ 44immomok, \ COVER PLATE r I/ ". A CHAMBER LID^LASER SHEET WINDOW  Figure 2.5 Cross section of the chamber. (The view is perpendicular to the one in the previous picture.)  14 Three types of injectors were used in this work. A commercial diesel fuel injector, and a prototype gas fuel injector were kindly provided by the Detroit Diesel Corporation (DDC). The third injector was developed at the UBC and is a poppet type dual-fuel (gasdiesel) injector. DDEC SOLENOID  CAMSHAFT  PLUNGER SOLENOID VALVE DIESEL FUEL  NEEDLE VALVE  Figure 2.6 Commercial DDC diesel fuel electronic unit injector schematic.  Figure 2.6 shows the DDC diesel fuel electronic unit injector schematic. It uses a camshaft driven plunger to generate injection pressure in the chamber below the plunger when the solenoid valve is closed. The pressure opens the needle valve which allows the fuel to enter the cylinder. The injection occurs only when the electronically controlled solenoid valve is closed, thus stopping recirculation of fuel through the chamber under the plunger. The timing and duration of the solenoid valve closure, which is controlled by a Detroit  15 Diesel Electronic Control (DDEC) system (its description can be found in Hames et al. (1985)), determines the beginning of injection (B01) and the quantity of injected fuel. The tip of the DDC Diesel injector tested had 9 holes; each of 0.147 mm in diameter and directed at 7.5 ° down from the plane of the cylinder head (165 ° included angle). DDEC SOLENOID GAS SUPPLY  SOLENOID VALVE  GAS CHAMBER  4 INJECTOR NOZZLE  Figure 2.7 Prototype DDC gas injector schematic. Figure 2.7 shows a schematic of the prototype DDC gas injector. It is actuated solely by a solenoid and does not require mechanical connection to the camshaft. The timing and duration of injection is still controlled by the solenoid valve, but in this case the valve directly controls admission of fuel into the cylinder. The tip of the gas injector tested has 6 holes, each of 0.381 mm in diameter, directed at 10 ° to the plane of the cylinder head (160° included angle).  16  DDEC SOLENOID  PLUNGER  UNIT INJECTOR  DIESEL SUPPLY /RETURN SPOOL VALVE  PUSH ROD DIESEL PILOT METERING VALVE CHECK VALVE  RETURN SPRING  MIXING RESERVOIR -  •  CNG  POPPET NOZZLE  -  POPPET SEAT ANGLE  Figure 2.8 UBC dual-fuel poppet injector schematic. (Courtesy of B. Hodgins.)  Figure 2.8 shows a schematic of the UBC dual-fuel poppet injector. A commercial DDC diesel fuel injector was modified to include a gas supply line, a diesel fuel metering valve to vary the gas-diesel fuel ratio, a mixing reservoir where gas and diesel fuel mix together, a push rod which acts directly on the poppet nozzle causing it to open, and a check valve in the diesel fuel line after the metering valve which prevents the high-pressure gas from entering that line when the pressure in it is lower than that of the gas. The injector nozzle consists of a poppet valve which opens when the hydraulic pressure of the diesel fuel acting on the push rod overcomes the return spring preload. Two versions of the injector -  17 with 20 ° and 10 ° poppets - were used. Fuel is injected into the cylinder in the shape of a conical sheet jet. Timing and metering of injection, and actuation of the plunger are analogous to those in the DDC commercial diesel injector.  Two systems of flow visualization - schlieren and laser sheet - were employed in the present work to investigate the propagation of jets created by these diesel engine injectors. Schlieren was used in the cases when only gas was injected and sometimes for diesel and diesel-gas injections. The laser sheet method was used exclusively for liquid and gas-liquid jets. The schlieren method (whose detailed description is given in Appendix C) allows one to distinguish areas of different density in the flow. It gives a picture of the injection flow boundaries. The laser sheet method (whose detailed description is given in Appendix D) allows one to get cross-sectional pictures of the jet. It can also be used to reveal directions and velocities of the moving droplets (in these experiments the liquid particles were too small and thoroughly mixed with gas to leave measurable streaks).  2.3 IMAGE ACQUISITION AND PROCESSING General arrangement of the image acquisition system is shown in Figure 2.9. A single-shot black-and-white high-shutter-speed video camera was used at maximum shutter speed (1/10,000 of a second). The output of the camera was directly connected to an Imaging Technology PC-based frame grabber board which converted the video signal to digital information. This allowed storage of the acquired pictures in the form of files on computer disks.  The processes of injection and image acquisition were synchronized to crank angle. This was achieved with the aid of a controller, specially constructed for this purpose. It uses  18 80C196KB microcontroller for precise timing that can not be done by an ordinary personal computer.  Computer  Flowvis. controller  C OM 1  Power supply 12V, 12A  LPT 1 0 Cam shaft  Frame grabber board  DDEC Injector  Monitor Camera  Power supply  Figure 2.9 General arrangement of the image acquisition system.  The controller receives a signal from an optical shaft encoder positioned on the axis of the cam shaft. The angular position of the cam shaft and the speed of its rotation are determined from the shaft encoder by the controller and displayed on the controller front panel. The controller allows one to set the beginning and duration of injection, and the period after the beginning of injection at which a picture is taken. More information on the controller is given in Appendix E.  Two computer programs in C language were used for image processing. They allow one to enhance image and to take measurements on it. Enhancement is especially needed for processing of pictures of gas injection into non- or low-pressurized chamber. At such  19 cases subtraction of the background (picture of the area of interest before the injection) is often needed to clearly identify the boundaries of the jet on schlieren images.  One background picture was taken for every set of snapshots of injection. Figures 2.10 and 2.11 show typical background pictures for schlieren and laser sheet methods of flow visualization. Only half of the chamber is shown on these snapshots. The tip of the injector is clearly visible near the top wall. As the dimensions of the windows are slightly smaller than the dimensions of the chamber, the side walls are not seen.  Figure 2.10 Typical schlieren background picture. (Injector tip is seen in the upper right corner.)  The black rectangle in Fig. 2.11 is a 50.8 by 25 4 mm piece of cardboard used for scaling while processing laser sheet pictures. In the processing of schlieren snapshots the  dimensions of the chamber were used. The background pictures were also used for  20 identifying the coordinates of the injector nozzle and, in some cases, for subtracting background from the image.  Figure 2.11 Typical laser sheet background picture. (Injector tip is seen in the upper left corner.)  Images captured by the camera and displayed on a computer screen were inevitably distorted as it was almost impossible to position the camera exactly perpendicular to the beam of light in the schlieren system, or exactly parallel to the "cutting" sheet of light in the laser sheet system. Therefore scaling was done in both horizontal and vertical directions. The same computer program was used for scaling and measurements. A background picture displayed on a computer screen was scaled by choosing (with the aid of a mouse) two pairs of points (first in the horizontal, then in the vertical direction), the distances between which were known, and entering these distances in the computer. The location of the exit of the injector nozzle was also indicated to give to the computer its  21 axis coordinates. These coordinates and scaling factors were retained in the computer memory and were used for taking measurements on subsequent injection snapshots having the same background. Determination of the nozzle exit coordinates on the background image was necessary because soon after the beginning of injection the injector tip was hidden by the injection cloud. The jet penetration is defined as the distance from the nozzle exit to the farthest point on the jet boundary (see Figure 2.12).  INJECTOR  JET  Ae-  JET PENETRATION  Figure 2.12 Definition of the jet penetration.  Processing of images was done after a complete set had been taken for given conditions of injection. One set usually had the same background picture. In many cases additional snapshots for the same conditions of injection were needed. Quite often they were taken on another day and have a different background picture. To insure compatibility of measurements on images with different backgrounds, the same points (the same chamber dimensions or the same rectangle) were always used for scaling.  Hard copies of pictures were obtained by converting images into postscript files and printing them on a laser printer. As the resulting pictures are of much inferior quality compared to those displayed on a computer monitor, the latter were used for analysis.  22  2.4 ERROR ANALYSIS The major errors in measurements of the jet penetration in the present experimental work were due to the following:  1.  Scattering of experimental data due to the process of the turbulent jet propagation, in which each case of the injected fluid traveling is slightly different from another even at the same injection conditions. This is the single most important factor affecting the accuracy of the measurements.  2.  Difficulty in distinguishing the jet tip on schlieren pictures at the beginning of injection when the tip velocity is high. The image of the tip does not have a clear edge and blends with the background.  3.  Optical distortion caused by use of short-focus-length lenses in the laser sheet system of flow visualization. To minimize the effect of this error, the camera is positioned in such a way that its axis passes through approximately the center of the area of interest.  4.  Limited accuracy of the scaling process. The accuracy of the jet penetration measurements on a picture of the jet depends on accuracy of the picture scaling. This error was found to be less than one percent.  To evaluate the difference between the jet penetration measurement and actual average jet penetration, sets of pictures were taken at the same conditions of injection and the same time interval after the beginning of injection. The standard deviation of the jet penetration measurements obtained with the use of the apparatus was found to be 1.7 percent from the  23 average on a set of 20 pictures for the DDC gas injector, and 3.7 percent on a set of 15 pictures for the UBC poppet gas-diesel injector. Three quarters of the obtained experimental data are supposed to lie (on the assumption of a normal distribution) in the ranges of standard deviation. Another quarter, theoretically, can be scattered anywhere.  24  3 EXPERIMENTAL RESULTS 3.1 INTRODUCTION This chapter presents results of experimental investigation of propagation of fuel jets created by different types of injectors. The round nozzle gas injector and the poppet gasdiesel injector are the main objectives of the present work. The commercial Detroit Diesel Corporation diesel fuel injector was investigated for the purpose of comparison with the previous two.  In the process of the experiment the following parameters were varied to investigate their effect on the jet penetration rate: pressure in the chamber into which the injection took place, upstream-to-chamber pressure ratio for gas and gas-diesel injection, diesel-gas mass ratio for gas-diesel injection, and duration of injection. Also, propagation of a carbon dioxide jet was compared with propagation of a methane jet.  3.2 ROUND NOZZLE GAS INJECTOR This section presents experimental results of investigation of the jet created by the prototype DDC gas injector. A schlieren system was used for flow visualization of the jet. In the process of the experiment gas-to-chamber pressure ratio, as well as the chamber pressure, were varied. At the end of this section comparison between propagation of a carbon dioxide and a methane jet is given.  Below are examples of the flow visualization pictures taken. Figures 3.1, 3.2 and 3.3 show development of the jet created by injection of methane at pressure ratio 1.5 and pressure  25 inside the chamber of 3550 kPa. Figures 3.4 and 3.5 show development of the jet at the pressure ratio of 5.0 and the chamber pressure of 2170 kPa.  The images were obtained by a single-shot camera at different times from the beginning of injection of different jets at the same conditions. Therefore, a set of snapshots at the same conditions of injection does not represent propagation of the same jet. Also, since this injector has 6 equally-spaced nozzles, parts of three jets from the adjacent nozzles appear on the schlieren pictures. This, nevertheless, does not obstruct the view of the head of the jet aligned to be perpendicular to the beam of light used for schlieren. The actual location of the top wall of the chamber in the plane passing through the axis of the aligned jet is about 3 mm (in scaled dimensions) above the edge of the black area at top of the pictures. This is due to the fact that some of the view is blocked by the edge of the cylinder head.  Beginning of the jet (BOJ) is defined here as the first visible appearance of the jet emerging from the nozzle. It is different from beginning of injection (B01), which is defined as the moment of the solenoid valve closure in the Detroit Diesel Electronic Control (DDEC) system type injector. The difference in time between the BOJ and the BOI is the delay of injection. It varies with injector design and with injection condition with the same injector.  26  0.14 ms after beginning of the jet  0.37 ms after beginning of the jet  1.08 ms after beginning of the jet  Figure 3.1 DDC gas injector jet propagation. Pch=3550 kPa, PR=1.5 (first of a sequence of 3 figures).  27  1.54 ms after beginning of the jet  2.72 ms after beginning of the jet  3.89 ms after beginning of the jet  Figure 3.2 DDC gas injector jet propagation. Pch=3550 kPa, PR=1.5 (second of a sequence of 3 figures).  28  5.06 ms after beginning of the jet  6.23 ms after beginning of the jet  7.39 ms after beginning of the jet  Figure 3.3 DDC gas injector jet propagation. Pch=3550 kPa, PR=1.5 (third of a sequence of 3 figures).  29  0.40 ms after beginning of the jet  0.63 ms after beginning of the jet  0.87 ms after beginning of the jet  Figure 3.4 DDC gas injector jet propagation. Pch=2170 kPa, PR=5.0 (first of a sequence of 2 figures).  30  1.22 ms after beginning of the jet  1.69 ms after beginning of the jet  2.39 ms after beginning of the jet  Figure 3.5 DDC gas injector jet propagation. Pch=2170 kPa, PR=5.0 (second of a sequence of 2 figures).  31 3.2.1 EFFECT OF CHAMBER PRESSURE  During the experiments the jet penetration (the distance from the nozzle exit to the farthest from it point on the jet boundary - see Figure 2.12) was measured at different moments after the beginning of injection. Figures 3.6 and 3.7 represent experimental data for the cases when the pressure ratio was equal to 2.0 and 3.0 respectively, and different pressures in the chamber. 60  6o  50 EE 40  e  30  0 Pch=690 kPa A Pch=2170 kPa  15 c  et 20  El Pch=3550 kPa  10 0 0  1  2^3 Time after BOJ, ms  4  5  Figure 3.6 DDC gas injector penetration at the pressure ratio of 2.0. (Continuous injection.)  The data points for different pressure ratios do not exactly coincide because of the  scattering of experimental data (see Section 2.3), but the experiments strongly indicate invariance of the jet penetration rate with different chamber pressures provided the pressure ratio is maintained to be the same. Therefore, the jet penetration rates for different pressure ratios can be compared even if the chamber pressure in different cases was different.  6  32  60 50 E E  g:  AA -ry  30 0 Pch=690 kPa  A Pch=2170 kPa  cr. 20  10 0  ^  0  0.5  1  Pch=3550 kPa  2.5  1.5^2 Time after BOJ, ms  3  3.5  Figure 3.7 DDC gas injector penetration at the pressure ratio of 3.0. (Continuous injection.)  3.2.2 EFFECT OF PRESSURE RATIO 60  PR=8 0 PR=5 pR 3  PR=2  00  77PAA  50  O v° W,^On  E 40  2- 30  ^  0  PR=1.5  0  0  2 tu tu  ct 20  10 0  0  1  2^3^4^5^6^7^8 Time after BOJ, ins  Figure 3.8 DDC gas injector jet penetration for different pressure ratios. (Continuous injection.)  33 Figure 3.8 shows dependence of the jet penetration rate on the pressure ratio with various chamber pressures. For reference: the data for the cases of PR equal to 1.5, 2.0, and 3.0 were taken at the chamber pressure 3550 kPa, for PR=5.0 the chamber pressure was 2170 kPa, and for PR=8.0 it was 690 kPa.  As the data show, the jet penetration rate depends significantly on the pressure ratio. The greater the pressure ratio, the greater the jet penetration rate, especially after 0.5 ms.  3.2.3 VIRTUAL BEGINNING OF THE JET  As shown by prior experiments (see Witze (1980), for example), and analytically in Appendix G, the penetration of an impulsively started jet is proportional to the square root of time during the period of injection. As can be seen from Figures 3.9 and 3.10, that is not the case for the initial half of a millisecond, but a good approximation thereafter for the injector used in the present experiment. Evidently, the flow is not "impulsively started" and there is valve opening with flow initiation period of the order of 0.4 ms.  t1/2, (ms) /2 Figure 3.9 DDC gas injector jet penetration for different pressure ratios. Squareroot-of-time dependence. (Continuous injection.)  34 The jet penetration rate right after the beginning of the jet is substantially lower than the expected one. To explain this lets compare, for example, observed jet penetration rate at the pressure ratio of 5.0 with the best fit which is proportional to the square root of time (curve A in Figure 3.10). 70 60 50  E E  d  .  40 30  822 20 0 Experiment  10 0  Best fit (with penetration proportional to t 1R ) 0  0.5^1^1.5  Time after BOJ, ms  2  2.5  Figure 3.10 DDC gas injector observed and calculated jet penetration at PR=5.0. (Continuous injection.)  A significantly bend fit of the experimental data can be achieved if the beginning of the fitting curve is shifted from the actual beginning of the jet to the time which will be later referred to as the virtual beginning of the jet or BOJN (curve B in Fig. 3.10). The measured jet penetration rate at the beginning is much less than expected from the squareroot-of-time dependence. This is due to the fact that some time is needed to fully open the valve admitting gas to the injector nozzle. As a result, the mass flow through the valve does not increases from zero to nominal steady-state value instantaneously. Another factor is the time needed to start the flow of the gas in the injector gas passage from the valve seat to the nozzle (see Fig. 2.7). Even in the absence of friction between the gas and the passage walls, there is a time delay because of the inertia of the fluid.  35 The differences in time between the actual beginning of the jet (the moment of its first appearance emerging from the nozzle - BOJ) and virtual beginning of the jet (or virtual starting time, which can be defined as the time origin when an impulsively-started jet would have originated - BOJN) are given in Table 3.1. The carbon dioxide injection data in the table are for the cases described in the next section. As can be seen from these tables the flow initiation period increases with the increase of the pressure ratio an the chamber pressure; it is greater for the carbon dioxide jet compared to the methane jet.  PR 1:5  PR=3.0  0.23 ms 0.28 ms  0.26 ms  0.23 ms  0.38 ms  0.32 ms  0.24 ms  0.32 ms  0.45 ms 0.72 ms  0.38 ms  PR=5.0  0.30 ms  Table 3.1 Round nozzle gas injector. Difference between BOJ and BOJN. • Pch=6901cPa 0.80 ms  P11= 1-5 -  0.77 ms  0.77 ms  0.77 ms  0.91 ms  0.80 ms  0.77 ms  PR=5.0' • .  PR=8.0  Table 3.2 DDC gas injector injection delay.  0.89 ms 0.82 ms  36 A very important characteristic of an injector is observed difference in time between the BOI (the moment of the solenoid valve closure) and BOJ - the injection delay - for different cases. It is also necessary for analysis of the flow visualization pictures. These data are summarized in Table 3.2.  3.2.4 COMPARISON BETWEEN METHANE AND CARBON DIOXIDE JETS  One of the interesting questions raised during the experiment was the dependence of the jet penetration rate on the kind of gas being injected. To investigate this dependence, carbon dioxide (molecular mass is 44.01) instead of methane (molecular mass is 16.04) was used as the gas injected by the DDC gas injector. Figures 3.11 and 3.12 compare the jet penetration rate of methane with that of carbon dioxide at the pressure ratio of 2.0 and 3.0 respectively.  60 50 E 40  17-3 0  A  82 20  0 CO2, Pch=33201cPa  ,  CH4, Pch=3550 kPa  1:1 CO2, Pch=2170 IcPa  10 0  0  1  2^3 Time after BOJ, ms  4  5  Figure 3.11 DDC gas injector. Comparison between methane (CH 4) and carbon dioxide (CO 2) jets penetrations. PR=2. (Continuous injection.)  37  1  ^  ^ ^^ 1.5^2 2.5 3 3.5 Time after BOJ, ms  Figure 3.12 DDC gas injector. Comparison between methane and carbon dioxide jets penetrations. PR=3, Pch=2170 kPa. (Continuous injection.)  The experimental data shows that the carbon dioxide jet initially propagates slower than the methane jet, but after a short period of time the jet penetration rate for carbon dioxide is greater than for methane. Solid lines in Fig 3.12 represent the best fit to the experimental data. They show that the methane jet in the "established region" (where the jet penetration is proportional to the square root of time from the virtual beginning of the jet) propagates slightly faster.  3.3 POPPET GAS-DIESEL INJECTOR This section presents results of investigation of a prototype 20 ° poppet gas-diesel injector. Two types of flow visualization techniques were employed in the injector testing: schlieren and laser sheet. Comparison of the pictures obtained with the use of both techniques for the same conditions of injection showed that the liquid fuel appears to be well atomized and its tiny droplets seem to be dispersed evenly throughout the whole volume of gas, creating something similar to a cloud of mist. The experiment appeared to show that at all  38 stages of injection both fuels travel inseparably. Figures 3.13 (schlieren) and 3.14 (laser sheet) taken at the same conditions illustrate this statement.  Figure 3.13 Schlieren picture of the poppet gas-diesel injector jet. PR=2.0, Pch=3550 kPa. 4.6 ms after BOI.  Figure 3.14 Laser sheet picture of the poppet gas-diesel injector jet. PR=2.0, Pch=3549 kPa. 4.6 ms after BOI.  39 The laser sheet method of flow visualization was employed most of the time since it allows one to see the structure of the jet in one plane, and is more accurate in measuring the jet penetration at the earlier stages of injection when the jet velocity is high (the jet boundary is clearly identifiable).  The pictures shown below are examples of propagation of the conical sheet jet at two different conditions. Figures 3.15 and 3.16 show development of the jet injected into the chamber pressurized to 3550 kPa with the pressure ratio of 1.5 and diesel-gas mass ratio of 0.5. The solenoid valve closure (BOI) was at 160 crank angle degrees. The pulse width (PW) during which the injector solenoid valve was closed was equal to 2.33 ms. The first appearence of the jet (BOJ) was detected around 0.45 ms after BOI. Figures 3.17 and 3.18 show development of the jet with the following conditions: Pch=3550 kPa , PR=3.0, diesel-gas mass ratio of 0.25, BOI at 170 crank angle degrees, PW continuous (injection did not stop before a snaphot was made); the difference between the BOJ and BOI was 0.47 ms.  40  0.16 ms after BOJN  0.40 ms after BOJN  0.86 ms after BOJN  Figure 3.15 Poppet injector jet propagation. Pch=3550 kPa, PR=1.5 (first of a sequence of 2 figures).  41  2.03 ms after BOJN  3.19 ms after BOJN  6.68 ms after BOJN  Figure 3.16 Poppet injector jet propagation. Pch=3550 kPa, PR=1.5 (second of a sequence of 2 figures).  42  0.23 ins after BOJN  0.70 ms after BOJN  1.41 ms after BOJN Figure 3.17 Poppet injector jet propagation. Pch=3550 kPa, PR=3.0 (first of a  sequence of 2 figures).  1.88 ms after BOJN  3.05 ms after BOJN  4.23 ms after BOJN  Figure 3.18 Poppet injector jet propagation. Pch=3550 kPa, PR=3.0 (second of a sequence of 2 figures).  44  3.3.1 EFFECT OF CHAMBER PRESSURE AND PRESSURE RATIO  Figure 3.19 shows measured penetrations of the jet at different conditions with the pulse width held constant at 2.33 ms. The actual jet pulse width (the pulse width minus the injection delay) was about 1.31 ms. The position of the diesel fuel metering valve, which controls diesel-gas ratio (see Fig. 2.8) was at 6 turns open. 50  A  40  A  PR=2 Pch=1820  A  PR=1.5 Pch=3550  o^aQ  2  PR=2 Pch=450  O PR=2 Pch=3550  E  30  PR=3 Pch=3550  (Pch is in kPa)  20  10 0  0  ^^ ^ ^ ^ 1 2^3^4^5^6 7 8 9 Time after BOJN, ms  Figure 3.19 Poppet gas-diesel injector jet penetration. PW=2.33 ms (actual injection stopped about 1.31 ms after BOJ or about 0.86 ms after BOJN).  The data on the above figure is plotted versus time after virtual beginning of the jet (BOJN). The difference in time between the moment of the solenoid valve closure (B01) and the BOJN was equal to 1.47 ms for PR-13 and Pch=3550 kPa, 1.30 ms for PR=2.0 and Pch-3550, 1.33 ms for PR=2.0 and Pch-1820 kPa, 1.35 ms for PR=2.0 and Pch=450 kPa, and 1.28 ms for PR=3.0 and Pch=3550 kPa Immediately after the beginning of the jet (before BOJN) its penetration is similar to that of gas from the gas injector described in the previous section.  45 Unlike the gas jet penetration rate (see Section 3.2.1), the gas-diesel jet penetration rate for the same pressure ratio is weakly dependent on the chamber pressure. This is explained by the fact that the diesel-gas mass ratio for the same position of the diesel fuel metering valve and the same pressure ratio is higher for a case of a lower chamber pressure (see Figure 3.21). For the above jets for the pressure ratio of 2.0 the diesel-gas mass ratio is estimated to be 0.38 for Pch=3550 kPa, 0.6 for Pch=1820 kPa, and about 0.8 for Pch=450 kPa. The dependence of the jet penetration rate on the diesel-gas mass ratio, as it is shown in Section 3.3.3, is weak.  3.3.2 EFFECT OF INJECTION DURATION Analysis of the experimental data shows that penetration of the jet in the "established region" is proportional to the square root of time during the duration of injection. After the injection ceases, the movement of the jet was found to slow down significantly, almost to a stop, and the jet loses its initial structure. Figure 3.20 shows dependence of the jet penetration rate on the duration of injection. 50  0 0 00  a  40 E  30  0  0  2  2 20 ci)  ^ Injection stopped 1.05ms after BOJN  El  0  10  Continuous injection  0 0  0  1  ^  ^^ ^ 7 6 5 Time after BOJN, ms  2^3^4  Figure 3.20 Poppet gas-diesel injector jet penetration for different durations of injection. PR=3.0. Pch=3550 kPa.  46 3.3.3 EFFECT OF DIESEL-GAS MASS RATIO  One of the major problems in interpreting experimental results for the gas-diesel injection was determining of exact liquid-gas mass ratio at different conditions of injection. No practically acceptable and accurate measurement of this ratio was possible on the experimental rig. Instead, averaged fuel-flow data of a test engine with the same injector was used. Mass flow ratio of the injected fuels at different positions of the metering valve, different pressure ratios, and different upstream pressures of the injected gas were calculated from the data. Figure 3.21 represents the averaged data for pressure ratios greater than two (labels indicate position of the diesel fuel metering valve). 1 0.9  •  a 0.8 0.7 s 0.6 0.5 0.4  0  9 turns  O  7 turns  .21111111111141110■4  8 turns 6 turns 5 turns  1 41*  V  0.3 0.2  5  ^  ^ 6^7 8 Upstream gas pressure, MPa  Figure 3.21 Diesel-gas mass ratio for 20° poppet injector (PR > 2).  Figures 3.22 and 3.23 show observed jet penetration at different diesel-gas mass ratios for the pressure ratios of 1.5 and 3.0 respectively. The jet with considerably larger amount of diesel fuel (Fig. 3.22) initially penetrates faster, but then loses its momentum faster, so both jets reach the boundary of the view at approximately the same time.  47 40  0  0 0  00  0  ^0 O  Diesel-gas mass ratio O ^  0.9 0.2  0 0^1^2^3^4^5^6^7 Time after BOJ, ms  Figure 3.22 Poppet injector jet penetration at different diesel-gas mass ratios. PR=1.5, Pch=3550 kPa.  0^  50 40 E E  6:  30  0  81.!  20  Diesel-gas mass ratio O 0.25 ^ 0.05  10 0  1  0  2^3^4 Time after BOJ, ms  5  6  Figure 3.23 Poppet injector jet penetration at different diesel-gas mass ratios. PR=3.0, Pch=3550 kPa.  The data shows that change in diesel-gas mass ratio does not have significant effect on the jet penetration rate.  48 3.3.4 EFFECT OF INJECTOR POPPET ANGLE All of the above statements considering the 20 ° poppet injector are also valid for the 10 ° poppet injector, as the jet propagation rate of the latter is only marginally better (see Figure 3.24, for example). 40  E  a  30  0 :I 20  E3 0 10 deg. poppet  c w  10  El 20 deg. poppet  0 ^ ^ ^^ 2^3^4^5 6 7 0 8 Time after BOJN, ms Figure 3.24 Comparison of jet penetration of 20° and 10° poppet injectors. Pch=3550 kPa, PR=2.0, PW=2.33 ms.  3.3.5 COMPARISON BETWEEN METHANE AND CARBON DIOXIDE JETS.  Figure 3.25 shows comparison between penetrations of methane and carbon dioxide jets. The dependence of the jet penetration rate on the kind of gas is similar to that for the round gas jet (see Section 3.2.4) There is greater time delay between the beginning and the virtual beginning of the jet for the carbon dioxide jet than for the methane jet. This can explained by greater inertia of carbon dioxide.  49 40  30  1  20  tE  0 CH4  10  El CO2 Best fit (with penetration porportional to tin) 1  2^3 Time after BOJ, ms  4  5^6  Figure 3.25 Poppet gas-diesel injector. Comparison between methane (CH 4) and carbon dioxide (CO 2) jets' penetrations. PR=2, Pch=2170 kPa.  The differences in time between the actual beginning of the jet (BOJ) and the virtual beginning of the jet (BOJN) are given in Table 3.3.  Co  CH4 Pch=3550 kPa PR=1.5  Pch=21701cPa  Pch=2170 kPa  0.18 ms  0.38 ms  0.12 ms  PR=2.0 PR-3.0  ,  0.51 ms  Table 3.3 Poppet diesel-gas injector. Difference between BOJ and BOJN.  50  3.4 ROUND NOZZLE DIESEL INJECTOR As part of the present work, some flow visualization of injection from the commercial DDC diesel injector was done for the purpose of comparison with the other two types of injectors. Figures 3.26, 3.27, and 3.28 show pictures of propagation of diesel fuel jet from the injector with the chamber pressure of 3550 kPa. The first two figures show propagation of the diesel jet with continuous pulse width (PW). The third picture shows later stages of propagation of the jet with PW=1.16 ms, which corresponds to the actual injection period of about 0.49 ms.  51  0.44 ms after BOJN  0.68 ms after the BOJN  1.14 ms after BOJN Figure 3.26 DDC diesel injector jet propagation. Pch=3550 kPa (first of a sequence of 2 figures).  52  1.84 ms after BOJN  2.30 ms after BOJN  3.70 ms after BOJN  Figure 3.27 DDC diesel injector jet propagation. Pch=3550 kPa (second of a sequence of 2 figures).  53  2.30 ms after BOJN  4.17 ms after BOJN  6.49 ms after BOJN Figure 3.28 DDC diesel injector jet propagation. Pch=3550 kPa. PW=1.16 ms.  54 3.4.1 EFFECT OF CHAMBER PRESSURE Figure 3.29 shows the observed rate of the jet penetration for different pressures in the chamber and the PW=1.67 ms (actual injection period is 0.49 tns).  60 Pch=101 kPa  50  0  Pch=1820 kPa  A  A  —  E 40  CI  ° 30  a  47. a  Pch=3550 kPa  A  A  A  C  ti 20 10 0 0  1  2  3^4 Time, ms  5  6  7  Figure 3.29 DDC diesel injector jet penetration for different pressures in the chamber. PW-1.67 ms (actual injection period is 0.49 ms).  The jet penetration rate from the diesel fuel injector depends very much on the pressure in the chamber because the diesel fuel supply pressure does not change. This is due to the fact that the upstream diesel pressure is held constant and a change in the chamber pressure leads to a change in the upstream-to-ambient pressure difference, which determines the velocity of fuel leaving the nozzle.  55 3.4.2 CALCULATED DIESEL JET PENETRATION  In this section a comparison is done between experimental and calculated diesel fuel spray tip penetration rates for injection into quiescent air. The calculations were done using the following formula developed by Dent (1971): 1/4^  S 3.07(1 (td. )n 294 i Pa^T.  y4  (3.1)  where S is the tip penetration, AP is the pressure drop across the injector nozzle, p a is the ambient density (density of air in the chamber), T a is the ambient (chamber) temperature, t is time, and d o is the diameter of the nozzle (all quantities are expressed in SI units). Figures 3.30 and 3.31 show comparison between experimentally observed and calculated spray penetration rates for different chamber pressures and for the diesel injection pressure assumed equal to 12 MPa.  Figure 330 DDC diesel injector. Comparison between experimental and calculated spray penetrations. Pch=3550 kPa. (Continuous injection.)  56  Figure 3.31 DDC diesel injector. Comparison between experimental and calculated spray penetrations. Pch=1820 kPa. (Continuous injection.)  The Dent's formula is applicable only for t > OS ms. Therefore there is no comparison given for the case of Pch=101 kPa as the jet tip reached the boundary of the view before t-0.45 ms.  The exact magnitude of the injection pressure for the above cases is not known. For the calculations it was taken to be equal to 12 MPa. This pressure has a significant effect on the calculated jet penetration rate. Nonetheless, analysis of the above graphs indicates that the Dent's formula is applicable only within a certain range of injection pressures.  3.4.3 COMPARISON WITH GAS AND GAS-DIESEL INJECTORS  To conclude this chapter, Figure 3.32 compares penetration rates of jets from the three types of injectors discussed earlier. The comparison is done for the cases when the pressure in the chamber was equal to 3550 kPa, the gas pressure ratio equal to 3.0, and the pulse width was continuous.  57 60 50 E 40  ^  0  DDC diesel injector DDC gas injector UBC poppet gas/diesel injector  10 0 0  1  2  Time, ins  3  4  5  Figure 3.32 Comparison of penetration of jets from different injectors. Pch=3550 kPa, PR=3.0, PW continuous. As it can be seen from the above figure, it is possible with a gas injector to achieve jet  penetration rate comparable to that for the commercial diesel fuel injector. The dual-fuel poppet injector also demonstrated a good jet propagation, especially considering the differences between the round and conical sheet jets.  3.5 SUMMARY OF EXPERIMENTAL OBSERVATIONS Results of the experimental investigation of the transient single- and two-phase jets propagation presented in this chapter can be summarized as follows:  1.^The penetration rate of the gas and gas-diesel transient jets do not depend significantly on the pressure in the chamber as long as the injection pressure ratio is constant.  58 2.  Penetration of the transient jet is proportional to the square root of time from the virtual beginning of the jet. The virtual beginning of the jet is defined as the moment in time found by extrapolation of experimental data in the "stabilized region" of the jet development on the beginning of the jet.  3.  Penetration rate of the gas and gas-diesel transient jets depends little on the molecular weight of the gas being injected (at the same conditions of injection the penetration rate is slightly different for different gases), and the liquid-to-gas mass ratio for a two-phase injection.  4.  Once the injection of fresh gas ends, the jet slows down considerably and eventually comes to a complete stop.  5.  For a two-phase injection with a high liquid-gas mass ratio, atomization of the liquid phase is not sufficient to prevent propagation of a part of it in the from of quite large droplets. For such cases the mixture cannot be treated as gas. When atomization is good, tiny droplets of the liquid phase mix thoroughly with the gas and the two phases propagate together.  59  4 INTEGRAL MODEL OF A TRANSIENT TWO-PHASE JET This chapter describes a model of the transient jet used to estimate the jet penetration rate. After a short introduction, outlining the development of the model, and sections describing steady-state jets, the model of a transient single- and two-phase jet is presented. The last sections show model sensitivity and comparison between predicted and experimentally observed jet penetration rates.  4.1 INTRODUCTION The process of simultaneous injection of natural gas and diesel fuel in diesel engines takes place in the form of a transient two-phase jet. Both these characteristics of the jet significantly complicate its theoretical analysis. To get practically applicable results one inevitably must use approximations (they are often called assumptions and models). The model of the transient jet which will be used in this work originates from observation of thermal plumes by J.S. Turner, who in 1962 modeled a starting plume as a steady buoyant plume feeding a vortex structure. That a similar model can be used for analyzing transient jets was suggested by flow visualization pictures of impulsively started jets (Batchelor (1967)), which clearly reveal a vortex structure in the shape of mushroom or ball at the head of the jet. Abramovich and Solan (1973) modeled a starting laminar jet as a quasisteady state jet feeding a vortex structure. The same model was successfully applied to transient turbulent round free jets by Witze (1980) and to transient laminar, turbulent, and spray jets by Kuo and Bracco (1982). It was shown to be quite accurate in predicting penetration of the jet. Ouellette and Hill (1992) modified this model for transient turbulent conical sheet jets. In this work that model is used and extended to include two-phase transient jets.  60 The model is based on the following considerations. It is possible to identify at the front of a suddenly operated jet, a spherical ball or vortex of fluid which increases in diameter and moves forward on the axis of the jet. Figure 4.1 shows an example of such a ball or spherical vortex. The movement of the ball is slowed down because of the interaction with the surrounding fluid. The resulting loss of momentum is due to viscous forces. At the same time, because of the decrease in velocity of the ball, some jet fluid enters it, carrying with it linear momentum and vorticity which are added to the momentum and vorticity of the fluid inside the ball.  Figure 4.1 An example of a spherical vortex at the front of a transient jet. (Only head  of the jet is clearly identifiable, as view of other parts is blocked by two neighboring jets propagating at the angle of 60 ° to the considered jet.)  For the purpose of simplification, which does not obscure understanding of the physical processes in the jet, we will use a model, which considers the flow at the front of a suddenly operated jet as propagation of a spherical vortex interacting with a steady jet and the surrounding fluid. The model is based on an integral momentum balance (see Winnikov and Chao (1966) or Abramovich and Solan (1973)). The validity of this  61 simplification was confirmed by Kuo and Bracco (1982) who showed that the stem of a transient jet can be considered to be in a steady state to which steady-state equations can be applied.  The model described above requires knowledge of the steady-state jet parameters. Therefore, before considering transient axisymmetric and conical-sheet jets (Sections 4.3 and 4.4 respectively), the steady-state jet must be analyzed.  4.2 STEADY - STATE CIRCULAR JET Consider a turbulent steady-state submerged round jet of incompressible fluid. Figure 4.2 shows a simplified diagram of the jet.  110  Urn/2 r 1r2  MEM  MEW MIMI&  \•,).144MPse.:  UMW,  0, ..M .`X-MMU^  MINIM WO' 111/  U  Zc INITIAL REGION  TRANSITION REGION  FULLY DEVELOPED REGION  Figure 4.2 Diagram of an axisymmetrical submerged jet. Fluid is discharged with a uniform initial velocity U o from a round nozzle of the radius ro and spread through a medium at rest. Axial velocity of the jet is denoted by the symbol U and the maximum axial velocity in a given cross section by the symbol U. The jet can be  62 separated into three regions. In the initial region the velocity in the potential core of the jet remains constant and equal to the initial velocity. The end of the initial region is marked by disappearance of the potential core because of the thickening of the jet boundary layer. The transition region may be defined as the region in which the jet velocity distribution becomes fully developed. The latter is characterized by invariance of the dimensionless velocity profile with distance from the nozzle. The jet in the fully developed region is similar in appearance to a flow of fluid from a source of infinitely small thickness. The linearity of the increase in the jet thickness can be derived theoretically (see, for example, Abramovich (1963)) and confirmed experimentally when the velocity profiles in the submerged jet are universal.  The similarity of the velocities profiles in different cross-sections of the fully developed region can be expressed as follows: r U = f(), where t = — , U.^r112  (4.1)  r is the distance from the axis of the jet in radial direction, and r u2 is the distance from the axis at which U=(0.5)U.. It is common practice in consideration of jets to extend the principle of similarity of velocity (as well as temperature and concentration) profiles to the beginning of the jet. In this analysis we employ the following formulae proposed by Warren as they are given in Witze (1980); if an axial distance z from the nozzle exit is less than the length of the potential core region z, r2 - r 2 e2 )], rIt2 - I.,  U = U. expr ln(2.0)(  (4.2)  where I., is the radius of the potential core at the distance z; if z is greater than z, U = U. exp[- ln(2.0)(rirv2 )2 1.^(4.3)  63 The real process of injection of natural gas is much more complicated than a jet of incompressible fluid. Nonetheless, its analysis can be significantly simplified if we assume that the effects of the gas compressibility are important only in the vicinity of the nozzle, and treat the rest of the jet as being incompressible. This assumption is validated by experiments which show that the static pressure in the jet is virtually invariable and equal to the pressure in the surrounding space.  Now let's consider a gas-liquid injection where a mixture of natural gas and diesel fuel form a single jet. If the liquid phase is finely atomized and uniformly dispersed throughout the gaseous phase, we can treat this two-phase mixture as a gas. In the case when the volume occupied by the liquid phase is negligible compared to that occupied by the gaseous phase, we can introduce the equivalent specific heats and gas constant of the twophase fluid as follows: cv = (1 Y)c„ + Yc1,^  (4.4)  c p = (1- y )cps + ye1,^  (4.5)  -  R = c p - c v = (1- y)(c pg - c n ),^(4.6) where y - ml ms + ml  (4.7)  is the mass fraction of the liquid phase in the mixture, ; and c p are the specific heats of the mixture at constant volume and pressure, c nt and cpg are the specific heats of the gaseous phase, c 1 is the specific heat of the liquid phase, R is the gas constant of the mixture, m 1 is the mass of the liquid phase, and m g is the mass of the gaseous phase.  Another way to determine the gas constant of the mixture is to use the equivalent molecular weight of the mixture M defined as  64  M = Mg (1+ i) where rl =  m  I  mg  (4.8)  in the following expression: R=  (4.9)  In the above equations Mg is the molecular weight of the gaseous phase, R is the universal gas constant, and rl is the liquid to gas mass ratio, which is related to the mass fraction of the liquid in the mixture y as follows: y=  T1 . 1 11^1 y  (4.10)  The equivalent gas constant of the two-phase mixture calculated by using both equations (4.6) and (4.9) was found to be identical. Now one can develop a mathematical model of the jet employing equations for gases and using the equivalent parameters given above, plus the equivalent density of the mixture p f: Pr = P 1/ (1 +1),^  (4.11)  where P g is the density of the gaseous phase.  The above formulae represent two-phase flow modifications to the transient jet model as it is described by Ouellette and Hill (1992).  The velocity of the flow at the exit of the nozzle U. can be found from the following relations:  (4.12)  65  T, -  To k -1 1+ —M2 ' 2  U. -^R(T. -^ k -1  (4.13)  (4.14)  where M is the Mach number, P. is the upstream pressure, P, is the ambient pressure, k is the specific heat ratio, ; is the static temperature of the gas leaving the nozzle, T. is the upstream temperature of the gas, and R is the gas constant.  Assuming similarity of the jet velocity profiles and constant pressure throughout the jet and surroundings, the momentum conservation equation for an axisymmetrical steadystate jet can be written in the following form: 00  C d po nr.2 U,2, = f pj 2nrU 2 dr or 0  (4.15)  C d po ro2 U,2, = 2r12, 2 U.,2 f pi f 2 (t)tclt,^(4.16) CO  where Cd is the discharge coefficient, and p i is the density of mixture of the jet and ambient fluids at a point in the jet. It can be calculated as follows: ^ pi apf + (1- a)p, or  Pi,  Pi -  (4.17)  (4.18)  /a + 1 Pf  where p, is the density of the ambient fluid, p f is the density of the injected fluid at ambient pressure, x is the concentration by mass or the mass fraction of the injected fluid in the jet, a is the concentration by volume of the injected fluid at a point:  66  a-  P. ^X Pf  (4.19)  0 - 1)+1 . Pr  As was shown by experiments (see Abramovich (1963), for example), the distributions of the concentration by mass in different cross-sections of the jet are similar. From the Taylor theory of turbulence for axisymmetric jets, which is confirmed by experimental data, the concentration and the velocity profiles are related in the following manner: g(  ^  (4.20)  ^Xm^Um  where Xm is the concentration at the axis of the jet. Now Eq. (4.16) can be rewritten in the following way:  f2 (t)tdt  Cd po r:U.2 = 2r12, 2 U:,p„ j 0 xm g(t)(-1-- -1)+1  (4.21)  Pf  The mass conservation equation for the injected fluid in the jet can be written as follows: Of  C d p o/rr,,2 U. = j a p f lyrrUdr or  (4.22)  0  C d por,,2 U 0 42, 2 1.J. j ap f f (t)tdt•^(4.23) 0 Replacing the volume fraction a by the mass fraction x (see Eq. 4.19), we can write Eq. (4.23) in the following way:  67  g(t)f(t)tdt  U o = 2r12, 2 11.X.P.  XJ(t)( EI 1) Pr  (4.24)  +1  To determine the concentration of the fluid of the jet at the jet axis at different locations the following experimental formula is used (see Birch et al. (1978)): Xm _  (4.25)  X. z+z.'  where k i is the decay constant, z o is the distance from the apparent origin of the jet to the nozzle exit (see Fig.4.2), and r e is the effective radius. The effective radius takes into account differences between the densities of the injected and ambient fluids at ambient pressure, and non-uniformity of the exit velocity distribution across the nozzle. For a round orifice the effective radius can be calculated as follows: = ro 11C d  IL) P.  The system of the three equations (4.21), (4.24), and (4.25) can be solved to find U  (4.26)  m at  different distances from the nozzle z by the process of iteration, when, at first, the value of the velocity at a definite location is estimated in order to find r in from Eq. (4.24), the value of which is then used to calculate U r. from Eq. (4.21). If the estimated and calculated velocities have different values, we repeat the calculations for another estimated value until the difference between it and the calculated one can be neglected.  The results for the velocity decay can be fitted with the following equation: k2 r. U. (z,, + zY  (4.27)  68  where k2 is another decay constant. This formula will be used for calculating the velocity at the axis of the "steady-state part" of the transient jet.  There is another aspect of a gas flow expansion which must be addressed here. In the process of injection for a gas flowing through a converging nozzle, when the pressure ratio across the nozzle reaches its critical value (1.86 for natural gas), the Mach number at the nozzle is equal to one and the flow is choked. If we continue to increase the pressure ratio, the expansion of the gas continues outside the nozzle. The resulting jet is called underexpanded. The expansion of the gas outside the nozzle makes it supersonic and results in formation of expansion waves, which are reflected as compression waves from the flow boundary. The coalescence of these compression waves forms a barrel-shape shock, which surrounds the supersonic region and ends in the axial direction as a normal shock (Mach disk) and subsequent reflected shocks (see Fig. 4.3). This process is repeated a number of times if the underexpansion is large.  FLOW BOUNDARY  EXPANSION WAVES M>1  MACH DISK M= 1  M»1  M<1 REFLECTED SHOCK  BARREL SHOCK Figure 4.3 Underexpanded jet.  69 If an appropriate scale factor is employed to describe the effective size of the jet source, the behavior of an underexpanded jet is similar to that of a classical free jet. The so-called pseudo-radius rp, can be used to account for the expansion of the gas outside the nozzle, which results in a jet behaving as if it was produced by a nozzle of a larger diameter than the actual one. Birch et al. (1983) derived the following formula: r  = ro 111c 3C d  Pa  (4.28)  where k3 is a constant. Eq. (4.28) was derived assuming sonic velocity after the Mach disk. An alternative derivation of a similar equation without this assumption can be found in Appendix F. These equations suggest that if the jet penetration is divided by the pseudoradius, the curves representing the jet penetration rates for different pressure ratios should collapse. This happens to be the case, as shown in Figure 4.4 where data of Fig. 3.8 is presented with the penetration divided by square root of the pressure ratio. 50 40 30 PR=1.5  20  40 PR=/0 PR=3.0 PR=5.0 PR=8.0  14.-;  (1.) 10 a. 0  0  1  2^3^4^5 Time after BOJ, ms  6  7  Figure 4.4 DDC gas injector. Normalized jet penetration for different pressure ratios.  8  70 The equivalent radius req combines both the effective radius (Eq. 4.26) and the pseudoradius (Eq. 4.28): 1/2^)1/2  Pr fog^EL o  P.^P.  Ik3C d (-11 3). P.  (4.29)  This equivalent radius is used instead the actual radius of the nozzle to account for differences in densities of the injected and ambient fluid and for the expansion of the jet fluid outside the nozzle. It should be used instead of the effective radius in Eqs. (4.25) and (4.27) whenever underexpansion of the jet occurs.  4.3 STEADY-STATE CONICAL SHEET JET In this section we will consider a jet formed by the poppet injectors developed at the Department of Mechanical Engineering of the UBC. They create a conical sheet jet of which a schematic 2-D section is shown in Fig. 4.5.  Figure 4.5 Conical sheet jet. There is no experimental data on velocity and concentration profiles for a conical sheet jet available. However, for small angles of the jet axis they may to be assumed to be Gaussian, i.e. as in the case of an axisymmetrical jet. Ouellette and Hill (1992), using the approach and assumptions presented in the previous section for describing the  71 axisymmetrical jet, give derivation of similar equations for the case of the compressible conical sheet jet. The resulting relations are: Um k4  (4.30)  U.^(z. + z) xm  X°  k5  (4.31)  (Z o + Z)  l eg = k6C,11-P-f-)i— P° ' - Pa Pa ) ^  (4.32)  where 1 is the lift, 1 64 is the equivalent lift, lt s is the seat radius, k 4 , k5 and k6 are constants.  4.4 TRANSIENT CIRCULAR JET Having completed the description of the steady state jet, which is employed in the model of the transient jet, we now can derive some useful equations for the latter. Figure 4.6 shows the assumed structure of the starting circular jet.  Ut  Zc STEADY STATE REGION  Figure 4.6 Characteristic structure of a circular transient jet.  TRANSIENT VORTEX REGION  -  72 The jet consists of a spherical vortex flow interacting with a steady-state jet. The vortex of radius Rv moves away from the nozzle at a bulk velocity that decays with the distance z from the nozzle. The size of the vortex continually grows due to the entrainment of mass from the steady-state jet which pushes it from behind. This growth adds additional velocity gradient along the diameter of the sphere, such that the velocity of its center U, moves faster than the trailing edge velocity (which is assumed to be equal to the velocity U v of the plane i where the steady-state jet interacts with the sphere) but not as fast as the tip velocity U r The radius re in the plane i is the radius where velocity of the steady-state jet is equal to that of the sphere at its outer radius. The jet behind the vortex is considered to be in a steady state, which is confirmed by the work of Kuo and Bracco (1982).  There are four unknown quantities in the transient portion of the model: the location, size, mass, and velocity of the spherical vortex. Determination of these unknowns is achieved by solving the time-dependent governing equations at the plane i. Velocity of the vortex is defined as follows: U=  dz dt  (4.33)  Because the plane i is almost tangent to the rear of the sphere, we can write the following equations: z t = z v + 2R v ,^ dR dR U, = Uv+^and U t = U + 2 " . dt^dt v  (4.34) (4.35)  The rate of change of mass m„, of the vortex is equal to the fraction of flow in the central portion of the steady-state jet that moves faster than the vortex, such that dm v - 2ir j p(U - U v )rdr, dt o  (4.36)  73 where p is the density in the steady-state jet. The later is related to the mass concentration X in the steady-state part as follows (see Eq. 4.18):  P  P.  (4.37)  -  -P-t - +1  x( Pf  The mass concentration or the mass fraction of the vortex x v can be defined as Xv  ^Inf,^ mfv may m y  (4.38)  where mf, is the mass of the injected fluid in the vortex and m 11 is the mass of the air in the vortex. We assume that the mixture of the injected fluid and the air in the vortex is uniform. The density of the vortex p v is defined as follows:  (4.39)  xv( CA - 1) +1 Pf  The change in the injected fluid mass content inside the vortex can be written as dmf" - 27r7 a p f (U - Ujrdr,,^ (4.40) dt^o  where a is the volume concentration of the injected fluid in the steady-state part of the jet at the plane i. Substituting the volume concentration by the mass concentration x (Eq. 4.23), Eq. (4.40) can be written as follows:  dmfv^  dt^  xu (  °X pa -1 +1 Pr  ^rdr.  (4.41)  74 Finally, the change of momentum M y of the vortex van be expressed as follows: dM v 27r7 p(U - UJUrdr - FsF - FD , dt 0  (4.42)  where FsF is the change of momentum due to acceleration of the surrounding fluid, F D is the drag force. The change of momentum due to acceleration of the surrounding fluid is equal to the change of momentum of the virtual mass of the surrounding fluid. The virtual mass is the product of a fraction (one-half for a sphere) of the displaced volume and the density of the surrounding fluid (Milne-Thomson (1968)). Thus, F  1 d(U„V„) ^pa 2^dt  (4.43)  The drag force is 1 Tp2,/lax D2 FD =^ CD — Al2^"  ,  (4.44)  where CD is the drag coefficient, which can be approximated by the drag coefficient of a sphere in a turbulent flow.  The system of Eqs. (4.33), (4.36), (4.40) and (4.42) can be solved for determining location, mass, injected fluid content, and momentum of the vortex as a function of time. The volume and the radius of the vortex can be derived from its mass and density, and the velocity from its momentum and mass. The initial conditions are: 3 3 at t 0 z, = z., m, = p,, — ar ,^1:11„ M v = m,U..^(4.45) 4 Ps  75  4.5 TRANSIENT CONICAL SHEET JET Ouellette and Hill (1992) suggested using the same approach which was used for modeling transient axisymmetrical jet to model the transient conical jet. For this case the vortex structure has a toroidal shape (see Figure 4.7).  1111  PLane i  El_  jig  Figure 4.7 Characteristic structure of a transient conical sheet jet.  Using assumptions identical to those in the pervious section, they expressed the change in location, mass, injected fluid content, and momentum of the vortex structure of the transient conical sheet jet similar to those for the axisymmetrical jet: velocity of the vortex U=  U"  dz ", dt  (4.46)  the rate of change of mass of the vortex (0 is the angle between the jet axis and a horizontal plane)  dm v^(U U„) - 270^p(U^cos(13)dr^cos(fl)p. U v )z„^= 47rz, dt^  o X pa  —  Pf  -  +1  (4.47)  76 the change in the injected fluid mass content inside the vortex  din fv = 4717  X(U  ^dr, cos(v)P. dt^10 (P. _1)+1 X pf v  (4.48)  the change in momentum of the vortex  dM V etnz v cos(P)P. dt  (1..J - UJU dr  _ FsF FD'  (4.49)  ° XVI"^+ 1 Pr  the change of momentum due to acceleration of the surrounding fluid d(U Vv ) Fs,- p, ^d; ,  (4.50)  FD = CD 2P,U vir(Z, + R v ) COS (3)R v  (4.51)  V,, = 27r2 (z v + R v )cos(13)11!.  (4.52)  the drag force  volume of the vortex  The initial conditions are: 1 at t = 0 z v = z 0 , U v = U., V,, = 27r 2 iz v + -m)cos(13)1 2„ 2 my^mfy =^MV = M V U V ,  (4.53)  where 1p, is the lift adjusted to account for underexpansion if applicable: = 1k6 C d 114-:).^  (4.54)  77  4.6 SAMPLE CALCULATIONS In this section results of sample calculations obtained with the use of the mathematical model of the two-phase transient jet are discussed. A listing of the computer program (written in FORTRAN) used for calculation of the round jet penetration rate is given in Appendix F.  One of the major unknown parameters used in the program, is the nozzle discharge coefficient Cd . The model, as it is shown at Fig. 4.8, is very sensitive to the choice of this coefficient. Unfortunately, the exact magnitude of the coefficient was not determined. In all subsequent calculations its value was taken to be equal to 05. 90  Cd0.8  80  Cd 0 .6  70  Cd0.5  60 50 40 gt 30 20 10 0  0  1  2^3^4^5 Time, ms  6  7  8  Figure 4.8 Dependence of the round jet penetration on the nozzle discharge coefficient. (Pch=3550 kPa, PR= 1.5.) The calculated jet penetration rate was also found to be sensitive to the choice of the sphere drag coefficient (see Figure 4.9), which is used in calculation of the loss of  9  78 momentum due to interaction of the vortex with the surrounding fluid. In all subsequent calculations its value was taken to be equal to 0.5. 70 DC-1).5 DC).75 DC=1.0  60 50  e 40 4.)  30 20 10 0  Figure  0  1  2^3^4 Time, ms  5  6  7  8  7  8  4.9 Dependence of the round jet penetration on the sphere drag coefficient (DC). (Pch=3550 kPa, PR=1.5.)  70 60 50  e 40 t 30 20 10 0  0  1  2^3^4 Time, ms  5  6  Figure 4.10 Dependence of the round jet penetration on the turbulent Reynolds  number (Ret). (Pch=3550 kPa, PR=1.5.)  79 The sensitivity of the model to the turbulent Reynolds number is shown in Figure 4.10. In subsequent calculations it was taken to be equal to 45 to match Warren empirical constant (see Witze(1980)) used in calculations of the center-line velocity of the steady-state jet.  Calculated propagation of the jet done with the use of the model showed that the jet penetration does not depend on the ambient pressure if the upstream to ambient pressure ratio does not change.  The most interesting result obtained from sample calculations of the jet penetration for different conditions was practically invariance of the jet penetration with the kind of gas being injected and the liquid-to-gas mass ratio (for the case of a two-phase injection). Calculated penetration rates of the carbon dioxide jet (R=188.9), air jet (R-286.9), methane jet (R=518.3), and hydrogen jet (R=4124) differed from one another by less than 0.5 percent. The same result was obtained for two-phase jets with the liquid-to-gas mass ratio being changed from 0.0 to 0.5. Experimental results given in Chapter 3 do not entirely support this predicted behavior of the jet, as the jet penetration rate was found to be slightly dependent on the kind of gas being injected and on the liquid-to-gas mass ratio for a well-atomized jet. This phenomenon can be explained by the fact that a jet of a more dense fluid, though having lower exit velocity at the nozzle, propagates being not so much affected by the surrounding fluid as a jet of a less dense fluid. Also, lower or higher velocity at the exit of the same nozzle means smaller or larger volumetric flow rate for different fluids or mass flow rate for the same fluid. Thus, in a case of a more dense flow less fluid is injected by volume than in a case of a less dense flow.  80  4.7 COMPARISONS OF CALCULATIONS WITH MEASUREMENTS 4.7.1 ROUND JET  Calculations of the round methane jet penetrations for different pressure ratios showed their similarity to experimental measurements. The results are presented in Figure 4.11. Figure 4.12 shows the same data plotted as a function of the square root of time. (Unless otherwise stated the chamber pressure for the calculations mentioned in the following figures was 3550 kPa.)  70  PR=8 PR=5 PR=3 PR=2  60 50 0G <1.) a.  PR=1.5  IWO  40 30 20 10 0  ^^ 5 0^1^2^3^4 6 Time, ms Figure 4.11 Calculated penetration of the round jet of methane for different pressure ratios.  The data shows increase in the jet penetration rate with increase of the pressure ratio in the manner similar to that observed experimentally (see Section 3.1.2). The calculated  7  81 penetration of the jet is proportional to the square root of time during the whole period of injection.  70 ^ PR=8 PR=5  =3 PR=2^PR=1.5  60 50 e 40 0  30 a.  20  Om,  10 0 0  ^  ^ ^ ^ 2 2.5 3 Square root of time  0.5^1^1.5  Figure 4.12 Calculated penetration of the round jet of methane for different pressure ratios.  Figures 4.13-4.17 show comparison between experimentally observed and calculated penetration rates of the round methane jet for different pressure ratios. On each of these graphs the time indicated is that from the virtual beginning of the jet (BOJN) (see Section 3.2.3). The injection was continuous. The difference in time between the first appearance of the jet (BOJ) and BOJN for the shown cases is given in Table 3.1.  82  70 60 E 50 E e 40 0 t i 30 c  cu a_  20 10 0  -1  ^ ^^ ^ ^ ^ 1 2^3^4^5 0 6 7 8 Time after BOJN, ms  Figure 4.13 Round methane jet. Comparison between experimentally observed and calculated penetrations. PR= 15  80 70 E  60  E 50 e 0 t 2" 40 Iri g 30  ta_  20  10  0  -1  ^  1^2^3 Time after BOJN, ms  ^  4^5  Figure 4.14 Round methane jet. Comparison between experimentally observed and calculated penetratios. PR=2.0  83  60 50 40 t 30 17) et 20 10 0  -1  0^1 Time after BOJN, ms  3  2  Figure 4.15 Round methane jet. Comparison between experimentally observed and calculated penetratios. PR=3.0  60 50 E 40 Calculated and exp. data fit  %1 30 -.  20 10 0  0 o O 0 -0.5  0  0.5^1^1.5 Time after BOJN, ms  2  Figure 4.16 Round methane jet. Comparison between experimentally observed and calculated penetrations. PR=5.0  2.5  84  60 50 E 40 0  :f5- 30 Calculated and exp. data fit  a.". 20 10 0  -0.5  ^ ^ ^^ 0 1 0.5 1.5 Time after BOJN, ins  Figure 4.17 Round methane jet. Comparison between experimentally observed and calculated penetrations. PR=8.0  4.7.2 CONICAL SHEET JET Calculated rates of penetration of the two-phase 20 ° conical sheet jet for different pressure ratios showed very little variation (less than 0.5 percent) when diesel-to-gas mass ratio was changed from 0.0 to 0.5. Also, for the same pressure ratios and the same diesel-gas mass ratios the calculated jet penetration rate was exactly the same for different pressures in the chamber, which should be expected since the two-phase jet is treated as a gas jet of equivalent density in the model. The calculated jet penetration rate for different pressure ratios is represented in Figure 4.18. Comparison between observed and predicted conical sheet jet penetration rate for different pressure ratios is given in Figures 4.19 - 4.21. The experimental data presented is for a continuous jet. The time indicated is that from the  85 virtual beginning of the jet (BOJN). The difference in time between the first appearance of the jet emerging from the nozzle (BOJ) and BOJN for different cases is given in Table 3.1. 120 ^  PR=8.0 PR=5.0  100  PR=3.0  80  PR=2.0 PR=1.5  0  01 .4:  60  a. 40 20 0 0  1  ^  2^3^4 Time, ms  5  ^ ^ 6 7  Figure 4.18 Poppet injector calculated jet penetration.  70 60 E 50 E  4)d, '40 30 20 10 0  -1  0  1  2^3^4 Time after BOJN, ms  5  6  Figure 4.19 Conical sheet jet. Comparison between experimentally observed and calculated penetrations. PR=1.5.  7  86  80 70 60 50 o *4:1 40 i 6 30 a. 20  10 0  -1  ^ ^^ ^ 0 1 2^3 4^5^6 Time after BOJN, ms  Figure 4.20 Conical sheet jet. Comparison between experimentally observed and calculated penetrations. PR=2.0.  80 70 60 E E 50 g 4= 1:3 40 .01-  g 0.. 41)  30 20  10 0  -1  ^ ^^ ^ ^ ^ 1 0 2^3 4 5 6 Time after BOJN, ms  Figure 4.21 Conical sheet jet. Comparison between experimentally observed and calculated penetrations. PR=3.0.  87 The calculated jet penetration rate for the poppet injector is significantly higher than the observed one. The difference is much larger than for the case of the round jet. That means that, in addition to the initial development of the jet, the model is not accurate enough in describing the transient conical two-phase sheet jet from the given injector. The main reason for this is that the propagation of the jet is very different from that described by the model. As was observed in experiments, the jet right after the beginning of injection clings to the top wall and propagates practically as a wall jet.  88  5 CONCLUSIONS AND RECOMMENDATIONS As the result of present experimental and analytical investigation of development of transient jets created in the process of injection of fuel by three types of diesel engine injectors in a pressurized chamber, the following can be concluded:  1.  The penetration rate of the transient gas and gas-diesel jets depends strongly on pressure ratio but does not depend significantly on the pressure in the chamber as long as the injection pressure ratio is constant. For gas injection the penetration at a given time is proportional to the square root of the pressure ratio. In all cases the stagnation temperature of the injected fluid was close to 290 K.  2.  Penetration of the gas, diesel, and gas-diesel transient jets is proportional to the square root of time from the virtual beginning of the jet. Owing to the valve opening transient the virtual beginning of the jet is 0.2-0.8 ms after first appearance of the injected fluid. This delay depends on the type of injector, fluid density, and somewhat on pressure ratio and chamber pressure.  3.  Penetration rate of the transient gas jet depends slightly on the molecular weight of gas being injected. For two-phase injection with liquid-gas mass ratios in the range 0.0-0.6 the penetration rate was shown to be almost independent of the liquid-gas mass ratio.  4.  Once the injection of fresh gas ends, the penetration rate of the head of the jet appears to be immediately reduced.  5.^For a two-phase injection with liquid-gas mass ratio higher than 0.6, atomization of the liquid phase is not sufficient to prevent propagation of a part of it in the  89 form of quite large droplets. For such cases the mixture cannot be treated as gas. With lower liquid-gas ratios comparison of schlieren with laser sheet pictures show that the two phases propagate together. 6.  The "head vortex model" of the transient jet proved to be helpful in analysis of influence of different factors on the jet propagation. The application of the model to the conical sheet jet should be modified because it does not correctly describe propagation of the jet (in the experiments the jet adhered to the top wall, whereas the model does not account for the wall presence) and the calculated jet penetration rate is significantly greater than the observed one.  7.  The model of the transient jet was modified to be applicable to two-phase jets when the gas-liquid mixture in a jet can be treated as a gas (with adequate droplet atomization). Predicted penetration rate for two-phase jets was shown to be independent of the diesel-gas mass ratio.  For a future work in the area of the present project the following can be recommended:  1.^It is necessary to thoroughly investigate initial development of the transient jet and determine exactly the process of flow initiation. Two aspects should be considered: time of the valve opening, and delay in establishing the steady flow rate due to internal friction. The latter can be estimated, for example, by determining the mass of a gas entered into a sufficiently long pipe (of a diameter close to the diameter of the gas passage in the injector) in specified intervals of time at conditions (pressures) close to those in the injector. Knowing that, it will be possible to make necessary changes in the model of the jet to improve its accuracy in predicting the initial propagation of the jet.  90 2.  In experiments with two-phase transient jets it is recommended to introduce a device allowing direct measurements of liquid-gas mass ratios of mixture forming the jet and homogeneity of the mixture.  3.  Two-phase transient jets should be investigated in conditions where it is possible to vary just one important parameter at a time, thus having an opportunity to accurately determine the influence of each factor on the jet propagation. In the present experiment, a change in the number of turns of the diesel fuel metering valve, for example, affects not only the diesel-gas mass ratio but also the injection delay. The position of the metering valve determines the amount of liquid fuel removed from the pressurized chamber under the injector plunger, thus affecting the chamber pressure increase rate and the poppet opening time. For example, the injection delay for the pressure ratio of 3.0, the chamber pressure of 3550 kPa, and the beginning of injection (B01) at 170 ° was 0.44 ms for the position of the metering valve at 1 turn open and 0.62 ms for the position of the metering valve at 6 turns open.  4.  It is desirable to have a system which would allow one to have several pictures of the same jet taken at different time intervals from the beginning of the jet (in the present experiment only one picture per injection can be taken). That would give an opportunity to see continuous development of the jet.  5.  It is desirable to increase dimensions of the chamber to investigate propagation of the jet at larger distances from the nozzle to increase the range of applicability of the results.  6.^Model of the conical sheet jet should be modified to improve its accuracy (for example, the jet adherence to the top wall should be taken into account).  91  6 REFERENCES Abramovich, G.N., 1963. The Theory of Turbulent Jets. M.I.T. Press, Massachusetts. Abramovich, S. and Solan, A., 1973. "The Initial Development of a Submerged Laminar Jet." Journal of Fluid Mechanics, Vol. 59, pp. 791-801. Abramovich, S. and Solan, A., 1973. "Turn-on and Turn-off Times for a Laminar Jet? Transactions of the ASME, Journal of Dynamic Systems, Measurement, and Control,  June, pp.155-160. Batchelor, G.K., 1967. An Introduction to Fluid Dynamics. Cambridge Press, Cambridge. Beck, NJ., Johnson, W.P., George, A.F., Petersen, P.W., Van Der Lee, B., Klopp, G., 1989. "Electronic Fuel Injection for Duel Fuel Diesel Methane.", SAE Technical Paper 891652. Bradshaw, P., 1964. Experimental Fluid Mechanics. Pergamon Press, New York. Birch, A.D., Brown, D.R., Dodson, M.G., and Thomas, J.R., 1978. "The Turbulent Concentration Field of a Methane Jet." Journal of Fluid Mechanics, Vol. 88, pp. 431-449. Birch, A.D., Brown, D.R., Dodson, M.G., and Swaffield, F., 1984. "The Structure and Concentration Decay of High Pressure Jets of Natural Gas." Combustion Science and Technology, Vol. 36, pp. 249-261. Danon, H., Wolfshtein, M., Hetsroni, G., 1977. "Numerical Calculations of Two-Phase Turbulent Round Jet". International Journal of Multiphase Flow, Vol. 3, pp. 223- 234. Dent, J.C., 1971. "Basis for the Comparison of Various Experimental Methods for Studying Spray Penetration." SAE Paper 710571, SAE Trans., Vol. 80. Einang, P.M., Koren, S., Kvamsdal, R., Hansen, T., Sarsten, A., 1983. "High-Pressure, 1983. Digitally Controlled Injection of Gaseous Fuel in a Diesel Engine, With Special Reference to Boil-Off from LNG Tankers? CIMAC Conference Proceedings. Paris, France. Ewan, B.C. and Moodie, K., 1986. "Structure and Velocity Measurements in Underexpanded Jets." Combustion Science and Technology, Vol. 45, pp. 275-288. Hames, RJ., Straub, R.D. and Amann, R.W., 1985. "DDEC - Detroit Diesel Electronic Control." SAE Paper 850542. Henqrussamee, D., 1975. "Mixing of Hot Starting-Jets with Cold Surroundings." Ph.D. Thesis, University of London.  92 Heywood, J.B., 1988. Internal Combustion Engine Fundamentals. McGraw Hill Book Company, New York. -  Hiroyasu, H., Kadota, T., Arai, M., 1980. "Supplementary Comments: Fuel Spray Characterization in Diesel Engines." Combustion Modeling in Reciprocating Engines. Edited by Mattavi, J.N. and Amann, C.A.. Plenum Press, New-York. Hiroyasu, H.,1985. "Diesel Engine Combustion and Its Modelling." Diagnostics and Modeling of Combustion in Reciprocating Engines, pp. 53 75, COMODIA 85, Proceedings of Symposium, Tokyo,Sept. 4-6, 1985. -  Khalil, E.E., Spalding, D.B., Whitelaw, J.H., 1975. "The Calculation of Local Flow Properties in Two-Dimensional Furnace." Journal of Heat and Mass Transfer, Vol. 18, p. 775. Kuo, T.-W. and Bracco, F.V., 1982. "On the Scaling of Transient Laminar, Turbulent, and Spray Jets." SAE Paper 820038. Loitsyanskii, L.G., 1966. Mechanics of Liquids and Gases. Pergamon Press, New York. Melville, W.K. and Bray, K.N.C., 1979. "A Model of the Two-Phase Turbulent Jet."  International Journal of Heat and Mass Transfer, Vol. 22, pp. 647 656. -  Minami, T., Yamaguchi, I., Shintani, K., Tsujimura, K., and Suzuki, T., 1990. "Analysis of Fuel Spray Characteristics and Combustion Phenomena under High Pressure Fuel Injection." SAE Transactions. Vol. 99, pp. 948-959. Miyake, M., Biwa, T., Endoh, Y., Shimotsu, M., Murakami, S., and Komoda, T., 1983. "The Development of High Output, Highly Efficient Gas Burning Diesel Engines." Proceedings of CIMAC Conference, Paris, France. Ouellette, P. and Hill, P., 1992. "Visualisation of Natural Gas Injection for a Compression Ignition Engine." SAE Paper 921555. Patankar, S.V., "Numerical Prediction of Three-Dimensional Flows." Studies in Convection Theory, Measurement and Application. Edited by Launder, B.E.. Academic Press, 1975. -  Reitz, R.D. and Bracco, F.V., 1979. "On the Dependence of Spray Angle and Other Spray Parameters on Nozzle Design and Operating Conditions." SAE Paper 790494. Schlichting, H., 1968. Boundary Layer Theory. McGraw-Hill, New-York, 6th edition. Shraiber, A.A., Yatsenko, V.P., Gavin, L.B., Naumov, V.A.;edited by Dolinsky, A.A., 1990. Turbulent Flows in Gas Suspensions. Hemisphere Publishing Corporation, NewYork. Turner, J.S., 1962. "The 'Starting Plume' in Neutral Surroundings." Journal of Fluid Mechanics, Vol. 13, pp. 356-368.  93 Wakenell, J., O'Neal, G., Baker, Q.A., 1987. "High-Pressure Late Cycle Direct Injection of Natural Gas in a Rail Medium Speed Diesel Engine." SAE Technical Paper 872041. Winnikow, S. and Chao, B.T., 1966. "Droplet motion in purified systems." Phys. Fluids, Vol. 9, p. 50. Witze, P.O., 1980. "The Impulsively Started Incompressible Turbulent Jet." SAND80 8617, pp. 3-15. Wygnanski, I. and Fiedler, H., 1969. Some Measurements in the Self-Preserving Jet. Journal of Fluid Mechanics, Vol. 41, pp. 577 612. -  -  94  Appendix A. APPARATUS DRAWINGS This appendix contains major design drawings of the experimental apparatus. It does not include drawings of the standard diesel engine parts incorporated in the rig.  List of the drawings: Page Figure A.1^Apparatus upper part assembly drawing. Figure 1 of 2. ^95 Figure A.2^Apparatus upper part assembly drawing. Figure 2 of 2. ^96 Figure A.3^Apparatus mounting plate.^  97  Figure A.4^Bearing support 1.^  98  Figure A.5^Bearing supports 2 and 3.^  99  Figure A.6^Bearing support 4.^  100  Figure A.7^Cam follower plate.^  101  Figure A.8^Cam follower guide.^  102  Figure A.9^Rocker arm assembly.^  103  Figure A.10 Chamber assembly drawing.^  104  Figure A.11 Chamber side 1. ^  105  Figure A.12 Chamber sides 2 and 4.^  106  Figure A.13 Chamber side 3.^  107  Figure A.14 Chamber cover plate.^  108  Figure A.15 Chamber lid.^  109  BEARING SUPPORT 4  BEARING SUPPORT 3 BEARING SUPPORT 2 BEARING SUPPORT 1  MOUNTING PLATE FOLLOWER PLATE FOLLOWER GUIDE  UBC  MECHANICAL ENGINEERING DE  ASSEMBLY DRAWING Drown by A. CHEPAKOVICII Approvwd  BEARING SUPPORT 4  BEARING^ BEARING^ BEARING S UPPORT 3^SUPPORT 2^[ SUPPORT 1  FOLLOWER GUIDE  FOLLOWER PLATE  MOUNTING PLATE  UBC  MECHANICAL ENGINEERING DEPARTMENT  ASSEMBLY DRAWING Drown by A. CHEPAKOVICH Approved  13.091 12 HOLES SNUG(ti FIT 5/8' BOLTS  O O 0  7.309 12.40  00.375 `•C ,41141:1LES --  0 0  tri  8.00 ^ 4.117 ----N.. F79_40  O  1.500  0 0 O  In  0.50  17)  NO  co  0  h.^1.100  ei  —•  0 (U  C.)  (U  1.100  13.195 ^ 15.633 ^ 17.312 ^ 21.800 ^  NOTE: 1. DIMENSIONS ANO TOLERANCES ARE IN INCHES. 2. UNLESS OTHERWISE SPECIFIED. TOLERANCES ARE: DIMENSION^TOLERANCE X.XX^0.01 X.XXX^0.001 3. MATERIAL OF THE PLATE IS CARBON STEEL 4. THE THICKNESS OF THE PLATE IS 0.5 INCHES.  UBC  MECHANICAL ENGINEERING DEPARTMENT  MOUNTING PLATE Preen by A. 04EPAKOVIOI Approved  ^  —no  0  0.938^0.938  r  3.200^4.750 --4-1  r.^0.250  1.13  0.88  0.925  3 SOCKETS FOR 3/8" SCREWS 6.363  1.50 0.750  2 HOLES SNUG—FIT 5/8" BOLTS  10.000 ^ 1 11.50  NOTE:^ 1. DIMENSIONS AND TOLERANCES ARE IN INCHES. 2. UNLESS OTHERWISE SPECIFIED, TOLERANCES ARE: DIMENSION^TOLERANCE X.XX^0.01 X.XXX^0.001 3. THE MATERIAL OF THE PART IS ALUMINUM. 4. THE HOLES, DIMENSIONS OF WHICH ARE MARKED WITH •, SHOULD BE DRILLED WITH TOLERANCES TO FIT EXISTING PARTS.  UBC  MECHANICAL ENGINEERING DEPARTMENT  BEARING SUPPORT 1 Drown by A. CHEPAKOVICH Approved  SOCKET FOR 5/16" BOLT  2 HOLES SNUG— FIT 3/8" BOLTS  VI MI  ai  2 HOLES SNUG— FIT 5/8" BOLTS  _H+0.750  0.750  ^1.50  6.50  NOTE: 1. DIMENSIONS AND TOLERANCES ARE IN INCHES. 2. UNLESS OTHERWISE SPECIFIED, TOLERANCES ARE: DIMENSION^TOLERANCE X.XX^0.01 X.XXX^0.001 3. THE MATERIAL OF THE PART IS ALUMINUM. 4. THE HOLES, DIMENSIONS OF WHICH ARE MARKED WITH •, SHOULD BE DRILLED WITH TOLERANCES TO FIT EXISTING PARTS.  UBC  MECHANICAL ENGINEERING DEPARTMENT  BEARING SUPPORTS 2&3 Drawn by A. CHEPAX0Y101 Atgwomt  WE^  OM OS.^  we.  0.250 ^ 0.925 I  0.88^1.13  3 SOCKETS FOR 3/8" SCREWS 6.363  1.50 0.750  2 HOLES SNUG—FIT 5/8" BOLTS  10.000 11.50 NOTE: 1. DIMENSIONS AND TOLERANCES ARE IN INCHES. 2. UNLESS OTHERWISE SPECIFIED, TOLERANCES ARE: DIMENSION^TOLERANCE X.XX^0.01 X.XXX^0.001 3. THE MATERIAL OF THE PART IS ALUMINUM. 4. THE HOLES, DIMENSIONS OF WHICH ARE MARKED WITH s, SHOULD BE DRILLED WITH TOLERANCES TO FIT EXISTING PARTS.  ENGINEERING U BC^MECHANICAL DEPARTMENT  BEARING SUPPORT 4 Drown by A. 01EPAK0b101  Olt^  PO .b■  Approwd  §  4X .375-16UNC M  0.^. 0^0 z  Pr)^  cO  co _ . —^  D cNi^ —^to  N  N T  CO  d . rn  1.750—  0.38 A 0.600  2.300 3.50 NOTE: 1. DIMENSIONS AND TOLERANCES ARE IN INCHES. 2. UNLESS OTHERWISE SPECIFIED, TOLERANCES ARE: DIMENSION^TOLERANCE X.XX^0.01 X.XXX^0.001 3. THE MATERIAL OF THE PART IS CARBON STEEL.  ENGINEERING UBC^MECHANICAL EPARTMENT D  FOLLOWER PLATE  Drawn by A. CHEPAKOVICH Approved  Al^ —  Iowa Mo.  1 :I^"T`  4 HOLES SNUGFIT 3/8' BOLTS  2.300  0.600  in  1.750 3.50 NOTE1 I. DIMENSIONS AND TOLERANCES ARE IN INCHES. 2. UNLESS OTHERWISE SPECIFIED, TOLERANCES ARES DIMENSION^TOLERANCE X.XX^0.01 X.XXX^0.001 3. THE MATERIAL OF THE PART IS CARBON STEEL. 4. w - TO BE DRILLED WITH TOLERANCES TO FIT EXISTING PART.  ENGINEERING U BC^MECHANICAL RTMENT DEPA  FOLLOWER GUIDE Drawn by A. CHEPAKOVICH Approved  I  IMAIC  I  DWO NO.  OAT  4.80 4.000 ^  L  NOTE: 1. DIMENSIONS AND TOLERANCES ARE IN INCHES. 2. UNLESS OTHERWISE SPECIFIED, TOLERANCES ARE: DIMENSION TOLERANCE X.XX^0.01 X.XXX^0.001 3. MATERIAL OF THE PARTS, EXCEPT THE AXLE, IS CARBON STEEL. MATERIAL OF THE AXLE IS STAINLESS STEEL. 4. THE ROCKER ARM ASSEMBLY IS TO BE MOUNTED ON THE MOUNTING PLATE. 5. PARTS, DIMENSIONS OF WHICH ARE MARKED WITH^, SHOULD FIT BEARINGS NO. 202.  0.180  —  R0.195 o co  cv  ti  3.25  in  4 HOLES SNUG—FIT 1 / BOLTS  cp Cl  o  ^  U BC 10.590*  MECHANICAL ENGINEERING EPARTMENT D  ROCKER ARM ASSEMBLY  1.380m 8.1 Approved  j  unta' ea*^Irmo  CHAMBER LID COVER PLATE  CHAMBER SIDE 4  CHAMBER SIDE 1 CHAMBER SIDE 2  NOTE: 1. BEFORE WORKING ON THE PARTS PLEASE CALL ALEXANDER AT 822-5968. 2. THREE QUARZTZ WINDOWS (NOT SHOWN) SHOULD FIT INTO THE CHAMBER SIDES.  UBC  MECHANICAL ENGINEERING DEPARTMENT  ASSEMBLY DRAWING Onvon by A. 04EPAKOVICH Approved  Mt^  WM IR^  NM  ^  7.000 ^  ^ 4X .125 —40UNC  1  1^o  0 0 r4^sc,s1  = =-._ -  ==  1^I^2 1  I  2  +  I itA 0°3  A. Au-  1^III i ii  I :i  II  II_ n 1•  n  "a _,  I I  g  •  Etii i il Iii t  il^I  L __=  ==  ill  3.300  2X .625-11UNC  0.180  0.88 0 Cs1  =—  X Cs' Z  NOTE: 1. DIMENSIONS AND TOLERANCES ARE IN INCHES. 2. UNLESS OTHERWISE SPECIFIED, TOLERANCES ARE: DIMENSION^TOLERANCE X.XX^0.01 X.XXX^0.001 3. MATERIAL OF THE PART IS CARBON STEEL. 4. DIMENSIONS MARKED WITH "a" SHOULD CORRESPOND TO DIMENSIONS OF EXISTING PARTS.  0.560  O  01  = O  co -4 so ci  O C.1 tO  (  ci 0  O O O  4-1.040 ^  crs  1.500  0  1.74  U, 0 0  UBC  ^ 2.50 ^ ^ 4.750* ^ 5.000  MECHANICAL ENGINEERING DEPARTMENT  CHAMBER SIDE 1 Orem by A. citrPAxovico  to  I  2 HOLES 5/8"  0  L  N N  O  N  N  0  In  0 N  O  O  L 1.340  -  4.440  -  ■ 1.340  10.000  1^r 0.780  0.780  0 O  1  1■••  I I  I I I I I  I I I I I 1^I  I  I  I  NOTE: 1. DIMENSIONS AND TOLERANCES ARE IN INCHES. 2. UNLESS OTHERWISE SPECIFIED, TOLERANCES ARE: DIMENSION^TOLERANCE^  UBC  X.XX^0.00^ X.XXX^0.000^  MECHANICAL ENGINEERING DEPARTMENT  CHAMBER SIDES 2 & 4  I^I  3. MATERIAL OF THE PART IS CARBON STEEL..... ... Dram  by A. OWPAKCA1101 °ft  Approved  w..  r 0 Nic`41 0  1  1  7.000 ^  1 1 =-_ =., —_-4 1:1 I I r^I A I III II 1 II Id  = '=—  +  I1 I  NOTE: 1. DIMENSIONS AND TOLERANCES ARE IN INCHES. 2. UNLESS OTHERWISE SPECIFIED, TOLERANCES ARE: DIMENSION^TOLERANCE X.XX^0.01 X.XXX^0.001 3. MATERIAL OF THE PART IS CARBON STEEL. 4. DIMENSIONS MARKED WITH " 41" SHOULD  1  _, :, --== L  4, I rq 111 '`-II^III 1 I it^1^III I  I  CORRESPOND TO DIMENSIONS OF EXISTING PARTS.  2X .625-11UNC  0.88  3.300 O 41 2  O O  O O O  O  VI I— VI  41 EZ 1— _1 -J  r (. co N z  2.7 5: ^  010 1  4.750•  fn  5.000  03  In  IO  0  UBC  MECHANICAL ENGINEERING DEPARTMENT  CHAMBER SIDE 3 Omen by A. CHEPAX0V1134 Approved  lc'  '  0.18  0.75  1.24 NOTE: 1. MATERIAL OF THE PART IS CARBON STEEL. 2. DIMENSIONS MARKED WITH "*" SHOULD CORRESPOND TO DIMENSIONS OF EXISTING PARTS.  ENGINEERING UBC^MECHANICAL DEPA RTMENT  Drawn by A. CHEPAKOVICH  sia A  Approved  SOLE  COVER PLATE  1  0WO NO.^  1 2 roux Dor :  r  En  I NEV.  NOTE: 1. MATERIAL OF THE PART IS CARBON STEEL. 2. DIMENSIONS MARKED WITH "*" SHOULD CORRESPOND TO DIMENSIONS OF EXISTING PARTS.^  E3  U BC MECHANICAL ENGINEERING Drawn by A. CHEPAKOVICH  SZE  A  Approved^SCAUL  I  r.  CHAMBER LID NO  , :2  ''  DATE  110  Appendix B. APPARATUS DETAILS The engine cylinder head is used as the base for mounting other parts of the apparatus. Located on the top of it are the mounting plate, cam shaft bearing supports, cam shaft, flywheel, sheaves for belt transmission, cam shaft and rocker arm assemblies. The chamber for flow visualization is mounted on the bottom of the cylinder head. The cylinder head, in turn, is mounted on an angle-iron frame. The electrical motor used for rotating the cam shaft and diesel fuel pump assembly are mounted on the same frame.  One of the main concerns in designing the "mechanical" - top part - of the apparatus was to make it reproduce, as closely as possible, the mechanical actuation of the diesel injector. Figure B.1 shows a graph representing the injector lift in the engine as a function of the crank angle, 180 ° being the top dead center.  12 10 8 6 4 2  0  100  ^  150  ^  ^ ^ 200 250 300 Crank angle, deg.  Figure B.1 DDC diesel injector lift as a function of the crank angle.  111 The major part of this problem was solved by using an original diesel engine cam shaft, thus making sure that the cam profile is exactly the same as in the engine. The linear motion of the cam shaft follower is transferred into linear motion of the injector plunger by a rocker arm assembly. The rocker arm provides a mechanical advantage which increases injector plunger displacement by a factor of 1.246 (as in the engine) over the cam lobe lift. The measured injector lift at a given crank angle in the experimental apparatus differed from that in the engine by a maximum of 0.05 mm.  Other main concerns were to make the apparatus withstand high dynamic loads and to maintain uniform rotational speed of the cam shaft during the actual process of injection, when the pressure of diesel fuel under the injector plunger can increases up to 200 MPa. These were done by using four sturdy bearing supports and a 23 kg flywheel 0.46 m in diameter. Testing of the apparatus at working conditions, during which the cam shaft speed was measured at each quarter of a degree, showed no variation in the rotational speed of the shaft.  The cam shaft bearings are lubricated by gravity oil flow from small oil caps mounted on top of each of the bearing supports which are refilled before each start of the apparatus. A very small amount of oil is also needed to be applied to the stem of the cam follower to ease its movement through the follower guide.  A three-phase two-horse-power 1725 rpm AC electrical motor with a two-groove "A" belt transmission drives the cam shaft. The speed of the cam shaft is 716 rpm, which roughly corresponds to the idle speed of the engine (600 rpm). Originally, the apparatus was built with the cam shaft speed at 1800 rpm but vibration was very high and the apparatus operation did not appear to be safe, so the speed was reduced.  112 The chamber for flow visualization is attached to the bottom part of the cylinder head. It has two 113 x 38 mm windows for which 122 x 56 x 25 mm fused quartz plates are used, and one 38 x 5 mm window for which a 38 x 14 x 13 mm fused quartz plate is used. The two big windows are positioned on the opposing sides of the chamber and allow the schlieren system to be used for flow visualization. The rectangular shape of the chamber is necessitated by the need to be able to use it for schlieren. Either of the big windows can also be used for taking pictures in the laser sheet visualization. The small window is positioned on the side of the chamber perpendicular to the viewing windows. It is solely used for admitting the laser sheet into the chamber. The side of the chamber opposing the small window is used for mounting a pressure gauge and for connection of the compressed air supply to the chamber.  The chamber was designed for the maximum internal pressure of 6.9 MPa. After its assembly it was tested by pressurizing to 5.5 MPa. Access to the inside of the chamber is possible after removal of its lid, which is secured by four bolts. This is the only element of the chamber designed for rapid installation and removal. The windows are sealed with paper gaskets and silicon sealant. The chamber lid is sealed with an 0-ring.  An integral part of the experimental apparatus is a diesel fuel system. It consists of a 20liter fuel tank, fuel pump with electrical motor, fuel lines, and restrictor (orifice) in the return line maintaining diesel fuel pressure before the injector at about 450 kPa. Due to corrosive nature of aged diesel fuel, a test fuel, which consists of three parts of kerosene and one part of turbine oil, was used as a substitute for diesel fuel. The test fuel density was 884 kg/m 3 .  As the sources of high pressure air and gas, bottles of compressed air and methane with their own pressure regulators were used.  113  Appendix C. SCHLIEREN SYSTEM Figure C.1 shows general arrangement of the schlieren system used for flow visualization in present work. It consists of a light source S (a 200 W mercury arc lamp), a pinhole PH, two spherical mirrors M1 and M2, two spherical lenses C and FL, two knife edges KE (only one is shown on the picture), and a camera CAM. The object under investigation is placed in test section TS.  TS M1 CAM  - IKE  M2  Figure C.1 General arrangement of the schlieren system. (Courtesy of P. Ouellette) The schlieren method of flow visualization is based on the phenomenon of deflection of a parallel beam of light passing through a region having a gradient of refractive index in the direction perpendicular to the direction of the beam. This gradient may be caused, as in the present experiment, by a non-homogeneous density field.  An angle 0 of deflection of each ray in the beam passing through a region with a gradient of refractive index in the direction perpendicular to that of the beam movement can be calculated using the following formula (see Bradshaw (1964)) if the direction of the beam propagation is denoted as x and direction perpendicular to it is denoted as y:  114  e.  ^dx,^ 1-1  (C.1)  where p is the refractive index: (p-1) is proportional to density for a given gas and equal to 0.00029 for air at standard density. If after that the beam falls on a screen, the illumination will be increased where the rays converge, that is where 00/ay or 02 p/dy 2 is negative, and decreased where  a6/ay or 0 2 p/Oy 2 is positive. If this beam of light is now  brought into focus, the linear deflection of a particular ray at the focus will be proportional to the density gradient. Inserting a knife edge at the focus in such a way as to cut off a fraction of the image of the light source, one can uniformly reduce by the same fraction the intensity of illumination of a screen placed beyond the focus, except for the regions illuminated by the deflected rays. These regions will be lighter if the ray is deflected away from the knife edge, and darker if it is deflected towards the knife edge. The resulting change of illumination will be therefore a function of the density gradient, and not of the rate of change of density gradient as in the case of absence of the knife edge (shadowgraph method).  It should be noted here that the schlieren method is only sensitive to density gradients in the direction perpendicular to the knife edge. The quality of obtained pictures and amount of information they carry with them depends to a very large extent on the correct positioning of the knife edge.  To create a parallel beam of light and later focus it at the camera, two spherical mirrors 305 mm in diameter and with the focal lengths 2440 mm were used. To make the beam of light reflect from a spherical mirror in only one direction (i.e. to have a parallel beam after the mirror) one should have a point light source positioned exactly at the mirror's focus. This was achieved by positioning a plate with a small hole in it in the focus of the lens and  115 by focusing the light from the real light source (a quartz lamp) with the aid of a spherical lens at this hole.  The light source, the mirrors, and the camera were assembled in the Z-configuration (the expanding and focusing mirrors were positioned at opposite sides and at the same angles to the parallel beam of light). This configuration allows one to eliminate the aberration caused by positioning mirrors at an angle to the light beam. This aberration termed "coma" occurs because the direction of the light reflected from the mirror depends on the position of the point of reflection on the mirror. Thus, a light ray falling on the center of the mirror will be deflected in a slightly different direction than that falling on the edge of the mirror. If one has two mirrors with the same focal lengths positioned at exactly the same angle to the axis of the beam of light but on opposite sides of it, the aberration caused by this effect can be totally eliminated due to the fact that coma caused by the second mirror will have the opposite direction than that caused by the first mirror.  In an off-axis mirror system the effects of another aberration, termed astigmatism, also need to be considered. If a point light source is used, astigmatism will result in the image of the source consisting not of a point, but of two lines at different positions from the focusing mirror, one in the plane of the axis of the beam and the light source (horizontal in our case), and the other perpendicular to that plane. In our system we used this effect for our advantage, inserting two knife edges, one horizontal and one vertical, at this points. This allowed us, by adjusting the knife edges, to get pictures showing the density gradient simultaneously in horizontal and vertical directions with a desired degree of intensity in each direction.  116 Because of the aberrations, particularly astigmatism and spherical aberration, in an off-axis system errors may arise in the representation of angles in the image of the flow. To eliminate these arrors scaling of the images was used (see Section 2.2).  A spherical lens was installed after the knife edges to focus the beam onto the camera. Its position , as far as the distance from the focusing mirror is concerned, did not have significant effect on the image, because the camera was positioned in such a way as to get a focused picture at any position of the lens.  117  Appendix D. LASER SHEET SYSTEM The laser sheet method of flow visualization was used to investigate the structure of a flow in two dimensions. The light constituting the laser sheet reflected normal to the sheet by particles in a flow field can be captured by a camera to create an image of the flow. If a fluid containing particles or droplets is injected into a non-reflective fluid (like air, for example), the difference in illumination of the laser sheet picture of such injection allows one to distinguish areas of different concentration of the injected fluid. Also, the magnitudes of streaks on a picture of given time exposure created by moving particles represent their velocities.  Unlike the schlieren method of flow visualization, where the resulting picture contains contours of the injection "cloud", the laser sheet method allows to make a "cut" through the "cloud", making visible only that portion of it which is in the plane of the laser sheet. The laser sheet method requires the presence of an illuminating agent since reflection of light, not density gradient is required. The advantage of this method is the ability to observe the flow in one plane.  Figure D.1 shows the general arrangement of the laser sheet system used for flow visualization in the present work. It consists of a laser (Spectra-Physics Model 165 Argon Ion Laser with Model 265 Power Supply), two plane mirrors M (for simplicity only one is shown on the picture) for directing the laser beam, a Melles Griot 01LCP002/116 pianocylindrical positive glass lens Ll with paraxial focal length of 12.7 mm for expanding the beam into a sector plane, a Melles Griot 01LPX307/066 plano-convex glass lens L2 with paraxial focal length of 300.0 mm and diameter of 66 0 mm for converting the sector plane into a stripe of light with parallel edges (both lenses have multilayer coatings intended to  118 prevent scattering of light which for lenses without coating constitutes about 16 percent), and a camera CAM. The gas flow to be illuminated is placed in test section TS.  CAM  Figure D.1 General arrangement of the laser sheet system.  As the thickness of the sheet of light does slightly change with the distance from the spherical lens (due to the finite thickness of the laser beam), the area of interest is positioned in such a way that its center is at the focal point of the lens where the sheet thickness is minimal.  The regulation of intensity of illumination is achieved by changing the power output of the laser (maximum up to 3 W). An increase in the power output increases the thickness of the laser beam and, consequently, the thickness of the "cutting" sheet of light (up to 4 mm in the area of interest), which, in turn, also contributed to increase of illumination of the resulting picture.  119 In the test rig the sheet of light passes into the chamber through a narrow quartz window on its side. It is positioned in such a way that the tip of the injector is illuminated. The camera is located in front of one of the two large quartz windows of the chamber. The second window is covered from inside the chamber to prevent reflection of light from it.  To minimize the effect of distortions caused by the use of a short-focus camera lens, the camera is positioned in such a way that the axis of its lens passes approximately through the middle of the area of interest. The camera is focused on the tip of the injector and the "cutting" sheet of light, making all objects in front and behind that plane barely distinguishable, which contributes to clearer pictures.  120  Appendix E. FLOW VISUALIZATION CONTROLLER A flow visualization controller is used in the present work to control timing of injection initiation (B01) and duration (PW), and picture acquisition. It uses 80C196KB microcontroller for precise timing that cannot be done by an ordinary personal computer (PC). It works in conjunction with FLOWVIS.EXE program executing on PC equipped with frame grabber card.  The front panel of the controller (see Figure E.1) has three multi-turn pots, a toggle switch, four LED displays, and a power supply switch. The pots allow one to set the crank angle of beginning of injection (B01), the duration of injection (or pulse width) in crank angle degrees (PW), and the crank angle at which a picture is taken (SNAP) with resolution of a quarter of a degree. BOI  ^  1170.01  PW  ^  110 .001  SNAP ANGLE/SPEED  1178.51  I 7161  POWER RUN ON  8 0  STANDBY OFF  Figure E.1 Front panel of the controller.  The toggle switch controls the injector driver output. In the up ("run") position the injector driver outputs are enable and the injector fires, in the down ("standby") position they are inhibited (the injector cannot be fired in that mode). The program 80C 196, which resides in the host PC detects the position of the toggle switch. When the program detects  121 a down-to-up mode switch transition, it initiates the injector firing and picture acquisition cycle staring at the next bottom dead center (BDC).  The front panel LED displays show BOI, PW, SNAP settings, and crank angle/speed. The crank angle/speed readout is set to show crank angle at shaft speeds less than 120 rpm, and to show shaft speed otherwise. Display of crank angle is needed during calibration. The 4-digit readouts utilize Motorola MC14499P BCD display/driver chip. Since the LED displays can only show 4 digits, crank angle degrees are truncated to the 4 most significant digits: Displayed value  Actual angle  Internal integer representation  000.0  0.00°  0 + offset  000.2  0.25°  1 + offset  000.5  0.50°  2 + offset  000.7  0.75°  3 + offset  001.0  1.00°  4 + offset  359.0  359.00°  1436 + offset  359.2  359.25°  1437 + offset  359.5  359.50°  1438 + offset  359.7  359.75°  1439 + offset  A firing sequence is initiated by flipping the front panel toggle switch from down to up. Once this transition has been detected, the controller enables injection and video event generation (if the switch is flipped down before a firing sequence is completed, it will  122 abort the current sequence and return to the standby state). When the next BDC is reached the calculations begin for injection and image acquisition to occur somewhere in the range of 0°- 45 ° . The calculations differ depending on whether high or low speed of the shaft is detected. In the normal, high-speed case, it is assumed that the motor is turning the shaft at a constant speed and the calculations are based on the predicted time when a specified angle will be reached. Otherwise, it is assumed that the shaft is being turned by hand at a low speed and calculations are based on actual angles.  The flow visualization controller can use either an Intel 80C196KB Evaluation Board (EvalBoard), or the CPU-196 board designed for general 80C196-based embedded control applications. The current version of the controller uses the program FVC196e running on an EvalBoard. The program must be downloaded from a PC using ECM96 each time the controller is powered up.  123  Appendix F. PSEUDO-RADIUS FOR UNDEREXPANSION Lees consider a supercritical release of gas from an infinite reservoir through an orifice of radius rc, (see Figure F.1).  P.  To  EXPANSION REGION I  Po  Un I  INFINITE RESERVOIR Pir Tn ,ft2ro  Pa, Pa rp s  Figure F.1 Diagram of a supercritical gas release.  The parameters of the gas in the reservoir are: pressure P 0 , temperature T 0 , and density p.. In the nozzle the gas parameters are: Pa, Ta, pa. At the end of the expansion region they are: Pa , pa. The velocity of the gas in the nozzle is Un , and at the end of the expansion region Uo. Radius of the of the end of the expansion region is denoted as r te .  Assuming uniform pressure outside the reservoir (P a ), no ambient fluid entrainment, adiabatic and one-dimensional flow between the nozzle and the end of the expansion region, the momentum equation for this system can be written as follows: 7rr:(P, - P.) = m(U. - U.), ^ (F.1) where m is the gas mass flow rate.  The parameters of the gas in the nozzle can be found from the following equations for choked flow:  124 2 ° k +1  Pa = P (— =  r")  (F.2)  2  (F.3)  2 1/(k-1)^p^2  )  1/(k-1)  (F.4)  Pa Po( -k +1^RT. k +1 where k is the specific heat ratio, and R is the gas constant.  The gas velocity in the nozzle (sonic) is determined as: un jcRT„ = ^  ( 2k  (F.5)  Now the equation for the gas mass flow rate can be written as follows: k^( 2 ) m = U n p a nra2 C d = irra2 C d P0 li— — RT0 k + 1  (k+1)/(2k-2)  (F.6)  where Cd is the nozzle discharge coefficient.  From Eqn. (F.1) the velocity at the exit of the expansion region: ( 2 rk-1) 7r 2^ri^ n U. = U. + ^°P -U+  m  La, P.  icjr1 )(k+1)/(2k-2) k^2^ Cda RT. k+1)  •  (F.3)  The continuity equation for the system can be written as follows: (F.4)  C d p aU a nr: = pa U a rr g ,  =  from where^ ro Cd 121)( p a^U0  = ra^C d -PJL Pa  LaU.  (F.5)  125  Eq. (F.9) assumes that temperature of the gas T. does not change during the expansion. After substitution of P., U., and U. in the last formula with the corresponding relation derived earlier, one can write the expression for the pseudo radius as follows:  rp, = ro  d  1.--S—) X  ( 2 rk -0 k + 1J [1_(.P4k +1)k/("1 1 1+ — kC d^k 2 )  (F.10)  That equation can be written in the form used by Birch et al (1984): = roilC d (-1-1 )K , Pit  where K 1+  ( 2 r k-1) k +1) 1 [ 1 _ (Pik + ly/(k-1) • Y3 2) kCd^  (F.11)  (F.12)  0 ^  Below are given equations allowing to calculate the magnitude of the underexpansion coefficient K without assumption of constant gas temperature during the gas expansion.  Momentum equation: 2 7rr 2 - C d p.U 2.nr.2 , -13.)Irro2 = p a U ..,  or (P. - Pa )r.2 = 1c13.M 20 r 2 - C d kP.M 2.r.2 , where M. is the Mach number at the end of the expansion region and M nis the Mach number in the nozzle. The last equation can be rewritten as follows:  (F.13) (F.14)  126  1  r )2 = 1+ km(- 1 0 11 -  k  p  M2.Cd  (F.15)  r  1+kM21-L-s  from where  Pn - ^  (F.16)  P.^1+ kM 2.C d •  Continuity equation: (F.17)  C d p.U.7r02 p.U oirrp2. Or Cd  -^M. ritT k e r;„ RT,,^RT.  (F.18)  where T. is temperature of the gas at the end of the expansion region. From the last equation: 2  P.^1 rp, M. 11--C Pa Cd ro M o  or  Pa^1  from where  2  ic,,) M. Cd ro M.  1+  (F.19)  k - 1 M2 2^°  (F.20)  k -1 ng 2 2^n  k-1 ‘ , 2 2 r) p 2^n Cd n n k-1 M2 r.^P. M. \ 1 ++---ivt 2^°  (F.21)  Combining Eqns. (F.21) and (F.15) we can get the following relationship:  P^ Pa Mn 0d pa m a 1 1+ CdkMa/= 1+ kM %form which it is possible derive the following formula:  1+ 1÷  k -1  M  2  2^n  2^°  (F.22)  127  1+  kC dM ni E1)1 -  M. —  P  k  2  1 M2  --. (1 ÷ C d ICM:) 1  k -1 2  (F.23)  For a choked flow (M. --- 1) this formula can be rewritten as follows:  M. =  \  1  kCd 1 + k - 1 (1+ C d k) -  2  P ( 2 ) ki(k-1)-1  k -1 2  (F.24)  k+1  Using this formula it is possible to calculate the magnitude of the Mach number at the end of the expansion region for different pressure ratios.  From Eqn. (F.21) it is possible to write a formula for rye exactly as is given in Eqn. (F.11). Only now the underexpansion coefficient is expressed as follows: ( 2 r( " -i)^k -1 K - Uc+1)^11^2 M.11+ M2  (F.25)  k2 1  Birch et al (1984) assume that the coefficient K is a constant, equal to 0.582 for methane. According to Eqns. (F.12), (F.25) and (F.24) the coefficient K for a given gas is dependent on the upstream-to-ambient pressure ratio and the nozzle discharge coefficient Cd. Figure F.1 shows comparison between the value of the coefficient K used by Birch et  al. and that calculated using Eqns. (F.12) and (F.25) assuming Cd to be constant and equal  128 to 0.85. The lines on the chart intersect around pressure ratio equal to 1.86, which corresponds to the critical pressure ratio for natural gas (average specific heat ratio k is equal to 1.35). 0.7 0.6 0.5  According to Birch et al. (1984)  0.4  According to Eqn. (F.12)  0.3  According to Eqn. (F.25)  0.2 ^ ^^^ 1 2^3^4^5^6 8 9 7  Upstream-to-ambient gas pressure ratio  Figure F.1 Underexpansion coefficient.  Birch et al used experimental data to show validity of using constant coefficient K. Unfortunately, in their experiments they used only estimated values of the nozzle discharge coefficient, therefore it is impossible to say whether the value of the coefficient K calculated with the use of the formulae (F1.2) or (F.25) would describe the results of the experiment better.  129  Appendix G. COMPUTER CODE OF A TRANSIENT CIRCULAR JET This computer code was originally developed by P. Ouellette and substantially modified in the present work.  C^COMPUTES PENETRATION OF A TRANSIENT ROUND FREE JET C OF METHANE INTO AIR IMPLICIT DOUBLE PRECISION (A-H,L-Z) OPEN(10,FILE='B:R15.0UT) PA = 3549000D0 TA = 290D0 TO = 290D0 PR = 1.5 PO = PR*PA RADO= 1.905D-4 RAD=RADO DIAM = 2.*RAD PI = 3.141592654 CD =0.5D0 C^EVALUATION OF PROPERTIES GK = 1.31 RA = 287. RG = 518.3 VISCOS = 1.1D-5 RHOA = PA/(RA*TA) RHOO = PO/(RG*TO) RHOG = PA/(RG*TA) RET = 45. C^COMPUTATION OF INITIAL VALUES MA = (2./(GK-1.)*((PO/PA)**((GK-1.)/GK)-1.))**(0.5) IF ( MA .GT.1) MA=1.0 TN = TO/(1.+ .5*(GK-1.)*MA**2.) UO = (2.*GK*RG*(TO-TN)/(GK-1.))**0.5 RHON = RH00/(1.+(GK-1.)*MA**2./2.)**(1^(GK-1.)) VISKIN=VISCOS/RHON  130 MOM = CD*PI*RHON*(U0**2.)*(RAD**2.) AREA = PI*RAD**2. RE = UO*2.*RADNISICIN RADEQ = RAD*(0.5439*CD*(PO/PA)*(RA/RG))**0.5 WRITE(*,*) U0=',U0 C^SET INITIAL VALUES RAD=CD*RAD*(RA/RG)**0.5 MA=(2J(GK-1.)*((PO/PA)**((GK-1.)/GK)-1.))**0.5 IF (MA.GE.1) RAD=RADEQ RPRO=0.1D0 DECU=13.6D0 DECC=4D0 VOLB=4.0DO*PI*((RADO)**3.)/3.0D0 MASSMP=RHOG*VOLB MASSBP=MASSMP VOLBP=VOLB RHOBP=RHOG CONCBP=1.0D0 MOMEBP=MASSBP*UO ZBP=RAD/(2.57756*RPRO) ZC=DECU*RAD ZO=RAD/(2.57756*RPRO) UBG=UO*0.5 UBP=UO T=0.0D0 RB=(VOLB*3.0D0/(4.0DO*P1))**(1.0D0/3.0D0) TIPPO=ZBP+2.*RB WRITE(*,20) ZBP,ZC 20 FORMAT(//,'INITIAL POSITION ZBP:',D15.5,/,'LENGTH OF CORE:',D15.5) 1  DT=1.0D-006 DO 500 T=DT,0.008D0,DT C^CALULATES ZB,UM,XM,RHALF 200 ZB=UBG*DT+ZBP RHALF=RPRO*ZB IF (ZB.LT.(ZC+ZO)) THEN UM=UO XM=1 ELSE UM=UO*DECU*RAD/ZB XM=DECC*RAD/ZB ENDIF C^NUMERICAL INTEGRATIONS  131 SUMF=0.0D0 SUMG=0.0D0 SUMH=0.0D0 RC=RAD*(ZC-ZB+ZO)/2C IF (ZB.GT .(ZC+ZO)) RC=0.0 IF (ZB.GT.(ZC+ZO)) GO TO 37 RO=SQRT(RC**2.+LOG(IJM/UBG)/LOG(2.0D0)*(RHALF**2.-RC**2.)) GO TO 40 37 RO=SQRT(RHALF**2.*LOG(UM/UBG)/LOG(2.0D0)) 40 CONTINUE HS'TEP=R0/11D0 DO 100 1=1,9,2 R 1=I*HSTEP R2=(I+ 1)*HSTEP U1=UM/(2.**((R1**2.-RC**2.)/(RHALF**2.-RC**2.))) U2=UM/(2.**((R2**2.-RC**2.)/(RHALF**2.-RC**2.))) X1=XM/(2.**(0.5*(R1**2.-RC**2.)/(RHALF**2.-RC**2.))) X2=XM/(2.**(0.5*(R2**2.-RC**2.)/(RHALF**2.-RC**2.))) IF (R1.LE.RC) THEN U1=UM X I =XM ENDIF IF (R2.LE.RC) THEN U2=UM X2=XM ENDIF RHO1=RHOA/(X1*(RHOA/RHOG-1)+ 1) RHO2=RHOA/(X2*(RHOA/RHOG-1)+ 1) F1=(U1-UBG)*RHO1*R1 F2=(U2-UBG)*RHO2*R2 SUMF=SUMF+4.*F1+2.*F2 G1=(U1-UBG)*R1 G2=(U2-UBG)*R2 SUMG=SUMG+4.*G1+2.*G2 H1=(U1-UBG)*U1*RHO1*R1 H2=(U2-UBG)*U2*RHO2*R2 SUMH=SUMH+4.*H1+2.*H2 100 CONTINUE SUMF=SUMF*HSTEP/3. SUMG=SUMG*HSTEP/3. SUMH=SUMH*HSTEP/3.  132 C CALCULATES MASS AND MOMENTUM MASSB=2.0D0*PI*SUMF*DT + MASSBP DVOLB=SUMG*DT DUB=UBP-UBG VOLB=DVOLB+VOLBP RB=(VOLB*3.0D0/(4.0DO*PI))**(1.0D0/3.0D0) FD=0.5*(0.5*RHOA*UBG**2.)*(PI*RB**2.) B 1=2*PI*SUMH B2=0.5*RHOA*(UBG*DVOLB+VOLB*DUB)/DT MOMEB=(B1+B2-FD)*DT+MOMEBP UB=MOMEB/MASSB C CHECKS CONVERGENCE IF(ABS(UBG-UB).LT.1.0D-3) GOTO 400 UBG=UBG+0.25*(UB-UBG) GOTO 200 400 CONTINUE MOMEBP=MOMEB VOLBP=VOLB MASSBP=MASSB TIPP=ZB+RB*2D0-ZO UBP=UB ZBP=ZB PFLAG=5.0D-005 IF (T.NE.0) VAL = ABS(T/PFLAG-ANINT(T/PFLAG)) IF (T.EQ.0) VAL=0 IF (VAL.LT.1D-5) WRITE(10,35) T*1000.,(TIPP-TIPPO)*1000. IF (VAL.LT.1D-5) WRITE(*,35) T*1000.,(TIPP-TIPPO)*1000. 30 FORMAT(5X,'TIME',9X, 1^7X,'TIP') • 35 FORMAT(2(1X,F12.4,2X)) 500 CONTINUE END  133  Appendix G. TIME-DEPENDENCE OF A TRANSIENT JET PENETRATION In this appendix the square-root-of-time dependence of a transient jet penetration is derived on a basis of a simple model of the jet.  The model assumes the jet shape similarity during the whole period of the jet propagation and no loss of momentum of the jet due to interaction with the surrounding fluid. For such conditions the momentum equation can be written as follows: k 1 pD 3 U = M a t ,^  (G.1)  where k 1 is a constant, p is the density of the injected fluid, D is the characteristic radial dimension of the jet, U is the average velocity of the whole volume of the jet, I■il a is the rate of momentum supply to the jet through the nozzle, and t is time.  Because of the assumed transient jet shape similarity D can be expressed as follows: D = k 2 z,  (G.2)  where z is the jet penetration (distance from the nozzle to the jet tip), and k2 is a constant. The average velocity of the jet can be written as follows: (G.3)  = k 3^, where k3 is another constant. Now Eqn. (G.1) can be rewritten as follows: 3 dz M^1 z^- ^ ° k1k2k3 dt p t  ,  (G.4)  12  (G.5)  from which z = (m.) 1/4 (  p  2^) 1/4  kik.2k3  134 Eqn. (G.5) shows that for a constant momentum rate through the nozzle the transient jet penetration rate is proportional to the square root of time.  

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