Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

High pressure injection of natural gas for diesel engine fueling Ouellette, Patric 1992

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-ubc_1992_spring_ouellette_patric.pdf [ 3.72MB ]
Metadata
JSON: 831-1.0080922.json
JSON-LD: 831-1.0080922-ld.json
RDF/XML (Pretty): 831-1.0080922-rdf.xml
RDF/JSON: 831-1.0080922-rdf.json
Turtle: 831-1.0080922-turtle.txt
N-Triples: 831-1.0080922-rdf-ntriples.txt
Original Record: 831-1.0080922-source.json
Full Text
831-1.0080922-fulltext.txt
Citation
831-1.0080922.ris

Full Text

HIGH PRESSURE INJECTION OF NATURAL GAS.FOR DIESEL ENGINE FUELINGbyPATRIC OUELLETI’EB.Eng., Ecole Polytechnique, 1989A THESIS SUBMITED IN PARTIAL FULFILLMENT OF- THE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinTHE FACULTY OF GRADUATE STUDIESMechanical Engineering DepartmentWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAJanuary 1992@ Patric OuelletteIn presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.Department of R4&kJCL. XuThe University of British ColumbiaVancouver, CanadaDate -4( I (izDE-6 (2188)11ABSTRACTThe high velocity unsteady methane jet emerging from a suddenly-opened conical poppettype nozzle is investigated, with the objective of characterising the penetration rate and the jetdistribution under different injection conditions. The results are to be utilised in the developmentand optimization of a prototype injector for late-cycle injection of natural gas in a diesel engine.Transient underexpanded turbulent jets of methane were visualized utilising schlieren andshadowgraph photography. The methane injections were principally performed in ambient air,with lateral visualization of the jet. Axial visualization of the methane injected into a pressurizedcylinder was also executed. Pressure ratios between 1.5 and 8 were utilised to generate the jets.The Reynolds number of the jets covered a range between 7x103 to 5.6x iOn.The steady-state turbulent conical sheet jet originating from the conical poppet nozzle ischaracterised using an integral approach in conjunction with published empirical results. Amodel of the transient conical sheet jet is developed, in which the transient jet is described as aquasi-steady jet feeding a moving vortex structure. The model is found to predict similarpenetration rates as the ones observed experimentally for different conditions, except in the earlymoments of the injection where the proposed modelling does not describe adequately the initialjet behaviour.The penetration of the methane jet is found to be proportional to the square root of thetime and initial velocity, and to the 1/4 power of the methane to air density ratio (taken atambient conditions), the upstream to ambient pressure and the product of the poppet lift by theseat radius. The jet penetration is also dependent on the ratio of methane to air densities atstandard temperature and pressure, the poppet angle and the injection duration. The conical sheetpenetration is shown to be approximately half of that of round holes, given the same flow area.U’Observations of the jet revealed that the conical sheet jet has a distinct curvature towardshe inside of the sheet, resulting in the jet collapsing under the nozzle for poppet angles greaterthan approximately 200. When the injector is positioned near a top wall, the jet exhibits a bistable behaviour, either collapsing under the poppet or clinging to the top wall.The immediate effect of the jet collapsing and clinging to the top wall is a reduction inmixing between the gas and the air and a slower penetration rate. Both these conditions areundesirable for an optimum combustion of the methane in a diesel environment. It is deducedthat with the current conical poppet nozzle design the distribution of the gas within the chamberis inadequate and the penetration rate of the jet is insufficient.Conical sheet interruptions at the nozzle is investigated as a potential solution for theclinging and collapsing problems. It is found that interruptions can successfully prevent bothphenomena. In addition, proper interruption arrangement generates jets of a different type thatare propagating significantly faster than the conical sheet jet.ivRÉSUMÉLe jet transitoire de methane débouchant a haute vitesse d’une fine fente annulaireconique soudainement ouverte est etudié, avec pour objectif la caractérisation du taux depénétration et de la distribution du methane injecté sous diverses conditions d’injection. L’orificeannulaire est obtenu par le déplacement d’une tige a bout conique a l’extrémité d’un cylindreconcentrique a la tige. Les résultats de 1’étude serviront au development et a l’optimisation d’uninjecteur prototype pour injection de gaz naturel en fin de compression dans un moteur diesel.Des jets turbulents transitoires ont éte visualisés au moyen des techniques schlieren etshadowgraph. Le methane a été injecté dans l’air ambiant dans la majorité des experiences, lejet étant visualisé latéralement. Des vues a.xiales du jet de methane injecte clans un cylindre souspression ont aussi ete obtenues. Des rapports de pression entre 1.5 et 8 ont été utilisés pourgénérer l’écoulement. Le nombre de Reynolds des jets observes varient entre 7x103 et 5.6x104Le jet turbulent sous forme de nappe conique s’écoulant en condition permanente del’orifice annulaire conique a été analyse au moyen des equations intégrales décrivant le jet et enadaptant des résultats empiriques trouvés dans Ia littérature. Un modèle du jet transitoire a étédéveloppé, dans lequel le jet transitoire est représente par un jet a écoulement quasi-permanentfournissant masse et momentum a un vortex s’éloignant de l’orifice. Le modèle prédit des tauxde pénétration similaires a ceux observes expérimentalement, sauf dans les premiers moments dujet oü le modèle surestime la pénétration.Les résultats indiquent que la pénétration du jet de methane est directement proportionellea la racine carrée du temps et de la vitesse initiale, a la puissance 1/4 du rapport de pression etdu rapport de densité (entre le methane et l’air aux conditions ainbiantes), et a la puissance 1/4du produit entre le rayon de l’orifice annulaire et le déplacement de la tige a bout conique. LaVpénétration depend aussi de l’angle de la partie conique, du rapport de densité entre le methaneet l’air aux conditions ste, ard, et de Ia durée de l’injection. La pénétraticn de la nappe coniquede methane est appoximativement Ia moitié de la pénéiration de jets débouchant d’orificescirculaires ayant Ia même surface d’écoulement que l’orifice annulaire conique.Les photographies du jet de methane révèlent une courbure de la nappe conique, dans ladirection du dessous de la nappe. Pour des angles de la partie conique supérieurs aapproximativement 200, cette courbure conduit a l’effondrement de la nappe qui s’agglomèreen un jet quasi-circulaire. Quand l’orifice de l’injecteur est place juste sous une paroi supérieure(comme c’est le cas dans le moteur), la nappe de methane affiche un comportement bi-stable; elleadhere a cette paroi ou s’effondre sous l’injecteur selon, entre autre, de l’angle de la partieconique et le rapport de pression.L’implication directe de cet effondrement ou de cette adhesion a la paroi supérieure estune r&luction du mélange entre le methane et l’air et un taux de penetration plus lent. Ces deuxconditions ne sont pas avantageuses pour une combustion efficace du methane dans unenvironnement diesel. Ii est déduit des résultats obtenus que le design actuel de l’orifice entraineune penetration et une distribution inadéquates du methane dans la chambre de combustion.L’interruption de la nappe de methane a l’orifice a été étudié brièvement en tant quesolution potentielle aux problèmes mentionnés. Les résultats indiquent que l’effondrement dujet et l’adhésion a Ia paroi supérieure peuvent être prévenus. De plus, un hon arrangement desinterruptions change le type de jet s’écoulant de l’orifice et entraine une pénétrationsignificativement supérieure a celle de la nappe continue.viTABLE OF CONTENTSABSTRACTRÉSUMÉ ivLIST OF SYMBOLS ixLIST OF TABLES xivLIST OF FIGURES XVACKNOWLEDGEMENTS XX1 INTRODUCTION 11.1 GLOBAL PROJECT 11.2 BRIEF REVIEW OF DIESEL INJECTION 51.3 PROTOTYPE INJECTOR 71.4 LATE-CYCLE HIGH PRESSURE GAS INJECTION:UNKNOWNS AND PROBLEMS 91.5 RESEARCH AND DEVELOPMENT STRATEGY 121.6 OBJECTIVE AND ORGANISATION OF THIS ThESIS 132 STEADY-STATE TURBULENT CONICAL SHEET JET 152.1 DIESEL FUEL SPRAY PENETRATION 162.2 INCOMPRESSIBLE STEADY-STATE TURBULENT ROUND FREE JET 182.3 INCOMPRESSIBLE STEADY-STATE TURBULENT CONICAL SHEET JET 252.4 COMPRESSIBLE TURBULENT ROUND FREE JET OF METHANE INTO AIR 312.5 COMPRESSIBLE TURBULENT CONICAL SHEET JET OF METHANE IN AIR 362.6 UNDEREXPANDED TURBULENT ROUND FREE JET 40VII2.7 UNDEREXPANDED CONICAL SHEET TURBULENT JET 433 TRANSIENT TURBULENT JET 463.1 INCOMPRESSIBLE TRANSIENT ROUND FREE JET 463.2 TRANSIENT ROUND FREE JET OF METHANE INTO AIR 523.3 TRANSiENT CONICAL SHEET JET OF METHANE INTO AIR 573.3.1 Scaling and Dimensional Analysis 603.3.2 Model Sensitivity 654 EXPERIMENTAL APPARATUS AND PROCEDURE 684.1 DESCRIPTION OF EXPERIMENTAL WORK 684.2 SIMILARITY 704.3 DESCRIPTION OF APPARATUS 754.3.1 Injection System and Control 754.3.2 Atmospheric Injection Rig & Cylindrical Chamber 814.3.3 Flow Visualization Set Up 834.3.4 Picture Acquisition 874.4 PICTURE ANALYSIS 914.5 EXPERIMENTAL CASES AND PROCEDURE 965 RESULTS 995.1 FREE PENETRATION OF THE CONICAL SHEET JET 1025.1.1 Comparison Between Model and Experiments 1025.1.2 Effect of Pressure ratio and Lift on Penetration 105viii5.1.3 Scaling 1075.1.4 Effect of Injection Duration 1115.1.5 Effect of Poppet Angle 1125.2 EFFECT OF GEOMETRICAL CONSTRAINTS ON THE JET 1175.2.1 Top Wall 1175.2.2 Bottom Wall 1195.2.3 Conical Sheet Jet Interruption 1205.2.4 Enclosed Area Effect 1285.2.5 Higher Reynolds Number Effect 1295.3 EXTENSION OF RESULTS TO ENGINE APPLICATION 1315.3.1 Penetration Rate 1315.3.2 Pulse Width Effect 1355.3.3 Jet Distribution 1356 CONCLUSIONS 1376.1 RECOMMENDATIONS AND FUTURE WORK 1457 REFERENCES 1478 APPENDICES 1498.1 APPENDIX A - NON-DIMENSIONAL ANALYSIS 1498.2 APPENDIX B - REPEATABILITY STUDY 1548.3 APPENDIX C - INTERNAL FLOW IN TEST INJECTOR 1558.4 APPENDIX D - TABLES OF RESULTS 161ixLIST OF SYMBOLSa Constant in Toilmien’s solution.A Area.A Effective area.A Nozzle area.A.1,, Pseudo-area for underexpansion.Cd Nozzle discharge coefficient.CD Drag coefficient of vortex.Effective diameter (to take into account the difference in density).d0 Diameter of the orifice.Pseudo-diameter for underexpansion.D Diameter of combustion chamber.FBV Body forces.FD Drag force.Surface forces.H Distance between the top and bottom wall in the combustion chamber.k Specific heat ratio.Ic n=l,2,3... Various constants.1 Poppet lift.Effective lift.1eq Equivalent lift.li,, Pseudo-lift for underexpansion.L (R, 1)’.xmay Mass of air within the vortex.mg1, Mass of second gas within the vortex.m Mass of the vortex structure.M Mach number.M Vortex integral momentum.P Pressure.Pressure of the ambient air or pressure of the air in the combustion chamber.Pressure in the jet at the end of the expansion.P0 Upstream pressure of the injected gas.Q Mass flow at end of expansion.Q Mass flow at nozzle.r Radial position normal to the jet axis.Radius of the inviscid core.re Radius where the steady state jet velocity = vortex velocity.1q Equivalent radius.r0 Radius of the orifice.Pseudo-radius for underexpansion.r112 Radial position where the velocity is half the axial velocity Urn.r1,r2 Radial penetration on left and right side of the injector in flow visualization pictures.R Radius of jet at a position z.Ra Air gas constant.R0 Injected gas constant.R Poppet seat radius.R Radius of the vortex.xiRe, Turbulent Reynolds number.Re Reynolds number of the vortex.t Time.Time between valve closing signal and actuationInjection duration.T Temperature at a point (z,r).Ta Temperature of the ambient air or of the air in the combustion chamber.Te Temperature of the injected gas at the end of expansion.Tm Temperature on the axis of the jet at a position z.T Static temperature of the injected gas at the nozzle.T0 Stagnation temperature of the injected gas.U Velocity at a position (r,z) in the steady-state jet.U Velocity of vortex centre.Ue Velocity of the jet at the end of expansion.Urn Velocity on the axis of the steady-state jet.U Velocity of the jet at the nozzle exit.U0 Velocity of the jet at the nozzle exit.U Velocity of the front of the vortex (tip velocity).U.k. Velocity of the vortex at its back plane.V Volume of the vortex.y1, Y2 Average axial penetration (downward) on left and right side of the injector on flowvisualization pictures.z Position along the jet axis, from virtual origin.z’ Position along the jet axis, from nozzle.xliLength of the potential core region.Position of the virtual origin relative to the orifice.z, Position of the jet tip, also define as penetration of the jet.Position of the back of the vortex structure.GREEK LETTERSa Concentration by volume. In velocity profile a=ln(2).a Volume concentration in the vortex.Poppet seat angle and jet axis angle.= r/r1 Non-dimensional radius r/R.p Viscosity.lit Turbulent viscosity.Turbulent kinematic viscosity.Non-dimensional radius r/ria.p Density.Pa Density of the ambient air or of the air in the combustion chamber.Pe Density of the injected gas at the end of expansion.Pg Density of the injected gas at same temperature and pressure as PaDensity at a point (z,r) in the jet.p, Density of the injected gas at the nozzle.p° Stagnation density of the injected gas.p, Vortex density.Shear stress.xliix Concentration by mass.Xxn Axial mass concentration.Mass concentration of the second gas within the vortex.ABBREVIATIONSCCD Charge coupled devices.CNG Compressed Natural gas.DDC Detroit Diesel Corporation.PM Particulate Matter.PR Pressure ratio.PW Pulse width.TA Turbocharged Aftercooled.TDC Top Dead Centre.xivLIST OF TABLESTable 1.1 - Emission Standards for Trucks and Buses. 2Table 2.1 - Corresponding values of the decay constant for experimentallyencountered values for constant a in Tollmien’s solution. 25Table 4.1 - Effects of pressure ratio, actuation pressure and pulse width on the lift. 80Table 4.2 - Summary of the components used in the experimental set-up. 92-93Table 4.3 - List of experiments performed. 97-98Table B.1 - Repeatability study. Upstream pressure of 173,7 kPa (1.7 atm), 100 anglepoppet, 0.056 mm lift at time 1 ms. 154Table B.2 - Repeatability study. Upstream pressure of 506,7 kPa (5 atm), 10° anglepoppet, 0.056 mm lift at 3 ms. 155Table C.1 - Mach number and pressure drop in the test injector. 159Table C.2 - Nozzle conditions for internally choked flow. 160xvLIST OF FIGURESFigure 1.1 - Schematic of natural gas injector with pilot diesel fuel. 8Figure 1.2 - Detail of the prototype injector tip. 10Figure 1.3 - Parameters relevant to the injection of gas into a combustion chamber. 11Figure 2.1 - Characteristic structure and parameters of a round free jet. 20Figure 2.2 - Control volume for momentum integral equation. 22Figure 2.3 - Conical sheet jet. 26Figure 2.4 - Detail of nozzle area. 28Figure 2.5 - Velocity decay for the conical sheet jet. 30Figure 2.6 - Velocity decay of the round free jet and the conical sheet jet. 31Figure 2.7 - Concentration and velocity profile in a turbulent jet. 33Figure 2.8 - Velocity and concentration decay for the round free jet of methane. 36Figure 2.9 - Velocity and concentration decay for the conical sheet jet of methane. 39Figure 2.10 - Expansion process for an underexpanded jet. 40Figure 2.11- Schematic expansion with pseudo-diameter. 41Figure 2.12 - Velocity and concentration decay for underexpanded round free jet. 44Figure 2.13 - Velocity and concentration decay for underexpanded conical sheet jet. 45Figure 3.1 - Proposed Transient Jet Model. 47Figure 3.2 - Comparison between model and Witze experiments. 51Figure 3.3 - Proportionality between the penetration and the square root of time. 53xviFigure 3.4 - Comparison between the tip velocity and the steady-state axial velocity. 53Figure 3.5 - Comparison between the penetration of the air jet and of the methane jet. 57Figure 3.6 - Model for the transient conical sheet jet. 58Figure 3.7 - Comparison between the penetration of a round jet and a conical sheet. 61Figure 3.8 - Penetration of a conical sheet jet as a function of time. 63Figure 3.9 - Penetration of a conical sheet jet as a function of the square root of time. 63Figure 3.10 - Effect of turbulent Reynolds number on the conical sheet jet penetration. 66Figure 3.11 - Effect of discharge coefficient on the conical sheet jet penetration. 66Figure 3.12 - Effect of vortex drag coefficient on the conical sheet jet penetration. 67Figure 4.1 - Experimental set 1; flow visualization of jet under atmospheric conditions. 69Figure 4.2 - Experimental set 2; flow visualization of jet within the pressurized chamber. 69Figure 4.3 - Principal parameters relevant to similarity. 71Figure 4.4 - Pneumatic actuator and prototype injector. 76Figure 4.5 - Injection System. 77Figure 4.6 - Lift trace obtained from a proximitor. 79Figure 4.7 - Injector holder for atmospheric injection set-up. 82Figure 4.8 - Cylindrical chamber with top and bottom quartz for flow visualization. 83Figure 4.9 - Beam deflection in a typical schlieren configuration. 85Figure 4.10 - Principal dimensions of the schlieren apparatus. 86Figure 4.11 - Vertical blank and odd/even status indicators used in triggering control. 89Figure 4.12 - Overall experimental set-up. 92Figure 4.13 - Rows of pixel to be reconstructed. 93Figure 4.14 - Principal steps of contour finding. 95xviiFigure 4.15 - Axial and radial penetrations. 96Figure 5.1 - Free conical sheet jet from 10 degree angle poppet. PJP=5’ 1=0.056 iim. 99Figure 5.2- Comparison between the model and experimental results for the penetrationof the conical sheet. 103Figure 5.3 - Comparison between the model corrected for friction and experimentalresults for the penetration of the conical sheet. 104Figure 5.4 - Free conical sheet jet from 10 degree angle. PcJPa=2, l—J.056 mm. 108Figure 5.5 - Free conical sheet jet from 10 degree angle. PJPa=2, 1=0.081 mm. 108Figure 5.6- Variation of the penetration with lift and upstream pressure, according toexperiments. 109Figure 5.7- Variation of the penetration with lift and upstream pressure as predictedby the model. 109Figure 5.8 - Variation of the penetration with lift and upstream pressure as predictedby the model corrected for internal flow behaviour. 110Figure 5.9 - Scaled model and experimental penetration in function of t*1a. 110Figure 5.10 - Post-injection penetration. Poppet angle of 10°, Po/Pa=2, 1=0.056 mm. 111Figure 5.11 - Post-injection penetration plotted as function •of t1,. 113Figure 5.12 - Free conical sheet jet from 20° angle poppet. Po/Pa=2, 1=0.056 mm. 114Figure 5.13 - Free conical sheet jet from 20° angle poppet. Pc/Pa=5’ 1=0.056 mm. 114Figure 5.14 - Free conical sheet jet from 30° angle poppet. PJP=2, 1=0.08 1 mm. 115Figure 5.15 - Free conical sheet jet from 30° angle poppet. PJPa=5, 1=0.08 1 mm. 115Figure 5.16-Proposed curving mechanism for conical sheet jet. 116xviiiFigure 5.17 - Penetration comparison between the free jet and the jet propagatingalong the top wall. 117Figure 5.18 - Effect of the top wall on the conical sheet jet. 100 angle poppet. 118Figure 5.19 - Effect of the top wall on the conical sheet jet. 20° angle poppet. 118Figure 5.20 - Effect of the bottom wall on the conical sheet jet. 100 angle poppet.PoIPa=5, 1=0.081 mm. 119Figure 5.21 - Propagation of the conical sheet from the 100 angle poppet between twowalls. H = 14.25 mm, Pc/Pa = 5, lift = 0.056 mm. 121Figure 5.22 - Propagation of the conical sheet from the 30° angle poppet between twowalls. H = 17.1 mm, Pa/P8 = 5, lift = 0.056 mm. 121Figure 5.23 - Velocity profile taken from numerical simulation of the conical sheet jet.30° angle initial velocity, H=16 mm, 3.6 ms after injection. Courtesyof Paul Walsh. 122Figure 5.24 - Fences for jet interruption. 123Figure 5.25 - Difference in initial velocity profile for full and interrupted conical jet. 124Figure 5.26 - Interrupted conical jet from 30° poppet. Interruption is performed by 4fences 2 mm wide at tip of copper cartridge. P0/P8 = 5, lift = 0.08 1 mm. 125Figure 5.27 - Interrupted conical jet from 10° poppet. Interruption is performed by 6fences of 2 mm width. Pc/Pa = 5, lift = 0.056 mm. 125Figure 5.28 - Shadowgraph of jet from 10° angle poppet (newest injector prototype).Frames 1 and 2 show full conical jet at 1 and 3 ms. Frames 3 and 4 showjet interrupted by two 6 mm wide fences at same times. 126Figure 5.29 - Shadowgraph of different interruption arrangements. In respective order:full conical sheet, 6x2 mm, 6x1 mm, and 8x1 mm. New prototype,xix100 poppet. 126Figure 5.30 - Shadowgraph of different interrupthn arrangements. In respective order:4x3mm, 4x2 mm, 4x1 mm and 4x2 mm with modified copper cartridge.New prototype, 100 poppet. 127Figure 5.31 - Difference in penetration for the free jet, the jet propagating along thetop wall and the enclosed jet. Data taken from new prototype 100poppet, 0.23 mm lift and pressure ratio of 2.64. 129Figure 5.32 - Penetration comparison between jets of different Reynolds number.The indicated pressure is the cylinder pressure before injection.10° angle poppet, pressure ratio of 2.64. 130Figure 5.33 - Axial shadowgraph visualization of the jet in the cylinder. For the caseillustrated, the chamber pressure is 3 atm and the upstream pressure is7.9 atm. 131Figure 5.34 - Approximation of jet penetration for the diesel fuel and the natural gas.Employed engine conditions are cylinder pressure and temperature of 24atm and 900 K, diesel holes diameter of 0.15 mm. 134Figure 5.35 - Approximate penetration for the diesel and natural gas injection for theconditions prevailing in the 6V-92 engine. Employed cylinder pressure andtemperature of 100 atm and 900 K. 134Figure C.1 - Model of the methane ports inside the test injector. 157xxACKNOWLEDGEMENTSI wish to express my gratitude to Dr. P.G. Hill for his invaluable help, judicious adviceand encouragements during the realisation of this project and the writing of this thesis. Thisthesis would not have been possible without the help of numerous people that I would like tothank Dr. E.G. Hauptmann for his suggestions regarding the flow visualization system, Dr. Y.Altintas for the usage of his magnetic displacement sensor, and Bruce Hodgins, research engineerand project manager, for his help and numerous suggestions. A special thanks to Paul Walsh forthe numerous late saturday nights spent debating the gas injection related mysteries.I want to offer very special thanks to the one person who during these two years offeredincessant moral support and encouragements - even during my worst impatient and grouchymoods - and who actively participated to the realisation of this thesis, my wife, Patty.Finalement je tiens a remercier spécialement toute ma famille qui malgré leur éloignementm’ont soutenus par leur constant soutien et leurs prières.11 INTRODUCTION1.1 GLOBAL PROJECTThe importance of using the earth’s resources efficiently and responsibly has becomeevident. Alarming levels of pollutants in American and European urban areas, generalatmospheric pollution and global warming are direct consequences of our massive use of fossilfuels for transportation and industrial processes. In an effort to ameliorate urban air quality andto reduce general atmospheric pollution, the EPA (Environmental Protection Agency) in theUnited States established the Clean Air Act Amendments (CAAA). The CAAA sets regulationsthat target, among other sources of pollution, passenger cars, buses and trucks.The majority of passenger cars are powered by internal combustion gasoline engineswhich produce nitrogen oxides (NOj, carbon dioxide (CO2), carbon monoxide (CO) andunburned or partially burned hydrocarbons (HC). Buses and trucks have been traditionallypowered by diesel engines, because of their greater durability and thermal efficiencies. Dieselexhaust is characterized by similar concentrations of NO1 as that of gasoline engines, slightlylower unburned hydrocarbon content and small amounts of CO and CO2. However, dieselengines are a major source of particulate matter (PM) emissions. Typically, between 0.2% and0.5% of the fuel mass is emitted as particulates Heywood [1988]’; these are composed primarilyof soot with some absorbed hydrocarbons. Both diesel and gasoline fuels contain small amountsof sulphur, which is oxidized during the combustion and forms sulphur dioxide (SO2). Dieselcontains more sulphur than gasoline, but the sulphur content in both fuels has been reducedsignificantly in the recent years. All of the above mentioned pollutants have separate and‘In this thesis, the year of the referenced publication is in brackets. The full references canbe found in alphabetical order at the end of the thesis.i2Recognizing the impact of diesel exhausts in urban areas, the EPA has set stringentrequirements on emissions from urban buses and heavy-duty trucks. The new regulations callfor a reduction of 90% in particulate matter and 15% in nitrogen oxides for urban buses betweenthe years 1990 and 1994, bringing PM at the 0.05 g/bhp-hr and NO1 at 5.0 g/bhp-hr. Bothrequirements are difficult to obtain simultaneously even with the latest diesel technology.Together with a light time schedule, these requirements have placed the diesel enginemanufacturers in a difficult situation. Table 1.1 summarizes emission standards for buses andtrucks.YEAR URBAN BUSES HEAVY-DUTY HEAVY-DUTY TRUCK ENGINEENGINE EMISSION STANDARDS EMISSION STANDARDS(gfbhp-hr measured during EPA heavy- (gfbhp-hr measured during EPAduty engine test) heavy-duty engine test)NO1 HC CO PM NO1 HC CO PM1990 6.0 1.3 15.5 0.60 6.0 1.3 15.5 0.601991 5.0 1.3 15.5 0.25’ 5.0 1.3 15.5 0.251993 5.0 1.3 15.5 0.10 5.0 1.3 15.5 0.251994 5.0 1.3 15.5 0.052 5.0 1.3 15.5 0.101998 4.02 1.3 15.5 0.052 4.02 1.3 15.5 0.10Table 1.1 - Emissions standards for trucks and buses. Reproduced from Detroit DieselInformation Update. ‘PM was previously set at 0.1 for 1991, and latter delayed to 1993.California has somewhat stricter standards and kept the 0.1 standard for 1991.2 Proposedstandards.Different strategies are being pursued in order to find a solution. Improving dieselengine design and electronic control, and using particulate traps are some of the alternatives.Electronic control of the injection already significantly improves emission characteristics, butfurther improvements are required to meet the 1993 standards. Particulate traps have beendeveloped and are being field tested with success, but their reliability and cost is a concern. So3far they have yet to satisfy the 290 000 miles life requirement. The other major alternative isto use an alternative fuel. Both methanol and natural gas are being tested extensively asalternative fuels for diesel engines.Methanol engines have been developed and field tested, and have met the standards bothfor NO1 and PM. Methanol is derived either from coal or natural gas, making its conversion costand therefore its purchase cost relatively high. As a consequence of its corrosive characteristics,most of the fuel system original components must be replaced by more resistant materials,making methanol a less attractive fuel for retrofit. Finally, methanol combustion producesaldehydes which are pollutants as of yet not regulated pollutants. All of these factors deter theusage of methanol.Natural gas has a longer history than methanol as an internal combustion engine fuel, andhas now been used in gasoline engines for a number of years. Natural gas can be stored ingaseous form (compressed natural gas : CNG) or in liquifled form (liquified natural gas LNG).Because of its availability, low cost and potential for clean burning, natural gas is a promisingalternative fuel. However its utilisation in diesel engine presents some challenges2.Different methods to implement the use of natural gas in diesel engines have beeninvestigated. Dual-fuel conversion can be performed, in which the percentage of diesel andnatural gas admitted in the chamber can either be fixed or variable. Ignition in dual-fuel enginesis ensured by the diesel fuel. Because the auto-ignition temperature of natural gas is higher thanthat of conventional diesel liquid fuel, the ignition must be assisted by spark plugs or glow plugsfor dedicated use of natural gas in a diesel engine.2 At Detroit Diesel, the biggest manufacturer of diesel engine in North America, efforts werefirst directed to the methanol engine. Recent efforts are directed to the development of a naturalgas-fuelled diesel engine.4To introduce the natural gas into the cylinder, one of the first methods to be used wasnatural fumigation, where the gas is pre-mixed with the air before the intake. Part-load operationwith natural fumigation in a diesel engine is characterised by poor combustion due to leanmixtures (there is no throttling in a conventional diesel engine). As an attempt to obtain somestratification of the fuel in the intake air, timed port injection of the gas at low pressure near theintake valve is being investigated. Stratification refers to the combustible mixture being localisedin the upper part of the cylinder, and is preventing the deterioration of the combustion at lowload (since full mixing of the natural gas with the full charge of air results in a mixture too weakfor complete combustion). To date, timed port injection has not fully overcome the problemassociated with the natural fumigation. Reduction in compression ratio, throttling and relativelylarge diesel proportion are needed to obtain acceptable part load combustion, with the overalleffect of reduced efficiency.A third approach being investigated is the late-cycle direct injection of natural gas intothe combustion chamber. Late-cycle refers to the injection of the gas near the end of thecompression stroke. Full stratification can be obtained with this method, providing thereforegood combustibility over the complete operating range. A small amount of pilot diesel fuel isinjected with the gas to provide ignition. Successful conversion of large diesel engines to directinjection of natural gas has been accomplished Miyake et al.; Einang [1983] ; Wakenell [1987].In all cases good efficiency, power rating, stable operation and low emissions were obtained, withpilot diesel fuel quantity as low as 5% (operation was acceptable down to 2%, but thermalefficiency decreased at this level).A project to convert a Detroit Diesel 6V-92 turbocharged and after-cooled (TA) diesel5engine3 to late-cycle electronically controlled direct injection of natural gas is currently underway at the department of Mechanical Engineering at UBC. The project consists of the designand development of an injector for natural gas. Ignition is ensured by injecting a smallproportion of diesel fuel with the natural gas through the same orifice, while in previous researchthe pilot fuel and the natural gas were injected through separate orifices. Injecting both fuelsthrough the same orifice permits gas blast atomization of the diesel fuel, and limits themodification necessary for the conversion. The aim is to develop a dual-fuel injector that willreplace the existing diesel injector and will therefore be easily implemented in existing engines.In order to inject the natural gas late in the cycle, high pressure is required. Consequently, anintensifier is being developed to bring the natural gas to the required pressure. The objective isto meet or exceed the thermal efficiency of a diesel fueled engine while reducing emissions.1.2 BRIEF REVIEW OF DIESEL INJECTIONThe success of this project is intimately related to the quality of the gas injection. Inorder to establish requirements for the gas injection, a brief review of the conventionalcompression ignition engine process is necessary. Diesel fuel is injected through small holes athigh velocity in the combustion chamber late in the compression stroke. The liquid fuelundergoes atomization as it is injected, vaporizes and mixes with the hot air in the combustionchamber. The properly mixed portion ignites shortly after the beginning of the injection sincethe pressure and temperature are above the fuel ignition point. The combustion causes anincrease in pressure and temperature that accelerates evaporation and ignition of the incomingfuel. The process of atomization, evaporation, mixing and ignition continues until the end of theApproximately 95% of the urban buses in North-America are powered by Detroit Dieseltwo-strokes engines.6injection. -The high initial velocity is necessary for two reasons. First it is largely responsible forthe atomization, in conjunction with very small injection holes (0.1 to 1 mm, a fairly large LIDratio is also required). Second it gives the fuel the necessary momentum to traverse thecombustion chamber in the available time, ensuring adequate air utilization. High initial velocityis attained by providing a large pressure difference between the fuel supply and the combustionchamber. Typically, the cylinder pressure is in the range of 50 to 100 atm. Fuel injectionpressures between 200 and 2000 atm are employed depending on the engine type. For theDetroit Diesel turbocharged 6V-92 engine, cylinder pressure of 100 to 120 atm are common.Injection pressure of the liquid fuel can be as high as 2000 atm.The combustion can be separated into different stages. There is first an ignition delay,the time between injection and ignition. This delay results from the processes that the fuel mustundergo (atomization, evaporation, mixing), and is of the order of 3 to 10 crank angle degreesdepending on engine operating conditions. Some of the fuel injected during this delay periodmixes with air within combustibility limits, resulting in a rapid combustion phase (correspondingto a peak in heat release). When all the premixed fuel accumulated during the ignition delayperiod is burned, the combustion becomes dependent on the incoming fuel. This is the mixing-controlled combustion phase, in which the rate of burning is essentially dependent on the rate atwhich the mixture becomes available for combustion. Approximately 75% of the fuel is burnedin this phase. Combustion continues late into the expansion stroke, and some of the unburnedfuel may burn in a late combustion phase. The mixing-controlled aspect of diesel combustionindicates that the combustion is directly related to the characteristics of the jet of fuel injected.Heywood [1988] points out some relevant characteristics of the compression ignitionengine while describing its process. First, because the fuel is not compressed with the air during7the compression stroke, there is no knocking limit to diesel engines. Higher compression ratiocan be used, increasing the efficiency of the cycle. Second, since the combustion timing iscontrolled by the injection timing, the delay between injection and combustion must be repeatableand short. Third, the torque is controlled by the amount of fuel injected, consequently the needfor throttling is eliminated, leading to increased mechanical efficiency. Fourth, there may be aproblem with air utilization at high load leading to formation of soot that cannot be burned beforeexhaust. The excessive amount of smoke limits the relative air fuel ratio to about 1.2, where therelative air fuel ratio is the actual air/fuel ratio over the stoichiometric air/fuel ratio.Diesel combustion depends on different physical processes, of which the proper diffusionof the fuel in the chamber is still the most important one:“The major problem in diesel combustion chamber design is to achieve sufficientlyrapid mixing between the injected fuel and the air in the cylinder to completecombustion in the appropriate crank angle interval close to top-centre” (Heywoodp.4.92)1.3 PROTOTYPE INJECTORA prototype injector for high pressure injection of natural gas with pilot diesel wasdesigned and patented by P.G. Hill, K.B. Hodgins from the Department of MechanicalEngineering at UBC, and R.J. Pierik, a former graduate student and research engineer in thedepartment. The prototype injector is intended to replace the existing diesel injector in the series60 and 71 Detroit Diesel engines without modifications to the engine itself. Figure 1.1 is aschematic of the natural gas injection system. Timing and fuel quantity are controlledelectronically by a modified Detroit Diesel Electronic Control (DDEC) system. The electroniccontrol closes a supply/return valve in the diesel lines towards the end of the compression stroke.The diesel in the injector is then compressed by a cam-actuated plunger, forcing the poppet valveto open once the pressure is high enough to counteract the spring. When a sufficient amount of8PILOTDIESELTHRO1TLE CNG STORAGEU.S. PATENT #5067467(20-200 atm)Figure 1.1 Schematic of natural gas injector with pilot diesel fuelgas and pilot fuel have been admitted into the cylinder, the supplyfteturn valve opens, andinjection stops. A controllable throttle regulates the percentage of pilot fuel admitted in thecombustion chamber with the natural gas. The pilot fuel is gas-blast atomized by the natural gasflow at the nozzle. In order to provide high pressure natural gas at all times, an intensifier bringsthe stored natural gas to the required injection pressure. The intensifier is driven by an accessoryshaft of the engine.Details of the tip of the injector can be found in Figure 1.2. The poppet valve and itsconical tip aie not a conventional design for diesel engines, where small holes are normally usedto inject and atomize the diesel fuel. The conical poppet design results in an axisymetric conicalsheet jet rather than a number of round jets. This design was chosen for several reasonsDIESELSUPPLYI RETURNIDDECCONTROLACCESSORY SHAFTDRIVEN ACTUATORINJECTORINTENSIFIERACCUMULATOR(-200 8AR)91) Because of its lower density, the total volume of natural gas per injection is greaterthen the corresponding volume of diesel. A larger orifice size is then necessary toallow the natural gas in the chamber within the time available. The conical shapeprovides more area to inject the gas. A small lift permits the design to keep goodatomization characteristics.2) Machining and manufacturing costs may be reduced significantly with this design,reducing total cost of the conversion.3) It is easier with this design than with the conventional pintle nozzle design to ensurechoking at the nozzle itself, providing better control on the gas injection.4) The design permits mixing the gas and the pilot fuel immediately before the nozzle;this would have been difficult with pintle type design.5) Sealing is a major challenge in the design of a high pressure gas injector, and theconical tip design may be easier to manufacture with appropriate sealingcharacteristics.1.4 LATE-CYCLE HIGH PRESSURE GAS INJECTION : UNKNOWNS AND PROBLEMSA prototype injector was designed and manufactured to gain knowledge and experienceregarding the implementation of the conversion. However numerous questions are unexploredand unanswered. The following paragraphs underline some of these questions.The injector is the most important part of the diesel engine. The injection dictates thequality of the combustion, and therefore of the fuel conversion efficiency, and has definite effectson emissions characteristics. Although there is a reasonably good knowledge of thecharacteristics of diesel injection, very little has been done on the direct injection of gases intocombustion chambers. In order to use natural gas successfully, it is of primary importance to10POPPET CAPINJECTOR NUT RETURN SPRINGPILOT FUELCNG PORTPOPPET VALVEFigure 1.2 Detail of the prototype injector tip.correlate the injector design and the operating parameters to injection and combustioncharacteristics. Injector design influences the injection by the shape, angle and diameter of itsnozzle and by the lift of the poppet. Operating parameters includes the length of injection,upstream pressure and temperature, and chamber pressure and temperature. Another importantfactor is the shape of the combustion chamber. These parameters are illustrated in Figure 1.3.Following the review of diesel injection in the previous section, we can now identify someimportant considerations for the gaseous injection. While the gas starts mixing immediately asit exits the nozzle, the pilot fuel must atomize, evaporate and mix with the air before it ignites,resulting in an ignition delay. This delay must be reproducible to ensure proper ignition timing;therefore the gas velocity must be kept constant. This is done by ensuring choking conditions11IiftI- J4seat radius Rs Iat the nozzle. A high gas velocity is required for atomization of the pilot fuel and to ensuresufficient diffusion of the gas in the chamber in the short time available. While under-penetration causes problems with air utilization, over-penetration in low-swirl chamber causesimpingement of the fuel on the wall, lowering mixing rate and increasing unburned species inthe vicinity of the wall. Penetration of the gas as a function of time or crank angle is unknownand must be investigated. The penetration depends on the geometry of the injector tip, the initialmomentum of the jet and the conditions in the combustion chamber. The initial momentum isrelated to the upstream gas condition and the nozzle flow area. For best air utilization, the jetmust be properly distributed in the chamber. This distribution is mainly dependent on the nozzlegeometry. Since the poppet geometry is not a conventional one, and no information was foundloFigure 1.3 Parameters relevant to the injection of gas in a combustion chamber.12on gas flow from such a nozzle, diffusion for this specific shape must be characterised.Because of the simultaneous presence of liquid fuel, droplets and evaporated diesel fuelin a jet of natural gas, the auto-ignition is not fully understood. The length and repeatability ofthe ignition delay are two unknowns.Other unknowns which must be investigated experimentally are operation variables suchas timing and fuel quantity for different engine operation conditions experimentally. Finally,detailed information regarding turbulence intensity, turbulence enhancement, and localised speciesformation have provided a better understanding of mixing rates and pollutants formation in dieselengine, and could be investigated for natural gas fueling.1.5 RESEARCH AND DEVELOPMENT STRATEGYAn experimental assessment of all the unknowns mentioned in the previous section is anenormous task. It was decided to limit experimental work, and to utilize computer simulationto characterize as much as possible the natural gas injection and combustion. The followingefforts were therefore undertaken:- Extensive testing of the prototype injector in a fully instrumented one cylinder DetroitDiesel 71 series research engine. The task can be divided in two categories. First, theinstrumentation must be adequate and reliable. Second, the prototype injector must betested. These efforts have already led to modification of the injector for better sealingand reliability. Research will follow on a turbocharged 6V-92 Detroit Diesel engine.- Analysis and flow visualization of the turbulent transient gas jet is being done and isthe subject of this particular project and thesis. Analytical work should provide a goodunderstanding of the jet diffusion mechanism, while indicating important variables andtheir respective effects on the jet. Potential scaling factors will also be examined. Flow13visualization will provide diffusion characteristics of the jet, and show evidence of theeffects of parameters variation.- Computer simulation using a modified TEACH code will provide some informationabout the effects of the piston motion on the jet dispersion and will provide furtherinsight as to the distribution of natural gas within the chamber. This is the subject ofa separate project.- More elaborate and complete simulation will be done using the KIVA code and shouldprovide detailed information about velocity profile, concentration profile, turbulenceintensity, species location and concentration, ignition characteristics and combustioncharacteristics as a function of crank angle. Both computer models and flowvisualization will provide information necessary to accelerate the design process of theinjector, reducing costly experimental development.1.6 OBJECTIVE AND ORGANISATION OF THIS THESISThe project being the subject of this thesis was launched because of the need for anexperimental investigation of the injection. Computer models can not provide exact simulationof the injector tip and need to be verified by experimental data. Flow visualization was chosenas the experimental method, since it provides a concrete representation of the injection of naturalgas from a conical nozzle poppet not available in the literature, and since it provides thenecessary information to investigate the effects of most parameters. Flow visualization has beenused widely in diesel injection research.Only the cold gas flow has been studied in this investigation. It is assumed that the gasflow dictates the pilot fuel diffusion and that the combustion does not significantly affect the flowdistribution and penetration. This is a reasonable assumption since diesel combustion is a14mixing-controlled combustion. The effect of the moving piston on the jet will not be investigatedin this projecx -The objective of this work is to obtain knowledge about the cold gas injection from theprototype injector, investigating in particular the penetration characteristics and the effect of thenozzle tip geometry on the diffusion of the gas. The effects of lift, pressure ratio and injectionlength on the gas diffusion will be investigated through a parametric study. An analyticaldescription of the conical sheet jet, based on previous work done on transient jets, will bepresented and provides understanding and scaling for the flow visualization results. The resultsof this work will be discussed, with the main goal of identifying important characteristics fornatural gas injection and potential improvements for the existing prototype injector.The analytical investigation of the gas diffusion from a conical nozzW design will bepresented in the two first chapters. A brief review of previous work done on transient diesel fuelsprays will be done as an introduction, and will lead to a more detailed analysis of transient jets,since it is the driving mechanism of fuel injection. In order to develop a model for transient jets,the velocity and concentration distribution in the steady-state jet must be known. The propertiesof the steady conical sheet jet are estimated in chapter 2, following previous work done on theturbulent round free jet. Then a model for the transient turbulent conical sheet jet will bepresented in chapter 3. The relevant literature is reviewed as each case is examined. Theexperimental apparatus and procedure will be described in detail in chapter 4. Results of flowvisualization will be presented and discussed in chapter 5. Finally, the potential implications ofthese results for the global project and potential improvements will be addressed in theconclusions.In this thesis a conical nozzle describes the type of nozzle illustrated in Figures 1.2 and 1.3.The type of jet emerging from this conical nozzle will be referred as a conical sheet jet.152 STEADY-STATE TURBULENT CONICAL SHEET JETThe mechanism of the injection of fuel into a combustion chamber is that of a transientturbulent jet. In a mixing-controlled combustion, the attributes of this transient jet dictate thequality of the combustion. In turn this transient jet is influenced by its surroundings (air motionin the cylinder, piston shape) and by its thermodynamics (evaporation, heat transfer, combustion).In spite of these influences, the investigation of the transient jet itself has always been a first stepin diesel injection research. One of the first and most fundamental aspects of transient jets tobe considered in diesel research is the penetration rate of the fuel spray. The penetration rate isdefined as the position of the tip of the jet relative to the nozzle as a function of time. The studyof the penetration rate does not provide a complete characterisation of the jet, but it establishesa basic requirement of the injection, that is the appropriate diffusion of the fuel through thecombustion chamber. Considerable work, both analytical and experimental, has been done ondiesel spray penetration. In most cases, simplified theoretical expressions that agree well withexperimental data can be established. These expressions are based on turbulent jet knowledgeand a particular expression will be reviewed briefly in the first part of this chapter. This reviewshall however serve more as an introduction, since in order to apply a similar theory to aturbulent conical sheet jet, the characteristics of this type of jet must be first examined.The steady-state round free turbulent jet will be reviewed, and a similar characterisationof the steady-state turbulent conical sheet jet will be presented. First, the incompressible jet ofair into air case will be examined, then the analysis will be extended to consider the injection ofa different gas into air. Underexpansion will also be discussed. The appropriate literatureconcerning each case will be reviewed as the case is presented.162.1 DIESEL FUEL SPRAY PENETRATIONThe literature on diesel fuel spray penetration is vast and dates back as far as 1937 withthe work of Schweitzer on oil sprays. Many empirical correlations have been established overthe years to predict penetration of the fuel spray tip in a quiescent chamber as a function of time.The model proposed by Dent 11971] has been shown to best correlate experimental data by Hayand Jones 11972]. The penetration prediction developed by Dent is based on the work of Forstalland Shapiro [1950] on mixing of coaxial gas jets. The velocity decay for a steady-state roundjet in their analysis has the following form:UmZc/da (2.1)U0 z/d0when the secondary fluid velocity is null. U0 and Urn are respectively the initial jet velocity andthe velocity on the axis of the jet, d0 is the diameter of the orifice, z is the distance along the jetaxis and z is the length of the potential core region. A top hat initial velocity profile is assumed.The parameters are illustrated in Figure 2.1. The potential core length was found to bez=4 d0 (2.2)A correction must be made to Equation 2.1 to account for density differences between theinjected fuel and the surrounding medium. It has been found by Thring and Newby [1952] thatthe density difference can be treated using an effective diameter dE instead of the actual diameterd0. The effective diameter is the size of the orifice that would yield, given a different injectedfluid density, the same momentum as if air was injected:1/2d=d0[._] (2.3)Pawhere Pg is the gas or fuel density and Pa is the air density, both taken at ambient temperatureand pressure. Equation 2.1 can then be rewrittenand the potential core length becomes ; = 4 d. Substituting z into Equation 2.4, the velocity17L z0/d (2.4)U0 z/ddecay becomes -U 4d (2.5)U0 zThe position z=O is a virtual origin situated in recess of the actual orifice. The jet can be thoughtas originating from a point source. Replacing Urn = dzjdt , where z is the position of the tip ofthe jet, in Equation 2.5 and integrating with the initial condition ;=0 at t=O, the transient natureof the jet can be described byz= {8U3td] 1/2 (2.6)The validity of the substitution is questionable, since it implies that the tip of the jet is travellingwith the same velocity as the steady jet. However, it seems to be a good approximation forliquid fuel injection. From the Bernoulli equation for incompressible fluids:p 1/2U0=C[2—) (2.7)Pgwhere iW = P0- a• P0 is the upstream pressure and a is the quiescent air pressure. Cd is thedischarge coefficient. Substitution of Equations 2.3 and 2.7 into Equation 2.6, results injp 1/2z= 3.36 C2[(—) td0]’12 (2.8)PaA discharge coefficient Cd of 0.8 is a good approximation for Reynolds number greater than i04and orifice length-to-diameter ratio between 2 and 4. With this approximation, Equation 2.8reduces top 1/2 1/2= 3.O1[(—) td0i (2.9)PaEquation 2.9 assumed that the density of the fuel and the air were at the same temperature. Incases where the temperature in the chamber is high, the equation must be modified. Assuming18that the injected fluid is at an ambient temperature of 298 K, Equation 2.9 becomesAP 1/2 1/2 298= 3.O1[(—) td] ( ) 4 (2.10)pa Twhere Ta is the temperature in the chamber. Equations 2.9 and 2.10 give the penetration inmeters when SI units are used for pressure, density and diameter. Dent shows that the aboveequations correlate well with experimental data on cold and hot bomb studies of jet penetrationfor temperature Ta from ambient to 800 K, orifice sizes from 0.25 mm to 0.7 mm and upstreampressures in the range 100 to 500 atm.Apparently, this model is a reasonable approximation for the penetration of round transientliquid fuel jets. It should be possible to establish a priori a similar relation for the conical sheetjet. Unfortunately, there is no known relationship for the velocity decay of a jet emerging froma conical nozzle design. The velocity decay must first be established, using integral equations.It must be mentioned that more recent work has been done on fuel spray penetration fromround orifices, but most of these recent studies consider more complex effects, such as swirl,piston movement and combustion chamber design. Those effects are certainly important, but area step ahead of the present work.2.2 INCOMPRESSIBLE STEADY-STATE TURBULENT ROUND FREE JETThe injection of natural gas into a combustion chamber is considered to be a compressibletransient turbulent jet involving two different gases (natural gas and air). Because chokingconditions are to be maintained at the nozzle, an upstream to cylinder pressure ratio larger thanthe critical pressure ratio will be required, and underexpansion could occur. Furthermore theconical geometry of the prototype injector tip (Figure 1.2) is not one commonly described in theliterature. The majority of the knowledge regarding turbulent jets concerns basic incompressible19steady-state jets of air into air, but there are a number of fundamental considerations and anun’’: r of approximations can be used to extend the analysis to compressible, underexpandedtransient turbulent jets. Starting from the simplest case, the appropriate papers will be reviewed,and the corresponding analysis applied to the round free jet first, for which experimental evidenceis available. Then the analysis will be extended to the case of a conical sheet jet of gas.Figure 2.1 illustrates a round free jet and its principal parameters. The jet can beseparated into three main region. The initial region is characterised by a central inviscid coreof length z in which the velocity is uniform and equal to the orifice velocity U0. This core issurrounded by a free shear layer where the exchange of mass and heat with the surroundingsbegins. At the end of the central core, a region of transition occurs before the fully developedpart of the jet. In this last region, the jet behaves as if it originates from a point source, locatedat a distance z0 from the orifice. The jet in the fully developed region has the property of self-similarity, meaning that the non-dimensional velocity profile is independent of the distance zalong the axis. The similarity concept is conveniently expressed as:-2=(’i) 1). (2.11)where U is the velocity at a position (r,z), Urn the velocity on the axis (O,z), and R is the radiusof the jet at the position z. There are different approximations of the velocity profile. Thevelocity profile suggested by Schlichting is often used:f(i) =_L=(l_i1.5)2 (2.12)UrnBut the definition of the radius of the jet R at a position z is not defmite, so that the profile dueto Warren (Witze [1980]) will be employed in this analysis:20(2.13)r a=1n2Urn r12where r112 is the radius where the velocity is half of the axial velocity Urn. This profile is validonly in the fully developed part of the jet.rr0r1TRANSITIONREGIONINITIALREGIONUrnDEVELOPEDREGIONFigure 2.1 Characteristic structure and parameters of a round free jet.A quantitative description of an incompressible round free jet can be found in theliterature (Abramovich [19631 and Witze [1980J). The half radius r112 and the axial velocity Urnof the jet can be expressed as a function of the axial distance z. The following assumptions mustbe made for this analysis:- In the fully developed region, the jet possesses the property of self-similarity. Thetransition region extends to approximately 20 diameters.- The pressure is constant throughout the jet and the surroundings. As long as the21surrounding medium is large in comparison to the size of the jet, and that the initialvelocity is low, the pressure uniformity is an experimentally observed fact.- The density is uniform in the jet, requiring that the injected fluid be the same as thefluid in the surroundings, and that compressible effects are very small in the cases ofgases, requiring low initial velocity.- The initial velocity profile is square. Alternatively, the initial momentum can becorrected by the discharge coefficient Cd.With these assumptions, the conservation of momentum is expressed as:tCdpr=27tfpU2rdr=27tpUr,,ff2() (214)Since the velocity profile is independent of z, the integral is a constant. It follows thatconstant (2.15)The increase ofr as a function of z can be obtain from the momentum integral equation appliedto a control volume located inside the steady-state jet, as illustrated in Figure 2.2, and isexpressed as:FSZ+FBV=fUpUdA (2.16)where are the surface forces and FBV are the body forces in the z direction. In the case ofa jet of air into air, the body force term can be neglected since convection is dominant in the jet.The surface forces are shear induced only, the pressure gradient being assumed null. The shearstress is expressed as a function of the turbulent viscosity:t=tIr12=pV.!L /2 P’b’t f’(l) (2.17)in which i is the turbulent viscosity. The right hand side of Equation 2.16 can be separated intotwo terms. The first is the momentum flux through the normal surfaces of the control volume.22r _—+ dzZ CONTROLVOLUMEFigure 2.2 Control volume for momentum integral equation.The second is the momentum at the half-radius, equal to the product of the mass flow throughthe lateral surface by the velocity at r112, UJ2. The momentum integral equation is then:-18)27tPVtUmf’(1)dZThe self-similarity property states that the profile f() is independent of z. Consequently, the firstintegral in the left-hand side of Equation 2.18 is a constant. According to Equation 2.15, theremaining part of that term is also a constant. The equation simplifies then toa — —2v f’(i)--(2.19)u112ffdGeneral empirical knowledge on turbulent round free jets states that the radius or the half radiusof the jet is directly proportional to the axial distance. To reflect that fact, a turbulent Reynoldsnumber Re is defined as23Re=UmZii2 (2.20)VtEquation 2.19 can now be integrated and yields—2f’(l) — k1Z—ReZ (2.21)RetJ f()d t0where k1 is a constant dependent on the velocity profile, and ReL is found experimentally. WithWarren’s velocity profile (Equation 2.13),k1=3.84. The half-radius r1,.2 is now expressed as afunction of z. To obtain an evaluation of Urn, Equation 2.21 can be replaced in the momentumconservation Equation 2.14:CdrO2r,ff2()d(2.22)CdrOU Re2ff2()d k1zThe distance z is actually the distance from the virtual origin of the jet. The relation betweenz and z’, the actual distance from the nozzle orifice, isz=z’+za(2.23)where z0 is the position of the virtual origin relatively to the orifice, and can be seen in Figure2.1. Setting Re = 45 to match Warren empirical constant (Witze [1980]) and assuming a squarevelocity profile (Cd=l), the following expressions are obtained for the half radius and the axialvelocity as a function of z:24Urn k2 13.8U0 (z’+z3)/r0 (z’+z0)/r0 (2.24)where Ic2 is a decay constantr112=0 .085 (z’±z0) (2.25)This solution agrees very well with Toilmien’s solution (Abramovich [1963]), Equation 2.26, forwhich experimental evidence is available. In section 2.1, the solution of Forstall and Shapiro wascharacterised by the same decay equation, but with a constant of 8 instead of 13.8.L1rn 0.96 (ToIlmien)U3 a(z’+z) (2.26)The constant a in Toilmien’s solution was found to be dependent on the initial velocity profile.Typical experimental values aie 0.066 for a uniform velocity profile, while values of 0.07 and0.076 have been reported for initial velocity profiles not completely uniform. The correspondingvalues for the decay constant in Equation 2.24 are given in Table 2.1. In his analysis, Witze[1980] takes into account the velocity profile in the core region, and obtains a similar relationfor the velocity decay:U 14.27 (Witze)U z (2.27)3r0According to these relationships, the core length (obtained when Urn = U0) is found to beapproximately 12 to 14 times the orifice radius. As for the virtual origin, it is dependent on thenozzle configuration. As an example, good agreement between Tolimien’s solution andexperiments were found when the virtual origin was set back about 4 times the orifice radius.The general form of Equation 2.24 indicates that results should be properly scaled when thevelocity and the axial distance are non-dimensionalized with the orifice velocity and the orificeradius.25constant a in Tolimien’s Equation 2.26 decay constant k2 in Equation 2.240.066 14.60.07 13.70.076 12.6Table 2.1 - Corresponding values of the decay constant in Equation 2.24 forexperimentally encountered values for constant a in Tolimien’s solution.2.3 INCOMPRESSIBLE STEADY-STATE TURBULENT CONICAL SHEET JETThe velocity decay and the spreading of a turbulent round free jet were obtained usingthe momentum integral equations and assuming a Gaussian velocity profile in the jet.Presumably, the velocity decay and the spreading of a turbulent conical sheet jet could beobtained following the same procedure if the velocity profile is known. Unfortunately,experimental data concerning the velocity profile in such a jet are not available. However forsmall jet axis angles, it will be assumed that the velocity profile within the jet is Gaussian.Figure 2.3 illustrates the conical poppet design and the main parameters of a conical sheet jet.Making the assumptions stated in the previous section, the conservation of momentum equationcan be written as:pCdA=2fpUUdA(2.28)2fpU227x [zcos () ÷rsin()] drThe term r sin(f3) is small compare to z cos({3) since the angle is assumed to be small, leadingtopCdA=2fpU227rzcos () dr(2.29)=47tpUr1,,2zcos()ff2 () dSince the velocity profile is a constant, Equation 2.29 leads to26Figure 2.3 Conical sheet jet.Urn!2r112zr112=constant (2.30)The momentum integral equation can be applied inside the jet, to a similar control volume(extending to r, as for the round free jet (Figure 2.2). The area of the top and bottom of thesheet are in fact different, but with the small angle assumption, that difference can be neglected’.The shear stress is similar to the one expressed in Equation 2.17. The momentum integralequation is‘By actually comparing the areas at any position z, it is possible to show that for an angleof 10 degrees, the top area is 3% larger. For 20 and 30 degrees, the top areas are respectively5% and 9 % larger.27[2fhhl’2U2pdA] —-.- [2fh1’2UpdA] =t2dA--[47czr112Ucos (3) pf’f () d] dz(2.31)- _[4Jtpzcos(P)Um.ri,f’f()d dzU /= 4ipzcos()v f (1)dzThe velocity profile is constant, and considering Equation 2.30, the first term on the left-handside is zero. Rearranging and substituting for the turbulent Reynolds number, yields8 -2ZVf’(1) 2ZUm f’(l)[ZUIj1]= 1 (2.32)f () d Reef f () dDividing by zUm2rlR = constant (Equation 2.30), results in1 8 [1]_ -2f’(l) 1ZUm8Z rn Ref’f()d (zUr112)(2.33)Substituting the transformation18 1 18 1 0 1UmZOZ(-;)Z()i3Z(2.34)we obtain8 —2f’(l)OZ Ref’f()d (Uzr112)(2.35)Multiplying by ZUm2ri, = constant, we fmally get8 — —2f”(l)---[zr2]— (2.36)UZ RetJ f()d0Once integrated and substituting the actual distance from the nozzle, Equation 2.36 yields28-2f”l’ k1 “‘ (z”÷z0) Re(z’+z0) (2.37)Reff()d t0and with Warren’s velocity profile, k1=1.71 14. Replacing r112 in Equation 2.28 we obtain anexpression for the velocity decay of the conical sheet jet:pCdAL 1%j 47rpcos(I3)ff2()d 1/2Z______________________________(2.38)-AVRef’f()d 1\ _8cos(p)f!(1)f2()d (z’+z0)Referring to Figure 2.4, the area at the nozzle isA=2itRlcos (13)and R=R5--cos (13) sin(13) (2.39)where R is the seat radius. In cases where theangle is small and when the lift is smallcompare to the seat radius, Equation 2.39reduces toA=27tR5lcos (13) (2.40)In the case of the prototype injector, the lift isFigure 2.4 Detail of nozzle area. approximately 0.1 mm compared to a seatradius of 3.4 imn. Equation 2.40 will be utilised to approximate the area at the nozzle.Replacing the area in Equation 2.38 yields1 (2.41)4j _4f(1)ff2()d (z”+z)Rearranging and saying Cd = 1,29_______________ _______= (2.42)_4f’(i)f2()d (z+z0) (z÷z0)where k2 = k (Re)1 and k = 0.623 for Warren’s velocity profile. Apparently, the results for theconical sheet jet should scale when the axial distance is non-dimensionalized with the square rootof Rl (seat radius multiplied by lift).The turbulent Reynolds number for a conical sheet jet is unknown. Its value is estimatedby assuming that the conical sheet jet will have the same spreading angle as the round free jetand as the plane jet. For these two jets, the angle between the jet axis and the surface of the jet(spreading angle) is approximately the same and is equal to roughly 13 degrees. For the roundfree jet, Re is approximately 45. For the plane jet, Re is lower, in the range 15-20 (Abramovich[1963]). Since the velocity profiles are the same for each jet, the increase of the half-radius r112with z should be the same. For the round free jet, r112 = 0.085 z. To yield the same constant forthe conical sheet jet, the turbulent Reynolds number must be approximately 20 (from Equation2.37). With this turbulent Reynolds number, the velocity decay given by Equation 2.42 becomesU 28--= withRe=20U3 z’+z0 t (2.43)Equation 2.43 indicates that the velocity decay is not dependent on the jet angle. However, thisis only true because of the area approximation in Equation 2.40. The velocity decay wascomputed for different cases, with the exact value of the area, and is plotted in Figure 2.5. Thescaling established on the area approximation is seen to be appropriate.In typical diesel injectors, the fuel is admitted through a number of small holes placed onthe circumference of the tip. The performance of the conical poppet design relative to a series30Urn1U00.80.60.40.20 ao 100Figure 2.5 Velocity decay for the conical sheet jet from Equation 2.43, scaled with (Rj)”2.Theturbulent Reynolds number is 20.of circular holes can be readily evaluated by comparing the axial velocity decay of the jetsemerging from each of these nozzles. The velocity decay for the turbulent conical sheet jet iscompared to the one of the turbulent round free jet in Figure 2.6. The comparison is based onan equivalence between the conical nozzle area and the combined area of 7 holes (number ofholes chosen because the Detroit Diesel injectors for the 71 series have 7 holes). The actualcomparison is performed between the jet from the conical poppet nozzle and the jet from one ofthe 7 holes. The initial velocity is the same in the two cases. The velocity decay of the conicalsheet jet occurs more rapidly then for the round free jet, that is a disadvantage since it willcorrespond to a lower penetration rate of the jet. The initial core length is shorter, as expectedfor a source with a smaller transverse scale. For the same total area, the jet from the conical+ Uo=127.2rrils, I =0.101mmV Uo = 41.4 mIs, I — 0.101 mmo Uo=127.2m/s, I =0.203mm20Z,q_31u1U00.80.60.40.20Figure 2.6 Velocity decays of the round jet and the conical sheet jet from Equations 2.24 and2.43. Re = 20 for the conical sheet jet, and Re= 45 for the round jet.poppet design will travel slower through the combustion chamber then the jets from 7 holes.So far we have discussed the simplest case of a low speed jet of air into air. In thefollowing section the injection of a gas with a different density will be discussed.2.4 COMPRESSIBLE TURBULENT ROUND FREE JET OF METhANE INTO AIRChoking is required at the nozzle to ensure high velocities and reproducibility. Abovea Mach number of about 0.3, compressibility effects are no longer negligible. Nozzle conditionsmust be modified to account for these compressibility effects. First the Mach number iscomputed from one-dimensional isentropic gas dynamics. The temperature, the density and thevelocity at the nozzle exit can be obtained from the Mach number.z(mm)32(k-i)(2.44)T-T3(2.45)—PCk1 (2.46)(1+ 21M2) k-iu f 2k R T -T (2.47)0 k—i ‘ o fl’The specific heat ratio k was taken as 1.35 for methane. In the immediate surrounding outsidethe nozzle, velocities are high and compressibility effects are also present. The density profilein this area will differ from the incompressible case. However experimental results show thatthe velocity profile still possesses the property of similarity (Abramovich [1963]). For thepresent analysis the details of the jet in the immediate surrounding of the nozzle (z < 1O(R l)1t2)are not required and will not be considered.The observation of the momentum conservation equation underlines the challenge oftreating an incoming gas of a different density in air.CdPflrQU—27tUrl,2fPf2 () (2.48)where p is the density at a point (r,z) anywhere in the jet. While the velocity profile at any axialdistance z remains Gaussian, the density is now a function of the axial distance and of the radius.At a point j(z,r) in the incompressible part of the jet (i.e. not near the nozzle), the density of themixture depends on the local concentration of the incoming gas. Assuming that air and methanebehave as ideal gases, it can be shown that at a point j in the jet33PjPg (1—a) Pa= Pa (2.49)P3x(-—1) +1Pgwhere cx is the concentration by volume of the injected gas at a point (z,r) and X is theconcentration by mass. The subscripts a and g refer respectively to the ambient gas and to theinjected gas. The densities of the air and the injected gas are taken at the same temperature andpressure. The concentration by mass within a jet is known to possess also the property of selfsimilarity (Abramovich [1963]). The Taylor theory of turbulence for axisymmetric jets predictsthat the concentration and the temperature profile are related to the velocity profile in thefollowing manner:.. AT....Xm ATm U1 (2.50)where x is concentration by mass,AT = T6 and ATm = TaTmThis relationship is well validated by numerous experimental data (Abramovich [1963]). Therespective velocity, concentrationand temperature profiles areplotted in Figure 2.7 according to iLUrnEquations 2.13 and 2.50. The x 0.75difference between the velocity ATATm 0.5profiles and the concentration0.25profile is due to the faster0:5 i 2:5 3diffusion of the mass relative to—r! rthe momentum. Figure 2.7 Concentration and velocity profile in aturbulent jet.The conservation ofUrn34momentum equation is obtained by replacing the density by its relation to the mass fractionconcentration, and by making the necessary transformation to take into account the concentrationprofile.7tCdPflroU-27Uri/2Pafif2 ()Q7(2.51)x() (_-—‘)+‘Pgwhere g() = y/ and Xm is the axial concentration. Since we now have a new variable, themass conservation equation is also required:7cdPnroUo_27rfapgurdr=27umri,2faP f() (2.52)The volume fraction is related to the mass fraction byPaP(Pa_1)÷ (2.53)PgReplacing Equation 2.53 in Equation 2.51 yieldsltCdPnrOUO—2ICUmXmri/PaJg()f()d(2.54)x() (—_—‘)+‘PgWhen treating the incompressible jet of air into air, the momentum integral equation was usedto obtain the half radius of the jet r1. Unfortunately, because the integral in Equations 2.51 and2.52 are no longer independent of z, the momentum integral becomes intractable for binarymixtures. Consequently empirical information is utilised to pursue this analysis. A good sourceof information is found in a paper written by a group from the British Gas Corporation (Birch,Brown, Dodson and Thomas [1978]), in which the turbulent concentration field of a methane jetis examined. The decay of the axial concentration was shown experimentally to closely followthe following relationship:35Xm k3d (2.55)xo z÷zowhere d1 is the effective diameter, presented in section 2.1. For a round orifice, the effectivediameter is1/2d=d0(!2) (2.56)Pawhere d0 is the actual diameter of the orifice. The decay constant k3 takes values between 4 and6 in the literature. The group from the British Gas Corporation found that a value of k3 of 4matches well the experiments in the far field (z>25d), while in the near field region (l0ckz<30d)a value of 4.7 fits better the results. The virtual origin was found to be -5.8d0.Since the concentration decay is well predicted by Equation 2.53, it can serve as the thirdequation needed to complete the analysis of the round free jet of methane into air. The solutionof the system of equations is no longer explicit but simple to solve by iteration. The integralscan be evaluated explicitly. The following steps were performed to obtain the solution:for 0 <z <50 mmI - compute axial concentration according to Equation 2.55 and with k3 = 4,2 - guess the axial velocity Urn’,3 - compute the half radius r1 from mass conservation 2.54,4 - compute the axial velocity Urn from momentum conservation 2.51,5 - repeat steps 3 and 4 until the difference between Urn’ and Urn is small.Equation 2.55 indicates that the concentration decay for different cases will be scaledwhen the axial distance is non-dimensionalized with the effective diameter. Figure 2.8 showsthat this is an appropriate scaling also for the velocity decay. In Figure 2.8, results are scaledwith the effective radius that is half the effective diameter. The obtained velocity decay can befitted with a decay equation similar to 2.24 and a decay constant of 11.2; this contrasts with a0.80.80.40.2036velocity decay constant of 13.8 for the incompressible jet of air into air. The half-radius r1 isfound to be approximately 0.1 1(z+z0), while a value of .085(z+;) was obtained for theincompressible case.Urn1U0Xmxo+V0Uo— 122,8mIs, r0— 0,3 mmUo=345,9m!s,r0=0,6mmUo=122,8m/s,r0=0,3mmUrnU0z IFigure 2.8 Velocity and concentration decay for the round free jet of methane into air.So far no mention was made of the buoyancy forces that occur when a jet of different densityis injected into air. At a certain distance away from the nozzle, where velocities are small,buoyant effects will become important. However, within the time scale relevant to engineoperation, buoyancy effects could not be observed experimentally.2.5 COMPRESSIBLE TURBULENT CONICAL SHEET JET OF METHANE INTO AIRThe previous discussion about compressible effects is applicable for the turbulent conical37sheet jet. The same treatment for the density can be applied, assuming that the concentrationprofile is equal to the square root of the velocity profile, as for the round free jet. Themomentum and mass conservation equations for a conical sheet are then writtenpflCdAflV=4TrUrl,2zcos(3) Paf0f2 () d(2.57)x() (——‘)÷‘pnCnUo=4mXmni,zc0s() Paf0 g() f() d (2.58)x() (—a—’) +1PgIn the previous section, experimental results from the British Gas Corporation were utilised toobtain the concentration decay of a binary mixture for a round free jet. For the conical sheet jet,such data are not available. Since concentration and velocity decay take a similar form for theround free jet, it is assumed that it is also true for the conical sheet. According to thisassumption, the equation for the concentration decay would take the formXm_ k4Z+Zc, (2.59)where the subscript E denotes the use of an effective area used to consider the difference indensity between the incoming gas and the ambient. We can derive the effective area from theequivalent momentum concept of Thring and Newby, and replacing for the approximate area atthe conical poppet nozzle (Equation 2.40):38A0PgV=4Pap (2.60)2 (R1)€cos (3) =2’n (R51)dosPa(Rs1)e(Rs1)PaTo get the equivalent momentum, changing only one of these two dimension (R, or 1) issufficient. In our case the seat radius is fixed and it is more convenient to define an effectivelift:= 1 (fg) (2.61)PaEquation 2.59 then takes the following formXm_ IC4Xc, Z1+Zt, (2.62)Rs1eThe constant k4 is unknown, but it can be evaluated by assuming again that the spreading angleis similar to the one of a round free jet of methane into air. The solution of the system ofequation was obtained for different values of k4 until one was found that yieldedr11O.1 1(z+z0).A concentration decay constant k4 = 2.14 was found. With this constant, a velocity decayconstant of 2.5 is obtained, while for the incompressible conical sheet jet of air into air, thevelocity decay constant is 2.8. It is important to note that decay constants vary throughout theliterature, and that the values proposed here are intended to be approximations.There are three equations and three unknowns to express as a function of the axialdistance z. The integral in Equations. 2.57 and 2.58 must be solved numerically. The solutionremains simple and follows the following stepsfor 0 < z < 50 mm391 - compute axial concentration from Equation 2.62,2 - numerical integration in Equation 2.57,3 - numerical integration in Equation 2.58,4- guess a value of the axial velocity Urn’,5 - compute r112 from mass conservation Equation 2.58,6 - compute Urn from momentum conservation Equation 2.57,7 - repeat steps 5 and 6 until the difference between Urn’ and Urn is small.The concentration decay should be properly scaled when the axial distance is nondimensionalized with (Rl)1. Figure 2.9 shows that this scaling is also appropriate for thevelocity decay. The data plotted in Figure 2.8 were computed without making the approximationfor the nozzle area (Equation 2.40).UrnU0Xmxo0.2Figure 2.9 Velocity and concentration decay for the conical sheet jet. The concentration andvelocity decay constants are 2.2 and 2.6 respectively.1oUo-123m/s,I=O.lmmUo-346m/s,I-O.1 mmUo = 123 mIs, I = 0.2 mm0.4 U0402.6 UNDEREXPANDED ROUND FREE JETAt this point it is unknown at which pressure ratio the natural gas injection will take placein the engine. Choking is necessaiy at the nozzle so that repeatable injection velocity and massflow can be obtained. For natural gas flowing trough a converging nozzle, choking occurs whenthe pressure ratio across the nozzle is greater than 1.86. To increase the penetration rate, pressureratio greater than the critical one might be required. When the pressure ratio is greater than 1.86,the jet is not fully expanded at the nozzle, and expansion occurs outside the nozzle. Also,because the geometry of the nozzle is similar to a converging-diverging nozzle, supersonicvelocities could occur at the nozzle exit. In both cases, the jet is underexpanded. Themechanism of the complex expansion process is well summarized in a paper by Ewan andMooclie [1986] and briefly in the next paragraph (see Figure 2.10).Figure 2.10 Principal characteristics of the expansion process for an underexpanded jet.When choking conditions are reached (M=1), further increase in upstream pressure forcesthe exit plane pressure to increase. As a result the jet expands outside the nozzle, where itaccelerates. Expansion waves originate around the expansion point. They propagate in the highEXPANSIONWAVESM= 1FLOW BOUNDARYDISKBARREL SHOCK41velocity expansion region and are reflected as compression waves when they meet the outer layer.The coalescence of these compression waves results in a barrel shape shock surrounding theimmediate surrounding of the supersonic region, and expanding for a few diameters. The barrelshock ends up in the axial direction as a normal shock (Mach disk) and subsequent reflectedshocks. If the underexpansion is large, this process is repeated a number of times.This complex problem has however been treated simply and successfully for a round freejet by at least two groups Moodie and Ewan [19861 and Birch, Brown, Dodson and Swaffleld[1984]. The immediate effect of the underexpansion can be seen on the flow visualizationpictures presented in the first of these papers. The jet increases in diameter suddenly as itexpands outside the nozzle. It is possible to retain the analysis for correctly expanded jetsdescribed in the previous sections by defining a pseudo-diameter larger than the actual diameter.The underexpanded jet behaves therefore as if it is a correctly expanded jet emerging from alarger orifice. This concept is only valid of course at a certain distance away from the nozzle,where the jet is known to have little memory of its origin, but barrel lengths are shown to be nomore than 3 diameters atpressure ratios up to 10.p.The pseudo-diameterINFINITERESERVOIR________can be obtained from theassumption that the mass flow PaT0pais conserved throughout theexpansion, meaning that themixing is negligible duringthe expansion process. Figure2.11 illustrates anFigure 2.11 Schematic expansion with pseudo-diameter.PnTPI,42underexpanded jet and the parameters used in the analysis. It must be underlined that therepresentation in Figure 2.11 is a simplified illustration to describe the pseudo-diameter concept.The mass flow at the orifice and at the pseudo-diameter are given respectively byQ=- CddpflUfl(2.63)QedsPeUeBecause Q = Q, the pseudo-diameter can be related to the real diameter by the followingrelationship:d 2(E!) =C (2.64)d0 dUepeThe velocity is sonic both at the nozzle and at the pseudo-diameter. We can relate the conditionsat the nozzle to the upstream conditions using compressible isentropic flow relationships andideal perfect gas law.d 2 [n(PS)=Vn F’____) k-id0 d_ Pe k+1(2.65)2 )k-1dVrTpT k+1T3=T( k-f1) and PeP6 so that(2.66)d 2 2ps...ç e o____\ k-i—/ ‘ ‘ ‘.k+ 1 ‘o n aIn Birch et al., the temperature at end of expansion Te and the temperature in the reservoir areassumed to be equal to the ambient temperature. Here it is preferred to assume that temperaturesare similar at the nozzle and in the plane of the pseudo diameter, since the conditions are sonicat both locations. Ewans shows that for an upstream pressure of 20 atm the nozzle T .85 T0and at the pseudo diameter Te = 0.8 to 0.9 T0, justifying this assumption. We therefore obtain43for natural gasd 2 p k -(—a) =C (0) 2 (k-i) (2.67)d0 d p k41that reduces tod —d 53f(PO\ (2.68)Ps °I d’p ‘N aBased on the different assumption for the temperature, Birch et al. obtained the same relation butwith a constant of .582 instead of .537. This difference does not change the validity of theirresults, since the coefficient Cd is somehow empirical. Their experiments show very well thatthe axial concentration decay for underexpanded jets behaves just like a correctly expanded jetwhen scaled with the pseudo-diameter. The experimental evidence of that the pseudo-diametercan be used successfully to describe underexpanded jets shall be used in this research to applyour previous analysis to underexpanded jets. The concept can readily be applied to the roundfree jet analysis done in section 2.5. The radius must be replaced by the pseudo-radius, half thepseudo-diameter, before computing the results if the pressure ratio is greater than 1.86. Differentcases were computed, and results are plotted in Figure 2.12. The concentration and velocitydecay collapse when the axial distance is scaled with the following equivalent radius:r= r5 (f) 2 = [r0(P-) 2]j O.537Cd.2 (2.69)2.7 UNDEREXPANDED CONICAL SHEET JETThe same idea is exploited for the turbulent conical sheet jet thin sheet. An expressioncan be obtained for a pseudo-lift to replace the actual lift if the jet is underexpanded. We findthat441UrnU00.75Xmxo0.50.250Figure 2.12 Velocity and concentration decay for underexpanded round free jet of methane.0.537 A Cd(2)(2.70)27t (R31) cos(f3) =0.537 (2)nR1cos(P) Cd(2)p(R1)5=0.537 RB1Cd(-2)A change in the lift only is sufficient to provide equivalent mass flow, so that Equation 2.70 canbe writtenlP$=O.537 (2.71)0 PoIPa = 1.5, r0= 0.31 mmo PoIPa =2, = 0.31 mmPoIPa=4, r0= 0.62 mmScaling should then be provided by the equivalent lift451 =1 (f2eq ps’,I’a (2.72)leq=O.537 JCd() ()Pa E’aThe pseudo-lift l.a,, is replaced in the calculation of the conical sheet jet velocity and concentrationdecays when the pressure ratio is greater than 1.86. Again when different cases are computed,they collapse on a unique curve if the axial distance is non-dimensionalized with the square rootof the R1 (Figure 2.13).UrnU00.75Xmxo0.2540Figure 2.13 Velocity and concentration decay for underexpanded conical sheet jet.oPoIPa=1.5,I=O.1 mmcPo/Pa=2,I=Oi mmPa/Pa =4,1=0.2 mm0.5a’lo 2463 TRANSIENT TURBULENT JETJ.S. Turner in 1962 modelled a starting plume as a steady buoyant plume feeding a vortexstructure. His model was inspired by the observation of thermal plumes. Flow visualization ofthe early stages of impulsively started jets Batchelor [1967] revealed the formation of a vortex“mushroom” or “ball”, suggesting that a model similar to the one used by Turner could beutilized for transient jets. Abramovich and Solan [1973] exploited that idea, and modelled astarting laminar jet as a quasi-steady state jet feeding a vortex structure. Witze [1980] appliedthe same model to a turbulent round free jet. The model predictions for the penetration of thejet compare veiy well with experimental measurements in the papers by Abramovich and Solan[1973] and Witze [1980]. In this section, the transient model will be presented first for aturbulent round free jet of air into air. Then the model will be adapted to take into account theinjection of a different gas into air. Finally, the possibility of building such a model for thetransient turbulent conical sheet jet will be examined.3.1 INCOMPRESSIBLE TRANSIENT TURBULENT ROUND FREE JETThe transient model for the starting jet from a round orifice is illustrated in Figure 3.1.The jet is modelled as the combination of a quasi-steady turbulent jet feeding a spherical vortexstructure. In the quasi-steady state region, the velocity profile is the one of the steady-state jet,described in chapter 2. The vortex structure is considered as a whole. It is modelled as a sphereof radius R, possessing mass and momentum, travelling away from the nozzle in the z direction.The location, mass and momentum of the vortex change with time. The momentum of thestructure is reduced by a drag force and by the need to accelerate the surrounding fluid.There is a plane i at the back of the vortex where mass and momentum are being fed to47Figure 3.1 Proposed transient jet model.the vortex structure by the quasi-steady jet. The plane is at a distance z from the orifice. Theposition of the tip, also defined as the penetration, is;. Assuming that the back plane is closeto the surface of the sphere at the axis, the relation between ; and z isz=z+2R (3.1)The velocity U is the velocity of the back of the vortex structure, at the plane i. Because thevortex is expanding, the velocity at the centre of the vortex U and the tip velocity U differ fromU,, but are related bydR dRU=U÷ (3.2)C V•dt V dtAt a point (z,r) on the back plane i, there is exchange of momentum from the jet to the vortexonly if the velocity in the jet U(z,r) is greater than the velocity of the vortex U.,. The radius rer048is the radius in the plane i where U(;,re) = U.Given that the velocity profile in the steady state jet is known, the location, mass andmomentum of the vortex as a function of time can be calculated. For the incompressible jet, thefollowing assumptions are made1) The vortex structure is modelled as a whole. It is assumed that the density is uniformin the structure and that its internal velocity field has no influence on its meanvelocity.2) The vortex receives mass from the jet only. It is assume that no mixing takes placebetween the surface of the vortex and the surrounding fluid.3) The expansion of the vortex is small compare to its velocity. The momentum of thejet can then be approximated by the product of the mass of the vortex and U.The internal structure of the vortex is believed to have some effects on the penetrationof the jet (McGregor [1974], Middelton [1975]), but these effects are small, and would addgreatly to the difficulty of this analysis. Also, while most of the mass is fed by the jet, somesurrounding gas will be entrained on the surface of the vortex. However the good predictionsreported in the literature suggest that the effects of assumptions 1) and 2) are secondary. Thepurpose of the third assumption is to simplify the calculation, but if the expansion dR/dt wasfound to be significant compare to U, it could be taken into account.In the steady-state part of the jet, the axial velocity isUrn 13.8U,., (z+z0) (3.3)and the velocity at a radius r is49—ln(2) (-r)2 (3.4)UUm e r11, -where r is the radius of the inviscid core, which is taken into account for the Iransient model.In the inviscid core of length z, the axial velocity is equal to the initial velocity. The radius ris evaluated by assuming that the central core vanishes linearly with the axial distance z. Whenz is greater than z, r = 0. At the interface between the steady state jet and the vortex, plane i,we can write(3.5)‘ dtFor an incompressible jet of air into air, the density is uniform in the jet and in the vortex, andthe rate of change in volume can be written:dv (3.6)V....2I (U-U)rdrdtwhere V is the volume of the vortex, and re is illustrated in Figure 3.1. The momentum changeisaccel ofv2f Pa(0v) Urdr - surrounding - F (3.7)dt fluidwhere M is the momentum of the vortex and FD is the drag force. The momentum loss due tothe acceleration of the surrounding fluid is equal to the change in momentum of a virtual massof surrounding fluid, where the virtual mass is the product of a fraction of the displaced volumeby the density of the surrounding fluid (Milne-Thomson [1968]). For an accelerating sphere, thefraction is 1/2. The momentum change equation then becomesdtf 1 d(UV)dt2fo p (U-U) U rdr---p j” -Fr, (3.8)Equation 3.8 can be expressed as a function of U only by performing the followingtransformation:50Vp d(Uv)=p [U Zr+v dU1 (3.9)dt a dt Vdt Vdtreplacing Equation 3.6 and 3.9 in Equation 3.8 yieldsdU,, 4. f’(UU)Ud 2f’9(UU)rdr2 Fd (3.10)dt 3V o 3 V.f)The drag force isFnCD(paU2v) (itR,) (3.11)where CD is the drag coefficient, and can be approximated by the drag coefficient of a sphere ina turbulent flow. Its value can be determined according to the Reynolds number of the vortexstructure defme as Re = 2 I v. Equations 3.5, 3.6 and 3.10 can be solved by successiveiterations. The initial conditions are:zzo, U,=U0 v,=4itr at t=O (3.12)For given initial conditions, a solution for the system of equations is obtained in thefollowing manner:1) increment the time,2) guess the vortex velocity U (the previous velocity is a good guess),3) calculate ; from 3.5,4) calculate r112 and Urn for the steady state region at z=z,5) calculate the radius re where U(r,z) U,,. This radius is evaluated from Equation 3.4,replacing U by U. After rearrangement:re=rc+(r112-r) —1n() /ln(2) (3.13)6) Integrate Equation 3.6 and obtain the vortex volume V,7) integrate Equation 3.10 and obtain a new vortex velocity U,, from the momentum51equation.8) If the new value U differs from the guessed value repeat steps 3) to 7), otherwiseincrement time and repeat.A solution was obtained for the round free jet of air into air and the results are comparedwith the data of Witze that can be found in a paper by Kuo and Bracco [1982]. The comparisonis illustrated in Figure 3.2, and it can be seen that the model represents the data well. A constantdrag coefficient CD of 0.5 was used in the comparison computations. Witze matches the databetter by utilizing a drag coefficient proportional to the velocity and size of the ball at a giventime. The vortex expansion rate dR/dt was found to be in the worst case less than 5% of thevelocity U,,, indicating that assumption 3 is reasonable.EEgFigure 3.2 Comparison between computed case and Witze experiments. Case 1: U0 = 53 m/s.Case 2 U0 = 103 rn/s. In both case the diameter of the orifice is 1.2 mm.As shown briefly in section 2.1 on diesel sprays, and also shown in the literature, the tippenetration is proportional to the square root of time. This proportionality is illustrated in FigureTime (ms)523.3 where the penetration for two different cases is plotted against the square root of time. Thepenetration is scaled by the orifice radius, while the time is scaled by r>/U. The proportionalityto t’ is evident except in the early moments of the jet. The two cases are seen to collapse toa common curve, but that result is true only if the drag coefficient is independent of the vortexvelocity and size.Numerical simulation of the turbulent jet performed by Kuo and Bracco [1982] shows thatthe jet penetration is mildly dependent on the Reynolds number. They suggest that for theturbulent jet, the tip penetration should be scaled usingr0•Re°°53,and that the time be scaled withr0Re°°53/U.Witze’s experimental data are shown to be well scaled with that Reynolds numberdependency. Another interesting characteristic of the transient jet is illustrated in Figure 3.4where the tip velocity and the axial velocity of the steady state are plotted as a function of theaxial distance. It can be seen that the vortex head velocity is about half the steady-state velocityat any given point.In the literature the model is analyzed for a jet of air into air. In the following section,the model is extended to a round free jet of methane into air.3.2 TRANSIENT TURBULENT ROUND FREE JET OF METHANE INTO AIRWhen a gas with a different density is injected into air, the model must be modified totake into account the fact that the rate of change of the vortex mass depends on the extent of themixing between the gas and the air in the jet. The vortex is now composed of a mixture of twogases of different densities. Its mass depends on the respective amount of each gas. There istherefore an extra variable required to describe the vortex structure. The methane content’ ofTo keep the analysis applicable to any gas, it should be called the secondary gas content.Methane content is utilised for clarity.53180160140120100Z 1r0806040200Figure 3.3 Proportionality between tip penetration and the square root of time.8Figure 3.4 Comparison between the tip velocity and the steady-state axial velocity. U0 =53 mls,d0 1.2 mm.Axial position or tip penetration (mm)the vortex m is defined, as the mass of methane present in the vortex at a given time.54The same assumptions as in section 3.1 are made, adding the following one:- The mixture of gas in the vortex is uniform.With this assumption, the mass concentration of the vortex , can be defined asm m= 9” =_i (3.14)V TV) + TV)“1gv £uav LIVwhere is the mass of air in the vortex and m is the total mass of the vortex. Similarly thevortex density can be defined, and is related to the concentration by:Pap (3.15)PgThere are now four equations: I) the change in position, ii) the change in total vortex mass, iii)the change in methane content and iv) the change in momentum.i) The change in position of the vortex is(3.16)“dtii) The change in mass is expressed by=2fre (U-U) rdr (3.17)where p is the density at a radius r and at position ; in the steady-state section. The density isrelated to the mass concentrationPat (3.18)x(-—1) +1Pgand the concentration in the steady state part is given by:—ln(2) (r—r)2XXme2 (r1,2zc)2and Xm (z±z0) (3.19)r.The velocity U is obtained from Equation 3.4. The velocity Urn is obtained from the steady-state55solution. It is convenient for the transient case to express the axial velocity decay in the steady-state jet with an equation similar to 3.3. The decay constant can be obtained by fitting the resultsof the steady-state calculation.iii) The change in methane mass content:_27tf0apg(U_U)rd.r(3.20)where cx is the volume concentration of methane at the back plane of the vortex at a radius r.Recalling Equation 2.53 for the relationship between the volume and mass fraction, Equation 3.20yieldsdt Paj0 p (3.21)x(—-1) +1Pgiv) The change in momentum:dMv 2qrep (U-U) U zdr--p6d(UV) -F (3.22)A different transformation than for the previous case is performed here since the density of thevortex differs from then the ambient density and changes with time:dM d(pVU) d(u,,v,.) dpi, (323)dt dt V dt VVdtthis can be rearranged tod(UV) ...i dMy.j v dPv1 (3.24)dt p dt vvdtUsing Equation 3.24 in the momentum equation 3.22, replacing the density with Equation 3.18and rearranging yields(if) cliv2irfr. (U-U) U (3.25)Vx(——1)÷1PgThe density change is obtained by differentiating Equation 3.15:56dp Pa(1) Er (3.26)dt [x(_1)÷112 dtPgPa dm dmdp Pa(1) m dm dtV.... g_____________(327)dttX(_1)+1]2The solution of Equations 3.16, 3.17, 3.21 and 3.25 provides the location, total mass,methane content and momentum of the vortex as a function of time. The volume and the radiusof the vortex can be inferred from its mass and density, and the velocity from its momentum andmass. The initial conditions are the followingz,=z0 M—mU0 at tO (3.28)where p is the density of the gas at the nozzle, and r1, is the pseudo-radius so thatunderexpansion can be considered if applicable. The solution of the system of equations followssimilar steps to the ones outlined in section 3.1. More details regarding the non-dimensionalsolution of a transient jet of methane into air are given in section 3.3.2.The solution for the penetration of a round free jet of methane was obtained using thesame drag coefficient as for the air jet. Results are illustrated in Figure 3.5, where thepenetration of the methane jet is compared with the penetration of an air jet with a same orificesize and a same initial velocity2. The methane jet penetration is slower then the air jet, sincethe initial momentum of the methane jet is almost 50% smaller than the one of the air jet. Thecircles on Figure 3.5 are representatives of the vortex size, and are obtained by plotting the2 A different pressure ratio across the nozzle is required to yield the same initial velocityfor a methane jet and an air jet.57penetration at the back plane ; as well as the tip penetration z.EE0Figure 3.5 Penetrations of the air jet and of the methane jet. U0 = 256.8 m/s and r(, = 0.6 mm.The pressure ratio is smaller for the methane jet.Unfortunately, there are no experimental data to verify the validity of the model.However the comparison with the jet of air into air indicates that the model is reasonable.Compressibility effects are partially taken into account; the gas expansion in the nozzle isconsidered, but the local compressibility effects in the area close to the nozzle exit are notconsidered. By using the solution for the steady-state jet of methane, underexpanded jets canalso be taken into account in the solution of the transient jet.3.3 TRANSIENT CONICAL SHEET JET OF METHANE INTO AIRExploiting the same idea, the conical sheet jet can be modelled as a quasi steady-stateTime (ms)dzdt58conical sheet jet feeding a vortex structure. The model is ifiustrated in Figure 3.6. The vortexstructure has a toroidal shape. The assumptions are identical to the one stated in the previoussections. For the steady-state section of the jet, the velocity and concentration profiles are theones developed in chapter 2. The change in location, in total mass, in methane content and inmomentum of the vortex structure at the back plane of the torus can be expressed in formssimilar to those derived for the round free jet of methane into air.IFigure 3.6 Model for the transient conical sheet jet.I) The change in location:(3.29)ii) The rate of change in total mass:59(U-U) 2zcos () dir (U—U ) (3.30)4TtzvCOS(13)Paf dr0PgThe concentration and velocity decays are obtained from the steady-state solution.iii) The rate of change in methane content:___rX(U-U)didt =47CZvCOS(P)Paf p (3.31)X(—-1) +1Pgiv) The change in momentum:dtf r (U-U)U accel. ofdt40s(1PJOV dr- surrounding- FD (3.32)x(!1) +1PgThe acceleration of the surrounding fluid can be approximated by the case of an acceleratingcylinder, for which it is given byd(U,,.V,,) (333)a dtReplacing in Equation 3.32 and utilizing the substitution given by Equation 3.24, the change inmomentum is(i+f) (P)f’° (U-U)U dr+VPg (3.34)PaTTTF PV_r,,...The change in density is given by Equation 3.27. The drag force is proportional to the frontalarea:60FD=CD(-P6UV) (4iu (z÷R) COS (f3)R) (3.35)where R is the radius of the torus. CD can be approximated by the drag coefficient of a cylinder,that is equal to one if the vortex Reynolds number Re is greater than i0. The volume of thetorus is given byV27t2(z+R) cos (f3) R, (3.36)and the initial conditions arez=z0, U,=U0 V=272(z+1PS)cos(p) (1)2, (337)m=pV, m=m, M=mU at t=Owhere l. is the lift corrected for underexpansion if applicable. The solution is discussed insection 3.3.1. The penetration of the conical sheet jet is readily compared with the penetrationof a round jet in Figure 3.7. The pressure ratio in both cases is 2, and the size of the roundorifices was chosen so it would yield 117th of the total area of the conical nozzle (since theDetroit Diesel 71-series injectors have 7 holes). The tip penetration of the conical sheet iscompared with the tip penetration of the round jet from one of the 7 holes. It can be seen thatpenetration is approximately 30% lower for the conical sheet jet.3.3.1 Scaling and Dimensional AnalysisIn the analysis of the steady-state conical jet, some scaling factors were obtained. Thefollowing equations summarize the conditions in the steady-state part, taken at the back plane ofthe vortex, at z =;.Ir112=k_____1/R3leq 3/Rs1eq1_1Cdf2.5371ififa(3.41)61140120100806040207 ROU iD HOLEb CONIC L POPPE0u 4 1 ‘10alime (ms)Figure 3.7 Penetration comparison between a round jet and a conical jet. U0=422,8 mis, 1=0.1mm,r0=0.31 mm, CD=O.5 for round jet, CD=l for conical jet.Urn—ln(2) (1)211/2 Urnand0k1zvs/Rsl eq.1n(2) (1)211/2Xrnk2and Xrn4[Rsleqwhere 1eq is given by(3.38)(3.39)(3.40)Also621 -Pax(--—1)÷1(3.42)PgThe term (R L)1’2 is seen to be a natural scaling factor having length dimension for the jetemerging from the conical nozzle. The velocity U0 is the scaling factor for velocities. For thetransient case, the time needs to be scaled. For the round free jet, it is shown in the literaturethat r,/U0 is an appropriate time scaling factor for the round free jet (Kuo and Bracco [1982]).Following the same idea, the time can be scaled with (R l)”2/U0for the conical sheet jet. Twocases were computed and scaled using these parameters and are illustrated in Figure 3.8, whereit is seen that the proposed time scaling factor is adequate. It was shown in section 3.1 that forthe round free the jet penetration is proportional to the square root of time. The two cases inFigure 3.8 are plotted in Figure 3.9 where it is seen that the penetration of the conical sheet jetis also directly proportional to the square root of time. In Figure 3.9, the data are also scaledwith the proposed scaling parameters.Utiising the scaling factors and the steady-state Equations 3.38 to 3.42, the equationsdescribing the rate of change of position, mass and momentum of the vortex can be nondimensionalized. The non-dimensional transient vortex equations are given in appendix A. Thefollowing dimensionless parameters are first defmed:__tuL./R1. . z-j L(3.43)_____ __— mgv_________—, mT,— —L3 L3 nL3U Lra ra 0It is found that, given PJPa’ f and the steady-state constants k1, k2 and k3, the change in position,mass, methane content and momentum of the vortex can be expressed as function of thefollowing parameters:63175Zt 150VRsIac1251007550250Figure 3.8 Penetration of a conical sheet jet as a function of time. For the case illustrated,Re=2O, Cd=O.85 and CD=l.500Figure 3.9 Penetration of the conical sheet jet as a function of the square root of time. Samecases as in figure 3.8.tuoqR3I200150Zt/R10064___(344)dt*dfl?vf (i;, u) (3.45)drng,f (z, U) (3.46)dt*(z, u;,R;) (3.47)The initial conditions can also be stated in dimensionless form:at t=O z=_?, R— u=i (3.48)The solution of the system of equations is obtained by solving simultaneously Equation 3.44,3.45, 3.46 and 3.47. The general method of solution follows these steps:For O<t*<t*efld1) U is guessed,2) ; is obtained from 3.44,3) is obtained from 3.45,4) m is obtained from 3.46,5) is obtained from 3.47,6) U is computed from:*(3.49)7) if the vortex velocity and the guessed value differ, repeat step 2) to 7), otherwisecontinue.8) calculate the radius R from the mass and density of the vortex,9) calculate the tip penetration from:65z=z+2R, (3.50)10) increment time and repeat. -The tip penetration of the turbulent conical sheet jet in an unbounded space is seen to bedependent on the following initial parameters:Z tU0 3 P9) (3.51)Pagiven the steady-state constants k1, k2 and k3. The equivalent lift for a nozzle choked at the exitplane is1 =0.537CdlfH.!2 (3.52)Pa1’3.3.2 Model SensitivityThe turbulent Reynolds number for the conical sheet jet could only be estimated and itsvalue could not be obtained experimentally. Penetration computation for different turbulentReynolds number were performed in order to establish its effect on the model. The turbulentReynolds number Umrin/vt is seen in Figure 3.10 to have a small effect on the conical sheet jetpenetration rate.Similarly, the nozzle discharge coefficient is not known accurately, so the sensitivity ofthe model to its variation has been verified. It is seen in Figure 3.11 that the model is not verysensitive to a change in discharge coefficient.The drag coefficient of the vortex was approximated by the one of a cylinder given aReynolds number greater than iO. A drag coefficient 20% larger was tried and showed verysmall effect on the penetration of the vortex, as seen in Figure 3.12. For all cases, the pressureratio is 2 and the lift is 0.056 mm.66EE0Figure 3.10 Effect of turbulent Reynolds number on penetration of the conical sheet jet. Thepressure ratio is 2 and the lift is 0.056 mm.EE0Figure 3.11 Effect of discharge coefficient on conical sheet jet penetration. Pressure ratio of2 and lift of 0.056 mm.Time (ms)Time (ms)67EE00..Time (ms)Figure 3.12 Effect of vortex drag coefficient on the jet penetration. Pressure ratio of 2 and liftof 0.056 mm.684 EXPERIMENTAL APPARATUS AND PROCEDURE4.1 DESCRIL TION OF EXPERIMENTAL WORKThe objective of the experimental work was to obtain knowledge about the natural gasinjection from the prototype injector, investigating in particular the penetration characteristics andthe effects of tip geometry on the gas diffusion. Flow visualization was chosen as theexperimental method, providing the qualitative and quantitative information necessary to meetthe experimental objectives. Since experimental data regarding the conical sheet jet could notbe found in the literature, flow visualization was particularly suited to obtain a first descriptiveaccount of this type of jet’. It is interesting to note that flow visualization has been widely usedin diesel research, and specifically in diesel spray penetration.There are three methods especially suited to visualize flows involving gas of differentdensities. All of them are based on the principle that the refraction index in a medium isproportional to its density. The three methods are shadowgraph, schlieren and interferometzyphotography. Without entering into the details of each method, it can be said that schlierenphotography is more sensitive to density change than the shadowgraph method. Interferometryis interesting when actual density measurements are desired, but also requires a more elaborateexperimental apparatus. Schlieren photography was the main method employed in this project,but shadowgraph photographs were also taken. More details on the flow visualization methodwill be given in section 4.3.3.The visualization of the gas injection in a pressurized cylindrical chamber has limitations.1 Hot wire anemomeiry was also considered and would be very useful to verify velocityprofiles in the steady-state jet. In retrospect, however, it would have been difficult to obtainresults without any certain knowledge of the conical sheet. The use of a concentration probe andof laser doppler velocimetry were discarded because of their limits and difficult usage in shortduration jets. Laser induced fluorescence was also considered.69Visualization can either be done through the top and bottom of the cylinder, or through sidewindows. The curvature of the wall diminishes the potential of visualization through sidewindows; the field of view is limited when conventional optics are utilised, unless the geometryof the chamber can be modified. Alternatively corrective cylindrical lenses can be used. A topview gives only the radial aspect of the flow, withholding valuable information about theunknown flow pattern in the axial direction. For these reasons, it was decided to perform twovisualization experiments. First, injection of gas from the prototype injector into atmosphericconditions would be performed, and the jet visualized laterally. Second, the gas would beinjected into a cylindrical chamber, and visualization would be done radially. These experimentsare illustrated in Figures 4.1 and 4.2.The first method provides a basis for the penetration characteristics of conical sheet jets,and will supply data to verify the integral model used to predict jet penetration in chapter 3. Inaddition, it gives qualitative and quantitative information about axial and radial penetration, andabout the jet angle. Pressure ratios similar to or larger than the ones used in the engine can beattained, and the effect of pressure ratio variation can be assessed. Geometrical parameters suchUGHT BEAM— RADIAL PENETRATIONF- *%% OPTICAL.VISUAUZATION AREA QUARTZFigure 4.1 Experimental set 1; flow Figure 4.2 Experimental set 2; flowvisualization of jet under atmospheric visualization of jet within the pressurizedconditions. chamber.INJECTORAXIAL PENETRATIONIINJECTOR—70as the poppet lift and angle, the presence of a top wall, the presence of a bottom and side wallswith different spacing from the top wpll will also be studied.In the second set of experiments, the gas injection will be first performed into acylindrical chamber at atmospheric pressure, permitting to study the effects of the pressure riseand of the cylinder walls on the jet penetration. The pressure rise is caused by the injection ofgas into a sealed cylinder. The jet penetration can be compared to results obtained in the firstset of experiments. The initial pressure in the cylinder will be increased, while keeping the samepressure ratios as the one previously used, in order to investigate the Reynolds number effect.However, it was decided to limit the pressure in the cylinder to a fraction of the engine cylinderpressure, reducing the time, the technical difficulties and the experimental cost. It should bementioned that the early stages of injection will be hidden by the presence of the injector itself(see Figure 4.2).The effect of the swirl and of the piston motion on the jet diffusion have not been studiedexperimentally as a consequence of both technical and time constraints. As mentionedpreviously, combustion, and the pressure rise associated with it, will not be studiedexperimentally in this particular project.Each component and aspects of the experimental set-up and procedure are described inmore details in the following sections, but first similarity questions are discussed.4.2 SIMILARITYIn this section the relation between the flow visualization experimental conditions and theengine conditions is examined. As mentioned in the first section of this chapter, the conditionsof the experiments will not match all conditions of the injection in a diesel engine. In order toestablish the consequences of this incomplete similarity, the major parameters on which the jetV 71penetration depends are identified. From the observation of these parameters, the relationshipbetween the experiment and the engine condition cn be assessed.“nh 4Lseat radius Rs I i‘JoFFigure 4.3 Principal parameters relevant to similarity.Figure 4.3 illustrates the major parameters for the injection of gas into a combustionchamber. The parameters can be divided into two distinct groups. The first one contains theparameters directly related to the penetration of the free turbulent conical sheet jet (unbounded).The second group contains the geometrical parameters regarding the combustion chamber.The parameters regarding the conical sheet were identified in chapter 3 and aresummarized here: VD72z tU pt___,_L, I) (4.1)/R3l JRl Pa -The equivalent radius l ispP0.537 Cd l(1)() (4.2)Pa l)when PJPa is greater than 1.86. Tn the density ratio PIPa’ the densities of air and methane aretaken at the same temperature and pressure. The penetration is also dependent on two otherparameters that were not considered in the model. First is the Reynolds number of the flow atthe nozzle, which for large enough values was assumed to have little effect on the jet penetration.Second is the injection duration t. that was not modelled in the previous chapter. The Reynoldsnumber is already dimensionless. The injection duration can take the same scaling as the time.tU p t.U pUl_____0 g p fl 0.pS (4.3)/Rl /RJCI P0Methane will be injected in the flow visualization experiments, so that the ratio P’Pa Sroughly the same as in the engine (where natural gas is utilised). Different poppet angles 3 weremanufactured to match the ones proposed for usage in the engine. The seat radius R, of thepoppet is the same for the injector used in the flow visualization experiments and the one usedin the engine. Then if U0, l, Re and t1 are the same for the flow visualization experiments andfor the engine, the penetration of the conical jet should be the same.1) For a choked flow at the nozzle, and assuming that in both cases the temperature ofthe gas before injection is ambient, the initial velocity U0 will be the same.2) The equivalent lift must be the same. The methane to air density ratio is practically73the same as the natural gas to air density ratio. The pressure ratio can also be matched.Then, given that the nominal lift can be matched, the equivalent lift will be the same.3) The injection time t in the flow visualization will be shown to be longer than the onein the engine. Nevertheless, the effect of the injection duration on the jet penetrationwill be investigated experimentally and is discussed in section 4.3.1.4) Finally the Reynolds number will differ in the engine because the upstream pressureis higher2. With a pressure ratio of 2, and a lift of 0.1 mm, the Reynolds number inthe engine is in the order of 5x10, while in the rig, allowing for correction to the liftbecause of underexpansion, the Reynolds number for a pressure ratio of 3.5 isapproximately 4x10. Roughly, the Reynolds number in the rig is 10 times lower thanin the engine. Fortunately, turbulent jets are moderately dependent on the Reynoldsnumber. In Kuo and Bracco [19821, the turbulent round free jet is found to bedependent on Re°°53. This dependency would cause small differences between theatmospheric rig and the engine conditions. The effect of the Reynolds number wasinvestigated experimentally to determine the extent of the Reynolds number dependencyfor the turbulent conical sheet jet.The second set of parameters includes the height and diameter of the chamber at a givenpoint. These parameters can be non-dimensionalized with (R leq)1fl. The penetration thendepends on the following parameters:2 The lift could in principle be increased to increase the Reynolds number. However thereis a point where the lift can no longer be increased while conserving choked flow conditions atthe nozzle.74z 0 Pg tU0 pU0l H D (4.4)1/RJ ,/Rl P0 */R1q JRj ijR3lThe diameter of the cylindrical chamber that will be used in the second set of flow visualizationexperiments is the same as the engine chamber (series 71). The height can be adjusted. Theoffset from the top wall could also have been considered, but its effect is more qualitative thanquantitative. In the experiments, the offset will be kept the same as in the engine. The pistonshape is another factor not included in the list of parameters. A piston shape was modelled forutilization in the atmospheric rig.In summary, the experiments relate to the engine conditions in the following manner: forboth sets of experiments, the penetration should be similar to the one occurring in the engine ifthe equivalent lift (nominal lift, pressure ration and density ratio) and the initial velocity arematched and if the effects the Reynolds number is small. Because the injection duration is longerin the flow visualization experiments, the penetration would be similar only during the time ofthe injection. The similitude between the penetration in the engine and the one in theatmospheric experiments depends also on the magnitude of the sealed cylinder effect.754.3 DESCRIPTION OF APPARATUS4.3.1 Injection System And Control -In the engine the injector is actuated with a cam, that is not ideal for a flow visualizationrig. Since only one injection at a time is needed, a simpler actuation mechanism can be used.A pneumatic actuation system was chosen because it is simple and clean. Also, compressed airis readily available, and there are some compact fast-acting valves for compressed air. Theinjector and the actuator are illustrated in Figure 4.4.The pneumatic actuator was designed so that it would replace the upper part of theprototype injector. The body and internal parts of the prototype injector used for the engineexperiments were used in the flow visualization experiments. High pressure air is allowed intothe upper chamber by a fast-acting 3-way solenoid valve, causing the main plunger to force thepoppet down via an intermediate rod. When power to the solenoid valve stops, the air in theupper chamber escapes by a vent port which opens when the valve closes, and the return springcloses the poppet. The high speed valve is a 3-way Servojet HSV 3000, with an opening timeof 2 ms. The valve is operated from a controller board, which provides power to the solenoidwhen a trigger signal is input to the board. A line from the computer parallel port is used as thetrigger signal. The power is supplied by a 12V, 4 amperes regulated power supply. Compressedair regulated at 3.45 MPag (500 psig) is used to actuate the plunger, ensuring quick opening.Since the actuating pressure is smaller than in the engine, the return spring was changed for onewith an appropriate spring constant. Methane was used as an injected gas. Since a very smallquantity is being injected during each injection, and since the time between each injection isrelatively long (15 - 30 seconds), the methane is released directly into the air. A solenoid shutoff valve was placed in the gas line, and the switch kept accessible to immediately shut off thegas in case of a leak at the nozzle.76I NTERM EDIATERODINJECTOR—. POPPET CAPRETURNSPRINGPOPPETVALVEVENTSOLENOIDHIGH PRES”AIR PORT 1*UPPER CHAMBERACTUATORPLUNGERCNG PORTI0Figure 4.4 Pneumatic actuator and prototype injector.77HIGH SPEEDVALVECOM PRESSEDAIRACTUATCINJECTORC - HIGH SPEED VALVE CONTROLLERS - SHUT OFF SOLENOID VALVEFigure 4.5 Injection system.The displacement of the poppet is limited by the seat under the poppet cap (see Figure4.4). The poppet cap is screwed onto the poppet stem, allowing the lift to be varied by the extentto which the cap is screwed on the stem3. The actual lift of the poppet could be measured witha dial displacement meter with an accuracy of 0.006 mm (0.25 thousandth of an inch). The dialmeter was placed under the poppet, and measurement was taken with the poppet kept open. Theadjustment is better made when the injector is disassembled. To verify that lift values andcharacteristic times of the poppet lift were repeatable, the trace of the lift was obtained using anon-contact magnetic displacement sensor (proximitor). With the appropriate power supply, theThis is true only of the first version of the prototype injector. The newest versions havea fixed lift and a different design to limit the lift.POWERSUPPLYINJECTED GAS78sensor outputs a signal proportional to the displacement. The calibration of the sensor is 200mV/thousandth of an inch (7874 mV/mm). Calibration was double-checked with the valuesobtained by the dial displacement gage and found to be in good agreement. The output signalfrom the proximitor was recorded on a Nicolet 3071 oscilloscope, and then transferred to an 286AT computer for further analysis. The signal sent to the high speed valve triggered theacquisition on the scope so that the delay between the signal and the poppet opening would beknown. Figure 4.6 shows a typical lift trace.Preliminary results indicated that the lift was increasing due to a slow unscrewing of thepoppet cap as injections were performed. This problem was solved and subsequently the lift wasfound to be repeatable. The delay between the trigger pulse to the high speed valve and thebeginning of opening is of approximately 5 ms. The duration of opening is in the order of 1 ms,the poppet being fully open just before 6 ms. The effects of pressure ratio, actuation pressureand pulse width to the high speed valve were analyzed with the proximitor, and the results arereported in Table 4.1.The results are characterized by some scattering, partially due to the noise and thevibration of the injection system rending difficult the precise identification of the time of theobserved parameters. According to these results, the delay between the thgger signal to the highspeed valve and the beginning of opening is fairly constant at 4.6 ± 0.1 ms when the actuationpressure is 3.45 MPag. Remarkably the duration of the opening process is not very sensitive tochange in upstream pressure or nominal lift. The scattered data renders it difficult to ascertaindefinite effects when these parameters are changed. The length of the opening is approximately1.25 ± 0.1 ms., but a careful examination of the lift traces shows that in fact 90% of the opening(starting at 10% of total lift and ending at total lift) is done in approximately 0.62 ms. Thisdifference is caused by a slow rise in the early stage of pressurization, and can be seen in Figure79444asSa52-J140.5C.0.50.012 0015 0.02 0024 0.025Time (seconds)Figure 4.6 Lift trace obtained from a proximitor. In this case, the pressure ratio was 1 and thepulse width 5 ms.4.6. A minimum pulse width of 4 ms is required to obtain a full opening of the poppet.Increasing the pulse width results in a proportional increase of the total length of injection. Anincrease of 1 ms roughly increases the total length by about 3.5 ms. The actuation pressure hasa very definite effect on the transient characteristics of the opening. Smaller actuation pressureincreases significantly the length of the opening, and if too low, does not provide a completeopening of the poppet. An actuation pressure of 3.45 MPag (500 psig) was judged to be,adequate, yielding complete opening at each trial in a reasonably short time. When the injectoris operated in the engine, the pressure build-up to open the poppet is much greater (30000 psig,202.7 MPag), but the return spring is also much stronger. At this stage, the exact opening timeof the poppet in the engine is unknown, but is estimated to be 0.1 ms. The length of injection0 0.004 0.00580# AP PR PW NL BO EO CL OD TL1 2.45 1 4 4 4.49 5.44 11.26 0.95 6.772 3.45 1 5 4 4.62 5.78 15.46 1.16 10.843 3.45 1 5 4 4.38 5.70 15.66 1.32 11.284 3.45 1 6 4 4.65 5.76 19.22 1.11 14.575 3.45 1 8 4 4.63 5.77 25.39 1.14 20.766 3.45 1 10 4 4.55 5.76 31.28 1.21 26.737 3.45 3 5 4 4.8 5.94 14.78 1.14 9.988 3.45 3 6 4 4.81 5.94 19.29 1.13 14.489 3.45 3 8 4 4.65 5.92 26.2 1.27 21.5510 3.45 5 5 4 4.64 5.87 16.55 1.23 11.9111 3.45 5 6 4 4.42 5.80 21.83 1.38 17.4112 3.45 5 8 4 4.57 5.94 27.24 1.37 22.6713 3.45 1 5 8 4.37 5.63 17.83 1.26 12.214 3.45 1 5 12 4.53 5.76 18.13 1.23 13.615 3.10 1 6 4 4.30 5.92 19.01 1.62 14.7116 1.21 1 6 4 3.64 6.01 16.68 2.37 13.0417 1.03 1 6 4 3.03 7.03 14.37 4.00 11.34Table 4.1 AP : actuation pressure (MPag), PR : pressure ratio, PW : pulse width (ms), NLnominal lift (thou), BO : beginning of opening (ms, 1% of NL), EO : end of opening (ins, topof 1st peak), CL: closure (ms, 10% of NL), OD : duration of opening (ms, EO-BO), TL : totallength of opening (ms, CL-BO). t = 0 ms when signal is sent to high-speed valve.can be anywhere between 1.0 ms to 2.0 ms4. It is seen that the actuator does not provide aquick enough opening (0.6 ins) or closing (15 ms total length) to match engine conditions. Thelonger opening time should not have a major effect, since it could be corrected by saying thatGiven an engine speed of 1000 RPM, and a injection duration of 13 degrees (idleconditions), the injection length is approximately 2.2 ms. For an engine speed of 2000 RPM anda duration of 15 degrees, the injection length is 1.25 ms.81the jet starts later then the actual opening. The longer total opening will however prevent anaccurate study of the deleration rte of the jet once its feeding stops. -An important consideration linked with the lift is choking. To maintain constantoperation, the flow must be choked at the nozzle. To obtain choking, the upstream pressure toambient pressure ratio must be greater than the critical pressure ratio. Also, the area at thenozzle must be smaller than the smallest orifice size in the CNG port. Since ports in the injectorhave large lengths compared to their diameters, friction choking can occur. According toapproximate calculations using one-dimensional isentropic flow with friction described inappendix C, the maximum lift yielding choking at the nozzle for the version of the prototypeinjector employed is 0.089 mm (0.0035”).4.3.2 Atmospheric Injection Rig And Cylindrical ChamberAs discussed in section 4.1, two separate sets of experiments were conducted. The firstone was a lateral visualization of an injection in an atmospheric pressure, while the second onewas the axial visualization of the injection in a pressurized chamber (Figures 4.1 and 4.2). Inthis section the two arrangements required for these two experiments are described.The first set up is a simple adjustable holder for the injector, and is illustrated in Figure4.7. The threaded rods allow the positioning of the top or bottom wall, either for the purposeof flow visualization or for observing wall effects. Configuration #1 is used for a free injection,without any constraint on the flow. Configuration #2 positions the injector tip just below the topwall, as in the engine. The offset is 1.6 mm. Walls of different heights were used to simulatewall effects, and a model of the piston bowl could be placed under the injector. The second setup consists of a cylindrical chamber with the same inside diameter as the bore diameter in theseries 71 engine, 4.25 inches or 108 mm. The cylinder was designed by Paul Walsh, another82Total heigth: 2iriches ), cmTotal width: 8.5 x 8.5 inches, 21,6 x 21,6 cmgraduate student in the Department of Mechanical Engineering. Figure 4.8 illustrates the cylinderand its adjustable support for the flow visualization system. The aluminium walls are 6.35 mmthick (1/4”), and the quartz are 12.7 mm thick (1/2”). According to manufacturer specifications,the quartz windows can withstand a pressure of approximately 450 KPa. The cylinder is sealedby 3 gaskets, one on each side of the top quartz, and the .third one on the inside part of thebottom quartz. An 0-ring seal ensures sealing between the injector and the top quartz. Differentheight spacers were manufactured to give the possibility of varying the distance between the twoquartz.Two ports permits charging and scavenging of the chamber (scavenging is the evacuationof the gas mixture in the chamber after injection). Each port is connected to a solenoid valve.Injector holder83INSIDE DIAMETER : 4.25 “, 10.8 cmSPACING BETWEEN QUARTZ : V.IABLEMAXIMUM INSIDE PRESSURE : 400 KPaLENGTH OF CYLINDER : 6”, 15.24cmINJECTOR HOLDER QUARTZ WINDOWSSPACER\4ir‘II IIFigure 4.8 Cylindrical chamber with top and bottom quartz for flow visualization.Before injection, the input valve opens and fills the chamber with air at the regulated pressure,while the output valve is kept closed. After the injection, the output valve is opened first, thenthe input valve is opened. Scavenging occurs for few seconds, and then the output valve isclosed so that the cylinder is pressurized for the next injection. The air in the chamber mustsettle down for a few seconds before the next injection.4.3.3 Flow Visualization Set UpSchlieren photography is based on the proportionality between the refractive index andthe density. A ray of light is deflected when it passes through a medium in which the densityis changing in a direction normal to its path. The bending is associated with the light travellingat a different speed in a different refractive index medium, and the refractive index beingI84proportional to the density. The natural gas injection call be visualized using a schlieren methodbecause there is a density gradient associated with the mixing cf gases with different densities.In a typical schlieren apparatus, the test section is illuminated by a parallel beam of light,obtained by placing a light source at the focal point of a lens or concave mirror. A second lensor mirror produces an image of the source at its focal plane. A schematic of a typical schlierensystem is illustrated in Figure 4.9.If there is a density gradient in the test section, some of the light rays will be deflected,and will generate another image of the source. If at this point the image is projected on a screen,shadowgraph visualization is obtained. If a focusing lens is placed between the image and thescreen, the image and the disturbed image are superimposed, and the disturbance is not apparent.The Toepler method rends the disturbance visible by reducing the intensity of the undisturbedsource image, utilizing a knife-edge. Because the disturbed image is not affected in the sameway by the knife edge, zones of illumination and shadings will appear corresponding to the zonesof density change in the test section. The orientation of the knife-edge determines the densitygradient orientation that will be observed.The set up used to visualize the methane injection is illustrated in Figure 4.10. Twoschlieren mirrors with a diameter of 304 mm (12 inches) and a focal length of 2.4385 meters (8feet) were available in the department. Their size is more appropriate for wind tunnelexperiments, and not required for this experiment where the area of interest lies in a diameter inthe order of 127 mm (5 inches). Given the cost of optical equipment, the set up was adapted totheir size. The distance between the mirrors should be approximately 2 times their focal length.One mirror was placed at the extremity of a 3.66 m (12 feet) long table, while a smaller tablewith adjustable height and a sliding top surface allowing front and back movement of the mirrorwas designed and build to accommodate the second one. A 200 watts mercury arc lamp was85LS: LIGHT SOURCEMl, M2 : SCHLIEREN MIRRORSTS : TEST SECTIONKE: KNIFE EDGEFL: FOCUSSING LENSP: SCREEN OR PHOTOGRAPHiC PLATELSM2Figure 4.9 Beam deflection in a typical schlieren configuration.used as a continuous light source, producing a bright white light with radiation in the ultra-violetregion. The light that was not directed to the apparatus was blocked by a metallic curtain thatacts as a shield for the UV. The dimensions of the arc is estimated to 2.5x1.3 mm (Holder andNorth [1963]). The light from the source is condensed by a lens, generating a slightly magnifiedimage of the source at its focal point. In its current configuration, the magnification is around1.2, yielding an image width of 1.2x1.3 mm = 1.56 mm = 0.0615 inch 1/16th of an inch. Acircular pin-hole of 1/16” diameter was placed at the focal point of the schlieren mirror (Ml inFigure 4.10). The test section (apparatus 1 or 2 discussed in the previous section) is placed atthe focal point of the second mirror (M2 in Figure 4.10). Originally a circular knife-edge wasused since there was no preferred direction for the density gradient. An adjustable plate withMl86different size holes was designed and tried, but the manufacturing of sharp circular orifices wasnot of good enough quality, and visualization was unclear. Straight knife-edge were foundsimpler to use, and the single gradient orientation was not found to be a handicap in visualizingthe flow. The knife-edge and the pin-hole were positioned in the 3 directions by precisionadjustable holders. The light-source, the lenses, the pin-hole and the knife-edge were allsupported by optical sliding holders, while the mirrors were self-supported and providedadjustment in rotation and inclination. Some of the lenses used were not in perfect conditionand, combined with stains on the light source glass tube, resulted in a background not perfectlyclear or uniform. Nevertheless the jet appears very clearly in contrast to the background.S: LIGHTSOURCE - MERCURYARC LAMP 200WCL: CONDENSING LENS 4)= 114,3mm (4.5”), FL= 101,6mm 4”PH : PIN HOLE 4) = 1,5875mm (1116”)KE: KNIFE EDGE, HORIZONTAL OR VERTICALFL: FOCUSSING LENS 4 = 88,9 mm (3.5”), FL= 139,7 mm (5.5”)M1,M2: SCHLIEREN MIRRORS 4)= 304,8mm (12”), FL= 2,44 m (8’)TS : TEST SECTIONCAM : CAMERA0=7.5°Dimensions in mmFigure 4.10 Principal dimensions of the schlieren apparatus.NOT TO SCALE874.3.4 Picture AcquisitionHigh speed photography would be ideal for the visualization of a transient jet. In theabsence of funds to purchase a high speed video camera, a single shot camera was purchased.The history of the jet was obtained by varying the timing between the injection of the jet and thetime of exposure. Since continuous light sources were available in the department, a shutteredcamera was acquired. The camera purchased is a black and white CCD video camera, with anelectronic shutter speed of 1110000thof a second. This shutter speed was judged acceptable forthis application, recognizing however that at the early stages of the injection the image of the jetwould most likely be blurred. The principal characteristics of the camera are:- High resolution; 968 (V) x 493 (H) array,- Low light sensitivity: 0.5 lux,- Adjustable shutter speed in step from 1/60 to 1110000th of a second,- Standard 75Q video signal output,- Price with power supply and cables : approximately $2500,- Distributed in Richmond B.C. by Infrascan.Charge coupled devices (CCD) are arrays of photosensitive pixels that are very efficientphoton collectors compared to regular photographic emulsions (CCD detect up to 70% ofincoming photons, compared to 1% for photographic films). As a results they are very sensitiveeven in low light or short exposure time conditions. Solid-state cameras (CCD) usually producea standard video signal, carrying the video information at a rate of 30 frames per second. In thestandard interlace mode, each frame is composed of two fields, the first carrying the videoinformation of all odd lines, while the second carries the even lines. For each field, every pixelis charged to the extent of light received. When it is time to regenerate, the pixels are “emptiedand their charge converted to a 8 bit digital signal. For black and white cameras, this means that88each pixel detects a grey level in the range 0 (black) to 255 (white). The digital signal is thenconverted to a video signal. CCD cameras are especially well suited for image digitization, andmany areas of science now use solid-state cameras in conjunction with image digitizationsystems. This option is very attractive because it permits automatic image analysis andprocessing and eliminates film processing time and costs.An Imaging Technology PC-based frame grabber board for image digitization waspurchased from the same distributor. It was installed in a PC-AT, and the output of the camerawas directly input to the frame grabber board. The board reconverts the video signal to digitalinformation and reconstructs an image of 512x512 pixels, each of 256 shades of grey. Theacquired pictures were recorded on standard 3.5” high density computer disks. A library ofsubroutines controlling the board and permitting image processing and analysis was alsopurchased.The time between the moment the signal is sent to the actuator valve and the moment thepicture is taken is controlled by monitoring the synchronization pulses of the video signal. Thevideo signal contains vertical blanks; a portion of the signal that carries no video information andthat marks the end of a field and the beginning of the following one. The vertical blank statusis extracted from the video signal by the frame grabber board, and its value (0 or 1) placed ina special register. This register can be accessed and the value of the vertical blank monitoredby a computer program. Another indicator in the same register (a register is composed of eightbits and each bit or group of bit is assign specific information), is the odd/even status andindicates if the current field is the first (odd) or second (even) field of a frame. Figure 4.11illustrates these two indicators.By comparison, the human eye can detect approximately 30 levels of grey.89tc : time between valve actuation and expositionto : time between valve dosing signal and actuation, could beafter t=33.33 mstc - to: pulse width of signal sent to valvet=o t=33.331 frame = 33.33 msVBSI U Li Li7 UOES I I II Iodd even tcfield field I to’I . . *SGi aCqUiSi1iOfl acquire imagecount-loop wait*T image acquired during that time is the 0.1 ms exposition of the arrayFigure 4.11 Vertical blank and odd/even status indicators used in triggering control.The frame grabber board also contains control registers that allow one to decide what theboard will do next. For example, the registers can be set so that the image from the camera isdisplayed live, or they can be set so that the image will be frozen or “grabbed”. Freezing thepicture at a specific moment is the goal that must be achieved. When the control register is setto freeze a picture, the board waits for the beginning of the next frame before capturing it. Thetiming is then obtained the following way : knowing that acquisition will only occur at thebeginning of a frame, corresponding to a rise on the vertical blank status and a low on theodd/even status, the injection signal will be sent at a given time before the acquisition. Thevertical blank and the odd/even status indicators are monitored and as soon as a new framebegins, the control register is set so that the next frame will be captured. A counter is established90between that moment and the beginning of the next frame. Each frame takes 1130th of a second(33.33 ms) to complete. The counter is utilised to control the time at which the opening andclosing signals are sent to the high speed valve before the picture is taken. On the 16 MHz 286PC-AT, there are 1849 counts in 33.33 ms, including the two outputs command to the valve.Therefore it is possible to control the opening and the closing with an accuracy of 18 microseconds. In practice, the count number is not always 1849 because of other tasks the computerco-processor must do during the counting (verify state of other registers, increment time etc...).However the value the counter reaches is known and cases in which the counter did not reach1849 are rejected. The timing was verified with a Nicolet 3071 digital oscilloscope, and the erroron the timing was found to be in the order of 0.05%, except when very short times wererequired, where the error could be as much as 2% (when a delay of 0.25 ms was requested, arepeated value of .256 ms was obtained on the scope). The timing control was judged to beadequate for the experiment. The program written to control the acquisition first requests thedesired time for exposition after the opening signal to the valve, then the desired length of theopening signal. A key must be pressed to initiate the above procedure. If the count is right, thenthe picture can be saved for further processing; otherwise the operation is repeated.One problem was discovered when the first flow visualization images were obtained.Both fields of the captured frame had been exposed for 1110000th of a second, resulting in twopictures being superimposed, one at the desired time, and one 1160th of a second later. Accordingto the manufacturer specifications, a non-interlaced mode can be set, but proper functioning inthat mode could not be obtained. As a result, the second field had to be erased by removingevery other line. The resulting image suffered from being only half the resolution anticipated.To somewhat mend this problem, a reconstruction program was written; this will be discussedin the next section. Reconstruction was performed immediately before saving the pictures.91The system described above was found to be very practical. Results from adjusting theschlieren system or from different cases were immediately seen, offering a distinct advantage onregular photography. Automatic processing of the picture was also found to be a useful toolwhen consistent quantification of a large number of images must be performed. Of course, it isnot high speed photography, and it is expected that irregularity in the jet will cause the timehistory data to be a bit scattered. Repeatability will be investigated in the next chapter. Otherdisadvantages are the large memory space required by each picture, and the limitations inproducing good quality hard copies of the picture.Figure 4.12 and Table 4.2 summarize the experimental set up.4.4 PICTURE ANALYSISBeside general qualitative observation of the picture, the penetration of the jet in timemust be obtained and compared with the analytical prediction. A program was written toautomatically calculate the penetration length from the digitized picture. Automatic processingensures greater consistency than a manual approach, and also reduces the time required foranalysis.The picture is composed of 5l2x5l2 pixels, each with an integer value between 0 and 255corresponding to a grey level. The value of each pixel can be accessed, modified and replaced,allowing for two categories of processing : image enhancement and image analysis. Imageenhancement permits one to improve the visual aspect of some characteristics of the image.92INJECTION SYSTEM AND CONTROL1 Prototype injector with pneumatic actuator (fig. 3.X). Compressed air at 500 psigis admitted in actuator by high speed valve (HSV 3000, Servojet). Usual lift is.004” or 0.1 mm. 90% of poppet opening occurs in 0.6 ms. Total duration is inthe order of 15 ms. Delay between trigger to HSV and poppet opening is 5 ms.2 Control board for the HSV, power from power supply (4) is allow to valve whentrigger is received from computer.3 Trigger signal taken on parallel port of computer (5V)4 Regulated 12V power supply, 4 Amps.5 Test rig, either straight support or cylinder (Figures 3.7 and 3.8)6 Compressed air and regulator7 Compressed methane and regulator8 Emergency shut-off valve, powered from power supply, manual switch nearcomputerFigure 4.12 Over all experimental set-up. Numbers refer to Table 4.2.NOT TO SCALE93FLOW VISUALIZATION9 St Concave Mirror, 12” diameter, 8’ focal length10 2.Concave mirror, 12” diameter, 8’ focal length11 Adjustable support table12 200 Watt continuous wave mercury arc lamp13 Condenser lens, 4.5” diameter, 9” focal length14 3-axis adjustable pm hole, 1/16” diameter15 3-axis adjustable knife-edge16 Focusing lensPICTURE ACQUISITION17 Pulnix TM-745 high resolution CCD shutter camera. 768x493 pixels array.1/0000thof a second shutter speed.18 Shutter control SC-745 for camera. Choice of manually selectable shutter speedfrom 1160th to1/0000th of a second.19 Power supply 12P-02 for Pulnix camera and power cable K25-12V20 Imaging Technology PCVISION Plus board, with ITEX PCplus subroutine library21 80286 PC AT Computer from ANO.‘able ‘i.z iuhimary ot experimentaL set up ana equipment.Image analysis extracts from the image some specific quantity.The first processing performed on theimage obtained from the flow visualization is renstructimage reconstruction. As previously ililii i iiiiiiidiscussed in the last section, every other line i i_’ki i i i i i i I I I II I I LU1+1____________________hadtobeerasedbecausetwopictureswere il”iiiiiiiiiiiiiiisuperimposed. The image can be improved j -0 J - mby giving the erased pixels a value based on Figure 4.13 Rows of pixel. The row i must beits immediate neighbours. Although complexreconstructedalgorithms exist that consider the values and the gradients associated with a large number of94pixels in the neighbourhood of the pixel to reconstruct, it was decided to use a very simplealgorithm, mainly because the long processing time associated with a complex algorithm appearedunjustified by the accuracy gain. The algorithm employed is the following one: given a row iof pixel to reconstruct (see Figure 4.13), the pixel at position i,j is given by the value:pix(ij) =- [pix(i—lj) +pix(i + 1 ,j)] (4.5)The quality of the reconstruction was verified by comparing the reconstructed image of adeliberately altered image with the original. Subtracting these two images revealed the situationswhere the reconstruction is not perfect. In general it was found that the reconstruction was verygood, except in areas containing sharp curved edges.Once the image is reconstructed, the contour can be found. The following steps,illustrated in Figure 4.14, outline the principle6:1-Subtract from the image to analyze an image of the background. The areacorresponding to the jet is isolated, minus a low level background difference due tonoise, vibration and air movement.2-Threshold the resulting image. The threshold will give a value of zero (black) to allpixels that are less then a fixed value, and 255 (white) to all the others. The thresholdvalue is typically fixed to 8 or 3%. The resulting image is a white jet on a blackbackground.3-Scan the image and detect edges, recording the coordinates.Once the coordinates of the edges are known, the radial penetrations r1 and r2 and the6 The algorithm that was used to find the contour of the jet is different than the usual edgedetection algorithms usually employed. The method described was preferred because it identifiedonly the edges of interest by contrast to all edges present inside and outside the jet, resulting ina simpler algorithm required to obtain the contour coordinates.951)2) thresholdIscan3) -• :__apixel valueFigure 4.14 Principal steps of contour finding.axial penetrations Yi and y2 are computed (illustrated in Figure 4.15). Their real dimension isobtained from previously-defined scaling factors. The penetration Yi and Y2 are taken asaverages. The apparent angle of the jet can also obtained. It is called the apparent angle becauseit does not necessarily correspond to the axis of the conical sheet jet. It is more an indicationof the travel tendency of the jet. Also a general penetration can be obtained from r and y suchas p = (r2+y)”. This will however overestimate slightly the actual penetration. Radial and axialpenetrations are illustrated schematically in Figure 4.15. A manual measurement subroutine wasalso written so that measurement between two points indicated with the mouse could be obtained.The accuracy of the method was evaluated by taking picture of objects of knowndimensions and comparing the value obtained with the automatic measurement program. It was96found that the automatic programoverestimated slightly the size in a mannerproportional to the threshold value. Thephenomena is caused by the presence of asmall region of shade immediatelysurrounding the objects. This region of shadeis small, but is considered “the object”, by the Figure 4.15 Axial and radial penetration.program. With a threshold value of 3%, theerror on different dimensions is of the order of 0.8 mm. For a threshold of 8%, the error dropsto 0.6 mm. Manual measurements (pointing the edges of the object with the mouse on thedigitized picture) yielded dimensions within 0.4 mm of the real values. It must however be saidthat the measurement depends on the scaling, that is done manually by pointing the edges of awell defined object of known dimension in the picture. The overall uncertainty on themeasurement of the jet penetration is in all cases less then 1 mm.4.5 EXPERIMENTAL CASES AND PROCEDUREThe experimental cases were chosen so that they would provide sufficient informationregarding the effect of a given parameters. As previously discussed, the parameters to study are:•pres sure ratio,•tip geometry: includes angle and lift,.environment: includes effect of top wall, bottom wall at different distances from the topwall, and sealed cylinder,•duration of injection,97•Reynolds number.The effect of these parameters will be determined by looking at the peneiration rate of the jet andat its distribution. Table 4.3 lists the main experiments to bç performed. The injection in a freeenvironment (experiments #1, 9 and 13) will permit to verify the validity of the model proposedin chapter 3. The angle effect can be studied by comparing cases 1, 9 and 13. Cases 1, 2 and3 should reveal the effects of varying the lift. The duration of the injection on the penetrationwill be observed in case 8. Many cases provide information about the effects of top wall, bottomplate and sealed cylinder. The repeatability of the injection is investigated in case 4. Finally,the Reynolds number effect will be observed in cases 16, 17, 18.Once the set-up is installed to study specific parameters, the light source is turned on andallowed to warm-up for few minutes. The desired pressure ratio is adjusted and pictures of thejet are taken at different times following the trigger signal to the high speed valve. The firstpicture taken is always the one of the undisturbed background, and must be retaken every timea new configuration is used, or the schlieren system is adjusted. The pictures that are accepted(count is right, and no major irregularities) are reconstructed and saved. Once all the requiredpictures for a given configuration and pressure ratio are done, the latter can be modified and a# environment lift j3 PR PW times (ms)(mm) — (ms)1 free 0.056 10 1.5, 2, 5 5 .25, .5, .75, 1,1.5, 2, 3, 5, 102 free 0.081 10 2, 5 5 .25, .5, .75, 1,1.5, 2, 3, 5, 103 free 0.15, 10 2, 2.64, 5 .25, .5, .75, 1,0.2 — 3.43, 5 1.5, 2, 3, 5, 104 repeatability 0.056 10 1.7,5 5 1, 3985 top wall 0.056, 10 2, 2.64, 5 0.5, 0.75, 1, 1.5,0.2 3.43, 5 2, 3, 5, 106 top and bottom wall H=17.8 0.056 10 2, 5 5 1, 2, 3, 5, 10mm, 7.95 mm, 14.25 mm —7 interrupted jet 0.056 10 2, 5 5 1, 2, 3, 5, 108 free 0.056 10 2 5, 6 1, 3, 5, 10, 11,12, 13, 14, 15,16, 17, 189 free 0.081 30 2, 5 5 .25, .5, .75, 1,1.5, 2, 3, 5, 1010 top wall 0.081 30 5 5 1, 2, 3, 5, 1011 top and bottom wall H17.8 0.081 30 5 5 1, 2, 3, 5, 10mm, 7.95 mm —12 top and bottom wall + 0.081 30 2,5 5 1, 2, 3, 5, 10interruptions13 free 0.056, 20 2, 2.64, 5 5 1, 2, 3, 5, 100.214 top waIl 0.056 20 2,5 5 1, 2, 3, 5, 1015 top and bottom walls, H = 0.056 20 5 5 1, 2, 3, 5, 1038.1 mm, 14.25 mm —16 in-cylinder Pa = latm (not 0.2 10 2.64, 3.43 5 1, 2, 3, 5, 10pressurized)17 in-cylinder Pa 2, 3 and 0.2 10 2.64 5 1, 2, 3, 5, 103.7 atm18 in-cylinder Pa = 2.85 atm 0.2 10 3.43 5 1, 2, 3, 5, 10T_ ——able 4.3 List of experiments performed.new set of picture taken. When all the pressure ratios required for the given configuration aredone, the easiest parameter to modified is changed, and the process is repeated.995 RESULTSThe results regarding the parameters studied with the flow visualization and with themodel are presented in the following discussion. A conical sheet jet is first examined, and thereproducibility is discussed. In section 5.1, the penetration rate of a conical sheet jet in anunbounded space is discussed, comparing experimental results with the model developed inchapter 3. The effects of the upstream pressure, lift and poppet angle on the free jet and thescaling of the results are also addressed. In the second section, the effects of the environmenton the jet are discussed. In section 5.3, the implications of the results for engine operation areexamined.Figure 51 Schlieren photography of the free conical jet sheet at 4 different times.lift is 0.056 mm, the upstream (tank) to atmospheric pressure ratio is 5, and the poppetangle is 10 degrees.Figure 5.1 illustrates a typical jet progression in atmospheric conditions without wall100constraints. For the case illustrated the upstream pressure, the lift and the poppet angle arerespectively 506,7 kPa (5 atm), 0.056 mm and 10 degrees. The schlieren was obtained with ahorizontal knife edge. In the jet, intense zones of blaãk or white indicate large densitydifferences with the surrounding. The abrupt change between the black zone and the white zonein the vicinity of the nozzle indicates a change in density gradient sign, also identifying amaximum density at that junction. Schlieren photography is sensitive to all planes normal to thelight beam, rending difficult the density analysis of a two-dimensional representation of a three-dimensional jet. The axis visible at the junction of the black and white zone is not necessarilythe axis of the jet, defined as the location where the velocity and the methane content aremaximal at any normal plane away from the nozzle. The schlieren of the three-dimensional jetshould yield a visible axis lower then the actual axis of the jet. The visible axis angle in Figure5.1 is approximately 25 degrees, comparatively with the poppet angle of 10 degrees.The jet in Figure 5.1 is not evenly distributed on either side of the axis, whether thevisible axis or the real axis is considered. The jet is seen to develop more on the bottom sideof the conical sheet. In Figure 5.4, in which the jet from the same nozzle is seen but with alower pressure ratio, the jet appears bent in the last frame. With larger angle poppets, thisphenomenon causes dramatic effects on the jet, as it is discussed in section 5.1.5. The jetdistribution differs then from the geometry of the transient conical sheet model proposed inchapter 3. The observed curvature is attributed to the lower pressure associated with airentrainment taking place in the enclosed area formed by the conical sheet, and is discussed insection 5.1.5.The jet is also seen to propagate further and with a slightly different angle on the rightside. This difference is attributed to an unequal opening of the poppet. For this reason,measurements on both sides of the injector were always taken.101The Reynolds number of the jet, define as p U0 1 I v, is approximately 7000 in Figure5.1. In the engine the Reynolds number is an order of magnitude higher. Reynolds numberdependency is discussed in section 5.2.5 and shown to be small. Results obtained from theinjection of gas in atmospheric conditions should then be representative of the jet behaviour athigher Reynolds number.The four frames illustrated in picture 5.1 are single shots from different injections, andconsequently the first question to be addressed is the reproducibility of the experiments. Keepingthe conditions constant, several pictures of the jet at the same time after the beginning of theinjection were taken. This reproducibility experiment was done for two different cases anddetails of the results are reported in appendix B. For the first case investigated, 8 injections withthe 100 angle poppet were photographed, with an upstream pressure of 1.7 atm and 1 ms afterthe beginning of injection. The average penetration’ of the jet was 11.5 mm on the left side and12.6 mm on the right side. The standard deviation was 0.4 mm (3.5%), with a maximumdeviation from the average of 0.7 mm (6.1%). For the second case, 9 injections from the samepoppet were photographed, this time with an upstream pressure of 5 atm, and 3 ms after thebeginning of injection. The average penetration for this second case was 29.9 mm on the leftand 35.1 mm on the right. The standard deviation was 0.9 mm (3%), with a maximum deviationfrom the average of 1.7 mm (5.7%). The standard deviation indicates that in most cases thepenetration is reproducible to within 1 mm. While penetration data will show a definite trend,the variation from injection to injection results in a source of uncertainty on the measurementsgreater than the uncertainty atthbuted to the measurement procedure discussed in chapter 4.‘The penetration of the jet is taken as the distance between the nozzle and the far-most pointreached by the jet radially (left or right) and downward.1025.1 FREE PENETRATION OF THE CONICAL SHEET JET5.1.1 Comparison Between I’de1 and ExperimentThe model does not take into account the jet curvature observed in Figure 5.1. However,for the 100 angle poppet, the jet distribution is still reasonably close to the one utilised in themodel. Figure 5.2 compares the penetration predicted by the model described in chapter 3 withresults obtained experimentally, for the 100 angle poppet, a lift of 0,056 mm and three differentupstream pressures. The experimental penetration values are measured from schlierenphotographs. In the model, the discharge coefficient is set to 0.85, the turbulent Reynoldsnumber to 20 and the drag coefficient to 1 if the Reynolds number of the vortex is greater thaniO. In addition, the conditions at the nozzle are assumed to be those of a choked nozzle. It isseen that the general trend is correct, and that the model response to different pressure ratiocorresponds to experimental observations. However, the predicted penetration is significantlylarger than the one observed experimentally.The difference between the model and the experiments can be the consequence of anumber of factors. There are numerous assumptions made in the model which could affectsignificantly its accuracy. The first assumption to consider is the assumed geometry of the jetthat differs from the geometry observed experimentally. The geometry of the jet and themechanism that causes it are only partially known through schlieren photography. Consequently,the model could not be modified to consider this difference2. The sensitivity of the model tothe turbulent Reynolds number, the discharge coefficient and the drag coefficient is mild as it wasshown in section 3.3.3 (Figures 3.10 to 3.12). A realistic change in any of these parameterscould not render the model closer to the experimental values.2 The modification might be difficult to implement to the simple model.1034002OFigure 5.2 Comparison between the model and experimental results for the penetration of theconical sheet. = 100 , 1 = 0,056 mm. In the model Re = 20, Cd = 0.85 and CD = 1.In calculating the initial velocity in the model, choking at the nozzle exit was assumedand pressure losses in the injector were neglected. Since the CNG ports in the injector are ofsmall diameter and are relatively long (large LID), the flow reaches high subsonic Mach numberin the smallest passage. An investigation was made to see if the pressure drop is significantthrough these small passages, and to determine the conditions that cause internal friction choking.Approximate calculations using one dimensional isentropic and adiabatic flow in pipes withfriction were conducted and are described in Appendix C.The calculations are based on the assumption that the upstream pressure remains constantduring the injection and that the flow becomes steady in the injector. The latter assumption isacceptable in the case of the flow visualization experiments because the tip reservoir contains lessTime (ms) Time (ms)104then 10% of the injected gas mass. The tip reservoir is the annular space surrounding the poppetvalve in the tip of the injector, and can be seen in Fit’ re 1.2. The presence of sharp edgesbetween ports of different sizes and potential flow separation were not considered in thesecalculations. Calculations suggested that, for the gas port dimensions of the test injectoremployed in the experiments, the maximum lift that can be set without occurrence of internalchoking is approximately 0.089 mm. Calculations also showed that combined pressure losses inthe gas ports could lead to a pressure drop of 16% for a lift of 0.056 mm, and of 22% for a liftof 0.081 mm. The model was modified to consider a pressure drop according to initialconditions, and new results for the same case are illustrated in Figure 5.3. The details of themodifications are given in Appendix C. The modified model yields a penetration closer to the60g40C200Figure 5.3 Penetration of the conical jet sheet; same conditions as in figure 4.1. The model wasadjusted to consider pressure drop inside the injector.Time (ms) lime (ms)experimental one, but there is still an overestimation in the order of 5% for the higher pressure105ratio and of 20 % for the lower pressure ratio. It can {e seen that the model predicts a fasterpropagation in the early moments than the one observed experimentally, especially for the lowerpressure cases, suggesting that the modelling of the conical jet is inadequate in the early momentsof propagation.5.1.2 Effect of Pressure Ratio and Lift on PenetrationFigures 5.2 and 5.3 indicate a strong pressure effect. Scaling results presented in chapters2 and 3 indicate that the penetration z and the time t can be scaled with the following factors:z tUz=____t= ° (5.1)/Rsleqwhere R is the seat radius, U0 the nozzle velocity, and l is the equivalent lift given byl,=l f 1.86Pa a (5.2)pP Por 1 O.537 1 C .1 —s if —>1.86eq dp1.86 is the critical pressure ratio for methane. In chapter 3, the penetration of the modelledconical sheet jet was shown to be directly proportional to the square root of time. This can alsobe observed experimentally (shown is Figure 5.9). Applying the scaling from Equations 5.1 and5.2, and assuming a pressure ratio greater than 1.86, the penetration can be expressed asz JU (R51Cdf.! “0)1/4 (5.3)The penetration is directly related to the square root of time, to the square root of the initialvelocity, to (Pg/Pa)1”4’and to 1114, and to (Po/Pa)”4if the jet is underexpanded. If the pressure ratiois under the critical one, an increase in pressure will yield a higher velocity and a higher densityratio. Once the flow is choked at the nozzle, the initial velocity remains constant, and anincrease in pressure will yield an increase of l. In both cases, an increase in pressure ratio106causes an increase in penetration that is observed experimentally.Jets emerging from nozzles with lifts of 0.056 mm and of 0.08 1 -mm are presented inFigures 5.4 and 5.5 respectively. The pressure ratio is 2 and the poppet angle is 10.Corresponding penetration are plotted in Figure 5.6, along with other cases. For a same pressureratio, the penetration observed experimentally does not differ significantly for different lifts. Theobserved jet from the larger lift nozzle has a slightly larger downward penetration, and occupiesmore space (indicates a larger volume) then the jet from the smaller nozzle. In addition, the jetfrom the larger lift has a smaller downward curvature.The model prediction corresponding to the experimental results plotted in Figure 5.6 arepresented in Figure 5.7, without correction for the pressure drop inside the injector. The modelclearly shows a dependency of the penetration on the lift, that is not reflected by the experimentalpenetration measurements. The apparent insensitivity of the penetration to the lift in theexperiments can be explained in part by the conditions of the flow inside the injector. Two casesmust be addressed: i) choking conditions occur at the nozzle and internal friction is considered,ii) the lift is too large and internal choking occurs.i) When the flow is choked across the nozzle of the injector, an increase in lift also causesan increase in Mach number in the gas ports, leading to a larger pressure drop. The model wascorrected for the pressure drop and penetration results obtained with the corrected model arepresented in Figure 5.8. In Figure 5.8, the curves for lifts of 0.056 and 0.08 1 mm were correctedfor friction. The difference between the penetration is seen to be significantly smaller than inFigure 5.7.ii) If the lift is too large, the flow is choked internally. There is a maximum mass flowthat can be maintained given the upstream pressure and temperature. An increase in lift whileinternal choking occurs will cause a lower nozzle velocity and therefore a lower momentum.107Along with internal choking, the flow is also subject to friction, reducing the actual stagnationpressure at the nozzle. In Figure 5.6, the maximum lift is 0.15 mm, lift at which the flow isinternally choked. Values for the velocity and the density at the nozzle for the internally chokedflow were obtained (Appendix C) and were used in the model. The curve for the lift of 0.15 mmin Figure 5.8 depicts the prediction of the model when it is corrected for internal choking. Thecorrected model does predict a lower penetration for the larger lift of 0.15 mm than for smallerlift. This is not reflected in the experiments, where the lift is in fact slightly higher for the largerlift. This can be explained by the fact that the flow does not choke instantly as the poppet opens.In the early moments, the flow is choked at the nozzle, resulting in a high initial momentum.This high initial momentum is sufficient to compensate for the subsequent drop in velocityassociated with internal choking.5.1.3 ScalingThe experimental data were scaled according to the factor proposed in Equations 5.1 and5.2, and the results are reported in Figure 5.9. These scaling factors are calculated from theexpected conditions at the nozzle. The real pressure ratio, density ratio and discharge coefficientare not known accurately. The corrections performed to account for internal flow conditionswere considered in the scaling parameters. The experimental points are piotted as a function ofthe square root of time, to which they can be seen to be directly proportional, except in the earlymoments. It is seen that all cases lie on lines with similar slopes, indicating that the penetrationfar from the nozzle is scaled appropriately. However, higher pressure cases lie on a line offsetfrom the lower pressure cases. This seems to indicate that the jet development at the beginningof the injection depends on the pressure ratio. It should be noted again that the conditions at thenozzle are known only approximately. The scaling for the model is also indicated in Figure 5.9.The slope of the predicted penetration is similar to that of the experimental one, but is seen1085.4 - - conical sheet jet from thelift of 0.056 mm.conical sheet jet from the 100 angle poppet. Pressure ratio of 2 andlift of 0.081 mm.E00109X I — O.O5&m, P0 — P10 I — 0.058mm. P0 — P2__* 10.OBlmm,Po-P1E1 I—0.OBlmm,Po—P2+ I—0.l5mm,Po—P1I—0.l5mm,Po—P20Figure 5.6 Variation of the penetration with lift and upstream pressure, according toexperiments.506,7 kPa202,7 kPaTime (ms)120100Time (ms)Figure 5.7 Variation of the penetration with lift and pressure ratio as predicted by the model.110Figure 5.8 Variation of the penetration with lift and upstream pressure as predicted by the modelcorrected for internal flow behaviour.Figure 5.9 Experimental data and model scaled with the factors given in Equation 5.1. Thepenetration is plotted as a function of t4’1.E0‘Po 506,7 kPa‘P0 — 202,7 kPaInternally chokedTime (ms)160120804001-0.056, Po-1 52.0? 1-0.056, F’,_7MODELo 1-0.056, Po-506.7[] 1-0.081, Po-202.71-0.081 ,Po—506.7EJ0%aó 60 90111to be shifted towards the left on the graph, indicating again that the difference between themodel and the experiments occurs mainly in the early moments of the jet;5.1.4 Effect of Injection DurationIn the penetration results shown so far, the poppet remained open over the time periodthe penetration was considered. In the engine, the injection duration is shorter, between 1 and2 ms depending on operating conditions, and it is of interest to characterise the penetration whilethe injector is closed. Although the actuation used in the experiments does not permit a durationas short as that which occurs in the engine, it is possible to look at the jet penetration just afterthe actual closing time of the injector. For pulse widths of 5 ms and 6 ms (the length of thesignal sent to high speed valve) the injection durations are approximately 11 ms and 14.5 msrespectively.5.10 Free conical sheet jet from 100 angle poppet. Pressure ratio of 2, lift of0.056 mm. Post-injection penetration.112Pictures were obtained for the jet from a 100 angle poppet before and after the closingof ‘e poppet for both pulse widths. Figure 5.10 shows the jet at different stages for a pulsewidth of 6 ms. At 16 ms, no jet appears at the nozzle, and the jet penetration does not increasesubstantially after the end of the injection. The penetration data for two different pulse widthsare plotted as a function of t in Figure 5.11. The straight line is a fit to the previously obtainedpenetration data before the poppet starts to close (at approximately 7 ms for PW=5 ms). Thedeviation from the proportionality line indicates that the jet quickly slows down once its feedingstops. The scattering of the data is in part due to the difficulty of identifying low densitygradient areas characteristic of the jet edges far from its origin. For the same reason, theseresults are not conclusive regarding the magnitude of the change in penetration rate. For a pulsewidth of 5 ms, the jet is found to deviate from its original penetration rate before the injectionis finished (at approx 11 ms). This is a consequence of the long closing process of the poppet.At 10 ms (3.1 ms”2), the penetration is seen to be less then if the poppet was still open.5.1.5 Effect of Poppet AngleThe distribution of the jet within the chamber must provide good mixing between the gasand the air, and must be such that rich zones of fuel are avoided. The angle at which the jet isinjected is a major factor affecting the jet distribution. To relate the distribution to the angle,pictures of injection from poppets with seat angles of 10, 20 and 30 degrees were taken.Different pressure ratios were tried for each angle, since the pressure ratio also has a large effecton the distribution.The jet distribution for the 100 angle poppet is shown in Figures 5.1, 5.4 and 5.5. Figures5.12, 5.13, 5.14 and 5.15 were obtained for the 20° and 30° angle poppets at pressure ratios of2 and 5. The curvature observed for the 10° angle poppet jet radically change the jet distribution1130Figure 5.11 Penetration data plotted versus the square root of time. The deviation from thedirect proportionality results from the closing of the poppet.of the jet from the 200 and 30° angle poppets. Early after its emergence from the nozzle, the jetfrom the 20° angle poppet bends downward. For a relatively low pressure ratio (2) the jetcollapses under the poppet completely and propagates downward. For higher pressure ratio, thejet avoids the collapsing, and propagates radially with a very defmite curvature. The phenomenais even more definite for the 30° angle poppet, where the jet collapses very soon under thepoppet and propagates directly downward with little radial penetration, even at higher pressureratio.It is also observed for the 30° angle jet that the jet takes a preferred orientation after ithas completely collapsed (clearly seen on the 10 ms frame in picture 5.13). This phenomena is114angle poppet. 1 ratio of 2, lift ofFigure 5.13 Free conical sheet jet from0.056 mm.angle poppet.115- .14 Free conical sheet jet from 300 angle poppet. Pressure ratio of 2, lift ofangle poppet.0.081 mm.116less accentuated for higher pressure ratio.The process believed responsible for the observed curvature is described in this paragraph.The conical sheet forms an enclosed space under the poppet. Air entrained by the incoming jetat its inside surface depletes the air in this enclosed space. Consequently, the pressure in theenclosed space is reduced, and air from the surrounding flows in. There is a pressure differencebetween the top and bottom surfaces of the conical sheet. The curvature of the jet is attributedto the effect of this pressure difference on the sheet. A schematic of the mechanism is illustratedin Figure 5.16. The extent of the curvature is related to the velocity of the jet and to the pressuregradient. Under some combinations of angle and velocities, the jet is brought completely towardsthe middle and the conical sheet collapses under the poppet.Gas penetration directly towards thepiston is judged unacceptable for engineoperation, since it leads to a rich areaunderneath the poppet and poor overall airutilisation. The question arises if thisphenomenon is likely to occur in engineoperation. In the flow visualization Figure 5.16 Proposed curving mechanism forconical sheet jet.expenments, piston motion was notinvestigated; numerical simulation done by Paul Walsh shows that the piston motion has adefinite effect on the jet. For the 200 and 30° angle poppets, the jet does not propagatesdownward to the same extent when the piston goes up. However the jet does propagatesdownward under the poppet when the piston goes down. In either case, the jet diffusion fromthe .30° poppet is inadequate. Consequently, the usage of 30° angle poppet of the prototypeinjector employed in the engine was discontinued, and two other poppets with respective angles117of 10 and 20 were manufactured. -5.2 EFFECT OF GEOMETRICAL CONSTRAINTS ON JET5.2.1 Top WallIn the engine, the nozzle is offset by approximately 1.6 mm from the top wall of thecylinder. This condition was reproduced and it was found that the top wall has a definite effecton the jet behaviour. Figure 5.18 depicts clearly that the jet emerging from the 100 angle poppetclings to the top wall early in its progression, and subsequently propagates along the top wall.The clinging is caused by a similar phenomenon that caused the jet to collapse under the poppet.The air entrainment between the top surface of the jet and the top wall creates a low pressurezone acting on the sheet, forcing the jet to cling to the top wall. The immediate effect of theclinging is to reduce the extent of mixing between the jet and the air. This is clearly seen bycomparing the area occupied by the jet in Figure 5.18 with Figure 5.1. The total penetration isslower by about 10% for the jetpropagating along the wall as itCcan be seen on Figure 5.17. For80the jet emerging from the 20°angle poppet, a similar phenomena 40occurs. The jet first propagates TOP WALL PR -220 * FREEPR—2downward but is then attracted : - 0 TOP WALL PR -5D FP.EEPR—5towards the top wall. The 0 2 4 8 10phenomenon is depicted in Figure Time (ms)5.19. Once it has made contact Figure 5.17 Penetration comparison between the free jetand the jet propagating along the top wall.with the top wall, the jet continues118rlhre 5.18 E - t of the top wall on the conical sheet jet. 1 ° angle poppet, pressureratio of 5, lift of 0.056 mm.of the top wall on 1ratio of 5, lift of 0.056 mm.conical sheet jet. 2w.119its course along it, while the mass of gas initially propagating downward continues to diffuse.For the 300 poppet, the jet is unaffected by the top wall3.5.2.2 Bottom WallThe bottom wall represents a static piston placed at a distance H from the top wall.Pictures were taken with a bottom wall at different heights H for all 3 poppet angles in order todetermine the principal effect of the wall on the jet. Figure 5.21 shows the propagation of thejet from a 100 angle poppet between two plates distant of 14.25 mm. The jet travels along thetop wall until its thickness is in the order of the distance H between the two plates. The jet thenpropagates touching the two walls, permitting mixing with the air only at its tip. Figure 5.20shows the radial penetration of thejet as a function of time for the100 angle poppet and for three80different heights H. The radial50penetration for the case without a --.---.E40Ebottom wall is also indicated. For030V__________the heights observed, the jet20 + TOPWALLONLYpropagates radially faster in the A * H -17.810 / 0 H-14.25beginning and then slows down E1 H - 7.980 4because of friction on both top and Time (ms)bottom walls. The same Figure 5.20 Penetration for the100 angle poppet withbottom wall at three different heights. Pressure ratio of 5.phenomena is observed for a Lift of 0.056 mm.The jet from the 30° is unaffected by the top wall only if the nozzle is offset from the topwall. When the nozzle is placed flush with the top wall, the jet also clings to the top wall.120pressure ratio of 2. This phenomena indicates that within a certain range, the wall has an effecton the jet even before the jet touches the wall. -The jet emerging from the 200 poppet travels initially downward. When the bottom wallis at 14.25 mm from the top wall, the jet impinges onto the bottom wall to which it clings. Thepropagation continues radially and soon the jet clings also to the top wall. For the largerdistances between top and bottom wall tried, the jet clung to the top wall. The jet from the 20°angle is seen to have two different behaviour depending on the distance of the bottom wall.Either the bottom wall is close and the jet clings initially to it before filling the gap between thetwo walls, or it clings to the top wall only. For both the 10° and 20° poppet, a distant wall didnot have any effects.For the 30° angle poppet, the jet impinges on the bottom plate, and then propagatesradially clinging on the bottom plate, as seen in picture 5.22. When the jet reaches the bottomwall, air no longer access the enclosed area inside the conical sheet. As a result, a recirculationring is formed under the poppet. This recirculation zone is also associated with a low pressurezone forcing the sheet to curve. Results of computer flow simulation of the above jet by PaulWalsh using a modified TEACH Code are illustrated in Figure 5.23. The recirculation and thecurvature of the jet are clearly seen.The radial penetration rate between the two plates is similar for each poppet angle, exceptat the beginning of the injection, where radial penetration is slower for jets diffusing towards thebottom wall.5.2.3 Conical Sheet Jet InterruptionAs it has been shown, the conical sheet jet is subject to deviation from its expectedcourse. Either it clings to the top wall, or it propagates toward the piston, reducing greatly the121Figure 5.21 Propagation of the conical sheet from the 100 angle poppet between twowalls. H = 14.25 mm, PJPa = 5, lift = 0.056 mm.Figure 5.22 Propagation of the conical jet from the 3utWO WallS. H = 17.1 flm, Pa/Pa = 5, lift = 0.081 mflipoppet betweenCOMBUSTION CHAMBER VELOCITY FIELDTIME AFTER INJECTION START (see) = 0.00359VELOCITY SCALE: __, 100 rn/sec2 2 2 2UJULLJ. IFigure 5.23 Velocity profile taken from numerical simulation of the conical sheet jet. 300 angleinitial velocity, H=16 mm, 3.6 ms after injection. Courtesy of Paul Walsh.possibility of distribution control. This phenomenon is related to the fact that the continuity thesheet renders it sensitive to the difference in pressure between the top and bottom surface of thesheet. The immediate results of both these phenomena are a lower penetration rate and a smallerspatial distribution, leading to a reduced mixing between the natural gas and the air. In anattempt to correct this situation while still keeping the advantages of the conical poppet design,the sheet was interrupted to allow pressure communication between the top and the bottom ofthe conical sheet.The injector is seated within a copper cartridge in the engine head. It is possible tomodify this cartridge so that small fences cover the tip of the injector. This concept is illustratedin figure 5.24. An available cartridge was modified so that 4 fences with widths ofapproximately 2 mm would interrupt the jet as it emerges from the nozzle. It was found thatthese four fences were sufficient to prevent the jet from the 300 angle poppet to collapse122‘ . . 4 4•+ 4 + ••4 4 4 44 4 4•..• ..ø -4—4 —0123downward as illustrated in picture 5.26. However four fences were not sufficient to prevent thejet from clinging to the top wall for either the 100 or 20° angle poppets.To investigate ifmore interruptions wouldprevent the clinging of the INJECTOR’..Jjet to the top wall, smallslices of tape were placed COPPERCARTRIDGEon the tip of the injector sothat the jet would beinterrupted at regularintervals. As shown inFigure 5.24 Fences for jet interruption.picture 5.27, 6 fences 2mm wide are sufficient to prevent clinging to the top wall for the jet from the 100 angle poppet.In Figure 5.27, the 100 poppet jet does however exhibit a defmite curvature, suggesting that alow pressure zone is still present under the poppet.A new phenomenon was observed while investigating jet interruptions. For someinterruption configurations, the penetration of the jet is significantly faster then for the conicaljet. Picture 5.28 is a shadowgraph photograph of the jet from the 10° poppet from the newestversion of the prototype injector4. Frames 1 and 2 represent the full conical jet sheet at times1 and 3 ms. In frames 3 and 4, the jet is interrupted by two 6 mm wide fences placedperpendicularly to the plane of the picture. The pictures are also respectively at 1 and 3 ms. Inthis case the penetration after 3 ms is more then double. At first, it was hypothesized that theThe faster penetration occurring when the jet is interrupted was also observed with theolder test injector used in most of this experimental work.POPPET124flow was internally choked and that a reduction in area at the tip caused the flow to choke at thenozzle. This hypothesis was disproved since an equal reduction in area with a differentinterruption arrangement did not lead to a higher penetration.. To obtain an idea of the behaviourof the interrupted jet, axial visualization of the jet was performed for different interruptionarrangements.Figure 5.29 shows shadowgraphs of the jet for different interruption patterns at time 3 ms.The first frame is that of the uninterrupted jet. Frames 2, 3 and 4 are interrupted jets by 6 fencesof 2 mm, 6 fences of 1 mm and 8 fences of 1 mm respectively. The penetration in all cases islarger than for the full jet.The lateral spreading of each jet is small, indicating that the initial velocity at the nozzlehas a small radial component, contrarily to the profile expected for the non-interrupted conicalpoppet (see illustration 5.25). The jets emerging from the interrupted nozzle resemble more toa series of round jets.Figure 5.30 depicts different arrangements of 4 interruptions. In the first three frames,the jet is interrupted with 4 small slices of tape respectively of 1, 2 and 3 mm. The forth frameshow the jet interrupted with the modifiedcopper cartridge illustrated in Figure 5.24, atthe tip of which 4 fences of 2 mm weremanufactured. It is seen that for 4interruptions of 1 mm, the jet is larger anddoes not penetrates as deeply. Also observedis the fact that the jet is different whenFigure 5.25 Hypothesized difference in initialinterrupted with small pieces of tape and velocity profile for full and interrupted conicaljet.when interrupted with the thicker fences of1255.26 Interrupted conical jet from - poppet. Interrup - - penfences 2 mm wide at tip of copper cartridge. PC/Pa = 5, lift = 0.08 1 mm..5.27 Interrupted conical jet from 100 angle poppet.with 6 fences of 2 mm width. o/a = 5, lift = 0.056 mm.ruption is performed126Figure iadowgraph of jet from 1 angle poppet (newest injector prototype).Frames 1 and 2 show full conical jet at 1 and 3 ms. Frames 3 and 4 show jetinterrupted by two 6 mm wide fences at same times.Figure 5.29 Shadowgraph of different interruption arrangements. In respecLve order:full conical sheet, 6x2 mm, 6x1 mm, and 8x1 mm. New prototype, 100 poppet.127the copper cartridge.It is not possible to reach a defmite conclusion at this point regarding the ideal number,size and shape of jet interruptions. Nevertheless the following statements results from theobservations:- Interruption successfully prevents the jet from collapsing under the poppet. For the 10and 200 angle poppets, top wall clinging could be prevented by an appropriate numberand size of interruptions. However, the resulting jet can still exhibit a largecurvature.- The width, number and shape of the fences all have an effect on the penetration,most likely by their effect on the initial velocity proffle at the injector’s tip.- There is probably an arrangement that would yield a good gas distribution. It would beF ‘L wgraph of different interruption arrangements. In respective order4x3mm, 4x2 mm, 4x1 mm and 4x2 with modified copper cartridge. New prototype,10° poppet.128interesting to have a 15° angle poppet and 6 interruptions of 1 or 2 mm. At thispoint, both the 100 and 200 angle poppet should be tested in the engine with aninterruption arrangement of 6 x 1.5 mm. More experiments would be beneficial.- With adequate arrangement, the penetration is faster than for the continuous sheet.Generally it is observed that if the initial jets resulting from the interruptions are wide,they will exhibit the characteristics of the conical sheet jet and have a slower penetrationrate. On the other hand if the jets are narrow, they behave more like round jets andhave a larger penetration rate.The disadvantage of the interruption is a reduction in nozzle area, leading to lower massflow. However, if internal choking can be avoided, a higher lift can be set to compensate for thereduced area. Interruptions would allow a better control on the jet diffusion.5.2.4 Enclosed Area EffectIn the second series of experiments, gas was injected in a sealed cylinder. Schlierenphotography was difficult to perform, potentially because of the difficulty in aligning the beamof light in a perfectly parallel direction with the cylinder axis. Shadowgraph photography wastherefore utilised. Due to its small lift, the test injector initially utilised allowed very little gasinto the chamber and axial visualization was difficult to perform. Consequently, the newestprototype injector with a larger lift (0.2 mm) was utiuised in order to improve and facilitatevisualization. Injections were first performed in atmospheric pressure to investigate thedifference in penetration in an enclosed area.Figure 5.31 compares the total penetration of the free jet, the jet propagating along a topwall and the jet in an enclosed area. All these results were obtained from the newest injector.Because the pressure rises in the sealed cylinder as the gas is injected, the penetration rate should129in principle be smaller than for the jet propagating in constant atmospheric pressure. Also thejet must slow down as it approaches the cylinder wall. Neither of these effects could be observedwithin the accuracy of the measurements taken, as it is seen in Figure 5.31. The pressure risein the cylinder due to the injection is small and its effect is likely to be negligible. Insufficientexperimental data were obtained from the newest prototype injector to reach conclusionsregarding the deceleration of the jet as it approaches the cylinder wall.400C.2 0020C_____________00.. 0 TOPWALL100 LJFREEINCYUNDER0Time (ms)Figure 5.31 Difference in penetration for the free jet, the jet propagating along the top wall andthe enclosed jet. Data taken with the new prototype 100 poppet, 0.23 mm lift and pressure ratioof 2.64.5.2.5 Reynolds Number EffectTurbulent jets are known to be moderately dependent on the Reynolds number. It was130attempted to define the dependency of the conical sheet jet on the Reynolds number, since theReynolds number is one of the parameter that was not reproduced in the flow visualizationexperiments. When the gas is injected in atmospheric pressure, the Reynolds number at thenozzle for the new prototype injector is approximately 1.5x 10 for a pressure ratio of 2.64. Byraising the pressure in the cylinder while keeping the pressure ratio kept constant, the Reynoldsnumber can be increased. Limited by the maximum pressure that the cylinder can withstand, themaximum Reynolds number attained was in the order of 5.6x104 Figure 5.32 is a graph of thepenetration obtained for different Reynolds number at the nozzle. The pressure ratio is 2.64, thelift is 0.23 mm and the 100 poppet of the new prototype was utilised.50040-SEg300•!200 Pa —101.3 kPa, Re — 1 .5x10410 Pa - 202.7 kPa, Re- 3.OxlOPa-304.OkPa,Re-6XOPa-375.2kPa,Re- 5.6x1042 4 8Time (ms)Figure 5.32 Penetration comparison between jets with different Reynolds number. The indicatedpressure is the cylinder pressure before injection. 10° angle poppet, pressure ratio of 2.64.It is seen that within the small range of Reynolds number tried, no significant dependencycan be observed. In the engine the Reynolds number is in the order of 5x104. For the round freejet, the penetration is found to be dependent to Re°°53 (Kuo and Bracco [19821). Assuming a131similar dependency for the conical sheet jet:u0&°°53(R3lfi)h1f4 (5.4)one can see that for a Reynolds number 10 times higher, the penetration would be approximately5% higher. The injection of gas in the cylinder can be observed in picture 5.33.5.3 EXTENSION OF RESULTS TO ENGINE APPLICATIONTwo main objectives have been pursued in this project. The first one was to evaluate thepenetration rate of the fuel in the chamber and to see if it is adequate. The second was to getsome information about the fuel distribution within the chamber.5.3.1 Penetration RateAssuming that the Reynolds number effect is small, the penetration rate for a flow chokede Axial shadowgraph visualization of the jet in the cylinder. For the caseillustrated, the chamber pressure is 3 atm and the upstream pressure is 7.92 atm.132at the nozzle will take the form indicated in Equation 5.3:Pp (55)zt=K/iLi(O.537RS1Cdj—1)”4where K is a constant. The density ratio is approximately 0.55. The initial velocity is the sonicvelocity at the nozzle conditions (choked nozzle), and assuming a constant upstream temperatureof 300 K, is approximately 422 rn/s for natural gas. The discharge coefficient is taken as 0.85.Replacing these values in Equation 5.5 yieldsPz = 14.6K/ (Rlj)”4 (5.6)Equation 5.6 is a convenient relationship to approximate the natural gas penetration when injectedfrom a choked conical nozzle. The constant K can be found from experimental data. If themodel is utilised, K is found to be approximately 1.8. The experimental penetration data for the100 angle poppet along the top wall taken from the first prototype injector yields a value of Kof 1.6. Because the proportionality between the penetration and the square root of time holdsonly far from the nozzle, Equation 5.6 overestimates the penetration for P < 20 (R,l).It is easier to judge if the natural gas penetration is sufficient by comparing it with dieselfuel penetration. Diesel fuel penetration can be approximated by the following relationshipdeveloped in chapter 2 (from DENT [1971]):z= 3.01 [(iP)1/2tdllr2(298)1,4 (57)Pa TaThe diesel pressure at the nozzle is in the order of 750 atm and the holes diameter are typicallybetween 0.15 to 0.2 mm. The temperature and the density depends on the type of engine. Forthe Detroit Diesel research engine (series 71) on which preliminary tests are performed, thepressure at the end of compression is 2.5 Mpa and the temperature is approximately 900 K,133yielding an air density of 10 kg/rn3. Utilising these values, approximate penetration of the dieselfuel was compared to approximate penetration of the natural gas calculated with Equation 5.8.The lift and seat radius of the newest 100 prototype injector are utilised. Results are piotted inFigure 5.34. Different upstream pressures for both the gas and the diesel are plotted. Theseresults are approximations, and neglect the fact that the injection last only from 1 to 2 ms.Nevertheless, the order of magnitude indicates that natural gas penetration is slower than thediesel one for the present testing conditions. Similar results are obtained for the 6V-92 engine,in which the cylinder pressure can be as high as 100 atm. Approximation of the jet penetrationfor the conditions prevailing in the 6V-92 are illustrated in Figure 5.35.Jet penetration can be increased (almost doubled) by proper interruption arrangement orby redesigning the injector tip and utilising circular orifices. The pressure ratio can also beincreased, but it is a limited parameter in practice. Before attempting to increase the jetpenetration, the combustion characteristics must be taken into consideration, so that flow velocityand burning rates stay compatible.Figure 5.34 Approximation of the jet penetration for diesel fuel and natural gas. Employedengine conditions are cylinder pressure and temperature of 24 atm and 900 K, diesel holesdiameter of 0.15 mm.Figure 5.35 Approximate penetration for the diesel and natural gas injection for the conditionsprevailing in the 6V-92 engine. Employed cylinder pressure and temperature of 100 atm and 900K.134EE0÷*xD0P0 - 500 atmP0- 750 atmPo— 1000 atmPa -40 atmP0—60 atmP0-SO atmTime (ms)E0±x0Pa — 750 atmPa -1000 atmPo-l25OatmP0-150 atmP0- 200 atmPo - 250 atmTime (ms)1355.3.2 Pulse Width EffectThe propagation of the jet after the end of the injection could not be fully simulated.However experimental observations indicated that the jet tip slows down immediately as thepoppet closes. The jet tip should then be close to the cylinder wall at the moment the poppetcloses. For the series 71 engine the cylinder radius is 54 mm. It is seen in Figure 5.34 that thediesel jet tip reaches approximately 45 mm after 1 ms and 65 mm after 2 ms. The natural gason the other hand reaches 20 mm after 1 ins and 25 mm after 2 ms. Typically in diesel engines,the injection starts between 15 to 20 degrees before TDC (top dead center), and stops at TDC.Most of the fuel is burned at 20 degrees after TDC. Assuming an engine speed of 1200 RPM,the duration of the injection is approximately 2.5 ms, and the time between the starts of theinjection and 20 degrees after TDC is approximately 5 ms. When the injector closes, the dieseljet has reached the cylinder wall. For natural gas fueling, the proposed beginning of injectionis 25 degrees before TDC. The duration of the injection is similar to that of diesel, 2.5 ms, whilethe time between the beginning of the injection and 20 degrees after TDC is approximately 6.25ms. At the time the injector closes, the natural gas jet has barely reached half the distance acrossthe chamber. Because of the slow penetration rate of the conical sheet it would take an injectionduration of nearly 8 ms to reach the cylinder wall. It can be concluded that the actual gaspenetration is inadequate.5.3.3 Jet DistributionThe subject of flow distribution has been discussed in many sections of this chapter, andonly a summary will be discussed here. While the flow visualization performed did notconsidered piston motion, swirl and combustion, some characteristics of the gas injection fromthe conical poppet design were established.136The conical sheet injected near a top wall was shown to have a bi-stable behaviour. Iteither clings to.the top wall or collapses under the poppet. Both phenomena are caused by lowpressure zones created by the air entrainment and to the sensitivity of the sheet to a pressuredifference between its top and bottom surfaces. Both phenomena reduce greatly the mixingsurface between the gas and the air. Along with the slow penetration discussed in the lastsection, the poor distribution provided by the actual design is likely to result in excessive smokeand non-optimal efficiency.Sheet interruption has been investigated and showed some potential improvement both inimproving the flow distribution and the penetration rate. Appropriate interruption prevents bothjet collapse and clinging to the top wall. More research would be required to obtain an optimalinterruption arrangement if such a solution is considered.1376 CONCLUSIONSThe objective of this project was to obtain knowledge about the injection of a highvelocity gas emerging from a suddenly opened conical poppet type nozzle, investigating inparticular the penetration rate and the flow distribution characteristics. The effect of pressureratio, lift, injection duration and wall constraints on the jet were also to be determined.Flow visualization of transient sonic methane jets was performed in this project. In mostexperiments, the jet emerging from the test injector was underexpanded at the nozzle. TheReynolds number of the jets observed ranged from 7x103 to 5.6x104 Visualization was realizedwith schlieren and shadowgraph techniques, and single-shot images were obtained with a CCDblack and white camera at a shutter speed of 1110000th of a second. Images were digitized forrecording and further processing. In a first set of experiments, the jet was injected inatmospheric conditions and visualized laterally. Then axial visualization of methane injectionsin a sealed cylindrical chamber was performed. The jet penetration and general distribution wereestablished from photographs.The characteristics associated with the incompressible steady-state turbulent conical sheetjet were examined utilising a momentum-integral approach and assuming the similarity of profilesin the jet. For small jet axis angles, an expression for the axial velocity decay of the turbulentconical sheet was obtained. The velocity decay was found to be inversely proportional to theaxial distance z, as is the case for the round free jet. The turbulent Reynolds number wasestimated to be 20 for the conical sheet, while it is approximately 45 for the round free jet.Based on results from selected review papers, the analysis was extended to binary mixtures.Compressibility effects were partially considered. A simple treatment for underexpanded jet wasalso discussed.138A model of the transient turbulent conical sheet jet was developed. The transient conicaljet is modelled as a quasi-steady-st’Lte conical sheet feeding a vortex ring. The model is anextension of a similar model for the incompressible transient round jet discussed in the literature.In the quasi-steady-state section of the transient jet, the properties are the one established in thesteady-state analysis. The vortex structure is considered as a whole; it is fed mass andmomentum by the steady-state jet, and is slowed down by a drag force and the need to acceleratesurrounding fluid. The model permits one to obtain the tip penetration, the vortex mass and thevortex velocity as a function of time for a high-velocity turbulent transient conical sheet jet ofmethane into air. While in principle the model depends on some properties not known accurately- the turbulent Reynolds number, the drag coefficient and the discharge coefficient - its transientnature renders the model quite insensitive to a variation in these parameters.Before comparing the penetration rate obtained analytically and experimentally, a firstconclusion regarding the observed jet geometry must be stated:• (1) The free conical sheet jet is seen to have a definite curvature of its axis,towards its inside surface, that leads to the collapsing of the jet for large poppet angle.As a result, the geometry of the jet observed experimentally differs from the geometryproposed in the modelling of the transient jet.When the jet is free from any wall constraints, the jet sheet naturally forms anenclosed area under the poppet. Air entrained by the jet is depleted in this area, causinga lower pressure zone. This lower pressure zone is sufficient to have an effect on thesheet, since its continuity renders it sensitive to pressure. For the 100 angle poppet, thesheet exhibits a definite curvature, causing a downward penetration larger than expected.For the 20° angle poppet, the curvature is severe and causes the jet to collapse under the139poppet, except at higher pressure ratios (5 to 1) where the jet avoids collapsing but isstrongly curved. The jet from the 300 arle poppet collapses under all conditions tested.The difference between the jet geometry for the 100 angle poppet and the modelledgeometry was small. Consequently the penetration rate obtained from the model and the oneobtained experimentally with the 100 angle poppet could be compared. The following statementscan be stated regarding the agreement between the experimental and analytical results:- The compared penetration rates far from the nozzle are similar.- The predicted variation in penetration rate for different pressure ratios across thenozzle is consistent with the one observed experimentally. However, the magnitude ofthe variation observed experimentally is greater than the one predicted, potentiallybecause of pressure effects in the development of the jet.- Larger variations in penetration rate for different lifts were predicted than the onesobserved experimentally, but this difference was explained by non-ideal flow conditionsinside the test injector.- The model predicted that penetration rates in the early stages of the jet propagation arelarger than the ones observed experimentally, especially at lower pressure ratios, leadingto an overall penetration approximately 15% higher than that observed experimentallyfor a pressure ratio of 2.It appears that, in addition to a difference in overall geometry, the development of thehighly transient jet as it exits the nozzle is not adequately modelled by the proposed geometry.Nevertheless, the model is consistent in predicting the effect of parametric variation, and givessome insight regarding the mechanism of the jet penetration. Both model and experimentalresults support to the following conclusions:140• (2) The model, to a large extent in accord with experimental observations, showsthat the free jet tip penetration of the conical sheet is rojortionai to:- the square root of time: t”2,- the square root of the initial velocity: U01’2,- the methane to air density ratio at ambient conditions to the power 1/4: (Pg/Pa)1’- the upstream to ambient pressure ratio to the power 1/4: (P01Pa)”,- the product of the seat radius by the lift to the power 1/4: (1 Rj”4.The jet penetration is also dependent on:- the poppet angle: f,- the injection duration: t.In addition, it was found that the flow conditions inside the test injector wereimportant to consider. Relatively long passages of small diameter in conjunction withhigh subsonic velocities lead to considerable pressure drop due to friction inside the testinjector. Consequently, the pressure just upstream of the nozzle is smaller then expected.Internal friction choking can also occur if the lift is set such that the nozzle area is notsignificantly smaller than areas of the passages inside the test injector.Furthermore, the magnitude of the conical sheet jet penetration was found to besignificantly less (by about 30%) than that of a series of round jets, given that the totalflow area is the same.• (3) An increase in the upstream-to-ambient pressure ratio is always found to causean increase in jet tip penetration, given that it is caused by an increase in upstreampressure. This penetration increase is both observed experimentally and predicted by themodel. If the flow at the nozzle is not choked, an increase in pressure ratio causes an141increase in initial velocity. If the flow is choked at the nozzle, an increase in pressurecauses underexpansion to occur. The underexpanded jet behaves as if it originated froma larger source area. An increase in nozzle velocity and area will both result in anincrease in jet tip penetration.• (4) The model predicts an increase in penetration if the lift is increased.Experimental observations indicated that the lift has little effect of the jet penetration.It was shown however that the flow behaviour inside the test injector could be heldresponsible for the lack of effect of the lift variation. If the flow is choked at the nozzleexit, the pressure drop increases when the lift is increased, resulting in a momentum gainmuch smaller than the one predicted by the model. If the lift is increased too much,internal choking occurs and nozzle velocity diminishes, yielding again a much lowermomentum than the predicted one. It is believed that if the injector is designed to limitinternal friction, by increasing the size of the gas passages, an increase in lift will yielda larger penetration.• (5) The presence of the top wall was found to have a very significant effect on theconical sheet. A similar phenomenon to that described in the first conclusion occurswhen the nozzle is positioned near a top wall for the 100 angle poppet. The air entrainedby the jet causes a low pressure zone between the sheet and the wall, provoking theclinging of the jet to the top wall. Clinging to the top wall was also observed for the 20°angle poppet at large pressure ratios. The top wall was found to have no influence on thejet from the 30° angle poppet.142Conclusions (1) and (5) lead to some corollary statements:o The effect of the angle on the jet is related to the observed jet geometry. Forsmall angles, the jet bends; the larger the angle, the larger the curvature. If the angle islarge enough, the jet collapses under the poppet.o When the nozzle is situated near a top wall, the jet exhibits a bi-stable behaviourassociated with the poppet angle. For a given angle, the jet either clings to the top wallor collapses under the poppet, propagating downward. It is not apparent that anyintermediate case exists between these two situations. The switching from one case tothe other seems to occur in the vicinity of an angle of 200, since for this angle bothbehaviours were observed depending on the pressure ratio.• (6) The effect of the bottom wall was observed for different distances between thetop and bottom walls and for different poppet angles. In all cases it was observed thatfor a small distance (15 mm) the jet rapidly fills the gap between the two walls andsubsequently propagates radially, mixing with the air only at its front. The followingobservations were made for each poppet angle:100 poppet: The jet clings to the top wall first and propagates along it. If thewalls are separated by a distance larger than the jet thickness (approx. 20 mm), the jetdoes not reach the bottom wall. Even without contact, the presence of the bottom wallwas found to have a small effect on the jet penetration (provided the bottom wall is nottoo far, in which case it has no effect).20° poppet: The jet initially propagates downward. If the bottom wall is near thetop wall, the jet clings to the bottom wall first, then fills the space between the two walls.If the bottom wall is further (25 mm) and the pressure ratio is high (5 to 1), the jet will143cling to the top wall first.300 poppet: The jet propagates towards the bottom wall to-which it clings.The similarity between the experiments performed in this project and the conditions inthe engine were discussed in chapter 4 and it was found that all parameters on which thepenetration depends could be reproduced experimentally, with the exception of the Reynoldsnumber and of the injection duration. In the literature, it is stated that the penetration increasesmildly with an increase in Reynolds number. Some experiments performed in this project lookedat the effect of increasing the Reynolds number. This was accomplished by injecting the gas ina pressurised chamber, while maintaining the pressure ratio constant. The higher upstreamdensity results in a higher Reynolds number. The following conclusion can be drawn from theseexperiments:• (7) An increase in the Reynolds number from 1.5x 10 to 5.6x 10 produced nosignificant change in the penetration rate. Together with results reported in the literature,this result indicates a mild dependence of the turbulent jet on the Reynolds number.The injection duration in the flow visualization experiments was longer than the oneoccurring in the engine. However, the penetration of the conical sheet after the injector hadclosed was observed, and it can be concluded that• (8) The penetration rate of the jet tip decreases rapidly when the poppet closes.A consequence of this observation is that given a point at a determined distance from thenozzle to be reached by the jet tip within a specified time, the jet tip must have travelled144the majority of this distance before the injector closes.Conclusions #7 and #8 lead to another corollary statement:o If all other parameters are matched (initial velocity, density ratio, pressure ratio, seatradius and lift and poppet angle), during the time the injector is open the penetration rateobserved experimentally is similar to that occurring in the engine.Extending the conclusions and corollaries stated so far to the present use of the prototypeinjector in the series 71 diesel engine, the following corollaries can be stated:o The natural gas jet has reached only half way across the chamber at the time theinjector closes. For the series 71 engine, it is evaluated that the natural gas penetrationis approximately half of the diesel penetration for typical operating conditions. Thenatural gas penetration for the present injector and conditions utilised is not sufficient toyield optimal mixing with the surrounding air.o The actual flow distribution is inadequate. While the flow distribution cannot beclearly established because the motion of the piston, the swirl and the squish effect werenot considered, the jet distribution is limited by its dual behaviour. With the present 100and 20° angle poppets, clinging to the top wall is lilcely to occur, resulting in poor mixingnear the top wall. Clinging and slow penetration rate would result in an overall poormixing and in the presence of a rich zone near the top wall, leading to soot formation andnon-optimal fuel conversion efficiency. If the jet propagates downward, the same145phenomenon occurs since then a rich zone occurs on the surface of the piston. In bothcases, the flow distribution is inadequate.The continuity of the jet renders it sensitive to the pressure difference across its surfaces,and diffusion cannot be easily controlled. As a potential solution for this problem, jetinterruption was investigated as a mean to allow pressure equilibrium between the top and bottomsurfaces of the sheet. The following preliminary conclusion were drawn:• (9) Jet interruption is a successful method to avoid top wall clinging and jetcollapsing in most cases. In addition, appropriate jet interruption can provide a jetpenetration rate significantly higher (almost double penetration rate was observed in somecases). The number, width and thickness of the interruptions utilised are importantparameters to consider.6.1 RECOMMENDATIONS AND FUTURE WORKOne of the main goals regarding the injection of natural gas into diesel engines is toobtain adequate penetration and distribution of the fuel in the chamber. The actual natural gaspenetration is slower mainly because of the chosen nozzle geometry. A series of round orificescould probably yield a similar fuel penetration for the natural gas as for the diesel fuel. Theinjector tip could be redesigned so that the gas would be introduced through a series of holes.However if the actual design is to be kept, jet interruption is recommended. The optimal numberand width of the interruptions could be determined with little more experimental work involvingthe manufacturing of different interruption arrangements and flow visualization.Even if the conical nozzle is not retained, the modelling of the conical sheet is an146interesting problem and the results obtained are promising. In order to improve the actual modelfurther experiments could be performed. In this project, the experiments carried out were relatedto the transient jet. Experimental data concerning the steady-state jet would be useful inverifying the assumptions made regarding the conical sheet jet. Two axis hot wire measurementsof the velocity within the conical sheet jet would provide a good experimental basis to establishmore accurately the steady-state characteristics.The flow inside the injector is subject to friction and recirculation, and because theinjector tip geometry is complex, the exact nozzle conditions are not known accurately. Aspecial nozzle assembly could be manufactured for the steady-state experimental measurementsthat would ensure better knowledge of the nozzle conditions.Regarding the transient conical sheet jet, modelled starting conditions seems tomisrepresent the actual starting jet. If light sheet visualization could be performed, requiringsome means of rending the flow visible, the structure of the starting jet, and of the remainingjet, could be established more completely than with schlieren photography.1477 REFERENCESAbramovich, G.N., The Theory of Turbulent Jets, M. I. T. Press, 1963Abramovich, S., Solan, A., The Initial Development of a SubmergedLaminar Round Jet, Journal of Fluid Mechanics, Vol. 59, pg. 791-801, 1973Abramovich, S., Solan, A., Turn-ON and Turn-OFF Times for a Laminar Jet,Transactions of the ASME, Journal of Dynamic Systems, Measurements, and Control, pg. 155-160, June 1973Arcoumanis, C., Cossali, E., Paal, G., Whitelaw, J. H., TransientCharacteristics of Single-Hole Diesel Sprays, SAE Technical Paper Series 900480, pg. 380-396,March 1990Batchelor, G.K. An Introduction to Fluid Dynamics, Cambridge Press, 1967Beck, N. J., Johnson, W. P., George, A. F., Petersen, P. W., Van Der Lee, B., Klopp, G.,Electronic Fuel Injection for Dual Fuel Diesel Methane, SAE Technical Paper 891652, August1989Birch, A. D., Brown, D. R., Dodson, M. G., Swaffield, F., The Structure and ConcentrationDecay of High Pressure Jets of Natural Gas, Combustion Science and Technology, Vol. 36, pg.249-261, 1984Birch, A. D., Brown, D. R., Dodson, M. G., Thomas, J. R., The Turbulent Concentration Fieldof a Methane Jet, Journal of Fluid Mechanics, Vol. 88, pg 431-449, 1978Dent, J. C., A Basis for the Comparison of Various Experimental Methods for Studying SprayPenetration, SAE Transactions, Vol. 80:3, pg.1881-1884,1971Einang ,P.M., Engja, H., Vestergen, R., Medium speed 4-stroke diesel engine using high pressuregas injection technology.Einang, P.M., Koren, S., Kvamsdal,R., Hansen, T., Sarsten,A., High-Pressure, Digitally ControlledInjection of Gaseous Fuel in a Diesel Engine, With Special Reference to Boil-Off from LNGTankers. Proceedings CIM AC Conference, June 1983Ewan, B. C. R., Moodie, K., Structure and Velocity Measurements in Underexpanded Jets,Combustion Science and Technology, Vol. 45, pg. 275-288, 1986Fox, WR.W., McDonald, A.T., Introduction to fluid Mechanics, John Wiley and Sons, 1985Heywood, 3. B., Internal Combustion Engine Fundamentals, McGraw-Hill Book Company, 1988148Holder, D. W., North, R. 3., Schlieren Methods, Publisher: Her Majesty’s Stationary Office, 1964Kuo, T. W., Bracco, F. V., On the Scaling of Transient Laminar, Turbulent, and Spray Jets,Society of Automotive Engineers, 820038, 1982.Middleton, 3. H., The Asymptotic Behaviour of a Starting Plume, Journal of Fluid Mechanical,Vol. 72, part 4, pg. 753-771, 1975Midgeley, P., Natural Gas Intensifier/Injector for DDEC - Equipment Diesel Engines, MarketStudy by Canadian Resourcecan Limited, Vancouver, B. C., December 1989Mime-Thomson, L.M., Theoritical Hydrodymamics, MacMillan, 1968Miyake, M., Biwa, T., Endoh, Y., Shimotsu, M., Murakami, S., Komoda, T., The Developmentof High Output, Highly Efficient Gas Burning Diesel Engine., CIMACPaper Dll.2.Saber, A. 3., Georgallis, M., Fluid Dynamic Structures Relevant to Fuel Injection and Jet Ignition,December 1989Schlichting, H., Boundary-Layer Theory Seventh Edition, McGraw-Hill Publishing Company,1987Shapiro, A. H., The Dynamics and Thermodynamics of Compressible Fluid Flow, The RonaldPress CompanySolomon, A. S. P., Plasma-Jet Ignition of Fuel Sprays in a Rapid Compression Machine, SAETechnical Paper Series 880205, March 1988Tennekes, H., Lumley, I. L., A First Course in Turbulence, MIT Press, 1989Thring, M.W., Newby, M.P., Combustion Length of Enclosed Turbulent Jet Flames,4thSymposium on combustion, pp789-796, Baltimore, William and Wilkins, 1953Turner, J.S., The “starting plume” in neutral surroundings, Journal of Fluid Mechanics, Vol. 13,pg. 356-368, 1962Varde, K. S., Popa, D. M., Diesel Fuel Spray Penetration at High Injection Pressures, Society ofAutomotive Engineers, Inc., 1984Wakenell, J.F., O’Neal, G.B., Baker, Q.A., High Pressure Late Cycle Injection of Natural Gasin a Rail Medium Speed Diesel Engine. SAE Technical Paper 872041, November 1987Walsh, P. Numerical Analysis of High Pressure Injection of Natural Gas into a Diesel EngineCombustion Chamber, M.A.Sc. Thesis, The University of British Columbia, 1992Witze, P., The Impulsively Started Incompressible Turbulent Jet, SAND8O-8617, pg.3-15, 19801498 APPENDICES8.1 APPENDIX A - NON-DIMENSIONAL ANALYSISThe transient turbulent conical sheet jet was modelled in chapter 3 as a quasi-steady-statejet feeding a vortex structure. The equations describing the rate of change of mass, momentumand position of the vortex structure can be non-dimensionalised using the appropriate scalingfactors. Equations A. 1 to A.5 summarize the steady-state equations, taken at the back plane ofthe vortex, at z z.U 2 U k—e and in 1U0 ; (A.1)and X (A.2)________(A.3)/RJ /R3lwhere =r/r112 and cx=ln(2) and is given byif <1.86Pa a (A.4)pP P1 =O.537lC —--- f -.‘1.86eq dp pa aAlsoP 1p P (A.5)aPg150The transient equation for the position, mass, methane content and momentum of the vortexstructure (for the conical jet sheet) are given by:u (A.6)din_!=2fTlp(UU)2tzcos(p)dr&(U-U) (A.7)=4;(p)pfr. drPgdm X(UU)drgv_________& (A.8)Pg(1+!)’’=47rz,cos(P)p (U-U)U dr+ajo pcitx(——1)+1Pg (A.9)f!U V-!FDdtThe drag force is proportional to the frontal area:FD=CD(p0U)(4t (;+R)cos(P)R) (A.1O)and the change in density is:dpp0(1) mdin= Pg d “& (All)- PpgThe following dimensionless parameters are defined:(—e)—UzVthe radius re can also be non-dimensionalized from Equation 3.13 (neglecting r)iii) The rate of change in methane content:_1f2a2[..e _a2— U]zv—1)+1* Pg(A.15)151_tUL=/RJ,, z=-,(A.12)*m*mm=, m = , M =gvPaL3110The steady-state Equations A. 1 to A.5 and the non-dimensional parameters defined in EquationA.1 1 are replaced in the transient Equations A.6 to A.1O and after rearrangement, the followingnon-dimensional expression are established:i) The rate of change of position:(A.13)dt*ii) The rate of change in total vortex mass:4(L) (A.14)Ldt*Pg-1n(U)In(2)LLd,n*1*=47rzcosdt*(13)JL Z (A.16)iv)The rate of change in momentum:152r(1 +f) dM 4*(f3)fL zv zvpv dt’ JO k _!• o—e 2 (-——1)+1Pg (A.17)d(f!)-27tCCOS(P)(U)P dt* L2It is found that, given PIPa’ f3 and the steady-state constants k1, k2 and k3, the change in position,mass, methane content and momentum of the vortex can be expressed as function of thefollowing parameters:dz (A.18)dm * * (A.19)L1)____* * (A.20)dt*dM*_(A.21)f4(z,U,R)The initial condition can also be stated in dimensionless form:* zo (A.22)at t*=O : z=—, R=1-, U=1The solution of the system of equation is obtained by solving simultaneously Equation A.18,A.19, A.20 and A.21, according to the following steps:For O<t*<t*end1) the term is guessed,1532) is obtained from A.13,3) is obtained from A. 14,4) is obtained from A.16,5) Pv1Pa is obtained from:Py_ 1P0 m* p (A.23) -__!(_..!—1) +1m Pg6) M1,* is obtained from A.17,7) U is computed from:(A.24)8) if the vortex velocity and the guessed value differ, repeat step 2) to 8), otherwisecontinue.9) calculate the radius R from:R 33m___)(A.25)V seq (!)Pa10) calculate the tip penetration:z z R________-‘-2 ‘ (A.26)/R1eq iy/Rgleq /Rgleq11) increment time and repeat.1548.2 APPENDIX B - REPEATABILITY STUDYBecause the history of the jet was to be obtained from single shots photographsfrom different jets at different times, a certain repeatability had to be shown. For two differentcases, multiple pictures of different jets at the same time after the beginning of the injection andfor the same conditions were obtained. The results of each case are reported in Table B.1 andB.2.APL APR RPL RPR PL PR1 7.6 5.8 9.3 11.7 12.0 13.12 7.1 5.3 8.3 10.7 10.9 12.03 7.5 5.7 9.3 11.7 11.9 13.04 7.1 5.4 9.3 11.4 11.7 12.65 7.3 5.5 8.6 11.4 11.3 12.76 7.1 5.6 9.3 11.4 11.7 12.77 7.4 5.9 8.3 11.0 11.1 12.58 7.4 5.9 8.3 11.0 11.1 12.5AVERAGE 7.3 5.6 8.8 11.3 11.5 12.6STD 0.2 0.2 0.5 0.3 0.4 0.3MAX 0.3 0.3 0.6 0.6 0.6 0.7Table B.1 Repeatability study. Upstream pressure of 173,7 kPa (1.7 atm), 10° angle poppet0.056 mm lift at time 1 ms. RPL : radial penetration measured on left side, RPR right radialpenetration, APL left axial penetration, APR : right axial penetration, PL: total penetrationmeasured on left side, PR right total penetration. Measurements in mm.155APL APR RPL RPR PL PR1 18.5 17.4 22.1 28.9 28.9 33.82 18.7 16.2 23.1 31.0 29.8 35.03 19.3 16.6 22.1 30.3 29.4 34.54 19.0 16.1 22.5 32.7 29.5 36.45 19.5 16.2 24.8 31.7 31.6 35.56 19.3 16.6 22.1 30.3 29.4 34.57 19.6 17.3 24.2 32.0 31.1 36.48 18.3 17.1 22.5 29.6 29.0 34.29 18.0 17.2 24.5 31.3 30.4 35.7AVERAGE 18.9 16.7 23.1 30.9 29.9 35.1STD 0.5 0.5 1.0 1.1 0.9 0.9MAX 0.9 0.7 1.7 1.9 1.7 1.3Table B.2 Repeatability study. Upstream pressure of 506,7 kPa (5 atm), 10° angle poppet,0.056 mm lift at 3 ms.8.3 APPENDIX C - INTERNAL FLOW IN TEST INJECTORIt is desired to obtain choking at the nozzle of the injector to maintain good control overthe mass of fuel injected. The small diameter of some of the CNG port in the prototype injectoralong with high Mach number leads to potential friction choking inside the injector. Themaximum lift of the poppet that can be achieve without friction choking is calculated in thisappendix for different conditions. In addition, the condition that would be found at the nozzlegiven an internal friction choked flow are evaluated. Another consequence of the small passagesand of the high Mach number is the potentially significant pressure drop inside the injector. Anapproximation of this pressure drop will also be obtained. The goal of these calculations is to156obtain a reasonable approximation of the characteristics of the flow inside the injector.The injector was modelled as illustrated in Figure C. 1. Each section represents a specificsection in the injector. The size difference between each section is exaggerated on the figure,but the sharp junctions are present in the injector. The following assumptions will be made:- the flow in the injector is iseniropic and adiabatic,- only friction choking is considered in the passages, the effect of edges is notconsidered,- because the mass of gas in the tip reservoir is in most cases less then 10% of the totalmass injected, the flow will be assumed as steady-state. This is not a reasonableassumption in the early stages, but once the flow is developed, it should provide a goodunderstanding of the process and a good estimate of the mass flow.The different scenario for choking flow in the injector are the following ones:1) The area at the nozzle is the smallest restriction. In which case friction choking in theinside passages might occur in section B and C and must be verified. Also the pressure dropoccurring in the passages and due to friction can be evaluated.2) The area at the nozzle is no longer the smallest area. Choking is then likely to occureither at the end of section B, or at the end of section C.Case 1The nozzle area is the smallest. Given upstream stagnation pressure and temperature andgiven the downstream pressure, the Mach number is obtained at the nozzle using the followingrelationship:1571-Nozzb:A=27tRslcósD, Rs—2,58mnA- Tip Reservoir: annular spaceA= 1.22x10 m, Deq = 3,94mm,L — 21,8 mm, h — 093 mm, LIDeq — 5,53, LIh — 23,5Vol = 2,65x1073B - Port to reservoir: D = 1,5875 mm, L = 9,65 mm, LID = 6.1Vol=1,9x10m3C - Cng Port: D = 1,98 mm, L= 26,16 mm, LiD = 13,2, Vol = 8,lxlqrrl’D - Cng Port: D = 278 mm, L 20,03 mm, L.ID = 7,3, Vo’— 1,2x10 m3E- Cng Port: D= 3,18 mm, L=95,25 mm, Vol= 7,54x10 m3Iseion D—seon Cseion Bseion AFigure C.1 Model of the methane ports inside the test injector._(()k1) (C.1)\k-1The temperature, density, velocity and mass flow of the gas at the nozzle can be computed fromthe Mach number:7;T—k—i (C.2)2Pa(C.3)(1÷-M2)158Uflf(,J -R(T0T) (C.4)th=pU4 (C.5)The mass flow at point 3 is the same as at the nozzle. From that mass flow, the Machnumber at 3 is computed: -M3V’ (1÷ZM)21)(C.6)The temperature, density, velocity are also computed at 3, using the same equations (C2-C4).The Reynolds number is also calculated at 3. From Shapiro, the following term is evaluatedL1_M2 k+1 (k+1)M2D w2 2k 2(1+_M2)2where f is the average friction coefficient, L is the maximum length of duct that will handlethe initial mass flow without choking. The friction coefficient f can be evaluated from1 2O 1og(!+ 2.51 (C.8)(4f)05 37 J (4J)05where efD is the relative roughness, and for smooth pipe can be taken as 0.000001 (equationtaken from Fox and McDonald, Introduction to Fluid Mechanics). The maximum LID ratio isthen obtained, and compared with the actual one, If the actual L/D ratio is larger then thecomputed one, choking will occur in the injector. The previous computations were performedon a LOTUS spreadsheet. It was found that internal choking occurred at a lift of approximately0.089 mm. The Mach number and pressure drop for each section is indicated in Table C. 1 forlifts of 0.056 and 0.08 1 mm.159lift PR Mn M3 M2’ Po2 M4 M3’ Po3 M5 M4’ fç4Po3 PM Po5.056 1.5 .8 .355 .397 .91 .218 .232 .94 .108 .110 .982 1.0 .372 .419 .91 .228 .243 .94 .113 .115 .985 1.0 .372 .417 .91 .228 .243 .94 .113 .115 .98.081 1.5 .8 .584 .737 .89 .329 .371 .90 .159 .164 .972 1.0 .624 .800 .89 .344 .390 .90 .166 .171 .975 1.0 .624 .786 .89 .344 .387 .90 .166 .171 .97.-awe u.i Macn numbers and pressure drop ifl the injector. iNumbers reter to the ditterenisections in Figure C. 1. The primed numbers indicated the end of the previous section byopposition to the beginning of the current one. Because the pressure drop does not changesignificantly with the initial pressure, the initial conditions were not corrected (no iterations).It can be seen that the compounded pressure drop is 16% for a lift of 0.056 mm and 22% for alift of 0.081 mm. The pressure drop was calculated the following way: For the section Binwhich the flow is choked, the stagnation pressure change can be readily obtained with_________(C.9): MWhere the Mach number at the beginning of the section considered is taken (given the Machnumber is one at the end of the section). For the sections where the flow does not choked, thefollowing relationship is utilised:LL7L) (C.1O)where Mb and Me are the Mach number at the beginning and at the end of the sectionconsideredrespectively. The Mach number at the beginning of the section can be found from the mass flowand upstream conditions. The first term is also known. The Mach number at the end of the160section can then be calculated from the previous Equation (C.10). The pressure drop in thesection is then obtained from(C.11)‘ (PJP:)where the respective pressure drop are calculated from Equation C.9.Case 2The previous results show that if choking occurs, it will occur at the end of section B.Given Mach = 1 at location 2, we can evaluate the maximum Mach number at the entrance ofthe port (3) utilizing Equation C.7. Since the friction coefficient depends on the Reynoldsnumber, an iterative process is required to obtain M3. Once the Mach number is obtained atlocation 3, the mass flow can be obtained, and the Mach number at the nozzle can be calculated.Again pressure differences due to friction can be computed. The pressure drops are usediteratively to modify the initial conditions. Condition at the nozzle are then inferred from theMach number and from the equation stated previously. Some results for these calculaton arereported in Table C.2.LIFT (mm) UPSTREAM Mn Vn (m/s) pn (kg/rn3)PRESSURE(kPa)0.15 202.7 .334 151.8 1.233506.7 .343 155.8 3.0740.203 202.7 .243 110.8 1.266506.7 .249 113.5 3.594r‘able C.2 Conditions at nozzle when internal friction cnoking is occuring.It is seen that the initial velocity is much lower than for a choked nozzle, even if the161increase in lift is only of 1120th of a millimeter. The density however increases moderately.8.1 PICTURE PROCESSING RESULTSIn the next pages are reproduced the results of the automatic and manual processing ofthe digitized photographs. The dimensions are in mm. The distances are taken from the nozzle.Some of the indicators are illustrated in Figure 4.15. -Key to abbreviations:PYA1 : automatic average downward penetration on left side.PYA2 : automatic average downward penetration on right side.Ri : automatic radial penetration on left side.R2: automatic radial penetration on right side.P1 : automatic estimation of the jet penetration on the left side. Overestimate thepenetration.P2 : automatic estimation of the jet penetraion on the right side. Overestimate the jetpenetration.P1M : manual measurement (with the mouse) of the jet total penetration on right side.P2M: manual measurement of the jet total penetration on the left side.TETA 1 : automatic measurement of the apparent angle on right side.TETA2 : automatic measurement of the apparent angle on left side.AREA: automatic evaluation of the two-dimensionnal area occupied by the jet. Couldbe converted to the volume assuming the jet is perfectly axisymetric.PYMAX : maximal distance reached downward.PICTURE PROCESSING RESULTS1 — 10 DEGREE ANGLE POPPET— FREE JET162A — LIFT— 0.056 PR— 1.5TIME (nis) PYA1 PYA2 Ri0.50.75 5.3 4.6 5.9 7.6 7.9 8.91 6.9 5.4 7.6 10.0 10.3 11.41.5 9.4 7.5 10.4 13.1 14.0 15.12 11.4 9.1 13.5 16.6 17.6 18.93 14.4 12.0 17.6 22.1 22.7 25.15 19.0 16.3 22.1 26.9 29.1 31.510 27.8 26.1 33.5 37.3 43.5 45.53.0 4.25.7 7.8 41.9 31.3 109.1 6.06077.8 10.0 42.4 28.4 169.1 7.97511.4 12.6 42.2 29.9 258.9 10.52813.9 16.2 40.2 28.6 376.7 13.71718.5 20.6 39.2 28.5 594.7 16.91054.2 26.9 40.6 31.3 994.4 22.65338.8 41.4 39.7 35.0 1992.5 33.817B — LIFT - 0.056 PR 2 FILE NAME PREFIX : L1C2TIME (ins) PYA1 PYA2 Ri P.2 P1 P2 PIN P2)4 TETAI TETA2 AREA PYMA)C0.5 4.2 3.8 4.8 6.5 6.3 7.5 3.9 6.5 41.3 30.4 88.1 4.46780.75 5.4 4.8 7.5 9.2 9.2 10.4 7.7 9.3 35.9 27.5 167.7 6.0607I 7.1 6.7 11.6 13.6 13.6 15.2 11.7 13.0 31.6 26.1 279.3 8.29641.5 10.0 8.4 15.0 16.0 18.0 18.1 16.0 16.3 33.6 27.6 431.3 11.4852 11.3 9.0 18.4 21.1 21.6 22.9 19.1 21.4 31.6 23.1 598.9.13.7173 15.6 13.1 22.5 25.9 27.3 29.0 24.4 25.4 34.7 26.9 917.1 18.5035 22.5 20.9 30.6 36.4 38.0 42.0 36.4 37.7 36.3 29.9 1703.3 25.84210 31.6 31.3 42.6 48.7 53.0 57.9 46.3 53.7 36.6 32.8 2971.4 39.5604.5 8.3 7.9 9.9 9.1 8.95.8 10.7 10.7 13.3 12.2 11.510.0 15.2 15.9 19.5 18.8 16.010.2 20.4 19.3 24.3 21.9 22.416.4 22.8 23.8 29.0 28.9 25.123.1 32.4 28.6 41.5 36.8 37.531.7 45.9 44.5 56.4 54.7 48.38.4 33.0 29.7 158.3 6.382110.9 36.6 28.4 245.6 8.932116.7 38.7 32.2 464.3 14.99628.7 33.1 27.9 633.5 15.63227.0 38.2 34.5 962.0 21.69634.1 38.5 38.9 1641.9 30.62849.5 35.6 35.5 3004.0 39.242FILE NAME PREFIX L1C1P.2 91 P2 PiN 92)4 TETA1 TETA2 AREA PYMAXC — LIFT — 0.056 PR— 5TIME (ms) PYAI PYA2 Ri0.25FILE NAME PREFIX L1C3P.2 P1 P2 PiN P2)4 TETA1 TETA2 AREA PYMAX4.5 7.00.5 9.2 6.5 9.1 14.7 12.9 16.1 11.4 13.9 45.20.75 10.7 7.7 11.9 17.2 16.0 18.8 12.6 17.3 42.11 13.9 10.9 16.1 22.4 21.3 24.9 17.8 22.7 40.91.5 16.8 13.5 20.3 27.3 26.3 30.5 21.3 27.0 39.52 19.6 17.4 25.9 33.6 32.5 37.9 27.5 33.4 37.13 24.2 23.9 35.0 40.6 42.5 47.1 35.7 42.1 34.65 32.6 29.5 42.4 48.7 53.4 56.9 45.6 54.5 37.610 47.5 42.3 58.5 73.2 75.3 84.5 67.3 72.3 39.1o — LIFT — 0.081 PR— 2TIME (ins) PYA1 PYA2 Ri23.9 314.1 10.67824.1 419.1 12.34626.0 687.0 16.01726.4 970.9 20.02127.4 1395.1 23.02530.5 2132.4 29.03231.2 3165.7 40.04630.1 6160.2 55.7320.50.7511.523S10FILE NM4E PREFIX L2CIR2 P1 P2 PiN P2M TETAI TETA2 AREA PYMAX5.1 4.15.47.912.213.317.925.832.8163E_LIrT=0.081pR5:-;TIME (ins) PYA.1 PYA2 RT0.25 7.1 3.8 5.70.5 8.6 5.8 8.70.75 12.8 7.8 10.11 16.1 10.6 15.41.5 19.9 14.8 20.82 22.1 15.9 23.23 27.4 22.9 34.95 35.6 .29.0 43.310FILE NAME PREFIX L2C2R2 P1 P2 P114 P2145.7 9.1 6.9 6.9 6.310.1 12.3 11.6 10.8 10.113.4 16.3 15.6 13.0 13.518.8 22.3 21.6 17.0 18.024.9 28.8 28.9 23.3 25.230.9 32.0 34.8 25.6 27.234.9 44.4 41.8 38.6 38.046.3 56.0 54.7 50.0 47.268.1 66.5TETh1 TEfl2 AREA PYMAX51.1 33.8 113.0 8.5544.7 29.8 218.1 10.38251.9 30.3 356.1 14.65746.2 29.3 612.6 18.62543.7 30.9 1000.4 21.98243.6 27.3 1292.3 30.22838.2 33.3 2015.3 33.28239.4 32.1 3157.1 40.610C — LIFT — 0.15 PR— 5TIME (ms) PYA1 PYA21 19.0 13.92 24.6 20.45 37.7 36.910 50.6 47.5FILE NAME PREFIX L3C2P1 P2 P114 P21427.5 26.4 21.7 21.538.9 39.6 32.0 34.264.6 61.1 54.6 57.386.6 85.5 77.0 72.0TEfl1 1’ETA2 AREA PYMAX43.6 31.8 864.4 22.69239.3 31.0 1772.1 29.735.7 37.2 4237.8 45.38535.7 33.8 7518.7 63.4072 — 10 DEGREE ANGLE POPPET — FREE 3ET — REPEATABILITY DATAA — LIFT 0.056 PR 5TIME (ius) PYA1 PYA23.0 18.5 17.43.0 18.7 16.23.0 19.3 16.63.0 19.1 16.13.0 19.5 16.23.0 19.3 16.63.0 19.6 17.33.0 18.3 17.13.0 18.0 17.2B — LIFT — 0.056 PR = 1.7TIME (ms) PYA1 PTh2 RI1.0 7.6 5.8 9.31.0 7.1 5.3 8.31.0 7.5 5.7 9.31.0 7.1 5.4 9.31.0 7.3 5.5 8.61.0 7.1 5.6 9.31.0 7.4 5.9 8.31.0 7.4 5.9 8.3FILE NAME PREFIX : L1C5P1 P2 P114 P21412.0 13.110.9 12.011.9 13.011.7 12.611.3 12.711.4 11.7 12.711.0 11.1 12.511.0 11.1 12.5F — LIFT 0.15 PR = 2TIME (iiis) PYA1 PYA21 8.2 8.22 16.9 14.83 19.8 17.65 24.4 24.010 33.0 34.5FILE NAME PREFIX L3C1P1 P2 P114 9214 TETA1 TETA2 AREA PY)4AX15.6 15.6 13.4 13.4 31.7 31.5 318.3 9.678525.6 25.7 20.0 22.1 41.3 35.2 774.1 20.02131.5 35.2 25.1 27.8 38.9 30.0 1166.7 23.02541.8 39.9 35.5 35.5 35.7 37.0 1820.0 29.36759.0 56.3 50.3 47.1 33.9 37.8 3387.7 41.046Ri13.319.324.534.049.0Ri20.030.152.570.4R213.321.030.531.944.5R222.434.048.771.1Ri22.123.122.122.524.922.124.222.524.5FILE NAME PREFIX : LIC491 P2 9114 P2M28.9 33.829.8 35.029.4 34.529.5 36.431.6 35.529.4 34.531.1 36.429.0 34.230.4 35.7TETA139.939.041.140.338.142.139.039.236.3R228.931.030.332.731.730.332.029.631.3R211.710.711.711.411.4TETA2 AREA31.1 1249.127.6 1265.228.7 1239.526.3 1303.221.0 1251.928.7 1239.528.4 1313.930.0 1198.628.7 1206.0PYMAX21.721.122.020.821.722.022.021.122.0PYMAX8.68.08.68.38.68.38.68.6TETh1 TETA2 AREA39.3 26.4 246.740.6 26.5 216.438.7 25.8 235.337.3 25.4 218.940.3 25.9 222.937.1 26.1 218.641.9 28.0 228.841.7 28.0 221.83 — 10 DEGREE ANGLE POPPET — TOP WALL164A — LIFT - 0.056 PR 2TIME (ins) PYAI PYA2 Ri0.5FILE NAME PREFIX : L4C1P.2 P1 P2 PiN P2M6.2 4.77.5 6.3TETA1 TETA2 AREA PYMAX4 — 10 DEGREE ANGLE POPPET — TOP WALL AND BOTTOM PLATEA — LIFT — 0.056 PR — 5 H — 17.8 FILE NAME PREFIX LSC1TIME (ins) PYA1 PYA2 Ri P.2 P1 P2 PiN P2M TOTAl TETA2 AREA PYMAX1 5.2 19.4 23.4 19.6 26.132 10.1 28.1 37.5 29.8 38.83 15.2 31 46.2 32 48.95 15.6 38.4 51.3 40 54.5B — LIFT 0.056 PR 5 H 7.95 FILE NAME PREFIX : L5C2TIME (rns) PYA1 PYA2 Ri P.2 P1 P2 P1M P2M TOTAl TETA2 AREA PYMAX1 5.9 6.5 18.2 19.2 19.1 20.3 17.4 18.0 17.9 18.7 327.0 6.92 6.6 6.7 24.6 27.6 25.5 28.4 23.6 26.1 15.1 13.7 483.0 6.93 6.7 6.4 30.7 33.4 31.4 34.0 26.4 31.2 12.3 10.9 562.7 6.95 6.6 6.2 39.8 42.5 40.3 42.9 37.0 39.8 9.5 8.3 699.3 6.9C — LIFT 0.056 PR 2 H 7.95 FILE NAME PREFIX L5C3TIME (ms) PYRI PTh2 Ri R2 P1 P2 P1M P2M TOTAl TETA2 AREA PYMAX2 6.6 6.6 19.5 16.5 20.6 17.8 18.9 16.5 18.6 21.9 341.7 6.93 6.6 6.6 22.2 21.9 23.2 22.9 21.9 21.4 16.6 16.7 407.3 6.95 6.4 6.5 28.0 29.3 28.7 30.0 27.2 27.9 12.9 12.4 498.1 6.9D — LIFT 0.056 PR • 2 H — 24.25 FILE NAME PREFIX L5C4TIME (ins) PYA1 PYA2 R1 P.2 P1 P2 PiN P2M TOTAl TETA2 AREA PYMAX1 4.2 3.5 10.7 9.7 11.5 10.3 11.1 10.4 21.7 19.8 131.7 5.42 6.2 6.3 18.4 17.8 19.4 18.9 19.7 18.0 18.3 19.6 324.7 7.03 8.4 8.8 23.6 24.2 25.0 25.8 24.5 25.6 19.5 20.0 507.8 10.75 10.7 10.8 31.0 30.7 32.8 32.5 31.8 32.2 19.1 19.4 798.6 12.61 4.9 3.2 7.9 9.5 9.3 10.0 9.2 8.2 31.8 18.8 135.6 6.97851.5 5.5 3.6 12.3 13.9 13.5 14.3 12.5 14.9 24.1 14.4 213.2 6.72852 6.5 6.1 16.9 17.8 18.1 18.9 18.1 17.9 21 0 18.9 322.6 8.0753 8.8 8.8 21.7 23.0 23.4 24.7 21.7 23.4 22.0 20.9 533.6 11.0355 10.7 10.8 30.5 30.5 32.3 32.3 30.8 31.3 19.3 19.5 845.3 13.45710 14.3 15.0 47.7 46.4 49.8 48.7 47.9 47.2 16.7 27.9 1623.4 20.453B — LIFT 0.056 PR - 5 FILE NAME PREFIX : L4C2TIME (ins) PYA1 PYA2 Ri P.2 P1 P2 PiN P2M TOTAl TETA2 AREA PYMAX0.5 6.6 4.1 7.6 7.9 10.0 8.9 7.9 8.8 40.9 27.6 128.6 7.250.75 8.0 4.9 13.6 12.0 15.8 13.0 13.9 13.0 30.6 22.3 254.0 8.28571 9.5 5.8 15.8 15.8 18.4 16.8 25.1 16.4 31.0 20.0 338.5 10.3531.5 13.8 7.9 18.3 21.5 22.9 22.9 18.5 22.5 37.0 20.2 559.3 15.7922 11.0 9.3 26.5 25.9 28.7 27.5 26.9 27.0 22.5 19.7 701.6 13.7213 11.9 12.1 34.4 33.8 36.4 35.9 3.6 34.2 19.1 19.8 1049.2 18.1215 16.2 14.7 47.1 49.9 49.8 52.0 45.9 48.7 19.1 16.4 1737.9 19.4141 4.0 12.5 10.1 11.3 10.0165E — LIFT 0.056 PR - 5 H 14.25 FILE NAME PREFIX : LSCSTIME (ms) PYAI PYA2 Ri R2 P1 P2 PiN P2W TETA1 TETA2 AREA PYMAX1 11.9 7.7 19.4 20.0 22.8 21.5 19.9 20.3 31.6 21.1 495.3 12.62 10.1 10.6 27.4 29.7 29.2 31.5 28.0 30.7 20.2 19.6 734.6 12.63 11.9 11.8 35.2 35.5 37.2 37.4 35.2 36.0 18.7 18.3 1022.0 12.95 12.8 12.3 44.6 45.9 46.4 47.5 45.1 46.6 16.1 15.1 1342.6 12.9F — LIFT — 0.056 PR — 5 PISTON BOWL FILE NAME PREFIX : LSC6TIME (tns) PYA1 PYA2 Ri R2 P1 P2 P1W P2W TETA1 TETA2 AREA PYMAX0.25 6.6 4.90.5 9.8 8.81 18.2 16.51.5 23.2 22.15 — 10 DEGREE ANGLE POPPET — INTERRUPTED JET AND BOTTOM PLATEA — LIFT — 0.056 PR 5 H 13.9 TNT • 6x2 FILE NAME PREFIX : L6C1TIME (ms) PYA1 PYA2 Ri R2 P1 P2 P1!.! P2M TETA1 TETA2 AREA PYMAX0.25 9.5 7.5 8.4 8.7 12.7 11.5 8.8 9.1 48.6 40.6 191.2 11.20.5 9.2 7.0 7.1 8.1 11.6 10.7 7.7 8.8 52.2 40.8 168.8 11.21 12.5 10.4 13.9 20.0 18.7 22.5 14.3 13.1 41.9 27.4 463.9 12.82 12.5 12.6 22.9 28.7 26.1 31.4 23.3 29.2 28.6 23.7 732.7 12.85 12.4 12.4 47.5 56.2 . 49.1 57.5 48.8 56.9 14.7 12.4 1347.9 12.8B — LIFT 0.056 PR 5 H 38.1 INT 6x2 FILE NAME PREFIX L6C2TIME (ins) PYAI PYA2 Ri R2 P1 P2 P1W P2W TETA1 TETA2 AREA PYMAX1 15.3 11.8 17.8 21.0 23.5 24.1 19.0 22.4 40.8 29.3 612.7 18.52 21.7 19.8 26.5 31.6 34.2 37.3 28.5 30.6 39.3 32.0 1283.0 27.35 33.3 29.6 45.5 56.8 56.4 64.1 50.2 62.0 36.2 27.5 3266.4 37.3C — LIFT 0.056 PR 2 H 38.1 INT 6x2 FILE NAME PREFIX L6C3TIME (ins) PYAI PYA2 RI R2 P1 P2 P1W P2W TETA1 TETA2 AREA PYMAX1 7.2 7.3 10.0 9.7 12.4 12.1 10.3 11.4 35.9 36.9 198.3 9.12 14.1 15.8 18.4 19.4 23.2 25.0 16.4 19.8 37.5 39.2 596.9 18.55 24.4 26.6 22.9 26.5 33.5 37.6 29.7 36.8 46.8 45.2 1270.2 30.710 35.2 34.8 31.6 37.1 47.3 50.9 44.3 48.7 48.1 43.2 2110.3 37.30 — LIFT — 0.056 PR 2 H — 38.1 INT 8x1.5 FILE NAME PREFIX L6C4TIME (ins) PTh1 PYA2 R1 R2 P1 P2 P1W P2 TETAI TETA2 AREA PYMAX1 6.5 7.2 10.0 8.7 11.9 11.3 10.7 i0.& 32.9 39.7 191.7 8.02 11.9 11.8 20.7 16.1 23.8 20.0 21.5 18.4 29.9 36.1 534.4 37.35 17.1 18.0 39.4 32.0 42.9 35.8 41.6 32.8 23.4 30.1 1272.6 23.610 23.1 24.3 49.1 44.2 54.2 50.5 59.7 42.1 25.2 28.7 2361.5 37.36— 10 DEGREE ANGLE POPPET — PULSE WIDTH EFFECT166A—LIFT-0.t)56 PR2 PN5TIME (ms) PYA1 PYA2 RI R21 7.3 7.0 10.8 10.13 18.1 16.1 23.9 22.95 23.6 21.2 31.4 26.810 35.4 31.9 36.3 37.911 34.2 32.3 40.9 41.512 37.2 35.5 46.1 40.214 39.9 36.7 50.4 44.115 41.3 36.0 47.1 44.8B—LIFT—0.056 P8—2 PW—6TIME (ins) PYA1 PYA2 Ri R21 6.9 6.9 10.3 9.65 25.3 21.6 29.5 32.110 33.8 32.6 42.1 39.113 39.5 39.6 44.4 41.414 38.8 35.3 46.4 44.115 39.4 35.5 50.0 53.016 37.7 34.1 51.7 48.417 41.3 40.2 52.0 47.018 47.2 43.8 50.0 47.0FILE NAME PREFIX L7C1PiN P2M TETAI TETA2 AREA10.6 12.1 34.2 34.8 216.725.4 25.8 37.1 35.2 870.734.5 35.0 37.0 38.4 1380.244.5 43.4 44.3 40.1 2586.249.0 47.9 39.9 37.9 2715.848.9 45.8 38.9 41.4 3156.956.8 49.1 38.4 39.7 3662.057.1 46.9 41.2 38.8 3666.9FILE NAME PREFIX L7C2P1M P214 TETA1 TETA2 AREA10.1 11.0 33.7 35.3 205.032.2 33.4 40.7 33.9 1437.648.9 47.2 38.8 39.9 2694.550.1 47.3 41.7 43.0 3491.354.9 49.9 39.9 38.7 3465.955.8 58.4 38.2 33.8 3818.058.0 53.5 36.1 35.2 3654.461.0 56.1 38.4 40.5 4226.756.7 58.1 43.3 43.0 4398.99 — 30 DEGREE ANGLE POPPET — TOP WALL AND BOTTOM PLATEA — LIFT 0.082 PR 5 N 27.8TIME (ins) PYAI PYA2 Ri R21 12.0 7.8 4.82 15.1 15.3 18.7 16.8 24.1 22.73 15.3 15.3 27.4 22.3 31.4 27.05 15.1 15.3 42.9 34.6 45.5 37.838.9 42.4 489.5 15.529.2 34.5 685.6 15.519.3 23.9 1116.4 15.5P113.129.939.350.753.359.264.362.6P112.338.954.059.460.563.764.066.468.8P212.328.034.249.652.653.757.457.5P211.838.750.956.656.563.859.261.964.3PYMAX8.219.126.538.238.544.547.248.9PYMAX7.629.537.743.242.644.243.246.452.47— 30 DEGREE ANGLE POPPET — FREE JETA— LIFT 0.082 PR 2NOT pROCESSEDB—LIFT—0.081 PR5NOT PROCESSED8— 30 DEGREE ANGLE POPPET — TOP WAILA—LIFT—0.082 PR- 5NOT PROCESSEDFILE NAME PREFIX L8C1FILE NAME PREFIX L8C2FILE NAME PREFIX L8C3FILE NAME PREFIX L8C4P1 P2 P114 P214 TETA2 TETA2 AREA PYMAXB — LIFT = 0.081 PR — S N — 7.95TIME (ins) PYA1 PYA2 Ri R2 P1 P21 6.5 6.4 12.6 10.0 14.2 11.92 6.6 6.8 20.7 17.1 21.7 18.43 6.4 6.6 30.4 24.9 31.0 25.74 6.5 6.6 41.0 24.5 41.5 25.4FILE NAME PR1FIX : LBCSPiN P2M TETA1 TETA2 AREA PYMAX27.4 32.6 167.9 6.717.8 21.6 330.3 7.011.9 14.9 424.0 7.08.9 15.2 516.5 7.016710 — 30 DEGREE ANGLE POPPET — Top WALL AND INTERRUPTIONA — LIFT 0.081 PR 5 INT 6x1.5TIME (ins) PYA1 PYA2 Ri R21 14.0 13.6 9.4 6.1 16.8 14.92 21.0 22.3 29.4 24.5 36.1 33.13 25.6 26.0 40.4 32.6 47.8 41.7B — LIFT - 0.081 PR 5 INT 4x2 COPPER NUTTIME (ins) PYA1 PYA2 RI R2 P1 P21 15.6 16.0 8.4 9.4 17.7 18.52 20.4 21.9 16.8 18.7 26.4 28.93 29.2 30.3 24.5 29.1 38.1 42.05 40.9 42.7 33.9 42.6 53.2 60.3C— LIFT — 0.081 PR— 2 INT 4x2 COPPER NUTTIME (ins) PTh1 PYA2 Ri R2 P1 P21 8.5 9.2 4.8 4.8 9.8 10.42 16.8 18.7 10.7 11.0 19.9 21.73 20.8 22.8 13.6 14.2 24.8 26.95 28.9 28.1 15.8 25.5 32.9 38.0FILE NAME PREFIX L8C7PiN P2M TETA1 TETA2 AREA PYMAX61.7 59.6 356.8 18.150.5 49.5 804.5 24.450.0 46.2 1525.7 34.250.4 45.0 2766.7 46.9FILE NAME PREFIX : L8C8P1M P2M TETA1 TETA2 AREA PYMAX60.3 62.1 145.9 10.157.6 59.5 417.4 19.856.9 58.1 633.4 24.461.3 47.8 1033.4 31.3A — LIFT — 0.056 PR 5 FILE NAME PREFIX L9CITIME (ins) PYA1 PYA2 RI R2 P1 P2 PYI PY2 TETAI TETA2 AREA PYMAX2 20.2 22.9 20.6 20.9 28.8 31.0 7.7 9.1 44.5 47.7 1041.2 39.13 24.8 26.6 26.3 31.3 36.1 41.1 9.6 11.9 43.3 40.3 1706.3 46.05 28.3 25.3 41.8 55.6 50.4 61.1 14.2 15.6 34.1 24.5 2910.5 53.568.7 72.8 23.8 23.8B — lIFT = 0.056 PR 2NOT PROCESSEDFILE NAME PREFIX L9C212 — 20 DEGREE ANGLE POPPET— TOP WALL 4 BOTION PLATEFILE NAME PREFIX L9C30.75 9.2 7.9 6.1 3.6 11.1 8.6FILE NAME PREFIX L8C6P1 P2 PiN P2M TETA1 TETA2 AREA PYMAX56.3 65.7 125.4 10.156.2 65.6 286.6 15.835.5 42.2 1165.8 28.532.4 38.6 1725.6 34.811— 20 DEGREE ANGLE POPPET — TOP WALL10A LIFT = 0.056 PR— 5 N — 14.0NOT PROCESSED168B — LIFT — 0.056 PR — 5 mt 6x2 sun FILE NAME PREFIX L9C4TIME (ins) PYA1 PYA2 RI R2 P1 P2 PY1 PY2 TETA1 TETA2 AREA PYMAX1 13.1 12.1 10.12 12.7 13.8 25.3 22.2 28.3 26.2 26.7 31.9 758.9 14.83 12.8 11.4 27.3 39.1 30.2 40.7 25.2 16.3 939.8 14.85 43.5 41.4C — LIFT 0.056 PR 5 H — 7.9 FILE NAME PREFIX : L9C5TIME (ins) PYA1 PYA2 RI R2 P1 P2 PY1 PY2 TETA1 TETA2 AREA PYMA)C1 14.9 15.0 11.6 13.9 18.9 20.5 52.0 47.2 493.9 18.72 22.1 22.0 24.2 28.4 32.8 35.9 42.4 37.7 1317.1 25.33 26.5 26.5 32.3 33.9 41.8 43.0 39.3 38.0 1916.1 31.35 34.3 33.5 48.8 52.0 59.6 61.8 35.1 32.8 3459.5 39.013 — 20 DEGREE ANGLE POPPET — FREE JETA — LIFT 0.056 PR 5 FILE NAME PREFIX LAdNOT PROCESSEDB — LIFT 0.056 PR — 2 FILE NAME PREFIX LAC2NOT PROCESSEDC — LIFT— 0.1 PR - 5 FILE NAME PREFIX LAC3NOT PROCESSED14 — 20 DEGREE ANGLE POPPET NEW INJECTOR — TOP WALLA — LIFT 0.2 PR 2.64 FILE NAME PREFIX Z1C1TIME (ins) PYA1 PYA2 Ri R2 P1 P2 PY1 PY2 TETA1 TETA2 AREA PYMAX1 4.3 4.62 15.4 15.93 19.4 21.45 31.7 29B — LIFT 0.2 PR 2.64 INT 6X2 FILE NAME PREFIX Z1C2TIME (ins) PYAI PYA2 RI R2 P1 P2 PYI P12 TETA1 TETA2 AREA PYMAYI 14.32 18.33 32.85 47.3C— LIFT — 0.2 PR = 3.43 INT 6X2 FILE NAME PREFIX Z1C4TIME (ins) PYA1 P1A2 Ri R2 P1 P2 P11 P12 TETA1 TETA2 AREA PYMAX1 9.42 25.83 42.25 51.316915 — 10 DEGREE ANGLE POPPET NEW INJECTOR — TOP WALLA — LIFT 0.2 PR — 2.64 INT 6X2 FILE NAME PREFIX Z2CITIME (nis) PYA1 PYA2 Ri R2 P1 P2 PY1 PY2 TETA1 TETA2 AREA PYMAX1 15.82 24.73 34.25 48.5B — LIFT 0.2 PR = 2.64 FILE NAME PREFIX : Z2C2TIME (ins) PYA1 PYA2 RI R2 P1 P2 PYI PY2 TETA1 TETA2 AREA PYMAXI 8.12 213 28.15 36.4C — LIFT 0.2 PR 3.43 FILE NAME PREFIX Z2C3TIME (ins) PYA1 PYA2 Ri R2 P1 P2 PY1 PY2 TETA1 TETA2 AREA PYMAX1 9.7 10.62 24 22.63 32.2 325 43.4 42.616 — 1C) DEGREE ANGLE POPPET NEW INJECTORA — LIFT 0.2 PR - 3.43 FILE NAME PREFIX Z2C4TIME (ins) PYA1 PYA2 Ri R2 P1 P2 PY1 PY2 TETA1 TETA2 AREA PYMAX2 13.4 13.62 27.5 27.13 31.7 27.75 42.6 44.1B — LIFT 0.2 PR — 2.64 FILE NAME PREFIX Z2C5TIME (ins) PYA1 PYA2 RI R2 P1 P2 PY1 PY2 TETA1 TETA2 AREA PYMAX1 10.5 10.22 24.8 24.73 26.5 27.55 35.95 35.117017 — EXPERIMENTS IN—CYLINDER, 10 DEGREE ANGLE POPPET NEW INJECTOR -A — LIFT - 0.2 PR — 2.64 Pog 267.5 kPa Poc — 101.3 kPa FILE NAME PREFIX : 2301TIME (ms) PYA1 PYA2 Ri R2 P1 P2 PY1 PY2 TETA1 TEEA2 AREA PYMAX2 21.3 213 27.3 275 35.3 33.88 31.1B — LIFT — 0.2 PR 3.43 Pog — 347.6 kPa Poc — 101.3 kPa FILE NAME PREFIX : 2302TIME (ms) PYA1 PYA2 Ri R2 P1 P2 PY1 PY2 TETAI TETA2 AREA PYMAX2 25.3 24.83 34.4 32.45 41.6 43.18 46.9 44.8C — LIFT 0.2 PR 2.64 Pog 535.1 kPa Poc 202.7 kPa FILE NAME PREFIX : 2401TIME (ms) PYAI PYA2 Ri R2 P1 P2 PY1 PY2 TETA1 TETA2 AREA PYMAX2 20.1 22.43 29.6 26.85 36.6 37.88 48.1 50.1O — LIFT 0.2 PR 2.64 Pog — 802.6 kPa Poc 304.0 kPa FILE NAME PREFIX Z4C2TIME (ms) PYA1 PYA2 Ri R2 P1 P2 PY1 PY2 PETAl TETA2 AREA PYMAX2 14.1 17.73 28.1 30.85 41.1 34.58 46.1 45.6E — LIFT 0.2 PR 2.64 Pog 990.7 kPa Poc 375.2 kPa FILE NAME PREFIX Z4C3TIME (ms> PYAI PYA2 Ri R2 21 P2 PY1 PY2 PETAl TETA2 AREA PYMAX2 18.4 19.13 27.5 25.85 39.2 34.88 48.2 49.8F—LIFT — 0.2 PR — 3.43 Pog — 990.7 kPa Poc = 288.9 kPa FILE NAME PREFIX Z4C4TIME (ms) PYAI PYA2 Ri R2 P1 22 PYl PY2 TETAI TETA2 AREA PYMAX2 24.2 253 32.8 31.85 43.1 38.88 49.6 46.817118 — AIL VISUALISATION 20 DGREE ANGLE POPPET FREE OR INTERRUPTEDA — LIFT -0.2 PR-S FREE FILE NAME PREFIX Y1CITIME (ins) PYAI PYA2 Ri R2 P1 P2 PY1 PY2 TETA1 TETA2 AREA PYMAX2 33.6 30.763 38.75 38.15 55.2 51.6B — LIFT — 0.2 PR - 5 INT 2X6 FiLE NAME PREFIX Y1C2TIME (ins) PYAI PYA2 Ri R2 P1 P2 PY1 PY2 TETAI TETA2 AREA PYMAX1 28.312 63.4C — LIFT — 0.2 PR- 5 INT 4X3 FILE NAME PREFIX Y1C5TIME (ins) PYA1 PYA2 Ri R2 P1 P2 PY1 PY2 TETA1 TETA2 AREA PYMAX1 36.12 63.4 67.53 78.8 85D — LIFT - 0.2 PR - 5 INT 4X2 FILE NAME PREFIX Y1C6TIME (ins) PYAI PYA2 RI R2 P1 P2 PY1 PY2 TETA1 TETA2 AREA PYMAX2 61.4 633 83.7 85.4E — LIFT - 0.2 PR 5 INT 4X1 FILE NAME PREFIX Y1C7TIME (ins) PYA1 PYA2 RI R2 P1 P2 PY1 PY2 TETA1 TETA2 AREA PYMAX3 61.1 61F — LIFT - 0.2 PR - 5 INT 4X2 WITH COPPER CARTRIDGE FILE NAME PREFIX Y1C8TIME (ins) PYAI PYA2 Ri R2 P1 P2 PY1 PY2 TETA1 TETA2 AREA PYMAX3 55.7 54.6G — LIFT 0.2 PR - 5 INT 6X2 FILE NAME PREFIX Y1C9TIME (ins) PYA1 PYA2 RI R2 21 P2 PYI PY2 TETA1 TETA2 AREA PYMAX2 52.6 51.93 70.6 70.2F — LIFT - 0.2 PR - 5 INT 6X1 FILE NAME PREFIX Y1CATIME (ins) PYA1 PYA2 Ri R2 P1 P2 PY1 PY2 TETA1 TETA2 AREA PYMAX3 75 77G - LIFT - 0.2 PR - S INT 8X1 FILE NAME PREFIX Y1CBTIME (ins) PYAI PYA2 Ri R2 22 P2 PYI PY2 TETAI TETA2 AREA PYMAX3 71.5 72.5

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0080922/manifest

Comment

Related Items