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An image-based analysis of stratified natural gas combustion in a constant volume bomb Mezo, Andrew 2008

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    AN IMAGE-BASED ANALYSIS OF STRATIFIED NATURAL GAS COMBUSTION IN A CONSTANT VOLUME BOMB  by  ANDREW MEZO  B.A.Sc., The University of British Columbia, 2006    A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE  in  THE FACULTY OF GRADUATE STUDIES  (Mechanical Engineering)           THE UNIVERSITY OF BRITISH COLUMBIA  (Vancouver)    September 2008   ? Andrew Mezo, 2008   iiABSTRACT Current stoichiometric spark-ignited engine technologies require costly catalytic converters for reductions in tailpipe emissions.  Load control is achieved by using a throttle, which is a leading contributor to reductions in efficiency.  Spark-ignited lean burn natural gas engines have been proven  to  be  more  efficient  and  emit  fewer  pollutants  than  their  stoichiometric  counterparts.  Load  reduction  in  these  engines  can  be  achieved  by  regulating  the  air/fuel  ratio  of  the  intake charge thereby reducing the efficiency penalties inherent to throttling.  Partially stratified charge (PSC) can provide further reductions in emissions and improvements in efficiency by extending the lean limit of operation.  PSC is achieved by the ignition of a small quantity of natural gas in the vicinity of the spark plug.  This creates an easily ignitable mixture at the spark plug electrodes, thereby providing a high energy ignition source for the ultra-lean bulk charge.   Stratified charge engine operation using direct injection (DI) has been proposed as a method of bridging the throttleless load reduction gap between idle and ultra-lean conditions.  A previous study was conducted to determine if PSC can provide a high-energy ignition source in a direct injected stratified charge engine.  Difficulties with igniting the PSC injections in an air-only bulk charge were encountered.  This study focuses on a fundamental Schlieren image-based analysis of PSC combustion.  Natural gas  was  injected  through  a  modified  spark  plug  located in  an  optically  accessible  combustion bomb.  The relationships between PSC injection timing, fuel supply pressure and spark timing were investigated.  Spark timing is defined as the duration between commanded start of injection and the time of spark.  As the fuel supply pressure was increased, the minimum spark timing that lead  to  successful  combustion  also  increased.    The  largest  spark  timing  window  that  led  to successful combustion was determined to be 80 ms wide at an injection fuel supply pressure of 300 psi.  The amount of unburned natural gas increased with increasing spark timing.  A cold flow study of the PSC injection system was also conducted.  The PSC injection solenoid was  found  to  have  a  consistent  average  injection  delay  of  1.95  ms.    The  slope  of  the  linear response region of observed injection duration to commanded injection duration was 8.4.  Due to plenum effects, the average observed injection duration of the entire PSC system was an order of magnitude  longer  than  the  commanded  injection  duration  and  was  found  to  vary  significantly with fuel supply pressure.   iii TABLE OF CONTENTS Abstract ........................................................................................................................................... ii Table of Contents ........................................................................................................................... iii List of Tables .................................................................................................................................. vi List of Figures ............................................................................................................................... vii Nomenclature .................................................................................................................................. x Acknowledgements ....................................................................................................................... xii 1.  INTRODUCTION ................................................................................................................... 1 1.1  Background ..................................................................................................................... 1 1.2  Turbulent Transient Jets .................................................................................................. 4 1.3  Schlieren Visualization .................................................................................................... 6 1.4  Research Objectives ........................................................................................................ 8 2.  EXPERIMENTAL SETUP ..................................................................................................... 9 2.1  Schlieren Optical Apparatus ............................................................................................ 9 2.2  High Speed Camera ....................................................................................................... 10 2.3  Combustion Bomb Assembly ........................................................................................ 11 2.4  PSC Injection System .................................................................................................... 12 2.5  Data Aquisition and Triggering ..................................................................................... 14 2.6  Injection Solenoid Delay Study ..................................................................................... 16 3.  METHODOLOGY ................................................................................................................ 21 3.1  Experimental Matrix ...................................................................................................... 21   iv 3.2  Pressure Data Analysis .................................................................................................. 23 3.3  Image Analysis .............................................................................................................. 24 3.4  Uncertainty Analysis ..................................................................................................... 26 4.  RESULTS AND DISCUSSION ............................................................................................ 29 4.1  Cold Flow Injection Data .............................................................................................. 29 4.1.1  PSC Injection Mass Flux ....................................................................................... 31 4.1.2  PSC Injection Timing ............................................................................................ 31 4.1.3  Charge Motion Entrainment .................................................................................. 36 4.2  Combustion Analysis..................................................................................................... 40 4.2.1  Integrated Heat Release Analysis .......................................................................... 46 4.2.2  Heat Release Rate Analysis ................................................................................... 55 4.2.3  Combustion Duration Analysis ............................................................................. 57 4.2.4  Ignition Delay Study .............................................................................................. 61 4.2.5  Fuel Jet and Flame Growth Study ......................................................................... 62 4.3  Summary of Combustion Results .................................................................................. 70 5.  CONCLUSIONS AND RECOMMENDATIONS ................................................................ 72 5.1  Conclusions ................................................................................................................... 72 5.2  Recommendations ......................................................................................................... 74 6.  REFERENCES ...................................................................................................................... 76 APPENDIX A: Experiment Numbers ........................................................................................... 79 APPENDIX B: Select Images for Combusting Runs .................................................................... 80   vAPPENDIX C: Select Images for Non-Combusting Runs .......................................................... 100 APPENDIX D: Select Matlab Processing Code.......................................................................... 106 Part I: Combustion Calculation Functions .............................................................................. 106 Part II: Image Processing Functions ........................................................................................ 115 Part III: Image Binarization Functions .................................................................................... 119 APPENDIX E: Compressible Flow Calculations ........................................................................ 124    vi LIST OF TABLES Table 1 - Experimental Matrix ...................................................................................................... 23 Table 2 - Natural Gas Composition .............................................................................................. 24 Table 3 - Instrumentation Description and Uncertainty ............................................................... 27 Table 4 - Injected NG Mass and RAFR Data at Each Pressure Ratio .......................................... 31 Table 5 - PSC Injection Timing Parameters Based on Schlieren Photography ............................ 34 Table 6 - Spark Timing with 100% Combustion Success ............................................................ 41    viiLIST OF FIGURES Figure 1 - Fuel-Air Equivalence Ratios Required for Throttleless Operation from [Kubesh, 2001] ......................................................................................................................................................... 3 Figure 2 - Individual Realization Overlapped with Three Run Average for Turbulent Transient Jet .................................................................................................................................................... 5 Figure 3 - Simple Schlieren System Diagram, Adapted from Settles (2001) ................................. 7 Figure 4 - Schlieren Optical Apparatus ........................................................................................ 10 Figure 5 - Sample Raw Image Captured with Phantom Camera .................................................. 11 Figure 6 ? Combustion Bomb Assembly ..................................................................................... 12 Figure 7 - Bosch XR2CS Spark Plug Modified for PSC Injection, Illustration on Left by Gorby (2007) ............................................................................................................................................ 13 Figure 8 - PSC System Details ..................................................................................................... 13 Figure 9 - LabView Virtual Interface (.vi) Control Software Screen Output ............................... 15 Figure 10 - Image Compilation, Solenoid Timing Study, 21.312 ms Commanded Pulse Width . 17 Figure 11 ? Injection Solenoid Delay for Various Commanded Pulse Width .............................. 18 Figure 12 - Observed Solenoid Injection Duration vs. Commanded Injection Duration ............. 19 Figure 13 - Linear Region of OSID vs. CID Plot ......................................................................... 19 Figure 14 - Solenoid Chatter Depicted by Secondary Jet Pulse, CID = 1.00 ms ......................... 20 Figure 15 - Example of Raw Image and Image with Background Divided.................................. 25 Figure 16 - Example of Background Subtraction and Binarization .............................................. 26 Figure 17 - Cold Flow Injection Plots, Pressure Ratios 2, 3, 4 ..................................................... 30 Figure 18 - Cold Flow Pressure Curves for PRATIO = 4, 95%PMPI Left, 99%PMPI Right ............... 32 Figure 19 - End of Injection Time as a Function of Percent Mean Value Selected ..................... 33 Figure 20 - Comparison Beteen Pressure and Schlieren Photography EOI Study ....................... 34   viiiFigure 21 - Injection Start Detail of Cold Flow Pressure Data ..................................................... 35 Figure 22 - Progression of Fuel Jet and Combustion Event at PRATIO = 4 .................................... 37 Figure 23 - Schlieren Images of the Start of Injection (Top Left), PRATIO 2 EOI (Top Right), PRATIO 3 EOI (Bottom Left), PRATIO 4 EOI (Bottom Right) ........................................................... 38 Figure 24 - Cold Flow Injection Average Pixel Count ................................................................. 39 Figure 25 - Combustion Success as a Function of Spark Timing for Each Pressure Ratio .......... 40 Figure 26 - Examples of Incombustible Test Cases for PRATIO = 2: TS = 10 ms (Top Left), TS = 20 ms (Top Right), TS = 90 ms (Bottom Left), TS = 100 ms (Bottom Right) .................................... 43 Figure 27 - Examples of Incombustible Test Cases for PRATIO = 3: TS = 10 ms (Top Left), TS = 20 ms (Top Right), TS = 40 ms (Bottom Left), TS = 160 ms (Bottom Right) .................................... 44 Figure 28 - Examples of Incombustible Test Cases for PRATIO = 4: TS = 20 ms (Top Left), TS = 50 ms (Top Right), TS = 120 ms (Bottom Left), TS = 160 ms (Bottom Right) .................................. 45 Figure 29 - Net Heat Release Plot for Exp 043, PRATIO = 3, TS = 30ms ....................................... 47 Figure 30 - Schlieren Images Corresponding to TS (Top Left), 5% Max IHR (Top Right), Max HRR (Bottom Left), and 95% Max IHR (Bottom Right) for PRATIO = 3, Ts = 30 ms .................... 48 Figure 31 ? Net Integrated Heat Release for PRATIO = 2 ............................................................... 49 Figure 32 - Net Integrated Heat Release for PRATIO = 3 ................................................................ 50 Figure 33 - Net Integrated Heat Release for PRATIO = 4 ................................................................ 50 Figure 34 - Schlieren Images at Time of Spark (Left) and 95% Max IHR (Right) for TS = 40 ms (Top) and TS = 80 ms (Bottom) at PRATIO = 2 ................................................................................ 52 Figure 35 - Schlieren Images at Time of Spark (Left) and 95% Max IHR (Right) for TS = 30 ms (Top) and TS = 160 ms (Bottom) at PRATIO = 3 .............................................................................. 53 Figure 36 - Schlieren Images at Time of Spark (Left) and 95% Max IHR (Right) for TS = 80 ms (Top) and TS = 160 ms (Bottom) at PRATIO = 4 .............................................................................. 54 Figure 37 - Maximum Rate of Heat Release for PRATIO = 2 ......................................................... 56 Figure 38 - Maximum Rate of Heat Release for PRATIO = 3 ......................................................... 56   ix Figure 39 - Maximum Rate of Heat Release for PRATIO = 4 ......................................................... 57 Figure 40 - Combustion Duration for PRATIO = 2 .......................................................................... 58 Figure 41 - Combustion Duration for PRATIO = 3 .......................................................................... 59 Figure 42 - Combustion Duration for PRATIO = 4 .......................................................................... 59 Figure 43 - Combustion Duration Normalized by Integrated Heat Release ................................. 60 Figure 44 - Ignition Delay ............................................................................................................ 61 Figure 45 - Step 1, Background Image (Left); Step 2, Frame under Study (Right) ..................... 63 Figure 46 - Step 3, Subtracted Image (Left); Step 4, Binarized Image (Right) ............................ 63 Figure 47 - Simplified Example of Image Subtraction and Addition ........................................... 64 Figure 48 - Cold Flow Fuel Jet Development, PRATIO 2 and PRATIO 3 ........................................... 65 Figure 49 - Plots of Different Threshold Values for PRATIO = 3, TS = 30 ms ................................ 66 Figure 50 - Flame Kernel Development at the Point of Ignition .................................................. 67 Figure 51 - Cold Flow and Combusting Runs as PRATIO = 2 ........................................................ 68 Figure 52 - Cold Flow and Combusting Runs at PRATIO = 3 ......................................................... 68 Figure 53 - Cold Flow and Combusting Runs at PRATIO = 4 ......................................................... 69    xNOMENCLATURE SYMBOLS PRATIO  Injection Pressure Ratio %PMPI  Percent of Mean Post Injection Pressure B  Uncertainty Due to Instrumentation Error CI95%  95% Confidence Interval c  Speed of Light in Vacuum (3.0 ? 108 m/s) c0  Speed of Light in a Medium of Interest idur  Injection Duration iend  Injection End istart  Injection Start k  Gladstone-Dale Coefficient mNG  mass of injected natural gas mNG  Mass of Natural Gas Injected n  Refractive Index P  Uncertainty Due to Averaging of Individual Realizations p  Instantaneous Pressure Pair  Pressure of Air PNG  Pressure of Natural Gas Qhr  Gross Heat Release Qht  Transferred Heat Qnet  Net Heat Release RNG  Gas Constant for Natural Gas Sx  Standard Deviation T  Temperature t0.25, n-1  Two-tailed 95% Confidence Interval Parameter in Student's t-table tcomb  Combustion Duration tign  Ignition Delay TS  Spark Timing v  Instantaneous Volume Vbomb  Volume of Combustion Bomb g1850  Average wi  Combined Uncertainty for Measured Parameters WR  Overall Uncertainty for Calculated Parameter Z  Mass Fraction ?th  Thermal Efficiency   xi afii10038  Equivalence Ratio ?  Ratio of Specific Heats rho  Density ?  Mixture Fraction    ABBREVIATIONS BC  British Columbia BTDC  Before Top Dead Centre CAD  Crank Angle Degrees CID  Commanded Injection Duration CSOI  Commanded Start of Injection FFT  Fast Fourier Transform GDI  Gasoline Direct Injection HC  Homogeneous Charge HHR  Heat Release Rate ICE  Internal Combustion Engine IHR  Integrated Heat Release IHR95%  Combustion Duration LLC  Lean Limit of Combustion NG  Natural Gas OSID  Observed Solenoid Injection Duration PIV  Particle Image Velocimetry PLIF  Planar Laser Induced Fluorescence PSC  Partially Stratified Charge RAFR  Relative Air-Fuel Ratio RON  Research Octane Number UBC  The University of British Columbia     xiiACKNOWLEDGEMENTS I would like to thank my supervisors, Dr. Bob Evans and Dr. Martin Davy for the guidance and support they have given me during my studies at UBC.  I am thankful to David Gorby for his mentorship during my first weeks at CERC and for the valuable information he has given me even after his departure.    I am grateful to Malcolm Shield for the insightful research conversations during work and play, to James Saunders for being a great neighbour and Ed Chan for all the helpful bits of information and code.  I thank the people and staff at UBC Mechanical Engineering for their help and contributions.  I would like to recognize Glen Jolly for sharing his vast electronics and controls knowledge with me.  I?d also like to thank all my colleagues at Coanda for the support and warm wishes all throughout my graduate school.  I am grateful to my parents, who have encouraged me to take this path and have offered their continuous support throughout.   Lastly,  I  would  like  to  thank  my  girlfriend  Julie,  who  has  stood  by  me  and  encouraged  me throughout my studies here.    11.  INTRODUCTION The internal combustion engine (ICE), which dates back to the late 19th century, is still the prime mover in  today?s  transportation  industry.    Over  the  course  of  its  lifetime,  the  ICE  has  had  numerous improvements in every aspect ranging from size, durability, control, and tailpipe emissions.  In the last 50 years of operation, some great strides have been made in the field of engine control and management, which have made the internal combustion engine cleaner and more efficient.  Also, alternative fuels such as natural gas have become more popular due to their abundance and clean burning nature.  1.1  BACKGROUND The recent introduction of carbon taxation, increases in the price of oil, as well as continuously tightening emissions regulations, have motivated further research into clean burning, efficient engine technologies.  Spark ignited engine research at the University of British Columbia (UBC) is primarily focused on natural gas (NG) fuelling.  NG is an abundant fuel source in BC, consisting mainly of methane (>90% CH4) [Terasen  2008].    The  application  of  natural  gas  in  a  spark  ignited  ICE  is  attractive  due  to  its  high hydrogen to carbon ratio, as well as its relatively high research octane number (RON > 130) compared to gasoline.  The increased H/C ratio helps reduce CO2 emissions by as much as 30% in comparison to long chain hydrocarbon liquid fuels such as Diesel and gasoline [Pischinger 2003].  The increased RON of NG over that of gasoline reduces engine knock, and allows engine operation at higher compression ratios in homogeneous  charge  fuelling.    The  price  of  natural  gas  is  also  advantageous  over  that  of  gasoline, equalling about half the cost of gasoline on a kilowatt-hour basis [Pischinger 2003].   The majority of today?s spark ignited engines used for transport operate on stoichiometric, homogeneous air-fuel  mixtures.    Stoichiometric  engines  require  three  way  catalytic  converters  to  reduce  emissions   2levels below those imposed by legislation.  Since three way catalytic converters require stoichiometric combustion  for  efficient  operation,  air/fuel  charge  throttling  must  be  used  for  load  control.    Pumping losses inherent to throttling are a major contributor to the decreased brake thermal efficiency (etath) of spark ignited engines at part load [Heywood, 1988].  The  lean  burn  approach  has  been  shown  as  an  effective  method  of  load  control  and  NOX  emissions reduction [Reynolds, 2001].  There are several other advantages inherent to lean burn operation, which include  increased  thermal  efficiency  and  reduction  in  emissions  of  hydrocarbons  (HC),  and  carbon monoxide (CO).  The work of Reynolds demonstrates that load reduction can be easily achieved in the upper load range by leaning the overall air/fuel ratio rather than throttling.  Reynolds demonstrated that further load control is possible by using a partially stratified charge (PSC) [Evans 2000] to extend the lean operating envelope of a single cylinder engine (UBC Ricardo Hydra).  Reynolds extended the Ricardo Hydra load range an additional 10% beyond that attainable by conventional lean operation.  PSC extends the lean limit of operation by injecting a small quantity of fuel in the vicinity of the spark plug electrodes, thereby ensuring that there is a near-stoichiometric air-fuel ratio near the electrodes at the time of spark.  This is assumed to provide a high-energy ignition source for the ultra-lean bulk charge which is otherwise not ignitable by conventional spark.  Although a step in the right direction, a throttleless load reduction gap still exists between ultra-lean and idle conditions, thus further load control using overall air/fuel ratio is desired.  Previous  research  efforts  on  the  development  of  a  throttleless  natural  gas  engine  by  Kubesh  (2001), developed  a  prechamber  engine  design  that  successfully  extended  the  lean  limit  of  operation  to  near-idling  conditions.    Although  Kubesh  showed  increases  in  thermal  efficiency  compared  to  the stoichiometric  homogeneous  charge  engine,  the  increases  were  minimal  due  to  the  large  heat  and combustion losses inherent to prechamber design engines.  Kubesh also attempted to use a direct injected, split bowl-in-piston combustion chamber configuration as an alternative to the prechamber design.  The   3split bowl-in-piston design had poor operating and emissions characteristics and was deemed unfeasible with the gaseous direct injector technology of that time.    The introduction of a more robust and faster acting  series of direct injectors by Westport Innovations allowed Gorby (2007) to implement direct injection of NG in the UBC Ricardo Hydra engine.  The work conducted by Gorby was focused on extending the lean operating envelope of the Ricardo Hydra to near-idle conditions, by using direct injection in conjunction with PSC.  Although PSC operation was shown to be effective in ultra-lean air fuel ratio environments, Gorby found the PSC plume difficult to ignite in an air only background.  Without ignition of the PSC pilot charge, the main fuel jet provided by the Westport injector did not ignite either.  An air only background is necessary for a fully stratified charge operation capable  of  near-idle  throttleless  operation.    The  equivalence  ratios  (afii10038  =  1/lambda)  required  for  throttleless operation of the 8.1 L CNG engine used by Kubesh, are shown in Figure 1.  For a torque output of less Figure 1 - Fuel-Air Equivalence Ratios Required for Throttleless Operation from [Kubesh, 2001]    4than 50 N-m (<10% max torque), an equivalence ratio of less than 0.1 (lambda > 10) is required.  The lean limit of operation for a homogeneous charge natural gas engine was shown to be around afii10038 = 0.60 (lambda = 1.66).  Gorby?s  inability  to  ignite  the  PSC  pilot  charge  in  an  air  only  environment  suggested  that  a  better understanding of the PSC injection system timing and flow characteristics was necessary before moving forward with further engine testing.  To this end, a study of gaseous reacting jets is essential to elucidate the limits of the PSC ignition, and design viable control schemes to operate low-NOX lean burn NG spark ignition engines using PSC and direct fuel injection.  1.2  TURBULENT TRANSIENT JETS The injection of the PSC fuel charge is assumed to be turbulent, based on findings presented by Hill and Oulette (1999) on transient turbulent gaseous jets.  There are several fundamental characteristics which make  the  spark  ignition  of  turbulent  jets  very  difficult.    Turbulent  jet  imaging  performed  by  Lahbabi (1993) indicates that the instantaneous jet profile is very different from the averaged one.  This finding was also discussed by Oulette (1996), who researched direct injections of natural gas for Diesel engine fuelling.    Studies  conducted  by  the  present  author  also  show  the  transient  turbulent  jet  to  vary significantly in profile from an individual realization to a run-averaged result.  Figure 2 demonstrates the difference  between  the  instantaneous  jet  profile  and  a  three  run  averaged  profile  for  a  water  jet  of Reynolds number of 110,000.       5 Figure 2 - Individual Realization Overlapped with Three Run Average for Turbulent Transient Jet   Research  performed  by  Dahm  and  Dimotakis  (1988)  on  turbulent  transient jet  mixing  has  shown  that concentration gradients also vary between individual realizations and run-averages.  Dahm and Dimotakis found  the  concentration  gradients  of  the  instantaneous  profile  to  be  very  large,  while  those  of  the averaged jet were found to be well approximated by a smooth probability density function.  Since the concentration gradients of the instantaneous transient jet are very steep, and vary with each individual realization, spark ignition at the correct air-fuel ratio can be very challenging.    The design of the jet exit nozzle was found by Mi et al. (2001) to greatly influence the mixing rate of the fuel with the surrounding air.  Mi et al. determined that the mixing entrained by an orifice type jet to be superior  to  that  of  pipe  and  smooth  contraction  jets.    Dahm  and  Dimotakis  found  the  external  fluid entrainment to also be highly Reynolds number dependent.  In the case of the PSC injector, Reynolds number varies with pressure ratio.  Thus, any fluctuations in pressure upstream of the metering solenoid can dramatically alter the flammability of the PSC charge.    61.3  SCHLIEREN VISUALIZATION A method of visualizing the PSC plume was deemed necessary in order to gain a better understanding of the flow characteristics at several pressure ratios.  The Schlieren visualization technique was chosen for viewing the PSC fuel injections due to its simplicity of operation and availability within the department.  An optically accessible combustion bomb was outfitted with the PSC injection system, where the other instrumentation described in detail in the next chapter.    Schlieren visualization works on the basic principle that the refractive index (n) of gases is dependent on their molecular composition and density.  The refractive index of a medium is defined as the ratio of the speed of light through that medium (c0) to the speed of light in vacuum (c).  As the speed of light in vacuum is constant (3.0 ? 108 m/s), the refractive index of a gas is directly proportional to the speed of light  within  this  gas.    Thus,  the  refractive  index  of  a  gas  is  proportional  to  its  density  according  to Equation 1.1, where k is the Gladstone-Dale coefficient which is gas specific, and rho is the gas density.    uni006E g3398uni0031 g3404 uni006Buni03C1  (Eq. 1.1)  The  value  of  k  varies  according  to  the  molecular  composition  of  the  gas,  and  the  wavelength  of  the Schlieren light source.  Since the value of k decreases with increasing light wavelength, a mercury vapour Schlieren light source was selected due to the strong bias towards the ultraviolet range of the mercury emission spectrum [Settles, 2001].  It is important to note that gas composition inhomogeneities bend the light in proportion to the gradient of the refractive index; thus, only sections of the bomb with varying air-fuel composition or varying density will be visible.  Equation 1.2 taken from Settles (2001), gives the angular ray deflection in the x-y plane along the direction of the optical axis, z.  Therefore, according to Equation  1.2,  the  luminosity  of  a  Schlieren  image  corresponds  to  the  first  spatial  derivative  of  the refractive index.    7    g2013g3051 g3404uni0031g1866 g3505g2034g1866g2034g1876 g2034g1878uni002C uni0020uni0020uni0020uni0020uni0020uni0020uni0020uni0020 g2013g3052 g3404uni0031g1866 g3505g2034g1866g2034g1877 g2034g1878uni0020  (Eq. 1.2)  Schlieren images can be generated using various configurations of mirrors, lenses or combinations of the two.    Regardless  of  the  selected  arrangement,  a  knife  edge  is  required  at  the  point  where  the  light  is focused into the camera.  The knife edge is needed in order to block some of the refracted rays from entering the camera and obscuring the density gradients.  By blocking half the refracted light rays, the first order spatial derivatives of the refractive index become visible.  This behaviour is demonstrated in the simplified diagram shown in Figure 3.    Figure 3 - Simple Schlieren System Diagram, Adapted from Settles (2001)  Omitting to use the knife edge shown, all the refracted rays are displayed on the screen and the first order spatial derivative in refractive index becomes invisible.  The visualization method that does not use a knife edge is called Shadowgraphy, and it is only capable of displaying second order spatial derivatives in refractive index.   The Schlieren configuration used in these experiments is a Z-Type Herschellian system consisting of a condenser lens and two parabolic mirrors.  This setup if further discussed in Section 2.1.  *Point SourceLensesDisturbance Knife EdgeScreen+y+z+x  81.4  RESEARCH OBJECTIVES The objectives of the research presented in this thesis are to determine the range of pressure ratios and spark timings that lead to successful combustion of the PSC fuel charge in an air only environment.  The experiments are conducted in a fully instrumented optically accessible combustion bomb.    The  Schlieren  photographs  collected  are  used  to  explain  variations  in  combustion  success  between experimental runs, as well as to determine the PSC system injection timing parameters.  The pressure data acquired is processed to give a comparison of combustion parameters between experimental runs.  These combustion parameters are used to compare the combustion quality of runs at each pressure ratio and spark timing selected.     92.  EXPERIMENTAL SETUP The experimental work was conducted at the Clean Energy Research Centre at The University of British Columbia.  The Schlieren optical apparatus was assembled in the UBC Ricardo Hydra single cylinder research  engine  test  cell.    The  Ricardo  Hydra  PSC  injection  system  was  used  for  this  study.    The experimental apparatus consisted of five major components: the Schlieren optics, the high speed camera (used to capture the Schlieren images), the combustion bomb assembly, the PSC injection system and the data acquisition and triggering hardware.  Each major component is described in detail in the following sections.  2.1  SCHLIEREN OPTICAL APPARATUS The Schlieren apparatus is made up of two concave mirrors with a focal length of 8 feet, a convex lens, a mercury vapour compact arc lamp and a power supply for the lamp.  Mercury vapour arc illumination was selected since it provides a luminous existence of 10-100 times that of a tungsten filament bulb and it is more  sensitive  to  the  changes  in  the  light  refraction  index  [Settles,  2001].    The  mercury  emission spectrum is biased towards the blue-green side with significant emissions proportions in the ultraviolet range.  The incoherent light emitted by the mercury arc is focused by the convex lens at the focal point of the first concave mirror.  This mirror collimates the light, which is then passed through the combustion bomb test section and is collected by the second concave mirror.  The second mirror focuses the light back to a point, which is then projected into a 300 mm Nikkor lens mounted to the high speed camera.  A sketch of the light path and Schlieren setup is shown in Figure 4.   10Concave MirrorConcave MirrorPoint Source ?Hg Vapour BulbPhantom Camera with 300mm LensCombustion Bomb8 ftColumnated Light BeamsSpark PlugKnife EdgeCondenser Lens Figure 4 - Schlieren Optical Apparatus  2.2  HIGH SPEED CAMERA The  camera  used  to  capture  the  Schlieren  images  is  a  12  bit  gray  scale  digital  CCD  Phantom  v.  7.1, manufactured by Vision Research.  Images were taken at a resolution of 480 by 480 pixels through a 300 mm Nikkor f-ratio 4.0 AF-S fixed focal length lens.  At this resolution, the camera is capable of a sample rate of 9302 frames/s, with the ability to buffer 3021 images, resulting in a capture time window of 324.7 ms.  The image exposure time was maintained constant at 102 ?s.  Figure 5 shows a raw sample image captured with the aforementioned settings prior to any processing algorithms.    11 Figure 5 - Sample Raw Image Captured with Phantom Camera  2.3  COMBUSTION BOMB ASSEMBLY The optically accessible combustion bomb is made up of a stainless steel cylinder with an 80 mm bore, sealed at each end by a disc shaped quartz viewing window 25.4 mm thick.  The distance between the quartz  windows  is  46  mm.    The  measured  sealed  volume  of  the  combustion  bomb  is  231.1  cubic centimetres.  The bomb is instrumented with an Omega K-type thermocouple, an MSI calibration pressure transducer  and  a  high  speed  piezoelectric  transducer  with  a  charge  sensitivity  of  1.083  pC/psi.    An illustration of the combustion bomb assembly is shown in Figure 6.     12 Figure 6 ? Combustion Bomb Assembly  2.4  PSC INJECTION SYSTEM The PSC concept tested in the UBC Ricardo Hydra research engine by Reynolds (2001), Brown (2003) and Gorby (2007) has been unchanged for the purposes of this study.  It is intended for use in spark ignited internal combustion engines operating in a partially or fully stratified charge mode.  The system consists of a modified Bosch XR2CS spark plug, an injection solenoid that meters the fuel, and a driver box to control the solenoid.  The spark plug modifications necessary to achieve stratified charge are shown in Figure 7.  A 320 mm long capillary tube with a 0.47 mm ID is connected to the outlet of the injection solenoid.  High pressure natural gas is injected through the capillary tube, down the milled channel in the spark plug threads and exits through the 0.3 mm radial hole into the vicinity of the spark plug electrodes.  The PSC system layout, along with tubing dimensions is shown in  Figure 8.  K-type Thermocouple Manual Purge PSC Spark Plug  Injection Solenoid Purge Solenoid PCB Piezoelectric Transducer M5151 Pressure Transducer Ignition Coil   13 Figure 7 - Bosch XR2CS Spark Plug Modified for PSC Injection, Illustration on Left by Gorby (2007)     Figure 8 - PSC System Details  SolenoidValvePressureRegulatorPressureGauge (Solenoid Upstream)1/4? TubingHigh PressureNG Supply1/4? - 1/16" Reducer Fitting1/16" Capillary Tube 0.47mm ID, 320mm Long0.3mm Exit HolePressureTransducer (Combustion Bomb)  14For the purpose of these experiments, the injection pressure ratio (PRATIO) is defined as the ratio of the pressure  upstream  of  the  injection  solenoid  to  the  pressure  inside  the  combustion  bomb  prior  to  the injection event.  The pressure measurement locations are detailed in Figure 8.  Calculations based on the theory  of  compressible  flow  in  constant-area  ducts  with  friction  [Shapiro]  suggest  that  the  PSC  flow remains subsonic and therefore unchoked at all pressure ratios attempted.  The calculations, along with the critical capillary tube lengths required for a sonic exit condition are shown in Appendix E.  The  combustion  bomb  was  pressurized  and  depressurized  with  air  five  times  before  the  start  of  each experiment.  This procedure was followed in order to purge the natural gas remaining in the capillary tube, downstream of the injection solenoid and thus maintain consistency between runs.  2.5  DATA AQUISITION AND TRIGGERING The data acquisition and triggering hardware was linked to a computer running NI LabView software V.7.0.  The hardware used for triggering the high speed camera, injector driver box and spark discharge was a 47 channel PCI National Instruments data acquisition card.  An NI PCI-6601 20 MHz timer card was  used  to  for  the  high  speed  timing  required  in  these  experiments.    High  speed  pressure  data  was collected at a frequency of 50 kHz with an NI USB-9211 data acquisition card.  Temperature data was collected with an NI USB-9215 thermocouple card.  A separate voltage channel was used in the high speed data acquisition hardware to synchronize the triggering hardware.  The  LabView  software  collected  pressure  and  temperature  data  as  tab  separated  text.    This  data  was pegged,  zeroed and analysed with Mathworks Matlab.  The high speed image data from the Phantom camera was downloaded from the camera buffer and saved in raw video format.  These videos were later   15converted to 16 bit grayscale TIFF images which were further processed with Matlab.  A screen shot of the LabView control interface is included in Figure 9.   Figure 9 - LabView Virtual Interface (.vi) Control Software Screen Output   162.6  INJECTION SOLENOID DELAY STUDY In order to determine the injection timing characteristics of the PSC system, an injection solenoid timing study was necessary to characterize the PSC solenoid on a stand-alone basis.  The PSC capillary tube was disconnected from the solenoid body, thus leaving the 0.25? port hole exposed to the atmosphere.  By using high-speed Schlieren photography, the natural gas transient jet was visualized exiting the solenoid body at a frame rate of 4700 frames/s.  This study was performed under atmospheric conditions, at constant regulator pressure and with several commanded injection duration (CID) values.  In each of the 24 runs conducted, a transient gaseous jet as defined by Hill and Ouellette (1999) is clearly observed at the solenoid exit.  Injection solenoid delay is defined as the duration between the commanded start of injection (CSOI) and the first instance natural gas is observed exiting the solenoid.  The observed end of injection is defined as the duration between the CSOI and the time at which the transient jet plume detaches from the solenoid exit.  The duration between the observed start and observed end of injection is defined as the observed solenoid injection duration (OSID).   An example of the start, development, and end of the transient jet is shown in Figure 10.  The 1.819 ms slide depicts the observed start of injection while the 14.584 ms slide shows the observed end of injection.    17 Figure 10 - Image Compilation, Solenoid Timing Study, 21.312 ms Commanded Pulse Width  The commanded injection pulse width was varied between 0.666 ms and 21.312 ms.  These pulse width values correspond to 8 crank angle degrees (CAD) and 256 CAD respectively, in an ICE operating at 2000 rpm.  The injection pressure was maintained at a constant 29 bar (420 psi).  Figure 11 shows the injection solenoid delay as a function of commanded injection duration.  The error bars specify a 95% confidence interval (defined in Section 3.4), which indicate that all values are within experimental error   18and average a jet plume start delay of 1.95 ms (23.5 CAD at 2000 rpm).  The start delay is concluded to be independent of commanded injection duration.    Figure 11 ? Injection Solenoid Delay for Various Commanded Pulse Width  The observed solenoid injection duration is plotted against commanded injection duration in Figure 12.  The response of the OSID is linear with CID for CID values up to ~ 2.7 ms.  For CID values higher than 2.7 ms, the observed solenoid injection duration becomes constant within experimental error (12.5 ms).  Since the observed solenoid injection duration is expected to increase linearly with commanded injection duration, a deviation from this behaviour could mean that the control system is not allowing for CID values higher than 2.7 ms.   0.00.51.01.52.02.53.00 2 4 6 8 10 12 14 16 18 20 22Jet Plume Start Delay (ms)Commanded Injection Duration (ms)  19  Figure 12 - Observed Solenoid Injection Duration vs. Commanded Injection Duration  The  linear  region  of  Figure  12  is  re-plotted  in  Figure  13  with  trendline  and  R2  values  shown.    The intercept of the trendline suggests that CID values less than ~ 0.46 ms result in no observed injection at 0.02.04.06.08.010.012.014.00 2 4 6 8 10 12 14 16 18 20 22Observed Injection Duration (ms)Commanded Injection Duration (ms)y = 8.441x - 3.898R? = 0.8760.02.04.06.08.00.0 0.3 0.5 0.8 1.0 1.3 1.5Observed Injection Duration (ms)Commanded Injection Duration (ms)Figure 13 - Linear Region of OSID vs. CID Plot   20all.    The  trendline  slope  indicates  that  observed  injection  durations  are  significantly  longer  than commanded injection durations.  Both the trendline slope, which is much greater than one and the CID axis intercept indicate that the solenoid valve has significant delays due to inertial forces.  This is a strong sign  that  observed  PSC  system  injection  durations  will  likely  be  much  longer  than  the  commanded injection durations.  Also, as the capillary tube is connected for the PSC injections, plenum effects due to the pressurized system volume downstream of the solenoid exit will likely extend the observed injection duration even further.  Evidence  of  solenoid  chatter  was  observed  for  three  commanded  injection  duration  timings.    At  CID values of 1.000, 1.167, and 1.332 ms a secondary jet pulse is observed following the main jet pulse.  The secondary pulse observed is shorter in duration and smaller in size.  An example of this behaviour at CID =  1.00  ms  is  shown  in  Figure  14,  where  the  progression  of  the  secondary  jet  pulse  is  clearly  seen following the end of the primary jet pulse.  Since this chatter could introduce additional uncertainties in the PSC injection system, CID timings that cause solenoid chatter were avoided in later studies.   Figure 14 - Solenoid Chatter Depicted by Secondary Jet Pulse, CID = 1.00 ms   213.  METHODOLOGY An investigation into the flammability of the PSC pilot charge in an air only environment was performed using  a  Schlieren  image  analysis  technique  for  qualitative  combustion  observation.    For  cases  where combustion  was  present,  visualization  helped  to  determine  the  combustion  quality  by  the  amount  of unburned  gases  remaining  post-combustion.    The  Schlieren  images  gave  significant  insight  into  the amount of mixture present near the spark plug electrodes at the time of spark.  The high speed images were  also  useful  in  determining  the  PSC  system  delays  and  injection  durations  at  the  pressure  ratios studied.  High  speed  pressure  data  was  used  to  determine  combustion  parameters  such  as  ignition  delay, combustion  duration,  rate  of  heat  release  and  total  heat  release  for  all  combusting  cases.    Cold  flow pressure data was used to establish the amount of natural gas injected at each pressure ratio.  Pressure data was also used to validate the findings and conclusions derived from the Schlieren images.  3.1  EXPERIMENTAL MATRIX Previous studies of the PSC system conducted by Reynolds (2001) suggest that spark timing with respect to injection is a critical variable when tuning the PSC system for optimal operation.  Spark timing with respect  to  the  commanded  start  of  injection  was  also  shown  to  affect  parameters  such  as  combustion duration, ignition delay and amount of heat released [Huang et al., 2003].  For the purposes of this study, spark timing (TS) is defined as the duration between the commanded start of injection (CSOI) and the commanded  time  of  spark.    Work  performed  on  stratified  methane  mixtures  in  a  constant  volume combustion  bomb  by  Kitagawa  et  al.  (2002)  demonstrates  a  significant  influence  of  spark  timing  on maximum combustion pressure and mass fraction of fuel burned.  Kitagawa et al. have also shown the rate of pressure rise to be greatly affected by spark timing.     22Mass of fuel injected, exit momentum flux and the Reynolds number of transient jets are all very much dependent on injection pressure ratio (PRATIO) [Hill, 1999].  These transient jet characteristics were shown to greatly influence entrainment velocities and concentration gradients by Dahm and Dimotakis (1990).  Pressure  ratio  is  defined  as  the  ratio  of  the  injection  pressure  upstream  of  the  solenoid  to  the  initial pressure in the combustion bomb.  Although the injection pressure ratio was held constant in the studies performed by Reynolds, Brown and Gorby, it was deemed critical to learn how the injection pressure ratio affects the combustion quality and stability of the PSC charge.  The previous section suggests that commanded injection duration timings greater than 2.7 ms result in constant OSID values.  Also, at commanded injection durations less than 1.3 ms solenoid chatter was observed.  Thus, for the purpose of these experiments, the commanded injection duration was maintained at a constant value of 8.0 ms.   As described previously, Reynolds (2001) and Brown (2003) have shown successful application of PSC to an ICE operating in a partially stratified mode with bulk charge relative air fuel ratios of 1.3 to 1.7.  Gorby (2007) attempted to operate the Ricardo Hydra in a fully stratified mode, with a bulk charge of pure air.  He was unsuccessful and did not manage to ignite the pilot PSC charge.  There is much interest in the application of the PSC system to a fully stratified charge engine.  Consequently, all tests conducted for  this  study  were  performed  with  an  air  only  bulk  charge.    The  charge  pressure  was  determined  to replicate that of the Ricardo Hydra engine at 30 degrees before top dead centre (BTDC).  A summary of the experimental matrix conducted is shown in Table 1.  A minimum of three repeats were performed for each table entry.  The list of the experimental numbers and order of execution is given in Appendix A.       23 Table 1 - Experimental Matrix     3.2  PRESSURE DATA ANALYSIS Raw  pressure  data  was  collected  at  a  frequency  of  50  kHz  for  500  ms  per  experiment.    Since  the piezoelectric  pressure  transducer  is  dynamic,  a  secondary  pressure  transducer  was  used  to  peg  the piezoelectric  pressure  signal  to  the  correct  initial  value.    The  pressure  data  timing  was  zeroed  and synchronized according to the input trigger signal of the camera.  A fast Fourier transform (FFT) algorithm was applied to the raw pressure signal to remove high frequency noise.  The pressure signal was then differentiated and heat release rate (HRR) was calculated according to Equation 3.1 [Heywood].    g1856g1843g1856g1872 g3404g2011g2011 g3398uni0031g1842g1856g1848g1856g1872 g3397uni0031g2011 g3398uni0031g1848g1856g1842g1856g1872   (Eq. 3.1)  Since  the  overall  relative  air-fuel  ratios  in  the  combustion  bomb  were  ultra-lean  (lambda  =  5.2  ?  15.2)  the specific heat ratio of air (gamma = 1.4) was used for all combustion calculations.  Net integrated heat release (IHR) values were calculated by integrating Equation 3.1.  Other parameters such as ignition delay and Injection Pressure Ratio (PRATIO)2 10 20 30 40 50 60 70 80 90 100 - - -3 10 20 30 40 50 60 70 80 90 100 120 140 1604 10 20 30 40 50 60 70 80 90 100 120 140 160Constants:Charge pressure: 100 psi (6.89) barCommanded injection duration: 8.000 msSpark Timing, (TS) [ms]  24combustion  duration  were  calculated  from  the  integrated  heat  release  data  and  compared  for  each experiment.  Ignition delay (tign) is defined as the duration between the commanded time of spark and 5% IHR.  Combustion duration (tcomb) is defined as the duration between tign and 95% IHR.  Calculations for overall relative air/fuel ratio were performed based on the partial pressures of natural gas and air.  There were a total of eight cold flow natural gas injections performed for each pressure ratio.  Cold flow data was used to determine the average amount of gas injected for each pressure ratio, as well as the 95% confidence interval of the pressure rise.  The average cold flow pressure data of each pressure ratio  was  subtracted  from  the  pressure  data  of  the  combusting  experiments  to  determine  the  pressure change due solely to combustion.  The NG composition used for all calculations is shown in Table 2.  This table represents a 2005 measurement of BC gas at a nearby location (Westport Innovations), which is assumed to have a very similar composition to the UBC facilities.  Table 2 - Natural Gas Composition   3.3  IMAGE ANALYSIS An  average  background  image  was  calculated for  each  experiment  by  taking  the  mean  of the  first  50 images prior to the start of injection.  The only inconsistency observed in the images used for background averaging  was  a  very  faint  but  noticeable  light  intensity  variation,  which  can  be  explained  by  the Name Species Mole % Mole FractionMolecular Mass [kg/kmol]Lower Heating Value [KJ/kg]Ethane C2H6 6.60 0.0660 30.070 47511Propane C3H8 0.32 0.0032 44.097 46333Methane CH4 91.59 0.9159 16.043 50030Carbon Dioxide CO2 0.40 0.0040 44.010 0Nitrogen N2 1.09 0.0109 28.013 0Based on GC measurement, Westport Innovations, Oct 2005  25behaviour of the Schlieren light power source.  Once an average background image was obtained, the remaining  frames  were  then  divided  by  the  average  background  image  to  obtain  a  clean,  noise  free representation.  A sample raw image and its background divided counterpart are shown in Figure 15.   Figure 15 - Example of Raw Image and Image with Background Divided  Image binarization was required in order to perform jet and flame area calculations.  An algorithm was developed to eliminate the gray background from the images represented in Figure 15, which is further explained in Section 4.2.5.  The resulting image is shown on the left of Figure 16.  Pixels with values below  a  threshold  of  ?5000?  were  then  assigned  a  value  of  ?65535?  (white)  while  pixels  above  the threshold were assigned o value of ?0? (black).  The binarized image is shown on the right of Figure 16.  The threshold value of ?5000? was selected after conducting a threshold sensitivity analysis outlined in Section 4.2.5.  This analysis yielded consistent results in the time domain, and consistent trends in pixel area growth.  Variation of the threshold value resulted in slight changes to the jet areas reported, however, trends such as jet expansion rates, injection start time, injection duration and injection finish time were all found to be consistent.     26 Figure 16 - Example of Background Subtraction and Binarization  3.4  UNCERTAINTY ANALYSIS Experimental uncertainties resulting from repeats of individual realizations were calculated using a 95% confidence interval (CI95%) according to Equation 3.2.  Sx is the standard deviation,  uni0058 is the average and n the number of repeats.  The corresponding value for t0.25, n-1 is found in the Student?s t-table.      uni0043uni0049g2877g2873uni0025 g3404 uni0058uni0020 g3399uni0074g2868uni002Eg2868g2870g2873uni002Cg2924g2879g2869uni0053g2934uni221Auni006E  (Eq. 3.2)  Uncertainties related to instrumentation (B) were also included in the calculations, which resulted in a combined uncertainty, wi, where wi is specific to any measured parameter.  Equation 3.3 demonstrates the calculation of wi, which is a function of uncertainty due to instrument error and the uncertainty arising from the 95% confidence interval (P).  Instrument specific error values are reported in Table 3.      uni0077g2919 g3404 g3493uni0042g2870 g3397uni0050g2870  (Eq. 3.3)    27Table 3 - Instrumentation Description and Uncertainty Description  Model # / Serial #  Range  Uncertainty MSI Pressure Transducer  M5151-000005-500PG  0 - 500 PSIG  ? 0.1% FS (? 0.5 PSI) PCB Piezoelectric Transducer  112B11 / 20877  0 - 5000 PSIG  ? 0.01 PSI Omega K-Type Thermocouple  KQXL-18  -260 - 1360 ?C  2.2 ?C  For  a  parameter  of  interest  R,  which  is  a  function  of  several  measured  parameters  (xi)  the  overall uncertainty WR is represented by Equation 3.4.  WR is a function of the combined measured parameter uncertainty (wi) and the partial derivative of R to that of each measured parameter used.    uni0057g2902 g3404 g3496g3436uni2202uni0052uni2202uni0078uni0031 uni0077g2869g3440g2870g3397g3436uni2202uni0052uni2202uni0078uni0032uni0077g2870g3440g2870g3397g1710g3397uni0020 g3436uni2202uni0052uni2202uni0078uni0069uni0077g2919g3440g2870  (Eq. 3.4)  To put things into perspective, it is useful to look at an example.  The mass of natural gas injected was determined based on an 8 run average for each pressure ratio, and was calculated using the ideal gas equation (Eq. 3.5).    uni006Dg2898g2891 g3404uni0050g2898g2891uni0056g2912g2925g2923g2912uni0052g2898g2891uni0054   (Eq. 3.5)  The  uncertainty  of  the  pressure  measurement  (wP,NG)  is  calculated  according  to  Equation  3.6,  where wins,NG is the uncertainty of the pressure transducer and wexp,NG is the uncertainty resulting from the 8 run 95% confidence interval.    uni0077g2900uni002Cg2898g2891 g3404 g3495uni0077g2919g2924g2929uni002Cg2898g2891g2870 g3397uni0077g2915g2934g2926uni002Cg2898g2891g2870  (Eq. 3.6)  Similarly,  the  uncertainty  of  the  temperature  measurement  (wT)  is  a  function  of  the  thermocouple instrument error (wins,T) and the CI95% uncertainty (wexp,T) shown in Equation 3.7.   28   uni0077g2904 g3404 g3495uni0077g2919g2924g2929uni002Cg2904g2870 g3397uni0077g2915g2934g2926uni002Cg2904g2870  (Eq. 3.7)  The  combustion  bomb  volume  was  determined  by  filling  with  water  from  a  burette,  which  has  an uncertainty of wV = 0.5 mL.  Finally, the overall uncertainty for the mass of natural gas calculation is given by Equation 3.8.    uni0057g2923uni002Cg2898g2891 g3404 g3496g3436uni0056g2912g2925g2923g2912uni0052g2898g2891uni0054 uni0077g2900g3440g2870g3397g3436g3398uni0050g2898g2891uni0056g2912g2925g2923g2912uni0052g2898g2891uni0054g2870uni0077g2904g3440g2870g3397g3436 uni0050g2898g2891uni0052g2898g2891uni0054uni0077g2906g3440g2870  (Eq. 3.8)       294.  RESULTS AND DISCUSSION The primary research objective was to determine the range of injection pressure ratios and spark timings that lead to successful combustion of stratified natural gas injections in an air-only environment.  The overall air-fuel ratio for all tests was well beyond the lean limit of flammability for premixed natural gas in air.  Test cases at spark timings of less than 30 ms after commanded injection were not ignitable for any pressure ratio.  Test cases at spark timings above 30 ms were ignitable for some cases, where the highest frequency of successful ignition occurred at a pressure ratio of 3.  4.1  COLD FLOW INJECTION DATA A cold flow injection study was performed with eight repeats for each pressure ratio.  The commanded injection duration was the same as for the combusting experiments (8.0 ms).  Pressure data acquired from this testing was used to determine the injection repeatability of the PSC system.  Average overall relative air-fuel ratio (RAFR) and mass of natural gas injected (mNG) were determined from this study and are reported in Table 4.  An injection timing study was also performed based on the cold flow pressure data and is discussed in the next section.  The cold flow pressure plots shown in Figure 17 were subtracted from the pressure plots of the combusting cases, in order to determine the pressure change due solely to combustion.  A value of zero in the time domain represents the start of the commanded injection (CI).   30     Figure 17 - Cold Flow Injection Plots, Pressure Ratios 2, 3, 4  0 50 100 150 20000.10.20.30.40.50.60.70.8Time from CI start [ms]Pressure [psi]PRATIO = 2  MeanCI95%CI95%0 50 100 150 20000.20.40.60.811.2Time from CI start [ms]Pressure [psi]PRATIO = 3  MeanCI95%CI95%0 50 100 150 20000.511.52Time from CI start [ms]Pressure [psi]PRATIO = 4  MeanCI95%CI95%  314.1.1  PSC Injection Mass Flux The data presented in Table 4 shows parameter averages and confidence intervals based on eight runs for each pressure ratio.  In order to account for pressure regulator error due to the manual pressure changes required, the runs were fully randomized using the random number generator built into MS Excel v. 2007.  Table 4 - Injected NG Mass and RAFR Data at Each Pressure Ratio Injection pressure ratio, PR Main Charge Pressure [psi] Average Pressure Rise       [psi] Standard Deviation in Pressure Rise [psi] Mass of NG injected (95% CI) [mg] Overall RAFR, ? (95% CI) 2  100.0  0.65  0.042  7.53 ? 0.42  15.2 ? 0.80 3  100.0  1.30  0.024  14.8 ? 0.26  7.65 ? 0.12 4  100.0  1.87  0.025  21.3 ? 0.49  5.31 ? 0.06   Table 4 shows the mass of natural gas injected to be repeatable within a maximum of 1 mg for all three pressure ratios.  The largest error occurs at a pressure ratio of 2 where the CI95% interval of 0.82 mg is about 11% of the average value of 7.53 mg.  For pressure ratios of 3 and 4 the CI95% interval becomes even smaller with 3.5% and 4.6% of the average respective values.  Thus, for experiments at pressure ratios of 2, the author is 95% confident that the mass of NG injected is within 11% of the average value, while for pressure ratios of 3 and 4 mNG is within 5% of the average value.  4.1.2  PSC Injection Timing Although  the  commanded  injection  duration  was  maintained  at  8.0  ms  for  all  experiments,  the  actual observed  injection  duration  was  significantly  longer  and  also  varied  with  pressure  ratio.    An  end  of injection (EOI) timing study was performed based on the pressure data acquired in the cold flow study.  First, the pressure data was FFT filtered to remove the high frequency noise over 2 kHz.  Next, a mean   32post injection pressure value was calculated.  Finally, the end of injection time was defined as the time required  for  the  pressure  to  reach  a  certain  percentage  of  the  mean  post  injection  pressure  (%PMPI).  Figure 18 shows two plots of the eight pressure data sets collected at an injection pressure ratio of 4.  The circles on the left plot indicate the 95%PMPI, while those on the right indicate the 99%PMPI for each of the eight pressure data sets sampled.  The circle scatter observed in the time domain had an increasing trend as the percentage of mean pressure defining EOI was increased.       Figure 18 - Cold Flow Pressure Curves for PRATIO = 4, 95%PMPI Left, 99%PMPI Right  The increasing scatter with increasing %PMPI behaviour is also shown in Figure 19, where the error bars indicate  the  95%  confidence  intervals.    %PMPI  values  up  to  97.5%  exhibited  EOI  times  that  were statistically different for each pressure ratio.  %PMPI values of 98% and higher displayed overlapping error bars for pressure ratios of three and four and thus, the EOI times were not statistically different.  The higher level of uncertainty for %PMPI values approaching 100% is explained by the asymptotic pressure curves,  where  a  small  change  in  pressure  near  the  asymptote  causes  a  very  large  change  in  the  time 0 50 100 15000.511.52Time [ms]Pressure [psi]0 50 100 15000.511.52Time [ms]Pressure [psi]  33domain.    It  was  therefore  deemed  that  a  %PMPI  value  of  97.5%  should  be  used  to  define  the  end  of injection.   Figure 19 - End of Injection Time as a Function of Percent Mean Value Selected  An EOI time analysis based on the Schlieren photography was also conducted in order to validate the pressure-based injection timing study.  The Schlieren videos were visually analysed on a frame by frame basis for all cold flow cases and the following injection parameters were determined: injection start (istart), injection end (iend), and injection duration (idur).  Injection start was established as the time at which the fuel plume first appears at the spark plug electrodes.  Injection end was defined as the moment the fuel ceased to flow in the vicinity of the electrodes.  Injection duration is the difference between iend and istart.  These PSC injection parameters are shown in Table 5, along with their 95% confidence intervals.  506070809010011092 94 96 98 100EOI Time [ms]Threshold (%PMPI)PRATIO = 2PRATIO = 3PRATIO = 4  34Table 5 - PSC Injection Timing Parameters Based on Schlieren Photography   The PSC timing data based on the Schlieren photography fits in well with the EOI data determined using the  pressure  approach.    The  iend  parameters  determined  using  the  Schlieren  photography  are  plotted alongside the EOI 95% confidence intervals from the pressure measurements in Figure 20.  For injection pressure  ratios  of  two  and  three,  EOI  time  values  at  98  %PMPI  are  a  good  match,  while  for  injection pressure ratios of 4, %PMPI value of about 99.5 is required.      Figure 20 - Comparison Beteen Pressure and Schlieren Photography EOI Study  The  injection  start  values  shown  in  Table 5  were  observed  to  decrease  with  increased  pressure  ratio.  These istart values represent the amount of time it takes to first see the fuel plume after the commanded start of injection.  It is interesting to note that the istart values are significantly longer than the average 2 20.5 ? 2.2 72.9 ? 1.4 52.4 ? 3.63 16.2 ? 0.7 90.9 ? 1.7 74.7 ? 2.44 13.1 ? 0.4 115.3 ? 2.1 102.1 ? 2.5Duration, idur [ms]PSC Injection ParametersPRATIO Start, istart [ms] End, iend [ms]506070809010011012092 93 94 95 96 97 98 99 100EOI Time [ms]Threshold (%PMPI)     CI95%, PRATIO = 2      CI95%, PRATIO = 3       CI95%, PRATIO = 4      72.9 ms, PRATIO = 2     90.9 ms, PRATIO = 3     115.3 ms, PRATIO = 4   35solenoid delay time of 1.95 ms discussed in the previous chapter.  The temporal difference between the istart values, which range from 13.1 ms to 20.5 ms, and the solenoid delay, could be attributed to the time required for the fuel to travel through the capillary tube into the spark plug body.  The combustion bomb was  purged  with  air  by  means  of  pressurizing  and  depressurizing  several  times  between  each experimental run.  Consequently, prior to each experiment, the fuel system contained only air downstream of the solenoid valve exit.  This air had to be displaced by the fuel during each injection, which explains the  additional  delay  observed  between  the  solenoid  valve  opening  and  fuel  reaching  the  electrodes.  Figure 21 shows a close-up the pressure data shown in Figure 17 in order to demonstrate the difference in injection delay based on the pressure measurements.  According to Figure 21, a significant pressure rise is observed after ~ 5 ms, which means that the actual start of injection occurred several milliseconds before the natural gas was observed at the spark plug electrodes.       Figure 21 - Injection Start Detail of Cold Flow Pressure Data    The discrepancy in injection delay between that observed in the Schlieren images and that observed from the pressure data varies with pressure ratio from ~ 15 ms at PRATIO = 2 to ~ 7 ms at PRATIO = 4.  It is however  not  unlikely  that  the  actual  time  required  for  fuel  to  reach  the  spark  plug  electrodes  in  a reciprocating engine is closer to that observed in the Schlieren images.  Due to the blow-down during the 0 2.5 5 7.5 1012.51500.050.1Time from CI start [ms]Pressure [psi]PRATIO = 2  0 2.5 5 7.5 1012.51500.050.10.150.20.25Time from CI start [ms]Pressure [psi]PRATIO = 3  0 2.5 5 7.5 10 12.5 1500.10.2Time from CI start [ms]Pressure [psi]PRATIO = 4    36exhaust stroke and the back-flow of air into the capillary tube during the compression stroke, the gas composition inside the capillary tube may be similar to that observed in these experiments.  4.1.3  Charge Motion Entrainment Heywood (1988) attributes the engine cylinder charge motion as one of the major factors that controls the combustion process in both spark-ignition and compression ignition engines.  Heywood breaks down the charge motion into several types, namely: swirl, squish and tumble.  Swirl is defined as organized bulk gas rotation around the cylinder axis.  This type of motion is usually accomplished by discharging the intake flow tangentially into the cylinder through the intake valve.  Squish refers to the gas motion in the radial direction oriented from the perimeter of the cylinder towards its axis.  Squish motion is significant when the piston nears the firedeck and pushes the in-cylinder gases away from the low clearance volume formed near TDC.  Tumble is defined as the bulk gas motion around an axis that is perpendicular to the cylinder axis.  Tumble motion is usually attained by using two intake valves instead of one, which causes a bias in the flow direction.  Tumble  was  the  most  prominent  bulk  charge  motion  observed  in  this  study.    Due  to  the  lack  of  the moving parts present in a reciprocating ICE, swirl and squish motions were absent.  The tumble motion resulted from the orientation of the PSC spark plug, which injected the fuel with a directional bias.  The typical  tumble  motion  observed  at  a  pressure  ratio  of  four  is  illustrated  in  the  slides  of  Figure  22.  Vortices resulting from the shear flow of the injected fuel with the quiescent air were also observed.  The large scale vortices were in the order of 15 mm in size at a pressure ratio of four, ~ 7 mm at a pressure ratio of three and ~ 4 mm at a pressure ratio of two.  The turbulent motion was seen to dissipate earlier at the smaller pressure ratios.    37 Figure 22 - Progression of Fuel Jet and Combustion Event at PRATIO = 4  The amount of charge motion developed was found to vary with time and pressure ratio.  The variation with time is explained by the gaseous jet resulting from the fuel injection event, which begins to entrain the quiescent surrounding air near the beginning of injection.  The variation with pressure ratio is a result of the increased mass flux as the pressure ratio increases.  Figure 23 shows images taken at the end of injection for each pressure ratio.  An image representing the start of injection is also shown, where fuel is just visible exiting the spark plug body.  The air-fuel mixture perimeter is outlined with a white line to make the boundary between air and air-fuel mixture clear.  As the pressure ratio is increased, the air-fuel mixture occupies an increasing percentage of the combustion bomb.  Since the Schlieren images display density gradients inside the combustion bomb, all mixture fraction gradients above zero should be visible.  Mixture fraction (zeta) is a conserved scalar which represents the amount of gas that originated from the fuel stream at a certain location ?i".  Equation 4.1 shows the mixture fraction as a function of mass fraction (Z) of two fluids.  The subscripts ?1? and ?2? represent the fuel and the air streams.    38  Figure 23 - Schlieren Images of the Start of Injection (Top Left), PRATIO 2 EOI (Top Right), PRATIO 3 EOI (Bottom Left), PRATIO 4 EOI (Bottom Right)  uni03B6 g3404uni0020 uni005Ag2919 g3398uni005Ag2919g2870uni005Ag2919g2869 g3398uni005Ag2919g2870  (Eq. 4.1)  The rate of developing charge motion is also observed to increase with increasing pressure ratio.  Figure 24 shows the plot of non-zero density gradient area as a function of time for each pressure ratio.  The slopes of the lines which represent rate of jet expansion and air entrainment are seen to increase with   39increasing  pressure  ratio.  Also, the  maximum  area values reached  at  the end of injection  are seen  to increase  with  increasing  pressure ratio.   The  plots in  Figure 24  were  determined  based  on  the  image binarization technique further discussed in section 4.2.5.     Figure 24 - Cold Flow Injection Average Pixel Count  The pixel count for a pressure ratio of two in Figure 24 begins to slowly decay after ~ 150 ms.  This is due to the fact that Schlieren imaging works on density gradients, and the density gradients are slowly disappearing as the injected fuel continuously diffuses and mixed with the surrounding air.   0 0.05 0.1 0.15 0.200.511.522.533.544.55Time from CI Start [s]Pixel Count x 104  PRATIO 2PRATIO 3PRATIO 4  404.2  COMBUSTION ANALYSIS  A combustion analysis based on the pressure data for each combusting event was performed to determine the changes in combustion characteristics as the spark timing (TS) and pressure ratio (PRATIO) were varied.  Combustion characteristics including ignition delay (tign), combustion duration (tcomb), heat release rate (HRR), and integrated heat release (IHR) were investigated.  The ignitability of the jet plume was very dependent on spark timing as well as pressure ratio.  The combustion success shown in Figure 25 is a parameter that represents the ratio of combusting runs to the total runs performed at a certain spark timing and pressure ratio.  The error bars were determined using the 90% confidence intervals for proportions equation specified by Navidi (2006).  The combustion parameters previously mentioned were influenced by  both  the  spark  timing  and  the  injection  pressure  ratio,  although  pressure  ratio  was  found  to  alter combustion performance more significantly.  These findings will be further discussed in the following sections.     Figure 25 - Combustion Success as a Function of Spark Timing for Each Pressure Ratio  0255075100020 40 60 80100 140 180Combustion success [%]Spark timing [ms]0255075100020 40 60 80100 140 180Combustion success [%]Spark timing [ms]0255075100020 40 60 80100 140 180Combustion success [%]Spark timing [ms]  41The  combustion  success  parameter  in  Figure  25  is  a  good  indicator  of  the  combustion  reliability.  Repeated attempts to ignite the jet plume at less than ideal conditions, such as those with a combustion success of less than 100%, would result in poor performance and high emissions.  Spark time intervals that exhibit reliable combustion (100% success rate) are shown in Table 6 for each pressure ratio.  One point of interest in Figure 25 is at a pressure ratio of three and a spark timing of 30 ms.  Several repeats were  performed  at  this  test  point;  however,  combustion  success  remained  intermittent  (about  66%).  Although PRATIO and TS were maintained constant, the ignitability of the jet plume varied presumably due to the chaotic nature of turbulence.  The position of the jet plume at the time of spark became the leading factor governing the flammability.  This point will be further discussed in the image analysis sections to follow.  Points tested with spark timings just above and below this value (40 ms and 20 ms) showed no signs of combustion.    Table 6 - Spark Timing with 100% Combustion Success PRATIO  Range [ms]  Window [ms] 2  40  arrowright  60  20 3  60  arrowright  140  80 4  90  arrowright  100  10   Test cases with an injection pressure ratio of three demonstrated the widest spark timing window that results in successful combustion.  Minimum spark timings that lead to successful combustion were found to increase with increasing pressure ratio.  The least favourable pressure ratio was found to be four, as it required the highest spark timing retardation and it had the narrowest spark timing window (10ms).  It is interesting to note that the experiments conducted by Gorby on the Ricardo Hydra were at an average injection pressure ratio of four.  As mentioned above, this pressure ratio is the least favourable amongst the three tested and it requires a minimum spark delay of 90 ms between CSOI and the time of spark for   42reliable combustion to occur.  Although it is understood that the engine charge motion and mixing scales are much different from those observed in the combustion bomb, it is useful to point out the engine test conditions for comparative purposes.  Gorby maintained a constant CSOI of 41 CAD before the time of spark.  Since most of his testing was conducted at 2000 RPM, this translates to 3.42 ms between the commanded start of injection and the time of spark.  As previously shown in Section 4.1.2, the duration between  commanded  start  of  injection  and  the  time  the  fuel  jet  plume  is  observed  at  the  spark  plug electrodes is 13.1 ?  0.4 ms.  This result sheds some light on Gorby?s inability to ignite the PSC charge, since it is likely that there was no fuel present at the spark plug electrodes at the time of spark.  Also, according Table 6, a spark timing delay of 3.42 ms is ~ 25 times less than that required for the successful combustion  of  the  PSC  charge  in  the  constant  volume  bomb  at  the  pressure  ratio  used  by  Gorby.  Considering that a full engine cycle lasts 60 ms at 2000 RPM, some modifications may be necessary to the PSC injection system in order to reduce the required spark delay.  Examples of test cases which were not ignitable are shown at the time of spark for each pressure ratio in Figure 26, Figure 27, and Figure 28.  The top left images in Figure 26 and Figure 27 indicate that the spark was triggered before the fuel jet was present.  The top right images in Figure 26 and Figure 27 and the  top  left  image  in  Figure  28  correspond  to  snapshots  of  the  spark  near  the  head  of  the  jet.    It  is conjectured that because the amount of air that has been entrained into the jet plume near the beginning of injection is likely very small, the spatial distribution of ignitable mixture is very limited and ignition is not repeatedly achievable.  The bottom left and the top right images in Figure 27 and Figure 28 are examples of spark initiation near the beginning of injection, after the air that was present prior to injection has been displaced away from the electrodes.  At this point, the air-fuel mixture is believed to be outside its flammability limits, since it is likely very fuel rich near the electrodes.  Examples of four cases where the fuel is thought to have mixed past its flammability limits are shown in the bottom frames of Figure 26 and in the bottom right frames of Figure 27 and Figure 28.  In all four instances, the spark was triggered after the observed fuel injection had completed and the bulk gas motions nearly dissipated.  Since the   43overall relative air/fuel ratio in each case is most probably far beyond the lean limit of combustion, the spark initiated in a fuel-lean zone and no flame was observed.    Figure 26 - Examples of Incombustible Test Cases for PRATIO = 2: TS = 10 ms (Top Left), TS = 20 ms (Top Right), TS = 90 ms (Bottom Left), TS = 100 ms (Bottom Right)    44  Figure 27 - Examples of Incombustible Test Cases for PRATIO = 3: TS = 10 ms (Top Left), TS = 20 ms (Top Right), TS = 40 ms (Bottom Left), TS = 160 ms (Bottom Right)    45  Figure 28 - Examples of Incombustible Test Cases for PRATIO = 4: TS = 20 ms (Top Left), TS = 50 ms (Top Right), TS = 120 ms (Bottom Left), TS = 160 ms (Bottom Right)      464.2.1  Integrated Heat Release Analysis Although the primary interest of this study was to determine the pressure ratios and spark timings that lead to successful combustion, the quality of combustion was of interest as well.  One run is said to have better combustion quality than another if the amount of net heat released is higher, the heat is released at a higher  rate,  and  the  combustion  delay  is  lower.    The  cold  flow  study  demonstrated  that  at  constant injection pressure ratio, the injected amount of fuel will remain constant, in the worst case scenario to within 11% of the average value.  Therefore, in order to compare the combustion quality of different spark timings at constant pressure ratio, it is helpful to look at the amount of heat released in each test.  It is important to note that the heat release studies performed yield net heat release results only.  In order to determine the gross heat release, one must know the heat transfer through the walls of the combustion bomb.    Since  this  experiment  was  not  set  up  to  do  heat  flux  measurements  the  inefficiencies  due  to combustion  and  the  heat  losses  from  the  combustion  bomb  must  be  grouped  together.    Equation  4.2 defines the net heat release rate according to Stone (1999), where Qnet, Qhr and Qht are the net heat release, the gross heat release and the heat transfer respectively.    uni0064uni0051g2924g2915g2930uni0064uni03B8 g3404uni0064uni0051g2918g2928uni0064uni03B8 g3398uni0064uni0051g2918g2930uni0064uni03B8 g3404uni0020uni03B3uni03B3 g3398uni0031uni0070uni0064uni0076uni0064uni03B8 g3397uni0031uni03B3 g3398uni0031uni0076uni0064uni0070uni0064uni03B8  (Eq. 4.2)       Equation 4.2 gives the crank angle (?) resolved heat release (normally applied to an operating ICE) as a function of instantaneous pressure (p), instantaneous volume (v), and the ratio of specific heats (gamma).  In the case of the constant volume combustion bomb, Equation 4.2 is applied on a time varying basis and the volume varying term drops out.  The result is shown in Equation 4.3.    uni0064uni0051g2924g2915g2930uni0064uni0074 g3404uni0064uni0051g2918g2928uni0064uni0074 g3398uni0064uni0051g2918g2930uni0064uni0074 g3404uni0020uni0031uni03B3 g3398uni0031uni0076uni0064uni0070uni0064uni0074   (Eq. 4.3)        47  Considering  the  large  mass  of  the  combustion  bomb  steel  walls,  they  are  assumed  to  be  a  constant temperature heat sink.  The test cell ambient temperature was maintained at a near constant 15 ?C.  Also, the initial temperature of the charge was found to be within 5 ?C between runs.  Thus, the heat transfer out of the combustion bomb is assumed to be constant at constant pressure ratio.  The heat transfer is assumed to vary with pressure ratio, since the mass of injected fuel also varies with pressure ratio.  Since the heat transfer is assumed constant for a constant pressure ratio, the changes in gross heat release are reflected in the net heat release value.  A sample plot of net heat release rate and net integrated heat release is shown in Figure 29.  Figure 29 - Net Heat Release Plot for Exp 043, PRATIO = 3, TS = 30ms  The combustion parameters discussed in the following sections are determined based on the heat release data of each individual run, which are typical to that shown in Figure 29.  Start of combustion is defined as the point where 5% of the maximum integrated heat release has been reached.  End of combustion is defined as 95% of the maximum integrated heat release.  The duration between the time of spark and the 0 50 100 150 200-0.500.511.522.533.5Time [ms]Net Heat Release Rate [kW]  0 50 100 150 200010203040506070Net Integrated Heat Release [J]  IHR5% Max IHR95% Max IHRHRRMax HRR  48time of 5% max IHR is referred to as the ignition delay (tign).  Combustion duration (tcomb) is defined as the time between 5% max IHR and 95% max IHR.  The Schlieren images corresponding to the time of spark,  5%  max  IHR,  max  HRR  and  95%  max  IHR  are  shown  in  Figure  30.    The  flame  can  be distinguished from the unburned fuel by the increased luminosity gradients.  In this run, the ignition delay (tign) is 24.84 ms (top right), the maximum heat release rate is 3.2 kW (bottom left) and the combustion    Figure 30 - Schlieren Images Corresponding to TS (Top Left), 5% Max IHR (Top Right), Max HRR (Bottom Left), and 95% Max IHR (Bottom Right) for PRATIO = 3, Ts = 30 ms    49duration is 29.12 ms (bottom right).  Note that a significant amount of fuel has flown past the spark plug electrodes at the time of spark, which is clearly seen in the top right image.  The heat release due to combustion as a function of spark timing is shown in Figure 31, Figure 32, and Figure 33, for pressure ratios of two, three and four respectively.  It is expected that the longer the spark is delayed after commanded injection, the longer that the injected natural gas will have to mix with the surrounding air.  Some of this natural gas will inevitably mix past the lean limit of combustion (LLC) and will therefore not burn.  Thus, the heat release due to combustion is expected to decrease with increasing spark  delay.    The  study  of  stratified  methane  injections  in  a  constant  volume  bomb  conducted  by Kitagawa et al. (2002) found that the mass fraction burned decreased with increasing ignition timing due to bulk quenching of the flame in the over lean surroundings.   Figure 31 ? Net Integrated Heat Release for PRATIO = 2  24681012141630 40 50 60 70 80 90IHR95% [J]Spark Time [ms]  50 Figure 32 - Net Integrated Heat Release for PRATIO = 3   Figure 33 - Net Integrated Heat Release for PRATIO = 4  The combustion heat release seems to be a strong function of spark timing for pressure ratios of two and three.  At a pressure ratio of two, the heat release steadily decreases by more than three times that of the best case value of 14 J at 40 ms to 4 J at 80 ms spark delay.  Similar behaviour is seen from the results at 10203040506070809020 45 70 95 120 145 170IHR95% [J]Spark Time [ms]809010011012013014015016030 80 130 180IHR95% [J]Spark Time [ms]  51a pressure ratio of three, where the heat release decreases from ~ 65 J at 30 ms to ~ 25 J at 160 ms spark delay.    Although  the  average  values  of  heat  release  for  pressure  ratios  of  four  also  decrease  with increasing spark delay, the results are not statistically different due to the large uncertainties observed.  It is  thought  that  the  large  error  bars  in  Figure  33  are  primarily  due  to  increased  turbulence  in  the combustion bomb resulting from the high injection pressure.  The large turbulence generated at a pressure ratio of four is expected to introduce a high variability in the amount of fuel that mixes past the LLC and thus, the dependence of heat release on spark delay is not as apparent.    Since the amount of fuel injected is unchanged at constant pressure ratio, it is expected that the amount of unburned fuel should increase with decreasing integrated heat release.  Schlieren images of the time of spark and the time at which combustion ends are shown in Figure 34, Figure 35, and Figure 36 for pressure ratios of two, three and four.  A white line is drawn around the perimeter of the flame front to help distinguish the burned mixture from the unburned reactants.  The top frames in each figure represent the  most  advanced  spark  timing  that  lead  to  successful  charge  ignition  for  each  pressure  ratio.    The bottom frames represent the most retarded spark timing that can sustain successful charge ignition.      52  Figure 34 - Schlieren Images at Time of Spark (Left) and 95% Max IHR (Right) for TS = 40 ms (Top) and TS = 80 ms (Bottom) at PRATIO = 2    53  Figure 35 - Schlieren Images at Time of Spark (Left) and 95% Max IHR (Right) for TS = 30 ms (Top) and TS = 160 ms (Bottom) at PRATIO = 3    54  Figure 36 - Schlieren Images at Time of Spark (Left) and 95% Max IHR (Right) for TS = 80 ms (Top) and TS = 160 ms (Bottom) at PRATIO = 4  The expected trend is apparent at all three pressure ratios, as the amount of unburned fuel remaining at the end of combustion for the earlier spark timings is significantly less.  The difference between the early and late spark timings is most apparent for a pressure ratio of three.  Figure 35 shows that at a spark timing of 30 ms the amount of unburned fuel is minimal, while at TS = 160 ms the burned gases are only present in the vicinity of the spark plug and the unburned gases occupy nearly 2/3 of the combustion bomb.     554.2.2  Heat Release Rate Analysis According to Heywood (1988) the rate of heat release is governed primarily by flame type, i.e. premixed or diffusion.  The premixed flame speed varies with charge motion, charge composition and combustion chamber geometry.  Diffusion flame combustion rates are dependent on injection rate, fuel composition and charge motion.  The type of flame present in these experiments is dependent on both pressure ratio and spark timing.  Late spark timings allow the fuel and air to mix for a longer duration and thus the combustion consists of a premixed flame.  Early spark timings initiate combustion as a premixed flame, followed in some cases by a diffusion flame.  Pressure ratio affects the rate of heat release since fuel injected at a higher pressure ratio has an increased momentum flux and thus enhances the air entrainment into the fuel.  Also, the increased turbulence generated at higher pressure ratios increases the flame speed by ?wrinkling? the flame, which has the effect of increasing the flame surface area.  For a diffusion flame, increased turbulence results in steeper air-fuel concentration gradients. These increase the heat release rate by increasing local rates of diffusion.  The maximum rate of heat release in Figure 37, Figure 38, and Figure 39 is plotted against spark timing for pressure ratios of two, three and four respectively.  At a pressure ratio of two, the maximum HRR is a strong function of spark timing and it is observed to decrease with increasing spark timing.  The plot of maximum  HRR  in  Figure  38  indicates  a  similar  dependence  on  spark  timing  as  that  in  Figure  37, however, the uncertainties are higher.  The maximum rate of heat release graph in Figure 39 shows no statistical dependence of maximum HRR on spark timing for a pressure ratio of four, as HRR rate values are  all  within  the  error  bars  shown.    The  observed  injection  duration  at  a  pressure  ratio  of  four  is significantly longer than at pressure ratios of two and three.  Since the end of the observed fuel injection occurs long after the time of spark for pressure ratios of four, considerable charge motion in the form of bulk gas flows and turbulent vortices is still present during the combustion event.  This is believed to be   56the primary reason that the maximum rate of heat release is unaffected by spark timing at this pressure ratio.   Figure 37 - Maximum Rate of Heat Release for PRATIO = 2   Figure 38 - Maximum Rate of Heat Release for PRATIO = 3  0.00.20.40.60.81.01.21.430 40 50 60 70 80 90HRR [kW]Spark Time [ms]0.00.51.01.52.02.53.03.520 45 70 95 120 145 170HRR [kW]Spark Time [ms]  57 Figure 39 - Maximum Rate of Heat Release for PRATIO = 4  4.2.3  Combustion Duration Analysis Two factors that govern combustion duration in a stratified charge environment are fuel-oxidizer mixing rate  and  quantity  of  fuel  available.    The  mixing  rate  is  proportional  to  the  charge  motion  inside  the combustion chamber and the gas diffusion rates.  The charge motion in these experiments was entrained by the fuel injection event and was further described in Section 4.1.3.  As the fuel injection event nears completion, charge motion was observed to diminish until it is completely dissipated.  This observation was consistent with that of Alger et al. (2005) who conducted particle image velocimetry (PIV) studies in a gasoline direct injected (GDI) engine operating at 750 RPM.  Alger et al. determined that the charge motion  entrained  from  the  fuel  injection  event  dissipated  within  ~  9  ms  (40  CAD)  after  the  end  of injection.    As mentioned in the previous section, charge motion is a parameter that strongly influences the flame speed.    Therefore,  in  the  case  of  these  experiments,  the  flame  speed  should  increase  during  the  fuel 0.01.02.03.04.05.06.030 80 130 180HRR [kW]Spark Time [ms]  58injection process and decrease near the end of injection.  If combustion duration were governed solely on flame speed, it would be expected that ignition close to the end of injection should increase the burn time.  However, in a stratified environment, if the spark event is highly delayed, more fuel mixes past the lean limit.  When the spark initiates, the flame kernel grows, and consumes only reactants which are within the flammability limits of the fuel.  Since there is now less fuel available to burn at the later spark timings, the combustion duration will decrease.    Given that the charge motion inside the combustion bomb and the amount of fuel available to burn both decrease with increasing spark timing, a clear trend in combustion duration with spark timing is difficult to predict.   The combustion duration for a pressure ratio of two is plotted in Figure 40.  The only spark timing that stands out to be significantly different from the rest is at 40 ms.  At a pressure ratio of three (Figure 41), the combustion duration starts with a value of 37 ms at a spark timing of 30 ms, steadily increases to a maximum at a spark timing of 100 ms, and then abruptly drops again at TS = 120 ms.  It is likely that the fuel available to burn after 100 ms significantly decreases.  For a pressure ratio of four,    Figure 40 - Combustion Duration for PRATIO = 2 1015202530354030 40 50 60 70 80 90Combustoin Duration [ms]Spark Time [ms]  59which is shown in Figure 42, the combustion duration values are not statistically different for any spark timing.  Figure 41 - Combustion Duration for PRATIO = 3   Figure 42 - Combustion Duration for PRATIO = 4  25303540455055606520 45 70 95 120 145 170Combustion Duration [ms]Spark Time [ms]3540455055606530 55 80 105 130 155 180Combustion Duration [ms]Spark Time [ms]  60In order to account for the reduced amount of fuel available to burn with increasing spark timing, the combustion duration is normalized with the integrated heat release.  By normalizing tcomb with IHR, the heat release parameter becomes factored into the combustion duration time, leaving flame speed as the only  significant  parameter.    The  plot  of  normalized  combustion  duration  in  Figure  43  shows  an increasing  trend  with  decreasing  pressure  ratio.    This  behaviour  is  expected,  since  the  charge  motion induced increases as the pressure ratio is increased.  The study of PSC injection timing as a function of pressure ratio discussed earlier, found the following average injection durations: PRATIO = 2 : 72.9 ms, PRATIO = 3 : 90.9 ms, and PRATIO = 4 : 115.3 ms.  The normalized combustion duration is seen to increase for  spark  timings  that  are  near  or  past  the  end  of  injection.    As  the  pressure  ratio  was  increased,  the duration between end of injection and charge motion dissipation was observed to increase.  At pressure ratios of two, the normalized combustion duration increases for spark timings greater than 60 ms (10 ms before the end of injection).  For pressure ratios of three, the increase in normalized combustion duration begins 30 ms after the end of injection.  At a pressure ratio of four, an increase in normalized combustion    Figure 43 - Combustion Duration Normalized by Integrated Heat Release 0.01.02.03.04.05.06.07.020 45 70 95 120 145 170tcomb/ IHR [ms/J]Spark Time [ms]PRATIO 2PRATIO 3PRATIO 4  61duration is not detected, which may be due to the longer time required for the charge motion to dissipate.  4.2.4  Ignition Delay Study The ignition delay shown in Figure 44 has a definite increasing trend from pressure ratios of two.  The uncertainties are also observed to increase with increasing pressure ratio, which make it more difficult to compare ignition delay times of PRATIO = 3 to those of PRATIO = 4.  For PRATIO = 3, the uncertainties have a decreasing trend with increasing spark timing.  This is believed to be a result of the decreasing turbulence level with increasing spark timing.  There are three spark timings (90 ms, 100ms and 160 ms) where the ignition delay at a pressure ratio of three is seen to be less than at a pressure ratio of four.  At constant pressure ratio, the ignition delay remains statistically constant with spark timing at all pressure ratios.  However, the uncertainty in ignition delay is seen to decrease with spark timing for pressure ratios of three.  This trend could be explained by the decreasing level of turbulence near the spark plug electrodes as the fuel injection event nears completion.  Figure 44 - Ignition Delay 010203040506020 45 70 95 120 145 170Ignition Delay [ms]Spark Time [ms]PRATIO 2PRATIO 3PRATIO 4  62The increased velocities near the spark plug electrodes at higher pressure ratios are believed to adversely affect  the  ignition  delay.    Ahmed  et  al.  (2007)  studied  the  effects  of  fuel  and  air  velocity  on  the ignitability and flame stability of non-premixed flames.  They concluded that the ignitability region is much  narrower  than  the  flame  stability  region  when  plotted  against  air-fuel  velocity.    Ahmed  et  al. attribute this finding to the fact that a flame edge is much more susceptible to straining out during the ignition phase than the established flame phase.  Ahmed et al. propose that increased charge velocities cause an excessive reduction in flame front temperature, which can lead to extinction.  The experiments conducted by Ahmed et al. support the argument that during the ignition phase, the developing PSC flame kernel is more susceptible to extinction at the increased velocities resulting from increased pressure ratio.  Also, mixing air and fuel at a faster rate than the rate of reaction can result in localized flame extinction, which could explain the high ignition delay times at increased pressure ratio.  4.2.5  Fuel Jet and Flame Growth Study Quantitative results attained from the pressure data were useful in determining parameters of interest such as  integrated  heat  release,  heat  release  rate,  ignition  delay,  combustion  duration  and  PSC  injection duration.  In order to try and explain fuel jet ignition difficulties and discrepancies between experiments, the Schlieren photographs were analyzed.  The Schlieren photography was also used to generate some quantitative results, such as the PSC system injection timing parameters.    Two parameters of interest which could not be determined from the pressure data are the fuel jet and the flame kernel growth rates.  The development of both fuel jet and flame kernel could be studied from the Schlieren Videos acquired; however, it is a tedious process requiring a manual frame by frame study.  Instead, a systematic automated procedure was developed using a series of Matlab algorithms as listed below:   631)  Acquire a set of 25 images prior to start of injection.  Use average of these images as background.  Resulting image is shown in Figure 45 on the left. 2)  Load frame under study, shown in Figure 45 on the right.   Figure 45 - Step 1, Background Image (Left); Step 2, Frame under Study (Right)   Figure 46 - Step 3, Subtracted Image (Left); Step 4, Binarized Image (Right)   643)  Subtract the background image from the frame under study and subtract the frame under study from  the  background  image.    Add  the  two  subtractions  together  to  form  the  image  shown  in Figure 46 on the left.  The double subtraction was necessary to maintain the pixels in the image which  were  of  lower  value  (i.e.  more  ?black?)  than  the  background.  Since  the  images  were processed as 16bit rather than double precision matrices, pixel subtractions that yield negative numbers  are  truncated  to  a  value  of  zero.    A  simplified  example  of  this  process  is  shown  in Figure 47.   Figure 47 - Simplified Example of Image Subtraction and Addition  4)  Select threshold value and binarize image.  Set the grey pixels below the threshold to white and those above the threshold to black.  The resulting image is shown in Figure 46 on the right. 5)  Count the black pixels in each progressive image and store values in an array. 6)  Plot the pixel count array as a function of time for a plot of jet and flame kernel development.  The cold flow fuel jet development is shown as a function of time in Figure 48, for pressure ratios of two and three.  In order to better illustrate the growth trend, the plot of PRATIO = 4 has been omitted from Figure 48 and is found in Figure 53.  The Schlieren mercury vapour light is powered by an AC source, therefore some periodic amplitude fluctuations are observed in Figure 48.  These fluctuations were found Im Bk Result1 3 2 1 0 24 2 1 3 3 0Bk Im Result2 1 1 3 1 01 3 4 2 0 1Sum1 23 1- - = = +   65to have a frequency of 120 Hz.  This frequency is double that of the power source due to the process of background subtraction.  Since the background is subtracted from the image of interest and the image of interest is also subtracted from the background, the luminosity fluctuations occur at twice the frequency of the light.  These fluctuations are a result of the double subtraction between the image under study and the background, which has an effect of inverting the negative alternating signal and therefore doubling the peak to peak frequency.  An FFT filter algorithm was written and applied to the raw curves in order to eliminate this noise.  Both the raw and the FFT curves are shown in Figure 48.    Figure 48 - Cold Flow Fuel Jet Development, PRATIO 2 and PRATIO 3  A  threshold  sensitivity  study  was  conducted  to  determine  if  the  general  trends  remain  the  same  for different thresholds.  The 16 bit images were processed with a threshold pixel value of 5000.  A plot of a single reacting run is shown at different threshold values in Figure 49, where the pressure ratio is three and the spark time is 30 ms.  The signal response in the time domain is the same for all three threshold cases.  The slopes of the response curves decrease with increasing threshold value.  Since this study is focused on relative differences between runs, changes in absolute values in the pixel count domain do not affect the results.  Events such as first sighting of the jet plume and first detection of the flame kernel are  0 50 100 150 200012345Time [ms]Pixel Count x 104  PRATIO 2, Cold Flow FFT AveragePRATIO 2, Cold Flow AveragePRATIO 3, Cold Flow FFT AveragePRATIO 3, Cold Flow Average  66 Figure 49 - Plots of Different Threshold Values for PRATIO = 3, TS = 30 ms  constant  with  varying  threshold  value.    Thus,  a  threshold  value  of  5000  was  maintained  constant  for processing all experiments.  The Schlieren visualization study conducted by Namazian et al. (1981) in an optically accessible ICE suggests that there is a temporal phase shift between the increase of the volume of gases inflamed and the mass fraction burned.  Namazian found the lead time between volume fraction of flame developed and mass fraction burned to be about 10 CAD which corresponds to 1.2 ms in the internal combustion engine at 1380 rev/min.  This trend was also apparent in the current study, where the flame kernel was observed to  develop  significantly  before  the  IHR5%  point,  which  defines  the  start  of  ignition  according  to  the pressure data.  The images in Figure 50 illustrate the flame kernel growth at the point of ignition (IHR5%) for each pressure ratio.  According to the pressure data, only 5% of the fuel has burned at this point, however, it is clearly seen that the ratio of inflamed area to air-fuel area is much greater. 0 50 100 150 2000123456789Time [ms]Pixel Count x 104  Threshold = 3000Threshold = 5000Threshold = 7000Flame Detected (3000)Flame Detected (5000)Flame Detected (7000)Fuel Jet Detected (Common)  67 Figure 50 - Flame Kernel Development at the Point of Ignition  Figure 51, Figure 52, and Figure 53 show plots of the total pixel count from the binarized Schlieren images as a function of time for pressure ratios of two, three and four respectively.  The curve deviation from the cold flow case indicates the presence of a flame kernel.  As the flame kernel grows, the pixel count steadily increases, until the flame growth process has finished.  The slope of the flame growth line is proportional to the growth rate and thus the rate of heat release.    68 Figure 51 - Cold Flow and Combusting Runs as PRATIO = 2  Figure 52 - Cold Flow and Combusting Runs at PRATIO = 3 0 20 40 60 80 100 120 140 1600  0.51  1.52  2.53  3.54  Time [ms]Pixel Count x 104  Average, Cold FlowTS = 40 ms, IHR = 13.9 JTS = 60 ms, IHR = 6.9 JTS = 70 ms, IHR = 5.6 JTS = 90 ms, IHR = 3.0 J0 50 100 150 200 250012345678Time [ms]Pixel Count x 104  Average, Cold FlowTS = 30 ms, IHR = 66.3 JTS = 90 ms, IHR = 66.4 JTS = 140 ms, IHR = 41.6 JTS = 160 ms, IHR = 28.2 J  69 Figure 53 - Cold Flow and Combusting Runs at PRATIO = 4  The slopes of the combusting runs, beginning with the point where the curves deviate from the cold flow average, have a decreasing trend with increasing spark timing.  This trend is most noticeable for pressure ratios of two and three, which corresponds to the earlier findings that maximum HRR has a tendency to decrease with increasing spark timing.  This decreasing trend is not as apparent for a pressure ratio of 4 (Figure 53) where there is little difference in the slope values of the flame kernel development.  The integrated  heat release  values  determined  from  the  pressure  analysis  are  shown  in  the  legends of Figure 51, Figure 52 and Figure 53.  These IHR values are proportional to the maximum pixel count observed for each experiment.  For example, in Figure 52, the runs with spark timings of 30 ms and 90 ms release a net of 66 J each, whereas those with spark timings of 140 ms and 160 ms release less heat (41 J and 28 J).  Although, both spark timings of 30 ms and 90 ms release the same amount of heat, it is evident from the slope of the curves that the 30 ms run releases heat at a faster rate than the run at 90 ms.  0 50 100 150 200 250 3000 2 4 6 8 1012Time [ms]Pixel Count x 104  Average, Cold FlowTS = 80 ms, IHR = 149.1 JTS = 90 ms, IHR = 143.2 JTS = 160 ms, IHR = 111.7 J  70According to the combustion calculations performed based on the pressure data, the run with a 30 ms spark timing shown in Figure 52 has a maximum HRR of 3.2 kW, while the run with a 90 ms spark timing has a maximum HRR of 2.1 kW.  4.3  SUMMARY OF COMBUSTION RESULTS The highest frequency of combustion success occurred at a pressure ratio of three.  The spark timing window that leads to successful combustion decreased with increasing pressure ratio.  The spark timing retardation necessary for successful combustion was observed to increase with increasing pressure ratio.  Net integrated heat release values had a decreasing trend with increasing spark timing.  Since the amount of fuel injected increased with increasing pressure ratio, net integrated heat release values also increased.  Schlieren photographs of the combustion event indicate that the amount of unburned fuel increases with increasing spark timing.  Heat release rates were observed to decrease with increased spark timing and increase with increasing pressure ratio.    While combustion duration had no specific trend with either spark timing or pressure ratio, the ratio of combustion duration to IHR showed a trend in both.  The normalized combustion duration increased with spark timing for pressure ratios of two and three.  This is likely due to the decrease in charge motion as the  fuel  injection  nears  completion  at  the  later  spark  timings.    Since  charge  motion  increased  with increasing pressure ratio, normalized combustion duration decreased.    Localized flame extinction may be responsible for the increased ignition delay as the pressure ratio was increased.  The increased charge motion at higher pressure ratios causes increases in the rate of air-fuel   71mixing.  Since the reaction rates at the beginning of combustion are relatively slow, mixing rates exceed the reaction rates, resulting in flame quenching.      725.  CONCLUSIONS AND RECOMMENDATIONS Engine load control by varying the air/fuel ratio is a superior method to that of throttling because the pumping losses inherent to throttling are absent.  Lean burn operation has been previously shown to be an effective way of increasing engine efficiency and decreasing engine emissions.  The PSC concept has been previously shown to increase the lean operating limit of a spark ignited engine using natural gas (Reynolds,  2001).    Stratified  charge  operation  using  PSC  in  conjunction  with DI  has  been  previously attempted (Gorby, 2007).  The results of the previous DI study indicate that the PSC fuel injections failed to ignite in an air-only bulk charge.  The research presented in this thesis was aimed at mapping out a range of injection pressure ratios and spark timings that lead to successful combustion of the PSC charge.    5.1  CONCLUSIONS The experiments  described  herein  were  conducted in  an  optically  accessible  combustion  bomb  with  a pressurized  volume  of  231.1  cubic  centimetres.    The  PSC  system  utilized  in  the  previous  engine experiments was installed in the combustion bomb.  The Schlieren imaging technique was used to study the PSC injection and combustion characteristics.  An in-depth combustion analysis was performed based on the high speed pressure data acquired.  The main objectives of determining the range of pressure ratios and spark timings that lead to successful combustion were achieved.  Combustion parameters were compared for all successful experiments.  Cold flow studies were also performed to determine the PSC injection delay and duration.  The PSC injection solenoid was characterized as a separate entity from the PSC system in order to get an understanding of its contributions to the total system delays.  The following conclusions were made:    731.  The  PSC  solenoid  injection  delay  had  a  consistent  average  of  1.95  ms  and  was  found  to  be independent of commanded injection duration.  There is a linear response region, in the observed solenoid injection duration as a function of commanded injection duration, with a slope of 8.4.  Commanded  injection  durations  of  2.7  ms  or  higher  showed  no  further  increase  in  observed injection duration.  Some solenoid chatter was apparent at CID values between 1.00 and 1.33 ms.  2.  The PSC system injection delay was observed to decrease as the pressure ratio was increased.  By using the Schlieren images, the average PSC system injection delays were determined to be 20.5 ms, 16.2 ms and 13.1 ms for pressure ratios of two, three and four respectively.  These injection delay  values  are  thought  to  be  unacceptably  long  for  the  time  scales  present  in  an  internal combustion engine.  3.  The average PSC system injection durations were 52.4 ms, 74.7 ms and 102.1 ms for pressure ratios  of  two,  three  and  four,  which  were  several  times  higher  than  the  commanded  injection duration of 8 ms.  This large discrepancy in duration is likely attributed to the plenum effects of the PSC system downstream of the injection solenoid.  As stated in the previous point, at engine operating  time  scales,  this  discrepancy  between  commanded  injection  duration  and  observed injection duration needs to be addressed.  4.  PSC charge ignition was attainable at all pressure ratios; however, a pressure ratio of three had the largest successful combustion frequency.  The minimum spark timing that led to successful combustion  increased  with  increasing  pressure  ratio,  while  the  ignitable  spark  timing  window decreased as the pressure ratio was increased.  5.  Integrated heat release, heat release rate and ignition delay all varied with pressure ratio.  Due to the increased amount of fuel injected at the higher pressure ratios, integrated heat release was   74observed to increase as well.  Heat release rate also increased with increasing pressure ratio due to the increasing charge motion present at higher pressure ratios.  Ignition delay increased with increasing pressure ratio, most likely due to localized flame extinction during the reduced heat release rate of the ignition period.  6.  Increasing  the  spark  timing  resulted  in  decreasing  integrated  heat  release,  release  rate  and increasing normalized combustion duration.  The imaging results strongly suggest that the IHR decreased due to the increasing amount of fuel mixed beyond the lean flammability limit at the later  spark  timings.    It  is  believed  that  HRR  decreased  and  normalized  combustion  duration increased  with  increasing  spark  timing  because  the  charge  motion  present  at  the  earlier  spark timings dissipated at the later spark timings.    7.  The pixel count data resulting from the image binarization showed the same trends in integrated heat  release  and  heat  release  rate  as  the  pressure  data.    A  temporal  phase  shift  is  observed between  flame  kernel  development  and  integrated  heat  release,  which  is  in  agreement  with previous research in an optically accessible engine.  5.2  RECOMMENDATIONS The ability to ignite the PSC plume in a bulk charge of air demonstrates that further research is warranted with  PSC  and  DI  in  a  stratified  charge  engine.    Since  the  previous  engine  studies  were  performed  at constant pressure ratio, it is recommended that future studies consider varying this.  These experiments have shown a significant variability of the discussed combustion parameters with pressure ratio.  Since a pressure ratio of three showed the most promising results, it is suggested that future work focus on this pressure ratio as a starting point.   75Since  the  current  PSC  system  exhibits  significantly  longer  injection  durations  than  the  commanded injection duration, it is suggested that an alternative method of injecting the fuel charge near the spark plug be investigated.  The use of a fast acting direct injector with a minimal downstream plenum volume is desirable instead of the current injection solenoid.    The Schlieren imaging technique demonstrated the qualitative flow characteristics of the PSC jet plume.  Further  image  processing  such  as  image  binarization  leads  to  an  understanding  of  trends  in  plume expansion rate and flame kernel development rate but did not yield any quantitative data.  In order to gain a  more  in-depth  understanding  of  the  ignition  probability  at  the  spark  plug  electrodes,  a  method  of quantifying  the  mixture  fraction  is  highly  desirable.    A  logical  next  step  would  be  to  implement  a technique such as planar laser induced fluorescence (PLIF) to map out the ignitable regions of the PSC plume.             766.  REFERENCES Abata, D., 1986, ?A Review of the Stratified Charge Engine Concept,? Automotive Engine Alternatives, R. L. Evans, ed., Plenum Press, New York, pp. 1-36.  Ahmed,  S.  F.,  Balachandran,  R.,  Marchione,  T.,  Mastorakos,  E.,  (2007)  ?Spark  Ignition  of  Turbulent Nonpremixed Bluff-Body Flames?, Combustion and Flame, Vol. 151, pp. 366-385  Alger, T., Wooldridge, S., Gallant, E., (2005), ?The Effect of Fuel Injection on the Velocity Fluctuations in the Bowl of a DISI Engine.? SAE Paper 2005-01-2102  Amann, C. A., 1986, ?How Shall We Power Tomorrow?s Automobile?,? Automotive Engine Alternatives, R. L. Evans, ed., Plenum Press, New York, pp. 37-82.  Bowker, Albert H., Lieberman, Gerald J., Engineering Statistics, 2nd Edition, (1972), Prentice-Hall Inc. NJ, ISBN 0-13-279455-1  Brown G (2003). ?Performance of a Partially Stratified-Charge Gasoline Engine? University of British Columbia, Canada, M.A.Sc dissertation  Dahm,  Werner  J.A.,  and  Dimotakis,  Paul  E.,  (1990)  ?Mixing  at  Large  Schmidt  Number  in  the  Self-Similar Far Field of Turbulent Jets?, Journal of Fluid Mechanics, Vol. 217, pp. 299-330  Evans (2000), ?Control Method for Spark-Ignition Engines?, United States Patent No. 6,032,640, Issued March 2000  Gorby D (2007). ?An evaluation of Partially Stratified Charge Ignition in a Direct Injection Natural Gas Engine?, University of British Columbia, Canada, M.A.Sc dissertation  Heywood, J.B., Internal Combustion Engine Fundamentals, (1988), McGraw-Hill, New York NY, ISBN 0-07-100499-8   Huang,  Z.,  Shiga,  S.,  Ueda,  T.,  Nakamura,  H.,  Ishima,  T.,  Obokata,  T.,  Tsue,  M.,  Kono,  M.,  (2003), ?Combustion  Characteristics  of  Natural-Gas  Direct-Injection  Combustion  Under  Various  Fuel   77Injection Timings?, Proc. Instn Mech. Engrs., Vol. 217 Part D: J. Automobile Engineering pp. 393-401  Hill,  Phillip  G.,  and  Oulette,  P.,  (1999),  ?Transient  Turbulent  Gaseous  Fuel  Jets  for  Diesel  Engines.? Journal of Fluids Engineering, Vol. 121, pp. 93-101  Holman, J. P., 2002, ?Heat Transfer?, 9th Ed., McGraw Hill, ISBN 0-07-240655-0  Kitagawa, T., Kido, H., Kim, K., Koga, H., Fujioka, K., (2002), ?Flame Propagation into Lean Region in Stratified Methane Mixture.? SAE Paper 2002-01-2693  Kubseh, John T., (2001), ?Development of a Throttleless Natural Gas Engine? SAE Paper 2001-01-2522  Lahbabi,  Fatima  Z.,  Bor?e,  Jacques,  Nuglisch,  Hans  J.,  and  Charnay,  Georges,  (1993),  ?Analysis  of Starting  and  Steady  Turbulent  Jets  by  Image  Processing  Techniques.?  Experimental  and Numerical Flow Visualization, ASME FED, Vol. 172, pp. 315-321  Mi, J., Nathan, G. J., Nobes, D. S., (2001), ?Mixing Characteristics of Axisymmetric Free Jets From a Contoured Nozzle, an Orifice Plate and a Pipe.? Journal of Fluids Engineering, Vol. 123, pp. 878-883  Namazian, M., Hansen, S., Lyford-Pike, E., Sanchez-Barsse, J., Heywood, J., Rife, J., (1981), ?Schlieren Visualization of the Flow and Density Fields in the Cylinder of a Spark Ignition Engine.? SAE Paper 800044  Navidi, W., 2006, ?Statistics for Engineers and Scientists?, 1st Ed., McGraw Hill, ISBN 0-07-255160-7  Oulette, P., (1996), ?Direct Injection of Natural Gas for Diesel Engine Fuelling,? PhD thesis, University of British Columbia  Pischinger, S., Umierski, M., H?chtebrock, B., (2003), ?New CNG Concepts for Passenger Cars: High Torque with Superior Fuel Consumption.? SAE Paper 2003-01-2264    78Reynolds, C.C.O., (2001), ?Performance of a Partially Stratified-Charge Natural Gas Engine?, University of British Columbia, Canada, M.A.Sc. dissertation  Settles, G. S., Schlieren and Shadowgraph Techniques, (2001), 1st Ed., Springer Berlin Heidelberg NY, ISBN 3-540-66155-7  Shapiro, A. H., The Dynamics and Thermodynamics of Compressible Fluid Flow, (1953), Volume I, John Wiley and Sons, ISBN 0-471-06691-5  Stone, Richard, Introduction to Internal Combustion Engines, 3rd Edition, (1999), Society of Automotive Engineers, Warrendale PA, ISBN 0-7680-0495-0  Terasen Gas Inc., World Wide Web, Cited August 15, 2008: http://www.terasengas.com/_AboutNaturalGas/FactsandInformation/GasFacts/DetailedGasFacts.htm   Ting, D. S. ?K., and Checkel, M. D., (2001), ?The Effect of Mean Turbulent Strain Rate on the Flame Speed of Premixed, Growing Flames.? Journal of Engineering for Gas Turbines and Power, Vol. 123, pp. 175 - 181  White, Frank M., Fluid Mechanics, (1999), 4th Ed., McGraw Hill, ISBN 0-07-069716-7          79APPENDIX A: EXPERIMENT NUMBERS     10 20 30 40 50 60 70 80 90 100 120 140 1601 2 3 4 5 6 7 8 9 10 - - -31 32 33 34 35 36 37 38 39 40 - - -61 62 63 64 65 66 67 68 69 70 - - -11 12 13 14 15 16 17 18 19 20 101 102 10341 42 43 44 45 46 47 48 49 50 107 108 10971 72 73 74 75 76 77 78 79 80 113 114 11592 9193949521 22 23 24 25 26 27 28 29 30 104 105 10651 52 53 54 55 56 57 58 59 60 110 111 11281 82 83 84 85 86 87 88 89 90 116 117 118Spark Timing [ms]24Pressure Ratio3Experiment Order of Execution:  (R - Run #, E - Exp #)R E R E R E R E R E R E1 46 21 66 41 67 61 6 81 71 101 1122 31 22 47 42 43 62 33 82 11 102 1063 84 23 65 43 86 63 34 83 73 103 1044 2 24 50 44 27 64 88 84 90 104 1155 22 25 18 45 39 65 62 85 61 105 1086 69 26 35 46 83 66 55 86 45 106 1187 15 27 1 47 74 67 19 87 64 107 1028 14 28 32 48 70 68 37 88 51 108 1169 38 29 40 49 4 69 59 89 23 109 10710 76 30 29 50 21 70 26 90 42 110 10911 81 31 48 51 3 71 60 91 91 111 11012 24 32 54 52 7 72 52 92 92 112 11413 72 33 12 53 63 73 77 93 93 113 11314 41 34 28 54 79 74 16 94 9415 8 35 75 55 68 75 85 95 9516 56 36 5 56 9 76 58 96 10117 30 37 17 57 10 77 80 97 10318 49 38 13 58 78 78 89 98 11119 44 39 36 59 25 79 87 99 10520 20 40 57 60 82 80 53 100 117  80APPENDIX B: SELECT IMAGES FOR COMBUSTING RUNS The following is a compilation of images corresponding to the time of spark (left), time of max HRR (middle) and end of combustion (right) for the experiments that were successfully ignited. PRATIO = 2, TS = 40 ms arrowright Exp 4   PRATIO = 2, TS = 40 ms arrowright Exp 34  PRATIO = 2, TS = 40 ms arrowright Exp 64     81PRATIO = 2, TS = 50 ms arrowright Exp 5   PRATIO = 2, TS = 50 ms arrowright Exp 35  PRATIO = 2, TS = 50 ms arrowright Exp 65       82PRATIO = 2, TS = 60 ms arrowright Exp 6   PRATIO = 2, TS = 60 ms arrowright Exp 36   PRATIO = 2, TS = 60 ms arrowright Exp 66       83PRATIO = 2, TS = 70 ms arrowright Exp 37   PRATIO = 2, TS = 70 ms arrowright Exp 67   PRATIO = 2, TS = 80 ms arrowright Exp 8       84PRATIO = 2, TS = 80 ms arrowright Exp 38   PRATIO = 2, TS = 90 ms arrowright Exp 9   PRATIO = 2, TS = 100 ms arrowright Exp 10       85PRATIO = 3, TS = 30 ms arrowright Exp 43   PRATIO = 3, TS = 30 ms arrowright Exp 73   PRATIO = 3, TS = 30 ms arrowright Exp 91       86PRATIO = 3, TS = 30 ms arrowright Exp 92   PRATIO = 3, TS = 30 ms arrowright Exp 95   PRATIO = 3, TS = 50 ms arrowright Exp 15       87PRATIO = 3, TS = 60 ms arrowright Exp 16   PRATIO = 3, TS = 60 ms arrowright Exp 46   PRATIO = 3, TS = 60 ms arrowright Exp 76       88PRATIO = 3, TS = 70 ms arrowright Exp 17   PRATIO = 3, TS = 70 ms arrowright Exp 47   PRATIO = 3, TS = 70 ms arrowright Exp 77       89PRATIO = 3, TS = 80 ms arrowright Exp 18   PRATIO = 3, TS = 80 ms arrowright Exp 48   PRATIO = 3, TS = 80 ms arrowright Exp 78       90PRATIO = 3, TS = 90 ms arrowright Exp 19   PRATIO = 3, TS = 90 ms arrowright Exp 49   PRATIO = 3, TS = 90 ms arrowright Exp 79       91PRATIO = 3, TS = 100 ms arrowright Exp 20   PRATIO = 3, TS = 100 ms arrowright Exp 50   PRATIO = 3, TS = 100 ms arrowright Exp 80       92PRATIO = 3, TS = 120 ms arrowright Exp 101   PRATIO = 3, TS = 120 ms arrowright Exp 107   PRATIO = 3, TS = 120 ms arrowright Exp 113       93PRATIO = 3, TS = 140 ms arrowright Exp 102   PRATIO = 3, TS = 140 ms arrowright Exp 108   PRATIO = 3, TS = 140 ms arrowright Exp 114       94PRATIO = 3, TS = 160 ms arrowright Exp 109   PRATIO = 3, TS = 140 ms arrowright Exp 115   PRATIO = 4, TS = 60 ms arrowright Exp 56       95PRATIO = 4, TS = 80 ms arrowright Exp 28   PRATIO = 4, TS = 80 ms arrowright Exp 58   PRATIO = 4, TS = 90 ms arrowright Exp 29       96PRATIO = 4, TS = 90 ms arrowright Exp 59   PRATIO = 4, TS = 90 ms arrowright Exp 89   PRATIO = 4, TS = 100 ms arrowright Exp 30       97PRATIO = 4, TS = 100 ms arrowright Exp 60   PRATIO = 4, TS = 100 ms arrowright Exp 90  PRATIO = 4, TS = 120 ms arrowright Exp 116       98PRATIO = 4, TS = 140 ms arrowright Exp 105   PRATIO = 4, TS = 140 ms arrowright Exp 117   PRATIO = 4, TS = 160 ms arrowright Exp 106       99PRATIO = 4, TS = 160 ms arrowright Exp 112        100APPENDIX C: SELECT IMAGES FOR NON-COMBUSTING RUNS The following is a collection of images taken from a typical cold flow experiment at pressure ratios of two, three and four.  There are 18 slides shown for each pressure ratio, broken up in 9 slides per page.  Image progression order is to the right, then down. PRATIO 2: First slide at 25.26 ms after CSOI.  The rest of the slides are shown at time intervals of 5.05 ms.       101      102PRATIO 3: First slide at 19.02 ms after CSOI.  The rest of the slides are shown at time intervals of 6.34 ms.       103      104PRATIO 4: First slide at 16.13 ms after CSOI.  The rest of the slides are shown at time intervals of 8.06 ms.       105   106APPENDIX D: SELECT MATLAB PROCESSING CODE The first subset of Matlab program code was used to conduct the combustion calculations.  The second subset  of  code  was  used  for  image  processing.    The  third  subset  was  used  for  post-processing  image binarization.  For both combustion calculations and image processing a main routine called ?process.m? was written which calls other functions as required.  The important functions called by the main routine are also shown here.  PART I: COMBUSTION CALCULATION FUNCTIONS  MAIN FILE: ?process.m?  % Zero the starting time based on camera trigger: Z_DATA = zerodata(EXP_DATA);   % Look up initial temperature: TEMP = mean(EXP_DATA(1:3,5));   clear EXP_DATA;   TIME = (Z_DATA(:,1)); PIEZO = filterdata(Z_DATA, 2, 2000); %PIEZO_ERROR = abs(PIEZO - Z_DATA(:,2));   % Peg the Piezoelectric pressure: PIEZO = PIEZO - P_INIT(1) + P_INIT(2); Z_DATA(:,2) = Z_DATA(:,2) - P_INIT(1) + P_INIT(2);   % Subtract pressure rise due to injection for HR calculations: INJECTION_PRESS = dlmread(['cold_flow_pratio_' num2str(P_RATIO) '_PIEZO.txt']); PIEZO_COMB = PIEZO(1:45001) - INJECTION_PRESS(1:45001, 10) - P_INIT(2); clear INJECTION_PRESS;   % Calculate pressure derivatives for HR calculations: DP_DATA(:,1) = TIME(1:(length(PIEZO_COMB)-1)); DP_DATA(:,2) = dp(PIEZO_COMB);   % Filter the pressure derivative data: DPIEZO = filterdp(DP_DATA, 2, 300);   % Calculate heat release rate: DH_PIEZO = hrr(DPIEZO); DH_PIEZO_RAW = hrr(DP_DATA(:,2));   % Calculate net integrated heat release: H_PIEZO = ihrr(DH_PIEZO);   107H_PIEZO_RAW = ihrr(DH_PIEZO_RAW);   % Plot pressure values: figure(3); plot(TIME(FIRST:LAST), Z_DATA(FIRST:LAST,2), 'green', TIME(FIRST:LAST), PIEZO(FIRST:LAST), 'blue'); title('Overall Pressure - Pegged and Zeroed for Camera Trigger'); ylabel('Pressure [PSI]'); xlabel('Time [s]'); legend('Raw pressure signal', 'FFT pressure'); %  figure(4); plot(TIME(FIRST:LAST), PIEZO_COMB(FIRST:LAST), 'blue'); title('Combustion Pressure - Pegged and Zeroed for Camera Trigger'); ylabel('Pressure [PSI]'); xlabel('Time [s]');   % Plot net heat release rate: figure(5); plot(TIME(FIRST:LAST), DH_PIEZO_RAW(FIRST:LAST), 'r', TIME(FIRST:LAST), DH_PIEZO(FIRST:LAST), 'b'); title('Heat Release Rate, Piezoelectric'); ylabel('HRR [kW]'); xlabel('Time [s]'); legend('Unfiltered', 'FFT Filtered');   % Plot net integrated heat release: figure(6); plot(TIME(FIRST:LAST), H_PIEZO_RAW(FIRST:LAST), 'r', TIME(FIRST:LAST), H_PIEZO(FIRST:LAST), 'b'); title('Net Integrated Heat Release, Piezoelectric'); ylabel('IHRR [kJ]'); xlabel('Time [s]'); legend('Unfiltered', 'FFT Filtered');   Plot HRR and IHRR on the same plot: figure(7); plot(TIME(FIRST:LAST), H_PIEZO(FIRST:LAST), '. black', TIME(FIRST:LAST), DH_PIEZO(FIRST:LAST), 'black'); title('Net Rate and Integrated Rate of Heat Release'); ylabel('HRR [kW]'); xlabel('Time [s]'); legend('Net Integrated HR', 'Net HR Rate');   % Compute combustion data: POSN_SPARK = round(SPARK/(2e-05));   % Define new heat release vector starting from spark location: H_PIEZO_RAW_SPARK = H_PIEZO_RAW(POSN_SPARK:length(H_PIEZO_RAW));   [H_MAX, POSN_H_MAX] = max(H_PIEZO_RAW);   H_COMB = H_MAX - H_PIEZO_RAW(POSN_SPARK); FIVE_PERCENT_H_COMB = 0.05 * H_COMB; TEN_PERCENT_H_COMB = 0.10 * H_COMB;   108NINETY_PERCENT_H_COMB = 0.90 * H_COMB; NINETYFIVE_PERCENT_H_COMB = 0.95 * H_COMB;   POSN_FIVE_PERCENT_H_COMB = find(H_PIEZO_RAW_SPARK > (FIVE_PERCENT_H_COMB + H_PIEZO_RAW(POSN_SPARK)), 1) + POSN_SPARK; POSN_TEN_PERCENT_H_COMB = find(H_PIEZO_RAW_SPARK > (TEN_PERCENT_H_COMB + H_PIEZO_RAW(POSN_SPARK)), 1) + POSN_SPARK; POSN_NINETY_PERCENT_H_COMB = find(H_PIEZO_RAW_SPARK > (NINETY_PERCENT_H_COMB + H_PIEZO_RAW(POSN_SPARK)), 1) + POSN_SPARK; POSN_NINETYFIVE_PERCENT_H_COMB = find(H_PIEZO_RAW_SPARK > (NINETYFIVE_PERCENT_H_COMB + H_PIEZO_RAW(POSN_SPARK)), 1) + POSN_SPARK;   T_FIVE = TIME(POSN_FIVE_PERCENT_H_COMB) - TIME(POSN_SPARK); T_TEN = TIME(POSN_TEN_PERCENT_H_COMB) - TIME(POSN_SPARK); T_NINETY = TIME(POSN_NINETY_PERCENT_H_COMB) - TIME(POSN_SPARK); T_NINETYFIVE = TIME(POSN_NINETYFIVE_PERCENT_H_COMB) - TIME(POSN_SPARK);   [DH_MAX, POSN_DH_MAX] = max(DH_PIEZO_RAW); T_DH_MAX = TIME(POSN_DH_MAX) - TIME(POSN_SPARK);   Write data to file: dlmwrite('combustion_data.txt', [EXP_NO P_RATIO SPARK TEMP P_INIT(2) max(PIEZO_COMB) DH_MAX T_DH_MAX FIVE_PERCENT_H_COMB ...      TEN_PERCENT_H_COMB NINETY_PERCENT_H_COMB NINETYFIVE_PERCENT_H_COMB T_FIVE T_TEN T_NINETY ...      T_NINETYFIVE], '-append', 'roffset', 0, 'delimiter', '\t', 'precision', 6);   EXPORT(:,1) = TIME(1:45000); EXPORT(:,2) = PIEZO_COMB(1:45000); EXPORT(:,3) = DH_PIEZO_RAW(1:45000); EXPORT(:,4) = DH_PIEZO(1:45000); EXPORT(:,5) = H_PIEZO_RAW(1:45000); EXPORT(:,6) = H_PIEZO(1:45000); dlmwrite(['proc_data_' num2str(EXP_NO) '.txt'], EXPORT, 'delimiter', '\t', 'precision', 6);         109FUNCTION: ?loaddata.m?  function trace=loaddata(exp) % Loads data based on experiment # % Input by user   if exp < 10     expstr = ['00' num2str(exp)]; elseif exp < 100     expstr = ['0' num2str(exp)]; elseif exp < 1000     expstr = num2str(exp); else     fprintf('Error in experiment number'); end   location = 'RawData\'; file = ['data' expstr '.txt'];   trace = dlmread([location file]); %trace = dlmread(file);   FUNCTION: ?init_press.m?  function P_INIT=init_press(EXP_DATA, NO_POINTS)   % Function averages inital pressure and returns value   for i=1:2     INIT_PRESS_MEAN(i) = mean(EXP_DATA(1:100,(i+1)));     INIT_PRESS_MEDIAN(i) = median(EXP_DATA(1:100,(i+1)));     PERCENT_DIFF(i) = 100 * abs(INIT_PRESS_MEAN(i) - INIT_PRESS_MEDIAN(i)) / (INIT_PRESS_MEAN(i) + INIT_PRESS_MEDIAN(i)) / 2;     if (PERCENT_DIFF(i) > 5)         fprintf('Error in initial pressure calculation!');         fprintf('Revise averaging window extrema.');         fprintf('Percent difference is:');         PERCENT_DIFF(i)     end        P_INIT(i) = INIT_PRESS_MEDIAN(i); end       110FUNCTION: ?zerodata.m?  function z_data=zerodata(exp)   % Function zeroes the time of the pressure trace to have it coincide with % the camera trigger   N_points=length(exp);   % Find camera trigger and assign time and pressure vectors: first_point=1; while exp(first_point,4) < 5     first_point=first_point+1; end   z_data(:,1) = exp(first_point:N_points,1) - exp(first_point,1); z_data(:,2) = exp(first_point:N_points,2); z_data(:,3) = exp(first_point:N_points,3);    FUNCTION: ?filterdata.m?  function data_rev=filterdata(raw_file, COL_DATA, CUTOFF_FREQ) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Edward C. Chan, Mechanical Engineering % University of British Columbia % 28 February, 2008 % Rev. B % Modified by: Andrew Mezo % Date: February 29, 2008 % % This program basically removes ignition signal noise (low frequency, % high amplitude) using a window median filter.  Then it applies % a gaussian low-pass filter to get rid of the higher frequency  % noise components.  The difference between the raw and filtered % signal is available for verification. %  % User configurable Inputs % ------------------------ % % COL_TIME, COL_DATA - columns on data file denoting time and the %       unfiltered data. % % MEDIAN_BOUND - size of the window for the median filter %   (size = 2 x MEDIAN_BOUND + 1) % % PRUNE_THRESHOLD - if the noise-to-signal ratio of the median filter is %   greater than this value, it gets replaced by the median % % NYQUIST_FACTOR - amount of zero padding required for the guassian %   filter (new array size = # samples x NYQUIST_FACTOR) % % CUTOFF_FREQ - Cut off frequency of the guassian filter %   111% EXTEND_LENGTH - number of elements to extend the data on both ends of %   the array % % Outputs % ------- % % time_raw - array of time % data_raw - array of unfiltered data % data_rev - array of filterd data % delta    - abs. difference between filtered and unfiltered data sets % % Remarks % ------- % % (1) PRUNE_THRESHOLD should be at least 1 to prevent pruning of %       otherwise meaningful data % % (2) NYQUIST_FACTOR should be at least 2 (10 is quite ideal) to %       minimize aliasing % % (3) CUTOFF_FREQ should be high enough to avoid smearing of %       important data.  It should be at least 200 Hz (I think) % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%           %         % some information about the data file         %   COL_TIME = 1;           %         % configurations for the window median filter          %   MEDIAN_BOUND = 10; PRUNE_THRESHOLD = 1.1;           %         % configuations for the gaussian low-pass filter         %   NYQUIST_FACTOR = 10;           %         % data extension length         %          EXTEND_LENGTH = 1000;     %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % DO NOT CHANGE BELOW THIS LINE %   112%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%           %         % extract sample information         %   N_LINES     = length (raw_file); SAMPLE_TIME = raw_file (N_LINES, COL_TIME) - raw_file (1, COL_TIME); SAMPLE_FREQ = N_LINES / SAMPLE_TIME;           %         % extract padding information         %    N_PADDED = floor (N_LINES * NYQUIST_FACTOR); N_FREQ   = floor ((N_PADDED + 0.5)/2); MAX_FREQ = 0.5 * SAMPLE_FREQ * NYQUIST_FACTOR;           %         % extract data into arrays         %    time_raw = raw_file (:,COL_TIME); data_raw = raw_file (:,COL_DATA); data_pad = zeros (N_PADDED, 1); data_pad(1:N_LINES) = data_raw;   clear raw_file;           %         % perform running median filter         %   INDEX_LO = MEDIAN_BOUND+1; INDEX_HI = N_LINES - (MEDIAN_BOUND + 1);   for (i=INDEX_LO:INDEX_HI);       LOWER_BOUND = i - MEDIAN_BOUND;     UPPER_BOUND = i + MEDIAN_BOUND;       window_median = median (data_pad (LOWER_BOUND:UPPER_BOUND));     noise_signal_ratio = (abs(data_pad(i)) - abs(window_median)) / abs(window_median);       if (noise_signal_ratio > PRUNE_THRESHOLD)         data_pad(i) = window_median;     end   end           %         % extend data array (if not, data would for some reason         % drop off)   113        %   EXTEND_START = N_PADDED - EXTEND_LENGTH +1; EXTEND_END   = N_LINES + EXTEND_LENGTH;   data_pad(N_PADDED:-1:EXTEND_START) = data_pad(1:EXTEND_LENGTH); data_pad(N_LINES+1:1:EXTEND_END)   = data_pad(N_LINES:-1:N_LINES-EXTEND_LENGTH+1);           %         % obtain FFT of data         %   data_fft = fft (data_pad);           %         % generate filter         %   SIGMA = CUTOFF_FREQ / sqrt (2.0 * log(2.0));   filter = zeros (N_PADDED, 1); filter(1:N_FREQ) = exp ( -0.5*(((1:N_FREQ)-1)/SIGMA).^2.0 ); filter(N_FREQ+1:N_PADDED) = filter(N_FREQ:-1:1);           %         % apply filter         %   data_fil = data_fft .* filter;           %         % recover filtered data         %   data_ift    = ifft (data_fil); data_rev = real (data_ift(1:N_LINES));       114FUNCTION: ?dp.m?  function proc_slope=dp(p)   for i=2:length(p)     j=i-1;     dt=2.0000e-005;     proc_slope(j)=(p(i)-p(j))/dt; end   FUNCTION: ?hrr.m?  function DH=hrr(DP)   % Calculates heat release rate based on dp/dt   % *************** Constants ***************** GAMMA = 1.4; CONV_UNIT = 6.894757; % 1 PSI = CONV_UNIT kPA BOMB_VOLUME = 2.311e-004; %[m^3] % *******************************************   DH = (1/(GAMMA-1)) * BOMB_VOLUME * DP * CONV_UNIT;   FUNCTION: ?ihrr.m?  function H=ihrr(DH)   % Integrates the heat release rate   INC_VALUE = 0; for i=1:length(DH)     INC_VALUE = INC_VALUE + DH(i)*2.000e-005;     H(i) = INC_VALUE; end      115PART II: IMAGE PROCESSING FUNCTIONS MAIN FUNCTION: ?process.m?  function process(exp)   %------CONSTANTS--------- start_image=56; exposure_const=3;  %Divide by this number to get the gray scale exposure bk_ave_last_image=50; border_sensitivity = 12; %------------------------   bk=loadimages(exp,1,bk_ave_last_image); bk_ave=bkground(bk, bk_ave_last_image); bk_ave=bk_ave+1;    %Eliminate divide by 0 possibility bk_ave_dp=im2double(bk_ave); clear bk;   end_image = filenum(exp);   border = frame_map(bk_ave_dp, border_sensitivity);   for i=start_image:end_image     frame=loadimage(exp, i);     frame_dp=im2double(frame);     c_frame_dp=frame_dp./bk_ave_dp;     c_frame=uint16(round(c_frame_dp*(65535/exposure_const)));     c_frame = c_frame + border;   % Black out time increment pixels     c_frame(461:476,6:97)=frame(461:476,6:97);       writeimage(exp, c_frame, i, start_image);   end        116FUNCTION: ?loadimages.m?  function frame=loadimages(exp,first_image,last_image) % Loads images based on experiment # and number of images % Input by user   if exp < 10     expstr = ['00' num2str(exp)]; elseif exp < 100     expstr = ['0' num2str(exp)]; elseif exp < 1000     expstr = num2str(exp); else     fprintf('Error in experiment number'); end   location = ['exp' expstr '\'];   for i=first_image:last_image       if i < 10         file = ['000' num2str(i) '.tif'];     elseif i < 100         file = ['00' num2str(i) '.tif'];     elseif i < 1000         file = ['0' num2str(i) '.tif'];            else         file = [num2str(i) '.tif'];             end           frame(:,:,i) = imread([location file]);   end   FUNCTION: ?bkground.m?  function ave=bkground(exp, no_images) % Computes arithmetic average of images   ave = exp(:,:,1)-exp(:,:,1);   for i=1:no_images     ave = ave + exp(:,:,i)/no_images; end        117FUNCTION: ?filenum.m?  function no_files = filenum(exp)   if exp < 10     expstr = ['00' num2str(exp)]; elseif exp < 100     expstr = ['0' num2str(exp)]; elseif exp < 1000     expstr = num2str(exp); else     fprintf('Error in experiment number'); end   location = ['exp' expstr '\']; dirOutput=dir(fullfile(location, '*.tif')); no_files = length(dirOutput);   FUNCTION: ?frame_map.m?  % % A - pixel values for image % MAGIC - arbitrary value for calculating cutoff threshold (8 is good) %   function M = frame_map (A,MAGIC) D = 3; [R,C] = size(A); blacklines = [ A(:,D)' A(D,:) A(:,C-D)' A(R-D,:) ]'; mu = mean(blacklines); sigma = std(blacklines); black_threshold = mu + MAGIC*sigma;   % Black background: %M = uint16( max( sign (A - black_threshold) , 0.0) * 65535);   % White background: M = uint16(max ( sign (black_threshold - A), 0.0) * 65535);        118FUNCTION: ?writeimage.m?  function writeimage(exp,cframe,i,start_image) % exp -> experiment number % cframe -> processed image matrix to be written % i -> frame number   if exp < 10     expstr = ['00' num2str(exp)]; elseif exp < 100     expstr = ['0' num2str(exp)]; elseif exp < 1000     expstr = num2str(exp); else     fprintf('Error in experiment number'); end   if i==start_image     mkdir(['cexp' expstr]); end   location = ['cexp' expstr '\'];   if i < 10     file = ['000' num2str(i) '.tif'] elseif i < 100     file = ['00' num2str(i) '.tif'] elseif i < 1000     file = ['0' num2str(i) '.tif']        else     file = [num2str(i) '.tif']         end   imwrite(cframe,[location file]);         119PART III: IMAGE BINARIZATION FUNCTIONS MAIN FILE: ?process_calcsubfill.m?  % ---------------- CONSTANTS -------------------- inc_frame = 18; cutoff_freq = 200;   least_frame2 = 1800; %frame number threshold Pratio 2 least_frame3 = 2200; %frame number threshold Pratio 3 least_frame4 = 2600; %frame number threshold Pratio 4   nonflammable2 = [1,2,3,7,31,32,33,39,40,61,62,63,68,69,70]; nonflammable3 = [11,12,13,14,41,42,44,45,71,72,74,75,103,113]; nonflammable4 = [21,22,23,24,25,26,27,51,52,53,54,55,57,81,82,83,84,85,86,87,88,104,110,111,118];   flammable2 = [4,5,6,8,9,10,34,35,36,37,38,64,65,66,67]; flammable3 = [15,16,17,18,19,20,43,46,47,48,49,50,73,76,77,78,79,80,101,102,107,108,109,114,115]; flammable4 = [28,29,30,56,58,59,60,89,90,105,106,112,116,117];   % -----------------------------------------------   exp(1:200,2,1:118) = 0; cexp(1:200,2,1:118) = 0;   % Calculate area curves for i = 1 : 95     temp = calcsubfill(i);     l_temp = length(temp);     exp(1:l_temp,1:2,i) = temp(1:l_temp,1:2);     i end   for i = 101 : 118     temp = calcsubfill(i);     l_temp = length(temp);     exp(1:l_temp,1:2,i) = temp(1:l_temp, 1:2);     i end   % Filter area curves to remove 120Hz noise for i = 1 : 95     exptemp = exp(:,:,i);     filtemp = filterdata(exptemp,2,cutoff_freq);     cexp(:,1,i) = exp(:,1,i);     cexp(:,2,i) = filtemp; end   for i = 101 : 118   120    exptemp = exp(:,:,i);     filtemp = filterdata(exptemp,2,cutoff_freq);     cexp(:,1,i) = exp(:,1,i);     cexp(:,2,i) = filtemp; end   % Check that there are enough files to produce a good graph index = 0; for i = 1 : length(nonflammable2)     if filenum(nonflammable2(i)) > least_frame2         index = index + 1;         i2(index) = nonflammable2(i);     end end   index = 0; for i = 1 : length(nonflammable3)     if filenum(nonflammable3(i)) > least_frame3         index = index + 1;         i3(index) = nonflammable3(i);     end end   index = 0; for i = 1 : length(nonflammable4)     if filenum(nonflammable4(i)) > least_frame4         index = index + 1;         i4(index) = nonflammable4(i);     end end   first = 0.0101; inc = inc_frame/9302; last = (199 * inc) + first;   % Calculate averages ave2(1:200,1) = first:inc:last; ave3(1:200,1) = first:inc:last; ave4(1:200,1) = first:inc:last; cave2(1:200,1) = first:inc:last; cave3(1:200,1) = first:inc:last; cave4(1:200,1) = first:inc:last;   ave2(1:200,2) = 0; ave3(1:200,2) = 0; ave4(1:200,2) = 0; cave2(1:200,2) = 0; cave3(1:200,2) = 0; cave4(1:200,2) = 0;     for i = 1:length(i2);     ave2(:,2) = ave2(:,2) + exp(:,2,i2(i))/length(i2);     cave2(:,2) = cave2(:,2) + cexp(:,2,i2(i))/length(i2);     end   121figure(1); plot(ave2(:,1), ave2(:,2)); hold on plot(cave2(:,1), cave2(:,2)); hold on   for i = 1:length(i3);     ave3(:,2) = ave3(:,2) + exp(:,2,i3(i))/length(i3);     cave3(:,2) = cave3(:,2) + cexp(:,2,i3(i))/length(i3);     end %figure; plot(ave3(:,1), ave3(:,2), 'r'); hold on plot(cave3(:,1), cave3(:,2), 'r'); hold on   for i = 1:length(i4);     ave4(:,2) = ave4(:,2) + exp(:,2,i4(i))/length(i4);     cave4(:,2) = cave4(:,2) + cexp(:,2,i4(i))/length(i4); end %figure; plot(ave4(:,1), ave4(:,2), 'g'); plot(cave4(:,1), cave4(:,2), 'g');        122FUNCTION: ?calcsubfill.m?  function data = calcsubfill(exp)   % ----------- Constants ----------- first_frame = 94; %(10 ms equivalent) inc_frame = 18; %(2 ms equivalent) bk_ave_first_image = 56; bk_ave_last_image = 80; % ----------------------------------   no_files = filenum(exp);   index = 0;   bk=loadcimages(exp, bk_ave_first_image, bk_ave_last_image); bk_ave=bkground(bk, (bk_ave_last_image - bk_ave_first_image)); clear bk;   for frame_no = first_frame : inc_frame : no_files         index = index + 1;       im = subfill(exp, frame_no, bk_ave);       data(index,1) = frame_no / 9302;          data(index,2) = 0; % col 1 = time, col 2 = area.     for j = 1 : 480         for i = 1 : 480             if im(i,j,1) == 0                 data(index,2) = data(index,2) + 1;             end         end     end end       123FUNCTION: ?subfill.m?  function fillim = subfill(exp, im_no, bk_ave)   % ------------Constants------------- thresh = 7000; bk_ave_first_image = 56; bk_ave_last_image = 80;   % ----------------------------------   if bk_ave == 0     bk=loadcimages(exp, bk_ave_first_image, bk_ave_last_image);     bk_ave=bkground(bk, (bk_ave_last_image - bk_ave_first_image));     clear bk; end   frame = loadcimage(exp, im_no); image = (frame - bk_ave) + (bk_ave - frame); fillim(1:480,1:480,1) = image;   for i = 1 : 480     for j = 1 : 480         if image(i,j) > thresh             fillim(i,j,1) = 0;         else             fillim(i,j,1) = 65535;         end     end end   fillim(1:480,1:480,2) = image(1:480,1:480);   %Set time pixels: fillim(461:476,6:97,1) = frame(461:476,6:97) + 40000; fillim(461:476,6:97,2) = frame(461:476,6:97);      124APPENDIX E: COMPRESSIBLE FLOW CALCULATIONS The PSC capillary tube, which is connected downstream of the 1/4" fitting at the solenoid exit (Figure 8) has an internal diameter of 0.47 mm.  It is assumed to be a constant area duct, connected at each end to a reservoir at constant temperature and pressure, as shown in the simplified diagram below:          Reservoir conditions:  T01 = 288.15 K P01 = 200 psi (1.38E6 Pa) @ PRATIO 2, 300 psi (2.07E6 Pa) @ PRATIO 3, 400 psi (2.76E6 Pa) @ PRATIO 4 P4 = 100 psi (689475.7 Pa)  Governing equations [Shapiro]:    g1858g1191g1838g1499g1830 g3404uni0031 g3398g1839g1853g2870g2870g1863uni0020g1839g1853g2870g2870 g3397g1863 g3397uni0031uni0032uni0020g1863 g1864g1866g4666g1863 g3397uni0031g4667uni0020g1839g1853g2870g2870uni0032 g3397g4666g1863 g3398uni0031g4667uni0020g1839g1853g2870g2870  (Eq. E.1)    uni0031g3493g1858g3404 g3398uni0031uni002Euni0038uni0020g1864g1867g1859uni0031uni0030g3429g4678g2013 g1830g3415uni0033uni002Euni0037g4679g2869uni002Eg2869g2869g3397uni0036uni002Euni0039g1844g1857g3433  (Eq. E.2)    g1839g1853 g3404 g1874uni002Fg1853  (Eq. E.3)    g1853 g3404 uni221Ag1863g1844g1846  (Eq. E.4)    g1844g1857 g3404 g2025g1874g1830g2020   (Eq. E.5)  P01            1 T01 P03            4 T03 2  320 mm 3    125Where g2188g3364 is the length mean coefficient of friction, L* is the critical tube length required for a sonic exit condition, D is the internal diameter of the capillary tube, a is the local speed of sound and Ma is the local Mach number.  The Reynolds number (Re) was determined based on average properties in the tube.  The following gas properties were used for the calculations: k (ratio of specific heats, natural gas) = 1.31   RNG (gas constant, natural gas) = 518 m2/(s2K)   ?NG (dynamic viscosity, natural gas) = 1.34E-5 Ns/m2   The following dimensions were used for the capillary tube:   L (length) = 320 mm   D (inner diameter) = 0.47 mm   ? (surface roughness) = 1.5E-6 m  Method of analysis for determination of critical tube length (L*): 1)  The flow between point (1) and (2) is assumed isentropic, as suggested by Shapiro 2)  Initially, the flow is assumed to be choked at the exit (3), thus assume L = L* 3)  An initial velocity is guessed at point (2) arrowright ex: 100 m/s 4)  The Mach number, Reynolds number and friction factor are calculated based on the guessed velocity 5)  The ratio in the left hand side of Equation E.1 is calculated based on the tube diameter, roughness and calculated friction factor 6)  The ratio on the right hand side of equation E.1 is calculated based on the ratio of specific heats and calculated Mach number 7)  The answers from steps 5 and 6 are compared and a percent difference value is calculated 8)  Steps 4 to 7 are looped, until the percent difference value is smaller than 0.01%  9)  Once the iteration loop converges, the calculated Mach number is used in Equations E.6 arrowright E.9  to give the static and stagnation pressures at the capillary tube entrance (2) and exit (3) 10)  At the sonic exit condition, where the length of the tube (L) is exactly equal to the critical length (L*) the pressure at the tube exit (P3) must equal the back pressure in the discharge reservoir (P4).  Thus, the left hand side of Equation E.10 equals 1.  The ratios of P01 to P4 and P3 to P03 are calculated based on the values found from step 9.  This gives a numerical value to the ratio of P03 to P01   12611) The ratio of P03 to P01 from step 10 is used in the Fanno Line Equation (E.10) to calculate the new Mach number which satisfies the equation 12) Finally, the Mach number calculated from step 11 is used in Equation E.1 to determine the value of the critical pipe length (L*)    g1842g2870 g3404g1842g2868g2869g4670uni0031 g3397uni0030uni002Euni0035g4666g1863 g3398uni0031g4667g1839g1853g2870g2870g4671 g3038g2869  (Eq. E.6)    g1842g2868g2870 g3404 g1842g2870g4670uni0031 g3397uni0030uni002Euni0035g4666g1863 g3398uni0031g4667g1839g1853g2870g2870g4671  (Eq. E.7)    g1842g2871 g3404g1842g2870uni0031g1839g1853g2870 g3496g1863 g3397uni0031uni0032 g3397g4666g1863 g3398uni0031g4667g1839g1853g2870g2870 (Eq. E.8)    g1842g2868g2871 g3404g1842g2868g2870uni0031g1839g1853g2870g3496g3428uni0032 g3397g4666g1863 g3398uni0031g4667g1839g1853g2870g2870g1863 g3397uni0031 g3432g3038g2878g2869g3038g2879g2869 (Eq. E.9)  Fanno Line Equation: g1842g2868g2871g1842g2868g2869 g3404 g3436g1863 g3397uni0031uni0032 g3440g3038g2878g2869g2870g4666g3038g2879g2869g4667 g1839g1853g2870g4672uni0031 g3397g1863 g3398uni0031uni0032 g1839g1853g2870g2870g4673g3038g2878g2869g2870g4666g3038g2879g2869g4667  (Eq. E.10)  Identity Equation:  g1842g2871g1842g2872g3404 g1842g2868g2869g1842g2872g1842g2868g2871g1842g2868g2869g1842g2871g1842g2868g2871  (Eq. E.11)  Steps 1 arrowright 12 are repeated for each pressure ratio to give the following critical length values:  PRATIO = 2 arrowright L* = 15.4 mm  If the actual tube length ( 320mm) is longer than the critical tube length, the flow will be unchoked and remain subsonic all though the  tube.    Also,  the  tube  exit  pressure  will  be  equal  to  the combustion bomb pressure.  As demonstrated by the L* values, the flow remains unchoked at all pressure ratios. PRATIO = 3 arrowright L* = 70.7 mm PRATIO = 4 arrowright L* = 152.7 mm   

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