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An investigation of methane autoignition behaviour under diesel engine-relevant conditions Iaconis, Jean-Louis 2003

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An Investigation of Methane Autoignition Behaviour Under Diesel Engine-Relevant Conditions by Jean-Louis laconis B . A . S c , The University of British Columbia, 2001  A thesis submitted in partial fulfilment of the requirements for the degree of Master of Applied Science in the Faculty of Graduate Studies Department of Mechanical Engineering  We accept this thesis as conforming to the required standard  The University of British Columbia March 2003 ©Jean-Louis laconis, 2003  In  presenting  degree freely  this  at the  thesis  in  partial  University of  British Columbia,  available for reference  copying  of  department  this or  publication of  fulfilment  and study.  his  or  her  representatives.  E W ^ W N  The University of British Columbia Vancouver, Canada  Date  DE-6  (2/88)  Npr-'\  1s>  CLoo3  that the  may be It  this thesis for financial gain shall not  HexkayuCft'  requirements  I agree  thesis for scholarly purposes by  the  I further agree  permission.  Department of  of  €^r~.A  that  be  an  advanced  Library shall make it  permission for extensive  granted  is  for  by the  understood allowed  head  that without  of  my  copying  or  my written  ii  Abstract  Abstract "An Investigation of Methane Autoignition Behaviour Under Diesel Engine-Relevant Conditions" by Jean-Louis laconis As an extension to recent experimental methane ignition delay time measurements conducted at diesel engine-relevant temperatures and pressures, further work has been conducted in an attempt to more closely converge shock tube results with actual engine operating environments. This was performed in three phases that involved reviewing previous homogeneous autoignition delay time data, characterizing a gaseous fuel injector for use in non-premixed ignition studies, and finally conducting non-premixed autoignition delay time measurements in a shock tube. First, in response to recent homogenous methane autoignition delay results that questioned the applicability of existing induction time correlations at low temperatures/high pressures, a series of homogeneous methane autoignition experiments were conducted to isolate whether pressure or temperature differences between recent results and existing correlations were responsible for observed discrepancies. Shock tube experiments were conducted at pressures between 2-4 bar and temperatures between 1100-2000 K, facilitating direct comparison with existing correlations over high temperatures and with recent results at lower, engine-relevant temperatures. These experiments indicated existing correlations could predict ignition delay times at low pressures, but differences in ignition detection methods caused noticeable scatter between correlations. Subsequently, the characteristics of a gaseous fuel injector were investigated to determine the influence of injection parameters on the injector's performance and on the jet produced. These experiments investigated the influence of injection duration and pressure on resultant jets, along with exploring the effects of pulsed injection, and the effects of various obstructions and of an enclosure on overall jet development. These experiments yielded correlations for predicting the injector's behaviour under all intended operating conditions. Finally, the coupling between chemical kinetics and fluid mechanics was explored in a series of non-premixed autoignition delay experiments. These shock tube experiments utilized a standard reflected shock technique, but with fuel injected into the shock-heated air after reflection of the incident shock wave. Chemical kinetic effects were explored by varying air temperatures and pressures, while the effects of fluid mechanic parameters were investigated by varying the fuel injection pressure and duration. These experiments suggested that high-pressure, partially premixed, pulsed direct injection could form an autoignition delay reduction strategy for diesel engines.  Table of Contents  iii  Table of Contents Abstract  ii  Table of Contents  ii»  List of Tables  v  List of Figures  vii  1 Introduction  1  2 Homogeneous Methane Autoignition Delay Study  3  2.1 Introduction  3  2.2 Background  3  2.3 Experimental Investigation  4  2.3.1 Apparatus  4  2.3.2 Instrument Calibration  5  2.3.3 Procedure 2.3.4 Experimental Results 2.3.5 Error Analysis 2.4 Numerical Investigation  >  6 7 14 16  2.4.1 Reduced Mechanism  17  2.4.2 Governing Equations..  17  2.4.3 Ignition Delay Criteria Definition  18  2.4.4 Parameter Tuning Procedure  22  2.4.5 Numerical Results  22  2.5 Conclusions and Recommendations 3 Characterization of a Gaseous Fuel Injection System  25 27  3.1 Introduction  27  3.2 Background  27  3.3 Injector Hardware Characterization  28  3.3.1 Experimental Apparatus  29  3.3.2 Injection Delay Measurement  31  Table of Contents  iv  3.3.3 Mass Flow Rate Measurement  35  3.3.4 Pulsed Injection System Validation  40  3.4 Jet Flow Field Characterization  43  3.4.1 Experimental Apparatus  44  3.4.2 Single Injection Mode  45  3.4.3 Pulsed Injection Mode  54  3.4.4 Effects of Jet Impingement  60  3.4.5 Effects of an Enclosure  66  3.5 Conclusions and Recommendations  67  4 Non-Premixed Methane Autoignition Delay Study  71  4.1 Introduction  71  4.2 Background  71  4.3 Experimental Methods  73  4.3.1 Apparatus  73  4.3.2 Procedure  76  4.4 Experimental Results  78  4.4.1 Autoignition Sensitivity to Fluid Mechanic Parameters  79  4.4.2 Autoignition Sensitivity to Chemical Kinetic Parameters  84  4.4.3 Error Analysis  93  4.4.4 Autoignition Visualization  94  4.5 Conclusions and Recommendations  102  5 Conclusions and Recommendations  104  References  107  Appendix A: Vacuum Sensor Calibration Data  111  Appendix B: Homogeneous Autoignition Delay Data  113  Appendix C: Homogeneous Autoignition Delay Error Analysis  114  Appendix D: Numerical Combustion Equations Derivation  118  Appendix E: Injector Hardware Characterization Data  123  Appendix F: Jet Flow Field Characterization Data  129  Appendix G: Non-Premixed Autoignition Delay Data  136  Appendix H: Autoignition Visualization Images  139  Appendix I: Shock Tube Test Section Design Calculations  140  Appendix J: Shock Tube Optical Test Section Drawings  146  List of Tables  v  List of Tables 2 Homogeneous Methane Autoignition Delay Study Table 2.1: Experimental Test Matrix (Homogeneous Autoignition Study)  8  Table 2.2: Autoignition Delay Time Correlations Comparison  12  Table 2.3: Numerical Ignition Criteria Comparison  19  Table 2.4: Activation Energy Comparison  24  3 Characterization of a Gaseous Fuel Injection System Table 3.1: Experimental Test Matrix (Injection Delay Study)  32  Table 3.2: ANOVA Results for Injection Delay Backpressure Dependence  34  Table 3.3: Experimental Test Matrix (Mass Flow Rate Study)  35  Table 3.4: Mass Flux Model Parameters  39  Table 3.5: Comparison of Experimental Mass Fluxes to Model Results  40  Table 3.6: Experimental Test Matrix (Pulsed Injection System Validation)  41  Table 3.7: Experimental Test Matrix (Single Injection Visualization Study)  46  Table 3.8: Jet Penetration Number Comparison  54  Table 3.9: Experimental Test Matrix (Pulsed Injection Visualization Study)  55  Table 3.10: Experimental Test Matrix (Jet Impingement Visualization Study)  61  Table 3.11: Experimental Test Matrix (Jet Enclosure Visualization Study)  66  4 Non-Premixed Methane Autoignition Delay Study Table 4.1: Experimental Test Matrix (Non-Premixed Fluid Mechanic Parameter Study) ....79 Table 4.2: Experimental Test Matrix (Non-Premixed Chemical Kinetic Parameter Study)..86 Table 4.3: Experimental Test Matrix (Autoignition Visualization Study)  95  Appendices Table A.1: Vacuum Sensor Calibration  111  Table B.1: Homogeneous Autoignition Delay Data  113  Table E.1: Injection Delay Experimental Data  123  Table E.2: Injector Mass Flow Rate Data  125  List of Tables  vi  Table E.3: Pulsed Injection System Validation Experimental Data  126  Table F.1: Single Injection Mode Jet Flow Field Data  129  Table F.2: Pulsed Injection Jet Flow Field Data  132  Table F.3: Jet Impingement Flow Field Data (Circular Obstruction)  134  Table F.4: Jet Impingement Flow Field Data (Rectangular Obstruction)  134  Table F.5: Jet Enclosure Flow Field Data  135  Table G.1: Non-Premixed Autoignition Delay Data  136  Table 1.1: Maximum Stress and Deflection for Fully Constrained B.C  142  Table I.2: Maximum Stress and Deflection for Free B.C  142  List of Figures  vi[  List of Figures 2 Homogeneous Methane Autoignition Delay Study Figure 2.1: Experimental Apparatus (Homogeneous Autoignition Study)  5  Figure 2.2: Shock Velocity and Autoignition Delay Measurement From Pressure Signals ...7 Figure 2.3: Experimentally Measured Homogenous Autoignition Delay Times  8  Figure 2.4: Normalized Homogeneous Autoignition Delay Times  9  Figure 2.5: Characteristic Pressure Signals Over Three Ignition Regimes  10  Figure 2.6: Comparison of Present Experimental Results to Previous Correlations  11  Figure 2.7: Comparison of Threshold and Gradient Ignition Criteria  20  Figure 2.8: Representative Pressure Time History Slope and Curvature Plots  21  Figure 2.9: Modified Gradient Ignition Definition  21  Figure 2.10: Comparison of Present Experimental and Numerical Results  23  Figure 2.11: Comparison of Present Numerical Results to Previous Correlations  25  3 Characterization of a Gaseous Fuel Injection System Figure 3.1: J41 Injector with Control System  29  Figure 3.2: Experimental Apparatus (Injection Hardware Characterization Study)  30  Figure 3.3: Injection Delay Definition  32  Figure 3.4: Histogram of Measured Injection Delay Times  33  Figure 3.5: Probability Plots of Measured Injection Delay Times  33  Figure 3.6: Injection Delay Time vs. Backpressure/Pressure Ratio  34  Figure 3.7: Mass Flux Measurements (Nitrogen)  36  Figure 3.8: Mass Flux Measurements (Methane)  36  Figure 3.9: Pulse Delay and Pulse-to-Pulse Pressure Ratio Definitions  41  Figure 3.10: Normalized Pulse-to-Pulse Pressure Ratio vs. Pulse Delay  42  Figure 3.11: Successive Injections with Insufficient Pulse Delays  43  Figure 3.12: Experimental Apparatus (Jet Flow Field Characterization Study)  44  Figure 3.13: Schlieren Images of Single Jet Evolution in Time  47  Figure 3.14: Jet Length Evolution During/After Injection (Single Injection)  48  Figure 3.15: Jet Width Evolution During/After Injection (Single Injection)  49  List of Figures  Y!R  Figure 3.16: Numerical Jet Model  51  Figure 3.17: Normalized Jet Tip Penetration (During Injection)  52  Figure 3.18: Normalized Jet Tip Penetration (During/After Injection)  53  Figure 3.19: Schlieren Images of Pulsed Jet Evolution in Time  56  Figure 3.20: Jet Length and Width Evolution (Pulsed Injection)  57  Figure 3.21: Flow Obstructions for Jet Impingement Study  60  Figure 3.22: Schlieren Images of Impinging Jet Evolution in Time  62  Figure 3.23: Jet Length and Width Evolution (Circular Obstruction)  63  Figure 3.24: Jet Length, Width, and Deflection Angle Definition  64  Figure 3.25: Jet Length and Width Evolution (Rectangular Obstruction)  65  Figure 3.26: Schlieren Images of Enclosed Jet Evolution in Time  67  Figure 3.27: Jet Length and Width Evolution (Enclosure)  68  4 Non-Premixed Methane Autoignition Delay Study Figure 4.1: Experimental Apparatus (Non-Premixed Autoignition Study)  74  Figure 4.2: Incident Shock Velocity Measurement From Pressure Signals  77  Figure 4.3: Ignition Definition From Optical Emissions Signals  78  Figure 4.4: Autoignition Injection Duration Sensitivity  80  Figure 4.5: Characteristic Optical Ignition Signals Over Two Regimes  81  Figure 4.6: Autoignition Injection Pressure Ratio Sensitivity  84  Figure 4.7: Autoignition Temperature Sensitivity (31 bar)  87  Figure 4.8: Autoignition Temperature Sensitivity (17 bar)  88  Figure 4.9: Differences in Luminosity Threshold with Pressure  90  Figure 4.10: Autoignition Pressure Sensitivity  91  Figure 4.11: Characteristic Optical Emission Signals Over Three Ignition Regimes  93  Figure 4.12: Experimental Apparatus (Autoignition Visualization Study)  96  Figure 4.13: Compact Schlieren System Schematic  97  Figure 4.14: Autoignition Visualization Image Post-Processing Examples  98  Figure 4.15: Comparison of Hot and Cold Jets  99  Figure 4.16: Reacting Jet Schlieren Images at Various Ignition Stages  100  Figure 4.17: Reacting Jet Self-Illuminated Images at Various Ignition Stages  101  Appendices Figure C.1: Illustration of Pressure Measurement Error  115  Figure H.1: Autoignition Visualization Images  139  List of Figures  ;  ix  Figure 1.1: Maximum Window Deflection Under Dynamic Loading  143  Figure J.1: Optical Window  147  Figure J.2: Viewing Window  148  Figure J.3: Optical Test Section  149  Figure J.4: Endplate Flange  150  Figure J.5: Adaptor Flange  151  Figure J.6: Injector Mounting Plate  152  Figure J.7: 3" Slip-On Adaptor Flange  153  Figure J.8: 2.5" Slip-On Adaptor Flange  154  Figure J.9: Instrumentation Window  155  Figure J. 10: Clamping Plate  156  Figure J.11: Test Section Assembly  157  Figure J.12: Adaptor Assembly  158  Figure J.13: Complete Assembly  159  1  Chapter 1: Introduction  Introduction The thrust to develop clean diesel technology being driven by increasingly stringent emissions regulations has led many to consider the use of natural gas to achieve these objectives without adversely affecting performance. Such an attempt has been made by Westport Innovations Inc. with a High Pressure Direct Injection (HPDI) system that utilizes a minute amount of diesel fuel (as little as 2-5% of the total fuel energy) to ignite a natural gas charge. The diesel pilot is used solely for igniting the natural gas, which has a much longer ignition delay time than diesel and would otherwise not be suitable for late-cycle injection. While such a system is able to maintain most of the torque, power, and efficiency benefits inherent to diesel engines and dramatically reduce emissions, the presence of a diesel pilot requires onboard storage of both diesel fuel and natural gas along with the use of a complicated dual-fuel injector. The cost implications of having redundant fuel systems and complex injectors provide motivation to seek out alternative methods of minimizing natural gas' autoignition delay time without the use of a pilot fuel. Unfortunately, currently accepted techniques for reducing natural gas' prohibitively long ignition delay time are limited to the following: •  Using dual fuels (i.e. diesel pilot);  •  Blending natural gas with an appropriate ignition-promoting additive;  •  Using a glow plug or spark plug; or  •  Increasing compression ratios to achieve higher temperatures.  Among these four options only the first two are suitable for retrofit applications, with the latter two requiring substantial engine modifications. Therefore, if cost reductions beyond the use of dual fuels are to be achieved, fundamental research investigating the autoignition behaviour of methane in diesel environments is required. Such research requires the thorough investigation of the chemical kinetics involved in methane oxidation, the fluid mechanics governing transient gaseous fuel jets, and finally the coupling that occurs between both fluid mechanic and kinetic parameters in an engine. Correspondingly, the present investigation is segregated into three phases.  Chapter 1: Introduction In the first phase, the autoignition delay times of various methane/air mixtures are measured to validate the existing experimental apparatus (by verifying that previous researchers' results can be adequately reproduced) while also attempting to resolve discrepancies between autoignition delay results obtained at low pressure and high temperature and those obtained under enginerelevant conditions (high pressure and low temperature). Since many previous ignition studies have been conducted, the scope of the first phase of this investigation is simply to validate the existing apparatus and attempt to resolve observed discrepancies between various researchers' results. In the second phase of the investigation, transient jets produced by a Westport Innovations J41 fuel injector are studied to understand this injector's characteristics and quantify the effects of various injection parameters on the jet produced. As with the first phase of this investigation, an abundance of research is available in the literature describing the development of gaseous jets in addition to many scaling laws developed based on previous experimental studies. Therefore, the purpose of this study is to validate the existing fuel injector for future use in non-premixed autoignition delay time shock tube studies and to facilitate the application of previously deduced scaling laws and empirical relations. Finally, once the influence of kinetic parameters on the autoignition delay time of methane has been clarified, and the fluid mechanic parameters governing transient gaseous jets produced by a Westport injector have been characterized, both the kinetic and the fluid mechanic parameters are studied together in a series of non-premixed methane ignition experiments. This final phase of this investigation attempts to explore the coupling that occurs between both kinetic and fluid mechanic parameters in a diesel engine with the intent of more closely converging shock tube results with engine operating environments. It is hoped that in so doing, alternative techniques for minimizing methane's autoignition delay time will emerge.  2  Chapter 2: Homogeneous Methane Autoignition Delay Study  3  Homogeneous Methane Autoignition Delay Study 2.1 Introduction Driven by increasingly stringent environmental regulations, rapid developments are occurring in the field of combustion research, especially relating to internal combustion engines with a large part of this effort focussed on the conversion of diesel engines, notorious for their emission of smog-producing nitrogen oxides (NO ) and carcinogenic soot, to much cleaner burning natural x  gas. Unfortunately, natural gas, or specifically methane (the main component of natural gas), exhibits poor compression ignitability, requiring either excessive temperatures or prohibitively long residence times, to ignite. While in spark-ignited engines this impediment is overcome by the presence of an external ignition source, diesel engines do no have any such ignition source. Therefore, research has principally focussed on developing an appropriate ignition-promoting additive to blend with natural gas or, as Westport Innovations has done with their HPDI system, using a pilot fuel to ignite the natural gas. While this system has been successfully proven to enable diesel engines to operate on natural gas, such a dual-fuel system ultimately poses cost and emissions limitations. Thus if further emission and cost reductions are desired, the diesel pilot must be eliminated. To achieve this objective, alternative methods of reducing natural gas' ignition delay time must be explored and the first step in doing so requires measurement of the autoignition delay time of methane at various operating conditions.  2.2 Background While many previous researchers have measured the ignition delay time of methane mixtures, most of these investigations have been performed at relatively high temperatures (T > 1500 K) and low pressures (P < 10 bar), which are not directly engine-relevant. For operating conditions that are engine-relevant (P > 30 bar, T « 1500 K) few experimental investigations have been conducted. To remedy this, Huang recently explored this domain. This recent work involved 1  measuring the ignition delay times of CHV^/DME/air mixtures in a shock tube over a range of equivalence ratios between 0.7-1.3, pressures from 16-40 bar, and temperatures between 950-  Chapter 2: Homogeneous Methane Autoignition Delay Study  4  1400 K. This investigation provided compelling evidence that existing methane induction time correlations developed from high-temperature, low-pressure experimental data failed to predict ignition delay times at engine-relevant conditions. However, since previous investigations were conducted at low pressures/high temperatures, and Huang's recent work was conducted at high pressures/low temperatures, a need exists to confirm if the pressure or temperature difference is responsible for observed discrepancies. The present investigation therefore seeks to explore this issue by measuring the ignition delay time of various CHJ0 /Ar mixtures at low pressures 2  (2-4 bar) and over a wide temperature range (1100-2000 K). This will permit direct comparison with previous work at high temperatures (T > 1500 K) and demonstrate whether existing ignition delay correlations also correctly predict ignition delay times at low temperatures (T < 1500 K). In addition, to complement the experimental research and to further compare the present results with existing correlations, numerical simulations with simplified chemical kinetics are performed using a single-step reaction mechanism fit to the current experimental results.  2.3 Experimental Investigation To permit direct comparison with previously published methane ignition delay time correlations, the experimental portion of the present investigation involved measuring the ignition delay times of stoichiometric CHVCVAr mixtures in a shock tube at various experimental temperatures and pressures using a standard reflected shock technique. Experimental conditions were chosen to coincide with those previously investigated by other researchers while extending to low enough temperatures to be engine-relevant, and thus comparable with recent experiments. Details of the specific apparatus used and the test conditions that were investigated are presented below.  2.3.1 Apparatus Experimental autoignition delay measurements were conducted in a 7.37 m long shock tube (3.11 m driver section, 4.26 m driven section), 5.9 cm in inner diameter with five PCB Piezotronics 112B11 dynamic pressure transducers mounted at 0.763 m, 2.130 m, 3.958 m, 4.108 m, and 4.260 m from the diaphragm for detecting the passage of incident shock waves (refer to Figure 2.1 schematic). An Auto Tran 600D-117 vacuum sensor was used for preparing driven gas compositions and measuring initial driven gas pressure, while an Eclipse® high-pressure sensor was used for measuring the driver gas pressure. Voltage outputs from the driven section vacuum sensor and the driver section pressure transducer were measured with a Circuit-Test DMR-3600 multimeter when.recording initial pressures,  Chapter 2: Homogeneous Methane Autoignition Delay Study  5  while outputs from the dynamic pressure transducers were recorded by a Wavebook/512™ data acquisition system set to a sampling frequency of 167 kHz (6 us sampling interval).  Vacuum Pump  C H  4  °  A  r  2  He  Dry Air  Figure 2.1: Experimental Apparatus (Homogeneous Autoignition Study) To obtain low test pressures (~ 2-4 bar) paper diaphragms were used consisting of 1-4 layers of coated paper (0.1-0.3 mm thick) with an outer layer of 0.01 mm thick plastic film added to ensure air impermeability (refer to diaphragm illustration in Figure 2.1). Stacking varying numbers of diaphragms controlled their burst pressure, and air impermeability was verified prior to each experiment by evacuating the driven section and ensuring that there was no detectable leakage through the diaphragm for at least 20 minutes.  2.3.2 Instrument Calibration Since each of the five dynamic pressure transducers along the length of the driven section was used solely for detecting the passage of an incident shock wave, no static calibration was performed (as they were not used for explicitly measuring pressures). Instead, only results of a previous dynamic calibration were used to verify each sensor's response time.  Chapter 2: Homogeneous Methane Autoignition Delay Study  6  These were previously verified to have a dynamic response time of less than 3 us and a voltage-to-pressure conversion factor of approximately 930 psi/V . 1  The vacuum sensor used for measuring the driven section pressure was calibrated using a zero and span calibration corresponding to vacuum and atmospheric pressures prior to each experiment (atmospheric pressure was compared to that recorded from an Oakton® Aneroid barometer). Linear regression between these two calibration points was used for calculating all intermediate pressures and was found to agree well with the manufacturer's specifications (refer to Appendix A for calibration data). The driver section high-pressure transducer was not exhaustively calibrated since it was not used in any ignition measurements. This transducer was used solely for measuring the diaphragm's burst pressure (for estimating the loss coefficient across the diaphragm) and not used in any other calculations. Therefore, the manufacturer's calibration constant was used together with the barometric pressure recorded prior to each test.  2.3.3 Procedure Prior to each experiment, barometric pressure was recorded and the driven and driver gas pressure transducers calibrated as per the procedure outlined above. Both the driven and driver sections were evacuated using a Cenco Instruments Corp. Hyvac 7 vacuum pump and gas compositions prepared manometrically. Gas mixtures were subsequently allowed to settle for at least 30 minutes, with the driven gas pressure measured immediately after charging the driven section and again prior to conducting the experiment to ensure there was no leakage across the diaphragm. The data acquisition system was then armed (set to be triggered by the rising edge of the incident shock wave as it passed the first dynamic pressure transducer) and driver section gas pressure (Praxair 99.9% He) was increased until the diaphragm(s) ruptured. Throughout all experiments a single diaphragm was used, instead of a double diaphragm, due to the paper diaphragms' inconsistent burst pressure. Incident shock velocities were calculated from pressure traces obtained from each of the five dynamic pressure transducers along the length of the driven section by measuring the time interval between rising edges as the shock wave passed each successive transducer (see Figure 2.2 (a)). Autoignition delay was defined as the time interval between incident shock reflection from the driven section endplate and the time when maximum curvature in the pressure signal from the endplate transducer was observed (Figure 2.2 (b)). The  7  Chapter 2: Homogeneous Methane Autoignition Delay Study experimental pressure and temperature was assumed equal to that immediately behind  the reflected shock wave (as calculated from isentropic shock relations and the measured incident shock velocity ). 1,2  Pressure Signals  Time (ms)  (a) Shock Velocity Calculation <4— Ignition — • ! Delay  Ignition Signal  (b) Ignition Delay Time Measurement  Figure 2.2: Shock Velocity and Autoignition Delay Measurement From Pressure Signals A summary of all test conditions investigated is presented in Table 2.1 (including several test conditions that did not result in ignition). While ideally experimental pressures ranging from 1-10 bar and temperatures from 1000-2000 K were sought, limitations imposed by the paper diaphragms' rupture behaviour limited the minimum pressure attained to 1.5 bar and the maximum pressure to 7.7 bar, with most experimental pressures between 3-4 bar. Likewise, variability in individual diaphragms' burst pressure resulted in unpredictable test pressures and variability in the resultant test conditions.  2.3.4 Experimental Results Experimentally measured ignition delay times are presented in Figure 2.3 with tabulated data available in Appendix B. It should be noted that in this figure, five test points in which there was no detectable ignition have been omitted. While these conditions do not appear as test points on the graph they are nevertheless important in establishing ignition limits and have been noted in Table 2.1.  Chapter 2: Homogeneous Methane Autoignition Delay Study Table 2.1: Experimental Test Matrix (Homogeneous Autoignition Study) Temperature (K)  1.5 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.2 6-8  fO  co in  900 0  1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2400 0 ox X X X  XX  X  X X  X XX  X X X  X  X X  0 X X  X  X  0  X X  X  *Note: Each X represents a successful test; an O indicates an unsuccessful test (no ignition detected).  Figure 2.3 illustrates two key trends: •  Ignition delay times for temperatures greater than 1550 K (1000/T < 0.65) exhibit a much steeper slope than those over the lower temperature range; and  •  The point at which the slope sharply changes (1000/T = 0.65) corresponds with the strong ignition limit, such that higher temperatures exhibited detonation, and below it deflagration was the primary combustion mode.  • Present Results - Strong » Present Results - 2-Stage  in E  A Present Results - Mild  co E  >> JS CD Q c o  0.45  0.55  0.65  0.75  0.85  0.95  1000/Temperature (1000/K)  Figure 2.3: Experimentally Measured Homogenous Autoignition Delay Times  Chapter 2: Homogeneous Methane Autoignition Delay Study  9  Additionally, a discontinuity exists near the strong ignition limit where ignition delay times seem to exhibit a sudden decrease as temperature decreases. This is partly attributed to differences in test pressures between individual data points, and primarily to differences in initial fuel and oxidant concentrations. In order to achieve the relatively high temperatures in the strong ignition region, high argon mole fractions were used (> 90%), resulting in low initial fuel and oxidant concentrations. Since ignition delay is dependent on temperature, pressure, and initial fuel and oxidant concentrations, reduced initial concentrations yielded increased ignition delay times. To compensate for this diluting effect, experimental data was fit to an empirical correlation of the form: r = A[CH ]  a  4  [0 ] -e " b  E/  (2.1)  T  2  and normalized ignition delay times plotted against temperature in Figure 2.4. 1.E-04 + Present Results - Strong • Present Results - 2-Stage A Present Results - Mild  1.E-07 0.45  0.55  0.65  0.75  0.85  0.95  1000/Temperature (1000/K)  Figure 2.4: Normalized Homogeneous Autoignition Delay Times *Note: The methane exponent of 0.33 is very similar to the value found by previous researchers (Table 2.2).  Figure 2.4 demonstrates the importance of normalizing autoignition delay time data by the initial fuel and oxidant concentrations to account for pressure or concentration differences between individual test points. By normalizing the experimental data in this manner, the discontinuity observed in Figure 2.3 was completely eliminated. It is also worth noting that the change in slope originally noted in Figure 2.3 remains after normalization, suggesting that it is a genuine phenomenon and not simply due to pressure/concentration differences  Chapter 2: Homogeneous Methane Autoignition Delay Study  10  between test points. In particular, the slope change was sufficiently pronounced that over the high-temperature region the best fit was obtained by a linear, rather than exponential, regression while a standard exponential curve fit described the low-temperature data well. Although no obvious physical reason for a linear relationship exists, perhaps at elevated temperatures ignition is more strongly dependent on fuel and oxidant concentrations. If this is true then the temperature terms implicit in the fuel and oxidant concentrations ([X] = P/RT) which are raised to the power of a + b (-1.34 + 0.33 = -1.01 ~ -1) would explain the linear relationship. Alternatively, given the large experimental uncertainties at high temperatures, an exponential relationship may be equally plausible. Given different ignition behaviour observed over different temperature ranges, the current experimental results are compared with previous researchers' correlations over each of three ignition regimes: strong ignition, observed mostly at high temperatures; two-stage ignition, occurring at intermediate temperatures; and mild ignition, commonly seen at low temperatures (refer to Figure 2.5).  Mild Ignition Regime (T< 1350 K)  2-Stage Ignition Regime (1350 K<T< 1550 K)  *o  U — Strong Ignition Regime (T> 1550 K)  Figure 2.5: Characteristic Pressure Signals Over Three Ignition Regimes High Temperature/Strong Ignition Regime When the present experimental results are plotted alongside previous researchers' correlations noticeable discrepancies are observed (see Figure 2.6). In the high  Chapter 2: Homogeneous Methane Autoignition Delay Study  1J_  temperature range (T > 1550 K, 1000/T < 0.65) the slope is approximately equal to that of previous correlations (within experimental error), but an offset is present in absolute values. The present results consistently exhibit longer ignition delay times than those calculated from existing correlations. This large discrepancy is attributed mostly to experimental error (as indicated by large error bars over this temperature range), but also to variations in the definition of ignition delay time and the methods used to measure those ignition delay times. Ignition in the present investigation was defined as the time interval between reflection of the incident shock from the driven section endplate and observance of maximum curvature in the pressure signal from the driven section endplate transducer. While this is a common means of defining ignition in shock tube studies, variants on it including detecting maximum curvature from a transducer located some distance from the shock tube endplate , or defining 3  ignition as the time when sudden changes in temperature, C H concentration, or 4  maximum OH radical emissions are observed have also been previously used by other researchers . 4  •  Present Results - Strong  •  Present Results - 2-Stage  A  Present Results - Mild Zhou & Karim (1994) Ufshitzetal.(1971) Grillo & Slack (1976) Seery 8. Bowman (1970) Tsuboi & Wagner (1974) Cheng a Oppenheim  _  (1984)  0.95  Figure 2.6: Comparison of Present Experimental Results to Previous Correlations In addition, various researchers also define experimental temperature and pressure differently. In the present study, the pressure and temperature behind the reflected shock wave were defined as the experimental conditions, but others have previously also used a linear average between conditions behind the reflected shock wave and those immediately before ignition to define the experimental conditions . Variability 3  Chapter 2: Homogeneous Methane Autoignition Delay Study  12  in the definition of the ignition delay time and experimental conditions is responsible for some of the observed offsets between various researchers' results. Among all previous induction time correlations, the results of Zhou and Karim were 4  the only ones to predict the presence of a slope change experimentally observed in the present results. Zhou and Karim found that detailed numerical simulations using full chemistry suggested a variable activation energy and instead of assigning global values to the parameters A and E in equation (2.1) assigned different values to each parameter over three temperature ranges (650-1200 K, 1200-1600 K, 1600-2400 K). The variable parameters in Zhou and Karim's correlation correctly predicted both the presence and location of the experimentally observed slope change. Also worth noting is that Zhou and Karim used a variant of the standard correlation equation (2.1), by expressing the concentration terms as mole fractions and adding a second term to explicitly account for temperature and pressure: r = A-  T_  (2.2)  where ycH4,andy are the methane and oxygen mole fractions, respectively. 02  Their choice of parameters specifically weighted the methane mole fraction and the pressure terms more heavily than previous researchers' correlations, while reducing the weighting on temperature (see Table 2.2). This increased dependence on fuel concentration reflects the trend observed in the present study at high temperatures. Table 2.2: Autoignition Delay Time Correlations Comparison T=A  T_  [CH ] .[0 ]"-e "T a  4  T(K)  x  E/  2  E(J/mol)  -1.03  195000  Researcher(s) Lifshitz et al. (1971)°  0.33  -1.03  219000  Grillo and Slack (1976)  0.40  -1.60  215000  Seery and Bowman (1970)  0.32  -1.02  222000  Tsuboi and Wagner (1974)  0.48  -1.94  194268  Cheng and Oppenheim (1984)  1.929x 10"**  08  To  02  74989  1200-1600  7  5.055 x10"  0.8  -1.0  0.2  88124  1600-2400  2.337 x 10"  0.8  -1.0  0.2  155345  1500-2150  3.62x10717- 0.33  1640-2150  4.40x10  1350-1900  7.65 x 1 0  1200-2100  2.50 x 10"  800-2400  1.19 x 10"  650-1200  •15 1B  15  12  9  6  3  7  8  Zhou and Karim (1994)  4  *Note: In Zhou and Karim's correlation, the concentration terms are replaced with mole fractions.  Chapter 2: Homogeneous Methane Autoignition Delay Study  13  However, despite some agreement between Zhou and Karim's correlation and the present results, the magnitudes of their correlation's predicted ignition delay times are much shorter than both the present results and all previous correlations. It is unclear whether this is due to incorrectly reported correlation parameters or if their correlation was based on erroneous simulations and thus only capable of predicting trends (variable activation energy) but not absolute autoignition delays. Additionally, Zhou and Karim's correlation was optimized for an initial pressure of 1 bar and they claim that extending their results to a pressure of 3 bar results in errors of ±35% . 4  Since most experiments in the present study were conducted at pressures between 3-4 bar, errors in excess of 35% are expected. This uncertainty in Zhou and Karim's correlation is illustrated by shaded regions in Figure 2.6, highlighting regions ±40% around their predicted ignition delay times. Despite this adjustment, their correlation still fails to predict measured ignition delay times at high temperatures. Intermediate Temperature/Two-Stage Ignition Regime Over the intermediate temperature range (between approximately 1350-1550 K) the effects of differences in the definition and detection of ignition manifest themselves. Within this temperature range, two-stage ignition was common (see Figure 2.5), and the extent to which the current results agreed with particular correlations depended on the ignition definition used. If the initial mild pressure rise was used to define the onset of ignition, experimental autoignition delay times were in close agreement with induction times predicted by Cheng and Oppenheim , but under-predicted values of 8  most other correlations. If the second (detonation) pressure rise was used to signal ignition, the present results agreed well with both Seery and Bowman's and Tsuboi 3  and Wagner's results (the two that extended into this temperature range). Defining 7  ignition based on the second, strong (detonation) ignition signal is believed to agree more closely with some previous researcher's results because they may have used rapid changes in C H concentration or maximum OH radical emissions to signal the 4  4  onset of ignition. Such concentration-based criteria would be expected to coincide with strong ignition, rather than mild, since that is the point when most of the mixture is burning and thus the closer agreement when the second pressure rise is used to define ignition. This highlights the importance of utilizing a consistent ignition delay time definition when attempting to compare experimental or numerical results with previous researcher's work.  Chapter 2: Homogeneous Methane Autoignition Delay Study  14  Low Temperature/Mild Ignition Regime Over the low temperature range, few correlations exist from previous experimental studies that predicted either the slope or absolute values of measured ignition delay times. Cheng and Oppenheim's correlation agreed reasonably well with the current 8  results to a temperature of approximately 1250 K and Zhou and Karim's correlation 4  agreed well with the current results at low temperatures, but Tsuboi and Wagner's  7  correlation predicted much longer ignition delay times. In general it was observed that at high temperatures the presently measured autoignition delay times exceeded those reported by previous researchers, while at low temperatures the opposite was true. This is partially attributed to the fact that ignition detection from pressure traces is often difficult when ignition is mild (as it is at low temperatures) and this may bias results towards shorter ignition delay times. Over the low temperature range ignition was not detected in several cases, indicating ignition delay times exceeding the total experimental time. Had ignition been detected in each of these cases it would have resulted in several test points with long ignition delays and these would have shifted the present results closer to existing correlations. Instead, since only short ignition delay times were detectable, the data was biased. This bias at low temperatures is one of the main causes for observed discrepancies between the present results and previous researchers' correlations. In the absence of alternative ignition detection methods, it is impossible to decisively state that pressure signals yielded misleading results at low temperatures, but this is believed to be one of the primary causes of the observed discrepancies.  2.3.5 Error Analysis When analysing experimental results, many errors influenced the experimental data in the present investigation, which must be understood. These errors were introduced mainly by experimental errors in the following measured quantities: •  Ignition delay time;  •  Incident shock velocity;  •  Driven gas pressure;  •  Barometric pressure; and  •  Ambient temperature.  The influence of errors in each of these measurements on final calculated experimental  Chapter 2: Homogeneous Methane Autoignition Delay Study  15  variables of interest is discussed below, with a more thorough error analysis available in Appendix C. Ignition Delay Time Error The inherent error in the ignition delay times calculated from the measured pressure signals varied depending on the type of ignition that was observed. Throughout the present investigation, ignition was categorized into three regimes: strong ignition at high temperatures; two-stage ignition at intermediate temperatures; and mild ignition at low temperatures. Characteristic pressure traces from each ignition regime were presented in Figure 2.5 along with illustrations of how ignition delays were defined. It is important to note that minimal error was associated with strong ignition because the point of ignition was clearly defined, but certain mild ignitions and all two-stage ignitions introduced noticeable ignition delay time errors due to the often-ambiguous nature of their pressure signals. For two-stage ignition, it was often unclear whether the first or second pressure rise'should be defined as the point of ignition, while for mild ignition cases the pressure rise was often so gradual that the point of maximum curvature was difficult to discern. Average error over the strong ignition regime was +0.135 ms, over the two-stage region was ±0.241 ms, and in the mild ignition regime was ±0.135 ms. However, the average error throughout the low-temperature regime is rather misleading because in some cases the pressure rise was very well defined and in other cases ambiguous. When the pressure signal was well defined, average error was ±0.070 ms, when ambiguous it was ±0.210 ms. Additional errors introduced by the dynamic pressure transducers' response time, and the data acquisition system's sampling frequency are negligible relative to those discussed above. Driven Gas Composition Error The driven gas composition was calculated from the partial pressure of each gas as the driven section gas mixture was prepared. Thus, errors in the vacuum pressure, barometric pressure, and ambient temperature all contributed to this error. Errors in the vacuum pressure transducer were due to limitations imposed by the multimeter resolution (±0.001 V and ±0.01 V for voltages less than/greater than 4 V,  Chapter 2: Homogeneous Methane Autoignition Delay Study  16  respectively) and calibration error (±0.001 bar associated with the barometer used to calibrate the transducer). These cumulatively introduced an error of ±0.002 bar into individual gas partial pressures, which in conjunction with ambient temperature error of ±3 K, resulted in average errors of ±0.7% in the argon mole fraction, ±0.8% in the oxygen mole fraction, and ±0.7% in the methane mole fraction. Experimental Temperature/Pressure Error The experimental temperatures and pressures were calculated from the driven gas composition and pressure (errors discussed above) and the incident shock velocity. The incident shock velocity was determined from pressure signals as illustrated in Figure 2.2 (a). Throughout all of the present tests, the radius of convergence of the linear fit used to calculate all velocities always exceeded 0.996 (most > 0.999). The error in the incident shock velocity was therefore minimal and assumed to be ±5 m/s (due mainly to error in the measured separation distance between dynamic pressure transducers - ±0.2% ). These cumulatively resulted in errors ranging from 5-164 K 1  (0.5 - 8%) and ±0.2-0.6 bar (6 -11%). The large experimental errors calculated at certain conditions were due to the accumulated errors of the many measurements that were used to calculate experimental conditions. In particular, the largest errors (164 K) occurred at the highest temperatures because the high argon mole fractions necessary to achieve such high temperatures resulted in greater uncertainty in the measured initial fuel and oxidant concentrations. Errors in the initial fuel and oxidant concentrations were carried forward into experimental temperature uncertainty.  2.4 Numerical Investigation Since the preceding experimental study compared measured autoignition delay times with both previous experimental and numerical results, numerical simulations must also be conducted to gain insight into uncertainties associated with such calculations. This includes exploring various methods for defining the ignition delay time numerically, and fitting a single-step global reaction mechanism to the current experimental results. While many reduced mechanisms are available that reasonably approximate full chemistry results, these are usually incapable of autoignition as a consequence of the presence of radical species in each reaction step. Thus, the development of a global mechanism is intended to provide insight into errors introduced by various ignition definitions, and to provide a baseline for future mechanism development work.  Chapter 2: Homogeneous Methane Autoignition Delay Study  17  2.4.1 Reduced Mechanism To minimize the computational burden of implementing any reduced mechanism, ideally the simplest mechanism (fewest reactions and/or species) is desired. However, it is also anticipated that increased agreement with full chemistry results and experimental data will require increased mechanism complexity. For this reason, a single-step global mechanism was chosen as it represents the simplest possible mechanism and will provide a baseline for any future mechanism development work. The mechanism investigated consists of the global reaction mechanism with only one reaction and four species, presented below: CH +20 ^C0 +2H 0 A  Z  2  (2.3)  2  2.4.2 Governing Equations Ignition of the combustible gas mixture behind the reflected shock wave was modelled as a homogenous, constant volume, adiabatic process. These assumptions reduced all the conservation equations to the trivial case where each is constant. Previous studies have found that despite this model's apparent simplicity, it approximates the complex chemical and thermal interactions in the shock tube reasonably well  2,9,10  . The system's temperature,  pressure, and species concentrations may then be derived from the reduced form of the energy equation and the ideal gas law to yield the following system of coupled first-order ordinary differential equations (complete derivation available in Appendix D): _1_,  ^ dt =  y  1  p V^K  dT dt  R  0  oo ^feJ  dt  . r . Y i o o o . ^ J V dt  .n/ ./7 -R.ryiooo^teJ V dt K  K  +  K  K  P . ^ T dt  (2.4)  (2.5)  (2.6)  In the above equations, P is the system pressure (kPa), T is the temperature (K), p is the mixture density (kg/m ), and R is the universal gas constant (J/mol/K). Additionally / X J , 3  W , Y , c , and h are the concentration (mol/cm ), molecular mass (g/mol), mass fraction, 3  k  k  pk  k  Chapter 2: Homogeneous Methane Autoignition Delay Study  18  constant pressure specific heat capacity (J/g/K), and specific enthalpy (J/g), respectively, of the k species. The factors of 1000 in both the temperature and pressure expressions th  are included for dimensional homogeneity between the various terms in those equations. Finally, in the species concentration equation, stoichiometric coefficients for the forward and reverse reactions are denoted by v and v , and the forward reaction rate coefficient, R  p  k , for each reaction, /, is expressed in the following Arrhenius form: f  k =A T ' n  f/  r  - e  7  ^  (2.7)  where A, is the frequency factor, n, the pre-exponential temperature exponent, and £, the activation energy of the i  th  reaction. The reverse reaction rate coefficient, k , is calculated b  from the forward reaction rate coefficient and the equilibrium constant. The equations developed above were simultaneously solved using a MATLAB program developed for this purpose while species properties were calculated from JANAF tables.  2.4.3 Ignition Delay Criteria Definition Critical to the use of any numerical simulation for predicting autoignition delay times is the establishment of criteria to define ignition. Since the combustible mixture begins reacting immediately, albeit very slowly initially, and accelerates as the mixture temperature and pressure increase as a result of the combustion reaction's exothermic nature, the ignition delay is physically the time when the global reaction rate exceeds some threshold value. The problem of defining ignition therefore involves determining an appropriate threshold reaction rate to use as an ignition indicator. However, global reaction rates are not readily measurable experimentally and thus researchers have employed numerous techniques for deducing this threshold reaction rate, and thus the onset of ignition, using other readily measurable or calculable quantities. Zhou and Karim summarized some of the various ignition criteria that have been used in 4  both experimental and numerical studies and these are reproduced in Table 2.3. Although many ignition criteria exist, most can be broadly categorized as either "threshold" criteria, in which ignition is signalled by the temperature, pressure, or concentration of a particular species exceeding (or falling below) a prescribed threshold value, or "gradient" criteria, in which ignition is signalled by the rate of change of the pressure, temperature, or a species concentration reaching a maximum. Based on these broad classifications, the suitability  Chapter 2: Homogeneous Methane Autoignition Delay Study  19  of two ignition criteria was investigated; one threshold criterion, and one gradient criterion. Table 2.3: Numerical Ignition Criteria Comparison Ignition Definition 1. 2.  Threshold  Sudden increase in mixture temperature Rate of temperature rise reaching its maximum value  Gradient X X  3. Sudden increase in pressure  X  4.  Changes in the density of the mixture  x'  5.  Sudden change in the energy release rate  6.  Consumption of a specified fraction of the fuel  7.  Onset of a rapid decrease in the C H concentration  X  8.  Onset of a rapid decrease in the 0  X  9.  Emission of either C 0 or H 0  X X  4  2  2  concentration X  2  10. Emission of C O  X  11. Sudden changes in the distribution of some products  X  12. Concentration of the species 0 reaching a maximum  X  13. Emission rate of the species OH reaching a maximum  X  14. Emission of the OH radical 15. Maximum slope change on the absorption profiles of C H 16. Appearance of various chemi-luminescent emissions  X X  3  X  Concentration-Based (Threshold) Criterion Concentration-based ignition criteria, namely defining ignition as the time when the concentration of a particular reactant species falls below a certain level, or a product species exceeds a given threshold, is numerically easily implemented, but presents several limitations. In particular, it cannot be easily implemented experimentally and secondly, selecting the threshold value to use as the ignition indicator is arbitrary. A common threshold is to use the time when 5% of the initial fuel has been consumed to define ignition but this qualitatively corresponds to different points on the pressure time history curves for different initial conditions. Several representative pressure histories are plotted in Figure 2.7 to graphically illustrate how such a threshold does not qualitatively correspond to the point of maximum curvature at all temperatures. Since in shock tube experiments the autoignition delay is most commonly defined by changes in pressure, ideally a numerical ignition indicator should correlate well with the experimental ignition definition. Unfortunately, as shown in Figure 2.7, this is not the case for the simple concentration-based criterion. At low temperatures, the time when 8.4% of the initial fuel is consumed correlates well with the autoignition delay times defined by the point of maximum curvature in the pressure history, but at high  Chapter 2: Homogeneous Methane Autoignition Delay Study  20  temperatures a larger fraction of the initial fuel concentration is consumed before maximum curvature is observed. For a 5% consumed fuel threshold, the situation is even worse, with predicted ignition delay times corresponding to only 87% of those predicted by maximum curvature in the pressure signal at 1000 K and only 44% at 2000 K. Such qualitative disagreement between a threshold criterion and common experimental ignition definitions based on pressure traces suggests that threshold criteria are only appropriate if ease of implementation outweighs their limitations.  1000 K, 3 bar  2000 K, 3 bar  r  3 (0 </>  <D  5% Fuel Consumed /  5% Fuel Consumed  + 8.4% Fuel Consumed  + 8.4% Fuel Consumed  O Max Curvature 0.01  0.02  0.03  0.04  O Max Curvature 0.05  0.00004 0.00008 0.00012 0.00016 0.0002  Time (s)  Time (s)  Figure 2.7: Comparison of Threshold and Gradient Ignition Criteria Pressure-Based (Gradient) Criterion A second ignition indicator is based directly on the combustible mixture's pressure, defining ignition as the point of maximum curvature in the pressure time history. However, unlike the simplicity of the concentration-based (threshold) criterion, this criterion poses several problems in locating the point of maximum curvature. Direct calculation of the pressure time history curvature, d P/dr\ from the numerical 2  pressure and time data using a numerical differencing scheme proved problematic because the resultant curvature is not a smooth function of time. As a result of unevenly distributed time steps and rounding errors in the pressure history solution, the computed curvature frequently exploded to a large number or became negative (see Figure 2.8). Several data smoothing techniques were attempted, including fitting an exponential curve to the pressure data or using a high-order differencing scheme, but regardless, direct computation of the curvature remained difficult.  Chapter 2: Homogeneous Methane Autoignition Delay Study  0.01  0.015  0.02  0.025  0.03  0.01  21  0.015  Time (s)  0.02  0.025  0.03  Time (s)  - Figure 2.8: Representative Pressure Time History Slope and Curvature Plots As an alternative to the above criterion, a second technique, defining ignition as the intersection point of a pair of lines drawn tangent to the initial and maximum slope points was explored. Since both the maximum and initial pressure slopes are easily determined, this technique was also easily implemented. However, while it provided an extremely robust method of determining the autoignition delay time, qualitatively it agreed reasonably well with the maximum curvature point at high temperatures but over-predicted the point of maximum curvature at low temperatures. Defining ignition as the point on the pressure time history nearest the intersection of these two tangent lines improved agreement (see Figure 2.9).  Figure 2.9: Modified Gradient Ignition Definition  Chapter 2: Homogeneous Methane Autoignition Delay Study  22  Implementing such an ignition definition required determining the intersection of the two tangent lines and then trigonometrically calculating the point on the pressure time history nearest the intersection point. However, as a result of a large difference in scales between the pressure (in kPa) on the ordinate and the time (in ms) on the abscissa, normalization was required before such a calculation could be performed. While many normalization schemes are plausible, it seemed most appropriate to normalize both time and pressure by the time and pressure difference, respectively, between the maximum and initial slope tangent points. This normalization causes the resultant ignition point on the pressure history to correspond with the qualitative maximum curvature point. Although the normalization scheme chosen may seem like a trivial point, it is important because normalizing by different values has the effect of unequally stretching each axis such that the computed ignition point on the pressure trace no longer qualitatively corresponds to the maximum curvature.  2.4.4 Parameter Tuning Procedure With ignition formally defined, Adaptive Simulated Annealing (ASA) was used to tune the Arrhenius equation parameters to fit experimental ignition delay times. Ingber's ASA code was used in conjunction with a MATLAB interface written by Sakata . Details of 11  12  the simulated annealing algorithm used in the present investigation are available from each of these references along with an extensive list of references to various publications discussing simulated annealing methods in general. ASA was used in conjunction with a Nelder-Meed simplex algorithm (commonly referred to as an amoeba algorithm) after use of ASA proved extremely computationally expensive, and exclusive use of the NelderMeed algorithm failed to converge on a global minimum. Therefore, ASA was used for finding the vicinity of the global minimum, and the simplex algorithm converged to the final solution.  2.4.5 Numerical Results Using the procedure described above, the single-step reaction mechanism's Arrhenius equation parameters were fit to the present experimental data, with the following resulting forward reaction rate expression: „,,  *i-  p=1-3x10 T 1 0  s t e  2 3 3  -129000/  -e  /RT  (2.8)  Chapter 2: Homogeneous Methane Autoignition Delay Study  23  Results of the numerical simulations using the above simplified reaction mechanism with both a concentration-based definition of ignition (threshold criterion) and a pressure-based ignition criterion (gradient criterion) are presented in Figure 2.10 below. This figure illustrates that the threshold criterion agrees well with experimental data and the gradient criterion at low temperatures but under-predicts ignition delay times at higher temperatures (as previously illustrated in Figure 2.7). Qualitatively, this difference results in the pressure-based ignition definition yielding a shallower slope and longer delay times than the concentration-based criteria at high temperatures, and subsequently converging at low temperatures. This distinction is important because it further highlights the effect of various ignition definitions. Throughout the experimental portion of this investigation, the differences between various researchers results were often attributed to variations in the ignition definition used by each, and this numerical result reaffirms this. Despite using an identical single-step reaction mechanism, differences in the method used to define ignition had a pronounced effect on the resultant autoignition times. 1.E-04 •  Present Results - Strong Present Results - 2-Stage  *  o 1 E-05 -—-  Present Results - Mild  - - -Threshold Criterion  E Gradient Criterion  O B  1.E-06  o I—i «*  i o  1 E-07 045  0.55  0.65  0.75  0.85  0.95  1000/Temperature (1000/K)  Figure 2.10: Comparison of Present Experimental and Numerical Results Unfortunately since the Arrhenius equation parameters in the simplified global reaction mechanism were optimized based on the present experimental data, which as discussed previously may have been biased towards short ignition delay times at low temperatures, the optimized activation energy was lower than that reported by other researchers. Table  Chapter 2: Homogeneous Methane Autoignition Delay Study  _24  2.4 lists the activation energy reported by several researchers including those previously presented in Table 2.2. This table illustrates how the current activation energy was 19-42% lower than that of all previous correlations except Zhou and Karim's results. Although, the accuracy of Zhou and Karim's simulation is uncertain, it is encouraging to see that the present single-step reaction mechanism predicted an activation energy that is approximately equal to the average of their full chemistry results. The disagreement with other correlations is largely attributed to difficulties encountered in the experimental portion of this investigation, which may have biased the data used to optimize the single-step reaction mechanism. Table 2.4: Activation Energy Comparison T(K)  P (bar)  E (J/mol)  -  -  159000  Vandenabeele et al. (1960)  1350- 1900  1.5-4  215000  Seery and Bowman (1970)  1500-2150  2-10  195000  Lifshitz et al. (1971)  1200-2100  2-300  222000  Tsuboi and Wagner (1974)  -  -  188000  Cooke and Williams (1975)  1200-1800  3-20  195000  Dorkoetal. (1975)  1640-2150  1 -6  219000  Grillo and Slack (1976)  800 - 2400  1-3  194268  Cheng and Oppenheim (1984)  650-2400  1  75000-155000  Zhou and Karim (1994)  1100-2000  2.6-4.2  129000  Present Results (2002)  Researcher 1J  3  5  7  14  15  6  8  4  Figure 2.11 further compares the present numerical simulations with previous correlations and full-chemistry results of Zhou and Karim. These results were obtained using a singlestep mechanism to calculate ignition delay times of stoichiometric C r V 0 / A r mixtures at a 2  pressure of 3.5 bar using both the threshold (5% fuel consumed) and gradient (maximum curvature in pressure history) criteria. These conditions were chosen because they correspond with those investigated experimentally and thus Figure 2.11 is the "numerical" equivalent of ^the "experimental" Figure 2.6. This graph illustrates reasonable agreement between both the threshold and gradient criteria and previous correlations at intermediate temperatures, but divergence at both high and low temperatures. Additionally, over the entire temperature range shown, the slope of the single-step reaction mechanism is much shallower than the slope of all other correlations. These phenomena (the shorter ignition delays at low temperature, longer ignition delays at high temperatures, and the shallower slope) all reflect the trends observed in the experimental portion of the investigation. Thus  Chapter 2: Homogeneous Methane Autoignition Delay Study  25  the numerical simulation may be used to calculate ignition delay times over a broad range of temperatures, but additional experimental data would be required to further optimize the global mechanism's Arrhenius equation parameters if improved agreement with existing correlations is desired. 1.E-04  r  Zhou & Karim (1994) Lifshitz etal. (1971) Grillo & Slack (1976) Seery& Bowman (1970) Tsuboi & Wagner (1974) Cheng & Oppenheim (1984) Threshold Criterion Gradient Criterion  1.E-07 0.45  0.55  0.65  0.75  0.85  0.95  1000/Temperature (1000/K)  Figure 2.11: Comparison of Present Numerical Results to Previous Correlations  2.5 Conclusions and Recommendations The present experimental and numerical investigation of the autoignition behaviour of various stoichiometric CHVOVAr mixtures illustrated several important trends in autoignition data, while also emphasizing the many sources of uncertainty in such measurements. These observations are summarized below: 1. Experimentally measured autoignition delay times agreed with previous researchers' correlations over small temperature ranges but over-predicted ignition delay times at high temperatures and under-predicted them at low temperatures. These differences were attributed to experimental error, inability to detect mild ignitions using pressure traces alone, and differences in the definition of ignition. Since such differences in the definition of experimental conditions, the definition of ignition delay, and the method of detecting ignition may all result in different induction time correlations, care must be taken when using such correlations.  Chapter 2: Homogeneous Methane Autoignition Delay Study  26  2. A discontinuity in measured ignition delay times was initially observed but attributed to differences in initial fuel and oxidant concentrations. This emphasized the importance of normalizing experimental results by initial fuel/oxidant concentrations as a failure to do so could misleadingly suggest the presence of trends that are not genuinely there. 3. The activation energy change experimentally observed at approximately 1550 K (and confirmed by Zhou and Karim's simulations) is not reflected in standard induction time correlations, but clearly should be since failure to recognize the change in activation energy can result in severe over-prediction of ignition delay times at low temperatures. 4. Numerical simulations qualitatively illustrated the effects of various ignition criteria on the resultant ignition delay times but were unable to duplicate previous researchers' work since the Arrhenius parameters in the simulation were based on experimental results that were not in agreement with previous results at low temperatures. 5. The importance of a consistent ignition definition illustrated by both the experimental and numerical portions of this investigation suggests that multiple ignition detection methods should be used simultaneously when conducting autoignition delay studies. Differences in the ability of various techniques to detect ignition over given operating ranges may distort the measured results and subsequently adversely influence any numerical simulations based on those results.  Chapter 3: Characterization of a Gaseous Fuel Injection System  27  Characterization of a Gaseous Fuel Injection System 3.1 Introduction Increasing environmental and political pressures on both the automotive and power generation industries are encouraging the exploration of alternative fuels, moving towards decarbonisation. Along these lines, natural gas and eventually hydrogen are being rigorously explored as future fuel replacements for conventional gasoline- and diesel-powered engines. However, among the many challenges presented by the transition to such fuels includes the need to characterize and precisely control the injection and ignition of gaseous fuels to optimize engine performance and minimize emissions. In this study a J41 gaseous fuel injector provided by Westport Innovations Inc. is characterized for such operation, with particular emphasis on the requirements of nonpremixed autoignition delay studies. This requires validation of the injector hardware to ensure it is capable of performing adequately under intended operating conditions and characterizing the jet produced. Hardware characterization includes verifying the injection system can respond sufficiently rapidly to issued control signals and perform multiple injections in rapid succession, along with measuring mass flow rates under various operating conditions. Jet characterization involves observing the jet plume issued from the injector under the aforementioned operating conditions and studying the influences of impingement and of an enclosure on the transient jet's development.  3.2 Background Numerous previous experimental and numerical studies have been conducted on axisymmetric jets leading to a thorough understanding of the development and behaviour of such jets under a variety of operating conditions. Such studies have included elementary measurements of mass entrainment in axisymmetric jets like the well-known work of Ricou and Spalding , to studies of 16  velocity and species profiles in jets such as those of Abdel-Rahman et al. , Malmstrom et al. , 17  18  and many others. However, of most direct relevance to the current investigation is the work of Hill and Ouellette who reviewed a variety of previous jet studies, especially those pertaining to 19  Chapter 3: Characterization of a Gaseous Fuel Injection System  28  transient gaseous jets, deduced scaling laws from existing results, and summarized the present understanding of the development of transient turbulent gaseous jets. Their recent work made extensive use of a transient jet model proposed by Turner and Abramovich and Solan , which 20  21  models a transient jet as a spherical vortex fed by a self-similar steady-state jet. This particular model has been used successfully in various applications from atmospheric flows to gaseous fuel jets. Additionally, Hill and Ouellette's scaling laws and Turner's jet model have been used jointly by subsequent researchers such as Boyan and Furuyama , who used their results to 22  successfully predict the behaviour of a natural gas jet. In addition to the extensive research conducted on the fundamental study of axisymmetric jets, several researchers have also studied the interactions between multiple jet plumes (Jenkins et al. ), pulsed injection behaviour (Murase et al. , Ishii et al. ), and jet impingement onto objects 23  24  25  of various geometries and at various orientations (Donaldson and Snedeker , Donaldson et 26  al. , Looney and Walsh , Krothapalli et al. , etc.). However, these studies aimed at addressing 27  28  29  a specific application such as studying the early development of injection pulses, or mass, heat, and momentum transferred by impinging jets. Therefore, although they provide insight into the behaviour of gaseous jets, they are not directly applicable to the present problem. In addition, almost all studies (except for those studying the initial development of a pulsed jet) utilized fully developed steady-state jets rather than transient jets. Little work has been performed to study the development of transient gaseous jets other than the works cited by Hill and Ouellette in their investigation. In addition to the stated differences between previously studied jets and the transient gaseous jets of interest in the present application, even the well understood behaviour of axisymmetric jets requires basic knowledge of the particular injector's characteristics before any correlations may be successfully applied. Hence, before any of the results of previous researcher's work can be applied to predict or manipulate the behaviour of the given jet, that jet's properties, and specifically the injector's characteristics must be quantified. Thus the aim of this investigation is to quantify the flow characteristics unique to the J41 fuel injector such that existing correlations and scaling laws may be used in future to accurately model the injector's behaviour.  3.3 Injector Hardware Characterization The J41 injector is a magneto-restrictive, mono-fuel injector used to facilitate natural gas injection into spark-ignited engines for light duty vehicles. This injector operates in conjunction  Chapter 3: Characterization of a Gaseous Fuel Injection System  29  with Westport's WCut software, which is used to specify the fuel injection duration and delay, an injector control module, which generates the required square wave at the appropriate times and duration based on parameters specified by the control software, and a driver that amplifies the controller's signal to produce the large current required to actuate the fuel injector (see Figure 3.1). These components are shown below:  ftinnle T«*t Se u tp  hJM t»i*jW 'n iliput  I ^ 1 ,•  Control Software  Injectcr Controller  Injector Driver  *Note: J41 fuel injector shown at an exaggerated scale relative to controller and driver.  J41 Fuel Injector  Figure 3.1: J41 Injector with Control System Given the complexity of this injection system, there are inherent delays in the system requiring measurement to ensure accurate injection timing. Additionally, since the system was designed to perform only a single injection, modifications were made to facilitate pulsed injection and the system's response to such unconventional operation also requires validation.  3.3.1 Experimental Apparatus To quantify the intrinsic properties of the fuel injection system hardware a J41 injector was mounted to inject into a small test chamber created by two 2.5 in ANSI B16.5 blind flanges bolted together (as illustrated in Figure 3.2) and repeatedly fired under various operating conditions while recording the injector control signal and the test chamber pressure. Both the control signal and test chamber pressure were recorded using a Wavebook/512™ data acquisition system at a 140 kHz sampling frequency (corresponding to a 7.1 us sampling  Chapter 3: Characterization of a Gaseous Fuel Injection System  30  interval). The control signal was sampled directly from the signal line between the injector controller and driver using a voltage divider circuit to reduce the 0-20 V signal to a 0-10 V signal suitable for connection to the data acquisition system. Test chamber pressure was monitored with two PCB Piezotronics 112B11 dynamic pressure transducers. These had been previously calibrated and have a manufacturer-stated response time of 3 us, which 1  is sufficiently rapid to be negligible relative to the injection time scales of interest.  Pulse Generator  Manual Shutoff Valve  Figure 3.2: Experimental Apparatus (Injection Hardware Characterization Study) Initial test chamber pressure (backpressure) was recorded using a Matheson bourdon ctube pressure gauge mounted as shown in Figure 3.2 with a manual shutoff valve placed between the test chamber and the pressure gauge to facilitate separating the two during each experiment, minimizing the test chamber volume. Additionally, to further reduce the total internal test chamber volume, the 0.25 in steel tube connecting the test chamber and manual shutoff valve was filled with small-diameter electrical wires, leaving only capillary  Chapter 3: Characterization of a Gaseous Fuel Injection System  31_  passages for transmitting pressure. Minimizing the test chamber volume in this manner not only minimized the system's response time, but also caused a sufficient test chamber pressure rise during each experiment to allow the backpressure for the subsequent test to be controlled by either not draining at all or only partially draining the test chamber gases between experiments. The injector control system was a slightly modified version (to facilitate pulsed injection) of a standard J41 control system provided by Westport Innovations Inc. This system was modified to enable pulsed injection through insertion of an 8-channel BNC programmable pulse generator upstream of the injector controller (refer to Figure 3.2 inset). The injector controller and driver remained intact, and Westport's WCut software was used to control injection durations. The only difference between the present and standard control system configuration was that rather than triggering the injector controller directly with an external trigger signal, the pulse generator was used to issue multiple successive trigger signals to the controller. This allowed the fuel injector to operate in either a continuous or pulsed injection mode, with the injection duration controlled by Westport's WCut software and the delay between successive injections independently controlled by the programmable pulse generator.  3.3.2 Injection Delay Measurement The injection delay, defined as the interval between the time a control signal is issued to the injector driver and when injection begins, is an extremely important parameter in both non-premixed autoignition delay experiments, and in engine operation. In ignition delay experiments the injection delay is used in identifying the start of injection, from which the ignition delay itself is defined, while in engine operation the injection delay is important in ensuring optimal fuel injection timing. Unfortunately, since direct detection of the start of injection is not possible, the voltage or current sent to the injector is monitored instead to record the time when a control signal is issued to the injector, with the understanding that there may be a slight delay before injection actually begins. In the present configuration, the control signals between the injector controller and driver were most easily monitored owing to their low voltage, which facilitated direct connection to a data acquisition system. Therefore, the delay time between this directly measurable signal and the start of injection (attributable to any lag in the injector driver circuitry and any mechanical delay associated with the injector itself) was quantified.  Chapter 3: Characterization of a Gaseous Fuel Injection System  32  Procedure The injection delay was easily measured using the above-described apparatus by repeatedly injecting methane into the test chamber while recording both the injector control signal and test chamber pressure. The injection delay time was then defined as the time interval between the rising edge of the control signal and observance of an initial rise in the test chamber pressure (see Figure 3.3).  Figure 3.3: Injection Delay Definition Using the above procedure, an injection delay was measured for a range of injection durations and pressure ratios (by varying the initial chamber pressure) to determine the injection delay's dependence on each parameter. The operating conditions that were investigated are summarized in Table 3.1 with data available in Appendix E. Table 3.1: Experimental Test Matrix (Injection Delay Study) Injection Duration: Injection Pressure:  1.5-3.5 ms 110 bar (1600 psi)  Backpressure:  0-48 bar (0-700 psi)  Pressure Ratio:  2.3-111  *Note: All indicated pressures are gauge pressures.  Experimental Results In total 96 experiments were conducted yielding 192 measured injection delay data points (one from each dynamic pressure transducer). The average injection delay was calculated to be 180 us with a standard deviation of 20 ps. A histogram of all experimental measurements is presented in Figure 3.4, illustrating that most delay times fell between 150 and 200 ps, exhibiting a positive skew. For comparison, both  Chapter 3: Characterization of a Gaseous Fuel Injection System  33  normal and lognormal distributions have been superimposed upon this histogram. Each distribution fits the data reasonably well, with the lognormal fitting marginally better than the normal distribution upon examination of each probability plot (Figure 3.5). Although it may appear as though neither distribution accurately captures the spike at 200 us in the present data, it must be taken into consideration that 19 data points exhibited a delay of exactly 200 us, and thus the unusually low frequency at 190 us and high frequency at 200 us may have been exaggerated by the number of points which fell exactly on the boundary between those two bins. 45 42  CZZD Frequency Normal Distribution Lognormal Distribution  39  40  34  35  30 24  S*25 5  23  3  20  15 11 10  7  140  150  160  170  180  190  200  210  220  230  240  250  More  Injection Delay (us)  Figure 3.4: Histogram of Measured Injection Delay Times Normal Probability  Lognormal Probability  a  -4  -2  0  z Percentile  2  4  -4  -2  0  z Percentile  Figure 3.5: Probability Plots of Measured Injection Delay Times  2  4  Chapter 3: Characterization of a Gaseous Fuel Injection System  34  Finally, Figure 3.6 presents measured injection delay times sorted by backpressure (the numbers indicate the number of samples collected at each pressure; error bars represent one standard deviation from the mean). This figure qualitatively illustrates the injection delay time's backpressure independence, and an analysis of variance (ANOVA) quantitatively indicates the average injection delay is independent of the backpressure to a significance level of 0.481 (Table 3.2). Such a high significance level (and the F-value of 0.935) further shows the total backpressure independence. Additionally, among all of the tests conducted at three injection durations between 1.5-3.5 ms, no obvious injection duration dependence was observed either. The injection delay of 180±20 ps is therefore independent of both injection duration and backpressure. Table 3.2: ANOVA Results for Injection Delay Backpressure Dependence Source of Variation Between Groups:  SS 2614.32  df 7  MS 373.4737  Within Groups:  73520.72  184  39.5691  Total:  76135.04  191  F 0.9347  P-value 0.4810  220  0 (0)/ 111.3  7(100)/ 14.1  14 (200) / 7.5  21 (300)/ 5.1  28 (400) / 3.9  34 (500)/ 3.1  41 (600)/ 2.6  Backpressure (barg (psig)) / Injection Pressure Ratio  Figure 3.6: Injection Delay Time vs. Backpressure/Pressure Ratio  48 (700)/ 2.3  Chapter 3: Characterization of a Gaseous Fuel Injection System  35  3.3.3 Mass Flow Rate Measurement The mass flow rate through the injector is not easily measurable with standard mass flow devices, which are typically designed for steady-state operation, and must therefore be correlated to the injection duration and pressure. Such measurements were conducted at Westport prior to delivery of the J41 injector used in the present investigation and further validated after delivery, with results from both measurements presented below. Procedure Mass flow rates measured using nitrogen gas as the injected gas were supplied with the J41 injector and also validated after receiving the injector using an experimental apparatus similar to that depicted in Figure 3.2. These tests also included additional measurements using methane as the injected gas to observe the effects of using different gases on the measured mass flow rate. A range of injection pressures that were sufficiently high to yield measurable mass flow rates were investigated using several injection durations. The total mass injected was measured manometrically and converted to a mass flow rate assuming ideal gas behaviour. Test conditions , investigated are summarized in Table 3.3 with data available in Appendix E. Table 3.3: Experimental Test Matrix (Mass Flow Rate Study) Injection Duration: Injection Pressure:  0.3-1.75 ms 62-172 bar (1000-2500 psi)  Injection Temperature:  295 K  Injected Gas:  Nitrogen/Methane  *Note: All indicated pressures are gauge pressures.  Experimental Results Experimental nitrogen mass flow measurements injected at four injection pressures are plotted as mass fluxes in Figure 3.7. At each pressure the mass flux remains nearly constant regardless of injection duration indicating mass flux is independent of the injection period. While the mass fluxes for injection durations below 0.8 ms exhibit slight fluctuations, these do not exceed 10% of the average mass flux value and are mainly attributable to transient effects associated with the start and end of injection occupying a larger fraction of the total injection duration for short injections. Measured mass fluxes with methane gas exhibited similarly constant values across a range of injection durations and are plotted in Figure 3.8. Additionally worth noting  Chapter 3: Characterization of a Gaseous Fuel Injection System  36  2500 psi (Westport) -1850 psi (Westport) 1500 psi (Westport) -»-1000 psi (Westport) 1850 psi (UBC) 1500 psi (UBC) - • - 1 0 0 0 psi (UBC) 0.2  0.4  0.6  0.8  1  1.2  1.4  1.6  1.8  Injection Duration (ms)  Figure 3.7: Mass Flux Measurements (Nitrogen)  - A  1820 psi (UBC)  -s-1500 psi (UBC) - • - 1 0 0 0 psi (UBC)  0.6  0.8  1  1.2  1.4  1.6  1.8  Injection Duration (ms)  Figure 3.8: Mass Flux Measurements (Methane) *Note: Experimental data labelled "Westport" collected at Westport Innovations Inc., experimental data labelled "UBC" collected at the University of British Columbia by J. Huang, Research Engineer, Dept. of Mechanical Engineering (Combustion Laboratory).  Chapter 3: Characterization of a Gaseous Fuel Injection System  37  is that while this data only extends to injection durations of 1.75 ms, data collected during the injection delay time study (extending from 1.5-3.5 ms injection durations) indicated that the rate of change of the test chamber pressure (which is proportional to the mass flow rate) remained constant within experimental uncertainty (Figure 3.8 inset). The measured mass flow rates may therefore be assumed constant up to an injection duration of 1.75 ms and possibly up to 3.5 ms or greater. Numerical Results To predict the mass flow through the injector for any conditions, a model assuming an adiabatic, isentropic expansion from the fuel reservoir (stagnation state) to the injector nozzle, where choked flow was assumed (Ma=1), was found to agree well with actual measured mass fluxes for both nitrogen and methane. The governing equations for calculating the mass flux (m) from the given stagnation temperature (T ), pressure (P ), gas properties (y, R), and nozzle diameter (d„) are: 0  0  T„ =  (3-1)  y+1  v =a =ylrRT n  n  n  (j  Pn = ' n \  Pn =  T  (3.2)  (3.3)  0J  (3.4)  RT  n  m = PV n  n  (3.5)  where subscript 0 represents stagnation properties, n represents nozzle conditions. Although the assumption of isentropic flow initially yielded mass fluxes that were 2232% greater than those experimentally measured, several proposed modifications to this simple model reproduced the experimental data extremely well. These models each improved the original results by attempting to predict the losses in the injector. The assumptions made by each of four variants on the above model are described below along with the equation from the five listed above that each model replaces:  Chapter 3: Characterization of a Gaseous Fuel Injection System  38  Equivalent Diameter: This model assumes adiabatic, isentropic flow, but with an equivalent diameter instead of the actual nozzle diameter to compute the mass flow rate. The equivalent diameter, d , models the frictional losses in e  the injector as having the net effect of reducing the exit area, and is tuned to experimental mass flux data. In this model the mass flow rate is calculated using the following equation: nd  m = pV n  e  n  (3.6)  2. Discharge Coefficient: This model assumes adiabatic, isentropic flow, just as the equivalent diameter model, but an empirical discharge coefficient, Ca, is used to reduce the mass flow rate to fit experimental data. In this model the mass flow rate is calculated using the following equation: m=  C V dPn  n  (3.7)  Pressure Loss Coefficient: This model also assumes adiabatic, isentropic flow, but with a pressure loss to reduce the nozzle exit pressure slightly. The pressure loss is non-dimensionalized by modelling it as a loss coefficient, K , p  and is fit to experimental mass flux data. In this model the following equation is used for computing the nozzle exit pressure and must be solved iteratively due to the dependence of the nozzle density on pressure:  (j  V-i  'n  \  T  (3.8)  0 J  4. Non-1sentropic (Polytropic) Expansion: This models the flow in the injector as an adiabatic, but non-isentropic flow. Therefore, instead of using the specific heat ratio, y, in the polytropic expansion equation, an experimentally tuned polytropic expansion coefficient, k, is used. In this model the pressure at the nozzle is calculated as follows: (t  W  (3.9)  Of the models considered, the pressure loss coefficient and discharge coefficient models reproduced experimental data best. However, each model has its distinct  Chapter 3: Characterization of a Gaseous Fuel Injection System  39  advantages and may be suitable for certain applications. The equivalent diameter and discharge coefficient are advantageous for their simplicity as they only involve applying a correction factor to the final mass flow rate, which is otherwise calculated using the isentropic expansion equations. The pressure loss coefficient is favoured simply because it fit the present experimental data best, but it is the most difficult to implement since it requires an iterative calculation procedure. Finally, the polytropic expansion model is practical because unlike the equivalent diameter and discharge coefficient models, which rely purely on empirical mass flow rate corrections, this model has some physical significance. A summary of each model's coefficient that most closely reproduced experimental data is presented in Table 3.4. Table 3.4: Mass Flux Model Parameters Mean  Optimal Model Parameters Std. Deviation Mass Flux Error  Equivalent Diameter, d (mm) Discharge Coefficient, C  0.970 0.778  0.016 0.025  3.03 % 3.00 %  Pressure Loss Coefficient, K  0.417  0.050  2.53 %  Polytropic Coefficient, k  1.242  0.015  4.20 %  e  d  p  Interestingly, the tuned model parameters that most closely reproduce experimental results correspond to a stagnation pressure loss between 11-24%, which is greater than a 10% stagnation pressure loss suggested by Hill and Ouellette for gaseous 19  injections. This difference is believed to be caused by the different injector used in their investigation, which exhibited a smaller internal pressure loss partially due to internal flow passage differences and partially as a result of operating at a different Reynolds number. Modelling the flow between the fuel reservoir and the injector nozzle using each of the models described above (using the optimal parameters tabulated in Table 3.4) mass fluxes for both methane and nitrogen injected at various pressures are listed alongside their experimental measurements in Table 3.5. This illustrates the close agreement between the pressure loss coefficient model and experimental results at all injection pressures investigated for both gases. The model developed herein is therefore a valid predictive tool for estimating the mass flow rate from the present injector given only the fuel reservoir conditions.  Chapter 3: Characterization of a Gaseous Fuel Injection System  40  Table 3.5: Comparison of Experimental Mass Fluxes to Model Results Injection Pressure (psi) 1000 Experimentally Measured  X  1820/1850  13.24  16.04  Discharge Coefficient, C  8.88  13.25  16.05  Pressure Loss Coefficient, K  8.95  13.36  16.17  o  Polytropic Coefficient, k  9.83  14.67  17.77  4  8.87  X 3 U.  e  d  p  Experimentally Measured ^ 10  (o E n "5) ra _  5 E. z  2500  13.95±1.04 16.56±0.98  l Mass (mg/m  Equivalent Diameter, d  9.27±0.71  1500  12.03±0.69 17.42±0.88 21.27±1.09 2 8 . 9 9 ± 1 . 3 7  Equivalent Diameter, d  11.96  17.85  21.98  29.64  11.97  17.86  21.99  29.65  Pressure Loss Coefficient, K  11.91  17.77  21.88  29.51  Polytropic Coefficient, k  11.42  17.05  20.99  28.31  e  Discharge Coefficient, C  d  p  *Note: All Indicated pressures are gauge pressures.  3.3.4 Pulsed Injection System Validation While the J41 injector, controller, and driver were designed and tested for use in single injection operation, the modifications performed to enable pulsed injection were unproven. Although these control system modifications were relatively minor, consisting only of the additional programmable pulse generator inserted upstream of the controller to repeatedly trigger the injector, it remained uncertain whether the injector, driver, and controller could respond sufficiently rapidly to successive trigger signals. The purpose of the present tests was therefore to validate the system's response to pulsed injection operation.  Procedure To validate the injector's ability to respond to multiple successive trigger signals the experimental apparatus previously described was used. The injector's response to pulsed injection operation was investigated by rapidly issuing multiple trigger signals to the injector controller while monitoring signals from both the controller and test chamber pressure. The J41 injector  controller's response was verified by observing  if multiple control signals were issued in response to each trigger, while the injector  driver was verified to be responding to the multiple control signals by observing if distinct test chamber pressure rises were observed corresponding to each issued control signal. Additionally, in order to estimate if equal amounts of fuel were being injected during each injection pulse, the magnitude of each pressure rise was also  Chapter 3: Characterization of a Gaseous Fuel Injection System  41  measured. Figure 3.9 presents typical control and pressure signals obtained in the current study illustrating how the pulse delay and pressure ratio were defined.  Pulse Delay Control Signal  Figure 3.9: Pulse Delay and Pulse-to-Pulse Pressure Ratio Definitions This procedure was used to validate the pulsed injection system at several realistic injection durations with variable delays between successive injections to determine the minimum delay between successive pulses that the system could respond to. In all cases two successive injections were investigated to minimize the size of the test matrix, although up to eight successive injection pulses are possible with the current configuration. These operating conditions are summarized in Table 3.6, with the experimental data available in Appendix E .  Table 3.6: Experimental Test Matrix (Pulsed Injection System Validation) Injection Duration: Number of Injection Pulses:  1-3 ms (each injection pulse) 2  Injection Delay (Between Pulses):  0.5-50 ms  Injection Pressure:  95 bar (1400 psi)  *Note: All indicated pressures are gauge pressures.  Experimental Results Figure 3.10 presents the normalized pressure ratio (AP2/AP1) plotted against pulse delay (see Figure 3.9 for definition of pulse delay, AP1, and AP2). It was observed that even when a very long delay separated two injection pulses, the pressure rise associated with the second injection (AP2) was consistently smaller than the first (AP1). This may have been caused by changing test chamber pressure or mixture composition. Since the volume of the test chamber was so small, the pressure and  Chapter 3: Characterization of a Gaseous Fuel Injection System  42  density within it increased dramatically after the first injection. Therefore, while the first injection fired into a low-pressure, air-filled chamber, the second injection fired into a high-pressure methane/air mixture, resulting in a reduced mass flow and thus yielding a smaller pressure rise. To compensate for this effect, all values plotted in Figure 3.10 have been normalized by the AP2/AP1 ratio observed when long pulse delays separated the two injections.  Delay Between Pulses (ms)  Figure 3.10: Normalized Pulse-to-Pulse Pressure Ratio vs. Pulse Delay Figure 3.10 illustrates that for short injection durations (< 1.8 ms), the injector is fully capable of two successive injections even if pulses are separated by as little as 0.5 ms (this was the shortest delay tested, shorter delays may also be possible), but for long injection durations (> 1.8 ms), the pulse delay must exceed 20 ms if unequal injection pulses are to be avoided. Sample pressure traces are presented in Figure 3.11 to illustrate the effects of injection pulses with insufficient pulse delays. The required minimum separation time between injection pulses is attributable to the injector driver's internal capacitance requiring time to accumulate a sufficient charge after each injection and is therefore unavoidable. To predict its effects in the region where the two pressure rises are not equal (i.e. pulse widths > 1.8 ms, pulse delays < 20 ms), the following empirical correlation may be used:  Chapter 3: Characterization of a Gaseous Fuel Injection System  AP2 AP1  AM  43  PD + 1 if PW >^.Bmsand PD<20ms 20 otherwise 1  where PW is the pulse width (injection duration - ms), PD is the pulse delay (ms), and A is given by the following relation: A = 0.2744 PHr -0.4908 7  - — j _  !  '  _  •  Pressure Signal  Control Signal (a) 2.5 ms Injection Duration, 0.5 ms Pulse Delay (AP2/AP1 = 0.24)  Pressure Signal  Control Signal (b) 3.0 ms Injection Duration, 1.0 ms Pulse Delay (AP2/AP1 = 0)  Figure 3.11: Successive Injections with Insufficient Pulse Delays  3.4 Jet Flow Field Characterization The jet flow field characteristics of the J41 injector were the second set of properties requiring characterization after the hardware itself had been validated. The injector's jet characteristics are of relevance to the present investigation because it is desirable to understand whether the transient jet that develops during and after injection develops similarly under different injection conditions. Additionally, in cases where multiple successive injection pulses are produced, the interactions between each injection and the net effect they have on the overall jet length scales (penetration length and jet width) must be investigated. Finally, to gain insight into how the jet may respond during in-cylinder injection the effects of impingement and of an enclosure on the resultant jet's development require investigation.  3.4.1 Experimental Apparatus The impulsively started transient jet that develops during injection was investigated with a CCD camera-based Schlieren imaging system. This apparatus (illustrated in Figure 3.12) comprised of two 0.3048 m (12 in) diameter concave mirrors each with a 2.4384 m (8 ft) focal length aligned to produce a parallel light beam between them. A 200 W mercury arc lamp was focussed onto a 0.5 mm diameter pinhole to produce a point source of light and placed at the focal point of one of the concave mirrors, slightly off-axis to avoid interfering with any part of the parallel light beam. At the focal point of the other concave mirror, also slightly off-axis, a circular aperture filtered the focused image, yielding a Schlieren image (rather than a shadowgraph) before projecting it onto a camera.  Converging Lens  Arc Lamp  Injector  Figure 3.12: Experimental Apparatus (Jet Flow Field Characterization Study) A circular aperture was used to filter the images, as opposed to a conventional Schlieren system using a knife edge, because the aperture allows resolving spatial density gradients in all planar directions rather than only visualizing those gradients that are perpendicular to the knife edge. Alternatively, a graded filter consisting of concentric rings would have also resolved spatial density gradients in all directions simultaneously and may have been  Chapter 3: Characterization of a Gaseous Fuel Injection System  45  particularly useful if images were captured in colour. However, since the camera used in the present tests was only capable of capturing greyscale images, a graded filter was not deemed to provide any noticeable advantage over use of a circular aperture, and so the latter was used (since it was readily available). Images were captured with a Kodak Megaplus ES 1.0 digital camera, which has a spatial resolution of 1008 (H) by 1018 (V) pixels. This camera is capable of capturing two images in a triggered double-exposure mode, with the first image exposure duration variable from 127 u.s to 33 ms, while the second image has a fixed exposure of 33 ms. Unfortunately, the second image's exposure duration was too long to be of practical use in the present investigation, therefore the camera was used in the single exposure mode with exposure duration set to its shortest value; 127 us. Although this exposure duration was sufficiently short to capture large-scale details of the flow, noticeable blurring of the small turbulent length scales was inevitable with the existing equipment. The injector was mounted vertically (injecting downward) on a simple test stand that firmly secured the injector to a mounting plate during all experiments and provided the ability to adjust the injector's height for alignment with the focussing mirrors (see Figure 3.12 inset). This ensured that the largest possible area was visible to capture the entire jet plume and provided some flexibility in adjusting the location of the jet relative to the light source to compensate for any irregularities in the illumination level. Finally, a string was tied taught 30 mm below the face of the injector mounting plate to provide a reference scale for use during subsequent image processing. Injector and camera timing and synchronization were accomplished by triggering both with a BNC programmable pulse generator. Two separate channels were used such that the relative delay time (the interval between the start of injection and the image capture) could be varied to capture the transient jet at various stages in its evolution. Additionally, use of the pulse generator allowed the investigation of the flow field that develops during pulsed injection operation by configuring the pulse generator to trigger the injector multiple times, as was previously done when validating the pulsed injection system.  3.4.2 Single Injection Mode The single injection mode is the operating mode for which the J41 injector was specifically designed, in which the injector is triggered only intermittently, with delays on the order of  Chapter 3: Characterization of a Gaseous Fuel Injection System  46  20 ms (corresponding to a four stroke engine operating at 6000 rpm) or greater separating injections. The jet characteristics in this operating mode are therefore of great practical interest in optimizing internal combustion engine operation. Additionally, data collected in this operating mode provides a baseline for comparison to experimental and numerical jet studies. Procedure Jet characteristics, namely the jet tip penetration length and maximum width, were measured from a series of images (17-35 at each operating condition, depending on the injection duration) captured using the apparatus described above. Methane was repeatedly injected at various injection pressures into atmospheric air while images were captured at 200 us intervals throughout the injection duration and at intervals ranging between 200 ps and 1.2 ms once injection ceased. Throughout, the jet tip penetration length and width were measured (in pixels) from the digital images and subsequently converted to millimetres by way of the reference scale on the injector mounting apparatus (Figure 3.12 inset). Five injection durations between 0.5-5.0 ms were explored at each of two injection pressure ratios of 3 and 5, representative of those typical in engine operation. The test conditions are summarized in Table 3.7 with data available in Appendix F. Table 3.7: Experimental Test Matrix (Single Injection Visualization Study) Injection Duration: Injection Pressure:  0.5-5 ms 2-4 bar (30-60 psi)  Pressure Ratio:  3-5  *Note: All indicated pressures are gauge pressures.  Experimental Results Figure 3.13 below contains representative images typical of those captured at each of 10 distinct injection conditions (combination of injection duration and pressure) presently investigated. These images illustrate how the jet tip length and width were relatively easily defined from the sequence of images as a consequence of the large density gradients between the methane jet and surrounding still air. From many series of images such as those in Figure 3.13, the length and width of the methane jet was measured at several injection conditions with results presented  Chapter 3: Characterization of a Gaseous Fuel Injection System  47  in Figure 3.14 and Figure 3.15. These figures illustrate that despite collecting data over many successive injections (distinct realizations of the jet), the resultant length and width measurements are relatively smooth. This indicates that the jet produced for any given injection is very consistent and repeatable. Although fluctuations and deviations from the dominant trends are present for all injection durations these are relatively small, typically falling within 5-10% of the trend line. Width measurements (Figure 3.15) exhibit greater fluctuations than the lengths due to the high turbulence levels along the edges of the jet where vortices interact to stretch the jet in various directions, causing greater variability between jet realizations. Additionally, density gradients are not as pronounced along the edges of the jet as they are at the tip, making width measurements from Schlieren images much more difficult than length measurements.  Figure 3.13: Schlieren Images of Single Jet Evolution in Time A second noteworthy point from Figure 3.14 is the self-similarity exhibited by the jet throughout the full range of injection durations investigated. During injection, all jets regardless of their total injection duration collapse well onto a common curve. This further illustrates the consistent, repeatable nature of the jet and is not unexpected since all previous mass flow rate measurements illustrated similar injection duration independence (Figure 3.8). However, after the end of injection, the length ceases to increase as rapidly as during injection (illustrated by a deviation from the main trend line) since a lack of any further momentum injection causes the viscous drag forces on the jet to dominate, slowing the jet's penetration rate. While this effect is most pronounced in the penetration length curves, a similar effect is also observed on the jet width, but is partially masked by the larger fluctuations inherently present in those measurements.  48  Chapter 3: Characterization of a Gaseous Fuel Injection System  * 0.5 ms Injection (During) o 0.5 ms Injection (After) a 1.0 ms Injection (During) 1.0 ms Injection (After) * 1.5 ms Injection (During) A 1.5 ms Injection (After) * 3.0 ms Injection (During) o 3.0 ms Injection (After) x 5.0 ms Injection (During) x 5.0 ms Injection (After)  (a) Injection Pressure Ratio = 3  • 0.5 ms Injection (During) o 0.5 ms Injection (After) • 1.0 ms Injection (During) 1.0 ms Injection (After) * 1.5 ms Injection (During) A 1.5 ms Injection (After) • 3.0 ms Injection (During) o 3.0 ms Injection (After) $ Representative Error Bar  x 5.0 ms Injection (During) x 5.0 ms Injection (After)  3  4  5  6  7  8  Time (ms) (b) Injection Pressure Ratio = 5  Figure 3.14: Jet Length Evolution During/After Injection (Single Injection)  Chapter 3: Characterization of a Gaseous Fuel Injection System  49  • 0.5 ms Injection (During) o 0.5 ms Injection (After) • 1.0 ms Injection (During) 1.0 ms Injection (After) * 1.5 ms Injection (During) & 1.5 ms Injection (After) • 3.0 ms Injection (During) o 3.0 ms Injection (After)  Representative Error Bar  x 5.0 ms Injection (During) x 5.0 ms Injection (After) 3  4  5  8  Time (ms) (a) Injection Pressure Ratio = 3  • 0.5 ms Injection (During) o 0.5 ms Injection (After) • 1.0 ms Injection (During) 1.0 ms Injection (After) * 1.5 ms Injection (During) 6 1.5 ms Injection (After) • 3.0 ms Injection (During) o 3.0 ms Injection (After)  Representative Error Bar  x 5.0 ms Injection (During) x 5.0 ms Injection (After) 2  3  4  5  8  Time (ms) (b) Injection Pressure Ratio = 5  Figure 3.15: Jet Width Evolution During/After Injection (Single Injection)  Chapter 3: Characterization of a Gaseous Fuel Injection System  50  Finally, increasing the pressure ratio from 3 to 5 increased the jet length (measured at fixed time intervals after injection) by a factor of approximately 1.4, and the width by a factor of 1.3, indicating both increased axial and radial jet velocities. Although these increased velocities are not predicted by the previously developed mass flow model, which assumes choked flow, implying the nozzle exit velocity is independent of the pressure ratio, that model does.suggest a linear momentum flux dependence on the pressure ratio. Therefore, although the choked nozzle limits the mass flow rate, higher pressure at the sonic throat arising from a higher pressure ratio yields a higher exit momentum flux. This greater momentum flux yields a higher jet velocity after the gas exits the nozzle and expands to ambient pressure. Numerical Results Among the many previous researchers that have modelled transient axisymmetric jet development, the most relevant is the work of Hill and Ouellette , who reviewed 19  an array of previous studies and proposed scaling laws for transient axisymmetric gaseous jets. This development was based on dimensional analysis of the jet tip penetration length (Z ) as a function of the exit momentum flux (M ), jet density at r  the nozzle exit (p ), ambient density (p ), exit velocity (U ), and nozzle diameter (d). n  a  0  Two relations were derived depending on whether the jet and ambient gas densities were equal or not, and both made use of a dimensionless constant: the penetration number, r. The derived relations for equal and different densities, respectively, are reproduced below:  (3.10)  These results, which are based on dimensional analysis, may be solved analytically if one assumes a transient jet of the Turner variety. This model treats the transient 20  jet as a transient vortex ball in front of a steady-state jet (refer to illustration in Figure 3.16), and in conjunction with the well-known mass entrainment results of Ricou and Spalding can be used to derive analytical equations for the vortex ball's and jet's 16  Chapter 3: Characterization of a Gaseous Fuel Injection System  51  momentum. Substituting the penetration number equations into these momentum equations yields an analytical penetration number solution (Hill and Ouellette ). 19  Additionally, since the jet momentum, density, and penetration length in time are experimentally measurable, the penetration number may also be calculated from experimental data.  Transient Vortex Region  Steady-State Jet Region  Figure 3.16: Numerical Jet Model To examine the validity of the scaling laws presented above, the jet length data from Figure 3.14 is replotted in Figure 3.17 in non-dimensionalized form, whereby the jet penetration is normalized such that when plotted against the square root of time, the slope of the curve is the penetration number. In Figure 3.17 only those data points collected during injection are plotted to illustrate how well the data collapses onto a straight line when normalized. Figure 3.18 includes all the data collected to illustrate how the penetration number decreases at the end of injection as the jet slows and tends towards puff jet behaviour. Quantitatively, the value of the slope in Figure 3.17 depends upon the normalization that is performed on the jet tip penetration length. Of the two penetration numbers presented earlier, clearly the latter (different jet and ambient densities) is relevant in the present investigation, but the momentum flux, exit velocity, and jet density are all required, none of which are directly measured. Using the various mass flow models developed earlier, in which expansion from the fuel reservoir to the nozzle is treated as an adiabatic, isentropic process with corrections to compensate for any losses,  Chapter 3: Characterization of a Gaseous Fuel Injection System  52  • 0.5 ms Injection (During) • 1.0 ms Injection (During) A 1.5 ms Injection (During) • 3.0 ms Injection (During) x 5.0 ms Injection (During)  Normalized Time (ms  )  (a) Injection Pressure Ratio = 3  • 0.5 ms Injection (During) • 1.0 ms Injection (During) * 1.5 ms Injection (During) • 3.0 ms Injection (During) x 5.0 ms Injection (During)  Normalized Time (ms  )  (b) Injection Pressure Ratio = 5  Figure 3.17: Normalized Jet Tip Penetration (During Injection)  Chapter 3: Characterization of a Gaseous Fuel Injection System  53  • 0.5 ms Injection (During) o 0.5 ms Injection (After) * 1.0 ms Injection (During)  M  E £ 5  1.0 ms Injection (After)  O)  c CD  dCD  * 1.5 ms Injection (During) 4  A 1.5 ms Injection (After)  -3  _N  3  • 3.0 ms Injection (During)  15 O  2  c 3.0 ms Injection (After) H$H  Representative Error Bar x 5.0 ms Injection (During) x 5.0 ms Injection (After)  0.5  1  1.5  2.5  3.5  Normalized Time (ms ) 05  (a) Injection Pressure Ratio = 3  » 0.5 ms Injection (During) o 0.5 ms Injection (After) s 1.0 ms Injection (During) • 1.0 ms Injection (After) A 1.5 ms Injection (During) A 1.5 ms Injection (After) • 3.0 ms Injection (During) o 3.0 ms Injection (After) x 5.0 ms Injection (During) x 5.0 ms Injection (After)  Normalized Time (ms  )  (b) Injection Pressure Ratio = 5  Figure 3.18: Normalized Jet Tip Penetration (During/After Injection)  Chapter 3: Characterization of a Gaseous Fuel Injection System  54  uncertainty in the tuned model parameters and differences between various models result in uncertainties in the penetration number. For comparison, Table 3.8 lists the penetration number (the slope in Figure 3.17) calculated using various assumptions for determining the mass flow, momentum, and nozzle density. Table 3.8: Jet Penetration Number Comparison Width Ratio, D/Z , at Various Injection Stages t  Penetration Number, r, Assuming Various Stagnation Pressure Losses Uniform Density Solution, r Analytical Solution, r  PR = 3  PR = 5  Theoretical  During  0.37±0.05  0.33±0.04  0.25±0.05  After  0.37±0.05  0.36±0.05  0.5-0.6 (puff jet)  10% loss  2.42±0.04  2.74±0.04  -  20% loss  2.50±0.04  2.83±0.04  30% loss  2.58±0.04  2.92±0.04  _  2.25±0.04  2.89±0.04  -  2.71±0.13  2.82±0.10  2.99±0.10  It is seen, regardless of what stagnation pressure loss is assumed within the injector or even if the differential density equation is used at all, that the penetration number for a pressure ratio of 3 is markedly lower than that predicted. Improved penetration number agreement with predicted results is observed at a higher pressure ratio of 5. The discrepancies between the low pressure ratio jet and the analytical solution is attributed mostly to the low Reynolds number. This effect is somewhat expected since the correlations developed by Hill and Ouellette assumed fully turbulent jets (Re > 500,000) while the current pressure ratios corresponded to nozzle Reynolds numbers between 33,000-43,000 and 56,000-72,000 for pressure ratios of 3 and 5, respectively, depending upon the stagnation pressure loss assumption. The closer agreement between experimental and analytical results at the higher pressure ratio is believed due to closer Reynolds number agreement. Nevertheless, despite minor differences in the numerical values for the penetration number, overall the experimental data is seen to collapse well using the scaling laws derived by Hill and Ouellette. Additionally, as the jet Reynolds number is increased, even the quantitative agreement converges with previously stated analytical results.  3.4.3 Pulsed Injection Mode Pulsed injection mode is the operating mode in which each individual injection is split into multiple successive shorter fuel injections, such that the total fuel injected equals that that  Chapter 3: Characterization of a Gaseous Fuel Injection System  55  would have been injected in one continuous injection pulse. The motivation behind such pulsed injection operation is speculation that pulsing injection can increase jet turbulence levels thereby increasing mixing rates and accelerating the autoignition process. Procedure To investigate the effects of pulsed injection operation, a series of Schlieren images were captured of two successive injections of various injection durations, separated by several injection pulse delays. Methane was injected at a constant pressure into atmospheric air while 17-20 sequential images were captured at intervals between 200 us to 1.2 ms. Jet tip penetration length and width were subsequently measured from captured digital images. While two distinct injection pulses were identifiable in several images, the jet tip and jet width of the second injection was not consistently measurable and therefore only the penetration length and width of the large scale flow (not individual injection pulses) was measured. Three injection durations between 0.5-1.5 ms were investigated at each of three pulse delays between 0.5-2.0 ms. These particular conditions result in injection of an equivalent quantity of fuel as single injection durations ranging between 1.0-3.0 ms, previously chosen for their engine relevance. The pulse delay was defined as the time interval between the end of the first injection and the beginning of the next injection (see Figure 3.9). Throughout all tests, a constant pressure ratio of 3 was maintained to limit the size of the test matrix. Experimental conditions investigated are summarized in Table 3.9 and experimental data is available in Appendix F. Table 3.9: Experimental Test Matrix (Pulsed Injection Visualization Study) Number of Injection Pulses: Injection Duration:  2 0.5-1.5 ms (per injection pulse)  Injection Delay:  0.5-2.0 ms  Injection Pressure:  2 bar (30 psi)  Pressure Ratio:  3  *Note: All Indicated pressures are gauge pressures.  ) Experimental Results Representative images of those captured in the present investigation are included in Figure 3.19. These images highlight the difficulty of distinguishing each individual injection pulse. Although in several images the jet tip of the second injection pulse  Chapter 3: Characterization of a Gaseous Fuel Injection System  56  is discernible, in others it is not, and the overall flow field appears no different than that observed when operating the injector in single injection mode (Figure 3.13).  Figure 3.19: Schlieren Images of Pulsed Jet Evolution in Time The jet tip penetration and jet width evolution in time are presented in Figure 3.20. In addition to plotting results from pulsed injection experiments, each of the graphs in Figure 3.20 also includes the jet length and width corresponding to a comparable single injection pulse to illustrate the similarities between the jet that develops during single and pulsed injection. This figure highlights the irrelevance of the pulse delay. For all injection durations, varying the delay between 0.5-2.0 ms had no noticeable effect on the ensuing jet, with each data point falling within experimental error of all others at any given time after the start of injection. Although increasing pulse delays much further (by orders of magnitude) would produce an observable effect on the jet flow field, such long pulse delays are of no interest since then the jet is considered two distinct injections rather than one pulsed injection. Furthermore, similarities observed between the jet development for the case of two successive injections and one long, continuous injection (which may be considered two successive pulses with no pulse delay) implies that the jet development is solely dependent on the total momentum injected, regardless of whether it is continuous or pulsed. This is especially demonstrated by comparing the pulsed injection case at an injection duration of 1.5 ms with a single injection with an injection duration of 3.0 ms (Figure 3.20 (e)). The jet tip penetration length for these two cases is nearly identical, and this is due to the momentum injection being equal in each case (two 1.5 ms duration pulses inject an equivalent momentum as a single 3.0 ms injection). Similar trends are illustrated by the injection durations of 0.5 ms and 1.0 ms, with all pulsed injection data points lying between those of the single injection curves.  Chapter 3: Characterization of a Gaseous Fuel Injection System  57  *  0.5 ms Pulse Delay  *  1.0 ms Pulse Delay  *  2.0 ms Pulse Delay 0.5 ms Single Pulse 1.0 ms Single Pulse  (a) Jet Length (0.5 ms Injection Duration Per Pulse)  •  0.5 ms Pulse Delay  •  1.0 ms Pulse Delay  A  2.0 ms Pulse Delay  — 0.5 ms Single Pulse 1.0 ms Single Pulse  3  4  5  Time (ms) (b) Jet Width (0.5 ms Injection Duration Per Pulse)  Figure 3.20: Jet Length and Width Evolution (Pulsed Injection)  Chapter 3: Characterization of a Gaseous Fuel Injection System  58  160 •  0.5 ms Pulse Delay  •  1.0 ms Pulse Delay  A  2.0 ms Pulse Delay  140 120  1.0 ms Single Pulse  E 100 E O)  _l •t-J <D  ~)  1.5 ms Single Pulse  80 60  •  *  40 J Representative Error Bar 20 0 0  1  2  3  4  5  6  7  8  Time (ms) (c) Jet Length (1.0 ms Injection Duration Per Pulse)  •  0.5 ms Pulse Delay  •  1.0 ms Pulse Delay  A  2.0 ms Pulse Delay 1.0 ms Single Pulse 1.5 ms Single Pulse  3  4  5  Time (ms) (d) Jet Width (1.0 ms Injection Duration Per Pulse)  Figure 3.20: Jet Length and Width Evolution (Pulsed Injection) cont'd.  Chapter 3: Characterization of a Gaseous Fuel Injection System  59  •  0.5 ms Pulse Delay  »  1.0 ms Pulse Delay  A  2.0 ms Pulse Delay 1.5 ms Single Pulse 3.0 ms Single Pulse  (e) Jet Length (1.5 ms Injection Duration Per Pulse)  •  0.5 ms Pulse Delay  a  1.0 ms Pulse Delay  A  2.0 ms Pulse Delay 1.5 ms Single Pulse 3.0 ms Single Pulse  3  4  5  Time (ms) (f) Jet Width (1.5 ms Injection Duration Per Pulse)  Figure 3.20: Jet Length and Width Evolution (Pulsed Injection) cont'd.  60  Chapter 3: Characterization of a Gaseous Fuel Injection System  The effect of pulsing the jet therefore exclusively seems to affect internal strain rates within the jet, which unfortunately could not be quantitatively resolved in the present study. If pulsing the jet has any effect in combustion applications it must arise from the effects it has on the strain intensity and/or distribution within the jet, not from any large-scale effects on the transient jet's development. Additionally, since the largescale flow field properties of a pulsed injection seem identical to those of continuous injections of equal momentum flux, all scaling laws developed for the single injection mode are applicable to pulsed injection operation.  3.4.4 Effects of Jet Impingement Studying the effects of jet impingement on ensuing transient jet development is of interest because such a scenario may arise in the presence of a protruding spark or glow plug, or an obstruction intended to enhance mixing or, if coated with a catalyst, accelerate ignition. While many configurations for such impingements are possible, and in some cases have been previously investigated, only two simple geometries were investigated in the current study to gain insight into the jet's behaviour. Procedure To investigate the effects of jet impingement, two blunt bodies were chosen as flow obstructions (see Figure 3.21). These consisted of a circular cross-section, 1.575 mm diameter wire placed perpendicular to the jet's axis, and a rectangular crosssection body 2.896 mm wide and 1.067 mm thick, mounted so that the jet impinged  II Figure 3.21: Flow Obstructions for Jet Impingement Study  A  »  Front  Side  Chapter 3: Characterization of a Gaseous Fuel Injection System  61  on its widest side. Each obstruction was located a distance from the injector nozzle such that 80-100% of the jet's width impinged on the obstruction. Methane was then injected at a constant pressure into atmospheric air while a sequence of 19 images captured the jet impinging on the flow obstructions with both the jet length and width measured along with qualitative observations of the jet's behaviour. Each of the flow obstructions was tested at several axial distances from the injector nozzle. All other parameters, including injection duration and pressure, ratio were held constant throughout the experiments. The test conditions are summarized in Table 3.10 and data is available in Appendix F. Table 3.10: Experimental Test Matrix (Jet Impingement Visualization Study) Obstruction Distance from Injector:  Circular Rectangular  0.5-2.0 mm 10.0-15.0 mm  Injection Duration:  1.0 ms  Injection Pressure:  2 bar (30 psi)  Pressure Ratio:  3  *Note: All indicated pressures are gauge pressures.  Experimental Results Several sample images captured in this study are shown in Figure 3.22 to illustrate the markedly different jet behaviour with the circular and rectangular obstructions. The circular obstruction had the net effect of decreasing the length and increasing the width of the jet while also noticeably increasing the turbulence and unsteadiness of the jet. Throughout the injection, the jet was observed to meander from one side to the other of the obstruction, occasionally even splitting into two jets. Additionally, little, if any, effect from moving the obstruction closer or farther from the nozzle was observed. Contrarily, the rectangular obstruction was observed to create a very stable, repeatable flow pattern. The jet consistently split into two distinct jets upon impinging on the flat obstruction, with few instabilities, and the effect of moving the obstruction closer or farther from the injector nozzle was to change the angle of the two deflected jets relative to the initial impinging jet. Quantitatively, since the cylindrical obstruction only occasionally caused the jet to split in two, the same measures used to analyse the original undisturbed jet, namely the tip penetration length and width, were used. These are presented in Figure 3.23 alongside length and width measurements for undisturbed jets at the same injection  62  Chapter 3: Characterization of a Gaseous Fuel Injection System pressure and duration. As discussed above, these graphs illustrate how the effect  of the circular obstruction was to reduce the jet penetration length by approximately 39% and increase the jet's width by 43%. Additionally, they illustrate that varying the obstruction's distance from the nozzle had no identifiable effect, within experimental uncertainty. This may be caused by the fact that the circular obstruction was placed very near the nozzle (separation distance to nozzle diameter ratio, L/d, of 0.45-1.81) to ensure the entire jet width impinged on the obstruction. Perhaps if the obstruction were located much farther (4-8 mm from nozzle) a stronger relationship between the separation distance and the jet's development would have been observed. Lastly, the jet width plot demonstrates the unsteady nature of the deflected jet, as the width is observed to fluctuate wildly as the jet would drift from one side to the other of the obstruction and occasionally even split into two jets.  LI  IB  LB •  •  U  IE*. '  •  •  (a) Impingement on Circular Obstruction  m  M  • U 0.1 ms  • •  y  t - 0.3 ms  I " 0,7 ms  m  1-1.3 rr«  (b) Impingement on Rectangular Obstruction  Figure 3.22: Schlieren Images of Impinging Jet Evolution in Time Since the rectangular obstruction consistently caused the jet to split into two distinct jets, it was inappropriate to solely rely on the tip penetration length and width of the jet as quantitative measures of its response. Instead, the jet length and width were defined as shown in Figure 3.24 along with the deflection angle. Since the jet split  Chapter 3: Characterization of a Gaseous Fuel Injection System  63  160 * 0.5 mm Gap (During) 140  o 0.5 mm Gap (After)  120  * 1.0 mm Gap (During) • 1.0 mm Gap (After)  E 100 E,  * 2.0 mm Gap (During)  C  & 2.0 mm Gap (After) Infinite Gap  3  4  5  Time (ms) (a) Jet Length (Circular Obstruction)  • 0.5 mm Gap (During) o 0.5 mm Gap (After) • 1.0 mm Gap (During) 3 1.0 mm Gap (After) * 2.0 mm Gap (During) A 2.0 mm Gap (After) Infinite Gap  3  4  5  Time (ms) (b) Jet Width (Circular Obstruction)  Figure 3.23: Jet Length and Width Evolution (Circular Obstruction)  Chapter 3: Characterization of a Gaseous Fuel Injection System  64  into two jets, the "length" measure is no longer representative of the tip penetration length, but rather the maximum axial distance travelled and the "width" is a measure of the maximum radial distance travelled.  Figure 3.24: Jet Length, Width, and Deflection Angle Definition Using the above definitions of the jet length and width, Figure 3.25 presents both the measured values of each using the rectangular obstruction, and for comparison also plots the penetration length and width of an undisturbed jet. As one would expect, length and width differ greatly from those of an unobstructed jet since impingement on the rectangular obstruction caused such a large deflection of the jet. Depending on the distance the obstruction was placed from the nozzle, either 10 mm or 15 mm (L/d = 9.09-13.64), the jet was deflected by 86° and 69°, respectively. Such a strong relationship between the obstruction's distance from the nozzle and the deflection angle is expected since locating the obstruction close to the nozzle causes a greater portion of the jet to impinge on the obstruction, whereas as the obstruction is moved farther from the injector, a smaller fraction of the jet impacts the obstruction. This relationship is also responsible for differences between the jet length's and width's response to the obstruction's location, with the penetration length seemingly more sensitive than the width. However, this effect is due mostly to the deflection angle change that occurs, which trigonometrically results in a larger increase in the length than the width for the particular deflection angles observed in this study. The effects of an obstruction are thus to increase the surface area and turbulence by splitting a jet into multiple jets, with the degree of turbulence augmentation and/or the angle through which the jets are deflected controlled by the distance from the nozzle to the obstruction.  Chapter 3: Characterization of a Gaseous Fuel Injection System  65  160 • 10 mm Gap (During) 140 $ Representative Error Bar 120  e 10 mm Gap (After) a 15 mm Gap (During) 15 mm Gap (After)  E 100 E, .c o> 80 c  Infinite Gap  _l  o5 60 40 20  •• • 3  4  5  6  7  Time (ms) (a) Jet Length (Rectangular Obstruction)  •  10 mm Gap (During)  o 10 mm Gap (After) •  15 mm Gap (During)  • 15 mm Gap (After) Infinite Gap  (b) Jet Width (Rectangular Obstruction)  Figure 3.25: Jet Length and Width Evolution (Rectangular Obstruction)  Chapter 3: Characterization of a Gaseous Fuel Injection System  66  3.4.5 Effects of an Enclosure Finally, the effects of an enclosure on a transient jet are of interest to understand how the combustion chamber walls and piston affect the jet's development. As with impingement, many combinations are possible to study such effects so only one special case, with three variants, was investigated. This involved studying the behaviour of a jet confined between parallel plates of various separation distances, such as would be the case for a jet injected parallel to the surface of a flat piston approaching top dead centre in an engine.  Procedure To investigate the effects of an enclosure, two moveable parallel plates were installed on the apparatus previously described and methane injected between the plates. Methane was injected into atmospheric air at a constant injection pressure and duration while 19 sequential images were captured of the jet at various stages in its evolution. Subsequently both the jet's length and width were measured from the captured images. Three sets of experiments were conducted at three distinct wall separation distances with all injection parameters held constant. A summary of the experimental conditions is presented in Table 3.11 with data in Appendix F. Table 3.11: Experimental Test Matrix (Jet Enclosure Visualization Study) Wall Separation Distance: Injection Duration:  12-50 mm 1.0 ms  Injection Pressure:  2 bar (30 psi)  Pressure Ratio:  3  *Note: All indicated pressures are gauge pressures.  Experimental Results Representative images of those captured in the present study are presented below in Figure 3.26. Qualitatively, the images illustrate how confining the jet had minimal influence on the jet length. Although inevitably the jet width was compressed once it filled the gap between the plates, no apparent difference in jet length between each case was present. This is attributed to the fact that the boundary layer that forms along the edges of the plates is very narrow and despite decelerating the flow near the periphery of the jet, it has little influence along the jet centreline. Additionally, since the jet was free to expand parallel to the plates, any constraint posed by the presence of the walls was compensated for by increased jet spread out of plane.  Chapter 3: Characterization of a Gaseous Fuel Injection System  f\J J.<!111  1  67  IT  J  •  e  •  0  •  Figure 3.26: Schlieren Images of Enclosed Jet Evolution in Time The qualitative observations discussed above are further reaffirmed in Figure 3.27 where the jet length and width are plotted alongside length and width measurements from an unconfined jet at the same injection pressure ratio and duration. This figure illustrates that the presence of parallel plates had a minimal effect on the jet length, as it was just slightly longer than the length of the unconfined jet regardless of the wall separation. Expectedly the width of the confined jet was reduced relative to the unconfined jet, but even this effect is only observed once the jet width fills the entire gap. Prior to filling the space between the walls, the jet width evolves at a similar rate as an unconfined jet. Unfortunately, no comments can be made with regards to any recirculation that occurs between the plates since no such observable flow was resolved in any of the images. However, from limited observations and quantitative measurements that were made, one may conclude that the influence of the viscous boundary layer introduced by the presence of confining parallel plates fails to extend far enough into the jet to have any influence on the transient jet's development and thus the effects of confining walls are only of concern for their potential quenching effects in a reacting flow, and not for any effects on the transient jet's development.  3.5 Conclusions and Recommendations The present characterization of a Westport Innovations J41 fuel injection system involving both validation of the fuel injector hardware and the jet produced under various operating conditions led to several quantitative measures that can be used in future to predict, control, and optimize the injection system's performance. These have included the following observations of both the hardware's response and the jet's flow field characteristics:  Chapter 3: Characterization of a Gaseous Fuel Injection System  68  • 12 mm Walls (During) o 12 mm Walls (After) • 23 mm Walls (During) • 23 mm Walls (After) * 50 mm Walls (During) A 50 mm Walls (After) Free Jet  3  4  5  6  Time (ms) (a) Jet Length (Enclosure)  70 » 12 mm Walls (During) 60  « 12 mm Walls (After)  •  • 23 mm Walls (During)  50  • 23 mm Walls (After)  E E, 40  A  .c * — -<  5 30  A * *  -  ——-~-~  —  A 50 mm Walls (After)  A  —)  20 (-  10  * 50 mm Walls (During)  A A  A  A A  Baj^-efaooa  a  •  O  •  1 Representative Error Bar J0 o  » I  2  3  4  5  Time (ms) (b) Jet Width (Enclosure)  Figure 3.27: Jet Length and Width Evolution (Enclosure)  Free Jet  Chapter 3: Characterization of a Gaseous Fuel Injection System  69  1. A physical delay time of 180±20 us was found to exist in the injector driver that must be accounted for if using the control signal between the injector controller and driver to monitor injection. Failure to do so will lead to the introduction of a systematic error in non-premixed ignition delay experiments, or inaccurate injection timing during engine operation. 2. Mass flux measurements performed with both methane and nitrogen gas at several injection pressures between 62-172 bar(g) (1000-2500 psi(g)) were very well predicted by a simple model assuming choked, underexpanded flow at the nozzle. This model can be used to predict the mass flow through the injector by modelling the expansion from the stagnation state (reservoir) to the nozzle exit as an adiabatic, isentropic flow and then applying a correction using one of several proposed models. 3. The present injection system was successfully modified to facilitate pulsed injection, but caution must be used in selecting appropriate combinations of injection durations and injection pulse delays to fall within a specified operational envelope. For injection durations less than 1.8 ms, each injection pulse was found to inject equal amounts of fuel, but if operation at longer injection durations is required, an empirical correlation must be used to predict the differential mass injection rates between injection pulses. 4. Schlieren visualization of the jet produced by the injector at several injection durations was found to be extremely repeatable and consistent, with the jet's development being identical regardless of injection duration. Additionally, both the temporal evolution of the jet and the effects of pressure ratio were predicted by a dimensionless penetration number, especially at higher pressures where closer agreement with analytical results was observed. 5. Pulsed injection operation was found to have minimal influence on the jet's large scale flow field development and the effects of pulsed versus continuous injection were thus speculated to only influence internal flow structures, possibly increasing the turbulence intensity. This effect requires further investigation when optical instruments capable of resolving shorter time/length scales become available. 6. Impingement on a circular body resulted in an extremely unstable jet that drifted from side to side and split into multiple jets unpredictably, while decreasing the penetration length and increasing the jet width. Contrarily, impingement on a flat body produced a  Chapter 3: Characterization of a Gaseous Fuel Injection System  70  very stable jet that split into two upon impingement, with the angle at which each jet propagated relative to the undisturbed jet controlled by varying the separation distance between the obstruction and the injector nozzle. Use of such a device is suggested for turbulence augmentation or jet splitting if such properties are desired. Additionally, such a device coated with a catalyst may potentially be used to accelerate the ignition process and thus warrants future investigation. 7. Confining the jet between parallel plates was found to have no noticeable influence of the transient jet's development regardless of the separation distance between the plates. It was concluded that the effects of viscosity that act at the interface between the jet and wall are confined to such a thin boundary region that they have a negligible influence on the bulk centreline flow.  Chapter 4: Non-Premixed Methane Autoignition Delay Study  71  Non-Premixed Methane Autoignition Delay Study 4.1 Introduction In the continued evolution of alternative fuel powered diesel engines, such as the HPDI system developed by Westport Innovations Inc., natural gas' prohibitively long autoignition delay time impedes further progress in both emissions and cost reductions and therefore remains critically important. While homogeneous methane autoignition delay time studies have provided insight into methane's behaviour under engine-relevant temperatures and pressures, diesel engines do not operate with homogenous air/fuel mixtures. Thus a need still exists to study the autoignition behaviour of methane under conditions that more closely reflect diesel operating environments. This includes investigating the coupling between the kinetic parameters studied in homogenous autoignition experiments and the fluid mechanic parameters associated with transient gaseous fuel jets. Unfortunately, thus far the kinetic parameters governing methane autoignition and the fluid mechanic parameters governing gaseous jets have been studied independently. Therefore, in an effort to better converge shock tube results with actual diesel engine operating conditions, non-premixed autoignition experiments are conducted in the present investigation to understand the influence of both kinetic and fluid mechanic parameters on methane autoignition.  4.2 Background The ignition behaviour of non-premixed methane injected into shock-heated air at diesel engine relevant conditions differs from the autoignition behaviour of homogeneous mixtures due to the presence of a diffusion flame and thus the interaction that occurs between chemistry and fluid mechanics. Consequently, ignition delay times depend not only on experimental temperatures and pressures, which affect chemical reaction rates, but also parameters affecting the turbulent jet, including the injection duration and pressure ratio. While many ignition delay studies have been conducted investigating homogenous methane/air mixtures in shock tubes, and likewise a great deal of research has been conducted over many decades studying the flow characteristics of gaseous jets, studying the autoignition behaviour of gaseous jets in diesel environments has  Chapter 4: Non-Premixed Methane Autoignition Delay Study  72  thus far been limited to numerical simulations. While some experimental autoignition work has been conducted with coflow and counterflow diffusion flames to better understand reaction zone properties and ignition characteristics, these are not representative of the autoignition process in a diesel engine. Recent experimental autoignition research includes that of Fotache et a l .  30,31  who studied the  effects of strain rate, fuel concentration, and pressure on the ignition temperature of counterflow cold methane, butane, propane, and ethane against heated air. Additional experiments by such researchers as Starner and Bilger investigated mixture fraction distributions in methane jets, 32  Everest et al. studied field and temperature gradients in non-premixed reacting jets, Rolon et 33  al. studied the interactions between a vortex and a diffusion flame, and Phillips investigated 34  35  the ignition location in turbulent jets. These are only a few of many similar experimental studies that investigated various phenomena in either counterflow diffusion flames or steady reacting jets. While these all provide great insight into the general ignition and combustion behaviour of methane diffusion flames, no studies directly investigating the autoignition delay behaviour of methane in diesel environments were discovered. Numerically, the situation is much the same, with many studies investigating the fundamental behaviour of diffusion flames, but few closely related to the current study. Peters and Pitsch 36  and Peters work is the most commonly used when describing diffusion flames using a laminar 37  flamelet formulation, with many subsequent researchers using their laminar flamelet formulation to study diffusion flames. These have included studies of the methane-air flame structure and extinction behaviour by researchers such as Chan et a l .  38,39  , Yoshida et al. , and Seshadri and 40  Peters , as well as many additional studies investigating the diffusion flame's response to many 41  scenarios such as Im and Chen's investigation of a methane/air diffusion flame's response to 42  unsteady strain rate, for example. These represent a small sampling of the many studies that have been conducted and are included to highlight the fact that while diffusion flame behaviour is relatively well understood, none of these studies may be directly applied to understanding the ignition behaviour of non-premixed methane in diesel environments. Two numerical studies that are of close relevance to the current problem include the work of Mastorakos et al. , who studied autoignition in turbulent mixing flows, and Bi and Agrawal , 43  44  who studied autoignition of natural gas in diesel environments. The work of Mastorakos et al. involved conducting numerical simulations of various mixing flows of cold (300 K) fuel and hot (1000-1100 K) air to identify conditions favouring early ignition and subsequently compared their  Chapter 4: Non-Premixed Methane Autoignition Delay Study  ,  73  results with previous experimental results and laminar flame theory. Likewise Bi and Agrawal modelled natural gas combustion in diesel environments to compare their findings with existing experimental results. The purpose of the present investigation is to measure the autoignition delay times of methane injected into shock-heated air under engine relevant temperatures and pressures to facilitate comparison with both previously measured homogeneous autoignition delay times and previous numerical simulation results. Additionally, imaging techniques were used to photograph the autoignition event at various stages in its evolution so that comparisons can be made between reacting and inert gaseous jets, with the aim of better understanding the autoignition behaviour under diesel engine-relevant conditions.  4.3 Experimental Methods The current investigation involved conducting a series of shock tube experiments measuring the autoignition delay time of gaseous methane fuel injected into shock-heated air under various engine-relevant experimental temperatures and pressures using a standard reflected shock technique. Details of both the specific apparatus used and the test conditions investigated are presented below.  4.3.1 Apparatus Experimental ignition delay measurements were conducted in a 7.37 m long shock tube (3.11 m driver section, 4.26 m driven section), 5.9 cm in inner diameter previously used for homogeneous methane/air autoignition delay time studies (see Chapter 2 for details). The sole modifications performed to the experimental apparatus included replacement of the Auto Tran 600D-117 vacuum sensor (previously used for measuring initial driven gas pressures) with an Auto Tran 860, and the use of a double diaphragm, rather than a single diaphragm, system for controlling the pressure ratio between the driven and driver section (see Figure 4.1). The double diaphragm system used for controlling the pressure ratio between driven and driver sections consists of two diaphragms in series separated by a small chamber (-66 cm , 0.8% of the total driver section volume) that is charged to an intermediate pressure 3  between that of the driven and driver sections. The use of two diaphragms separated by a small chamber at an intermediate pressure ensures that the pressure difference across  Chapter 4: Non-Premixed Methane Autoignition Delay Study  74  each diaphragm does not exceed its burst strength until the pressure in the intermediate chamber is released (by a solenoid valve venting to atmospheric pressure). Each of the diaphragms consists of a 0.635 mm (0.025 in) aluminum or steel sheet, with five radial grooves (each 2.95 cm in length) machined to depths between 0.279-0.381 mm (0.0110.015 in), depending on the desired rupture strength. Such a system provides control of the pressure ratio between driven and driver sections, as the pressure difference across each diaphragm can be maintained safely below its burst strength until the intermediate chamber pressure is released. This makes the system insensitive to variability between individual diaphragm's burst pressure caused by material property or machining defects.  Fuel Inlet  Solenoid Valve Injector  Manual Valve  Rubber Gasket Steel/Aluminum Diaphragm \ Rubber Gasket \ Rubber Gasket Steel/Aluminum Diaphragm \ ^ Rubber Gasket  Driver Section  Pressure Transducer Injector Nozzle  Driven section  Quartz Window  Intermediate Chamber  Exploded View of Double Diaphragm  Injector Control System Injector Trigger  Photomultipliers  m  Vacuum Pumpj  Solenoid Delay Circuit « He  Dry Air  Figure 4.1: Experimental Apparatus (Non-Premixed Autoignition Study) Fuel injection was performed by a Westport Innovations J41 gaseous fuel injector located on the shock tube endplate as illustrated in Figure 4.1, facilitating the injection of methane fuel axially into the shock tube. This injector, which was previously tested to investigate its jet characteristics (refer to Chapter 3 for details), is a magneto-restrictive unit (allowing rapid opening and closing times) with a 1.1 mm diameter nozzle. Westport's WCut control  Chapter 4: Non-Premixed Methane Autoignition Delay Study  75  software was used for controlling the injection duration and the delay between detection of a trigger signal and the start of injection. The trigger signal was generated by the passage of an incident shock by one of the five dynamic pressure transducers along the length of the shock tube. Throughout the present tests, the delay between arrival of a trigger signal and the start of injection was adjusted to ensure injection began 100-800 ps after incident shock reflection from the endplate. Finally, to minimize any fuel leakage into the shock tube before injection, a manual shutoff valve and an Advanced Fuel Components solenoid valve were installed upstream of the injector (see Figure 4.1 inset). Although the fuel injector should have sealed unassisted, this was not found to be the case. Therefore, a manual shutoff valve was used for sealing the injector from fuel lines between experiments, while a solenoid was used to charge the injector immediately prior to injection; thereby minimizing the time it remained in a charged state, potentially leaking fuel into the shock tube. The injector-charging solenoid valve was controlled by the same signal used for opening the valve that vented the intermediate chamber pressure in the double diaphragm system. This was necessary since it could not be triggered by the shock wave itself because of its excessively long opening time, which exceeded the time available before the arrival of the incident shock. To compensate for the time necessary to drain the intermediate chamber (and thus generate a shock wave), an electronic delay circuit was introduced between the two solenoid valves' control signals such that the injector-charging valve could be opened 0-9999 ms after the solenoid used for venting the intermediate chamber was opened, with typical delays between 0-400 ms throughout the present investigation. This arrangement ensured the injector was pressurized for only a few hundred milliseconds prior to injection to minimize any fuel leakage into the shock tube. The delay between opening the injectorcharging solenoid valve and the start of injection was monitored by a Nicolet Instrument Corporation (NIC) 2090-I oscilloscope to measure how long the injector was in a charged state before injection to estimate total fuel leakage. Ignition itself was detected by light emission signals observed through a 10 mm diameter fused quartz window located on the shock tube endplate adjacent to the fuel injector such that any light emitted along the length of the shock tube was detectable. While ignition is commonly detected by pressure measurements in homogeneous shock tube experiments, such a technique is impractical for non-premixed ignition delay experiments because the  Chapter 4: Non-Premixed Methane Autoignition Delay Study  76  quantity of fuel injected is too small to produce any detectable pressure rise upon ignition. Hence two photomultipliers, an Electron Tubes P30A and a TSI 9162, monitored CH (with a bandpass filter of 470±15 nm) and broadband light emissions, respectively, from a pair of fibreoptic cables placed up against the endplate quartz window for detecting the onset of combustion. Signals from the photomultipliers, the injector control signal, and three of the five dynamic pressure transducers (due to limited available sampling channels) were acquired using a Wavebook/512™ data acquisition system sampling at a rate of 140 kHz (corresponding to a 7.1 us sampling interval).  4.3.2 Procedure Prior to each experiment, barometric pressure was recorded and the driven section gas pressure transducer was calibrated using a zero and span calibration corresponding to vacuum and atmospheric pressure (similar to the procedure used throughout all previous homogenous autoignition experiments). Both driven and driver sections of the shock tube were subsequently evacuated along with the tubing connecting the fuel injector, injectorcharging solenoid, and manual shutoff valve (refer to Figure 4.1). The driven section was filled with air (Praxair medical grade) to the desired initial pressure and the driver section gas composition prepared manometrically with a mixture of helium (Praxair 99.9% purity) and air (Praxair medical grade). The data acquisition system was armed (to be triggered by the rising edge of the incident shock wave as it passed the second of five piezoelectric pressure transducers - the first transducer was used for injector triggering), the injection delay and duration were set through Westport's WCut software and the delay between the solenoid for draining the intermediate chamber pressure in the double diaphragm system and the injector-charging solenoid was set. Finally, the intermediate chamber pressure was vented, initiating the rupture of the diaphragms, and generating the desired incident shock wave. In order to ensure a quiescent, constant pressure region behind the reflected shock wave (i.e. in the experimental test section), the specific heat ratio of the driver gas was carefully tuned. This was performed by blending air and He to yield a tailored interface between the driven and driver gases upon shock reflection from the endplate. A tailored interface is one where the pressure on either side of the contact surface is equal after the reflected shock passes through the interface (from driven to driver gas), ensuring that the contact  77  Chapter 4: Non-Premixed Methane Autoignition Delay Study surface remains stationary and maximizing the experimental time. If the shock velocity across the interface is not equal, the driver gas pressure will be greater than the driven gas pressure, or vice versa, after the reflected shock passes through the interface, and the interface is said to be under-tailored or over-tailored, respectively. An under-tailored  interface causes the test pressure to rise steadily as the contact surface encroaches into the driven section gas, while an over-tailored interface causes the experimental pressure to decrease due to the contact surface moving away from the experimental section. Both cases are undesirable, and thus by altering the composition (He fraction) of the driver gas, its specific heat ratio is tailored to tune the speed of sound across the contact surface and thus ensure that the pressure difference across the interface is zero. The procedure for calculating required initial conditions to produce a tailored interface was well documented by Huang , and a slightly modified version of the numerical code written by Huang was 1  used in the present investigation. Incident shock velocities were calculated from the pressure traces from each of the three monitored dynamic pressure transducers by measuring the time interval between rising edges as the shock passed each successive transducer location (see Figure 4.2). Using the measured incident shock velocity and initial driven gas properties, the experimental pressure and temperature were calculated by assuming them to be equal to the conditions immediately behind the reflected shock (as calculated using isentropic shock relations ). 1,2  4  3.5 3 2.5 2 1.5 1 0.5 0  Pressure Transducer Signals y = 0.8296x +0.0183 R = 0.9998 2  2  ^  3  Time (ms)  *Note: Only 3 transducers are used for computing the incident shock velocity (versus 5 used in previous homogeneous studies) because 2 DAQ channels were required for injector control signal and optical ignition detection.  Figure 4.2: Incident Shock Velocity Measurement From Pressure Signals The ignition delay time was defined as the time interval between the start of injection, as measured by the injector control signal (and corrected to compensate for an inherent 180  78  Chapter 4: Non-Premixed Methane Autoignition Delay Study  \is delay in the injector driver), and the observance of CH and broadband light emissions. In cases where the onset of ignition was not easily identifiable from light emission signals, the intersection of a line tangent to the curve at its inflection point (maximum slope) with its initial baseline was used (see Figure 4.3). Such a definition has been previously used by other researchers in homogeneous autoignition studies and was employed throughout 4  the current investigation, with ignition measured independently from both broadband and CH band emissions signals.  Injection Duration Injection Signal  Injector Lag Time (180 us)  -4— Ignition D e l a y — • >' — Ignition Delay  —p  Optical (CH) Signal  r~  i \~y  Optical (BB) Signal  Figure 4.3: Ignition Definition From Optical Emissions Signals  4.4 Experimental Results The autoignition behaviour of non-premixed methane injected into shock-heated air differs from the behaviour of homogeneous mixtures due to the presence of a diffusion flame and therefore the effects of both chemical kinetics and fluid mechanics on the ignition times were investigated. These included studying the effects of experimental temperature and pressure (directly affecting chemical reaction rates) and also studying parameters influencing the turbulent jet, such as the injection duration and pressure ratio. The results of experimental investigations examining the influences of each of these parameters are presented below.  Chapter 4: Non-Premixed Methane Autoignition Delay Study  79  4.4.1 Autoignition Sensitivity to Fluid Mechanic Parameters The ignition delay time's fluid mechanic dependence was explored by varying the injection duration and pressure ratio at nominal experimental pressures of 17 and 31 bar. Injection durations between 0.5-5.0 ms and injection pressure ratios between 3-5 were chosen for investigation, as they represent typical diesel engine operating parameters. These test conditions are summarized in Table 4.1 with experimental data available in Appendix G. Table 4.1: Experimental Test Matrix (Non-Premixed Fluid Mechanic Parameter Study) Experimental Temperature: Experimental Pressure:  1000-1400 K 17-31 bar (nominal)  Injection Duration:  0.5-5.0 ms  Injection Pressure Ratio:  3-5 (nominal)  Injection Duration Sensitivity Injection duration (the time interval during which fuel injection occurs) was the first fluid mechanic parameter governing a transient jet's influence on the establishment of a diffusion flame to be investigated. Injection duration was initially speculated to have a potential influence on methane's autoignition behaviour by virtue of its fuel metering properties, control of overall mixture equivalence ratio, and cooling effects. Additionally, the transient nature of short-duration impulsive jets produces a direct flow field dependence on injection duration, which dictates the temporal evolution of temperature, species, and velocity gradients in the flow, which in turn influence the thermodynamic, kinetic, and transport processes necessary for autoignition. These effects were investigated at a constant experimental pressure of 31.2±0.8 bar and a temperature of 1107±7 K, with the injection pressure ratio maintained at 3.0±0.1. Results of all measured autoignition times at each investigated injection duration are presented in Figure 4.4, illustrating the presence of two distinct ignition regimes; one strongly dependent on injection duration, and another independent of the injection duration. Short injection durations (< -3.0 ms) exhibited a strong autoignition delay time dependence on injection duration, with decreased injection durations resulting in shorter ignition delay times, but long injection durations yielded autoignition delay times that were approximately independent of the injection duration. Additionally, in the injection duration-dependent regime, autoignition times increased nearly linearly with injection duration, with the shortest autoignition times quantitatively just slightly  Chapter 4: Non-Premixed Methane Autoignition Delay Study  80  longer than the premixed autoignition delay time of 1-1.2 ms measured at similar experimental conditions . 1  0.5  0  I 0  1  2  3  '  '  4  5  6  Injection Duration (ms)  Figure 4.4: Autoignition Injection Duration Sensitivity The presence of the threshold below which ignition delay times depend on injection duration and above which are independent of injection duration also coincides with two distinct ignition modes observed in each regime. For injection durations shorter than 3.0 ms, ignition occurred after the end of injection and in most cases produced clear optical emission signals that unambiguously identified ignition (refer to Figure 4.5 (a)). In contrast, for injection durations greater than 3.0 ms, ignition occurred during injection, but optical emissions signals consistently exhibited a gradual rise or a slight initial plateau, indicative of mild reactivity, followed by a sudden increase in combustion intensity near the end of injection or shortly thereafter (Figure 4.5 (b)). Both the presence of injection duration dependent and independent regimes and the approach to premixed autoignition times for short injection durations are explicable if one adopts the notion of a "kinetic" and "physical" component to ignition delay times as done by Bi and Agrawal . They defined a kinetic delay as the ignition delay time 44  component attributable to the chemical reaction and a physical delay as the portion attributable to the time necessary for the fuel and oxidant to mix and create a locally combustible mixture with a sufficiently favourable strain rate to facilitate autoignition.  Chapter 4: Non-Premixed Methane Autoignition Delay Study  81  Employing such a model, infinitesimally short injection durations would be expected to nearly instantly produce a combustible mixture (negligible mixing time scales) and the autoignition time should approach the kinetically-limited premixed autoignition delay time. At the opposite extreme, long injection durations reach a steady state after a fixed period of time (regardless of total injection duration) and only produce a combustible mixture once the physical delay is exceeded. Between each extreme, injection ceases prior to sufficient time elapsing to overcome the physical delay, but the sudden decrease in strain that occurs immediately at the end of injection rapidly reduces strain rates to levels that allow ignition. Hence, for short injection durations, autoignition occurs shortly after the end of injection and scales linearly with injection duration.  Injection Signal Ignition * ~ Delay  Optical (CH) Signal (a) Clearly Defined Autoignition Delay Typical of Short Injection Durations (< 3.0 ms)  Injection Signal  M—  Ignition Delay — • •V /  L  Optical (CH) Signal  (b) Mild Reactivity Preceding Autoignition Typical of Long Injection Durations (> 3.0 ms)  Figure 4.5: Characteristic Optical Ignition Signals Over Two Regimes  Chapter 4: Non-Premixed Methane Autoignition Delay Study  82  Furthermore the .observed qualitative differences between optical emissions signals may also be explained by considering the physical and kinetic components of the ignition delay time. The clearly defined optical emissions signals observed for short injection durations are characteristic of those seen in premixed ignition experiments in which an ignition kernel is formed and rapidly spreads. This similarity suggests a shared ignition mode, reinforcing the theory that kinetics dominate ignition for short injection durations. Likewise, the region of mild reactivity preceding ignition for long injection durations is analogous to the "Luminosity Threshold" observed by previous researchers studying steady-state counterflow diffusion flames  30,31  . In their study of  counterflowing cold methane and heated air, they described the luminosity threshold as a state where the mixture glows but does not rigorously burn. In particular they described it as a threshold, because as they gradually increased the temperature of the air jet, the luminosity threshold was defined as the threshold temperature above which luminescence was observed. Observation of a phenomenon analogous to a luminosity threshold in the present study suggests a shared ignition mode between steady-state counterflow jets and the current results for long injection durations. In addition to qualitative evidence presented herein of the transition from kineticallylimited to mixing-limited combustion, quantitative data also exists supporting such a theory. The recent work by Fotache et al., who investigated the ignition behaviour 30  of counterflow methane-air diffusion flames, affirmed that the flame kernel governing ignition in diffusion flames is essentially a premixed system and behaves similar to homogenous systems, just as qualitatively observed in the present investigation for short injection durations. Additionally, they stated the kernel width was proportional to the square root of the density weighted strain rate and through this relationship all convective-diffusive transport processes influence ignition. Increased strain rates decrease the kernel width and allow heat and many of the stable radicals involved in methane oxidation to convect or diffuse away from the ignition kernel. This explains the observed lack of ignition while injecting, as high strain rates present in the jet convect and diffuse away the heat and radicals necessary for the flame kernel to grow. Additionally, this phenomenon may possibly be responsible for the observed "Luminosity Threshold". As an initial homogenous flame kernel forms, it is inhibited from spreading and further igniting surrounding regions of the jet, giving rise to mild reactivity or multiple ignition/extinction cycles before ignition. Subsequently when injection ends, or sufficient time elapses to convect the flame kernel to a low strain  Chapter 4: Non-Premixed Methane Autoignition Delay Study  83  or high temperature region of the flow, the flame kernel is able to spread, and hence the observed abrupt increase in light emission (Figure 4.5 (b)). The counteracting influences of the chemical heat release and the convective and diffusive losses from the ignition kernel identified by Fotache et al. as dominant forces governing ignition in diffusion flames may be used in conjunction with Bi and Agrawal's concept of a kinetic and physical delay to explain the present dependence on injection duration. Injection Pressure Sensitivity Having identified the concepts of a kinetic and physical delay as being relevant to the present results and the importance of strain rate in the autoignition process by its promotion or inhibition of flame kernel growth, experiments were conducted to further investigate the effects of strain rate. However, since the strain in a turbulent jet cannot be controlled as it can in counterflow diffusion flame studies, the injection pressure ratio was varied instead. The intention being that increasing the injection pressure would yield a higher Reynolds number and the increased turbulence would produce higher mean strain rates. Several tests were conducted at an experimental pressure of 17.0±0.9 bar and a temperature of 1199±34 K, at each of two injection pressure ratios, 2.7±0.2 and 5.0±0.3, chosen for their diesel engine relevance. The result of varying the injection pressure ratio was negligible and no noticeable difference between each pressure ratio at each of several injection durations tested was observed (see Figure 4.6). This was caused by several factors including very large experimental uncertainties inherent in autoignition delay measurements that may mask any differences (note the large error bars on some data points in Figure 4.6), the relatively small difference between each of the pressure ratios tested, and a genuine autoignition delay independence from injection pressure. This latter point is the most noteworthy. Although increasing injection pressure certainly improves mixing between fuel and oxidant and may be beneficial in certain pollutant formation processes, it does not appear to reduce autoignition delays. Support for this finding is provided by the work of Mastorakos et al.  43  Mastorakos et al. addressed seemingly contradictory findings whereby experiments had shown that turbulence decreases ignition delay times while laminar flame theory suggests that higher strain rates associated with turbulence should prevent ignition and thus increase ignition delay times. Their work involved conducting numerical  Chapter 4: Non-Premixed Methane Autoignition Delay Study  84  « 1.0 m s Injection (PR=5) 1.0 m s Injection (PR=3)  0.70  0.75  0.80  0.85  0.90  0.95  1.00  lOOGrremperatiire (1000/K) * 1.5 m s Injection (PR=5) i> 1.5 m s Injection (PR=3)  0.70  0.75  0.80  0.85  0.90  0.95  1.00  1000/Temperature (1000/K) * 3.0 m s Injection (PR=5) o 3.0 m s Injection (PR=3)  0.70  0.75  0.80  0.85  0.90  0.95  1.00  1000/Temperature (1000/K)  Figure 4.6: Autoignition Injection Pressure Ratio Sensitivity  Chapter 4: Non-Premixed Methane Autoignition Delay Study  85  simulations of various mixing flows of cold (300 K) fuel and hot (1000-1100 K) air to identify the conditions that favoured early ignition. They discovered that ignition was initiated at several locations simultaneously and that these locations were all at the "most reactive" mixture fraction where scalar dissipation rate is lowest. Furthermore the most reactive mixture fraction was found to be in the fuel lean regions, believed to be due to higher temperatures in the lean region compensating for the reduced fuel concentration through the reaction rate's exponential temperature dependence. However, in addition to mixture fraction requirements, ignition was also conditional upon the lowest possible scalar dissipation. This conditional dependence on scalar dissipation rate offered an explanation as to why (1) partially premixed flows have been found to ignite earlier than non-premixed flows, and (2) turbulent flows ignite earlier than laminar ones. Partially premixing the fuel and air yields smaller mixture fraction gradients and hence lower scalar dissipation rates, while turbulence, with its many length and time scales and its chaotic nature creates regions of both very high and low scalar dissipation rate. The regions of unusually low scalar dissipation rate preferentially ignite and hence result in shorter ignition delay times than in laminar flows despite the higher mean strain. Additionally, since ignition in turbulent flows always occurs in regions of unusually low strain rate, and such regions are present regardless of the turbulence intensity, ignition delay time is independent of turbulent time scales. So their conclusion was that the turbulent length and time scales and partial premixing affect ignition by their effect on the conditional scalar dissipation rate. Applying the concepts presented above to the current experimental findings, it is not surprising that increasing the injection pressure ratio did not have any effect on the measured ignition delay times. Since the flow is already turbulent at the lower of the injection pressures investigated, increasing injection pressure further only increases the turbulence and has minimal impact on the conditional scalar dissipation rates in the flow. Certainly, if the injection pressure were increased excessively, a negative impact on the ignition delay times would be expected since then the turbulence may inhibit autoignition by dissipating any heat released in the combustion process so rapidly that any small flame kernels that are formed are immediately extinguished. However, for the injection pressure ratios presented here, no autoignition delay time dependence on injection pressure was observed.  Chapter 4: Non-Premixed Methane Autoignition Delay Study  86  4.4.2 Autoignition Sensitivity to Chemical Kinetic Parameters The ignition delay time's kinetic dependence was investigated by varying the experimental temperature and pressure behind the reflected shock wave. Temperatures between the ignition limit and 1400 K were investigated at two nominal experimental pressures (17 bar and 31 bar) chosen to correspond with conditions previously explored in premixed ignition studies to facilitate direct comparison with existing results. Additionally, given the injection duration dependence discussed above, several injection durations between 0.5-5.0 ms were investigated at each test condition. These experimental conditions are summarized in Table 4.2. Table 4.2: Experimental Test Matrix (Non-Premixed Chemical Kinetic Parameter Study) Experimental Temperature: Experimental Pressure:  1000-1400 K 17-31 bar (nominal)  Injection Duration:  0.5-5.0 ms  Injection Pressure Ratio:  3 (nominal)  Experimental (Air) Temperature Sensitivity Results of measured autoignition delay times conducted at 31.1±1.4 bar (including data from the previously discussed injection duration sensitivity study) are presented in Figure 4.7. This figure illustrates the expected temperature dependence, namely decreased ignition delay times with increased experimental (air) temperature. Also, in addition to the present experimental results, two additional curves are included in this figure plotting ignition delays measured by Huang in a previous homogeneous 1  ignition delay study conducted at similar experimental conditions. Although at first the ignition delay reduction with increased experimental temperature from 1100 K to 1400 K does not appear to be as large as that observed in premixed ignition delay studies (partly due to the logarithmic scale), the absolute magnitude of the reduction (~600 us) is nearly identical. This is not unexpected since increasing experimental temperatures accelerate chemical reactions and correspondingly reduce the kinetic component of the autoignition delay time. Since both non-premixed and premixed ignition delay times exhibit nearly identical reductions with increasing temperatures, this suggests that only the kinetic delay is affected by temperature. The qualitative agreement between the present non-premixed results and previous homogeneous ignition delay times thus reinforces the theory of a kinetic and physical component to non-premixed ignition delay times.  87  Chapter 4: Non-Premixed Methane Autoignition Delay Study  10  •  0.5 ms Injection (CH)  •  1.0 ms Injection (CH)  *  1.5 ms Injection (CH)  •  3.0 ms Injection (CH)  x  5.0 ms Injection (CH) Stoich Premixed Data  - - - Lean Premixed Data  0.1 0.70  0.75  0.80  0.85  0.90  0.95  1.00  1000/Temperature (1000/K)  Figure 4.7: Autoignition Temperature Sensitivity (31 bar) Furthermore, numerical simulations by Bi and Agrawal similarly concluded that the 44  kinetic delay decreases as temperatures are increased, but in addition they stated that the physical delay also exhibited a reduction at increased temperatures. While in the present study, the magnitude of the ignition delay reduction was found to be approximately equal to only the kinetic reduction (no additional reduction attributable to the physical delay was observed), any physical delay reduction may have simply been too small to detect given large experimental uncertainties. While the ignition delay time's kinetic component is greatly reduced by increased temperatures (due to the chemical reaction rate's exponential temperature dependence), no such reason exists suggesting that the physical delay should exhibit a similar dependence. If the physical component of the ignition delay time is reduced at elevated temperatures it must be attributable to the increased thermal gradients between the heated air and relatively cold fuel, which enhance heat and mass transfer. However, kinetics are far more strongly dependent on temperature than mixing rates are, and therefore the physical delay remains approximately constant. Experimental (Air) Pressure Sensitivity To further explore the ignition delay time's kinetic dependence, the tests presented above were repeated at a lower pressure of 16.8±1.0 bar to observe the influence of  Chapter 4: Non-Premixed Methane Autoignition Delay Study  88  the reduced pressure on ignition delay times and explore whether the temperature dependence observed at higher pressures was preserved at a lower test pressure. These results are presented in Figure 4.8 illustrating that the reduced experimental pressure had a minimal impact on the magnitude of the ignition delay times relative to the high-pressure results, but the pressure reduction greatly affected the ignition limit (the temperature below which ignition was no longer observed).  0.1  1  '  0.70  0.75  ' 0.80  0.85  0.90  1  0.95  1.00  1000/Temperature (1000/K)  Figure 4.8: Autoignition Temperature Sensitivity (17 bar) At similar temperatures, ignition delay times at each injection pressure were equal (within experimental uncertainty). This was not unexpected since minimal pressure dependence was observed in a previous homogenous ignition study , and Fotache 1  et al. indicate that the flame kernel governing diffusion flame's ignition behaves like 30  homogenous systems. However, previous homogeneous autoignition studies found that the ignition delay times increased slightly at lower pressure (due to the reduced reactant concentrations) while the present results do not exhibit any increase at all. In fact, a slight reduction is seen for some injection durations. While this apparent reduction is not fully understood, it is believed to be partially a manifestation of the luminosity threshold phenomenon observed at higher pressures. Fotache et al. in their investigation of counterflow diffusion flames indicated that the luminosity threshold approached the ignition temperature at elevated pressures, and  Chapter 4: Non-Premixed Methane Autoignition Delay Study  89  eventually vanished altogether. Therefore, while at higher pressures, the luminosity threshold was easily identifiable because its magnitude was small (vanishing with increased pressure) relative to the ignition signal, at the reduced pressure of 17 bar, the magnitude of this luminosity was comparable to that of ignition signals, and may have been mistakenly interpreted as ignition. This theory is supported by noting that short injection durations exhibited equal autoignition delay times at both pressures, suggesting pressure has a negligible effect on ignition delay, while longer injection durations coincide with the lower error bounds of the data presented in Figure 4.7. These lower error bounds identify the luminosity threshold and interestingly, even at 31 bar several data points from the long injection durations exhibited ignition delay times as short as those seen at 17 bar. This further suggests that at low pressures, and occasionally at higher pressures, the luminosity can be of comparable intensity to the ignition signal and hence cause the observed apparent reduction in ignition times. Figure 4.9 below illustrates this phenomena by plotting several realizations of the "luminosity threshold" to illustrate how the magnitude of the light emission can vary widely. Bearing in mind that the slight apparent ignition delay time reduction for long injection durations may thus not be genuine but simply due to luminescence, then ignition in non-premixed combustion is essentially independent (or extremely weakly dependent) on experimental pressure. It should be expected that the kinetic component of the ignition delay would be slightly reduced with elevated pressures based on previous homogeneous ignition delay results, but the physical delay would not experience any such reduction if the injection pressure ratio were preserved. To further clarify the negligible change, or perhaps even slight reduction, in ignition delay times at low pressure, ignition delay times measured at each of four injection durations are plotted in Figure 4.10. At each injection pressure, measured ignition delay times fall within experimental error of each other. For short injection durations (1.0 ms and 1.5 ms) the data points collected at 17 bar are scattered equally above and below the trend line plotted based on 31 bar data. At longer injection durations of 3.0 ms and 5.0 ms, the 17 bar data remains within experimental error of the 31 bar data's trendline, but is slightly biased towards shorter ignition delay times. This bias is attributed to the luminosity threshold effects discussed above. Aside from the negligible impact on ignition delay times, experimental pressure did exhibit a very strong effect on the ignition limit and quantitatively, the magnitude of  Chapter 4: Non-Premixed Methane Autoignition Delay Study  90  the ignition limit shift agreed well with that observed in lean premixed experiments. In the present tests, the ignition limit shifted approximately 70 K (from 1050 K at 31 bar to 1120 K at 17 bar), while a similar pressure reduction yielded a 70 K increase in the ignition limit in lean homogeneous autoignition experiments. In addition to the remarkable agreement between these two cases it is also significant to note that this behaviour is markedly different from the response of stoichiometric mixtures at the same pressures. Unlike the lean data, stoichiometric mixtures failed to demonstrate any ignition limit pressure dependence. This close agreement with lean premixed results lends further support to the belief that autoignition in non-premixed mixtures occurs in fuel-lean regions. Such dependence has also been expressed by Bi and Agrawal and Mastorakos et al. in previous simulations who all suggested ignition preferentially occurs in fuel-lean regions due to higher temperatures in these areas.  Figure 4.9: Differences in Luminosity Threshold with Pressure  Chapter 4: Non-Premixed Methane Autoignition Delay Study  91  * 1.0 ms Injection (31 bar) • 1.0 ms Injection (17 bar)  0.70  0.75  0.80  0.85  0.90  0.95  1.00  1000/Temperature (1000/K) (a) 1.0 ms Injection Duration  * 1.5 ms Injection (31 bar) A 1.5 ms Injection (17 bar)  0.70  0.75  0.80  0.85  0.90  0.95  1000/Temperature (1000/K) (b) 1.5 ms Injection Duration  Figure 4.10: Autoignition Pressure Sensitivity  1.00  Chapter 4: Non-Premixed Methane Autoignition Delay Study  92  * 3.0 ms Injection (31 bar) o 3.0 ms Injection (17 bar)  0.70  0.75  0.80  0.85  0.90  0.95  1.00  1000/Temperature (1000/K) (c) 3.0 ms Injection Duration  10 x 5.0 ms Injection (31 bar) o 5.0 ms Injection (17 bar)  E,  -T  E  J2  1  o  Q  cr  0.1 0.70  0.75  0.80  0.85  0.90  0.95  1000/Temperature (1000/K) (d) 5.0 ms Injection Duration  Figure 4.10: Autoignition Pressure Sensitivity cont'd.  1.00  93  Chapter 4: Non-Premixed Methane Autoignition Delay Study 4.4.3 Error A n a l y s i s  Throughout all current experiments, all error sources previously present in homogeneous autoignition studies were present (Appendix C), with the exception of the error associated with ignition delay measurements and uncertainty in driven gas compositions. Uncertainty in ignition delay times attributable to ambiguous pressure traces in homogeneous ignition delay experiments was replaced by errors associated with ambiguous optical emissions signals, and although uncertainty in the driven gas composition was eliminated since the driven gas was now pure bottled air (eliminating errors in preparing the gas composition manometrically), leakage through the injector yielded uncertainty in the fuel injected. Ignition Delay Time Error Ignition delay time errors were primarily associated with the frequent uncertainty in identifying the onset of ignition from light emission signals. Several typical ignition signals are presented in Figure 4.11 to illustrate how upper and lower bounds were defined in such cases.  To  Mild Reactivity Preceding Ignition  Figure 4.11: Characteristic Optical Emission Signals Over Three Ignition Regimes In cases where ignition was very well defined and the optical emission signals were strong, minimal errors were introduced, and were on average approximately ±0.080  Chapter 4: Non-Premixed Methane Autoignition Delay Study  94  ms (Figure 4.11 (a)). When the ignition signal was preceded by weak light emission the lower error bound was defined as the time when the initial weak light emission occurred and upper bounds defined as the time when a slope change was observed in the light emission intensity, signalling a change from mild reactivity to much more rigorous burning (Figure 4.11 (b)). As a result, no quantitative mean error could be defined, since this varied widely from case to case. Finally, when optical emissions signals exhibited a very gradual rise (Figure 4.11 (c)) upper and lower error bounds were defined as shown, with average errors typically in the range of ±0.100 ms to ±0.400 ms. Fuel Mass Flow Error Uncertainty in the quantity of fuel present (due to leakage) produced no quantifiable effect on measured ignition delay times, but contributed to qualitative uncertainty in analysing the effects of injection durations. Despite previous characterization of the J41 injector used in the present investigation demonstrating a constant fuel mass flux regardless of injection duration (±10%), the effects of any fuel leakage prior to injection are not easily quantified. Though a leakage mitigation system was installed upstream of the fuel injector (Figure 4.1), the injector remained in a charged state for typically 200-800 ms prior to injection. Throughout this time, fuel leakage into the shock tube created a cloud of partially premixed fuel and air in the vicinity of the injector nozzle, which may have had the net effect of promoting ignition. It has been shown by previous researchers (and discussed in this investigation) that partially 43  premixing fuel and oxidant promotes ignition by reducing mixture fraction gradients in the flow. The effect of any leakage through the injector would produce precisely such an effect and, while extremely desirable if effective in reducing ignition delay times, this effect introduced an unquantifiable degree of uncertainty throughout all experimental results.  4.4.4 Autoignition Visualization While identifying the ignition delay time dependence on both kinetic and fluid mechanic parameters of interest, extensive reliance on concepts presented by Bi and Agrawal and 44  Mastorakos et al. was necessary. While the ignition delay data seemed to corroborate 43  those theories, many of the concepts they discussed were unrelated to the ignition delay itself, but rather focussed on the ignition location (fuel lean regions, multiple simultaneous  Chapter 4: Non-Premixed Methane Autoignition Delay Study  95  ignition sites, etc.). So to further explore the present interpretation of theories put forth by previous researchers, autoignition delay experiments were conducted with an optical test section in place to facilitate capturing high-resolution digital images of the ignition event at various stages in the autoignition process. Experiments were conducted at a pressure of 6 bar (nominal), with temperatures between 1250-1400 K (1250 K was determined to be the ignition limit at this pressure), and injection durations between 1.0-5.0 ms. These test conditions are summarized in Table 4.3 with digital images available in Appendix H. Table 4.3: Experimental Test Matrix (Autoignition Visualization Study) Experimental Temperature: Experimental Pressure:  1250-1400 K 6 bar (nominal)  Injection Duration:  1.0-5.0 ms  Injection Pressure Ratio:  4 (nominal)  Apparatus Modifications To facilitate high-speed digital photography of autoignition events, the experimental apparatus in Figure 4.1 was modified with the addition of an optical test section at the end of the driven section. The optical test section contained three fused quartz windows (for observing ignition events in the shock tube) and one instrumentation window (for mounting a pair of pressure transducers). Figure 4.12 illustrates this modified setup, with detailed drawings of the optical test section itself available in Appendix J. The addition of an optical test section lengthened the driven section by 0.54 m, thus resulting in a total shock tube length of 7.90 m (3.11 m driver section, 4.79 m driven section). With the addition of the optical test section, light emission signals could no longer be detected from the driven section endplate, since it could no longer accommodate a window and fibreoptic cable. Instead a fibreoptic cable was mounted up against one of the three large quartz windows along the sides of the test section. Although there was initial concern whether such an arrangement was capable of detecting any light emitted downstream of the fibreoptic cables' location, this was not found to be a problem. Additionally, since previous tests had demonstrated excellent agreement between CH and broadband optical emissions, only CH band emissions were used for detecting ignition, as the fibreoptic cable previously used for detecting broadband light was required by the Schlieren imaging system.  Chapter 4: Non-Premixed Methane Autoignition Delay Study  96  Manual Valve Solenoid Valve  Injector  Pressure Transducers  4  Adaptor Clamping Plates (4)  |j  »" •  ^  Rubber Gaskets (4)  '  Instrumentation Window  .  Ji>  Injector Control System cope ^  l n j e c t o r T r i 9 9 e r :  T  u  j  Photomultiplier  Driver Section  ^>  Vacuum Pump  EBBED Solenoid Delay Circuit  r 4  He  Dry Air  Figure 4.12: Experimental Apparatus (Autoignition Visualization Study) A Schlieren imaging system was assembled to facilitate visualization of the gaseous jet within the test section. This system was adapted from the one previously used for investigating the jet characteristics of the injector used in the current tests (refer to Chapter 3 for component descriptions). However, space limitations prevented the use of that system in its original configuration, so a modified version was developed to reduce its size (total distance between lenses and mirrors - refer to Figure 4.13). This modified Schlieren system focussed the light from a 200 W mercury arc lamp onto the end of a 0.5 mm diameter fibreoptic cable. This fibreoptic cable replaced a pinhole and allowed both the arc lamp and focussing lens to be located off-axis from the mirrors and lenses used to produce a parallel light beam. The light transmitted through the fibreoptic cable was passed through a 15.24 cm (6 in) diameter double convex lens with a 43.18 cm (17 in) focal length to produce a parallel light beam to pass through the test section's quartz windows. Additionally, to further minimize the  Chapter 4: Non-Premixed Methane Autoignition Delay Study  97  system's total length, rather than having a second converging lens on the opposing side of the test section to focus the parallel light onto a camera, a mirror was used. The mirror reflected the parallel beam back through the test section and through the convex lens, focussing the Schlieren image immediately adjacent to the fibreoptic cable. Although the use of such a fibre optic cable is unconventional for Schlieren systems, passing the parallel light beam through the test section twice and using the same lens to both produce the parallel light and focus the Schlieren image has been previously used successfully by others . 45  Digital Camera  Converging Lens  Plane Mirror  Pinhole Test Section Placed Here  Fibreoptic Cable  Mercury Arc Lamp and Focussing Lens  Distance from pinhole to lens: 0.432 m (17 in) Distance from lens to mirror: 0.254 m (10 in)  Figure 4.13: Compact Schlieren System Schematic Finally, since the circular parallel light beam was cropped as it passing through the rectangular quartz windows, the focussed image was correspondingly rectangular, not circular. Therefore, instead of using an aperture to resolve density gradients in all directions (as previously done when testing the injector) or using as a single knife edge to resolve density gradients perpendicular to the knife edge (as in conventional Schlieren systems) a rectangular aperture was created. This consisted of four knife edges that could be independently adjusted to "frame" the focussed image, allowing density gradients in two orthogonal directions to be resolved. The resulting image was photographed with a Kodak Megaplus ES 1.0 camera previously described in Chapter 3. To compensate for any foreign particles on the quartz windows, mirror, and lens, or non-uniformities introduced by the arc lamp, two images were captured during each  Chapter 4: Non-Premixed Methane Autoignition Delay Study  98  experiment; one before and one during ignition. Subsequently the "ignition" image was filtered to compensate for irregularities by using the initial image as a mask. In Figure 4.14 several examples are presented illustrating the initial "baseline" image, the second "ignition" image, and the final filtered image. Finally, to further highlight observed light intensity gradients in the flow, the greyscale intensities were mapped onto a colour scale. It should be emphasized that the colours presented in these figures simply represent a linear colour mapping of the original greyscale intensities and are not necessarily representative of any physical parameter.  Figure 4.14: Autoignition Visualization Image Post-Processing Examples Schlieren Photography Schlieren imaging of the autoignition process did not yield any quantitative results but did provide some further evidence supporting the theories presented throughout the discussion of the autoignition delay time data. In order to interpret these images reacting jets were first compared to equivalent non-reacting jets previously studied in Chapter 3. Several images of the reacting jet before the onset of combustion (i.e. before any reaction) indicate close agreement between the reacting jet and the nonreacting jet and are presented in Figure 4.15, which presents the reacting jet before ignition began alongside images of a non-reacting jet of same injection duration and injection pressure ratio. These illustrate that the jet penetration length and length to width ratio were qualitatively identical. In addition, close agreement was observed between the potential core length of the reacting and non-reacting jets, the location of high turbulence regions, the vortex ball location, and other qualitatively features. Interestingly, regions of the non-reacting jet that exhibited high turbulence intensity are nearly indistinguishable in the "reacting" jet images even before ignition. This illustrates the thorough mixing of fuel and oxidant that occurs in these regions.  Chapter 4: Non-Premixed Methane Autoignition Delay Study  99  Rigorous mixing in vortex ball (a) Cold Jet at t = 0.3 ms, Hot Jet at t = 0.35 ms  (c) Cold Jet at t = 1.9 ms, Hot Jet at t = 1.87 ms  Figure 4.15: Comparison of Hot and Cold Jets Since the regions in the non-reacting jet where high turbulence intensity and many eddies were observed correspond to regions of the reacting flow that are identical to "hot air" regions, this implies that thorough mixing and/or ignition was occurring in these areas. The images suggest ignition may be occurring in the ball vortex region of the jet that is relatively lean and hot due to extensive mixing and then spreading towards the injector nozzle (as evidenced by decreasing length of the cold jet region in the sequence of images in Figure 4.16). However, when comparing the reacting jet images captured during ignition (Figure 4.16) with those captured prior to ignition (Figure 4.15) little difference is observed in the ball vortex region. As a consequence of the external illumination (necessary to see the jet), it is unclear whether ignition is occurring in the ball vortex or if the hot air and cold fuel are simply very well mixed. Certainly, the two are not unrelated, since mixing is a prerequisite for ignition, but Schlieren images alone cannot conclusively prove that ignition is initiated in the ball vortex region since the external illumination source caused well-mixed regions and reacting regions to appear identical.  Chapter 4: Non-Premixed Methane Autoignition Delay Study  100  Figure 4.16: Reacting Jet Schlieren Images at Various Ignition Stages *Note: CH emissions plotted along the left with a square wave indicating the camera trigger time. Vertical white bar in each image indicates approximate location of jet tip.  Self-Illuminated Photography Given the difficulties encountered in distinguishing between well-mixed regions and ignition based solely on Schlieren images, additional experiments were conducted without external illumination. In these cases, the jet and other flow phenomena were invisible, and thus the only light detected was that caused by ignition. Several of the captured images are presented in Figure 4.17. The images in Figure 4.17 conclusively illustrate that autoignition does begin in the ball vortex region of the jet, not near the nozzle, or along the edges of the steady-  Chapter 4: Non-Premixed Methane Autoignition Delay Study  Dark  Light Intensity Scale  101  Light  Figure 4.17: Reacting Jet Self-Illuminated Images at Various Ignition Stages *Note: CH emissions plotted along the left with a square wave indicating the camera trigger time. Vertical white bar in each image indicates approximate location of jet tip.  Chapter 4: Non-Premixed Methane Autoignition Delay Study  f02  state self-similar portion of the jet. Although none of the images captured the start of ignition, the sequence shown clearly suggests ignition preferentially occurs in or around the ball vortex and then gradually spreads towards the injector nozzle. Such an ignition process is corroborated by the numerical simulations of Bi and Agrawal  44  who indicated autoignition preferentially occurs in the fuel-lean regions of the flow. Additionally, Bi and Agrawal's work suggested several ignition phenomena including the presence of multiple simultaneous ignition sites, the ignition sites moving closer to the nozzle at elevated temperatures, and the ignition originating from hot spots in the free jet that are convected downstream. Similarly, the present experiments seem to indicate similar trends. Several of the images in Figure 4.17 suggest multiple "hot spots" or ignition initiation sites, and collectively the sequence of images definitively shows autoignition occurring around the ball vortex of the jet and then spreading towards the nozzle. Although little more than such qualitative observations can be made from such images, the agreement between the ignition initiation location and growth presently observed and the mechanism described by Bi and Agrawal in their numerical work lends further support to the inferences that were drawn in analysing the autoignition delay time data.  4.5 Conclusions and Recommendations The present investigation of both the chemical kinetic and fluid mechanic parameters governing the autoignition behaviour of gaseous methane injected into shock-heated air at diesel enginerelevant conditions has led to the following observed dependencies: 1. Autoignition behaviour was found to correspond well with the concept of a kinetic and physical component to ignition delay times. The kinetic component, due to chemical reaction rates, governs the ignition delay time's response to experimental temperature and pressure, while the physical component, due to mixing, dictates the ignition delay time's response to flow parameters including the injection duration, strain rate, and partial premixing. 2. Injection duration and ignition delay times exhibited a linear relationship for injection durations less than 3.0 ms and were independent for longer injections. This behaviour was attributed to the physical component of the ignition delay time as excessive strain in the flow inhibits ignition until the end of injection or until a locally combustible pocket  Chapter 4: Non-Premixed Methane Autoignition Delay Study  103  is convected sufficiently far downstream into a low strain/high temperature region. This suggests use of pulsed injection could yield short ignition delay times when delivering the same quantity of fuel as a single, longer injection as multiple short injections may ignite faster than one long injection. 3. Injection pressure was observed to have a negligible effect on autoignition delay times and was not unexpected since previous numerical research had shown ignition occurs at a "most reactive" mixture fraction where the scalar dissipation rate is lowest. Since increasing the injection pressure has no effect on the conditional mixture fraction and scalar dissipation rate dependence, no increase/decrease in ignition delay times was observed. High injection pressures therefore do not reduce autoignition delay times directly, but may be useful in increasing fuel delivery rates and therefore may indirectly reduce autoignition delay times by reducing required injection durations. 4. Air temperature was found to influence autoignition delay times identically to the way it affected lean homogenous methane/air mixtures. Increasing air temperatures reduced ignition delay times by a magnitude equal to the reduction observed in lean premixed mixtures over the same temperature range. This effect was attributed to the reduction in the kinetic component of the ignition delay time that occurs as the air temperature is increased. Additionally, the close agreement between the ignition limit shift observed between the current results and previous lean homogenous mixtures suggests ignition preferentially occurs in lean regions of the flow. 5. Air pressure had a negligible effect on ignition delay times but dramatically affected the lowest temperature at which ignition was possible, with higher pressures having a lower ignition limit. Also, the magnitude of the ignition limit shift was identical to that observed for lean homogenous mixtures, further supporting the theory that ignition in gaseous jets preferentially occurs in fuel-lean regions. 6. Images of the autoignition process confirmed that ignition initiates in the fuel-lean ball vortex region of the flow. These images illustrated multiple simultaneous ignition sites and provided evidence indicating that ignition occurs along the edges of the ball vortex and then gradually spreads towards the injector nozzle. This finding is significant as it both confirms theories suggested by previous researchers and suggests increasing the mixing rate (reducing the time necessary to form a lean mixture) could effectively reduce ignition delay times.  Chapter 5: Conclusions and Recommendations  104  Conclusions and Recommendations The current three-phase investigation of methane's autoignition behaviour under diesel enginerelevant conditions has included a numerical and experimental study of homogeneous methane autoignition delay times, characterization of a fuel injector for methane injection in non-premixed autoignition studies, and a hon-premixed methane autoignition delay time study. Several of the most noteworthy findings from each study are summarized below: 1. The homogeneous methane autoignition delay time study illustrated the importance of using a consistent method for detecting and defining ignition in both experimental and numerical studies. A large portion of the observed discrepancies between previous researchers' results and correlations was attributed to the multitude of different ignition definitions used. In addition, the importance of using a variable activation energy over different experimental temperature regimes was illustrated by the inability of existing correlations to predict a distinct activation energy change observed at a temperature of approximately 1550 K. 2. The injector characterization study quantified the presence of a 180±20 us delay in the injector driver that must be accounted for to ensure proper injection timing, proposed several numerical models for predicting mass flows and exit conditions at the injector nozzle given only the fuel reservoir state, and verified the injector's ability to operate in a pulsed injection mode. Additionally, Schlieren visualization of the jet produced by the injector under a variety of operating conditions demonstrated the self-similarity of the jet and its close agreement with existing scaling laws. The effects of jet impingement onto objects of various geometries were also illustrated, showing that the penetration length and/or turbulence intensity of the jet could be controlled by varying the distance from the nozzle to the obstruction, and the effects of an enclosure on the transient jet's development were demonstrated to be negligible. 3. The non-premixed methane autoignition delay time study coupled the kinetics studied in the homogeneous autoignition delay time study with the jet fluid mechanics from the  Chapter 5: Conclusions and Recommendations  105  injector characterization study. This led to the finding that kinetic and fluid mechanic parameters influence the autoignition behaviour independently, and thus autoignition delay times can be split into their "kinetic" and "physical" components. Experimental temperatures and pressures affect autoignition delay times through their influence on the kinetic component identically to the manner in which homogeneous ignition times respond to similar temperature/pressure changes. The injection duration affects the physical component of ignition delay times, delaying autoignition until near the end of injection for long injection durations and exhibiting a linear relationship on autoignition times for short injections, with an asymptotic approach to homogeneous autoignition delay times as the injection duration is reduced. Moreover, these experiments agreed well with previous numerical simulations that suggested ignition preferentially occurs in fuel-lean regions of the flow. This was confirmed by capturing images of the ignition process, which clearly illustrated ignition occurring in the fuel-lean ball vortex of the jet. Following the initial intent of the present investigation, which was to discover potential strategies for reducing methane's prohibitively long autoignition delay time, the following potential ignition delay reduction strategies have emerged and warrant future investigation: 1. High-pressure injection. Although non-premixed autoignition delay time experiments showed no ignition delay reduction with increased injection pressure, the injector characterization study indicated increasing the injection pressure increases the mass flux and thus a shorter injection duration at a high injection pressure could deliver the same quantity of fuel as a longer injection duration at a low pressure. Therefore, this may achieve an ignition delay time reduction by virtue of its reduced injection duration. Additionally, increased injection pressure may be beneficial for pollutant formation processes not investigated in the present study. 2. Partial premixing. Leakage from the injector used in the present study was observed to act as an ignition promoter under certain conditions and numerical simulations have previously indicated that partial premixing of fuel and oxidant is beneficial for ignition promotion through its influence on reducing mixture fraction gradients. Therefore, if the "leakage" can be controlled, partially premixing or stratifying the fuel may reduce autoignition delay times. 3. Pulsed injection. Since effects of injection duration were so pronounced in reducing ignition delay times, using pulsed injection to deliver the desired quantity of fuel over  Chapter 5: Conclusions and Recommendations  106  multiple short injections rather than one long injection may reduce ignition delay times. The injector characterization study showed such a control strategy could be readily implemented using existing hardware and furthermore pulsed injection operation had no adverse impact on the jet's penetration length and width. 4. High-pressure, partially premixed, pulsed direct injection. Finally, given the present understanding of the effects of high-pressure injection at increasing fuel mass fluxes, partial premixing at reducing spatial mixture fraction gradients, and pulsed injection at creating regions of favourable strain, combining all three into a high-pressure, partially premixed, pulsed direct injection system should also be investigated as a potential ignition delay time reduction strategy for diesel engines. To proceed with implementing the above autoignition delay reduction strategies, the following work remains to be conducted: 1. Replace (or repair) the existing injector to eliminate the large uncertainties currently attributed to leakage. This should be the first priority before conducting any further non-premixed experiments! 2. Repeat the injection duration study (particularly for short injections that exhibited an injection duration dependence) and injection pressure ratio sensitivity experiments with a properly sealing injector to verify that the observed trends are not simply a byproduct of leakage effects. 3. Explore pulsed injection by investigating the effects of pulse duration, pulse width, and equal or unequal injection pulse widths on autoignition delay times. 4. Quantify the effects of partial premixing by conducting autoignition experiments with the shock tube's driven section filled with a lean mixture of methane and air (instead of pure air) and comparing autoignition delay times to non-premixed results. 5. 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S., "The Starting Plume in Neutral Surroundings", Journal of Fluid Mechanics, Vol.  13, p. 356, 1962. 21  Abramovich, S., and Solan, A., "The Initial Development of a Submerged Laminar Round Jet",  Journal of Fluid Mechanics, Vol. 59, p. 791,1973. 2 2  Boyan, X., and Furuyama, M., "Jet Characteristics of CNG Injector with MPI System", JSAE  Review, Vol. 19, p. 229, 1998. 2 3  Jenkins, R. M., Foster, W. A.-Jr., and Wirth, L. S., "Numerical Analysis of Unsteady Multiple  Jet Plume Interactions", Applied Mathematics and Computation, Vol. 79, p. 239, 1996. 2 4  Murase, E., Ono, S., Hanada, K., Nakahara, S., Endo, H., and Oppenheim, A. K.,  "Comparative Study of Pulsed Jet Ignition", JSAE Review, Vol. 13, p. 18, 1992. 2 5  Ishii, R., Fujimoto, H., Hatta, N., and Umeda, Y., "Experimental and Numerical Analysis of  , Circular Pulse Jets", Journal of Fluid Mechanics, Vol. 392, p. 129, 1999. 2 6  Donaldson, C. P. and Snedeker, R. S., "A Study of Free Jet Impingement. Part 1. Mean  Properties of Free and Impinging Jets", Journal of Fluid Mechanics, Vol. 45, p. 281, 1971.  References  2 7  109  Donaldson, C. D., Snedeker, R. S., and Margolis, D. P., "A Study of Free Jet Impingement.  Part 2. Free Jet Turbulent Structure and Impingement Heat Transfer", Journal of Fluid Mechanics, Vol. 45, p. 477,1971. 2 8  Looney, M. K. and Walsh, J . J., "Mean-Flow and Turbulent Characteristics of Free and  Impinging Jet Flows", Journal of Fluid Mechanics, Vol. 147, p. 397, 1984. 2 9  Krothapalli, A., Rajkuperan, E., A M , F., and Lourenco, L , "Flow Field and Noise  Characteristics of a Supersonic Impinging Jet", Journal of Fluid Mechanics, Vol. 392, p. 155, 1999. 3 0  Fotache, C. G., Kreutz, T. G., and Law, C. K., "Ignition of Counterflowing Methane versus  Heated Air under Reduced and Elevated Pressures", Combustion and Flame, Vol. 108, p. 442, 1997. 31  Fotache, C. G., Wang, H., and Law, C. K., "Ignition of Ethane, Propane, and Butane in  Counterflow Jets of Cold Fuel versus Hot Air Under Variable Pressures", Combustion and Flame, Vol. 117, p. 777, 1999. 32  Starner, S. H., and Bilger, R. W., "Mixture Fraction Imaging in a Lifted Methane Jet Flame",  Combustion and Flame, Vol. 107, p. 307, 1996. 33  Everest, D. A., Driscoll, J . F., Dahm, W. J. A., and Feikema, D. A., "Images of the Two-  Dimensional Field and Temperature Gradients to Quantify Mixing Rates within a Non-Premixed Turbulent Jet Flame", Combustion and Flame, Vol. 101, p. 58,1995. 34  Rolon, J . C , Aguerre, F., and Candel, S., "Experiments on the Interaction between a Vortex  and a Strained Diffusion Flame", Combustion and Flame, Vol. 100, p. 422, 1995. 3 5  Phillips, H., "Ignition in a Transient Turbulent Jet of Hot Inert Gas", Combustion and Flame,  Vol. 19, p. 187, 1972. 3 6  Peters, N., "Laminar Flamelet Diffusion Models in Non-Premixed Turbulent Combustion",  Progress in Energy and Combustion Science, Vol. 10, p. 319,1984. 37  Pitsch, H., and Peters, N., "A Consistent Flamelet Formulation for Non-Premixed Combustion  Considering Differential Diffusion Effects", Combustion and Flame, Vol. 114, p. 26, 1998. 3 8  Chan, S. H., Pan, X. C , and Abou-Ellail, M. M., "Flamelet Structure of Radiating CH -Air 4  Flames", Combustion and Flame, Vol. 102, p. 438, 1995.  References  3 9  110  Chan, S. H., Yin, J . Q., and Shi, B. J., "Structure and Extinction of Methane-Air Flamelet with  Radiation and Detailed Chemical Kinetic Mechanism", Combustion and Flame, Vol. 112, p. 445, 1998. 4 0  Yoshida, A., Igarashi, T., and Kotani, Y., "Extinction of Turbulent Diffusion Flames by  Kolmogorov Microscale Turbulence", Combustion and Flame, Vol. 109, p. 669, 1997. 41  Seshadri, K., and Peters, N., "Asymptotic Structure and Extinction of Methane-Air Diffusion  Flames", Combustion and Flame, Vol. 73, p. 23, 1988. 4 2  Im, H. G. and Chen, J . H., "Chemical Response of Methane/Air Diffusion Flames to Unsteady  Strain Rate", Combustion and Flame, Vol. 118, p. 204,1999. 4 3  Mastorakos, E., Baritaud, T. A., and Poinsot, T. J., "Numerical Simulations of Autoignition in  Turbulent Mixing Flows", Combustion and Flame, Vol. 109, p. 198, 1997. 4 4  Bi, H., and Agrawal, A. K., "Study of Autoignition of Natural Gas in Diesel Environments Using  Computational Fluid Dynamics with Detailed Chemical Kinetics", Combustion and Flame, Vol. 113, p. 289, 1998. 4 5  Holder, D. W., and North, R. J., "Notes on Applied Science No. 31: Schlieren Methods", Her  Majesty's Stationary Office, 1963.  111  Appendix A: Vacuum Sensor Calibration Data  Vacuum Sensor Calibration Data  A.1 Driven Section Pressure Transducer The Auto Tran 600D-117 vacuum sensor used to measure driven gas pressure was calibrated against an Oakton® Aneroid barometer, yielding extremely repeatable results (as is illustrated in Table A.1). The average slope of all calibrations was -2.997 psiA/ with a standard deviation of 0.002 psiA/, agreeing well with the manufacturer's value of -3 psiA/. Table A.1: Vacuum Sensor Calibration Atmospheric Pressure (V) (bar) (psi) 1.014 1.019 1.019 1.017 1.018 1.018 1.019 1.018 1.019 1.018 1.017 1.015 1.016 1.016 1.016 1.016 1.015 1.016 1.014 1.015 1.015 1.016 1.016 1.015 1.015 1.015  1.010 1.014 1.014 1.001 1.001 1.002 1.002 0.995 0.994 0.997 0.995 1.010 1.012 1.015 1.016 1.029 1.000 1.000 0.997 0.991 0.993 0.994 0.997 1.013 1.014 1.015  14.649 14.707 14.707 14.518 14.518 14.533 14.533 14.431 14.417 14.460 14.431 14.649 14.678 14.721 14.736 14.924 14.504 14.504 14.460 14.373 14.402 14.417 14.460 14.692 14.707 14.721  Vacuum Pressure (V) (bar) 5.90 5.93 5.93 5.86 5.87 5.87 5.87 5.83 5.83 5.84 5.83 5.90 5.91 5.93 5.93 5.99 5.85 5.85 5.84 5.81 5.82 5.83 5.84 5.92 5.93 5.93  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  Regression (psiA/) (barA/) -2.998 -2.995 -2.995 -2.998 -2.992 -2.995 -2.996 -2.999 -2.997 -2.999 -2.998 -2.999 -2.999 -2.999 -2.999 -3.000 -3.000 -3.000 -2.996 -2.998 -2.997 -2.995 -2.998 -2.995 -2.992 -2.995  -0.207 -0.206 -0.206 -0.207 -0.206 -0.207 -0.207 -0.207 -0.207 -0.207 -0.207 -0.207 -0.207 -0.207 -0.207 -0.207 -0.207 -0.207 -0.207 -0.207 -0.207 -0.206 -0.207 -0.207 -0.206 -0.207  112  Appendix A: Vacuum Sensor Calibration Data Table A.1: Vacuum Sensor Calibration cont'd. Atmospheric Pressure (bar) v (psi)  (.015 ) .014 .015 .015 .015 .015 .014 .015 .015  1.015 1.004 1.004 1.003 1.003 1.003 1.023 1.018 1.016  14.721 14.562 14:562 14.547 14.547 14.547 14.837 14.765 14.736  Vacuum Pressure (bar) (V) 5.93 5.87 5.87 5.87 5.87 5.87 5.96 5.94 5.93  0 0 0 0 0 0 0 0 0  Regression (bar/V) (psi/V) -2.995 -2.999 -2.999 -2.996 -2.996 -2.996 -3.000 -2.998 -2.998  -0.207 -0.207 -0.207 -0.207 -0.207 -0.207 -0.207 -0.207 -0.207  A.2 Driver Section Pressure Transducer The Eclipse® high-pressure sensor used for measuring driver section gas pressures was not calibrated since it was not used directly in any ignition delay studies (only used for estimating diaphragm burst pressure). However, a discrepancy was discovered between the manufacturersupplied conversion factor and the one currently used. The manufacturer indicates that the equation for converting measured voltages to pressures is: P(psi) = 1250*(V-0.5) but the equation currently being used is: P(psi) = 1200*(V-V ) 0  where V is determined by measuring the transducer output voltage at atmospheric pressure 0  prior to each experiment (pseudo-calibration) and was found to have an average value of 0.4632 V with a standard deviation of 0.0006 V over the course of the present experimental study. Throughout all experiments, the latter equation using the pseudo-calibration constant was used.  Appendix B: Homogeneous Autoignition Delay Data  113  Homogeneous Autoignition Delay Data Table B.1: Homogeneous Autoignition Delay Data V02  0.637 0.609 0.857 0.857 0.962 0.962 0.927 0.727 0.727 0.608 0.608 0.727 0.823 0.790 0.790 0.857 0.926 0.926 0.857 0.608 0.667 0.857 0.608 0.927 0.963 0.667 0.667 0.823 0.823 0.824  0.242 0.260 0.095 0.095 0.026 0.025 0.049 0.182 0.182 0.262 0.261 0.182 0.118 0.140 0.140 0.096 0.049 0.049 0.095 0.261 0.222 0.095 0.261 0.049 0.025 0.222 0.222 0.118 0.118 0.118  YCH4  EQR  0.121 0.999 0.131 1.002 0.048 1.000 0.048 1.000 0.013 0.980 0.013 1.000 0.025 1.020 0.091 1.004 0.091 1.000 0.130 0.993 0.130 0.998 0.091 1.002 0.059 1.004 0.070 1.000 0.070 0.997 0.047 0.990 0.025 1.000 0.025 ' 1.000 0.048 1.000 0.130 0.998 0.111 0.998 0.048 1.019 0.131 1.002 0.024 0.990 0.012 1.000 0.111 0.998 0.111 0.998 0.059 1.000 0.059 0.996 0.059 1.000  P Driven  P Driver  (psia)  (psia)  nominal  upper  1.109 1.107 1.198 1.199 1.200 1.199 1.199 1.185 1.170 1.529 1.500 1.500 1.470 1.498 1.499 1.499 1.497 1.469 1.018 1.795 1.797 1.198 1.199 1.500 0.989 1.199 1.199 1.500 1.499 1.499  135.85 30.12 42.13 48.02 58.86 58.83 83.05 73.48 67.52 57.94 41.32 48.10 48.10 36.06 70.77 58.80 67.22 61.26 68.69 60.31 62.72 61.52 58.96 61.36 60.15 34.95 68.55 68.84 43.56 90.34  0.3  PTest  TTest  lower  (bar)  (K)  0.426  0.24  0.972 1.02 0.582  1.488 1.104 0.642  0.882 0.96 0.522  0.732 0.504 0.612 0.612 1.386 1.23 1.272  0.792 0.828 1.578 1.248 1.446 1.29 1.472  0.672 0.444 0.552 0.432 1.326 1.17 1.072  0.498 1.086 1.146 1.482 0.738 0.96  1.032 1.146 1.26 1.77 0.876 1.134  0.438 1.026 0.99 1.422 0.66 0.9  0.81 0.63 1.452 0.378 2.412 0.36  1.23 1.071 1.56 0.438 2.472 0.714  0.75 0.57 1.116 0.306 2.352 0.3  6.65 2.414 2.857 3.044 3.415 3.294 3.637 3.865 3.263 3.586 3.26 3.416 3.243 2.589 4.254 3.748 4.022 3.65 3.394 4.152 4.224 3.417 3.536 3.746 3.201 2.58 3.981 1.512 3.252 7.787  1935 1103 1421 1475 1813 1769 1794 1491 1369 1143 1102 1229 1315 1120 1468 1462 1658 1581 1738 1135 1192 1578 1281 1587 1981 1141 1428 874 1302 2212  T  (ms)  1.494 1.614 1.374 0.01754 0.10754 0.00054  Appendix C: Homogeneous Autoignition Delay Error Analysis  114  Homogeneous Autoignition Delay Error Analysis C.1 Autoignition Delay Time Error Ignition delay time errors have been discussed in the body of this thesis. These are principally due to ambiguities in the pressure traces that made identifying the point of maximum curvature difficult. Throughout the present study, average errors over each of the three ignition regimes described earlier were: •  High Temperature/Strong Ignition Regime:  ±0.135 ms  •  Intermediate Temperature/Two Stage Ignition Regime:  ±0.241 ms  •  Low Temperature/Mild Ignition Regime (Weil-Defined):  ±0.070 ms  •  Low Temperature/Mild Ignition Regime (Ambiguous):  ±0.210 ms  Additional errors were also introduced by the dynamic pressure transducers' response time (3 ps) and the data acquisition system's sampling frequency (6 us) but these were both orders of magnitude smaller than errors introduced by ambiguous pressure traces.  C.2 Driven Gas Composition Error The driven gas composition was calculated by evacuating the driven section of the shock tube and successively adding individual gases while measuring their partial pressure with the Auto Tran 600D-117 vacuum sensor and Circuit-Test DMR-3600 multimeter. The vacuum sensor was calibrated using a zero and span calibration. At vacuum, the error in the voltage output is ±0.01 V (maximum multimeter resolution) and at atmospheric pressure the error is ±0.001 V due to the multimeter and ±0.001 bar due to the Oakton® Aneroid barometer used to calibrate the transducer. When measuring the partial pressure of a gas using the DMR-3600 multimeter, errors of ±0.001 V translated into errors of ±0.002 bar (0.028 psi) in all pressure measurements (refer to Figure C.1 to see how errors in calibration and voltage measurements carried forward into errors in measured pressures). Also, the order in which the shock tube was filled (Ar-0 2  Appendix C: Homogeneous Autoignition Delay Error Analysis  115  C H ) introduced variable errors in the pressure measurement and mole fractions of individual 4  gases. These are summarized below: Argon pressure: PAT -Pmeasured,1± 0-002 Oxygen pressure: - Pmeasured.2  ^Ar+Oj Po  - PAr+0  2  2  - 0.002  ^Ar  Po = Pmeasured, ± 0-002 - P 2  2  • PQ -  measured  , ± 0.002 1  Pmeasured,2 Pmeasured,1 — 0.004  =  —  2  Methane pressure: PAr+0 +CH 2  PcH  4  P H C  4  =  4  -Pmeasured,3 ±0.002  PAr+0 +CH 2  4  ~~ PAr+0  2  = Pmeasured,3 ± 0-002 - P  • • PcH - Pmeasured,3 4  -  measured  , ± 0.002 2  Pmeasured,2 - 0.004  Figure C.1: Illustration of Pressure Measurement Error *Note: Error bar magnitudes have been greatly exaggerated for illustrative purposes.  Appendix C: Homogeneous Autoignition Delay Error Analysis  116  For a given final pressure measurement: Ptotal Pmeasured.final - 0-002 _  The errors in the individual mole fractions of the gases are: _ Ar _ Pmeasured,1 - 0-002 = ^total Pmeasured.final - 0.002 P  y  Ar  Q  P  CH  P  _ measured,2 Rneasured.l — 0-004 P  2  °>" P,total  Y  Pmeasured.final - 0.002 _ Pmeasured,3 ~ Pmeasured,2 - 0-004 ± 0.002 measured,final  4  VCH -H total 4  Finally, the error in the equivalence ratio is given by: EQR = 2 ^ * — ^ easured,3 ~ measured,2 — 0-004 measured,2 measured,1 — 0.004 CH  m  P  P  — P  These produced average errors of 0.7% in the argon mole fraction, 0.8% in the oxygen mole fraction, and 0.7% in the methane mole fraction, with total driven gas pressure error of ~4.5%,  C.3 Experimental Temperature/Pressure Error Experimental temperature and pressure were found to be proportional to the following:  test «  P  test *  E  1 1 Q - — • driven • i • R  T  where:  EQR  P  V  .y r.Vi,To  (C2)  A  J  EQR is the equivalence ratio; y is the argon mole fraction; Ar  Pdnven  is the initial driven section pressure;  Vi is the measured incident shock velocity; and T is the initial driven section temperature. 0  (C1)  Appendix C: Homogeneous Autoignition Delay Error Analysis  117  The errors in the gas composition and pressure were discussed above. Errors in the incident shock velocity were minimal as the radius of convergence of the linear fit used to calculate the incident shock from dynamic pressure transducer signal exceeded 0.996 (average = 0.9989, standard deviation = 0.0038). Therefore, the main source of error was in measured distances between transducers and the data acquisition system's sampling rate. Errors in the measured distances were ± 0.2% plus the radius of the sensor (0.002 m), therefore the uncertainty in the distance may be expressed as: w = 0.002 • X + 0.002 x  The data acquisition system was set to sample data every 6 ps, therefore the error in the time measurement may be expressed as: Wt^e.OxlO"  6  The uncertainty in the velocity (which is a function of the distance errors and time errors) may be determined from the following formula: /  2  2  • W^ +  IdxJ f<\\  5V  X  V  wf  St  2  w =, v  7  (0.002•X + 0.002) +  (  y\  2  2  Vw  V t )  ,  ^  {G.Ox^J  From the configuration of the dynamic pressure transducers along the driven section, X=3.493 m and t=3.003-5.497 ms (based on shock velocities between 635.4-1163 m/s). This leads to an uncertainty in measured velocities of 1.78-2.34 m/s. To account for this uncertainty and that due to shock attenuation, the error in the calculated velocities were considered to be + 5 m/s. Using the errors calculated above for the gas composition, initial driven section pressure, initial temperature, and shock velocity, upper and lower error bounds on temperature and pressure were calculated using equations C.1 and C.2. For example, the maximum temperature was calculated as: ^max  - {EQ min<yAr,max> i T  R  V  max' ^"o.max)  These errors cumulatively produced errors in the experimental temperature between.5-164 K and errors in the experimental pressure between 0.2-0.6 bar, with the largest errors at high experimental temperatures due to large uncertainty introduced by the high Ar dilution necessary to produce such temperatures.  Appendix D: Numerical Combustion Equations Derivation  118  Numerical Combustion Equations Derivation D.1 Thermodynamic Development Premixed combustion in the shock tube was treated as an adiabatic, constant volume process. With these two assumptions, the first law of thermodynamics for a closed system was simplified by neglected all external heat transfer and work: Sq = du + Sw adiabatic => Sq = 0 const, vol. => Sw = P dv = 0 .-. du = 0  (D.1)  Transforming the above expression in terms of specific enthalpy: du = d(h-Pv)  =0  const, vol. => P • dv = 0  (D.2)  :.dh = vdP Since a solution in time is sought, the above may be restated as: dh dP — =v dt dt  v  (D.3) '  To further expand the above equation, an additional assumption that all gases involved in the combustion process behave as ideal gases is made (this is reasonable for the temperatures and pressures in the present investigation). With this final assumption, the enthalpy of the driven gas mixture is expressed as follows:  Ai = 5 > A K  where:  x is the mass fraction of species K; and K  h is the specific enthalpy of species K, (kJ/kg). K  (D.4)  Appendix D: Numerical Combustion Equations Derivation  119  Differentiating equation (D.4) with respect to time, an expression for the LHS of equation (D.3) is obtained:  The specific enthalpy of species K may be further expressed as (assuming ideal gas): dh =c dT K  (D.6)  PK  Additionally, the rate of change of the mass fraction of species K with time may be restated in terms of molar species production rate by expressing the rate of change of the mass of species K as a function of time and then dividing by the total mass in the driven section (a constant):  ^ - = iooo« yw v K  dt  K  dx dt  1000 • cb • M • V _ 1000 m p  K  where:  K  K  K  (b M  K  K  K  (D.7)  m is the mass of species K (kg); K  <b is the molar production rate of species K (mol/cm /s); 3  K  M is the molecular mass of species K (kg/kmol); K  V is the total mixture volume (m ); 3  m is the total mixture mass (kg); and p is the total mixture density (kg/m ). 3  Note: The factor of 1000 appearing in equation (D.7) is included to convert the units of the production term from mol/cm /s to kmol/m /s for dimensional homogeneity. 3  3  Substituting equations (D.6) and (D.7) into (D.5), an expression relating the change in mixture specific enthalpy as a function of the species production rate and the temperature change is obtained: *  _  ?  i  «  L  ^  A  +  ?  ^  .  £  ( D  .  8 )  This equation forms the LHS of expression (D.3). However, substituting (D.8) into (D.3) yields  Appendix D: Numerical Combustion Equations Derivation  120  an expression containing both the rates of change of temperature and pressure as a function of time. T o transform this equation further to a more useful form, the ideal gas law is used to eliminate the pressure term:  n-RT V dP R fdn dT} — = —• T+n dt V {dt dt). dP_^R IY1000 cb VT dt ~V P=  r  K K  ^ - .*L RT dt  +  dP = R T - Y l 0 0 0 <y + —• — dt 4* T dt  (D.9)  K  where:  n is the total number of moles in the driven section; and R is the universal gas constant (kJ/kmol/K).  Finally, substituting equations (D.9) and (D.8) into (D.3):  ]T1000 o) -M h dT _ P U dt ~ P K  K  i  -RT -^1000- <a  K  K  (D.10)  K V  if  While this equation is complete, it may be more convenient to express all of the terms in molar quantities. This transformation is performed by making the following substitutions:  1 p v  where:  V m  RT PM  _y M M K  '  PV m-T  p-T  M  K K  M  K  '  P  C  ~* r  =  c — M p  K  y is the mole fraction; K  h C  K  is the molar enthalpy (kJ/kmol); and  P K  is the molar specific heat (kJ/kmol/K).  Thus, the final expression for the rate of change of the system temperature becomes:  Appendix D: Numerical Combustion Equations Derivation RT dT_ dt  121  £ 1 0 0 0 -cb • h - R • T • £ 1 0 0 0 • <b VK K K  K  K  :  (D.11)  This final expression may be numerically integrated to solve for the mixture temperature, and equation (D.9) may be subsequently used to solve for mixture pressure.  D.2 Chemical Kinetic Development The above thermodynamic analysis yields an expression for the rate of change of temperature (and subsequently pressure) as a function of time, but this equation depends on an unknown molar species production rate. This production rate may be expressed as follows based upon the reaction stoichiometry:  (D.12)  where:  v ,v p  R  are stoichiometric coefficients of product and reactant species,  [XJ is the concentration of species j (mol/cm ); and 3  k , k are the forward and reverse reaction rate coefficients, respectively. f  b  The above production rate is tabulated by summing the production rate of species K in all reactions, /', included in the reaction mechanism. Forward reaction rate coefficients for each reaction are readily available in the literature in a modified Arrhenius form:  k =A T '-e n  fi  where:  r  RT  (D.13)  A , n and £, are experimentally determined coefficients. it  The reverse reaction rate coefficient is then calculated from the forward reaction rate and the equilibrium constant using the equation:  ' k  eq  keg,  in the above equation is the equilibrium constant, given by the following relation and  Appendix D: Numerical Combustion Equations Derivation calculated from the JANAF thermochemical data tables: n/c„ = eQl  where:  RT  AG is the change in Gibb's free energy (kJ/kmol).  122  Appendix E: Injector Hardware Characterization Data  123  Injector Hardware Characterization Data E.1 Injection Delay Experimental Data The following is the experimental data collected during the injection delay study: Table E.1: Injection Delay Data Filename  inj030 inj031 inj032 inj033 inj034 inj035 inj036 inj037 inj038 inj039 inj040 inj041 inj042 inj043 inj044 inj045 inj046 inj047 inj048 inj049 inj050 inj051 inj052 inj053 inj054 inj055 inj056 inj057 inj058 inj059 inj060  Injection Backpressure Duration (ms) (psig) 1.45 1.45 1.49 1.49 1.49 1.49 1.49 1.46 1.45 1.50 1.50 1.45 1.48 1.45 1.46 1.49 1.47 1.41 1.48 1.48 1.45 1.46 1.44 1.44 1.45 1.47 1.39 1.46 1.44 1.49 1.47  0 330 600 700 500 700 500 700 250 625 650 250 600 700 200 600 700 200 600 700 250 600 700 100 500 700 200 600 700 500 700  P1  P2  (ms)  (ms)  0.157 0.179 0.186 0.200 0.186 0.200 0.214 0.200 0.171 0.200 0.186 0.214 0.179 0.150 0.186 0.200 0.164 0.243 0.186 0.193 0.157 0.171 0.229 0.164 0.171 0.179 0.164 0.157 0.186 0.214 0.179  0.157 0.171 0.236 0.200 0.186 0.200 0.193 0.171 0.171 0.200 0.186 0.186 0.179 0.150 0.207 0.200 0.164 0.171 0.186 0.193 0.157 0.193 0.179 0.186 0.171 0.179 0.164 0.157 0.157 0.207 0.179  Appendix E: Injector Hardware Characterization Data  124  Table E.1: Injection Delay Data cont'd. Filename inj061 inj062 inj063 inj064 inj065 inj066 inj067 inj068 inj069 inj070 inj071 inj072 inj073 inj074 inj075 inj076 inj077 inj078 inj079 inj080 inj081 inj082 inj083 inj084 inj085 inj086 inj087 inj088 inj089 inj090 inj091 inj092 inj093 inj094 inj'095 inj096 inj097 inj098 inj099 injIOO inj101 inj102 inj103 inj 104  [jjJ^JJJJ  Backpressure  (ms)  (psig)  (ms)  1.47 1.45 1.45 1.47 1.45 1.44 1.45 1.46 1.46 1.47 1.49 1.45 1.49 1.44 1.45 1.46 1.46 1.48 1.46 1.49 1.48 1.49 1.46 1.49 1.39 1.45 1.47 1.46 1.49 1.47 2.48 2.51 2.43 2.49 2.48 2.53 2.50 2.51 2.49 2.48 2.50 2.52 2.47 2.51  300 600 700 600 600 700 200 600 700 250 600 700 200 500 700 200 500 700 150 500 700 400 600 500 150 500 700 150 500 650 200 300 600 0 0 600 0 500 400 300 700 0 500 200  0.221 0.157 0.200 0.179 0.164 0.157 0.164 0.164 0.193 0.186 0.221 0.157 0.221 0.164 0.164 0.200 0.171 0.193 0.171 0.221 0.187 0.193 0.171 0.200 0.171 0.157 0.186 0.171 0.221 0.171 0.157 0.207 0.143 0.164 0.164 0.207 0.193 0.193 0.164 0.150 0.200 0.207 0.179 0.193  P1  P2 (ms) 0.193 0.179 0.200 0.179 0.164 0.150 0.164 0.164 0.164 0.186 0.193 0.157 0.243 0.164 0.164 0.200 0.171 0.193 0.171 0.193 0.187 . 0.193 0.171 0.200 0.171 0.157 0.186 0.171 0.200 0.171 0.157 0.186 0.143 0.164 0.164 0.207 0.171 0.193 0.164 0.150 0.200 0.207 0.179 0.193  Appendix E: Injector Hardware Characterization Data  725  Table E.1: Injection Delay Data cont'd. Filename  Injection  Backpressure  P1  P2  (ms)  (psig)  (ms)  (ms)  2.50 2.49 2.51 2.50 2.51 2.48 3.55 3.51 3.54 3.54 3.54 3.55 3.51 3.53 3.53 3.51 3.51 3.49 3.45 3.52 3.53  600 250 600 200 600 300 400 600 200 400 600 300 400 250 600 300 600 400 500 300 300  0.164 0.164 0.186 0.179 0.186 0.157 0.193 0.179 0.164 0.179 0.193 0.200 0.150 0.157 0.164 0.157 0.150 0.193 0.164 0.157 0.164  0.164 0.164 0.186 0.179 0.186 0.157 0.186 0.150 0.164 0.179 0.193 0.193 0.157 0.157 0.164 0.157 0.150 0.193 0.164 0.157 0.164  Duration  inj105 inj106 inj107 inj108 inj109 inj110 inj111 inj112 inj113 inj114 inj115 inj116 inj117 inj118 inj119 inj120 inj121 inj122 inj123 inj124 inj125  .  E.2 Injector Mass Flow Rate Experimental Data The following is the injector mass flow data: Table E.2: Injector Mass Flow Rate Data CH  4  essur e (psi  Pulse Width  i_ CL  Qi  H "5 c iZ  Experiments ( U B C ) Injection P r e s s u r e (psi)  N  2  Pulse Width  Experiments ( U B C ) Injection P r e s s u r e (psi)  (ms)  1000  1500  1820  (ms)  1000  1500  1850  0.3 0.4 0.5 0.6 0.7 0.8  3.6 3.95 4.8 6.2 8.1 9.2 11.9 14.0 17.5 20.0  5.0 6.0 7.0 10.0 12.5 14.0 17.5 21.5 26.0 30.5  6.0 7.0 9.0 12.0 14.5 16.0 20.0 25.5 31.5 36.5  0.3 0.4 0.5 0.6 0.7 0.8 1.0 1.25 1.5 1.75  2.5 2.8 3.6 5.2 6.0 6.8 8.0 10.5 13.0 15.0  3.8 4.2 6.0 7.0 8.5 10.0 12.5 15.0 18.5 21.5  4.2 5.5 6.5 8.5 10.2 12.2 15.0 19.0 23.0 27.0  1.0 1.25 1.5 1.75  N E x p e r i m e n t s (Westport) 2  Pulse Width (ms)  Injection P r e s s u r e (psi) 1000  1500  1850  2500  Appendix E: Injector Hardware Characterization Data  126  Table E.2: Injector Mass Flow Rate Data cont'd. CH  4  Pulse Width  Experiments (UBC) Injection P r e s s u r e (psi)  N Experiments ( U B C ) Pulse Width  1000  1500  1820  (ms)  1000  1500  0.3 O) 0.4 0.5 ** 0.6 u 0.7 0.8 in in ra 1.0 S 1.25 re 1.5 o H 1.75  3.00 3.30 4.00 5.17 6.76 7.68 9.93 11.68 14.60 16.69  3.64 4.08 5.24 7.58 8.74 9.91 11.65 15.30 18.94 21.85 12.14 10.20 10.49 12.63 12.49 12.38 11.65 12.24 12.63 12.49  5.54 6.12 8.74 10.20 12.38 14.57 18.21 21.85 26.95 31.32  10.01 8.24 8.01 8.62 9.65 9.59 9.93 9.34 9.73 9.53  5.01 5.84 7.51 10.01 12.10 13.35 16.69 21.27 26.28 30.45 16.69 14.60 15.02 16.69 17.28 16.69 16.69 17.02 17.52 17.40  0.3 0.4 0.5 0.6 0.7 0.8 1.0 1.25 1.5 1.75  0.3 0.4 0.5 0.6 ra 0.7 CC 0.8 o 1.0 u. 1.25 (0 in ra 1.5 1.75  4.17 5.01 5.84 8.34 10.43 11.68 14.60 17.94 21.69 25.45 13.90 12.51 11.68 13.90 14.90 14.60 14.60 14.35 14.46 14.54  0.3 0.4 0.5 0.6 0.7 0.8 1.0 1.25 1.5 1.75  2  Injection P r e s s u r e (psi)  (ms)  in E ra E  N E x p e r i m e n t s (Westport)  2  Pulse Width  Injection P r e s s u r e (psi)  1850  (ms)  1000  1500  1850  2500  6.12 8.01 9.47 12.38 14.86 17.77 21.85 27.68 33.51 39.33 18:45 20.40 15.30 20.03 17.48 18.94 17.00 20.64 17.69 21.23 18.21 22.22 18.21 21.85 17.48 22.14 17.97 22.34 17.90 22.48  0.3 0.4 0.5 0.6 0.7 0.8 1.0 1.25 1.5 1.75  3.64 4.39 6.13 7.23 8.31 9.93 12.30 15.55 18.74 21.68 12.14 10.98 12.25 12.05 11.88 12.41 12.30 12.44 12.49 12.39  4.81 6.25 8.87 10.35 11.58 14.24 17.98 22.44 26.88 31.33 16.04 15.64 17.73 17.24 16.55 17.80 17.98 17.95 17.92  5.97 7.73 10.64 12.54 14.79 17.50 22.05 27.63 33.51 39.02  8.27 10.40 14.45 17.54 19.86 23.35 29.96 37.45 45.44 53.17  19.90 19.32 21.27 20.90 21.12 21.88 22.05 22.11 22.34 22.29  27.57 26.01 28.90 29.23 28.38 29.18 29.96 29.96 30.30 30.38  0.3 0.4 0.5 0.6 0.7 0.8 1.0 1.25 1.5 1.75  17:90  E.3 Pulsed Injection System Validation Experimental Data The following is the data collected when validating the pulsed injection system: Table E.3: Pulsed Injection System Validation Data Filename  multiOOl  Pulse Delay  Pulse Width  AP1  AP2  (ms)  (ms)  (V)  (V)  4.0  2.0  0.050  0.040  multi002  4.0  1.0  0.034  0.021  multi003 multi004  4.0 8.0  3.0 2.0  0.088  0.000 0.045  multi005 multi006  8.0  1.0 3.0  0.060 0.035  0.021  multi007  8.0 8.0  3.0  0.083  0.035 0.037  multi008  3.0  1.0  0.032  0.020  multi009 multi010  3.0 3.0  2.0 2.5  0.058  0.042 0.015  multiOH  1.5  multi012  1.5  1.0 0.5  0.085  0.075 0.037 0.020  0.021 0.010  Appendix E: Injector Hardware Characterization Data  127  Table E.3: Pulsed Injection System Validation Data cont'd. Filename  Pulse Delay (ms)  Pulse Width (ms)  AP1  AP2  (V)  (V)  0.5  0.021  0.009  multi013  1.0  multi014  1.0 1.5 1.5 1.5  1.0 0.5 1.0 1.5  0.060 0.020 0.035 0.085  0.000 0.010 0.022 0.000  2.0 2.0  0.5 1.0  0.010 0.024  2.0 2.5 2.5 2.5 2.5 3.0 3.0 3.0 3.0 3.0 4.0  1.5 0.5 1.0 1.5 2.0 0.5 1.0 1.5 2.0  0.020 0.033 0.047  2.5 0.2  0.073 0.021  4.0 4.0 4.0 4.0  1.0 1.5 2.0 2.5  0.033 0.045 0.060 0.070  0.034  4.0 4.5  3.0  0.085  0.000  3.0 3.0  0.085 0.085  0.006 0.018  3.0  0.085 0.085  0.029  multi015 multi016 multi017 multi018 multi019 multi020 multi021 multi022 multi023 multi024 multi025 multi026 multi027 multi028 multi029 multi030 multi031 multi032 multi033 - multi034 multi035 multi036 multi037 multi038 multi039 multi040  5.0 6.0 7.0  x  0.021 0.033 0.047 0.060 0.021 0.034 0.048 0.059  0.036 0.008 0.022 0.036 0.040 0.009 0.022 0.033 0.040 0.015 0.009 0.022 0.035 0.041  8.0  3.0 3.0  0.085  multi041.  9.0  3.0  0.085  0.040  multi042 multi043  10.0 10.0  3.0 2.0  0.085 0.058  0.044 0.046  multi044  10.0  1.0  0.033  0.022  multi045 multi046  12.0 12.0  3.0 2.0  0.085  0.049 0.047  multi047 multi048  12.0 15.0  multi049  18.0 21.0  multi050 multi051 multi052  1.0  0.058 0.033  0.022  3.0  0.085  0.057  3.0 3.0  0.085 0.085  0.067  21.0  2.0  0.058  0.047  24.0  3.0  0.085 0.085  0.072 0.072  0.058 0.034  0.048 0.022  multi053  50.0  3.0  multi054  50.0 50.0  2.0  multi055  0.035 0.039  1.0  0.070  128  Appendix E: Injector Hardware Characterization Data Table E.3: Pulsed Injection System Validation Data cont'd. Filename  Pulse Delay (ms)  multi056  50.0  multi057 multi058 multi059 multi060  5.0 6.0 7.0 8.0  multi061  9.0  multi062  10.0 12.0 15.0 18.0 21.0 24.0 5.0  multi063 multi064 multi065 multi066 multi067 multi068 multi069  Pulse Width (ms)  AP1  AP2  (V)  (V)  3.0  0.085  0.072  2.5 2.5 2.5 2.5  0.071 0.072 0.072 0.073  0.035  2.5 2.5  0.070 0.071  0.049  2.5 2.5 2.5 2.5 2.5  0.072 0.072 0.073 0.072 0.073 0.046  0.052 0.057 0.059 0.061 0.060 0.034  0.046 0.047 0.047 0.047  0.034 0.036 0.036  1.5  0.038 0.042 0.045 0.050  6.0 7.0 8.0  1.5 1.5 1.5  multi073 multi074  9.0 10.0 5.0  1.5 1.5 2.0  multi075  6.0 7.0 15.0  2.0 2.0 2.0  0.059  multi076 multi077  0.059 0.059  0.045 0.046 0.048  multi078  18.0  2.0  0.060  0.048  multi079 multi080 multi081 multi082  50.0 50.0 100.0 100.0  1.5 2.5 3.0  0.046 0.072 0.084  0.035 0.060 0.072  0.073  multi083  100.0  2.5 2.0  0.059  0.060 0.048  multi084  100.0  multi085  100.0  1.5 1.0  0.047 0.034  0.036 0.023  multi070 multi071 multi072  0.047 0.059  0.036 0.036 0.043  Appendix F: Jet Flow Field Characterization Data  129  Jet Flow Field Characterization Data F.1 Single Injection Mode Experimental Data The following is the data collected during the single injection jet flow field characterization study: Table  F.1: Single Injection Mode Jet Flow Field Data  Image  Time (ms)  1  0.127  2  0.327  3  0.527  4  0.727  5  0.927  c o  6  2 3 Q  Width (pixels)  PR = 3 Length Width (mm) (pixels)  0  ii)  E o  c ra  k_ 3  Q in C  p  Width (pixels)  PR = 5 Length Width (pixels) (mm)  1 20  Length (mm)  1  62  7  21  29  94  10  31  31  98  10  33  42  130  14  43  43  115  14  38  44  146  15  49  41  125  14  42  54  172  18  57  42  143  14  48  60  180  20  60  1.127  49  139  16  46  69  191  23  64  7  1.327  60  143  20  48  70  197  23  66  8  1.527  65  155  22  52  88  190  29  63  9  1.727  60  167  20  10  1.927  48  153  16  11  2.127  63  157  12  2.327  64  185  13  2.527  59  167  14  3.127  65  15  3.727  16 17 1  56  82  230  27  77  51  95  216  32  72  21  52  77  232  26  77  21  62  75  240  25  80  20  56  82  238  27  79  181  22  60  80  242  27  81  72  196  24  65  121  266  40  89  4.327  72  231  24  77  5.527  111  230  37  77  129  264  43  88  0.127  25  75  8  25  26  88  9  29  2  0.327  32  103  11  34  37  125  12  42  0  ^3  Length (mm)  *  1  1  3  0.527  39  113  13  38  50  154  17  51  4  0.727  46  119  15  40  59  184  20  61  5  0.927  51  142  17  47  62  188  21  63  6  1.127  60  159  20  53  67  213  22  71  7  1.327  66  165  22  55  87  234  29  78  8  1.527  58  173  19  58  71  222  24  74  9  1.727  55  186  18  62  72  243  24  81  Appendix F: Jet Flow Field Characterization Data  :  130  Table F.1: Single Injection Mode Jet Flow Field Data cont'd. Image  C  o O c o *3  h. IR  Q (A E o  c o ra Q (0  E  in  c o  2 3  Q (A  E p co  10 11 12 13 14 15 16 17 18 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 2 3 4 5 6 7 8 9 10 11  PR = 3 Length Width (pixels) (mm)  Time (ms)  Width (pixels)  1.927 2.127 2.327 2.527 2.727 2.927 3.527 4.127 5.327 6.527 0 0.127 0.327 0.527 0.727 0.927 1.127 1.327 1.527 1.727 1.927 2.127 2.327 2.527 2.727 2.927 3.127 3.727 4.327 5.527 6.727 0 0.127 0.327 0.527 0.727 0.927 1.127 1.327 1.527 1.727 1.927 2.127  66 86 79 68 81 74 90 86 103 102  199 180 210 215 205 229 236 266 274 278  25 33 39 48 51 54 63 72 66 79 76 73 95  62 78 121 128 140 144 160 182 184 187 210 208 212  89 104 120 103 120  241 258 265 293 310  25 36 37 51 65 58 61 67 76 74 78  62 93 112 114 136 142 149 183 201 194 209  22 29 26 23 27 25 30 29 34 34 1 8 11 13 16 17 18 21 24 22 26 25 24 32  30 35 40 34 40 1 8 12 12 17 22 19 20 22 25 25 26  Length (mm)  PR = 5 Width Length Width (pixels) (pixels) (mm)  66 60 70 72 68 76 79 89 91 93  85 87 81 109 106 93 124 140 117 160  263 281 295 294 311 309 309 331 361 360  21 26 40 43 47 48 53 61 61 62 70 69 71  80 86 88 98 103  28 42 59 60 72 73 67 75 89 83 87 116 105 102 113 101 127 149 129 160  96 132 158 169 190 212 226 240 251 278 281 288 305 310 329 334 348 382 389 419  21 31 37 38 45 47 50 61 67 65 70  24 40 64 55 73 69 85 89 84 91 73  97 142 160 183 188 215 222 225 247 266 287  28 29 27 36 35 31 41 47 39 53 1 9 14 20 20 24 24 22 25 30 28 29 39 35 34 38 34 42 50 43 53 1 8 13 21 18 24 23 28 30 28 30 24  Length (mm)  88 94 98 98 104 103 103 110 120 120 32 44 53 56 63 71 75 80 84 93 94 96 102 103 110 111 116 127 130 140 32 47 53 61 63 72 74 75 82 89 96  Appendix F: Jet Flow Field Characterization Data  131  Table F.1: Single Injection Mode Jet Flow Field Data cont'd.  i u ratio  C o O c  •  (A E  o to  Image  Time (ms)  Width (pixels)  PR Length (pixels)  12  2.327  85  13  2.527  78  14 15 16 17  2.727 2.927 3.127  23 24 25  3.327 3.527 3.727 3.927 4.127 4.327 4.527 4.727 5.327  26 27 28 29  18 19 20 21 22  1 2 3 4  c  =3 Width (pixels)  PR Length (pixels)  73  84  79  107  31 32 30  80 81 86  103 102 108  26  89 90 94 94  136  328 346  110 159 114 114 156 164  359 319 358 371 390 407  161 156  Width (mm)  Length (mm)  218  28  238  26  94 96 90  240 243 257  79 86 95 103 94 117  267 271  96 93 122  309 323 329  31 41  5.927 7.127 8.327  120 136 130  345 376 385  40 45 43  9.527  179  411  60  0 0.127 0.327 0.527 0.727  28 39 35 53  70 96 115 124  9 13 12 18  283 281 292 283  29 32 34 31 39 32  Width (mm)  Length (mm)  288  28  96  298  36  325 327  34 34 36  99 108 109 109  45 37 53 38 38 52  120 106 119 124 130  406 422  55 54 52  136 135 141  160  431  53  144  23 32 38 41  35 37 53 51  94 129 148 178  12 12 18 17  31 43 49 59  50  207 209  21 22  69 70  228 257  26 32  92 94  260  31  273  31  91  86 100  265 297  29  102  300  33 34  88 99 100  121  300 334  40 34  100 111  330  38  110  97 94 103 108 110 115 125  115  128 137  1  1  5 6  0.927  53  150  1.127  49  18 16  53  62 66  7  1.327  69  160 169  23  56  79  8  1.527 1.727  69 67  173 194  23 22  58 65  95  9  =5  76 86 87  o  10  1.927  68  201  23  67  2  11 12  2.127  73 99  212 195  24.  71  33  77  230  26  65 77  2.727  80  236  2.927 3.127  96 86  243 267  27 32  79 81  29  89  102 115  3.327  96  265  32  88  120  339  40  113  87  29 35  386  41 34  114  88  122 102  341  106  269 263  90  19  3.527 3.727  20  3.927  120  271  40  90  145  371  48  21 22  4.127 4.327  89 107  298 304  30 36  99  128  395  132  101  140  390  43 47  23 24  4.527  100 92  295  33 31  98  115 134  418 394  38 45  139  '•3  3 Q (0  E  13  in  14 15  o  16 17 18  2.327 2.527  4.727  328  109  129 124. 130 131  Appendix F: Jet Flow Field Characterization Data T a b l e F.1:  Single Injection Mode Jet Flow Field Data cont'd. PR = 3 Length Width (pixels) (mm)  Width (pixels)  25  4.927  104  317  26  5.127  308  27 28 29  5.327 5.527 5.727  109 114 111 127  30  5.927  31 32 33 34 35  6.127 6.827 7.427 8.627 9.827  >nfd.  Image  Time (ms)  o o c o  •3 IQ k. 3 Q (0 C C O IO  132  PR = 5 Length Width (mm) (pixels)  Length (mm)  Width (pixels)  35  106  131  434  44  145  36  103  153  410  51  137  303 333 325  38 37 42  101 111 108  143 167 184  420 404 443  48 56 61  140 135 148  126  355  42  118  153 119 121 185 156  331 371  51 40 40 62 52  110 124 122 124 135  366 372 404  Length (mm)  F.2 Pulsed Injection Mode Experimental Data The following is data collected during the pulsed injection jet flow field characterization study: T a b l e F.2:  Pulsed Injection Mode Jet Flow Field Data 0.5 m s P u l s e Delay  Img  c  o  "-3  2  3 Q  (0  Time (ms)  1.0 m s P u l s e Delay  2.0 m s P u l s e Delay  Width Length Width Length Width Length Width Length Width Length Width Length (pix) (pix) (mm) (mm) (pix) (pix) (mm) (mm) (pix) (pix) (mm) (mm)  1  0 0.127  23  64  8  21  27  58  25  64  8  21  0.327  33  94  11  31  33  29  38  92  13  31  3  0.527  35  121  12  40  41  86 121  9 11  19  2  14  40  47  105  16  35  4  0.727  116  16  39  47  131  16  44  49  125  16  42  5  0.927  48 47  132  16  44  59  131  20  44  55  135  18  45  6 7  1.127  58  137  19  46  54  148  18  49  55  143  18  48  1.327  58  157  19  52  64  21  48  49  50  1.527 1.727  60 58  154 175  20 19  51 58  62 67  49  148  21 22  49  69 57  150 141  16  8 9  145 147  161  23 19  47 54  1  1  1  E m 10 d 11 12  1.927  74  174  25  58  69  159  23  53  63  159  21  53  2.127 2.327  66 97  162 162  22 32  54 54  65 77  172 180  22 26  57  72  171  60  68  170  24 23  57 57  13  2.527  68  195  23  65  76  167  25  56  83  174  28  58  14  3.127  74  194  25  65  69  199  23  66  76  188  25  63  15  3.727  69  202  23  67  23  70  78  81  207  27  69  70 74  210  235  30 30  70  4.327  90 89  209  16  203  25  68  17  5.527  92  250  31  83  72  236  24  79  100  237  33  79  1  0 0.127  29  67  10  22  26  65  9  22  30  75  10  25  0.327 0.527  35 44  95 114  12  32 38  36 44  89 110  12 15  30 37  36 45  97 114  12 15  32  15  (0  E  p  2 3  1  1  1  38  Appendix F: Jet Flow Field Characterization Data  133  Table F.2: Pulsed Injection Mode Jet Flow Field Data cont'd. 0.5 m s P u l s e Delay  1.0 m s P u l s e Delay  2.0 m s P u l s e Delay  Img  Time (ms)  4  0.727  48  130  16  43  17  42  43  132  14  44  0.927  46  139  15  46  50 52  125  5  147  17  49  51  142  17  47  6 7 8  1.127 1.327 1.527  50 58 69  159 178 174  17 19 23  53 59 58  58 60 53  154 160 172  19 20 18  51 53 57  59 62 74  157 161 177  20 21 25  52 54 59  9 10 11  1.727 1.927 2.127  71 63 63  173 208 204  24 21 21  58 69 68  87 68 106  177 195 192  29 23 35  59 65  178 195 203  23 21 25  59 65 68  12  2.327 2.527 2.727 2.927 3.527 4.127 5.327 6.527  70 79 97  215 217 210  23 26 32  223 246 253  80 74 103 87 97 105  27  31 30 32 34 34  22 31 28 24 25 30  198 219 218  219 240 270 292 324  67 92 84 72 74 89 113 122  209 199 198  93 90 97  72 72 70 73 80 90 97 108  64 70 66 66 74 82 84  68 63 76  242 273 268  29 32 35  66 73 73 81 91 89  298 317  38 41  99 106  89 104  295 317  30 35  98 106  22  28 44  1 9  23  65 100 104 124 142  1 10 12  22  31 39 46 47  29 35 38 44 52  13 15 17  33 35 41 47  50  64  148  21  49  13 14 15 16 17 18 19 1 2  0 0.127  Width Length Width Length Width Length Width Length Width Length Width (pix) (mm) (mm) (mm) (mm) (mm) (Pix) (Pix) (Pix) (Pix) (Pix)  102 103  0.327 0.527 0.727 0.927  29 34 44 41 47  1.127  74  8  1.327 1.527  9  67 87  1 10 11 15 14 16  25 34  Length (mm)  46  42 45 48  69 94 117 138 141  25  48  62  151  15 16 21  165 180  20 26  55 60  55 66  170 180  18 22  57 60  59 79  165 166  20 26  55 55  198  24  66  75  193  25  64  68  183  23  61  69 72  205 207  23 24  68 69  69 74  212  71 72  74 74  195 198  25 25  65  216  23 25  2.327  76  214  71  96  32  239  29  80  93  238 253  26  230  81 86  83  2.727  72 77  85 77  28  217  32 27  220  81 95  216 248  72  2.527  25 27  31  73 79 84  15  2.927  88  243  29  81  112  247  37  82  75  260  25  87  16 17  3.127 3.727  106 116  260  35 39  87  99 84  260 293  33 28  87 98  100 92  265 287  18  4.327  114  38  96  99  292  33 31 33  88 96 97  19  5.527  32  114  41  108  6.727  58  111  124 111  325  20  392  37  131  3 4  115 131 139 144  1.727  61 78 71  10 11  1.927 2.127  12 13 14  5 6 7  29 38 44  120  268 292  40  89 97  109 121  333 357  36  111  95  289 342  40  119  173  332  15 14  66  F.3 Jet Impingement Experimental Data The following is experimental data collected when investigating the effects of jet impingement onto circular and rectangular cross-section obstructions:  Appendix F: Jet Flow Field Characterization Data  134  Table F.3: Jet Impingement Flow Field Data (Circular Obstruction) 0.5 m m G a p Img  Time (ms)  0 1 2  c o  1.0 m m G a p  1  0.127  39  3 4  0.327 0.527 0.727  5 6 7  45 54 60  38 51 75 77  14 16 19 21  0.927  66  87  23  1.127  72 84  88 104  74 77 97  1 13 18 26 27  30 42  30 31  65  25 29  110 112 104 121 121  10 15 14 20  62  90 95  23 22  36  69  98  24  34  26 27 34  38 39 36  95 109 98  42 42  40 40 38 39  33 38 34  31 33  116 116 109 112  40 58  ^3  8  3  9 10 11 12  1.727 1.927 2.127 2.327  13  2.527  89  113  31  39  14 15  2.727 2.927 3.527  100 139 92  138 113 133  35 48 32  48 39 46  138 172  133  48  46  94  18  4.127 5.327  138  48  19  6.527  162  180  60 57  63  Q CO  E p  16 17  88 94  1  35 52 67 72  1.327 1.527  2  2.0 m m G a p  Width Length Width Length Width Length Width Length Width Length Width Length (pix) (pix) (mm) (mm) (pix) (pix) (mm) (mm) (pix) (pix) (mm) (mm)  128  102 107  12 18 23 25 31  33 36 49 58  41  12  14  49 74 77  13 17 20  17 26 27  66  83  63 71  88 107  23 22  29  33  65 69  105 112 105  23 24 37  37  113 125  33 29  39 44  36 37  131  46 46 43  126 122 142  44  46 38  119 124 111  42  133 123  43 39  43 50  133  48  46  101  139  35  48  33 32  55 63  153  145  53  51  93  159 180  158  160  55  56  148  189  52  66  146  180  51  63  106 131 108 137  10 m m G a p Img  15 m m G a p  Width Length Width Length Width Length Width Length (pix) (pix) (mm) (mm) (pix) (pix) (mm) (mm)  0  1  1  1  0.127  45  38  16  13  42  51  15  18  2  0.327  57  47  20  16  72  61  25  21  3  74  51  26  18  76  24  80  58  28  20  85  68 71  27  4  0.527 0.727  30  25  5  0.927  59  36  21  92  80  32  28  6 re 3 7 Q  1.127  103 111  61  39  21  107  81  37  28  1.327  126  58  44  20  117  82  41  29  (0  8  1.527  138  60  48  21  136  86  47  30  E p  9  135  66  47  140  63  49  23 22  140 140  94 94  49  10  1.727 1.927  49  33 33  11  2.127  149  67  52  23  145  101  51  35  12  2.327  161  158  91 94  32  156  23 25  58  2.527  56 54  165  13  66 71  55  33  14  2.727  165  79  58  28  156  103  54  36  15  2.927  171  64  60  22  164  108  57  38  c  g  ^3  39 37  45 37  Table F.4: Jet Impingement Flow Field Data (Rectangular Obstruction) Time (ms)  105 96 84  25  31 37  Appendix F: Jet Flow Field Characterization Data  135  Table F.4: Jet Impingement Flow Field Data (Rectangular Obstruction) cont'd. 10 m m G a p Img  •p c o o  Time (ms)  15 m m G a p  Width Length Width Length Width Length Width Length (pix) (mm) (mm) (pix) (mm) (mm) (Pix) (Pix)  16  3.527  175  78  61  27  172  108  60  38  17  4.127  200  80  70  28  197  99  69  35  18  5.327  210  102  73  36  205  108  72  38  19  6.527  202  98  70  34  206  112  72  39  F.4 Jet Enclosure Experimental Data The following is data collected when investigating the effects of an enclosure: Table F.5: Jet Enclosure Flow Field Data 12 m m W a l l s Img  Time (ms)  23 m m Walls  50 m m W a l l s  Width Length Width Length Width Length Width Length Width Length Width Length (pix) (pix) (mm) (mm) (pix) (pix) (mm) (mm) (pix) (mm) (mm) (pix)  0  1  1  1  1  0.127  17  78  6  27  29  76  10  27  28  75  10  26  2  0.327  28  104  10  36  32  110  11  38  35  106  12  37  3  0.527  34  114  12  40  47  124  16  43  50  130  17  45  4  0.727  34  142  12  50  46  138  16  48  48  142  17  50  5  0.927  34  147  12  51  49  154  17  54  51  149  18  52  6  1.127  34  162  12  57  53  166  18  58  66  160  23  56  7  1.327  34  174  12  61  57  180  20  63  53  183  18  64  8  1.527  34  192  12  67  65  196  23  68  64  185  22  65  9  1.727  34  197  12  69  65  197  23  69  70  215  24  75  (0  10  1.927  34  199  12  69  65  212  23  74  70  207  24  72  E q  11  2.127  34  205  12  72  65  203  23  71  80  231  28  81  12  2.327  34  232  12  81  65  238  23  83  65  235  23  82  13  2.527  34  232  12  81  65  215  23  75  86  232  30  81  14  2.727  34  225  12  78  65  210  23  73  92  245  32  85  15  2.927  34  234  12  82  65  246  23  86  89  260  31  91  16  3.527  34  242  12  84  65  253  23  88  96  286  33  100  17  4.127  34  244  12  85  65  271  23  95  108  281  38  98  18  5.327  34  272  12  95  65  293  23  102  108  301  38  105  19  6.527  34  278  12  97  65  294  23  103  121  310  42  108  c o 2 3 Q  Appendix G: Non-Premixed Autoignition Delay Data  136  Non-Premixed Autoignition Delay Data G.1 Experimental Data The following is experimental data collected during the non-premixed autoignition experiments: Table  G.1: Non-Premixed Autoignition Delay Data  Pulse  Ini.  P  P  Width  Press.  Driven  Driver  (ms)  (psig)  (psia)  (psia)  0.5 0.5 0.5 0.5 0.5 0.5 0.5 1 1 1 1 1 1 1 1 1 1 1 1 1 1  1550 1550 1550 1530 1550 1550 1525 1500 1550 1500 1500 1480 1520 1500 1500 1500 1550 1525 1480 1480 1480 1550 1580 1575 1550 1530 1550 1550 1530 1550  11.163 11.163 11.161 11.164 11.160 13.359 13.360 11.164 11.165 11.163 11.163 11.160 11.162 11.151 11.160 11.163 11.164 11.163 8.619 7.497 13.150 11.164 11.165 11.159 11.165 11.153 11.160 13.362 13.361 13.357  624.23 622.92 623.51 622.98 623.04 665.02 665.61 623.64 624.23 623.03 622.32 622.90 622.90 623.54 622.98 622.99 623.06 623.54 609.35 614.16 594.97 623.05 623.01 622.99 624.14 622.98 623.04 665.03 665.02 665.02  1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5  T C H (ms) nominal upper  x B B (ms) lower  nominal  upper  PTest lower  1.50 1.56 1.58 1.13 1.49 1.40 1.15 1.60 1.50 1.35  1.50 1.68 1.68 1.26 1.49 1.46 1.21 1.60 1.55 1.38  1.20 1.24 1.24 0.91 1.46 1.06 0.95 1.53 1.45 1.24  1.38 1.55 1.44 1.11 1.38 1.24 1.06 1.47 1.43 1.28  1.38 1.70 1.58 1.23 1.56 1.33 1.21 1.53 1.55 1.41  0.88 1.19 1.15 0.89 1.11 0.94 0.98 1.31 1.31 1.23  1.28 0.95  1.28 0.95  1.28 0.87  1.08 1.21  1.08 1.21  0.95 0.94  1.48  1.80  1.39  1.48  1.58  1.31  1.96 1.18 1.99  1.96 1.18 1.99  1.88 1.18 1.86  1.97 1.24 1.89  1.97 1.24 1.89  1.85 1.24 1.81  TTest  (bar)  (K)  31.706 31.706 31.821 30.780 32.017 32.381 33.655 30.110 29.593 28.671 29.127  1142 1142 1144 1125 1148 1056 1076 1113 1103 1086 1095 1082 1090 1095 1105 1093 1154 1139 1273 1356 1020 1159 1136 1142 1139 1136 1136 1061 1061 1056  28.448 28.841 29.096 29.693 29.016 32.348 31.513 30.285 29.680 29.644 32.674 31.398 31.695 31.518 31.366 31.386 32.699 32.699 32.374  Appendix G: Non-Premixed Autoignition Delay Data  137  Table G.1: Non-Premixed Autoignition Delay Data cont'd. Pulse Width  Inj. Press.  (ms)  1.5 1.5 1.5 1.5 3 3 3 3 3 3 3 3 3 3 3 5 5 5 5 5 5 5 5 5 5 5 0.5 0.5 0.5 1 1 1 1 1 1 1 1 1.5 1.5 1.5 1.5 1.5 1.5 1.5  P Driven  P Driver  (psig)  (psia)  (psia)  1525 1475 1475 1475 1525 1525 1525 1525 1520 1520 1515 1510 1510 1510 1510 1500 1500 1500 1500 1500 1500 1500 1490 1480 1480 1480 1380 1380 1375  13.360 7.501 8.626 9.288 11.159 11.163 11.164 11.160 11.160 11.159 13.356 13.361 13.374 13.360 13.359 13.359 13.360 13.362 13.358 11.163 11.160 11.162 8.620 7.500 14.553 13.146 5.748 5.750 5.744 5.748 5.750 5.749 4.928 4.286 4.578 5.310 5.310 5.750 5.744 5.747 5.301 4.435 4.435 5.310  665.01 613.86 608.47 606.08 623.00 623.01 623.60 623.05 623.05 623.05 665.05 665.70 665.10 665.11 665.11 665.14 665.14 665.13 666.92 623.11 623.16 623.16 609.45 614.26 590.27 594.46 355.62 355.47 355.25 355.63 355.61 355.30 357.86 361.40 359.01 356.61 356.71 354.44  1390 1380 1375 1370 1350 1350 720 680 1390 1370 1380 1370 1350 1350 725  355.50 355.46 357.25 360.21 360.18 357.30  T C H (ms)  nominal upper  T BB  (ms)  lower  nominal  upper  lower  1.41 1.23 1.38 2.98 2.88 3.47 1.91 2.11 2.05 3.02  1.41 1.23 1.38 3.30 2.88 3.82 3.38 4.40 3.47 3.75  1.26 1.23 1.33 1.79 2.62 3.21 1.91 2.11 2.05 3.02  1.31 1.23 1.46 3.02 2.83 3.51 1.93 2.14 2.41 3.16  1.31 1.23 1.46 3.09 2.83 4.60 4.15 3.74 3.49 4.03  1.14 1.23 1.06 1.86 2.53 3.21 1.93 2.14 2.41 3.16  2.79 3.05 2.91 2.68 3.41 2.91 1.92 2.03 2.73 2.53 2.98 2.48  2.94 3.05 2.91 2.68 3.41 3.09 3.37 4.06 2.99 2.53 3.20 2.64  2.14 3.05 1.96 2.68 3.26 2.91 1.92 1.57 2.68 1.64 2.89 2,14  3.09 2.81 2.99 2.74 3.38 2.95 1.72 2.47 2.87 2.55 3.14 2.46  3.09 3.38 2.99 2.74 3.38 2.99 2.19 4.63 3.38 2.55 3.19 2.79  2.09 2.30 1.96 2.74 3.29 2.95 1.72 1.79 2,87 1.65 2.64 2.17  1.78 8.70 3.79 1.23 3.27 4.06 1.20 0.84 1.28  2.10 8.70 3.79 1.23 3.27 4.06 1.20 0.84 1.28  1.78 8.70 3.79 1.23 3.27 3.46 1.09 0.84 0.77  1.78 8.64 3.74  2.10 8.64 3.74  1.23 3.12 3.96 1.05 0.78 1.13  1.23 3.12 3.96 1.05 0.78 1.13  1.78 8.64 3.49 1.23 3.06 3.37 1.05 0.78 0.67  0.81 1.25 1.29 0.88 2.12 0.73 1.06 2.32  1.63 1.25 1.33 1.78 2.19 1.08 1.06 2.32  0.81 1.17 1.20 0.88 2.02 0.45 0.62 0.96  0.73 1.20 1.32 0.81 2.21 0.49 0.99 2.15  1.09 1.20 1.40 1.63 2.21 1.05 0.99 2.15  0.73 1.12 1.27 0.76 1.75 0.38 0.76 0.94  PTest  TTest  (bar)  (K)  32.818 30.864 29.801 29.545 31.696 32.346 32.028 32.017 31.625 31.381 32.493 33.659 32.972 32.696 33.009 32.816 32.383 33.016 33.007 31.393 31.384 31.389 29.662 31.219 29.921 29.464 16.961 15.758 15.586 18.170 15.759 15.600 15.419 17.919 15.427 17.419 17.130 17.559 17.085' 17.801 15.515 17.748 17.257 17.418  1063 1385 1262 1210 1142 1154 1148 1148 1141 1136 1058 1076 1065 1061 1066 1063 1056 1066 1066 1136 1136 1136 1260 1393 976 1017 1164 1122 1116 1206 1122 1116 1199 1397 1246 1229 1218 1185 1169 1193 1159 1364 1344 1229  Appendix G: Non-Premixed Autoignition Delay Data  138  Table G.1: Non-Premixed Autoignition Delay Data cont'd. Pulse Width  Inj. Press.  P Driven  P Driver  (ms)  (psig)  (psia)  (psia)  3 3 3 3 3 3 3 3 5 5 5 5 5 5  1390  5.744 5.752 5.749 4.287 4.436 5.937 5.939 5.310 5.746 5.747 5.750 5.749 5.308 5.309  354.43 359.10 355.45 361.45 360.81 354.20 354.80 357.20 354.43 355.47 355.47 355.26 356.64 356.71  1370 1390 1370 1350 1350 700 770 1390 1380 1380 1380 1370 700  X CH  (ms)  nominal upper  5.82  T BB  (ms)  PTest  TTest  lower  nominal  upper  lower  (bar)  (K)  1122 1212 1111 1402 1275 1154 1148 1222 1181 1122 1199 1122 1162 1225  6.20 1.68  5.82  5.85  15.742  1.61  1.65  6.38 1.69  5.85  1.65  1.48  1.51 1.99 2.63 2.40 1.91 2.63  1.56 2.05 2.72 2.40 1.91 2.80  1.46 1.86 2.37 2.40 1.49 1.59  1.30 1.93 2.73 2.34 1.88 2.55  1.35 2.05 2.73 2.34 3.02 2.74  1.15 1.93 2.53 2.34 1.78 1.37  1.96 3.07 2.14  2.04 3.07 2.14  1.86 2.89 1.73  2.01 3.11 2.24  2.20 3.17 2.45  1.52 2.02 1.11  18.370 15.448 18.042 15.620 17.204 17.037 17.241 17.439 15.750 17.992 15.754 15.594 17.305  Appendix H: Autoignition Visualization Images  Figure H.1: Autoignition Visualization Images  139  Appendix I: Shock Tube Optical Test Section Design Calculations  Shock Tube Optical Test Section Design Calculations  140  i  1.1 Design Variables In the design of the optical test section several key parameters were optimized to ensure that both the material strength and fatigue limits were not exceeded during "normal" operation. These parameters included: 1. Test section width; 2. Viewing window profile; and 3. Viewing window offset from test section endplate.  1.1.1 Test Section Width Increasing the test section width increases the overall strength and stiffness of the test section, but the increased width also requires increasing the width of the viewing window keyway to maintain the field of view. There are also limitations imposed on how wide the test section can be made by the fact that it must be mounted to a standard flange and must be smaller than the flange's bolt circle diameter.  1.1.2 Viewing Window Profile The viewing window profile consists of a narrow window, which is flush-mounted to the inner walls of the test section, and a much wider keyway, which is used for applying clamping force onto the window. Of these two, the keyway design offers the most flexibility. The keyway's width is fixed by the requirement to maintain a full field of view within the test section and is therefore purely a function of the test section width. Its minimum thickness is set by the strength of the fused quartz window and is calculated using the following empirical formula:  Appendix I: Shock Tube Optical Test Section Design Calculations where:  p  max  Omax  141  is the maximum design pressure differential across the quartz window; is the maximum stress (1000 psi (70 bar) for quartz with a S.F. of 7);  t is the quartz window thickness; and w is the unsupported quartz window width. Thus the only parameter available for optimization is the shape of the transition from the narrow inner window to the wider keyway. Previous tests with a small 10 mm diameter fused quartz window had shown that the only acceptable transition between the two was a smooth taper (i.e. no sharp corners or o-ring grooves) and so the design was set by these constraints.  1.1.3 Viewing Window End Offset Increasing the viewing window offset from the test section endplate increases both the strength and stiffness of the test section as well as reducing stresses on both the viewing window's inner radius (the point of maximum stress concentration) and the welds holding the test section to the endplate flange. However, the tip of the fuel injector must be flush with the end of the viewing window in order to see the entire gas jet during experiments, and so the injector dimensions (length) constrain the maximum end offset.  I.2 Stress Analysis (Static Loading) Given the three identified design variables, seven possible designs were analysed using finite element methods. For this preliminary comparison between the various options, static analysis was performed since only a relative comparison between options was desired, and static analysis is much less CPU-time intensive than dynamic analysis. In all cases the test pressure was 100 bar, and two sets of boundary conditions, "fully-constrained" and "free" were tested (since the actual constraints fall somewhere between these two). The design variations considered are summarized below, with results in Table 1.1 and Table 1.2: Baseline: Original design (J. Huang) but with a width of 4.5 in and a chamfered keyway. Opt 1: Baseline + increased viewing window end offset from 1.2 in to 1.5 in. Opt 2: Baseline + increased viewing window end offset from 1.2 in to 2.0 in. Opt 3: Baseline + increased viewing window end offset from 1.2 in to 3.0 in. Opt 4: Opt 3 + increased test section width from 4.5 in to 5.0 in. Opt 5: Opt 4 + increased viewing window end offset from 3.0 in to 4.0 in. Opt 6: Opt 5 + increased test section width from 5.0 in to 6.0 in.  Appendix I: Shock Tube Optical Test Section Design Calculations  Table 1.1:  142  Maximum Stress and Deflection for Fully Constrained B . C . Baseline  Opt1  Opt 2  Opt 3  Opt 4  Opt 5  Opt 6  Stress psi [Mpa]  54241 [374]  50823 [350]  54277 [374]  53123 [366]  49548 [342]  48671 [336]  N/A  Deflection in  0.00409  [mm]  [0.104]  0.00414 [0.105]  0.00404 [0.103]  0.00390 [0.099]  0.00294 [0.075]  0.00287 [0.073]  N/A  Table 1.2:  Maximum Stress and Deflection for Free B . C . Baseline  Opt 1  Opt 2  Opt 3  Opt 4  Opt 5  Opt 6  Stress psi [Mpa]  ....  91232 [629]  75723 [522]  57806 [399]  56650 [391]  50043 [345]  34684 [239]  Deflection in  ....  0.00650 [0.165]  0.00514 [0.131]  0.00408 [0.104]  0.00319 [0.081]  0.00292 [0.074]  0.00169 [0.042]  [mm]  Among the options analysed, the optimal design is somewhere between Opt 2 and Opt 3. While Opt 4 - 6 exhibited improved performance, their increased test section width was too large for mounting into standard flanges without interfering with the flange bolts. Additionally, the viewing window end offset of Opt 3 was longer than the available injector mounting length, so this had to be reduced.  1.3 Stress Analysis (Dynamic Loading) Some preliminary stress analysis with dynamically applied pressure indicated that the common convention of treating dynamic loads as equivalent to static loads of double the magnitude was reasonably accurate. Window deflections using both statically and dynamically applied loads are plotted in Figure 1.1. This shows that the maximum deflection at 100 bar is 0.090 mm under static loading and 0.180 mm under dynamic loading, while at 40 bar the maximum deflections are 0.036 mm and 0.071 mm under static and dynamic loading, respectively. The dynamic deflections are approximately double their static equivalents, mimicking the trend observed in maximum stresses. Additionally, when materials are subjected to dynamic loads for very short durations (~ milliseconds) material properties are greatly strengthened and catastrophic failure is therefore not a concern. From the limited stress analysis conducted, it was concluded that failure of the test section itself is not a concern.  1.4 Fatigue Analysis Given the location of the maximum stresses along the inner radius of the optical window slot, fatigue analysis was performed assuming this would be the location of failure.  Appendix I: Shock Tube Optical Test Section Design Calculations  0  0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8  0.9  143  1  Normalized Distance from End  Figure 1.1: Maximum Window Deflection Under Dynamic Loading Properties of Stainless Steel used in fatigue analysis: 304 SS Annealed Ultimate Tensile Strength, S = 82.4 kpsi ut  Endurance Limit: This is the endurance limit of the raw material for a polished rotating beam specimen undergoing fully reversed loading: S ; = 0.504 •  = 0.504 • 82.4 = 41.5 kpsi  Endurance Limit Modifying Factors: Surface Factor, k : a  Corrects for surface finish, with rough surfaces providing many crack initiation sites and thus resulting in smaller endurance limit. The constants (2.70, -0.265) were empirically derived for a "Machined or cold-drawn" surface finish: k = 2.70 • S ^ a  Size Factor, K : b  02 6 5  = 2.70 • 82.4  02 6 5  = 0.839  Appendix I: Shock Tube Optical Test Section Design Calculations  144  Corrects for the size of the component, with larger components having a smaller endurance limit:  where d is the effective diameter found by equating the area of the specimen stressed at and above 95% of the maximum stress to the equivalent area in a round specimen: A>5%, f reC  = 0 0 5 • h • b = 0.05 • 0.306 • 1.043 = 0.01596 in  2  0.01596 = 0.0766 • d => d = 0.456 in 2  0.1133  Load Factor, k : c  Corrects for the type of loading (axial, bending, torsion, shear). The location of maximum stress on the test section is primarily in bending, so the correction factor for bending is used: k =1 c  Temperature Factor, k : d  Corrects for increased likelihood of brittle failure during low temperature operation or yielding at high temperatures. Since the test section is only exposed to high temperatures for a few milliseconds, the nominal operating temperature is assumed to be room temperature and no correction is applied:  Miscellaneous Effects Factor, k : e  Corrects for corrosion, cyclic frequencies, stress concentrations, etc. Since stress analysis of the test section has already provided the maximum stress at the inner window radius (rather than the nominal) and all analysis has been performed based on this maximum  Appendix I: Shock Tube Optical Test Section Design Calculations  145  stress, the effects of stress concentration have already been implicitly accounted for. The only other potentially relevant factor is corrosion: k = 0.8 (?) e  Using the above endurance limit modifying factors, the endurance limit is: S =k k k k k S' = e  a  b  c  d  e  0.839 • 0.954 • 0.8 -41.5 = 26.6 kpsi  e  Additionally, to calculate the expected lifetime if the test section is subjected to a given loading, the following equation may be used:  N=  -  where:  a=  {0.9S f S ut  e  (0.9-82.4) 26.6  2  207  1. 0.9 S„, 1. 0.9-82.4 ^ = --log6 =--log = -0.088 3 26.6 a  N=  ,aj  [207  Since the calculated endurance limit is greater than the maximum stresses experienced at 40 bar, the test section has infinite life at this operating pressure. Using the above equation, the greatest stress that the test section may be subjected to while maintaining infinite life (1,000,000 cycles) is 61.1 kpsi. This is just slightly greater than the maximum stresses if the test section is operated continuously at 100 bar.  Appendix J: Shock Tube Optical Test Section Drawings  Shock Tube Optical Test Section Drawings  Appendix J: Shock Tube Optical Test Section Drawings  147  to o  Q  I  o  ^  m  |  <  Appendix J: Shock Tube Optical Test Section Drawings  148  Appendix J: Shock Tube Optical Test Section Drawings  149  Appendix J: Shock Tube Optical Test Section Drawings  150  Appendix J: Shock Tube Optical Test Section Drawings  151  Appendix J: Shock Tube Optical Test Section Drawings  152  Appendix J: Shock Tube Optical Test Section Drawings  153  Appendix J: Shock Tube Optical Test Section Drawings  154  Appendix J: Shock Tube Optical Test Section Drawings  155  Appendix J: Shock Tube Optical Test Section Drawings  156  Appendix J: Shock Tube Optical Test Section Drawings  157  Appendix J: Shock Tube Optical Test Section Drawings  158  Appendix J: Shock Tube Optical Test Section Drawings  159  

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