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Cycle-to-cycle variations in spark-ignition engines 1988
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Title | Cycle-to-cycle variations in spark-ignition engines |
Creator |
Kapil, Anil |
Publisher | University of British Columbia |
Date Created | 2010-09-09 |
Date Issued | 2010-09-09 |
Date | 1988 |
Description | Pressure data measurements have been made in a single-cylinder, spark-ignition engine over 100 consecutive cycles. The engine was operated on natural gas at a wide range of engine speed and equivalence ratios. The effects of spark electrode geometry, combustion chamber geometry, spark gap and throttling have also been examined. From these pressure measurements standard deviations in burning times in mass-fraction-burned values were determined. Because of the existing evidence that the origin of cyclic variations is in the early combustion period, the standard deviations of cyclic variation in time required for a small (almost zero) mass-fraction-burned is estimated by extrapolation. These extrapolated values of standard deviation are compared with the implication of a hypothesis that cyclic variations in combustion in spark-ignition engines originate in the small-scale structure of turbulence (after ignition). The nature of turbulence structure during combustion is deduced from existing knowledge of mixture motion within the combustion chamber of the engine. This research determines the turbulent parameters, such as turbulence intensity, turbulent length scales and laminar burning velocity. The standard deviation in burning times in the early stages of combustion is estimated, within experimental uncertainty, by the parameter ⋋/4uℓ where ⋋ is the Taylor microscale and uℓ is the laminar burning velocity of the unburned mixture. This parameter is the consequence of the Tennekes model of small-scale structure of turbulence and Chomiak's explanation of the high flame propagation rate in regions of concentrated vorticity and the assumption that theignition behaves as though it were from a point source. The general conclusion reached is that the standard deviation in the burning time for small mass-fraction-burned is associated with the early stages of burning-predictable from the knowledge of the Taylor microscale and the laminar burning velocity. |
Subject |
Spark Ignition Engines Spark Ignition Engines -- Testing |
Genre |
Thesis/Dissertation |
Type |
Text |
Language | Eng |
Collection |
Retrospective Theses and Dissertations, 1919-2007 |
Series | UBC Retrospective Theses Digitization Project [http://www.library.ubc.ca/archives/retro_theses/] |
Date Available | 2010-09-09 |
DOI | 10.14288/1.0080822 |
Degree |
Master of Applied Science - MASc |
Program |
Mechanical Engineering |
Affiliation |
Applied Science, Faculty of |
Degree Grantor | University of British Columbia |
Campus |
UBCV |
Scholarly Level | Graduate |
URI | http://hdl.handle.net/2429/28392 |
Aggregated Source Repository | DSpace |
Digital Resource Original Record | https://open.library.ubc.ca/collections/831/items/1.0080822/source |
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CYCLE-TO-CYCLE VARIATIONS IN SPARK-IGNITION ENGINES. By ANIL KAPIL Eng., Walchand College Of Engineering, India, 1981. A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTERS IN APPLIED SCIENCE. i n THE FACULTY OF GRADUATE STUDIES Department of Mechanical Engineering We accept the thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA May, 1988 © A n i l K a p i l , 1988 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. 1 further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of The University of British Columbia Vancouver, Canada Date DE-6 (2/88) ABSTRACT Pressure data measurements have been made i n a s i n g l e - c y l i n d e r , s p a r k - i g n i t i o n engine over 100 consecutive cycles. The engine was operated on natural gas at a wide range of engine speed and equivalence r a t i o s . The e f f e c t s of spark electrode geometry, combustion chamber geometry, spark gap and t h r o t t l i n g have also been examined. From these pressure measurements standard deviations i n burning times i n mass-fraction-burned values were determined. Because of the e x i s t i n g evidence that the o r i g i n of c y c l i c v a r i a t i o n s i s i n the e a r l y combustion period, the standard deviations of c y c l i c v a r i a t i o n i n time required for a small (almost zero) mass-fraction-burned i s estimated by extrapolation. These extrapolated values of standard deviation are compared with the i m p l i c a t i o n of a hypothesis that c y c l i c v a r i a t i o n s i n combustion i n s p a r k - i g n i t i o n engines o r i g i n a t e i n the small-scale structure of turbulence ( a f t e r i g n i t i o n ) . The nature of turbulence structure during combustion i s deduced from e x i s t i n g knowledge of mixture motion within the combustion chamber of the engine. This research determines the turbulent parameters, such as turbulence i n t e n s i t y , turbulent length scales and laminar burning v e l o c i t y . The standard deviation i n burning times i n the e a r l y stages of combustion i s estimated, within experimental uncertainty, by the parameter A/4u^ where A i s the Taylor microscale and u^ i s the laminar burning v e l o c i t y of the unburned mixture. This parameter i s the consequence of the Tennekes model of small-scale structure of turbulence and Chomiak's explanation of the high flame propagation rate i n regions of concentrated v o r t i c i t y and the assumption that the i i i g n i t i o n behaves as though i t were from a point source. The general conclusion reached i s that the standard deviation i n the burning time for small mass-fraction-burned i s associated with the early stages of burning-predictable from the knowledge of the Taylor microscale and the laminar burning v e l o c i t y . i i i TABLE OF CONTENTS Page: Abstract i i Table of Contents i v L i s t of Tables v i i i L i s t of Figures i x Nomenclature x i i Acknowledgements xv 1. INTRODUCTION 1 2. LITERATURE REVIEW 6 2.1 Introduction 6 2.2 E f f e c t of A i r - F u e l Mixture Composition 7 Equivalence Ratio 7 Fuel Type 9 Charge D i l u t i o n 10 2.3 E f f e c t of I g n i t i o n Variables 12 I g n i t i o n Systems 12 Spark Electrode Geometry 13 Spark J i t t e r 13 2.4 Engine Speed and Compression Ratio 14 2.5 E f f e c t of Combustion Chamber Geometry 15 Chamber Shape and Spark Location 16 Spark Timing 17 Valve Shrouding 17 2.6 Comments 20 3. APPARATUS AND INSTRUMENTATION 21 3.1 Introduction 21 3.2 Apparatus 21 Engine 21 A i r I n l e t System 21 Fuel Intake System 22 Coolant System 22 O i l System 23 Dynamometer 23 I g n i t i o n System 24 3.3 Instrumentation 24 Pressure Measurement 24 Volume Assignment 25 A i r Flow Measurement 26 Gas Flow Measurement 26 Fuel - A i r Ratio 27 Speed Measurement 27 i v TABLE OF CONTENTS (Continued) Page Torque Measurement 27 Data A c q u i s i t i o n System 28 3.4 Operational Control 29 Control Console 29 S t a r t i n g Procedure 30 3.5 Data A c q u i s i t i o n and Transfer 31 Data A c q u i s i t i o n 31 Data Transfer. 32 4. MEASUREMENTS WITH MOTORED ENGINE. 33 4.1 Introduction 33 4.2 Phasing of Pressure-Volume Data 33 4.3 Poly t r o p i c Exponents 37 4.4 Volumetric E f f i c i e n c y 40 4.5 Peak Pressure 41 5. FIRED DATA ANALYSIS 42 5.1 Introduction 42 5.2 Scalin g of Pressure 42 5.3 Volume C a l c u l a t i o n 43 5.4 Mass-Burned-Fraction C a l c u l a t i o n 43 I n i t i a l Conditions 44 Compression Stroke 45 Combustion Process 48 D i s s o c i a t i o n C a l c u l a t i o n 51 Stanjan 51 5.5 S t a t i s t i c a l Analysis 52 6 . FIRED ENGINE MEASUREMENTS AND RESULTS 54 6.1 Introduction 54 6.2 C y c l i c V a r i a t i o n s i n Pressure 55 6.3 C y c l i c V a r i a t i o n s i n Burning Time 57 6.4 E f f e c t of Spark Plug Geometry 63 6.5 E f f e c t of Spark Gap Width 63 v TABLE OF CONTENTS (Continued) Page 6.6 Effect of Part Throttle 64 6.7 Disk Combustion Chamber 65 6.8 Summary 68 7. TURBULENCE AND IGNITION IN ENGINES 70 7.1 Introduction 70 7.2 Homogenity and Isotropy In Engine Turbulence 70 7.3 Turbulence Measurements i n Engines 72 Mean Velocity 72 Turbulence Intens i t y 73 7.4 Turbulent Scales 74 7.5 Small Scale Structure of Turbulence 78 7.6 I n i t i a l Flame Propagation 80 7.7 Laminar Burning Velocity 84 7.8 Summary 85 8.0 COMPARISON OF MEASUREMENTS AND THEORETICAL ESTIMATES OF STANDARD DEVIATION 86 8.1 Introduction 86 8.2 Mean Random Time Delay 86 8.3 Comparison of Data 90 8.4 Summary 91 9.0 CONCLUSIONS 92 10. RECOMMENDATIONS 95 REFERENCES '. 96 APPENDICES A: CALIBRATION CURVES 100 B: COMBUSTION-VOLUME PHASING 102 C: LAMINAR BURNING VELOCITY 105 v i TABLE OF CONTENTS (Continued) Page D: PROPERTIES OF B.C.NATURAL GAS 109 E: SENSITIVITY ANALYSIS 110 v i i. LIST OF TABLES Page Table 1. Engine Specifications 112 Table 2. S e n s i t i v i t y of IMEP and PMEP to 1° Change i n Phasing Motored Engine 35 Table 3. Polytropic Exponents of Compression and Expansion i n a Motored Engine 39 Table 4. Typical Length and Velocity Scales For Engine Turbulence at 3000 RPM 89 Table A . l Pressure and Voltage values for Calibration of Piezo-Electric Pressure Transducer 101 Table B.l Peak Pressure and i t s Crank-Angle Occurance for Changes i n Phasing 103 v i i i LIST OF FIGURES Page F i g 1. C y c l i c Pressure Variations i n a Spark I g n i t i o n Engine 113 F i g 2. Engine, Dynamometer and Control Systems Layout 114 F i g 3. Ricardo Hydra Engine Cross-Sectional Views 115 F i g 4. Combustion Chamber Shapes a) Bath-Tub Chamber. b) Disc Chamber 116 « F i g 5. Instumentation Layout 117 F i g 6. Hardware Arrangement 118 F i g 7. Ensemble-Averaged Pressure [Motored Engine] 119 F i g 8. Indicator Diagram on Logarithmic Scale [Motored Engine]....120 F i g 9. Indicator Diagram on Logarithmic Scale 121 F i g 10. Indicator Diagram on Logarithmic Scale 122 F i g 11. Volumetric E f f i c i e n c y i n a Motored Engine 123 F i g 12. Ensemble-Averaged Peak Pressure i n a Motored Engine 124 F i g 13. T y p i c a l Pressure V a r i a t i o n s and Frequency Histogram for Peak Pressure. Speed = 3000 RPM, <f> = 1.015 125 F i g 14. T y p i c a l Pressure Variations and Frequency Histogram f o r Peak Pressure. Speed = 3000 RPM, $ = 0.674 126 F i g 15. Ensemble-Averaged Peak Pressure V a r i a t i o n with Speed And Equivalence Ratio 127 F i g 16. C o e f f i c i e n t of V a r i a t i o n f o r D i f f e r e n t Speeds and Equivalence Ratios 128 F i g 17. T y p i c a l Mass-Fraction-Burned V a r i a t i o n with Time, From I g n i t i o n . N=3000 RPM. <f> = 1.25 129 F i g 18. T y p i c a l Frequency Histogram f o r Burning Times (X=0.10, N = 3000,<j> - 1. 1.05.) 130 F i g 19. T y p i c a l Frequency Histogram f o r Burning Times (X=0.30,N = 3000 RPM. $ = 1.05.) 131 F i g 20. T y p i c a l Frequency Histogram f o r Burning Times (X=0.50,N = 3000 RPM. <f> = 1.05.) 132 i x L i s t of Figures (Continued) Page Fig 21. Typical Frequency Histogram for Burning Times (X=0.10, N = 3000 RPM. ci = 1.22.) 133 Fig 22. Typical Frequency Histogram'for Burning Times (X=0.10, N = 3000 RPM. <f> = 1.38.) 134 Fi g 23. Standard Deviation i n Burning Time. N = 2400 RPM. (Bath Tub Chamber) 135 Fig 24. Standard Deviation i n Burning Time. N = 2400 RPM. (Bath Tub Chamber) 136 Fig 25. Standard Deviation i n Burning Time. N = 3000 RPM. (Bath Tub Chamber) 137 Fig 26. Standard Deviation i n Burning Time. N = 3000 RPM. (Bath Tub Chamber) 138 Fig 27. Standard Deviation i n Burning Time. N = 3600 RPM. (Bath Tub Chamber) 139 Fig 28. Standard Deviation i n Burning Time. N = 3600 RPM. (Bath Tub Chamber) 140 Fig 29. Standard Deviation i n Burning Time. N = 4200 RPM. (Bath Tub Chamber) 141 Fig 30. Extrapolated Standard Deviation i n Early Burning Time 142 Fig 31. Extrapolated Standard Deviation i n Early Burning Crank Angle Interval 143 Fig 32. Cross Correlation Coefficient Of Standard Deviation In Burning Time 144 Fig 33. Modified Spark Plug With Fine Point Electrodes 145 Fig 34. Standard Deviation i n Burning Time. N = 3000 RPM. (Needle Point Electrode Geometry) 146 Fig 35. Standard Deviation i n Burning Time. N = 3000 RPM. (Needle Point Electrode Geometry) 147 Fig 36. Extrapolated Standard Deviation i n Early Burning Time. Different Electrode Geometries N = 3000 RPM 148 Fig 37. Modified Spark Plug With Wide Gap Electrodes 149 Fig 38. Standard Deviation i n Burning Time. N = 3000 RPM. (Spark Plug Gap = 2.3 mm) 150 x L i s t of Figures (Continued) Page Fig 39. Standard Deviation i n Burning Time. N = 3000 RPM. (Spark Plug Gap = 2.3 mm) 1 5 1 Fig 40. Extrapolated Standard Deviation i n Early Burning Time. Different Spark Gaps N •» 3000 RPM. • 152 Fig 41. Standard Deviation i n Burning Time. N = 3000 RPM. (Half Open Throttle) 153 Fig 42. Standard Deviation i n Burning Time. N = 3000 RPM. (Half Open Throttle) 154 Fig 43. Extrapolated Standard Deviation i n Early Burning Time. Different Throttle Settings N = 3000 RPM 155 Fig 44. Standard Deviation i n Burning Time. N = 2400 RPM. (Disc Chamber) 156 Fig 45. Standard Deviation i n Burning Time. N - 3000 RPM. (Disc Chamber) 157 Fig 46. Standard Deviation i n Burning Time. N = 3600 RPM. (Disc Chamber) 158 Fig 47. Standard Deviation i n Burning Time. N - 4200 RPM. (Disc Chamber) 159 Fig 48. Standard Deviation i n Burning Time. N •= 3000 RPM. (Disc Chamber- Fine Point Electrode Geometry) 160 Fig 49. Standard Deviation i n Burning Time. N = 3000 RPM. (Disc Chamber- Spark Plug Gap — 1.5 mm) 161 Fig 50. Standard Deviation i n Burning Time. N = 3000 RPM. (Disc Chamber- Half Open Throttle) 162 Fig 51. Extrapolated Standard Deviation i n Early Burning Time. (Disk Chamber) 163 Fig 52.Extrapolated Standard Deviation i n Early Burning Time. (Disk Chamber) Different Electrode Geometries N = 3000 RPM..164 Fig 53. Extrapolated Standard Deviation i n Early Burning Time. (Disk Chamber) Different Spark Gaps N = 3000 RPM 165 Fig 54. Extrapolated Standard Deviation i n Early Burning Time. (Disk Chamber). Different Throttle Settings N = 3000 RPM..166 x i L i s t of Figures (Continued) Page Fig 55.Effect of Different Combustion Chambers on Standard Deviation. N=2400 RPM 167 Fig 56. Effect of Different Combustion Chambers on Standard Deviation. N=3000 RPM 168 Fig 57.Effect of Different Combustion Chambers on Standard Deviation. N=3600 RPM 169 Fig 58.Effect of Different Combustion Chambers on Standard Deviation. N=4200 RPM 170 Fig 59.Effect of Different Combustion Chambers on Standard Deviation Different Spark Gaps 171 Fig 60.Effect of Different Combustion Chambers on Standard Deviation. Fine Point Electrodes 172 Fig 61. Effect of Different Combustion Chambers on Standard Deviation. Partly Opened Throttle 173 Fig 62. Model of Concentrated V o r t i c i t y Region as Proposed By Tennekes 174 Fig 63. Effect of Equivalence Ratio on Mean Random Time Delay 175 Fig 64. Comparison of Extrapolated Standard Deviation and Mean Random Time Delay with Equivalence Ratio. - 2400 RPM. (Bath-Tub Chamber) 176 Fig 65. Comparison of Extrapolated Standard Deviation and Mean Random Time Delay with Equivalence Ratio. - 3000 RPM. (Bath-Tub Chamber) 177 Fig 66. Comparison of Extrapolated Standard Deviation and Mean Random Time Delay with Equivalence Ratio. - 3600 RPM. (Bath-Tub Chamber) 178 Fig 67. Comparison of Extrapolated Standard Deviation and Mean Random Time Delay with Equivalence Ratio. - 4200 RPM. (Bath-Tub Chamber) 179 Fig 68. Relationship Between Mean Random Time Delay and Extrapolated Standard Deviation i n Burning Time Within a Bath-Tub Chamber 180 Fig 69. Relationship Between Mean Random Time Delay and Extrapolated Standard Deviation i n Burning Time Within a Disc Chamber 181 x i i L i s t of Figures (Continued) Page F i g 70. C a l i b r a t i o n Curve For Laminar Flow Element (Natural Gas)..182 F i g 71. C a l i b r a t i o n Curve For Laminar Flow Element (Air) ....183 F i g 72. C a l i b r a t i o n Curve For K i s t l e r Pressure Transducer 184 F i g 73. Combustion Time at 10% Mass-Fraction-Burned on P r o b a b i l i t y Paper 185 F i g 74. Combustion And Motored Pressure At D i f f e r e n t Crank Angle Intervals - 3000 RPM. ( For S e n s i t i v i t y Analysis) 186 F i g 75. Combustion Pressure Less Motored Pressure at D i f f e r e n t Crank Angle Intervals- 3000 RPM ( S e n s i t i v i t y Analysis)....187 F i g 76. Mass-Fraction-Burned and Time S e n s i t i v i t y at D i f f e r e n t Crank Angles ( S e n s i t i v i t y Analysis) 188 x i i i NOMENCLATURE 2 A Area (m ) BDC Bottom Dead Centre Cov Normalized Covariance COV Coefficient Of Variation C Constant pressure s p e c i f i c heat (kJ/kg-K) p C Constant volume s p e c i f i c heat (kJ/kg-K) V E Total energy (kJ) EVC Exhaust Valve Closing EVO Exhaust Valve Opening e Specific energy (kJ/kg) h° Enthalpy of formation (kJ/kmol) h Specific enthalpy (kJ/kmol) H Clearance height (mm) H Total Enthalpy (kJ) IMEP Indicated mean effective pressure (kPa) IVC I n l e t Valve Closing IVO I n l e t Valve Opening k 1 Isentropic Exponent L Connecting rod length (mm) L , l Integral length scale MBT Minimum for best torque MW Molecular weight(kg/kmol) N Number of Engine Cycles P Pressure (kPa) PMEP Pumping Mean Effective Pressure (kPa) Q Heat added or l o s t to the cylinder walls (kJ) x i v Qair 3 T o t a l Volume Of A i r Inhaled By the Engine i n m /min R Crank radius. R,r Radius (mm) Re L Reynolds number based on the i n t e g r a l length scale R 6 A Reynolds number based on the Taylor micro scale RPM Engine speed (Revolutions per minute) R Universal gas constant (kJ/kmol-K) ST Turbulent Burning V e l o c i t y . T Temperature (k) TDC Top dead centre U V e l o c i t y (m/s) U(t) Instantaneous v e l o c i t y (m/s) U(t) Turbulent mean v e l o c i t y (m/s) V t Laminar burning v e l o c i t y (m/s) u(t) F l u c t u a t i n g component of the instantaneous v e l o c i t y u' Turbulent i n t e n s i t y , RMS of v e l o c i t y f l u c t u a t i o n s (i V 3 Volume (m ) 3 S p e c i f i c volume (m /kg) WOT Wide open t h r o t t l e X,x Mass-burned-fraction X Mean of Sample Data 4> Equivalence r a t i o X Taylor microscale of turbulence (mm) X Normalised A i r f u e l r a t i o V 2 Kinematic v i s c o s i t y (m /s) 1 Kolmogorov scale of turbulence (mm) V Volumetric e f f i c i e n c y 9 Instantaneous Value of Crank P o s i t i o n a Standard Deviation of Sample Data. a Extrapolated Standard Deviation i n Burning time f o r o small mass-fraction-burned. 5q Quenching Distance (mm) 5c Width Of The Flame Kernel (mm) Subscripts amb Ambient conditions b Burned mixture intake Conditions i n the intake manifold ° Reference condition at 273°K u Unburned mixture t o t T o t a l c y l i n d e r conditions 1 I n i t i a l crank angle step i n the c a l c u l a t i o n s 2 F i n a l crank angle step i n the c a l c u l a t i o n s x v .1. ACKNOWLEDGEMENTS I would l i k e to acknowledge the guidance and support of Professor P.G. H i l l during the course of my program towards a masters degree i n mechanical engineering. I am extremely grateful to him for his u n t i r i n g support, stimulating discussions and the opportunities he presented to me. I am thankful to him for his confidence i n me. I would also l i k e to acknowledge other members of the faculty who provided t h e i r assistance and support to me.Special thanks to the Technical support s t a f f v i z : Shu Oshika, John Richards and Len Drake and my colleagues for helping me i n various forms towards the completion of the program. I also appreciate the support provided by Ragini during the course of my research. x v j. i 1 1.INTRODUCTION Cycle to cycle variations i n combustion process are ch a r a c t e r i s t i c of a l l spark i g n i t i o n engines and are observed at a l l operating conditions. The combustion process i n a spark i g n i t i o n engine i s controlled such that the chemical energy of the a i r - f u e l mixture i s released into useful mechanical work near the top-dead-centre (TDC) of the engine. The mechanical work i s the resul t of the gas pressure acting on the face of the piston at the time of the release of chemical energy i n the chamber. Cylinder pressure i s thus a direct indicator of the combustion process within the engine. Typical physical evidence of c y c l i c variations i s i l l u s t r a t e d i n Fig 1. This diagram shows sample pressure data versus crank angle for 10 consecutive engine cycles at 3000 rpm, wide open t h r o t t l e (WOT) and stoichiometric equivalence r a t i o . The engine was a four stroke cycle; hence two revolutions of the engine or 720 degrees of crank angle constitutes one cycle. In Fig 1 '0' corresponds to the bottom dead centre (BDC) at the beginning of the exhaust stroke, '180' corresponds to the top dead centre (TDC) at the beginning of the intake stroke, '360' corresponds to the BDC at the beginning of the compression stroke and '540' represents TDC at the beginning of the expansion stroke. The plot has no m i s f i r i n g cycles since a l l the pressure traces i n the sample l i e above the motored pressure values. The plot displays wide variations i n the maximum pressure development from one cycle to another 2 with steady operating conditions of speed, t h r o t t l e and spark timing. Variations i n the pressure-time plots are due to v a r i a t i o n i n combustion from cycle-to-cycle. These variations between the pressure-crank angle p l o t s , for the same set of operating conditions, between cycles i s termed cycle to cycle variations i n a spark ignited engine. Consistency i n cycle-to-cycle pressure development would mean an increase i n the mean peak pressure, thereby increasing the power output, improving the fu e l economy and the r e l i a b i l i t y . These improvements are especially useful at leaner f u e l - a i r mixtures because at th i s f u e l - a i r mixture strength we also have improved e f f i c i e n c y and reduced exhaust gas emissions. Thus, to achieve the benefits of the improvements due to decrease i n c y c l i c variations of pressure the combustion variations should be minimized. Cyclic variations i n combustion have been of interest for the past 30-35 years. I n i t i a l l y , the research was aimed at determining the influence of engine and operating variables on c y c l i c combustion varia t i o n s . The major parameters explored were equivalence r a t i o , fuel type, residuals, i g n i t i o n systems including spark energy, combustion chambers, speed, compression r a t i o and intake valve modifications. The consensus conclusions that emerged from the i n i t i a l studies were that: a) although engine operating variables s i g n i f i c a n t l y affect the combustion v a r i a t i o n of an spark i g n i t i o n engine they do not seem to cause them; and b) in-cylinder v e l o c i t y variations that exist near the spark plug at the time of i g n i t i o n affect the c y c l i c combustion variations. Later studies based on the previous experimental findings concentrated mainly on those design parameters which modify the in-cylinder flows near the spark plug at the time of i g n i t i o n . Young, [1] i n a review paper, has shown that such modifications are effective i n reducing c y c l i c variations. Pressure i s the most common parameter i n studying c y c l i c variations because of the ease and accuracy with which i t can be measured and because i t i s d i r e c t l y proportional to the amount of charge burned i n the combustion chamber. Pressure as a parameter i s , i n i t s e l f , i n e f f e c t i v e i n studying the i n i t i a l stages of combustion which i s the important area of interest i n studying the sources of c y c l i c variations. Pressure change i s a direct consequence of the mass - fraction-burned the mass - fraction-burned values at different crank angle positions can b obtained from the experimental pressure data. Though the design modifications that affect the i n i t i a l flame period have been shown to decrease the combustion va r i a t i o n s , the causes of these c y c l i c variations have s t i l l not been determined. The objective of this research i s to study the o r i g i n of these c y c l i c variations whose explanation has eluded researchers for over three decades. The work consists of three stages: a) analysis of experimental pressure data collected from engine tests. b) i d e n t i f i c a t i o n of the nature of turbulence at spark from recent trends i n research i n t h i s area. 4 c) comparison of experimental r e s u l t s with the reported values of turbulence parameters i n accordance with the hypothesis that " C y c l i c v a r i a t i o n s i n combustion i n spark i g n i t i o n engines are mainly due to (and predictable from) the small scale structure of turbulence and can be c o r r e l a t e d with the Taylor microscale and the laminar burning v e l o c i t y " , where the Taylor microscale i s a c h a r a c t e r i s t i c length scale of turbulence described i n d e t a i l l a t e r , and the laminar burning v e l o c i t y i s the burning v e l o c i t y of the f u e l - a i r mixture i n the engine. Experiments were conducted on an engine (described i n chapter 3) at d i f f e r e n t operating conditions of speeds, equivalence r a t i o s and geometries. F i r s t l y , the experimental pressure data i s processed to obtain the values of mass-fraction-burned at every crank angle p o s i t i o n fo r a l l the cycles within the sample data at a given set of operating conditions. Secondly, the standard deviation i n burning times i s determined at the d i f f e r e n t values of mass-fraction-burned within the sample data. The values of the standard deviation i n burning times at higher mass-fraction-burned values are used to extrapolate the values of standard d e v i a t i o n i n burning time i n the i n i t i a l burning period i . e . fo r zero mass-fraction-burned. This i n i t i a l period following spark i s the main area of i n t e r e s t . This randomness i n the i n i t i a l stages of combustion i s the extrapolated standard deviation i n burning time. Research i n the area of the nature of turbulence structure i n a spark i g n i t i o n engine provides quantitative information on the structure of turbulence, the turbulence parameters such as turbulence i n t e n s i t y , 5 and the length scale. Most of these studies aimed at understanding turbulence within the engine have been conducted i n a motored engine (without combustion) wherein the spark plug i s replaced by a hot wire and measurements taken using a Constant Temperature Anemometer (CTA). More recent studies i n the same area of in-cylinder flows within the engine are conducted using Laser Doppler Anemometry (LDA). Results using either of the two methods i n an engine show comparable results for the region near the spark plug at TDC during combustion. Inferences from experiments within the wind tunnel also help to obtain the nature of turbulence within the engines. The turbulent flow i n the cylinder at the TDC i s random and i s dependent on the engine operating conditions. The turbulence can be characterised by determining the nature, the length scales and the turbulence intensity of the flow. This characterization, along with the idea that the spark i s almost a point source, shows a random behaviour of the i n i t i a l flame-kernel propagation with time, c a l l e d the mean random time delay. The comparison between the value of the extrapolated standard deviation i n burning time and the mean random time delay i n burning time shows a l i n e a r l y increasing relationship between the extrapolated standard deviation i n burning time from the experimental data with the data on turbulence as inferred from the trends of recent research. The following chapters expand on the information provided here and then discuss the results obtained using the above mentioned hypothesis. 2. LITERATURE REVIEW 2.1 Introduction This chapter reviews the ava i l a b l e l i t e r a t u r e on c y c l i c v a r i a t i o n s i n spark i g n i t i o n engines i n combustion and pressure development. Most of the experiments described herein were c a r r i e d out by systematically changing one v a r i a b l e at a time and observing i t s e f f e c t on a parameter chosen to characterize c y c l i c v a r i a t i o n s . The various parameters used by researchers i n the study of c y c l i c v a r i a t i o n s are: a) Peak Pressure: the maximum cyl i n d e r pressure within each combustion cyc l e . b) Maximum rate of pressure r i s e c) Crank angle at which peak pressure occurs d) Flame a r r i v a l times: the time f o r the flame front to t r a v e l across the chamber or between flame detectors at s p e c i f i e d points. e) Burning times: the time duration from i g n i t i o n to s p e c i f i e d mass-burned-fraction or complete combustion. f) Indicated mean e f f e c t i v e pressure: the work per cycle divided by the displacement volume. The f i r s t f i v e parameters described above are d i r e c t l y r e l a t e d to the combustion process and help i n quantifying the c y c l i c v a r i a t i o n s . The s i x t h parameter i s an i n t e g r a l parameter which i s more useful i n determining the e f f e c t s of combustion v a r i a t i o n s on engine speed or ve h i c l e motion. The ease and accuracy of measuring the pressure i n the combustion chamber using p i e z o - e l e c t r i c transducers has made the peak pressure or rate of pressure r i s e the most commonly used parameter i n 7 studying c y c l i c variations i n engines. The i n i t i a l burning period i n an engine (following spark) i s of p a r t i c u l a r interest i n this research due to the evidence (which w i l l be discussed l a t e r ) that c y c l i c variations have been found to originate early i n the combustion period. The time to burn the f i r s t 5% of the fu e l may, therefore, be more s i g n i f i c a n t than the c y c l i c variations i n peak pressures i n any discussion of the causes of c y c l i c variations. The c y c l i c v a r i ations, which are the subject of this review, are not those which are associated with engine m i s f i r i n g or lack of homogeneity i n the f u e l - a i r mixture or malfunctioning of the i g n i t i o n system. They are those present i n a well designed, well tuned engine operating on f u l l y mixed high quality fuels. 2.2 Effect of Air-Fuel Mixture Composition The p r i n c i p a l characteristics of the inflammable a i r - f u e l mixture i n the engine are the equivalence r a t i o , f u e l type, and the degree of charge d i l u t i o n by residual gas from the previous cycle. Equivalence Ratio Warren and Hinkamp [44] studied the effects of change i n equivalence r a t i o on c y c l i c variations i n a single cylinder modified CFR engine using well mixed iso-octane fuel at a compression r a t i o of 9.5:1, WOT, and MBT spark timing at 1200 rpm. Using ion i z a t i o n gaps to detect the flame a r r i v a l times at 73mm from the spark plug, they observed minimum variations i n flame a r r i v a l times at 1.15 equivalence r a t i o . As a f r a c t i o n of mean a r r i v a l times, the minimum spread was reported to be 0.38. The spread i n flame a r r i v a l times increased with both richer and leaner mixtures. They also showed that this minimum v a r i a t i o n i n flame 8 a r r i v a l times occurred at the mixture strength corresponding to the maximum power. In th i s study, i t was found that minimum variations i n flame a r r i v a l times occurred when the mean a r r i v a l times were a minimum i. e . , mean flame speeds were the highest. Using a single cylinder Renault engine and iso-octane as the fuel Karim [11] observed minimum c o e f f i c i e n t of variations i n the range of 1.25 to 1.35 equivalence r a t i o for speeds of 3500 and 2500 rpm at 8.5:1 compression r a t i o . In a d d i t i on, Karim noted that the value of the mean co e f f i c i e n t of v a r i a t i o n a) approached the weaker mixture strength as the speed was increased; b) increased as the equivalence r a t i o was changed from the optimum value; and c) the value was never less than 5% even under the most steady operating conditions. Soltau [10] used a si m i l a r , but ipetrol f u e l l e d , engine and observed minimum v a r i a t i o n i n the peak pressure at 1.060 to 1.230 at 9:1 compression r a t i o at 3500 rpm and 500 rpm respectively. Both Soltau and Karim observed best-power values at the equivalence r a t i o corresponding to the minimum variations i n the measuring parameter. Thus, the equivalence r a t i o was found to be an important factor influencing c y c l i c variations i n combustion and subsequent pressure development i n the engine. Minimum c y c l i c variations i n combustion were found to occur at the equivalence r a t i o corresponding to the mixture strength for maximum power t y p i c a l l y i n the range of 1.06 to 1.35, depending on the speed, fuel and the compression r a t i o . At these mixture-strengths the combustion duration was the shortest and the values of peak pressure were the highest. 9 The e f f e c t of measuring parameter such as peak pressure, COV and flame a r r i v a l times being such that v a r i a t i o n s i n flame a r r i v a l times increase slowly away from the minimum point at both r i c h and lean equivalence r a t i o s and v a r i a t i o n s i n peak pressure increase r a p i d l y from the minimum point. Fuel Type Fuels with f a s t e r flame speeds can release a larger part of t h e i r energy near TDC where the volume change due to p i s t o n movement i s minimum. Pressure v a r i a t i o n s , therefore, are mainly due to the combustion v a r i a t i o n s . With slower burning v e l o c i t y , s u b s t a n t i a l energy i s released l a t e i n the cycle, past TDC, when the volume i s changing f a s t e r due to the increasing p i s t o n v e l o c i t y . The v a r i a t i o n s i n pressure due to the combustion v a r i a t i o n s then include the e f f e c t of the changing pressure due to r a p i d l y varying c y l i n d e r volume during t h i s part of the cycle motion. A numerical c a l c u l a t i o n undertaken i n appendix B shows the e f f e c t of t h i s combustion volume phasing on the magnitude of the pressure. Starkman, Strange and Dahm [54] performed experiments i n a single c y l i n d e r CFR engine i n which i o n i z a t i o n gaps were placed i n the path of the flame t r a v e l and were used to monitor flame a r r i v a l times of the r e a c t i o n front f o r many cycles. They found that f or each f u e l studied there ex i s t e d a minimum reaction front propagation rate which was a function of equivalence r a t i o . For the n i t r o p a r r a f i n family, the peak r e a c t i o n front propagation rate was approximately near 0 = 1 . 0 and for iso-octane and methanol the peaks were at 0 = 1.15 and 1.45 r e s p e c t i v e l y . Thus, the equivalence r a t i o at which minimum c y c l i c 10 variations occurred depended greatly on the fuel used. Starkman et a l . also showed that the maximum flame speeds for different fuels had dif f e r e n t magnitudes. Methanol had the highest normal rate of reaction front propagation of 180 ft/sec. The different rates of pressure r i s e i s thus related to the fuel used i n the study and better combustion-volume phasing of the fuels with faster flame speeds w i l l show less pressure variations compared to the slower burning fuels. To study the effects of different fuels, both l i q u i d and gaseous, on the flame development i n a combustion chamber using a Renault engine, Soltau [10] noted that for a certain equivalence r a t i o the mean va r i a t i o n i n pressure was not i d e n t i c a l for a l l the fuels and some pressure v a r i a t i o n was observed with each and every fuel fed to the engine. He also found that a pre-mixed charge obtained with gaseous fuels such as methane, towngas and butane did not display less pressure fluctuations than a well-mixed l i q u i d petrol f u e l - a i r mixture carburetted or sprayed into the intake manifold. Thus, the magnitude of.the propagation flame speed and the mixture strength at which i t occurs are the two important f u e l related c h a r a c t e r i s t i c s that influence c y c l i c variations i n pressure development. I t can also be deduced that the faster the fuel burns, the less the cycle i s troubled with peak pressure fluctuation from one cycle to another. Charge D i l u t i o n Karim performed tests i n which the l e v e l of the residuals i n the chamber was increased by pa r t l y closing the t h r o t t l e . From these tests he found the minimum c o e f f i c i e n t of v a r i a t i o n increased from 0.08 at WOT to 0.10 at 1/4 t h r o t t l e and 0.25 at 1/8 open t h r o t t l e . He concluded that increased residuals resulted i n higher c y c l i c pressure v a r i a b i l i t y . Karim found that increased d i l u t i o n of the fresh charge with either nitrogen or carbon dioxide resulted i n increased variations i n peak pressure. The difference i n the v a r i a t i o n of peak pressure using added carbon dioxide or nitrogen was r e l a t i v e l y small, which showed that the effect of the residual concentration on the pressure v a r i a b i l i t y did not depend on the major constituent of the residual gases. To eliminate residuals, Soltau operated his engine by "skip" f i r i n g every fourth cycle. From the P-V diagrams generated, heobserved that almost complete purging of residual gases resulted i n steadier operation although some v a r i a t i o n s t i l l occurred. This steady operation, he noted, was due to the fast burning that occurred i n the absence of residuals. The parameter (IMEP) used to study c y c l i c variations i n th i s case were qu a l i t a t i v e and the numerical results were not presented by the author. Patterson [40] investigated the influence of residuals by "skip" f i r i n g every fourth, second and every cycle on a CFR engine fueled with indolene at about 0.80, MBT spark timing and 1600 RPM. He observed that results of the c y c l i c variations i n maximum rate of pressure r i s e for a l l the cases tested showed no s i g n i f i c a n t changes. This results contradicts Soltau's or Karim's results and can be explained by noting that the results r e f l e c t the combined effects of residuals and MBT spark timing on c y c l i c variations. Thus, an increase i n d i l u t i o n whether with exhaust residuals or with other inert gases, was generally found to result i n increased c y c l i c 12 variations i n pressure development. This pressure development could have been due to decreased flame speeds i n the presence of residuals. 2.3 Effect of Ignition Variables The effects of the i g n i t i o n variables on c y c l i c combustion variations reviewed are- i g n i t i o n system, electrode geometry and spark j i t t e r . I g n i t i o n System Soltau used two different i g n i t i o n systems to investigate the influence of the spark energy on the burning process. The f i r s t one was a standard suppressed c o i l i g n i t i o n system. The other system was modified with a rheostat i n the primary winding to reduce the primary c o i l current and thus the spark energy. Both systems i n i t i a t e d a single spark at the plug electrode. He noted that at any load or speed the energy content of the spark had no influence on the rep e a t a b i l i t y of the cycles as long as no m i s f i r i n g occurred. However, at the fringe of a i r - f u e l i g n i t a b i l i t y , i f the energy was reduced, then m i s f i r i n g did occur. He also found that with a wide-open t h r o t t l e , the a i r f u e l r a t i o at which the engine started m i s f i r i n g was v i r t u a l l y the same for a l l p r a c t i c a l amounts of spark energy, as long as the gap length was greater than the quenching distance. Soltau found that pressure records taken under i d e n t i c a l conditions of load and speed but with spark energy varying from 0.20 to 200 mJ showed no difference i n peak pressure v a r i a t i o n . Patterson [40] studied the contribution of the i g n i t i o n system to the combustion variations by using a high energy fast-rise-time (40 usee) capacitive discharge system and an inductive system (120 /isec) and 13 observed no difference i n the mean torque at the dynamometer. Therefore, there i s l i t t l e evidence of the influence of the type of i g n i t i o n system on the c y c l i c v a r i a t i o n i n the absence of m i s f i r i n g . Spark Electrode Geometry Soltau [10] used different types of electrode shape on the spark plug i n a Renault engine and observed no difference i n the peak pressure variations and I.M.E.P. He used non standard forms of electrodes such as sharp points, special discharge surfaces and large mass plug points. The shape of the spark plug was thus i n s i g n i f i c a n t i n studying c y c l i c variations ( i . e . electrode shape was found to have no effect on c y c l i c variations of pressure). Spark J i t t e r Spark J i t t e r i s defined as the v a r i a t i o n i n the spark timing from cycle-to-cycle. This j i t t e r could be due to the v i b r a t i o n of the drive or d i s t r i b u t o r mechanism so that i t does not occur at the same crank angle for each cycle within the sample. Soltau [10], from his experiments using a standard type of d i s t r i b u t o r and Renault research engine, noted that the point of i g n i t i o n was repeatable. He used a quartz-window engine and high speed photography to f i n d that the point of i g n i t i o n did not vary by more than 2° crank angle due to the v i b r a t i o n i n the d i s t r i b u t i o n . Assuming that i n each combustion cycle the heat release diagram i s s i m i l a r , Soltau calculated that i t would require variations i n spark timing of over 15° at 2500 rpm to produce the observed differences i n peak pressure. Careful examination of the i g n i t i o n setting by Karim [11] revealed that spark at a point setting i s consistent to within 1.5°crank angle. 14 Albrecht et a l [53] studied the development of the spark discharge, as we l l as the i n i t i a t i o n of chemical reaction experimentally using high frequency measuring techniques i n an inflammable mixture. They noted that the ac t i v a t i o n radicals could be detected at an early stage (about 10 nanoseconds) and the s t a r t i n g point for combustion was determined to e x i s t between 10 to 20 microseconds. This led them to conclude that the spark process i s highly repeatable and does not contribute to the c y c l i c v a r i a t i o n s . Thus, Soltau and Karim noted that spark j i t t e r was too small to account for the observed c y c l i c variations. Summarizing the effects of i g n i t i o n variables on c y c l i c variations, previous research has shown that a) the improvement i n combustion using d i f f e r e n t i g n i t i o n systems i s i n s i g n i f i c a n t ; b) the shape of the electrode geometry does not affect c y c l i c variations;and c) the spark i n i t i a t i o n process i s highly repeatable. Thus, c y c l i c variations i n combustion are affected l i t t l e i f at a l l by changes i n the type of i g n i t i o n system, quantity of spark energy, presence of spark j i t t e r and the shape of the electrodes. 2.4 Engine Speed and Compression Ratio Karim [11] found that the influence of speed on combustion v a r i a t i o n i s related to the equivalence r a t i o . He observed that for the lean range of mixtures an increase i n speed reduces the COV. At best power mixture strengths, the speed had no v i s i b l e effect and at r i c h equivalence r a t i o s , an increase i n speed resulted i n a deterioration of COV. Soltau [10] found that the average peak pressure deviation from the 15 mean increased from 7.24 at compression r a t i o of 6:1 to 12.9 at a compression r a t i o of 9:1 and showed steadier influence at a large compression r a t i o when i t decreased from 12.9 to 9.8 at 12:1 compression r a t i o at 2000rpm and best-power equivalence r a t i o i n a Renault engine. Winsor and Patterson [20] found an increase i n peak pressure v a r i a t i o n as engine speed was increased. They conducted tests at an equivalence r a t i o of 1.06, at 8.5:1 compression r a t i o and spark advance of 35° before TDC. To study the effects of compression r a t i o and speed Barton et a l [14] increased the compression r a t i o from 7:1 to 16:1 and speed from 900 to 1800 rpm. Barton et a l observed a) increase i n pressure variations with increase i n speed and compression r a t i o b) increase i n flame speeds and variations i n flame speed with increase i n speed and compression r a t i o . Young [1], i n his review paper, reported that increasing engine speed usually results i n larger c y c l i c combustion v a r i a t i o n and pressure var i a t i o n s . He stated that increases i n flame speed has been attributed to increase i n engine turbulence with engine speed and this higher turbulence also probably causes an increase i n flame speed variations. The increase i n compression r a t i o s l i g h t l y decreases the c y c l i c v ariations because of the lower residuals and higher temperatures. Nevertheless, the values reported on the effect of engine speed and compression r a t i o on c y c l i c variations indicate that the relationship i s weak. 2.5 Effect of Combustion Chamber Geometry The design variables considered i n t h i s section are r e l a t i v e l y 16 r i g i d such as chamber shape, spark timing and valve shrouding. They are r i g i d i n the sense that they cannot be changed i n the course of experiments. Chamber Shape and Spark Location Young (1) made a comprehensive study of three di f f e r e n t combustion chambers and noted that the best chamber shape from the c y c l i c dispersion point of view i s the one that allows the greatest amount of cylinder volume to be engulfed per unit of t r a v e l of an assumed spherical flame front propagating from the spark plug. This e f f i c i e n t chamber with the e f f i c i e n t location of the spark plug would have the shortest combustion duration period of a l l possible locations of the spark plug and hence the lowest c y c l i c variations of the engine. Soltau [10] observed decreased peak pressure variations when the charge was ignit e d by moving the spark plug near or to the center of the combustion chamber rather than placing i t at the near wall location. Hirao and Kim [41], i n t h e i r experiment, moved the spark plug location from d i r e c t l y above the piston to the more open volume near the valves i n an L head engine. They observed lower c y c l i c variations and noted that any change which decreased the maximum flame travel distance or increased the rate of mass burning and thus decreased flame travel times resulted i n lowered c y c l i c variations. Thus, the best chamber and spark plug combination would have the shortest combustion duration. A short combustion duration implies a fast burning cycle since the fast burning cycle releases most of i t s energy at or near TDC where there exists a good volume-pressure phasing. This phasing results i n lower values of c y c l i c v a r i a b i l i t y i n combustion 17 duration. Spark Timing Karim [11] found that the effect of spark timing on the r e l a t i v e peak pressure variations was dependent on the mixture strength. From tests at the r i c h mixture of 1 . 1 5 0 , using iso-octane as the f u e l , Karim found that the effect of spark timing on the r e l a t i v e peak pressure variations were constant for a spark timing range of 30°to 70° BTDC and increased with retard i n spark less than 30° BTDC; As the equivalence r a t i o was made leaner, spark timing had an increasingly stronger effect on the r e l a t i v e peak pressure variations. For a l l the cases considered Karim found that minimum c y c l i c pressure variations occurred at MBT spark timing. Warren and Hinkamp [44], using i o n i z a t i o n gaps along the flame path, observed minimum variations i n flame a r r i v a l time near MBT spark timing. At thi s minimum the spread was about 35% of the t o t a l t r a v e l duration. The io n i z a t i o n gap was located 73mm from the spark plug so the t o t a l t r a v e l duration included both the i g n i t i o n delay and the actual propagation rate. There i s a general consensus regarding the views presented above that minimum variations occur at the MBT spark timing and that the effect of spark timing i s influenced by the mixture strength and spark plug location. Valve Shrouding Patterson [40] investigated the effect of turbulence and mixture motion on c y c l i c variations by observing the effect of shrouded intake valve. He observed a decrease i n the pressure rate v a r i a t i o n from about 18 55% with the normal unshrouded valve to about 30% with a shrouded intake valve. The shrouded intake valve induced s w i r l i n a propane fu e l l e d , CFR engine at 1600 rpm and WOT condition. The experiment showed that the absolute spread i n pressure rates remained e s s e n t i a l l y unchanged, while the mean rate was nearly doubled. Patterson postulated that s w i r l produced by th i s shrouded valve affects early flame kernel development by smearing the kernel and increasing i t s surface area. As s w i r l increased the combustion rates, Patterson postulated that c y c l i c variations i n mixture motion would lead to c y c l i c variations i n pressure or any other parameter used i n the study of c y c l i c variations. Broeze [42] used three different types of intake valves on a CFR research engine: a standard unshrouded intake valve, a shrouded valve and a ca s t e l l a t e d valve, to examine the effect of the change i n intake valve geometry on the delay period and the main combustion period. Broeze defined the delay period as the period without appreciable pressure r i s e on the f i r e d engine pressure curve from the motored engine pressure curve under the same operating conditions. The shrouded intake valve was f i l e d progressively such that a l l the three valves gave the same volumetric e f f i c i e n c y . Broeze found that the standard non-shrouded valve had the longest burning period for both the i n i t i a l and the main stage period. The castellated valve shortened the i n i t i a l and the main stage burning period, possibly due to the increased turbulence. The shrouded intake valve results showed that the i n i t i a l burning period was shortened more than with the castellated valve and the main burning stage was the same as with the castellated valve. Broeze [42] also found that the i g n i t i o n delay period was strongly 19 affected by the mixture strength for a l l the intake valves considered and the main combustion duration was nearly constant with change i n mixture strength. The shrouded valve produced enhanced turbulence as well as s w i r l . Broeze thus postulated that both s w i r l and turbulence decreased the boundary layer thickness and allowed the developing flame kernel to interact with the turbulent mainstream e a r l i e r . Furthermore, since s w i r l could p e r s i s t longer than the compression stroke, i t was thought to be more ef f e c t i v e than turbulence i n decreasing the i n i t i a l delay period. Thus, though Broeze did not consider c y c l i c v a r i a tions, h is experimental results using d i f f e r e n t intake valves show that the shrouded intake valve and a castellated valve have a strong effect of decreasing the i n i t i a l delay period. Young [1], i n his review paper, noted that mixture motions and turbulence are mostly responsible for c y c l i c variations i n combustion and subsequent pressure development. He also stated that due to the d i f f i c u l t y of measuring in-cylinder flows, the role of turbulence and mixture motion i n c y c l i c variations has been largely inferred from the physical changes made to the engine. Karim [11], i n his study of c y c l i c variations stated that "by far the greatest variable element i n engine operation i s that of charge motion inside the cylinder both i n quantity and di r e c t i o n . " Summarizing the effects of the different design variables, i t can be seen that valve shrouding and turbulence are the two factors that can improve c y c l i c v ariations. The effect of s w i r l induced by the shrouded 20 valve i s more than that of turbulence alone produced by the castellated valve. Valve shrouding has been shown to influence the i n i t i a l burning period although there s t i l l exists randomness of the flow within the engine at the time of the spark. The main conclusion from t h i s p a r t i c u l a r design variable i s that i f the i n i t i a l burning period can b e affected, then the c y c l i c variations can be reduced. 2.6 Comments The importance of the i n i t i a l burning period has also been shown b y various other researchers. Soltau [10] used coal dust for flow v i s u a l i z a t i o n i n a modified Renault engine using a quartz-window with no squish or s w i r l . He observed no conformity to any pattern within the engine from the high speed-movies collected by him from t h i s simple chamber. He then postulated that t h i s randomness i n flow contributes to the randomness i n c y c l i c variations i n engines. Peters and Borman [12] have reported that cycles with varied burning rates i n the i n i t i a l burning period continue to have lower burning rates even when combustion i s well under way. Belmont, Hancock and Birmingham [36], from viewing a succession of indicator diagrams from successive cycles, noted that the future of the combustion appeared to be defined at a very early stage i n the cycle. Young's review paper summarized the findings by stating that "cycle-to-cycle variations i n combustion originate early i n the combustion process. Although hard evidence i s s t i l l lacking, i t i s thought that a main cause of these variations i s the cycle-to-cycle variations of v e l o c i t y i n the v i c i n i t y of the spark plug at the time of i g n i t i o n , which affects the developing flame kernel." 3. APPARATUS AND INSTRUMENTATION 3.1 Introduction This chapter provides an overview of the experimental setup to study c y c l i c variations i n the engine. Fig 2 shows gives a b r i e f idea of the experimental setup. F i r s t a b r i e f description of the apparatus i s given. Second, the instrumentation used to evaluate the c y c l i c variations quantitatively i s described. Third, the controls are described, as well as the st a r t i n g procedure. F i n a l l y , an overview of the data acqu i s i t i o n and data transfer techniques i s presented. 3.2 Apparatus The apparatus consists of the engine and the dynamometer, a i r and * f u e l intake systems, o i l and cooling systems and the i g n i t i o n system. Engine The engine used throughout the investigation i s a Ricardo research engine. A cross - sectional view of the engine i s shown i n Fig 3. I t i s a four-stroke, single-cylinder, water cooled, spark-ignition engine, having an 80.2mm bore and 88.2mm stroke and compression r a t i o of approximately 8.9:1. The engine i s f i t t e d with the "bath-tub" combustion chamber shown i n Fig 4 and has v e r t i c a l overhead valves actuated from an overhead camshaft driven by a bel t through the crankshaft. The specifications of the engine are given i n Table 1. The combustion chamber forms the heart of the apparatus. The related components that form the whole assembly are now b r i e f l y described. A i r I n l e t System The a i r - i n l e t system consists of an a i r f i l t e r , aluminum a l l o y heater chamber with a 1 kW heater, t h r o t t l e body assembly with servo motor controlled t h r o t t l e , and i n l e t manifold. The position of the t h r o t t l e b u t t e r f l y i s remotely controlled from the control console. Signals for the temperature indicator are provided by a duplex thermocouple i n s t a l l e d i n the i n l e t manifold. A laminar flow element (Cussons VFAM-120C) i s mounted ju s t ahead of the a i r f i l t e r to enable accurate metering of the a i r flow. The pressure drop across the laminar flow element i s sensed by a d i f f e r e n t i a l manometer i n the control room. Fuel Intake System The fuel-intake system consists of a 1.5" Meriam laminar flow element, piping and a flow control valve which i s used to vary the a i r - f u e l r a t i o . The fuel (natural gas) from the mains passes through the regulator before i t goes through the laminar flow element. A Celesco P7D d i f f e r e n t i a l pressure transducer measures the pressure drop across the laminar flow element. This signal from the d i f f e r e n t i a l pressure transducer i s then amplified by the Celesco low cost c a r r i e r demodulator, and made compatible with the data acqu i s i t i o n system. The pressure drop across the laminar flow element i s also sensed by a d i f f e r e n t i a l manometer i n the control room. Coolant System The coolant system c i r c u i t i s closed and pressurized. The coolant, consisting of water and commercial an t i f r e e z e / i n h i b i t o r , i s drawn from the bottom of the header tank and pumped through the a heat exchanger before passing through to the engine block and cylinder head. The header tank contains low coolant l e v e l sensor and two thermocouples one t r i p s the system i f overheated and the other provides temperature data to the control console. The temperature of the cooling water can be controlled by the l i m i t switches on the cooling tank on the engine. Temperatures i n the range of 60 to 75°C were observed on the console i n the course of these experiments and the temperature was set to t r i p at 100°C due to the overheating of the coolant. O i l System The l u b r i c a t i n g o i l which i s contained i n the engine sump i s pressure fed to the crankshaft and the big end bearings and camshaft bearings. The o i l pressure i s lim i t e d to 4 bar by a r e l i e f valve i n the engine. A pressure switch on the engine t r i p s the engine i n case of o i l pressure f a i l u r e . A thermocouple t r i p s the system i f overheated, and another thermocouple provides o i l temperature data to the console. Dynamometer The dynamometer i s a D.C machine mounted on trunnion bearings supported by pedestals. Load i s measured by means of a torque arm mounted from the frame of the dynamometer. The arm carries a s t r a i n gauge load c e l l whose output provides a continuous display of the torque at the control console. A pedestal houses a c a l i b r a t i o n weight equivalent of 20 Nm for s t a t i c checking of the torque measuring system. The dynamometer i s operated through a KTK th y r i s t o r converter unit. The dynamometer can act as a d.c. motor to drive the engine during s t a r t i n g and motoring operations or as a d.c. generator when the engine i s i n f i r i n g mode. A tachometer mounted on the dynamometer shaft provides a speed signal to the closed loop speed control system. The engine i s coupled to a D.C dynamometer and u t i l i z e s regenerative load absorption which f a c i l i t a t e s motoring over variable speed range and assessment of the f r i c t i o n a l losses when required. The dynamometer unit i s capable 24 of absorbing up to 44 kW of engine power at up to 5500 rpm. Ig n i t i o n System The engine i g n i t i o n system i s a conventional c o i l and spark plug arrangement with the primary c o i l c i r c u i t operated by a "Lumenition" electronic i g n i t i o n unit. The p r i n c i p l e of the Lumenition unit i s that signal pickups of speed and TDC reference from the flywheel on the crankshaft are processed by the electronic system along with the desired remotely set signal of the i g n i t i o n timing from the control console. The lumenition system then provides the i g n i t i o n trigger signal at the correct spark advance. This electronic i g n i t i o n system model PHY 623 eliminates spark j i t t e r due to mechanical cams or d i s t r i b u t o r s . 3.3 Instrumentation The instrumentation on the research engine which aids i n monitoring the engine as well as obtaining quantitative data i s now described and i s as shown i n Fig 5. The pressure transducer, o p t i c a l pickup unit, a i r and gas flow metering units, lambda sensor, speed and torque measuring sensors constitute the instrumentation described below. The data a c q u i s i t i o n systems used are also described. Pressure Measurement The engine i s equipped with a K i s t l e r 6121 p i e z o - e l e c t r i c pressure transducer mounted i n an extension sleeve into the outer sleeve located i n the cylinder head of the engine. For the p i e z o - e l e c t r i c transducer no water jacket or cooling water i s necessary since i t i s s e l f cooling. The charge output from the transducer was integrated by the K i s t l e r model 5004 charge amplifier to y i e l d a voltage proportional to the cylinder pressure. Thus the signal from the transducer yielded the cylinder pressure and rate of pressure r i s e . The display of the pressure signal was monitored using a Textronix oscilloscope. One hundred consecutive cycles of pressure data were d i g i t i z e d at a rate of 1 sample/degree for each set of operating condition. The combination of the pie z o - e l e c t r i c pressure transducer and charge amplifier was calibrated with a dead weight tester i n the laboratory p r i o r to performing any tests. The c a l i b r a t i o n curve for the transducer i s provided i n appendix A. Volume Assignment The accuracy of the pressure measurement was complemented by an accurate measurement of the crank angle position using an AVL optical—pickup—unit. An o p t i c a l crank angle pickup unit model 360c/600 was mounted on the engine crank shaft. This sensor generated pulses every crank angle degree which were used to trigger the data acquisition system. A single pulse from the BDC i s used to synchronize the data with the po s i t i o n of the crank shaft. The volume at any instant of the piston motion i s then deduced from the physical dimensions of the engine and the crank posi t i o n . The physical dimensions can be determined quite accurately hence the accuracy of the t o t a l volume cal c u l a t i o n i s l i m i t e d by the accuracy of both the clearance volume measurement and the determination of crank angle. The synchronization of the pressure-volume data i s further v e r i f i e d by analyzing the motored engine data i n chapter 4. The data obtained using an engine driven o p t i c a l pulse generator synchronizes d i g i t a l scanning of pressure signal with crank angle . A BDC marker pulse on one channel of the pulse generator was used to i n i t i a t e scanning. The second channel provides 600 pulses which are further resolved to 1800 pulses through the pulse m u l t i p l i e r and depending on the number of pressure points to be scanned they are further divided by the pulse divider. In this p a r t i c u l a r case 360 pulses per revolution at one crank angle degree i n t e r v a l determines the actual scanning points. As the location of each scanning pulse was fi x e d i n r e l a t i o n to the marker pulse (BDC pulse) the locations of the other scanning pulses were determined by determining the crank angle at which the marker pulse of BDC occurred. A i r flow Measurement The metering of the a i r inducted into the engine i s done by reading the d i f f e r e n t i a l pressure across the laminar flow element i n inches of water gauge on an in c l i n e d d i f f e r e n t i a l manometer situated i n the control room. The laminar flow element i s an accurate measuring instrument which i s calibrated by the manufacturer. The c a l i b r a t i o n constant at standard normal conditions i s provided with the instrument. These c a l i b r a t i o n constants are used to translate the pressure into the volume flowrate. The c a l i b r a t i o n curve for the laminar flow element i s provided i n appendix A. Gas flow Measurement The metering of the f u e l inducted into the engine i s done by using the d i f f e r e n t i a l pressure across the laminar flow element i n inches of water gauge on an inc l i n e d d i f f e r e n t i a l manometer situated i n the control room. The laminar flow element i s an accurate measuring instrument which i s calibrated by the manufacturer and the c a l i b r a t i o n 27 constant at standard normal conditions are provided with the instrument. These c a l i b r a t i o n constant are used to translate the pressure into the volume flowrate of the gas into the engine. The c a l i b r a t i o n curve for the laminar flow element i s provided i n appendix A. Fuel-Air Ratio The normalized a i r - f u e l r a t i o i s the r a t i o of the actual a i r - f u e l r a t i o to the theoretical a i r - f u e l r a t i o . Control of the a i r - f u e l r a t i o was assisted by the use of a zirconium dioxide oxygen sensor i n the exhaust pipe. The output of the sensor was fed to a d i g i t a l voltmeter to indicate whether the engine was running r i c h (approx 0.8 volts),stoichiometric (approx 0.1 to 0.5 v o l t s ) , or lean (less than 0.Iv). However, this i s a rough indicator of the range of operation, and i s more useful i n a s s i s t i n g with the stoichiometric a i r - f u e l r a t i o . The actual values of f u e l - a i r r a t i o are shown on the PC monitor screen using the software. Speed Measurement Speed measurement i s made by the tachorrpter attached to the dynamometer shaft. Speed i s set by a set-speed potentiometer on the control console. A closed loop control system for the speed compares the actual and proposed speeds by the comparator. The error signal i s then sent to maintain a constant speed irrespective of t h r o t t l e setting changes, f u e l - a i r r a t i o change or spark advance. The engine speed range i s 1200-5500 rpm. Actual speed values on the console are steady to within +0.2%. Torque measurement The s t r a i n gage load c e l l s mounted on the torque arm which i s mounted on the frame of the dynamometer provides the torque values as they are seen on the control console. A test was conducted to examine the v a r i a t i o n i n the torque meter at 2000 rpm i n a motored engine. The s t a t i c c a l i b r a t i o n of the engine using 20 Nm weight both before and after running the engine for about 10 minutes showed a v a r i a t i o n i n the torque meter of about 0.60 Nm. The torque values from the dynamometer as seen on the console show a v a r i a t i o n i n the results that are collected from the torque meter at every measuring point of engine data c o l l e c t i o n . Data Acquisition System Two data a c q u i s i t i o n systems have been employed on this project to allow r e a l time data to be collected for processing as shown i n Fig 6. The analogue signals from the instrumentation on the engine v i z : i g n i t i o n advance, airflow, f u e l flow, speed and torque terminate near the f i r s t data acqu i s i t i o n system i n a mil-spec connector, which plugs into the c i r c u i t box i n control room. The c i r c u i t box contains screen terminal boards which connect to the data translation DT2801A data a c q u i s i t i o n board i n s t a l l e d inside the PC. Another c i r c u i t board provides trigger and clock pulses to the ISAAC 2000 where pressure data and BDC pulses are being recorded. Signals from the mil-spec connector entering the terminal boards are o p t i c a l l y isolated and ion-pass f i l t e r e d at 60 Hz before passing into the A/D converter inside the PC v i a the ribbon connector. The second system consists e n t i r e l y of an ISAAC 2000, which i s a fast data a c q u i s i t i o n unit and has 64K of buffer memory, off l i n e block transfer of data and highly f l e x i b l e sample control system. I t uses 29 Labsoft I I software and i s compatible with the IBM PC used for this experimental setup. Sampling rates of 200 kHz are available at 16 channels. 3.4 Operational Control The apparatus and procedure for engine control are now presented. The control console i n the control room i s f i r s t described followed by the s t a r t i n g procedure of the engine. Control-Console The control console i n the control room shows the d i g i t a l torque i n the range of 0-50 Nm and d i g i t a l speed i n the range of 0-120 rev/sec and i g n i t i o n advance +70 to -20 degrees analogue and running hours 0-999 d i g i t a l . I t also shows an 8 channel d i g i t a l temperature indicator for i n l e t a i r , f u e l , water (engine coolant) and o i l temperature, exhaust gas temperature. Three channels are l e f t open. The controls of the engine room on the console are: a) dynamometer motor mode of start/auto/absorb mode depending on the testing conditions. b) set speed potentiometer to set the required speed on the engine. c) emergency stop button to stop the engine i n case of emergency d) t h r o t t l e p o s i t i o n to control the volumetric e f f i c i e n c y , and e) i g n i t i o n timing to set the spark timing. The safety monitoring system on the console consists of the dynamometer temperature, o i l pressure-low indicator, emergency stop switch, water l e v e l indicator and water and o i l temperature indicators. 30 Starting Procedure After preliminary checking of a l l apparatus and instruments a standard routine as described below i s carried out before any actual f i r i n g or non-firing data i s collected. A check on the o i l l e v e l i n the crank case i s carried out followed by a minimum of two hand crank rotations on the engine to check for any seizing of the piston or to avoid any other seizing problem. The mains are then turned on along with the water for the dynamometer. The engine l u b r i c a t i n g o i l and water pump are started, and the charge amplifier i s l e f t on for about an hour i n a reset mode. The charge amplifier range adjustments should be set to give the longest system time constant without encountering signal d r i f t . The time constant of the pie z o - e l e c t r i c system i s not a measure of the time i t takes the system to respond to an input but rather a measure of the time required for a given pressure signal to decay. The lu b r i c a t i n g o i l temperature i s heated to approximately 40°C before the engine i s started. The engine i s f i r s t set to p a r t l y open t h r o t t l e and then started to rapidly reach a speed of about 1200rpm to avoid running at the natural frequency of vi b r a t i o n of the engine. This procedure described so far i s common to both f i r i n g and non-firing engine studies. For the motored case the design speed i s set and the t h r o t t l e opened wide to obtain WOT condition and the engine i s a l l set to acquire the motored engine data. For the f i r e d engine case the i g n i t i o n switch i s turned on and the fuel supply i s started u n t i l the engine starts stable f i r i n g . To reach the desired operating condition the speed and the t h r o t t l e are slowly coordinated and increased to reach the desired design state from the i n i t i a l condition. The engine i s then run i n f i r i n g mode u n t i l conditions s t a b i l i z e . The power output, e f f i c i e n c y and torque values are then monitored such that the setting of the minimum spark advance w i l l give the best values of torque and power. In both f i r i n g and non f i r i n g engine conditions the data c o l l e c t i o n program i s simultaneously loaded and run to c o l l e c t the data of 100 consecutive cycles at different operating conditions. This program scans the channels on the data acquisition board DT 2801A to read i n the data coming from the various transducers attached to the engine. A t o t a l of 100 values are read i n from each channel and averaged over a 5 second period. The values of voltages through appropriate signal conditioning systems and by integration with software from the PC are updated on the monitor screen of the PC every 5 seconds. For f i r e d engine testing MBT (Minimum spark advance for Best Torque) timing of the i g n i t i o n system i s the value of spark advance at the required t h r o t t l e setting which shows optimum values of brake power and thermal e f f i c i e n c y . After desired operating conditions on the engine are reached the data c o l l e c t i o n program i s loaded on the computer. 3.5 Data Acquisition and Transfer A discussion of the satisfactory set up of the apparatus and the instrumentation i s followed by the procedure for data acqu i s i t i o n and subsequently the transfer of data for processing. Data Acquisition The pressure signals from the charge amplifier and the signals from the AVL o p t i c a l pick up sensor are fed to the circuit-box to condition 32 the signals and then to the ISAAC 2000 data acqu i s i t i o n system for c o l l e c t i o n of data. The software used for data acquisition i s f l e x i b l e and i s an interactive program which asks for input such as the number of cycles for which data has to be collected, the number of channels to be read and the operating speed. This input i s l a t e r used by the IBM PC computer to communicate with the ISAAC 2000 to acquire cylinder pressure at the appropriate intervals following the trigger from the BDC pulses. The operating conditions set, a trigger from the DT2801A board sent to ISAAC 2000 starts acquiring 100 consecutive cycles of data after the expansion stroke. This data i s stored i n the ISAAC 2000 fast data ac q u i s i t i o n system. This stored data i n the ISAAC i s then transferred to the IBM PC onto a diskette. While the data i s being collected by the ISAAC relevant information from the console at that p a r t i c u l a r operating conditions such as speed, a i r flow, fuel flow, temperatures, and the performance results i s noted. Data Transfer The data collected on the PC, are then transferred to the mini computer VAX 11/750 by using a communication package. The data on VAX 11/750 i s now prepared for detailed analysis by reducing i t using a program c a l l e d ISAC2VAX. This program ISAC2VAX concatenates the data into one single f i l e of 100 consecutive cycles. I t s t r i p s the f i r s t seven characters that are transferred with the binary data sent over to VAX, leaving behind the Pressure and BDC pulse data points which are bundled up into one large f i l e for further s t a t i s t i c a l analysis. 4. MEASUREMENTS WITH MOTORED ENGINE 4.1 Introduction Preliminary checks of the motored engine (non-firing) performance are undertaken before f i r e d engine data i s recorded, to validate the d i g i t a l pressure and crank angle data. Pressure data collected from the motored engine shows l i t t l e cycle-to-cycle v a r i a b i l i t y but can y i e l d considerable information about the accuracy and r e l i a b i l i t y of the recording procedures. In a motored engine inhomogenieties, high heat transfer rates and combustion introduced quantities are largely absent. Hence i t i s worthwhile to c r i t i c a l l y analyze the motored pressure data before f i r i n g test data i s recorded. The monitored tests i n a motored engine were carried out at 2400, 3000, 3600 and 4200 rpm, with wide-open t h r o t t l e . While the pressure data are taken from an engine, other pertinent data from the console such as a i r flow rates, speed, temperature and atmospheric pressure are noted concurrently. The pressure data i s analyzed to ascertain: a) Proper phasing of pressure-volume data b) Polytropic exponents of compression and expansion c) Volumetric e f f i c i e n c y , and d) Peak pressures. 4.2 Phasing of Pressure-Volume Data The i n i t i a l check on the data i s to observe the occurrence of peak pressure on the ensemble-averaged pressure data of 100 cycles, with respect to the volume by observing the phasing of pressure vs crank angle plot from Fig 7. The occurrence of peak pressure occurs s l i g h t l y before TDC ( i n the range of TDC to 2° crank angle before TDC) serves as 34 an approximate check of pressure-crank angle phasing. The ensemble-averaged peak pressure does not occur at the same crank angle before TDC for a l l the speed ranges considered i n th i s research, but l i e s within the TDC to -2° before TDC range. The indicator (P-V) diagram, as shown i n Fig 8, serves as a qua l i t a t i v e check of the pumping loop (exhaust and intake stroke) pressure trace. The majority of the exhaust stroke pressure trace i s above the mean exhaust manifold pressure. S i m i l a r l y , during the intake stroke the cylinder pressure f a l l s below the mean intake manifold pressure. The spikes i n the pressure trace during the intake stroke may be due to the high instantaneous gas flow rate due to the changing valve movement during intake. The effect of phasing of the pressure volume data i s magnified i n the IMEP values of the motored engine. The indicated mean effec t i v e pressure (IMEP) i s the theoretical pressure at which a constant pressure expansion from minimum cylinder volume to maximum cylinder volume would produce an amount of work equal to the quantity being considered. The IMEP and PMEP (Pumping Mean Effective Pressure) values for the test cases considered are shown i n Table 2. Table 2 also shows that deliberately retarding or advancing the phasing, the s e n s i t i v i t y of IMEP to the phasing i s as high as 40% per degree crank angle, whereas the PMEP i s r e l a t i v e l y insensitive to changes i n phasing. 35 TABLE 2: S e n s i t i v i t y of IMEP and PMEP to 1° change i n phasing-Motored Engine. NORMAL 1° ADVANCED 1° RETARDED SPEED IMEP PMEP IMEP PMEP IMEP PMEP 2400 -39.3 -24.2 -57.5 -24.1 -21.1 -24.3 3000 -38.5 -39.5 -57.5 -39.6 -19.6 -39.3 3600 -32.9 -55.8 -52.3 -56.3 -13.4 -55.3 4200 -28.9 -86.9 -48.2 -87.7 -09.6 -86.0 Phasing i s , thus, an important check on motored pressure data as i t confirms the compatibility of the pressure transducer and the crank angle pick up unit. Figure 8 i s a logarithmic P-V diagram of motored pressure data. I t contains information about the scaling, phasing and the transducer performance. The compression curve from the IVC to near TDC can be approximated by a polytropic process PVn = constant. This function plots as a straight l i n e on the logarithmic diagram with slope= -n. The deviation from a straight l i n e of this function PVn= constant with slope equal to -n can be caused by several factors v i z : a) Improper Reference Pressure: I f the reference pressure i s improperly assigned at BDC (the transducer used i s piezo-electric) then a small curvature i s noticeable during the f i r s t part of the compression stroke after IVC. Fig 9 shows this effect of an incorrect reference pressure allocated to the p i e z o - e l e c t r i c transducer. Since this i s a simple scaling problem, i t can be e a s i l y corrected. b) Improper Clearance Volume:If the wrong clearance volume i s assigned to the engine similar d i s t o r t i o n of the curve i s observed at the top end of compression stroke towards TDC. The central portion of the compression curves remains r e l a t i v e l y unaffected by wrongful assignment of the values of Reference pressure and/or clearance volume. Deviations from the straight l i n e i n the central region i s an indication that the pressure data and/or pressure transducer maybe faulty . c) Improper Phasing: Improper phasing of the pressure-volume data d i s t o r t s the logarithmic P-V plot. I f the pressure data i s retarded w.r.t the volume then the pressure data at the TDC during expansion are greater than compression pressure data. Figure 10 shows the effect of phasing when the pressure was i n t e n t i o n a l l y retarded w.r.t volume. The higher values of pressure during expansion overlap the compression pressure data. A si m i l a r plot could also res u l t for a faulty transducer. F i n a l l y , the time constant setting on the charge amplifier also could give f a u l t y results by showing d i s t o r t i o n on the logarithmic P-V plot. The log plots of the motored data collected for this experiment d i d not show any of the above distortions and hence the scaling, and c a l i b r a t i o n of the transducer assembly was shown to be acceptable for further engine data c o l l e c t i o n . 4.3 Polytropic Exponents The compression and expansion curve.from the IVC (Inlet Valve Closing) to nearly TDC, and from TDC to EVO (exhaust valve opening) respectively, can be approximated by a polytropic process PVn = constant. Figure 8 shows how the motored pressure data for the four stroke cycle plots as a straight l i n e on a natural log plot. The slope of the plots for the compression and expansion gives the compression and expansion c o e f f i c i e n t s . The slope of the compression and the expansion l i n e represented as a polytropic process i s another indicator of the quality of motored data. The range of the polytropic exponents i s different for di f f e r e n t engine geometries. The expansion exponents are higher than the compression exponents as discussed below. From the f i r s t law of thermodynamics for the system per unit mass dq = du + dw (4.1) dw = Pdv (constant pressure) from the d e f i n i t i o n of enthalpy h = u + Pv (4.2) d i f f e r e n t i a t i n g (4.2) we have dh = du + Pdv + vdP! (4.3) rearranging we have du + Pdv = dh - vdP (4.4) dq = Tds (4.5) dh = CpdT (4.6) CP - - J ^ J - R (4.7) 38 using the relationship (4.2-4.7) we can write the f i r s t law from eq 1 as Tds = dh - vdP (4.8) Tds = CpdT - vdP (4.9) Tds k-1 R dT - vdP. (4.10) div i d i n g throughout by R T we have ds dT dP R k-1 (4.11) from the polytropic equation Pv = constant we have ln(P) + n ln(v) = In(const) (4.12) integrating above we have dP ^ dv — — + n = 0 v from the equation of state we have Pv = RT d i f f e r e n t i a t i n g the above and rearranging we get (4.13) dP dv — + dT from the above we get ds R ds R (k-1) k-1 1 k-1 ds R dP + dv dP P dP k-1 dP P dv v for an isentropic process dP 0 + k + n dv dv where n i s the isentropic exponent. (4.14) (4.15) (4.16) (4.17) (4.18) subtracting the above we get (k - 1 ) ds R - (k-n) dv v (4.19) ds i s negative due to the heat loss to the walls and any other i r r e v e r s i b i l i t y . The term dv i s negative during compression and positive during v expansion so that k > n during compression k < n during expansion. Sample calculations for the engine at the compression r a t i o of 8.93 and i n l e t temperature of 293°K showed that the isentropic exponent value (for both compression and expansion) i s approximately 1.365. The values of the compression and expansion exponents for the test cases i n a motored engine are shown i n Table 3. The results reported show a pattern s i m i l a r to the one discussed above. TABLE 3 : Polytropic Compression and Expansion Exponents- Motored Engine, Polytropic Index n SPEED COMPRESSION EXPANSION 2400 1.35 1.385 3000 1.352 1.385 3600 1.351 1.380 4200 1.352 1.380 40 For the Engine operating conditions of i n l e t a i r temperature = 294°K pressure at BDC = 101 kPa compression r a t i o f ̂ B D C ~) = 8.93 R V T D C J we can calculate the temperature at TDC using isentropic relations k-1 i.e. T = T [ ^ H £ _ ] TDC BDC ^ V T D C •> The above equation gives the temperature of a i r at TDC to be about 720°K at t h i s temperature the value of the isentropic exponent from the a i r tables i s about 1.365. Assuming the temperature v a r i a t i o n at TDC to be about 50°C then the v a r i a t i o n i n the value of k i s + 0.003 4.4 Volumetric E f f i c i e n c y Volumetric e f f i c i e n c y i s the percentage of theoretical charge inside the engine. The plot of the volumetric e f f i c i e n c y for different speeds i s shown i n Fig 11. From this Figure i t can be observed that there i s a loss of volumetric e f f i c i e n c y with increase i n speed of the engine. This loss i n volumetric e f f i c i e n c y i s responsible for the loss of power i n engines at high speeds. The volumetric e f f i c i e n c y rj for a four stroke engine may be defined as: r, = 2 Qair (4.20) v Vs RPM 3 where Qair i s the t o t a l amount of a i r i n m /min inhaled by the engine, Vs i s the stroke volume i n li t r e s / m i n and RPM represents the speed of the engine i n revolutions per minute. 41 4.5 Peak Pressure The ensemble-averaged peak pressures i n the motored engine at di f f e r e n t speeds are shown i n Fig 12. The difference i n the values of the peak pressures for the same compression r a t i o but different speeds i s due to the loss of the volumetric e f f i c i e n c y . In summary, The pie z o - e l e c t r i c transducer i s a r e l a t i v e pressure measuring instrument which can be calibrated using a s t a t i c dead weight tester i n the laboratory for a small range of pressures. A detailed analysis of the motored engine data using the pi e z o - e l e c t r i c transducer i s thus h e l p f u l i n confirming the c a l i b r a t i o n of the transducer. The phasing of the indicator diagram confirms the compatibility of the crank angle pick up unit and the piezo - e l e c t r i c transducer. Other checks l i k e the logarithmic plots of the data and the slopes of the polytropic exponents of compression and expansion further confirm the compatibility of the crank-angle unit and the transducer. 5.FIRED DATA ANALYSIS 5.1 Introduction D i g i t a l data processing was used to quantitatively analyze c y c l i c variations i n a spark i g n i t i o n engine. The data processing included the scaling of the analog pressure transducer output data at each crank angle point, c a l c u l a t i o n of the volume at every crank angle position, c a l c u l a t i o n of mass-burned-fraction from the pressure data and f i n a l l y the s t a t i s t i c a l analysis of the computed mass-fraction-burned data. 5.2 Scaling of Pressure The data from the data acquisition system exists i n an integer form. Two steps are taken to relate these integers to absolute cylinder pressure. a) The integer output data from the data acqu i s i t i o n system ranges of 0 to 4096 of the charge amplifier are f i r s t converted to the r e l a t i v e pressure values using the relationship Pressure = Integer 1 Q * 10 (5.1) 204.8 the integer value of 0 to 4096 corresponds to -10 volts to +10 volts output. The scaling factor of the charge amplifier which gives the voltage to mechanical units conversion i s then used to give the value of the r e l a t i v e pressure corresponding to the integer value. b) The pi e z o - e l e c t r i c transducer provides r e l a t i v e pressures. Hence i t i s necessary to have a means of determining the absolute pressure at some point i n the cycle and then a l l the data are scaled from this value of the reference pressure. We assume that the cylinder pressure at BDC after the intake stroke i s given by 43 where P represents the pressure at BDC and ambient condition, r\ i s the volumetric e f f i c i e n c y and T represents the temperature at intake and the ambient conditions. This value of pressure at BDC i s used as a reference pressure i n a l l the cases considered. The r e l a t i v e pressures are s h i f t e d by a constant value to obtain absolute cylinder pressures. A l l the data are thus scaled using this value of reference pressure to give the pressure values for the whole cycle of intake, compression, expansion and exhaust stroke. 5.3 Volume Calculation The absolute volume i s calculated at any crankshaft po s i t i o n for the engine geometry and the clearance volume of the combustion chamber using the following relationship. where V i s the instantaneous volume, H i s the clearance height, Area i s the cross - sectional area of the combustion chamber, R i s the crank radius, L i s the connecting rod length and 8 i s the instantaneous value of crank po s i t i o n (0=0 at TDC). Minimum volume i s assigned at TDC and i t increases to a maximum at BDC. 5.4 Mass-Burned-Fraction Calculation This section describes the program XPRESS used to calculate the mass-fraction-burned values from the experimentally obtained pressure data from the engine. Only the data for the compression stroke from BDC t i l l the occurrence of spark and the combustion process thereafter are V V = Area H + R (5.3) 44 used. The i n i t i a l conditions of pressure, temperature, and the energy of the i n i t i a l charge p r i o r to the compression are calculated from the constants of the engine geometry and the thermodynamic properties of the various species i n the charge. The thermodynamic properties during the compression process are calculated using the f i r s t law of thermodynamics, perfect gas law and the conservation of energy equations. The actual pressure data i s then read to calculate the mass-fraction-burned values using the conservation of energy and mass. The e f f i c i e n c y of t h i s program has been greatly enhanced by incorporating the application package "STANJAN". STANJAN calculates the thermodynamic properties of the hydrocarbon f u e l and the values generated by t h i s package are placed i n tables which are read by XPRESS. A f u l l l i s t i n g of the program i s given i n the appendix F. I n i t i a l conditions The i n i t i a l conditions of the mass and the energy of the charge i n the cylinder at the BDC are deduced from engine test data. The a i r and natural gas (fuel) flow rates , the intake manifold temperature, and the ambient pressure are entered before calculating the composition of the cylinder contents (charge) p r i o r to the compression stroke at BDC. The chemical equation for the combustion of a hydrocarbon fuel in a i r at a given r e l a t i v e f u e l - a i r r a t i o gives the mole f r a c t i o n of a l l the species present i n the charge. The chemical equation for the combustion of a hydrocarbon fuel i n the a i r at a s p e c i f i c a i r - f u e l r a t i o i s : CN HM + C N+M/4]A 0 + 3.76N 2 2 NCO + M/2 H 0 + [ N+M/4] (A-l)O +3.76A N 2 2 45 (5.4) where C,H,0, N,CÔ , H 2 n represents carbon, hydrogen, oxygen, nitrogen, carbon dioxide and water, respectively, A i s the r e l a t i v e a i r - f u e l r a t i o and subscripts N,M are the atoms of carbon and hydrogen i n the f u e l . The t o t a l number of kmols of charge present i n the cylinder at BDC i s obtained from the ideal gas law, P V BDC BDC NTot = -H f ( 5 " 5 ) MOL BDC The t o t a l mass of the charge i n the cylinder i s then c a l culated using the molecular weight of the charge. The molecular weight i s calculated from the weight of i t s constituents. The energy of the mixture i s calculated using the relationship E = (H-PV) = (H-RT) (5.6) Energy = £ ̂ ( h°. + Ah. - RT ) (5.7) where N i s the number of kmols of constituent 'i', h° i s the enthalpy i fi V J of formation 'i' i n kJ/kmol at 298°K and 1 bar, Ah i s the difference i i n enthalpy of the constituent 'i' between temperature T and 298°K obtained from Van Wylen and Sonntag [43], R i s the universal gas constant i n kJ/kmol°K and T i s the i n l e t temperature of the mixture. Knowing the mass composition and energy of the charge at BDC before compression, the mass-burned-fraction compression process can now be calculated. Compression Stroke The compression values of pressure, temperature, and t o t a l energy 46 are calculated at every crank angle degree increment from BDC u n t i l the occurrence of spark. In calculations, for every crank angle degree increment state 1 represents the i n i t i a l state and state 2 represents the f i n a l state at the end of the step. To calculate the value of the pressure, temperature and the t o t a l energy at the state 2 i n i t i a l values at state 1 are used as the st a r t i n g condition. These cal c u l a t i o n are accomplished by solving three equations simultaneously for every crank angle degree using the Newton-Raphson technique. The three equations are: a) The equation of state: P 2 - Pi ( V 1 / V 2 ) ( T 2 / T 1 ) (5.8) b) The f i r s t law of thermodynamics: E 2 = El - (Pi + P 2 ) ( V 2 - V i ) / 2 + DQ (5.9) c) Conservation of energy: E 2 = (M/MW)*Spec.Energy(T2) (5.10) where P, V, E, T represents pressure, volume, energy and temperature respectively, DQ represents the heat loss from the engine MW represents the molecular weight of the cylinder contents , Spec.Energy represents the molar s p e c i f i c energy of cylinder content, M i s the t o t a l mass i n the cylinder and subscripts 1 and 2 represents the state 1 and 2. These three equations are reduced to a single equation i n 1 unknown the temperature T 2 as follows: F ( T 2 ) = Ci + C 2 + C 3 . Spec. Energy ( T 2 ) =0 (5.11) where Cl = El - Pi ( V 2-Vi)/2 + DQ C 2 = - P 1 V 1 . ( V 2 - V i ) / 2 . V 2 . T 1 (5.12) C3 = -M/MW (5.13) 47 This equation i n one unknown i s solved i t e r a t i v e l y to get the temperature T 2 . Then, corresponding to that temperature the pressure, the energy and the mass-burned-fraction are calculated. The flow chart for this part of the program i s as shown below: Increment crank-angle Assume a f i n a l temperature using isentropic compression/expansion temperature as a f i r s t guess. t Solve 3 equations simultaneously using a Newton-Rapson technique O F i r s t law. O Perfect Gas law. O Conservation of energy. Do u n t i l occurrence of spark. ][ Obtain the f i n a l temperature, Pressure and Energy. \ ~ Next crank-angle Flow chart for compression u n t i l Spark These calculations at every crank angle step are done t i l l the occurrence of spark. 48 Combustion Process The ca l c u l a t i o n procedure of the mass-fraction-burned values i n the engine following spark i s now shown: The major assumptions made i n t h i s subroutine on progressive burning are: 1) The combustion chamber i s divided into two zones by a thi n , spherically expanding flame front separating the burned gas f r a c t i o n (X) from the unburned gas f r a c t i o n (1-X). 2) Both the burned and unburned gases have varying s p e c i f i c heats and obey the ideal gas law. 3) The unburned gas i s i s e n t r o p i c a l l y compressed by the expanding burned gases. 4) The pressure i s uniform throughout the combustion chamber. Calculations based on these assumptions are performed at every crank angle degree from spark u n t i l the end of combustion. The experimental pressure data i s now read by the program to calculate the mass-burned-fraction values using the conservation of mass and energy equations as shown below. From the conservation of Mass and Energy: + (l-X) * (5.14) M b u J L - X e + (1-X) e (5.15) M b u where V i s the volume of the combustion chamber, E i s the t o t a l energy i n the cylinder, M i s the molecular weight, X i s the mass-fraction burned, «• i s the s p e c i f i c volume, e i s the s p e c i f i c energy and the subscript b and u, represents the burned gas properties and the unburned gas properties respectively. At each step of the combustion process the values of energy , temperature and volume are known for both the burned and unburned gases at the previous ca l c u l a t i o n step, state 1, and these are used as the s t a r t i n g values for calculating values for the current step, state 2. The unknowns i n the equations 1, and 2 above are determined as shown below. a) The unknowns i n the unburned gases are calculated using isentropic compression from the i n i t i a l values of temperature, s p e c i f i c volume and the i n i t i a l and f i n a l pressure (experimental data) to give the f i n a l temperature and s p e c i f i c volume. From the assumption of isentropic compression of the unburned gases o = w (P / P ) 1 / k (5.16) u2 ul r 2 Assuming ideal gas behaviour T = P » / M R (5.17) U 2 u2 u which allows the s p e c i f i c energy of the unburned gas to be calculated e h u + 1 h° - h° > - R T f i L i ( l u ) i ( To )- u 2 N MW u u (5.18) where the values of h are obtained from formulae representing i(Tu) curvefits to the published enthalpy data for each constituent (Van Wylen and Sontag [43]) h° i s the heat of formation for the 'i' t h species and h , . i s the enthalpy of the species at the base i(To) 50 conditions. b) The new combustion chamber volume i s obtained from the volume-crank angle relationship for the engine using a l l the appropriate constants from the engine geometry. c) The unknown t o t a l energy of the control mass El, contained i n the combustion chamber i s given by the f i r s t law E 2 = E - P . ( V 2-Vi) + dq (5.19) The P(V2-Vi) term i s approximated by (P +P )/2 ( V 2 - V 1 ) d) The values of X2 ,Vb2 and Eb2 are unknown at th i s point, however (5.20) (5.21) according to the following relationship V = M RT / P (5.22) b2 b2 hZ' Z ' V - f(T. ,P ) and b2 62 2 e = f(T ,P ) b2 b2 2 I N ,-0 •< ,- o h + 1 h f j j (T b 2 ) j (To ) RT u b 2 N MW b b -. .(5.23) To calculate the values of X 2 , V b 2 and Eb2 we proceed as follows: Knowing the pressure and i t e r a t i v e temperature Tb2 we can read the values of the dissociated species from the table created by STANJAN and thus calculate the values of Vb2 and Eb2. The program proceeds by i t e r a t i n g the burned gas temperature Tb2 u n t i l the values of e and v calculated by equations 5.22 and b2 b2 J ^ 5.23 s a t i s f y equations 5.14 and 5.15. At this point X 2 , the mass-burned-fraction i s obtained. The above procedure i s repeated at each crank angle degree u n t i l the mass f r a c t i o n burned reaches a maximum value. In practice the values of x computed for adiabatic combustion r i s e to a maximum of approximately 0.8 and stay constant thereafter. Assuming that a l l of the fuel i s burned as x reaches a plateau, correction for the heat transfer effect i s made by dividing each value of x by the maximum value of x for that p a r t i c u l a r cycle. e) The laminar burning v e l o c i t y was calculated using the expression presented by Guilder for methane from his experiments i n constant volume bomb experiments. Laminar burning v e l o c i t y i s discussed i n appendix C. Dissociation Calculations The di s s o c i a t i o n calculations were performed by using the application package STANJAN. This package calculates the values of the species and places them i n the form of a table which i s then read by the program XPRESS. The dissociations considered i n this model are C02 ( ) CO + 1/2 02 H 2 O ( ) 1/2 H2 + OH H 2 O ( ) H2 + 1/2 02 1/2 N 2 + 1/2 02 ( ) NO H2 > 2H i 02 > 20 < STANJAN The application package STANJAN i s b r i e f l y described i n this section. This i s a general-purpose interactive program that can be used to solve chemical equilibrium problems. The basic data i n th i s program i s taken from the JANNAF tables. The user selects the species to be included i n each phase of the system, sets the atomic populations and state parameter and then solves for the equilibrium state using the method of element potentials. The user-specified state parameters may be temperature and pressure or pressure and entropy or other options available. The results include the composition of each phase such as the dissociated species and the products, and the thermodynamic properties of the system such as the internal energy, enthalpy and entropy. This value of the dissociated species i n the table eliminates the need for i t e r a t i v e calculations of dissociated products at high temperature and pressure thus saving a l o t of time. In t h i s case a series of calculations were made over a matrix of T and P values. These tabulated results for each f u e l - a i r r a t i o are stored i n a f i l e for l a t e r processing using user specified format. 5.5 S t a t i s t i c a l Analysis The s t a t i s t i c a l analysis used to determine the extent of cycle-by-cycle variations i n engines from the mass-burned-fraction values was done using Fortran programs. The s t a t i s t i c s calculated from the mass-burned-fraction values were the mean, standard deviation, and cross-correlation c o e f f i c i e n t . The mass-burned-fraction values at each crank angle calculated by XPRESS are used to calculate the values of the mass-burned-fraction i n terms of time after the occurrence of the spark using the relationship. Burning time for x crank angle after spark = ^ ^ R p M (5.24) S t a t i s t i c a l analysis i s then performed on the calculated values of the time taken for a s p e c i f i c discrete value of mass-fraction-burned for 100 cycles i n one set of sample data. The mass-burned-fraction values at each crank angle showed a continuous set of data values. This data was f i r s t arranged such that burning times at 2, 3, 4, 5, 7, 10, 20, 30 40, and 50 percent mass-fraction-burned were calculated using equation 24 above and the s t a t i s t i c a l analysis carried out to calculate the mean standard deviation and cross correlation c o e f f i c i e n t . An i n i t i a l test conducted with di f f e r e n t sample sizes of consecutive cycles at 3000 RPM, WOT and 1.25 equivalence r a t i o showed that increasing the number of cycles increased the r e l i a b i l i t y of r e s u l t s . A sample case of 50 and 100 cycles showed that the value of standard deviation was 4% lower with 50 cycles. A sample size of 100 consecutive cycles i s selected as an economical sample size as large number of tests can be e a s i l y conducted using the available computer siz e . The mean of the time for the same mass f r a c t i o n burned i calculated using the relationship i - ( 5 - 2 5 ) i=l wwhere x i s the i t h value and N i s the number of measurements. i The standard deviation i s calculated using the relationship a = ' 1 N 2 i n I <xj - x >2 1/2 (5.26) The normalized covariances (Cov) are calculated using the relationship N y i ^ l ( X l ( 1 ) - V * ( X 2 ( 1 ) - X 2 > C o V = (a )*(a )* (N-l) ( 5 ' 2 7 ) The raw data collected from the engine i n the form of integers i s thus processed through various stages to a form that can be evaluated to study c y c l i c variations i n the engines. 54 6.FIRED ENGINE MEASUREMENTS AND RESULTS. 6.1 Introduction. This chapter discusses the results obtained from the experiments conducted on the Ricardo research engine. The calculating procedures are as described i n chapter 5. Cylinder pressure measurements were made with dif f e r e n t configuration setups as described below. A variety of equivalence r a t i o s on either side of the stoichimetric a i r fuel r a t i o were considered, the range being approximately 0.70 < <j> < 1.15. A l l the measurements were made at MBT spark timing. The variables i n th i s experimental study are: a) speed: measurements were made at 2400, 3000, 3600 and 4200 rpm at WOT using a standard spark plug with an electrode diameter of 3mm and a spark gap of 0.7mm. b) spark plug geometry: In addition to the standard spark plug the effects on combustion of a modified spark plug with 1.3mm electrode diameter having pointed ends and 0.7mm spark gap at WOT and 3000 rpm were also studied. c) spark gap width: In addition to the standard spark plug the effects on combustion of another modified spark plug at WOT and 3000 rpm were also studied. The modified spark plug had spark gap width of 2.3mm for the bathtub chamber and about 1.5mm for the disc shaped combustion chamber. d) part t h r o t t l e : measurements were made at partly opened t h r o t t l e at 3000 rpm. Part-opened-throttle i s described i n terms of volumetric e f f i c i e n c y . The volumetric e f f i c i e n c y at 3000 rpm for f u l l y opened t h r o t t l e and partly-opened t h r o t t l e are 85% and 64% respectively. 55 e) chamber geometry : pressure measurements were made at a l l the configurations described above with two different combustion chamber geometries the "bathtub" chamber and the "disc" chamber. Section 6.3 to 6.6 discusses the results from the "bath-tub" chamber and section 6.7 discusses the results from the "disc" shaped chamber. 6.2 CYCLIC VARIATIONS IN PRESSURE The ease and accuracy with which pressure i n the combustion chamber can be measured using a pi e z o - e l e c t r i c transducer has made pressure the most common parameter for quantifying c y c l i c variations. Fig 13 i s a sample plot of the peak pressure d i s t r i b u t i o n for a sample of 100 consecutive cycles at 3000 rpm WOT, and <f> of 1.015. This plot shows the maximum and the minimum pressure curve within the sample for the compression and expansion phase of the cycle. Also shown i s the ensemble-averaged mean of the 100 cycles for the same sample data. The spread of peak pressures within a sample of 100 consecutive cycles i s shown on the histogram at the l e f t hand side of the plot. The standard deviation i n the peak pressure for this sample data i s 325.7 kPa and the c o e f f i c i e n t of v a r i a t i o n i s 0.0675. Fig 14 i s a s i m i l a r plot for a sample data of 100 consecutive cycles at 3000 rpm, WOT and an equivalence r a t i o of 0.674 i.e a very lean operating condition. This sample has 8 m i s f i r i n g cycles as shown by the peak pressure being less than the motored pressure. This m i s f i r i n g i n the engine increases the spread i n the peak pressure v a r i a t i o n . The standard deviation i n peak pressures i s about 450 kPa and the c o e f f i c i e n t of v a r i a t i o n i s about 0.188. This example of an extreme 56 case i s for i l l u s t r a t i o n only; i n none of the cases discussed hereafter i s there any evidence of m i s f i r i n g . This combined plot for a pa r t i c u l a r sample data presents the character of the c y c l i c variations i n engine pressure at that p a r t i c u l a r operating condition. The pressure curve shows the range i n the absolute values of pressure within the sample and the histogram shows the d i s t r i b u t i o n of the peak pressure within the sample data collected. Fig 15 shows the ensemble-averaged peak pressure for samples of 100 cycles at di f f e r e n t speeds and equivalence r a t i o s . Ensemble-averaged peak pressure increases with speed from 2400 rpm to 3600 and thereafter shows a tendency to decrease with increase i n speed. The lower values of peak-pressure at lower speed i s associated with the lower l e v e l of turbulence at lower speeds. This lower turbulence causes the flame to trav e l slower which affects the phasing and thereby magnifies the effect of pressure due to increasing piston speed (This concept i s discussed i n d e t a i l i n appendix B ). This phenomenon of loss of peak pressure at high speeds i s associated with reduced volumetric e f f i c i e n c y with increase i n speed. The maximum value of the ensemble-averaged peak pressure occurs near the stoichimetric f u e l - a i r r a t i o . The value of peak pressure decreases for both r i c h and lean mixtures away from the maximum value of the peak pressure. This decrease i n peak pressure i s associated with excess a i r i n case of lean mixtures and incomplete combustion i n case of r i c h mixtures; these decrease the temperature and hence the peak pressure i n the combustion chamber. The effect of equivalence r a t i o on the peak pressure i s s i g n i f i c a n t and follows a steady pattern at a l l speeds, where as the peak pressure increases with speed from 2400 rpm to 57 3600 rpm but decreases with speed with increase from 3600 to 4200 rpm. The standard deviation i n the ensemble-averaged peak pressure (within the sample data of 100 cycles) normalized by the ensemble-averaged mean of peak pressure for the sample i s termed the c o e f f i c i e n t of v a r i a t i o n (COV) [11]. The values of the c o e f f i c i e n t of v a r i a t i o n for the engine data at different speeds and equivalence r a t i o at WOT and MBT spark timing i s shown i n Fig 16. This plot of c o e f f i c i e n t of v a r i a t i o n against equivalence r a t i o shows that the minimum value of c o e f f i c i e n t of v a r i a t i o n occurs near the stoichimetric a i r - f u e l r a t i o for a l l the speeds considered. The c o e f f i c i e n t of v a r i a t i o n increases more rapidly with departure from <f> = 1, i.e. as the equivalence r a t i o i s made lean or r i c h , this increase being more rapid on the r i c h side than on the lean side. The c o e f f i c i e n t of v a r i a t i o n appears not to have a clear dependence with speed. Thus, the influence of equivalence r a t i o on c o e f f i c i e n t of v a r i a t i o n i s quite s i g n i f i c a n t while the effect of engine speed i s comparatively small. 6.3 CYCLIC VARIATIONS IN BURNING TIME Peak pressure i s d i r e c t l y influenced by the combustion i n the engine but i t s occurrence i s detached from the i n i t i a l burning period. Most researchers have concluded that combustion variations originate i n the early part of the burning period following spark. Young for example i n h i s review paper [1] concluded that "cycle-to-cycle variations i n combustion originate early i n the combustion process. Although hard evidence i s s t i l l lacking i t i s thought that a main cause of these variations i s the cycle-to-cycle variations of v e l o c i t y i n the v i c i n i t y 58 of the spark plug at the time of i g n i t i o n which affects the developing flame kernel". The main area of interest i n this research i s concentrated on the early stages of combustion following spark. By calculating mass-fraction-burned values from the pressure data we can make inferences about c y c l i c variations i n burning time early i n the combustion period. The pressure data collected from the engine i s not smoothed i n any way except for the pressure at the time of spark. The high energy at spark sometimes seems to interfere with the pressure output signal, giving an e r r a t i c value of pressure at spark. This drawback i s r e c t i f i e d by cal c u l a t i n g an average value for the compression exponent over the range from IVC to j u s t before spark and then using t h i s exponent 'n' calculate the value of the pressure at spark for every cycle using the simple relationship PiVi" = P2V21 1. State 1 represents the conditions of pressure and volume at 5 degrees before spark and condition 2 represents the conditions at spark. The mass-fraction-burned values are calculated from the pressure data collected using the energy and mass conservation equations. The d e t a i l s of these calculations are described i n the chapter 5. F i g 17 i s a sample plot of mass-fraction-burned values plotted against time. Three of the fastest and three of the slowest mass-fraction-burned curves are shown i n addition to the ensemble averaged mean curve from a sample of 100 consecutive cycles. The curve shows mass-fraction-burned value x ranging from 0 to 1. In practice the values of x computed for adiabatic combustion r i s e to a maximum of 59 approximately 0.8 and stay constant thereafter. Assuming that a l l of the f u e l i s burned as x reaches a plateau, correction for the heat transfer effect i s made by dividing each value of x by the maximum value of x for that p a r t i c u l a r cycle. Figure 17 shows t y p i c a l difference i n burning times between the fastest and the slowest burning cases. I t may be noted that the shapes of the burned curves are sim i l a r . At x = 0.5 a l l the curves seem to have about the same slope, however they appear to be shift e d i n time. I t seems that v a r i a t i o n i n the i n i t i a l burning period sets up the trend for l a t e r combustion, which then proceeds i n a sim i l a r manner for a l l cycles. The dispersion i n burning time increases as x increases. However, as w i l l be shown, the value of i n i t i a l spread i s not negligible i n the early combustion region. This denotes that there i s substantial randomness associated with the early stages of combustion following the spark. The values of the standard deviation i n burning time for each set of operating conditions at the appropriate x values can then be determined from s t a t i s t i c a l analysis. We now examine this value of standard deviation i n burning time at different a i r - f u e l r a t i o and x. Fig 18 shows the frequency histogram of burning time for 10% mass-fraction-burned at 3000 rpm and an a i r - f u e l r a t i o of 1.05. The standard deviation for this case i s 0.08334 ms. Fig 19 shows the frequency histogram of burning time for 30% mass-fraction-burned at 3000 rpm and an a i r - f u e l r a t i o of 1.05. The standard deviation for th i s case i s 0.1122 ms. Fig 20 shows the frequency histogram of burning time for 50% 60 mass-fraction-burned at 3000 rpm and an a i r - f u e l r a t i o of 1.05. The standard deviation for this case i s 0.1247 ms. Fig 18, 21 and 22 shows the frequency histograms and the values of the standard deviation of 10% mass-fraction-burned at a i r - f u e l r a t i o of 1.05, 1.22 and 1.38 respectively. The standard deviation i n burning times are 0.08334, 0.1137 and 0.2300 ms respectively. Thus Figs. 18-22 show that the standard deviation i n burning times increases a) as the mass-fraction-burned increases. b) as the equivalence r a t i o changes ( a l l other conditions remaining constant). The dependence of the standard deviation i n burning time on x values and equivalence r a t i o i s seen i n Figs 23-29 which show the effects of speed and equivalence r a t i o for MBT spark timing. These plots show that there i s an almost l i n e a r relationship between the standard deviation a i n burning time and x, with an almost l i n e a r increase i n a with x. The increase i n the value of standard deviation i n burning times with increasing values of x may be due to the combined effect of random flame development and the wall interaction with the developing flame; the larger the flame size , i .e. the larger the value of x, the greater the contribution which might be expected from this source of randomness. However t h i s effect should be neg l i g i b l e as x approaches zero. As equivalence r a t i o i s varied from the optimum, the flame temperature and the burning v e l o c i t y decline, and the combustion period 61 increases. An explanation for the increase i n c y c l i c v a r i a t i o n with decline i n laminar burning v e l o c i t y w i l l be proposed l a t e r i n chapter 8. Extrapolating the values of standard deviation to the i n i t i a l stages of combustion ( i . e . for x—>0 and disregarding the highly uncertain determinations for x less than 0.03 or 0.04 ) we obtain the extrapolated standard deviation a . The extrapolated standard deviation i n burning time a represents the standard deviation i n burning time for zero mass-fraction-burned. The calculated values of x less than 0.04 show very high values of standard deviation. The extrapolation i n these cases i s carried out from values of x greater than 5%. In theory, the value of CTq has to be determined at very small values of x i.e. j u s t as the developing flame kernel following spark h i t s the faster burning vortex tubes i n the turbulent structure. This average distance that has to be covered by the flame i s approximately 0.22mm. In practice, exact determination of the value of x from the pressure data i n the early stages following spark i s very d i f f i c u l t , as when the outer flame radius i s of the order of 10mm, the value of x i s well below 1% ( i . e within the uncertain region.) Hence, for a l l p r a c t i c a l purposes the value of a Q i s obtained by extrapolation from higher values of x . This value of standard deviation for very small values, almost zero, of x i s termed the standard deviation i n burning time at zero mass f r a c t i o n burned. Appendix E shows the effect of the small uncertainty i n the pressure data on the calculated burning time for small values of x. The pressure i s deliberately modified by a small amount equal to the uncertainty i n the pressure acquisition equipment. 62 Appendix E shows that t h i s pressure uncertainty prevents the determination of a for values of x less than about 0.03 (3%). o v The facts that the extrapolated standard deviation values are not not n e g l i g i b l e , and that the i n i t i a l spark process i s highly repeatable, suggests that the behaviour of the flame i n the i n i t i a l stages i s important i n locating the o r i g i n of c y c l i c variations. I t i s consistent with the idea that the burning curves appear to be the same except for a variable s h i f t i n the time for flame i n i t i a t i o n . We proceed to examine thi s dependence on x for different equivalence ratios and speeds. Fig 30 shows the behavior of the extrapolated standard deviation a at d i f f e r e n t speeds and equivalence r a t i o s . This p l o t shows that the values increase systematically on both sides of the minimum; the minimum occurs near the stoichimetric value. The s l i g h t tendency for the values of a to decrease with speed can be due to higher turbulence o levels at high speeds. The change i n a with speed at dif f e r e n t o equivalence r a t i o s shows a sim i l a r behaviour as the change of c o e f f i c i e n t of v a r i a t i o n (COV) under s i m i l a r operating conditions. This s i m i l a r i t y between < 7 Q ( i n the i n i t i a l stages) and COV (for peak pressures) appears consistent with the view that the variations i n the i n i t i a l stages sets the stage for further pressure development and that the pressure i s d i r e c t l y related to combustion v a r i a t i o n i n the engine. The value of plotted i n terms of crank angle values instead of time i n milliseconds exhibit somewhat less v a r i a t i o n i n standard deviation with speed, as seen i n Fig 31. They tend to f a l l around a li n e a r relationship pointing to the fact that i n terms of crank angle 63 the standard deviation values are independent of speed but behave systematically with change i n equivalence r a t i o , i.e increase as the fu e l i s made leaner. This i n d i r e c t l y shows that the turbulence increases l i n e a r l y with speed. The co r r e l a t i o n c o e f f i c i e n t between x values at two d i s t i n c t values of x determine how strongly they are related to each other. A value of 1 indicates a strong positive l i n e a r relationship and a value of 0 indicates no relationship at a l l . The correla t i o n c o e f f i c i e n t between the burning times at x= 0.07 and x = 0.10, 20, 30, 40 and 50 i s shown i n Fig 32 for an equivalence r a t i o of 1.05 at 3000 rpm and WOT condition. A high c o r r e l a t i o n exists between the i n i t i a l burning times and the burning times at a l a t e r stage. This high value of the cor r e l a t i o n c o e f f i c i e n t indicates that the standard deviation i n burning time i n the la t e r stages of burning i s strongly related to the standard deviation i n burning time i n the i n i t i a l stages. This sample case i s a true representative of most of the test cases considered. 6.4 EFFECT OF SPARK PLUG GEOMETRY: Fig 33 shows a modified spark plug used to determine the effect of electrode shape and size on c y c l i c variations. Fig 34 and 35 show the li n e a r behaviour of the standard deviation i n burning time with mass-fraction-burned for different equivalence ra t i o s at 3000 rpm and WOT. Fig 36 shows the plot of a values for dif f e r e n t equivalence ratios o - and i s compared with the standard configurations at the same speed. They exhib i t a si m i l a r trend of change i n standard deviation with change 64 i n equivalence r a t i o with a minimum at near stoichimetric f u e l - a i r r a t i o . This figure does not show any s i g n i f i c a n t improvement i n the standard deviations i n burning times with the modified spark plug point. This test shows that the size of the shape and size electrode has l i t t l e e ffect on c y c l i c variations. 6.5 EFFECT OF SPARK GAP WIDTH : Figure 37 shows the modified spark plug used to study the effects of long sparks at i g n i t i o n on the c y c l i c variations i n engines. Fig 38 and 39 show the li n e a r behaviour of the standard deviation i n burning time with x for different equivalence ratios at 3000 rpm and WOT. The case of <f> = 0.6739 has m i s f i r i n g cycles i n the sample data and i t demonstrates how m i s f i r i n g can affect the li n e a r relationship between a and x. o Fig 40 which shows the plot of a Q for different equivalence ratios and compared to the standard configuration at the same speed. They exhibit a s i m i l a r trend of change i n standard deviation with change i n equivalence r a t i o with a minimum at near stoichimetric. This curve does not show any s i g n i f i c a n t change i n a with the modified spark plug gap. o Thus, t h i s test shows that there i s a weak relationship between wide spark gaps (2.3mm) and c y c l i c variations. 6.6 EFFECT OF PART THROTTLE Tests with p a r t l y open t h r o t t l e were conducted to study the effects of increased residuals on c y c l i c variations. Fig 41 and 42 show the li n e a r v a r i a t i o n with x of the standard deviation i n burning time for dif f e r e n t equivalence ratios at 3000 rpm. 65 Fig 43 shows the plot of a for dif f e r e n t equivalence ratios at o 3000 rpm for the standard configuration and the pa r t l y open t h r o t t l e . They exhibit a l i n e a r relationship of increase i n standard deviation with change i n equivalence r a t i o with a minimum at near stoichimetric. This curve does not show any s i g n i f i c a n t change for the part t h r o t t l e . I t shows a weak relationship with change i n t h r o t t l e setting from WOT to p a r t l y open t h r o t t l e . This weak effect could be due to the combined effect of high compression r a t i o and MBT spark timing. 6.7 Disc Combustion Chamber This section discusses the results from the disc-shaped combustion chamber. Most of the tests were conducted for s i m i l a r operating conditions as with the "bath-tub" combustion chamber. Figs 44-50 shows the behaviour of standard deviation i n burning time with mass-burned-fraction values for dif f e r e n t operating conditions of speeds (2400, 3000, 3600 and 4200 rpm), spark plug geometry, spark plug gap and p a r t l y open t h r o t t l e respectively. These plots have one fundamentally d i f f e r e n t operating parameter such as speed, electrode shape or electrode gap and t h r o t t l e opening. A l l these plots show that there exists an increasing l i n e a r relationship between x and standard deviation i n burning time. Fig 51 shows the effect of change i n speed and equivalence r a t i o on the a . The influence of equivalence r a t i o on standard deviation has a o d i s t i n c t i v e pattern with a minimum value near the stoichiometric a i r - f u e l r a t i o and increases with change i n equivalence r a t i o for both r i c h and lean mixtures. The influence of speed on standard deviation i s 66 not very d i s t i n c t with a small amount of decrease i n standard deviation for increase i n speed from 2400 to 3600 rpm. Further increase i n speed over 3600 rpm shows an increase i n engine variations. Thus there i s a weak relationship of speed with standard deviation for a whole range of speeds. The influence of the equivalence r a t i o on standard deviation could be related to the effect of flame speed. Near stoichiometric a i r - f u e l r a t i o the flame speeds are the fastest and hence combustion rate i s increased. This flame speed i s a function of the temperature and pressure with a maximum near the stoichiometric a i r - f u e l r a t i o . As the equivalence r a t i o i s changed the maximum temperature i n the combustion chamber i s less than the maximum value near the stoichiometric value and thi s reduces the flame speed which increases the combustion duration and hence the variat i o n s . The turbulence l e v e l increases l i n e a r l y with speed and hence decreases the combustion duration which shows up as an improvement i n standard deviation. At higher l e v e l of speed the increase i n combustion rate i s made more complex by an increase of residuals due to the decreased volumetric e f f i c i e n c y and th i s may explain the increased values of standard deviation. Fig 52 shows the effect of spark plug geometry on c y c l i c variations at 3000 rpm, WOT and MBT spark timing. From the plot i t can be seen that there i s no improvement i n standard deviation for the two diff e r e n t shapes of spark plug points, which i s i n agreement with the results of bath-tub chambers and other researchers that the effect of spark plug point geometry i s i n s i g n i f i c a n t i n reducing c y c l i c variations. 67 Fig 53 shows the effect of an increased spark plug gap on c y c l i c v ariations at 3000 rpm, WOT and MBT spark timing. The spark gaps considered were the standard gap of 0.7mm and modified spark plug gap of 1.5mm. The influence of equivalence r a t i o on a appears to be simi l a r o for both types of spark plugs. The Figure shows a decrease i n extrapolated standard deviation with increased spark gap (1.5mm). This behaviour could be due to the increased size of the kernel which needs small amounts of i n i t i a l t r a v e l time to interact with the turbulence (This phenomenon i s better explained i n chapter 8). Fig 54 shows the effect of residuals due to pa r t l y open t h r o t t l e on combustion variations at 3000 rpm and MBT spark timing. This figure shows a s i g n i f i c a n t increase i n a for lean mixtures and a decrease i n o standard deviation for r i c h mixtures. The increase i n standard deviation for lean mixtures may be due to effects of increased residuals which influence the flame speed and hence decrease the combustion rate and hence increases the combustion variations. The effect of reduced volumetric e f f i c i e n c y due to part open t h r o t t l e and the residuals i n the r i c h mixture seem to have an effect of increase i n flame speed and hence reduces c y c l i c variations i n standard deviation. Thus, the effect of part-open t h r o t t l e i s such that there i s a increase i n value of a compared to the f u l l y open t h r o t t l e condition at o 3000 rpm. Figures 55 to 61 shows the effect of two dif f e r e n t combustion chambers on c y c l i c variations. The two chambers are the simple combustion chamber (disc-shaped) and the bath-tub chamber which has 68 squish at TDC. These figures shows that a) There is a dis t inct improvement in a for different values o of equivalence ratio and speed. b) the minimum value of a occurs at leaner equivalence ratio o for the "bath-tub" chamber as compared to the disc chamber. c) a decreases with increased speed as speed is proportional o to the turbulence leve l . This behaviour could be due to the increased level of turbulence in the "bath-tub" chamber as compared to the simple disc-shaped combustion chamber. The higher turbulence level increases the combustion rate which affects the phasing and gives decreased value of a for higher o turbulence leve l . 6.8 Summary In summary the experimental results computed from the engine pressure data shows that 1) The pressure data shows randomness at a l l operating conditions. 2) The ensemble-averaged peak pressures for a sample data at any speed shows a maximum value near the stoichiometric a ir- fuel ratio and changes with change in speed. 3) The COV in peak pressure shows a minimum value near the stoichiometric a i r- fuel rat io and changes with change in speed. 4 ) The x values calculated from the pressure data seem to suggest a substantial randomness in the burning times during combustion. 5) The standard deviation in burning times increases l inear ly as the 69 x increases and shows a minimum set of values near the stoichiometric a i r - f u e l r a t i o . 6) Extrapolated values of standard-deviation i n burning times vary with speed and shows a minimum near the stoichiometric a i r - f u e l r a t i o . 7) Extrapolated standard deviation shows less dispersion when plotted i n terms of crank angle. 8) A high c o r r e l a t i o n exists between the values of x at i n i t i a l stages and the l a t e r stages.. 9) The shape of the electrode has no s i g n i f i c a n t effect on c y c l i c variations for both "disc" shaped and "bath-tub" chamber. 10) The spark gap width has no s i g n i f i c a n t effect on c y c l i c variations i n "bath-tub" combustion chamber but has a s t a b i l i z a t i o n effect on c y c l i c variations i n the disc chamber, by showing lower values of a as compared to the standard spark plug gap values of a . o 11) The increased residuals had no effect on c y c l i c variations when the volumetric e f f i c i e n c y i s changed from 85% to 64% at MBT spark timing i n "bath-tub" chamber but for the "disc" chamber there i s a deterioration i n c y c l i c variations as seen by the higher values of the a compared to o the case of f u l l t h r o t t l e . 12) The corresponding values of standard deviation i n burning times i n the disc shaped combustion chamber has higher values than the "bath-tub" combustion chamber. An inference that can be drawn from these results i s that the "bath-tub" chamber generates more turbulence than the "disc" chamber. 70 7. TURBULENCE AND IGNITION IN ENGINES 7.1 Introduction This chapter reviews the available l i t e r a t u r e on turbulence structure within the engine during the combustion period. The chapter considers a) the nature of the turbulent structure i n spark i g n i t i o n engines. b) the d i s t r i b u t i o n of the major turbulence parameters v i z : turbulence inten s i t y , and turbulent scales and the i r dependence on speed. c) the model of the small scale structure of turbulence as presented by Tenneekes. d) o p t i c a l data on the i n i t i a l flame kernel. e) the th e o r e t i c a l step-by-step development of the i n i t i a l flame kernel following spark (as deduced from the turbulent structure model) and the nature of the early flame propagation. f) the laminar burning v e l o c i t y of methane (a major constituent i n natural gas). 7.2 Homogenity And Isotropy i n Engine Turbulence The flow f i e l d i n an engine i s primarily governed by the valve events and piston motion. During the early part of the compression process the influence of the intake process i s dominant; the combustion chamber shape (eg. pre-combustion chamber), i n l e t s w i r l and effe c t i v e valve area are mainly important i n establishing the i n i t i a l levels of turbulence from which the decay process begins. Combustion i n an engine occurs mostly i n the v i c i n i t y of Top Dead Centre (TDC) during the compression and expansion process. Measurements of turbulence have been i n t h i s region. Semenov [29] did extensive work on the d i s t r i b u t i o n of mean 71 v e l o c i t y and turbulent intensity across a disc-shaped combustion chamber. Using hot wire anemometry i n a motored engine he made measurements at various points i n the combustion chamber at diff e r e n t running conditions. He noted that during the compression stroke i n the v i c i n i t y of TDC the turbulence intensity at a given point does not vary with time by more than 10% and i t does not change by more than 15% with increasing distance from the chamber centre. Semenov thus concluded that combustion proceeds under conditions of p r a c t i c a l l y constant turbulence. Whitelaw et al.[52] made measurements of three v e l o c i t y components using a forward-scatter laser doppler anemometer i n the transparent cylinder motored with a disc type chamber having a compression r a t i o of 7.4. They found that the turbulence showed a tendency towards isotropy at TDC. Lancaster [16] used single point measurements with a t r i - a x i a l probe and obtained close agreement between the i n t e n s i t i e s measured by the three sensors near TDC; he concluded that the turbulence tended towards isotropy. The results of several other investigations [4][20] imply that i n chambers with no squish the turbulence i s nearly homogeneous and isot r o p i c . Daneshyar and F u l l e r [5] for example conclude that "When averaged over many cycles the turbulence i s v i r t u a l l y homogeneous and isot r o p i c towards the end of compression i n swi r l i n g and non swi r l i n g flows (except near the chamber wal l s ) " . The general consensus, on the turbulent structure for the engine operating conditions, i s that approximately constant conditions of homogeneous, isotro p i c turbulence p r e v a i l i n the engine during combustion. 7.3 Turbulence Measurements i n Engines Turbulence i s defined as the fluctuating v e l o c i t y component super-imposed on the mean v e l o c i t y of a viscous flow. The v e l o c i t y fluctuations which are measured at a fixe d point i n space can be envisioned as the resul t of turbulent eddies passing that point. Three parameters- mean v e l o c i t y .turbulent intensity and turbulent scale- can be used to describe the observed turbulence. Mean Velocity The mean v e l o c i t y i s the average v e l o c i t y measured during a spec i f i e d time i n t e r v a l and i t has both d i r e c t i o n and magnitude. This d e f i n i t i o n i s dependent on the time i n t e r v a l for which i t i s defined and thi s leads to stationary analysis of turbulence data. The mean ve l o c i t y i s then defined as U = U + u (7.1) where U i s the instantaneous v e l o c i t y , U i s the time averaged value and u i s the flu c t u a t i o n component. I f the mean v e l o c i t y varies slowly with time the mean v e l o c i t y could be defined as •U(t.i) = U(t) + U(i) + u ( t , i ) (7.2) where U ( t , i ) i s the instantaneous v e l o c i t y at any time t i n record i , U(t) i s the ensemble-averaged mean v e l o c i t y at any time t and U(i) i s the time-averaged mean v e l o c i t y for a portion ("window") of record i after U(t) has been subtracted from the instantaneous v e l o c i t y at each time i n the record. The turbulent component of ve l o c i t y i s u ( t , i ) . This d e f i n i t i o n of mean v e l o c i t y i s used for non-stationary analysis of 73 engine data. Turbulence Intensity Turbulence intensity i s defined as the root mean square value of the v e l o c i t y fluctuations about the mean. Whitelaw et a l . [51] made measurements of three v e l o c i t y components using a forward-scatter laser doppler anemometer i n the transparent cylinder motored engine with a "disc" type chamber having a compression r a t i o of 7.4. Using stationary analysis they found that the r a t i o of average turbulence intensity and the mean piston speed at TDC of compression increased from 0.47 to 0.59 i n the absence of induction s w i r l along the cylinder diameter with sim i l a r values being 10-25% lower i n the presence of s w i r l . Bracco et a l [51] noted that for a "disc" shaped combustion chamber the r a t i o of turbulence intensity to the mean piston speed has a upper l i m i t of about 0.5 at TDC. Boisvert [37] used a numerical model of the combustion process incorporating a l l the combustion implications of Tennekes model and found that the r a t i o of values of turbulence intensity to the mean piston speed are i n the range of 0.47 to 0.60. Ha l l and Bracco [51] used laser doppler velocimetry to make cycle- resolved v e l o c i t y and turbulence measurements under motoring conditions i n a "pancake" chamber engine having a compression r a t i o of 7.5. They found that the turbulence intensity had a linea r relationship with the engine speed and the magnitude of TDC turbulence intensity has a maximum value of about 0.5 times the mean piston speed for t h i s simple chamber. Semenov [29] reported that turbulent intensity was r e l a t i v e l y constant with time during the end of compression and beginning of expansion with the value of the constant depending on the geometry of the combustion chamber. Lancaster [50] showed that turbulence intensity increased with increasing speed. There i s substantial v a r i a t i o n i n the reported measurements of the turbulence i n t e n s i t y mainly because of different methods of analysis (stationary and non-stationary analysis). The mean v e l o c i t y signal from the engine i s non-stationary and non ergodic. The results of ensemble-averaged values of turbulence intensity (stationary analysis) d i f f e r s ubstantially from values obtained by non-stationary averaging with windows of various sizes [37]. Since the ensemble-averaged analysis for the engine contains fluctuations due to the mean ve l o c i t y i t produces values of turbulence intensity which are larger than si m i l a r values obtained using non-stationary analysis. Thus though the experiments carried out so far seem to point out the lack of s u f f i c i e n t engine data, a consensus conclusion reported by Heywood [39] i s that for chambers without s w i r l the turbulence intensity at TDC has a maximum value of about h a l f the mean piston speed and the turbulence intensity increases with increase i n engine speed. 7.4 Turbulence Scales Direct measurements of length scale requires simultaneous 2 point measurement of the s p a t i a l correlation c o e f f i c i e n t from which integral and perhaps microscales can be calculated. The s p a t i a l c o r r e l a t i o n of simultaneous v e l o c i t y measurements at two points Xo and (xo+x) i s given by Rc*> - " T T T S " ( X ° + * i ...'.(7.3) N-l i = l u ' ( X o ) U '(Xo+X) K ' where i refers to the i t h measurement, N i s the t o t a l number of 75 measurements, u i s the v e l o c i t y fluctuation, and u' i s the RMS v e l o c i t y fluctuations. The integral length scale Lx i s defined by a Lx = J R(«)dx . . . (7.4) o Due to the d i f f i c u l t y i n applying the technique of two point measurement to engine studies, single point autocorrelation has been widely used to calculates the integral length scale. This method f i r s t calculates the integral time scale defined by the correlation between two v e l o c i t i e s at a fixed point i n space but separated i n time r L = J Rrdt (7.5) o where, Rr = — L I U : r ) U ( : + t \ (7.6) N i=l u'(r) u'(r+t) where i refers to the i t h measurement, N i s the t o t a l number of measurements, u i s the v e l o c i t y fluctuation, and u' i s the RMS v e l o c i t y fluctuations. The i n t e g r a l length scales i s then related to the integral time scale by the r e l a t i o n Lx = U r ... (7.7) L where U i s the mean v e l o c i t y , and r^ i s the integral time scale. However equation 7.7 i s approximately v a l i d only for stationary, homogeneous and low turbulence intensity flows. I t therefore cannot be used for engine studies. The Taylor microscale, A, i s defined by the second derivative of the of the auto correl a t i o n c o e f f i c i e n t R(x) evaluated at the o r i g i n Xo. A 2 = -2/(62Rx/SxZ)Xo (7.8) where R(sc) i s the auto correlation c o e f f i c i e n t d i f f e r e n t i a t e d w.r.t 76 distance x. For single point auto correlation the micro time scale r i s m defined from the auto correlation function of equation 7-6 evaluated at the o r i g i n to. r 2 = -2/(5 2Rr/5t 2)to (7.9) m For homogeneous, isotropic turbulence the micro time and length scales are related by A = U r (7.10) m The turbulent scale i s a parameter representative of the size of the eddies i n the flow. In turbulent flows there i s a d i s t r i b u t i o n of energy over a continuous range of eddy sizes. The large eddies whose sizes are l i m i t e d by the system boundaries are c a l l e d the integral length scales. These scales create v e l o c i t y gradients i n the flow which re s u l t i n turbulent stresses. These turbulent stresses create smaller eddies which i n turn create s t i l l smaller eddies u n t i l the k i n e t i c energy of flow i s dissipated into heat through viscous action. Dissipation occurs at the smallest length scale i n the energy cascade. Turbulence length scales are of fundamental importance i n the characterization of turbulent flows and i n the formulation of turbulent models. For i s o t r o p i c and homogeneous turbulence the three length scale relationships are as calculated below. For i s o t r o p i c , homogeneous turbulence the rate of production of turbulent energy i s proportional to the k i n e t i c energy per unit mass of large eddies divided by the time scale of the large eddies L/u'. For steady state t h i s production i s equal to the rate of viscous d i s s i p a t i o n 77 therefore £ a (u' 3/L) (7.11) where e i s the rate of diss i p a t i o n of turbulent k i n e t i c energy per unit mass due to v i s c o s i t y , u' i s the turbulence intensity and L i s the inte g r a l length scale Taylor [7] has shown that for isotro p i c turbulence the rate of energy d i s s i p a t i o n per unit mass i s € = 15u (—£-) ....(7.12) where u' i s the RMS value of the fluctuating v e l o c i t y component, v i s the kinematic v e l o c i t y and A i s the Taylor microscale. Kolmogorov's length scale rj, v e l o c i t y t» for isotropic turbulence 3 1/4 1/4 are based upon e and ». They are n = (j/ /e) and «• = (ev) = v/r\ 3 A from the d e f i n i t i o n of the Kolmogorov length scale e = v fr\ . The scaling rules for l o c a l l y isotropic turbulence can thus be derived from the above as 3 2 U ' i c r U' > 2 U /-7 1 ON where e i s the rate of dis s i p a t i o n of turbulent k i n e t i c energy per unit mass due to v i s c o s i t y , v i s the kinematic v i s c o s i t y and L, A and r\ are the i n t e g r a l length scale, Taylor microscale and the Kolmogorov scales of turbulence respectively. These relationships imply that R 1 / 2 - 1 R L 15 A (7.14) •J 15 = ^ i r R 1 / 4 = (^i5-) 1 / 2 R 1 / 2 ( 7 - 1 5 ) i n which R r? L A u'L and R = A L V u'A 78 Fraser et a l [38] made dir e c t measurements of the l a t e r a l fluctuations i n t e g r a l length scale by means of LDV i n a motored engine with a disc shaped chamber and operated with s w i r l . They found that the fluc t u a t i o n i n t e g r a l length scale L reaches a minimum within 10 degrees BTDC and ri s e s thereafter, reaching approximately one-fifth the chamber height near TDC. At TDC the integral length scale was found to be about 2.25mm and i t scales with the instantaneous clearance height and varies l i t t l e with speed. Lancaster [50] noted that the integral scale normalized by TDC clearance height had values i n the range of 0.175 to 0.275 and reached a minimum at TDC, and was independent of speed. There seems to be some s i m i l a r i t y i n the results obtained by using hot wire and laser doppler velocimetry. Lancaster [50] from his measurements i n a motored CFR engine using hot wire anemometry calculated.the Taylor microscales i n the range of 0.63mm to 0.84mm. He also noted that the temporal microscale was nearly independent of engine variables other than the engine speed. In summary, i t i s shown by almost a l l researchers that the integral length scale i s about one-fifth the chamber height and i t i s independent of speed. Heywood [39] i n his review paper has reported a range of 2-5 mm for the int e g r a l length scales i n an automotive engine. 7.5 Small Scale Structure Of Turbulence Given that during i g n i t i o n and combustion the turbulence within the engine i s homogeneous and isotropic and that we have approximate knowledge of the turbulence intensity and integral length scale, we can make estimates concerning the small scale structure of turbulence. Tests conducted i n the wind tunnels by various researchers using hot wire anemometry reveal that the flow may not be continuously turbulent on a very small scale but i t may exhibit intermittency. The intermittency factor at a point i s defined as that f r a c t i o n of time for which the flow i s turbulent. This phenomenon has been found to be c h a r a c t e r i s t i c of a l l turbulent flows. To explain t h i s intermittency Tennekes used a hypothesis that "the small scale structure of turbulence may be modelled as vortex tubes of diameter r) which are stretched by eddies of size A where rj i s the Kolmogorov scale and A i s the Taylor microscale". Tennekes proposal of the small scale structure of turbulence i s indicated i n Fig 62 i n which a single vortex tube i s shown with t y p i c a l spacings A and more or less uniform v e l o c i t y u' within these A-sized regions where the flow i s laminar. The di s s i p a t i o n process i s concentrated i n the vortex tube of c h a r a c t e r i s t i c size rj. The Taylor microscale i s consistent with the experimental observations of the length scale corresponding to the zero crossing frequency. This model, with regions of concentrated di s s i p a t i o n i n the vortex tubes and the intermittency i n between, i s dimensionally compatible with the scaling rules. The d i s s i p a t i o n rate per unit mass within the tube w i l l be of the order of where c i s a constant. The r a t i o of the mass within the tube to the t o t a l w i l l be proportional to f u 1 (7-16) 2 ....(7-17) so the average di s s i p a t i o n rate i n the f l u i d as a whole w i l l be • « - C - f ) 2 ^ = - ( - r ) 2 • • • ( 7 - 1 8 ) which i s i n agreement with the relationship ( 7 - 1 1 ) above. The Taylor microscale i s given a physical meaning by showing i t as the spacing of the spaghetti - l i k e structure the vortex tubes of Kolmogorov thickness assume. The Tennekes model implies that a l l of th d i s s i p a t i o n takes place within the vortex tube. In b r i e f , the Tennekes model implies that a large eddy of the size of i n t e g r a l length scale contains several A-sized regions i n which the burning rate i s slow, probably at laminar burning v e l o c i t y , but the boundaries of these regions are rapidly inflamed because of the rapid flame propagation along the vortex tubes of size rj. 1. 6 I n i t i a l Flame Propagation Before the turbulent flame propagation process can begin the existence of a viable flame kernel must be established. Theoretical analysis of the i g n i t i o n process requires estimation of the heat generated by i g n i t i o n and combustion and the heat loss due to heat conduction from burned to the unburned gases. The minimum i g n i t i o n energy i s usually determined by balancing the heat produced by chemical reaction and the heat dissipated v i a turbulence. Of c r i t i c a l importance i s the size of the flame kernel when i t s temperature has f a l l e n to the adiabatic flame temperature of the mixture. At this point the c r i t e r i o n for successful i g n i t i o n i s that the rate of heat release from the reaction zone be greater than the heat loss from the volume. We now review the available o p t i c a l data for the early flame development period. Khalghatgi [45] studied the effects of change i n compression r a t i o from 3.5 to 7 and fuels l i k e propane, methane, and iso-octane on the early flame development i n a spark i g n i t i o n engine using an o p t i c a l technique. This o p t i c a l technique t imes the passage of the flame front across two p a r a l l e l adjustable laser beams. Khalghatgi observed that c y c l i c variations i n combustion are reduced i f the flame kernel reaches a c r i t i c a l size more quickly i.e. i f the laminar burning v e l o c i t y i s increased. In his experiments laminar burning v e l o c i t y was increased by increasing compression r a t i o and by using different fuels. Increase i n compression r a t i o increased the laminar burning v e l o c i t y due to a decrease i n residual mass-fraction. Laminar burning v e l o c i t y varies from propane to iso-octane to methane i n the descending order. V i s u a l i z a t i o n techniques are p a r t i c u l a r l y useful i n the very early stages of combustion. Parameters l i k e pressure and burning times can only y i e l d l i m i t e d information. Photographs of the combustion chamber during the combustion process show that although a substantial volume f r a c t i o n i s occupied by burned gas, the corresponding mass burned f r a c t i o n i s too small to be measured. I t i s interesting to note that when the outer flame radius i s of the order of 10 mm the mass-fraction-burned i s s t i l l well below 1%. Gatowski, Heywood and DeLeplace [26] examined schlieren photographs > the early stages of flame development i n a square cross section engine taken at 1400 rpm using premixed propane (0.9 equivalence ratio) as the f u e l . They observed that the flame started at the spark plug as a smooth surfaced roughly spherical kernel and this i n i t i a l l y spherical kernel about 1mm diameter interacts with the turbulent flow f i e l d to produce a wrinkled and convoluted outer surface of the flame within the f i r s t few degrees. They also noted that the di r e c t i o n of motion of the kernel varies from cycle to cycle. Tagalian and Heywood [47] used a square piston engine and schlieren photography at 1400 rpm using premixed propane at 0.9 equivalence r a t i o . An enlarged view of the spark plug region permits the study of flame t r a v e l during the f i r s t few crank angle degrees after spark. They noted that the flame started from a smooth-surfaced spherical kernel about 1 mm i n diameter formed during the f i r s t crank angle degree following the spark and grows spherically for the next few degrees. They found that the flame radius was found to increase l i n e a r l y with time over the f i r s t 15°. During t h i s period of 15° following spark the amount of mass burned i s small and the burning speed can be derived from the flame speed (dr/dt) and the r a t i o of densities i.e. Sb = p b dr This p dt u burning speed for small amount of mass burned i s found to be si m i l a r to the laminar burning speed for the fuel considered (propane i n this case). Thus concluding that laminar l i k e burning process immediately follows the spark discharge. Keck, Heywood and Noske [48] analysed the high speed schlieren photographs of Gatowski and Heywood to obtain information on early flame development i n t h e i r square piston, premixed, spark-ignition engine. They suggested that the variations i n the growth rate of the flame kernel and i t s location i n the i n i t i a l stages were the major causes of c y c l i c variations i n spark-ignition engines. They f i t t e d a theoretical c i r c l e on the schlieren photographs from the engine such that they had the same area and the centre as the schlieren shadows to give a 1/2 t h e o r e t i c a l shadow radius r = (A^/TT) . S i m i l a r l y they obtained the burned radius r^ from the burned gas volume. They calculated shadow radius r and i t s rate of change from the o p t i c a l data. S i m i l a r l y they calculated the burned gas radius and i t s rate of change from the pressure data. By p l o t t i n g these two they found that for regions less than 1 cm the shadow expansion speed approaches the burned gas expansion speed. Extrapolating to zero size of the shadow radius the value of the flame speed i s approximately the laminar burning v e l o c i t y for the dif f e r e n t design configurations. The burning speed i s also shown to be l i n e a r l y dependent on the kernel size for r a d i i less than 20mm. They also concluded that v a r i a t i o n i n flame speed at the spark plug i s the major source of c y c l i c variations. Opinions d i f f e r on the development character of the kernel i n the very early stages of combustion. Zur Loye and Bracco [49]suggested that the integrating nature of the schlieren technique makes i t very d i f f i c u l t to draw firm conclusions about the structure of the kernel. Their technique produced a two dimensional image of a t h i n s l i c e of the flame front rather than an image which corresponds to an integration along the path of the l i g h t . A pulsed laser sheet was passed through the engine and Mie scattering by TiO^seeding p a r t i c l e was collected by a 100x100 p i x e l diode array with a f i e l d of view of 1cm x 1cm and l a t e r d i g i t i z e d . They noted the influence of turbulence on the structure of the kernel at a l l engine speeds and even at 0.6° after spark at 300rpm. They observed flame kernels at different speeds 300, 1200, and 3000 rpm and at diff e r e n t times and noticed that the shape of the flame kernel was f a r from spherical and the shape and size varied considerably from cycle to cycle and the convolutions increased with speed. One pa r t i c u l a r frame at 3000rpm and 100/is after spark showed a kernel of 2-3mm from end to end but only 0.2-0.5mm wide i n certain protuding ligaments. The p r i n c i p a l shortcoming of these observations i s that even a size as small as 1mm i s too large i n scale to show the early flame development. The c r i t i c a l (self-sustaining) kernel size i s about lOa/U^, where a i s the thermal d i f f u s i v i t y which under engine conditions i s of the order of 0.01mm. The Taylor microscale i s of the order of 2 (15i/L/u') , where v i s the kinematic v i s c o s i t y and L i s the integral length scale, which under engine conditions i s of the order of 0.2mm. Extrapolation with the present diagnostic and v i s u a l i z a t i o n techniques i s required to i n f e r the random behaviour of the e a r l i e s t stages of flame kernel growth. An important inference from the research done i n the early flame development period i s that the flame propagation during this period i s approximately at the laminar burning v e l o c i t y of the f u e l . 7.7 Laminar Burning Velocity The laminar burning v e l o c i t y or flame v e l o c i t y i s the v e l o c i t y at which unburned f u e l a i r gas mixture moves through the combustion wave i n the d i r e c t i o n normal to the wave surface. For a given f u e l , the laminar burning v e l o c i t y i s a function of the mixture strength, the unburned mixture temperature and pressure. The wholly empirical c o r r e l a t i o n proposed by Guilder [35] was used i n this research Su(0,T,P) = Suo(0). (Tu/To)" (P/Po)^ 7.19 Suo i s the v e l o c i t y measured at Tu = To and P = Po for a given mixture strength, a and B are constants or mixture strength dependent terms and subscripts u and o represent the unburned and standard conditions. Extensive experimental values for the laminar burning v e l o c i t y of methane are available but not enough evidence of these values for natural gas .since methane constitutes over 94% of natural gas the laminar burning v e l o c i t y values for methane are used here. Comparison of the laminar burning v e l o c i t y values from different sources i s compiled i n appendix C. 7.8 Summary In summary, based on the l i t e r a t u r e review undertaken the general findings on engine turbulence measurements are: a) Turbulence i s nearly homogeneous and i s t r o p i c near TDC. b) Turbulence i n t e n s i t y varies l i n e a r l y with speed. c) Turbulence in t e n s i t y varies from about 0.4 to 0.6 times the mean piston speed. d) The in t e g r a l length scale i s about one f i f t h the chamber height at TDC. e) There i s some uncertainty i n determining the size of the kernel following spark from the schlieren and other modes of photography. f) Flame travels with laminar burning v e l o c i t y following spark u n t i l i t h i t s the vortex tubes whereby i t travels at turbulent v e l o c i t y . 86 8. COMPARISON OF MEASUREMENTS AND THEORETICAL ESTIMATES OF STANDARD DEVIATION. 8.1 Introduction: This chapter compares a cha r a c t e r i s t i c from the experimental data with a chara c t e r i s t i c estimated value of the nature of turbulence within the engine. The nature of the turbulence i s deduced from the trends of continuing experimental research as discussed i n chapter 7. The comparison i s made i n accordance with the hypothesis presented by H i l l [55]. The hypothesis states that "Cyclic variations i n Combustion i n Spark Ignition engines are mainly due to (and predictable from) the small scale structure of turbulence and can be correlated with the Taylor microscale and the laminar burning v e l o c i t y . " where the Taylor microscale i s a cha r a c t e r i s t i c length scale of turbulence, and the laminar burning v e l o c i t y i s the burning v e l o c i t y of the f u e l - a i r mixture i n the engine, as discussed i n appendix C. To have a comparable ch a r a c t e r i s t i c of the turbulence with the experimental value of the standard deviation i n burning time during the early stages of combustion following spark or for zero mass-fraction-burned we calculate the mean random time delay X/UV^ from the Tennekes model of turbulence. In the following sections we f i r s t determine a comparable ch a r a c t e r i s t i c mean random time delay. Then we compare the two cha r a c t e r i s t i c time values for zero mass - fraction-burned i.e for the region following spark. 8.2 Mean Random Time Delay From the small scale structure model and the i n i t i a l flame development review we can now picture the flame development stages following spark i n an engine. Chomiak [2] pointed that a flame should propagate rapidly along a vortex tube owing to the collapse of the vortex tube caused by the density change associated with the flame. Daneshyar and H i l l [9] showed by a simple model that the propagation v e l o c i t y produced by this hydrodynamic effect should be of the order of the square root of the density r a t i o across the flame (unburned to burned gas density r a t i o ) times the turbulent fluctuating v e l o c i t y u = u +-J2/3 p /p u' and this t 1 u b quantity i s much faster than the laminar speed. This implies that the flame propagates rapidly along the vortex tube of diameter n and r e l a t i v e l y slowly i n the quiescent regions of length scale A. The flame kernel i n the A-sized region propagates at the laminar burning v e l o c i t y u^ but once the kernel h i t s the vortex boundary the flame propagates at the turbulent rates that are much faster than the laminar burning rates. Assuming spark i g n i t i o n as almost a point source then the randomness of i g n i t i o n i s related as to where the effec t i v e point source i s located near to or far from the vortex tubes of diameter rj. In the A-sized region the flame i s taken to propagate at the laminar v e l o c i t y U^. So the maximum difference i n time for the flame to reach the fast burning zone of the turbulence structure w i l l range from 0 to A/(2U^,) . The mean value of the random time delay i s then A/(4U^). There i s an equal p r o b a b i l i t y of location of the spark within these extreme values. Figure 73, which shows time at x=10% on pro b a b i l i t y paper, indicates normal d i s t r i b u t i o n of the sample test of 100 cycles, except perhaps for 88 some cycles towards the end of the data set. Thus i n th i s study, the d i s t r i b u t i o n of the mean random time delay i s assumed to be normally dis t r i b u t e d . Based on th i s i d e n t i f i a b l e structure of homogeneous,isotropic turbulence we can calculate the random time delay period A/4Û , as —^— = —-— ( U ^ ) ( Homogeneous Isentropic relationship) A 15 v A _ — / 15 vL 4u^ Ul 16 u' where u' i s the ch a r a c t e r i s t i c turbulence RMS v e l o c i t y L i s the int e g r a l length scale v i s the kinematic v i s c o s i t y A i s the Taylor microscale u^ i s the laminar burning v e l o c i t y The value of u' i s assumed to be 0.5 times the mean piston speed i n the case of the "Bath-tub" chamber and 0.42 times the mean piston speed i n the case of the disk chamber being considered. The uncertainty i n the cal c u l a t i o n of u' can be +30% for both the chambers. The cal c u l a t i o n of i s made from the results presented by Guilder [35] as shown i n section 8.5 and the uncertainty i n the value of the laminar burning v e l o c i t y can be of the order of 2. The cal c u l a t i o n of L i s based on the general consensus that i t i s one-fifth the chamber height and the uncertainty i n t h i s value i s of the order of 2. Typical length and v e l o c i t y scales of a spark i g n i t i o n engine are shown i n Table 4. 89 Table 4. Typical length and v e l o c i t y scales for engine turbulence. (3000 RPM). u'm/sec 0.5 Up 4.41 R L u ' L V 1654 U^m/sec 0.48 9.2 L mm 0.2H 2.25 A mm 0.213 rj mm A /15 R L 0.0087 Sq mm 10a - ( S T - 0.63u') 0.01 5c mm S T 0 . 7 5 [ 1+10 ( U'5 L / S L . L ) ( U ' / S L ) 0 - 3 7 5 ] 0.004 In the above table u' i s the turbulent i n t e n s i t y , RL i s the Reynolds number for the int e g r a l length scale, U^ and ST are the laminar and turbulent burning v e l o c i t i e s , L,A,»j are i n t e g r a l , Taylor and Kolmogorov scales respectively, 5q [58] i s the quenching distance, 5c i s the width of the flame kernel, and a i s the thermal d i f f u s i v i t y . The random time delay t h e o r e t i c a l l y calculated above for the turbulent structure i n an engine has a d i s t r i b u t i o n of values for neg l i g i b l e mass-fraction-burned. The experimental data shows a spread i n burning times for zero mass-fraction burned by extrapolation. I t would be inter e s t i n g to examine the relationship i f any between these two. This comparison i s done i n the following sections. 90 Figure 63 shows the trend i n the estimated values of the mean random time delay with equivalence r a t i o for different speeds. Increase i n speed tends to decrease the value of the mean random time delay. This i s due to the increase i n turbulence l e v e l with increase i n speed. Increase i n turbulence l e v e l decreases the value of X as i t i s inversely proportional to the Reynolds number (Chapter 7). Also an increase i n speed increases the temperature and pressure which increases the value of the laminar burning v e l o c i t y . Thus there i s a decrease i n the value of X/UV^ with increase i n speed. Recollect that a sim i l a r phenomenon of decrease i n the value of extrapolated standard deviation i s observed for the experimental data and also si m i l a r to the experimental data there exists a minimum value of X/kM^ near the stoichiometric f u e l - a i r r a t i o . 8.3 Comparison of Data In t h i s section we compare the value of extrapolated standard deviation and the mean random time delay for different speeds and operating conditions. Figures 64 to 67 show the behaviour of the two ch a r a c t e r i s t i c time constants at di f f e r e n t speeds and equivalence r a t i o . These Figures show that i n the lean f u e l region the two curves follow the same trend for a l l the speeds and configurations considered. Also the magnitudes of the two variables correspond very closely to each other. There seems to be no si m i l a r relationship for r i c h mixtures. F i n a l l y , a comparison of the estimated value of the mean random time delay i s made with the extrapolated standard deviation i n burning time, for both the "bath-tub" and "disc" chamber. The f u e l - a i r r a t i o considered i n these comparisons i s 0 < 1.05 . Figures 68 and 69 show these comparisons for the "bath-tub" and "disc" chamber respectively. From these plots we observe that there exists a simple r e l a t i o n between the extrapolated standard deviation and the mean random time delay for both the chambers. This r e l a t i o n i s a = 0.75 A/4u, for the bath-tub chamber, and O %i a= 0.85 A/4u, for the disc chamber. O t/ where a i s the extrapolated standard deviation i n burning time from the o experimental data and A/4u^ i s the estimated mean random time delay. These simple relations suggest that the d i s t r i b u t i o n of extrapolated standard deviation a f a l l s around the mean value of A/4U. where the o -C mean value of random time delay i s normally distributed. 8.4 Summary a) The random time delay period A/4U^,in the early stages of burning can be estimated from the Tennekes model of the small scale structure of turbulence. b) Combining the Tennekes model of small scale structure of turbulence, Chomiak's concept of rapid flame t r a v e l along the vortex tubes and the approximate point source of i g n i t i o n we can give an explanation of the i n i t i a l flame propagation within an engine. 9. CONCLUSIONS. The objective of this research was to investigate the o r i g i n of c y c l i c variations i n combustion by r e l a t i n g the mass-fraction-burned values calculated from the experimental data to the small scale structure of turbulence prevalent i n the engine. The conclusions, based on the experiments and estimates of turbulence parameter are: 1) Standard deviation i n burning time increases l i n e a r l y with increase i n the value of x and the mass-fraction-burned (x) values i n the l a t e r stages of combustion are strongly dependent on the x values i n the i n i t i a l stages. 2) The values of the standard deviation i n burning time, extrapolated to kernels of vanishing sizes, are s i g n i f i c a n t and show that randomness exists at zero mass-fraction-burned. 3) At the same speed, the extrapolated standard deviation values at diff e r e n t equivalence ratios shows a minimum value near the stoichiometric a i r - f u e l r a t i o and thi s value increases as the a i r - f u e l r a t i o i s increased both towards lean and the r i c h side ( i n the absence of m i s f i r i n g ) . 4) The modified spark plug electrode shape did not show any change i n combustion v a r i a t i o n as compared with the standard spark plug. 5) The modified spark plug spark gap decreases combustion v a r i a t i o n i n case of a disc shaped combustion chamber, but i t shows no combustion improvement i n case of a Bath tub combustion chamber. 6) The effe c t of the part-open-throttle on the change i n standard deviation was negli g i b l e i n the case of Bath tub combustion chamber but 93 an increase i n the values of standard deviation was observed i n the case of a disc shaped combustion chamber. An increase i n mean time for complete combustion was observed i n both cases. 7) Comparison of the bath-tub and the disc chamber at diff e r e n t speeds and configurations at similar operating conditions show that the Bath tub chamber has lower values of extrapolated standard deviation. 8) The minimum value of extrapolated standard deviation s h i f t s towards the leaner equivalence r a t i o (around the stoichiometric a i r - f u e l r a t io) with increase i n turbulence le v e l s . 9) The mean random time delay shows a linea r relationship when compared to the extrapolated standard deviation i n burning time value for both the bath-tub and the disc chamber. The simple relationship suggests that the d i s t r i b u t i o n of values of extrapolated standard deviation f a l l around the normally distributed values of mean random time delay. The mean random time delay estimated from the Tennekes model of small-scale-structure of turbulence resulted from the following assumptions: a) Turbulence i s nearly homogeneous and i s t r o p i c near TDC. b) Turbulence in t e n s i t y varies from about 0.4 to 0.6 times the mean piston speed for chambers with no s w i r l . c) The int e g r a l length scale i s about one f i f t h the chamber height at TDC. d) Flame travels with laminar burning v e l o c i t y following spark u n t i l i t h i t s the vortex tubes whereby i t travels at turbulent v e l o c i t y . e) Chomiak's concept of rapid flame travel along the vortex tubes and the approximate point source of i g n i t i o n can give an explanation of the i n i t i a l flame propagation within an engine. The results presented above do not prove that these assumptions are true, nevertheless the results have shown that the o r i g i n of c y c l i c variations can be predicted from the small-scale-structure of turbulence i n the engine during spark. RECOMMENDATIONS It i s suggested that further work be conducted i n order to determine the turbulence parameters such as the turbulence intensity, length scales and the nature of turbulence during combustion using the Laser Doppler Anemometery for the "Bath-tub" and "Disc" combustion chamber that have been used i n these studies. Further, pressure data should be collected for the modified spark-plug gaps with both an increase and decrease i n spark-gap size for the Bath-tub and Disc shaped combustion chamber. Also the effect of gradually increasing residuals on c y c l i c variations should be observed by changing the t h r o t t l e opening. F i n a l l y , a study of the v i s u a l i z a t i o n of i n i t i a l flame growth following spark w i l l be highly useful i n determining the i n i t i a l flame growth. 96 REFERENCES 1. Young, Michael B., "Cyclic Dispersion i n the Homogeneous-charge Spark-Ignition Engine", A Literature Survey Society of Automotive Engineers Paper, SAE 810020 , 1981. 2. Chomiak, J . , "Flame Development from an Ignition Kernel i n Laminar and Turbulent Homogeneous Mixtures", The Combustion I n s t i t u t e , Seventeenth Symposium (International) on Combustion, 255-263,1979. 3. Amann, C.A.,"Cylinder Pressure Measurement and i t s use i n Engine Research", SAE 852067. 4. Dent, J.C., and Salama, N.X., "The Measurement of the Turbulence Characteristics i n an Internal Combustion Engine Cylinder", SAE 750886 Automobile Engineering Meeting, Detroit, (1975). 5. Daneshyar, H., and F u l l e r , D.E., "Mixture Motion i n an Engine Cylinder", Cambridge University Engineering Department/A/Thermo/TR.15 (1981) . 6. Smith, J.R., "The Influence of Turbulence on Flame Structure i n an Engine", ASME conference Phoenix, Arizona, Paper W014-19 (1982). 7. Taylor, G.I., "Production and Dissipation of V o r t i c i t y i n a Turbulent F l u i d " , Proc. Roy. Soc. A, 1938. 8. Tennekes, H., "Simple Model for the Small Scale Structure of Turbulence", The Physics of Fluids, v o l . 1, No. 3. (1968). 9. Daneshyar, H., and H i l l , P.G., "the Structure of Small Scale Turbulence and i t s Effects on Combustion i n Spark Ignition Engines", Proc. i n Energy and Combustion Science. 10. Soltau, J.P., "Cylinder Pressure Variations i n Petrol Engines," Proceedings of the I n s t i t u t e of Mechanical Engineers, No. 2, 1960-1961. 11. Karim, G.A., "An Examination of the Nature of the Random Cyclic Pressure Variations i n a Spark i g n i t i o n Engine," J. of the In s t i t u t e of Petroleum, v o l . 53, No 519, March 1967. 12. Peters, B.D., Borman, G.L., "Cyclic Variations and Average Burning Rates i n a S.I.Engine," SAE 700064, 1970. 13. Harrow, G.A., Orman, P.L., "A Study of Flame Propagation and Cyclic Dispersion i n a Spark-Ignition Engine," Advanced School of Automotive Engineering (Part IV) Combustion Processes i n the Spark Ignition Engine, Pergamon Press, July 1965. 14. Barton, R.K., Kenemuth, D.K., Lestz, S.S., Meyer, W.E., "Cycle-by-Cycle Variations of a Spark Ignition Engine- A S t a t i s t i c a l 97 Analysis," SAE 700488, 1970. 15. Winsor, R.E., Patterson, D.J., "Relationship of Cyclic Combustion Variations and Mixture Motion i n a Spark-Ignition Engine," Tech. Report No.l, Dept. of Mechanical Engineering, University of Michigan, September 1972. 16. Lancaster, D.R., "Effects of Engine Variables on Turbulence i n a Spark-Ignition Engine," SAE 761059, 1976. 17. Lancaster, D.R., Krieger, R.B., Sorenson, S.C., H u l l , W.L., "Effects of Turbulence on Spark-Ignition Engine Combustion," SAE 760160, 1976. 18. Andrews, G.E., Bradley, D., Lwakabamba, S.B. "Turbulence and Turbulent Flame Propagation -A C r i t i c a l Appraisal," Combustion and Flame, Vol. 24, 1975. 19. Hansel, H.G., "A Turbulent Combustion Model of Cycle-to-Cycle Combustion Variations i n Spark-Ignition Engines," Combustion Science and Technology, Vol. 2, 1970. 20. Winsor, R.E., Patterson, D.J., "Mixture Turbulence-A key to Cyclic Variations," SAE 730086., 1973. 21. Annand, W.J.D., "Heat Transfer i n the Cylinder of Reciprocating Internal Combustion Engines," Proc. Instn. Mech. Engrs., Vol. 177, No. 36, pp.973-996, 1983. 22. Beretta, G.P., Rashidi, M., Keck, J.C., "Turbulent Flame Propagation and Combustion i n Spark-Ignition Engines," Combustion and Flame, Vol. 52, pp 217-245, 1983. 23. Bopp, S., V a f i d i s , C, and Whitelaw, J.H., "The Effect of Engine Speed on the TDC Flow f i e l d i n a Motored Reciprocating Engine," SAE 860023, 1986. 24. Chomiak, J . , "Dissipation Fluctuations and the Structure and Propagation of Turbulent Flames i n Premixed Gases at high Reynolds Numbers," Sixteenth Symposium (International) on Combustion, The Combustion I n s t i t u t e , pp 1665-1673, 1977. 25. Fraser, R.A., Felton, P.G., Bracco, F.V., and Santavicca, D.A., "Preliminary Turbulence Length Scales Measurements i n a Motored IC Engine," SAE 860021, 1986. 26. Gatowski, J.A., Heywood, J.B., and Delaplace, C, "Flame Photographs i n a Spark-Ignition Engine," Combustion and Flame, Vol. 56, pp 71-81, 1984. 27. Kuo, A.Y.S., and Corrsin, S., "Experiments on Internal Intermittency and Fine Structure D i s t r i b u t i o n Functions i n F u l l y Turbulent F l u i d , " Journal of F l u i d Mechanics, Vol. 50, Part 2, pp. 285-319, 1971. 28. Lancaster, D.R., Krieger, R.B., Lienesch, J.H., "Measurement and Analysis of Engine Pressure Data," SAE 750026, 1975. 29. Semenov, E.S., "Studies of Turbulent Gas Flow i n Piston Engines, NASA Technical Translation F-97, 1963. 30. Tabaczynski, R.J., "Turbulence and Turbulent Combustion i n Spark-Ignition Engines," Prog. Energy Combustion Science, Vol. 2, pp. 143-165,1976. 31. Tabaczynski, R.J., "Turbulence Measurement and Modelling i n Reciprocating Engines-An overview," I Mech. Eng. 1983. 32. Taylor, G.I., " S t a t i s t i c a l Theory of Turbulence," Proceedings of Royal Society (London), Ser.A., Vol. 151, pp 421, 1935. 33. Andrews, G.F., Bradley, D., "The Burning Velocity of Methane A i r Mixtures," Combustion and Flame, Vol. 19, pp 275-288, 1972. 34. Sharma, S.P., Agarwal, D.D., Gupta, CP., "The Pressure and Temperature Dependence of Burning Velocity i n a Spherical Combustion Bomb," Eighteenth Symposium (International) on Combustion, The Combustion I n s t i t u t e , pp 493-501, 1981. 35. Gulder, O.L., "Correlations of Laminar Combustion Data For Alternative S.I.Engine Fuels," SAE 841000, 1984. 36. Belmont, Hancock and Buckingham " S t a t i s t i c a l Aspects of Cyclic V a r i a b i l i t y , " SAE 860324. 37. Boisvert, J . , "Turbulent Combustiono of Gas-Air Mixtures i n a Spark-Ignition Engine." M.A.Sc Thesis U.B.C. AFL-86-05 1986. 38. Fraser, Felton, Bracco and Santavicca "Preliminary Turbulence Length Scale Measurement i n a Motored IC Engine." SAE 860021. 39. Heywood, J.B., "Fluid Motion within the Cylinder of Internal Combustion Engines. - The 1986 Freeman Scholar Lecture". J. of Fluids Engineering March 1987 Vol 109/3. 40. Patterson, D.J., "Pressure Variations, A fundamental Combustion Problem". SAE paper No.660129, 1966. 41. Hirao, 0., Kim, Y., "Combustion Variation Analysis on Flame Propagation i n 4 Cycle Gasoline Engines". Japan Automobile Research I n s t i t u t e , Inc., 1970. 42. Broeze, J . J . , "Combustion i n Internal Combustion Engines. I I . Th Spark I g n i t i o n Engines,". Engineering Vol. 169, A p r i l 28, 1950. 99 43. Van Wylen. G.J.,Sonntag. R.E., "Fundamentals i n C l a s s i c a l Thermodynamics". 44. Warren, J.A., Hinkamp. J.B., "New Instrumentation For Engine Combustion Studies", SAE Transactions, Vol 64, 1956. 45. Kalghatghi, G., "Early Flame Development i n a Spark-Ignition Engine", Combustion and Flame 60, 299,308, 1985. 46. Gatowski, J.A., Heywood, J.B. and DeLePlace, C, "Flame Photographs i n a Spark-Ignition Engine"., Combustion and Flame, 56, 71-81, 1984. 47. Tagalian, J . , and Heywood, J.B., "Flame I n i t i a t i o n i n a Spark-ignition Engine", Combustion and Flame, 64, 243-246, 1986. 48. Keck, J.C., and Heywood, J.B., "Early Flame Development and Burning Rates Spark-ignition Engines and Their Cyclic V a r i a b i l i t y " , SAE 870164 (1987) . 49. Zur Loye, A.O. and Bracco, F.V., "Two-Dimensional V i s u a l i s a t i o n of Ig n i t i o n Kernels i n an IC Engine"., Combustion and Flame, 69, N0.1 60-69, 1987. 50. Lancaster, D.R., "Effects of Engine Variables on Turbulence i n a Spark-Ignition Engine". SAE 760159. 51. Bracco, F.V., and H a l l , M.J, "A Study of V e l o c i t i e s and Turbulence i n t e n s i t i e s i n F i r i n g and Motored Engines". SAE 870453. 52. Whitelaw, J.H., V a f i d i s , Bopp, S., "The Effect of Engine Speed on TDC F i e l d i n a Motored Reciprocating Engine". SAE 860023. 53. Albrecht, H., Bloss, W.H., Herden, W. , Maly, R. , Saggan, B. , and Wagner, E., "New Aspects on Spark Ignition". SAE 770853. 54. Starkman, E.S., Strange. F.M., and Dahm. T.J., "Flame Speeds and Pressure Rise Rates i n Spark Ig n i t i o n Engines." SAE paper 83V, 1959. 55. H i l l . P.G., "Cyclic Variations and Turbulence Structure i n Spark Ign i t i o n Engines". Combustion and Flame. 56. "The Ricardo/Cussons Standard Hydra Engine and Test Bed Manual". 57. Hung. J . , "Effects of Propane and Ethane Addition on the Laminar Burning Velocity Of Methane". 100 APPENDIX A.CALIBRATION CURVES This appendix presents the c a l i b r a t i o n curves for a) the Meriam laminar flow element, used to monitor the natural gas flow b) the Meriam Laminar flow meter to monitor the a i r flow to the Ricardo engine, and c) the c a l i b r a t i o n curve for the pie z o - e l e c t r i c transducer. LAMINAR FLOW ELEMENT The c a l i b r a t i o n curves for the two Meriam laminar flow elements a) a i r model 50MC2-4F and b) fuel model 50MW20-1.5 are supplied by the manufacturer with the instrument giving the r e l a t i o n between pressure head across the meter elements i n inches of water and the volume flow i n 3 f t /min. To calculate the standard cubic feet per minute temperature and pressure correction factors from charts supplied by the manufacturer are used. QUASI-STATIC CALIBRATION OF PIEZO-ELECTRIC PRESSURE TRANSDUCER The pressure transducer was calibrated i n the laboratory to confirm the c a l i b r a t i o n constant supplied by the manufacturer. The pressure transducer was attached to i t s sleeves [56] and i n s t a l l e d i n the deadweight tester. The pie z o - e l e c t r i c transducer i s calibrated q u a s i - s t a t i c a l l y on a deadweight tester using a K i s t l e r 5001 charge amplifier. The charge amplifier was set on i t s "long" time constant to provide high input resistance. The large input resistance of the charge amplifier makes i t suitable to calibrate this dynamic response producing pressure transducer. The s e n s i t i v i t y and the range are set to the settings normally used on the engine. The s e n s i t i v i t y ( c a l i b r a t i o n constant) i s provided by the manufacturer and the c a l i b e r a t i o n range of pressures i s between 10-110 bars (this i s the pressure range within the 101 engine). After the preliminary i n s t a l l a t i o n i s done the dead weight tester i s loaded with known weights. These weights provide a hydraulic pressure on the pressure transducer which gives an output signal. The value of the output signal i s determined using the oscilloscope. Thus the values of the voltages corresponding to the known pressure are collected. A plot i s then made of the charge output versus pressure applied. The best f i t t i n g straight l i n e i s then drawn through the points and the gradient of the l i n e gives us the s e n s i t i v i t y . I f the gradient i s dif f e r e n t from the one supplied by the manufacturer the c a l i b r a t i o n i s repeated with the s e n s i t i v i t y set at the new value of the gradient. The c a l i b r a t i o n curve supplied by the manufacturer and the caliberation curve determined from the measurements obtained i n the laboratory are both reported. The values of the pressure and the output from the charge amplifier are as shown i n Table A . l . Table A . l : Pressure and Voltage Values for Calibration of Piezo-electric Pressure-Transducer. Pressure Voltage Input (psi) Output (mV) 15 99 25 168 35 240 45 297 55 359 105 695 155 1017 205 1363 APPENDIX B.COMBUSTION-VOLUME PHASING This appendix examines the e f f e c t of the p i s t o n movement on combustion within the engine. The piston p o s i t i o n changes while the combustion occurs within the engine. This change i n pi s t o n motion being small at TDC, when the v e l o c i t y of the pi s t o n approaches zero and then increases s i n u s o i d i a l l y on the expansion stroke with the maximum v e l o c i t y occuring midway between the stroke. The Engine simulation model by Boisvert [37] c a l c u l a t e s the pressure i n an engine from BDC p r i o r to compression to TDC and into the expansion stroke. The c a l c u l a t i o n s f o r the compression stroke u n t i l the occurrence of the spark are the same as i n the program XPRESS described i n chapter 4 but the c a l c u l a t i o n s following spark i n the combustion period are done combining a thermodynamic analysis of the cy l i n d e r contents coupled with the turbulent entrainment model. This program was used to show the importance of combustion volume phasing. The input to the program i s the i n i t i a l conditions of intake and ambient temperature, ambient pressure, speed, r e s i d u a l f r a c t i o n , spark advance and the equivalence r a t i o . To understand the e f f e c t of the pressure occuring at or near TDC we maintain a l l the conditions of input the same but change the value of the spark advance such that the peak pressure occurs over a range of crank angles a f t e r spark. The r e s u l t s of t h i s experiment are shown i n Table B . l 103 Table B . l : Peak-Pressure and i t s Crank Angle Occurrences for Changes i n Phasing. Spark Advance Before TDC Crank Angle at Peak Pressure Peak Pressure 26 16 5340.80 28 14 5705.94 30 12 6068.03 32 10 6394.30 34 8 6658.30 36 6 6940.91 38 4 7128.25 I f we consider these cycles to be true for a p a r t i c u l a r set of operating conditions then we can see that the cycle which has the peak pressure near the TDC shows the highest value of the pressure or conversely i f the cycle i s faster burning i.e i t travels faster i n the chamber then most of the heat release occurs near TDC and subsequently the value of the peak pressure i s higher. The phasing of the pressure and the volume position plays an important role i n determining the character of the pressure and the output vari a t i o n s . For fast burning cases a large f r a c t i o n of the energy release occurs near TDC when the combustion chamber volume i s changing very slowly. As a result the pressure variations are due mainly to the combustion variations. For the slower burning cases a large part of energy release occurs l a t e r i n the cycle, the variations i n pressure due to the combustion v a r i a t i o n i s augmented by the changing pressure due to rapidly varying cylinder volume during t h i s part of the cycle. By burning most of the mixture while the piston i s at or very near TDC i.e by faster burning the c y c l i c variations have been known to decrease. Obviously then to minimize cycle to cycle variations i n an engine combustion variations should be minimized and or combustion rates maximized. APPENDIX C.Laminar Burning Velocity This appendix reviews some of the l i t e r a t u r e on the laminar burning v e l o c i t y of methane at high temperatures and pressures as presented by various authors, engine. The laminar burning v e l o c i t y or flame v e l o c i t y i s the v e l o c i t y at which unburned f u e l a i r gas mixture moves through the combustion wave i n the d i r e c t i o n normal to the wave surface. For a given f u e l , the laminar burning v e l o c i t y i s a function of the mixture strength, pressure and the unburned mixture temperature. Guilder [35] suggested that closed vessel explosions techniques accompanied by density corrections can give good p o s s i b i l i t i e s for the accurate measurement of burning v e l o c i t y . Various forms of empirical relationships have been proposed for laminar burning v e l o c i t i e s and the simplest form of the wholly empirical corre l a t i o n proposed by Guilder i s Su(<£,T,P) = Suo(^) (Tu/To)a (P/Po)^ Suo i s the v e l o c i t y measured at Tu = To and P = Po for a given mixture strength, a and /9 are constants or mixture strength dependent terms and subscripts u and o represent conditions of the unburned gases and at standard conditions respectively. Guilder made measurements i n a constant volume bomb. He proposed empirical expression to represent the room temperature burning v e l o c i t y of methane Suo($) = W exp [-£($-1.075)2] where the n=0.15 , £-=5 .18 , W=0.422 m/sec are for methane. 106 The effect of pressure and temperature on the burning v e l o c i t y of methane and propane have been correlated by various kinds of relationships including the power law. Guilder proposed the following relations for temperature and pressure. Pressure Dependency For the pressure dependence of the laminar burning v e l o c i t y a power law expression i s deduced by Guilder from the available data from various sources Su($,P) = Suo(3>) [P/Po]*6 for methane th i s pressure exponent 6 i s around -0.5 i n the range of 4-100 pressure i n kpa. Temperature dependency For the temperature dependency of the burning v e l o c i t y the power law proposed by Guilder i s Su($,T) = Suo($) [Tu/To]" for the temperature exponent of methane the proposed values of a ranges from 1.37 to 2.33 at various pressure ranges and equivalence r a t i o s . This value i s taken to be 2 i n our case. Andrew and Bradley [33] obtained the value of laminar burning v e l o c i t y using bomb hot wire and corrected density r a t i o techniques. They proposed separate formulae for the dependence of methane laminar burning v e l o c i t y on unburned gas pressure and temperature St = 43 P i f ° - 5 (constant Tu) 107 S^ = (10 + 0.000371 Tu*Tu) (constant Pu) where P i s i n atm. Combing these two equations to get the laminar burning v e l o c i t y we have Ŝ = (10 + 0.000371 Tu*Tu) P u " 0 5 t h i s i s j u s t i f i e d by Sharma Aggarwal and Gupta who show that the rate of increase of burning v e l o c i t y with temperature does not vary with increasing pressure. Sharma, Aggarwal and Gupta [34] obtained laminar burning v e l o c i t y of methane-air for pressures of 0.5 to 8 atm, temperature of 300 to 600°K and equivalence r a t i o i n the range of 0.8 to 1.2. They correlated the pressure, temperature and mixture strength dependence i n to the relations given by St - CA (TU / 3 0 0 ) 1 - 6 8 / * $ < 1.0 Ŝ = C« (Tu / 300) 1-68*<* $ > i . o where C4= -418 + 1287/$ -1196/$2 + 360/$3- 150(log Pu ) they stated that though the working fuel was natural gas they computed the burning v e l o c i t y assuming this gas to be Methane. Hung [57] obtained laminar burning v e l o c i t y of stoichiometric mixtures of methane-air and methane with ethane or propane additives by making measurements i n a constant volume chamber for pressures of 1 to 80 atm and with unburnt gas temperature i n the range of 300 to 500 K. She correlated the pressure and temperature dependence of the burning v e l o c i t i e s for the whole range of experimental conditions by the r e l a t i o n Su = Suo [Tu/To]a [P/Po]'9 where Suo = 33.7. /3 = -.315 and a = 1.87 for methane. She also reported that the greatest r e l a t i v e increase i n burning v e l o c i t y was at the highest pressure, for a given temperature and trace amounts of propane and ethane do not appear to have s i g n i f i c a n t effects on the burning v e l o c i t y . APPENDIX D - PROPERTIES OF B.C. NATURAL GAS Composition (Volume %) Methane 94. 00 Ethane 3. 30 Propane 1. ,00 Iso-Butane 0. ,15 N-Butane 0, .20 Iso-Pentane 0. .02 N-Pentane 0 .02 Nitrogen 1. .00 Carbon-Dioxide 0 .30 Hexane 0 .01 Water content: 3 to 4 l b s / m i l l i o n cubic feet. APPENDIX E - SENSITIVITY ANALYSIS The effect of uncertainty i n the pressure data i n determining the mass - fraction-burned values w.r.t the crank angles i n the i n i t i a l stages after spark i s i l l u s t r a t e d i n the following discussion. The s e n s i t i v i t y of raw pressure data w.r.t time (after spark) can be established from the relationship AP At S?/6t where At i s the uncertainty i n time corresponding to the uncertainty AP i n the pressure data. The derivative 5P/5t i s the slope of the combustion pressure (less motored pressure) w.r.t time after spark. The term AP i s the minimum uncertainty i n the pressure corresponding to the d i g i t i z a t i o n error of +1 units. For the transducer assembly, the d i g i t i z a t i o n of analog data was such that a d i g i t a l value of 4096 at the data a c q u i s i t i o n system corresponded to 100 bars of pressure within the engine. Thus 2 units of raw pressure data would equal 5 kPa. Figure 74 shows the t y p i c a l f i r e d and motored pressure curves. Figure 75 shows the difference between the combustion pressure and the motored pressure and ( i n a broken curve) the same curve plus the d i g i t i z a t i o n error of 100 bar/ 4096 = 5 kPa. The f u l l curve i s used to P i + l " P i estimate 5P/5t = — . This estimate becomes unreliable when 5P/5t i+1 I i s small. Figure 76 shows both the mass-fraction growth with crank angle (computed from the f i r e d pressure curve) and the estimate of the AP time uncertainty At = corresponding to the d i g i t i z a t i o n error 6?/St and affected by the fluctuations i n the estimate of 5P/5t. 111 This graph shows the estimates of burning time uncertainty are necessarily unreliable for x < 2%. TABLE 1 RICARDO HYDRA ENGINE SPECIFICATIONS Number of Cylinders Bore Stroke Con-rod Length Swept Volume Clearance Volume Compression Ratio Max Speed Max Power Max Cylinder Pressure Valve Timing: Inlet Opens Inlet Closes Exhaust Opens Exhaust Closes 1 80.26 mm 88.90 mm 158.0 mm 0.45 SL 0.0563 I 9:1 90 rev/sec 15 kW 120 bar 12° BTDC 56° ABDC 56° BBDC 12° ATDC Normal Working Temperatures: Oil 80°C Water 80°C 6000 CYCLIC PRESSURE VARIATIONS IN A SPARK IGNITION ENGINE Speed - 3000 RPM (p - 1.00 P R E S S U R E / k P a 5000 . 4000 3000 . 2000 1000 Motored;; P r e s s u r e v.. T •1 W - f T 720 .440 2160 2880 3600 4320 5040 5760 6480 7200 CRANK ANGLE DEGREES Fig 1. Cyclic Pressure Variations in a Spark Ignition Engine. NAT. GAS GASOLINE COOLING 4, WATER *— HYDRA ENGTNT OIL COOL INC — < — WATER DYNAMOMETER T f TACHO IETER TORQUE LOAD CELL control Dgiull Mt CONVERTER CABINET Ctntrol ' SlpMll I* *vmr A U or V out TRANSFORMER POWER SUPPLY g 2. Engine, Dynamometer and Control Systems Layout. 115 C D Cross S e c t i o n L o n g i t u d i n a l S e c t i o n Fig 3. Ricardo Hydra Engine Cross-Sectional Views. Fig 4. Combustion Chamber Shapes a) Bath-Tub Chamber, b) Disc Chamber. NATURAL OAS INLET APPROXIMATE RELATIVE AM/FUEL5 RATIO •DC PULSCS- o .a»puLSEs- AP- »AWFLOW INLET TEMPERATURE I L OAS LAMINAR FLOW ELEMENT IEXHAUST X SENSOR CZ EXHAUST PRESSURS AVL •SPCEOITDROUI AM INLET / FILTER ' AM LAMINAR FLOW ELEMENT *AIR TEMPERATURE ' AM TEMPERATURE OASOLME INLET INSTRUMENTATION L A Y O U T Fig 5 . Instumentation Layout. 118 F I G U R E fl - H A R D W A R E A R R A N G E M E N T RS232 Unk to PC \ BOC ^ Pickup* Fig 6. Hardware Arrangement. E n s e m b l e A v e r a g e d P r e s s u r e 3500-1 3000- 2500- 0_ 0-| 1 1 1 1 1 1 1 -I -200 -150 -100 -50 0 50 100 150 200 C r a n k A n g l e ( d e g r e e s ) F i g 7. Ensemble-Averaged Pressure [Motored Engine] Fig 8. Indicator Diagram on Logarithmic Scale [Motored Engine] -10 - 9 . 5 - 9 - 8 . 5 - 8 - 7 . 5 L o c ^ V o l u m e " . Fig 9. Indicator Diagram on Logarithmic Scale [Incorrect reference Pressure] 10-1 Fig 10 . Indicator Diagram on Logarithmic Scale [Pressure Retarded] Fig 11. Volumetric Efficiency i n a Motored Engine. 2500-1 I 1 ! 1 1 1 1 1 1 1 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 S p e e d / ( R P M ) 4^ Fig 1 2 . Ensemble-Averaged Peak Pressure i n a Motored Engine. 6000-1 Frequency Crank Angle Fig 13. Typical Pressure Variations and Frequency Histogram for Peak Pressure. Speed - 3000 RPM, - 1.015. 6000-t 5000- 0 5 10 15200 -100 0 100 200 Frequency Crank Angle Fig 14. Typical Pressure Variations and Frequency Histogram for Peak Pressure. Speed - 3000 RPM, 4> - 0.674. Peak Pressure Variation vs Equivalence Ratio 6OOO-1 5000 O 4000 UJ ^ 3000- w u i cc ^ 2000 < u i Q . 1000- H a • XX X A X A X • >e x A A A 6 A X • 0 r i i i [ i i i i [ 0.5 0.6 0.7 0.8 0.9 1 E q u i v a l e n c e R a t i o T—i—i i | i i i i [—i i i i |—i i i—r—j—i i i i |—i i i i | 1.1 1.2 1.3 R P M A 2400 X 3000 • 3600 H 4200 Fig 15. Ensemble-Averaged Peak Pressure Variation with Speed and Equiv.Ratio. Coefficient of Variation vs Equivalence Ratio 0.25-1 0.20 C o "a > c .«> 0.10 o o CJ 0.05 BA X • A I X • X R P M A 2400 X 3000 • 3600 B 4200 0.00 I • ' • • i ' ' • • i ' • • ' i • 1 1 ' I 1 1 ' ' I ' ' ' ' I ' ' ' ' I ' ' ' ' 1 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 E q u i v a l e n c e R a t i o F i g 16. C o e f f i c i e n t of V a r i a t i o n for Dif f e r e n t Speeds and Equivalence Fig 17. Typical Mass-Fraction-Burned Variation with Time, From Ignition. N-3000 RPM. <f> - 1.37 Frequency Histogram - Time for 10% Mass-Fraction-Burned 15 10 >-o c a> D V a> 0.0 5.0 T 10.0 1 15.0 20.0 Time for 10% Mass-Fraction-Burned/Csec) *10~ 4 Fig 18. Typical Frequency Histogram for Burning Times (X-0.10, N - 3000 ,0 - 1. 1.05.) to O Frequency Histogram - Time For 30% Mass-Fraction-Burned l5-i Time/(msec) 19. Typical Frequency Histogram for Burning Times (X-0.30, N - 3000 RPM. <f> - 1.05.) Frequency Histogram - Time For 50% Mass-Fraction-Burned Time/(msec) 20. Typical Frequency Histogram for Burning Times (X-0.50, N - 3000 RPM. <f> - 1.05.) Frequency Histogram - Time for 10% Mass-Fraction-Burned '5-| 10- u c a> D cr 0.0 5.0 10.0 15.0 Time for !0% M a s s - F r a c t l o n - B u r n e d / 1 s e c 20.0 •10" 21. T y p i c a l Frequency Histogram for Burning Times (X-0.10, N - 3000 RPM. 0 - 1 . 2 2 . ) Frequency Histogram - Time for 10% Mass-Fraction-Burned 12 T 10 8- >~ o c 3 6 cr CD 0.0 5.0 UL 10.0 15.0 20.0 25.0 Time for ! 0 % M a s s - F r a c t l o n - B u r n e d | s e c 30.0 • 1 0 " Fig 22. Typical Frequency Histogram for Burning Times (X-0.10, N - 3000 RPM. <f> - 1.38.) S t a n d a r d D e v i a t i o n in B u r n i n g T i m e o 0.5 -i 0.4- c~ 0.3 o o "> <u Q "D v. D TJ C o CO 0.2- 0 . 1 - 0.0 G A • • • • • • i i i i • i i i I i i i i I i i i i I i i i i I < i i 0.0 0.1 0.2 0.3 0.4 0.5 M a s s - F r a c t i o n - B u r n e d 0.6 E q u i v . R a t i o A 1.1767 X 1.0915 a 1.0173 B 0.9884 F i g 23. Standard Deviation i n Burning Time. N - 2400 RPM. (Bath Tub Chamber) S t a n d a r d D e v i a t i o n in B u r n i n g T i m e 0.4 0.3 c I 0.2 Q i _ O TJ C a CO 0.1 0.0 a a a a a a • a • 8 a a a • • X X X • n x ^ x • X X A A A A 0.0 I ' ' ' ' I 0.1 I I I I I 0.2 0.3 0.4 M a s s - F r a c t i o n - B u r n e d i—•—1—'—<—i 0.5 0.6 E q u i v . R a t i o A 0.9509 X 0.8801 O 0.7987 B 0.7530 O 0.7393 Fig 24. Standard Deviation in Burning Time. N - 2400 RPM. (Bath Tub Chamber). S t a n d a r d D e v i a t i o n in B u r n i n g T i m e A A A X X X *K< X X H § B 3̂ • D B Equiv. Ratio B r P „ j H A t . 1 3 5 8 x 1.0772 D 1.0162 8 0.9513 T—1—1—,—j—1—1—1—1—1—1—1—1—1—1—1—1—1—"—1—1—1—1—1—1—1—1—' 1 I 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Mass-Fraction-Burned Fig 25. Standard Deviation i n Burning Time. N - 3000 RPM. (Bath Tub Chamber) S t a n d a r d D e v i a t i o n in B u r n i n g T i m e o 0.4 n O c D (?) 0.3 c o I 0.2 Q 0.1- 0.0 2 H X A • X A X A 5 • X A -! T » 1 0.0 i — 1 — 1 — • — 1 — r 0.1 X A 0.2 0.3 0.4 M a s s - F r a c t i o n - B u r n e d H • x A 1—.—i—i—.—| 0.5 0.6 E q u i v . R a t i o A 0.8824 X 0.8210 • 0.8068 • 0.7610 H 0.7241 H 0.6902 Fig 26. Standard Deviation in Burning Time. N - 3000 RPM. (Bath Tub Chamber). O o OO S t a n d a r d D e v i a t i o n / m s e c o b o. b o P 9 9 K> * I I , i • • I i i i I a 9. in N> to I ? Q o ^ o O* CM ' 3 H LK BO 0 0 Q " ID Q . Q Q . O CD < Q _ • • O ZS CO Q. *" C D C 3 D * o In" X 3 CD o p I* • X O — m i § S c io S w ?• oo o» > Q 6 £ I S t a n d a r d D e v i a t i o n i n B u r n i n g T i m e 0.25-1 u c o > Q o x> c o CO 0.20- 0.15- 0.10- 0.05- • n x x 0.00- 0.0 — I — 0.1 • X A a x A X A 0.2 0.3 0.4 M a s s - F r a c t i o n - B u r n e d 0.5 Equiv. Ratio A 0.8652 X 0.8U0 • 0.7544 0.6 28 Standard Deviation i n Burning Time. N - 3600 RPM. (Bath Tub Chamber S t a n d a r d D e v i a t i o n i n B u r n i n g T i m e u I o > Q TJ o X ) c a CO 0.35 ^ 0.30 ~ 0.25- 0.20 0.15 0.10 0.05 0.00 fi 2 2j fi 0.0 0.1 X • T Q T" 0.2 0.3 0.4 M a s s - F r a c t i o n - B u r n e d 0.5 1—i 0.6 Equiv. Ratio A 1.075 X 1.028 • 0.9J7 B 0.862 B 0.792 Fig 29. Standard Deviation i n Burning Time. N - 4200 RPM. (Bath Tub Chamber) E x t r a p o l a t e d S t a n d a r d - D e v i a t i o n 0.4 o 0.3 H c o I 0.2 <u Q "D i _ O X> c O 0.1 CO 0.0 X A • X B X • B X • A £g X & R P M A 24 0 0 X 3 0 0 0 • 3 6 0 0 B 4200 -1 1 1 1 ! f 1 1 1 1 " I T I -| 1 T—1 1 1 1 • T ! " I 1 T I ! I ] 1—T f" T J I 1 1 T" 0.5 0.6 0.7 0.8 0.9 1 E q u i v a l e n c e R a t i o 1.1 1.2 1.3 tsJ Fig 30. Extrapolated Standard Deviation in Early Burning Time. Extrapolated Standard-Deviation in Burning Time 3 . 5 -i D 3 - A X 2 . 5 - 0 X c o 2 - ~h •> <u Q T ) 1 . 5 - i_ O ~ Q C o t _ u RPM CO 1 A 2 4 0 0 X 3 0 0 0 0 . 5 - • 3 6 0 0 S 4 2 0 0 0 - c . 1 T • | • 1 . 5 0 . 6 -» ' I • ' ' • 1 ' ' ' ' 1 ' ' ' ' 1 ' ' ' ' ' ' • " ' > ' ' 0 . 7 0 . 8 0 . 9 1 t.1 1-2 1.3 E q u i v a l e n c e Ratio Fig 31. Extrapolated Standard Deviation i n Early Burning Crank Angle Interval CO C r o s s C o r r e l a t i o n c o e f f i c i e n t * 1.2- (— X A V cu • A v A A X QJ /™» 0.8- O - at io n - at io n 0.6- 0 ) 1̂ o o (/) 0.4^ t/i O v_ - O 0.2-^ n Legend A 7% > X 10% > — i 111111 • i • 1111111111111111111111 , , , , i 0 0 0.1 0.2 0.3 0.4 0.5 . . . , , 0.6 Mass-Burned_fraction Fig 32. Cross Correlation Coefficient Of Standard Deviation In Burning Time. 145 h— 1 . 7 m m A F I G 3 3 . M o d i f i e d S p a r k P l u g w i t h F i n e P o i n t E l e c t r o d e s S p a r k P l u g G a p 0 . 7 m m . Standard Deviation in Burning Time (Fine Point Electrode) o c o > CD Q o c a CO 0.25n x 0.20 0.15 0.10 0.05- 0.00 x X K a a • • 0.0 0.1 0.2 0.3 0.4 M a s s - F r a c t i o n - B u r n e d i — i — i 0.5 1 i 0.6 Equiv. Ratio H 1.0785 X 1.0596 • 1.0255 8 0.9562 34. Standard Deviation i n Burning Time. N - 3000 RPM. (Needle Point Electrode Geometry). •Standard Deviation in Burning Time (Fine Point Electrode) 0.35 0.30T o a> 0.25 c o > a o X) c a 0.20 0.15 0.10 0.05 0.00 *X X AAA X A 0.0 0.1 x A 0 • X A 0.2 0.3 0.4 M a s s - F r a c t i o n - B u r n e d 0.5 0.6 Equiv. Ratio A 0 . 8 B J J X 0.8179 O 0.7578 S 0 .7083 Fig 35. Standard Deviation i n Burning Time. N - 3000 RPM. (Needle Point Electrode Geometry). Effect of Spark Plug Geometry (3000 RPM) o c O 0.25-1 0.20 > Q T > i _ O "D C a to T > ~h o a. a X 0.05 0.15 - 0.10 0.00 X X X 0.5 0.6 0.7 0.8 0.9 Equivalence Ratio i.i Legend A STDCONFIG X FINEP0INT -1 1.2 Fig 36. Extrapolated Standard Deviation i n Early Burning Time. Different Electrode Geometries N - 3000 RPM. 4^ OO 149 FIG 3 7 . Modi f ied Spark P lug with Wide Gap E l e c t r o d e s Spark P lug Gap 2 . 3 m m . Standard Deviation in Burning Time (Spark Gap 2.3mm) u c o a > a> Q o •o c o 0.20 0.15 y o.io- O 0.05 10 0.00 • A X A D A X • X a A s A 6 Equiv. Ratio A 1.0838 X 1.0193 • 0 .9489 0.0 0.1 0.2 0.3 ' 0.4 M a s s - F r a c t i o n - B u r n e d 0.5 0.6 38. Standard Deviation i n Burning Time. N - 3000 RPM. (Spark Plug Gap - 2.3 mm) Standard Deviation in Burning Time (Spark Gap 2.3mm) o I o > a) Q o C a ui 0.6 0.5- 0.4- 0.3 0.2 0.1 0.0^ Q 0 0.0 I 1 0.1 3 A 9 0.2 0.3 0.4 M a s s - F r a c t i o n - B u r n e d 9 A 0.5 '—I 0.6 Equiv. Ratio A 0.8797 X 0.8129 • 0.771J 8 0.7154 B 0.67J9 39. Standard Deviation i n Burning Time. N - 3000 RPM. (Spark Plug Gap - 2.3 mm) E f f e c t o f S p a r k P l u g G a p ( 3 0 0 0 R P M ) u c o > ID a o 7 3 c CO T > <D o Q_ O i_ X UJ 0.35-, 0.30- 0.25 0.20- 0.15- 0.10 0.05 0.00 0.5 0.6 A X >A X A — I — 0.7 0.8 0.9 1 Equivalence Ratio —T— 1.1 - 1 1.2 Legend A STDCONFIG X WIDEGAP Fig 40. Extrapolated Standard Deviation i n Early Burning Time. Different Spark Gaps N - 3000 RPM. i—• Ln Standard Deviation in Burning Time (Half Open Throttle) 0.30 -i 0.25- o o w I o D '> <u O n V. O X> c o ui 0.20- « 0.15- 0.10- 0.05- 0.00- 6 X • X • 0.0 0.1 0.2 0.3 0.4 M a s s - F r a c t i o n - B u r n e d A x a Equiv. Ratio X 10539 • 0.9923 0.5 • — l 0.6 Standard Deviation i n Burning Time. N - 3000 RPM. (Half Open Throttle) Standard Deviation in Burning Time (Half Open Throttle) u a> VI I .o "a *> a> a X) O "a c o t7) 0.25 0.20 0.15- 0.10 0.05 0.00 A A 0.0 0.1 0.2 • I ' 0.5 a 0.4 Mass-Fractlon-Burnad x • 0.5 0.6 Equlv. RoUo A 0.94)9 X 0.8621 • 0.S2W • 0.7342 Fig 42. Standard Deviation i n Burning Time. N - 3000 RPM. (Half Open Throttle) 4̂ Effect of Part Throttling (3000 RPM) o 0.25- c o 0.20- > 4) Q "2 0.15 H o X) c D to ~h o a. o X- 0.05 H 0.10- 0.00- 0.5 — I — 0.6 — I — 0.7 0.S 0.9 Equivalence Ratio t.i Legend L. STDCONTIG X H.O.T - 1 1.2 Extrapolated Standard Deviation i n Early Burning Time. Different Throttle Settings N - 3000 RPM. S t a n d a r d D e v i a t i o n i n B u r n i n g T i m e s B B S B B A A c r m • D s s s s H A X U x a • xxxx x E q u i v . Rat io M a s s - F r a c t i o n - B u r n e d A 1.1120 X 1.0420 Q 0.9910 8 0.7120 O 0.6050 • • • . I • • • • I • • • ' I 1 ' ' ' ' ' ' ' ' ' N ' K 0.0 0.1 0.2 0.3 0.4 0.5 0.6 u CD 1/1 > CD O D C Standard Deviation in Burning Time -3000 RPM 0.5 0.4 0.3 0.2 0.1 0.0 E2 S axno D o.o o.i n A x • n A Q A n A 1 i i ' 0.2 0.3 0.4 Mass-F rac t i on -Burned 0.5 0.6 Equiv. Ratio A 1.1020 X 1.0530 • 0.9900 B 0.8720 B 0.7150 Fig 45. Standard Deviation i n Burning Time. N - 3000 RPM. (Disc Chamber) ^1 Standard Deviation in Burning Time -3600 RPM 0 . 5 - 1 n 0.4- C 0.3 H o "o '> cu a \_ D X» C o o cu 0.2 C O 0.1- 0.0 fif* a a a • a B • a • 0.0 0.1 •T T 'T'" 1 t I | I I I I | 0.2 0.3 0.4 M a s s - F r a c t i o n - B u r n e d a 64 • i | i i i > | 0.5 0.6 E q u i v . R a t i o A 1.1080 X 1.0570 • 0.9250 8 0.8240 B 0.7210 Fig 46. Standard Deviation i n Burning Time. N - 3600 RPM. (Disc Chamber) Standard Deviation in Burning Time -4200 RPM 0.5 -1 o a) 0 . 4 - c .2 *g *> 0J Q TJ i_ O X ) c to 0 . 3 - a 8 S 0 . 2 - 0.1- 0.0- • a x x • i — 1 — • — r - X • B a 0.0 0.1 0.2 0.3 0.4 0.5 M a s s - F r a c t i o n - B u r n e d i i i i • 0.6 E q u i v . R a t i o A 1.0930 X 0.9490 • \.D0X SB 0.7740 n 0.7090 Fig 47. Standard Deviation in Burning Time. N - 4200 RPM. (Disc Chamber) Standard Deviation in Burning Time (Fine Point Electrode) 0.51 0.4- o 0 ) I o > CD Q a c D 0.3- 0.2- 0.1- X M X AAA A n A 0.0- n A n A s A 0.0 0.1 0.2 0.3 0.4 M a s s - F r a c t i o n - B u r n e d n A 0.5 0.6 Equiv. Ratio A 1.1320 X 1.0550 O 0.9950 B 0 .8500 8 0 .8000 H 0.6550 Fig 48. Standard Deviation in Burning Time. N - 3000 RPM. (Disc Chambe (Fine Point Electrode Geometry). Standard Deviation in Burning Time (Spark Gap 1.5mm) 0.4 n O <u I o '> Q O c o in 0.3- 0.2- 0.1- n n A A A A A A rrro • o.o- x a x a X • 1 ' • I ' ' ' 1 I ' ' ' 1 I • ' ' ' ) ' 0.0 0.1 0.2 0.3 0.4 M a s s - F r a c t i o n - B u r n e d ~ 1 0.5 • — 1 0.6 Equiv. Ratio A UJJO X 1.0470 O 0.9870 B 0.8520 B 0.E530 Fig 49. Standard Deviation i n Burning Time. N - 3000 RPM. (Disc Chamber). (Spark Plug Gap - 1.5 mm) t—• ON Standard Deviation in Burning Time (Half Open Throttle-) 0.5 . 0.4- O to c/i I o ~o '> CP a o ~o c _o 0.3- 0.2- 0.1- 0.0- n n x A f f i g g XXX X 0.0 —I— 1 0.1 • X 0 • X X r—] . • 1 r — | r 0.2 0.3 0.4 M a s s - F r a c t i o n - B u r n e d • X 0.5 1 — i 0.6 Equiv. Ratio A 1.1850 X 1.1030 O 0.9200 B 0.8620 B 0.7600 50 Standard Deviation i n Burning Time. N - 3000 RPM.(Disc Chamber) (Half Open Throttle) E x t r a p o l a t e d S t a n d a r d - D e v i a t i o n 0 .5 n 0 .4 C * 0.3 o o 0) V) JE *> a> Q TJ i _ O -a c o CO 0.2 H 0.1 0 .0 A X X B A X A A B X v • * • • • X H • • R P M A 24 0 0 X 3 0 0 0 • 3 6 0 0 B 4 2 0 0 0 .4 i • 1 ' <—|—i—i—i—i—f—i—i—i—i—j—r- 0.6 0 .8 1 1.2 Equivalence Ratio 1.4 Fig 51. Extrapolated Standard Deviation i n Early Burning Time.(Disk Chamber) Effect of Spark Plug Geometry (Disk Chamber 3000 RPM) 0.5 n 52. o CJ I O > Q X> i_ O X I c _a (75 X I ai ~o o a o u 0.4 0.3 0.2 0.1 0.0 0.4 X A AX XA 0.6 — I — 0.8 l 1.2 Equivalence Ratio CONFIGURATION A 1000 X rin« Point I 1.4 Extrapolated Standard Deviation i n Early Burning Time.(Disk Chamber) Different Electrode Geometries N - 3000 RPM. Effect of Spark Plug Gap (Disk Chamber 3000 RPM) 0.5 o <u f 0 . 4 > o <u 0.3 i_ O T > C a 0.2 o 0.0 A A A A X X A x A x X 0 . 4 0.6 0.8 1 Equivalence Ratio 1.2 CONFIGURATION A 1000 - 1 1.4 Fig 53. Extrapolated Standard Deviation i n Early Burning Time.(Disk Chamber) Different Spark Caps N - 3000 RPM. U l Effect of Part Throttling (Disk Chamber 3000 RPM) 0.5 n o <u to F 0.4 > q a> 0.3- Q "O l_ D X) C D 0.2- Hn XD o 0.0 x x A A X >A A X CONFIGURATION A 3000 X Hdl Throllk 0.4 0.6 0.8 1 1.2 1.4 Equivalence Ratio 54. Extrapolated Standard Deviation In Early Burning Time.(Disk Chambe Different Throttle Sewings N - 3000 RPM. Effect on Standard Deviation of Different Chambers-2400 RPM 0.5-1 o Q) £ 0.4 C o ai 0.3 o TJ O 0.2 (7) TJ CD 15 o ~x 0.0 X X A A A X X x A A X X X X 0.4 - i—•—,— I — 0.6 1 - T 1 t I 1 1 I I I * I I * 0.8 1 E q u i v a l e n c e R a t i o 1.2 C H A M B E R A DISK X B A T H T U B 1.4 Fig 55. Effect of Different Combustion Chambers on Standard Deviation-2400 RPM Effect on Standard Deviation of Different Chambers-3000 RPM 0.5-1 o £ 0.4 c o o j 0.3-Q D J 0-2 CO CL D ~x UI 0.1- 0.0 A . t T • f •— f * | ' " I T " ' T T 1 I I I " f T ' ' I I r • — f i . . | | | | CHAMBER A DISK X B A T H T U B 0.4 0.6 0.8 1 Equivalence Ratio 1.2 - 1 1.4 Fig 56. Effect of Different Combustion Chambers on Standard Deviation-3000 RPK Effect on Standard Deviation of Different Chambers-3600 RPM 0.5 -1 o Q) I q '> 0) Q X> t_ O X ) c o ( 7 5 XI _a> 15 o Q . D v_ ~x UI 0 . 4 - 0 . 3 - 0 . 2 - 0 .1- 0.0 A X A A A A X x x x CHAMBER A DISK X B A T H T U B 0.4 0.6 0.8 1 Equivalence Ratio 1.2 1.4 Fig 57. Effect of Different Combustion Chambers on Standard Deviation-3600 RPM Effect on Standard Deviation of Different Chambers-4200 RPM 0.5-1 u CO in £ 0.4 c o cu 0.3 Q TJ o TJ O 0.2 CO TJ CO J3 §. 0.1 D *x UJ 0.0- -i »—-r- 0.4 "1— 1 —'— 1 —'—I—<- 0.6 0.8 1 Equivalence Ratio 1.2 CHAMBER A DISK X B A T H T U B i i i i i i i i i i —1 1.4 Fig 58. Effect of Different Combustion Chambers on Standard Deviation-4200 RPM Effect of Spark Plug Gap(Different Chambers-3000 RPM) 0.5-1 u <u I o "a *> OJ Q 0.4- 0.3- o * D C _D c o X) JO ~o o Q . D i_ IK UI 0.2- 0.1- 0.0- X X A A v X x x X CHAMBER A DISK X B A T H TUB 0.4 G.S 0.8 1 1.2 Equivalence Ratio — i 1.4 59. Effect of Different Combustion Chambers on Standard Deviation Different Spark Gaps. Effect of Spark Plug Geometr(Different Chambers-3000 RPM) 0.5 o 0J £ 0.4 c o v 0.3 Q X) v. O X) S 0.2 CO T3 0J ]5 O O. O -0.1 0.0 X A A X A A X X X C H A M B E R A DISK X B A T H T U B 0.4 0.6 0.8 1 Equivalence Ratio 1.2 i 1.4 Fig 60. Effect of Different Combustion Chambers on Standard Deviation Fine Point Electrodes. Effect of Throtling (Different Chambers-3000 RPM) 0.5 u o a> 0.3 O O •o c D 0.2 (7i £ g . o.i o 0.0 A A A A A A X A X X X x x x CHAMBER A DISK X B A T H TUB '—1—1—I—•—'—'—'—I—1—'—'—1—I—'—•—1—1—I—•—•—>—•—I 0.4 0.6 0.8 1 1.2 1.4 Equivalence Ratio 61. Effect of Different Combustion Chambers on Standard Deviat Partly Opened Throttle. 174 F i g 62. Model of Concentrated V o r t i c i t y Region as Proposed by Tennekes 0.30-1 Mean Random Time Delay v 0.25 £ 0.20 a> Q a> E 0.15 0.10 o TJ C o cc c o J | 0.05 0.00 0.4 — 1 — 0.6 —v~ 0.8 1 1.2 Equivalence Ratio —r- 1.4 Speed 2400 3000 3600 4200 1.6 Fig 63. Effect of Equivalence Ratio on Mean Random Time Delay. Ul Extrapolated Standard Deviation & Mean Random Time Delay o > a 0.4 n 0.3 ii 0.2 o T ) c _o Zn •a o o a. o i _ X U J 0.1 0.0 0.4 0.6 0.8 1 1.2 Equivalence Ratio 1.4 2400 rpm M«on Tlm> 0«loy X Cilropolaltd Vakj« I 1.6 Fig 64. Comparison of Extrapolated Standard Deviation and Mean Random Time Delay with Equivalence Ratio'. - 2400 RPM. (Bath-Tub Chamber) ON 65. Comparison of Extrapolated Standard Deviation and Mean Random Time Delay with Equivalence Ratio. - 3000 RPM. (Bath-Tub Chamber) Extrapolated Standard Deviation & Mean Random Time Delay o 0) (SI c "> OJ Q O T> c a tn X) 0) jg o a. o 0.20 0.15 0.10- 0.05- 0.00 X X Configuration U » o n Tlm« D«loy X ( > l r a p o l a l * d V a k j . 0.4 0.6 0.8 1 1.2 Equivalence Ratio 1.4 1.6 Fig 66. Comparison of Extrapolated Standard Deviation and Mean Random Time Delay with Equivalence Ratio. - 3600 RPM. (Bath-Tub Chamber) Extrapolated Standard Deviation & Mean Random Time Delay o <u </) E > o > 0,25-i 0.20- 0.15- O X) c a <u o Q . a 0.10 0.05 0.00 4200 rpm Utan Tlm« D«lay X CvtrapolaUd Voiu* 0.4 0.6 0.6 1 1.2 Equivalence Ratio 1.4 67. Comparison of Extrapolated Standard Deviation and Mean Random Time Delay with Equivalence Ratio. - 4200 RPM. (Bath-Tub Chamber) Extrapolated Standard Deviation vs Mean Random Time Delay 0.30 al 0.25 to X- A A X >» 0.20- _D CD Q CD E 0.15- X 0.10- E o TJ C o cc c a a> 0.05 0.00-Ih „ ^ A S • XX H 0 • • 0.00 0.05 0.10 0.15 0.20 Extrapolated Standard Deviation /(msec) 0.25 Conf igurat ion a 24 0 0 R P M X 3 0 0 0 R P M • 3 6 0 0 R P M H 4 2 0 0 R P M H H a l l T h r o l l l . M F l n « P o i n t • W i d e G a p Fig 68. Relationship Between Mean Random Time Delay and Extrapolated Standard Deviation i n Burning Time within a Bath-Tub Chamber. I Extrapolated Standard Deviation vs Mean Random Time Delay 0.4 u in Q E o XI c D c o 0.3 0.2 0.1- 0.0 • H XA X ens 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Extrapolated Standard Deviation / ( m s e c ) 0.35 Configuration o. 2400 RPU x 3000 RPU • 3600 RPU a 4200 RPU n Holf throtlU M Tint Polnl • Wldt Cap Fig 69. Relationship Between Mean Random Time Delay and Extrapolated Standard Deviation i n Burning Time within a Disc Chamber. 182 Fig 70. Ca l i b r a t i o n Curve For Laminar Flow Element (Natural Gas) 183 reuiiie oeiaioonag« Calibration sr>*el FSe zeHnstiumentafjori •kISTLER D r u c k a u f n e h m e r C a p l e u r d e p r e s s i o n P r e s s u r e t r a n s d u c e r Type 6 1 2 1 SN 2 8 2 7 3 7 KjJibrierier Bereicn Gamme etalonnee [ b a r ] Calibrated range 0 .250 0...25 0...2.5 Betriebsiemperaiurbereicft Gamme de temp, d'utilisation (*C] -60.-350 Operating temperature range Emptindlitftkeit Sensibilite [ p C / b a r ] Sensitivity Kalibnert bei Elalortne a 20 *C Calibrated at by Sh Date 15.12.86 Linearitat r-crs Linearite < i « F S O Ltneariry 0,3 0,3 0,3 1bar = 10*Nm-*= 1,019...al= 14.50...psi lai = l k p c m _ , = i k g ! c m - ' = 0.980655 bar 1psi = 0.O6B94...bar 000 — -400 1 40 -I—f--M Q[PC] BEE xi I S y 1 / •3 000 -300 3 52 7 ; i z 2 2 000 20- 55 •100 25 - H - i - - t-t- ±± P [bar] 0 25 so 7 5 100 125 150 175 200 225 2S0 0 2.5 5 7.5 10 12.5 15 17.5 20 2 2 . 5 25 0 0 . 2 5 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2. Abhangigkeit der Empfindlictikeit von der Temperatur Sensibility en (onction de la temperature Sensitivity versus temperature o C / b a f 300 ' 3 5 0 ' C 72. Calibration Curve For K i s t l e r Pressure Transducer 185 * . 0 . 90 0 . 80 0 . 70 7 3 0 .01 1.70 1.80 Combustion Time at 10% Mass-Fraction-Burned on P r o b a b i l i t y Paper. 1.40 1 . 50 1 .60 10% Burning Time(rnsec) COMBUSTION AND MOTORED P R E S S U R E S AT 3 0 0 0 RPM Fig 74. Combustion And Motored Pressure At Different Crank Angle Intervals - 3000 RPM.( For S e n s i t i v i t y Analysis) oo ON 3500 3000 . 450 500 550 600 650 700 Fig 75. Combustion Pressure Less Motored Pressure at Different Crank Angle Intervals- 3000 RPM ( S e n s i t i v i t y Analysis) 0 0 T! era O 3 1-1 P» (u in 3 in TV* 1 TJ > * 3 P CTQ O H-1 rt <D K* U) O 3 to e in 3 rt O- to p . H 3 rt $ P CD I-1 CO W (t> H . 3 m in p. rt Pi rr Hi CD n 3 rr ( — ) B u r n i n g T i m e A t ( m s e c ) C ) M a s s - F r a c t i o n - B u r n e d o o o o CO ^ o\ o CD 881
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