誌謝 vi 摘 要 vii 第一章 簡介 x 第二章 實驗設備及方法 xii 第三章 數值方法介紹 xiv 第四章 振盪之拉伸火焰 xv 第五章 實驗與數值模擬之結果 xvi 第六章 討論 xix 第七章 結語 xxi ABSTRACT xxii NOMENCLATURE xxv CONTENTS xxix LIST OF TABLES xxxiii LIST OF FIGURES xxxiv CHAPTER Ⅰ INTRODUCTION 1 1-1 Background 1 1-2 Investigation of Stretch Flat Flame 4 1-2.1 Steady Stretch 5 1-2.2 Unsteady Stretch 7 1-3 Investigation of Oscillation 8 1-3.1 Oscillation of Stagnation Plane 8 1-3.2 Reflection and Refraction of Acoustic Wave 10 1-4 Investigation of Instability 15 1-4.1 Sivashinsky Instability 15 1-4.2 Rayleigh Instability 17 1-4.3 The Influence of Heat Release Rate 20 1-5 Motivations and Objectives 23 CHAPTER II EXPERIMENTAL APPARATUS 25 2-1 Basic Setup 25 2-1.1 Burners and Fuel Systems 25 2-1.2 Wall Oscillation and Speaker Excitation System 26 2-1.3 Acoustic Measurement 26 2-1.4 Temperature Measurement 27 2-1.5 Image Capture Device 29 2-1.6 Ion Probe 29 2-1.7 Hot Wire 31 2-2 Quantitative Flow Visualization 34 2-2.1 Lasers 34 2-2. 2 Control Unit 34 2-2.3 Recording System 35 2-2.4 Rotating Disk Calibration 36 2-3 Experiment Design 37 CHAPTER III NUMERICAL METHOD 39 3-1Jet-Wall Impingement 39 3-1.1 Governing Equations 39 3-1.2 Boundary and Initial Conditions 43 3-2 Finite Difference Approximations 45 3-2.1 Spatial Discretizations 46 3-2.2 Temporal Discretizations 47 3-2.3 Temporal and Spatial Discretizations 48 3-3 Starting Estimates 49 3-4 Adaptation of Mesh Point 50 3-5 Time Stepping 52 3-6 Solution Procedure 53 CHAPTER Ⅳ THE OSCILLATORILY STRETCHED FLAME 55 4-1 Basis Structure of Flat Flame and Verification with References 55 4-2 Phase Delay of Oscillating Premixed Flame 56 4-3 Structural Response of Oscillating Premixed Flame 61 4-4 Detailed Pathway of NO Formation 63 4-5 Heat Release Rate and Pressure Fluctuations 67 4-6 Identifying Global Strain Sate 72 CHAPTER Ⅴ EXPERIMENTAL AND NUMERICAL RESULTS 75 5-1 Measuring Oscillatory Equivalence Ratio 76 5-3 Influences of Strain Rate 82 5-4 The Coupling Effects of Oscillatory Equivalence Ratio and Strain Rate 84 CHAPTER Ⅵ DISCUSSION 87 6-1 Dimensionless and Simplification of Energy Equation 88 6-2 The Effect of Unsteady Equivalence Ratio 90 6-3 The Effect of Unsteady Strain Rate 92 6-4 The Coupling Effects of Unsteady Strain Rate and Equivalence Ratio 97 6-4.1 Illustration of Physical Phenomena 101 6-5 Confirmation of Unstable Region 103 6-5.1 Verification with reference 104 6-5.2 Physical Analysis 107 6-6 Relative Number 108 CHAPTER Ⅶ CLOSURES 112 7-1 Conclusions 112 7-2 Future Work 115 APPENDIX 116 A1. Derivation of Global Strain Rate 116 A2 Simplification of Jet Flow to One Dimensional Flow 117 A3. Assumption of Unsteady One Dimensional Flow 119 REFERENCES 122 PUBLICATION LIST 220 VITA 222 著作權聲明 223 LIST OF TABLES TABLE 4-5.1 Data Set For Heat Release Rate Calculation 130 TABLE 6-6.1 Symbol Descriptions 131 TABLE 6-6.2 The Detailed Classification For Operating Conditions 132 LIST OF FIGURES Fig. 1-1.1 The lower NO formation in lean premixed combustion 134 Fig. 1-1.2 In well-stirred reactor, the effect of oscillatory (a) mass flow rate (b) equivalence ratio and (c) temperature on reaction rate in the lean premixed combustion 135 Fig. 1-2.1 Schematic of surface element S with velocity V and unit normal vector n in a flow field v 136 Fig. 1-2.2 Examples of the stretched flames 137 Fig. 1-2.3 Principle of counterflow methodology in determining : (a) velocity profile and definition of reference and (b) extrapolation of reference to yield 138 Fig.1-4.1a Thermo-acoustic feedback cyclic. 139 Fig.1-4.1b Thermo-acoustic feedback cyclic 139 Fig. 1-5.1a The Schematic of oscillatory jet-wall impingement. 140 Fig. 1-5.1b Mechanisms of Combustion Instability. 140 Fig. 2-1.1 Essentials of the experimental arrangements. 141 Fig. 2-1.2a The schematic diagram of ion probe 142 Fig. 2-1.2b The schematic of the ion measurement in single jet-wall impingement 142 Fig. 2-1.3 The distribution of temperature, heat release rate and ion concentration in flat flame (Lawton et al. 1969). 143 Fig. 2-1.4 a photograph of the single-type hot wire probe. 144 Fig. 2-1.4 b photograph of parallel hot wire probe for exit velocity and concentration measurements. 144 Fig. 2-2.1 Arrangements of lasers and optics of PIV device. 145 Fig. 2-2.2 The schematic plots of CCD control and laser trigger occasions. 146 Fig. 2-2.3(a) Rotating disk calibration of PIV device ( = 5 cyclic/second). 147 Fig. 2-2.3(b) Real velocity and velocity measured by PIV against the radius of location ( = 5 cyclic/second). 147 Fig. 2-3.1a The schematic of oscillatory strain rate induced by oscillatory domain in jet-wall impingement. 148 Fig. 2-3.1b The schematic of oscillatory strain rate induced by oscillatory exit flow rate (Fuel +Air) in jet-wall impingement. 148 Fig. 2-3.2a The schematic of oscillatory equivalence ratio induced by oscillatory fuel flow rate in jet-wall impingement. 149 Fig. 2-3.2b The signal fluctuations of exit velocity under the conditions by oscillatory equivalence ratio. 149 Fig.2-3.3 The schematic plot of oscillatory strain rate and equivalence rate. 150 Fig.2-3.4 The schematic plot of oscillatory strain rate and equivalence rate, induced at the same time by wall and speaker excitation respectively. 151 Fig.2-3.5 The schematic plot of oscillatory strain rate and equivalence rate, induced not at the same time by wall and speaker excitation respectively. 152 Fig. 4-1.1a The comparisons of the distributions of the temperature, velocity, OH and NO concentration are shown in the jet-wall impingement at the equivalence ratio, 0.8. 153 Fig. 4-1.1b The comparisons of the distributions of the temperature, velocity, OH and NO concentration are shown in the jet-wall impingement at the equivalence ratio, 0.6. 153 Fig. 4-1.1c The photograph of flat flame at different equivalence ratio in single jet-wall impingement. 154 Fig. 4-1.2a Verification of cyclic variation of flame location at frequency, f=51Hz, with A=0.1, where A is the amplitude fraction of domain between burner exit and wall in oscillatory wall case. 155 Fig. 4-1.2b Verification of cyclic variation of extinction strain rate, a=2650(1/s), for equivalence ratio, 0.8(CH4/air) by using cyclic variation of relative OH concentration, where B is the amplitude fraction of exit mean velocity. 155 Fig. 4-2.1 Temporal variation of Tmax and relative NO concentration at B=0.1 with f=10 and 100Hz, respectively. 156 Fig. 4-2.2 Dynamic response of flame thickness, relative NO concentration and Tmax vs. strain rate for oscillatory frequency f=10 and 100 Hz with B=0.1 156 Fig. 4-2.3 Dynamic response of flame thickness, relative NO concentration and Tmax vs. strain rate for B=0.1 and 0.3 at fixed oscillatory frequency f=10 Hz 157 Fig. 4-2.4 Temporal variation of Tmax and relative NO concentration at f=10 Hz with B=0.1 and 0.3, respectively. 157 Fig. 4-3.1 Comparison of cyclic variation of opposite strain (out-of-phase) for relative NO concentration and max flame temperature at frequency, f=10 Hz, with A=0.1 at equivalence ratio, 0.8(CH4/air) in oscillatory wall case, where A is the amplitude fraction of domain between burner exit and wall. 158 Fig. 4-3.2 Comparisons of oscillatory exit velocity and wall for the location of max flame temperature (normalized), d (d/L), and flame thickness (normalized), f (f/L), at frequency, freq=10 Hz, for equivalence ratio, 0.8(CH4/air) with A=B=0.1 where B and A are the amplitude fraction of exit mean velocity and domain between burner exit and wall respectively. 159 Fig. 4-3.3 Comparison of dynamic response of oscillatory exit velocity and wall for the max flame temperature at various frequency for equivalence ratio, 0.8(CH4/air) with A=B=0.1, where B and A are the amplitude fraction of mean velocity and domain between burner exit and wall respectively. 160 Fig. 4-3.4 Comparison of dynamic response of oscillatory exit velocity and wall for relative NO concentration at various frequency for equivalence ratio, 0.8(CH4/air) with A=B=0.1, where B and A are the amplitude fraction of mean velocity and domain between burner exit and wall respectively. 160 Fig. 4-4.1 At equivalence ratio, 0.8(CH4/air), the cyclic variations of oscillatory exit velocity and wall for the detailed NO pathway at various frequency with A=B=0.1, where B and A are the amplitude fraction of mean velocity and domain between burner exit and wall respectively. 161 Fig. 4-4.2 At equivalence ratio, 0.6(CH4/air), the cyclic variations of oscillatory exit velocity and wall for the detailed NO pathway at various frequency with A=B=0.1, where B and A are the amplitude fraction of mean velocity and domain between burner exit and wall respectively. 162 Fig. 4-4.3a At equivalence ratio, 0.8(CH4/air), the comparison of spatial variation of detailed NO pathway at strain rate 60.19(1/s), phase=90o, and 73.59(1/s), phase=270o, with frequency, f=10 Hz, and B=0.1 in the oscillatory exit velocity case. 163 Fig. 4-4.3b At equivalence ratio, 0.8(CH4/air), the comparison of spatial variation of detailed NO pathway at strain rate 60.8(1/s), phase=90o, and 74.3(1/s), phase=270o, with frequency, f=10 Hz, and A=0.1 in the oscillatory wall case. 163 Fig. 4-4.4a At equivalence ratio, 0.6(CH4/air), the comparison of spatial variation of detailed NO pathway at strain rate 18.0(1/s), phase=90o, and 22.0(1/s), phase=270o, with frequency, f=10 Hz, and B=0.1 in the oscillatory exit velocity case. 164 Fig. 4-4.4b At equivalence ratio, 0.6(CH4/air), the comparison of spatial variation of detailed NO pathway at strain rate 18.2(1/s), phase=90o, and 22.2(1/s), phase=270 o, with frequency, f=10 Hz, and A=0.1 in the oscillatory wall case. 164 Fig. 4-5.1 The profile of ion concentration and heat release rate 165 Fig. 4-5.2 The spectral density of ion probe signal without excitation at equivalence ratio, 0.6, 0.7 and 0.8(methane/ air). 166 Fig. 4-5.3a The spectral density of ion probe signal with oscillatory wall at 10 Hz of equivalence ratio, 0.6, 0.7 and 0.8(methane/ air). 167 Fig. 4-5.3b The spectral density of ion probe signal with oscillatory exit velocity at 10 Hz of equivalence ratio, 0.6, 0.7 and 0.8(methane/ air). 168 Fig. 4-5.4a The spectral density of ion probe signal with oscillatory wall at 20 Hz of equivalence ratio, 0.6, 0.7 and 0.8(methane/ air). 169 Fig. 4-5.4b The spectral density of ion probe signal with oscillatory exit velocity at 20 Hz of equivalence ratio, 0.6, 0.7 and 0.8(methane/ air). 170 Fig. 4-5.5a The spectral density of ion probe signal with oscillatory wall at 500 Hz of equivalence ratio, 0.6, 0.7 and 0.8(methane/ air). 171 Fig. 4-5.5b The spectral density of ion probe signal with oscillatory exit velocity at 500 Hz of equivalence ratio, 0.6, 0.7 and 0.8(methane/ air). 172 Fig. 4-5.6a The spectral density of ion probe signal with oscillatory wall at 1000 Hz of equivalence ratio, 0.6, 0.7 and 0.8(methane/ air). 173 Fig. 4-5.6b The spectral density of ion probe signal with oscillatory exit velocity at 1000 Hz of equivalence ratio, 0.6, 0.7 and 0.8(methane/ air). 174 Fig. 4-5.7a The comparisons of Pressure fluctuation incoming from burned and un-burned side at various frequency for equivalence ratio =0.8(CH4/air) with A=B=0.1, where B and A are the amplitude fraction of mean velocity and domain between burner exit and wall respectively 175 Fig. 4-5.7b The comparisons of Pressure fluctuation incoming from burned and un-burned side at various frequency for equivalence ratio =0.6(CH4/air) with A=B=0.1, where B and A are the amplitude fraction of mean velocity and domain between burner exit and wall respectively 175 Fig. 4-5.8 Comparisons of dynamic response of oscillatory exit velocity and wall for wall temperature at various frequency with A=B=0.1, where B and A are the amplitude fraction of mean velocity and domain between burner exit and wall respectively. 176 Fig 4-6.1a The velocity distribution in single jet-wall field. The domain (L) is 1.1cm and the exit velocity is 70 cm/sec at equivalence ratio, =0.8. 177 Fig 4-6.1b The velocity distribution in single jet-wall field. The domain (L) is 0.9 cm and the exit velocity is 70 cm/sec at equivalence ratio, =0.8. 177 Fig 4-6.2a The velocity distribution in single jet-wall field. The domain (L) is 1.0 cm and the exit velocity is 60 cm/sec at equivalence ratio, =0.8. 178 Fig 4-6.2a The velocity distribution in single jet-wall field. The domain (L) is 1.0 cm and the exit velocity is 75 cm/sec at equivalence ratio, =0.8. 178 Fig. 4-6.3a Relations between global strain rate (the ratio of exit velocity to domain between wall and burner exit) and strain rate (the velocity gradient before the zero strain) at equivalence ratio, =0.8, while the exit velocity is changed. 179 Fig. 4-6.3b Relations between global strain rate (the ratio of exit velocity to domain between wall and burner exit) and strain rate (the velocity gradient before the zero strain) at equivalence ratio, =0.8, while the domain is changed. 179 Fig. 4-6.4a Relations between global strain rate (the ratio of exit velocity to domain between wall and burner exit) and strain rate (the velocity gradient before the zero strain) at equivalence ratio, =0.6, while the exit velocity is changed. 180 Fig. 4-6.4b Relations between global strain rate (the ratio of exit velocity to domain between wall and burner exit) and strain rate (the velocity gradient before the zero strain) at equivalence ratio, =0.6, while the domain is changed. 180 Fig. 4-6.5 The comparisons of extinction strain rate at lean mixtures (methane/air) in stagnation field 181 Fig. 5-1.1a The calibration between methane exit velocity and signal output of hot wire. 182 Fig. 5-1.1b The velocity distribution of three flow rate of methane (i.e., 2565, 3802 and 4800 ml/min) at the burner exit 182 Fig. 5-1.2 The cycle variations of signal output of hot wire. The flow rate of methane are 2565, 3802 and 4800 ml/min with speaker excitation (55, 70 and 85 dB) at 10 Hz, respectively. 183 Fig. 5-1.3 The cycle variations of signal output of hot wire. The flow rate of methane are 2565, 3802 and 4800 ml/min with speaker excitation (55, 70 and 85 dB) at 10 Hz, respectively. 184 Fig. 5-1.4 Phase average of cycle variations of hot-wire signal at the phases of 90o, 180o, 270o and 360o, respectively. 185 Fig. 5-1.5a Calibration of the square anemometer (two parallel hot-wire probe) output as function (U*RHO)1/2 for both wires at different concentration. 186 Fig. 5-1.5b The square anemometer (two parallel hot-wire probe) output normalized by the concentration difference. 186 Fig. 5-1.6 The relation between equivalence ratio and mixture density of the CH4/air flow. 187 Fig. 5-1.7 The verification of oscillatory equivalence ratio and invariable exit velocity by two parallel hot-wire probe at the equivalence ratio with 10 Hz, 55dB excitation. 188 Fig. 5-1.8 The verification of oscillatory equivalence ratio and invariable exit velocity by two parallel hot- wire probe at the equivalence ratio with 1000 Hz, 85 dB excitation. 189 Fig. 5-2.1a The cycle variations of the relative heat release rate at the cases of initial slope of the oscillatory strain rate, (i.e., the strain rate is kept constant) and equivalence ratios, with 1, 10, 100 and 1000 Hz. The initial equivalence ratio and strain rate at time, t=0.0 are 0.52 and 25(1/s), respectively. 190 Fig. 5-2.1b The cycle variations of the relative heat release rate at the cases of initial slope of the oscillatory strain rate, (i.e., the strain rate is kept constant) and equivalence ratios, with 1, 10, 100 and 1000 Hz. The initial equivalence ratio and strain rate at time, t=0.0 are 0.52 and 25(1/s), respectively. 190 Fig. 5-2.2a The cycle variations of the relative heat release rate at the cases of initial slope of the oscillatory strain rate, (i.e., the strain rate is kept constant) and equivalence ratios, with 1, 10, 100 and 1000 Hz. The initial equivalence ratio and strain rate at time, t=0.0 are 0.55 and 110(1/s), respectively. 191 Fig. 5-2.2b The cycle variations of the relative heat release rate at the cases of initial slope of the oscillatory strain rate, (i.e., the strain rate is kept constant) and equivalence ratios, with 1, 10, 100 and 1000 Hz. The initial equivalence ratio and strain rate at time, t=0.0 are 0.55 and 110(1/s), respectively. 191 Fig. 5-2.3 The cycle variations of ion probe signal output at the cases of initial slope of the oscillatory strain rate, (i.e., the strain rate is kept constant) and equivalence ratios, with (a)1 Hz, (b)10 Hz, (c)100 Hz and (d)1000 Hz. The initial equivalence ratio and strain rate at time, t=0.0 are 0.55 and 110(1/s), respectively. 192 Fig. 5-2.4 The cycle variations of ion probe signal output at the cases of initial slope of the oscillatory strain rate, (i.e., the strain rate is kept constant) and equivalence ratios, with (a)1 Hz, (b)10 Hz, (c)100 Hz and (d)1000 Hz. The initial equivalence ratio and strain rate at time, t=0.0 are 0.55 and 110(1/s), respectively. 193 Fig. 5-2.5 The cycle variations of ion probe signal output at the cases of initial slope of the oscillatory strain rate, (i.e., the strain rate is kept constant) and equivalence ratios, with (a)1 Hz, (b)10 Hz, (c)100 Hz and (d)1000 Hz. The initial equivalence ratio and strain rate at time, t=0.0 are 0.6 and 300(1/s), respectively. 194 Fig. 5-2.6 The cycle variations of ion probe signal output at the cases of initial slope of the oscillatory strain rate, (i.e., the strain rate is kept constant) and equivalence ratios, with (a)1 Hz, (b)10 Hz, (c)100 Hz and (d)1000 Hz. The initial equivalence ratio and strain rate at time, t=0.0 are 0.6 and 300(1/s), respectively 195 Fig. 5-2.7a The cycle variations of the relative heat release rate at the cases of initial slope of the oscillatory strain rate, (i.e., the strain rate is kept constant) and equivalence ratios, with 1, 10, 100 and 1000 Hz. The initial equivalence ratio and strain rate at time, t=0.0 are 0.65 and 590(1/s), respectively. 196 Fig. 5-2.7b The cycle variations of the relative heat release rate at the cases of initial slope of the oscillatory strain rate, (i.e., the strain rate is kept constant) and equivalence ratios, with 1, 10, 100 and 1000 Hz. The initial equivalence ratio and strain rate at time, t=0.0 are 0.65 and 590(1/s), respectively. 196 Fig. 5-2.8 The cycle variations of ion probe signal output at the cases of initial slope of the oscillatory strain rate, (i.e., the strain rate is kept constant) and equivalence ratios, with (a)1 Hz, (b)10 Hz, (c)100 Hz and (d)1000 Hz. The initial equivalence ratio and strain rate at time, t=0.0 are 0.65 and 590(1/s), respectively. 197 Fig. 5-2.9 The cycle variations of ion probe signal output at the cases of initial slope of the oscillatory strain rate, (i.e., the strain rate is kept constant) and equivalence ratios, with (a)1 Hz, (b)10 Hz, (c)100 Hz and (d)1000 Hz. The initial equivalence ratio and strain rate at time, t=0.0 are 0.65 and 590(1/s), respectively. 198 Fig. 5-3.1 The cycle variations of the relative heat release rate with the cases of initial slope of the oscillatory equivalence ratios, and strain rate, with 1, 10, 100 and 1000 Hz. The initial equivalence ratio and strain rate at time, t=0.0 are 0.6 and 300(1/s), respectively. 199 Fig. 5-3.2 The cycle variations of ion probe signal output at the cases of initial slope of the oscillatory equivalence ratios, (i.e., the equivalence ratio is kept constant) and strain rate, with (a)1 Hz, (b)10 Hz, (c)100 Hz and (d)1000 Hz. The initial equivalence ratio and strain rate at time, t=0.0 are 0.60 and 300(1/s), respectively. 200 Fig. 5-3.3 The cycle variations of ion probe signal output at the cases of initial slope of the oscillatory equivalence ratios, (i.e., the equivalence ratio is kept constant) and strain rate, with (a)1 Hz, (b)10 Hz, (c)100 Hz and (d)1000 Hz. The initial equivalence ratio and strain rate at time, t=0.0 are 0.60 and 300(1/s), respectively. 201 Fig. 5-4.1 The cycle variations of the ion probe signal output with the cases of positively initial slope of the oscillatory equivalence ratios , and strain rate , with (a)1 Hz, (b)10 Hz, (c)100 Hz and (d)1000 Hz. The initial equivalence ratio and strain rate at time, t=0.0 are 0.6 and 300(1/s), respectively. 202 Fig. 5-4.2 The cycle variations of the ion probe signal output with the cases of initial slope of the oscillatory equivalence ratios, and strain rate, with (a)1 Hz, (b)10 Hz, (c)100 Hz and (d)1000 Hz. The initial equivalence ratio and strain rate at time, t=0.0 are 0.6 and 300(1/s), respectively. 203 Fig. 5-4.3a The cycle variations of the relative heat release rate with the cases of strain rate, , and initial slope of the oscillatory equivalence ratios, from to with oscillations at 1 Hz 204 Fig. 5-4.3b The cycle variations of the relative heat release rate with the cases of strain rate, and initial slope of the oscillatory equivalence ratios, from to with oscillations at 1 Hz 204 Fig. 5-4.4 The cycle variations of the relative heat release rate with the cases of slope of the oscillatory equivalence ratios, and strain rate, with 1, 10, 100 and 1000 Hz. 205 Fig. 5-4.5 The cycle variations of the ion probe signal output with the cases of initial slope of the oscillatory equivalence ratios, and strain rate, with (a)1 Hz, (b)10 Hz, (c)100 Hz and (d)1000 Hz. The initial equivalence ratio and strain rate at time, t=0.0 are 0.6 and 300(1/s), respectively. 206 Fig. 6-1.1 The schematic plot of the temperature gradient in lean condition. 207 Fig. 6-4.1 The cyclic response of the flame thickness and location to the opposed excitation at 1 and 1000 Hz. The initial slope of oscillatory strain rate and equivalence ratio are and , respectively. 208 Fig. 6-5.1a The dependence of normalized chemical reaction time on equivalence ratio. 209 Fig. 6-5.1b The dependence of normalized slope, in figure 6-5.1 on the equivalence ratio. 209 Fig. 6-5.2 The dependence of normalized chemical reaction time and slope, on equivalence ratio near extinction strain rate. 210 Fig. 6-5.3a The relations between thermal diffusivity and equivalence ratio at lean condition in methane/air mixture. 211 Fig. 6-5.3b The relations between laminar flame speed and equivalence ratio by Law (1989) and Lawn et al. (2004). 211 Fig. 6-5.4 The difference between the value of zero and RHS of equation (6-5.11) at various equivalence ratios. The solutions of equation (6-5.11) are near 1.0 and 0.6. 212 Fig. 6-6.1a The cyclic variations of the relative number at the cases of initial slope of the oscillatory strain rate, (i.e., the strain rate is kept constant) and equivalence ratios, with 1, 10, 100 and 1000 Hz. The initial equivalence ratio and strain rate at time, t=0.0 are 0.52 and 25(1/s), respectively. 213 Fig. 6-6.1b The cyclic variations of the relative number at the cases of initial slope of the oscillatory strain rate, (i.e., the strain rate is kept constant) and equivalence ratios, with 1, 10, 100 and 1000 Hz. The initial equivalence ratio and strain rate at time, t=0.0 are 0.52 and 25(1/s), respectively. 213 Fig. 6-6.2a The cyclic variations of the relative number at the cases of initial slope of the oscillatory strain rate, (i.e., the strain rate is kept constant) and equivalence ratios, with 1, 10, 100 and 1000 Hz. The initial equivalence ratio and strain rate at time, t=0.0 are 0.55 and 110(1/s), respectively. 214 Fig. 6-6.2b The cyclic variations of the relative number at the cases of initial slope of the oscillatory strain rate, (i.e., the strain rate is kept constant) and equivalence ratios, with 1, 10, 100 and 1000 Hz. The initial equivalence ratio and strain rate at time, t=0.0 are 0.55 and 110(1/s), respectively. 214 Fig. 6-6.3a The cyclic variations of the relative number at the cases of initial slope of the oscillatory strain rate, (i.e., the strain rate is kept constant) and equivalence ratios, with 1, 10, 100 and 1000 Hz. The initial equivalence ratio and strain rate at time, t=0.0 are 0.65 and 590(1/s), respectively. 215 Fig. 6-6.3b The cyclic variations of the relative number at the cases of initial slope of the oscillatory strain rate, (i.e., the strain rate is kept constant) and equivalence ratios, with 1, 10, 100 and 1000 Hz. The initial equivalence ratio and strain rate at time, t=0.0 are 0.65 and 590(1/s), respectively. 215 Fig. 6-6.4 The cyclic variations of the relative number with the cases of initial slope of the oscillatory equivalence ratios, and strain rate, with 1, 10, 100 and 1000 Hz. The initial equivalence ratio and strain rate at time, t=0.0 are 0.6 and 300(1/s), respectively. 216 Fig. 6-6.5a The cyclic variations of the relative number with the cases of strain rate, , and initial slope of the oscillatory equivalence ratios, from to with oscillations at 1 Hz 217 Fig. 6-6.5b The cyclic variations of the relative number with the cases of strain rate, and initial slope of the oscillatory equivalence ratios, from to with oscillations at 1 Hz 217 Fig. 6-6.6 The cyclic variations of the relative number with the cases of slope of the oscillatory equivalence ratios, and strain rate, with 1, 10, 100 and 1000 Hz. 218 Fig. 6-6.7 Schematic diagram of the stable regime for oscillatory strain rate and equivalence ratio at lean condition 219