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Turbulent combustion of gas-air mixtures in a spark ignition engine Boisvert, Julie 1986

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TURBULENT COMBUSTION OF G A S - A I R MIXTURES I N A SPARK IGNITION ENGINE by J U L I E BOISVERT A THESIS SUBMITTED I N PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n THE FACULTY OF GRADUATE STUDIES Depar tmen t o f M e c h a n i c a l E n g i n e e r i n g We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF B R I T I S H COLUMBIA J u n e , 1986 © J U L I E BOISVERT, 1986 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e a n d s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e h e a d o f my d e p a r t m e n t o r by h i s o r h e r r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f )\&g\Acm\caA ^ n c ^ n e e n ^ The U n i v e r s i t y o f B r i t i s h C o l u m b i a 2075 W e s b r o o k P l a c e V a n c o u v e r , C a n a d a V6T 1W5 D a t e i> Ob jg(p  ABSTRACT An engine simulation model has been developed to describe turbulent combustion of gas-air mixtures i n a s p a r k - i g n i t i o n engine. The model incorporates a turbulent entrainment combustion theory proposed by Daneshyar and H i l l which i s based on Tennekes' model of turbulence and the vortex bursting p r i n c i p l e of Chomiak. Flame propagation was based on turbulent entrainment. The flame was modelled as a thick s p h e r i c a l s h e l l composed of burned and unburned gases. Inside the thick flame, pockets of i n i t i a l s i z e A, the Taylor microscale, are consumed at a rate of the order of the laminar burning v e l o c i t y . To compare the model to experimental data, turbulence l e v e l s were measured i n a motored Ricardo Hydra engine using hot wire anemometry. Combustion pressure data were measured with a p i e z o e l e c t r i c transducer. Results i n d i c a t e that the model i s successful i n pred i c t i n g trends i n o v e r a l l combustion rates when the engine speed and a i r - f u e l r a t i o are v a r i e d . The model a l s o provided i n s i g h t i n t o the structure of turbulent flames i n engines. - i i -TABLE OF CONTENTS Page Abstract i i L i s t of Figures v L i s t of Tables x i Nomenclature x i i Acknowledgements x v i i 1. INTRODUCTION 1 2. REVIEW OF PREVIOUS WORK 5 2.1 A B r i e f Summary of Experimental Findings 5 2.2 Review of the Thin Flame Model 8 2.3 Turbulent Entrainment Models 9 2.4 Background on the Turbulent Entrainment Model 10 2.4.1 Turbulent Entrainment V e l o c i t y 10 2.4.2 Thick Burning Zone 11 3. TURBULENT ENTRAINMENT ENGINE SIMULATION MODEL 13 3.1 I n i t i a l Conditions 13 3 .2 Compression and Expansion 13 3.3 Combustion Calculations 13 3.3.1 Assumptions 14 3.3.2 Governing Equations 15 3.3.3 Geometric Considerations 16 3.3.4 Thick Burning Zone Modelling 16 3.3.5 Laminar Burning V e l o c i t y 17 3.3.6 D i s s o c i a t i o n Calculations 18 3.3.7 Heat Loss Calculations 18 3.3.8 I g n i t i o n Delay 19 3.3.9 Sp e c i a l L i m i t i n g Cases: I n i t i a l and F i n a l Burning 19 3.3.10 Solving Scheme 20 4. EXPERIMENTAL INVESTIGATION 21 4.1 Objectives 21 4.2 Instrumentation 21 4.2.1 Engine Description 21 4.2.2 Pressure Measurements 23 4.2.3 Hot Wire Measurements 23 4.2.4 Crank Angle Measurements 23 4.2.5 Data A c q u i s i t i o n 24 4.2.6 Other Measurements 24 - i i i -TABLE OF CONTENTS ( C o n t i n u e d ) Page 4 . 3 M o t o r i n g T e s t s 24 4 . 3 . 1 P r o c e d u r e and D a t a A n a l y s i s 24 4 . 3 . 2 R e s u l t s 26 4 . 4 C o m b u s t i o n T e s t s 27 4 . 4 . 1 P r o c e d u r e and D a t a A n a l y s i s 27 4 . 4 . 2 R e s u l t s 28 5 . SIMULATION PROGRAM RESULTS 30 5 . 1 C o m p a r i s o n w i t h E x p e r i m e n t a l R e s u l t s 30 5 . 1 . 1 Mass F r a c t i o n B u r n e d C u r v e s 30 5 . 1 . 2 P r e s s u r e H i s t o r i e s 32 5 . 1 . 3 C o m b u s t i o n I n i t i a t i o n 32 5 . 1 . 4 C o m b u s t i o n D u r a t i o n 33 5 . 2 M o d e l P r e d i c t i o n s 34 5 . 2 . 1 F lame T h i c k n e s s 34 5 . 2 . 2 C F a c t o r V a r i a t i o n w i t h E n g i n e Speed 35 5 . 2 . 3 Thermodynamic and G e o m e t r i c P r o p e r t i e s 35 5 . 2 . 4 T u r b u l e n t E n t r a i n m e n t and S c a l e s 35 5 . 3 P a r a m e t r i c S t u d y 37 5 . 3 . 1 E f f e c t o f Vo lume D i s t r i b u t i o n i n t h e T h i c k F lame . . 37 5 . 3 . 2 E f f e c t o f C F a c t o r i n T u r b u l e n t B u r n i n g E q u a t i o n . . 38 5 . 3 . 3 I n t e g r a l L e n g t h S c a l e 38 6 . DISCUSSION OF UNCERTAINTIES 39 6 . 1 M o d e l A s s u m p t i o n s 39 6 . 2 E x p e r i m e n t a l Measu remen t s 41 6 .3 I n t e r p r e t a t i o n o f R e s u l t s 41 7 . CONCLUSIONS 43 8 . RECOMMENDATIONS 45 REFERENCES 46 APPENDICES A : TURBULENT ENTRAINMENT MODEL - ENGINE SIMULATION PROGRAM . . . . 120 B : PRESSURE MEASUREMENTS - MOTORED TEMPERATURE CALCULATIONS . . . 139 C : HOT WIRE ANEMOMETER MEASUREMENTS 148 D : RICARCO HYDRA GEOMETRY CALCULATIONS 171 - i v -LIST OF FIGURES Page 1. Microshadographs of flame fronts measured by Smith [40] 50 2. Flame photographs taken by Namazian et a l . [31] i n the MIT square p i s t o n engine 51 3. Schematic of the Tennekes model; d e f i n i t i o n of turbulent length scales 52 4. Schematic of turbulent combustion as shown by Tabaczynski [44] 53 5. Schematic of the thick combustion zone 54 6. Compression and expansion c a l c u l a t i o n s flowchart 55 7. Ricardo combustion chamber from manufacturer supplied drawings 56 8. Approximate combustion chamber geometry 57 9. Combustion ca l c u l a t i o n s flowchart 58 10. Engine t e s t i n g f a c i l i t i e s 59 11. Photograph of the pressure transducer mounted i n the c y l i n d e r head 60 12. Hot wire anemometer measuring positions 61 13. Photograph of the hot wire probe l o c a t i o n 62 14. Mean v e l o c i t y as a function of crank angle degrees for a l l investigated engine speeds, baseline p o s i t i o n 63 15. Turbulence i n t e n s i t y as a function of crank angle degrees f o r a l l investigated engine speeds, baseline p o s i t i o n 64 16. Relative turbulence i n t e n s i t y as a function of crank angle degrees f o r a l l investigated engine speeds, baseline p o s i t i o n 65 17. Mean v e l o c i t y at 30° BTDC and at top dead center as a function of engine speed, baseline p o s i t i o n 66 18. Turbulence i n t e n s i t y at 30° BTDC and at top dead center as a fu n c t i o n of engine speed, baseline p o s i t i o n 67 19. Comparison of top dead center turbulence i n t e n s i t y with other i n v e s t i g a t o r s ' r e s u l t s , from Bopp et a l . [7] 68 - v -LIST OF FIGURES (Continued) Page 20. E f f e c t of wire o r i e n t a t i o n on turbulence i n t e n s i t y at 1200 rpm 69 21. E f f e c t of p o s i t i o n along the spark plug axis on turbulence i n t e n s i t y at 1200 rpm 70 22. Experimental pressure curves at 1200 rpm for three a i r - f u e l r a t i o s 71 23. Experimental pressure curves at 1800 rpm for three a i r - f u e l r a t i o s 72 24. Experimental pressure curves at 2400 rpm for three a i r - f u e l r a t i o s 73 25. Experimental pressure curves at 3000 rpm for three a i r - f u e l r a t i o s 74 26. Mass f r a c t i o n burned curve calculated from experimental pressures at 1800 rpm f o r three a i r - f u e l r a t i o s 75 27. Indicated mean e f f e c t i v e pressure as a function of a i r - f u e l r a t i o s f o r a l l operating speeds 76 28. Brake mean e f f e c t i v e pressure as a function of a i r - f u e l r a t i o s f o r a l l operating speeds 77 29. Comparison of calculated and experimental mass f r a c t i o n burned f o r 1200 rpm, X = 1.01 78 30. Comparison of calculated and experimental mass f r a c t i o n burned f o r 1200 rpm, X = 1.16 79 31. Comparison of calculated and experimental mass f r a c t i o n burned f o r 1200 rpm, X = 1.27 80 32. Comparison of calculated and experimental mass f r a c t i o n burned f o r 1800 rpm, X = 1.00 81 33. Comparison of calculated and experimental mass f r a c t i o n burned f o r 1800 rpm, X = 1.15 82 34. Comparison of calculated and experimental mass f r a c t i o n burned f o r 1800 rpm, X = 1.28 83 35. Comparison of calculated and experimental mass f r a c t i o n burned f o r 2400 rpm, A = 1.04 84 36. Comparison of calculated and experimental mass f r a c t i o n burned f o r 2400 rpm, X = 1.20 85 - v i -LIST OF FIGURES (Continued) Page 37. Comparison of calculated and experimental mass f r a c t i o n burned f o r 2400 rpm, X = 1.36 86 38. Comparison of calculated and experimental mass f r a c t i o n burned f o r 3000 rpm, X = 1.08 87 39. Comparison of calculated and experimental mass f r a c t i o n burned f o r 3000 rpm, X = 1.22 88 40. Comparison of calculated and experimental mass f r a c t i o n burned f o r 3000 rpm, X = 1.37 89 41. Comparison of calculated and experimental pressure h i s t o r i e s f o r 1200 rpm, X = 1.01 90 42. Comparison of calculated and experimental pressure h i s t o r i e s for 1200 rpm, X = 1.16 91 43. Comparison of calculated and experimental pressure h i s t o r i e s for 1200 rpm, X = 1.27 92 44. Comparison of calculated and experimental pressure h i s t o r i e s for 1800 rpm, X = 1.00 93 45. Comparison of calculated and experimental pressure h i s t o r i e s for 1800 rpm, X = 1.15 94 46. Comparison of calculated and experimental pressure h i s t o r i e s for 1800 rpm, X = 1.28 95 47. Comparison of calculated and experimental pressure h i s t o r i e s for 2400 rpm, X = 1.04 96 48. Comparison of calculated and experimental pressure h i s t o r i e s for 2400 rpm, X = 1.20 97 49. Comparison of calculated and experimental pressure h i s t o r i e s for 2400 rpm, X = 1.36 98 50. Comparison of calculated and experimental pressure h i s t o r i e s f o r 3000 rpm, X = 1.08 99 51. Comparison of calculated and experimental pressure h i s t o r i e s f o r 3000 rpm, X = 1.22 100 52. Comparison of calculated and experimental pressure h i s t o r i e s for 3000 rpm, X = 1.37 101 53. Comparison of calculated and experimental time to burn the f i r s t 5% of t o t a l mass i n the c y l i n d e r 102 - v i i -LIST OF FIGURES (Continued) Page 54. Comparison of calculated and experimental time to burn 5 to 95% of t o t a l mass i n the c y l i n d e r 103 55. Predicted flame thickness as a function of a i r - f u e l r a t i o and engine speed 104 56. V a r i a t i o n of c factor over the engine speed range 105 57. Predicted mass f r a c t i o n entrained and burned for 1800 rpm and X = 1.00 106 58. Predicted inner and outer flame radius f o r 1800 rpm and X - 1.00 107 59. Predicted outer flame area for 1800 rpm and X = 1.00 108 60. Predicted unburned, burned and flame volumes for 1800 rpm and X = 1.00 109 61. Predicted i n t e g r a l length scale at 1800 rpm, X = 1.00, X = 1.15, 3000 rpm X = 1.08 110 62. Predicted Taylor microscale at 1800 rpm, X = 1.00, X = 1.15, 3000 rpm X = 1.08 I l l 63. Enhanced turbulence i n t e n s i t y at 1800 rpm, X = 1.00, X = 1.15, 3000 rpm X = 1.08 112 64. Predicted turbulent entrainment v e l o c i t y at 1800 rpm, X = 1.00, X = 1.15, 3000 rpm X = 1.08 113 65. E f f e c t of the volume d i s t r i b u t i o n i n the thick flame on mass f r a c t i o n burned, 3000 rpm, X = 1.08, c f a c t o r = 2.2 114 66. E f f e c t of c factor on the mass f r a c t i o n burned, 3000 rpm, X = 1.08, x V o l = 90% 115 67. Predicted and calculated mass f r a c t i o n burned f or L = h c at spark timing, 3000 rpm, X = 1.08 116 68. Predicted and calculated mass f r a c t i o n burned f o r L = h c/5 at spark timing, 3000 rpm, X = 1.08 117 69. E f f e c t of c o e f f i c i e n t a i n the heat loss equation on pressure h i s t o r i e s 118 70. Comparison of mass f r a c t i o n burned curves extracted from experimental pressures, extracted from predicted pressures and c a l c u l a t e d from model 119 - v i i i -LIST OF FIGURES (Continued) Page A . l Two dimensional vortex i n the unburned mixture 133 A.2 Vortex bursting due to combustion 134 A.3 Burned mass f r a c t i o n i n flame zone 135 A.4 Laminal burning of spher i c a l pockets 136 A.5 D e f i n i t i o n of unburned cone and flame zone cone; flame zone cone radius vs distance through flame 137 A. 6 Volume d i s t r i b u t i o n i n flame zone, = 10 mm 138 B. l Ensemble averaged motored and combustion pressures 145 B.2 Relative rms flu c t u a t i o n s of pressures about the ensemble averaged mean 146 B. 3 Calculated motored temperatures 147 C. l Heat balance of wire element 159 C.2 Anemometer bridge c i r c u i t 160 C.3 Hot wire c a l i b r a t i o n curve 161 C.4 D e f i n i t i o n s of mean window v e l o c i t y , f i t t e d true mean v e l o c i t y , rms window i n t e n s i t y and true rms i n t e n s i t y 162 C.5 Comparison of ensemble averaged mean v e l o c i t y with true mean v e l o c i t y obtained by non-stationary cycle-by-cycle a n a l y s i s using various window s i z e s , 1200 rpm, baseline p o s i t i o n 163 C.6 Comparison of ensemble averaged turbulence i n t e n s i t y with i n t e n s i t y obtained by non-stationary cycle-by-cycle a n a l y s i s using various window s i z e s , 1200 rpm, baseline p o s i t i o n 164 C.7 Comparison of ensemble averaged mean v e l o c i t y with true mean v e l o c i t y obtained by non-stationary cycle-by-cycle analysis using various window s i z e s , 1800 rpm, baseline p o s i t i o n 165 C.8 Comparison of ensemble averaged turbulence i n t e n s i t y with i n t e n s i t y obtained by non-stationary cycle-by-cycle a n a l y s i s using various window s i z e s , 1800 rpm, baseline p o s i t i o n 166 C.9 Comparison of ensemble averaged mean v e l o c i t y with true mean v e l o c i t y obtained by non-stationary cycle-by-cycle a n a l y s i s using various window s i z e s , 2400 rpm, baseline p o s i t i o n 167 - i x -LIST OF FIGURES (Continued) Page C I O Comparison of ensemble averaged turbulence i n t e n s i t y with i n t e n s i t y obtained by non-stationary cycle-by-cycle a n a l y s i s using various window s i z e s , 2400 rpm, baseline p o s i t i o n 168 C l l Comparison of ensemble averaged mean v e l o c i t y with true mean v e l o c i t y obtained by non-stationary cycle-by-cycle a n a l y s i s using various window s i z e s , 3000 rpm, baseline p o s i t i o n 169 C12 Comparison of ensemble averaged turbulence i n t e n s i t y with i n t e n s i t y obtained by non-stationary cycle-by-cycle a n a l y s i s using various window s i z e s , 3000 rpm, baseline p o s i t i o n 170 D.l Integration coordinates 183 D.2 Integration l i m i t s 184 D.3 Geometry: clearance volume 185 D.4 Area of e l l i p s e sections 186 D.5 Flame i n t e r s e c t i o n areas 187 D.6 E l l i p s e perimeter intersected 188 D.7 Geometry: cylinder volume 189 D.8 Non-dimensional flame volume vs non-dimensional flame radius 190 D.9 Non-dimensional flame front area vs non-dimensional flame radius 191 D.10 Non-dimensional wetted cylinder area vs non-dimensional flame radius 192 - x -LIST OF TABLES Page 1. Ricardo Hydra engine c h a r a c t e r i s t i c s 22 2. Operating conditions, motoring tests 25 3. Operating conditions, combustion tests 28 4. Model parameters 31 5. I g n i t i o n delay for the twelve base operating conditions ...... A . l Comparison of mass and volume d i s t r i b u t i o n s through flame f o r various d e f i n i t i o n s of flame thickness (exponential burning law) 126 C l Wire c h a r a c t e r i s t i c s 149 C.2 Time associated with each window size 157 - x i -NOMENCLATURE A Area (m2) A C o r r e l a t i o n constant, hot wire c a l i b r a t i o n A u Area of the outer flame boundary (m 2) ABDC A f t e r bottom dead center ATDC After top dead center a Cylinder bore (mm) B Correlation constant, hot wire c a l i b r a t i o n BDC Bottom dead center BBDC Before bottom dead center BTDC Before top dead center BMEP Brake mean e f f e c t i v e pressure (kPa) b Short axis length of e l l i p t i c a l clearance area (mm) C Carbon CA Crank angle (deg) 0^ Constant pressure s p e c i f i c heat (kJ/kg-K) C v Constant volume s p e c i f i c heat (kJ/kg-K) c Factor i n the model turbulent burning v e l o c i t y equation D,d Diameter E Energy (kJ) E Hot wire bridge voltage (V) EVC Exhaust valve c l o s i n g EVO Exhaust valve opening e S p e c i f i c energy (kJ/kg) e Molar S p e c i f i c energy (kj/kmol) - x i i -F Residual f r a c t i o n i n the c y l i n d e r res H Hydrogen h Convective c o e f f i c i e n t (W/m2-K) h c Clearance height (mm) I Current (A) IVC Intake valve c l o s i n g IVO Intake valve opening IMEP Indicated mean e f f e c t i v e pressure (kPa) K Constant i n the general turbulent burning v e l o c i t y equation Constant i n the Daneshyar and H i l l turbulent burning v e l o c i t y equation k Thermal conductivity (W/m2-K) L , l Length (m) L In t e g r a l length scale (m) M,m Mass (kg) Mw Molecular Weight (kg/kmol) N,n Number of moles (m) N Nitrogen N C o r r e l a t i o n exponent, hot wire c a l i b r a t i o n Nu Nusselt number (h d/k) 0 Oxygen P Pressure (kPa) Q Heat added or l o s t to the c y l i n d e r walls (kJ) Q Heat f l u x (W) Q Volumetric flow rate (m 3/s) R Connecting rod length (mm) R,r Radius (mm) - x i i i -R Resistance (ohms) R Gas constant (kJ/kg-K) R^ Inner flame radius (mm) Re Reynolds number (Vd/v) Re Reynolds number based on the i n t e g r a l length scale (VL/v) L i Re^ Reynolds number based on the Taylor microscale (VA/v) RPM Engine speed (rpm) Rmol Universal gas constant (kJ/kmol-K) R Outer flame radius (mm) u T Temperature (K) TDC Top dead center T,t Time (s) t Time f o r complete burning through the turbulent flame (s) 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) U^ Laminar burning v e l o c i t y (m/s) U Turbulent burning v e l o c i t y (m/s) u(t) Fluctuating component of the instantaneous v e l o c i t y (m/s) u' Turbulent i n t e n s i t y , RMS of v e l o c i t y fluctuations (m/s) V Volume (m 3) V g Swept volume (m 3) V Voltage (V) v S p e c i f i c volume (m3/kg) WOT Wide open t h r o t t l e w Tangential v e l o c i t y (m/s) X,x Mass f r a c t i o n X , Volume f r a c t i o n burned i n the turbulent flame v o l - xiv -y Distance through turbulent flame from outer edge (mm) a Temperature c o e f f i c i e n t of resistance of wire (1/C) 6 Turbulent flame thickness (mm) <|> Crank angle (deg) cj> Equivalence r a t i o p Density (kg/m3) p R e s i s t i v i t y (ohm-cm) X Taylor microscale of turbulence (mm) X Relative f u e l - a i r r a t i o v Kinematic v i s c o s i t y (m 2/s) y Dynamic v i s c o s i t y (N-s/m2) n Kolmogorov scale of turbulence (mm) n v Volumetric e f f i c i e n c y Q Angular v e l o c i t y (rad/s) T Time (s) T C h a r a c t e r i s t i c laminar burning time scale (s) Subscripts a i r Refers to intake a i r amb Refers to ambient conditions b.bnt Refers to burned mixture f,flame Refers to the thick burning zone f c Refers to a section of the turbulent flame formed by a cone of base radius X and height Ry gas Refers to gas properties i n the hot wire c a l c u l a t i o n s intake Refers to conditions i n the intake manifold ° Refers to a reference temperature of 273K - xv -p R e f e r s t o t h e u n b u r n e d p o c k e t s i n t h e t u r b u l e n t f l a m e r e s R e f e r s t o t he r e s i d u a l s i n t h e c y l i n d e r s p a r k R e f e r s t o c o n d i t i o n s a t t h e t i m e o f s p a r k sup R e f e r s t o t he w i r e s u p p o r t s o r p r o n g s t o t R e f e r s t o t h e t o t a l c y l i n d e r c o n t e n t s u , u n b R e f e r s t o unburned m i x t u r e 0,1,2 R e f e r s t o a n i n i t i a l , f i r s t and s e c o n d g u e s s i n a n i t e r a t i o n 1 R e f e r s t o t h e i n i t i a l c r a n k a n g l e s t e p i n t h e c a l c u l a t i o n s 2 R e f e r s t o t h e f i n a l c r a n k a n g l e s t e p i n t h e c a l c u l a t i o n s oo R e f e r s t o c o n d i t i o n s f a r away f rom the p r e s e n t p o s i t i o n window R e f e r s t o t h e a v e r a g i n g window i n c y c l e by c y c l e a n a l y s i s w i r e R e f e r s t o the h o t w i r e wop R e f e r s t o t h e o p e r a t i n g t e m p e r a t u r e o f t h e w i r e - x v i -ACKNOWLEDGEMENTS The author wishes to acknowledge Dr. P.G. H i l l f o r his guidance and encouragement throughout the course of t h i s work. Professors Hauptmann, Evans and Daneshyar are also thanked; t h e i r contribution through enlighten-ing discussions i s appreciated. Special thanks go to Alan Jones f o r the design of the data a c q u i s i t i o n system. The s t a f f and graduate students of the Department of Mechanical Engineering are al s o thanked f o r t h e i r support. - x v i i -1. INTRODUCTION Combustion phenomena i n engines are known to be affected by pre-flame turbulence, equivalence r a t i o , geometry of the combustion chamber and spark l o c a t i o n . These e f f e c t s are known q u a l i t a t i v e l y and understood quan-t i t a t i v e l y to a c e r t a i n extent. There are s t i l l many unresolved questions about the e f f e c t of lean combustion on c y c l i c v a r i a t i o n and burning rates, and how they are influenced by the engine flow f i e l d and the properties of the mixture. Turbulence i n engines and i t s e f f e c t on combustion has been a subject of extensive t h e o r e t i c a l and experimental research. It i s generally known that engine turbulence, which i s generated by the high shear flow past the intake valve and decays during the compression stroke, enhances the propa-gation of the reacting gases i n t o the unburned mixture. Turbulence i n motored engines has been measured using hot wire anemometry and more recently with l a s e r Doppler velocimetry. The e f f e c t of turbulence on flame development has been observed i n bombs and engines by v i s u a l i z a t i o n techniques, and by i n d i r e c t methods such as pressure measurements and ion probe s i g n a l s . It i s known that turbulent flame speed can be an order of magnitude l a r g e r than the laminar burning v e l o c i t y . Although researchers disagree on the exact nature of t h i s phenomena, the consensus seems to be that the flame i s stretched by the turbulent eddies for low l e v e l s of turbulence, but for higher l e v e l s , such as those encountered i n engines at operating speeds, the wrinkled flame breaks into l i t t l e islands or 'flamelets' which tend to burn at a rate c l o s e r to the laminar burning v e l o c i t y . Experimental evidence supports th i s l a s t theory. 2. Experimenters have known f o r quite some time that the flame kernel, i n i t i a t e d by the spark discharge, develops into a r a p i d l y propagating s e l f -s ustaining flame which reaches the ends of the chamber before a l l the combustion mixture has been consumed. It i s also known that flame propagation time and o v e r a l l combustion duration can be decreased by increasing turbulence or modifying the combustion chamber geometry. To understand the complex phenomena of combustion i n engines, researchers have developed mathematical models to simulate flame front propagation and thus predict burning rates, burned gas temperatures and exhaust emissions. Combustion modelling has been quite successful as a p r e d i c t i v e t o o l and i s used frequently by engine designers. The use of these models has however been l i m i t e d by the fa c t that up to now they tend to be engine dependent and thus have l i t t l e p r e d i c t i v e capacity when a t o t a l l y new design i s introduced. The complete d e s c r i p t i o n of combustion i n s i d e an engine i s a formid-able task. Such a model must take into account the momentum and energy balance, k i n e t i c s of oxidation, and i s complicated by the formation of thermal layers and other such phenomena. These types of models are i n t h e i r infancy and as yet have only been used to solve some simple 2-D problems at r e l a t i v e l y high computer costs. The turbulent entrainment models are most promising as they have proven successful i n design work. They combine a thermodynamic analysis of c y l i n d e r contents along with an entrainment equation f o r the flame front and equations describing the burning region l e f t behind the flame f r o n t . Thus the e f f e c t s of turbulence and reactant properties are combined. These models are successful i n p r e d i c t i n g trends and performing parametric studies. However, they are somewhat engine-dependent and a c e r t a i n amount 3. of t a i l o r i n g i s necessary to extend them to another a p p l i c a t i o n . Also, the e f f e c t of lean burning on c y c l i c v a r i a t i o n and thus on i g n i t i o n delay has not been predicted s u c c e s s f u l l y . These models could examine the geometry of the burning zone, i t s thickness and i t s e f f e c t on the o v e r a l l burning rate and engine performance. There i s need f o r further work i n t h i s area e s p e c i a l l y i n l i g h t of recent experimental findings about the structure of turbulent flames i n engines. Recently, Daneshyar and H i l l [1] formulated a s e r i e s of equations describing the propagation v e l o c i t y and thickness of the turbulent flame as a function of turbulence l e v e l s and reactant properties. This model has led to encouraging r e s u l t s i n l i m i t e d t e s t i n g . The objective of t h i s work i s to develop an engine simulation program incorporating these ideas, and to use i t to perform extensive t e s t i n g of the model. The s p e c i f i c objectives of t h i s work are summarized below: 1) Develop an engine simulation program which describes the rapid entrainment of the flame front across the c y l i n d e r and the r e l a t i v e l y slow burning i n the thick flame. This program, w i l l incorporate a thermodynamic an a l y s i s of the c y l i n d e r contents, a flame entrainment equation and a series of equations describing the geometry of the thick burning zone based on e x i s t i n g experimental evidence. 2) Conduct turbulence measurements i n s i d e the c y l i n d e r of the Ricardo Hydra engine with a hot wire anemometer. The purpose of these te s t s i s to determine the order of magnitude of turbulence l e v e l s around the spark f i r i n g time f o r various engine speeds and t h r o t t l e s e t t i n g s . 4. 3) Perform a s e r i e s of combustion t e s t s i n the Ricardo to measure pressure h i s t o r i e s and performance data over a range of engine speeds and a i r f u e l r a t i o s . 4) Submit the model to extensive t e s t i n g against the combustion data. The simulation program w i l l be tested f o r i t s a b i l i t y to predict o v e r a l l burning rates and pressure h i s t o r i e s over the range of engine speeds and equivalence r a t i o s . The model w i l l a l s o be tested i n p r e d i c t i n g i g n i t i o n delay. F i n a l l y , i t w i l l be used to gain greater understanding of the structure of the thick burning zone and i t s e f f e c t s on the o v e r a l l burning rates i n the engine. 5 . 2. REVIEW OF PREVIOUS WORK 2.1 Summary of Experimental Findings Turbulence i s known to enhance combustion [2,3,4,5,6]. The turbulent burning v e l o c i t y i s i n c e r t a i n cases ten times the laminar v e l o c i t y . Laminar burning v e l o c i t y i s a property of the mixture established by experimental measurement that depends on chemical composition and thermodynamic state. Turbulence i n engines i s created by the shear flow past the intake valve and decays ra p i d l y thereafter. In the absence of turbulence genera-tors (squish, s w i r l ) , i t tends to decay near top dead center and be governed by chamber geometry. Turbulence can be described by scale and i n t e n s i t y . Turbulent scale i s a parameter representative of the s i z e of the eddies i n the flow. The turbulence i n t e n s i t y i s the root mean square value of the f l u c t u a t i n g v e l o c i t y component about the mean. This d e f i n i -t i o n was formulated for a s i t u a t i o n where the mean v e l o c i t y i s steady with time i . e . , c l e a r l y definable. In an engine, the turbulent f l u c t u a t i o n s are of the same order as the mean v e l o c i t y and s i g n i f i c a n t c y c l i c v a r i a t i o n i s present. Thus there i s disagreement on an appropriate d e f i n i t i o n of mean v e l o c i t y and i n t e n s i t y i n engines. The r e s u l t s of experimenters depend highly on the way they have inte r p r e t e d t h e i r measurements. To understand the e f f e c t of turbulence on combustion, researchers have measured turbulence l e v e l s i n motored engines using hot wire anemometry and more recently laser doppler velocimetry. The general findings [5,7,8] are: 1) Turbulence i n t e n s i t y i s l i n e a r l y dependent on engine speed; 6. 2) Time scales are of the order of milliseconds; 3) The i n t e g r a l length scale i s of the order of the chamber height. There i s also evidence that f o r a simple combustion chamber geometry such as a disk chamber, the turbulence near top dead center tends to be homogeneous and i s o t r o p i c [9,7,8,10]. Turbulence i n the pre-flame f i e l d of an engine has been measured with la s e r Doppler anemometry. Witze [11,12] found that the turbulence inten-s i t y j u s t ahead of the flame undergoes an increase of up to two times i n the d i r e c t i o n of the flame propagation caused by the one-dimensional compression of preflame gases. This has been explained by the rapid d i s t o r s i o n theory [13]. Turbulent flames i n engines have a l s o been investigated. Smith [10] observed the e f f e c t of turbulence on flame structure i n engines. Using a micro-Schlieren technique, he photographed images of the flame front as i t propagated towards the camera. The flame front i s defined as the boundary separating a region of burned, burning and unburned gases from a region where i t i s s t a t i s t i c a l l y improbable to f i n d any burned gas. Examples of h i s photographs are shown i n Figure 1. Since i n t e n s i t y varied l i n e a r l y with engine speed, and there was evidence that the turbulence was i s o t r o p i c and homogeneous near top dead center, he set out to discover i f the s i z e of the flame wrinkles diminished with increasing RPM. Indeed they scaled with Re , where the Taylor microscale was derived from i s o t r o p i c turbulence A r e l a t i o n s h i p s . He also found the scale to decrease with progressing combustion, consistent with rapid d i s t o r s i o n theory. The siz e of the flame structures were found to be of the order of the Taylor microscale. 7. Smith [14] also observed turbulent flame thicknesses i n engines using Rayleigh s c a t t e r i n g . One important f i n d i n g was that as engine speed increased, the l i k e l i h o o d of islands of unburned gases being engulfed by the burned gases increased. Namazian, Hansen, Lyford-Pike, Sanchez-Barsse, Heywood and R i f e [15] observed thick burning regions (10 to 15 mm) through a side window i n the MIT square piston engine. Some of t h e i r photographs are reproduced i n Figure 2. They estimated that the thick flames were composed of a majority (50 to 70%) of burned gases. From t h e i r observations, they formulated an equation for the c h a r a c t e r i s t i c burning time of the entrained gases which l e d to a c h a r a c t e r i s t i c flame thickness. The rapid propagation of the outer flame edge with respect to the unburned gases i s defined as the turbulent entrainment or burning v e l o c i t y . Measurements of the turbulent burning v e l o c i t y have been conducted i n engines as w e l l as i n bombs. Although there i s s t i l l controversy i n the formulation of an adequate model describing the turbulent burning v e l o c i t y , experiments [2,3,7,16] i n d i c a t e a dependence on i n t e n s i t y as well as laminar burning v e l o c i t y i n the general form: U T = U £ + K u' A promising approach to modelling turbulent combustion i s found i n Tennekes' [17] model f o r i s o t r o p i c turbulent structure. A p a r a l l e l can be drawn between the structure of i s o t r o p i c turbulence and that of turbulent flames. The rapid propagation of the flame front would occur along vortex tubes of t y p i c a l diameter n (the Kolmogorov scale) by a mechanism known as 'vortex bursting' formulated by Chomiak [18]. Turbulent entrainment models are based on these fundamental assumptions. 8. 2.2 A Review of the Thin Flame Model Rassweiler and Withrow [19] were the f i r s t to c o r r e l a t e c y l i n d e r pressure development with the progress of the flame f r o n t . They extracted p i s t o n motion from the pressure curve and ca l c u l a t e d heat release r a t e s . Later, the two-zone thermodynamic model was introduced by Patterson and Van Wylen [20], who divided the chamber i n t o a region of burned gas and a region of unburned gas. Subsequently Krieger and Borman [21] added d i s s o -c i a t i o n and ca l c u l a t e d heat release r a t e s . Lancaster [4] introduced the geometric assumptions: s p h e r i c i t y and apparent p o s i t i o n of the flame. The thermodynamic or t h i n flame model combines a thermodynamic analysis of cylinder contents with an empirical burning law describing the progression of a t h i n r e a c t i o n front across the chamber. Mattavi, Groff, Lienesch, Matekunas and Noyes [22] demonstrated the c a p a b i l i t i e s of the t h i n flame model when they used i t to improve the design of a combustion chamber. The model was f i r s t used i n a diagnostic mode i n which engine pressure h i s t o r i e s were used to derive a c o r r e l a t i o n of flame speed r a t i o as a function of the laminar burning v e l o c i t y and motored turbulence i n t e n s i t y . The flame speed r a t i o i s defined as the r a t i o of turbulent burning v e l o c i t y ( r e l a t i v e to the unburned gas ahead of the flame) to the laminar burning v e l o c i t y at the unburned gas conditions. Next t h i s model was used i n a p r e d i c t i v e mode where the same c o r r e l a t i o n was applied to predict pressure h i s t o r i e s f o r d i f f e r e n t chamber configura-tions . It was found that the predicted improvements i n the o v e r a l l burning rate s u c c e s s f u l l y matched combustion data i n the new chamber. Groff and Matekunas [6] used pressure traces and flame photographs to develop a r e f i n e d expression f o r the flame speed r a t i o which included the 9. apparent combustion-induced compression of the unburned gas and the d i s t o r -t i o n of the flame geometry during the i g n i t i o n phase. They concluded that an accurate d e s c r i p t i o n of combustion i n engines should include a f i n i t e flame thickness. The d e f i c i e n c i e s of the t h i n flame model reside mainly i n the f a c t that i t does not describe the actual turbulent flame as observed through v i s u a l i z a t i o n techniques. The flame speed r a t i o obtained from c o r r e l a t i n g experimental data leads to an u n r e a l i s t i c 'slowing down' of the turbulent flame towards the end of combustion. Also, since t h i s kind of model was f i r s t developed, more facts have been discovered about the structure of the turbulent flame which are now being incorporated i n a new breed of models. 2.3 Turbulent Entrainment Models The new generation of combustion models have incorporated most of the recent experimental f i n d i n g s . B l i z a r d and Keck [23] and l a t e r Beretta, Rashidi and Keck [24] developed a turbulent entrainment model with slow burning behind the flame f r o n t . The entrained gas was assumed to burn at a rate proportional to the amount of unburned gas present i n the thick zone. This model agreed well with experiments over the range of conditions Investigated. The authors used both pressure h i s t o r i e s and flame photo-graphs to develop t h e i r model. Tabaczynski, Ferguson and Radhakrishnan [25] formulated an entrainment model with slow laminar burnup of eddies i n i t i a l l y of the siz e of the i n t e g r a l length scale. This was an attempt to model the burning mechanism inside the thick combustion zone through an understanding of the inherent structure observed i n flame photographs, as w e l l as i n the turbulent flow f i e l d . Hires, Tabaczynski and Novak [26] used t h e i r model to predict 10. i g n i t i o n delay and o v e r a l l combustion rates once an engine c h a r a c t e r i z i n g parameter had been determined. There i s s t i l l a need f o r a model describing the thick burning zone and i t s observed structure. 2.4 Background on the Turbulent Burning Model The present model i s based on the Tennekes [17] concept of the struc-ture of i s o t r o p i c turbulence. Tennekes formulated the model to account f o r experimental evidence of intermittency i n viscous d i s s i p a t i o n . The turbu-lent structure was modelled as vortex tubes of t y p i c a l s i z e n> the Kolmogorov scale, being stretched by eddies of s i z e X, the Taylor micro-s c a l e . A schematic of the Tennekes model and the d e f i n i t i o n of the scales of turbulence are i l l u s t r a t e d i n Figure 3. There i s experimental evidence i n support of the Tennekes model, notably the works of Narayan [27] and Ku and C o r r s i n [28]. The implications of the Tennekes model f o r combustion are: f a s t burn-ing i n the vortex tubes, and slow burning i n the X s i z e eddies. As i s l a n d s of unburned gas are engulfed by the t h i c k turbulent flame, the n regions w i l l r a p i d l y enflame due to a hydrodynamic mechanism causing the fast pro-pagation of the flame f r o n t . This i s i l l u s t r a t e d schematically i n Figure 4. 2.4.1 Turbulent Entrainment V e l o c i t y The mechanism behind f a s t burning i n the vortex tubes i s explained by the vortex bursting theory developed by Chomiak [18]. He deduced an expression f o r the propagation v e l o c i t y of the flame front along the vortex tubes as a function of the de n s i t i e s and the turbulence i n t e n s i t y i n the unburned gases ahead of the flame. This equation i s developed i n Appendix A. From t h i s , Daneshyar and H i l l developed an expression for the turbulent entrainment v e l o c i t y : 11. U = U + K, u' (1) T £ 1 v ' where K. < ^2/3 p /p, . i u b For a density r a t i o of 5 or 6 which i s close to what i s encountered i n engines, t h i s equation becomes: U w = U + 2u' T £ Similar r e s u l t s have been obtained by Abdel-Gayed, A l - K h i s h a l i and Bradley [1] i n measuring turbulent burning v e l o c i t i e s i n w e l l s t i r r e d bombs for engine l i k e conditions Re > 1000 and u'/U > 1. The equation i s also very s i m i l a r to the ones used by Tabaczynski and Keck i n t h e i r models. 2.4.2 Thick Burning Zone According to the theory, pockets of average s i z e A are engulfed by the turbulent flame and burn at a rate governed by the laminar burning v e l o c i t y . Thus a c h a r a c t e r i s t i c burn-up time scale of these pockets would be: £ Daneshyar and H i l l proceed to apply the burn rate equation dr = (1-r) dt T to get r (3) t f c - T c £n(l-r) (4) 12. and i n t e g r a t i n g f o r complete burning (90% burned) t t (99% burned) F i n a l l y the combustion zone thickness i s deduced 6 = (5) Preliminary c a l c u l a t i o n s by Daneshyar and H i l l using t y p i c a l engine values for u' and X lead to thicknesses of the order This compares well with experimental investigations [15,29]. The combustion zone i s i l l u s t r a t e d i n Figure 5. The model has proven to be very promising i n preliminary c a l c u l a t i o n s of burn rates i n bombs and engines. The true t e s t l i e s i n i t s incorporation i n t o an engine simulation program. 3 < 6 < 10 mm 13. 3. TURBULENT ENTRAINMENT ENGINE SIMULATION MODEL 3.1 I n i t i a l Conditions The engine simulation program begins c a l c u l a t i o n s at bottom dead center at the s t a r t of the compression stroke. The intake and exhaust strokes are not modelled. The i n i t i a l conditions are deduced from engine test data. The a i r and gas flow rates f or a given run as well as intake manifold temperature are used i n c a l c u l a t i n g the pressure and temperature at BDC as well as the mass of the cy l i n d e r contents. These c a l c u l a t i o n s are discussed i n Appendix A. 3.2 Compression and Expansion Stroke The compression and expansion c a l c u l a t i o n s are i d e n t i c a l . In both cases three equations are solved simultaneously by a Newton-Rapson technique. These equations are: 1) The equation of state; 2) The F i r s t law of thermodynamics; 3) Conservation of energy. A flowchart representing the c a l c u l a t i o n s i s presented i n Figure 6. The compression/expansion c a l c u l a t i o n s are d e t a i l e d i n Appendix A. 3.3 Combustion Calculations The engine simulation combines a thermodynamic analysis of the cyl i n d e r contents coupled with the turbulent entrainment model. I t describes the propagation of a thick turbulent flame which divides the chamber into three zones: burned, unburned and a mixture of burned and unburned gases. 14. 3.3.1 Assumptions Regarding the turbulence i n the chamber, the following assumptions are made: 1) The turbulence i n t e n s i t y i s i s o t r o p i c and homogeneous and thus the r e l a t i o n s of i s o t r o p i c turbulence [30] can be used to i n f e r the length sc a l e s . Y = — R l ' 2 (6) X •IT L 2) The turbulence i s relaxed at the time of spark f i r i n g which means that the large scale eddies are c l o s e to the chamber dimensions. The i n t e g r a l length scale L i s of the order of the chamber height. 3) Once the flame i s propagating, both the i n t e g r a l length s c a l e and the turbulence i n t e n s i t y are enhanced according to rapid d i s t o r t i o n theory [13]. The eddies are assumed to be compressed r a p i d l y , thus conserving angular momentum. U u spark ^ Pu^ Pu,spark^ L = L s P a r k ( p u / p u , s P a r k > ' 1 / 3 <8> With respect to the thick burning zone: 1) The burning zone i s a thick s p h e r i c a l s h e l l propagating from spark l o c a t i o n to the ends of the chamber. 2) The burning zone i s composed of unburned gas pockets i n i t i a l l y of s i z e A engulfed by burned gas. It i s assumed that a l l burned as well as a l l unburned gas i n the chamber i s at the same thermodynamic state. F i n a l l y , the c l a s s i c a l assumptions for the thermodynamic model were made: 15. 1) Pressure i s uniform throughout the combustion chamber. 2) Burned gases are at chemical equilibrium. 3) Unburned gases are compressed i s e n t r o p i c a l l y . It i s assumed that the heat loss to the cylinder walls i s compensated by the heat gain from the burned gases. 4) The gases are assumed to be i d e a l . 3.3.2 Governing Equations The equations that are solved simultaneously as the program steps through the f i r i n g stroke i n one degree crank angle increments are the following: Conservation of Mass M, tot = M u + M f + M^ (9) F i r s t law p AV + AQ (10) Entrainment equation dme dt = p A U. K u u t (11) with U t = U £ + c / p 7 ^ «• (12) Burning zone thickness equation (13) 16. Volume constraint V = V + V, + V. (14) tot u f b 3.3.3 Geometric Considerations The Ricardo 'bathtub' head configuration o f f e r s an i n t e r e s t i n g geometric problem. A schematic drawing of the cylinder head design i s depicted i n Figure 7. It was decided to s i m p l i f y the geometry somewhat to f a c i l i t a t e the ca l c u l a t i o n s of i n t e r s e c t i o n volumes and areas between the sphere and the chamber i t s e l f . This new geometry shown i n Figure 8 consists of an e l l i p t i c a l shaped clearance area occupying the same volume as the r e a l clearance space. The s i m p l i f i e d flame o r i g i n i s also shown on the f i g u r e . Some erro r i s introduced by s i m p l i f y i n g the geometry but i t appears to be minor compared to the assumptions of flame s p h e r i c i t y and immobility of the flame center. Because of the complexity of the c a l c u l a t i o n s involved i t was decided to generate tables of volume, flame area and wetted cylinder wall area f o r a range of r a d i i and crank angle degrees that would be encountered during combustion. The simulation program would simply search the table when a volume or area i s desired. The complete i n t e g r a t i o n procedure i s explained i n Appendix D. 3.3.4 Modelling the Thick Burning Zone One of the d i f f i c u l t i e s i n modelling the burning zone i s e s t a b l i s h i n g a l o c a l mass d i s t r i b u t i o n function f o r the burned and unburned gas. Experimental combustion v i s u a l i z a t i o n by Namazian et a l . [15] l e d to the statement that 50-70% of the mass i n the thick flame zone was burned gas. 17. Two theories, one based on the exponential burning law i n the zone, the other based on geometric considerations were proposed. Both are explained i n d e t a i l i n Appendix A. The two l e d to s i m i l a r r e s u l t s . It was found that the l o c a l volume f r a c t i o n of burned to unburned gas i n the burn-i n g zone i s approximately: X , ~ 75 to 85% v o l The l o c a l volume f r a c t i o n i s defined as the r a t i o of burned gas volume i n the flame to the t o t a l flame volume. It was decided to use a volumetric f r a c t i o n i n the thick burning zone instead of a mass f r a c t i o n because t h i s s i m p l i f i e s the model c a l c u l a t i o n s considerably. 3.3.5 Laminar Burning V e l o c i t y The expression used f o r c a l c u l a t i n g laminar burning v e l o c i t y was the same as that used by Jones [31]. For engine-like conditions, he combined two equations determined by Andrews and Bradley [32] i n constant volume bomb experiments. The f i r s t of these equations was a c o r r e l a t i o n of with varying pressure while the second described the v a r i a t i o n with temper-ature. The r e s u l t i n g combined equation for laminar burning v e l o c i t y at stoi c h i o m e t r i c conditions used i n the program i s : U £ = p-1/2 [io + 0.000371 T u 2 ] cm/sec (15) To obtain the laminar burning v e l o c i t y at other a i r - f u e l r a t i o s , a non-dimensional f a c t o r was c a l c u l a t e d from Andrews and Bradley's r e s u l t s at atmospheric conditions, and applied to the burning v e l o c i t y . Since natural gas i s composed of 95% or more of methane, these equations were used to model the laminar burning v e l o c i t y of natural gas. 18. 3.3.6 D i s s o c i a t i o n C a l c u l a t i o n s The d i s s o c i a t i o n c a l c u l a t i o n s were performed by a subroutine w r i t t e n by Jones [31]. It of f e r s the option of choosing two, four or s i x d i s s o c i a -t i o n reactions. For t h i s study the four following reactions were used. C0 2 = CO + 1/2 0 2 R\0 = h\ + 1/2 0„ 2 2 2 H 20 = OH + 1/2 H 2 NO = 1/2 N 2 + 1/2 0 2 3.3.7 Heat Loss Calculations The heat t r a n s f e r to the w a l l was estimated by Annand's [33] formula i n which a Nusselt vs Reynolds c o r r e l a t i o n i s applied i n the following way ^ = A w a l l °' 8 I < R e> b < V T w a l l > A t < 1 6> cylinder bore (m) V mpxD v 2LN/60 mean pi s t o n v e l o c i t y (m/s) 450 K Stroke (m) Engine speed (rev/min) The c o e f f i c i e n t s used i n t h i s study were: where D Re V mp T wall L N A = 0.8 B = 0.7 19. 3.3.8 Ig n i t i o n Delay I g n i t i o n delay i n t h i s case i s defined as the time f o r the ke r n e l to grow to a c e r t a i n s i z e such that the rapid propagation along the vortex tubes i s i n i t i a t e d . This i s a random time delay because the spark could create a flame kernel anywhere i n the p r e - i g n i t i o n flow f i e l d which was i l l u s t r a t e d i n Figure 3. As can be seen i n Figure 3, the maximum distance the flame would have to t r a v e l to reach t h i s next vortex tube would be A/2. The mean distance would be A/4. Thus the random time delay before r a p i d flame propagation would be: *delay " X ~T <17> The flame propagates at the laminar burning v e l o c i t y , u n t i l a vortex tube i s reached at which time the flame i s rap i d l y entrained along these tubes. The burned mass f r a c t i o n at the end of the i g n i t i o n delay i s n e g l i g i b l e . In the program, compression was extended and combustion c a l c u l a t i o n s were started at the end of i g n i t i o n delay. 3.3.9 Special L i m i t i n g Cases: I n i t i a l and F i n a l Burning Two a d d i t i o n a l models were developed f o r handling the early burning stages and the f i n a l burn-up. The f i r s t burning stage i s defined as the f i r s t c a l c u l a t e d step a f t e r the i g n i t i o n delay. Thus the kernel has reached the mean size A/2. In the early model development the turbulent entrainment c a l c u l a t i o n were started from a n e g l i g i b l e s i z e kernel. Thus i t was impossible to apply Eq. (1) since the i n i t i a l flame area was zero. Instead, the 20. following assumptions were made regarding the f i r s t burning step. The density v a r i a t i o n s i n the kernel were considered n e g l i g i b l e compared to the r a p i d growth rate of the flame. Also the o v e r a l l density i n the small kernel was assumed to be equal to the burned gas density. Thus the entrainment equation f o r the f i r s t burning step i s d R p U = U - H . (18 ) dt t p, D When the outer edge of the flame has reached the ends of the chamber, the thickness equation i s no longer a p p l i c a b l e . Since there i s no more flame entrainment, the remaining unburned gas regions are consumed at the laminar burning v e l o c i t y . Thus, the exponential burning law i s applied dm m T T = - r <»> c 3.3.10 Solving Scheme A simple flowchart was prepared to i l l u s t r a t e the c a l c u l a t i o n procedure of the combustion phase of the program. Calculations s t a r t a f t e r i g n i t i o n delay and end when a l l or a prefixed amount of the mass i n the cylinder i s consumed. The flowchart i s shown on Figure 9. 4 . EXPERIMENTAL INVESTIGATION 2 1 . 4 . 1 O b j e c t i v e s The p u r p o s e o f t h e m o t o r e d i n v e s t i g a t i o n was t o g a i n i n f o r m a t i o n a b o u t t h e t u r b u l e n c e l e v e l s i n s i d e t h e R i c a r d o e n g i n e . The o b j e c t i v e o f t h e c o m b u s t i o n t e s t s were t o g e n e r a t e d a t a o v e r a w i d e r ange o f o p e r a t i n g c o n d i t i o n s t o compare w i t h t h e s i m u l a t i o n p r o g r a m . 4 . 2 I n s t r u m e n t a t i o n A s c h e m a t i c o f t h e c o m p l e t e t e s t s e t up i s shown i n F i g u r e 1 0 . The R i c a r d o H y d r a t e s t f a c i l i t i e s c o n s i s t o f t h e e n g i n e and dc dynamometer and i n s t r u m e n t a t i o n f o r m o n i t o r i n g o i l a n d c o o l a n t t e m p e r a t u r e s , i n t a k e and e x h a u s t t e m p e r a t u r e s and i n t a k e a i r f l o w r a t e . The dynamometer e n a b l e s v a r i a b l e s p e e d r a n g e , and a m a g n e t i c p i c k - u p o n t h e f l y w h e e l r e g u l a t e s t h e i g n i t i o n t i m i n g . I n a d d i t i o n t o t h e s t a n d a r d R i c a r d o i n s t r u m e n t a t i o n , a p i e z o e l e c t r i c p r e s s u r e t r a n s d u c e r was mounted i n t h e h e a d . An A V L o p t i c a l p i c k u p was a l s o i n s t a l l e d on t h e f l y w h e e l f o r d a t a a c q u i s i t i o n p u r p o s e s . V a r i o u s o t h e r i n s t r u m e n t s w h i c h were u s e d i n t h e d a t a c o l l e c t i o n a r e i l l u s t r a t e d i n F i g u r e 1 0 . 4 . 2 . 1 E n g i n e D e s c r i p t i o n The R i c a r d o H y d r a i s a s i n g l e c y l i n d e r g a s o l i n e r e s e a r c h e n g i n e f e a t u r i n g a b a t h t u b c o m b u s t i o n chamber w i t h o v e r h e a d camshaf t and v e r t i c a l v a l v e s . The e n g i n e b o r e and s t r o k e a r e 8 0 . 2 6 mm and 8 8 . 9 mm r e s p e c t i v e l y , and t h e c o m p r e s s i o n r a t i o i s 8 . 9 3 t o 1. The e n g i n e c a n be o p e r a t e d a t a maximum s p e e d o f 5 , 4 0 0 rpm and p r o d u c e s maximum power o f 15 k w . The e n g i n e s p e c i f i c a t i o n s a r e p r e s e n t e d i n T a b l e 1. Table 1 Ricardo Hydra Engine C h a r a c t e r i s t i c s Number of cylinders 1 Bore (mm) 80.26 Stoke (mm) 88.9 Swept Volume (£) 0.45 Maximum speed (rpm) 5400 Maximum power (kW) 15 Compression Ratio 8.93:1 Valve Arrangement: Overhead camshaft, v e r t i c a l valves Valve L i f t (mm) 9 Intake port diameter (mm) 32 Valve events: Inlet opens (IVO) 12° BTDC Inle t closes (IV) 56° ABDC Exhaust opens (EVO) 56° BBDC Exhaust closes (EVC) 12° ATDC 23. 4.2.2 Pressure Measurements The pressure was measured with a K i s t l e r 6121 p i e z o e l e c t r i c transducer which was f l u s h mounted i n the c y l i n d e r head of the Ricardo engine. The r e s u l t i n g charge s i g n a l was fed to a . K i s t l e r model 5004 charge a m p l i f i e r to y i e l d a voltage proportional to cylinder pressure. One hundred cycles of pressure data were d i g i t i z e d at a r a t e of 1 sample/degree f o r each measur-ing condition. A photograph of the p o s i t i o n of the transducer i s shown i n Figure 11. 4.2.3 Hot Wire Measurements A TSI 12 26 high temperature probe with a DISA M-10 constant tempera-ture bridge were used to measure hot wire voltages. The s i g n a l was f i l t e r e d at 20 kHz with a DISA 55D26 s i g n a l conditioner before being d i g i t i z e d every 0.2 degree crank angle. These settings remained unchanged over a l l engine speeds. The wire m a t e r i a l was a platinum-iridium a l l o y . 6.3 micrometers i n diameter and 1.5 mm i n length. The wire was operated at 600°C. The probe was inserted through the spark plug hole using a s p e c i a l l y designed f i t t i n g . Figure 12 shows the probe measuring positions while Figure 13 i s a photograph of the probe i n s t a l l a t i o n i n the spark plug hole. 4.2.4 Crank Angle Measurements An AVL model 360c/600 o p t i c a l crank angle pick-up was mounted on the engine flywheel. This sensor generated pulses every crank angle degree which were used to t r i g g e r the data a c q u i s i t i o n , and a s i n g l e pulse at BDC used to synchronize the data with the p o s i t i o n of the crankshaft. 24. 4.2.5 Data A c q u i s i t i o n A l l data were taken by an ISAAC 2000 high speed data a c q u i s i t i o n u n i t . The ISAAC then executed a data transfer to an IBM PC, and the values were checked f o r proper phasing before they were copied onto floppy d i s k . Sampling was continuous u n t i l 40 consecutive cycles were acquired for the motored data, or 100 cycles f o r f i r e d pressure data. 4.2.6 Other Measurements Volumetric a i r and gas flow rates were measured with laminar flow elements. The a i r flow meter was mounted i n the intake of the Ricardo and was equipped with b u i l t - i n compensation for pulsating flows. Engine coolant and o i l temperatures were monitored through a l l t e s t s . 4.3 Motored Tests 4.3.1 Procedure and Data An a l y s i s Table 2 l i s t s the operating conditions f o r a l l the motoring t e s t s . A l l motored tests were cold s t a r t s which means that the engine was operated at room temperature. These tests were performed i n two phases. F i r s t motored pressures were recorded for the range of operating conditions. One hundred cycles of pressure data were c o l l e c t e d and ensemble-averaged. They were then analyzed to y i e l d motored temperatures using the following procedure: i s e n t r o p i c compression was assumed up to intake valve c l o s i n g , then the perfect gas law was applied f o r the remaining of the compression and expansion strokes. Further de s c r i p t i o n s of these methods are found i n Appendix A. Each wire was c a l i b r a t e d against a p i t o t tube, at atmospheric temperature and pressure i n a small wind tunnel. An anay t i c a l model was Table 2 25. Operating Conditions - Motoring Tests TEST #1: P o s i t i o n A, Orientation 1 RPM Thrott l e 1200 1800 2400 3000 WOT WOT WOT WOT PART ( n v PART ( n v PART ( T 1 v PART (n , v 75%) 75%) 75%) 75%) TEST #2: P o s i t i o n A, B, C Orientation 1, 2 WOT Engine speed 1200,1800 used to obtain the following Nusselt vs Reynolds number c o r r e l a t i o n which extended the c a l i b r a t i o n to any pressure and temperature The equations of the a n a l y t i c a l model were taken from Lancaster [28] and are based on heat trans f e r studies of e l e c t r i c a l l y heated c y l i n d e r s to a moving f l u i d [34,35]. These methods are explained i n d e t a i l i n Appendix C. Once the hot wire anemometer was c a l i b r a t e d , i t was mounted i n the engine. Forty cycles of data were taken at every f i f t h of a crank-angle degree f o r each condition. Gas properties deduced from the motored pressures were then used i n the analysis of the hot wire s i g n a l to obtain instantaneous v e l o c i t i e s . These properties were evaluated i n the same way as suggested by Witze [36]. Nu = A + B Re N (18) 26. The raw v e l o c i t y data was reduced using a non-stationary cycle by cycle time averaging method developed by Catania and M i t t i c a [37] . An 8 degree window was deduced for the frequency cut-of f between mean v e l o c i t y and turbulence i n t e n s i t y . Appendix C also describes i n d e t a i l the p a r t i c u l a r aspects of the hot wire measurements along with the procedure for choosing the window s i z e . 4.3.2 Results Figure 14 i s a p l o t of the mean v e l o c i t y at wide open t h r o t t l e as a function of engine speed. Figures 15 and 16 show respectively the turbu-lence i n t e n s i t i e s and r e l a t i v e i n t e n s i t i e s f o r the same conditions. It appears that the mean v e l o c i t y and i n t e n s i t y vary l i n e a r l y with engine rpm as expected. Figure 17 i s a p l o t of the mean v e l o c i t y vs engine speed f o r two s p e c i f i c points i n the cycle: top dead center and a t y p i c a l spark tim-ing (30 BTDC). Figure 18 shows the same r e l a t i o n f o r i n t e n s i t i e s . The f l o w f i e l d i n the engine at the defined spark time was assumed to represent the standard conditions p r e v a i l i n g i n the c y l i n d e r at the beginning of combustion. In order to compare the present data to previous measurements, Figure 19 was reproduced from a paper by Bobb, V a f i d i s and Whitelaw [38]. This graph i s a compilation of top dead center turbulence i n t e n s i t y measured i n various motored engines by d i f f e r e n t researchers. The data obtained i n t h i s study was p l o t t e d on the graph. Both ensemble averaged and cycle-by-cycle resolved data were plotted. It can be seen that even the ensemble averaged data i s low compared to previous experimentors. There are some events i n the data that can only be explained by the i r r e g u l a r shape of the chamber and the p o s i t i o n of the probe. For example a hump occurs a f t e r top dead center. If t h i s were ordinary squish, the hump should l i e symmetric-a l l y about top dead center as found by other researchers [39] . The low l e v e l s can a l s o be a t t r i b u t e d to the l a r g e r s i z e and l i f t of the intake valve which i s at the source of the engine turbulence. In addition, the chamber configuration, the proximity of the wire to the w a l l and the f a c t that the Ricardo i s a new engine could also explain the low turbulence l e v e l s measured. The assumptions of isotropy and homogeneity that are commonly used f o r simple disk chambers were tested on the Ricardo data. Figures 20 and 21 show the e f f e c t s of the probe o r i e n t a t i o n and p o s i t i o n along the spark plug axis on the turbulence i n t e n s i t y at 1200 rpm. The e f f e c t s were s i m i l a r at higher speeds. Since the objectives of the motored te s t s were to get an idea of the turbulence l e v e l s , p o s i t i o n i n g the probe i n the spark hole was appropriate although i t l i m i t e d the s p a t i a l r e s o l u t i o n of the f l o w f i e l d . F i n a l l y i t i s important to mention that we are interested i n the turbulence i n t e n s i t y during the compression stroke and p a r t i c u l a r l y at the time of spark f i r i n g . From the present data the values selected as c h a r a c t e r i s t i c i n t e n s i t i e s f o r each engine rpm are: RPM V (m/s) u' (m/s) mp 1200 3.56 0.85 1800 5.33 1.36 2400 7.11 1.67 3000 8.89 1.95 The estimated uncertainty associated with these values i s 50-70%. Again the reader i s r e f e r r e d to Appendix B f o r d e t a i l s . 4.4 Combustion Measurements The range of operating conditions for the f i r e d tests i s shown i n Table 3. 4.4.1 Procedure and Data Analysis The procedure f o r acquiring f i r e d pressure data was i d e n t i c a l to the 2 8 . Table 3 Operating Conditions - Combustion Tests Engine Speed (rpm) Throt t l e Spark Timing Relative A i r / F u e l Ratio X = 1.0 X 3 1-15 X = 1.30 1200 WOT MBT 1.01 1.16 1.27 1800 WOT MBT 1.00 1.15 1.28 2400 WOT MBT 1.04 1.20 1.36 3000 WOT MBT 1.08 1.22 1.37 one used i n measuring motored pressures. One hundred cycles of data were taken at each operating condition. Appendix B describes the d e t a i l s of pressure s c a l i n g and ensemble-averaging. 4.4.2 Results Figures 22 to 2 5 show the ensemble-averaged pressure h i s t o r i e s f o r the operating conditions measured. The spark timing was set at minimum for best torque. It can be seen that the peak pressure decreases as the mixture i s leaned. From t h i s combustion data, the pressure r i s e due to p i s t o n motion was a r t i f i c i a l l y extracted to y i e l d graphs of pressure r i s e due to combustion only. This was accomplished by c a l c u l a t i n g what the pressure i n the cylinder would have been i f combustion had e n t i r e l y taken place at the c y l i n d e r volume at spark timing. The r e s u l t i n g curves were s i m i l a r to constant volume combustion pressure h i s t o r i e s . It was then assumed that the normalized pressure r i s e was p r o p o r t i o n a l to the normalized mass f r a c t i o n burned, an assumption used by Rassweiler and Withrow [19]. S t a r t i n g from the occurrence of spark, f o r each subsequent crank angle, the pressure was expanded p o l y t r o p i c a l l y from i t ' s value at the current volume, to the value i t would have had at the spark volume by using the following equation: 29. P , (n) = P(n) (-r i s e V V(n) 1.30 ( 1 9 ) spark A pol y t r o p i c index of 1.3 was used as a mean value over the range of temperatures covered. Thus constant volume combustion was simulated. Typical r e s u l t s are presented i n Figure 26 which i s a plot of r e l a t i v e pressure r i s e , (the zero value being the pressure at spark f i r i n g and the . one value being the peak pressure achieved) as a function of degrees a f t e r spark f i r i n g f o r 1800 rpm. The assumption that r e l a t i v e pressure r i s e i s representative of o v e r a l l burning rate was made. It can be seen from these graphs that both i g n i t i o n delay and o v e r a l l burning rate are influenced by the mixture strength. The leaner mixture has a longer i g n i t i o n delay and burns more slowly. Figures 27 and 28 show the in d i c a t e d and brake mean e f f e c t i v e pressure as a function of r e l a t i v e a i r - f u e l r a t i o with engine speed as a parameter. It can be seen that the work done by the engine decreases as the mixture i s leaned and increases with engine speed. The increase with RPM i s due to the increase i n volumetric e f f i c i e n c y over the speed range and the reduction i n heat transfer at higher speeds. 5. SIMULATION PROGRAM RESULTS 30. In t h i s chapter, the r e s u l t s of the simulation program development are presented. The engine simulation program was f i r s t tested against experimental combustion data to e s t a b l i s h the v a l i d i t y of the model. Next the model pre d i c t i o n s were examined and interpreted. F i n a l l y a parametric study was conducted to determine the e f f e c t of c e r t a i n c o n t r o l l i n g variables on the combustion r e s u l t s . 5.1 Comparison with Experimental Results The basis used f o r comparison between ca l c u l a t e d and experimental data were the mass f r a c t i o n burned curves. The engine simulation program c a l c u l a t e s t h i s value d i r e c t l y . These curves were compared to the mass f r a c t i o n burned data obtained from extracting piston motion from experi-mental pressure h i s t o r i e s as described i n Section 4.4.2. Next the calculated combustion duration and i g n i t i o n delay were compared to experimental values. F i n a l l y the model predictions were examined. 5.1.1 Mass F r a c t i o n Burned Curves It was found that, i n order to obtain best agreement between calculated and experimental mass f r a c t i o n burned curves, the c factor i n the turbulent burning equation must be va r i e d with engine speed. This conclusion became apparent when comparing the program r e s u l t s and data at stoi c h i o m e t r i c a i r - f u e l r a t i o s . 31. The other model parameters were determined from l o g i c a l implications of the model. A l i s t of the model parameters i s presented i n Table 4. The c f a c t o r was chosen as best f i t to the near stoichiometric experimental mass burn curve, such that the rates of mass burned were as close as po s s i b l e over the period between 5 and 95% mass burned.. Table 4. Simulation Program Parameters I g n i t i o n Delay ( t d e l a y ) j - ^ h Integral Length Scale at Spark (L) — Burned Gas Volume Fr a c t i o n i n Thick Flame (X ]_) 0.82 c f a c t o r @ 1200 rpm 3.1 1800 rpm 2.4 2400 rpm 2.3 3000 rpm 2.6 Figures 29 through 40 show comparisons of calculated and experimental mass f r a c t i o n burned curves f o r a l l twelve operating conditions. It can be seen that there i s good agreement between calculated and experimental values with regards to combustion i n i t i a t i o n and mass burn r a t e s . The curves are also i n agreement over the range of a i r - f u e l r a t i o s i n v e s t i -gated. There i s however some discrepancy i n the l a s t stages of burning which w i l l be discussed i n the next se c t i o n . The c f a c t o r i n the turbulent burning equation was v a r i e d over the speed range. This could be explained by the inherent uncertainty i n the turbulent i n t e n s i t y measurements which was estimated at 50-70%. When t h i s uncertainty i s considered, the v a r i a t i o n i n c factor over the speed range i s acceptable. However, there i s some discrepancy between the c f a c t o r at 1200 rpm and that at higher speeds. 32. The experimental r e s u l t s at 1200 rpm were suspect as the combustion duration did not follow the same trend than at higher speeds. It i s believed that MBT spark timing was not achieved during these t e s t s . The factor which m u l t i p l i e s the turbulence i n t e n s i t y i n the turbulent burning equation i s high compared to r e s u l t s obtained by other engine modelers [25]. In the l a s t chapter i t was shown that the turbulence l e v e l s measured In t h i s work were low compared to published experimental r e s u l t s . As well, the cycle-by-cycle averaging technique leads to i n t e n s i t y values as much as half of the ensemble averaged r e s u l t s . Some researchers have used ensemble averaged i n t e n s i t y values i n t h e i r models. The i n t e g r a l length scale was chosen as one f i f t h of the clearance chamber height at the time of spark. A s i m i l a r r e s u l t had been obtained experimentally by Fraser, Felton, Bracco and Santavicca [40] who used l a s e r Doppler velocimetry to make two-point s p a t i a l c o r r e l a t i o n measurements of v e l o c i t y f l u c t u a t i o n s . 5.1.2 Pressure H i s t o r i e s Figures 41 to 52 are p l o t s of the c a l c u l a t e d and experimental pressures generated from the runs described i n Table 4. Although agreement was exc e l l e n t i n the mass burn curves, the c a l c u l a t e d pressure curves show peak pressures as much as 20% higher than experimental values, the expansion curves, however i n d i c a t e that the heat l o s s predictions are i n agreement with experimental values. It i s believed that the main reason f o r t h i s overestimation of peak pressures i s due to the method of comparing calculated and experimental mass burn curves. This w i l l be discussed i n d e t a i l i n the following chapter. 5.1.3 Combustion I n i t i a t i o n Table 5 shows the values of i g n i t i o n delay obtained f o r the twelve base operating conditions. The i g n i t i o n delay was defined as the average 33. time f o r the flame to reach a r\ vortex tube, and was modelled i n the following way = _X T d e l a y 4 U I It can be seen from Table 5 that the mean random time delay increases as the mixture i s leaned. This i s due to a reduction of the laminar burning v e l o c i t y . It can also be seen that, although there i s l i t t l e v a r i a t i o n with engine speed, the i g n i t i o n delay tends to decrease as a d i r e c t r e s u l t of the decrease i n Taylor microscale with speed. Table 5 Ig n i t i o n Delay f o r the Twelve Base Operating Conditions Engine Speed (rpm) Relative A i r / F u e l Ratio I g n i t i o n Delay (deg) (msec) 1200 1.01 2 0.28 1200 1.16 2 0.28 1200 1.27 3 0.42 1800 1.00 2 0.19 1800 1.15 3 0.28 1800 1.28 4 0.37 2400 1.04 3 0.21 2400 1.20 4 0.28 2400 1.36 5 0.35 3000 1.08 4 0.22 3000 1.22 5 0.28 3000 1.37 6 0.33 The time to burn the f i r s t 5% of the t o t a l mass i n the c y l i n d e r was deduced from the mass f r a c t i o n burned curves. This time has been pl o t t e d i n Figure 53 i n crank angle degrees as a function of a i r - f u e l r a t i o with engine speed as parameter, i t can be seen that agreement i s better at higher speeds due to the f a c t that the times involved are much smaller. 5.4.4 Combustion Duration Combustion duration was defined as the time i n crank angle degrees to burn 5 to 95% of the t o t a l mass i n the c y l i n d e r . Due to the previously 34. mentioned discrepancy towards the end of combustion, there i s some d i s -agreement between calculated and experimental values. Figure 54 shows the c a l c u l a t e d and experimental combustion duration as function of a i r - f u e l r a t i o with speed as a parameter. The calculated combustion durations are short compared to experimental values. A p l o t of 5 to 80% mass f r a t i o n burned would show better agreement. 5.2 Model Predictions 5.2.1 Flame Thickness The burning zone thickness at 50% t o t a l mass burned i s p l o t t e d i n Figure 55 for the twelve program runs described i n the l a s t section. I t can be seen that the thickness increases as the a i r - f u e l mixture becomes leaner. The trend with engine speed indicates much thicker flames at 3000 rpm compared to the three slower engine speeds. The equation used to describe flame thickness i n the program was: 6 = The flame thicknesses v a r i e s from 6 to 9 mm at stoichiometric a i r -f u e l r a t i o s and increases as the mixture i s leaned. This i s a r e s u l t of slower laminar burning v e l o c i t y and lower f u e l energy l e v e l s which lead to low temperatures and pressures. Thicker flames were predicted at 3000 rpm than at lower speeds. This i s d i f f i c u l t to explain as the thickness was expected to increase s t e a d i l y with turbulence i n t e n s i t y . The increase i n flame thickness with engine speed was achieved i n the model by a decrease i n Taylor microscale and general increase i n turbulent burning v e l o c i t y due to increased turbulence l e v e l s . These trends are consistent with experimental observations made by Smith [14] . The thicknesses are consistent with measurements made by Namazian and a l . [15]. 35. 5.2.2 c Factor V a r i a t i o n with Engine Speed Figure 56 i s a plot of c factor with engine speed. The experimental r e s u l t s f o r 1200 rpm are believed to be suspect. If t h i s data i s d i s -regarded, the v a r i a t i o n of c factor over the higher speed range i s within 15%. In a d d i t i o n there does not seem to be a c l e a r trend with engine speed, i t i s d i f f i c u l t to draw meaningful conclusions from these r e s u l t s . More work i s necessary to understand the r o l e of t h i s f a c t o r . 5.2.3 Thermodynamic and Geometric Properties The following curves are t y p i c a l model predictions for thermodynamic properties other than those discussed previously. Figure 57 show the mass f r a c t i o n entrained and mass f r a c t i o n burned as a function of crank angle degrees f o r 1800 rpm and near s t o i c h i o m e t r i c a i r -f u e l r a t i o . I t can be seen that the two curves are s i m i l a r and are repre-sentative of the f a c t that the burning zone thickness i s quite constant during combustion. Figure 58 i s a plot of the inner and outer flame r a d i i f o r the same program run. This f i g u r e shows the constant flame thickness throughout combustion. It i s i n t e r e s t i n g to note that when the outer flameradius i s of the order of 10 mm the mass f r a c t i o n burned i s s t i l l w e l l below 1%. The outer flame area i s p l o t t e d i n Figure 59 against crank angle f o r the same conditions. The area increases i n i t i a l l y as the flame grows, reaches a maximum and then decreases due to the confinement of the chamber. This e f f e c t i s r e f l e c t e d i n the mass f r a c t i o n entrained curve shown previously. The volumes of the three zones are p l o t t e d i n Figure 60. The thick burning zone has a r e l a t i v e l y constant volume during the combustion process. 5.2.4 Turbulent Entrainment and Scales This set of curves show the model predictions for turbulent length 36. scales, enhanced turbulent i n t e n s i t y and flame entrainment v e l o c i t y . Figure 61 and 62 show the i n t e g r a l length scale and Taylor microscale v a r i a t i o n s with crank angle f o r three p a r t i c u l a r conditions: 1800 rpm at near stoichiometric and lean a i r - f u e l r a t i o s and 3000 rpm at near stoi c h i o m e t r i c a i r - f u e l r a t i o . In the case of the i n t e g r a l length s c a l e s , the i n i t i a l values are s i m i l a r since i t was assumed that L = h /5. The c i n t e g r a l length scale was then enhanced according to the r e l a t i o n : ^ ^spark ^ pu^ pu,spark^ The Taylor microscale curves show the e f f e c t of unburned gas density between near stoichiometric and lean. The Reynolds number e f f e c t i s r e f l e c t e d i n the smaller scales at higher engine speed. I t can be seen that the Taylor microscale diminishes as combustion progresses, which i s a di r e c t consequence of the decrease of the i n t e g r a l length scale. The behaviour of the c a l c u l a t e d Taylor microscale and thus the scale of the turbulent flame structure agreed with measurements performed by Smith [14] and Keck [29]. I t was found through v i s u a l i z a t i o n techniques, that the flame structure s i z e decreased with engine speed and also as combustion progressed. The enhanced turbulence i n t e n s i t y i s p l o t t e d i n Figure 63 for the same three conditions described above. The s l i g h t differences i n the curves at 1800 rpm are a r e s u l t of d i f f e r e n t unburned gas d e n s i t i e s . The i n t e n s i t y was enhanced i n the following way: U u,spark ^ pu^ pu,spark^ Figure 64 shows the turbulent entrainment v e l o c i t y at 1800 rpm f o r X « 1.00, X a 1.30 and 3000 rpm for 1 = 1.00. 37. 5.3 Parametric Study The purpose of the parametric study was to gain i n s i g h t i n t o the r e l a -t i v e e f f e c t of c e r t a i n parameters. This enabled the i d e n t i f i c a t i o n of key fa c t o r s which were shown to predominately influence combustion. The para-metric study was also an evaluation of the model i n showing that i t led to r e a l i s t i c r e s u l t s when c e r t a i n parameters were changed. The key v a r i a b l e s examined were the volume d i s t r i b u t i o n i n the thick burning zone, the constant c i n the turbulent entrainment equation and the i n t e g r a l length scale. 5.3.1 E f f e c t of Volume D i s t r i b u t i o n i n the Thick Flame These s e r i e s of program runs were generated to examine the e f f e c t of the volume d i s t r i b u t i o n i n the thick flame zone on the rate of t o t a l mass burned. For t h i s t e s t , the flame propagation f a c t o r C was a r b i t r a r i l y set at 2.2 and the i n t e g r a l length scale was assumed to be equal to the c l e a r -ance chamber height at time of spark. These te s t s were performed f o r a l l the twelve experimental operating conditions. I g n i t i o n delay had not been included at t h i s point of the study. The range of volume f r a c t i o n s was i n i t i a l l y chosen from 75 to 95% burned volume to t o t a l flame volume. I t was found that 80 to 90% l e d to mass burn curves c l o s e s t to experimental values. Figure 65 shows a t y p i c a l r e s u l t of the program runs along with the experimental mass burned curves for 3000 rpm and near stoichiometric a i r -f u e l r a t i o . The r e s u l t s i n d i c a t e d that the e f f e c t of volume f r a c t i o n was more important at higher speeds. This i s again due to the fa c t that the times involved between crank angle degrees are smaller at higher engine speeds. Thus changes i n the mass burn rate are r e f l e c t e d more strongly at higher speeds. The volume d i s t r i b u t i o n had an e f f e c t on flame thickness through changes i n thermodynamic properties due to f a s t e r or slower burning. The 38. choice of the volume d i s t r i b u t i o n f a c t o r was shown to have s i g n i f i c a n t e f f e c t on combustion duration. 5.3.2 E f f e c t of c Factor i n Turbulent Burning Equation The program was run at the f o l l o w i n g conditions to examine the e f f e c t of factor c i n the turbulent entrainment equation. The volume d i s t r i b u t i o n was set at 90% f o r these runs and the i n t e g r a l length scale was assumed to be the chamber height at time of spark. These te s t s were run at a l l twelve experimental conditions with c taking the values 2.0, 2.2 and 2.4. A representative r e s u l t i s plotted i n Figure 66 for 3000 rpm and near s t o i c h i o m e t r i c a i r - f u e l r a t i o . These curves show a strong dependance of rate of t o t a l mass burned on c f a c t o r . 5.3.3 Integral Length Scale One of the assumptions of the model was that the turbulence was relaxed at top dead center. According to these arguments, the si z e of the larger eddies would be of the order of the l i m i t i n g dimension of the chamber. Fraser et a l . [40] measured the i n t e g r a l length scale and found that i t was approximately one f i f t h of the chamber height at top dead center. These two values were tested i n thr model to see the e f f e c t of t h i s v a r i a t i o n and to see which l e d to the best r e s u l t s . Figures 67 and 68 show a set of program runs d i f f e r i n g only i n the d e f i n i t i o n of the i n t e g r a l length scale. The operating conditions were 3000 rpm and near stoichiometric a i r - f u e l r a t i o . These tests were performed with a l l other parameters set according to Table 5. The choice of i n t e g r a l length scale had s i g n i f i c a n t e f f e c t on the c a l c u l a t e d i g n i t i o n delay and mass burn rates. The model predictions are improved when the i n t e g r a l length scale i s chosen as h c/5. Similar trends were observed at the other operating conditions. 39. 6. DISCUSSION OF UNCERTAINTIES 6.1 Model Assumptions One of the major assumptions of the model was that the r e l a t i o n s h i p s of i s o t r o p i c turbulence could be used to describe the f l o w f i e l d i n the engine. This assumption was based on findings of experimenters such as Semenov [9] and Lancaster [8], who measured the turbulence i n a motored engine with a hot wire anemometer. The general conclusion was that i n a simple combustion chamber, the turbulence at top dead center tended towards isotropy and homogeneity. This> assumption was extended, i n t h i s case, to the Ricardo combustion chamber which has a squish configuration. The turbulence i n t e n s i t i e s obtained i n the Ricardo engine d i d not give evidence of a turbulent i n t e n s i t y increase around top dead center which has been shown to be c h a r a c t e r i s t i c of squish chambers [39] . Instead a hump was present a f t e r top dead center which might be a t t r i b u t e d to j e t t i n g of a i r out from the various c a v i t i e s of the chamber. The smooth decrease i n mean v e l o c i t y and turbulence i n t e n s i t y from intake valve c l o s i n g to top dead center tends to i n d i c a t e that the turbulence i s r e l a x i n g as the p i s t o n i s nearing the end of i t s t r a v e l . A simple combustion chamber would have been a better medium f o r t e s t i n g the model. However i n the present s i t u a t i o n the i s o t r o p i c assumption was used and the r e s u l t s should be interpreted with these l i m i t a t i o n s i n mind. Along with the i s e n t r o p i c turbulence assumption, the s p h e r i c i t y assumption would also be more r e a l i s t i c i n a simple combustion chamber. I t has however been observed that the flames are very close to s p h e r i c a l except i n chambers where there i s strong s w i r l [15]. 40. The engine simulation program runs were c a l c u l a t e d from the experi-mental operating conditions. Assumptions were made i n determining the pressure and temperature at bottom dead center, the r e s i d u a l f r a c t i o n i n the chamber and the heat loss to the cylinder walls. The error associated i n determining the reference pressure i s n e g l i g i b l e f o r experimental pressure data since the whole curve i s simply s h i f t e d by a constant. Thus an er r o r of a few ki l o P a s c a l s at bottom dead center i s n e g l i g i b l e at top dead center. However, the i n i t i a l pressure and temperature had s i g n i f i c a n t impact on the simulation c a l c u l a t i o n s since they determine the i n i t i a l thermodynamic state i n the c y l i n d e r . The r e s i d u a l f r a c t i o n was set at 5% since t h i s i s a t y p i c a l value encountered i n experiments. The uncertainty could have been diminished by attempting to model intake and exhaust strokes but i t was judged that t h i s was unnecessary at th i s stage, since a v a l i d comparison could s t i l l be made between model and experiment. The heat l o s s equation was developed by Annand [33] . The c o e f f i c i e n t s of the equation were chosen because they were t y p i c a l values observed f o r various engines. The comparison of c a l c u l a t e d and experimental pressure h i s t o r i e s gave an i n d i c a t i o n that the heat transfer was close to the ac t u a l heat t r a n s f e r as the expansion strokes were s i m i l a r . It was a l s o found through t e s t i n g the model with d i f f e r e n t c o e f f i c i e n t s i n the Annand equation, that the di f f e r e n c e s observed between ca l c u l a t e d and experimental pressure h i s t o r i e s could not be explained by an inaccurate heat transfer factor. Figure 69 shows the e f f e c t of varying the f a c t o r a i n Annand's equation. It was mentioned i n Chapter 3 that two assumptions were made with regards to burning rate. The f i r s t was to assume that the flame could be approximated by a quarter sphere f o r the very f i r s t c a l c u l a t i o n step. In addition, the entrainment equation was reduced to the following expression f o r t h i s f i r s t step only: dR p T i - U -± dt t p b This was necessary because the amount of mass entrained i s determined from the turbulent burning v e l o c i t y , the unburned gas density and the flame area. Since no flame area was a v a i l a b l e i n i t i a l l y , t h i s assumption was proposed. It was tested against flame geometry c a l c u l a t i o n s and found to be v a l i d f o r r a d i i i n the 0 to 10 mm range. This assumption i s not believed to introduce error as the mass f r a c t i o n entrained and burned are much less than 1% at the end of t h i s f i r s t step. 6.2 Uncertainties Associated with the Measurements The uncertainty associated with the hot wire measurements and averag-ing technique has been discussed extensively. One consequence of the averaging technique used was that the turbulence i n t e n s i t y was low compared to other researchers and thus the c factor i n our model seems high compared to other modelers. In addition, the meaning of the hot wire s i g n a l recorded must be interpreted with reservation because of the low magnitude of the mean v e l o c i t y coupled with the f a c t that the flow f i e l d i n the chamber i s unknown due to the i r r e g u l a r shape of the combustion chamber. 6.3 Uncertainties i n Interpretation of Results The basis of comparison of the model with experimental r e s u l t s was the mass f r a c t i o n burned curves. The experimental mass f r a c t i o n burned curves 42. were determined from the pressure h i s t o r i e s using a pi s t o n motion extraction method described i n Chapter 4. Comparing pressure h i s t o r i e s o f f e r s a good check of the model but more information would be gained i f a d i r e c t comparison of flame structure had been possible through flame v i s u a l i z a t i o n techniques. One d i f f i c u l t y encountered during t h i s work was that i t i s r e l a t i v e l y easy to match pressure h i s t o r i e s and mass burn rate curves with a given combination of c fac t o r , flame density d i s t r i b u t i o n and flame thickness. Unfortunately, we can only rely on previous experimenters r e s u l t s with respect to these parameters. A d i r e c t comparison over a wide range of conditions would be quite informative. The method used to extract the mass burn rate from the combustion pressures must also be approached with reservation. I t was based on the observed f a c t that pressure r i s e due to combustion i s proportional to mass f r a c t i o n burned. The method used a polytropic compression or expansion of the c y l i n d e r contents back to the volume at spark. The choice of the poly-t r o p i c index was based mainly on the f a c t that the r e s u l t i n g curve should be s i m i l a r to a constant volume bomb pressure r i s e curve. An index of 1.3 was chosen as the experimental curves showed the rapid pressure r i s e followed by a decrease supposedly due to heat l o s s . The pis t o n e x t r a c t i o n method was tested on a ca l c u l a t e d pressure curve from the thick flame simulation model. The r e s u l t i s shown i n Figure 70. This f i g u r e shows the experimental mass burn curve calculated from the piston motion extraction program, the ca l c u l a t e d mass f r a c t i o n burned and the r e s u l t of e x t r a c t i n g the piston motion from the calculated pressure curve. It can be seen that there i s a problem at the end of combustion a t t r i b u t e d to the f a c t that the pressure r i s e didn't reach a maximum u n t i l the exhaust valve opened. This o f f e r s some i n s i g h t i n the general poor agreement between c a l c u l a t e d and experimental runs at the end of combustion. A better method should be proposed to deal with t h i s inconsistency. 43. 7. CONCLUSIONS The objective of t h i s work was to develop an engine simulation program incorporating a turbulent entrainment model developed by Daneshyar and H i l l . In addition, a series of experiments were to be performed to deter-mine the turbulence l e v e l s i n the Ricardo engine and the combustion pressures associated with burning a gaseous f u e l i n the engine. The model was to be tested against experimental data and evaluated. The steps taken were: 1. An engine simulation program was developed incorporating the turbulent entrainment model. This program simulates the f i r i n g strokes of the Ricardo Hydra engine operating on a gaseous f u e l . The model features i g n i t i o n delay and turbulent entrainment of a thick r e a c t i o n f r o n t accompanied by slow laminar burning i n s i d e the thick flame. 2. The turbulence l e v e l s i n the motored engine were measured using hot wire anemometry. Measurements were conducted at four engine speeds and at various p o s i t i o n s along the spark plug axis i n the chamber. The r e s u l t i n g turbulence i n t e n s i t y l e v e l s were low compared to published r e s u l t s at comparable engine speeds. 3. Combustion pressure h i s t o r i e s were measured over a range of engine speeds and a i r - f u e l r a t i o s . The engine was operated on n a t u r a l gas. From the pressure data, mass f r a c t i o n burned curves were calcu l a t e d . The conclusions that can be drawn from t h i s work are the following: The o r i g i n a l form of the proposed model underestimated combustion 44. durations when compared to experiments. A constant was added to increase the e f f e c t of the turbulence i n t e n s i t y . This constant was adjusted for best agreement with experimental mass f r a c t i o n burned data obtained at stoichiometric a i r - f u e l r a t i o s . This led to good agreement between c a l c u l a t i o n s and experiments with regards to combustion i n i t i a t i o n and mass burn rates over the speed and a i r - f u e l r a t i o range investigated. There was however discrepancy towards the end of combustion which i s believed to be a re s u l t of the method used to c a l c u l a t e the experimental mass f r a c t i o n burned. The model predicted higher peak pressures by about 10%. The corre c t trend was obtaining over the speed and a i r - f u e l r a t i o range. The constant added to the turbulence i n t e n s i t y was speed dependent showing variations of 15% over the higher speed range. The parametric study l e d to the following r e s u l t s : The model i s very s e n s i t i v e to the c factor i n the turbulent burning equation and to the volume d i s t r i b u t i o n i n the thick flame. The choice of the i n t e g r a l length scale also had s i g n i f i c a n t e f f e c t on i g n i t i o n delay and combustion duration. The value retained i n the model was one f i f t h of the clearance height at time of spark. The predicted flame thicknesses agreed w e l l with published experimental r e s u l t s . The correct trend with engine speed and a i r - f u e l r a t i o was al s o achieved by the model. 8. RECOMMENDATIONS It i s recommended that t h i s model be tested against combustion data obtained from a simple geometry engine or a w e l l - s t i r r e d bomb. This would enable easier diagnosis of experimental data. It i s al s o recommended that flame v i s u a l i z a t i o n or other s u i t a b l e techniques be used to measure flame structure and thickness over a range of engine speeds (or turbulence l e v e l s ) and a i r - f u e l r a t i o s . Since the model i s based on the structure of the turbulent flame, e f f o r t s should be d i r e c t e d towards v e r i f y i n g the p a r a l l e l proposed by Tennekes and the mechanism developed by Chomiak. 46. REFERENCES [1] Daneshyar, H. and H i l l , P.G., "The Structure of Small Scale Turbulence and I t s E f f e c t on Combustion i n Spark-Ignition Engines," Report to be published. [2] Andrews, G.E. and Bradley, D., "Turbulence and Turbulent Flame Propagation - A C r i t i c a l A p praisal," Combustion and Flame, Vol. 24, pp. 285-304, 1975. [3] Abdel-Gayed, R.G., A l - K h i s h a l i , K.J., Bradley, D., "Turbulent Burning V e l o c i t i e s and Flame St r a i n i n g i n Explosions," Proceedings of the Royal Society, London, Ser. 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[17] Tennekes, H., "Simple Model for the Small-Scale Structure of Turbulence," The Physics of F l u i d s , V ol. 11, No. 3, pp. 669-670, 1968. [18] Chomiak, J . , " D i s s i p a t i o n 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. [19] Rassweiler, G.M. and Withrow, L., "Motion Pictures of Engine Flames Correlated with Pressure Cards," SAE Transactions, Vol. 42, No. 5, pp. 185-204, 1938. [20] Patterson, D.J. and Van Wylen, G.V., "A D i g i t a l Computer Simulation f o r Spark Ignited Engine Cycles," SAE Paper No. 633 F, 1963. [21] Krieger, R.B. and Borman, G.L., "The Computation of Apparent Heat Release f o r I n t e r n a l Combustion Engines," ASME 66-WA/DGP-4, 1966. [22] Mattavi, J.N., Groff, E.G., Lienesch, J.H., Matekunas, F.A. and Noyes, R.N., "Engine Improvements Through Combustion Modelling," Combustion Modelling i n Reciprocating Engines, pp. 537-587, Mattavi, J.N. and Annand, C A . E d i t o r s , Plenum Press, New York-London, 1980. [23] B l i z a r d , N.C. and Keck, J.C., "Experimental and Theoretical Investigation of Turbulent Burning Model f o r Internal Combustion Engines," SAE Transactions, V o l . 83, Paper No. 740191, pp. 846-864, 19 74. [24] 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. [25] Tabaczynski, R.J., Ferguson, C.R. and Radhakrishnan, K., "A Turbulent Entrainment Model f o r Spark-Ignition Engine Combustion," SAE Transactions, V o l . 86, Paper No. 770647, pp. 2414-2433, 1977. [26] Hires, S.D., Tabaczynski, R.J. and Novak, J.M., "The P r e d i c t i o n of I g n i t i o n Delay and Combustion Intervals f o r a Homogeneous Charge Spark-Ignition Engine," SAE 780232, 1978. [27] Narayanan, M.A.B., Rajogopalan, S. and Narasimha, R., "Experiments on the Fine Structure of Turbulence," J . F l u i d Mech., Vol. 80, Part 2, 1977. 48. [28] 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 In F u l l y Turbulent F l u i d , " Journal of F l u i d Mechanics, V o l . 50, Part 2, pp. 285-319, 1971. [29] Keck, J.C., "Turbulent Flame Structure and Speed i n Spark-Ignition Engines," Nineteenth Symposium (International) on Combustion, The Combustion I n s t i t u t e , 1982, pp. 1451-1466. [30] Taylor, G.I., " S t a t i s t i c a l Theory of Turbulence," Proceedings of the Royal Society (London), Ser. A., Vol. 151, p. 421, 1935. [31] Jones, A.L., "The Performance of a Turbocharged Spark-Ignition Engine Fuelled with Natural Gas and Gasoline", M.A.Sc. Thesis, U n i v e r s i t y of B r i t i s h Columbia, 1985. [32] Andrews, G.F. and Bradley, D., "The Burning V e l o c i t y of Methane A i r Mixtures", Combustion and Flame, Vol. 19, pp. 275-288, 1972. [33] 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. [34] C o l l i s , D.C. and Williams, M.J., "Two-Dimensional Convection from Heated Wires at Low Reynolds Numbers," Journal of F l u i d Mechanics, V o l . 6, pp. 357-384, 1959. [35] Davies, P.O.A.L. and Fisher, M.J., "Heat Transfer from E l e c t r i c a l l y Heated Cylinders," Proceedings of the Royal Society, London, Ser. A, V o l . 280, pp. 486-527, 1964. [36] Witze, P.O., "A C r i t i c a l Comparison of Hot-Wire Anemometry and Laser Doppler Velocimetry f o r I.C. Engine Applications," SAE 800132, 1980. [37] Catania, A.E. and M i t t i c a , A., "A Contribution to the D e f i n i t i o n of Turbulence i n a Reciprocating I.C. Engine," ASME 85-DGP-12, 1985. [38] Bopp, S., V a f i d i s , C. and Whitelaw, J.H., "The E f f e c t of Engine Speed on the TDC F l o w f i e l d i n a Motored Reciprocating Engine," SAE 860023, 1986. [39] Witze, P.O., "Measurement of the S p a t i a l D i s t r i b u t i o n and Engine Speed Dependance of Turbulent A i r Motion i n an I.C. Engine," SAE 770220, 1977. [40] Fraser, R.A., Felton, P.G., Bracco, F.V. and Santavicca, D.A., "Preliminary Turbulence Length Scale Measurements i n a Motored IC Engine," SAE 860021, 1986. [41] Tabaczynski, R.J., Trinker, F.H. and Shannon, B.A.S., "Further Refinements and V a l i d a t i o n of a Turbulent Entrainment Model f o r Spark-Ignition Engines," Combustion and Flame, V o l . 39, pp. 111-121, 1980. 49. [42] McCormack, P.D., Scheller, K., Mueller, G. and Tisher, R., "Flame Propagation i n a Vortex Core", Combustion and Flame, Vol. 19, pp. 297-303, 1972. [43] Brown, W.L., "Methods f o r Evaluating Requirements and Errors i n Cylinder Pressure Measurements," SAE 670008, 1968. [44] Lancaster, D.R., Krieger, R.B. and Lienesch, J.H., "Measurement and Analysis of Engine Pressure Data," SAE 750026, 1975. [45] Moore, C , "UBC Curve-Curve F i t t i n g Routines", Computing Centre, U n i v e r s i t y of B r i t i s h Columbia, 1984. [46] N i c o l , T., "UBC Integration", Computing Centre, University of B r i t i s h Columbia, 1982. [47] Amann, C.A., " C l a s s i c a l Combustion Diagnostics f or Engine Research," SAE 850395, 1985. [48] Cameron, CD., "An Investigation of Squish Generated Turbulence i n an In t e r n a l Combustion Engine," M.A.Sc. Thesis, U n i v e r s i t y of B r i t i s h Columbia, 1985. [49] Daneshyar, H. and F u l l e r , D.E., " D e f i n i t i o n and Measurement of Turbulence Parameters i n Reciprocating IC Engines," Cambridge Univ e r s i t y Engineering Department, 1985. [50] 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. [51] Heywood, J.B., "Engine Combustion Modelling. An Overview," Combustion Modelling i n Reciprocating Engines, pp. 1-38, Mattavi, J.N. and Annand, C A . E d i t o r s , Plenum Press, New York-London, 1980. [52] Horvatin, M. and Hussmann, A.W., "Measurement of A i r Movement i n In t e r n a l Combustion Engine Cylinders," DISA Information, No. 8, pp. 13-22, July 1969. [53] Rajan, S., Smith, J.R. and Rambach, G.D., "Internal Structure of a Turbulent Premixed Flame Using Rayleigh Scattering," Combustion and Flame, V o l . 57, pp. 95-107, 1984. [54] Rask, R.B., "Comparison of Window, Smoothed-Ensemble and Cycle-by-Cycle Data Reduction Techniques f o r Laser Doppler Anemometer Measurements of In-Cylinder V e l o c i t y , " Symposium on F l u i d Mechanics of Combustion Systems," ASME, FED Spring Meeting, 1981. [55] Ricou, J.P. and Spaulding, D.B., "Measurement of Entrainment by Axialsymmetric Turbulent J e t s , " J . F l u i d Mech., 9, 21, 1961. 5 0 . Figure 1. Microshadographs of flame fronts measured by Smith [14] 51. m + l8° n + 2 4 ° p + 36* q + 4 2 ° f • 1 o + 3 0 s 1 "1 I J r + 48' 1 H|. 13 - Photographs of a t y p i c a l combustion process reproduced from a a o v l e w i t h i n t e r v a l s of 6 detreea(0.72 ms). Spark timing l e 55* ITC. For i n t e r p r e t a t i o n of photographs eee F i g . 14 i Figure 2. Flame photographs taken by Namazian et a l . [15] i n the MIT square piston engine. 52. Figure 3. . Schematic of the Tennekes model; d e f i n i t i o n of turbulent length scales. Figure 4. Schematic of turbulent combustion as shown by Tabaczynski [4l] . 54. Motionless Reactants Products Figure 5., Schematic of th i c k combustion zone. Do u n t i l Occurrence of Spark (compression) Bottom Dead Center (expansion) Increment crank-angle Assume a f i n a l temperature using i s e n t r o p i c compression/expansion temperature as a f i r s t guess Solve 3 equations simultaneously using a Newton-Rapson technique • F i r s t Law . Perfect Gas Law • Conservation of Energy Obtain the f i n a l temperature, pressure and energy Next crank-angle Figure 6. Engine Simulation Program Flowchart, Compression and Expansion COTTIER DETAIL O F COMBUST ION C H A M B E R 3 y v ALL OVER. VOLUME WITH PLUG &L VALVES IM POSlTOkl TO BE CC ure 7. Ricardo combustion chamber from manufacturer supplied drawings 5 7 . Figure 8. Approximate combustion chamber geometry. 58. Do u n t i l Mass f r a c t i o n > 0.99 Increment crank-angle CA„ Calculate new volume V, Assume new pressure P, Calculate f i n a l properties of unburned gas T u » U £ ' e u » Pu ? *"> . ? Z2_ Assume burned gas temperature Calculate properties of burned gas include or not d i s s o c i a t i o n e^ , Calculate mass of unburned gas entrained m„ Calculate turbulent flame thickness 8, Deduce new flame p o s i t i o n and mass f r a c t i o n burned Calculate heat loss to walls Calculate new t o t a l energy from f i r s t law Figure 9. Engine Simulation Program Flowchart, Combustion Phase NATURAL GAS| INLET APPROXIMATE RELATIVE AIR/FUEL' 1 RATIO BOC PULSE S -0 .2* PULSES-OAS F L O W . INLET TEMPERATURE JL ,AP GAS A I R HEATER 033 OAS LAMINAR FLOW E L E M E N T •X SENSOR I EXHAUST TEMPERATURE / EXHAUST PRESSURE KISTLER TRANSDUCER RICARDO HYDRA ENGINE AVL AIR FLOW ^ SPEED I TORQUE INLET PRESSURE AIR INLET / FILTER A M LAMINAR FLOW ELEMENT AIR TEMPERATURE T AIR TEMPERATURE INSTRUMENTATION LAYOUT Figure 10. Engine testing f a c i l i t i e s . 60. Figure 11. Photograph of the pressure transducer mounted in the cylinder head. 61. P o s i t i o n A : W i r e measures a x i a l and r a d i a l componen t s . P o s i t i o n B : W i r e measu res t a n g e n t i a l ( s w i r l ) component . F i g u r e 1 2 . Hot w i r e anemometer m e a s u r i n g p o s i t i o n s . Figure 13. Photograph of the hot wire probe l o c a t i o n . Figure 14. Mean v e l o c i t y as a function of crank angle degrees f o r a l l investigated engine speeds, baseline p o s i t i o n . 0-\ 1 1 r -140 -120 -100 -80 T 1 1 r -20 TDC 20 40 Crank Angle deg 60 80 100 120 140 Figure 15. Turbulence i n t e n s i t y as a function of crank angle degrees f o r a l l investigated engine speeds, baseline p o s i t i o n . 1-1 -140 -120 -100 •40 -20 TDC 20 40 Crank Angle deg 140 Figure 16. Relative turbulence i n t e n s i t y as a function of crank angle degrees for a l l investigated engine speeds, baseline p o s i t i o n . 10 8 6 0-Legend A Spark 30 deg BTDC X Top Dead Center i i — 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200 Engine speed rpm ON Figure 17. Mean v e l o c i t y at 30 BTDC and at top dead center as a function of engine speed, baseline p o s i t i o n . Legend A Spark 30 deg BTDC X Top Dead Center n 1 1 i i i i i i i i i 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200 Engine speed rpm Figure 18. Turbulence i n t e n s i t y at 30° BTDC and at top dead center as a function of engine speed, baseline p o s i t i o n . 68. Figure 19. Comparison of top dead center turbulence i n t e n s i t y with other in v e s t i g a t o r s ' r e s u l t s , from Bopp et a l . [38] . 5-1 BDC -150 -120 -90 -60 -30 TDC 30 60 90 120 150 BDC Crank Angle deg Figure 2 0 . Effect of wire orientation on turbulence i n t e n s i t y at 1200 rpm. 8 6-1 CO c CO or Legend A Distance 5 mm X Distance *=• lfrmm • Distance = 15 mm • 2l A i v c A" -180 -150 -120 -90 -60 -30 0 30 60 Crank Angle deg 180 Figure 21. Effect of position along the spark plug axis on turbulence i n t e n s i t y at 1200 rpm. o 6000 5500 5000 4500 ^ 4000 'co 3500 ^ 3000 co to a> 2500 2000 1500 1000 500 0 Legend A Lambda - 1.01 X Lambda - 1.16 • Lambda = 1.27 A — A——A A A ' •A" Lambda =1.16 Lambda =1.01 g Lambda =1.27 "A< 'A- 'A-' A . .A -180 -150 •120 •90 -60 •30 30 60 90 120 150 180 Crank Angle (deg) Figure 22. Experimental pressure curves at 1200 rpm for three a i r - f u e l r a t i o s . 5500-j 5000-1 4500 4000-3500-3000-2500-2000 1500-1000-500-0 ^ Legend A Lambda ™ 1.00 X Lambda = -LI5. • Lambda = 1.28 -90 •A- 'A- 'A--180 -150 -120 0 •A T -60 -30 30 60 Crank Angle (deg) 90 120 150 180 Figure 23. Experimental pressure curves at 1800 rpm for three a i r - f u e l r a t i o s . 6000-1 5500 5000 4500 ^ 4000 'co 3500 CD ^ 3000 CO co 0) 2500 2000 1500 1000 500 0 Legend A Lambda - 1.04 X Lambda - 1.20 • Lambda = 1.36 •A- •A . • •A •180 -150 -120 •90 -60 -30 0 30 60 Crank Angle (deg) 90 120 150 180 Figure 24. Experimental pressure curves at 2400 rpm for three a i r - f u e l r a t i o s . 6000 5500-5000-4500-4000-3500-3000-2500-2000-1500-1000-500 Legend A Lambda ™ 1.08 X Lambda " 122 • Lambda = 1.37 •A' •A« •180 -150 -120 -90 -60 -30 0 30 60 Crank Angle (deg) 90 120 150 - A —I 180 Figure 25. Experimental pressure curves at 3000 rpm f o r three a i r - f u e l r a t i o s . Figure 26. Mass f r a c t i o n burned curve calculated from experimental pressures at 1800 rpm for three a i r - f u e l r a t i o s . 1200 1100-Legend A 1200 RPM X 1800 RPM • 2400 RPM El 3000 RPM 1000-900-X A 800-700 + 1 1.05 1.10 T T 1.15 1.20 1.25 Relative Air-Fuel Ratio 1.30 1.35 1.40 Figure 27. Indicated mean e f f e c t i v e pressure as a function of a i r - f u e l r a t i o s for a l l operating speeds. 1000-T 900 Legend A 1200 RPM X 1800 RPM • 2400 RPM H 3000 RPM 800H 700 H A X 600 + 1 —I 1 1 1.15 1.20 1.25 Relative Air-Fuel Ratio 1.05 1.10 1.30 1.35 1.40 Figure 28. Brake mean e f f e c t i v e pressure as a function of a i r - f u e l r a t i o s f o r a l l operating speeds. Figure 29. Comparison of calculated and experimental mass f r a c t i o n burned for 1200 rpm, X = 1.01. Crank Angle After Spark (deg) Figure 30. Comparison of calculated and experimental mass f r a c t i o n burned for 1200 rpm, X = 1.16. Crank Angle After Spark (deg) Figure 31. Comparison of calculated and experimental mass f r a c t i o n burned for 1200 rpm, X = 1.27. Figure 32. Comparison of calculated and experimental mass f r a c t i o n burned for 1800 rpm, X = 1.00. 9 Figure 33. Comparison of calculated and experimental mass f r a c t i o n burned for 1800 rpm, X = 1.15. Figure 34. Comparison of calculated and experimental mass f r a c t i o n burned for 1800 rpm, X = 1.28. Figure 35. Comparison of calculated and experimental mass f r a c t i o n burned for 2400 rpm, X = 1.04. Figure 36. Comparison of calculated and experimental mass f r a c t i o n burned for 2400 rpm, X = 1.20. A <T 10 20 30 40 50 60 70 80 90 100 Crank Angle After Spark (deg) Figure 37. Comparison of calculated and experimental mass f r a c t i o n burned for 2400 rpm, X = 1.36. Figure 38. Comparison of calculated and experimental mass f r a c t i o n burned for 3000 rpm, X = 1.08. Figure 39. Comparison of calculated and experimental mass f r a c t i o n burned for 3000 rpm, X = 1.22. Figure 40. Comparison of calculated and experimental mass f r a c t i o n burned for 3000 rpm, X = 1.37. 6000 5500 5000-4500-^ 4000 "To i 3500H ^ 3000H w CO O 2500H 2000 1500-1000-500-Legend A FP015 C FACTOR = 3.1 — A — A — A A" -180 -150 -120 -90 •60 -30 0 30 60 Crank Angle (deg) 90 120 150 180 o Figure 41. Comparison of calculated and experimental pressure h i s t o r i e s for 1200 rpm, X = 1.01. 6000-1 5000 H 4500 4000 H 3500 3000-2500-2000-1500-1000-500-Legend A FP020 C FACTOR = 3.1 - A — A - ^ A — A - A — A — A ' A -180 -150 -120 •90 -60 -30 0 30 60 Crank Angle (deg) 90 120 150 180 Figure 42. Comparison of calculated and experimental pressure h i s t o r i e s for 1200 rpm, X = 1.16. 6000 5500-6000-4500-^ 4000-co ^ 3500-1 CD ^ 3000H co co d> 2500H 2000 1500H 1000 500-1 Legend A FP021 C FACTOR = 3.1 , A — A - r A — f t A-A - A - -•A- :A •180 -150 -120 -90 -60 -30 0 30 60 Crank Angle (deg) 90 120 150 180 Figure 43. Comparison of calculated and experimental pressure h i s t o r i e s for 1200 rpm, X = 1.27. 6000 5500 5000-4500-^ 4000 "cO 3500 ^ 3000-1 CO CO <D 2500 H 2000-1500-1000-500 0 Legend A FP009 C FACTOR = 2.4 • A — A - p A — f t ' A A " • A - A C A-T -180 -150 -120 -90 T -60 -30 0 30 60 Crank Angle (deg) •A 90 120 150 180 Figure 44. Comparison of calculated and experimental pressure h i s t o r i e s for 1800 rpm, X = 1.00. 6000-1 5500-1 5000 4500 ^ 4000-1 * 3500 CD ^ 3000H to to CD 2500 2000-1 1500 1000-500-Legend A F P010 C FACTOR = 2.4 — A — A - — A ^ ' , A — A T A — A A -180 -150 -120 -90 •60 -30 0 30 60 Crank Angle (deg) 90 120 150 180 Figure 45. Comparison of calculated and experimental pressure h i s t o r i e s for 1800 rpm, X = 1.15. 6000-5500-5000 4500 ^ 4000H "to -* 3500H ^ 3000 CO CO O 2500 2000 1500-1000-500 0 Legend A FP011 C F A C T O R - 2.4 120 -90 -60 -30 0 30 60 Crank Angle (deg) 90 120 150 180 Figure 46. Comparison of calculated and experimental pressure h i s t o r i e s for 1800 rpm, X = 1.28. 6000 5500-Crank Angle (deg) Figure 47. Comparison of calculated and experimental pressure h i s t o r i e s for 2400 rpm, X = 1.04. 6000-1 5500 5000-4500-^ 4000-co Q_ ^ 3500H 5 3000H to Q) 2500 H 2000-1500-1000 500 Legend A FP013 C F A C T O R = 2.3 A — A A A —A—A-""*A' A ~~"" A ^A^ -180 -150 -120 •90 -60 -30 0 30 60 Crank Angle (deg) 90 120 A — i 1 150 180 Figure 48. Comparison of calculated and experimental pressure h i s t o r i e s for 2400 rpm, X = 1.20. Legend A FP014 C F A C T O R - 2.3 •180 -150 •60 -30 0 30 60 Crank Angle (deg) 180 Figure 49. Comparison of calculated and experimental pressure h i s t o r i e s for 2400 mm. X = 1.36. 6000 -1 5500-Crank Angle (deg) Figure 50. Comparison of calculated and experimental pressure h i s t o r i e s for 3000 rpm, X = 1.08. 6000-1 •180 -150 -120 -60 -30 0 30 60 Crank Angle (deg) 180 Figure 51. Comparison of calculated and experimental pressure h i s t o r i e s for 3000 rpm, X = 1.22. 6000 5500 5000 4500 4000-3500-3000-2500-2000 1500 1000 500 Legend A FP018 C FACTOR = 2.6 A — A — A — A — A •A' A " ^ - A ^ A A r -180 -150 -120 -90 -60 -30 0 30 60 Crank Angle (deg) 90 120 150 -1 180 Figure 52. Comparison of calculated and experimental pressure h i s t o r i e s for 3000 rpm, A = 1.37. 30 Legend 1200 RPM CALCULATED X 1200 RPM EXPERIMNETAL 1800 RPM CALCULATED _ H 1800 RPM EXPERIMENTAL 2400 RPM CALCULATED 1.40 Air-Fuel Ratio M O N) Figure 53. Comparison of calculated and experimental time to burn the f i r s t 5% of t o t a l mass i n the cylinder. 55 50-45-40 Legend 1 2 0 0 R P M C A L C U L A T E D X 1 2 0 0 R P M E X P E R I M N E T A L 1 8 0 0 R P M C A L C U L A T E D _ H 1 8 0 0 R P M E X P E R I M E N T A L * 2 * 0 0 , B f M E X P E R I M E N T A L 52°.9J?.pEc.^ c.ykAXLP... ffi 3 0 0 0 R P M E X P E R I M E N T A L X ©- y r ^ ® ^ " -X-•X" 30-25-1.05 1.10 1.15 1.20 1.25 Air-Fuel Ratio 1.30 1.35 — t 1.40 o Figure 54. Comparison of calculated and experimental time to burn 5 to 95% of t o t a l mass i n the cylinder. 15 6 -i i i i i 1 1 1 r 1 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 Air-Fuel Ratio M O Figure 55. Predicted flame thickness as a function of a i r - f u e l r a t i o and engine speed. -1 1 1 1 1 1 1 1 1 1 r 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200 RPM Figure 56. Variation of c factor over the engine speed range. Figure 57. Predicted mass f r a c t i o n entrained and burned f o r 1800 rpm and X = 1.00. 80-1 Crank Angle (deg) Figure 58. Predicted inner and outer flame radius f o r 1800 rpm and X = 1.00. Crank Angle (deg) Figure 59. Predicted outer flame area f o r 1800 rpm and X = 1.00. Figure 60. Predicted unburned, burned and flame volumes for 1800 rpm and \ = 1.00. S 35.0 Legend 1800 RPM Lambda - 1.00  1800 RPM Lambda - 1.30  3000 RPM Lambda - 1.00 Crank Angle (deg) Figure 61. Predicted i n t e g r a l length scale at 1800 rpm, A = 1.00, X = 1.15, 3000 rpm X = 1.08. Crank Angle (deg) Figure 62. Predicted Taylor microscale at 1800 rpm, X = 1.00, X = 1.15, 3000 rpm X = 1.08. 5-1 Figure 63. Enhanced turbulence i n t e n s i t y at 1800 rpm, X = 1.00, X = 1.15, 3000 rpm X = 1.08. Legend 1800 RPM Lambda - 1.00  1800 RPM Lambda « 1.30  3000 RPM Lambda - 1.00 n 1 1 1 1 1 1 -30 -20 -10 0 10 20 30 Crank Angle (deg) Figure 64. Predicted turbulent entrainment v e l o c i t y at 1800 rpm, X = 1.00, X = 1.15, 3000 rpm X = 1.08. Mass Fraction Burned 09 c l-t r+l M I - l l-Ti ft) r-h O n> rr n H- rr O 3 § a4 C rr i-t 3* 3 iU rt> Cu < - o L O o o o I - l 3 c a ca cr o 00 o 3 l-ti (0 PJ O rr rr p* O H* n o II r-h N> I-1 • PJ N> 3 • CD O 3 9 PJ ca CO Q I o I t\J I CD -L. o c n i o CO o \1 o CO I o CD _ L _ CO o ' O ~) a D x" D ca c— (D ID <— (D ~) CO "O a "5 a_ c a O ' O cn CD O 00 O CD O O a X X X VOL VOL VOL • :• • o ? 9 CD O m cn bo o •*TT Crank Angle After Spark (deg) Figure 67. Predicted and calculated mass f r a c t i o n burned for L = h at spark timing, 3000 rpm, X = 1.08. ° Crank Angle After Spark (deg) h-* Figure 68. Predicted and calculated mass f r a c t i o n burned f or L = b /5 at spark timing, 3000 rpm, A = 1.08. c Crank Angle After Spark (deg) Figure 70. Comparison of mass f r a c t i o n burned curves extracted from experimental pressures, extracted from predicted pressures and calculated from model. 120. APPENDIX A TURBULENT ENTRAINMENT MODEL - ENGINE SIMULATION PROGRAM 1. Development of the turbulent burning equation 2. Volume D i s t r i b u t i o n i n Thick Burning Zone 2.1 Exponential Burning Law 2.2 Geometric Considerations 3. I n i t i a l Mixture Composition 4. Compression and Expansion Strokes 5. I n i t i a l and F i n a l Burning 1 2 1 . 1. Development of the Turbulent Burning Equation Chomiak [18] developed a theory for rapid propagation of a flame i n a turbulent f i e l d . At very high Reynolds, a t h i n continuous flame sheet becomes disrupted and the strong d i s s i p a t i v e eddies play a key r o l e i n the propagation process. McCormack [42] has observed that a flame propagates very r a p i d l y when ig n i t e d i n the midst of a laminar vortex, the flame v e l o c i t y being proportional to the vortex strength. He also observed that combustion causes a discontinuous breakdown of the vortex. Chomiak presents a simple equation f o r momentum balance at the flame i n t e r f a c e : / (p-pJdA = / p b U 2 dA A A This simply means that the pressure forces induced by the r o t a t i o n of the f l u i d are equal to the momentum f l u x due to the p u l l i n g of the flame insi d e the vortex. To determine the pressure d i s t r i b u t i o n i n s i d e the vortex l e t us consider a two-dimensional vortex of strength ft and diameter n shown i n u u Figure A - l . This vortex i s i n the unburned mixture ahead of the flame and i t s maximum v e l o c i t y i s of the order u' the turbulent i n t e n s i t y . The momentum equation (neglecting r a d i a l or a x i a l motion): 1 dP w2 p dr r w i s the tangential v e l o c i t y and i s equal to 1 2 2 . w = Q r 0 < r < n / 2 u u Q ri 2 w = -TT- V 2 < r < It i s assumed that the tube has a viscous core and i s a po t e n t i a l vortex outside t h i s region. The pressure d i s t r i b u t i o n thus obtained i s n 2 2 4 1 2 n/2 p ft 'n * u u u u P -P -i 1 / 2 2 » 1 r , U . i * r, 2 2 8 r u u u u The v e l o c i t y and pressure p r o f i l e s are plotted i n Figure A - l . Daneshyar and H i l l c a l c u l a t e the mean pressure d i f f e r e n c e by i n t e g r a t i n g the pressure d i s t r i b u t i o n equation out to two times the vortex radius. P -P = — / (P -P) 2TT r dr ' V 0 £2 2 n 2 £ (2) u u r3 _ J L _ 1 " p u ~ 4 \-Tb + — J n n and since the maximum tangential v e l o c i t y of the cone i s — ^ — = u' they get p u ' 2 u 2.77 1 2 3 . The p r o p a g a t i o n o f t h e f l a m e i n t h e v o r t e x i s m o d e l l e d i n t h e f o l l o w i n g way . L e t us assume t h a t t h e r i g h t s i d e o f t h e v o r t e x o f F i g u r e A - l b u r n s c o n s e r v i n g mass and a n g u l a r momentum ( s e e F i g u r e A - 2 ) . c o n s e r v a t i o n o f mass p n 2 = p,n, 2 u u b b c o n s e r v a t i o n o f a n g u l a r momentum ft n 2 = ft, n , 2 ° u u b b I t i s t h e n e a s i l y shown t h a t t h e p r e s s u r e d r o p t h r o u g h t h e u n b u r n e d s i d e o f t h e v o r t e x i s f a r g r e a t e r t h a n t h a t t h r o u g h t h e b u r n e d s i d e . P b , (P - P ) , = ( — ) 2 (P - P ) oo b P oo U U A t y p i c a l v a l u e f o r P u / p ^ i s 5 , w h i c h l e a d s t o : (P - P ) » (P - P ) , oo 'u oo 't> D a n e s h y a r and H i l l deduce t h e momentum b a l a n c e P u ' 2 . u 1 and the v e l o c i t y (P - P ) « 7 7 = T p U 2 oo ' u 2 . 7 7 2 b a 2 P u ! ' 2 a v 2 . 7 7 p, b T h i s i s t he a x i a l p r o p a g a t i o n v e l o c i t y i n d u c e d by the v o r t e x b u r s t i n g m e c h a n i s m . The t u r b u l e n t e n t r a i n m e n t o f t h e f l a m e i s t h i s h y d r o d y n a m i c v e l o c i t y p l u s t h e l a m i n a r b u r n i n g v e l o c i t y . 124 . U 1/2 This expression accounts for both chemical and hydrodynamic e f f e c t s . The equation was used i n the simulation program to describe the propagation of the outer edge of the burning zone. 2. Volume D i s t r i b u t i o n i n the Thick Burning Zone As mentioned i n Chapter 2, two d i s t i n c t theories were developed to calculate the approximate volume (or mass) d i s t r i b u t i o n i n the thick burning zone. F i r s t l e t us define the volume f r a c t i o n of burned gas i n the flame zone. 2 .1 Exponential Burning Law It has already been discussed that the burning rate i n the flame zone i s assumed proportional to the amount of unburned gas present i n the zone. X bflame v o l V,. flame dm. mf flame dt T flame T X c Let us define the reacted f r a c t i o n i n the flame m. flame r m flame The equation becomes 1 2 5 . dr dt T 1-r c Solving t h i s d i f f e r e n t i a l equation we obtain t - - x c * n ( l - r ) or = 1 -r e Now we express the reacted f r a c t i o n as a function of distance from the outer edge of the flame. This i s shown i n Figure A-4. where t' i s the time a f t e r entrainment of the flame. We can express the reacted f r a c t i o n i n terms of the distance through the flame. The mean reacted f r a c t i o n i s obtained by inte g r a t i n g t h i s function through the flame y = U t t ) dy and remembering that 6 = U t we get 126. T "T It r = 1 + ^  (e C C - l ) for 99% burned, t f c = 2.3 A/U^, and r = 1 + _ i _ ( e - 2 - 3 + l ) = 0.609 Now the average volume f r a c t i o n can e a s i l y be derived from the average mass f r a c t i o n V. = Pb b f r p. V. + p V K b b f *u u f 1 1 - p b / p u ( i - ¥ For P u / p ^ = 5, and defining d i f f e r e n t thresholds for flame thickness Table A - l has been prepared to show the trends of r and X , . It can be v o l seen that the mean volume f r a c t i o n l i e s i n the range 75-85%. Table A - l Comparison of Mass and Volume D i s t r i b u t i o n s Through Flame f o r Various D e f i n i t i o n s of Flame Thickness (Exponential Burning Law) % burned 6 r X v o l 0.90 1.15 X 0.406 0.774 0.95 1.5 X ut/u 0.482 0.823 0.99 2.3 X u X 0.609 0.886 127. 2.2 Geometric Considerations A second theory was developed based on the laminar burning of s p h e r i c a l pockets of i n i t i a l radius X. This argument i s purely geometric and i t s objective was to e s t a b l i s h a l i m i t i n g case i n the d i s t r i b u t i o n . The pockets are assumed to burn at laminr TJ . See Figure A-4. dmu -rr— = -p A U„ dt u u I We neglect the e f f e c t of compression on the unburned gas density i n the pockets. dR .*. R = X - U„t P A Thus the radius of the pockets decreases l i n e a r l y as a function of time. Once again we define y as the distance from the outer edge of the flame, and we express the pocket radius with respect to y. RP = x - u ; y Since R = 0 a t y = 6 , 6 = X 77— > and R = 4- (6-y) p 6 128 . To determine the r e l a t i v e volume of the pockets to the t o t a l volume i n the flame zone the following arguments are proposed. Lets take a section of the burning zone defined by the arc length X as shown i n f i g u r e A-5. We assume as a worst case that the volume of unburned pockets i n t h i s section i s that of a cone of base diameter 2X and height 6. The f r a c t i o n of unburned to t o t a l volume i n t h i s section i s obtained i n the following way: The radius of the flame s e c t i o n as a function of distance through the zone i s R f c " X ~ T- Y u The area of the flame s e c t i o n A, = TT R 2 f c f c The volume of the section i s thus calculated 6 V f c = TT / R 2 dy 0 = { ^ - [R 3 - (R X) 3] R 2 U U £ u The t o t a l pocket volume i s obtained i n the same way 129. 6 F i n a l l y the volume r a t i o i s derived V R 2 6 u u (R - 6 )3 u For 6 = 10 mm which i s a t y p i c a l observed thickness, the r a t i o i s p l o t t e d i n Figure A-6 against outer flame radius. We can see that i n t h i s worst case the minimum r a t i o i s around 70%. 3. I n i t i a l Mixture Composition Since the intake and exhaust strokes were not modelled, a few assumptions had to be made regarding these processes. For i n i t i a l pressure and temperature at bottom dead center, the motoring test assumptions were used. In c a l c u l a t i n g the composition of the mixture, the r e l a t i v e a i r f u e l r a t i o was f i r s t c a l c u l a t e d from gas flow rates and input to the program. The t o t a l number of moles was calculated TINTAKE BDC AMB n v T AMB BDC 130. P V = BDC BDC T 0 T = ^OL TBDC The r e s i d u a l f r a c t i o n was accounted for (assumed at 5%) i n c a l c u l a t i n g the molar f r a c t i o n of each specimen. The mass f r a c t i o n of each r e s i d u a l component was estimated by assuming complete combustion of the f u e l . H X(C + 7^) A [ l - F ] 0„ H res res_ 1 + 4.76 X(C + -A U2 The same type of c a l c u l a t i o n was performed for each component of the cy l i n d e r mixture. 4. Compression and Expansion Strokes For compression and expansion, the following three equations were solved using a Newton-Rapson method. E 2 = E1 ~ pAV + AQ E 2 = I x. e i ( T 2 ) P1V1 P2V2 T T 1 2 5. I n i t i a l and F i n a l Burning The entrainment equation i s r e c a l l e d 131. An approximate equation was needed f o r the f i r s t burning step since no unburned area was a v a i l a b l e . The i n i t i a l kernel i s very small and grows very r a p i d l y . It has a n e g l i g i b l e mass compared to the charge. For t h i s f i r s t step i t i s assumed that the density in s i d e the kernel i s the burned gas density and that density v a r i a t i o n s are small compared to the growth of the flame. d K V A dt = P u A u U T dp, dR V. — - + p A _-H - P A U_ f , u u dt u u T dt dR p = — u dt p b t F i n a l burn-up. Once the outer edge of the flame has engulfed the chamber, the d e f i n i t i o n of 6 i s no longer f e a s i b l e . In t h i s case, the simple burning rate equation i s used to describe the laminar burn-up of the remaining pockets. According to the exponential burning law, the rate of mass burned i s proportional to the amount of unburned gas l e f t i n the flame zone. d dt ~ x c 2 U L Amu = mu, — r — At 1 3 2 . This simple equation i s used up to complete burning of the charge which may be defined at a f i x e d percentage of the t o t a l mass i n the c y l i n d e r . 1 1 1 1 r r Figure A.1. Two dimensional vortex i n the unburned mixture. p b p u Figure A.2. Vortex bursting due to combustion. 135. Figure A.3. Burned mass f r a c t i o n i n flame zone. Figure A. 4. Laminal burning of s p h e r i c a l pocket 137 . Figure A.5. D e f i n i t i o n of unburned cone and flame zone cone; flame zone cone radius vs distance through flame. Figure A.6. Volume d i s t r i b u t i o n i n flame zone, 6 = 10 mm. APPENDIX B PRESSURE MEASUREMENTS — MOTORED TEMPERATURE CALCULATIONS Introduction 1. Pressure Data Reduction 2. Pressure Scaling 3. Temperature Calculations from Motored Pressure Data 4. Uncertainty Analysis 140 . Introduction The f i r s t part of t h i s appendix describes the procedures f o r averaging the pressure data for both motored and f i r e d experiments. The second part deals with the c a l c u l a t i o n s of motored c y l i n d e r temperatures which are needed to in t e r p r e t the hot wire data. The techniques used here were i n s p i r e d by previous work by Lancaster [8] and Witze [36]. The recommend-ations of Brown [43] and Lancaster et a l [44] for measurement and analysis techniques were c l o s e l y followed. B .1 Pressure Data Reduction As mentioned i n Chapter 4, one hundred consecutive cycles of pressure data were c o l l e c t e d at a rate of one sample per degree crank angle, f o r both motored and f i r e d engine conditions. The d i g i t i z e d voltages from the transducer were ensemble-averaged to obtain one mean curve f o r each engine operating condition. This method consists of averaging the instantaneous value at a given crank-angle over many cycles: Once the data i s reduced, the transducer c a l i b r a t i o n constant was applied to y i e l d r e l a t i v e pressure values. V(4>) = N E V(i,4>) i = l p kPa (<t>) = V(c)>) x 200 kPa Volt 1 4 1 . B .2 P r e s s u r e D a t a S c a l i n g S i n c e t h e p i e z o e l e c t r i c t r a n s d u c e r i s a r e l a t i v e p r e s s u r e m e a s u r i n g d e v i c e , t h e s e r e l a t i v e p r e s s u r e s were t h e n s h i f t e d by a c o n s t a n t v a l u e t o o b t a i n a b s o l u t e p r e s s u r e s . The mos t common p r o c e d u r e i s t o assume t h a t t h e p r e s s u r e a t BDC a t t he b e g i n n i n g o f t he c o m p r e s s i o n s t r o k e i s e q u a l t o t h e mean i n t a k e m a n i f o l d p r e s s u r e [43,44]. F o r w i d e - o p e n t h r o t t l e m o t o r i n g , t h i s a s s u m p t i o n was v e r i f i e d . However i t was found t h a t t h e f o l l o w i n g r e l a t i o n b a s e d o n t h e measu red v o l u m e t r i c e f f i c i e n c y l e d t o i d e n t i c a l BDC p r e s s u r e s a t w i d e - o p e n t h r o t t l e , and a l s o p r e d i c t e d p a r t t h r o t t l e as w e l l a s c o m b u s t i o n BDC p r e s s u r e s : D / * u n > "o T I N T A K E P k P a ( * = 3 6 0 ) - AMB n v - T — AMB F o r m o t o r i n g , i s o t h e r m a l f i l l i n g was assumed and t h e t e m p e r a t u r e r a t i o was 1. The v o l u m e t r i c e f f i c i e n c y may be d e f i n e d a s : 2 0 @ T P w a i r A M B ' AMB M o t o r i n g n = V V RPM 2 0 @ T P ^ w TOT A M B ' AMB F i r i n g TI = V V RPM T y p i c a l e x p e r i m e n t a l ensemble a v e r a g e d p r e s s u r e c u r v e s a r e shown i n F i g u r e B - l f o r b o t h m o t o r e d and f i r e d c o n d i t i o n s . T h e i r r e s p e c t i v e r e l a t i v e rms f l u c t u a t i o n s a r e a l s o p l o t t e d i n F i g u r e s B - 2 . 1 4 2 . B.3 Temperature Calculations From Motored Pressure Data As mentioned before, the pressure data were sampled once every degree crank angle. However the hot wire data were acquired every f i f t h of a degree crank angle. The mean pressure data were thus interpolated to generate 4 data values i n between each crank angle degree. This was done using smoothing and i n t e r p o l a t i n g routines SMOOTH and SMTH [45]. The f i t t e d curve was made to coincide with each r e a l data point. The f i n a l r e s u l t was a pressure data array which was used i n c a l c u l a t i n g the cy l i n d e r temperature, and i n analyzing the hot wire data. An assumption had to be made to choose a reference temperature. As mentioned, isothermal f i l l i n g was assumed so that the temperature at BDC at the beginning of compression stroke was set to ambient. This choice was reasonable as the cooling water was close to ambient during the motored t e s t s . Three options were investigated f o r temperature c a l c u l a t i o n s : 1) assume adiabatic compression and expansion, 2) determine the slopes of the log p vs log V curves to obtain o v e r a l l polytropic indices f o r compression and expansion, 3) assume adiabatic compression up to IVC and c a l c u l a t e temperatures from the perfect gas law for the compression and expansion strokes up to exhaust valve c l o s i n g (EVO). It was found that the l a s t method l e d to the l e a s t u n c e r t a i n t i e s i n peak temperatures. The adiabatic assumption leads to erroneous expansion temperatures as demonstrated by Witze [36]. F i t t i n g s t r a i g h t l i n e s to l o g pl o t s also y i e l d e d u n c e r t a i n t i e s i n the c r i t i c a l peak values of pressure and temperature. 1 4 3 . The perfect gas method gave best r e s u l t s , following more c l o s e l y the measured pressure values e s p e c i a l l y around TDC which i s a c r i t i c a l region f o r hot wire data c a l c u l a t i o n s i n engines. A b r i e f d e s c r i p t i o n of the c a l c u l a t i o n procedure follows. Ambient temperature was assumed at BDC on intake stroke T(* = 360) = T a m b Isentropic compression was assumed to IVC and the temperature from each previous step was used to c a l c u l a t e the i s e n t r o p i c index 1 -1 P2 Y T 2 - T ^ — ) y = C p C T ^ / C ^ ) The perfect gas law was then applied from IVC to EVO, P 2 V 2 T„ = T, •2 1 p i V l The r e s u l t i n g temperature array was used i n analyzing the hot wire data. The temperature curve corresponding to the pressure curve of Figure B - l i s plotted i n Figure B-3. The program written f o r ensemble averaging and c a l c u l a t i n g the temperatures i n PRESISAACTEMPPERF. The program that processes the f i r e d pressures i s FIREDPRES. 144 . B . 4 U n c e r t a i n t y A n a l y s i s The u n c e r t a i n t i e s a s s o c i a t e d w i t h e a c h i n s t r u m e n t u s e d i n t h i s p a r t o f t h e e x p e r i m e n t a r e l i s t e d i n T a b l e B - l . These combined u n c e r t a i n t i e s r e s u l t i n a 2% e r r o r i n t h e u n s e a l e d p r e s s u r e s . The p h a s i n g o f p r e s s u r e and c r a n k a n g l e was t h o r o u g h l y c h e c k e d as s u g g e s t e d by L a n c a s t e r e t a l [ 4 4 ] . A l s o c e r t a i n e v e n t s s u c h a s v a l v e o p e n i n g s and s p a r k a r e c l e a r l y v i s i b l e on s i n g l e c y c l e p l o t s a t t h e p r o p e r t i m e . The a s s u m p t i o n s u s e d i n s c a l i n g t h e p r e s s u r e and t e m p e r a t u r e d a t a i n v o l v e g r e a t u n c e r t a i n t i e s . I s e n t r o p i c c o m p r e s s i o n up t o IVC i s a l s o a m a j o r s o u r c e o f e r r o r . Thus i t i s e s t i m a t e d t h a t t h e u n c e r t a i n t y i n peak p r e s s u r e l i e s a r o u n d 5%. The u n c e r t a i n t y i n t e m p e r a t u r e i s f a r g r e a t e r a t 10-15%. These l a s t e f f e c t s ove r shadow t h e i n s t r u m e n t e r r o r . The a d v a n t a g e o f s i m u l t a n e o u s l y m e a s u r i n g a b s o l u t e p r e s s u r e s and t e m p e r a t u r e s i s c l e a r l y d e m o n s t r a t e d . T r a n s d u c e r K i s t l e r 6121 L i n e a r i t y ± 1.0% F S C h a r g e A m p l i f i e r K i s t l e r L i n e a r i t y ± 0.05% FS AVL O p t i c a l P i c k - u p 3 6 0 c / 6 0 0 A c c u r a c y 0 . 1 ° r e s o l u t i o n A i r f l o w measurement R i c h a r d A l c o c k v i s c o u s f l o w a i r me te r l i n e a r i t y < 3% N a t u r a l gas f l o w measurement Neuman L F E 50 M W 2 0 - 1 1 / 2 ± 0 . 5 % T a b l e B - 4 . U n c e r t a i n t y i n M e a s u r i n g I n s t r u m e n t s 4500 Figure B . l . Ensemble averaged motored and combustion pressures. Figure B .2. Relative rms fluctuations of pressures about the ensemble averaged mean. 150 -100 -50 0 50 100 Crank RngLe deg Figure B.3. Calculated motored temperatures. 150 200 APPENDIX C  HOT WIRE ANEMOMETER MEASUREMENTS Introduction 1. Thermal Equilibrium of Hot Wire 2. C a l i b r a t i o n of Hot Wire 3. Hot Wire Operation 4. S e n s i t i v i t y Analysis 5. Hot Wire Data Reduction 6. Uncertainty i n Hot Wire Measurements 149 . I n t r o d u c t i o n The t h e o r y b e h i n d t h e o p e r a t i o n o f t h e h o t w i r e has b e e n f u l l y d e s c r i b e d i n p r e v i o u s s t u d i e s [8,34,35,36]. The e q u a t i o n s d e s c r i b i n g t h e h e a t b a l a n c e o f t h e h o t w i r e a r e b a s e d o n r e s e a r c h p e r f o r m e d by C o l l i s and W i l l i a m s [34] and D a v i e s and F i s h e r [35] on h e a t t r a n s f e r f r o m e l e c t r i c a l l y h e a t e d c y l i n d e r s t o a m o v i n g f l u i d . The d e t a i l e d d e v e l o p m e n t o f t h e e q u a t i o n s u s e d i n t h i s work c a n be found i n L a n c a s t e r ' s [8] p a p e r . E v a l u a t i o n o f gas p r o p e r t i e s a t t h e mean gas t e m p e r a t u r e was b a s e d o n t h e f i n d i n g s o f W i t z e [36] i n h i s c r i t i c a l c o m p a r i s o n o f h o t w i r e anemometry t o l a s e r d o p p l e r v e l o c i m e t r y f o r e n g i n e f l o w measu remen t s . P r e s e n t e d i n t h i s a p p e n d i x a r e the m a i n a s s u m p t i o n s and e q u a t i o n s u s e d t o i n t e r p r e t h o t w i r e d a t a and d e t a i l s o f w i r e c a l i b r a t i o n and o p e r a t i o n . A l s o p r e s e n t e d a r e the a v e r a g i n g t e c h n i q u e and window s i z e a n a l y s i s . T a b l e C - l l i s t s t h e c h a r a c t e r i s t i c s o f t h e p r o b e and w i r e u s e d . T a b l e C - l W i r e C h a r a c t e r i s t i c s T S I P 12.5 P l a t i n u m I r i d i u m A l l o y 6.3 ym 1.5 mm 1 8 . 0 W/m-K 9 x l 0 _ l t ° C _1 C l T h e r m a l E q u i l i b r i u m o f H o t W i r e F i g u r e C - l shows t h e h e a t b a l a n c e o n a n e l e m e n t o f e l e c t r i c a l l y h e a t e d w i r e . The f o l l o w i n g a s s u m p t i o n s were made, ba sed on w i r e d i m e n s i o n s and p r o p e r t i e s : • The r a d i a l t e m p e r a t u r e g r a d i e n t i s n e g l i g i b l e Type M a t e r i a l s D i a m e t e r , d w ± r e L e n g t h , £ w i r e T h e r m a l C o n d u c t i v i t y , K w i r e T h e r m a l c o e f f i c i e n t o f R e s i s t a n c e , a 150. • The diameter and material properties are i n v a r i a n t along the wire length • Radiation from the wire to i t s surroundings i s n e g l i g i b l e • The thermal conductivity K . i s independent of the wire wxre temperature • The convective c o e f f i c i e n t h i s uniform on the whole wire surface The equation describing the heat balance of the wire and i t s surroundings can be written i n the following way: ^ e l e c t r i c ^conduction + ^convection where 3 2T . j. . ,. wire , Q j . , = A . K . dx ^conduction wxre wire „ o 9x^ Q „. = TT d . h (T . - T ) dx convection wxre wire gas I 2 P(T , ) • K V wire' , Q i ^ • = 1 d x e l e c t r x c A The wire r e s i s t i v i t y i s a function of the wire temperature: p . = p [1 + a(T . - T )1 H w i r e ^o 1 v wire o'J The values of K . , d . , 1 . are common to a l l wires and can be found wxre wxre' wire i n Table C - l . The value of p must be measured for each wire. o 1 5 1 . The heat balance equation i s a second order l i n e a r non-homogeneous d i f f e r e n t i a l equation which was solved [8] to give an expression f o r the wire temperature as a function of the distance from the center point: cosh ( /C~^ x) T . (x) = (T - C.) - + C. wire^ sup 1' c Q s h j— 1 x 2 wire where and C l IT d . 1 . h T + I 2 R (1 - a r ) wire wire gas T wo o_ TT d . 1 . h - I 2 R a wire wire wo C , 4 R I 2 a = 4 r h wo •> 2 K d L ir d 1 - " wire wire wire wire R P 1 • o wire wo A . wire The mean wire temperature was obtained by integrating t h i s temperature function along the wire. 2(T - C.) 1 , - v sup 1' , . /•— wire. , „ T w l r e = tanh (/C2 - g - ) + C x wire 2 This mean temperature i s assumed to be the equivalent temperature determined from the resistance of the hot wire. 1 5 2 . C . 2 C a l i b r a t i o n B e f o r e o p e r a t i o n , t h e r e s i s t a n c e o f t h e w i r e a t a m b i e n t t e m p e r a t u r e must be d e t e r m i n e d . The h o t w i r e b r i d g e was u sed t o measure t h e r e s i s t a n c e o f t h e w i r e , p r o b e and c a b l e a s s e m b l y . A s c h e m a t i c o f t h e b r i d g e c i r c u i t i s i l l u s t r a t e d i n F i g u r e C - 2 . R „ = R . + R V 1 + R m e a s u r e d w i r e c a b l e p r o b e The c a b l e and p robe r e s i s t a n c e s were measured s e p a r a t e l y . R = 0 . 2 8 5 fi c a b l e R , = 0 . 5 2 ft p robe Once the w i r e r e s i s t a n c e a t a m b i e n t was known, t he r e s i s t a n c e f o r any o p e r a t i n g t e m p e r a t u r e c o u l d e a s i l y be o b t a i n e d . R = R . / [ I + ot(T , - T )1 w w i r e ' 1 v amb o / J o amb R = R [1 + a ( T T )1 wop WQ L wop O -> The o p e r a t i n g t e m p e r a t u r e was c h o s e n a t 6 0 0 ° C as s u g g e s t e d by W i t z e [36] . C a l i b r a t i o n o f t h e anemometer s y s t e m was p e r f o r m e d a t a m b i e n t c o n d i t i o n s i n a w i n d t u n n e l . The a i r v e l o c i t y was measured w i t h a p i t o t t u b e . S i n c e mos t o f t h e p r e s e n t e d r e s u l t s were o b t a i n e d w i t h w i r e #3, t h e c a l i b r a t i o n c u r v e i s p r e s e n t e d f o r t h i s c a s e i n F i g u r e C - 3 . 153 . Since the anemometer was c a l i b r a t e d at ambient conditions, the heat balance equations were used to cal c u l a t e an o v e r a l l convection c o e f f i c i e n t h f o r each measured data point. A Nusselt vs. Reynolds numbers c o r r e l a t i o n was calculated for the c a l i b r a t i o n which was of the form: N N = A + B Re u Vd , hd . , _ wire , „ wire where Re = and Nu = —; v k gas gas The convection c o e f f i c i e n t h was solved for i t e r a t i v e l y and a curve f i t t i n g routine NL2S0L [45] was used to f i n d the best f i t c o e f f i c i e n t s A, B and N. These c a l c u l a t i o n s were performed by the program HWCAL2. C .3 Hot Wire Operation The hot wire voltage s i g n a l measured during engine motoring was d i g i t i z e d every f i f t h of a degree crank angle. The gas properties were evaluated at the mean pressure and temperature obtained from motoring pressure data (see Appendix A). This time the Nu vs Re c o r r e l a t i o n was used to c a l c u l a t e instantaneous v e l o c i t i e s f o r each data point i . e . 1800 times per engine re v o l u t i o n . These c a l c u l a t i o n s were performed by HOTWIRE. C .4 S e n s i t i v i t y Analysis Many researchers have conducted s e n s i t i v i t y a n alysis on the c a l c u l a t e d v e l o c i t i e s to varia t i o n s i n the gas temperature [8,36]. Since temperatures are c a l c u l a t e d from motored pressures there i s uncertainty e s p e c i a l l y at peak values at TDC. Compounding t h i s problem i s the fac t that the 1 5 4 . anemometer i s l e s s s e n s i t i v e to f l u c t u a t i o n s i n v e l o c i t y as the temperature difference between the wire and the f l u i d i s reduced. And f i n a l l y the turbulent i n t e n s i t y around top dead center i s of greatest i n t e r e s t to the engine researcher. Lancaster [8] estimated that using c a l c u l a t e d temperatures from measured pressures (based on a polytiropic r e l a t i o n s h i p ) added 10% to the uncertainty i n the v e l o c i t i e s . The method used here i s thought to estimate the actual mean cylinder temperature within 10-15%. A s e n s i t i v i t y a n alysis was conducted on the data using two d i f f e r e n t temperature curves but keeping the pressures v i r t u a l l y constant. At TDC the peak temperatures were the following: run 1 T T D C = 618 K run 2 T T D C = 587 K This resulted i n a 5% di f f e r e n c e . The r e s u l t i n g difference at TDC i s i n mean v e l o c i t y ~ 28% i n turbulent i n t e n s i t y ~ 24% The same s e n s i t i v i t y a n a l y s i s conducted on other data sets at d i f f e r e n t engine speeds led to s i m i l a r r e s u l t s . C .5 Hot Wire Data Reduction The cycle-by-cycle non-stationary time averaging method i s f u l l y described i n the paper by Catania and M i t t i c a [37], and w i l l be discussed very b r i e f l y here. 155. The instantaneous v e l o c i t y i n the engine can be thought of as a mean flow on which i s superimposed turbulent f l u c t u a t i o n s . U ± ( t ) = U i ( t ) + u ± ( t ) C.5.1 Mean V e l o c i t y U^(t) the mean v e l o c i t y f o r c y c l e i was determined i n the following way: A period or window s i z e was chosen. The instantaneous v e l o c i t y U^(t) was time averaged (using a trapezoidal rule) over the crank angle i n t e r v a l . This y i e l d e d an average v e l o c i t y value which was centered i n the window (see Figure C-4). Next a cubic spline was f i t t e d to these mean values to obtain a mean v e l o c i t y curve u\^(t) f o r cycle i . No attempt was made to adjust the mean v e l o c i t y curve so that f i t t e d curve and ac t u a l instantaneous v e l o c i t y curve had the same mean i n each window (as recommended by Catania and M i t t i c a ) . Instead an exact f i t to every window mean was used. The window mean of the f i t t e d curve was found to never diverge by more than 3% from the actual mean, and t h i s was judged s a t i s f a c t o r y i n view of the other u n c e r t a i n t i e s i n the measurements. The r e s u l t i n g mean v e l o c i t y curves (one per cycle) were ensemble averaged over a l l cycles to give the true mean v e l o c i t y <U i , window' > =\ I U ±(t+T) dT 1 N N U true (t) = Z U,(t) i = l 156 . C.5.2 Turbulence Intensity For each i n d i v i d u a l cycle, the f l u c t u a t i n g v e l o c i t y component was calculated from instantaneous v e l o c i t y and the f i t t e d mean v e l o c i t y curve (see Figure C-4) . The squared average i n t e n s i t y f o r each previously defined window was then calculated as follows: 1 T <u' , . 2> = i f u 2(t+x) dx .window 0 1 1 = | J [U ±(t+T) - U . ( t + t ) ] 2 d t Next these squared average i n t e n s i t i e s were ensemble averaged over the N cycles, and the root extracted. 1 N <u' . > - / i - Z <u' , . 2> ,window N ,window A cubic spline was then f i t t e d to the mean window turbulence i n t e n -s i t i e s f o r graphing purposes. C.5.3 Window Size For a n a l y s i s purposes, we separate the instantaneous v e l o c i t y i n t o two components: U ± ( t ) = U ± ( t ) + u ± ( t ) 157 . Transport on a scale that i s comparable to c y l i n d e r dimensions i s att r i b u t e d to the mean v e l o c i t y , while mixing on a much smaller scale i s a t t r i b u t e d to turbulent f l u c t u a t i o n s . The choice of the averaging window si z e establishes a frequency cut-off point between mean v e l o c i t y and f l u c t u a t i o n s . I f the window i s too small there i s loss of higher frequency informa-t i o n as turbulence i s interpreted as mean flow v a r i a t i o n s and u' i s under-estimated. If the window i s chosen too large the mean flow patterns are att r i b u t e d to turbulent f l u c t u a t i o n s and we tend to overestimate u'. Catania and M i t t i c a [37] recommend that the choice of an appropriate window size be made by reducing the data over a number of window sizes and s e l e c t i n g the best r e s u l t . They found that 8 degrees at 1600 RPM was the best choice which corresponds to a time scale 0.9 msec t y p i c a l l y much larger than the d i s s i p a t i v e time scales. Our r e s u l t was a l s o 8 degrees at a l l engine speeds. Table C-2 shows the time associated with each window s i z e . Table C-2 Time Associated With Each Window Size Engine Speed RPM Time (msec) 2° 4° 6° 8° 10° 12° 15° 1200 1800 2400 3000 0.278 0.185 0.139 0.111 0.556 0.370 0.278 0.222 0.833 0.556 0.417 0.333 1.111 0.741 0.556 0.444 1.389 0.926 0.694 0.556 1.667 1.111 0.833 0.667 2.083 1.389 1.042 0.833 Figures C-5 to C-12 present the window analysis for wide open t h r o t t l e at the four engine speeds. I t i s i n t e r e s t i n g to note how the non-158 . stationary averaged i n t e n s i t i e s are reduced i n comparison to the ensemble averaged rms f l u c t u a t i o n s , i n d i c a t i n g s u b s t a n t i a l c y c l i c v a r i a t i o n s . A f o r t r a n program (HOTWIREREDUCTION) was wr i t t e n to perform ensemble as well as non-stationary time averaging. C.6 Uncertainty i n Hot Wire Measurements Tabaczynski [42] stated r i g h t l y that hot wire measurements can at best be interpreted q u a l i t a t i v e l y . Many uncertainties l i e i n the fac t that the wire has no d i r e c t i o n a l r e s o l u t i o n or i n the task of separating f l u c t u a -tions from mean v e l o c i t y when there i s l i t t l e or no mean flow. However, Tabaczynski mentions that up to now l a s e r doppler measurements have confirmed hot wire findings i n magnitude and trend. The inherent uncertainty i n the measurement technique i s compounded i n th i s experiment by the proximity of the wire to the wall and the i r r e g u -l a r i t y of the chamber i t s e l f . The hump i n turbulent i n t e n s i t i e s a f t e r top dead center i s an example of data behaviour d i f f i c u l t to explain. Since we must put numbers i n the estimation of uncertainty, a approxi-mate estimate i s 50-70% error on the magnitude of both mean v e l o c i t y and rms f l u c t u a t i o n s i s proposed. 159 . 160. Figure C . 2 . Anemometer bridge c i r c u i t . 1.2-1 4 5 Reynolds Nb Figure C.3. Hot wire c a l i b r a t i o n curve. Figure C.4. Def i n i t i o n s of mean window v e l o c i t y , f i t t e d true mean v e l o c i t y , rms window i n t e n s i t y and true rms in t e n s i t y . 60-1 40 co 1 o o c CO CD 2 30-Legend A Ensemble Averaged X 6 deg window _ • 8 deg window H 10 deg window H 12 deg window_ X ]5_dej_wjndow • 18 deg window BDC -150 -120 -90 -30 TDC 30 Crank Angle deg Figure C.5. Comparison of ensemble averaged mean v e l o c i t y with true mean v e l o c i t y obtained by non-stationary cycle-by-cycle analysis using various window size s , 1200 rpm, baseline p o s i t i o n . BDC ON CO Legend A Ensemble Averaged X 6 deg window • 8 deg window  G3 10 deg window _ ffi 12 deg window * 16 jiejj ^ window • 18 deg window _ l 1 1 T -140 -120 -100 -80 -60 •40 -20 TDC 20 40 Crank Angle deg 120 140 Figure C.6. Comparison of ensemble averaged turbulence i n t e n s i t y with i n t e n s i t y obtained by non-stationary cycle-by-cycle analysis using various window s i z e s , 1200 rpm, baseline p o s i t i o n . BDC -150 Figure C.7, -30 TDC 30 Crank Angle deg Comparison of ensemble averaged mean v e l o c i t y with true mean ve l o c i t y obtained by non-stationary cycle-by-cycle analysis using various window si z e s , 1800 rpm, baseline p o s i t i o n . 180 ON 10 8 £ CO c c tn Legend A Enaemble Averaged X 8 deg window • 8 deg window  E3 10 deg window _ X 16^egj « indow -i 1 T -140 -120 -100 -80 -60 •40 -20 TDC 20 40 Crank Angle deg 120 140 Figure C.8. Comparison of ensemble averaged turbulence i n t e n s i t y with i n t e n s i t y obtained by non-stationary cycle-by-cycle analysis using various window s i z e s , 1800 rpm, baseline p o s i t i o n . 50 Legend 0 I i h 1 1 1 1 1 1 i 11 i f BDC -150 -120 -90 -60 -30 TDC 30 60 90 120 150 BDC Crank Angle deg O N Figure C.9. Comparison of ensemble averaged mean v e l o c i t y with true mean v e l o c i t y obtained by non-stationary cycle-by-cycle analysis using various window s i z e s , 2400 rpm, baseline p o s i t i o n . 12 -r 10 8-L e g e n d A Ensemble Averaged X 6 deg window • 8 deg window G3 10 deg window K !? fieg window X 15^eg^|ndow * lf..deJ..,^i!L<!.ow_ OH r -140 -120 -100 -40 -20 TDC 20 40 Crank Angle deg i i 60 80 100 120 140 <JN 00 Figure C.10. Comparison of ensemble averaged turbulence i n t e n s i t y with i n t e n s i t y obtained by non-stationary cycle-by-cycle analysis using various window s i z e s , 2400 rpm, baseline p o s i t i o n . 50-1 0 | i 11 i i i i I I i i i BDC -150 -120 -90 -60 -30 TDC 30 60 90 120 150 BDC Crank Angle deg CTN Figure C . l l . Comparison of ensemble averaged mean v e l o c i t y with true mean v e l o c i t y obtained by non-stationary cycle-by-cycle analysis using various window s i z e s , 3000 rpm, baseline p o s i t i o n . 14 12 10 Legend A Ensemble Averaged X 8 deg window • 8 deg window 0 10 deg window _ ffl 12 deg window X 15 jleg j*jndo w • 18 deg window _ -140 Figure C.12, -40 -20 TDC 20 40 Crank Angle deg Comparison of ensemble averaged turbulence i n t e n s i t y with i n t e n s i t y obtained by non-stationary cycle-by-cycle analysis using various window s i z e s , 3000 rpm, baseline p o s i t i o n . 140 o APPENDIX D RICARDO HYDRA GEOMETRY CALCULATIONS Introduction 1. Hydra Geometry and Approximate Geometry 2. Integration Procedure 3. I n t e r s e t i o n of Flame and E l l i p t i c Clearance Volume 3.1 Geometric Relations 3.2 AFS1 - Area of Int e r s e c t i o n 3.3 GAMMA1 - Angle of In t e r s e c t i o n 3.4 WPER1 - Wetted Perimeter 4. In t e r s e c t i o n of Flame and C y l i n d r i c a l Volume 4.1 Geometric Relations 4.2 AFS2 - Area of Int e r s e c t i o n 4.3 GAMMA2 - Angle of In t e r s e c t i o n 4.4 WPER2 - Wetted Perimeter 5. Solving the I n t e g r a l 1 7 2 . Introduction This s e c t i o n reports the development of equations describing the i n t e r s e c t i o n of a sph e r i c a l flame (centered at the spark location) and the Hydra combustion chamber. Two parameters a f f e c t i n g the geometry: flame radius and crank p o s i t i o n were varied to encompass a l l possible geometries encountered during r e a l engine operation. For each case the volume enclosed by the flame, the flame area and the wetted cylinder wall area were ca l c u l a t e d . A l l t h i s information was then w r i t t e n to a 3-dimensional array which would be accessed by the simulation program. 1. Hydra Geometry and Approximate Geometry The Ricardo Hydra c y l i n d e r head was i l l u s t r a t e d schematically i n Figure 7. Note the spark plug l o c a t i o n at a 45 degree angle at one side of the head. On the other side i s an access port f o r a pressure transducers. To f a c i l i t a t e the c a l c u l a t i o n s , the complex shaped clearance volume was modelled as an e l l i p t i c a l c y l i n d e r of equal height and volume. The approximate chamber geometry was i l l u s t r a t e d i n F i g . 8. The large axis of the e l l i p s e i s the c y l i n d e r bore; the short axis was calculated as follows: (see Figure D-l for symbol d e f i n i t i o n ) V = V clearance approximate = TT a b h c V , , clearance b = r IT a h c = 31.571 mm For the approximate chamber, the spark i s located at the top corner of the head. The er r o r introduced by t h i s s i m p l i f i e d geometry i s judged 1 7 3 . minimal compared to other assumptions such as flame s p h e r i c i t y and f i x e d center of propagation. This has been discussed i n the model chapter. 2. Integration Procedure The following formulas r e f e r to F i g . D - l . Volume Integration dV = d(rcos6) rcos6dydz = Area(z) dz = AFSl(z) dz i n clearance region = AFS2(z) dz i n cylinder region Flame Area Intersection dA = r d9 rcos6 dy = r dy dz at each z = constant plane, y varies from -y to +y due to flame symmetry = 2r y dz A = 2r / y dz 2r J GAMMAl(z) dz i n clearance region 2r / GAMMA2(z) dz i n c y l i n d e r region Wetted Area Integration dA = Perimeter (z) dz = WPERl(z) dz i n clearance region = WPER2(z) dz i n c y l i n d e r region 174 . Integration L i m i t s These l i m i t s apply for a l l c a l c u l a t i o n s : volume, flame area and wetted c y l i n d e r w a l l area. See F i g . D-2 f o r i l l u s t r a t i o n of the 3 possible geometries. If R- < h t c h Volume enclosed by flame i s c VOLUME = f AFSl(z) dz , , -, JQ V ' i n clearance region; Case 1 I f R, > h r c V0L1 = / AFSl(z) dz 0 Volume enclosed by flame i n clearance region If R f < h V0L2 = / AFS2(z) dz h c Volume enclosed by flame i n cylinder area, flame hasn't h i t piston; Case 2 If R r > h h V0L2 = / AFS2(z) dz flame has h i t piston; Case 3 h Volume = V0L1 + V0L2 The same l i m i t s apply for flame area and wetted area i n t e g r a t i o n . 1 7 5 . 3. Intersection of Flame and E l l i p t i c a l Clearance Volume 3.1 Geometric Relations The following r e l a t i o n s are derived from the geometry as shown i n F i g . D-3. Lets take a section z 1 1 r2 = r f 2 - Z2 2 rsin-y = Rsing 3 b = rcosy + rcos3 4 R 2 [ b 2 c o s 2 e + a 2sin20] = a 2 b 2 5 6 = TT/2 - 3 3 < IT/2 6 = B - IT/2 3 > TT/2 where R^ : flame radius z : v e r t i c a l p o s i t i o n w/r to top of chamber a : Bore/long axis of e l l i p s e b : short axis of e l l i p s e R : E l l i p s e Radius r : projected flame radius i n z=const plane Y,3,6 J angles as defined i n Figure D-3 These r e l a t i o n s are v a l i d for a l l r a d i i subject to the r e s t r i c t i o n s 0 < r < 2b i . e . the projected flame does i n t e r s e c t the e l l i p s e . These f i v e equations can be reduced to the following expressions: 176. R 2 = - f ± \ /B 2 - 4C with B = 2 ( b 2 - r 2 ) + 4 b <* (a2-b2) C = ( b 2 - r 2 ) 2 _ _4_a£b^ (a2-b2) and f i n a l l y the angles are deduced. -1 u r b 2 ( a 2 - R 2 ) n l / 2 i 6 = cos  |± [ — t-J } R2 ( a2-b 2) i f r > /aT+b2" then 3 > TT/2, take negative sig n - i rb r. _ ra 2-R 2 1/2 y = cos 1 {- [1 + ( — — ] ]} a^-b^ i f 3 > TT/2, take p o s i t i v e sign. 3.2 AFS1 - Area of Inte r s e c t i o n In t h i s section, equations f o r the area of i n t e r s e c t i o n of the projected flame and e l l i p s e are developed. The basic problem i s to c a l c u l a t e the area of a sec t i o n of an e l l i p s e . Refer to F i g . D-4. TOTAL AREA of e l l i p s e : nab AREA of 1/4 e l l i p s e : irab/4 R 6 A - / / r dr d6 0 0 0 1 7 7 . Using a previously derived r e l a t i o n : we get r 2 ( b 2 C 0 S 2 6 + a 2 s i n 2 e ) = a 2 b 2 • 1 + ( — - l ) s i n 2 e b 2 a 2 / l + Q 2sin 2 e Q2 - - - - 1 b 2 6 R A = / de / r dr 0 0 8 R2 0 e a_2 r u d6 2 0 (1 + Q2 sin2e) This i n t e g r a l can be found i n a handbook. 1 9 A = t a n - 1 [7140.2 tane] B /1+Q2" 0 — - t a n " 1 (T~ tan6) / b Now we can express the area of the e l l i p s e swept by angle 3 (Fig* D-4). 1 7 8 . 23 = ~~2~ t a n "b t a n e ^ for 3 > TT/2, take p o s i t i v e s i g n F i n a l l y the area intersected by the projected flame area and the e l l i p s e : AFS1 i s obtained by summing the following areas (see Figure D-5). AFS1 = Area of c i r c l e swept by 2y y r 2 - Area of t r i a n g l e ABC r 2 s i n y c o s y nab — T , a + Area of e l l i p s e swept by 23 — ; J — + abtan 1 (-g tan6) + Area of t r i a n g l e BCD R 2 sin3cos3 AFSl(z) = y r 2 - r 2 s i n y c o s y + + ab tan - 1(-|- tan9) - R 2sin3cos3 f o r 3 < TT/2 top sign and 9 = TT/2-3 3 > TT/2 bottom sign and 6 = 3~TT/2 3.3 GAMMA1 - Angle of Inte r s e c t i o n In Section 2 of t h i s appendix an expression was developed f o r the flame area A = 2Rf / y dz In the clearance region, the integrand i s simply y and i s r e f e r r e d to as GAMMAl(z). 3.4 WPER1 - Wetted Perimeter In t h i s case, the basic problem i s to c a l c u l a t e the perimeter of a section of the e l l i p s e . See F i g . D-6. 179. ^ e l l i p s e ~ 2TT/-|- (a 2+b 2) approximate equation e P = a f / l - K 2 s i n 2 0 d6 exact equation 6 0 /a*-b z with K = - — — This i s an e l l i p t i c a l i n t e g r a l of the second kind and i s tabulated. To solve the i n t e g r a l i n our program, the integrand was expressed as a binomial s e r i e s , and the in t e g r a t i o n was performed term by term. [1 + ( - K 2 s i n 2 e ) ] l / 2 = 1 - ^ - K 2 s i n 2 6 - K^sin^e - -^j^r K&sin6e L J 2 2.4 2.4.6 Integrating term by term and a f t e r algebraic manipulation we get e / (1 - K 2 s i n 2 6 ) 1 / 2 d6 = 0.893596 + 0.05464 sin26 - 7.164xl0 - l t sin4e 0 + 7.574xl0 - l t sinSecose + 1.144xl0 - l tsin 7 e cos6 - G(6) P a = a G(9) 1 8 0 . This equation was v e r i f i e d against tabulated values. F i n a l l y the expression for the perimeter of the e l l i p s e section formed by i n t e r s e c t i o n with the projected flame i s : (Refer to F i g . D-6). WPERl(z) = e l ^ ± p s e + 2a G(6) for 3 < TT/2 top sign and 6 = TT/2 - 3 3 > TT/2 bottom sign and 6 = 3 - TT/2 4. I n t e r s e c t i o n of Flame and C y l i n d r i c a l Volume 4.1 Geometric Relations These r e l a t i o n s are derived f o r the geometry shown i n F i g . D-7. 1 r * = r f 2 - z2 2 r siny = a sin3 3 a cos3 + r cosy = b These equations are v a l i d f o r a l l r a d i i subject to the r e s t r i c t i o n : a-b < r < a+b i . e . , the flame must i n t e r s e c t the c i r c l e of radius a. These equations are reduced to y i e l d expressions f o r the angles: = cos _ ! ra2+b2- r2 1 L 2ab J 181. - i r b 2 - a 2 + r 2 i Note that when r < a-b 3 = 0 y = n r > a+b 3 = ir y = 0 4.2 AFS2 - Area of Intersection The equations f o r area of i n t e r s e c t i o n are developed i n the same way as f o r the clearance area. Refer to F i g . D-9 For a-b < r < a+b AFS2 = Area of flame c i r c l e swept by 2y y r 2 ± Area of t r i a n g l e ABC + r 2 sinycosy + Area of c y l i n d e r c i r c l e swept by 23 3a 2 + Area of t r i a n g l e BCD ± a 2 sin3cos3 AFS2 = y r 2 - r 2 s i n y c o s y + 3a 2 - a 2sin3cos3 0 < g < TT for r < a-b AFS2 = i r r 2 4.3 GAMMA2 - Angle of Inte r s e c t i o n As before A = 2R f / y dz GAMMA2(z) = y a-b < r < a+b GAMMA2(z) = ir r < a-b 1 8 2 . 4.4 WPER2 - Wetted Perimeter It can e a s i l y be shown from F i g . D-7 that: WPER2(z) = 26a a-b < r < a+b WPER2(z) =0 r < a-b If the flame has touched the piston, the area intersected on the piston must be added to the wetted w a l l area. I f R f > h Wetted piston area = AFS2 (r f=h) h u c h A t r I WPERl(z) dz + / WPER2(z) dz + AFS2(h) wetted Q h c 5. Solving the Integral The expressions were integrated numerically using the i n t e g r a t i o n + routine CADRE [46]. This routine uses a cautious adaptive Romberg extrapolation which can handle d i s c o n t i n u i t i e s of slope i n the integrand function. Figures D-8 to D-10 are p l o t s of non-dimensionalized flame volume, area and wetted area. The non dimensionalizing parameters are for Volume: VOLCYL = Cylinder volume at given crank angle degree f o r flame area: AWPCYL = Area of a hemisphere of radius equal to each cylinder radius f o r wetted area: AWPCYL = T o t a l area of cy l i n d e r i n c l u d i n g head, walls and piston at a given crank angle These parameters were taken from the B l i z a r d & Keck paper [23]. Figure D.l. Integration Coordinates. 1 8 4 . Figure D.2. Integration l i m i t s . 1 8 5 . 1 8 < IT/2 2 g > TT/2 t 1 1 1 Figure D.3. Geometry: clearance volume. 3 ^ TT/2 Figure D.4. Area of e l l i p s e sections. Figure D.5. Flame i n t e r s e c t i o n areas. Figure D.6. E l l i p s e perimeter intersected. e « TT/2 B > TT/2 Figure D . 7 . Geometry: c y l i n d e r volume. CYL.HEIGHT C/A A H=14.2S0 C/A=0 x H=16.184 C/A=15 • H=21.776 C/A =30 • H =30.427 C/A=45 • M=4t2M___C/» f60 . . . . M ^i^ 4 0 _ _ C ^ A = 7 5 _ _ • HfS-LO.8.' fa*???...-0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 NON DIMENSIONAL FLAME RADIUS Rf/ZMAX l.l re D.8. Non-dimensional flame volume vs non-dimensional flame radius. 0.8 0.0 | & CYLHQGHT C/A & H-14.a»0 C/»»0 H°l«l«4 C/*«B • H=30.«2? C/X»4> • tttV?.^ .....^ .?*?.... » t«3J4?__C^»=75__ » («f«i5«!_..e^.;»o I I I I I 0.1 0.2 0.3 0.4 0.5 NON DIMENSIONAL FLAME RADIUS RF/ZMAX \ \ \ \ \ \ ' 0.6 0.7 0.8 0.9 \ 1.1 Figure D.9. Non-dimensional flame front area vs non-dimensional flame radius (/// / CYL???????????1 A H=14.2S0 C/A -0 x H-16.184 C/A=I5  o H=21.776 C/A=iO • H=S0.427 C/A-4S x H=53J40 C f^c=75 • *!f?.;L??.l_.<?/*=?P. 0.3 0.4 O.S 0.6 0.7 0.8 0.9 NON DIMENSIONAL FLAME RADIUS RF/ZMAX i.i Figure D.10. Non-dimensional wetted cylinder area vs non-dimensional f l radius. 

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