UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

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

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1986_A7 B64.pdf [ 6.67MB ]
Metadata
JSON: 831-1.0096891.json
JSON-LD: 831-1.0096891-ld.json
RDF/XML (Pretty): 831-1.0096891-rdf.xml
RDF/JSON: 831-1.0096891-rdf.json
Turtle: 831-1.0096891-turtle.txt
N-Triples: 831-1.0096891-rdf-ntriples.txt
Original Record: 831-1.0096891-source.json
Full Text
831-1.0096891-fulltext.txt
Citation
831-1.0096891.ris

Full Text

TURBULENT COMBUSTION OF G A S - A I R MIXTURES I N A SPARK I G N I T I O N ENGINE  by JULIE  BOISVERT  A T H E S I S SUBMITTED I N P A R T I A L FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF A P P L I E D SCIENCE  in THE FACULTY OF GRADUATE STUDIES Department  We a c c e p t  of Mechanical E n g i n e e r i n g  this  to the  thesis  required  as c o n f o r m i n g standard  THE U N I V E R S I T Y OF B R I T I S H COLUMBIA June,  1986  © J U L I E BOISVERT,  1986  In  presenting  requirements of  British  it  freely  agree for  this  thesis  i n partial  f o r an advanced  Columbia, I agree available  that  that  f o rreference  permission  scholarly  degree  f o rextensive  fulfilment of the at the University  the Library  shall  and study.  I  copying  p u r p o s e s may b e g r a n t e d  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 .  understood  that  for  financial  copying  gain  or publication  shall  of  n o t be a l l o w e d  )\&g\Acm\caA  The U n i v e r s i t y o f B r i t i s h 2075 Wesbrook P l a c e Vancouver, Canada V 6 T 1W5  Date  i> O b jg(p  thesis  o f my  I t i s thesis  w i t h o u t my  ^ n c ^ n e e n ^ Columbia  of this  of this  permission.  Department  further  by t h e head  department  make  written  ABSTRACT  An engine s i m u l a t i o n model has been developed t o d e s c r i b e combustion  of g a s - a i r m i x t u r e s i n a s p a r k - i g n i t i o n engine.  i n c o r p o r a t e s a t u r b u l e n t entrainment combustion  turbulent  The model  theory proposed  by  Daneshyar and H i l l which i s based on Tennekes' model of t u r b u l e n c e and the v o r t e x b u r s t i n g p r i n c i p l e of Chomiak. t u r b u l e n t entrainment.  Flame p r o p a g a t i o n was  based  on  The flame was m o d e l l e d as a t h i c k s p h e r i c a l s h e l l  composed of burned and unburned  gases.  I n s i d e the t h i c k flame, pockets of  i n i t i a l s i z e A, the T a y l o r m i c r o s c a l e , a r e consumed a t a r a t e of the o r d e r of  the laminar burning v e l o c i t y .  To compare the model t o e x p e r i m e n t a l  data, t u r b u l e n c e l e v e l s were measured i n a motored R i c a r d o Hydra u s i n g hot wire anemometry. p i e z o e l e c t r i c transducer. predicting  Combustion  p r e s s u r e data were measured w i t h a  R e s u l t s i n d i c a t e t h a t the model i s s u c c e s s f u l i n  trends i n o v e r a l l combustion  a i r - f u e l r a t i o are v a r i e d .  engine  r a t e s when the engine speed  The model a l s o p r o v i d e d i n s i g h t i n t o the  s t r u c t u r e of t u r b u l e n t flames i n e n g i n e s .  - i i -  and  TABLE OF CONTENTS Page  Abstract L i s t of Figures L i s t of T a b l e s Nomenclature Acknowledgements  i i v xi x i i xvii  1.  INTRODUCTION  1  2.  REVIEW OF PREVIOUS WORK  5  2.1  A B r i e f Summary o f E x p e r i m e n t a l F i n d i n g s  5  2.2  Review of the T h i n Flame Model  8  2.3  T u r b u l e n t Entrainment Models  9  2.4  Background on the T u r b u l e n t Entrainment Model 2.4.1 T u r b u l e n t Entrainment V e l o c i t y 2.4.2 T h i c k Burning Zone  3.  4.  TURBULENT ENTRAINMENT  ENGINE SIMULATION MODEL  10 10 11 13  3.1  I n i t i a l Conditions  13  3 .2  Compression  13  3.3  Combustion C a l c u l a t i o n s 3.3.1 Assumptions 3.3.2 Governing E q u a t i o n s 3.3.3 Geometric C o n s i d e r a t i o n s 3.3.4 T h i c k Burning Zone M o d e l l i n g 3.3.5 Laminar B u r n i n g V e l o c i t y 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 3.3.7 Heat L o s s C a l c u l a t i o n s 3.3.8 I g n i t i o n Delay 3.3.9 S p 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 B u r n i n g 3.3.10 S o l v i n g Scheme  and Expansion  13 14 15 16 16 17 18 18 19 19 20  EXPERIMENTAL INVESTIGATION  21  4.1  Objectives  21  4.2  Instrumentation 4.2.1 Engine D e s c r i p t i o n 4.2.2 P r e s s u r e Measurements 4.2.3 Hot Wire Measurements 4.2.4 Crank Angle Measurements 4.2.5 Data A c q u i s i t i o n 4.2.6 Other Measurements  21 21 23 23 23 24 24  - i i i-  TABLE OF CONTENTS  (Continued) Page  4.3  Motoring Tests 4.3.1 Procedure 4.3.2 Results  4.4  5.  6.  and D a t a A n a l y s i s  24 24 26  Combustion Tests 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 4.4.2 Results  27 27 28  SIMULATION PROGRAM RESULTS  30  5.1  Comparison 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 5.1.2 5.1.3 5.1.4  30 32 32 33  Mass F r a c t i o n Burned C u r v e s Pressure Histories Combustion I n i t i a t i o n Combustion D u r a t i o n  5.2  Model P r e d i c t i o n s 5.2.1 Flame T h i c k n e s s 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 5.2.3 Thermodynamic and G e o m e t r i c P r o p e r t i e s 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  5.3  P a r a m e t r i c Study 5.3.1 E f f e c t o f Volume D i s t r i b u t i o n i n the T h i c k Flame 5.3.2 Effect of C Factor i n Turbulent Burning Equation 5.3.3 Integral Length Scale  DISCUSSION 6.1 6.2 6.3  34 34 35 35 35 .. ..  OF UNCERTAINTIES  37 37 38 38 39  Model Assumptions E x p e r i m e n t a l Measurements Interpretation of Results  39 41 41  7.  CONCLUSIONS  43  8.  RECOMMENDATIONS  45  REFERENCES  46  APPENDICES A : TURBULENT ENTRAINMENT MODEL - ENGINE SIMULATION PROGRAM . . . .  120  B:  139  PRESSURE MEASUREMENTS - MOTORED TEMPERATURE CALCULATIONS  ...  C : HOT WIRE ANEMOMETER MEASUREMENTS  148  D : RICARCO HYDRA GEOMETRY CALCULATIONS  171  -  iv  -  LIST OF FIGURES Page  1.  Microshadographs of flame f r o n t s measured by Smith  2.  Flame photographs taken by Namazian e t a l . [31] i n the MIT square p i s t o n engine  3.  Schematic of the Tennekes model; d e f i n i t i o n of length  [40]  50  51  turbulent  scales  52  4.  Schematic of t u r b u l e n t  combustion as shown by T a b a c z y n s k i [44]  5.  Schematic of the t h i c k combustion zone  6.  Compression and expansion c a l c u l a t i o n s  7.  R i c a r d o combustion chamber from manufacturer  53 54  flowchart  55  supplied  drawings  56  8.  Approximate  combustion chamber geometry  9.  Combustion  10.  Engine t e s t i n g f a c i l i t i e s  11.  Photograph of the p r e s s u r e t r a n s d u c e r mounted i n the  calculations  flowchart  57 58 59  c y l i n d e r head  60  12.  Hot w i r e anemometer measuring p o s i t i o n s  61  13.  Photograph of the hot w i r e probe l o c a t i o n  62  14.  Mean v e l o c i t y as a f u n c t i o n of crank a n g l e degrees f o r a l l i n v e s t i g a t e d engine speeds, b a s e l i n e p o s i t i o n T u r b u l e n c e i n t e n s i t y as a f u n c t i o n of crank angle degrees f o r a l l i n v e s t i g a t e d engine speeds, b a s e l i n e p o s i t i o n  63  15. 16.  17.  18.  19.  64  R e l a t i v e t u r b u l e n c e i n t e n s i t y as a f u n c t i o n of crank a n g l e degrees f o r a l l i n v e s t i g a t e d e n g i n e speeds, b a s e l i n e p o s i t i o n  65  Mean v e l o c i t y at 30° BTDC and a t top dead c e n t e r as a f u n c t i o n o f engine speed, b a s e l i n e p o s i t i o n  66  T u r b u l e n c e i n t e n s i t y a t 30° BTDC and a t top dead c e n t e r as a f u n c t i o n o f engine speed, b a s e l i n e p o s i t i o n  67  Comparison of top dead c e n t e r t u r b u l e n c e i n t e n s i t y w i t h o t h e r i n v e s t i g a t o r s ' r e s u l t s , from Bopp e t a l . [7]  68  - v -  LIST OF FIGURES  (Continued) Page  20.  Effect  21.  E f f e c t of p o s i t i o n along the spark plug a x i s on t u r b u l e n c e i n t e n s i t y a t 1200 rpm  70  E x p e r i m e n t a l p r e s s u r e curves a t 1200 rpm f o r t h r e e a i r - f u e l ratios  71  E x p e r i m e n t a l p r e s s u r e curves a t 1800 rpm f o r t h r e e a i r - f u e l ratios  72  E x p e r i m e n t a l p r e s s u r e curves a t 2400 rpm f o r t h r e e a i r - f u e l ratios  73  E x p e r i m e n t a l p r e s s u r e curves a t 3000 rpm f o r t h r e e a i r - f u e l ratios  74  Mass f r a c t i o n burned curve c a l c u l a t e d from e x p e r i m e n t a l p r e s s u r e s a t 1800 rpm f o r t h r e e a i r - f u e l r a t i o s  75  I n d i c a t e d mean e f f e c t i v e p r e s s u r e as a f u n c t i o n of a i r - f u e l r a t i o s f o r a l l o p e r a t i n g speeds  76  Brake mean e f f e c t i v e p r e s s u r e as a f u n c t i o n of a i r - f u e l r a t i o s f o r a l l o p e r a t i n g speeds  77  Comparison of c a l c u l a t e d and e x p e r i m e n t a l mass burned f o r 1200 rpm, X = 1.01  fraction 78  Comparison of c a l c u l a t e d and e x p e r i m e n t a l mass burned f o r 1200 rpm, X = 1.16  fraction  Comparison of c a l c u l a t e d and e x p e r i m e n t a l mass burned f o r 1200 rpm, X = 1.27  fraction  Comparison of c a l c u l a t e d and e x p e r i m e n t a l mass burned f o r 1800 rpm, X = 1.00  fraction  Comparison of c a l c u l a t e d and e x p e r i m e n t a l mass burned f o r 1800 rpm, X = 1.15  fraction  Comparison of c a l c u l a t e d and e x p e r i m e n t a l mass burned f o r 1800 rpm, X = 1.28  fraction  Comparison of c a l c u l a t e d and e x p e r i m e n t a l mass burned f o r 2400 rpm, A = 1.04  fraction  Comparison of c a l c u l a t e d and e x p e r i m e n t a l mass burned f o r 2400 rpm, X = 1.20  fraction  22.  23.  24.  25.  26.  27.  28.  29.  30.  31.  32.  33.  34.  35.  36.  of wire o r i e n t a t i o n  on t u r b u l e n c e i n t e n s i t y  - vi -  a t 1200 rpm  69  79  80  81  82  83  84  85  LIST OF FIGURES ( C o n t i n u e d ) Page 37.  38.  39.  40.  41.  42.  43.  44.  45.  46.  47.  48.  49.  50.  51.  52.  53.  Comparison of c a l c u l a t e d and e x p e r i m e n t a l mass f r a c t i o n burned f o r 2400 rpm, X = 1.36  86  Comparison of c a l c u l a t e d and e x p e r i m e n t a l mass f r a c t i o n burned f o r 3000 rpm, X = 1.08  87  Comparison of c a l c u l a t e d and e x p e r i m e n t a l mass f r a c t i o n burned f o r 3000 rpm, X = 1.22  88  Comparison of c a l c u l a t e d and e x p e r i m e n t a l mass f r a c t i o n burned f o r 3000 rpm, X = 1.37  89  Comparison of c a l c u l a t e d f o r 1200 rpm, X = 1.01  and e x p e r i m e n t a l p r e s s u r e h i s t o r i e s 90  Comparison of c a l c u l a t e d f o r 1200 rpm, X = 1.16  and e x p e r i m e n t a l p r e s s u r e h i s t o r i e s  Comparison of c a l c u l a t e d f o r 1200 rpm, X = 1.27  and e x p e r i m e n t a l p r e s s u r e h i s t o r i e s  Comparison of c a l c u l a t e d f o r 1800 rpm, X = 1.00  and e x p e r i m e n t a l p r e s s u r e h i s t o r i e s  Comparison of c a l c u l a t e d f o r 1800 rpm, X = 1.15  and e x p e r i m e n t a l p r e s s u r e h i s t o r i e s  Comparison of c a l c u l a t e d f o r 1800 rpm, X = 1.28  and e x p e r i m e n t a l p r e s s u r e h i s t o r i e s  Comparison of c a l c u l a t e d f o r 2400 rpm, X = 1.04  and e x p e r i m e n t a l p r e s s u r e h i s t o r i e s  Comparison of c a l c u l a t e d f o r 2400 rpm, X = 1.20  and e x p e r i m e n t a l p r e s s u r e h i s t o r i e s  Comparison of c a l c u l a t e d f o r 2400 rpm, X = 1.36  and e x p e r i m e n t a l p r e s s u r e h i s t o r i e s  Comparison of c a l c u l a t e d f o r 3000 rpm, X = 1.08  and e x p e r i m e n t a l p r e s s u r e h i s t o r i e s  Comparison of c a l c u l a t e d f o r 3000 rpm, X = 1.22  and e x p e r i m e n t a l p r e s s u r e h i s t o r i e s  Comparison of c a l c u l a t e d f o r 3000 rpm, X = 1.37  and e x p e r i m e n t a l p r e s s u r e h i s t o r i e s  91  92  93  94  95  96  97  98  99  100  101  Comparison of c a l c u l a t e d and e x p e r i m e n t a l f i r s t 5% o f t o t a l mass i n t h e c y l i n d e r - vii-  time t o burn the 102  LIST OF FIGURES (Continued) Page 54.  55.  Comparison of c a l c u l a t e d and e x p e r i m e n t a l 95% o f t o t a l mass i n t h e c y l i n d e r  time to burn 5 t o 103  P r e d i c t e d flame t h i c k n e s s as a f u n c t i o n 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 f a c t o r over the engine speed range  105  57.  P r e d i c t e d mass f r a c t i o n e n t r a i n e d and burned f o r 1800 rpm and X = 1.00  106  58.  P r e d i c t e d i n n e r and outer  flame r a d i u s f o r 1800 rpm and  X - 1.00  107  59.  Predicted  60.  P r e d i c t e d unburned, burned and flame volumes f o r 1800 rpm and X = 1.00  109  61.  P r e d i c t e d i n t e g r a l l e n g t h s c a l e a t 1800 rpm, X = 1.00, X = 1.15, 3000 rpm X = 1.08  110  62.  63.  64.  65.  66.  outer  flame area  f o r 1800 rpm and X = 1.00  108  P r e d i c t e d T a y l o r m i c r o s c a l e a t 1800 rpm, X = 1.00, X = 1.15, 3000 rpm X = 1.08  I l l  Enhanced t u r b u l e n c e i n t e n s i t y a t 1800 rpm, X = 1.00, X = 1.15, 3000 rpm X = 1.08  112  P r e d i c t e d t u r b u l e n t entrainment v e l o c i t y a t 1800 rpm, X = 1.00, X = 1.15, 3000 rpm X = 1.08  113  E f f e c t of the volume d i s t r i b u t i o n i n the t h i c k 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  E f f e c t of c f a c t o r on the mass f r a c t i o n burned, 3000 rpm, X = 1.08, x = 90%  115  P r e d i c t e d and c a l c u l a t e d mass f r a c t i o n burned f o r L = h spark t i m i n g , 3000 rpm, X = 1.08  116  V o l  67.  68.  69.  70.  c  at  P r e d i c t e d and c a l c u l a t e d mass f r a c t i o n burned f o r L = h / 5 a t spark t i m i n g , 3000 rpm, X = 1.08  117  E f f e c t of c o e f f i c i e n t a i n the heat l o s s e q u a t i o n histories  118  c  on  pressure  Comparison of mass f r a c t i o n burned curves e x t r a c t e d from e x p e r i m e n t a l p r e s s u r e s , e x t r a c t e d from p r e d i c t e d p r e s s u r e s and c a l c u l a t e d from model  - viii  -  119  LIST OF FIGURES (Continued) Page A.l  Two d i m e n s i o n a l  v o r t e x i n the unburned mixture  A.2  Vortex  A.3  Burned mass f r a c t i o n i n flame zone  135  A.4  L a m i n a l burning  136  A.5  D e f i n i t i o n of unburned cone and flame zone cone; flame zone cone r a d i u s vs d i s t a n c e through flame  137  A. 6  Volume d i s t r i b u t i o n i n flame zone,  138  B. l  Ensemble averaged motored and combustion p r e s s u r e s  145  B.2  R e l a t i v e rms f l u c t u a t i o n s averaged mean  146  b u r s t i n g due t o combustion  of s p h e r i c a l  133 134  pockets  = 10 mm  of p r e s s u r e s  about the ensemble  B. 3  C a l c u l a t e d motored temperatures  147  C. l  Heat balance  159  C.2  Anemometer b r i d g e c i r c u i t  160  C.3  Hot wire  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 t r u e mean v e l o c i t y , rms window i n t e n s i t y and t r u e rms i n t e n s i t y  162  Comparison of ensemble averaged mean v e l o c i t y with t r u e mean v e l o c i t y o b t a i n e d by n o n - s t a t i o n a r y c y c l e - b y - c y c l e a n a l y s i s u s i n g v a r i o u s window s i z e s , 1200 rpm, b a s e l i n e p o s i t i o n  163  Comparison of ensemble averaged t u r b u l e n c e i n t e n s i t y w i t h i n t e n s i t y o b t a i n e d by n o n - s t a t i o n a r y c y c l e - b y - c y c l e a n a l y s i s u s i n g v a r i o u s window s i z e s , 1200 rpm, b a s e l i n e p o s i t i o n  164  Comparison of ensemble averaged mean v e l o c i t y w i t h t r u e mean v e l o c i t y o b t a i n e d by n o n - s t a t i o n a r y c y c l e - b y - c y c l e a n a l y s i s u s i n g v a r i o u s window s i z e s , 1800 rpm, b a s e l i n e p o s i t i o n  165  Comparison of ensemble averaged t u r b u l e n c e i n t e n s i t y w i t h i n t e n s i t y o b t a i n e d by n o n - s t a t i o n a r y c y c l e - b y - c y c l e a n a l y s i s u s i n g v a r i o u s window s i z e s , 1800 rpm, b a s e l i n e p o s i t i o n  166  Comparison of ensemble averaged mean v e l o c i t y w i t h t r u e mean v e l o c i t y o b t a i n e d by n o n - s t a t i o n a r y c y c l e - b y - c y c l e a n a l y s i s u s i n g v a r i o u s window s i z e s , 2400 rpm, b a s e l i n e p o s i t i o n  167  C.5  C.6  C.7  C.8  C.9  of wire  element  c a l i b r a t i o n curve  - ix -  LIST OF FIGURES (Continued) Page CIO  Comparison of ensemble averaged t u r b u l e n c e i n t e n s i t y with i n t e n s i t y o b t a i n e d by n o n - s t a t i o n a r y c y c l e - b y - c y c l e a n a l y s i s u s i n g v a r i o u s window s i z e s , 2400 rpm, b a s e l i n e p o s i t i o n  168  Comparison of ensemble averaged mean v e l o c i t y w i t h t r u e mean v e l o c i t y o b t a i n e d by n o n - s t a t i o n a r y c y c l e - b y - c y c l e a n a l y s i s u s i n g v a r i o u s window s i z e s , 3000 rpm, b a s e l i n e p o s i t i o n  169  Comparison of ensemble averaged t u r b u l e n c e i n t e n s i t y w i t h i n t e n s i t y o b t a i n e d by n o n - s t a t i o n a r y c y c l e - b y - c y c l e a n a l y s i s u s i n g v a r i o u s window s i z e s , 3000 rpm, b a s e l i n e p o s i t i o n  170  D.l  Integration coordinates  183  D.2  Integration limits  184  D.3  Geometry: c l e a r a n c e  D.4  Area of e l l i p s e s e c t i o n s  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  188  D.7  Geometry: c y l i n d e r volume  189  D.8  Non-dimensional flame volume vs non-dimensional flame r a d i u s  190  D.9  Non-dimensional flame f r o n t a r e a vs non-dimensional flame radius  191  C l l  C12  volume  185  intersected  D.10 Non-dimensional wetted c y l i n d e r a r e a vs non-dimensional flame radius  -  x  -  192  LIST OF TABLES Page 1.  R i c a r d o Hydra engine c h a r a c t e r i s t i c s  22  2.  O p e r a t i n g c o n d i t i o n s , motoring t e s t s  25  3.  O p e r a t i n g c o n d i t i o n s , combustion  28  4.  Model parameters  5.  I g n i t i o n d e l a y f o r the twelve base o p e r a t i n g c o n d i t i o n s  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 v a r i o u s d e f i n i t i o n s o f flame t h i c k n e s s ( e x p o n e n t i a l b u r n i n g law)  126  C l  Wire c h a r a c t e r i s t i c s  149  C.2  Time a s s o c i a t e d w i t h each window s i z e  157  tests  31  -  xi  -  ......  NOMENCLATURE  2  A  Area  A  C o r r e l a t i o n constant, hot wire  A  u  (m ) calibration  Area o f the o u t e r flame boundary  2  (m )  ABDC  A f t e r bottom dead c e n t e r  ATDC  A f t e r top dead c e n t e r  a  C y l i n d e r bore  B  C o r r e l a t i o n c o n s t a n t , hot w i r e  BDC  Bottom dead c e n t e r  BBDC  Before bottom dead c e n t e r  BTDC  B e f o r e t o p dead c e n t e r  BMEP  Brake mean e f f e c t i v e p r e s s u r e (kPa)  b  Short a x i s l e n g t h o f e l l i p t i c a l c l e a r a n c e a r e a  C  Carbon  CA  Crank a n g l e (deg)  0^  Constant  C  Constant volume s p e c i f i c heat  v  (mm) calibration  p r e s s u r e s p e c i f i c heat  (mm)  (kJ/kg-K)  (kJ/kg-K)  c  F a c t o r i n t h e model t u r b u l e n t b u r n i n g v e l o c i t y e q u a t i o n  D,d  Diameter  E  Energy ( k J )  E  Hot w i r e b r i d g e v o l t a g e (V)  EVC  Exhaust v a l v e c l o s i n g  EVO  Exhaust  e  S p e c i f i c energy  e  Molar S p e c i f i c energy  valve  opening (kJ/kg) (kj/kmol)  - xii-  F  R e s i d u a l 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  h  c  2  (W/m -K)  C l e a r a n c e h e i g h t (mm)  I  C u r r e n t (A)  IVC  Intake v a l v e c l o s i n g  IVO  Intake v a l v e  IMEP  I n d i c a t e d mean e f f e c t i v e p r e s s u r e (kPa)  K  Constant  opening  i n the g e n e r a l t u r b u l e n t burning v e l o c i t y  Constant i n t h e Daneshyar and H i l l equation  t u r b u l e n t burning  2  k  Thermal c o n d u c t i v i t y (W/m -K)  L,l  Length (m)  L  I n t e g r a l l e n g t h s c a l e (m)  M,m  Mass (kg)  Mw  M o l e c u l a r Weight (kg/kmol)  N,n  Number  N  Nitrogen  N  C o r r e l a t i o n exponent, hot w i r e  Nu  N u s s e l t number (h d/k)  0  Oxygen  P  P r e s s u r e (kPa)  Q  Heat added o r l o s t t o t h e c y l i n d e r w a l l s ( k J )  Q  Heat f l u x (W)  Q  V o l u m e t r i c flow r a t e (m /s)  R  Connecting  R,r  Radius (mm)  of moles (m)  3  rod l e n g t h (mm)  - xiii -  equation  calibration  velocity  R  R e s i s t a n c e (ohms)  R  Gas c o n s t a n t (kJ/kg-K)  R^  Inner flame r a d i u s  Re  Reynolds number  Re  (mm)  (Vd/v)  Reynolds number based on t h e i n t e g r a l l e n g t h s c a l e  (VL/v)  Li  Re^  Reynolds number based on t h e T a y l o r m i c r o s c a l e (VA/v)  RPM  E n g i n e speed  R  mol  R  u  (rpm)  U n i v e r s a l gas c o n s t a n t Outer flame r a d i u s  (kJ/kmol-K)  (mm)  T  Temperature  TDC  Top dead  T,t  Time ( s )  t  Time f o r complete b u r n i n g through t h e t u r b u l e n t flame ( s )  U  Velocity  U(t)  Instantaneous v e l o c i t y  U(t)  T u r b u l e n t mean v e l o c i t y  U^  Laminar b u r n i n g v e l o c i t y  U  Turbulent burning v e l o c i t y  u(t)  F l u c t u a t i n g component o f t h e i n s t a n t a n e o u s v e l o c i t y  u'  T u r b u l e n t i n t e n s i t y , RMS  V  Volume  V  g  (K)  center  (m/s) (m/s) (m/s) (m/s) (m/s)  of v e l o c i t y  fluctuations  3  (m )  Swept volume  3  (m )  V  V o l t a g e (V)  v  S p e c i f i c volume (m /kg)  WOT  Wide open t h r o t t l e  w  Tangential velocity  X,x  Mass f r a c t i o n  X  Volume f r a c t i o n burned i n t h e t u r b u l e n t flame  3  , vol  (m/s)  - xiv -  (m/s) (m/s)  y  D i s t a n c e through  a  Temperature c o e f f i c i e n t of r e s i s t a n c e of wire  6  T u r b u l e n t flame t h i c k n e s s  <|>  Crank angle  (deg)  cj>  Equivalence  ratio  p  Density  p  R e s i s t i v i t y (ohm-cm)  X  T a y l o r m i c r o s c a l e of t u r b u l e n c e  X  Relative fuel-air  v  Kinematic v i s c o s i t y  y  Dynamic v i s c o s i t y  n  Kolmogorov s c a l e of t u r b u l e n c e  n  (mm)  (1/C)  (mm)  3  (kg/m )  Volumetric  v  t u r b u l e n t flame from o u t e r edge  (mm)  ratio 2  (m /s) 2  (N-s/m ) (mm)  efficiency  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 b u r n i n g time s c a l e  (s)  Subscripts air  Refers to intake a i r  amb  R e f e r s to ambient c o n d i t i o n s  b.bnt  R e f e r s t o burned  mixture  f , f l a m e R e f e r s to the t h i c k b u r n i n g  zone  fc  R e f e r s t o a s e c t i o n o f the t u r b u l e n t flame formed by a cone o f base r a d i u s X and h e i g h t Ry  gas  R e f e r s t o gas p r o p e r t i e s i n t h e h o t w i r e  intake  R e f e r s to c o n d i t i o n s i n the i n t a k e m a n i f o l d  °  R e f e r s t o a r e f e r e n c e temperature  - xv -  of 273K  calculations  p  Refers  to the unburned  res  Refers  to  spark  Refers  to conditions at  sup  Refers  to  tot  Refers  to the  u,unb  Refers  to unburned  0,1,2  Refers  to an i n i t i a l ,  first  1  Refers  to  crank angle  2  Refers  to the  oo  Refers  to c o n d i t i o n s  window  Refers  to  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  wire  Refers  to  the  wop  Refers  to the  the  pockets  residuals  i n the  i n the the  the w i r e s u p p o r t s or  the  spark  prongs  contents  mixture  initial final  hot  flame  cylinder  time of  total cylinder  turbulent  and second guess i n an  crank angle far  step i n the  step i n the  away f r o m t h e  calculations  calculations  present  wire  operating  temperature of the  -  xvi  -  iteration  wire  position analysis  ACKNOWLEDGEMENTS  The author wishes t o acknowledge Dr. P.G. H i l l encouragement throughout t h e c o u r s e o f t h i s work. Evans and Daneshyar  f o r h i s guidance and P r o f e s s o r s Hauptmann,  a r e a l s o thanked; t h e i r c o n t r i b u t i o n through e n l i g h t e n -  ing discussions i s appreciated.  S p e c i a l thanks go t o A l a n Jones f o r t h e  d e s i g n o f the data a c q u i s i t i o n system.  The s t a f f and graduate s t u d e n t s o f  the Department o f M e c h a n i c a l E n g i n e e r i n g a r e a l s o thanked f o r t h e i r support.  - xvii -  1.  INTRODUCTION  Combustion phenomena i n engines a r e known to be a f f e c t e d by t u r b u l e n c e , e q u i v a l e n c e r a t i o , geometry o f the combustion  chamber and  location.  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  titatively  to a c e r t a i n extent.  about  spark  quan-  There a r e s t i l l many u n r e s o l v e d q u e s t i o n s  the e f f e c t of l e a n combustion  and how  pre-flame  on c y c l i c v a r i a t i o n and burning  rates,  they a r e i n f l u e n c e d by the e n g i n e f l o w f i e l d and the p r o p e r t i e s o f  the m i x t u r e . T u r b u l e n c e i n engines and i t s e f f e c t on combustion of e x t e n s i v e t h e o r e t i c a l and e x p e r i m e n t a l r e s e a r c h .  has been a s u b j e c t  I t i s g e n e r a l l y known  t h a t engine t u r b u l e n c e , which i s g e n e r a t e d by the h i g h shear f l o w p a s t the i n t a k e v a l v e and decays d u r i n g the compression  s t r o k e , enhances the propa-  g a t i o n o f the r e a c t i n g gases i n t o t h e unburned m i x t u r e .  Turbulence i n  motored engines has been measured u s i n g hot w i r e anemometry and more r e c e n t l y w i t h l a s e r Doppler v e l o c i m e t r y . The e f f e c t of t u r b u l e n c e 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 t e c h n i q u e s , and by i n d i r e c t methods such as p r e s s u r e measurements and i o n probe  signals.  I t i s known that  turbulent  flame speed can be an o r d e r o f magnitude l a r g e r t h a n t h e l a m i n a r b u r n i n g velocity.  Although r e s e a r c h e r s d i s a g r e e on the exact nature of  phenomena, the consensus  this  seems t o be t h a t t h e flame i s s t r e t c h e d by  the  t u r b u l e n t e d d i e s f o r low l e v e l s of t u r b u l e n c e , but f o r h i g h e r l e v e l s ,  such  as t h o s e encountered i n engines a t o p e r a t i n g speeds, the w r i n k l e d flame breaks i n t o l i t t l e  i s l a n d s or  ' f l a m e l e t s ' which tend to burn a t a r a t e  c l o s e r t o the l a m i n a r b u r n i n g v e l o c i t y . this last  theory.  Experimental evidence supports  2. Experimenters have known f o r q u i t e some time t h a t t h e flame k e r n e l , initiated  by the spark d i s c h a r g e , develops i n t o a r a p i d l y p r o p a g a t i n g s e l f -  s u s t a i n i n g flame which reaches t h e ends o f t h e chamber b e f o r e a l l the combustion m i x t u r e has been consumed.  I t i s a l s o known that  flame  p r o p a g a t i o n time and o v e r a l l combustion d u r a t i o n can be d e c r e a s e d by increasing  t u r b u l e n c e or m o d i f y i n g the combustion  chamber geometry.  To understand the complex phenomena o f combustion i n e n g i n e s , r e s e a r c h e r s have developed mathematical models to s i m u l a t e flame  front  p r o p a g a t i o n and thus p r e d i c t b u r n i n g r a t e s , burned gas temperatures exhaust e m i s s i o n s .  Combustion  m o d e l l i n g has been q u i t e s u c c e s s f u l as a  p r e d i c t i v e t o o l and i s used f r e q u e n t l y by engine d e s i g n e r s .  The use o f  these models has however been l i m i t e d by the f a c t t h a t up to now t o be engine dependent totally  new  they tend  and thus have l i t t l e p r e d i c t i v e c a p a c i t y when a  design i s introduced.  The complete d e s c r i p t i o n o f combustion able task.  and  i n s i d e an engine i s a f o r m i d -  Such a model must take i n t o account the momentum and  energy  b a l a n c e , k i n e t i c s o f o x i d a t i o n , and i s c o m p l i c a t e d by the f o r m a t i o n o f thermal l a y e r s and o t h e r such phenomena.  These  types of models are i n  t h e i r i n f a n c y and as y e t have o n l y been used t o s o l v e some simple problems  a t r e l a t i v e l y h i g h computer  2-D  costs.  The t u r b u l e n t entrainment models a r e most p r o m i s i n g as they have proven s u c c e s s f u l i n d e s i g n work.  They combine a thermodynamic a n a l y s i s o f  c y l i n d e r c o n t e n t s a l o n g w i t h an entrainment e q u a t i o n f o r the flame and e q u a t i o n s d e s c r i b i n g the b u r n i n g r e g i o n l e f t  behind the flame  front front.  Thus the e f f e c t s o f t u r b u l e n c e and r e a c t a n t p r o p e r t i e s a r e combined. models are s u c c e s s f u l i n p r e d i c t i n g studies.  These  trends and performing p a r a m e t r i c  However, they a r e 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 n e c e s s a r y t o extend them t o a n o t h e r a p p l i c a t i o n .  Also,  the  e f f e c t of l e a n b u r n i n g 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 d e l a y has n o t been p r e d i c t e d s u c c e s s f u l l y .  These models c o u l d examine the geometry  of the b u r n i n g zone, i t s t h i c k n e s s and i t s e f f e c t on the o v e r a l l b u r n i n g r a t e and engine performance.  There i s need f o r f u r t h e r work i n t h i s a r e a  e s p e c i a l l y i n l i g h t of r e c e n t e x p e r i m e n t a l f i n d i n g s about  the s t r u c t u r e o f  t u r b u l e n t flames i n e n g i n e s . R e c e n t l y , Daneshyar and H i l l  [1] f o r m u l a t e d a s e r i e s o f e q u a t i o n s  d e s c r i b i n g the p r o p a g a t i o n v e l o c i t y and t h i c k n e s s of the t u r b u l e n t flame as a f u n c t i o n o f t u r b u l e n c e l e v e l s and r e a c t a n t p r o p e r t i e s . l e d t o encouraging r e s u l t s i n l i m i t e d  T h i s model has  testing.  The o b j e c t i v e o f t h i s work i s t o d e v e l o p an engine s i m u l a t i o n program i n c o r p o r a t i n g these i d e a s , and to use i t t o perform e x t e n s i v e t e s t i n g of t h e model.  The s p e c i f i c o b j e c t i v e s o f t h i s work a r e summarized below:  1)  Develop  an engine s i m u l a t i o n program which d e s c r i b e s the r a p i d  entrainment o f the flame f r o n t a c r o s s the c y l i n d e r and the r e l a t i v e l y b u r n i n g i n the t h i c k flame.  T h i s program, w i l l  slow  i n c o r p o r a t e a thermodynamic  a n a l y s i s o f the c y l i n d e r c o n t e n t s , a flame entrainment e q u a t i o n and a s e r i e s of e q u a t i o n s d e s c r i b i n g the geometry of the t h i c k burning zone based on e x i s t i n g e x p e r i m e n t a l e v i d e n c e .  2)  Conduct  t u r b u l e n c e measurements i n s i d e the c y l i n d e r o f the R i c a r d o  Hydra engine w i t h a hot w i r e anemometer. determine firing  The purpose o f t h e s e t e s t s i s t o  the o r d e r of magnitude of t u r b u l e n c e l e v e l s around  time f o r v a r i o u s engine speeds and t h r o t t l e  settings.  the spark  4. 3)  P e r f o r m a s e r i e s o f combustion  p r e s s u r e h i s t o r i e s and performance air fuel  4)  t e s t s i n the R i c a r d o t o measure d a t a over a range of engine speeds  ratios.  Submit  t h e model t o e x t e n s i v e t e s t i n g a g a i n s t the combustion d a t a .  The s i m u l a t i o n program w i l l be t e s t e d f o r i t s a b i l i t y t o p r e d i c t  overall  b u r n i n g r a t e s and p r e s s u r e h i s t o r i e s over the range of engine speeds equivalence r a t i o s . delay.  and  The model w i l l a l s o be t e s t e d i n p r e d i c t i n g  and  ignition  F i n a l l y , i t w i l l be used t o g a i n g r e a t e r u n d e r s t a n d i n g of the  s t r u c t u r e o f the t h i c k b u r n i n g zone and i t s e f f e c t s on the o v e r a l l b u r n i n g r a t e s i n the engine.  5. 2.  2.1  REVIEW OF PREVIOUS WORK  Summary o f E x p e r i m e n t a l F i n d i n g s Turbulence  i s known t o enhance combustion [2,3,4,5,6].  b u r n i n g v e l o c i t y i s i n c e r t a i n cases t e n times the laminar  The t u r b u l e n t velocity.  Laminar b u r n i n g v e l o c i t y i s a p r o p e r t y o f t h e m i x t u r e e s t a b l i s h e d by e x p e r i m e n t a l measurement t h a t depends on c h e m i c a l composition and thermodynamic s t a t e . T u r b u l e n c e i n engines i s c r e a t e d by t h e shear f l o w p a s t t h e i n t a k e v a l v e and decays r a p i d l y t h e r e a f t e r .  I n the absence of t u r b u l e n c e  genera-  t o r s ( s q u i s h , s w i r l ) , i t tends t o decay near t o p dead c e n t e r and be governed by chamber geometry. intensity.  Turbulence  can be d e s c r i b e d by s c a l e and  T u r b u l e n t s c a l e i s a parameter r e p r e s e n t a t i v e o f t h e s i z e o f  the eddies i n the f l o w .  The t u r b u l e n c e i n t e n s i t y i s the r o o t mean  v a l u e o f t h e f l u c t u a t i n g v e l o c i t y component about t h e mean.  square  This d e f i n i -  t i o n was f o r m u l a t e d f o r a s i t u a t i o n where the mean v e l o c i t y i s steady time i . e . , c l e a r l y d e f i n a b l e .  In an engine,  with  the turbulent f l u c t u a t i o n s a r e  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 t h e r e i s disagreement  v e l o c i t y and i n t e n s i t y i n e n g i n e s .  on an a p p r o p r i a t e d e f i n i t i o n o f mean The r e s u l t s of experimenters  depend  h i g h l y on t h e way they have i n t e r p r e t e d t h e i r measurements. To understand  the e f f e c t of t u r b u l e n c e on combustion, r e s e a r c h e r s have  measured t u r b u l e n c e l e v e l s i n motored engines u s i n g h o t w i r e anemometry and more r e c e n t l y l a s e r doppler v e l o c i m e t r y .  The g e n e r a l f i n d i n g s  [5,7,8]  are:  1)  T u r b u l e n c e 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 s c a l e s a r e o f the o r d e r o f m i l l i s e c o n d s ;  3)  The i n t e g r a l l e n g t h s c a l e i s of the o r d e r of the chamber h e i g h t .  There i s a l s o e v i d e n c e t h a t f o r a s i m p l e combustion chamber geometry such as a d i s k chamber, the t u r b u l e n c e near top dead c e n t e r tends to be homogeneous and i s o t r o p i c  [9,7,8,10].  T u r b u l e n c e i n the pre-flame f i e l d o f an engine has been measured w i t h l a s e r Doppler anemometry.  Witze  [11,12] found that the t u r b u l e n c e i n t e n -  s i t y j u s t ahead o f the flame undergoes the  an i n c r e a s e o f up t o two  times i n  d i r e c t i o n of the flame p r o p a g a t i o n caused by the one-dimensional  compression o f preflame gases.  T h i s has been e x p l a i n e d by the r a p i d  d i s t o r s i o n theory [ 1 3 ] . T u r b u l e n t flames i n engines have a l s o been i n v e s t i g a t e d .  Smith  observed the e f f e c t of t u r b u l e n c e on flame s t r u c t u r e i n e n g i n e s . m i c r o - S c h l i e r e n t e c h n i q u e , he photographed propagated  towards  the camera.  s e p a r a t i n g a r e g i o n o f burned, where i t i s s t a t i s t i c a l l y his  photographs  b u r n i n g and unburned  w i t h engine speed, and t h e r e was  boundary  gases from a r e g i o n  to f i n d any burned gas.  a r e shown i n F i g u r e 1.  Using a  images o f the flame f r o n t as i t  The flame f r o n t i s d e f i n e d as the  improbable  [10]  Since i n t e n s i t y varied  Examples o f linearly  e v i d e n c e t h a t the t u r b u l e n c e was  isotropic  and homogeneous near top dead c e n t e r , he s e t out t o d i s c o v e r i f the s i z e o f the Re  flame w r i n k l e s d i m i n i s h e d w i t h i n c r e a s i n g RPM. , where the T a y l o r m i c r o s c a l e was  Indeed  they s c a l e d w i t h  d e r i v e d from i s o t r o p i c t u r b u l e n c e  A relationships. combustion,  He a l s o found the s c a l e t o d e c r e a s e w i t h p r o g r e s s i n g  c o n s i s t e n t with r a p i d d i s t o r s i o n theory.  The s i z e of the flame  s t r u c t u r e s were found t o be o f the o r d e r o f t h e T a y l o r m i c r o s c a l e .  7. Smith [14] a l s o observed t u r b u l e n t flame t h i c k n e s s e s i n engines u s i n g Rayleigh scattering.  One  important f i n d i n g was  that as engine  i n c r e a s e d , the l i k e l i h o o d o f i s l a n d s o f unburned the burned gases  speed  gases b e i n g e n g u l f e d by  increased.  Namazian, Hansen, L y f o r d - P i k e , Sanchez-Barsse, Heywood and R i f e observed t h i c k b u r n i n g r e g i o n s (10 to 15 mm) MIT  square p i s t o n engine.  F i g u r e 2.  [15]  through a s i d e window i n the  Some o f t h e i r photographs  a r e reproduced i n  They e s t i m a t e d t h a t the t h i c k flames were composed of a m a j o r i t y  (50 t o 70%)  o f burned gases.  From t h e i r o b s e r v a t i o n s , they f o r m u l a t e d an  e q u a t i o n f o r the c h a r a c t e r i s t i c b u r n i n g time of the e n t r a i n e d gases l e d t o a c h a r a c t e r i s t i c flame  which  thickness.  The r a p i d p r o p a g a t i o n of the o u t e r flame edge w i t h r e s p e c t to the unburned  gases i s d e f i n e d as the t u r b u l e n t entrainment o r b u r n i n g v e l o c i t y .  Measurements of the t u r b u l e n t b u r n i n g v e l o c i t y have been conducted i n e n g i n e s as w e l l as i n bombs.  A l t h o u g h t h e r e i s s t i l l c o n t r o v e r s y i n the  f o r m u l a t i o n of an adequate model d e s c r i b i n g the t u r b u l e n t 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 w e l l as  l a m i n a r b u r n i n g v e l o c i t y i n the g e n e r a l form:  U  T  =  U  £  + K u'  A p r o m i s i n g approach t o m o d e l l i n g t u r b u l e n t combustion i s found i n Tennekes'  [17] model f o r i s o t r o p i c t u r b u l e n t s t r u c t u r e .  drawn between the s t r u c t u r e of i s o t r o p i c flames.  A p a r a l l e l can be  t u r b u l e n c e and t h a t of t u r b u l e n t  The r a p i d p r o p a g a t i o n o f the flame f r o n t would o c c u r a l o n g v o r t e x  tubes of t y p i c a l diameter n (the Kolmogorov s c a l e ) by a mechanism known as ' v o r t e x b u r s t i n g ' f o r m u l a t e d by Chomiak [ 1 8 ] . are based on these fundamental  assumptions.  T u r b u l e n t entrainment models  8. 2.2  A Review o f the T h i n Flame Model R a s s w e i l e r and Withrow [19] were t h e f i r s t  p r e s s u r e development  to c o r r e l a t e c y l i n d e r  w i t h the p r o g r e s s of the flame f r o n t .  They e x t r a c t e d  p i s t o n motion from t h e p r e s s u r e c u r v e and c a l c u l a t e d heat r e l e a s e r a t e s . L a t e r , the two-zone thermodynamic model was i n t r o d u c e d by P a t t e r s o n and Van Wylen [20], who d i v i d e d t h e chamber i n t o a r e g i o n o f burned gas and a r e g i o n o f unburned  gas.  Subsequently K r i e g e r and Borman [21] added  c i a t i o n and c a l c u l a t e d heat r e l e a s e r a t e s . geometric assumptions:  disso-  L a n c a s t e r [4] i n t r o d u c e d t h e  s p h e r i c i t y and apparent p o s i t i o n o f the flame.  The thermodynamic o r t h i n flame model combines a thermodynamic a n a l y s i s of c y l i n d e r c o n t e n t s w i t h an e m p i r i c a l b u r n i n g law d e s c r i b i n g t h e p r o g r e s s i o n o f a t h i n r e a c t i o n f r o n t a c r o s s t h e chamber. M a t t a v i , G r o f f , L i e n e s c h , Matekunas and Noyes [22] demonstrated t h e c a p a b i l i t i e s o f t h e t h i n flame model when they used i t t o improve t h e d e s i g n o f a combustion  chamber.  The model was f i r s t  used i n a d i a g n o s t i c  mode i n which engine p r e s s u r e h i s t o r i e s were used t o d e r i v e a c o r r e l a t i o n of  flame speed r a t i o as a f u n c t i o n of the l a m i n a r b u r n i n g v e l o c i t y and  motored t u r b u l e n c e i n t e n s i t y .  The flame speed r a t i o i s d e f i n e d as t h e  r a t i o o f t u r b u l e n t burning v e l o c i t y the  ( r e l a t i v e t o the unburned  flame) t o 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 a t t h e unburned  gas ahead o f  gas c o n d i t i o n s .  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 a p p l i e d t o p r e d i c t p r e s s u r e h i s t o r i e s f o r d i f f e r e n t chamber c o n f i g u r a tions .  I t was found t h a t the p r e d i c t e d improvements i n the o v e r a l l b u r n i n g  r a t e s u c c e s s f u l l y matched combustion d a t a i n t h e new chamber. G r o f f and Matekunas [6] used p r e s s u r e t r a c e s and flame photographs t o d e v e l o p a r e f i n e d e x p r e s s i o n f o r t h e flame speed r a t i o which i n c l u d e d t h e  9. apparent combustion-induced  compression o f the unburned  t i o n of the flame geometry d u r i n g the i g n i t i o n phase.  gas and the d i s t o r They concluded t h a t  an a c c u r a t e d e s c r i p t i o n o f combustion i n engines s h o u l d i n c l u d e a flame  finite  thickness. The d e f i c i e n c i e s o f the t h i n flame model r e s i d e m a i n l y i n the f a c t  t h a t i t does not d e s c r i b e the a c t u a l t u r b u l e n t flame as observed v i s u a l i z a t i o n techniques.  The flame speed r a t i o o b t a i n e d from c o r r e l a t i n g  e x p e r i m e n t a l data l e a d s to an u n r e a l i s t i c flame towards first  the end o f combustion.  A l s o , s i n c e t h i s k i n d o f model  was  the s t r u c t u r e of the  b e i n g i n c o r p o r a t e d i n a new  breed o f models.  T u r b u l e n t Entrainment Models The new  the  'slowing down' of the t u r b u l e n t  developed, more f a c t s have been d i s c o v e r e d about  t u r b u l e n t flame which a r e now  2.3  through  g e n e r a t i o n o f combustion models have i n c o r p o r a t e d most of  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,  R a s h i d i and Keck [24] developed a t u r b u l e n t entrainment model w i t h slow b u r n i n g behind the flame f r o n t .  The e n t r a i n e d gas was  r a t e p r o p o r t i o n a l t o the amount o f unburned T h i s model agreed w e l l w i t h experiments Investigated. graphs  assumed to burn a t a  gas p r e s e n t i n the t h i c k  zone.  over the range of c o n d i t i o n s  The a u t h o r s used b o t h p r e s s u r e h i s t o r i e s and flame photo-  to develop t h e i r model.  T a b a c z y n s k i , Ferguson and Radhakrishnan  [25] f o r m u l a t e d an entrainment  model w i t h slow laminar burnup of e d d i e s i n i t i a l l y i n t e g r a l length scale.  T h i s was  i n s i d e the t h i c k combustion  an attempt  of the s i z e of the  t o model the b u r n i n g mechanism  zone through an u n d e r s t a n d i n g of the i n h e r e n t  s t r u c t u r e observed i n flame photographs, as w e l l as i n the t u r b u l e n t f l o w field.  H i r e s , T a b a c z y n s k i and Novak [26] used t h e i r model to p r e d i c t  10. i g n i t i o n d e l a y and o v e r a l l combustion r a t e s once an engine parameter had  been  characterizing  determined.  There i s s t i l l a need f o r a model d e s c r i b i n g the t h i c k b u r n i n g zone and  i t s observed  2.4  structure.  Background on the T u r b u l e n t B u r n i n g Model The p r e s e n t model i s based  t u r e of i s o t r o p i c t u r b u l e n c e .  on t h e Tennekes [17] concept of the s t r u c Tennekes f o r m u l a t e d the model to account  e x p e r i m e n t a l e v i d e n c e of i n t e r m i t t e n c y i n v i s c o u s d i s s i p a t i o n . l e n t s t r u c t u r e was  modelled  as v o r t e x tubes of t y p i c a l s i z e n>  Kolmogorov s c a l e , b e i n g s t r e t c h e d by e d d i e s o f s i z e X, scale.  A schematic  of the Tennekes model and  o f t u r b u l e n c e a r e i l l u s t r a t e d i n F i g u r e 3.  The  for  turbu-  the  the T a y l o r m i c r o -  the d e f i n i t i o n of the s c a l e s  There i s e x p e r i m e n t a l  evidence  i n support of the Tennekes model, n o t a b l y the works of Narayan [27] and  Ku  and C o r r s i n [28]. The  i m p l i c a t i o n s of the Tennekes model f o r combustion a r e : f a s t  i n g i n the v o r t e x tubes, and  slow b u r n i n g i n the X s i z e e d d i e s .  As  burnislands  of unburned gas a r e e n g u l f e d by the t h i c k t u r b u l e n t flame, the n r e g i o n s w i l l r a p i d l y enflame due  t o a hydrodynamic mechanism c a u s i n g the f a s t  p a g a t i o n o f the flame f r o n t .  pro-  This i s i l l u s t r a t e d schematically i n Figure  4.  2.4.1  T u r b u l e n t Entrainment  Velocity  The mechanism behind f a s t b u r n i n g i n the v o r t e x tubes i s e x p l a i n e d by the v o r t e x b u r s t i n g theory developed  by Chomiak [18].  He deduced  an  e x p r e s s i o n f o r t h e p r o p a g a t i o n v e l o c i t y o f the flame f r o n t a l o n g the v o r t e x tubes as a f u n c t i o n of the d e n s i t i e s and unburned gases ahead o f the flame. A.  From t h i s , Daneshyar and H i l l  entrainment  velocity:  the t u r b u l e n c e i n t e n s i t y i n the  T h i s e q u a t i o n i s developed developed  i n Appendix  an e x p r e s s i o n f o r the t u r b u l e n t  11. U  where K. i  < ^2/3  =  T  U  £  + K, u' 1  v  (1) '  p /p, . u b  F o r a d e n s i t y r a t i o of 5 o r 6 which i s c l o s e t o what i s encountered engines, t h i s  equation becomes:  U  w  T  = U  £  +  2u'  S i m i l a r r e s u l t s have been o b t a i n e d by Abdel-Gayed, A l - K h i s h a l i Bradley  [1] i n measuring  f o r engine  in  and  t u r b u l e n t b u r n i n g v e l o c i t i e s i n w e l l s t i r r e d bombs  l i k e c o n d i t i o n s Re  > 1000  and u'/U  > 1.  The  equation i s a l s o  very s i m i l a r t o the ones used by T a b a c z y n s k i and Keck i n t h e i r models.  2.4.2  T h i c k Burning Zone A c c o r d i n g t o the t h e o r y , pockets o f average  turbulent velocity.  flame and  burn a t a r a t e governed  s i z e A a r e e n g u l f e d by  the  by the laminar burning  Thus a c h a r a c t e r i s t i c burn-up time s c a l e of these pockets would  be:  £  Daneshyar and H i l l  proceed  to apply the burn r a t e  dr dt  (1-r)  =  equation  (3)  T  to get r 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%  t  Finally  (99% burned)  t  the combustion zone t h i c k n e s s  6  Preliminary values  f o r u' and  i s deduced  =  (5)  c a l c u l a t i o n s by Daneshyar and X l e a d to t h i c k n e s s e s  of the  3 < 6 < 10  T h i s compares w e l l w i t h  experimental  promising  engines. program.  The  H i l l using  t y p i c a l engine  order  mm  i n v e s t i g a t i o n s [15,29].  combustion zone i s i l l u s t r a t e d i n F i g u r e 5. very  burned)  The model has  The  proven t o  be  i n p r e l i m i n a r y c a l c u l a t i o n s of burn r a t e s i n bombs and t r u e t e s t l i e s i n i t s i n c o r p o r a t i o n i n t o an engine s i m u l a t i o n  13. 3.  3.1  TURBULENT ENTRAINMENT ENGINE SIMULATION MODEL  I n i t i a l Conditions The engine s i m u l a t i o n program b e g i n s c a l c u l a t i o n s a t bottom  c e n t e r a t the s t a r t of the compression s t r o k e . s t r o k e s a r e not m o d e l l e d . test data.  The i n t a k e and  The a i r and gas f l o w r a t e s f o r a g i v e n run as w e l l as i n t a k e  as w e l l as the mass of the c y l i n d e r c o n t e n t s .  a r e d i s c u s s e d i n Appendix  3.2  exhaust  The i n i t i a l c o n d i t i o n s a r e deduced from engine  m a n i f o l d temperature a r e used i n c a l c u l a t i n g t h e p r e s s u r e and at BDC  dead  Compression  These  temperature  calculations  A.  and E x p a n s i o n S t r o k e  The compression and e x p a n s i o n c a l c u l a t i o n s a r e i d e n t i c a l .  In b o t h  cases t h r e e equations are s o l v e d s i m u l t a n e o u s l y by a Newton-Rapson technique.  These e q u a t i o n s a r e :  1)  The e q u a t i o n of s t a t e ;  2)  The F i r s t law o f  3)  C o n s e r v a t i o n of energy.  thermodynamics;  A f l o w c h a r t r e p r e s e n t i n g the c a l c u l a t i o n s i s p r e s e n t e d i n F i g u r e 6. The compression/expansion c a l c u l a t i o n s a r e d e t a i l e d i n Appendix  3.3  Combustion  A.  Calculations  The engine s i m u l a t i o n combines a thermodynamic a n a l y s i s o f the c y l i n d e r c o n t e n t s coupled w i t h the t u r b u l e n t entrainment model.  It  d e s c r i b e s the p r o p a g a t i o n o f a t h i c k t u r b u l e n t flame which d i v i d e s  the  chamber i n t o t h r e e zones: burned, unburned  and  unburned  gases.  and a mixture of burned  14. 3.3.1  Assumptions Regarding  t h e t u r b u l e n c e i n t h e chamber, the f o l l o w i n g assumptions a r e  made:  1)  The t u r b u l e n c e 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 t u r b u l e n c e [30] can be used t o i n f e r the l e n g t h scales. Y  =  X  2)  The  R l '  —  2  (6)  L  •IT  t u r b u l e n c e i s r e l a x e d a t the time of spark f i r i n g which means t h a t  t h e l a r g e s c a l e e d d i e s a r e c l o s e t o t h e chamber dimensions.  The  integral  l e n g t h s c a l e L i s of the order of the chamber h e i g h t .  3)  Once t h e flame  i s propagating,  both the i n t e g r a l l e n g t h s c a l e and  t u r b u l e n c e i n t e n s i t y are enhanced a c c o r d i n g to r a p i d d i s t o r t i o n [13].  the  theory  The e d d i e s a r e assumed t o be compressed r a p i d l y , thus c o n s e r v i n g  angular momentum.  U  u  L  =  L  spark  s ark P  ( p  P  P  ^ u^ u,spark^  u  / p  u,s ark>'  With r e s p e c t to the t h i c k burning  1)  1 / 3  8  <>  P  zone:  The b u r n i n g zone i s a t h i c k s p h e r i c a l s h e l l p r o p a g a t i n g from  spark  l o c a t i o n to the ends of the chamber.  2)  The b u r n i n g zone i s composed o f unburned gas pockets i n i t i a l l y  s i z e A e n g u l f e d by burned gas.  of  I t i s assumed t h a t a l l burned as w e l l as  a l l unburned gas i n t h e chamber i s a t t h e same thermodynamic s t a t e . Finally, made:  the c l a s s i c a l assumptions f o r the thermodynamic model were  15. 1)  P r e s s u r e i s u n i f o r m throughout the combustion  2)  Burned gases a r e a t c h e m i c a l e q u i l i b r i u m .  3)  Unburned gases a r e compressed  isentropically.  chamber.  I t i s assumed t h a t the  heat l o s s to the c y l i n d e r w a l l s i s compensated by the heat g a i n from the burned  4)  3.3.2  gases.  The gases a r e assumed t o be  ideal.  Governing E q u a t i o n s The e q u a t i o n s t h a t a r e s o l v e d s i m u l t a n e o u s l y as the program s t e p s  through the f i r i n g  s t r o k e i n one degree crank angle increments a r e the  following:  C o n s e r v a t i o n o f Mass =  M, tot  First  M  u  + M  f  +  M^  (9)  law p AV +  AQ  (10)  Entrainment e q u a t i o n dme = p A U. dt u u t  (11)  K  with U  t  = U  £  + c/p7^  «•  (12)  B u r n i n g zone t h i c k n e s s e q u a t i o n (13)  16. Volume c o n s t r a i n t V  3.3.3  tot  = V  u  + V, + V. f b  (14)  Geometric C o n s i d e r a t i o n s The R i c a r d o 'bathtub' head c o n f i g u r a t i o n o f f e r s an i n t e r e s t i n g  geometric problem.  A schematic drawing o f the c y l i n d e r head d e s i g n i s  d e p i c t e d i n F i g u r e 7. facilitate  I t was d e c i d e d t o s i m p l i f y t h e geometry somewhat t o  the c a l c u l a t i o n s o f i n t e r s e c t i o n volumes and areas between the  sphere and t h e chamber i t s e l f .  T h i s new geometry shown i n F i g u r e 8  c o n s i s t s o f an e l l i p t i c a l shaped as t h e r e a l c l e a r a n c e space. the  c l e a r a n c e a r e a occupying the same volume  The s i m p l i f i e d flame o r i g i n i s a l s o shown on  figure. Some e r r o r i s i n t r o d u c e d by s i m p l i f y i n g t h e geometry but i t appears t o  be minor the  compared t o the assumptions  o f flame s p h e r i c i t y and i m m o b i l i t y o f  flame c e n t e r . Because o f t h e c o m p l e x i t y o f t h e c a l c u l a t i o n s i n v o l v e d i t was d e c i d e d  to  generate t a b l e s o f volume, flame a r e a and wetted c y l i n d e r w a l l a r e a f o r  a range o f r a d i i and crank a n g l e degrees t h a t would be encountered d u r i n g combustion.  The s i m u l a t i o n program would simply s e a r c h the t a b l e when a  volume o r a r e a i s d e s i r e d . i n Appendix  3.3.4  The complete i n t e g r a t i o n procedure i s e x p l a i n e d  D.  M o d e l l i n g the T h i c k B u r n i n g Zone One o f t h e d i f f i c u l t i e s  i n m o d e l l i n g t h e b u r n i n g 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 f u n c t i o n f o r the burned and unburned g a s . E x p e r i m e n t a l combustion v i s u a l i z a t i o n by Namazian e t a l . [15] l e d t o t h e statement  t h a t 50-70% o f the mass i n the t h i c k flame zone was burned gas.  17. Two  t h e o r i e s , one based on the e x p o n e n t i a l b u r n i n g law i n t h e zone,  the o t h e r based  on geometric  c o n s i d e r a t i o n s were proposed.  e x p l a i n e d i n d e t a i l i n Appendix A. found  Both  are  The two l e d t o s i m i l a r r e s u l t s .  t h a t the l o c a l volume f r a c t i o n of burned  It  to unburned gas i n the  was  burn-  i n g zone i s a p p r o x i m a t e l y : X  The  , ~ 75 to vol  85%  l o c a l volume f r a c t i o n i s d e f i n e d as the r a t i o of burned  i n t h e flame t o the t o t a l flame volume.  I t was  gas volume  d e c i d e d t o use a v o l u m e t r i c  f r a c t i o n i n the t h i c k b u r n i n g zone i n s t e a d of a mass f r a c t i o n because  this  s i m p l i f i e s the model c a l c u l a t i o n s c o n s i d e r a b l y .  3.3.5  Laminar B u r n i n g  Velocity  The e x p r e s s i o n used f o r c a l c u l a t i n g l a m i n a r b u r n i n g v e l o c i t y was same as t h a t used by Jones two e q u a t i o n s determined bomb experiments.  The  [31].  For e n g i n e - l i k e c o n d i t i o n s , he  the  combined  by Andrews and B r a d l e y [32] i n c o n s t a n t volume  first  of these e q u a t i o n s was  a c o r r e l a t i o n of  w i t h v a r y i n g p r e s s u r e w h i l e the second d e s c r i b e d the v a r i a t i o n w i t h temperature.  The r e s u l t i n g combined e q u a t i o n f o r laminar burning v e l o c i t y a t  s t o i c h i o m e t r i c c o n d i t i o n s used i n t h e program i s :  U  £  =  p-1/2  [io  + 0.000371 T  2 u  ]  cm/sec  (15)  To o b t a i n the laminar b u r n i n g v e l o c i t y a t other a i r - f u e l r a t i o s , non-dimensional atmospheric  f a c t o r was  a  c a l c u l a t e d from Andrews and B r a d l e y ' s r e s u l t s a t  c o n d i t i o n s , and a p p l i e d t o the b u r n i n g v e l o c i t y .  Since n a t u r a l  gas i s composed o f 95% o r more o f methane, these e q u a t i o n s were used model the l a m i n a r burning v e l o c i t y of n a t u r a l  gas.  to  18. 3.3.6  Dissociation Calculations 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 s u b r o u t i n e w r i t t e n  by Jones  [ 3 1 ] . I t o f f e r s the o p t i o n of c h o o s i n g two, f o u r or s i x d i s s o c i a -  tion reactions.  F o r t h i s study the f o u r f o l l o w i n g r e a c t i o n s were used.  C0  2  = CO + 1/2  0  2  R\0 = h\ + 1/2 0„ 2  2  H0  = OH + 1/2  NO  = 1/2 N  2  3.3.7  2  H  2  + 1/2  2  0  2  Heat L o s s C a l c u l a t i o n s The heat t r a n s f e r t o the w a l l was e s t i m a t e d by Annand's [33] f o r m u l a  i n which a N u s s e l t  vs Reynolds c o r r e l a t i o n i s a p p l i e d i n the f o l l o w i n g  ^  where  D  A  = wall °'  c y l i n d e r bore  Re V mp  8  I  <  R e  >  b  L  A  t  (m)  V mpxD v 2LN/60  mean p i s t o n v e l o c i t y (m/s)  T  wall  T  <V wall>  450 K Stroke  (m)  N 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: A  =  0.8  B  =  0.7  16  < >  way  19. 3.3.8  I g n i t i o n Delay I g n i t i o n d e l a y i n t h i s c a s e i s d e f i n e d as t h e time f o r t h e k e r n e l t o  grow t o a c e r t a i n s i z e such t h a t the r a p i d p r o p a g a t i o n a l o n g the v o r t e x tubes i s i n i t i a t e d .  T h i s i s a random time d e l a y because t h e spark c o u l d  c r e a t e a flame k e r n e l anywhere i n the p r e - i g n i t i o n f l o w f i e l d  which was  i l l u s t r a t e d i n F i g u r e 3. As c a n be seen i n F i g u r e 3, t h e maximum d i s t a n c e t h e flame would have to t r a v e l to reach t h i s next v o r t e x tube would be A/2. would be A/4.  The mean d i s t a n c e  Thus t h e random time d e l a y b e f o r e r a p i d flame p r o p a g a t i o n  would be:  *delay "  The  X  17  ~T  <>  flame propagates a t the laminar burning v e l o c i t y , u n t i l a v o r t e x  tube i s reached a t which time t h e flame i s r a p i d l y e n t r a i n e d a l o n g t h e s e tubes.  The burned mass f r a c t i o n a t the end of the i g n i t i o n d e l a y i s  negligible.  I n t h e program, compression was extended and combustion  c a l c u l a t i o n s were s t a r t e d a t the end of i g n i t i o n d e l a y .  3.3.9  S p 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 Two a d d i t i o n a l models were d e v e l o p e d f o r h a n d l i n g t h e e a r l y b u r n i n g  stages and the f i n a l  burn-up.  The f i r s t b u r n i n g s t a g e i s d e f i n e d as t h e f i r s t c a l c u l a t e d s t e p a f t e r the i g n i t i o n d e l a y .  Thus the k e r n e l has reached the mean s i z e A/2.  In t h e e a r l y model development were s t a r t e d  t h e t u r b u l e n t entrainment  from a n e g l i g i b l e s i z e k e r n e l .  calculation  Thus i t was i m p o s s i b l e t o  apply E q . (1) s i n c e t h e i n i t i a l flame a r e a was z e r o .  Instead, the  20. f o l l o w i n g assumptions were made r e g a r d i n g the f i r s t b u r n i n g s t e p .  The  d e n s i t y v a r i a t i o n s i n the k e r n e l were c o n s i d e r e d n e g l i g i b l e compared to r a p i d growth r a t e of the flame. k e r n e l was entrainment  assumed to be  A l s o the o v e r a l l d e n s i t y i n the s m a l l  equal to the burned gas d e n s i t y .  Thus the  equation f o r the f i r s t burning step i s  d R U  dt  =  U  When the outer edge of the flame has  p -H. t p, D  reached  t h e t h i c k n e s s e q u a t i o n i s no l o n g e r a p p l i c a b l e . flame entrainment,  the remaining  laminar burning v e l o c i t y .  unburned gas  (18)  the ends of the  TT=  chamber,  S i n c e t h e r e i s no more  r e g i o n s are consumed a t  Thus, the e x p o n e n t i a l b u r n i n g law  dm  3.3.10  the  the  i s applied  m -  r c  <»>  S o l v i n g Scheme  A simple f l o w c h a r t was  prepared  t o i l l u s t r a t e the  procedure of the combustion phase of the program.  calculation  Calculations start  after  i g n i t i o n d e l a y and end when a l l o r a p r e f i x e d amount of the mass i n the c y l i n d e r i s consumed.  The  f l o w c h a r t i s shown on F i g u r e  9.  21. 4.  4.1  INVESTIGATION  Objectives The  the  EXPERIMENTAL  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  turbulence The  engine.  o b j e c t i v e of the combustion t e s t s were t o g e n e r a t e d a t a over a  wide range  4.2  l e v e l s i n s i d e the Ricardo  of o p e r a t i n g c o n d i t i o n s to  compare w i t h t h e  s i m u l a t i o n program.  Instrumentation A schematic of the complete t e s t  R i c a r d o Hydra t e s t  facilities  consist  set  u p i s shown i n F i g u r e 1 0 .  of the  e n g i n e a n d d c dynamometer  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 and c o o l a n t temperatures, exhaust  temperatures  and i n t a k e a i r  v a r i a b l e speed range, ignition  timing.  4.2.1  enables  Ricardo instrumentation,  flywheel  for  data  the a  An AVL o p t i c a l  a c q u i s i t i o n purposes.  i n s t r u m e n t s which were used i n the d a t a c o l l e c t i o n  are  i n Figure 10.  Engine D e s c r i p t i o n The  Ricardo Hydra 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 research  featuring valves. and  The dynamometer  t r a n s d u c e r was m o u n t e d i n t h e h e a d .  p i c k u p was a l s o i n s t a l l e d on t h e  illustrated  standard  and  i n t a k e and  and a m a g n e t i c p i c k - u p on t h e f l y w h e e l r e g u l a t e s  In a d d i t i o n to the  p i e z o e l e c t r i c pressure  Various other  flowrate.  The  the  a bathtub  c o m b u s t i o n chamber w i t h o v e r h e a d c a m s h a f t  The e n g i n e b o r e and s t r o k e a r e compression r a t i o  i s 8.93  to  1.  engine and  8 0 . 2 6 mm a n d 8 8 . 9 mm r e s p e c t i v e l y , The e n g i n e c a n be o p e r a t e d a t  maximum s p e e d o f 5 , 4 0 0 rpm a n d p r o d u c e s maximum p o w e r o f 15 k w . specifications  are  presented  i n Table  1.  vertical  a  The e n g i n e  Table 1 R i c a r d o Hydra Engine C h a r a c t e r i s t i c s  Number of c y l i n d e r s  1  Bore (mm)  80.26  Stoke (mm)  88.9  Swept Volume (£)  0.45  Maximum speed  5400  (rpm)  Maximum power (kW) Compression  Ratio  V a l v e Arrangement:  15 8.93:1  Overhead  camshaft,  v e r t i c a l valves Valve L i f t  (mm)  Intake p o r t diameter (mm)  Valve  9 32  events: I n l e t opens (IVO)  12° BTDC  I n l e t closes (IV)  56° ABDC  Exhaust opens (EVO)  56° BBDC  Exhaust c l o s e s (EVC)  12° ATDC  23. 4.2.2  P r e s s u r e Measurements The  p r e s s u r e was measured w i t h a K i s t l e r 6121  which was  piezoelectric  transducer  f l u s h mounted i n the c y l i n d e r head of the R i c a r d o engine.  r e s u l t i n g charge s i g n a l was  The  f e d t o a . K i s t l e r model 5004 charge a m p l i f i e r t o  y i e l d a v o l t a g e p r o p o r t i o n a l to c y l i n d e r p r e s s u r e .  One  hundred c y c l e s of  p r e s s u r e d a t a were d i g i t i z e d a t a r a t e o f 1 sample/degree f o r each measuring  condition.  Figure  4.2.3  A photograph of the p o s i t i o n of the t r a n s d u c e r i s shown i n  11.  Hot Wire Measurements A TSI 12 26 h i g h temperature  t u r e b r i d g e were used f i l t e r e d a t 20 kHz  to measure hot wire v o l t a g e s .  The  constant signal  temperawas  w i t h a DISA 55D26 s i g n a l c o n d i t i o n e r b e f o r e b e i n g  d i g i t i z e d every 0.2  degree crank a n g l e .  over a l l engine speeds. 6.3  probe w i t h a DISA M-10  These s e t t i n g s remained unchanged  The w i r e m a t e r i a l was  micrometers i n diameter  and  1.5  mm  a platinum-iridium a l l o y .  i n length.  The wire was  operated  at  600°C. The probe was designed  fitting.  i n s e r t e d through  the spark p l u g h o l e u s i n g a s p e c i a l l y  F i g u r e 12 shows the probe measuring p o s i t i o n s w h i l e  F i g u r e 13 i s a photograph o f the probe i n s t a l l a t i o n i n the spark p l u g hole.  4.2.4  Crank A n g l e Measurements An AVL model 360c/600 o p t i c a l crank a n g l e p i c k - u p was  engine  flywheel.  T h i s sensor generated  mounted on  p u l s e s every crank angle degree  which were used t o t r i g g e r the d a t a a c q u i s i t i o n , and a s i n g l e p u l s e a t used  the  to s y n c h r o n i z e the data w i t h the p o s i t i o n of the c r a n k s h a f t .  BDC  24. 4.2.5  Data A c q u i s i t i o n A l l d a t a were t a k e n by an ISAAC 2000 h i g h speed d a t a a c q u i s i t i o n u n i t .  The ISAAC then executed a data t r a n s f e r to an IBM PC, and the v a l u e s were checked f o r p r o p e r p h a s i n g b e f o r e they were c o p i e d onto f l o p p y d i s k . Sampling was continuous u n t i l 40 c o n s e c u t i v e c y c l e s were a c q u i r e d f o r t h e motored  4.2.6  d a t a , o r 100 c y c l e s f o r f i r e d p r e s s u r e d a t a .  Other Measurements V o l u m e t r i c a i r and gas f l o w r a t e s were measured w i t h laminar f l o w  elements.  The a i r f l o w meter was mounted i n t h e i n t a k e o f the R i c a r d o and  was equipped w i t h b u i l t - i n  compensation  f o r pulsating flows.  Engine c o o l a n t and o i l temperatures were monitored through a l l t e s t s .  4.3  Motored T e s t s  4.3.1  Procedure and Data A n a l y s i s T a b l e 2 l i s t s the o p e r a t i n g c o n d i t i o n s f o r a l l t h e m o t o r i n g t e s t s .  A l l motored at  t e s t s were c o l d s t a r t s which means that the engine was o p e r a t e d  room temperature. These t e s t s were performed  i n two phases.  F i r s t motored p r e s s u r e s  were r e c o r d e d f o r the range of o p e r a t i n g c o n d i t i o n s . p r e s s u r e d a t a were c o l l e c t e d and ensemble-averaged. a n a l y z e d to y i e l d motored  One hundred  cycles of  They were then  temperatures u s i n g the f o l l o w i n g p r o c e d u r e :  i s e n t r o p i c compression was assumed up t o i n t a k e v a l v e c l o s i n g ,  then t h e  p e r f e c t gas law was a p p l i e d f o r the remaining of the compression and expansion s t r o k e s . Appendix  F u r t h e r d e s c r i p t i o n s o f t h e s e methods a r e found i n  A.  Each w i r e was c a l i b r a t e d a g a i n s t a p i t o t tube, a t atmospheric temperature and p r e s s u r e i n a s m a l l wind  tunnel.  An a n a y t i c a l model was  25. Table 2 Operating C o n d i t i o n s - Motoring Tests  TEST #1:  P o s i t i o n A, O r i e n t a t i o n 1 RPM 1200 1800 2400 3000  Throttle WOT WOT WOT WOT  PART PART PART PART  (n , v (n ( ( v  n v  T1v  75%) 75%) 75%) 75%)  TEST #2: P o s i t i o n A, B, C O r i e n t a t i o n 1, 2 WOT Engine speed 1200,1800  used t o o b t a i n the f o l l o w i n g N u s s e l t vs Reynolds extended  t h e c a l i b r a t i o n t o any p r e s s u r e and  Nu = A + B Re  number c o r r e l a t i o n which  temperature  N (18)  The e q u a t i o n s o f the a n a l y t i c a l model were taken from L a n c a s t e r [28] and a r e based on heat t r a n s f e r s t u d i e s o f e l e c t r i c a l l y heated c y l i n d e r s t o a moving f l u i d  [34,35].  These methods a r e e x p l a i n e d i n d e t a i l i n Appendix  C. Once t h e h o t w i r e anemometer was c a l i b r a t e d , engine.  i t was mounted i n t h e  F o r t y c y c l e s of data were taken a t every f i f t h o f a c r a n k - a n g l e  degree f o r each c o n d i t i o n .  Gas p r o p e r t i e s deduced from t h e motored  p r e s s u r e s were then used i n the a n a l y s i s o f the hot wire s i g n a l to o b t a i n instantaneous v e l o c i t i e s . as suggested by Witze [ 3 6 ] .  These p r o p e r t i e s were e v a l u a t e d i n t h e same way  26. The raw cycle  v e l o c i t y d a t a was  time a v e r a g i n g method developed  degree window was and  reduced u s i n g a n o n - s t a t i o n a r y c y c l e  turbulence  by C a t a n i a and M i t t i c a  deduced f o r the frequency  cut-off  [37] .  by An 8  between mean v e l o c i t y  intensity.  Appendix C a l s o d e s c r i b e s i n d e t a i l t h e p a r t i c u l a r a s p e c t s of the hot wire measurements along with the procedure  4.3.2  f o r choosing the window s i z e .  Results F i g u r e 14 i s a p l o t of the mean v e l o c i t y a t wide open t h r o t t l e as a  f u n c t i o n of engine  speed.  F i g u r e s 15 and  16 show r e s p e c t i v e l y  the t u r b u -  l e n c e 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 c o n d i t i o n s . appears  t h a t the mean v e l o c i t y and  as expected.  i n t e n s i t y vary l i n e a r l y with engine  rpm  F i g u r e 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 p o i n t s i n the c y c l e :  ing  (30 BTDC).  flowfield  It  top dead c e n t e r and  a t y p i c a l spark t i m -  F i g u r e 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 .  i n the engine at the d e f i n e d spark time was  the s t a n d a r d c o n d i t i o n s p r e v a i l i n g  i n the c y l i n d e r  The  assumed to r e p r e s e n t  a t the b e g i n n i n g of  combustion. In o r d e r t o compare the p r e s e n t d a t a t o p r e v i o u s measurements, F i g u r e 19 was  reproduced  from a paper by Bobb, V a f i d i s and Whitelaw [38].  This  graph i s a c o m p i l a t i o n of top dead c e n t e r t u r b u l e n c e i n t e n s i t y measured i n v a r i o u s motored engines t h i s study was cycle  plotted  by d i f f e r e n t on the graph.  r e s o l v e d data were p l o t t e d .  averaged  researchers.  The  data o b t a i n e d i n  Both ensemble averaged  and c y c l e - b y -  I t can be seen t h a t even the ensemble  d a t a i s low compared t o p r e v i o u s experimentors.  There a r e some  events i n the data that can o n l y be e x p l a i n e d by the i r r e g u l a r shape of the chamber and dead c e n t e r . ally  the p o s i t i o n of the probe.  F o r example a hump o c c u r s a f t e r  top  I f t h i s were o r d i n a r y s q u i s h , the hump should l i e symmetric-  about top dead c e n t e r as found by o t h e r r e s e a r c h e r s [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 t o t h e l a r g e r s i z e and l i f t v a l v e which i s a t the source of the engine  turbulence.  o f the i n t a k e  In a d d i t i o n ,  the  chamber c o n f i g u r a t i o n , the p r o x i m i t y o f t h e w i r e t o the w a l l and the f a c t t h a t the R i c a r d o i s a new  engine  c o u l d a l s o e x p l a i n the low  turbulence  l e v e l s measured. The assumptions of i s o t r o p y and homogeneity t h a t a r e commonly used f o r simple d i s k chambers were t e s t e d on the R i c a r d o d a t a .  F i g u r e s 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 a l o n g the spark p l u g a x i s on the t u r b u l e n c e i n t e n s i t y a t 1200 h i g h e r speeds.  rpm.  The e f f e c t s were s i m i l a r a t  S i n c e the o b j e c t i v e s o f t h e motored t e s t s were t o get  i d e a of the t u r b u l e n c e l e v e l s , p o s i t i o n i n g  the probe i n the spark h o l e  a p p r o p r i a t e a l t h o u g h 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 o f the F i n a l l y i t i s important  to mention t h a t we  t u r b u l e n c e i n t e n s i t y d u r i n g the compression time of spark f i r i n g .  1200 1800 2400 3000  The  are i n t e r e s t e d i n the  s t r o k e and p a r t i c u l a r l y a t the  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  V  (m/s) mp 3.56 5.33 7.11 8.89  was  flowfield.  From the p r e s e n t d a t a the v a l u e s s e l e c t e d  RPM  an  as  are:  u'  (m/s) 0.85 1.36 1.67 1.95  e s t i m a t e d u n c e r t a i n t y a s s o c i a t e d w i t h these v a l u e s i s 50-70%.  A g a i n the r e a d e r i s r e f e r r e d t o Appendix B f o r d e t a i l s .  4.4  Combustion Measurements The  Table  4.4.1  range of o p e r a t i n g c o n d i t i o n s f o r the f i r e d  t e s t s i s shown i n  3.  Procedure  and Data A n a l y s i s  The procedure  f o r a c q u i r i n g f i r e d p r e s s u r e d a t a was  i d e n t i c a l t o the  28. Table 3 O p e r a t i n g C o n d i t i o n s - Combustion T e s t s  Relative Air/Fuel Ratio Throttle  Engine Speed (rpm) 1200 1800 2400 3000  one used  Spark Timing  WOT WOT WOT WOT  i n measuring motored p r e s s u r e s .  p r e s s u r e s c a l i n g and  X 3  1.0  1.01 1.00 1.04 1.08  MBT MBT MBT MBT  t a k e n a t each o p e r a t i n g c o n d i t i o n .  4.4.2  X =  One  X =  1-15  1.30  1.27 1.28 1.36 1.37  1.16 1.15 1.20 1.22  hundred c y c l e s of d a t a were  Appendix B d e s c r i b e s the d e t a i l s o f  ensemble-averaging.  Results F i g u r e s 22 t o 2 5 show the ensemble-averaged p r e s s u r e h i s t o r i e s f o r t h e  o p e r a t i n g c o n d i t i o n s measured. best torque. mixture  The  spark t i m i n g was  s e t a t minimum f o r  I t can be seen t h a t t h e peak p r e s s u r e decreases as  the  i s leaned.  From t h i s combustion d a t a , the p r e s s u r e r i s e due t o p i s t o n motion artificially only.  e x t r a c t e d to y i e l d graphs of p r e s s u r e r i s e due  T h i s was  accomplished  to combustion  by c a l c u l a t i n g what the p r e s s u r e i n the  c y l i n d e r would have been i f combustion had c y l i n d e r volume a t spark t i m i n g .  The  e n t i r e l y taken p l a c e a t the  r e s u l t i n g c u r v e s were s i m i l a r t o  c o n s t a n t volume combustion p r e s s u r e h i s t o r i e s . the n o r m a l i z e d p r e s s u r e r i s e was f r a c t i o n burned, an assumption  I t was  then assumed t h a t  p r o p o r t i o n a l t o the n o r m a l i z e d mass  used by R a s s w e i l e r and Withrow [ 1 9 ] .  S t a r t i n g from the o c c u r r e n c e of spark, f o r each subsequent a n g l e , the p r e s s u r e was  was  expanded p o l y t r o p i c a l l y  crank  from i t ' s v a l u e a t  the  c u r r e n t volume, t o the v a l u e i t would have had a t the spark volume by u s i n g the f o l l o w i n g e q u a t i o n :  29. 1.30 V(n) P , (n) = P ( n ) (rise V spark  (19)  A p o l y t r o p i c index of 1.3 was used as a mean v a l u e over temperatures  covered.  Thus c o n s t a n t volume combustion was s i m u l a t e d .  T y p i c a l r e s u l t s a r e presented pressure r i s e ,  the range o f  i n F i g u r e 26 which i s a p l o t of r e l a t i v e  ( t h e z e r o v a l u e b e i n g t h e p r e s s u r e a t spark f i r i n g and t h e .  one v a l u e being the peak p r e s s u r e a c h i e v e d ) spark f i r i n g f o r 1800 rpm.  as a f u n c t i o n of degrees  after  The assumption t h a t r e l a t i v e p r e s s u r e r i s e i s  r e p r e s e n t a t i v e o f o v e r a l l burning  r a t e was made.  I t can be seen from  these  graphs t h a t both i g n i t i o n d e l a y and o v e r a l l b u r n i n g r a t e a r e i n f l u e n c e d by the mixture  strength.  The l e a n e r m i x t u r e  has a l o n g e r i g n i t i o n d e l a y and  burns more s l o w l y . F i g u r e s 27 and 28 show t h e i n d i c a t e d and brake mean e f f e c t i v e as a f u n c t i o n of r e l a t i v e a i r - f u e l r a t i o w i t h engine It  speed as a parameter.  c a n be seen t h a t t h e work done by t h e engine decreases  leaned and i n c r e a s e s with engine  speed.  as t h e m i x t u r e i s  The i n c r e a s e with RPM i s due t o  the i n c r e a s e i n v o l u m e t r i c e f f i c i e n c y over t h e speed range and t h e r e d u c t i o n i n heat  transfer at higher  pressure  speeds.  30. 5.  SIMULATION PROGRAM RESULTS  In t h i s c h a p t e r , the r e s u l t s of the s i m u l a t i o n program development  are  presented. The engine s i m u l a t i o n program was  first  tested against experimental  combustion d a t a to e s t a b l i s h the v a l i d i t y of the model. p r e d i c t i o n s were examined and i n t e r p r e t e d . conducted  to determine  Next the model  F i n a l l y a p a r a m e t r i c study  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 v a r i a b l e s on  was the  combustion r e s u l t s .  5.1  Comparison w i t h E x p e r i m e n t a l R e s u l t s The b a s i s used f o r comparison between c a l c u l a t e d and e x p e r i m e n t a l  were the mass f r a c t i o n burned c u r v e s . c a l c u l a t e s t h i s value d i r e c t l y .  The  engine  data  s i m u l a t i o n program  These c u r v e s were compared t o t h e mass  f r a c t i o n burned data o b t a i n e d from e x t r a c t i n g p i s t o n motion from e x p e r i m e n t a l p r e s s u r e h i s t o r i e s as d e s c r i b e d i n S e c t i o n 4.4.2. Next the c a l c u l a t e d combustion d u r a t i o n and compared t o e x p e r i m e n t a l v a l u e s .  Finally  i g n i t i o n d e l a y were  the model p r e d i c t i o n s were  examined.  5.1.1  Mass F r a c t i o n Burned Curves It was  found t h a t , i n o r d e r t o o b t a i n b e s t agreement between  c a l c u l a t e d and  e x p e r i m e n t a l mass f r a c t i o n burned c u r v e s , the c f a c t o r i n  t h e t u r b u l e n t b u r n i n g e q u a t i o n must be v a r i e d w i t h engine speed.  This  c o n c l u s i o n became apparent  data a t  stoichiometric a i r - f u e l  when comparing the program r e s u l t s and  ratios.  31. The o t h e r model parameters were determined of the model. c f a c t o r was  A list  from l o g i c a l  implications  of the model parameters i s presented i n T a b l e 4.  chosen as b e s t f i t t o t h e near s t o i c h i o m e t r i c  The  experimental  mass burn curve, such t h a t the r a t e s of mass burned were as c l o s e as p o s s i b l e over the p e r i o d between 5 and 95% mass burned..  T a b l e 4.  S i m u l a t i o n Program Parameters  I g n i t i o n Delay ( t  d  e  l  a  y  j-^  ) h  I n t e g r a l Length  F i g u r e s 29  S c a l e a t Spark (L)  —  Burned Gas Volume F r a c t i o n i n T h i c k Flame (X ]_)  0.82  c f a c t o r @ 1200 1800 2400 3000  3.1 2.4 2.3 2.6  rpm rpm rpm rpm  through 40 show comparisons of c a l c u l a t e d and  experimental  mass f r a c t i o n burned c u r v e s f o r a l l twelve o p e r a t i n g c o n d i t i o n s . seen t h a t t h e r e i s good agreement between c a l c u l a t e d and  I t can  experimental  v a l u e s w i t h regards t o combustion i n i t i a t i o n and mass burn r a t e s . curves a r e a l s o i n agreement over the range of a i r - f u e l r a t i o s gated.  The  investi-  There i s however some d i s c r e p a n c y i n t h e l a s t s t a g e s of b u r n i n g  which w i l l be d i s c u s s e d i n the next  section.  The c f a c t o r i n the t u r b u l e n t b u r n i n g e q u a t i o n was speed  range.  v a r i e d over  e s t i m a t e d a t 50-70%.  When t h i s  u n c e r t a i n t y i s c o n s i d e r e d , the v a r i a t i o n i n c f a c t o r over the speed i s acceptable. rpm  and  the  T h i s c o u l d be e x p l a i n e d by the i n h e r e n t u n c e r t a i n t y i n t h e  t u r b u l e n t i n t e n s i t y measurements which was  1200  be  range  However, t h e r e i s some d i s c r e p a n c y between the c f a c t o r a t  that at higher  speeds.  32. The e x p e r i m e n t a l r e s u l t s a t 1200  rpm were s u s p e c t as the combustion  d u r a t i o n d i d not f o l l o w the same t r e n d than a t h i g h e r speeds. b e l i e v e d t h a t MBT The  spark t i m i n g was  not a c h i e v e d d u r i n g t h e s e  It i s tests.  f a c t o r which m u l t i p l i e s the t u r b u l e n c e i n t e n s i t y i n the t u r b u l e n t  b u r n i n g e q u a t i o n i s h i g h compared t o r e s u l t s o b t a i n e d by o t h e r modelers  [25].  In the l a s t  chapter i t was  engine  shown t h a t the t u r b u l e n c e  measured I n t h i s work were low compared t o p u b l i s h e d e x p e r i m e n t a l As w e l l , the c y c l e - b y - c y c l e a v e r a g i n g  used  ensemble averaged  results.  A s i m i l a r r e s u l t had  e x p e r i m e n t a l l y by F r a s e r , F e l t o n , Bracco and  5.1.2  Some r e s e a r c h e r s have  chosen as one f i f t h of the c l e a r a n c e  chamber h e i g h t a t the time of spark.  v e l o c i m e t r y to make two-point  velocity  been o b t a i n e d  S a n t a v i c c a [40] who  used  laser  s p a t i a l c o r r e l a t i o n measurements of  fluctuations.  Pressure  Histories  F i g u r e s 41 t o 52 are p l o t s of the c a l c u l a t e d and p r e s s u r e s generated was  values  i n t e n s i t y v a l u e s i n t h e i r models.  The i n t e g r a l l e n g t h s c a l e was  Doppler  results.  t e c h n i q u e l e a d s to i n t e n s i t y  as much as h a l f of the ensemble averaged  levels  experimental  from the runs d e s c r i b e d i n T a b l e 4.  Although  agreement  e x c e l l e n t i n the mass burn c u r v e s , the c a l c u l a t e d p r e s s u r e curves show  peak p r e s s u r e s as much as 20% h i g h e r than e x p e r i m e n t a l v a l u e s ,  the  expansion c u r v e s , however i n d i c a t e t h a t the heat l o s s p r e d i c t i o n s are i n agreement with e x p e r i m e n t a l v a l u e s .  I t i s b e l i e v e d t h a t the main reason  f o r t h i s o v e r e s t i m a t i o n of peak p r e s s u r e s i s due c a l c u l a t e d and  e x p e r i m e n t a l mass burn  curves.  t o the method of comparing  T h i s w i l l be d i s c u s s e d i n  d e t a i l i n the f o l l o w i n g chapter.  5.1.3  Combustion  Initiation  T a b l e 5 shows the v a l u e s of i g n i t i o n d e l a y o b t a i n e d f o r the base o p e r a t i n g c o n d i t i o n s .  The  i g n i t i o n d e l a y was  d e f i n e d as the  twelve average  33. time f o r t h e flame t o r e a c h a r\ v o r t e x tube, and was m o d e l l e d i n t h e f o l l o w i n g way = T  delay  _X 4 U I  I t c a n be seen from T a b l e 5 t h a t t h e mean random time d e l a y i n c r e a s e s as the mixture i s leaned. velocity.  T h i s i s due t o a r e d u c t i o n of t h e l a m i n a r b u r n i n g  I t can a l s o be seen t h a t , a l t h o u g h t h e r e i s l i t t l e  w i t h engine speed,  variation  t h e i g n i t i o n d e l a y tends t o d e c r e a s e as a d i r e c t  of the decrease i n T a y l o r m i c r o s c a l e w i t h  result  speed.  Table 5 I g n i t i o n Delay f o r t h e Twelve Base O p e r a t i n g C o n d i t i o n s  I g n i t i o n Delay Engine Speed (rpm)  Relative Air/Fuel Ratio  1200 1200 1200 1800 1800 1800 2400 2400 2400 3000 3000 3000  1.01 1.16 1.27 1.00 1.15 1.28 1.04 1.20 1.36 1.08 1.22 1.37  The time t o burn t h e f i r s t  (deg)  (msec)  2 2 3 2 3 4 3 4 5 4 5 6  0.28 0.28 0.42 0.19 0.28 0.37 0.21 0.28 0.35 0.22 0.28 0.33  5% o f t h e t o t a l mass i n t h e c y l i n d e r was  deduced from the mass f r a c t i o n burned  curves.  T h i s time has been p l o t t e d  i n F i g u r e 53 i n crank a n g l e degrees as a f u n c t i o n o f a i r - f u e l r a t i o w i t h engine speed as parameter,  i t can be seen that agreement i s b e t t e r a t  h i g h e r speeds due t o t h e f a c t t h a t t h e times i n v o l v e d a r e much s m a l l e r .  5.4.4  Combustion D u r a t i o n Combustion d u r a t i o n was d e f i n e d as the time i n crank angle degrees t o  b u r n 5 t o 95% of t h e t o t a l mass i n t h e c y l i n d e r .  Due t o t h e p r e v i o u s l y  34. mentioned d i s c r e p a n c y towards the end of combustion, t h e r e i s some d i s agreement between c a l c u l a t e d and  experimental values.  F i g u r e 54 shows the  c a l c u l a t e d and e x p e r i m e n t a l combustion d u r a t i o n as f u n c t i o n of r a t i o w i t h speed  as a parameter.  The  air-fuel  c a l c u l a t e d combustion d u r a t i o n s a r e  s h o r t compared t o e x p e r i m e n t a l v a l u e s .  A p l o t of 5 t o 80% mass f r a t i o n  burned would show b e t t e r agreement.  5.2  Model P r e d i c t i o n s  5.2.1  Flame Thickness The b u r n i n g zone t h i c k n e s s a t 50%  t o t a l mass burned i s p l o t t e d i n  F i g u r e 55 f o r the twelve program runs d e s c r i b e d i n the l a s t  section.  It  can be seen t h a t the t h i c k n e s s i n c r e a s e s as t h e a i r - f u e l m i x t u r e becomes leaner. rpm  The  t r e n d w i t h engine  speed  i n d i c a t e s much t h i c k e r flames a t 3000  compared t o the t h r e e slower engine speeds.  d e s c r i b e flame  t h i c k n e s s i n the program  6  The flame  The e q u a t i o n used  was:  =  t h i c k n e s s e s v a r i e s from 6 t o 9 mm  at stoichiometric a i r -  f u e l r a t i o s and i n c r e a s e s as the m i x t u r e i s l e a n e d . slower  laminar burning v e l o c i t y and  low temperatures  lower  l e v e l s which l e a d  to e x p l a i n as the t h i c k n e s s was  than a t lower speeds.  expected  The i n c r e a s e i n flame  a c h i e v e d i n the model by a decrease  to  This  to i n c r e a s e s t e a d i l y  thickness with  engine  i n T a y l o r m i c r o s c a l e and  g e n e r a l i n c r e a s e i n t u r b u l e n t b u r n i n g v e l o c i t y due levels.  of  and p r e s s u r e s .  with turbulence i n t e n s i t y . speed was  This i s a result  f u e l energy  T h i c k e r flames were p r e d i c t e d a t 3000 rpm is difficult  to  to increased turbulence  These t r e n d s are c o n s i s t e n t w i t h e x p e r i m e n t a l o b s e r v a t i o n s made by  Smith [14] .  The t h i c k n e s s e s a r e c o n s i s t e n t w i t h measurements made by  Namazian and a l . [ 1 5 ] .  35. 5.2.2  c F a c t o r V a r i a t i o n w i t h Engine Speed F i g u r e 56 i s a p l o t of c f a c t o r w i t h engine speed.  r e s u l t s f o r 1200 regarded, 15%.  rpm  a r e b e l i e v e d t o be s u s p e c t .  The  experimental  If t h i s data i s d i s -  the v a r i a t i o n of c f a c t o r over the h i g h e r  speed range i s w i t h i n  In a d d i t i o n t h e r e does not seem t o be a c l e a r t r e n d w i t h engine  speed,  i t is difficult  More work i s necessary  5.2.3  to draw m e a n i n g f u l c o n c l u s i o n s  results.  t o u n d e r s t a n d t h e r o l e of t h i s f a c t o r .  Thermodynamic and The  from these  Geometric P r o p e r t i e s  f o l l o w i n g curves  are  t y p i c a l model p r e d i c t i o n s f o r thermodynamic  p r o p e r t i e s o t h e r t h a n those d i s c u s s e d p r e v i o u s l y . F i g u r e 57 show the mass f r a c t i o n e n t r a i n e d and a f u n c t i o n of crank a n g l e degrees f o r 1800 fuel ratio.  I t can be seen t h a t the  two  s e n t a t i v e of the f a c t t h a t t h e b u r n i n g d u r i n g combustion.  F i g u r e 58  f o r the same program run. throughout combustion. flameradius below  rpm  curves  mass f r a c t i o n burned  and near s t o i c h i o m e t r i c a i r are s i m i l a r and  zone t h i c k n e s s i s q u i t e  i s a p l o t of the i n n e r and  are  repre-  constant  outer flame  T h i s f i g u r e shows the c o n s t a n t  flame  radii  thickness  I t i s i n t e r e s t i n g to note t h a t when the  i s of the o r d e r of 10 mm  outer  t h e mass f r a c t i o n burned i s s t i l l  well  1%. The  o u t e r flame a r e a i s p l o t t e d i n F i g u r e 59 a g a i n s t crank a n g l e f o r  the same c o n d i t i o n s .  The  reaches a maximum and  t h e n d e c r e a s e s due  This e f f e c t  area i n c r e a s e s i n i t i a l l y  as the flame grows,  t o the confinement of the chamber.  i s r e f l e c t e d i n the mass f r a c t i o n e n t r a i n e d  curve  shown  previously. The burning  volumes of the t h r e e zones a r e p l o t t e d i n F i g u r e 60. zone has a r e l a t i v e l y c o n s t a n t  volume during  the  The  thick  combustion  process.  5.2.4  as  Turbulent  Entrainment and  T h i s s e t of curves  Scales  show the model p r e d i c t i o n s f o r t u r b u l e n t  length  36. s c a l e s , enhanced t u r b u l e n t i n t e n s i t y and flame entrainment v e l o c i t y . F i g u r e 61 and 62 show the i n t e g r a l l e n g t h s c a l e and T a y l o r m i c r o s c a l e v a r i a t i o n s w i t h crank a n g l e f o r t h r e e p a r t i c u l a r c o n d i t i o n s :  1800 rpm a t  near s t o i c h i o m e t r i c and l e a n a i r - f u e l r a t i o s and 3000 rpm a t near stoichiometric a i r - f u e l ratio.  In t h e c a s e o f t h e i n t e g r a l l e n g t h s c a l e s ,  the i n i t i a l  v a l u e s a r e s i m i l a r s i n c e i t was assumed t h a t L = h /5. c i n t e g r a l l e n g t h s c a l e was then enhanced a c c o r d i n g t o the r e l a t i o n :  ^  ^spark  p  p  ^ u^ u,spark^  The T a y l o r m i c r o s c a l e curves show the e f f e c t of unburned between near s t o i c h i o m e t r i c and l e a n .  gas d e n s i t y  The Reynolds number e f f e c t i s  r e f l e c t e d i n the s m a l l e r s c a l e s a t h i g h e r engine speed. t h a t t h e T a y l o r m i c r o s c a l e d i m i n i s h e s as combustion d i r e c t consequence  The  I t can be seen  p r o g r e s s e s , which i s a  of the decrease of the i n t e g r a l l e n g t h  scale.  The b e h a v i o u r o f t h e c a l c u l a t e d T a y l o r m i c r o s c a l e and thus t h e s c a l e of the t u r b u l e n t flame s t r u c t u r e agreed w i t h measurements performed by Smith  [14] and Keck [ 2 9 ] . I t was found through v i s u a l i z a t i o n t e c h n i q u e s ,  t h a t the flame s t r u c t u r e s i z e decreased w i t h engine speed and a l s o as combustion p r o g r e s s e d . The enhanced t u r b u l e n c e i n t e n s i t y i s p l o t t e d i n F i g u r e 63 f o r t h e same t h r e e c o n d i t i o n s d e s c r i b e d above.  The s l i g h t d i f f e r e n c e s i n the curves a t  1800 rpm a r e a r e s u l t o f d i f f e r e n t unburned was enhanced i n the f o l l o w i n g  U  u  gas d e n s i t i e s .  The i n t e n s i t y  way:  ,spark  p  p  ^ u^ u,spark^  F i g u r e 64 shows the t u r b u l e n t entrainment v e l o c i t y a t 1800 rpm f o r X « 1.00, X a 1.30 and 3000 rpm f o r 1 = 1.00.  37. 5.3  P a r a m e t r i c Study The purpose o f the p a r a m e t r i c study was  tive effect  of c e r t a i n parameters.  t o g a i n i n s i g h t i n t o the r e l a -  T h i s enabled the i d e n t i f i c a t i o n of key  f a c t o r s which were shown t o p r e d o m i n a t e l y i n f l u e n c e combustion. m e t r i c study was  a l s o an e v a l u a t i o n of the model i n showing  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 p a r a -  t h a t i t l e d to  The key  examined were the volume d i s t r i b u t i o n i n the t h i c k burning zone, c o n s t a n t c i n the t u r b u l e n t entrainment e q u a t i o n and the i n t e g r a l  variables the length  scale.  5.3.1  E f f e c t o f Volume D i s t r i b u t i o n i n the T h i c k Flame These s e r i e s of program runs were g e n e r a t e d t o examine t h e e f f e c t of  the volume d i s t r i b u t i o n i n the t h i c k flame zone on the r a t e of t o t a l mass burned. a t 2.2  For t h i s t e s t , the flame p r o p a g a t i o n f a c t o r C was and the i n t e g r a l l e n g t h s c a l e was  ance chamber h e i g h t a t time o f s p a r k .  assumed to be equal to the c l e a r -  These t e s t s were performed f o r a l l  the twelve e x p e r i m e n t a l o p e r a t i n g c o n d i t i o n s . i n c l u d e d a t t h i s p o i n t of the s t u d y . initially was  a r b i t r a r i l y set  I g n i t i o n d e l a y had not been  The range of volume f r a c t i o n s  chosen from 75 t o 95% burned  was  volume to t o t a l flame volume.  It  found t h a t 80 t o 90% l e d t o mass b u r n c u r v e s c l o s e s t t o e x p e r i m e n t a l  values. F i g u r e 65 shows a t y p i c a l r e s u l t of the program runs a l o n g w i t h the e x p e r i m e n t a l mass burned fuel ratio.  curves f o r 3000 rpm and near s t o i c h i o m e t r i c a i r -  The r e s u l t s i n d i c a t e d t h a t t h e e f f e c t of volume f r a c t i o n  more important a t h i g h e r speeds.  T h i s i s a g a i n due to the f a c t t h a t  was the  times i n v o l v e d between crank a n g l e degrees a r e s m a l l e r a t h i g h e r engine speeds.  Thus changes i n the mass burn r a t e are r e f l e c t e d more s t r o n g l y a t  h i g h e r 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 t h i c k n e s s through changes i n thermodynamic p r o p e r t i e s due  to f a s t e r or slower b u r n i n g .  The  38. c h o i c e of the volume d i s t r i b u t i o n f a c t o r was e f f e c t on combustion  5.3.2  program was  Burning  Equation  r u n a t the f o l l o w i n g c o n d i t i o n s t o examine t h e  of f a c t o r c i n the t u r b u l e n t entrainment e q u a t i o n . was be  s e t a t 90%  significant  duration.  E f f e c t of c F a c t o r i n T u r b u l e n t The  shown t o have  f o r these runs and  the chamber h e i g h t at time of  The  volume d i s t r i b u t i o n  t h e i n t e g r a l l e n g t h s c a l e was  assumed t o  spark.  These t e s t s were r u n a t a l l twelve e x p e r i m e n t a l and  effect  2.4.  conditions with c  t a k i n g the v a l u e s 2.0,  2.2  A representative result  i s plotted i n  F i g u r e 66 f o r 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 s t r o n g dependance of r a t e of t o t a l mass burned on c f a c t o r .  5.3.3  I n t e g r a l Length One  Scale  of the assumptions of the model was  r e l a x e d at top dead c e n t e r .  According  t h a t the t u r b u l e n c e  to these arguments, the s i z e of  l a r g e r e d d i e s would be of the o r d e r of t h e l i m i t i n g dimension of chamber.  approximately  These two  t h i s v a r i a t i o n and F i g u r e s 67 and  one  f i f t h of the chamber h e i g h t a t top dead  t o see which l e d t o t h e b e s t  and  results.  The  o p e r a t i n g c o n d i t i o n s were  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 t e s t s were  performed w i t h a l l o t h e r parameters s e t a c c o r d i n g t o T a b l e The  of  show a s e t of program runs d i f f e r i n g o n l y i n the  d e f i n i t i o n of the i n t e g r a l l e n g t h s c a l e . 3000 rpm  found  v a l u e s were t e s t e d i n t h r model to see the e f f e c t  68  the  the  F r a s e r et a l . [40] measured the i n t e g r a l l e n g t h s c a l e and  t h a t i t was center.  was  c h o i c e of i n t e g r a l l e n g t h s c a l e had  s i g n i f i c a n t e f f e c t on  c a l c u l a t e d i g n i t i o n d e l a y and mass burn r a t e s .  c  operating conditions.  the  The model p r e d i c t i o n s a r e  improved when the i n t e g r a l l e n g t h s c a l e i s chosen as h / 5 . were observed a t the other  5.  Similar  trends  39. 6.  6.1  DISCUSSION OF UNCERTAINTIES  Model Assumptions One  of the major assumptions of t h e model was  that the  relationships  of i s o t r o p i c t u r b u l e n c e c o u l d be used to d e s c r i b e the f l o w f i e l d i n the engine.  T h i s assumption was  Semenov [9] and L a n c a s t e r  based on f i n d i n g s of experimenters  [ 8 ] , who  engine w i t h a hot w i r e anemometer.  such  measured the t u r b u l e n c e i n a motored The g e n e r a l c o n c l u s i o n was  that i n a  simple combustion chamber, the t u r b u l e n c e a t top dead c e n t e r tended i s o t r o p y and homogeneity.  as  This> assumption was  towards  extended, i n t h i s case,  the R i c a r d o combustion chamber which has a s q u i s h c o n f i g u r a t i o n .  to  The  t u r b u l e n c e i n t e n s i t i e s o b t a i n e d i n t h e R i c a r d o engine d i d not g i v e  evidence  of a t u r b u l e n t i n t e n s i t y i n c r e a s e around top dead c e n t e r which has  been  shown t o be c h a r a c t e r i s t i c of s q u i s h chambers [39] .  I n s t e a d a hump  was  p r e s e n t a f t e r top dead c e n t e r 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 t h e v a r i o u s c a v i t i e s of the chamber.  i n mean  The  smooth d e c r e a s e  v e l o c i t y and  turbulence i n t e n s i t y  c e n t e r tends  t o i n d i c a t e t h a t the t u r b u l e n c e i s r e l a x i n g as the p i s t o n i s  n e a r i n g the end  of i t s t r a v e l .  from i n t a k e v a l v e c l o s i n g to top dead  A simple  a b e t t e r medium f o r t e s t i n g t h e model. the i s o t r o p i c assumption was  used and  combustion chamber would have been However i n the p r e s e n t  situation  the r e s u l t s should be i n t e r p r e t e d  w i t h t h e s e l i m i t a t i o n s i n mind. A l o n g w i t h the i s e n t r o p i c t u r b u l e n c e assumption, the s p h e r i c i t y assumption would a l s o be more r e a l i s t i c has however been observed except  i n a simple combustion chamber.  t h a t the flames a r e very c l o s e t o s p h e r i c a l  i n chambers where t h e r e i s s t r o n g s w i r l  [15].  It  40. The engine s i m u l a t i o n program runs were c a l c u l a t e d from t h e e x p e r i mental o p e r a t i n g c o n d i t i o n s .  Assumptions were made i n d e t e r m i n i n g the  p r e s s u r e and temperature  a t bottom dead c e n t e r , t h e r e s i d u a l f r a c t i o n i n  the chamber and the heat  l o s s t o the c y l i n d e r w a l l s .  The e r r o r a s s o c i a t e d  i n determining the reference pressure i s n e g l i g i b l e f o r experimental p r e s s u r e data s i n c e the whole curve i s simply s h i f t e d by a c o n s t a n t .  Thus  an e r r o r o f a few k i l o P a s c a l s a t bottom dead c e n t e r i s n e g l i g i b l e a t top dead c e n t e r . impact  However, the i n i t i a l  p r e s s u r e and temperature  on t h e s i m u l a t i o n c a l c u l a t i o n s s i n c e they determine  had s i g n i f i c a n t the i n i t i a l  thermodynamic s t a t e 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 s e t a t 5% s i n c e t h i s i s a t y p i c a l v a l u e encountered  i n experiments.  The u n c e r t a i n t y c o u l d have been d i m i n i s h e d by  a t t e m p t i n g t o model i n t a k e and exhaust was  unnecessary  s t r o k e s b u t i t was judged t h a t t h i s  a t t h i s s t a g e , s i n c e a v a l i d comparison c o u l d s t i l l  be made  between model and experiment. The heat l o s s e q u a t i o n was developed of  by Annand [33] .  The c o e f f i c i e n t s  the equation were chosen because they were t y p i c a l values observed f o r  v a r i o u s engines.  The comparison o f c a l c u l a t e d and e x p e r i m e n t a l  h i s t o r i e s gave an i n d i c a t i o n t h a t the heat  t r a n s f e r was c l o s e t o the a c t u a l  heat t r a n s f e r as t h e e x p a n s i o n s t r o k e s were s i m i l a r . through  pressure  I t was a l s o  found  t e s t i n g the model w i t h 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  e q u a t i o n , t h a t t h e d i f f e r e n c e s observed between c a l c u l a t e d and e x p e r i m e n t a l p r e s s u r e h i s t o r i e s c o u l d not be e x p l a i n e d by an i n a c c u r a t e heat factor.  transfer  F i g u r e 69 shows t h e e f f e c t o f v a r y i n g t h e f a c t o r a i n Annand's  equation. I t was mentioned i n Chapter regards to burning r a t e .  3 t h a t two assumptions were made w i t h  The f i r s t  was t o assume t h a t the flame  c o u l d be  approximated  by a q u a r t e r sphere f o r t h e very f i r s t c a l c u l a t i o n s t e p .  a d d i t i o n , the entrainment for  this first  e q u a t i o n was  reduced  to the f o l l o w i n g e x p r e s s i o n  step only: dR T  p  i - U  dt  T h i s was  -± t  p  b  necessary because the amount of mass e n t r a i n e d i s  determined  from the t u r b u l e n t b u r n i n g v e l o c i t y , t h e unburned gas d e n s i t y and the area.  Since no flame area was  proposed.  In  I t was  available i n i t i a l l y ,  t h i s assumption  flame  was  t e s t e d a g a i n s t flame geometry c a l c u l a t i o n s and found  be v a l i d f o r r a d i i i n the 0 t o 10 mm  range.  T h i s assumption  to  i s not  b e l i e v e d t o i n t r o d u c e e r r o r as t h e mass f r a c t i o n e n t r a i n e d and burned a r e much l e s s than 1% a t the end  6.2  of t h i s f i r s t  step.  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 the Measurements The u n c e r t a i n t y a s s o c i a t e d w i t h t h e hot w i r e measurements and  ing  technique has been d i s c u s s e d e x t e n s i v e l y .  a v e r a g i n g t e c h n i q u e used was to  other r e s e a r c h e r s and  to  o t h e r modelers.  One  consequence of  t h a t the t u r b u l e n c e i n t e n s i t y was  averagthe  low  compared  thus the c f a c t o r i n our model seems h i g h compared  In a d d i t i o n , the meaning of the hot w i r e  signal  r e c o r d e d must be i n t e r p r e t e d w i t h r e s e r v a t i o n because of the low magnitude of  the mean v e l o c i t y c o u p l e d w i t h the f a c t t h a t the flow f i e l d  chamber i s unknown due  6.3  i n the  to the i r r e g u l a r shape of the combustion chamber.  U n c e r t a i n t i e s i n I n t e r p r e t a t i o n of R e s u l t s The b a s i s of comparison of the model w i t h e x p e r i m e n t a l r e s u l t s was  mass f r a c t i o n burned c u r v e s .  The  e x p e r i m e n t a l mass f r a c t i o n burned  the  curves  42. were determined from t h e p r e s s u r e h i s t o r i e s u s i n g a p i s t o n motion e x t r a c t i o n method d e s c r i b e d i n Chapter 4. Comparing  p r e s s u r e h i s t o r i e s o f f e r s a good check o f t h e model b u t more  i n f o r m a t i o n would be gained i f a d i r e c t comparison of flame s t r u c t u r e had been p o s s i b l e through flame v i s u a l i z a t i o n t e c h n i q u e s .  One d i f f i c u l t y  encountered d u r i n g t h i s work was t h a t i t i s r e l a t i v e l y easy t o match p r e s s u r e h i s t o r i e s and mass b u r n r a t e c u r v e s w i t h a g i v e n c o m b i n a t i o n o f c f a c t o r , flame d e n s i t y d i s t r i b u t i o n and flame t h i c k n e s s .  U n f o r t u n a t e l y , we  can only r e l y on p r e v i o u s experimenters r e s u l t s w i t h r e s p e c t t o t h e s e parameters.  A d i r e c t comparison over a wide range of c o n d i t i o n s would be  quite informative. The method used t o e x t r a c t t h e mass burn r a t e from t h e combustion p r e s s u r e s must a l s o be approached w i t h r e s e r v a t i o n .  I t was based on t h e  observed f a c t t h a t p r e s s u r e r i s e due t o combustion i s p r o p o r t i o n a l t o mass f r a c t i o n burned.  The method used a p o l y t r o p i c compression or expansion of  the c y l i n d e r c o n t e n t s back t o t h e volume a t s p a r k .  The c h o i c e o f t h e p o l y -  t r o p i c index was based mainly on t h e f a c t t h a t the r e s u l t i n g be s i m i l a r t o a c o n s t a n t volume bomb p r e s s u r e r i s e c u r v e . was  curve should  An i n d e x o f 1.3  chosen as the e x p e r i m e n t a l curves showed the r a p i d p r e s s u r e r i s e  f o l l o w e d by a d e c r e a s e supposedly due t o h e a t l o s s .  The p i s t o n e x t r a c t i o n  method was t e s t e d on a c a l c u l a t e d p r e s s u r e curve from the t h i c k s i m u l a t i o n model.  The r e s u l t i s shown i n F i g u r e 70.  flame  T h i s f i g u r e shows t h e  e x p e r i m e n t a l mass burn curve c a l c u l a t e d from the p i s t o n motion  extraction  program, t h e c a l c u l a t e d mass f r a c t i o n burned and t h e r e s u l t o f e x t r a c t i n g the p i s t o n motion from the c a l c u l a t e d p r e s s u r e c u r v e .  I t can be seen t h a t  t h e r e i s a problem a t t h e end o f combustion a t t r i b u t e d t o t h e f a c t t h a t t h e p r e s s u r e r i s e d i d n ' t r e a c h a maximum u n t i l  the exhaust v a l v e opened.  This  o f f e r s some i n s i g h t i n t h e g e n e r a l poor agreement between c a l c u l a t e d and e x p e r i m e n t a l runs a t the end of combustion. proposed t o d e a l w i t h t h i s  inconsistency.  A b e t t e r method s h o u l d be  43. 7.  CONCLUSIONS  The o b j e c t i v e of t h i s work was  to develop an engine s i m u l a t i o n program  i n c o r p o r a t i n g a t u r b u l e n t entrainment model developed by Daneshyar and Hill.  In a d d i t i o n , a s e r i e s of experiments were to be performed  mine the t u r b u l e n c e l e v e l s i n the R i c a r d o engine and the p r e s s u r e s a s s o c i a t e d w i t h b u r n i n g a gaseous was  to d e t e r -  combustion  f u e l i n the engine.  The model  t o be t e s t e d a g a i n s t e x p e r i m e n t a l d a t a and e v a l u a t e d . The steps taken were:  1.  An engine s i m u l a t i o n program was  entrainment model.  developed i n c o r p o r a t i n g the t u r b u l e n t  T h i s program s i m u l a t e s the f i r i n g s t r o k e s of the  R i c a r d o Hydra engine o p e r a t i n g on a gaseous  fuel.  The model f e a t u r e s  i g n i t i o n d e l a y and t u r b u l e n t entrainment of a t h i c k r e a c t i o n f r o n t accompanied  2.  by slow laminar b u r n i n g i n s i d e the t h i c k flame.  The t u r b u l e n c e l e v e l s i n the motored engine were measured u s i n g h o t  wire anemometry.  Measurements were conducted a t f o u r engine speeds and a t  v a r i o u s p o s i t i o n s a l o n g the spark p l u g a x i s i n the chamber.  The  resulting  t u r b u l e n c e i n t e n s i t y l e v e l s were low compared to p u b l i s h e d r e s u l t s a t comparable  3.  engine  Combustion  speeds.  p r e s s u r e 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  the p r e s s u r e d a t a , mass f r a c t i o n burned  o p e r a t e d on n a t u r a l gas.  curves were c a l c u l a t e d .  The c o n c l u s i o n s t h a t can be drawn f r o m t h i s work a r e the f o l l o w i n g : The o r i g i n a l form of the proposed model underestimated  combustion  From  44. d u r a t i o n s when compared t o experiments.  A c o n s t a n t was added t o i n c r e a s e  the e f f e c t  T h i s constant was a d j u s t e d f o r  of the t u r b u l e n c e i n t e n s i t y .  b e s t agreement w i t h e x p e r i m e n t a l mass f r a c t i o n burned d a t a o b t a i n e d a t stoichiometric a i r - f u e l ratios. c a l c u l a t i o n s and experiments burn r a t e s over the speed  T h i s l e d to good agreement between  w i t h regards  t o combustion i n i t i a t i o n and mass  and a i r - f u e l r a t i o range i n v e s t i g a t e d .  There was  however d i s c r e p a n c y towards t h e end o f combustion which i s b e l i e v e d t o be a r e s u l t of the method used  t o c a l c u l a t e the e x p e r i m e n t a l mass f r a c t i o n  burned. The model p r e d i c t e d h i g h e r peak p r e s s u r e s by about 10%. t r e n d was o b t a i n i n g over the speed  and a i r - f u e l r a t i o  range.  The c o n s t a n t added t o t h e t u r b u l e n c e i n t e n s i t y was speed showing v a r i a t i o n s of 15% over the h i g h e r speed The p a r a m e t r i c study  The c o r r e c t  dependent  range.  l e d t o the f o l l o w i n g r e s u l t s :  The model i s very s e n s i t i v e to the c f a c t o r i n the t u r b u l e n t b u r n i n g e q u a t i o n and t o t h e volume d i s t r i b u t i o n i n t h e t h i c k flame.  The c h o i c e o f  the i n t e g r a l l e n g t h s c a l e a l s o 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 d e l a y and combustion d u r a t i o n .  The v a l u e r e t a i n e d i n t h e model was one f i f t h o f t h e  c l e a r a n c e h e i g h t a t time of s p a r k . The p r e d i c t e d flame experimental r e s u l t s .  t h i c k n e s s e s agreed w e l l w i t h p u b l i s h e d  The c o r r e c t t r e n d with engine  r a t i o was a l s o a c h i e v e d by t h e model.  speed  and a i r - f u e l  8.  RECOMMENDATIONS  I t i s recommended t h a t t h i s model be t e s t e d a g a i n s t combustion o b t a i n e d from a simple geometry engine o r a w e l l - s t i r r e d bomb.  data  T h i s would  enable e a s i e r d i a g n o s i s of e x p e r i m e n t a l d a t a . I t i s a l s o recommended t h a t flame v i s u a l i z a t i o n o r o t h e r s u i t a b l e t e c h n i q u e s be used t o measure flame s t r u c t u r e and t h i c k n e s s over a range o f engine speeds  ( o r t u r b u l e n c e l e v e l s ) and a i r - f u e l  ratios.  Since the model i s based on t h e s t r u c t u r e of the t u r b u l e n t e f f o r t s s h o u l d be d i r e c t e d towards  flame,  v e r i f y i n g t h e 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 S t r u c t u r e of S m a l l S c a l e T u r b u l e n c e and I t s E f f e c t on Combustion i n S p a r k - I g n i t i o n E n g i n e s , " Report t o be p u b l i s h e d .  [2]  Andrews, G.E. and B r a d l e y , D., "Turbulence and T u r b u l e n t Flame P r o p a g a t i o n - A C r i t i c a l A p p r a i s a l , " Combustion and Flame, V o l . 24, pp. 285-304, 1975.  [3]  Abdel-Gayed, R.G., A l - K h i s h a l i , K.J., B r a d l e y , D., "Turbulent Burning V e l o c i t i e s and Flame S t r a i n i n g i n E x p l o s i o n s , " Proceedings o f t h e R o y a l S o c i e t y , London, Ser. A., V o l . 391, pp. 393-414, 1984.  [4]  L a n c a s t e r , D.R., K r i e g e r , R.B., Sorensen, S.C. and H u l l , W.L., " E f f e c t o f Turbulence on S p a r k - I g n i t i o n Engine Combustion," SAE 760160, 1976.  [5]  T a b a c z y n s k i , R.J., "Turbulence and T u r b u l e n t Combustion i n SparkI g n i t i o n E n g i n e s , " Prog. Energy Combust. S c i . , Vo. 2, pp. 143-165, 1976.  [6]  G r o f f , E.G. and Matekunas, F.A., "The Nature of T u r b u l e n t Flame P r o p a g a t i o n i n a Homogeneous S p a r k - I g n i t e d E n g i n e , " SAE 800133, 1980.  [7]  T a b a c z y n s k i , R.J., "Turbulence Measurement and M o d e l l i n g i n R e c i p r o c a t i n g Engines - An Overview," I Mech. Eng. 1983.  [8]  L a n c a s t e r , D.R., " E f f e c t of Engine V a r i a b l e s on Turbulence i n a S . I . Engine," SAE 760159, 1976.  [9]  Semenov, E.S., " S t u d i e s of T u r b u l e n t Gas Flow i n P i s t o n E n g i n e s , " NASA T e c h n i c a l T r a n s l a t i o n F-97, 1963.  [10]  Smith, J.R., "The I n f l u e n c e of Turbulence on Flame S t r u c t u r e i n an E n g i n e , " ASME Conference Phoenix, A r i z o n a , Paper WO 14-19, 1982.  [11]  Witze, P.O., M a r t i n , J.K. and Borgnakke, K., "Measurements and P r e d i c t i o n F l u i d M o t i o n and Combustion Rates i n a S p a r k - I g n i t i o n E n g i n e , " SAE 831697, 1983.  [12]  Witze, P.O., M a r t i n , J.K and Borgnakke, K., "Combustion E f f e c t s on t h e Preflame Flow F i e l d i n a Research Engine," SAE 850122, 1985.  [13]  Wong, V.W. and H o u l t , D.P., "Rapid D i s t o r s i o n Theory A p p l i e d t o T u r b u l e n t Combustion," T r a n s a c t i o n s o f t h e SAE, V o l . 88, Paper Nb. 790357, pp. 1243-1262, 1979.  [14]  Smith, R.J., "Turbulent Flame S t r u c t u r e i n a Homogeneous Charge E n g i n e , " SAE 820043, 1982.  47.  [15]  Namazian, M., Hansen, S., L y f o r d - P i k e , E., Sanchez-Barsse, J . , Heywood, J . and R i f e , J . , " S c h l i e r e n V i s u a l i z a t i o n o f t h e Flow and D e n s i t y F i e l d s i n the C y l i n d e r of a S p a r k - I g n i t i o n E n g i n e , " SAE 800044, 1980.  [16]  Andrews, G.E. and B r a d l e y , D., "Determination of Burning V e l o c i t i e s : A C r i t i c a l Review," Combustion and Flame, V o l . 18, pp. 133-153, 1972.  [17]  Tennekes, H., "Simple Model f o r the S m a l l - S c a l e S t r u c t u r e o f Turbulence," The P h y s i c s o f F l u i d s , V o l . 11, No. 3, pp. 669-670, 1968.  [18]  Chomiak, J . , " D i s s i p a t i o n F l u c t u a t i o n s and the S t r u c t u r e and P r o p a g a t i o n o f T u r b u l e n t Flames i n Premixed Gases a t High Reynolds Numbers," S i x t e e n t h Symposium ( I n t e r n a t i o n a l ) on Combustion, The Combustion I n s t i t u t e , pp. 1665-1673, 1977.  [19]  R a s s w e i l e r , G.M. and Withrow, L., "Motion P i c t u r e s of Engine Flames C o r r e l a t e d w i t h P r e s s u r e Cards," SAE T r a n s a c t i o n s , V o l . 42, No. 5, pp. 185-204, 1938.  [20]  P a t t e r s o n , D.J. and Van Wylen, G.V., "A D i g i t a l Computer S i m u l a t i o n f o r Spark I g n i t e d E n g i n e C y c l e s , " SAE Paper No. 633 F, 1963.  [21]  K r i e g e r , R.B. and Borman, G.L., "The Computation o f Apparent Heat R e l e a s e f o r I n t e r n a l Combustion Engines," ASME 66-WA/DGP-4, 1966.  [22]  M a t t a v i , J.N., G r o f f , E.G., L i e n e s c h , J.H., Matekunas, F.A. and Noyes, R.N., "Engine Improvements Through Combustion M o d e l l i n g , " Combustion M o d e l l i n g i n R e c i p r o c a t i n g Engines, pp. 537-587, M a t t a v i , J.N. and Annand, C A . E d i t o r s , Plenum P r e s s , New York-London, 1980.  [23]  B l i z a r d , N.C. and Keck, J.C., "Experimental and T h e o r e t i c a l I n v e s t i g a t i o n o f T u r b u l e n t B u r n i n g Model f o r I n t e r n a l Combustion Engines," SAE T r a n s a c t i o n s , V o l . 83, Paper No. 740191, pp. 846-864, 19 74.  [24]  B e r e t t a , G.P., R a s h i d i , M., Keck, J.C., "Turbulent Flame P r o p a g a t i o n and Combustion i n S p a r k - I g n i t i o n Engines," Combustion and Flame, V o l . 52, pp. 217-245, 1983.  [25]  T a b a c z y n s k i , R.J., Ferguson, C.R. and Radhakrishnan, K., "A T u r b u l e n t Entrainment Model f o r S p a r k - I g n i t i o n Engine Combustion," SAE T r a n s a c t i o n s , V o l . 86, Paper No. 770647, pp. 2414-2433, 1977.  [26]  H i r e s , S.D., T a b a c z y n s k i , R . J . and Novak, J.M., "The P r e d i c t i o n o f I g n i t i o n Delay and Combustion I n t e r v a l s f o r a Homogeneous Charge S p a r k - I g n i t i o n Engine," SAE 780232, 1978.  [27]  Narayanan, M.A.B., Rajogopalan, S. and Narasimha, R., "Experiments on the F i n e S t r u c t u r e o f T u r b u l e n c e , " J . F l u i d Mech., V o l . 80, P a r t 2, 1977.  48.  [28]  Kuo, A.Y.S. and C o r r s i n , S., "Experiments on I n t e r n a l I n t e r m i t t e n c y and F i n e - S t r u c t u r e D i s t r i b u t i o n F u n c t i o n s I n F u l l y T u r b u l e n t F l u i d , " J o u r n a l of F l u i d Mechanics, V o l . 50, P a r t 2, pp. 285-319, 1971.  [29]  Keck, J.C., "Turbulent Flame S t r u c t u r e and Speed i n S p a r k - I g n i t i o n Engines," N i n e t e e n t h Symposium ( I n t e r n a t i o n a l ) on Combustion, The Combustion I n s t i t u t e , 1982, pp. 1451-1466.  [30]  T a y l o r , G.I., " S t a t i s t i c a l Theory of Turbulence," P r o c e e d i n g s of R o y a l S o c i e t y (London), Ser. A., V o l . 151, p. 421, 1935.  [31]  Jones, A.L., "The Performance of a Turbocharged S p a r k - I g n i t i o n E n g i n e F u e l l e d w i t h N a t u r a l Gas and G a s o l i n e " , M.A.Sc. T h e s i s , U n i v e r s i t y o f B r i t i s h Columbia, 1985.  [32]  Andrews, G.F. and B r a d l e y , D., "The Burning V e l o c i t y of Methane A i r M i x t u r e s " , Combustion and Flame, V o l . 19, pp. 275-288, 1972.  [33]  Annand, W.J.D., "Heat T r a n s f e r i n the C y l i n d e r of R e c i p r o c a t i n g I n t e r n a l Combustion E n g i n e s , " Proc. I n s t n . Mech. E n g r s . , V o l . 177, No. 36, pp. 973-996, 1983.  [34]  C o l l i s , D.C. and W i l l i a m s , M.J., "Two-Dimensional C o n v e c t i o n from Heated Wires a t Low Reynolds Numbers," J o u r n a l o f F l u i d Mechanics, V o l . 6, pp. 357-384, 1959.  [35]  Davies, P.O.A.L. and F i s h e r , M.J., "Heat T r a n s f e r from E l e c t r i c a l l y Heated C y l i n d e r s , " P r o c e e d i n g s o f the R o y a l S o c i e t y , 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 Doppler V e l o c i m e t r y f o r I.C. E n g i n e A p p l i c a t i o n s , " SAE 800132,  [37]  C a t a n i a , A.E. and M i t t i c a , A., "A C o n t r i b u t i o n to the D e f i n i t i o n of T u r b u l e n c e i n a R e c i p r o c a t i n g 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 R e c i p r o c a t i n g E n g i n e , " 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 E n g i n e Speed Dependance of T u r b u l e n t A i r M o t i o n i n an I.C. E n g i n e , " SAE 770220, 1977.  [40]  F r a s e r , R.A., F e l t o n , P.G., B r a c c o , F.V. and S a n t a v i c c a , D.A., " P r e l i m i n a r y T u r b u l e n c e L e n g t h S c a l e Measurements i n a Motored IC Engine," SAE 860021, 1986.  [41]  T a b a c z y n s k i , R.J., T r i n k e r , F.H. and Shannon, B.A.S., " F u r t h e r Refinements and V a l i d a t i o n of a T u r b u l e n t Entrainment Model f o r S p a r k - I g n i t i o n E n g i n e s , " Combustion and Flame, V o l . 39, pp. 111-121, 1980.  the  Laser 1980.  49.  [42]  McCormack, P.D., S c h e l l e r , K., M u e l l e r , G. and T i s h e r , R., "Flame P r o p a g a t i o n i n a V o r t e x Core", Combustion and Flame, V o l . 19, pp. 297-303, 1972.  [43]  Brown, W.L., "Methods f o r E v a l u a t i n g Requirements and E r r o r s i n C y l i n d e r P r e s s u r e Measurements," SAE 670008, 1968.  [44]  L a n c a s t e r , D.R., K r i e g e r , R.B. and L i e n e s c h , J.H., "Measurement and A n a l y s i s of E n g i n e P r e s s u r e Data," SAE 750026, 1975.  [45]  Moore, C , "UBC Curve-Curve F i t t i n g R o u t i n e s " , Computing 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 I n t e g r a t i o n " , Computing Columbia, 1982.  [47]  Amann, C.A., " C l a s s i c a l Combustion D i a g n o s t i c s f o r Engine R e s e a r c h , " SAE 850395, 1985.  [48]  Cameron, C D . , "An I n v e s t i g a t i o n of Squish Generated T u r b u l e n c e i n an I n t e r n a l Combustion E n g i n e , " M.A.Sc. T h e s i s , 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 o f T u r b u l e n c e Parameters i n R e c i p r o c a t i n g IC E n g i n e s , " Cambridge U n i v e r s i t y E n g i n e e r i n g Department, 1985.  [50]  Gatowski, J.A., Heywood, J.B. and D e l a p l a c e , C , "Flame Photographs i n a S p a r k - I g n i t i o n E n g i n e , " Combustion and Flame, V o l . 56, pp. 71-81, 1984.  [51]  Heywood, J.B., "Engine Combustion M o d e l l i n g . An Overview," Combustion M o d e l l i n g i n R e c i p r o c a t i n g E n g i n e s , pp. 1-38, M a t t a v i , J.N. and Annand, C A . E d i t o r s , Plenum P r e s s , New York-London, 1980.  [52]  H o r v a t i n , M. and Hussmann, A.W., "Measurement of A i r Movement i n I n t e r n a l Combustion Engine C y l i n d e r s , " DISA I n f o r m a t i o n , No. 8, pp. 13-22, J u l y 1969.  [53]  Rajan, S., Smith, J.R. and Rambach, G.D., " I n t e r n a l S t r u c t u r e of a T u r b u l e n t Premixed Flame U s i n g R a y l e i g h S c a t t e r i n g , " Combustion and Flame, V o l . 57, pp. 95-107, 1984.  [54]  Rask, R.B., "Comparison of Window, Smoothed-Ensemble and C y c l e - b y C y c l e Data R e d u c t i o n Techniques f o r L a s e r D o p p l e r Anemometer Measurements of I n - C y l i n d e r V e l o c i t y , " Symposium on F l u i d Mechanics of Combustion Systems," ASME, FED S p r i n g Meeting, 1981.  [55]  R i c o u , J.P. and S p a u l d i n g , D.B., "Measurement of Entrainment by A x i a l s y m m e t r i c T u r b u l e n t J e t s , " J . F l u i d Mech., 9, 21, 1961.  Centre,  Centre, U n i v e r s i t y of B r i t i s h  50.  F i g u r e 1.  Microshadographs o f flame f r o n t s measured by Smith [14]  51.  m + l8°  p + 36*  n +24°  q +42°  f1  1  •  o  +30 s  "1  I J r + 48'1  H | . 13 - Photographs o f a t y p i c a l combustion p r o c e s s r e p r o d u c e d from a a o v l e w i t h i n t e r v a l s o f 6 d e t r e e a ( 0 . 7 2 ms). Spark t i m i n g l e 55* ITC. F o r i n t e r p r e t a t i o n o f photographs eee F i g . 14  i F i g u r e 2.  Flame photographs taken by Namazian et a l . [15] i n the MIT square p i s t o n engine.  52.  F i g u r e 3.  . Schematic of t h e Tennekes model; d e f i n i t i o n of turbulent length scales.  F i g u r e 4.  Schematic of t u r b u l e n t T a b a c z y n s k i [4l] .  combustion as shown by  54.  Motionless Reactants  F i g u r e 5.,  Products  Schematic o f t h i c k combustion  zone.  Do u n t i l  Occurrence o f Spark (compression) Bottom Dead Center (expansion)  Increment c r a n k - a n g l e  Assume a f i n a l temperature u s i n g i s e n t r o p i c compression/expansion temperature as a f i r s t guess  Solve using • . •  3 equations simultaneously a Newton-Rapson technique F i r s t Law P e r f e c t Gas Law C o n s e r v a t i o n o f Energy  O b t a i n t h e f i n a l temperature, p r e s s u r e and energy  Next c r a n k - a n g l e  F i g u r e 6.  Engine S i m u l a t i o n Program F l o w c h a r t , Compression and E x p a n s i o n  COTTIER  DETAIL 3  OF  COMBUSTION  CHAMBER  y  v ALL OVER. VOLUME WITH PLUG &L VALVES IM POSlTOkl TO BE CC ure 7.  Ricardo combustion  chamber from manufacturer s u p p l i e d  drawings  57.  F i g u r e 8.  Approximate combustion chamber  geometry.  58. Do u n t i l  Mass f r a c t i o n > 0.99  Increment  c r a n k - a n g l e CA„  C a l c u l a t e new volume V,  Assume new p r e s s u r e P,  C a l c u l a t e f i n a l p r o p e r t i e s of unburned gas T  U  u  » £ ?  e  ' u *"> .  » Pu ?  Z2_  Assume burned gas temperature  C a l c u l a t e p r o p e r t i e s of burned gas i n c l u d e o r n o t d i s s o c i a t i o n e^ ,  C a l c u l a t e mass o f unburned gas e n t r a i n e d m„  C a l c u l a t e t u r b u l e n t flame t h i c k n e s s 8,  Deduce new flame p o s i t i o n and mass f r a c t i o n burned  C a l c u l a t e heat l o s s t o w a l l s  C a l c u l a t e new t o t a l energy from f i r s t law  F i g u r e 9.  Engine S i m u l a t i o n Program F l o w c h a r t , Combustion  Phase  AIR F L O W  OAS FLOW.  AIR INLET  ,AP GAS  A  I  /  R  HEATER  INLET TEMPERATURE  JL  N A T U R A L GAS| INLET  033  FILTER  O A S LAMINAR F L O W ELEMENT  A M LAMINAR FLOW ELEMENT  APPROXIMATE RELATIVE AIR/FUEL' RATIO  EXHAUST TEMPERATURE  1  KISTLER TRANSDUCER  AIR  TEMPERATURE  •X SENSOR I T AIR T E M P E R A T U R E RICARDO HYDRA  /  ENGINE  EXHAUST PRESSURE  BOC PULSE S -  INLET PRESSURE  0.2* PULSES-  AVL  INSTRUMENTATION ^  F i g u r e 10.  S P E E D I TORQUE  Engine t e s t i n g  facilities.  LAYOUT  60.  Figure 11.  Photograph of the p r e s s u r e t r a n s d u c e r mounted i n the c y l i n d e r head.  61.  Position Position  A : W i r e measures B : Wire measures  Figure  12.  a x i a l and r a d i a l components. t a n g e n t i a l ( s w i r l ) component.  H o t w i r e anemometer m e a s u r i n g positions.  F i g u r e 13.  Photograph of the hot w i r e probe  location.  F i g u r e 14.  Mean v e l o c i t y as a f u n c t i o n of crank angle degrees f o r a l l i n v e s t i g a t e d engine speeds, b a s e l i n e p o s i t i o n .  0-\ 1 -140 -120  1  -100  r  -80  T  1  1  r  -20  TDC  20  40  Crank Angle F i g u r e 15.  deg  60  80  100  Turbulence i n t e n s i t y as a f u n c t i o n of crank angle degrees f o r a l l i n v e s t i g a t e d engine speeds, b a s e l i n e p o s i t i o n .  120  140  1-1  -140 -120  -100  •40  -20 TDC  Crank Angle F i g u r e 16.  20  40  deg  R e l a t i v e t u r b u l e n c e i n t e n s i t y as a f u n c t i o n of crank angle degrees f o r a l l i n v e s t i g a t e d engine speeds, b a s e l i n e p o s i t i o n .  140  10  Legend 8  A  Spark 30 deg BTDC  X  Top Dead Center  6  0i i — 1000 1200 1400  1600 1800 2000 2200 2400 2600 2800 3000 3200 Engine speed rpm ON  F i g u r e 17.  Mean v e l o c i t y a t 30 BTDC and a t top dead c e n t e r of engine speed, b a s e l i n e p o s i t i o n .  as a f u n c t i o n  Legend  n  A  Spark 30 deg BTDC  X  Top Dead Center  1  1  1000 1200 1400  F i g u r e 18.  i  1600  i  i  i  i  i  i  i  i  1800 2000 2200 2400 2600 2800 3000 3200 Engine speed rpm  Turbulence i n t e n s i t y a t 30° BTDC and a t top dead c e n t e r as a f u n c t i o n o f engine speed, b a s e l i n e p o s i t i o n .  68.  F i g u r e 19.  Comparison of top dead c e n t e r t u r b u l e n c e i n t e n s i t y w i t h o t h e r 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 . [38] .  5-1  BDC  -150  -120  -90  -60  -30  TDC  Crank Angle Figure 20.  E f f e c t of w i r e o r i e n t a t i o n  30  60  90  120  150  deg  on t u r b u l e n c e i n t e n s i t y at 1200  rpm.  BDC  8  Legend A Distance 6-  mm = • lfrmm X Distance * •  1  5  Distance =  CO  15  mm  ivc  c  CO  or 2  •  l A  A"  -180 -150  -120  -90  -60  -30  0  Crank Angle  30  180  60  deg o  F i g u r e 21.  E f f e c t of p o s i t i o n along t h e spark p l u g a x i s on i n t e n s i t y at 1200 rpm.  turbulence  6000 5500  Legend  5000  A  Lambda - 1.01  4500  X  Lambda - 1.16  Lambda =1.16  •  Lambda = 1.27  Lambda  ^ 4000 'co 3500  g  =1.01  Lambda =1.27  ^ 3000 co to  a > 2500 2000 1500 1000 "A<  500 A — A——A  0 -180 -150  F i g u r e 22.  A  A ' •A"  •120  •90  -60  •30  30  Crank Angle (deg)  60  90  'A- 'A-  120  Experimental p r e s s u r e curves a t 1200 rpm f o r t h r e e a i r - f u e l  'A.  150  ratios.  .A  180  5500-j  Legend  5000-1  A Lambda ™ 1.00  4500  X Lambda =-LI5. •  Lambda =1.28  40003500300025002000 15001000-  •A- ' A 'A•A  5000^ -180 -150 -120  T  -90  -60  -30  0  30  60  90  120  150  Crank Angle (deg) F i g u r e 23.  Experimental p r e s s u r e curves a t 1800 rpm f o r t h r e e a i r - f u e l  ratios.  180  6000-1  5500 5000 4500 ^ 'co  4000  Legend A  Lambda - 1.04  X  Lambda - 1.20  •  Lambda = 1.36  3500 CD  ^  3000  CO  co  0) 2500 2000 1500  •  1000 500 •A-  •A.  0 •180 -150 -120  •90  -60  -30  0  30  60  90  120  150  Crank Angle (deg) F i g u r e 24.  Experimental p r e s s u r e curves a t 2400 rpm f o r t h r e e a i r - f u e l  ratios.  •A  180  6000 5500-  Legend  5000-  A  Lambda ™ 1.08  4500-  X  Lambda "122  •  Lambda =1.37  4000350030002500200015001000500  •A' •A« -A  —I  •180 -150 -120 -90  -60  -30  0  30  60  90  120  150  Crank Angle (deg) F i g u r e 25.  Experimental p r e s s u r e curves at 3000 rpm f o r t h r e e a i r - f u e l  ratios.  180  Figure  26.  Mass f r a c t i o n burned curve c a l c u l a t e d from e x p e r i m e n t a l at 1800 rpm f o r three a i r - f u e l r a t i o s .  pressures  1200  Legend 1100-  A  1200 RPM  X  1800 RPM  •  2400 RPM  El 3000 RPM 1000-  900XA  800-  700 + 1  1.05  1.10  T  T  1.15  1.20  1.25  1.30  1.35  Relative Air-Fuel Ratio F i g u r e 27.  I n d i c a t e d mean e f f e c t i v e pressure f o r a l l o p e r a t i n g speeds.  as a f u n c t i o n o f a i r - f u e l  ratios  1.40  1000-T  Legend 900  A  1200 RPM  X  1800 RPM  •  2400 RPM  H  3000 RPM  800H  AX  700 H  600 + 1  —I  1.05  1.10  1.15  1  1.20  1  1.25  1.30  1.35  Relative Air-Fuel Ratio F i g u r e 28.  Brake mean e f f e c t i v e p r e s s u r e a l l o p e r a t i n g speeds.  as a f u n c t i o n o f a i r - f u e l r a t i o s f o r  1.40  F i g u r e 29.  Comparison of c a l c u l a t e d and e x p e r i m e n t a l mass f r a c t i o n burned f o r 1200 rpm, X = 1.01.  Crank Angle After Spark (deg) F i g u r e 30.  Comparison of c a l c u l a t e d and e x p e r i m e n t a l mass f r a c t i o n burned f o r 1200 rpm, X = 1.16.  Crank Angle After Spark (deg) F i g u r e 31.  Comparison of c a l c u l a t e d and e x p e r i m e n t a l mass f r a c t i o n burned f o r 1200 rpm, X = 1.27.  F i g u r e 32.  Comparison of c a l c u l a t e d and e x p e r i m e n t a l mass f r a c t i o n burned f o r 1800 rpm, X = 1.00.  9  F i g u r e 33.  Comparison of c a l c u l a t e d and e x p e r i m e n t a l mass f r a c t i o n f o r 1800 rpm, X = 1.15.  burned  F i g u r e 34.  Comparison of c a l c u l a t e d and experimental mass f r a c t i o n burned f o r 1800 rpm, X = 1.28.  F i g u r e 35.  Comparison o f c a l c u l a t e d and e x p e r i m e n t a l mass f r a c t i o n f o r 2400 rpm, X = 1.04.  burned  F i g u r e 36.  Comparison o f c a l c u l a t e d and e x p e r i m e n t a l mass f r a c t i o n burned f o r 2400 rpm, X = 1.20.  A  <T  10  20  30  40  50  60  70  80  90  Crank Angle After Spark (deg) F i g u r e 37.  Comparison of c a l c u l a t e d and e x p e r i m e n t a l mass f r a c t i o n burned f o r 2400 rpm, X = 1.36.  100  F i g u r e 38. Comparison o f c a l c u l a t e d and e x p e r i m e n t a l mass f r a c t i o n burned f o r 3000 rpm, X = 1.08.  F i g u r e 39.  Comparison of c a l c u l a t e d and e x p e r i m e n t a l mass f r a c t i o n f o r 3000 rpm, X = 1.22.  burned  F i g u r e 40.  Comparison o f c a l c u l a t e d and e x p e r i m e n t a l mass f r a c t i o n f o r 3000 rpm, X = 1.37.  burned  6000 5500 50004500^  Legend A FP015 C FACTOR = 3.1  4000  "To i  3500H  ^ w  3000H  CO  O  2500H 2000 15001000500—  A — A — A  -180 -150  -120  A"  -90  •60  -30  0  30  60  90  120  150  180  Crank Angle (deg) o F i g u r e 41.  Comparison of c a l c u l a t e d and experimental p r e s s u r e h i s t o r i e s f o r 1200 rpm, X = 1.01.  6000-1  5000 H  Legend A  4500  FP020 C FACTOR = 3.1  4000 H 3500 30002500200015001000500A — A — A ' - A — A - ^ A- —  A  A  -180 -150 -120  •90  -60  -30  0  30  60  90  120  Crank Angle (deg) F i g u r e 42.  Comparison of c a l c u l a t e d and e x p e r i m e n t a l p r e s s u r e h i s t o r i e s f o r 1200 rpm, X = 1.16.  150  180  6000 550060004500^ 4000co ^ 3500-1  Legend A  FP021 C FACTOR = 3.1  CD  ^  3000H  co co  d>  2500H 2000 1500H 1000 500-1 A - A A-  , A — A - r A — f t  •180 -150  -120  -90  -60  -30  0  30  60  90  120  Crank Angle (deg) F i g u r e 43.  Comparison of c a l c u l a t e d and experimental p r e s s u r e h i s t o r i e s f o r 1200 rpm, X = 1.27.  - •A- :A 150  180  6000 5500 50004500^  4000  Legend A  FP009 C FACTOR = 2.4  "cO  3500 ^  3000-1  CO CO  <D  2500 H 200015001000500  • -AC A  0•A — A - p A — f t -180 -150 -120  A  ' T -90  A  "  T  -60  -30  0  30  60  90  120  Crank Angle (deg) F i g u r e 44.  Comparison of c a l c u l a t e d and e x p e r i m e n t a l p r e s s u r e f o r 1800 rpm, X = 1.00.  histories  A- •A  150  180  6000-1 5500-1  Legend  5000 A  4500  FP010  C FACTOR = 2.4 ^  4000-1  *  3500  CD  ^  3000H  CD  2500  to to  2000-1  1500 1000500— TAA — A-—A , A—A — A  -180 -150  -120  -90  ^'  A •60  -30  0  30  60  90  120  Crank Angle (deg) F i g u r e 45.  Comparison of c a l c u l a t e d and e x p e r i m e n t a l p r e s s u r e h i s t o r i e s f o r 1800 rpm, X = 1.15.  150  180  600055005000 4500 ^ "to  4000H  -*  3500H  ^  3000  Legend A  FP011 C FACTOR -  2.4  CO CO  O  2500 2000 15001000500 0 120  -90  -60  -30  0  30  60  90  120  Crank Angle (deg) F i g u r e 46.  Comparison of c a l c u l a t e d and e x p e r i m e n t a l p r e s s u r e h i s t o r i e s f o r 1800 rpm, X = 1.28.  150  180  6000 5500-  Crank Angle (deg) F i g u r e 47.  Comparison o f c a l c u l a t e d and experimental p r e s s u r e f o r 2400 rpm, X = 1.04.  histories  6000-1 5500 50004500^ co Q_ ^  4000-  5  3000H  to Q)  2500 H  Legend A  FP013 C F A C T O R = 2.3  3500H  200015001000 500 A  —A—A-""* ' A A A  A— A -180 -150  -120  •90  ~~"" ^A^ A —i  -60  -30  0  30  60  90  120  Crank Angle (deg) F i g u r e 48.  A  Comparison o f c a l c u l a t e d and e x p e r i m e n t a l p r e s s u r e h i s t o r i e s f o r 2400 rpm, X = 1.20.  150  1  180  Legend A  FP014 C FACTOR -  •180  -150  2.3  •60  -30  0  30  180  60  Crank Angle (deg)  F i g u r e 49.  Comparison of c a l c u l a t e d and e x p e r i m e n t a l p r e s s u r e f o r 2400 mm. X = 1.36.  histories  6000-1 5500-  Crank Angle (deg) F i g u r e 50.  Comparison of c a l c u l a t e d and e x p e r i m e n t a l p r e s s u r e h i s t o r i e s f o r 3000 rpm, X = 1.08.  6000-1  •180 -150  -120  -60  -30  0  30  180  60  Crank Angle (deg) F i g u r e 51.  Comparison of c a l c u l a t e d and e x p e r i m e n t a l p r e s s u r e f o r 3000 rpm, X = 1.22.  histories  6000 5500 5000  Legend A  4500 4000-  FP018 C FACTOR = 2.6  3500300025002000 1500 1000 500 A  A — A — A — A — A  -180 -150  r -120  F i g u r e 52.  •A'  " ^ - A ^  A  A  -1  -90  -60  -30  0  30  60  90  120  Crank Angle (deg)  Comparison of c a l c u l a t e d and e x p e r i m e n t a l p r e s s u r e f o r 3000 rpm, A = 1.37.  histories  150  180  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)  F i g u r e 53.  Comparison of c a l c u l a t e d and e x p e r i m e n t a l time t o burn the f i r s t 5% o f t o t a l mass i n the c y l i n d e r .  55 Legend 1200 R P M C A L C U L A T E D  50-  X  1200 R P M EXPERIMNETAL 1800 R P MCALCULATED _  H  1800 R P M EXPERIMENTAL  *  2 * 0 0 , B f M EXPERIMENTAL  45-  p c  c  A  52°.9J?.E.^.ykXLP... ffi  3 0 0 0 R P M EXPERIMENTAL  y  ©-  40  X  r^®^"  -X•X"  30-  25-  — t  1.05  1.10  1.15  1.20  1.25  1.30  1.35  1.40  Air-Fuel Ratio o F i g u r e 54.  Comparison of c a l c u l a t e d and e x p e r i m e n t a l time t o burn 5 t o 95% of t o t a l mass i n the c y l i n d e r .  15  6-  i  1  i  i  i  1.05  1.10  1.15  F i g u r e 55.  i  1.20  Air-Fuel Ratio  P r e d i c t e d flame t h i c k n e s s engine speed.  1  1  1  1.25  1.30  1.35  as a f u n c t i o n of a i r - f u e l r a t i o  r  1.40 M O  and  -1  1  1200  1400  1  1600  1  1800  1  2000  1  2200  1  1  1  1  r  2400  2600  2800  3000  3200  RPM F i g u r e 56.  V a r i a t i o n of c f a c t o r over the engine speed range.  F i g u r e 57.  P r e d i c t e d mass f r a c t i o n e n t r a i n e d and burned f o r 1800 X = 1.00.  rpm  and  80-1  Crank Angle (deg) F i g u r e 58.  P r e d i c t e d i n n e r and o u t e r flame r a d i u s f o r 1800 rpm and X =  1.00.  Crank Angle (deg) F i g u r e 59.  P r e d i c t e d outer flame area f o r 1800 rpm and X =  1.00.  F i g u r e 60.  P r e d i c t e d unburned, burned and flame volumes f o r 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) F i g u r e 61.  P r e d i c t e d i n t e g r a l l e n g t h s c a l e at 1800 rpm, A = 1.00, X = 1.15, 3000 rpm X = 1.08.  Crank Angle (deg) F i g u r e 62.  Predicted Taylor microscale 3000 rpm X = 1.08.  at 1800 rpm, X = 1.00, X =  1.15,  5-1  F i g u r e 63.  Enhanced t u r b u l e n c e i n t e n s i t y at 1800 3000 rpm X = 1.08.  rpm,  X = 1.00,  X =  1.15,  Legend 1800 RPM Lambda - 1.00 1800 RPM Lambda « 1.30 3000 RPM Lambda - 1.00  n  -30  1  1  1  1  1  1  -20  -10  0  10  20  30  Crank Angle (deg) F i g u r e 64.  P r e d i c t e d t u r b u l e n t entrainment v e l o c i t y a t 1800 rpm, X = 1.00, X = 1.15, 3000 rpm X = 1.08.  Mass Fraction Burned o  CD  Q I  I  t\J I  -L.  o  cn i  o  o  o  o  CO  \1  CO  CD  I  _L_  09  c  l-t  l-Ti  CO o '  ft) r-h  O n> rr n H- rr O  C  rr  i-t  3*  O ~) a  <  x"  3  a  4  §  rt> Cu  -  LO  o o o  I-l  O  D  3 iU  o  c a  D  ca  ca c— (D  3  O  ID  cr  <—  cn  (D  ~)  o o  3  CO "O CD  00  a l-ti  PJ O rr O  O  "5  (0 rr p* H*  a_  n o II  r-h N> I• PJ N> 3  ca  1  •  CD O  00 O  3  9  PJ  ca  CO  CD O  O  a  •*TT  VOL  I-l  X  VOL  r+l M  X  VOL  X  •  :•  o  CD O  '  ? m  cn  •  9 bo o  Crank Angle After Spark (deg) F i g u r e 67.  P r e d i c t e d and c a l c u l a t e d mass f r a c t i o n burned f o r L = h at spark t i m i n g , 3000 rpm, X = 1.08. °  Crank Angle After Spark (deg) h-*  F i g u r e 68.  P r e d i c t e d and c a l c u l a t e d mass f r a c t i o n burned f o r L = b /5 a t spark t i m i n g , 3000 rpm, A = 1.08. c  Crank Angle After Spark (deg) F i g u r e 70.  Comparison of mass f r a c t i o n burned c u r v e s e x t r a c t e d from e x p e r i m e n t a l p r e s s u r e s , e x t r a c t e d from p r e d i c t e d p r e s s u r e s and c a l c u l a t e d from model.  120. APPENDIX A TURBULENT ENTRAINMENT  MODEL - ENGINE SIMULATION PROGRAM  1.  Development of the t u r b u l e n t b u r n i n g e q u a t i o n  2.  Volume D i s t r i b u t i o n i n T h i c k B u r n i n g Zone 2.1  E x p o n e n t i a l Burning Law  2.2  Geometric C o n s i d e r a t i o n s  3.  Initial  Mixture  Composition  4.  Compression and E x p a n s i o n  5.  Initial  and F i n a l  Burning  Strokes  121. 1.  Development of the T u r b u l e n t Burning Chomiak [18] developed  turbulent f i e l d .  Equation  a theory f o r r a p i d  At v e r y h i g h Reynolds,  p r o p a g a t i o n of a flame i n a  a t h i n continuous  becomes d i s r u p t e d and  the s t r o n g d i s s i p a t i v e  propagation process.  McCormack [42] has observed  v e r y r a p i d l y when i g n i t e d  flame  sheet  eddies p l a y a key r o l e i n the t h a t a flame  propagates  i n the midst of a laminar v o r t e x , the  v e l o c i t y b e i n g p r o p o r t i o n a l t o the v o r t e x s t r e n g t h .  He  flame  a l s o observed  that  combustion causes a d i s c o n t i n u o u s breakdown of the v o r t e x . Chomiak p r e s e n t s a simple e q u a t i o n f o r momentum b a l a n c e a t the  flame  interface:  / A  (p-pJdA  =  /  p  b  U  2  dA  A  T h i s simply means t h a t the p r e s s u r e f o r c e s induced by the r o t a t i o n the f l u i d inside  a r e e q u a l t o the momentum f l u x due  t o the p u l l i n g o f the  of  flame  the v o r t e x .  To determine  the p r e s s u r e d i s t r i b u t i o n i n s i d e the v o r t e x l e t us  c o n s i d e r a two-dimensional  Figure A - l .  v o r t e x of s t r e n g t h ft and diameter u  T h i s v o r t e x i s i n the unburned mixture  n  shown i n u  ahead of the flame  i t s maximum v e l o c i t y i s o f the o r d e r u' the t u r b u l e n t i n t e n s i t y . momentum e q u a t i o n ( n e g l e c t i n g r a d i a l or a x i a l  1 dP p dr  w i s the t a n g e n t i a l v e l o c i t y and  w r  2  i s equal t o  motion):  The  and  122. w = Q r u  0 < r < n / 2 u  Q ri w  2  2  r  V < <  = -TT-  I t i s assumed t h a t the tube has a v i s c o u s c o r e and i s a p o t e n t i a l v o r t e x outside t h i s region. The p r e s s u r e d i s t r i b u t i o n thus o b t a i n e d i s  n 2 2 puft 'n * u u  4  P -P »  -i  1  r, 2 2 u u u  The  2  1  r ,  8  n/2 u  1 /2 U  .  i  2 *  r  u  v e l o c i t y and p r e s s u r e p r o f i l e s a r e p l o t t e d i n F i g u r e A - l .  Daneshyar and H i l l c a l c u l a t e t h e mean p r e s s u r e d i f f e r e n c e by i n t e g r a t i n g the p r e s s u r e d i s t r i b u t i o n e q u a t i o n out t o two times the v o r t e x r a d i u s .  P -P  =  —  /  ' V  (P -P)  "  r dr  0  £2 n 2 u u u ~ 4 2  p  2TT  (2) _JL_1 — J £  r  3  \-Tb  +  n n and  s i n c e the maximum t a n g e n t i a l v e l o c i t y of the cone i s — ^ — = u' they  get u'2 u 2.77  p  123. The p r o p a g a t i o n  of the  i n the v o r t e x i s modelled i n  following  way.  A-l  c o n s e r v i n g m a s s a n d a n g u l a r momentum ( s e e  burns  It  is  L e t us  flame  assume t h a t  conservation  o f mass  conservation  of angular °  then  e a s i l y shown t h a t  s i d e of the v o r t e x i s  far  the  right  side of  momentum  the  vortex of  2  = p,n, b b  n u u  2  = ft, n , b b  ft  that through  Figure  Figure A-2).  p n u u  p r e s s u r e drop  greater than  the  the  through  2  2  the  the burned  unburned side.  P  b, (P - P ) , = ( — ) oo b P  2  (P  oo  -P) U  U  A t y p i c a l value for  P /p^ i s  5,  u  (P - P )  and H i l l  deduce  (P - P ) oo ' and t h e  (P - P ) ,  't>  oo  t h e momentum  P u' u « 2.77 7  u  to:  7  2  =  balance  . 1 p U 2 b a  2  T  velocity  a  This i s mechanism. velocity  »  'u  oo  Daneshyar  which leads  the  axial  the  2 2.77  propagation  The t u r b u l e n t  plus  v  u !' p, b  2  velocity  entrainment  laminar burning  P  o f the  velocity.  i n d u c e d by t h e flame i s  this  vortex  bursting  hydrodynamic  124.  1/2  U  T h i s e x p r e s s i o n accounts f o r both c h e m i c a l and hydrodynamic e q u a t i o n was  effects.  The  used i n the s i m u l a t i o n program t o d e s c r i b e the p r o p a g a t i o n o f  the o u t e r edge of the b u r n i n g zone.  2.  Volume D i s t r i b u t i o n i n the T h i c k B u r n i n g Zone As mentioned  i n Chapter 2, two d i s t i n c t t h e o r i e s were developed t o  c a l c u l a t e the approximate burning  volume (or mass) d i s t r i b u t i o n i n the t h i c k  zone.  F i r s t l e t us d e f i n e the volume f r a c t i o n o f burned gas i n the flame zone. X  2 .1  Exponential Burning  bflame V,. flame  vol  Law  It has a l r e a d y been d i s c u s s e d t h a t the b u r n i n g r a t e i n the flame zone i s assumed p r o p o r t i o n a l t o the amount of unburned  dm. flame dt  mf  flame T  T  c  L e t us d e f i n e the r e a c t e d f r a c t i o n i n the flame  m. r The e q u a t i o n becomes  gas p r e s e n t i n the  flame m  flame  X  zone.  125. 1-r  dr dt  T  S o l v i n g t h i s d i f f e r e n t i a l e q u a t i o n we  t  -  c  obtain  -x * (l-r) c  n  or r = 1 - e  Now  we express the r e a c t e d f r a c t i o n as a f u n c t i o n of d i s t a n c e from the  o u t e r edge o f the flame.  T h i s i s shown i n F i g u r e  y = U  t  A-4.  t  where t ' i s the time a f t e r entrainment of the f l a m e . We the  can e x p r e s s the r e a c t e d f r a c t i o n i n terms of the d i s t a n c e  through  flame.  The mean r e a c t e d f r a c t i o n i s o b t a i n e d  by i n t e g r a t i n g t h i s f u n c t i o n  through the flame  ) dy  and remembering t h a t 6 = U t  we  get  126. T  r  f o r 99% burned, t  f c  =  It - l )  "T  1 + ^  (e  C  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 d e r i v e d from the average mass f r a c t i o n  P  = r  b  p. V. b b  K  f  b  V. f + p V *u u  f  1 1  For  - p  P / p ^ = 5, and d e f i n i n g d i f f e r e n t u  / p b  u  ( i  -  ¥  t h r e s h o l d s f o r flame t h i c k n e s s  T a b l e A - l has been p r e p a r e d t o show the t r e n d s o f r and X , . vol seen that the mean volume f r a c t i o n l i e s i n the range 75-85%.  I t can be  Table A - l Comparison o f Mass and Volume D i s t r i b u t i o n s Through Flame f o r V a r i o u s D e f i n i t i o n s o f Flame T h i c k n e s s ( E x p o n e n t i a l B u r n i n g Law)  % burned  r  6  0.90  1.15 X  0.95 0.99  1.5 2.3  u /u  X t X u  X  X  vol  0.406  0.774  0.482 0.609  0.823 0.886  127. 2.2  Geometric C o n s i d e r a t i o n s A second  spherical  t h e o r y was  developed based on the laminar b u r n i n g o f  p o c k e t s o f i n i t i a l r a d i u s X.  and i t s o b j e c t i v e was  to e s t a b l i s h  T h i s argument i s p u r e l y geometric  a l i m i t i n g case i n the  The p o c k e t s a r e assumed t o burn a t l a m i n r TJ .  dmu -rr— dt  We  distribution.  See F i g u r e A-4.  -p A U„  =  u u I  n e g l e c t the e f f e c t of compression  on the unburned gas d e n s i t y i n  the pockets. dR  .*. R  = X - U„t A  P  Thus the r a d i u s of the pockets d e c r e a s e s l i n e a r l y as a f u n c t i o n o f time.  Once a g a i n we d e f i n e y as the d i s t a n c e from the o u t e r edge o f the  flame, and we  express the pocket r a d i u s w i t h r e s p e c t to y.  R  =  x  P  Since R  = 0 a t y = 6 ,  - u ;  6 = X 77— > and  R  = p  46  (6-y)  y  128. To determine t h e r e l a t i v e the  volume o f t h e pockets t o t h e t o t a l volume i n  flame zone the f o l l o w i n g arguments a r e proposed.  Lets  take a s e c t i o n  of t h e b u r n i n g zone d e f i n e d  by t h e a r c l e n g t h X as shown i n f i g u r e A-5.  assume as a worst case t h a t  the volume o f unburned  pockets i n t h i s  i s t h a t o f a cone o f base diameter 2X and h e i g h t 6. unburned  t o t o t a l volume i n t h i s  The f r a c t i o n o f  The r a d i u s o f t h e flame s e c t i o n as a f u n c t i o n o f d i s t a n c e  R  X  f c "  ~ T-  Y  u  The a r e a of the flame  A, = fc  section  TT  R  2  fc  The volume of the s e c t i o n i s thus c a l c u l a t e d  V  f c  =  TT  6 / R 0  = {^R u  2  section  s e c t i o n i s o b t a i n e d i n the f o l l o w i n g  zone i s  2  [R  dy  3  3  - (R U  X) ] U  £  The t o t a l pocket volume i s o b t a i n e d i n the same way  We  way:  through the  129. 6  Finally  the volume r a t i o  i s derived  V  R 2 6 u u  For in  6 = 10 mm  u  -  6)  3  which i s a t y p i c a l o b s e r v e d t h i c k n e s s , t h e r a t i o i s p l o t t e d  F i g u r e A-6 a g a i n s t outer flame r a d i u s .  c a s e t h e minimum r a t i o i s around  3.  (R  We  can see that i n t h i s  worst  70%.  I n i t i a l M i x t u r e Composition S i n c e t h e i n t a k e and exhaust s t r o k e s were not modelled, a few  assumptions had to be made r e g a r d i n g these p r o c e s s e s . For  i n i t i a l p r e s s u r e and temperature a t bottom dead c e n t e r , the  motoring t e s t  assumptions were used.  T  BDC  AMB  n  v  INTAKE T AMB  BDC  In c a l c u l a t i n g r a t i o was  first  t h e c o m p o s i t i o n o f t h e m i x t u r e , the r e l a t i v e  c a l c u l a t e d from gas f l o w r a t e s and i n p u t t o t h e  The t o t a l number of moles was  calculated  a i r fuel program.  130.  =  T  The r e s i d u a l  0  T  =  P V BDC BDC T  ^OL  BDC  f r a c t i o n was accounted f o r (assumed a t 5%) i n c a l c u l a t i n g  the molar f r a c t i o n o f each specimen. component was e s t i m a t e d by assuming  The mass f r a c t i o n o f each  residual  complete combustion of the f u e l .  H X(C  7^)  +  A  [l-F  0„  ] H  1 + 4.76 X(C  +  -A  res r e s _ U  2  The same type of c a l c u l a t i o n was performed f o r each component of the c y l i n d e r mixture.  4.  Compression For  and E x p a n s i o n S t r o k e s  compression and expansion, t h e f o l l o w i n g t h r e e e q u a t i o n s were  s o l v e d u s i n g a Newton-Rapson method.  E  2  = E  E  2  = I x.  P  5.  V  11 T 1  1  ~ pAV + AQ  P  e i  (T ) 2  V  22 T 2  I n i t i a l and F i n a l B u r n i n g The entrainment e q u a t i o n i s r e c a l l e d  131. An approximate e q u a t i o n was unburned area was very r a p i d l y . first  available.  needed f o r t h e f i r s t b u r n i n g s t e p s i n c e no  The  initial  k e r n e l i s very s m a l l and  I t has a n e g l i g i b l e mass compared t o t h e charge.  grows  For  this  s t e p i t i s assumed t h a t the d e n s i t y i n s i d e the k e r n e l i s the burned  gas d e n s i t y and t h a t d e n s i t y v a r i a t i o n s a r e s m a l l compared t o the growth o f the  flame.  d  K V  A =  dt  dp, V. — f , dt  dR  A  U  u u T  dR + pA _-H u u dt  -  A U_ u u T  P  p  = — dt  P  p  u t  b  F i n a l burn-up.  Once the o u t e r edge of the flame has d e f i n i t i o n of 6 i s no l o n g e r f e a s i b l e .  e n g u l f e d the chamber,  In t h i s case, the simple  r a t e e q u a t i o n i s used to d e s c r i b e the laminar burn-up of the  the burning  remaining  pockets. A c c o r d i n g t o the e x p o n e n t i a l b u r n i n g law, p r o p o r t i o n a l to the amount of unburned gas  left  d dt  ~ x c  2 U  Amu  = mu,  L  —r—  At  t h e r a t e o f mass burned i s i n the flame  zone.  132. T h i s s i m p l e e q u a t i o n i s used up t o complete b u r n i n g o f t h e charge which may cylinder.  be d e f i n e d a t a f i x e d percentage of the t o t a l mass i n the  11  1  1  r  r  Figure  A.1.  Two  d i m e n s i o n a l v o r t e x i n the unburned  mixture.  p  F i g u r e A.2.  u  V o r t e x b u r s t i n g due t o combustion.  p  b  135.  F i g u r e A.3.  Burned mass f r a c t i o n i n flame zone.  F i g u r e A. 4.  Laminal b u r n i n g of s p h e r i c a l  pocket  137.  F i g u r e A.5.  D e f i n i t i o n of unburned cone and flame zone cone; flame zone cone r a d i u s v s d i s t a n c e through flame.  F i g u r e 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 C a l c u l a t i o n s from Motored P r e s s u r e Data  4.  Uncertainty  Analysis  140. Introduction The  f i r s t p a r t o f t h i s appendix d e s c r i b e s t h e procedures  the p r e s s u r e data f o r both motored and f i r e d experiments.  The second  d e a l s w i t h the c a l c u l a t i o n s o f motored c y l i n d e r temperatures needed t o i n t e r p r e t  the hot wire d a t a .  f o r averaging part  which a r e  The techniques used here were  i n s p i r e d by p r e v i o u s work by L a n c a s t e r [8] and Witze  [ 3 6 ] . The recommend-  a t i o n s o f Brown [43] and L a n c a s t e r e t a l [44] f o r measurement and a n a l y s i s t e c h n i q u e s were c l o s e l y f o l l o w e d .  B .1  P r e s s u r e Data  Reduction  As mentioned i n Chapter 4, one hundred c o n s e c u t i v e c y c l e s o f p r e s s u r e data were c o l l e c t e d a t a r a t e o f one sample per degree crank a n g l e , f o r b o t h motored and f i r e d engine c o n d i t i o n s . The  d i g i t i z e d v o l t a g e s from the t r a n s d u c e r were ensemble-averaged t o  o b t a i n one mean curve f o r each engine o p e r a t i n g c o n d i t i o n .  T h i s method  c o n s i s t s o f a v e r a g i n g the i n s t a n t a n e o u s v a l u e a t a g i v e n crank-angle  over  many c y c l e s :  V(4>)  Once the data i s reduced,  =  N E V(i,4>) i=l  the t r a n s d u c e r c a l i b r a t i o n c o n s t a n t was  applied to y i e l d r e l a t i v e pressure values.  p  (<t>) = V(c)>) x 200 kPa  kPa Volt  141. B.2  Pressure  Data  Scaling  Since the p i e z o e l e c t r i c transducer device,  these r e l a t i v e  obtain absolute pressure at  p r e s s u r e s were  pressures.  BDC a t  the  then s h i f t e d  b e g i n n i n g of the  is  is  equal to  For wide-open t h r o t t l e  H o w e v e r i t was f o u n d t h a t  value  to  t o assume t h a t  compression stroke  [43,44].  a s s u m p t i o n was v e r i f i e d .  measuring  by a c o n s t a n t  T h e m o s t common p r o c e d u r e  mean i n t a k e m a n i f o l d p r e s s u r e this  i s a r e l a t i v e pressure  the  the the  motoring, following  r e l a t i o n b a s e d o n t h e m e a s u r e d 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 pressures at  wide-open 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  throttle  as  well  a s c o m b u s t i o n BDC p r e s s u r e s :  D P  For m o t o r i n g ,  (  kPa  /* un> * =  3  6  0  )  isothermal f i l l i n g  T  "o AMB  n  INTAKE v - T — AMB  was assumed a n d t h e  temperature  ratio  was 1. T h e 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  @T P A M B ' AMB  2 0 air w  Motoring  n  = V  V  TI  =  V  T y p i c a l e x p e r i m e n t a l ensemble  V  averaged  F i g u r e B - l f o r b o t h motored and f i r e d relative  rms f l u c t u a t i o n s  2 0 TOT w  ^ Firing  are  also  as:  RPM  @T P A M B ' AMB RPM  pressure curves are  conditions.  plotted  Their  shown i n  respective  i n Figures B-2.  142. B.3  Temperature  C a l c u l a t i o n s From Motored P r e s s u r e Data  As mentioned crank a n g l e .  b e f o r e , the p r e s s u r e data were sampled  once every degree  However t h e h o t w i r e d a t a were a c q u i r e d every f i f t h o f a  degree crank a n g l e . The mean p r e s s u r e d a t a were thus i n t e r p o l a t e d t o g e n e r a t e 4 d a t a v a l u e s i n between each crank angle degree.  T h i s was done u s i n g  and i n t e r p o l a t i n g r o u t i n e s SMOOTH and SMTH [ 4 5 ] . to c o i n c i d e w i t h each r e a l d a t a p o i n t .  smoothing  The f i t t e d c u r v e was made  The f i n a l r e s u l t was a p r e s s u r e  d a t a a r r a y which was used i n c a l c u l a t i n g t h e c y l i n d e r temperature, and i n a n a l y z i n g the hot wire d a t a . An assumption had t o be made t o choose a r e f e r e n c e temperature. mentioned,  isothermal f i l l i n g  As  was assumed so that the temperature a t BDC a t  the b e g i n n i n g o f compression s t r o k e was s e t t o ambient. r e a s o n a b l e as the c o o l i n g water was c l o s e t o ambient  T h i s c h o i c e was  d u r i n g the motored  tests. Three o p t i o n s were i n v e s t i g a t e d f o r temperature  calculations:  1)  assume a d i a b a t i c compression and expansion,  2)  determine t h e s l o p e s o f t h e l o g p vs l o g V c u r v e s t o o b t a i n o v e r a l l p o l y t r o p i c i n d i c e s f o r compression and expansion,  3)  assume a d i a b a t i c compression up t o IVC and c a l c u l a t e temperatures from the p e r f e c t gas law f o r the compression and expansion s t r o k e s up t o exhaust v a l v e c l o s i n g  (EVO).  I t was found t h a t t h e l a s t method l e d t o the l e a s t u n c e r t a i n t i e s i n peak temperatures.  The a d i a b a t i c assumption l e a d s t o erroneous expansion  temperatures as demonstrated by Witze  [36].  Fitting  s t r a i g h t l i n e s to l o g  p l o t s a l s o y i e l d e d u n c e r t a i n t i e s i n t h e c r i t i c a l peak v a l u e s o f p r e s s u r e and  temperature.  143. The p e r f e c t gas method gave b e s t r e s u l t s , f o l l o w i n g more c l o s e l y measured p r e s s u r e v a l u e s e s p e c i a l l y around TDC  which i s a c r i t i c a l  the  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 f o l l o w s . temperature was assumed a t BDC  on i n t a k e s t r o k e  T ( * = 360) =  I s e n t r o p i c compression was  Ambient  T  a  m  b  assumed to IVC and the temperature from each  p r e v i o u s s t e p was used t o c a l c u l a t e the i s e n t r o p i c i n d e x  1 -1 P  2  T  2  Y  y =  - T^—)  The p e r f e c t gas law was  then a p p l i e d from IVC t o  P V 2  T„ = T, •2 1 p  The r e s u l t i n g  CpCT^/C^)  temperature a r r a y was  i  V  EVO,  2  l  used i n a n a l y z i n g the hot w i r e  data. The temperature c u r v e c o r r e s p o n d i n g t o the p r e s s u r e c u r v e o f F i g u r e B-l i s plotted i n Figure  B-3.  The program w r i t t e n f o r ensemble a v e r a g i n g and c a l c u l a t i n g the temperatures i n PRESISAACTEMPPERF. p r e s s u r e s i s FIREDPRES.  The program  that p r o c e s s e s the f i r e d  144. B.4  Uncertainty Analysis The u n c e r t a i n t i e s  the  experiment are  result  a s s o c i a t e d w i t h each instrument used i n t h i s part  listed  i n Table B - l .  These combined  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 .  a n d 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 a s [44].  Also c e r t a i n events  visible  on s i n g l e c y c l e p l o t s a t  involve great u n c e r t a i n t i e s . source of e r r o r .  pressure  lies  10-15%.  These l a s t  of  pressure  by L a n c a s t e r e t  s u c h as v a l v e openings and s p a r k a r e the proper  and temperature  overshadow the i n s t r u m e n t  simultaneously measuring absolute  pressures  is  far  error.  greater  The  and t e m p e r a t u r e s  is  demonstrated.  Transducer K i s t l e r  6121  Linearity Charge A m p l i f i e r  ± 1.0% F S Kistler  Linearity  ± 0.05% F S  AVL O p t i c a l P i c k - u p 3 6 0 c / 6 0 0 0.1°  Accuracy  Air  flow  resolution  measurement  R i c h a r d A l c o c k v i s c o u s flow a i r meter N a t u r a l gas f l o w  linearity  measurement  Neuman L F E 50 M W 2 0 - 1  Table B - 4 .  data a  i s e s t i m a t e d t h a t the u n c e r t a i n t y i n peak  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  effects  clearly  I s e n t r o p i c c o m p r e s s i o n up t o I V C i s a l s o  Thus i t  a r o u n d 5%.  al  time.  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  major  uncertainties  The p h a s i n g o f  suggested  of  1 / 2  ±0.5%  Uncertainty i n Measuring  Instruments  < 3%  at  advantage clearly  4500  Figure B . l .  Ensemble  averaged motored and combustion  pressures.  Figure B.2.  R e l a t i v e rms f l u c t u a t i o n s of p r e s s u r e s about the ensemble averaged mean.  150  -100  F i g u r e B.3.  -50 0 C r a n k RngLe  C a l c u l a t e d motored  50 deg  100  temperatures.  150  200  APPENDIX C HOT WIRE ANEMOMETER MEASUREMENTS  Introduction 1.  Thermal E q u i l i b r i u m o f Hot W i r e  2.  C a l i b r a t i o n o f Hot Wire  3.  Hot Wire O p e r a t i o n  4.  Sensitivity  5.  Hot W i r e D a t a R e d u c t i o n  6.  Uncertainty  Analysis  i n Hot Wire Measurements  149. Introduction 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 described  i n previous studies  [8,34,35,36].  The e q u a t i o n s  fully  describing  the  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 Williams heated  [34] a n d D a v i e s a n d F i s h e r  c y l i n d e r s to a moving f l u i d .  equations  of Witze  at  Presented to interpret  appendix are  are  the  electrically the  paper.  was b a s e d o n  the  c o m p a r i s o n o f h o t w i r e anemometry  to  measurements.  the main assumptions  hot w i r e d a t a and d e t a i l s  Also presented  [8]  t h e mean g a s t e m p e r a t u r e  [36] i n h i s c r i t i c a l  i n this  from  The d e t a i l e d d e v e l o p m e n t o f  l a s e r doppler velocimetry for engine flow  C-l  transfer  u s e d i n t h i s w o r k c a n be f o u n d i n L a n c a s t e r ' s  E v a l u a t i o n o f gas p r o p e r t i e s findings  [35] o n h e a t  and  and e q u a t i o n s  used  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 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 .  Table  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 .  Table C - l Wire C h a r a c t e r i s t i c s Type Materials Diameter, d Length, £ Thermal C o n d u c t i v i t y , K Thermal c o e f f i c i e n t of R e s i s t a n c e , a w  w  i  r  ±  r  e  e  w  C l  i  r  e  T S I P 12.5 Platinum Iridium 6.3 ym 1.5 mm 1 8 . 0 W/m-K 9xl0 °C 1 _ l t  Alloy  _  Thermal E q u i l i b r i u m of Hot Wire 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  wire.  The f o l l o w i n g  a s s u m p t i o n s w e r e made,  based on w i r e d i m e n s i o n s and  properties: • The r a d i a l  temperature  gradient  heated  is negligible  150. • The diameter and m a t e r i a l p r o p e r t i e s a r e i n v a r i a n t a l o n g the w i r e length • R a d i a t i o n from the wire to i t s s u r r o u n d i n g s i s n e g l i g i b l e • The t h e r m a l c o n d u c t i v i t y K . wxre  i s independent o f the w i r e  temperature • The c o n v e c t i v e c o e f f i c i e n t h i s u n i f o r m on the whole w i r e  surface  The e q u a t i o n 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 w i r e and i t s s u r r o u n d i n g s can be w r i t t e n i n the f o l l o w i n g  ^electric  ^conduction  j. Q j ., ^conduction  . ,. A . K . wxre w i r e  way:  +  ^convection  where 2  Q  „. convection  • Q i ^ • electrxc  =  =  d . h (T . - T ) dx wxre wire gas  TT  I  3 T . wire , dx „ o 9x^  2  P(T , ) wire' , 1 A  K V  d  =  x  The wire r e s i s t i v i t y i s a f u n c t i o n of the wire  p . = p [1 + a(T . wire ^o wire H  1  v  temperature:  - T )1 o' J  The v a l u e s of K . , d . , 1 . a r e common t o a l l wires and can be found wxre wxre' w i r e i n Table C - l .  The v a l u e of p  must be measured f o r each w i r e . o  151. The heat b a l a n c e e q u a t i o n i s a second o r d e r l i n e a r non-homogeneous d i f f e r e n t i a l e q u a t i o n which was s o l v e d [8] t o g i v e an e x p r e s s i o n f o r t h e w i r e temperature  as a f u n c t i o n o f t h e d i s t a n c e from t h e c e n t e r p o i n t :  /  cosh (C~^ x) T . (x) = (T - C.) wire^ sup 1' j— 2 wire c  Q  s  h  + C. 1  x  where  IT d . 1. hT + I wire wire gas  2  R wo  2  R  T  C  l  TT d . 1. h - I wire wire  C  wo  a  2  , 4  =  (1 - a r ) o_  2  K d wire wire  wo  Po 1wire • A . wire  r L  4 R I wo • > ir d 1 - " wire wire a  h  and  R  The mean wire temperature  was o b t a i n e d by i n t e g r a t i n g t h i s  temperature  f u n c t i o n along the wire.  T  2(T - C.) sup 1' v  w  l  r  e  =  2  wire  T h i s mean temperature determined  1 , , . /•— wire. , „ tanh (/C - g - ) + C  x  2  i s assumed t o be the e q u i v a l e n t temperature  from t h e r e s i s t a n c e o f t h e h o t w i r e .  152. C.2  Calibration Before operation,  must be d e t e r m i n e d .  the r e s i s t a n c e of the w i r e at  ambient  The h o t w i r e b r i d g e was u s e d t o m e a s u r e  of  the wire,  probe and c a b l e a s s e m b l y .  is  i l l u s t r a t e d i n Figure C-2.  R  „ measured  =  R . wire  The c a b l e a n d p r o b e r e s i s t a n c e s  R R  Once t h e w i r e r e s i s t a n c e operating temperature  w o  wop  at  = R . wire  = R  W  L Q  The o p e r a t i n g t e m p e r a t u r e  the  resistance  A schematic of the bridge  circuit  + R + R cable probe V  1  were measured  separately.  = 0 . 2 8 5 fi  , = 0 . 5 2 ft probe  a m b i e n t was k n o w n ,  could easily  R  R  cable  temperature  resistance  for  any  be o b t a i n e d .  / [ I + ot(T , ' amb 1  amb  the  v  [1 + a ( T wop  was c h o s e n a t  T  T )1 o / J  )1  O>  600°C as  suggested  by W i t z e  [36] . C a l i b r a t i o n o f t h e a n e m o m e t e r s y s t e m was p e r f o r m e d a t conditions tube.  i n a wind  tunnel.  ambient  The a i r v e l o c i t y was m e a s u r e d w i t h a  pitot  S i n c e m o s t o f t h e p r e s e n t e d r e s u l t s w e r e o b t a i n e d w i t h w i r e #3,  calibration  curve i s presented  for  this  case i n F i g u r e C - 3 .  the  153. S i n c e t h e anemometer was c a l i b r a t e d a t ambient  c o n d i t i o n s , t h e heat  balance equations were used to c a l c u l a t e an o v e r a l l c o n v e c t i o n c o e f f i c i e n t h f o r each measured d a t a p o i n t . was  A N u s s e l t v s . Reynolds numbers c o r r e l a t i o n  c a l c u l a t e d f o r the c a l i b r a t i o n which was of the form:  N  , where  _ Re =  Vd , wire v gas  , and  u  =  A + B Re  N  hd . „ wire Nu = —; k gas  The c o n v e c t i o n c o e f f i c i e n t h was s o l v e d f o r i t e r a t i v e l y and a c u r v e f i t t i n g r o u t i n e NL2S0L [45] was u s e d t o f i n d t h e b e s t f i t and N.  C .3  c o e f f i c i e n t s A, B  These c a l c u l a t i o n s were performed by the program HWCAL2.  Hot Wire O p e r a t i o n The h o t w i r e v o l t a g e s i g n a l measured d u r i n g engine m o t o r i n g was  d i g i t i z e d every f i f t h  of a degree crank a n g l e .  The gas p r o p e r t i e s were  e v a l u a t e d a t t h e mean p r e s s u r e and temperature o b t a i n e d from m o t o r i n g p r e s s u r e data (see Appendix A ) .  T h i s time t h e Nu vs Re c o r r e l a t i o n was  used t o c a l c u l a t e i n s t a n t a n e o u s v e l o c i t i e s f o r each d a t a p o i n t i . e . 1800 times per engine r e 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  Sensitivity  Analysis  Many r e s e a r c h e r s have conducted s e n s i t i v i t y a n a l y s i s on t h e c a l c u l a t e d velocities  to v a r i a t i o n s i n the gas temperature  [8,36].  S i n c e temperatures  a r e c a l c u l a t e d from motored p r e s s u r e s t h e r e i s u n c e r t a i n t y e s p e c i a l l y a t peak v a l u e s a t TDC.  Compounding t h i s problem i s the f a c t t h a t t h e  154. anemometer i s l e s s s e n s i t i v e t o 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 d i f f e r e n c e between the wire and the f l u i d  i s reduced.  And  finally  the  t u r b u l e n t i n t e n s i t y around top dead c e n t e r i s of g r e a t e s t i n t e r e s t t o the engine r e s e a r c h e r . Lancaster  [8] e s t i m a t e d t h a t u s i n g c a l c u l a t e d temperatures from  measured p r e s s u r e s (based on a p o l y t i r o p i c 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 t o e s t i m a t e  the a c t u a l mean c y l i n d e r temperature w i t h i n 10-15%. A s e n s i t i v i t y a n a l y s i s was temperature  conducted on the d a t a u s i n g two  different  curves but keeping the p r e s s u r e s v i r t u a l l y c o n s t a n t .  At  TDC  t h e peak temperatures were t h e f o l l o w i n g :  run 1  T  T D C  =  618  K  run 2  T  T D C  =  587  K  T h i s r e s u l t e d i n a 5% d i f f e r e n c e .  The r e s u l t i n g d i f f e r e n c e a t 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 o t h e r d a t a s e t s a t d i f f e r e n t engine speeds l e d to s i m i l a r  C .5  results.  Hot Wire Data R e d u c t i o n The c y c l e - b y - c y c l e n o n - s t a t i o n a r y time a v e r a g i n g method i s f u l l y  d e s c r i b e d i n the paper by C a t a n i a and M i t t i c a very b r i e f l y  here.  [37], and w i l l be  discussed  155. The i n s t a n t a n e o u s v e l o c i t y i n t h e engine c a n be thought o f as a mean f l o w on which i s superimposed  turbulent  U (t) ±  C.5.1  =  fluctuations.  U (t) + u (t) i  ±  Mean V e l o c i t y U ^ ( t ) t h e mean v e l o c i t y f o r c y c l e i was determined i n t h e f o l l o w i n g  way: A p e r i o d o r window s i z e was chosen. was time averaged  The i n s t a n t a n e o u s v e l o c i t y U ^ ( t )  ( u s i n g a t r a p e z o i d a l r u l e ) over the crank a n g l e  interval.  T h i s y i e l d e d an average v e l o c i t y v a l u e which was c e n t e r e d i n t h e window (see  F i g u r e C-4).  <U  > =\  Next a c u b i c s p l i n e was f i t t e d v e l o c i t y c u r v e u\^(t) f o r c y c l e i . v e l o c i t y c u r v e so t h a t f i t t e d had  I  i , window'  U (t+T) dT ±  t o these mean v a l u e s t o o b t a i n a mean No attempt was made t o a d j u s t t h e mean  c u r v e and a c t u a l i n s t a n t a n e o u s v e l o c i t y  curve  the same mean i n each window (as recommended by C a t a n i a and M i t t i c a ) .  I n s t e a d an e x a c t f i t t o every window mean was used. fitted  The window mean o f t h e  curve was found to never d i v e r g e by more than 3% from the a c t u a l  mean, and t h i s was judged s a t i s f a c t o r y i n view o f t h e o t h e r 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 c u r v e s (one p e r c y c l e ) were ensemble averaged  over a l l c y c l e s t o g i v e the t r u e mean v e l o c i t y  U  true  (t)  =  1 N  N Z U,(t) i=l  156. C.5.2  Turbulence For  Intensity  each i n d i v i d u a l c y c l e ,  calculated  t h e f l u c t u a t i n g v e l o c i t y component was  from i n s t a n t a n e o u s 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 F i g u r e C-4) . The squared average i n t e n s i t y f o r each p r e v i o u s l y then c a l c u l a t e d  as  defined  window was  follows:  <u' , . 2> .window  =  T  1 i  1 = | J  f u 2(t+x) dx 0  1  [U (t+T) ±  U.(t+t)]  2  dt  Next these squared average i n t e n s i t i e s were ensemble averaged over t h e N c y c l e s , and t h e r o o t  extracted.  N  1 <u' . > - /i,window N  A cubic  s p l i n e was then f i t t e d  sities  f o r g r a p h i n g purposes.  C.5.3  Window For  Z  <u' , . 2> ,window  to the mean window t u r b u l e n c e i n t e n -  Size  a n a l y s i s purposes, we s e p a r a t e t h e i n s t a n t a n e o u s v e l o c i t y i n t o two  components:  U (t) = U (t) + u ( t ) ±  ±  ±  157. T r a n s p o r t on a s c a l e t h a t i s comparable t o c y l i n d e r dimensions i s attributed  to the mean v e l o c i t y , w h i l e mixing  attributed to turbulent fluctuations. s i z e e s t a b l i s h e s a frequency  on a much s m a l l e r s c a l e i s  The c h o i c e o f t h e a v e r a g i n g window  c u t - o f f p o i n t between mean v e l o c i t y and  fluctuations. I f t h e window i s t o o s m a l l t h e r e i s l o s s o f h i g h e r frequency t i o n as t u r b u l e n c e estimated.  informa-  i s i n t e r p r e t e d as mean flow v a r i a t i o n s and u' i s under-  I f t h e window i s chosen t o o l a r g e t h e mean flow p a t t e r n s a r e  a t t r i b u t e d to t u r b u l e n t f l u c t u a t i o n s and we tend t o o v e r e s t i m a t e u'. C a t a n i a and M i t t i c a  [37] recommend t h a t t h e c h o i c e o f an a p p r o p r i a t e  window s i z e be made by r e d u c i n g s e l e c t i n g the best r e s u l t .  the data over a number of window s i z e s and  They found  best c h o i c e which corresponds  t h a t 8 degrees a t 1600 RPM was t h e  t o a time s c a l e 0.9 msec t y p i c a l l y  l a r g e r than t h e d i s s i p a t i v e time s c a l e s . all  engine speeds.  Table  much  Our r e s u l t was a l s o 8 degrees a t  C-2 shows the time a s s o c i a t e d with each window  size.  Table  C-2  Time A s s o c i a t e d With Each Window S i z e  Engine Speed RPM 1200 1800 2400 3000  Time (msec) 2°  4°  6°  8°  10°  12°  15°  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  F i g u r e s C-5 t o C-12 present a t t h e f o u r engine speeds.  the window a n a l y s i s f o r wide open t h r o t t l e  I t i s i n t e r e s t i n g t o n o t e how t h e non-  158. s t a t i o n a r y averaged i n t e n s i t i e s a r e reduced i n comparison t o t h e 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 w r i t t e n t o p e r f o r m ensemble as w e l l as n o n - s t a t i o n a r y  C.6  time  averaging.  U n c e r t a i n t y i n Hot Wire Measurements Tabaczynski  [42] s t a t e d r i g h t l y  be i n t e r p r e t e d q u a l i t a t i v e l y .  t h a t h o t w i r e measurements c a n a t b e s t  Many u n c e r t a i n t i e s l i e i n the f a c t t h a t the  w i r e has no d i r e c t i o n a l r e s o l u t i o n o r i n t h e t a s k o f s e p a r a t i n g  fluctua-  t i o n s from mean v e l o c i t y when t h e r e i s l i t t l e  However,  Tabaczynski confirmed  o r no mean f l o w .  mentions t h a t up t o now l a s e r d o p p l e r measurements have  hot wire  f i n d i n g s i n magnitude and t r e n d .  The i n h e r e n t u n c e r t a i n t y i n t h e measurement t e c h n i q u e t h i s experiment by the p r o x i m i t y l a r i t y o f t h e chamber i t s e l f .  of the wire  i s compounded i n  t o the w a l l and the i r r e g u -  The hump i n t u r b u l e n t i n t e n s i t i e s a f t e r t o p  dead c e n t e r i s an example of data behaviour d i f f i c u l t  to explain.  S i n c e we must p u t numbers i n t h e e s t i m a t i o n o f u n c e r t a i n t y , a a p p r o x i mate estimate  i s 50-70% e r r o r 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 b r i d g e  circuit.  1.2-1  4  5  Reynolds Nb F i g u r e C.3.  Hot wire c a l i b r a t i o n  curve.  F i g u r e C.4.  D e f i n i t i o n s o f mean window v e l o c i t y , f i t t e d t r u e mean v e l o c i t y , rms window i n t e n s i t y and t r u e rms intensity.  60-1 Legend  40 co  1  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  _  30o o c CO CD  2  BDC  -150  -120  -90  -30  TDC  Crank Angle  30  BDC  deg ON CO  F i g u r e C.5.  Comparison o f ensemble averaged mean v e l o c i t y w i t h t r u e mean v e l o c i t y obtained by n o n - s t a t i o n a r y c y c l e - b y - c y c l e a n a l y s i s u s i n g v a r i o u s window s i z e s , 1200 rpm, b a s e l i n e p o s i t i o n .  Legend A  Ensemble Averaged  X  6 deg window  •  8 deg window  G3 10 deg window _ ffi 12 deg window  l  *  16 jiejj ^window  •  18 deg window  1  1  _  T  -140 -120 -100 -80  -60  •40  -20 TDC  Crank Angle F i g u r e C.6.  20  40  120  140  deg  Comparison of ensemble averaged t u r b u l e n c e i n t e n s i t y w i t h i n t e n s i t y obtained by n o n - s t a t i o n a r y c y c l e - b y - c y c l e a n a l y s i s u s i n g v a r i o u s window s i z e s , 1200 rpm, b a s e l i n e p o s i t i o n .  BDC  -150  -30  TDC  30  180  Crank Angle deg ON  F i g u r e C.7,  Comparison of ensemble averaged mean v e l o c i t y w i t h t r u e mean v e l o c i t y obtained by n o n - s t a t i o n a r y c y c l e - b y - c y c l e a n a l y s i s u s i n g v a r i o u s window s i z e s , 1800 rpm, b a s e l i n e p o s i t i o n .  10 Legend  8  A  Enaemble Averaged  X  8 deg window  •  8 deg window  E3 10 deg window _  £  X  16^egj«indow  CO  c  c tn  -i  1  T  -140 -120 -100 -80  -60  •40  -20 TDC  20  40  120  140  Crank Angle deg F i g u r e C.8.  Comparison o f ensemble averaged t u r b u l e n c e i n t e n s i t y w i t h i n t e n s i t y obtained by n o n - s t a t i o n a r y c y c l e - b y - c y c l e a n a l y s i s u s i n g v a r i o u s window s i z e s , 1800 rpm, b a s e l i n e p o s i t i o n .  50 Legend  0  I  i  BDC  -150  h -120  1  1  1  1  1  1  i  1  -90  -60  -30  TDC  30  60  90  120  1  i  150  f BDC  Crank Angle deg ON  F i g u r e C.9.  Comparison o f ensemble averaged mean v e l o c i t y w i t h t r u e mean v e l o c i t y o b t a i n e d by n o n - s t a t i o n a r y c y c l e - b y - c y c l e a n a l y s i s u s i n g v a r i o u s window s i z e s , 2400 rpm, b a s e l i n e p o s i t i o n .  12 -r Legend 10  A  Ensemble Averaged  X  6 deg window  •  8 deg window  G3 10 deg window  8-  OH  K  !? fieg window  X  15^eg^|ndow  *  lf.. J.. ^i!L !. _  de  ,  <  ow  r  - 1 4 0 -120  -100  -40  -20 TDC  20  40  60  i  i  80  100  120 140  Crank Angle deg <JN  00  F i g u r e C.10. Comparison of ensemble averaged t u r b u l e n c e i n t e n s i t y w i t h i n t e n s i t y o b t a i n e d by n o n - s t a t i o n a r y c y c l e - b y - c y c l e a n a l y s i s u s i n g v a r i o u s window s i z e s , 2400 rpm, b a s e l i n e p o s i t i o n .  50-1  0 | BDC  i  -150  1  1  -120  i  i  i  i  I  I  i  i  -90  -60  -30  TDC  30  60  90  120  i  150  BDC  Crank Angle deg CTN  F i g u r e C . l l . Comparison o f ensemble averaged mean v e l o c i t y w i t h t r u e mean v e l o c i t y obtained by n o n - s t a t i o n a r y c y c l e - b y - c y c l e a n a l y s i s u s i n g v a r i o u s window s i z e s , 3000 rpm, b a s e l i n e p o s i t i o n .  14 Legend  12  10  -140  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  _  -40  -20 TDC  20  40  140  Crank Angle deg F i g u r e C.12, Comparison of ensemble averaged t u r b u l e n c e i n t e n s i t y w i t h i n t e n s i t y obtained by n o n - s t a t i o n a r y c y c l e - b y - c y c l e a n a l y s i s u s i n g v a r i o u s window s i z e s , 3000 rpm, b a s e l i n e p o s i t i o n .  o  APPENDIX D RICARDO HYDRA GEOMETRY CALCULATIONS  Introduction 1.  Hydra Geometry and Approximate  2.  Integration  3.  I n t e r s e t i o n o f Flame and E l l i p t i c C l e a r a n c e Volume  4.  5.  Geometry  Procedure  3.1  Geometric R e l a t i o n s  3.2  AFS1 - Area o f I n t e r s e c t i o n  3.3  GAMMA1 - A n g l e o f I n t e r s e c t i o n  3.4  WPER1 - Wetted P e r i m e t e r  I n t e r s e c t i o n o f Flame and C y l i n d r i c a l Volume 4.1  Geometric R e l a t i o n s  4.2  AFS2 - Area o f I n t e r s e c t i o n  4.3  GAMMA2 - A n g l e o f I n t e r s e c t i o n  4.4  WPER2 - Wetted P e r i m e t e r  S o l v i n g the I n t e g r a l  172. Introduction T h i s s e c t i o n r e p o r t s the development i n t e r s e c t i o n of a s p h e r i c a l flame Hydra combustion chamber.  Two  of equations d e s c r i b i n g the  ( c e n t e r e d a t the spark l o c a t i o n ) and  parameters a f f e c t i n g the geometry: flame  r a d i u s and crank p o s i t i o n were v a r i e d to encompass a l l p o s s i b l e e n c o u n t e r e d d u r i n g r e a l engine o p e r a t i o n .  A l l t h i s i n f o r m a t i o n was  geometries  For each case t h e volume  e n c l o s e d by the flame, the flame a r e a and the wetted were c a l c u l a t e d .  the  cylinder wall area  then w r i t t e n t o a 3-dimensional  a r r a y which would be a c c e s s e d by the s i m u l a t i o n program.  1.  Hydra Geometry and Approximate  Geometry  The R i c a r d o 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  F i g u r e 7.  Note the spark p l u g l o c a t i o n a t a 45 degree a n g l e a t one s i d e of  the head.  On the o t h e r s i d e i s an a c c e s s p o r t f o r a p r e s s u r e t r a n s d u c e r s .  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 c l e a r a n c e volume  was m o d e l l e d as an e l l i p t i c a l c y l i n d e r o f e q u a l h e i g h t and volume. approximate  chamber geometry was  illustrated  i n F i g . 8.  t h e e l l i p s e i s t h e c y l i n d e r bore; the s h o r t a x i s was f o l l o w s : (see F i g u r e D - l f o r symbol  V  clearance  = V =  TT  The  The l a r g e a x i s o f  c a l c u l a t e d as  definition)  approximate a b h  c V , , clearance b = r IT a h c = 31.571  For the approximate t h e head.  mm  chamber, the spark i s l o c a t e d a t the top c o r n e r of  The e r r o r i n t r o d u c e d by t h i s s i m p l i f i e d geometry i s judged  173. m i n i m a l compared t o o t h e r assumptions such as flame s p h e r i c i t y and center  2.  of p r o p a g a t i o n .  T h i s has  been d i s c u s s e d  i n the model  fixed  chapter.  I n t e g r a t i o n Procedure The  f o l l o w i n g formulas r e f e r t o F i g . D - l .  Volume I n t e g r a t i o n dV  =  d ( r c o s 6 ) rcos6dydz  =  A r e a ( z ) dz  =  A F S l ( z ) dz  i n clearance  =  AFS2(z) dz  i n cylinder region  region  Flame Area I n t e r s e c t i o n dA  =  r d9 rcos6  =  r dy  dy  dz  at each z = constant  plane,  y v a r i e s from -y  to +y  symmetry = 2r y A  =  dz  2r / y dz 2r J GAMMAl(z) dz  i n clearance  2r / GAMMA2(z) dz  i n cylinder region  region  Wetted Area I n t e g r a t i o n dA  =  P e r i m e t e r ( z ) dz  =  WPERl(z) dz  i n clearance  =  WPER2(z) dz  i n cylinder region  region  due  to flame  174. Integration Limits  These l i m i t s a p p l y f o r 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 o f t h e 3 p o s s i b l e  geometries.  I f R- < h t c h VOLUME  =  f Q  J  Volume e n c l o s e d by flame i s  c A F S l ( z ) dz ' V  , , i n clearance region;  -, Case 1  I f R, > h r c Volume e n c l o s e d by V0L1  =  /  i n clearance region  0  If R  f  flame  A F S l ( z ) dz  < h Volume e n c l o s e d by flame i n V0L2  =  /  AFS2(z) dz h  h i t piston;  c  If R  r  c y l i n d e r a r e a , flame  hasn't  Case 2  > h h V0L2  =  /  AFS2(z) dz  flame has h i t p i s t o n ;  h  Volume = V0L1 + V0L2  The  same l i m i t s a p p l y f o r flame a r e a and wetted area  integration.  Case 3  175. 3.  I n t e r s e c t i o n o f Flame and E l l i p t i c a l C l e a r a n c e  3.1  Geometric R e l a t i o n s The  Volume  f o l l o w i n g r e l a t i o n s a r e d e r i v e d from the geometry as shown i n F i g .  D-3. Lets  take a s e c t i o n 1  r  2  = r 2  z  1  Z  2  -  f  2  rsin-y =  3  b = rcosy +  4  R [ b c o s e + a sin20] =  5  6 = TT/2 - 3  3 < IT/2  6 = B - IT/2  3 >  2  2  Rsing  2  rcos3 2  2  a b  2  TT/2  where R^  : flame r a d i u s  z  : v e r t i c a l p o s i t i o n w/r  a  : Bore/long a x i s of  b  : s h o r t a x i s of  R  : Ellipse  r  : p r o j e c t e d flame r a d i u s i n z=const p l a n e  Y,3,6  J angles  These r e l a t i o n s are v a l i d  ellipse  ellipse  Radius  as d e f i n e d  i n Figure  for a l l r a d i i  0 < r <  i . e . the p r o j e c t e d  t o top o f chamber  subject  D-3  to the  restrictions  2b  flame does i n t e r s e c t the  ellipse.  These f i v e e q u a t i o n s can be reduced t o the f o l l o w i n g  expressions:  176.  R  with  B  =  C  =  2  2  4  2(b -r ) +  ( b  2  - f ±\  =  /B  2  - 4C  b<  * (a2-b2)  2 - r 2 ) 2 _ _4_a£b^ (a2-b2)  and  f i n a l l y the angles a r e deduced.  2  6  =  u [r—b ( a 2 - R 2t-J ) l / 2 }i cos-1 |± R2 ( 2 - b ) 1  n  2  a  2  if  r > /aT+b "  2  =  if  3.2  3 > TT/2,  take n e g a t i v e  sign  2  - i b r. _ a - R 1/2 cos 1 {- [1 + ( — — ] ]} a^-b^ r  y  then  r  3 > TT/2, take p o s i t i v e  sign.  AFS1 - A r e a o f I n t e r s e c t i o n In t h i s s e c t i o n , e q u a t i o n s f o r t h e a r e a o f i n t e r s e c t i o n o f t h e  projected  flame and e l l i p s e  The b a s i c problem  a r e developed.  i s t o c a l c u l a t e t h e a r e a o f a s e c t i o n o f an e l l i p s e .  R e f e r t o F i g . D-4.  TOTAL AREA o f e l l i p s e :  nab  AREA o f 1/4 e l l i p s e :  irab/4  A  0  R 6 / / r d r d6 0 0  177. Using a previously derived r e l a t i o n :  r  2  ( b  2  C 0 S  2  6  + 2 a  s i n  2  = 2 2  e )  a  b  we get • 1 + (—  -  l)sin2e  2  b  2  Q2  -  a ---1 b 2  2  / l + Q sin e 2  6 A  =  R  / de 0  /  r dr 0  8  R2  0  a_2 2  This i n t e g r a l  u r  e  d6  0  (1 + Q 2 i n 2 e ) s  can be found i n a handbook.  9  1  A  = B  tan  - 1  /1+Q2"  [7140.2 tane] 0  — - t a n " (T~ tan6) / b 1  Now we can express the a r e a of the e l l i p s e swept by angle 3 ( F i g * D-4).  178.  23  =  ~~2~  t  a  n  "b  f o r 3 > TT/2, take p o s i t i v e  Finally AFS1  AFS1  a  n  e  ^  sign  the a r e a i n t e r s e c t e d by the p r o j e c t e d  flame a r e a and the e l l i p s e :  i s o b t a i n e d by summing t h e f o l l o w i n g a r e a s ( s e e F i g u r e D-5).  =  A r e a o f c i r c l e swept by 2y  -  Area o f t r i a n g l e  +  Area o f e l l i p s e  +  Area of t r i a n g l e BCD  AFSl(z)  for  3.3  t  =  2  yr  2  2  ABC  r sinycosy nab — — ; J — + abtan  1  swept by 23  R  2  2  ,a (-g tan6)  sin3cos3  -1  y r - r sinycosy +  T  2  + ab tan (-|- tan9) - R s i n 3 c o s 3  3 < TT/2  t o p s i g n and 9 = TT/2-3  3 > TT/2  bottom  s i g n and 6 = 3~TT/2  GAMMA1 - A n g l e o f I n t e r s e c t i o n In S e c t i o n 2 o f t h i s appendix an e x p r e s s i o n was developed f o r t h e  flame a r e a A  =  2R  f  / y dz  In t h e c l e a r a n c e r e g i o n , t h e i n t e g r a n d i s s i m p l y y and i s r e f e r r e d t o a s GAMMAl(z).  3.4  WPER1 - Wetted P e r i m e t e r In t h i s case, t h e b a s i c problem i s t o c a l c u l a t e t h e p e r i m e t e r o f a  s e c t i o n o f the e l l i p s e .  See F i g . D-6.  179.  ^ellipse  P  =  2  ~  2  e f / l- K sin 0 0 2  a  6  2  TT/-|- ( a + b )  2  approximate  d6  exact  equation  equation  z  with  K =  /a*-b - — —  T h i s i s an e l l i p t i c a l  integral  of the second  k i n d and i s t a b u l a t e d .  To  s o l v e t h e i n t e g r a l i n o u r program, t h e i n t e g r a n d was e x p r e s s e d as a b i n o m i a l s e r i e s , and the i n t e g r a t i o n was performed  [1 + ( - K s i n e ) ] l / 2  2  L  2  Integrating  term  2  =  J  2  1 - ^-K sin 6 2  -  2.4  term  by term.  K ^ s i n ^ e - -^j^r 2.4.6  K&sin6e  by term and a f t e r a l g e b r a i c m a n i p u l a t i o n we g e t  e 2  /  2  (1 - K s i n 6 )  1 / 2  d6  =  0.893596 + 0.05464 sin26 - 7 . 1 6 4 x l 0  +  7.574xl0  -  G(6)  =  a G(9)  -lt  sin4e  0  P  a  -lt  sinSecose + 1 . 1 4 4 x l 0  - l t  sin e 7  cos6  180. T h i s e q u a t i o n was  Finally  v e r i f i e d against tabulated  the e x p r e s s i o n  f o r the p e r i m e t e r  values.  of the e l l i p s e  i n t e r s e c t i o n w i t h the p r o j e c t e d flame i s : ( R e f e r t o F i g .  WPERl(z)  f o r 3 < TT/2 3 > TT/2  =  e  l  ^  ±  p  s  e  + 2a  6 = TT/2 - 3  bottom s i g n and  6 = 3 - TT/2  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  4.1  Geometric R e l a t i o n s  D-6).  Volume  These r e l a t i o n s a r e d e r i v e d f o r the geometry shown i n F i g .  1  r* = r 2  2  r siny = a  3  a cos3 + r cosy = b  f  -  z  D-7.  2  sin3  These e q u a t i o n s are v a l i d  f o r a l l r a d i i subject  a-b  i.e.,  by  G(6)  top s i g n and  4.  s e c t i o n formed  the flame must i n t e r s e c t  < r <  to the  a+b  the c i r c l e of r a d i u s  a.  These e q u a t i o n s a r e reduced t o y i e l d e x p r e s s i o n s  =  _! cos  restriction:  ra2+b2- 2 L 2ab J r  1  f o r the  angles:  181.  -i  Note t h a t when  4.2  r  b  2  -  a  2  +  r  2  i  r < a-b  3 = 0  y = n  r > a+b  3 = ir  y = 0  AFS2 - A r e a o f I n t e r s e c t i o n The e q u a t i o n s f o r a r e a o f i n t e r s e c t i o n a r e developed i n t h e same way  as f o r the c l e a r a n c e a r e a .  For  R e f e r t o F i g . D-9  a-b < r < a+b AFS2  =  A r e a o f flame c i r c l e  ±  Area o f t r i a n g l e ABC  +  A r e a o f c y l i n d e r c i r c l e swept by 23  +  Area o f t r i a n g l e BCD  2  2  AFS2 = y r - r s i n y c o s y + 3 a  for  2  yr + r  2  - a sin3cos3  2  GAMMA2 - A n g l e o f I n t e r s e c t i o n As b e f o r e A = 2R  f  / y dz  GAMMA2(z) = y  a-b < r < a+b  GAMMA2(z) = ir  r < a-b  2  3a ± a  r < a-b AFS2 = i r r  4.3  swept by 2y  2  2  sinycosy 2  sin3cos3  0 < g < TT  182. 4.4  WPER2 - Wetted  Perimeter  I t can e a s i l y be shown from F i g . D-7 t h a t :  WPER2(z)  = 26a  a-b < r < a+b  WPER2(z)  =0  r < a-b  I f the flame has touched the p i s t o n , the area i n t e r s e c t e d on the p i s t o n must be added t o t h e wetted w a l l a r e a .  If  R  > h  f  Wetted p i s t o n a r e a = AFS2  h  t  r  wetted  I  f  u h  c A  (r =h)  WPERl(z) dz + / Q  WPER2(z) dz + AFS2(h)  h  c  5.  S o l v i n g the I n t e g r a l The  +  e x p r e s s i o n s were i n t e g r a t e d n u m e r i c a l l y  r o u t i n e CADRE [ 4 6 ] .  using the i n t e g r a t i o n  T h i s r o u t i n e uses a c a u t i o u s a d a p t i v e  Romberg  e x t r a p o l a t i o n which c a n h a n d l e d i s c o n t i n u i t i e s o f s l o p e i n t h e i n t e g r a n d function. F i g u r e s D-8 t o D-10 a r e p l o t s o f n o n - d i m e n s i o n a l i z e d a r e a and wetted a r e a .  flame volume,  The non d i m e n s i o n a l i z i n g parameters a r e  f o r Volume:  VOLCYL = C y l i n d e r volume a t g i v e n crank angle  f o r flame area:  AWPCYL = Area o f a hemisphere o f r a d i u s e q u a l t o each cylinder  degree  radius  f o r wetted a r e a : AWPCYL = T o t a l a r e a o f c y l i n d e r i n c l u d i n g head, w a l l s and p i s t o n a t a g i v e n crank  angle  These parameters were taken from t h e B l i z a r d & Keck paper  [23].  Figure D.l.  Integration  Coordinates.  184.  F i g u r e D.2.  Integration  limits.  185.  1  2  t  1  1 F i g u r e D.3.  1  Geometry: c l e a r a n c e volume.  8  <  IT/2  g > TT/2  3 ^ TT/2  F i g u r e D.4.  Area of e l l i p s e  sections.  F i g u r e D.5.  Flame i n t e r s e c t i o n  areas.  F i g u r e 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 x  H=16.184  •  H=21.776  •  H =30.427  C/A=0 C/A=15 C/A =30 C/A=45  •  M=4t2M___C/»f60....  M  ^i^40__C^A=75__ 8  • HfS-LO..' fa*???...-  0.2  0.3  0.4  0.5  0.6  0.7  0.8  0.9  l.l  NON DIMENSIONAL FLAME RADIUS Rf/ZMAX  re D.8.  Non-dimensional flame volume vs n o n - d i m e n s i o n a l flame r a d i u s .  0.8  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  \ 0.0 |  &  I 0.1  F i g u r e D.9.  I 0.2  \  \ \ \  \ '  \  I I I 0.6 0.7 0.8 0.9 0.3 0.4 0.5 NON DIMENSIONAL FLAME RADIUS RF/ZMAX  Non-dimensional flame f r o n t area v s n o n - d i m e n s i o n a l  1.1  flame r a d i u s  (/// /  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  x  H=53J40  C/A-4S  C^fc=75  ;  • *!f?.L??.l_.<?/*=?P.  0.3  0.4  O.S  0.6  0.7  0.8  0.9  i.i  NON DIMENSIONAL FLAME RADIUS RF/ZMAX  F i g u r e D.10.  Non-dimensional wetted c y l i n d e r a r e a v s n o n - d i m e n s i o n a l f l radius.  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0096891/manifest

Comment

Related Items