UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

An investigation of venturi type air-fuel mixers for gaseous fuelled engines Troesch, Ernst Urs 1983

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

Notice for Google Chrome users:
If you are having trouble viewing or searching the PDF with Google Chrome, please download it here instead.

Item Metadata

Download

Media
831-UBC_1983_A7 T76.pdf [ 10.55MB ]
Metadata
JSON: 831-1.0095788.json
JSON-LD: 831-1.0095788-ld.json
RDF/XML (Pretty): 831-1.0095788-rdf.xml
RDF/JSON: 831-1.0095788-rdf.json
Turtle: 831-1.0095788-turtle.txt
N-Triples: 831-1.0095788-rdf-ntriples.txt
Original Record: 831-1.0095788-source.json
Full Text
831-1.0095788-fulltext.txt
Citation
831-1.0095788.ris

Full Text

AN INVESTIGATION OF VENTURI TYPE AIR-FUEL MIXERS FOR GASEOUS FUELLED ENGINES By ERNST URS TROESCH Dipl.Ing.ETH, Swiss Federal I n s t i t u t e of Technology, 1979 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE 1n THE FACULTY OF GRADUATE STUDIES Department of Mechanical Engineering We accept t h i s t h e s i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA J u l y 1983 © Ernst Urs Troesch, 1983 \ In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. D e p a r t m e n t o f Mechanical Eng ineer ing The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 DE-6 ( 3 / 8 1 ) i i ABSTRACT A study has been made of the fundamental f a c t o r s a f f e c t i n g the a b i l i t y of a venturi type a i r - f u e l mixer to hold a constant a i r - f u e l r a t i o . The v a l i d i t y of simple flow equations used to p r e d i c t the performance of a i r - f u e l mixers was examined, and values of pressure drop across the mixer were determined f o r s i x d i f f e r e n t c o n f i g u r a t i o n s . The o v e r a l l conclusion i s that i t should be p o s s i b l e to c o n s t r u c t v e n t u r i a i r - f u e l mixers which supply the engine with a s t o i c h i o m e t r i c a i r -f u e l mixture, provided that the pressure r e g u l a t o r maintains a constant o u t l e t pressure. The venturi type gas mixer system i n v e s t i g a t e d ( i n c l u d i n g pressure r e g u l a t o r ) was found to accurately c o n t r o l the a i r - f u e l r a t i o under t r a n s i e n t c o n d i t i o n s . I t was found that accurate flow c a l c u l a t i o n s are i n general not p o s s i b l e , so that the design of v e n t u r i type a i r - f u e l mixers w i l l be e m p i r i c a l i n nature. i i i TABLE OF CONTENTS Page ABSTRACT 11 LIST OF TABLES v LIST OF' FIGURES v i ACKNOWLEDGMENTS x i i NOMENCLATURE x l i 1 I. INTRODUCTION 1 1.1 Requirements f o r The A i r - F u e l Mixer 2 1.2 Introd u c t i o n to The Venturi Type A i r - F u e l Mixer 4 1.3 Purpose 6 I I . REVIEW OF PREVIOUS WORK AND STUDY OBJECTIVES 7 2.1 Review of Previous Work 7 2.2 Objectives and Scope of Work 10 I I I . EXPERIMENTAL APPARATUS AND PROCEDURE 12 3.1 Steady-State Experiments 12 3.1.1 Design of Venture Elements 12 3.1.2 Experimental Arrangement of Flow Bench 15 3.1.3 Experimental Procedure 18 3.1.4 C o e f f i c i e n t s of Discharge 20 3.1.5 Data Reduction 22 3.2 Dynamic Experiments 24 3.2.1 Experimental Arrangement and Procedure 24 IV. DISCUSSION OF RESULTS 27 4.1 Steady-state Experiments 27 4.1.1 Measurements of mass flow r a t i o s 27 4.1.2 C o e f f i c i e n t s of discharge 29 4.1.3 Pressure drop across the venturi element 33 4.2 Dynamic Experiments 35 i v Page V. CONCLUSIONS AND RECOMMENDATIONS 39 5.1 Conclusions 39 5.2 Recommendations 41 TABLES 43 FIGURES 45 REFERENCES 101 APPENDICES 105 APPENDIX A: Thermodynamic P r o p e r t i e s Used In This Thesis 106 APPENDIX B: Flow Equations 107 APPENDIX C: Influence of F l u i d C o m p r e s s i b i l i t y 110 APPENDIX D: C o e f f i c i e n t s of Discharge 113 APPENDIX E: E r r o r A n a l y s i s 121 V LIST OF TABLES Table Page 1. Measured and c a l c u l a t e d venturi throat depression APyj. f o r the highest measured a i r flow i f i j . Measurements and c a l c u l a t i o n s f o r neutral case ( P 0 I " Pon* 4 4 2. Comparison between incompressible and compressible flow as a f u n c t i o n of A P W T 112 LIST OF FIGURES Figure Page 1. I d e a l i z e d pressure and v e l o c i t y d i s t r i b u t i o n along the v e n t u r i tube a x i s 46 2. Sketch of a t y p i c a l conversion k i t , showing a i r - f u e l gas mixer and pressure r e g u l a t o r . Mixer mounted i n a i r cleaner case 47 3. Mass flow r a t i o m^/m^ versus a i r flow mj f o r three d i f f e r e n t values of AP Q = P Q I - P Q I j . C a l c u l a t i o n s were done with B e r n o u l l i ' s equation f o r incompressible f l u i d s 48 4. Drawing of venturi assembly with V-4H-5.3mm i n s e r t 49 5. Photos of venturi assembly with V-16H-2.6mm i n s e r t 50 6. Drawing of common shape f o r a l l the venturi elements 51 7. Drawing of venturi element V-16H-2.6mm 52 8. Drawing of venturi element V-4H-5.3mm 53 9. Drawing of venturi element V-1H-I2.3mm 54 10. Drawing of venturi element V-90D-12.3mm 55 11. Drawing of venturi element V-45D-12.3mm 56 12. Drawing of venturi element V-0D-12.3mm 57 13. Lay-out of flow bench f o r steady-state experiments 58 14. Photos of flow bench (steady-state measurements) 59 15. D e t a i l s of fuel supply f o r a l l the c o n f i g u r a t i o n s , with the exception of V-0D-12.3mm 60 v i i F igure Page 16. D e t a i l s of fuel supply f o r V-0D-12.3mm 61 17. Lay-out of flow bench f o r dynamic experiments 62 18. Location of hot wire probes 63 19. Photos of hot wire probes mounted i n ve n t u r i assembly 64 20. Measured and c a l c u l a t e d mass flow r a t i o s iTij/mjj versus a i r flow m^  f o r three d i f f e r e n t values of A P 0 = P 0 I " P 0 I I * Curves c a l c u l a t e d using CDI = C D I I = 1 ' 0 , C o n f i 9 u r a t l o n : V-16H-2.6mm 65 21. Measured and c a l c u l a t e d mass flow r a t i o s mj/ifijj versus a i r flow f o r three d i f f e r e n t values of A P 0 = P 0 I " P 0 I I " Curves c a l c u l a t e d using C n T = C n T T = 1.0. Co n f i g u r a t i o n : V-4H-5.3mm 66 DI DII 3 22. Measured and c a l c u l a t e d mass flow r a t i o s m^/m^ versus a i r flow nij f o r three d i f f e r e n t values of APQ = PQJ - P Q J J . Curves c a l c u l a t e d using CDI = C D I I = C o n f i g u r a t i o n : V-1H-I2.3mm 67 23. Measured and c a l c u l a t e d mass flow r a t i o s m^/m^ versus a i r flow mj f o r three d i f f e r e n t values of A P 0 = P 0 I ~ P0ir C u r v e s c a l c u l a t e d using CDI = C D I I = 1 C o n f i g u r a t i o n : V-90D-12.3mm 68 24. Measured and c a l c u l a t e d mass flow r a t i o s n^/m^ versus a i r flow m^  f o r three d i f f e r e n t values of A P 0 = P 0 I " P 0 I I * C u r v e s c a l c u l a t e d using CDI = C D I I = C o n f 1 9 u r a t 1 o n : V-45D-12.3mm 69 25. Measured and c a l c u l a t e d mass flow r a t i o s m^/m^ versus a i r flow mj f o r three d i f f e r e n t values of A P Q = P Q I - P Q I . . Curves c a l c u l a t e d using C n T = C n T T = 1.0. Co n f i g u r a t i o n : Y-0D-12.3mm 70 v i i i Figure Page 26. Measured c o e f f i c i e n t s of discharge f o r s i n g l e main flow ( a i r ) and f o r s i n g l e second flow ( f u e l ) , with f i t t e d curves. C o n f i g u r a t i o n : V-16H-2.6mm 71 27. Measured c o e f f i c i e n t s of discharge f o r s i n g l e main flow ( a i r ) and f o r s i n g l e second flow ( f u e l ) , with f i t t e d curves. C o n f i g u r a t i o n : V-4H-5.3mm 72 28. Measured c o e f f i c i e n t s of discharge f o r s i n g l e main flow ( a i r ) and f o r s i n g l e second flow ( f u e l ) , with f i t t e d curves. C o n f i g u r a t i o n : V-1H-I2.3mm 73 29. Measured c o e f f i c i e n t s of discharge f o r s i n g l e main flow ( a i r ) and f o r s i n g l e second flow ( f u e l ) , with f i t t e d curves. C o n f i g u r a t i o n : V-90D-12.3mm 74 30. Measured c o e f f i c i e n t s of discharge f o r s i n g l e main flow ( a i r ) and f o r s i n g l e second flow ( f u e l ) , with f i t t e d curves. C o n f i g u r a t i o n : V-45D-12.3mm 75 31. Measured c o e f f i c i e n t s of discharge f o r s i n g l e main flow ( a i r ) and f o r s i n g l e second flow ( f u e l ) , with f i t t e d curves. C o n f i g u r a t i o n : V-0D-12.3mm 76 32. Measured and c a l c u l a t e d mass flow r a t i o s m^/m^ versus a i r flow f o r three d i f f e r e n t values of A P 0 = P 0 I " P 0 I I " C u r v e s c a l c u l a t e d using c o e f f i c i e n t s of discharge Cp = f ( R e ) , as obtained from s i n g l e flow measurements. C o n f i g u r a t i o n : V-16H-2.6mm 77 33. Measured and c a l c u l a t e d mass flow r a t i o s m^/m^ versus a i r flow m^  f o r three d i f f e r e n t values of A P 0 = P 0 I " P 0 i r C u r v e s c a l c u l a t e d using c o e f f i c i e n t s of discharge C D = f ( R e ) , as obtained from s i n g l e flow measurements. C o n f i g u r a t i o n : V-4H-5.3mm 78 Figure i x Page 34. Measured and c a l c u l a t e d mass flow r a t i o s m^/m^ versus a i r flow mj f o r three d i f f e r e n t values of A P Q = P Q I - PQJJ* Curves c a l c u l a t e d using c o e f f i c i e n t s of discharge C D = f ( R e ) , as obtained from s i n g l e flow measurements. C o n f i g u r a t i o n : V-1H-12.3mm 79 35. Measured and c a l c u l a t e d mass flow r a t i o s mj/ifijj versus a i r flow nij f o r three d i f f e r e n t values of AP^ = Pm - P n... Curves c a l c u l a t e d using 0 01 O i l . . 3 c o e f f i c i e n t s of discharge C D = f ( R e ) , as obtained from s i n g l e flow measurements. C o n f i g u r a t i o n : Y-90D-12.3mm 80 36. Measured and c a l c u l a t e d mass flow r a t i o s iTij/mjj versus a i r flow m^  f o r three d i f f e r e n t values of AP Q = P Q I - PQJJ- Curves c a l c u l a t e d using c o e f f i c i e n t s of discharge C D= f ( R e ) , as obtained from s i n g l e flow measurements. C o n f i g u r a t i o n : V-45D-12.3mm 81 37. Measured and c a l c u l a t e d mass flow r a t i o s mj/irijj versus a i r flow m ^ f o r three d i f f e r e n t values of AP Q = P Q I - P Q I J - Curves c a l c u l a t e d using c o e f f i c i e n t s of discharge C Q = f ( R e ) , as obtained from s i n g l e flow measurements. C o n f i g u r a t i o n : V-OD-12.3mm 82 38. Measured c o e f f i c i e n t s of discharge f o r main flow ( a i r ) with various flow c o n d i t i o n s . C o n f i g u r a t i o n : V-16H-2.6mm 83 39. Measured c o e f f i c i e n t s of discharge f o r main flow ( a i r ) with various flow c o n d i t i o n s . C o n f i g u r a t i o n : V-4H-5.3mm 84 40. Measured c o e f f i c i e n t s of discharge f o r main flow ( a i r ) with various flow c o n d i t i o n s . C o n f i g u r a t i o n : V-1H-I2.3mm 85 X Figure Page 41. Measured c o e f f i c i e n t s of discharge f o r main flow ( a i r ) with various flow c o n d i t i o n s . C o n f i g u r a t i o n : • V-90D-12.3mm 86 42. Measured c o e f f i c i e n t s of discharge f o r main flow ( a i r ) with various flow c o n d i t i o n s . C o n f i g u r a t i o n : V-45D-12.3mm 87 43. Measured c o e f f i c i e n t s of discharge f o r main flow ( a i r ) with vvarious flow c o n d i t i o n s . C o n f i g u r a t i o n : v-0D-123mm 88 44. Measured c o e f f i c i e n t s of discharge f o r main flow ( a i r ) with various flow c o n d i t i o n s . C o n f i g u r a t i o n : V-0D-12.3mm 89 45. Measured c o e f f i c i e n t s of discharge f o r second flow ( f u e l ) with various flow c o n d i t i o n s . C o n f i g u r a t i o n : V-16H-2.6mn 90 46. Measured c o e f f i c i e n t s of discharge f o r second flow ( f u e l ) with various flow c o n d i t i o n s . C o n f i g u r a t i o n : V-4H-5.3mm 91 47. Measured c o e f f i c i e n t s of discharge f o r second flow ( f u e l ) with various flow c o n d i t i o n s . C o n f i g u r a t i o n : V-1H-I2.3mm 92 48. Measured c o e f f i c i e n t s of discharge f o r second flow ( f u e l ) with various flow c o n d i t i o n s . C o n f i g u r a t i o n : V-90D-12.3mm 93 49. Measured c o e f f i c i e n t s of discharge f o r second flow ( f u e l ) with various flow c o n d i t i o n s . C o n f i g u r a t i o n : V-45D-12.3mm 94 50. Measured c o e f f i c i e n t s of discharge f o r second flow ( f u e l ) with various flow c o n d i t i o n s . C o n f i g u r a t i o n : V-0D-12.3mm 95 51. Experimental arrangement of pressure taps f o r measurements of pressure drop across v e n t u r i elements 95 Figure x i Page 5 2 . Measured s t a t i c pressure d i f f e r e n c e s across the venturi element f o r d i f f e r e n t c o n f i g u r a t i o n s , P 0I = P0II 9 6 5 3 . V e l o c i t y (top trace) and t h r o t t l e p l a t e angle (bottom trace) versus time. Pressure r e g u l a t o r not connected to venturi assembly 97 54 . V e l o c i t y Wj (top trace) and t h r o t t l e p l a t e angle (bottom trace) versus time. Pressure r e g u l a t o r connected to venturi assembly 97 5 5 . V e l o c i t y WJJ (top trace) and t h r o t t l e p l a t e angle (bottom trace) versus time. Pressure r e g u l a t o r not connected to venturi assembly 98 5 6 . V e l o c i t y WJJ (top trace) and t h r o t t l e p l a t e angle (bottom trace) versus time. Pressure r e g u l a t o r connected to venturi assembly 98 5 7 . V e l o c i t y (top trace) and t h r o t t l e p l a t e angle (bottom trace) versus time. Pressure r e g u l a t o r not connected to venturi assembly 9 9 5 8 . V e l o c i t y (top trace) and t h r o t t l e p l a t e angle (bottom trace) versus time. Pressure r e g u l a t o r connected to venturi assembly 9 9 5 9 . V e l o c i t y (top trace) i n hose j u s t a f t e r pressure r e g u l a t o r and t h r o t t l e p l a t e angle (bottom t r a c e ) versus time 100 x i i ACKNOWLEDGMENTS I wish to express my ap p r e c i a t i o n to the members of the Thesis Committee f o r t h e i r i n t e r e s t and support. Thanks are also due to Dr. R.L. Evans f o r h i s supervision of t h i s p r o j e c t . Special thanks to the te c h n i c a l s t a f f of the Mechanical Engineering Department, e s p e c i a l l y Mr. L. Drake, who provided i n v a l u a b l e a s s i s t a n c e with the experimental work. The assi s t a n c e of Mrs. M. Lewis i n preparing the manuscript i s g r a t e f u l l y acknowledged. NOMENCLATURE Area, [m 2] Polynomial c o e f f i c i e n t s V e l o c i t y of sound, [m/s] C o e f f i c i e n t of discharge Constant-pressure s p e c i f i c heat, [J/(kg K)] Constant-volume s p e c i f i c heat, [J/(kg K)] Diameter, [m] S p e c i f i c heat r a t i o Molecular weight, [kg/kmol] Mass flow r a t e , [kg/s] Mass r a t i o of a i r to mixture of a i r and water Mass r a t i o of water to mixture of a i r and water nij + m n, [kg/s] Number of moles Pressure, [N/m2] Gas constant, [J/(kg K) ] Universal gas constant = 8314.34 J/(kmol K) Radius, [m] Reynolds number Temperature, [K] Volume flow r a t e , [m 3/s] S p e c i f i c volume V e l o c i t y , [m/s] XIV A = D i f f e r e n c e X = Normalized a i r / f u e l r a t i o v = Kinematic v i s c o s i t y , [m 2/s] p = Density, [kg/m 3] <}> = R e l a t i v e humidity S u b s c r i p t s 0 = Stagnation c o n d i t i o n s 1 = Main flow ( a i r ) II = Second flow ( f u e l ) mix = Mixture of a i r and water vapour PD = Pressure drop VT = Venturi t h r o a t 1 I. INTRODUCTION Natural gas has been used as an automotive f u e l f o r about s i x t y y e a r s . I t o f f e r s c e r t a i n advantages when compared to gasoline; f o r example, i t has a higher octane number and produces lower exhaust emissions. Natural gas was f i r s t used i n Europe as an a l t e r n a t i v e f u e l , e s p e c i a l l y i n I t a l y , because i t was a v a i l a b l e at a s u b s t a n t i a l l y lower p r i c e than g a s o l i n e . C u r r e n t l y there are approximately 250,000 I t a l i a n cars operating on natural gas. In North America and New Zealand there has r e c e n t l y been renewed i n t e r e s t i n r e p l a c i n g o i l based t r a n s p o r t a t i o n f u e l s with domestically produced natural gas [1]*, [ 2 ] . Most automobile engines running on natural gas are converted g a s o l i n e engines which run on both gasoline and natural gas. To enable a g a s o l i n e engine to run on natural gas, an a i r - f u e l mixer- has to be i n s t a l l e d . This mixer- should be able to provide an optimal a i r - f u e l r a t i o under steady-s t a t e and dynamic c o n d i t i o n s for- the whole flow range of an engine. Since the a i r - f u e l r a t i o i s one of the most important v a r i a b l e s for- an i n t e r n a l combustion engine, accurate metering i s very important. While gasoline carburetors have been developed to a c e r t a i n degree of s o p h i s t i c a t i o n , only l i t t l e research has so far- been done on a i r - f u e l mixers f o r gaseous f u e l l e d engines.. This t h e s i s w i l l t h e r e f o r e deal with a few aspects of a i r - f u e l r a t i o c o n t r o l . * Numbers i n square brackets designate references at the end of t h i s r e p o r t . 2 1.1 Requirements f o r the A i r - F u e l Mixer It i s common p r a c t i c e to determine q u a n t i t i e s of i n t e r e s t of an i n t e r n a l combustion engine, such as power output, thermal e f f i c i e n c y or exhaust gas emissions, as a fu n c t i o n of the normalized a i r - f u e l r a t i o x. The normalized a i r - f u e l r a t i o X has the advantage of perm i t t i n g comparisons of the q u a n t i t i e s of i n t e r e s t for d i f f e r e n t f u e l s . X i s defined as f o l l o w s : x m A i r actual  A i r required f o r s t o i c h i o m e t r i c combustion or x z ^AiAuel^ actual (mAl-j./mpuel) stoichiometric Recent reviews i n references [1] and [2] noted that X a f f e c t s : (i) power output : (ii) thermal e f f i c i e n c y (iii) exhaust gas emissions ( i v ) laminar flame v e l o c i t y (v) I g n i t i o n delay ( v i ) combustion d u r a t i o n , e t c . Consequently each engine speed and load point requires a s p e c i f i c a i r - f u e l r a t i o i n order to obtain optimum performance. Of course, each engine designer has to f i n d the optimum for the engine under design according to d i f f e r e n t emission r e g u l a t i o n s , fuel p r i c e s and a p p l i c a t i o n s . 3 Furthermore, i f a i r and fuel are not homogeneously mixed, the combustion process w i l l vary from c y c l e to c y c l e , i n a d d i t i o n to v a r i a t i o n s due to changing turbulence i n t e n s i t i e s . The gas mixer should provide an optimal a i r - f u e l r a t i o under both steady-state and dynamic co n d i t i o n s over the whole flow range of an engine. As an example f o r a t y p i c a l a i r flow range, the 1.8 l i t e r Toyota engine i n the A l t e r n a t i v e Fuels Laboratory at the U n i v e r s i t y of B r i t i s h Columbia has an a i r flow range of about 0.0033 kg/s ( i d l e at 800 rpm) to 0.067 kg/s ( f u l l load at 5000 rpm) while running on natural gas [ 3 ] . In designing a i r - f u e l mixers, the pressure drop through the a i r - f u e l mixer i s important. At f u l l load a higher pressure drop causes a higher pumping l o s s and therefore reduced power output and e f f i c i e n c y . Note that t h i s i s only v a l i d f o r f u l l load, because at part load i t does not make any d i f f e r e n c e whether the a i r flow i s t h r o t t l e d at the t h r o t t l e p l a t e or r e s t r i c t e d i n the mixer. Gasoline engines converted to run on natural gas have a s i g n i f i c a n t l y smaller maximum power output while running on natural gas. This i s due to the longer i g n i t i o n delay, the slower flame speed and the replacement of a i r by gaseous f u e l i n the c y l i n d e r [4]. Although automobile engines are operated f o r only b r i e f periods at f u l l l o a d , the pressure drop across the a i r - f u e l mixer should be as small as p o s s i b l e to prevent a d d i t i o n a l power l o s s . The a i r - f u e l mixer a l s o a f f e c t s a carbureted engine while running on g a s o l i n e . The r e s t r i c t i o n of the mixer has a s i m i l a r e f f e c t to the choke p l a t e and therefore the a i r - g a s o l i n e mixture w i l l be r i c h e r . 4 In summary, an ide a l a i r - f u e l mixer should: ( i ) Provide a s p e c i f i c X f o r each engine speed and load p o i n t . For t h i s t h e s i s t h i s c o n d i t i o n was reduced to: x = 1 = constant over the whole flow range, ( i i ) Mix a i r and fuel homogeneously. ( i i i ) Provide c o r r e c t operation under both steady-state and dynamic c o n d i t i o n s . ( i v ) Have minimal pressure drop across the a i r - f u e l mixer, (v) Be a simple device, ( v i ) Be easy to maintain, ( v i i ) Have a low manufacturing c o s t . 1.2 I n t r o d u c t i o n to the Venturi Type A i r - F u e l Mixer According to [ 5 ] , the p r i n c i p l e s of the venturi tube were f i r s t i n v e s t i g a t e d around 1791 by the I t a l i a n p h y s i c i s t G.B. V e n t u r i . In 1886 the American engineer Clemens Herschel used a venturi tube to measure the flow of water. He i s genera l l y c r e d i t e d as the inventor. The p r i n c i p l e of the v e n t u r i tube i s shown i n Figure 1. The e f f e c t of the c o n s t r i c t i o n i s to increase the v e l o c i t y and thus to decrease the s t a t i c pressure i n the v e n t u r i t h r o a t . The reduced pressure created i n the venturi throat i s a measure of the flow rate and can a l s o be used to suck i n a second f l u i d . That i s why the two main a p p l i c a t i o n s of the venturi tube are i n the measurement of the flow rate of f l u i d s and i n carburetors and gas mixers. Commercially a v a i l a b l e a i r - f u e l mixers can be c l a s s i f i e d i n t o two groups: v a r i a b l e area gas mixers and v e n t u r i type gas mixers. A v e n t u r i type gas mixer i s a simple device and has a f a s t t r a n s i e n t response. 5 One of the most convenient ways to add the a i r - f u e l mixer f o r the conversion i s to mount i t i n t o the a i r cleaner case, on c o n d i t i o n that there i s enough free room a v a i l a b l e . Figure 2 shows the arrangement of a i r cleaner case, a i r f i l t e r element, gas mixer, gasoline carburetor and pressure r e g u l a t o r . A pressure r e g u l a t o r must be i n s t a l l e d with a v e n t u r i type gas mixer i n order to control the f u e l pressure. Approximate steady-state c a l c u l a t i o n s showed that the a i r - f u e l r a t i o at low flow rates deviates s i g n i f i c a n t l y from the s t o i c h i o m e t r i c value, due to very small e r r o r s i n the pressure r e g u l a t o r and/or small f r i c t i o n pressure losses i n the connecting pipe between pressure r e g u l a t o r and a i r - f u e l mixer, as can be seen by reference to Figure 2 and to the c a l c u l a t i o n s below. The stagnation pressure PQJJ i n the pressure r e g u l a t o r cannot be kept e x a c t l y equal to PQJ. Due to changing s t i f f n e s s e s of the s p r i n g and the diaphragm of the l a s t stage i n the pressure r e g u l a t o r , the pressure d i f f e r e n c e APQ = PQJ - PQJ J w i l l vary with changing temperatures. Born [6] estimated the pressure r e g u l a t o r accuracy to be w i t h i n i50 N/m2 f o r a t y p i c a l pressure r e g u l a t o r . Although the r e l a t i v e inaccuracy i s very small (±0.05% f o r PQJJ = 1 b a r ) , i t causes s i g n i f i c a n t problems at low flow r a t e s . In order to show t h i s , i t i s assumed that there are no f r i c t i o n l o s s e s . The mass-flow r a t i o s are c a l c u l a t e d as a f u n c t i o n of a i r flow f o r three d i f f e r e n t cases: (a) neutral 01 - P Oil = 0 N/m2 (b) overpressure 01 - P Oil = -50 N/m2 (c) underpressure AP 0 = P 01 - P Oil = +50 N/m2. 6 With the assumptions stated i n Appendix B, the flow of an incompressible f l u i d i s described by equations (B.1) to (B.4) i n the appendix. As an example of the r e s u l t of such a c a l c u l a t i o n see the curves i n F i g . 3. These c a l c u l a t i o n s were done f o r the venturi c o n f i g u r a t i o n V-16H-2.6mm (see Section 3.1.1), and the fuel was simulated with a i r . The mass flow r a t i o s m^/m^ are p l o t t e d versus the a i r flow i T i j . F i g . 3 shows the unacceptable d e v i a t i o n i n the a i r - f u e l r a t i o at low flow rates due to small pressure r e g u l a t o r e r r o r s . The d e v i a t i o n s are very prominent at low flow r a t e s , where the metering s i g n a l APyy = P Q I - P Y T i s weak. The i n f l u e n c e of AP Q decreased with i n c r e a s i n g mass flow r a t e , because of the decreasing APQ/AP u t r a t i o : a P 0 I " PVT = 1 "ii a poir PVT 1 " V ^ V T 1.3 Purpose As yet l i t t l e research has been done on a i r - f u e l mixers f o r gaseous f u e l l e d engines and d e t a i l e d explanations and measurements of gas mixer performance are not r e a d i l y a v a i l a b l e . The purpose of t h i s t h e s i s i s to provide basic information f o r an improved gas mixer design. The aim i s not to develop a new a i r - f u e l mixer, but to explore the fundamental f a c t o r s a f f e c t i n g the a b i l i t y of a venturi type gas mixer to hold \ = constant, to i n v e s t i g a t e the v a l i d i t y of flow equations i n order to p r e d i c t a c c u r a t e l y the performance of a i r - f u e l mixers, to obtain values of pressure drop across the mixer f o r d i f f e r e n t c o n f i g u r a t i o n s , and to i n v e s t i g a t e the dynamic behaviour of a venturi type a i r - f u e l mixer system ( i n c l u d i n g a pressure r e g u l a t o r ) under t r a n s i e n t c o n d i t i o n s . I I . REVIEW OF PREVIOUS WORK AND STUDY OBJECTIVES 7 2.1 Review of Previous Work The l i t e r a t u r e review included t o p i c s of gas mixers, carburetors, flow measuring devices, venturi elements, gas engines and converted engines. Although gas and gasoline engines have been operated f o r many decades, there i s an amazing lack of useful information i n the l i t e r a t u r e about gasoline carburetors and a i r - f u e l mixers f o r gaseous f u e l s . I t can be concluded that the design and development of both a i r - f u e l mixers and gasoline carburetors are experimental i n nature. There are more reports about gasoline carburetors than about a i r - f u e l mixers because carburetors are more widely used. T h e o r e t i c a l analyses given i n textbooks t r e a t both a i r flow and f u e l flow s e p a r a t e l y . Because of the i n t e r a c t i o n of one flow with the other i n the actual device the r e s u l t i n g equations are of only l i t t l e value i n a c c u r a t e l y p r e d i c t i n g the performance of the device, so they can only be used as a f i r s t approximation. To give an example, Grohe i n [7] recommends incompressible f l u i d equations and constant c o e f f i c i e n t s of discharge ( C n = 0.80, C n r ... = 0.85) f o r a gasoline carburetor. He s t a t e s D A i r D Gasoline t h a t these empirical values are s u f f i c i e n t f o r an e s t i m a t i o n of a i r and f u e l opening diameters, and that the f i n a l diameters must be experimentally determined. T a y l o r i n [8] went a step f u r t h e r . He suggests compressible f l u i d equations f o r the a i r flow and t r e a t s the gasoline flow as incompressible. L i k e Grohe he c o r r e c t s the id e a l flow equations with c o e f f i c i e n t s of discharge i n order to p r e d i c t the real flow r a t e s . Taylor does not mention 8 values f o r c o e f f i c i e n t s of discharge. However, from an example c a l c u l a t i o n i t was found that he assumes a constant C n .. /C n r r a t i o . In t h e i r u A i r u basoime textbooks n e i t h e r Grohe nor T a y l o r , corroborate the r e s u l t s of c a l c u l a -t i o n s with measurements. A few years ago more rigorous exhaust emission r e g u l a t i o n s were followed by i n v e s t i g a t i o n s i n t o the t r a n s i e n t a i r - f u e l response of g a s o l i n e engines'[9], [10], [11]. The r e s u l t s of these papers show th a t sudden t h r o t t l e changes i n carburated gasoline engines cause an a i r - f u e l r a t i o excursion i n the c y l i n d e r . The mixture gets leaner during t h r o t t l e openings and r i c h e r during t h r o t t l e c l o s i n g s . The main reason f o r t h i s behaviour i s the l i q u i d f i l m on the surfaces of the i n d u c t i o n system. This f i l m cannot reach i t s new e q u i l i b r i u m immediately, and the r e s u l t i n g dynamic l a g i n the fuel flow from carburetor to c y l i n d e r causes the a i r - f u e l r a t i o excursion. Tanaka and Durbin show i n [9] that a i r and f u e l flow i n the carburetor respond instantaneously to t h r o t t l e p o s i t i o n changes. A l l these r e s u l t s lead to the supposition that there should be no dynamic l a g with natural gas, since natural gas i s i n the gas phase. However, there could be a dynamic l a g caused by the pressure r e g u l a t o r , which must be i n s t a l l e d with a v e n t u r i type a i r - f u e l mixer. There i s no l i t e r a t u r e a v a i l a b l e about the t r a n s i e n t response of gaseous f u e l l e d engines, with the exception of the paper [12] by Hamburg and Hyland. They report on a prototype vaporized gasoline engine metering system, where a v e n t u r i type a i r - f u e l mixer with a feedback c o n t r o l system was used to provide a 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 . The l i q u i d gasoline was vaporized before e n t e r i n g the "carburetor". Note that the problems are s i m i l a r f o r natural gas and vaporized gasoline because both f u e l s are gaseous. In order to take care of changes i n temperatures, f u e l composition e t c . , a 9 feedback system with an exhaust gas sensor c o n t r o l l e d the area of the f u e l metering o r i f i c e to keep the a i r - f u e l r a t i o s t o i c h i o m e t r i c . I t was demonstrated that with vaporized gasoline the steady-state high-frequency f l u c t u a t i o n s i n the a i r - f u e l r a t i o were minimal, the t r a n s i e n t a i r - f u e l r a t i o v a r i a t i o n s were n e g l i g i b l e f o r changes i n engine load and the a i r -f u e l r a t i o d i s t r i b u t i o n from c y l i n d e r to c y l i n d e r was uniform. The two authors used standard compressible f l u i d equations to e x p l a i n the e f f e c t of the v a r i a b l e area of the f u e l metering o r i f i c e . However, as w i l l be shown in t h i s t h e s i s , these equations w i l l not p r e d i c t accurately the flow r a t e s , because no c o e f f i c i e n t s of discharge were introduced. A huge amount of l i t e r a t u r e e x i s t s on venturi elements which are used to measure a s i n g l e flow (see f o r example, Li n d l e y [ 1 3 ] ) . However, l i t e r a t u r e i s very scarce about venturi elements i n which two gaseous  f l u i d s are mixed over a large flow range. The B r i t i s h Hydromechanics Research A s s o c i a t i o n (B.H.R.A.) [31] have published extensive data on l o s s c o e f f i c i e n t s f o r pipe "T" j u n c t i o n s , but t h i s data i s only f o r s i n g l e entry j u n c t i o n s and can not be a p p l i e d to m u l t i p l e entry venturi c o n f i g u r a t i o n s . Andreopoulos [14] presents measurements i n a j e t - p i p e flow i s s u i n g p e r p e n d i c u l a r l y i n t o a cross stream. In t h i s i n v e s t i g a t i o n a p i p e - j e t flow was driven by a compressor and issued Into a cross stream. V e l o c i t y measurements were taken which showed that the flows a f f e c t each other. Research work i n t h i s f i e l d s t a r t e d only r e c e n t l y , and no general r e s u l t s have y e t been obtained. Although the c o n f i g u r a t i o n i n v e s t i g a t e d by Andreopoulos i s not a venturi one, i t i s not much d i f f e r e n t , so that i t can be concluded that the f u e l flow m T T i n t o a venturi t h r o a t w i l l a f f e c t the 10 a i r flow irij and vice versa. Thus c o e f f i c i e n t s of discharge obtained with a s i n g l e flow w i l l be a l t e r e d when a second flow i s present. L i t e r a t u r e about engine conversions to gaseous f u e l s mainly c o n s i s t s of papers which describe the p r a c t i c a l part of conversions, such as power l o s s e s , pay back times, a v a i l a b i l i t y of f u e l , r e l i a b i l i t y , e t c . The authors of these a r t i c l e s are more concerned with showing t h a t conversions are p r a c t i c a l and o f f e r c e r t a i n advantages compared to ga s o l i n e , than i n pr o v i d i n g information about the performance of the gas mixer system. 2.2 Objectives and Scope of Work The o v e r a l l o b j e c t i v e of t h i s work was to obtain design information on a i r - f u e l mixers f o r gaseous f u e l l e d engines and to determine whether or not accurate p r e d i c t i o n s of the mass flow r a t i o produced by such mixers can be determined a n a l y t i c a l l y . A secondary o b j e c t i v e was to i n v e s t i g a t e the dynamic response of an a i r - f u e l mixer system, i n c l u d i n g a pressure r e g u l a t o r . In p a r t i c u l a r , s i x d i f f e r e n t c o n f i g u r a t i o n s of venturi type a i r - f u e l mixers were designed and constructed to be tested on a flow bench. The flow bench was used f o r both the steady-state measurements and i n modified form f o r the dynamic response measurements. During the steady-state experiments the mass flow r a t i o was determined as a f u n c t i o n of a i r flow and the c o e f f i c i e n t s of discharge were determined f o r both s i n g l e and combined flows i n the mixer. A l l of these measurements were taken at three d i f f e r e n t values of the pressure d i f f e r e n c e , A P Q = P Q J - P Q J J . 2 corresponding to the neutral case, A P Q = 0 N/m ; overpressure, A P Q = -50 2 2 N/m ; and the underpressure case, AP N = +50 N/m . In a d d i t i o n , values of 11 the pressure drop across the venturi element as a f u n c t i o n of a i r flow ra t e were obtained f o r a l l s i x c o n f i g u r a t i o n s . Transient response t e s t s were c a r r i e d out using a spring operated t h r o t t l e p l a t e to provide a steep t h r o t t l e opening ramp, and hot wire anemometer probes to measure the dynamic response of both the a i r and f u e l flow. These measurements were done both with and without a pressure r e g u l a t o r i n the system i n order to i n v e s t i g a t e the e f f e c t of the r e g u l a t o r i n determining the dynamic a i r - f u e l response of the system. Because of safety problems with natural gas the experiments were conducted using a i r to simulate natural gas i n the fu e l stream. A l l the i n v e s t i g a t i o n s were done f o r " a i r - a i r mixers" ( f u e l = a i r ) ; the back c a l c u l a t i o n s to a real a i r - f u e l mixer ( f u e l = natural gas) i s beyond the scope of t h i s Master's Thesis. 12 I I I . EXPERIMENTAL APPARATUS AND PROCEDURE 3.1 Steady-State Experiments 3.1.1 Design of Venturi Elements S i x d i f f e r e n t venturi elements were designed to be teste d on a flow bench. To minimize the t e c h n i c i a n ' s work involved the ven t u r i elements were designed as i n s e r t s which could be put i n t o a main body (-••venturi assembly). The ven t u r i assembly consisted of a pipe i n t o which could be screwed the venturi element, the fue l supply connections, the t h r o t t l e ( i n c l u d i n g a potentiometer) and the pressure taps to measure the pressure drop, see F i g s . 4 and 5, and F i g . 50. This assembly was connected to the stagnation chamber I . The shape of the venturi element was kept the same f o r a l l c o n f i g u r a t i o n s , see F i g s . 4 and 6, and only the fuel supply arrangement was a l t e r e d , see F i g . 7 to F i g . 12. The d i f f e r e n t elements are i d e n t i f i e d by the f o l l o w i n g codes: ( i ) V-16H-2.6mm : 16 fue l holes, fuel hole diameter = 2.6 mm, see F i g . 7. ( i i ) V-4H-5.3mm : 4 fue l holes, f u e l hole diameter = 5.3 mm, see F i g . 8. ( i i i ) V-1H-I2.3mm : 1 fuel hole i n venturi w a l l , diameter = 12.3 mm see F i g . 9. ( i v ) V-90D-12.3mm: f u e l pipe i s cut at 90 degrees to the ven t u r i t h r o a t , inner diameter = 12.3 mm, see F i g . 10. (v) V-45D-12.3mm: fue l pipe i s cut at 45 degrees to the ve n t u r i t h r o a t , inner diameter = 12.3 mm, see F i g . 11. 13 ( v i ) V-0D-12.3mm : fuel pipe i s cut at 0 degrees to the venturi t h r o a t , inner diameter = 12.3 mm, see F i g . 12. The expression "spud-in" r e f e r s to the c o n f i g u r a t i o n s V-90D-12.3mm and V-45D-12.3mm, and " p a r a l l e l v e n t u r i " to V-0D-12.3mm. The main design c o n s i d e r a t i o n f o r the venturi elements are l i s t e d and discussed below: ( i ) The venturi elements must f i t i n t o the l i m i t e d room i n the a i r cleaner case. Only exception : p a r a l l e l v enturi V-0D-12.3mm. ( i i ) The venturi elements must f i t onto the e x i s t i n g gasoline carburetor. The carburetor connection was simulated with a pipe whose inner diameter was 57 mm. ( i i i ) The a i r flow range should be approximately the same as f o r a 1.8 l i t r e 4 c y l i n d e r engine (see Section 1.1). However, the ven t u r i elements were designed f o r a flow r a t e , which was increased by a f a c t o r of about 1.4 i n order to match the flow ranges of the laminar flow elements. ( i v ) The smaller the venturi t h r o a t diameter the b e t t e r the metering s i g n a l w i l l be and the worse the pressure drop over the element w i l l be. In the l i t e r a t u r e there i s no standard maximum depression recommended. For example, Hamburg [12] chooses a AP.. T = 11200 N/m2, Grohe [7] recommends AP., t = 8600 N/m2 VTmax VTmax fo r a 4 c y l i n d e r gasoline engine, and Harrington [20] reports A PVTmax = N/m2. For the flow bench experiments the engine was simulated by vacuum cleaners. Because of t h e i r l i m i t e d blower capacity the maximum venturi depression was put i n t o the lower range of the values l i s t e d above. The r e s u l t i n g v e n t u r i t h r o a t diameter was chosen to be D = 35 mm. 14 (v) To keep the entry l o s s s m a l l , the r a t i o of i n l e t radius to ve n t u r i throat diameter, r/D, should be l a r g e . However, the a v a i l a b l e room i n the a i r cleaner case l i m i t s t h i s r a t i o . Entrance l o s s values f o r a smooth converging bellmouth are l i s t e d i n [ 2 1]. S t a r t i n g at r/D = 0, the entrance losses decrease q u i c k l y with i n c r e a s i n g r/D r a t i o . For r/D > 0.20 t h i s decrease T i s very slow. For the venturi elements under design, the r/D r a t i o was chosen to be 0.25. ( v i ) The a v a i l a b l e room i n the a i r cleaner case was not s u f f i c i e n t f o r a long d i f f u s o r (see F i g . 2 ) . Therefore a "short d i f f u s o r " was chosen. A short d i f f u s o r i s a d i f f u s o r which has a gradual, tapered enlargement at the beginning and then an abrupt enlargement to the f i n a l area [22]. Such a d i f f u s o r can have an e f f i c i e n c y which i s close to that of a d i f f u s o r with a small angle of divergence between the i n i t i a l and the end area. The information about short d i f f u s o r s i s very scarce, so that i t i s not c e r t a i n whether, i n t h i s a p p l i c a t i o n , the short d i f f u s o r i s r e a l l y b e t t e r compared to one with the same length which has no abrupt area enlargement but a steeper angle of divergence. I n t u i t i v e l y i t was concluded that a short d i f f u s o r has a b e t t e r pressure recovery e f f i c i e n c y , ( v i i ) I t was impossible to p r e d i c t p r e c i s e l y the diameters of the f u e l i n l e t corresponding to X = 1. They had to be found by an experimental t r i a l and e r r o r method. Because the fuel was simulated by a i r , f i r s t the flow rate had to be estimated allowing f o r the density d i f f e r e n c e between a i r and 15 methane as f o l l o w s : [ 7 A F ^ A i r . A p a i r V p a i r _ >/ p a i r _ ^methane _ ^ 34 V t h a n e A pmethane. P ^ I ^methane N pmethane rfij/mj^ 17.2 f o r a s t o i c h i o m e t r i c air-methane mixture [23]. Thus mj/ifijj = 17.2/1.34 = 12.8 f o r a " s t o i c h i o m e t r i c " a i r - a i r mixture. Note that natural gas was approximated by methane. The diameters f o r the 16-, 4- and 1- hole venturi element were determined experimentally by i n c r e a s i n g the fu e l hole diameters i n small steps u n t i l the c o r r e c t mass flow r a t i o mj/ifijj was found. A t r i a l and e r r o r method would have been very tedious f o r the spud-in c o n f i g u r a t i o n s and the p a r a l l e l v e n t u r i . Therefore the inner diameter f o r a l l one-hole c o n f i g u r a t i o n s was chosen to be the same, recognizing that the c o n d i t i o n of x = 1 would not be met e x a c t l y . 3.1.2 Experimental Arrangement of Flow Bench A flow bench had to be s p e c i a l l y designed and b u i l t f o r these experiments (see F i g s . 13 to 16). The engine was simulated by three vacuum c l e a n e r s , which sucked atmospheric a i r through the flow bench. The vacuum cleaners used were two SEARS Craftsman, model no.758.17860, and one Acklands model no.650. For the steady-state experiments the t h r o t t l e p l a t e was removed and the flow rates were c o n t r o l l e d by v a r i a b l e autotransformers (Staco Energy Products Co., type 3PN 1100) and by the b a l l valves I and I I . A b a r r e l was used as a surge tank to reduce pressure f l u c t u a t i o n s ( f o r values see Appendix E: E r r o r a n a l y s i s ) . 16 Stagnation chambers I and II were used to measure the stagnation pressures and temperatures. P r e l i m i n a r y measurements showed that the temperatures i n the two chambers were equal to the laboratory temperature: T f t T = T O T T = T, . . . Thus, only T. . . was K 01 O i l Laboratory * J Laboratory measured during the main i n v e s t i g a t i o n s . In order to smooth out the v e l o c i t y p r o f i l e and to reduce v o r t i c e s , wire-mesh screen and honeycomb were i n s t a l l e d i n the stagnation chambers. The flow through these chambers was v i s u a l i z e d with o i l smoke to check the e f f e c t of these measures. The pressure d i f f e r e n c e A P Q = P Q J - P Q J J f o r the three cases ( n e u t r a l , overpressure, underpressure) were adjusted with the b a l l valves to simulate pressure r e g u l a t o r e r r o r s . The b a l l valves could completely shut o f f the flows, i f d e s i r e d . For example, while performing the experiments to obtain the c o e f f i c i e n t of discharge f o r the s i n g l e main flow, the b a l l valve II was cl o s e d . The volume flow rates [m 3/s] were measured with laminar flow elements manufactured by Meriam Instruments. Model 50MH10-4NT was used to measure the main a i r flow and model 50MH10-1.25NT f o r the f u e l flow. For a pressure drop of 2000 N/m2 across the laminar flow element the volume a i r flow rates are about 0.077 m3/s and 0.0078 m3/s r e s p e c t i v e l y , at 21°C and 1.01 b a r ) . To get the mass flow rate [ k g / s ] , the density p f o r humid a i r must be known. The density can be c a l c u l a t e d as p = = - (0.00348 P, . - 0.00132 P . „ ), l a b o r a t o r y Laboratory water vapor 17 w h e r e P L a b o r a t o r y a n d P w a t e r vapor a r e 1 n N / m 2 ' s e e R e f . [ 1 5 ] . According to the users manual, the laminar flow elements had to be i n s t a l l e d with a 10 diameter s t r a i g h t run of pipe up and downstream of the elements. The pressure d i f f e r e n c e s were measured with four d i f f e r e n t types of manometers. Two Men am Instruments i n c l i n e d manometers (model 40HE35WM) were used to measure the pressure drop across each of the two laminar flow elements up to a pressure drop of 1500 N/m2. Two Lambrecht type alcohol manometers, which could be i n c l i n e d at d i f f e r e n t angles, were used to measure the stagnation chamber pressure d i f f e r e n c e A PQ and to measure the venturi t h r o a t depression APy T up to 1600 N/m2. A manometer board with seven i d e n t i c a l manometers was constructed f o r t h i s i n v e s t i g a t i o n . The range of these manometers was 0 to 10700 N/m2 with water as manometer f l u i d . They were used to measure the pressure d i f f e r e n c e s between laboratory and the stagnation chambers I and I I , the pressure drop across the venturi elements, the pressure drop across the laminar flow elements and the venturi t h r o a t depression f o r pressure d i f f e r e n c e s which exceeded the range of the i n c l i n e d manometers, and f i n a l l y A P Q was a l s o measured on t h i s board. For very coarse measurements the experiments could be conducted with the manometer board only. This reduced s i g n i f i c a n t l y the l i k e l i h o o d of the i n c l i n e d manometer overflowing while experimenting with the apparatus. The atmospheric pressure i n the la b o r a t o r y was determined with a mercury manometer. 18 3.1.3 Experimental Procedure There are two flows through the venturi elements; the a i r flow and the fuel flow. Each flow was trea t e d as a one-dimensional flow with a uniform v e l o c i t y p r o f i l e over the c r o s s - s e c t i o n . As discussed i n Appendix C the B e r n o u l l i equation f o r incompressible f l u i d s i s not accurate enough f o r t h i s i n v e s t i g a t i o n , and the c a l c u l a t i o n s were therefore done f o r i s e n t r o p i c and compressible flow of a p e r f e c t gas (see Appendix B). This i d e a l c a l c u l a t e d flow was then cor r e c t e d by i n t r o d u c i n g c o e f f i c i e n t s of discharge, defined as f o l l o w s : r r , . . . r . . . r _ actual mass rate of flow C o e f f i c i e n t of discharge t n = n^,, „->i - ,4 . , ,J , •4.L. 3 D mass flow rate c a l c u l a t e d with compress-i b l e i s e n t r o p i c flow of a p e r f e c t gas The r e s u l t i n g equations to describe the a i r - f u e l r a t i o m^/m^ as a fun c t i o n of nij are derived i n Appendix B. As o u t l i n e d i n Section 2.2, a l l the i n v e s t i g a t i o n s were done using a i r i n the fuel stream. The r e s u l t s found with a i r w i l l not ne c e s s a r i l y be the same as f o r natural gas, since these two gases have not the same thermodynamic p r o p e r t i e s and the physical s i m i l a r i t i e s are not completely f u l f i l l e d . There are three types of s i m i l a r i t i e s which are of i n t e r e s t : geometric, kinematic and dynamic s i m i l a r i t y [18], [ 1 9]. In order to leave the option open of doing engine experiments with natural gas l a t e r , the v e n t u r i elements were designed f o r natural gas. Therefore the geometric s i m i l a r i t y was f u l f i l l e d . The flow i s mainly a f f e c t e d by i n e r t i a , pressure, viscous and buoyancy f o r c e s . The use of a i r to simulate the natural gas fue l stream e l i m i n a t e s the buoyancy e f f e c t s of the l i g h t e r natural gas stream. 19 This was not f e l t to be important i n the present i n v e s t i g a t i o n , however, since the emphasis i s on o v e r a l l mass flow r a t i o s r a t h e r than on mixing of the fue l and a i r streams. An experimental research program was set up to determine: ( i ) m j / i T i j j r a t i o s as a f u n c t i o n of m^  f o r three d i f f e r e n t values of the pressure d i f f e r e n c e , as discussed i n Section 1.2: neutral P 0 I r 0 I I = 0 N/m2 overpressure P0I = -50 N/m2 underpressure P0I r 0 I I = +50 N/m2 The mass flows m^  and nijj were measured using the laminar flow elements described i n Section 3.1.2; ( i i ) C o e f f i c i e n t of discharge C D J f o r s i n g l e main flow (no second f l o w ) , ( i i i ) C o e f f i c i e n t of discharge C D I I f o r s i n g l e second ( f u e l ) flow (no main f l o w ) . ( i v ) Cpj and C ^ j f o r combined flow (both main and second flow are present i n venturi t h r o a t ) , (v) Pressure drop through the venturi element. The c o e f f i c i e n t s of discharge were determined as a fu n c t i o n of the Reynolds number ( f o r d e t a i l s see Section 3.1 .4). Note that C D I I includes the pressure l o s s due to f r i c t i o n i n the connecting l i n e between stagnation chamber II and the venturi t h r o a t . In the a i r - f u e l mixer design the main quantity of i n t e r e s t i s the a i r - f u e l r a t i o n^/m^ as a f u n c t i o n of the a i r flow mj, where both ^ and mjj are a fu n c t i o n of the venturi throat pressure P V j . In order to show the v a l i d i t y of equations (B.8) and (B.9) i n p r e d i c t i n g accurately the flows, the f o l l o w i n g procedure was followed: 20 (a) The measured and the c a l c u l a t e d mass flow r a t i o s m^/m^ were p l o t t e d as a f u n c t i o n of the a i r flow . In t h i s f i r s t step the c a l c u l a t i o n s were done using C^j = C ^ j j = 1.0. (b) The measured and c a l c u l a t e d r a t i o s mj/m^j were again p l o t t e d , but t h i s time the c o e f f i c i e n t s of discharge as measured f o r s i n g l e flows were s u b s t i t u t e d i n t o the equations (B.8) and (B.9). (c) The venturi throat depression APy-j. = P Q J - Py-j. was compared i n Table 1 f o r the maximum measured a i r flow m^ . The measured values are l i s t e d together with those obtained from the c a l c u l a t i o n s (using f i r s t C^j = = 1.0, and secondly the measured s i n g l e flow c o e f f i c i e n t s of di s c h a r g e ) . 3.1.4 C o e f f i c i e n t s of Discharge The c o e f f i c i e n t of discharge f o r a compressible flow, i n reference to the measured s t a t i c pressure and to the c r o s s - s e c t i o n where the pressure i s measured, i s defined by the r e l a t i o n : c _ Actual mass rate of flow  D ~ Mass flow rate c a l c u l a t e d with compressible i s e n t r o p i c flow " See Appendix B f o r assumptions and equations f o r i s e n t r o p i c and compressible flow of a p e r f e c t gas. The c o e f f i c i e n t of discharge f o r a s i n g l e flow i s mainly a f f e c t e d by the geometry and the Reynolds number [ 1 6 ] , since i t i s influenced by the boundary-layer thickness (displacement t h i c k n e s s ) , flow separation phenomena, v e l o c i t y d i s t r i b u t i o n and whether the flow i s laminar or t u r b u l e n t [ 1 7 ] , Therefore, the c o e f f i c i e n t s of discharge Cp were c a l c u l a t e d as a f u n c t i o n of the Reynolds number f o r the d i f f e r e n t v e n t u r i c o n f i g u r a t i o n s . 21 There were d i f f e r e n t p o s s i b i l i t i e s to choose the c h a r a c t e r i s t i c lengths i n order to compute Re = wL/v. The most convenient way was to take the t h r o a t diameter (D = 35 mm) f o r the main flow, and to take the diameter of the fuel openings i n t o the venturi t h r o a t f o r the second flow. The experimental data were obtained with atmospheric a i r , i . e . with a mixture of dry a i r and water vapor. The thermodynamic p r o p e r t i e s f o r the dry air/water vapor mixture were c a l c u l a t e d f o r a mixture of p e r f e c t gases: m. n . M . + n . M . #.% u _ mix _ a i r a i r water water I1) M . w - - — — -7—z m i x "mix n a i r + "water m. m . + m . c • „ „ _ i « j _ a i r water Since n. = rs— , thus M_. = i M. mix m . m . i a i r water M . M . a i r water l e t MH20 = m . /m . water mix, MAIR = m . /m. = 1-MH20 a i r mix t h e n Mmix = MAIR A MH20 W~ + M . a i r water C . MAIR C . + MH20 C ( i i ) k - p mix _ p a i r p water tin 9) k " i i x C v m . x MAIR Cyr a 1 r + MH20 t[ ^ ( I I I - 2 ) A computer program was developed to c a l c u l a t e C D = f( R e ) , see Appendix D. The program c a l c u l a t e d C = f ( R e ) , and used least-square c u r v e - f i t methods to obtain C n vs Re f o r polynomials of the form 22 Cp(Re) = A x + A 2Re + A 3 R e 2 + A 4Re 3 + AgRe1*. Comparing the c a l c u l a t e d Cp = f(Re) with the f i t t e d curve on the p l o t s , i t was found that the polynomial f i t worked well f o r most of the cases, but f o r a few i t was necessary to transform f i r s t the Re-a x i s and then to make the polynomial c u r v e - f i t . The two transformations used were Re' = ln(Re + 100) and Re' = v^ RT. I t was not p r a c t i c a l to f i t a s i n g l e curve to C D I I of V-0D-12.3mm. The values had to be approximated with two d i f f e r e n t curves. The values f o r a l l the r e s u l t i n g c u r v e - f i t s are l i s t e d i n Appendix D. I t should be noted that the expressions stagnation pressures and temperatures ( P Q , T Q ) used i n the program r e f e r to the c o n d i t i o n s i n the stagnation chamber I ( * P Q J , T q i ) and II (^ 01 r T0II^  r e s p e c t i v e l y . I t follows that C D I I f o r the f u e l flow already i n c l u d e s the pressure l o s s due to the flow f r i c t i o n i n the connecting l i n e between stagnation chamber II and venturi t h r o a t . 3.1.5 Data Reduction In t h i s s e c t i o n the measured q u a n t i t i e s are l i s t e d and t h e i r use i s described. Note that the pressure d i f f e r e n c e s were measured with manometers, which were operated with alcohol ( s p e c i f i c g r a v i t y = 0.8), water and mercury as manometer f l u i d . The conversion f a c t o r s to determine the pressure i n [N/m2] are 1 mm H 20 = 9.80665 N/m2 and 1 mm Hg = 133.322 N/m2, [24]. One of the most important q u a n t i t i e s was the atmospheric pressure l a b o r a t o r y * S i n c e t h e stagnation pressure P Q J i n the stagnation chamber I , and P Q J J i n stagnation chamber II r e s p e c t i v e l y , was measured as a pressure d i f f e r e n c e to atmosphere, the value of 23 P. . . must be known. P, . was also used to c a l c u l a t e the Laboratory Laboratory mass flow rates through the laminar flow elements. P r e l i m i n a r y measurements showed that the pressure drop through the pipe from atmosphere to the f i r s t pressure taps of the laminar flow elements was about 100 N/m2 at maximum flow. Therefore the r e s u l t i n g e r r o r i n c a l c u l a t i n g the a i r density was only about 0.1%. To c a l c u l a t e the a i r density as o u t l i n e d i n Section 3.1.2, the temperature T L a D O r a t . o r y a n c* ^ e P a r t i a ^ Pressure of water vapor i n a i r must be known besides P L a D O r a t o r y * T h e r e l a t 1 v e humidity <t> was determined with a s l i n g psychrometer (measuring wet and dry bulb temperatures). The p a r t i a l pressure p w a t e r v a p 0 r could be c a l c u l a t e d a s P w a t e r vapor = * P s a t ' w h e r e P s a t i s t h e s a t u r a t i o n P r e s s u r e o f water at the measured temperature T L a b o r a t o r y - T d r y b u l | ) . For values of the s a t u r a t i o n pressure as a fu n c t i o n of the temperature, see [ 2 5 ] . P r e l i m i n a r y measurements showed that T Q I = T Q I I = T L a D O T a t o r y (= T ^ bu-|D)» and thus i t was not necessary to measure T Q I and T Q I I i n the stagnation chambers. The laminar flow elements were c a l i b r a t e d at Meriam Instruments. The volume flows could be obtained from the c a l i b r a t i o n curves f o r each measured pressure drop across the laminar flow elements. Due to de v i a t i o n s i n T. . . from the c a l i b r a t i o n temperature, the flow Laboratory rates obtained from the c a l i b r a t i o n curves had to be correcte d according to a c o r r e c t i o n chart i n the users manual of the laminar flow elements. A f t e r t h i s f i r s t step i n the data r e d u c t i o n , the f o l l o w i n g q u a n t i t i e s were a v a i l a b l e f o r each data p o i n t : P Q I and T Q I 1n 24 stagnation chamber I , P Q J J and T Q J J i n stagnation chamber I I , a i r mass flows nij and m^, mass flow r a t i o iTij/m^, A P q = P Q I -PQJJ> venturi t h r o a t depression A P y T = P Q I - P y T (to c a l c u l a t e CDJJ: A P y T = P Q I I -P V T ) , a i r / w a t e r mixture (= MH20), and the pressure drop A P p Q across the venturi element. At t h i s stage the mass flow r a t i o m^/m^ could be p l o t t e d as a f u n c t i o n of the a i r flow IT^  , and the pressure drop APpp across the venturi elements as a f u n c t i o n of m ^ = mj+m^j. In the next step, the c o e f f i c i e n t s of discharge were c a l c u l a t e d with a computer program which was s p e c i a l l y developed f o r these i n v e s t i g a t i o n s , see Section 3.1.4 and Appendix D. F i n a l l y the mass flow r a t i o s nij/iTijj could be c a l c u l a t e d using the c o e f f i c i e n t s of discharge, and were compared with those from the measurements. An e r r o r a n a l y s i s i s given i n Appendix E. Dynamic Experiments 3.2.1 Experimental Arrangement and Procedure The goal of the dynamic experiments was to obtain information about the t r a n s i e n t behaviour of the venturi type a i r - f u e l mixer both with and without a pressure r e g u l a t o r i n the system. An experimental arrangement was designed to measure the two flow responses as a f u n c t i o n of t h r o t t l e motion. The flow bench f o r steady-state measurements was modified as shown i n F i g . 17. The laminar flow elements and the stagnation chambers were removed, and hot wire anemometer probes were i n s t a l l e d . In the f i r s t set of experiments, i n order to t e s t the v e n t u r i element i t s e l f , the two openings f o r the main and f o r the f u e l flow 25 were open to the atmosphere. For the second set of experiments to determine the t r a n s i e n t response of the element together with a pressure r e g u l a t o r the fue l opening was connected with a hose to a Renzo Landi Type M pressure r e g u l a t o r . The hose length was 0.70 m, and i t s inner diameter was 19 mm. This pressure r e g u l a t o r was equipped with an i d l e device which was, however, shut o f f f o r these experiments. The pressure r e g u l a t o r was fed with compressed a i r from a c y l i n d e r . The t r a n s i e n t flow response was measured with a hot wire anemometer u n i t . The hot wire DISA probes Type 55P11 were put i n t o the flows as shown i n F i g s . 18 and 19. The probes were operated by a DISA type 55D01 constant temperature anemometer. The hot wire s i g n a l was l i n e a r i z e d i n a DISA type 55D10 L i n e a r i z e r and then displayed on an o s c i l l o s c o p e . The t h r o t t l e motion was measured with a p o t e n t i -ometer and i t s sig n a l was also d i s p l a y e d on the o s c i l l o s c o p e , so that i t was p o s s i b l e to see the t r a n s i e n t flow response as a fun c t i o n of the t h r o t t l e angle. The o s c i l l o s c o p e used was a Tektronix dual beam storage o s c i l l o s c o p e , model 5113, and photographs were taken from the stored d i s p l a y with a Tektronix C-59A o s c i l l o s c o p e camera. The experiments were conducted with the V-16H-2.6mm c o n f i g u r a t i o n . There i s no c l e a r understanding of what t h r o t t l e opening speeds are f o r t y p i c a l d r i v i n g . DeLosh et a l , [ 2 6 ] , used t h r o t t l e ramps from about 3° (from close d p l a t e ) to 30° at a t h r o t t l e opening ra t e of 40 degrees/second. Aquino [ 1 0 ] , did a s e r i e s of one-second t h r o t t l e ramp measurements of various magnitudes, each s t a r t i n g at 10° and ramping up to 13°, 15°, 17°, 19° and 21°, r e s p e c t i v e l y . He states t h a t 26 t y p i c a l d r i v i n g often includes f a s t e r t h r o t t l e openings. Hires/Overington [11], increased the t h r o t t l e angle l i n e a r l y from 12.2° to 15.9° at a rate of 23 degrees/second. F i n a l l y Tanaka/Durbin [ 9 ] , did very f a s t t h r o t t l e openings/closings from 34° to 90° and v i c e - v e r s a . They do not mention the opening ra t e ; however, from a f i g u r e the opening time was estimated to be about 0.005 to 0.010 seconds. ( A l l these papers dealt with gasoline engines.) No t y p i c a l t h r o t t l e openings were found i n the l i t e r a t u r e . Therefore a step change had to be defined. In order to see the dynamic behaviour b e t t e r a steep ramp was chosen, opening the t h r o t t l e from 0° to 90° i n 0.050 seconds. The t h r o t t l e was opened with a spring mechanism, which guaranteed a repeatable opening r a t e . As an example of a t y p i c a l ramp see the bottom trace of F i g . 53. The spr i n g was released manually. The experiments were conducted with the same maximum flow rate f o r a l l the t e s t s . The maximum a i r flow rate mT was 0.045 kg/s. 27 IV. DISCUSSION OF RESULTS Steady-State Experiments 4.1.1 Measurements of mass flow r a t i o s Both mass flow rates and i T i j j were measured f o r the three cases n e u t r a l , overpressure and underpressure corresponding to a pressure d i f f e r e n c e AP Q = P Q I - P Q I I of 0 N/m2, -50 N/m2 and +50 N/m2. The mj/nijj r a t i o s as a f u n c t i o n of irij are p l o t t e d i n F i g s . 20 to 25 f o r the s i x d i f f e r e n t c o n f i g u r a t i o n s described p r e v i o u s l y . Note that the measured m^/m^ r a t i o s as a f u n c t i o n of mj are p l o t t e d twice, i n F i g s . 20 to 25 and i n F i g s . 32 to 37. This was necessary i n order to allow the comparison of the measured values with those from the flow equation c a l c u l a t i o n s . For F i g s . 20 to 25 the curves were c a l c u l a t e d , using CDj = CD j ^  = 1.0, and f o r F i g s . 32 to 37 the c o e f f i c i e n t s of discharge were used as obtained from s i n g l e flow measurements (see Section 4.1.2). Since i n t h i s Section only the measured values are discussed, only the measured values shown i n F i g s . 20 to 25 should be considered. The measurements showed that f o r a l l c o n f i g u r a t i o n s the mj/rfijj r a t i o was s e n s i t i v e to the pressure d i f f e r e n c e APQ = P Q I - P Q I I between the two stagnation chambers. This s e n s i t i v i t y was very prominent at low flow r a t e s , where the metering s i g n a l APyy was weak. The i n f l u e n c e of AP Q decreased with i n c r e a s i n g mass flow r a t e , because of the decreasing APQ/AP^ r a t i o (see Table 1 f o r values of APyy). The tendency of t h i s behaviour was already p r e d i c t e d i n Section 1.2 28 and was confirmed by these measurements. The conclusion from these measurements i s that the pressure r e g u l a t o r has to work very a c c u r a t e l y i n order to prevent unacceptable excursions from the 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 . A p e r f e c t l y operating pressure r e g u l a t o r would cause mj/mjj r a t i o s as measured f o r the neutral case ( A P Q = 0 N/m2). A l l the i n v e s t i g a t e d c o n f i g u r a t i o n s showed problems at low flow rates up to about 0.015 kg/s. For the r e s t of the i n v e s t i g a t e d flow range with 2 * * A P Q = 0 N/m the mj/m j j r a t i o s remained constant w i t h i n j u s t a few percent (t 2%), with the exception of V-0D-12.3mm ( F i g . 25). The m^/m^ r a t i o was nearly constant f o r V-1H-I2.3mm, V-90D- 12.3mm and V-45D-12.3mm f o r A P Q = 0 N/m2 ( F i g s . 22 to 24). Note, that the spud-in versions V-45D-12.3mm and V-90D-12.3mm could not be measured over the whole flow range, because the blower capacity of the vacuum cleaners was not s u f f i c i e n t to overcome the high pressure drop over these v e n t u r i c o n f i g u r a t i o n s . For d e t a i l s of pressure drop see Sectio n 4.1.3. Concerning m^/m^ r a t i o s , the V-0D-12.3mm ( F i g . 25) was an i n t e r e s t i n g case. The mixture was very lean at i d l e flow and never reached a constant value f o r the r e s t of the flow range. The shape of the mj/mjj c h a r a c t e r i s t i c at low flow rates l e d to the specul a t i o n t h a t the pipe f r i c t i o n between surge tanks II and the venturi throat i n f l u e n c e d the flow more at low flow r a t e s . Although the pipe flow was not f u l l y developed, the pressure drop due to pipe f r i c t i o n was estimated with equations f o r f u l l y developed flow. The r a t i o A P p i p e f r i c t i o n ^ V T w a s ( ' u 1 t e n l 9 n » * r m 36% at the f i r s t data p o i n t down to 28% f o r the l a t e s t . This decrease was not enough to support the 29 s p e c u l a t i o n s a f e l y , however, and f u r t h e r i n v e s t i g a t i o n s need to be done to f i n d the explanation f o r t h i s behaviour. The example of V-0D-12.3mm showed the importance of the varying A P r „ ^ + . - ^ „ / A P W T r a t i o with changing flow r a t e s . In order to make pipe f r i c t i o n vi t h i s n e g l i g i b l e and to have small fuel diameters i n the venturi t h r o a t t h e A p p i p e f r i c t i o n / A P V T r a t i o h a s to b e s m a 1 1 ' In general, flow s e p a r a t i o n , flow reattachment, secondary flow and flow f r i c t i o n i n f l u e n c e the fu e l flow i n the connecting pipe from the pressure r e g u l a t o r chamber to the venturi t h r o a t . Consequently t h i s p art of a conversion k i t has to be designed very c a r e f u l l y . I t i s pr e f e r a b l e to use short pipes of la r g e diameter with only moderate bends and well rounded entrances. 4.1.2 C o e f f i c i e n t s of discharge In the a i r - f u e l mixer design the main quantity of i n t e r e s t i s the a i r - f u e l r a t i o m^/m^ as a f u n c t i o n of a i r flow m^  , where both ifij and rrijj are a f u n c t i o n of the venturi t h r o a t pressure P y T . In Appendix B the general equations (B.8) and (B.9) were derived. The next phase of t h i s work was to determine the c o e f f i c i e n t s of discharge from the experimental data using equation (B.8). The c o e f f i c i e n t s of discharge were c a l c u l a t e d from experimental data and c o r r e l a t e d to the Reynolds number. The c h a r a c t e r i s t i c length i n Re = wL/v was chosen to be L = D = 35 mm f o r the main flow f o r a l l c o n f i g u r a t i o n s , and f o r the second flow L = the diameter of the fue l openings i n t o the venturi throat (See Section 3.1.4). The area Aj f o r the main flow was taken to be the thr o a t area f o r a l l c o n f i g u r a t i o n s : AI = 0.0352n/4 = 9.62 10 _ i t m 2 , T n i s d e c i ' s i ° n w a s s i g n i f i c a n t f o r the 30 spud-in and the V-0D-12.3mm ve r s i o n s , e.g., the flow area f o r V-OD-12.3mm was AJ = (0.035 2 - 0.0143 2)n/4 = 8.02 l O ' 4 m2. Therefore the c o e f f i c i e n t s of discharge C^j i n reference to the annular area A|, where P V T was measured, was 9.62/8.02 = 1.20 times bigger than the c a l c u l a t e d C p j . In order to have a uniform method, a l l the c o e f f i c i e n t s of discharge were c a l c u l a t e d i n reference to the f u l l c r o s s - s e c t i o n area. The c o e f f i c i e n t s of discharge f o r s i n g l e flows are p l o t t e d i n F i g s . 26-31. The meaning of c o e f f i c i e n t s of discharge f o r a s i n g l e flow i s : (a) C D j f o r s i n g l e flow: measurements only f o r flow mj, no flow m^; (b) C D J J f o r s i n g l e flow: measurements only f o r flow m^, no flow The measured c o e f f i c i e n t s of discharge are p l o t t e d together with curves, which approximate the data. These curves were the r e s u l t s of c u r v e - f i t s , which were done to get a mathematical expression f o r c o e f f i c i e n t s of discharge as a fu n c t i o n of Reynolds number. For d e t a i l s see Section 3.1.4 and Appendix D. These mathematical expressions were used i n the computer program as described below. A computer program was developed to show the e f f e c t s of using c o e f f i c i e n t s of discharge. This program c a l c u l a t e d mj/mjj as a f u n c t i o n of rrij, according to equations (B.8) and (B.9). The f l u i d used was atmospheric a i r under the same co n d i t i o n s ( PQ , T Q , Q>) as when conducting the experiments. So the measured m^/m^ r a t i o s could be compared with those from the c a l c u l a t i o n with c o e f f i c i e n t s of discharge. The r e s u l t s of these c a l c u l a t i o n s are presented i n F i g s . 20-25, i n F i g s . 32-37 and i n Table 1, as described below. 31 F i r s t , the c a l c u l a t i o n s were done f o r CQJ = C D I I = 1.0. Comparing the measured values with the c a l c u l a t e d ones i n F i g s . 20-25 and i n Table 1, i t must be concluded that the c o r r e l a t i o n was very poor. Secondly, the c o e f f i c i e n t s of discharge f o r s i n g l e flows were used. The r e s u l t of these c a l c u l a t i o n s are shown i n F i g s . 32-37. The r e s u l t was a great improvement on the previous method. The ven t u r i t h r o a t depression APy T f o r maximum flow showed an acceptable c o r r e l a t i o n , see Table 1. However, the c a l c u l a t e d iTij/mjj r a t i o s s t i l l d i d not c o r r e l a t e with measurements, with the exception of V-1H-I2.3mm and V-90D-12.3mm. In order to see the i n f l u e n c e of a second flow on another flow, the c o e f f i c i e n t s of discharge f o r the combined flows were c a l c u l a t e d and compared with those f o r s i n g l e flows. C o e f f i c i e n t s of discharge f o r a combined flow means that the values f o r the venturi t h r o a t depression APy T were measured while both flows irij and mjj were present. CQJ and Cpj j f o r the combined flow were then c a l c u l a t e d f o r these A P V T v a l u e s the same computer program which was used to obtain the c o e f f i c i e n t s of discharge f o r s i n g l e flow, see Appendix D. APy T was measured as APyj = PQJ - P y T i n order to c a l c u l a t e C D I f o r combined flow, and as A P V T = P 0 I I " PVT t 0 C A ^ C U ^ A T E CQJJ f o r combined flow. The experimental data was the same as used to p l o t mj/ irijj = f ( m j ) , see F i g s . 20 to 25. The c o e f f i c i e n t s of discharge f o r combined flow had to be determined f o r three cases: n e u t r a l , overpressure and underpressure. They w i l l e x a c t l y match the data [m^/m^ = f ( i r i j ) , A P y j ), and the values from equations (B.8) and (B.9). The d i f f e r e n c e between the c o e f f i c i e n t s of discharge 32 f o r s i n g l e flow and those f o r w combined flow i s a measure of the i n f l u e n c e of a second flow on another flow. The comparison of C n j f o r combined flow with those f o r s i n g l e flow i s shown i n F i g s . 38-43. The tendencies are: ( i ) Neutral case : C_.T . . . < C n T . . . DI combined DI s i n g l e ( i i ) Overpressure : Same as f o r neutral case. Tendency at low flow rates that C D I was l e s s than or equal to that of neutral case. ( i i i ) Underpressure: Same as f o r neutral case. Tendency at low flow rates f o r C Q I to be greater than or equal to t h a t of neutral case. A p o s s i b l e explanation f o r t h i s behaviour i s that the second flow c o n s t r i c t e d the main flow, i f i s s u i n g from the side i n t o the main flow. The smaller the m^/m^ r a t i o the greater the i n f l u e n c e of the second flow. I f the second flow was p a r a l l e l to the main one, as i n c o n f i g u r -a t i o n V-0D-12.3mm ( F i g . 43), then there was no c o n s t r i c t i o n a C D j was about the same f o r a l l four cases. The comparison of Cpjj f o r combined flow with those f o r s i n g l e flow i s shown i n F i g s . 44-49. There appeared to be no t y p i c a l pattern i n the d i f f e r e n c e s as seen f o r C ^ j . C ^ J J f o r combined flow was f o r a few co n f i g u r a t i o n s greater ( F i g s . 44, 45, 48), while f o r the r e s t ( F i g s . 46, 47, 49), l e s s than those f o r s i n g l e flow. T y p i c a l again were the l a r g e d e v i a t i o n s at low flow rates f o r overpressure and underpressure compared to n e u t r a l . The r e s u l t s of these measurements i n d i c a t e that i n general i t i s not p o s s i b l e to c a l c u l a t e a c c u r a t e l y m^/rn^ as a f u n c t i o n of m^  and to p r e d i c t the venturi throat pressure P without using c o e f f i c i e n t s of 33 discharge f o r combined flow. Using c o e f f i c i e n t s of discharge f o r a s i n g l e flow i s i n general s t i l l not s a t i s f a c t o r y , because i n most of the a p p l i c a t i o n s the c o e f f i c i e n t s of discharge f o r s i n g l e flow are not the same as those f o r combined flow, e s p e c i a l l y at low flow rates where the c o e f f i c i e n t s of discharge are very s e n s i t i v e to varying m^/m^ r a t i o . 4.1.3 Pressure Drop Across the Venturi Elements I t was noted i n Section 1.1 t h a t the o b s t r u c t i o n of the a i r - f u e l mixer a f f e c t s power output and thermal e f f i c i e n c y . The r e s t r i c t i o n of the mixer has a s i m i l a r e f f e c t to the choke p l a t e i n a gasoline carburetor and thus the a i r - f u e l r a t i o w i l l be r i c h e r , while running on gas o l i n e i n a dual fuel engine. Therefore, i t i s very important f o r the designer to know the order of magnitude of the pressure drop f o r d i f f e r e n t elements. In order to determine the average pressure drop exper i m e n t a l l y , four pressure taps were put i n t o the pipe piece j u s t behind the ve n t u r i element and connected together. The pressure taps are e q u a l l y d i s t r i b u t e d on the circumference as shown i n F i g . 50. The pressure drop across the element was measured as shown i n F i g . 50. The measurements were taken f o r the neutral case ( P Q I = P Q J J ) and t h e i r values are p l o t t e d versus the t o t a l mass flow through the element ( m t o t - nij + m^) i n F i g . 52. The measured pressure a f t e r the venturi element i s a s t a t i c pressure. Since the flow s t i l l has q u i t e a high v e l o c i t y there i s a considerable dynamic pressure ^ w2. The t o t a l pressure at the pressure taps i s the s t a t i c pressure plus the dynamic pressure. Therefore the t o t a l pressure drop across the element, as a d i f f e r e n c e of the t o t a l pressures, i s the measured s t a t i c pressure d i f f e r e n c e minus the dynamic pressure. 34 To get an approximation of the value of the dynamic pressure i n the c r o s s - s e c t i o n where the pressure taps are l o c a t e d , i t i s assumed that there i s : ( i ) a uniform v e l o c i t y p r o f i l e ; ( i i ) a constant a i r density p = 1.2 kg/m3; and ( i i i ) a c r o s s - s e c t i o n a l area, A, at the s t a t i c pressure taps which i s c a l c u l a t e d f o r an imaginary extended d i f f u s o r , as shown i n F i g . 51. Hence, w = m t 0 . j . / ( A p ) , and ^ w2 = f u n c t i o n ( m t o t ) can e a s i l y be c a l c u l a t e d . Note that i n F i g . 52, the s t a t i c pressure d i f f e r e n c e s are p l o t t e d without any c o r r e c t i o n f o r the dynamic pressure. The approximate dynamic pressure, as j u s t c a l c u l a t e d , i s also p l o t t e d to show i t s order of magnitude. While comparing the pressure drops of the d i f f e r e n t c o n f i g u r a t i o n s , i t has to be taken i n t o c o n s i d e r a t i o n that the mj/mjj r a t i o s are not the same f o r a l l c o n f i g u r a t i o n s , as can be seen i n the measured m^/m^ r a t i o s i n F i g s . 20-25. The s p u t - i n versions V-900-12.3mm ( F i g s . 23 and 24), e s p e c i a l l y , have to high a second flow m j j . This means that the diameters of the spud-ins would have to be reduced to obtain the c o r r e c t r a t i o mj/mjj, so that the r e s i s t a n c e f o r the main flow mj, and therefore the pressure drop, would decrease. How much do the diameters have to be reduced? When only the inner diameter of a spud-in i s reduced, w i l l decrease with about the square of the diameter r a t i o s . A smaller inner diameter w i l l a lso allow the reduction of the outer diameter of the spud-in. Therefore, the venturi t h r o a t depression w i l l decrease f o r a given main flow nij. Thus w i l l decrease. 35 As j u s t shown, a small change i n the diameter s i z e w i l l a l t e r the second flow m^ s i g n i f i c a n t l y . Regarding the two spud-in versions under i n v e s t i g a t i o n , i t can be concluded that the diameters have to be reduced, but i t w i l l be a moderate change. The measurements showed such an increased pressure drop f o r the spud-in c o n f i g u r a t i o n s compared with the other c o n f i g u r a t i o n s that even f o r reduced spud-in diameters the pressure drop has to be expected to be so high that spud-in c o n f i g u r a -t i o n s are of only l i t t l e i n t e r e s t f o r i n t e r n a l combustion engine a p p l i c a t i o n s . This i s i l l u s t r a t e d with the f o l l o w i n g example of the reduction i n power due to the pressure drop. As a f i r s t approximation the power i s propor t i o n a l to the manifold pressure, since the mass of the a i r - f u e l charge i n the c y l i n d e r i s nearly p r o p o r t i o n a l to t h i s pressure. The higher pumping l o s s and changes i n the combustion process are not taken i n t o c o n s i d e r a t i o n . At f u l l load, where the t h r o t t l e i s wide open, the manifold pressure i s approximately atmospheric, i f there i s only l i t t l e r e s t r i c t i o n due to the a i r - f u e l mixer and the carburetor. Therefore, f o r an atmospheric pressure of 1 bar, the power w i l l decrease by 1% f o r each 1000 N/m2 pressure drop. For example, the s t a t i c pressure drop d i f f e r e n c e between V-45D-12.3mm and V-16H-2.6mm i s about 5000 N/m2 at ^ t o t = 0 , 0 7 0 k g / s ^ s e e 5 2^» a n d t n u s t n e P o w e r W l 1 1 b e approximately S% l e s s with the V-45D-12.3mm mixer compared to the V-16H-2.6mm. 4.2 Dynamic Experiments Dynamic experiments were conducted to show the time response of the flows under the i n f l u e n c e of f a s t t h r o t t l e opening. The t h r o t t l e was opened from 0° ( f u l l y closed) to 90° (wide open) i n 0.050 s, (see Section 36 3.2.1). The v e l o c i t y was measured with hot wire probe I and WJJ with hot wire probe II (see F i g s . 18 and 19). The r e s u l t s of the dynamic experiments are presented i n F i g s . 53 to 59 and each f i g u r e i s discussed below. In these o s c i l l o s c o p e p i c t u r e s the t h r o t t l e p l a t e angle (bottom trace) and the v e l o c i t i e s Wj and WJJ r e s p e c t i v e l y (top t r a c e ) , are p l o t t e d versus time. The scales are: ( i ) T h r o t t l e Angle: 1 d i v i s i o n = 30°. The zero l i n e was set f o r a l l the f i g u r e s on the f i r s t h o r i z o n t a l screen 1 i ne. ( i i ) V e l o c i t i e s : 1 d i v i s i o n = 6 m/s. The zero l i n e was set f o r Wj ( F i g s . 53 and 54) on the second h o r i z o n t a l screen l i n e , f o r WJJ ( F i g s . 55 t 59) on the t h i r d one. ( i i i ) Time: 1 d i v i s i o n = 0.100 s f o r F i g s . 53, 54, 55, 56 and 59. 1 d i v i s i o n = 0.020 s f o r F i g s . 57 and 58. I t was t y p i c a l f o r a l l experiments that the flow j u s t a f t e r opening the t h r o t t l e was momentarily greater than the new steady-state value. The reason f o r t h i s was the i n c r e a s i n g a i r density i n the surge tank due to t h r o t t l e opening. The same behaviour has been observed i n t r a n s i e n t experiments with engines. DeLosh et al [26] c a l l i t "manifold f i l l i n g " , Aquino [10] describes i t as "manifold a i r charging". D e s c r i p t i o n of the f i g u r e s : In F i g s . 53 and 54 the main flow v e l o c i t y Wj was measured with hot wire probe I (see F i g s . 17 to 19). F i g . 54 was obtained with the pressure 37 r e g u l a t o r connected to the venturi* assembly, and F i g . 53 without pressure r e g u l a t o r . As expected, the main flow instantaneously responded to t h r o t t l e motion and there was no d i f f e r e n c e between these two cases. F i g s . 55 and 56 show the v e l o c i t y WJJ measured with hot wire probe I I . For F i g . 55 the f u e l connection was open to the atmosphere, while f o r F i g . 56 the fuel connection was connected to the pressure r e g u l a t o r . A small response l a g could be observed with the pressure r e g u l a t o r i n place. In order to see that b e t t e r , the data i s repeated i n F i g s . 57 and 58 with an expanded time s c a l e . Note that the flow could not be p r o p o r t i o n a l to the t h r o t t l e angle because of the b u t t e r f l y valve c h a r a c t e r i s t i c . Therefore i t was assumed that i n F i g . 57 the flow instantaneously responded to t h r o t t l e motion, so that the time lag i n F i g . 58 could be estimated i n reference to F i g . 57. The time l a g was about 0.010 seconds. Figure 59 i s added to show an i n t e r e s t i n g observation. In F i g s . 56 and 58, with the pressure r e g u l a t o r i n place, a v e l o c i t y f l u c t u a t i o n was observed. The question was whether t h i s f l u c t u a t i o n was caused by the hose or by the pressure r e g u l a t o r i t s e l f . The hose was disconnected from the pressure r e g u l a t o r and the same v e l o c i t y f l u c t u a t i o n was observed as i n F i g . 56. This i n d i c a t e s that the f l u c t u a t i o n i s caused by turbulence (Re « 20000) and secondary flow i n the hose. To check the v e l o c i t y f l u c t u a t i o n from the pressure r e g u l a t o r , hot wire probe II was mounted i n the hose j u s t a f t e r the pressure r e g u l a t o r . The r e s u l t was an extreme v e l o c i t y f l u c t u a t i o n , as shown 1n F i g . 59. The conclusion i s that the pressure r e g u l a t o r causes an extreme v e l o c i t y f l u c t u a t i o n which, however, i s dampened i n the connecting hose to the v e n t u r i element. The cause of the f l u c t u a t i o n was not i n v e s t i g a t e d . 38 In summary, the flows instantaneously responded to t h r o t t l e motion when the venturi assembly was opened to the atmosphere. When the pressure r e g u l a t o r was connected, a time l a g of about 0.010 seconds was observed i n the f u e l flow. In comparison, the time between two working cyc l e s f o r 1 c y l i n d e r of a 4-stroke engine at 3000 rpm i s 0.040 seconds. The conclusion i s t h a t the response time f o r the venturi type a i r - f u e l mixer i s good and no dynamic enrichment devices are necessary as f o r gasoline engines. 39 V. CONCLUSIONS AND RECOMMENDATIONS 5.1 Conclusions S i x d i f f e r e n t c o n f i g u r a t i o n s of venturi type a i r - f u e l mixer were designed to be tested on a s p e c i a l l y constructed flow bench. Steady-state measurements were conducted to obtain experimentally: (a) mass flow r a t i o mj/mjj as a f u n c t i o n of a i r flow rate mj; (b) c o e f f i c i e n t s of discharge f o r s i n g l e and combined flow; (c) pressure drop across the venturi element. The mass flow r a t i o s and c o e f f i c i e n t s of discharge were determined f o r three d i f f e r e n t cases: n e u t r a l , overpressure and underpressure corresponding to a pressure d i f f e r e n c e APQ = PQJ - PQJJ of 0 N/m2, -50 N/m2 and +50 N/m2. T r a n s i e n t response t e s t s were c a r r i e d out by using a steep t h r o t t l e opening ramp i n order to get information about the dynamic behaviour of the v e n t u r i type a i r - f u e l mixer by i t s e l f and of the mixer together with a pressure r e g u l a t o r . In general i t i s impossible to use flow equations (B .8) and (B .9) without c o e f f i c i e n t s of discharge f o r combined flow 1n order to p r e d i c t a c c u r a t e l y mass flow r a t i o s irij/mjj as a f u n c t i o n of a i r flow mj, where both flows depend on the venturi t h r o a t pressure Pyy. The c a l c u l a t i o n s with CQJ = CQJJ =1.0 produce values f a r o f f the measured ones, and even with c o e f f i c i e n t s of discharge obtained from the i n d i v i d u a l s i n g l e flows, the c a l c u l a t i o n s give i n general only an approximation of the real flow r a t e s . A l l t h i s was demonstrated on s i x d i f f e r e n t c o n f i g u r a t i o n s of venturi type a i r - f u e l mixers. 40 The c o e f f i c i e n t of discharge depends on the c o n f i g u r a t i o n , the Reynolds number and the mj/m^ r a t i o . The c o e f f i c i e n t s of discharge for the combined flow, which were obtained f o r s i x d i f f e r e n t c o n f i g u r a t i o n s , can be used f o r s i m i l a r c o n f i g u r a t i o n s . However, these c a l c u l a t i o n s w i l l only be approximate because v a r i a t i o n s i n the design parameters w i l l change the c o e f f i c i e n t s of discharge. This leads to the conclusion that a i r - f u e l mixer design i s experimental i n the f i n a l stage. The venturi type a i r - f u e l mixer i s s e n s i t i v e to the stagnation pressure d i f f e r e n c e APQ. This s e n s i t i v i t y i s very prominent at low flow r a t e s , where A P Q / A P V T i s not n e g l i g i b l e . An already very small APQ e r r o r causes considerable excursions from the 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 . The requirements on the accuracy of a pressure r e g u l a t o r can be relaxed i f the venturi element i s designed f o r high venturi t h r o a t depression A P V J . However, a high depression causes a high pressure drop over the element unless p a r t i c u l a r care i s taken i n the design. The spud-in versions V-90D-12.3mm and V-45D-12.3mm have such a high pressure drop over the element, t h a t they are of l i t t l e i n t e r e s t f o r i n t e r n a l combustion engine a p p l i c a t i o n . Much work needs to be done on p a r a l l e l Venturis, such as the investigated V-0D-12.3mm, to get a constant a i r - f u e l r a t i o and to dimension the mixer so that i t w i l l f i t i n t o an a i r c l e a n e r case. The pressure drop of the three remaining c o n f i g u r a t i o n s decreased with i n c r e a s i n g number of holes, or with decreasing f u e l opening diameters r e s p e c t i v e l y . Therefore the V-16H-2.6mm c o n f i g u r a t i o n i s p r e f e r a b l e . The dynamic response of the i n v e s t i g a t e d venturi type gas mixer system was very f a s t . When a pressure r e g u l a t o r was included i n the system, there 41 was a small response l a g i n the f u e l flow. This time l a g was about 0.010 seconds f o r experiments with a Renzo Landi Type M pressure r e g u l a t o r . The o v e r a l l conclusion of t h i s work i s that i t should be p o s s i b l e to c o n s t r u c t venturi a i r - f u e l mixers, which supply the engine with a s t o i c h i o m e t r i c a i r - f u e l mixture, provided that the pressure r e g u l a t o r works very a c c u r a t e l y . The i n v e s t i g a t e d venturi type gas mixer system ( i n c l u d i n g a pressure r e g u l a t o r ) was found to a c c u r a t e l y c o n t r o l the a i r - f u e l r a t i o under t r a n s i e n t c o n d i t i o n s . Since the flow s i t u a t i o n i n a v e n t u r i t h r o a t , where a i r and f u e l meet, deserves to be c a l l e d "complex", i f not "extremely complex", and accurate flow c a l c u l a t i o n s are i n general not p o s s i b l e , the design of a venturi a i r - f u e l mixer w i l l be experimental i n nature. 5.2 Recommendations The 16-hole c o n f i g u r a t i o n was the most promising one of the i n v e s t i g a t e d venturi elements. Consequently an experimental i n v e s t i g a t i o n i n t o the design parameters of t h i s c o n f i g u r a t i o n should be conducted. Some of the design parameters are: main venturi t h r o a t diameter D, i n l e t r a d i u s r a t i o r/D, p o s i t i o n and s i z e of f u e l holes, wall thickness between fue l r i n g channel and venturi t h r o a t , arrangement of f u e l hose, d i f f u s o r angle, rounding of fuel hole entrances, e t c . A b e t t e r understanding of the flow ( s e p a r a t i o n , r e c i r c u l a t i o n , etc.) can be obtained by using flow v i s u a l i z a t i o n techniques. A f u r t h e r extension of the flow bench i s necessary f o r i n v e s t i g a t i o n s i n t o the mixing of the two gaseous f l u i d s . This problem was not t r e a t e d i n the present i n v e s t i g a t i o n , but i t could be i n t u i t i v e l y concluded that the two gases w i l l be b e t t e r mixed than l i q u i d g asoline with a i r i n a 42 conventional carburetor. Nevertheless, i t would be i n t e r e s t i n g to see the change of mixing q u a l i t y f o r d i f f e r e n t c o n f i g u r a t i o n s . Flow bench experiments are important f o r i n v e s t i g a t i o n s of the design parameters, although these r e s u l t s should be confirmed on natural gas powered engines. F i n a l l y , i t would be i n t e r e s t i n g to t r y a D a l l tube Instead of a ve n t u r i element f o r a i r - f u e l r a t i o c o n t r o l . Cousins [27] i n v e s t i g a t e d the design parameters of a D a l l tube f o r measuring a s i n g l e flow. However, no information i s a v a i l a b l e as to whether a "Dall tube a i r - f u e l mixer" i s f e a s i b l e . 43 T A B L E S Venturi m I Venturi Throat Depression APy T = P 0 I " PVT Configuration measured c a l c u l a t e d , using CDI = C D I I = 1 , 0 c a l c u l a t e d , using C D = f(Re) as ob-tained from s i n g l e flow measurements. [kg/s] [N/m2] [N/m2] [N/m2] V-16H-2.6mm 0.095 6560 4310 6140 V-4H-5.3mm 0.094 6590 4270 6020 V-1H-I2.3mm 0.093 6120 4220 6150 V-90D-12.3mm 0.076 ' 5870 2730 5510 V-45D-12.3mm 0.062 4160 1790 4060 V-0D-12.3mm 0.091 7790 4110 8000 Table 1: Measured and c a l c u l a t e d venturi throat depression A P y T f o r the highest measured a i r flow i f i j . Measurements and c a l c u l a t i o n s f o r neutral case ( P n T = P n T T ) . 45 F I G U R E S 46 w ^ 9 - T' I d e a l i z e d pressure and v e l o c i t y d i s t r i b u t i o n along the v e n t u r i tube a x i s . 47 TO INLET MANIFOLD F i g . 2: Sketch of a t y p i c a l conversion k i t , showing a i r - f u e l gas mixer and pressure r e g u l a t o r . Mixer mounted i n a i r cleaner case. 48 F i g . 3: Mass flow r a t i o mj/mjj versus a i r flow riij f o r three d i f f e r e n t values of APQ = P Q I - PQJJ. C a l c u l a t i o n s were done with B e r n o u l l i ' s equation f o r incompressible f l u i d s . 49 F i g . 4: Drawing of v e n t u r i assembly with V-4H-5.3mm i n s e r t . F i g . 6: Drawing of common shape f o r a l l the v e n t u r i elements. F i g . 7: Drawing of v e n t u r i element V-16H-2.6mm. SECTION A-A Fig. 8: Drawing of v e n t u r i element V-4H-5.3mm. SECTION A-A F i g . 9: Drawing of v e n t u r i element V-1H-I2.3mm. SECTION A-A F i g . 10: Drawing of v e n t u r i element V-90D-12.3mm. SECTION A-A F i g . 11: Drawing of ve n t u r i element V-45D-12.3mm. 57 F i g . 12: Drawing of v e n t u r i element V-0D-12.3mm. 1 BALL VALVE I 2 WIRE-MESH SCREEN 3 HONEYCOMB 4 STAGNATION CHAMBER I 5 VENTURI ASSEMBLY, INCL. THROTTLE 6 VACUUM CLEANER 7 SURGE TANK 8 LAMINAR FLOW ELEMENT II 9 LAMINAR FLOW ELEMENT I 10 BALL VALVE II 11 STAGNATION CHAMBER II F i g . 13: Lay-out of flow bench f o r steady-state experiments. cn Co 14: Pho to s o f f l o w bench ( s t e a d y - s t a t e m e a s u r e m e n t s ) . F i g . 15 : D e t a i l s o f f u e l s u p p l y f o r a l l t h e c o n f i g u r a t i o n s , w i t h t h e e x c e p t i o n o f V-0D-12.3mm. F i g . 16: D e t a i l s of f u e l supply f o r v-0D-12.3mm. THIS SECTION ONLY FOR EXPERIMENTS WITH PRESSURE REGULATOR 1 HOT WIRE PROBE II 2 HOT WIRE PROBE I 3 HOT WIRE EQUIPMENT (BRIDGE,LINEARIZER) 4 OSCILLOSCOPE 5 VACUUM CLEANER 6 SURGE TANK 7 VENTURI ASSEMBLY, INCL. THROTTLE, POTENTIOMETER 8 CONNECTION TO POTENTIOMETER 9 COMPRESSED AIR CYLINDER 10 PRESSURE REGULATOR g. 17: Lay-out of flow bench f o r dynamic experiments 63 Fig. 18: Location of hot wire probes. F i g . 19: Pho to s o f ho t w i r e p robes mounted i n v e n t u r i a s s e m b l y . 65 25 rti-r /m II 20 h 15 10 0 -i 1 r i — r " i— r -I 1 L _i i i_ P 01 — P on P oi — P on P oi ~ P on +50 N/m2 0 -50 N/m2 _j i i_ _ i i i_ -i i i_ 0 0 . 0 2 0 0 . 0 4 0 0 . 0 6 0 IH-0 .080 0.100 [kg/s] F i g . 20: Measured and c a l c u l a t e d mass flow r a t i o s m^/m^ versus a i r flow rhj f o r three d i f f e r e n t values of APQ = P Q I - P Q I I . Curves c a l c u -l a t e d using C D I = C D I I = 1.0. Configuration:V-16H-2.6mm. 66 21: Measured and c a l c u l a t e d mass flow r a t i o s irij/m^j versus a i r flow irij f o r three d i f f e r e n t values of APQ = P Q I - P g i r Curves c a l c u -l a t e d using C D I = Cpjj = 1.0. C o n f i g u r a t i o n : V-4H-5.3mm. 67 0 _i i i 1 • ' • J , L _ i . _i I i_ _i L 0 0.020 0.040 0.060 ffl-0 .080 0.100 [kg/sl F i g . 22: Measured and c a l c u l a t e d mass flow r a t i o s m^/m^ versus a i r flow rhj f o r three d i f f e r e n t values of APQ = P Q I - P Q I j . Curves c a l c u -l a t e d using C D I = C D I I = 1.0. C o n f i g u r a t i o n : V-1H-I2.3mm. 68 F i g . 23: Measured and c a l c u l a t e d mass flow r a t i o s mj/m^ versus a i r flow m f o r three d i f f e r e n t values of APQ = P Q I - P Q I I . Curves c a l c u -l a t e d using C n T = C n T T = 1.0. C o n f i g u r a t i o n : V-90D-12.3mm. 69 F i g . 24: Measured and c a l c u l a t e d mass flow r a t i o s mj/ifijj versus a i r flow m f o r three d i f f e r e n t values of APQ = P Q I - P Q I I . Curves c a l c u -l a t e d using C n T = C n T T = 1.0. C o n f i g u r a t i o n : V-45D-12.3mm. 70 25 III 20 1 5 10 0 1 1 1 | ' 1 ' | • 1 1 1 ' ' I 1 1 -• : P o i — P on = + 5 0 N / m 2 -- x P o : — P on _ 0 -— a : P M — P on = - 5 0 N / m 2 — X -X -X I + -X \ •» - \ + V * x x • e & S * -— \ B B ° — - B \ ~ o — -- — e — D -- ° / i 1 , 1 , 1 . 1 , 1 , i i 0 . 0 2 0 0 . 0 4 0 0 . 0 6 0 0 .080 0.100 mT [kg/s] 25: Measured and c a l c u l a t e d mass flow r a t i o s mj/mjj versus a i r flow riij f o r three d i f f e r e n t values of AP Q = P Q I PQJJ. Curves calcu-l a t e d using C Q I = C D I I = 1.0. C o n f i g u r a t i o n : V-0D-12.3mm. 71 o.o 5 0 0 0 0 1 0 0 0 0 0 1 5 0 0 0 0 2 0 0 0 0 0 2 5 0 0 0 0 3 0 0 0 0 0 Re=D*w/z/ 1 0 0 0 0 15000 2 0 0 0 0 2 5 0 0 0 3 0 0 0 0 Re=D*wA/ F i g . 26: Measured c o e f f i c i e n t s of discharge f o r s i n g l e main flow ( a i r ) and f o r s i n g l e second flow ( f u e l ) , with f i t t e d curves. C o n f i g u r a t i o n : V-16H-2.6mm. r- , , , , I . . . • I • • • • I • • i i I i — i — i — i — i — i _ i — 0 50000 100000 150000 200000 250000 300000 Re=D *w/z/ C D „ 0.8 0.6 0.4 0.2 °'°0 10000 20000 30000 40000 50000 60000 Re=D *w/z/ g. 27: Measured c o e f f i c i e n t s of discharge f o r s i n g l e main flow ( a i r ) and f o r s i n g l e second flow ( f u e l ) , with f i t t e d curves. C o n f i g u r a t i o n : V-4H-5.3mm. 1 .0 CD, 0.8 h i ,i • » - i — i — i — i —I— i — i — i — i — r — i — i — i — i —i— i — i — i— r — i— i — i i i—a 0.6 0 .4 0.2 0.0 50000 100000 150000 200000 250000 300000 Re=D *w/i/ "•T 1 1 I 0.8 0.6 §-0.4 f-0 . 2 ^ 0.0 - 1 — i — I — i — i — i — i — r — i — I — i — i — r ~ ~ T — ' — i — i ' — T , , M I "i t i—q 1 1 I I I 1 I 1 , 1 . A.—t, 20000 40000 60000 80000 1O0OOO 120000 Re=D*w/z/ F i g . 28: Measured c o e f f i c i e n t s of discharge f o r s i n g l e main flow ( a i r ) and f o r s i n g l e second flow ( f u e l ) , with f i t t e d curves. C o n f i g u r a t i o n : V-1H-I2.3mm. 1 .0 -1 r — i r 0.8 0.6 0 .4 0.2 - | — i — i r — l 1—l 1 — r — i — | 1 — l 1 — l — | — l 1 — ' 1—| 1 — l '—I-1 0.0 • I i i i i 1 — t -50000 100000 150000 200000 250000 300000 Re=D*w/V 1 .0 CD„ i-0.8 i -I — i — i — r -j—i—i—i i | i — i — i — i — | — i — i — i i | i — i — r — i — | — i — i i i 0.6 0 .4 0.2 0.0 • ' • • • i I i i i i 1 — i — > — i — i — I — i — i — i — i — I — i — i — ' — 20000 40000 60000 80000 100000 120000 Re=D*w/i/ F i g . 29: Measured c o e f f i c i e n t s of discharge f o r s i n g l e main flow ( a i r ) and f o r s i n g l e second flow ( f u e l ) , with f i t t e d curves. C o n f i g u r a t i o n : V-90D-12.3mm. °'° 0 50000 100000 150000 200000 250000 ' 300000 Re=D*w/i/ °'° 0 20000 40000 60000 80000 100000 120000 Re=D*w/i/ 30: Measured c o e f f i c i e n t s of discharge f o r s i n g l e main flow ( a i r ) and f o r s i n g l e second flow ( f u e l ) , with f i t t e d curves. C o n f i g u r a t i o n : V-45D-12.3mm. 76 1 .0 CD, V O.B £-0.6 0 .4 fr 0.2h 0.0 50000 100000 150000 200000 250000 300000 Re=D *w/z/ 1 .0 0.8 I-0.6 0 .4 0.2 0.0 - i — i — l — i — i — i — i — l — i — i — r — i — I — i — i — i — i — i — i — i — i — i — | — i i i "T _J • * * • I I I • 1 1 1 20000 40000 60000 80000 100000 120000 Re=D*w/y F i g . 31: Measured c o e f f i c i e n t s of discharge f o r s i n g l e main flow ( a i r ) and f o r s i n g l e second flow ( f u e l ) , with f i t t e d curves. C o n f i g u r a t i o n : V-0D-12.3mm. 77 iti 7 / i i i II 20 h 15 10 0 1 1 1 1 1 1 ' 1 1 1 1 • : Poi 1 ' — P on 1 I = + 5 0 1 ' 1 N / m 2 1 x : Poi ~ Pon 0 -— \ a : Poi - P on = - 5 0 N / m 2 — -_ • ' — X """" X + */ * x * / * X X ~ / a ° ~ / a \ XQJ * B -/ ° — / a -- _ - B 1 . 1 . 1 . 1 1 1 , 1 1 1 , i 0 0 . 0 2 0 0 . 0 4 0 0 . 0 6 0 0 . 0 8 0 0 . 1 0 0 mj. [kg/s] F i g . 32: Measured and c a l c u l a t e d mass flow r a t i o s irij/ifij.j versus a i r flow rhj f o r three d i f f e r e n t values of APQ = P Q I - P o i r Curves c a l c u -l a t e d using c o e f f i c i e n t s of discharge C Q = f ( R e ) , as obtained from s i n g l e flow measurements. C o n f i g u r a t i o n : V-16H-2.6mm. 78 [Tl-2 5 I / m i l 20 h 15 10 "I 1 r - i 1 r "1 1-+ 50 N/m 2 0 - 5 0 N/m 2 J 1 L I I 1 L. _i I i 1 I L 0 . 0 2 0 0 . 0 4 0 0 . 0 6 0 . 0 . 0 8 0 riij [kg/s] 0 . 1 0 0 F i g . 33: Measured and c a l c u l a t e d mass flow r a t i o s mj/ihjj versus a i r flow ihj f o r three d i f f e r e n t values of APQ = PQJ PQJJ. Curves calcu-l a t e d using c o e f f i c i e n t s o f discharge CQ = f ( R e ) , as obtained from s i n g l e flow measurements. C o n f i g u r a t i o n : V-4H-5.3mm. 79 F i g . 34: Measured and c a l c u l a t e d mass flow r a t i o s riij/mjj. versus a i r flow m f o r three d i f f e r e n t values of APQ = PQJ - PQJJ- Curves c a l c u -l a t e d using c o e f f i c i e n t s of discharge C Q = f ( R e ) , as obtained from s i n g l e flow measurements. C o n f i g u r a t i o n : V-1H-I2.3mm. 80 25 - i — r mT / f i i II 20 15 h 10 0 -i 1 r _i I i L -i 1 1 1 r -i 1 r P oi — P on P oi — P on P oi _ P on +50 N/m2 0 -50 N/m2 J I 1 1 I I I i _ l u 0 0 . 0 2 0 0 . 0 4 0 0 . 0 6 0 0 . 0 8 0 0 . 1 0 0 fii! [kg/s] F i g . 35: Measured and c a l c u l a t e d mass flow r a t i o s mj/rhjj versus a i r flow m f o r three d i f f e r e n t values of APQ = PQJ - PQJJ. Curves c a l c u -l a t e d using c o e f f i c i e n t s of discharge C Q = f ( R e ) , as obtained from s i n g l e flow measurements. C o n f i g u r a t i o n : V-90D-12.3mm. 81 25 mT/m II 20 15 10 h -i 1 r " i—r 0 0 j i i_ -i 1 r- -i 1 r P.i - Pan = +50 N/m2 P.: " Pan = 0 P., - Pan = -50 N/m2 _j L 0.020 0 .040 0.060 0.080 J L J 0.100 rhx [kg/s] F i g . 36: Measured and c a l c u l a t e d mass flow r a t i o s ihj/ i f i j j versus a i r flow ihj f o r three d i f f e r e n t values of APQ = PQJ PQJJ. Curves c a l c u -l a t e d using c o e f f i c i e n t s of discharge CQ = f ( R e ) , as obtained from s i n g l e flow measurements. C o n f i g u r a t i o n : V-45D-12.3mm. 82 riix. [kg/s] F i g . 37: Measured and c a l c u l a t e d mass flow r a t i o s mj/rfijj versus a i r flow m f o r three d i f f e r e n t values of APQ = PQJ - PQJJ. Curves c a l c u -l a t e d using c o e f f i c i e n t s of discharge CQ = f ( R e ) , as obtained from s i n g l e flow measurements. C o n f i g u r a t i o n : V-0D-12.3mm. CD: • « • 0.8 h 0.6 |-s i n g l e flow o.B K 0.6 combined f l o w , neutral 0.8 0.6 E-combined f l o w , overpressure 0.8 £-0.6 h combined f l o w , underpressure • i ' • ' i i i • • • i • • • ' i — i — i — i — i — i — i i i i—I 50000 100000 150000 • 200000 250000 300000 Re=D*w/V F i g . 38: Measured c o e f f i c i e n t s of discharge f o r main flow ( a i r ) with various flow c o n d i t i o n s . C o n f i g u r a t i o n : V-16H-2.6mm. I 1 ' ' ' 1 1 I ' ' ' 1 I T I "f ' *T" 84 CD, t» «• « • « 0.6 0.6 £-0.6 §-0.6 E-0.8 h 0.6 E-0.8 0.6 s i n g l e flow combined f l o w , neutral combined f l o w , overpressure combined f l o w , underpressure -L . - . I . , , 1 I 50000 100000 150000 • 200000 250000 300000 Re=D*w/z/ F i g - 39: Measured c o e f f i c i e n t s of discharge f o r main flow ( a i r ) with various flow c o n d i t i o n s . Configuration:V-4H-5.3mm. 85 CD: 0.8 0.6 0.B E-. * - • • • 0.6 0.8 0.6 0.8 0.6 s i n g l e flow combined f l o w , neutral combined f l o w , overpressure combined f l o w , underpressure _i i i i — l — i -1 I I L . -L J ' 1 ' 50000 100000 150000 200000 250000 300000 Re=D*w/z/ F i g . 40: Measured c o e f f i c i e n t s of discharge f o r main flow ( a i r ) w i t h various flow c o n d i t i o n s . C o n f i g u r a t i o n : V-1H-I2.3mm. 86 i i • -i 1 1 1 r 1 j r—I 1 1 1 1 1 1 1 1 1 1 P-O.B h 0.6 fr 0.6 0.6 V O.B f-0.6 O.B h 0.6 • • K s i n g l e flow combined flow, neutral combined f l o w , overpressure combined f l o w , underpressure i i i i i i i , 50000 100000 150000 200000 250000 300000 Re=D*w/V F i g . 41: Measured c o e f f i c i e n t s of discharge f o r main flow ( a i r ) with various flow c o n d i t i o n s . C o n f i g u r a t i o n : V-90D-12.3. 1 I I'-'T 1 '•• I I •I'T'l T T 1 1 I T 87 CDi 0.8 0.6 0.B 0.6 0.8 p-O . B I - , 0.8 h 0.6 h s i n g l e flow combined f l o w , neutral combined f l o w , overpressure combined f l o w , underpressure i , I J—• • ' F i i i i i i i 50000 100000 150000 200000 250000 300000 Re=D*w/i/ F i g . 42: Measured c o e f f i c i e n t s of discharge f o r main flow ( a i r ) with various flow c o n d i t i o n s . C o n f i g u r a t i o n : V-45D-12.3mm. - i — i — 1 1 1 1 * 1 — i — I I I I I I I — I 1 I I—I 1 — I I—I i — i r — i — CD, 0.8 0.6 6-X K M m 0.8 I-0.6 £-0.8 0.6 §-0.8 |-0.6 h s i n g l e flow combined f l o w , neutral combined f l o w , overpressure combined f l o w , underpressure 88 _ i — i — i I i i—i—i— i i J I I L_J I I l_ 50000 100000 150000 200000 250000 300000 R e = D * w / z / F i g . 43: Measured c o e f f i c i e n t s of discharge f o r main flow ( a i r ) with various flow c o n d i t i o n s . C o n f i g u r a t i o n : V-0D-12.3mm. - i 1 — i 1 I — i — i r — i — I — i 1 — i 1 — I 1 — i 1 — I — 1 — I r — i — — i — i 1 — I T -0.6 p-0 .4 s i n g l e flow 89 O.B h 0.6 tr 0.4 h combined f l o w , neutral o.e P-0.6 0 .4 V combined f l o w , overpressure 0.8 P-0.6 f-0.4 I-combined f l o w , underpressure - l , 1 . I . . . L - , I „ . J .1 ml 1. i 5000 10000 15000 20000 25000 30000 R e = D * w / i / F i g . 44: Measured c o e f f i c i e n t s of discharge f o r second flow ( f u e l ) w i t h various flow c o n d i t i o n s . C o n f i g u r a t i o n : V-16H-2.6mm. 90 - 1 1 1 1 1 1 T —1 I 1 | I T I I I I I 1 I CD„ 0.6 0 .4 t-0.8 h 0.6 E-0.4 E-0.8 £-0.6 fc-0 .4 •« - « • • • 0.8 |-0.6 t-0 .4 s i n g l e flow combined f l o w , neutral combined flow, overpressure combined f l o w , underpressure I • I I I 1 I t I L—J 1 1 1 • i-10000 20000 30000 40000 50000 60000 Re=D *w/z/ F i g . 45: Measured c o e f f i c i e n t s of discharge f o r second flow ( f u e l ) w i t h various flow c o n d i t i o n s . C o n f i g u r a t i o n : V-4H-5.3mm. "T I I I I T "I ' T II 'T"'"T"1 IT I T 1 1 T I I T 1 T" I I I I I 91 C D „ 0.6 f-0 .4 0.8 0.6 0 .4 0.8 h 0.6 0.4 0.8 p-0.6 0 .4 • m ' 1 • ' I i i i i I i « i i I s i n g l e flow combined f l o w , neutral  combined f l o w , overpressure combined f l o w , underpressure i . J 20000 40000 60000 80000 100000 120000 Re=D*w/z/ F i g . 46: Measured c o e f f i c i e n t s of discharge f o r second flow ( f u e l ) w i t h various flow c o n d i t i o n s . C o n f i g u r a t i o n : V-1H-I2.3mm. 92 1 1 I T " T 1 I 1 •-T"y™| ' T ' ' T"" *T I "I'"' 1' ""1 ' 'T ' 0.6 h 0 .4 tr 0.8 £-0.6 0 .4 I-0.8 h 0.6 0 .4 f-0.8 0.6 0 .4 I 1 I 1 1 • B s i n g l e flow combined f l o w , neutral combined f l o w , overpressure combined f l o w , underpressure _J I J 1 — 1 L__l 1 L. ••1 „, , t I I l__J I I 1 1 > J • •— • 20000 40000 60000 80000 100000 120000 Re=D*wA/ F i g . 47: Measured c o e f f i c i e n t s of discharge f o r second flow ( f u e l ) w i t h various flow c o n d i t i o n s . C o n f i g u r a t i o n : V-90D-12.3mm. -T — i i - 1 1 1 1 1 1 1 1 1 1 1—T—1 1 1 1 I I 93 O.B 0.6 0.8 p-0.6 0.8 p-0.6 p-0.8 p-0.6 p-s i n g l e flow combined flow, neutral combined flow, overpressure combined flow, underpressure ' • • • I 1 * ' • I i • i i i i j _ 20000 40000 60000 80000 100000 120000 Re=D *w/z/ F i g . 48: Measured c o e f f i c i e n t s of discharge f o r second fl o w ( f u e l ) w i t h various flow c o n d i t i o n s . C o n f i g u r a t i o n : V-45D-12.3mm. i i r — r - T • i - j i—i 1 i "™r" |"r ' CD I I 0.4 E-0 . 2 ^ X • 0.6 h 0.4 h 0 . 2 ^ 0.6 fe-0 .4 tr 0-2 r X « • 0.6 p-0 .4 I-0 . 2 ^ I ' ' ' ' I ' s i n g l e flow combined f l o w , neutral combined f l o w , overpressure •combined f l o w , underpressure 94 F i g . 49: 0 20000 40000 60000 80000 100000 120000 R e = D * w / i / Measured c o e f f i c i e n t s of discharge f o r second flow ( f u e l ) w i t h various flow c o n d i t i o n s . C o n f i g u r a t i o n : V-0D-12.3mm. 95 F i g . 50: Experimental arrangement of pressure taps f o r measurements of pressure drop across v e n t u r i elements. S \ S A. \ k \ \ \ \ \ \ \ ^ \ \ , / , j "l AREA A (046.4) Flow 1 — . \ \ \ \ N n \ \ \ \ s v \ \ \ \ \ F i g . 51: Imaginary extended d i f f u s o r w i t h area A. 96 D 10000 h 5000 h 0 . 0 2 0 0 . 0 4 0 0 . 0 6 0 0 . 0 8 0 0 . 1 0 0 mi + rtiII [kg/s] F i g . 52: Measured s t a t i c pressure d i f f e r e n c e s across the v e n t u r i element f o r d i f f e r e n t c o n f i g u r a t i o n s , PQJ = P g i r F i g . 53: V e l o c i t y nr. ( t o p t r a c e ) and t h r o t t l e p l a t e a n g l e (bo t tom t r a c e ) v e r s u s t i m e . P r e s s u r e r e g u l a t o r n o t c o n n e c t e d t o v e n t u r i a s s e m b l y . F i g . 54: V e l o c i t y Wj ( t o p t r a c e ) and t h r o t t l e p l a t e a n g l e (bo t tom t r a c e ) v e r s u s t i m e . P r e s s u r e r e g u l a t o r c o n n e c t e d t o v e n t u r i a s s e m b l y . F i g . 56: V e l o c i t y w n ( t o p t r a c e ) and t h r o t t l e p l a t e a n g l e ( bo t t om t r a c e ) v e r s u s t i m e . P r e s s u r e r e g u l a t o r c o n n e c t e d t o v e n t u r i a s s e m b l y . 99 F i g . 57: V e l o c i t y WJJ ( t o p t r a c e ) and t h r o t t l e p l a t e a n g l e (bo t tom t r a c e ) v e r s u s t i m e . P r e s s u r e r e g u l a t o r n o t c o n n e c t e d t o v e n t u r i a s s e m b l y . F i g . 58 : V e l o c i t y ( t o p t r a c e ) and t h r o t t l e p l a t e a n g l e ( bo t t om t r a c e ) v e r s u s t i m e . P r e s s u r e r e g u l a t o r c o n n e c t e d t o v e n t u r i a s s e m b l y . F i g . 59: V e l o c i t y ( t o p t r a c e ) i n hose j u s t a f t e r p r e s s u r e r e g u l a t o r and t h r o t t l e p l a t e a n g l e ( bo t t om t r a c e ) v e r s u s t i m e . 101 R E F E R E N C E S 102 REFERENCES 1. Perry, C , Evans, R.L., H i l l , P.G., A Review of Performance of Natural  Gas Otto Cycle Engines, Report AFL-82-5, U n i v e r s i t y of B r i t i s h Columbia, 1982. 2. G e t t e l , L.E., Evans, R.L., H i l l , P.G., Review of I g n i t i o n and  Combustion Processes i n Methane-Air Mixtures, Report AFL-82-4, U n i v e r s i t y of B r i t i s h Columbia, 1982. 3. Goharian, F., p r i v a t e communication, 1983. 4. Baets, J.E., Combustion of Natural Gas and Gasoline i n a Spark-Ignited  Engine, Report AFL-82-2, U n i v e r s i t y of B r i t i s h Columbia, 1982. 5. The Encyclopedia Americana, Americana Corporation, I n t e r n a t i o n a l E d i t i o n , 1970. 6. Born, G., p r i v a t e communication 1982. 7. Grohe, H., Otto - and Dieselmotoren. Vogel V e r l a g , 6th ed., 1982. 8. T a y l o r , C.F., The Internal-Combustion Engine i n Theory and P r a c t i c e , Vol.11, Chapter 6, The M.I.T. Press, 1968. 9. Tanaka, M., Durbin, E.J., Transient Response of a Carburetor Engine, SAE Paper No.770046, 1977. 10. Aquino, C.F., Transient A/F Control C h a r a c t e r i s t i c s of a 5 L i t e r  C entral Fuel I n j e c t i o n Engine, SAE Paper No.810494, 1981. 11. H i r e s , S.D., Overington, M.T., Tra n s i e n t Mixture Strength Excursions -An I n v e s t i g a t i o n of T h e i r Causes and the Development of a Constant  Mixture Strength F u e l i n g Strategy, SAE Paper No.810495, 1981. 12. Hamburg, D.R., Hyland, J.E., A Vaporized Gasoline Metering System f o r In t e r n a l Combustion Engines, SAE Paper No.760288, 1976. 103 13. L i n d l e y , D., An Experimental I n v e s t i g a t i o n of the Flow i n a C l a s s i c a l  Venturimeter, Proc. I n s t . Mech. Eng. 1969-70, Vol.184, Pt.7, No.8. 14. Andreopoulos, I . , Measurements i n a J e t - P i p e Flow Issuing  P e r p e n d i c u l a r l y i n t o a Cross-Stream, Journal of F l u i d Engineering, Vol.184, 1982. 15. B e r c h t o l d , M., Thermodynamik I I , AMIV-Verlag, 3rd ed., 1973. 16. Ower, E., Pankhurst, R.C., The Measurement of A i r Flow, Pergamon Press, 4th ed. 1966. 17. S c h l i c h t i n g , H., Boundary-Layer Theory, McGraw-Hill, 7th ed., 1979. 18. Massey, B.S., Mechanics of F l u i d s , Chapter 8, Van Nostrand Reinhold Company, 3rd ed., 1978. 19. Daugherty, R.L., F r a n z i n i , J.B., F l u i d Mechanics with Engineering  A p p l i c a t i o n s , Chapter 7, McGraw-Hill, 7th ed., 1977. 20. Harrington, D.L., B o l t , J.A., A n a l y s i s and D i g i t a l S i mulation of  Carburetor Metering, SAE Paper No.700082. 21. ASHRAE Handbook, 1977 Fundamentals Volume, Chapter 31. 22. Eck, B., Techm'sche Stromungslehre, Chapter IV, Springer Verlag, 7th ed., 1966. 23. R. Bosch, Automotive Handbook, Chapter F u e l s , VDI-Verlag, 1976. 24. Anderton, P., Bigg, P.H., Changing to the metric system, National P h y s i c a l Laboratory, 4th ed., 1972. 25. Keenan, J.H., Keyes, F.G., H i l l , P.G., Moore, J.G., Steam Tables, John Wiley & Sons, 1978. 26. DeLosh, R.G., Brewer, K.J., Buch, L.H., Ferguson, T.F.W., Tobler, W.E., Dynamic Computer Simulation of a V e h i c l e w i t h E l e c t r o n i c Engine  C o n t r o l , SAE Paper No.810447, 1981. 104 27. Cousins, T., An Experimental I n v e s t i g a t i o n i n t o the Design Parameters  of the P a l l Tube, Department of Industry National Engineering Laboratory, Proceedings Paper J-2, 1975. 28. Van Wylen, G.J., Sonntag, R.E., Fundamentals of C l a s s i c a l  Thermodynamics, John Wiley & Sons, 2nd ed., 1978. 29. VDI - Warmeatlas, Db7, 2. Auflage, 1974. 30. Handbook of Chemistry and P h y s i c s , F-45, The Chemical Rubber Co., 52nd e d i t i o n , 1971. 31. M i l l e r , D.S., Internal Flow Systems, B.H.R.A., F l u i d Engineering S e r i e s , Vol.5, 1978. 105 A P P E N D I C E S 106 APPENDIX A: THERMODYNAMIC PROPERTIES USED IN THIS THESIS Property Source [28] R • 8314.34 R a i r •  287.00 R -methane = 518.35 M a i r = 28.97 M w a t e r * 18.015 k a i r = 1.400 k = methane •  1.299 C p a i r = 1003.5 °v a i r = 716.5 ^p water = 1872.3 ^v water = 1410.8 Sa t u r a t i o n pressure v a i r = [13.41 J kmol K J J kgHT J YgT _J kg K J VcgT J [28] [28] raSr C28] IcmoT [ 2 8 ] [28] [28] at 300 K [28] v at 300 K [28] at 300 K [28] at 300 K [28] - = fu n c t i o n (Temperature) [25] f5(T-273.15)] 10" 6 ^ ( t h i s equation was developed to approximate data from [29] f o r temperatures between 0°C and 40°C) K i r = 1 5 , 1 7 1 0 " 6 s~ a t 2 0 ° C ) = 16.49 10" 6 ^- at 20°C [30] methane s 107 APPENDIX B: FLOW EQUATIONS Each s i n g l e flow through the venturi elements w i l l be tre a t e d as a one-dimensional flow with a uniform v e l o c i t y p r o f i l e over the cross-s e c t i o n . The q u a n t i t i e s of i n t e r e s t are: (a) s t a t e of the f l u i d : P,T,v (b) v e l o c i t y : w (c) mass flow r a t e : m The unknowns as a f u n c t i o n of the pressure can be c a l c u l a t e d with the f o l l o w i n g set of equations: ( i ) d e n s i t y : p = 1/v (B.1) ( i i ) c o n t i n u i t y : m = Apw (B.2) ( i i i ) s t a t e ( i d e a l or p e r f e c t gas): Pv = RT (B.3) The remaining equations are d i f f e r e n t f o r incompressible and compressible f l u i d s . Incompressible F l u i d s Under the assumptions: ( i ) f l u i d i s incompressible: p = constant ( i i ) steady-state/steady-flow process ( i i i ) f r i c t i o n l e s s ( i v ) a d i a b a t i c (v) no work done by or on the f l u i d ( v i ) i n f l u e n c e of f i e l d o f force n e g l i g i b l e , the B e r n o u l l i equation describes the flow: £ w 2 + P = P Q (B.4) 108 Compressible F l u i d s Assumptions: ( i ) steady-state/steady-flow process ( i i ) i s e n t r o p i c flow ( a d i a b a t i c , f r i c t i o n l e s s ) ( i i i ) f l u i d i s a p e r f e c t gas: C p = constant, C y = constant hence k * C^/C„ = constant P v ( i v ) no work done by or on the f l u i d (v) i n f l u e n c e of f i e l d of force n e g l i g i b l e , then, the r e s u l t i n g equations are: k-1 P u *0 '0 Equation (B.2) can now be w r i t t e n as: T+T w • fe " V 1 - TT) { B - 6 ) m - AP Q J|K A l l the equations described above are well known (see General References about Thermodynamic/Fluid Mechanics [ 1 5 ] ) . I t i s i n d i c a t e d i n Appendix C when the incompressible B e r n o u l l i equation may be used without l o s s of accuracy. In Section 3.1.2 the c o e f f i c i e n t s of discharge are introduced to c o r r e c t the i d e a l c a l c u l a t e d flow r a t e , as obtained with equation (B.7), The equations to describe the a i r - f u e l r a t i o m^/m^ as a f u n c t i o n of mj become: itlr = C n TA TP, 2 k I + l 2 k I 1 [ PVT [PVT1 k I • kj-1 R j T 0 I \ P 0 I 1 ["on (B . 8 ) rfi II C D I A I P O I 1 2k I 1 irpr R j T 0 I VT 01 2k C D I I A I I P O I I II k H " 1 R I I T O I I POII ) VT 5 O i l (B.9) APPENDIX C: INFLUENCE OF FLUID COMPRESSIBILITY 1 1 0 The quantity of i n t e r e s t i s the a i r - f u e l r a t i o m^/m.- as a fu n c t i o n of the a i r flow m.. The question i s , whether the c a l c u l a t i o n s can be c a r r i e d out assuming the f l u i d s to be incompressible, or whether they must be done f o r the compressible case. Mass flows are c a l c u l a t e d below f o r incompressible as well as compressible flow as a f u n c t i o n of APyj. The values f o r these two cases are compared with each other; the c a l c u l a t e d r e l a t i v e e r r o r s give a measure to answer the above question. The comparisons are done f o r both natural gas and a i r . Note that natural gas i s approximated by methane. The governing equations (assumptions see Appendix B) are: (a) For incompressible f l u i d s : m pincompr " "RT^  ( n ) w. incompr ^ P 1 n c o m p r mincompr = A R E A p1ncompr wincompr (b) For compressible f l u i d s : (1) Pyy - P,, - A P V T k-1 nr. ( i i ) PVT pcompr = -Kr ( i v ) wcompr = J C T R T 0 ^ " TT ) comp (v) a = W I l l ( v i ) Mach = w/a ( v 1 i ) "compr = A R E A pcompr wcompr ' A computer program was developed to carry out the computing work, Values used f o r the c a l c u l a t i o n s are: ( i ) P Q = 1 bar ( i i ) T 0 = 300 K ( i i i ) f o r a i r : R = 287.00 --JJ, k=1.400 ( i v ) f o r methane : R = 518.35 j ^ - y , k=1.299. The r e s u l t i n g mass flows and r e l a t i v e e r r o r s are l i s t e d i n Table 2, together with other q u a n t i t i e s which might be of i n t e r e s t . The d e c i s i o n as to whether the incompressible flow equations describe the flow s a t i s f a c t o r i l y depends on the accepted e r r o r , and ther e f o r e on the metering s i g n a l APyj i n the venturi t h r o a t . APyj depends on the design. I f , f o r example, a venturi t h r o a t i s designed f o r 4000 N/m2 at maximum flow, then the small inaccuracy r e s u l t i n g from using incompressible flow equations can c e r t a i n l y be accepted, see Table 2. The ve n t u r i elements used i n the present i n v e s t i g a t i o n s have maximum APyj values up to about 8000 N/m2. The r e s u l t i n g e r r o r 1n the mass flow i s about 5%; i t i s th e r e f o r e important to use the compressible flow equations and to accept the e x t r a computing work i n v o l v e d . F l u i d = Air DPVT RH01ncompr w1ncompr mlncompr RHOcompr wcompr mcompr Mach wcompr-w1ncompr mcompr-mlncompr wcompr mcompr [N/m**2] [kg/m**3] [m/s] [kg/s] [kg/m**3] [tn/s] [kg/s] [-] [-] [-] 2000.0 1.161 58.7 AREA* 68.2 1 . 145 58.9 AREA* 67 4 0. 17 0.0036 -.0108 4000.0 1 . 161 83.0 AREA* 96.4 1 . 128 83.6 AREA* 94 3 0.24 0.0072 -.0221 6000.0 1.161 101 .6 AREA*118.1 1.111 102 .8 AREA*114 2 0.30 0.0109 -.0338 8000.0 1 . 161 117.4 AREA*136.3 1 .094 1 19. 1 AREA*130 3 0.35 0.0147 -.0458 10000.0 1 . 161 131.2 AREA*152.4 1 .077 133.7 AREA*144 0 0.39 0.0184 -.0583 12000.0 1 . 161 143.7 AREA*167.0 1 .060 147 .0 AREA*155 9 0.43 0.0223 -.0712 14000.0 1 . 161 155.3 AREA*180.3 1 .043 159.4 AREA*166 3 0.47 0.0262 -.0846 16000.0 1 . 161 166.0 AREA*192.8 1 .025 171.1 AREA*175 5 0.51 0.0301 -.0985 18000.0 1 . 161 176. 1 AREA*204.5 1 .008 182.3 AREA*183 7 0.54 0.0341 -.1130 20000.0 1 . 161 185.6 AREA*215.5 0.990 192 .9 AREA*191 1 0.57 0.0382 -.1280 Flu i d = Methane DPVT RHO1ncompr wlncompr mlncompr RHOcompr wcompr mcompr Mach wcompr-w1ncompr mcompr-m1ncompr wcompr mcompr [N/m**2] [kg/m**3] [m/s] [kg/s] [kg/m**3] [m/s] [kg/s] [-] [-] [-] 20O0.0 0.643 78.9 AREA* 50.7 0.633 79.2 AREA* 50 1 0. 18 0 0039 -.0117 4000.0 0.643 111.5 AREA* 71.7 0.623 112.4 AREA* 70 1 0.25 0 0078 -.0238 6000.0 0.643 136.6 AREA* 87.8 0.613 138.2 AREA* 84 8 0.31 0 01 18 -.0364 8000.0 0.643 157.7 AREA*101.4 0.603 160.3 AREA* 96 7 0.36 0 0158 -.0495 10000.0 0.643 176.4 AREA*1 13.4 0.593 179.9 AREA*106 7 0.41 0 0199 -.0630 12000.0 0.643 193.2 AREA*124.2 0.583 197.9 AREA*115 4 0.45 0 0240 -.0769 14000.0 0.643 208.7 AREA*134.2 0.573 214.7 AREA*122 9 0.49 0 0282 - . 0915 16000.0 0.643 223. 1 AREA*143.5 0.562 230.5 AREA*129 6 0.52 0 0324 -.1066 18000.0 0.643 236.6 AREA*152.2 0.552 245.6 AREA*135 6 0.56 0 0367 -.1223 20000.0 0.643 249.4 AREA*160.4 0.542 260. 1 AREA*140 9 0.59 0 041 1 -.1386 Table 2: Comparison between incompressible and compressible flow as a fu n c t i o n of A P V T . ^ ro 113 APPENDIX D: COEFFICIENTS OF DISCHARGE This Appendix D i s organized i n the f o l l o w i n g way: (a) Computer program, (b) Example of an input f i l e and an output f i l e , (c) L i s t of the r e s u l t i n g mathematical expressions of the c u r v e - f i t s f o r c o e f f i c i e n t s of discharge. 115 a •a > Ui o I i in •> I s ?r | ? s o- so-; 5 iM S « j ? • I I I ? ?! ik | i f is. zi ill t u h - h f ? -. , ! . ! ! : . 5 1 . ! 5 JS i 18 ill . U ! » s iJiili , & I mm , II | I fi5?il,f Hit \ I fi [K j \ 15'BHiJ — (j — «- «- <j w — *- •-u u u u u n u L> u n «o u u n r> 241 DO 670 I"1.4 342 DO 660 J-1.30 243 C»Ll PIOM,7.0.3 0»0.,*FlOAT(l|»O.S'FLOAT(d-t),31 244 CALL PLOT(,6.9.3.0*0.,'F10AT(11*0.S^FLOATIJ-,),3) 245 660 CONTINUE 246 670 CONTINUE 24 7 C 248 C»Ll PALPHAI 'STANDARD '.0.01 249 INTEGER OPD/73BC9C940/ 250 C»Ll PST«(3.2.13.74.0 S3.'CO'.0.0,2) 25, C4LL PSTN14.3. 13.74.0.33.ORO.0.0.4.0) 252 CALL PS»»{ "3.0.3 7.0 S3.'R»-0»«/'.0.0.7) 253 CALL PALPHAI'GREEK. , -.0.0) 254 DATA NUU/ZS3404040/ 255 CALL PSYFM ,6 .0. 3 .7.0. S3.NUU.O.0. I) 256 C 257 C Plo t data potnta and F i t t e d curve 25B C 259 DO 700 I'l.NOATA 260 CALL SYMBOLIRf (l),CO(I).0. 1.04.0.0.-I) 261 700 CONTINUE 262 CALL L1WEIREF.CDF.131.I) 263 C 264 CALL PLOTND 265 STOP 266 END , C 2 C 3 SUBROUTINE LSOFIT( X. V .•t.M.NP.NAO, A, SUMX. COEFF, VAR) 4 DIMENSION X(M).Y(M),A(N).SUDX(NM2).COEFF(N.NP) 5 C 6 C I n i t i a l i z a t i o n OF SLMXll). COEFF(l.iJ) and A l l ) 7 C 8 00 10 L-I.NM2 9 SUMXHI-O. 10 10 CONTINUE 11 DO 30 1-1.5 12 DO 20 J-1.6 13 COEFFU.JI-O. 14 20 CONTINUE 13 30 CONTINUE 16 DO 40 I-1.3 17 A ( I ) . 0 . 18 40 CONTINUE 19 C 20 C C a l c u l a t i o n OF I-SUMS. T-SUMS and Forming oF COEFF-Matr l« 2, C 22 00 70 K-l.N 23 C 24 C C a l c u l a t i o n OF X-SUMS 33 C 26 TENP-XCKI 37 00 50 L-I.NN3 26 SUMX(L).SU«IX(L)»TE»IP 39 TENP»TEI4P*X(K) 30 30 CONTINUE 31 C 33 C C a l c u l a t t o n of v-SUMS 33 C 34 TEMP-Y(K) 35 DO 60 I-I.N 36 COEFMI.MP)-COEFF(I,NP)*TEMP 37 TEMP-TEWP»X(K > 3B 60 CONTINUE 39 70 CONTINUE 40 C 4 1 C Form rest of the matrix 42 c 43 00 100 I-I.N 44 00 90 0-1.N 45 IF1I GT.1-OR.J.GT.1) 00 TO 00 46 COEFF(I,J)-FLO»T(«) 47 GO TO 90 40 00 l-!*d-2 49 COEFMl.dl-SlWXLU) 50 90 CONTINUE 51 100 CONTINUE 52 c 53 c Solve f o r unknown A-valuaa 54 c 55 CALL CHOLtCOEFF.A.N.NP) 56 c 5? c C a l c u l a t i o n of variance 50 c 59 SUM-O. 60 DO 110 I»1,M . . 6 1 FX-»(M**(2)»X(I)»*(3)*X (n**2*»(<)*X(I)**3**(5)«X(I)**4 63 SUM-SUM*<I 1-FX)**2 63 110 CONTINUE 64 VAR-SUN/<M-N) 65 c 66 RETURN 67 1 c END a c 3 SUBROUTINE CH0L(A,X.N.NP) 4 DIMENSION A(N.NP).X(N) 9 INTEGER RN.RI1 6 c 7 c Location of r o * RN with largest A(N.I) 0 c 9 RN-1 10 BIG-ABS(A<1.1)1 11 00 10 I-2.N 13 A8-ABS(A(I.1)1 13 IF(AB.LE.BIG) GO TO 10 14 BIG"AB 15 BN- I 16 10 CONTINUE IF(RN.EQ.1) GO TO 30 10 c 19 c Row interchange If RN.NE.1 30 c 3 1 DO 20 0-1.NP 23 TEMP-A<RN.J) 33 A<RN.J)-A<1,0) 24 A( t.J)» TEMP 25 30 CONTINUE 26 c 27 c F i r s t row of U-matrlx CTl 28 C 29 30 OO 40 J-2.NP 30 4(1.<)>•»( 1.J)/»(1.D 31 40 CONTINUE 32 C 33 00 120 1-2.N 34 C 35 c Uth coluwn of L-»»trlH 36 c 37 J - l 38 JM-J-1 39 00 60 1-J.N 40 SUW"0. 4 1 00 50 IC-1.JM 42 su"-sim»M I.K )•»<».. J) 43 50 CONTINUE 44 *<l.i»-*(I.O>-SIM 45 SO CONTINUE 46 C 47 C Location of row HI! with l i r j n l 1 48 c 49 I f ( L EO N) 00 TO 90 SO 51 RIl'N 52 m»M'i 53 B1G*«BS(«(*.M>) 54 00 70 l-NP.N 55 A B ' t B S M M . M M 56 ir(«B LE BIO) 00 TO 70 57 BIG-»B 58 RII'I 59 70 CONTINUE 60 IFIRIl EO.N) 0 0 TO 90 61 C 62 c Row Intarchanga If P.II.NE.M 63 c 64 0 0 80 J-I.NP 65 TE«-*(PlI.d) 66 MRU . J)-»<M. J) 67 MN.tll'TEM 68 80 CONTINUE 69 70 c c Ith row of U-Natrl* 71 c 72 90 I-L 73 IP-I»1 74 IM-I-1 75 00 110 J-IP.NP 76 SUW.-0. 77 00 IOO K-1.IM 78 SUM-SUM*M1.KI*MK.<I) 79 100 CONTINUE 80 »(l.d)-(MI.J)-SUtl)/«tl.l> 81 110 CONTINUE 82 120 CONTINUE 83 c 84 c 85 c Back s u b s t i t u t i o n 86 c 87 NM'N-I 88 X(N)>XN.NP) 89 00 140 NN- 1 ,N*t 90 SUH'O 91 I-N-NN 92 IP'I't 93 DO 130 J»IP.N 9» SU»>SU»>»< 1 .0)' 95 96 130 CONTINUE »(I)-«(1,NP)-SUM 97 140 CONTINUE 98 99 C RE TURN IOO END of f 11a — o t x n i M P i f i i n v o c s * o — ooooodoooooo » e o n r i s ' i p i i n M i B — —• - N D ^ U ) ' * 0 ) N l * » n • < — *- — c» tt — — 000060600000 B I I 1 I t I I I I I > 1 ~ CN o i i n o i n v i f i t D a h r i v o i S~ o6o6b6oobci66 <D § *- — e 4-> * ~ \ ^ OOOimtt>nQm»Oir-t~ j "3 *» **• n r t r t n t i n n n N r i n n o • C »- t *« — rt.nniDr-ffitno>r» O > — « «4T B3 — r>0)BNS (— tt> a 2 — — IP 01 tr « o — 8 • 1 • a a cx *• « *t > > > 0 2^ 81888888888" " B  8 8 PSS . t i bbbbbbbbbbbb 888 £ v 000 • • OOO L X — • «-rxmf«0«OOOOOO > I £ « o — - o n n <C 8 i £ i i d — t t L (. ^ 1 »-r»ri*#»i(cr-»pc»0 — « 0 0 0 O OJ 3 r>e>r>0>r-crO**intf)*)Q *- ooooooooooc < 4 -o QJ 1888888888 - « m w « 0) CD W I-«t w o> ip 066666666666 CN |0*-«iPC>0)*«*jC0a*<P<P*-8 o8K^g25^2:=S5S 1 • tp 5 OOOOOOOOOOOO - o - « o - - - » - - - - - ~ - - - , - L ... . Q . E x ; The mathematical expressions as the r e s u l t s of the c u r v e - f i t s are l i s t e d below f o r the d i f f e r e n t v e n t u r i c o n f i g u r a t i o n s : V-16H-2.6mm: - C D I = 0.8408 + 0.2620 10" 7 Re - C D I I = 0.6410 + 0.6065 10" 5 Re - 0.1121 10" 9 Re 2 V-4H-5.3mm: - C D I = 0.8504 - C D I I = 0.6440 - 0.2470 10" 6 Re + 0.1672 1 0 " 1 0 Re 2 V-1H-I2.3mm: - C D I = 0.8198 + 0.6853 10' 7 Re - C D n = 0.5611 + 0.2493 10" 6 Re V-90D-12.3mm: - C D I = 0.6652 + 0.1042 10" 5 Re - 0.8165 1 0 " 1 1 Re 2 + 0.2759 1 0 " 1 6 Re 3 - 0.3359 1 0 " 2 2 Re1* - C D n = -0.4040 10" 1 + 0.1282 Re' - 0.5819 10" 2 ( R e ' ) 2 where Re' = ln(Re+100) V-45D-12.3mm: - C D I = 0.6227 + 0.4680 10" 6 Re - 0.1079 1 0 - " Re 2 - C D n = -0.2662 10 1 + 0.9124 Re' - 0.8378 10" 1 ( R e ' ) 2 + 0.2570 10~ 2 ( R e ' ) 3 , where Re' = ln(Re+100) C D I = 0.5934 + 0.1075 10' 2 Re' - 0.3713 10" 5 (Re' + 0.4078 10" 8 ( R e ' ) 3 , where Re' = /Re C D I I = 0.2736 + 0.3131 10" 4 Re - 0.9183 10" 9 Re 2 + 0.8624 1 0 " 1 4 Re 3 f o r Re < 40000 C n T T = 0.59 + 4.73 IQ" 7 Re f o r Re > 40000. 121 APPENDIX E: ERROR ANALYSIS Mass flow rates and m^ The errors for and m.. were ident ical , because the inaccuracy of the calibration curves, the reading errors and the changes in T, . ^ and P. . were the same. The equation for mass flow Laboratory Laboratory rate can be written as m = pV . Thus the error can be calculated from M - ^ + ^ , where l 1 " ^ ^ = ( 0 ' 0 0 3 4 8 M o r a t o r y " 0 - ^ 2 P w a t e r v a p o r ) (see Section 3.1.4). Since P w a t e r v a p Q r « P L a b o r a t o r y , the second term is negligible. .-. p « 0.00348 P, . . /T. . «. and H Laboratory Laboratory Ap h ^Laboratory _ ^Laboratory p Laboratory Laboratory Reading errors and changes in T L a b o r a t o r y and P L a b o r a t o r y were estimated to be tO.25% for both. ... . +0.25% - tO.25% = ±0.5% P A V (•ji) BL : This relative error is influenced by the calibration curve V inaccuracy, the reading error from the calibration curve and the uncertainty in determining the pressure drops across the laminar flow elements. The laminar flow elements were calibrated to within ±0.5%. The reading errors from the calibration curves were estimated to be within ±0.5%. These two errors together make an error of +1%. The pressure drops across the laminar flow elements were 122 estimated to be w i t h i n tl% (at low flow rates the reading e r r o r s were the cause f o r the u n c e r t a i n t y , while at higher flow rates pressure f l u c t u a t i o n s were the cause). Since pressure drop and volume flow were c o r r e l a t e d nearly l i n e a r l y the r e s u l t i n g e r r o r from the pressure drops was al s o ±1*. ... M « +0.5% + ±2% = 12.5% m (b) A i r - f u e l r a t i o m^/m^j • • • ^ m j / m j j ) ACVJ/VJJ) AVJ "A I " V I / V I I "~i AV II - ±2% - ±2% = U% I I (c) C o e f f i c i e n t of discharge The c o e f f i c i e n t of discharge e r r o r was estimated t r e a t i n g the f l u i d as incompressible; that i s the c o e f f i c i e n t of discharge was expressed as m V C n = = — . Thus the e r r o r can be c a l c u l a t e d from Apw Aw —5- « — - — - — , where C D V A w ( i ) "• - 2 % * s e e above) V (•H) ML : A = 5f2L f :. M - ?AD . AD W A S E S T I R N A T E D T O B E W I T H I N A A D D ... £ - +2% A 123 1 1 1 1 1 W w ^ P ' " w 7 A P V T 7 P Due to reading e r r o r s and pressure f l u c t u a t i o n s A ( A P V T ) / A P V T was estimated to be w i t h i n 12%. ... Aw . 1. (+ 2% _ + 0 < 5 %^ = + 1 > 2 5 % AC n .-. — - 12% - 12% - 11.25% = 15.25% CD Note that t h i s u ncertainty appears to be qu i t e high. Since i n t h i s i n v e s t i g a t i o n the i n t e r e s t was more the comparison of the c o e f f i c i e n t s of discharge f o r s i n g l e and combined flow than the absolute values, the e r r o r s due to AA/A and Ap/p are c a n c e l l e d out. Thus Aw/w » l l % and th e r e f o r e AC D/C D - 13%. 

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}]}"
                            data-media="{[{embed.selectedMedia}]}"
                            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:
https://iiif.library.ubc.ca/presentation/dsp.831.1-0095788/manifest

Comment

Related Items