A contribution to 1D Modeling of Diesel Sprays and Combustion

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HAL Id: tel-03134907

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Submitted on 12 Feb 2021

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A contribution to 1D Modeling of Diesel Sprays and

Combustion

Alejandro Aljure Osorio

To cite this version:

Alejandro Aljure Osorio. A contribution to 1D Modeling of Diesel Sprays and Combustion. Reactive fluid environment. Ecole Centrale de Nantes, 2019. English. �tel-03134907�

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1

D

OCTORAL

T

HESIS OF

ÉCOLE

CENTRALE

DE

NANTES

COMUE UNIVERSITY OF BRETAGNE LOIRE

DOCTORAL SCHOOL N°602 SPI(Sciences pour l'Ingénieur)

Specialty: Energetics, Thermal Sciences, Combustion

A contribution to 1D Modeling of Diesel Sprays and Combustion

Thesis presented and defended at École Centrale de Nantes, on October 21st_{of 2019}

Research Unit: CNRS UMR 6598 By

Alejandro Aljure Osorio

Revisers before defense:

Pascale Domingo Directrice de Recherche CNRS, CORIA

José Garcia-Oliver Professeur, CMT - Université Polytechnique de Valence (Espagne)

Jury Composition:

President

Pascal Higelin Professeur, PRISME – Polytech Orléans

Examinators

José Garcia-Oliver Professeur, CMT – Université Polytechnique de Valence (Espagne)

Pascale Domingo Directrice de Recherche CNRS, CORIA

Thesis Director

Xavier Tauzia Professeur, LHEEA ECN

Co-supervisor

Alain Maiboom Maître de conférences HdR, LHEEA ECN

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ACKNOWLEDGEMENTS

I would like to thank Dr Xavier Tauzia and Dr Alain Maiboom, not only for directing this thesis work but also for their guidance during all my master and PhD process and their help in allowing me to obtain the grant to pursue my PhD studies.

I would also like to thank the French Ministry of Higher Education and Research (MESR) for giving me the grant for the PhD studies.

Special thanks to the members of the jury: Dr Pascale Domingo, Dr José María García Oliver, Dr Pascal Higelin and Dr Alessio Dulbecco, for taking the time to review and comment this work.

A special mention goes to Mme Anne-Laure Fremondière, who helped me in the admissions process to Ecole Centrale de Nantes, which allowed me to pursue both my masters and PhD degrees. Another special mention to Dr Pascal Chesse and all the TSM team, who hosted me in their lab during my studies.

And most of all, I would like to thank my wife and family for always supporting me in all the challenges I undertake and encouraging me to perform my best.

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LIST OF FIGURES

FIGURE 1 :HEAT RELEASE RATE AS A FUNCTION OF CRANK ANGLE FOR DIESEL COMBUSTION [2] ... 21

FIGURE 2 :OH-PLIF AND SOOT IMAGE OF CONVENTIONAL DIESEL COMBUSTION (TOP) AND LTC(BOTTOM), DIESEL JET PENETRATING FROM LEFT TO RIGHT [9] ... 22

FIGURE 3 :VAPOR FUEL EQUIVALENCE RATIO MEASUREMENTS AFTER END OF INJECTION (EOI) BY TOLUENE TRACER FLUORESCENCE [10] IN INERT JET.THE CIRCLED NUMBER SHOW THE TIME IN CRANK ANGLE DEGREES FOR THE JET TO REACH THE POSITION OF EACH CIRCLE. ... 23

FIGURE 4 :DEC’S MODEL OF COMBUSTION IN THE QUASI-STEADY STATE OF DIFFUSION FLAME [8] ... 24

FIGURE 5 :DEC CONCEPTUAL COMBUSTION MODEL [8] ... 25

FIGURE 6:LTC CONCEPTUAL MODEL (RIGHT) FROM SANDIANATIONAL LABS, COMPARED TO THE CONVENTIONAL DEC MODEL (LEFT) [14] ... 26

FIGURE 7 :ALL THE NON-VAPORIZING PENETRATION DATA PLOTTED ON TOP OF THE PENETRATION CORRELATION [19]. ... 27

FIGURE 8 :WALL JET VELOCITY AND TEMPERATURE PROFILES AT R=6[25] ... 30

FIGURE 9 :WALL JET VELOCITY AND TEMPERATURE PROFILES AT R=10[25] ... 30

FIGURE 10 :WALL IMPINGING JET [27] ... 30

FIGURE 11 :PREDICTED TIP PENETRATIONS OF WALL-IMPINGING JETS FOR THREE IMPINGING DISTANCES (L)[27] AND MEASUREMENTS OBTAINED FROM [31]. ... 32

FIGURE 12PROFILE OF ROUND JET (A) AND RADIAL JET (B)[27] ... 32

FIGURE 13 :RATIOS OF TIP PENETRATIONS OF HALF-RADIAL AND WALL-IMPINGING JETS TO THAT OF THE ROUND JET [27] ... 34

FIGURE 14 :RATIOS OF ENTRAINED MASS OF HALF-RADIAL AND WALL-IMPINGING JETS TO THAT OF THE ROUND JET [27] ... 34

FIGURE 15 :RATIOS OF ENTRAINED MASS OF HALF-RADIAL AND WALL-IMPINGING JETS TO THAT OF THE ROUND JET [27] ... 34

FIGURE 16 :TIP PENETRATIONS OF THE ROUND AND WALL-IMPINGING JETS AS A FUNCTION OF TIME (STARTING WALL JET)[27] ... 35

FIGURE 17 :ENTRAINED MASS OF THE ROUND AND WALL-IMPINGING JETS AS A FUNCTION OF TIME (STARTING WALL JET)[27] ... 35

FIGURE 18 :ENTRAINED MASS OF THE ROUND AND WALL-IMPINGING JETS AS A FUNCTION OF TIME (DEVELOPED WALL JET)[27] ... 35

FIGURE 19 :STRUCTURE OF AN IMPINGING JET [34] ... 36

FIGURE 20 :MEASURED (SYMBOLS) AND COMPUTED (CURVES) TIP PENETRATIONS OF FREE AND IMPINGING JETS [34] ... 36

FIGURE 21 :COMPUTED JET PENETRATIONS WITH NO-SLIP AND FREE-SLIP BOUNDARY CONDITIONS [34] ... 37

FIGURE 22 :COMPUTED PENETRATIONS WITH DIFFERENT CUT-OFF VALUES FOR FUEL MASS FRACTION (F)[34] ... 37

FIGURE 23 :SIMILARITY VELOCITY PROFILES IN WALL JETS [34] ... 38

FIGURE 24 :VARIATION OF THE HALF-WIDTH OF THE JET WITH DISTANCE FROM THE POINT OF IMPINGEMENT [34] ... 38

FIGURE 25 :VARIATION OF THE MAXIMUM RADIAL VELOCITY WITH DISTANCE FROM THE POINT OF IMPINGEMENT [34] ... 38

FIGURE 26 :RICH, FLAMMABLE AND LEAN FRACTION OF FUEL IN THE JETS [34] ... 39

FIGURE 27 :ENTRAINED VOLUME OF THE JETS FOR A CUT-OFF VALUE OF 0.01[34] ... 39

FIGURE 28 :ENTRAINED VOLUME OF THE JETS FOR A CUT-OFF VALUE OF 0.03[34] ... 39

FIGURE 29 :VARIATION OF WALL JET MOMENTUM FLUX WITH NOZZLE HEIGHT [38] ... 40

FIGURE 30 :EFFECT OF NOZZLE HEIGHT ON WALL JET TO FREE JET TURBULENCE INTENSITY [38] ... 40

FIGURE 31 :CORRELATION FOR WALL JET HALF-THICKNESS WITH NOZZLE HEIGHT [38] ... 41

FIGURE 32 :EFFECT OF MODIFIED TURBULENCE MODELS ON WALL JET SPREADING [38] ... 41

FIGURE 33 :IMPINGING JET FLOW FIELD AND CO-ORDINATE SYSTEM [43] ... 42

FIGURE 34 :NON-DIMENSIONAL FREE-JET VELOCITY PROFILES FOR VARYING PROBE POSITION (HN/DN=10.0 AND NPR=1.05)[43] ... 42

FIGURE 35:NON-DIMENSIONAL WALL-JET VELOCITY PROFILES FOR VARYING RADIAL POSITION (HN/DN=10.0 AND NPR=1.05)[43] ... 43

FIGURE 36 :PEAK NON-DIMENSIONAL VALUES OF MEASURED MEAN AND TURBULENT QUANTITIES IN THE WALL JET FOR VARYING NOZZLE HEIGHTS (NPR=1.05)[43] ... 44

FIGURE 37 :VARIATION OF WALL JET GROWTH RATES WITH NOZZLE HEIGHT [43] ... 45

FIGURE 38 :WALL JET VARIABLES AS DESCRIBED IN [44]... 45

FIGURE 39 :SCHEMATIC LAYOUT OF THE THUNDERSTORM WIND TUNNEL [45] ... 46

FIGURE 40 :DEFINITION OF TERMS FOR FLAT SURFACE [45] ... 46

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FIGURE 42 :RADIAL DEVELOPMENT OF THE MEAN VELOCITY PROFILE, SURFACE TAKEN AT A DISTANCE 2D FROM JET [45] ... 47

FIGURE 43 :NORMALIZED MEAN VELOCITY PROFILES, SURFACE TAKEN AT A DISTANCE 2D FROM JET [45] ... 48

FIGURE 44 :COMPARISON OF CURRENT IMPINGING WALL JET WITH PUBLISHED DATA [45] ... 49

FIGURE 45 :VELOCITY PROFILE COMPARISON FROM LIN [44] ... 49

FIGURE 46 :MEASURED AND PREDICTED WALL SPRAY RADIUS AND WALL SPRAY HEIGHT, AFTER IMPACT WITH THE WALL (CROSS FLOW OF 9.4 M/S)[47] ... 50

FIGURE 47 :EFFECT OF CRITICAL WEBER NUMBER ON THE PREDICTED WALL SPRAY RADIUS (GAS PRESSURE 13.8 BAR, CROSS-FLOW VELOCITY 0.0 M/S, NORMAL INJECTION)[47] ... 51

FIGURE 48 :SCHEMATIC REPRESENTATION OF THE WALL ROUGHNESS AND OF THE ANGLE OF IMPACTION [47] ... 51

FIGURE 49 :ILLUSTRATION OF THE MEASUREMENT LOCATIONS [54] ... 52

FIGURE 50 :COMPARISON BETWEEN COMPUTATIONAL [63] AND EXPERIMENTAL VELOCITY PROFILES [54] ... 54

FIGURE 51 :SCHEMATICS OF LIEF IMAGES CONFIGURATION IN THE JET WALL CASE AND PALLET CONNECTING IMAGE COLORS AND FUEL MASS CONCENTRATIONS [70] ... 55

FIGURE 52 :TIME EVOLUTION OF MEAN VAPOR FUEL MASS CONCENTRATION FIELDS FOR THE REFERENCE CONDITION [70] ... 56

FIGURE 53 :COMPARISON OF MEAN JET VOLUME EVOLUTION TO THE DIFFERENT CONDITIONS IN THE JET WALL AND FREE JET CONFIGURATIONS [70] ... 56

FIGURE 54 :MEAN VAPOR FUEL MASS RADIAL CONCENTRATION PROFILE COMPARISON FOR REFERENCE CONDITIONS AT T =0.8 MS, AT A DISTANCE OF 20 MM FROM THE NOZZLE (6.6 MM FROM THE WALL)[70] ... 57

FIGURE 55 :MEAN VAPOR FUEL MASS AXIAL CONCENTRATION PROFILE COMPARISON FOR REFERENCE CONDITIONS AT T =0.8 MS, ALONG THE JET AXIS [70] ... 57

FIGURE 56 :COMPARISON OF PROBABILITY DENSITY FUNCTIONS OBTAINED AT SEVERAL LOCATIONS (LOWER PART).LOCATION POSITIONS IN THE JET (UPPER PART) FOR REFERENCE CONDITIONS AT T=0.8 MS [70] ... 58

FIGURE 57 :COMPARISON OF VOLUME HISTOGRAMS CALCULATED IN THE WHOLE VAPOR JETS BETWEEN THE WALL AND FREE JET CONFIGURATIONS FOR THE REFERENCE CONDITIONS AT T =1 MS [70] ... 58

FIGURE 58 :CALCULATION DOMAIN FOR VOLUME HISTOGRAMS IN THE FREE AND WALL JET CONFIGURATIONS [70] ... 59

FIGURE 59 : A)SCHEMATIC OF THE RELOCATION OF EQUIVALENT VOLUMES TO MODEL THE IMPACT WITH THE WALL. B)DETAIL OF THE DISCRETIZATION APPROACH FOR THE ZONES CLOSE TO THE WALL, PARTICULARLY THE LAST ZONE “N”[73]... 60

FIGURE 60 :QUALITATIVE COMPARISON OF THE WALL JET PENETRATION BETWEEN THE MODEL AND THE OBSERVATIONS MADE BY BRUNEAUX [70], FOR THE REFERENCE CONDITIONS [73] ... 60

FIGURE 61 :SCHEMATIC DIAGRAM OF THE OPTICAL DIESEL ENGINE AND DIAGNOSTICS SETUP [74] ... 61

FIGURE 62 :THE LASER BEAM PATH AREA COVERAGE (TOP), SCHEMATIC OF THE FIELD OF VIEW (BOTTOM-LEFT), ILLUSTRATION OF THE LASER SHEETS FOR VARIOUS DISTANCES FROM THE CYLINDER HEAD (BOTTOM-RIGHT)[74] ... 62

FIGURE 63 :MOTORING (BLACK LINE) AND FIRING (ORANGE) IN-CYLINDER PRESSURE TRACES (TOP).APPARENT HEAT RELEASE RATE (AHRR) AND FUEL INJECTION RATE (BOTTOM).THE SYMBOLS ILLUSTRATE THE LOCATION OF THE IMAGES TAKEN:CIRCLES FOR STAGE A IMAGES, SQUARES FOR STAGE B IMAGES AND TRIANGLES AND DIAMONDS FOR STAGE C IMAGES [74] ... 63

FIGURE 64 :PLIF IMAGES OF FUEL FLUORESCENCE DURING COMBUSTION STAGE A AT A PLANE 7 MM BELOW THE CYLINDER HEAD (LEFT).ESTIMATION OF THE WALL JET TIP PENETRATION LENGTH (TOP RIGHT).PENETRATION FOR UP-SWIRL AND DOWN-SWIRL SIDES OF THE DIESEL JET (BOTTOM-RIGHT)[74] ... 64

FIGURE 65 :COOL FLAME CHEMILUMINESCENCE IMAGES (LEFT), OFFLINE OH-PLIF IMAGES (MIDDLE) AND ONLINE OH-PLIF IMAGES (RIGHT) DURING COMBUSTION STAGE B(LOW-TEMPERATURE REACTION).THE PLIF IMAGES WERE TAKEN AT 7 MM BELOW THE CYLINDER HEAD.THE BOUNDARIES OF OFFLINE IMAGES ARE OVERLAID ON THE ONLINE IMAGES FOR COMPARISON PURPOSES [74] ... 65

FIGURE 66 :OH*CHEMILUMINESCENCE IMAGES (LEFT), OFFLINE OH-PLIF IMAGES (MIDDLE) AND ONLINE OH-PLIF IMAGES (RIGHT) DURING COMBUSTION STAGE C(HIGH-TEMPERATURE REACTION) BETWEEN 9.5 AND 13.5°CA ATDC WHEN THE APPARENT HEAT RELEASE RATE INCREASES.THE PLIF IMAGES WERE TAKEN AT 7 MM BELOW THE CYLINDER HEAD.THE BOUNDARIES OF OFFLINE IMAGES ARE OVERLAID ON THE ONLINE IMAGES FOR COMPARISON PURPOSES.THE RED ARROWS SHOWN ON THE ONLINE IMAGES AT 12.5 AND 13.5°CA ARE TO ANNOTATE THE EXPANSION OF OH SIGNALS BEHIND THE JET HEAD.EOI DENOTES THE END OF INJECTION [74] ... 66

FIGURE 67 :ILLUSTRATION OF DIESEL FLAME DEVELOPMENT INSIDE THE CYLINDER OF SMALL-BORE DIESEL ENGINES, WITH THE START OF COMBUSTION AFTER WALL IMPINGEMENT [74] ... 67

FIGURE 68SCHEMATIC OF A COMMON-RAIL INJECTION SYSTEM [82] ... 69

FIGURE 69SCHEMATIC OF A MULTIPLE INJECTION SEQUENCE [5]. ... 69

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FIGURE 71SOOT,NOX AND HRR FOR ENGINE OPERATING POINT 1500 X 5 AS A FUNCTION OF DWELL TIME (DT) AND INJECTION

DURATION (ET) OF THE PILOT INJECTION [82]. ... 71

FIGURE 72SOOT,NOX AND HRR FOR ENGINE OPERATING POINT 2000 X 2 AS A FUNCTION OF DWELL TIME (DT) AND INJECTION DURATION (ET) OF THE PILOT INJECTION [82]. ... 72

FIGURE 73SOOT,NOX AND HRR FOR ENGINE OPERATING POINT 2500 X 8 AS A FUNCTION OF DWELL TIME (DT) AND INJECTION DURATION (ET) OF THE PILOT INJECTION [82]. ... 72

FIGURE 74SOOT AND NOX EMISSIONS WITH RESPECT TO TEMPERATURE AT THE START OF COMBUSTION (TSOC)[82]... 73

FIGURE 75NOX EMISSIONS, NOISE, SOOT EMISSIONS AND FUEL CONSUMPTION VERSUS CA10[82]. ... 74

FIGURE 76PENETRATION OF VAPOR FUEL FOR CASE 1(15/85%)[88] ... 75

FIGURE 77FLAME LUMINOSITY IMAGES (IN FALSE COLOR) FOR A DWELL TIME OF 0.17 MS (LEFT),0.77 MS (CENTER) AND 1.37 MS (RIGHT).THE IMAGES ARE LABELED IN TIME AFTER THE START OF THE MAIN INJECTION (AMI).INJECTION PENETRATES FROM RIGHT TO LEFT [88] ... 75

FIGURE 78FLAME LUMINOSITY INTEGRATION PLOT FOR CASE 1(15/85%), WITH A) DWELL TIME OF 0.17 MS, B) DWELL TIME OF 0.77 MS AND C) DWELL TIME OF 1.37 MS.PLOT D) SHOWS THE HEAT RELEASE RATE PLOT FOR ALL CASES [88] ... 76

FIGURE 79CFD SIMULATION RESULT AT 1 MS AFTER THE START OF THE MAIN INJECTION FOR CASE 1[88] ... 77

FIGURE 80QUALITATIVE COMBUSTION INTERACTION MODEL FOR MULTIPLE-INJECTIONS: A)SINGLE INJECTION; B) SHORT DWELL TIME; C) MEDIUM DWELL TIME; D) LONG DWELL TIME.SPRAY PENETRATIONS ARE INDICATED WITH RESPECT TO THE START OF THE FIRST INJECTION [88] ... 77

FIGURE 81EMISSIONS AND HRR PLOT FOR STRATEGY 2[5] ... 79

FIGURE 82EMISSIONS AND HRR PLOT FOR STRATEGY 4B [5] ... 80

FIGURE 83RATE OF INJECTION OF SPLIT INJECTION TYPE 0.5/0.5/0.5[91].BOTH MEASURED AND MODELED RATE OF INJECTIONS ARE SHOWN.THE MODELED INJECTION IS USED TO SIMULATE THE SPRAY USING THE 1D MODEL OF MUSCULUS [9]. ... 81

FIGURE 84PENETRATION OF SINGLE AND MULTIPLE INJECTION SPRAYS AT 900K, BOTH INERT AND REACTING [91] ... 82

FIGURE 85PRESSURE RISE AND APPARENT HEAT RELEASE RATE (AHRR) PLOTS VERSUS TIME FOR THE REACTIVE CASES AT DIFFERENT AMBIENT INITIAL TEMPERATURES [91] ... 82

FIGURE 86SCHLIEREN AND PLIF IMAGES FOR THE REACTIVE CONDITION AT 900K.DASHED LINES INDICATE AXIAL DISTANCES FROM THE INJECTOR AND RED LINES INDICATE THE PLIF CONTOUR [91] ... 83

FIGURE 87SCHLIEREN AND PLIF IMAGES FOR THE REACTIVE CONDITION AT 800K.DASHED LINES INDICATE AXIAL DISTANCES FROM THE INJECTOR AND RED LINES INDICATE THE PLIF CONTOUR [91]. ... 84

FIGURE 88SCHLIEREN AND PLIF IMAGES FOR THE REACTIVE CONDITION AT 750K.DASHED LINES INDICATE AXIAL DISTANCES FROM THE INJECTOR AND RED LINES INDICATE THE PLIF CONTOUR [91]. ... 85

FIGURE 89INERT VAPOR PENETRATION AND LIQUID LENGTH FOR CASE 2[94]... 86

FIGURE 90PENETRATION OF THE SECOND INJECTION FOR CASES 3 AND 4(SHIFTED TO T =0) AND PENETRATION OF THE SINGLE INJECTION (CASE 1), BOTH FROM EXPERIMENT AND 1D MODEL [94] ... 86

FIGURE 91CENTERLINE MIXTURE FRACTION (LEFT) AND MOMENTUM FLUX (RIGHT) FOR DWELL TIME CASES (CASE 1, CASE 3 AND CASE 4) AT THE INDICATED TIME AFTER START OF THE SECOND INJECTION [94]. ... 87

FIGURE 92PENETRATION OF THE SECOND INJECTION FOR CASES 5 AND 6(SHIFTED TO T =0) AND PENETRATION OF THE SINGLE INJECTION (CASE 2), FROM THE 1D MODEL [94] ... 88

FIGURE 93IGNITION DELAY AND LIFT-OFF LENGTH FOR THE INDICATED CASES AND FOR BOTH INJECTIONS, WITH VARIATION IN DWELL TIME (LEFT) AND FIRST INJECTION DURATION (RIGHT)[94]. ... 88

FIGURE 94INTEGRATED SOOT MAP, APPARENT HEAT RELEASE RATE AND INJECTION PULSE FOR CASE 2(LEFT) AND CASE 3(RIGHT), SHOWING THE EFFECT OF DWELL TIME [94]. ... 89

FIGURE 95INTEGRATED SOOT MAP, APPARENT HEAT RELEASE RATE AND INJECTION PULSE FOR CASE 5(LEFT) AND CASE 6(RIGHT), SHOWING THE EFFECT OF DURATION OF THE FIRST INJECTION [94]. ... 90

FIGURE 96TIME PLOT OF TOTAL SOOT MASS WITH DWELL TIME VARIATION (LEFT) AND INJECTION DURATION VARIATION (RIGHT)[94]. ... 90

FIGURE 97 :1D DISCRETE CONTROL VOLUME MODEL FOR A TRANSIENT DIESEL JET ... 96

FIGURE 98.RADIAL DISTRIBUTION OF SPECIES FRACTION FOR AN INERT SPRAY (TOP) AND REACTIVE SPRAY (BOTTOM), AT AN AXIAL POSITION WHERE THE FUEL FRACTION AT THE AXIS IS 0.4.YF DENOTES FUEL FRACTION,YO2 DENOTES OXYGEN FRACTION, AND YB DENOTES THE REST OF THE SPECIES PRESENT (N2,CO2, AND H2O) ... 100

FIGURE 99. PACKET DISTRIBUTION IN HIROYASU'S LAGRANGIAN MODEL... 101

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FIGURE 101.PROCESSED SCHLIEREN IMAGES OF THE EXPERIMENTAL SPRAY, INERT (TOP, BLUE LINE MARKS THE LIQUID PORTION [107])

AND REACTIVE (BOTTOM, THE BLUE LINE MARKS THE FLAME [108]). ... 104

FIGURE 102.INERT SPRAY PENETRATION.THE EXPERIMENTAL VALUES ARE GREEN (WITH UNCERTAINTY BARS); THE EULERIAN MODEL IN BLUE (DOTTED) AND THE LAGRANGIAN MODEL IN RED (DASHED). ... 105

FIGURE 103.REACTIVE SPRAY PENETRATION.THE EXPERIMENTAL PENETRATION IS IN ORANGE (WITH UNCERTAINTY BARS); THE LAGRANGIAN MODEL IS IN RED (DASHED LINE) AND THE EULERIAN MODEL IS IN BLUE (DOTTED LINE) ... 105

FIGURE 104.INERT SPRAY PROFILE, AT T =2 MS AFTER START OF INJECTION ... 106

FIGURE 105.REACTIVE SPRAY PROFILE AT T =2 MS ... 107

FIGURE 106.INERT AND REACTIVE EXPERIMENTAL SPRAY PROFILE, TAKEN FROM SCHLIEREN IMAGING AT T =2 MS ... 107

FIGURE 107.ROHR CURVE ... 108

FIGURE 108.INERT PRESSURE TRACE AND PRESSURE RISE... 109

FIGURE 109.REACTIVE PRESSURE CURVE, SHOWING THE EXPERIMENTAL ABSOLUTE PRESSURE (GREEN-SQUARES), THE EXPERIMENTAL FILTERED PRESSURE RISE (ORANGE, WITH ERROR BARS), THE EULERIAN MODEL ABSOLUTE PRESSURE (BLUE-DOTTED), THE LAGRANGIAN MODEL ABSOLUTE PRESSURE (RED-DASHED) AND THE MEAN-TEMPERATURE-LAGRANGIAN MODEL ABSOLUTE PRESSURE (BLACK-SOLID)... 109

FIGURE 110.INERT 2D GRAPHS SHOWING THE FUEL FRACTION DISTRIBUTION ON THE EULERIAN MODEL (RIGHT) AND LAGRANGIAN MODEL (LEFT).THE BLACK REGION REPRESENTS THE ZONE WITH THE STOICHIOMETRIC VALUE. ... 110

FIGURE 111.REACTIVE 2D GRAPHS FROM THE EULERIAN MODEL (LEFT) AND THE LAGRANGIAN MODEL (RIGHT).ON THE TOP ROW, THE FUEL FRACTION DISTRIBUTION, AT THE MIDDLE ROW THE OXYGEN DISTRIBUTION, AND AT THE BOTTOM ROW THE MIXTURE FRACTION DISTRIBUTION.THE BLACK REGION REPRESENTS THE ZONE WITH THE STOICHIOMETRIC VALUE. ... 111

FIGURE 112.SCHEMATIC OF EULERIAN GRID, SHOWING RADIAL DILATATION OF ONE ELEMENT BY INCREASING THE OUTLET RADIUS, WHILE MAINTAINING THE INLET RADIUS AND AXIAL DISTANCE CONSTANT... 112

FIGURE 113.PENETRATION PLOT OF THE NEW EULERIAN MODEL AND THE EXPERIMENTAL SPRAY, FOR BOTH INERT AND REACTIVE CASES. ... 113

FIGURE 114.SPRAY PROFILE FOR THE NEW EULERIAN MODEL, OLD EULERIAN MODEL (WITHOUT RADIAL DILATATION) AND THE EXPERIMENTAL SPRAY, FOR THE REACTIVE CASE. ... 114

FIGURE 115.ROHR CURVE FOR THE NEW EULERIAN MODEL (BLUE-SOLID LINE), OLD EULERIAN MODEL (GREEN-DOTTED LINE, WITHOUT RADIAL DILATATION) AND THE EXPERIMENTAL SPRAY (ORANGE-SQUARES), FOR THE REACTIVE CASE. ... 115

FIGURE 116.PRESSURE RISE CURVE FOR THE NEW EULERIAN MODEL (BLUE-SOLID LINE), OLD EULERIAN MODEL (GREEN-DOTTED LINE, WITHOUT RADIAL DILATATION) AND THE EXPERIMENTAL SPRAY (ORANGE-ERROR BARS), FOR THE REACTIVE CASE. ... 115

FIGURE 117.2D GRAPH FOR THE FUEL FRACTION OF THE SPRAY CALCULATED WITH THE NEW EULERIAN MODEL. ... 116

FIGURE 118.2D GRAPH FOR THE OXYGEN FRACTION OF THE SPRAY CALCULATED WITH THE NEW EULERIAN MODEL. ... 116

FIGURE 119.2D GRAPH FOR THE MIXTURE FRACTION OF THE SPRAY CALCULATED WITH THE NEW EULERIAN MODEL. ... 117

FIGURE 120 :SCHEMATIC OF THE VOLUME OF ONE ZONE OF THE WALL JET.THE WALL CORRESPONDS TO THE PLANE X-Y (WITH THE Y AXIS PERPENDICULAR TO THE PAGE). ... 121

FIGURE 121 :AXIAL VELOCITY PROFILES FOR WALL JET ... 123

FIGURE 122 :AXIAL VELOCITY PROFILES AND FUEL FRACTION PROFILE FOR WALL JET ... 124

FIGURE 123 :MODELING OF IMPINGEMENT ZONE... 126

FIGURE 124 :COMPUTATIONAL DOMAIN FOR THE CALCULATION OF AN IMPINGING JET (FREE JET, THEN WALL JET) ... 127

FIGURE 125 :AXIS OF THE 1D MODEL FOR THE IMPINGING JET: FIRST ALONG THE FREE JET AXIS, THEN ALONG THE WALL IN THE RADIAL DIRECTION OF THE WALL JET ... 128

FIGURE 126 :PENETRATION OF THE FREE JET VS. THE MEASURED BRUNEAUX WALL JET AND THE LIQUID PENETRATION ... 129

FIGURE 127 :WALL JET VOLUME CURVES FOR DIFFERENT VALUES OF CMOMENTUM ... 129

FIGURE 128 :WALL JET VOLUME CURVES FOR DIFFERENT VALUES OF CMOMENTUM_W ... 130

FIGURE 129:WALL JET VOLUME WITH BEST MATCH VALUES ... 130

FIGURE 130 :PENETRATION OF THE CALCULATED WALL JET WITH THE SELECTED VALUES FOR CMOMENTUM AND CMOMENTUM_W ... 131

FIGURE 131 :TIP VELOCITY OF THE FREE JET AND THE CALCULATED WALL JET ... 132

FIGURE 132 :ENTRAINMENT RATE OF THE FREE JET AND THE CALCULATED WALL JET (LEFT AXIS), AND FREE JET PENETRATION (RIGHT AXIS) ... 132

FIGURE 133 :RICH, FLAMMABLE AND LEAN MASS FRACTIONS OF THE FREE JET AND THE CALCULATED WALL JET ... 133

FIGURE 134 :STEADY STATE VELOCITY OF THE FREE JET AND THE CALCULATED WALL JET, AT T =1.3 MS ... 134

FIGURE 135 :AVERAGE FUEL MASS FRACTION OF THE FREE JET AND THE CALCULATED WALL JET, AT T =1.3 MS ... 135

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FIGURE 137 :STEADY STATE FLAMMABLE MASS FRACTION FOR FREE AND WALL JET, AT T =1.3 MS ... 136

FIGURE 138 :STEADY STATE FLAMMABILITY PROFILE FOR FREE AND WALL JET, AT T =1.3 MS ... 137

FIGURE 139 :STEADY STATE TEMPERATURE PROFILE FOR FREE AND WALL JET, AT T =1.3 MS ... 138

FIGURE 140 :SCHEMATIC OF THE WALL JET INTERPRETATION.THE DASHED BOLD LINE REPRESENTS THE MODEL WALL JET PENETRATION, AND THE SOLID BOLD LINE REPRESENTS THE ACTUAL WALL JET DEVELOPMENT.THE EXTRA LENGTH OF THE CALCULATED WALL JET IS “CURLED” TO FORM THE TIP VORTEX. ... 138

FIGURE 141 :EXPERIMENTAL AND CALCULATED VOLUME OF WALL JET FOR AN INJECTION PRESSURE OF 1500 BAR AND 2000 BAR 139 FIGURE 142 :ENTRAINMENT RATE OF WALL JET FOR AN INJECTION PRESSURE OF 1500 BAR AND 2000 BAR... 140

FIGURE 143 :TIP VELOCITY OF WALL JET FOR AN INJECTION PRESSURE OF 1500 BAR AND 2000 BAR ... 140

FIGURE 144 :RICH, FLAMMABLE AND LEAN MASS FRACTIONS OF WALL JET FOR AN INJECTION PRESSURE OF 1500 BAR AND 2000 BAR ... 141

FIGURE 145 :STEADY VELOCITY OF WALL JET FOR AN INJECTION PRESSURE OF 1500 BAR AND 2000 BAR, AT T =1.3 MS ... 141

FIGURE 146 :AVERAGE EQUIVALENCE RATIO OF WALL JET FOR AN INJECTION PRESSURE OF 1500 BAR AND 2000 BAR, AT T =1.3 MS ... 142

FIGURE 147 :STEADY STATE RICH AND LEAN FRACTION LIMITS OF WALL JET FOR AN INJECTION PRESSURE OF 1500 BAR AND 2000 BAR, AT T =1.3 MS ... 142

FIGURE 148 :STEADY STATE FLAMMABLE MASS FRACTION OF WALL JET FOR AN INJECTION PRESSURE OF 1500 BAR AND 2000 BAR, AT T =1.3 MS ... 143

FIGURE 149 :FLAMMABILITY PROFILE OF WALL JET FOR AN INJECTION PRESSURE OF 1500 BAR AND 2000 BAR, AT T =1.3 MS ... 143

FIGURE 150AXIAL TEMPERATURE PROFILE OF WALL JET FOR AN INJECTION PRESSURE OF 1500 BAR AND 2000 BAR, AT T =1.3 MS144 FIGURE 151INERT FUNCTIONS IN THE MIXTURE FRACTION (Z) DOMAIN FOR MASS FRACTION OF SPECIES ... 147

FIGURE 152INFINITELY FAST CHEMISTRY FUNCTIONS IN THE MIXTURE FRACTION (Z) DOMAIN FOR MASS FRACTION OF SPECIES ... 147

FIGURE 153INERT AND INFINITELY FAST CHEMISTRY FUNCTION IN THE MIXTURE FRACTION (Z) DOMAIN FOR TEMPERATURE ... 147

FIGURE 154SCHEMATIC MAPPING OF VAPOR FUEL FRACTION (YFG, SOLID LINE) AND LIQUID FUEL FRACTION (YFL, DASHED LINE) IN THE MIXTURE FRACTION (Z) DOMAIN (NOT TO SCALE).THE DOTTED LIGHT LINES ARE CONSTRUCTION LINES FOR THE PLOT. ... 148

FIGURE 155SCHEMATIC MAPPING OF OXYGEN FRACTION (YO) IN THE MIXTURE FRACTION (Z) DOMAIN (NOT TO SCALE).THE DOTTED LIGHT LINES ARE CONSTRUCTION LINES FOR THE PLOT. ... 149

FIGURE 156SCHEMATIC MAPPING OF TEMPERATURE (T) IN THE MIXTURE FRACTION (Z) DOMAIN (NOT TO SCALE).THE DOTTED LIGHT LINES ARE CONSTRUCTION LINES FOR THE PLOT. ... 149

FIGURE 157VAPOR FUEL REACTION RATE USING THE INERT MASS FRACTIONS DISTRIBUTIONS.THE MOST REACTIVE ZONE IS LOCATED AROUND Z=0.02. ... 151

FIGURE 158MASS FRACTIONS AND TEMPERATURE DISTRIBUTION IN THE MIXTURE FRACTION DOMAIN FOR CST =0(INERT REGIME). ... 153

FIGURE 159MASS FRACTIONS AND TEMPERATURE DISTRIBUTION IN THE MIXTURE FRACTION DOMAIN FOR CST =0.5. ... 153

FIGURE 160MASS FRACTIONS AND TEMPERATURE DISTRIBUTION IN THE MIXTURE FRACTION DOMAIN FOR CST =0.9. ... 153

FIGURE 161MASS FRACTIONS AND TEMPERATURE DISTRIBUTION IN THE MIXTURE FRACTION DOMAIN FOR CST =1(INFINITELY FAST CHEMISTRY REGIME). ... 153

FIGURE 162REACTION ZONE THICKNESS FUNCTION ... 158

FIGURE 163PRESSURE RISE VS TIME FOR CASE 1 ... 161

FIGURE 164HEAT RELEASE RATE VS TIME FOR CASE 1 ... 162

FIGURE 165SPRAY PROFILE FOR CASE 1(Y-AXIS EXTENDED, NOT TO SCALE) ... 162

FIGURE 166REACTION ZONE IN SPRAY PROFILE FOR CASE 1(Y-AXIS EXTENDED, AXES NOT TO SCALE) ... 163

FIGURE 167AXIAL TEMPERATURE DISTRIBUTIONS, AT A SIMULATION TIME OF 2 MS ... 163

FIGURE 168AXIAL FUEL FRACTION DISTRIBUTIONS, AT A SIMULATION TIME OF 2 MS ... 164

FIGURE 169AXIAL OXYGEN FRACTION DISTRIBUTIONS, AT A SIMULATION TIME OF 2 MS ... 164

FIGURE 170VOLUME FRACTION OF LIMIT AND REACTIVE ZONE AT A SIMULATION TIME OF 2 MS ... 165

FIGURE 1712D MIXTURE FRACTION PLOT AT T =2 MS.THE REGION BELOW Z=0(IN WHITE) MARKS THE SPRAY BOUNDARY.THE BLACK ZONE BETWEEN Z=0.04 AND Z=0.05 MARKS THE STOICHIOMETRIC REGION (ZST=0.0425) ... 165

FIGURE 1722DTEMPERATURE PLOT AT T =2 MS.THE REGION BETWEEN T=900K AND T=903K CORRESPONDS TO THE ZONE OF PURE AIR, THEREFORE IT MARKS THE BOUNDARY OF THE SPRAY.THE BLACK LINE MARKS THE STOICHIOMETRIC REGION. ... 166

FIGURE 1732D FUEL MASS FRACTION PLOT AT T =2 MS.THE BLACK LINE MARKS THE STOICHIOMETRIC REGION. ... 166

FIGURE 1742D OXYGEN MASS FRACTION PLOT AT T =2 MS.THE REGION ABOVE YO=0.15 INDICATES THE ZONE OF PURE AIR, AND THE BLACK LINE MARKS THE STOICHIOMETRIC REGION. ... 166

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FIGURE 179INJECTION PROFILES OF SPLIT [115] AND SINGLE INJECTIONS ... 172

FIGURE 180SPLIT AND SINGLE INJECTION PENETRATIONS, WITH THE SECOND INJECTION PENETRATION SHOWN SEPARATELY ... 173

FIGURE 181COPY OF FIGURE 84PENETRATION OF SINGLE AND MULTIPLE INJECTION SPRAYS AT 900K, BOTH INERT AND REACTING [91] ... 173

FIGURE 182AXIAL VELOCITY PROFILE AT TIME T=1.45 MS, THE SQUARES INDICATE THE AXIAL POSITION OF EACH CONTROL VOLUME (CENTER OF VOLUME) ... 174

FIGURE 183AXIAL TIME-DIFFERENTIAL VELOCITY PROFILE AT TIME T=1.45 MS, THE SQUARES INDICATE THE AXIAL POSITION OF EACH CONTROL VOLUME (CENTER OF VOLUME) ... 174

FIGURE 184SPRAY PROFILE WITH MIXTURE FRACTION (Z)2D PLOT OF THE INERT SPRAY FROM THE MODEL, AT 500,1200 AND 1500 ΜS ASOI ... 175

FIGURE 185SCHLIEREN IMAGES FROM INERT SPRAY, AT 500,1200 AND 1500 ΜS ASOI[115] ... 175

FIGURE 186HRR AND PRESSURE RISE PLOT FOR REACTIVE SPLIT INJECTION AND SINGLE 1.0 MS INJECTION AT 900K, EXPERIMENTAL (TOP, AS SEEN IN FIGURE 85) AND CALCULATED FROM THE MODEL (BOTTOM) ... 176

FIGURE 187EXPERIMENTAL IMAGES (SCHLIEREN - LEFT AND PLIF- CENTER, AS SHOWN IN FIGURE 86[91]) AND MODEL VISUALIZATION (TEMPERATURE FIELD - RIGHT) FOR THE REACTIVE SPRAY AT 900K ... 177

FIGURE 188TEMPERATURE FIELD OBTAINED FROM THE MODEL FOR BOTH REACTIVE SPLIT AND REACTIVE SINGLE 1.0 MS INJECTION CASES ... 178

FIGURE 189HRR AND PRESSURE RISE PLOT FOR REACTIVE SPLIT INJECTION AT 800K, EXPERIMENTAL (TOP, AS SEEN IN FIGURE 85) AND CALCULATED FROM THE MODEL (BOTTOM) ... 179

FIGURE 190HRR AND PRESSURE RISE PLOT FOR REACTIVE SPLIT INJECTION AT 750K, EXPERIMENTAL (TOP, AS SEEN IN FIGURE 85) AND CALCULATED FROM THE MODEL (BOTTOM) ... 180

FIGURE 191INJECTION PROFILE VS CRANK ANGLE FOR PILOT-MAIN INJECTION MODELING WITH DWELL TIME VARIATION ... 183

FIGURE 192INJECTION PROFILE VS TIME FOR PILOT-MAIN INJECTION MODELING WITH DWELL TIME VARIATION ... 183

FIGURE 193RATE OF HEAT RELEASE (HRR) FOR PILOT-MAIN INJECTION IN ENGINE GEOMETRY WITH DWELL TIME VARIATION ... 184

FIGURE 194MAIN RATE OF HEAT RELEASE (HRR) FOR PILOT-MAIN INJECTION IN ENGINE GEOMETRY WITH DWELL TIME VARIATION 184 FIGURE 195TEMPERATURE OF THE SURROUNDING ZONE AND INJECTION PROFILE VS SIMULATION TIME FOR THE DIFFERENT INJECTION CASES ... 185

FIGURE 196SPRAY TEMPERATURE VS AXIAL DISTANCE FROM THE INJECTOR, FOR THE DIFFERENT INJECTION CASES, AT A SIMULATION TIME OF 19.6 MS ... 185

FIGURE 197TEMPERATURE PLOT FOR INJECTION CASE DT500 AT A TIME OF 19.6 MS AFTER THE START OF SIMULATION ... 186

FIGURE 201HRR VS CRANK ANGLE FOR AN OPERATING POINT OF 1500 X 5 FOR DIFFERENT DWELL TIMES [82] ... 187

FIGURE 202NOISE (TOP) AND BRAKE SPECIFIC FUEL CONSUMPTION (BSFC, BOTTOM) WITH RESPECT TO DWELL TIME FOR THE 1500 X 5 CASE [82] ... 187

FIGURE 203PILOT RATE OF HEAT RELEASE (HRR) FOR PILOT-MAIN INJECTION IN ENGINE GEOMETRY WITH DWELL TIME VARIATION 188 FIGURE 204INDICATED MEAN EFFECTIVE PRESSURE (IMEP) FOR PILOT-MAIN INJECTION WITH DWELL TIME VARIATION ... 188

FIGURE 205PRESSURE RISE FOR PILOT-MAIN INJECTION IN ENGINE GEOMETRY WITH DWELL TIME VARIATION ... 189

FIGURE 206PRESSURE RISE PLOT AND RATE OF INJECTION FOR PILOT INJECTION ONLY CASE ... 190

FIGURE 207PRESSURE RISE CLOSE UP FOR PILOT INJECTION ONLY CASE... 190

FIGURE 208INJECTION PROFILE FOR PILOT-MAIN INJECTION IN ENGINE GEOMETRY WITH INJECTION DURATION VARIATION ... 191

FIGURE 209HRR CURVES FOR DIFFERENT PILOT INJECTION DURATIONS ... 191

FIGURE 210PILOT (CLOSE-UP)HRR CURVES FOR DIFFERENT PILOT INJECTION DURATIONS ... 192

FIGURE 211MAIN (CLOSE-UP)HRR CURVES FOR DIFFERENT PILOT INJECTION DURATIONS ... 192

FIGURE 212PRESSURE RISE CURVES FOR DIFFERENT PILOT INJECTION DURATIONS ... 193

FIGURE 213INDICATED MEAN EFFECTIVE PRESSURE (IMEP) FOR PILOT-MAIN INJECTION WITH ENERGIZING TIME VARIATION.THE SINGLE INJECTION CASE (ET0) IS SHOWN FOR REFERENCE. ... 193

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FIGURE 214INJECTION PROFILE VS CRANK ANGLE FOR PILOT-MAIN-AFTER INJECTION MODELING WITH DWELL TIME VARIATION, AS IN

STRATEGY 3A [5] ... 195

FIGURE 215HRR VS CRANK ANGLE FOR PILOT-MAIN-AFTER INJECTION MODELING WITH DWELL TIME VARIATION, AS IN STRATEGY 3A [5] ... 195

FIGURE 216CLOSE UP VIEW OF THE MAIN INJECTION HRR VS CRANK ANGLE FOR THE PILOT-MAIN-AFTER STRATEGY ... 196

FIGURE 217CLOSE UP VIEW OF THE AFTER INJECTION HRR VS CRANK ANGLE FOR THE PILOT-MAIN-AFTER STRATEGY ... 196

FIGURE 218EXPERIMENTAL NOISE,BSFC AND HRR PLOT FOR STRATEGY 3A [5] ... 197

FIGURE 219PRESSURE TRACE VS CRANK ANGLE FOR THE PILOT-MAIN-AFTER STRATEGY ... 197

FIGURE 220INDICATED MEAN EFFECTIVE PRESSURE (IMEP) FOR PILOT-MAIN-AFTER SIMULATED CASES (STRATEGY 3A FROM [5]), WITH EQUAL AMOUNT OF FUEL INJECTED ... 198

FIGURE 221TEMPERATURE FIELD OF THE SPRAY WITH INJECTION PROFILE DT300 AT A SIMULATION TIME OF 21.1 MS (START OF AFTER INJECTION) ... 198

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LIST OF TABLES

TABLE 1.MEASURED CONSTANTS IN WALL-IMPINGING JETS ... 31

TABLE 2SPREADING RATE CORRELATION CONSTANTS [44] ... 45

TABLE 3DISSIPATIVE ENERGY LOSS RELATIONSHIPS AND CORRESPONDING OBSERVATIONS [54] ... 53

TABLE 4OPERATING CONDITIONS FOR THE JET WALL CONFIGURATION [70] ... 55

TABLE 5ENERGIZING TIME FOR PILOT AND MAIN INJECTIONS AND PERCENT DISTRIBUTION OF THE MAIN INJECTION AT THE DIFFERENT OPERATING POINTS [82] ... 70

TABLE 6TEST CONDITIONS FOR MULTIPLE-INJECTION IN CONSTANT VOLUME COMBUSTION CHAMBER [88] ... 74

TABLE 7PILOT-PILOT-MAIN INJECTION STRATEGIES [5] ... 78

TABLE 8PILOT-MAIN-AFTER INJECTION STRATEGIES [5] ... 79

TABLE 9EXPERIMENTAL CASES FOR SPLIT INJECTION TESTING [94] ... 85

TABLE 10.INERT AND REACTIVE EXPERIMENTAL DATA FROM THE ECN DATA SEARCH [106] ... 102

TABLE 11VALUES FOR TAN Α ... 122

TABLE 12WALL JET MODEL CONSTANTS ... 125

TABLE 13EXPERIMENTAL PARAMETERS FOR WALL JET MODEL TESTING ... 128

TABLE 14REACTIVE EXPERIMENTAL DATA FROM THE ECN DATA SEARCH [106] ... 146

TABLE 15INJECTIONS FOR MULTIPLE INJECTION TESTING ... 171

TABLE 16SIMULATION PARAMETERS FOR MULTIPLE INJECTIONS TESTING ... 172

TABLE 17ENGINE GEOMETRY AND PARAMETERS FOR PILOT-MAIN INJECTION SIMULATION WITH ENGINE GEOMETRY ... 182

TABLE 18ESTIMATED INJECTION PARAMETERS FOR PILOT-MAIN INJECTION IN ENGINE GEOMETRY ... 182

TABLE 19START OF INJECTION FOR THE PILOT-MAIN INJECTION SCHEME WITH DWELL TIME VARIATION ... 183

TABLE 20INJECTION PARAMETERS FOR PILOT-MAIN INJECTION IN ENGINE CONDITIONS WITH INJECTION DURATION VARIATION ... 191

TABLE 21ENGINE GEOMETRY AND PARAMETERS FOR PILOT-MAIN-AFTER INJECTION SIMULATION WITH ENGINE GEOMETRY ... 194

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ABBREVIATIONS

0D Zero dimensional 1D One dimensional 2D Two dimensional 3D Three dimensional A Area

aHRR Apparent Heat Release Rate

AMI After start of the Main Injection

Ar Combustion mapping parameter

ASI After Start of Injection

aTDC after Top Dead Center

aSOI after Start of Injection

BMEP Brake Mean Effective Pressure

BSFC Brake Specific Fuel Consumption

c Empirical coefficient

CA Crank Angle

Cf Fraction that defines the boundary for the jet tip

CFD Computational Fluid Dynamics

CHEMKIN® Chemical Kinetics

CI Compression Ignition

Cimp1 Empirical coefficient Cimp2 Empirical coefficient Cmomentum, Cmom Empirical coefficient Cmomentum_w, Cmom_w Empirical coefficient

CO Carbon Monoxide

Cp Specific heat at constant pressure

cst Progress variable from mixing to combustion regime

Ct Empirical coefficient

D,d Orifice/nozzle diameter

d0h Hydraulic diameter of nozzle

d0w Height of impingement zone exit area

dBA A-weighted decibels

DBI Diffused Background Illumination

dbv Thickness of the outer boundary layer

dd Droplet diameter

de Thickness of the inner boundary layer

diff vel Time difference of velocity

Dn Orifice/nozzle diameter

dnw Impinging distance

dr Change in spray radius

DSM Differential Reynolds Stress Model

dt Time step

DT Dwell Time

Ea Activation energy

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ECU Electronic Control Unit

Ed Dissipative energy loss

EGR Exhaust Gas Recirculation

entr Entrained

EOI End of Injection

erf Error function

ET Energizing Time

exp Experimental

Fm Empirical constant

Fn Empirical constant

FWHM Full Width at Half Maximum of axial velocity

h Heat convection coefficient

H Increase of elevation above the terrain (embankment)

HC unburned HydroCarbons

HCCI Homogeneous Charge Compression Ignition

Hn Impinging distance

HRR Heat Release Rate

i Control volume index

I Pre-calculated integral

IMEP Indicated Mean Effective Pressure

inj Injection

k Entrainment constant

kk Total number of species in combustion reaction

K Momentum flux leaving the orifice/nozzle

L Impinging distance

LL Liquid Length

LIEF Laser Induced Exciplex Fluorescence

LOL Lift-Off Length

LTC Low Temperature Combustion

Lv Latent Heat (of Vaporization)

m Empirical constant

𝑚̇(𝑥) Total mass flow rate

map Mapped (zone)

Me Entrained mass

Mf Momentum flux

Mfn Momentum flux leaving the orifice/nozzle

𝑚̇𝑖 Injected mass flow rate

mod Model

n Empirical constant

NOx Nitrous Oxides

NPR Nozzle Pressure Ratio

NZ Number of Zones

NZF Number of Zones in the Free jet

OH Hydroxyl radical

PAH Polycyclic Aromatic Hydrocarbons

PCCI Premixed Charge Compression Ignition

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Pil Pilot (injection)

Pinj Injection pressure

PLIF Planar Laser-Induced Fluorescence

PM Particulate Matter

Q Arrhenius reaction progress variable

r Radial coordinate

R Radius

Re Reynolds number

reac Reactive

red Reduced

Revap Evaporation coefficient

RNG Re-Normalization Group

ROHR Rate Of Heat Release

ROI Rate Of Injection

RPM Revolutions Per Minute

s Oxidizer to fuel ratio

S Penetration

SI Spark Ignition

SMD Sauter Mean Diameter

SOI Start of Injection

t Time

T Temperature

Ta Air temperature in the combustion chamber

tb Breakup time

Temp Temperature

timp Time of impingement (contact with the wall)

tinj Injection duration time

trf Transfer

U Axial velocity

Uc Velocity along the central axis

UHC Unburned HydroCarbons

Um Velocity leaving the orifice/nozzle

Unorm Droplet velocity component normal to the wall

Uo Velocity leaving the orifice/nozzle

Utang Droplet velocity component tangential to the wall

u’ Free jet fluctuation intensity

𝑢2

̅̅̅ Mean axial turbulent velocity

V Velocity, radial velocity

Vav Mean velocity

Vm Radial peak velocity

Vmax Maximum radial velocity at a given radial location

Vol Volume

v’ Wall jet fluctuation intensity

𝑣2

̅̅̅ Mean radial turbulent velocity

We Weber number

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X1/2 Jet half width

y Radial coordinate

Y Mass fraction

Y1/2 Jet half width or half thickness

ytip Total tip penetration

z Coordinate perpendicular to the wall

Z Passive scalar for mixture fraction

Z1/2 Jet half width or half thickness

Greek letters

α Empirical coefficient, wall jet spreading angle

β Multiplier for the species mass flux radial integration

Γ Progress variable from mixing to infinitely fast chemistry

regime

δ Half-thickness

θ Angle

k-ϵ Kappa-Epsilon turbulence model

ν Kinematic viscosity

ξ Non dimensional radius (r/R)

𝜌̿ Mean density

ρa Ambient density

ρd Density of the liquid phase (in droplets)

ρf Fuel density

ρi Injected fluid density

σ Droplet surface tension

Ф Equivalence Ratio

𝜔̇ Molar reaction rate

Subindexes a Air av Average b Burned comb Combustion cr Critical evap Evaporation f fuel g Gaseous phase

i Control volume index

ini Initial

k Species identifier

l Liquid phase

max Maximum

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1 INTRODUCTION

Compression ignition engines (such as those using diesel fuel) in propulsion have the potential to be more efficient than their gasoline counterparts. Large diesel engines have big-bore cylinders (150 mm or more), therefore the contact of the diesel spray with the cylinder wall generally is not an issue to consider. Also, big engines have small rotation speeds, which give plenty of time for the diesel fuel to mix before being burned. They are already widely used as industrial heavy-duty stationary engines and in heavy-duty transportation systems (trucks, trains, ships), since the accessories they require (turbo/super charging, post-treatment systems, high pressure fuel injection system, etc.) that take up considerable space and weight are not a constraint for these applications.

However, for automotive and light duty commercial applications, the trend is to “downsize” the engines, to make them more efficient for the propulsion application and less polluting. With downsizing, the speed of the engine increases and the bore decreases; therefore the spray wall interaction and the mixing dynamics now become even more important parameters to consider for the design and performance of the engine. Techniques such as Low Temperature Combustion (LTC), that are used to reduce pollutant emissions at the source, can be achieved by making multiple injections during one engine cycle.

Creating models to simulate diesel injection has also become increasingly important to understand the dynamics of diesel injection and combustion. CFD models can describe accurately the fluid dynamics related to diesel injection, but are very time-consuming and require plenty of computing power. This is where 1D models become useful, to reduce the computational time and obtain fairly acceptable results. They are often calibrated and validated with experiments in a constant volume bomb, which is necessary to understand the variations in the spray dynamics independently of compression and expansion phenomena that exist in real engines.

The objective of this work is to continue working with an existing 1D diesel injection and combustion model, which includes a module of detailed chemistry (CHEMKIN in this case). A literature review is presented in chapter 2, which includes information on some basics of compression ignition engines, modeling, spray-wall interaction and multiple injections. The improvement of the model accuracy is the main objective, through a comparison between eulerian and lagrangian model approaches and the inclusion of a sub-model of radial dilatation, which is presented in chapter 3. Additionally, a sub-model to consider the spray-wall interaction and a radial distribution of variables (pseudo-2D condition) is added (presented in chapter 4), as an intermediate step in taking the 1D model to be adapted for real engine calculations, which include small bore cylinders with spray contact with the wall. Finally, an application of the model with multiple injections and real engine geometry is presented in chapter 5 as a validation of the model improvements.

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Les moteurs à allumage par compression (comme ceux utilisant du carburant diesel) en propulsion pourraient être plus efficaces que leurs équivalents à essence. Les moteurs diesel industriels ont des cylindres de gros diamètre (150 mm ou plus). Par conséquent, le contact du spray diesel avec la paroi du cylindre n'est généralement pas un problème à prendre en compte. En outre, les gros moteurs ont de petites vitesses de rotation, ce qui laisse suffisamment de temps au carburant diesel pour qu'il se mélange avant d'être brûlé. Ils sont déjà largement utilisés comme moteurs fixes industriels et dans les systèmes de transport lourds (camions, trains, navires), car les accessoires nécessaires (système de suralimentation, systèmes de post-traitement, système d'injection de carburant à haute pression, etc. .) qui prennent beaucoup de place et de poids ne constituent pas une contrainte pour ces applications.

Toutefois, pour les applications automobiles et utilitaires légers, la tendance est à la réduction de la taille des moteurs afin de les rendre plus efficaces pour l’application de la propulsion et moins polluants. Avec la réduction de la taille, la vitesse du moteur augmente et l'alésage diminue; par conséquent, l'interaction spray-paroi et la dynamique de mélange deviennent des paramètres encore plus importants à prendre en compte pour la conception et les performances du moteur. Des techniques telles que la combustion à basse température (LTC), utilisées pour réduire les émissions de polluants à la source, peuvent être obtenues en faisant plusieurs injections au cours d'un cycle de moteur.

Créer des modèles pour simuler l'injection de diesel est également devenu de plus en plus important pour comprendre la dynamique de l'injection et de la combustion de diesel. Les modèles CFD peuvent décrire avec précision la dynamique des fluides liée à l'injection de carburant diesel, mais prennent beaucoup de temps et nécessitent beaucoup de puissance de calcul. C'est ici que les modèles 1D deviennent utiles pour réduire le temps de calcul et obtenir des résultats assez acceptables rapidement. Ils sont souvent calibrés et validés à l'aide d'expériences dans une bombe à volume constant, ce qui est nécessaire pour comprendre les variations de la dynamique du spray indépendamment des phénomènes de compression et de dilatation existant dans les moteurs réels.

L'objectif de ce travail est de continuer à travailler avec un modèle d'injection et de combustion diesel 1D existant, qui comprend un module de chimie détaillée (CHEMKIN dans ce cas). Une revue de la littérature est présentée au chapitre 2, qui comprend des informations sur certaines bases des moteurs à allumage par compression, de la modélisation, de l’interaction spray-paroi et des injections multiples. L’amélioration de la précision du modèle est l’objectif principal, par une comparaison entre les approches modélisées eulérienne et lagrangienne et par l’inclusion d’un sous-modèle de dilatation radiale, présenté au chapitre 3. En outre, un sous-modèle pour l’interaction spray-paroi et une sous-modèle de distribution radiale des variables (condition pseudo-2D) sont ajoutées (présentées au chapitre 4), constituant une étape intermédiaire pour adapter le modèle 1D pour les calculs de moteurs réels, qui incluent des cylindres à petit alésage avec paroi. Finalement, une application du modèle à injections multiples et à géométrie réelle du moteur est présentée au chapitre 5 en tant que validation des améliorations du modèle.

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2 DIESEL ENGINE FUNDAMENTALS

Compression ignition (CI) engines operate slightly different than spark ignition (SI) engines. Pure air is compressed by a piston in a cylinder, contrary to the fuel-air mixture that is compressed by SI engines. The fuel is then directly injected into the cylinder, where it auto-ignites and generates high pressure gases to drive the crankshaft.

CI engines can be more efficient than SI engines. They have a higher compression ratio, which makes the thermodynamic cycle more efficient. They have less pumping losses, since no throttle valve is required. And they operate with a lower general equivalence ratio of fuel to air, since fuel is locally concentrated in the injected spray instead of being all around the cylinder [1].

However, these advantages come with a price. Due to the higher compression ratio required and higher specific power desired for operation, turbocharging or supercharging is important and almost often mandatory for the CI engines, therefore increasing the parts that a working engine must have (making it bulky and expensive). Due to the direct fuel injection, the mixture preparation happens directly inside the cylinder during the end of the compression stroke of the engine; therefore, the speed of the engine is limited by this mixing process. As the automotive engines become smaller (downsizing), their speed becomes bigger; therefore, this mixing constraint becomes even more influential [2].

Since the flame inside the CI engine is a diffusion flame (burning happens at the same time as the injection process), the combustion will happen in the zone where the local mixture is close to stoichiometric. This causes the flame temperature to be the highest possible, leading to increased emissions of nitrous oxides (NOx). There is also a zone where the mix is highly rich, leading to increased emissions of soot.

Conventional CI engines therefore have bulky after-treatment systems to deal with these increased emissions. However, reduction of emissions at the source is a focus of major studies, since it could drastically reduce the number and size of after-treatment systems. This is one of the reasons why it is crucial to understand the injection and combustion phenomena underlying diesel fuel.

In this line of work, there are new combustion methods being studied, such as PCCI (Premixed Charge Compression Ignition) and HCCI (Homogeneous Charge Compression Ignition), where all the fuel mass is pre-mixed with the air before combustion starts, having a fully pre-mixed combustion with lower flame temperature. Both methods aim to increase the mixing time available to have more pre-mixed combustion in the cylinder with lower temperatures, therefore reducing the emissions mentioned before. [1]

To reduce pollution at the source, it is necessary to understand in detail the process by which the diesel fuel is burned in the cylinder. In this chapter, an overview of the compression ignition theory and low temperature combustion is given in section 2.1, the different approaches to modeling the injection and combustion process are discussed in section 2.2, the interaction between the fuel spray and the combustion chamber wall is shown in section 0, and the concept of multiple injections is introduced in section 2.4.

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2.1 CI COMBUSTION

The process of CI combustion can be split into 4 parts, according to Heywood [2] and shown in Figure 1:

 Ignition delay: From the moment when the injector starts injecting fuel into the cylinder until the first significant heat is released. It takes some time to prepare the mixture and create the appropriate conditions for the auto-ignition process to happen, including fuel atomization and vaporizing, mixture formation and initial oxidation reactions; it is a very complex phenomenon, not fully understood.

 Premixed combustion phase: When inflammation starts, the fuel already mixed with the air will burn very fast, leading to a peak in cylinder pressure. The heat release rate depends directly in the amount of fuel already mixed with the air at the start of the combustion phase. The mixture will be close to stoichiometric, but it can have a relatively high variation within the flammability limits.

 Mixing controlled combustion phase: After the initial premixed combustion, fuel continues to be injected into the cylinder, being mixed and burned at the same time, creating a diffusion flame. Since mixing and burning are simultaneous, the mixing process controls the reaction rate, which is considerably slower than the premixed combustion. The reaction will happen at the physical location where the mixture is stoichiometric, in between the injected fuel (too rich) and the surrounding air (too lean). Since the combustion is always stoichiometric, the flame temperature will be the maximum temperature possible (adiabatic flame temperature).

 Late combustion phase: Combustion continues at a lower rate, due to the temperature and pressure reduction during the expansion stroke of the engine. There are also left-overs of fuel and fuel-rich combustion products that burn during this stage.

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2.1.1 Low Temperature Combustion

In an effort to reduce engine emissions in diesel engines, Low Temperature Combustion (or LTC) has been gradually implemented in the engines. LTC uses dilution, either by exhaust gas recirculation (EGR) or by using locally lean mixtures. This way, NOx emissions are reduced, due to the lower flame temperature, and soot formation can also be reduced due to the reduction of fuel-rich areas. Diesel fuel is injected earlier in the engine cycle, where the in-cylinder gases have lower temperature and density; therefore, the delay of ignition can be extended until the end of injection (EOI), making the transient ramp-down of injection more important for the mixing and combustion processes inside the cylinder. The concepts of homogeneous charge compression ignition (HCCI) [3] and EGR dilution [4] come from this LTC concept, and multiple injections [5] can also be used to reach LTC conditions.

Images of OH Planar Laser-Induced Fluorescence (OH-PLIF) and soot Laser-Induced Luminosity ( [6], [7]) show the difference between a conventional diesel jet and a LTC diesel jet. The conventional diesel jet ignites before the end of injection (EOI) and has a soot region (Figure 2, red region inside white dashed line) expanding almost throughout its entire cross-section. A small ring of OH (green region) is seen around the soot area. Soot is formed where mixtures are greater than Ф≈2, and OH forms at around Ф≈1. This shows strong gradients of equivalence ratio that are confirmed by direct vapor-fuel measurements [8].

Figure 2 : OH-PLIF and soot image of conventional diesel combustion (top) and LTC (bottom), diesel jet penetrating from left to right [9] The LTC jet shows that the ignition happens after EOI, and OH is seen throughout most of its cross-section. Soot only appears at the downstream part of the jet. This indicates that there is more mixing in the diesel jet to bring the equivalence ratio down close to stoichiometry, without increasing the size of the jet, and despite the fact that the LTC condition has less oxygen (due to dilution).

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Vapor-fuel measurements in inert conditions (0% O2) equivalent to the LTC condition [10] show that equivalence ratios become much lower upstream of the jet near the injector than at the downstream side, and also that this reduction of equivalence ratio moves downstream faster than the jet itself (Figure 3).

Figure 3 : Vapor fuel equivalence ratio measurements after end of injection (EOI) by toluene tracer fluorescence [10] in inert jet. The circled number show the time in crank angle degrees for the jet to reach the position of each circle.

However, having very lean mixtures contributes to the formation of unburned hydrocarbons (UHC) and carbon monoxide (CO), indicating incomplete combustion in these regions.

These observations are similar for single-phase transient gas jets ( [11], [12] ). Johari and Paduano [11] proposed that since less jet flow is available for vortex growth, entrainment must increase to compensate for the vortex formation process.

2.2 COMBUSTION MODELS

The combustion models are descriptions of the combustion process, constantly being updated and improved as imaging techniques become available to visualize the injection and combustion processes.

There are two general families of models: Conceptual (or qualitative) and Systematic (or quantitative). The conceptual models make a description of the combustion process according to observations of combustion phenomena. They distinguish different zones inside the combustion chamber, according to their function. There are conceptual models with and without fuel spray calculations.

The systematic models are those where the division of zones is not done according to function, but rather in a methodical way depending on the analysis to be done, which can be Lagrangian (moving frame of reference) or Eulerian (fixed frame of reference).

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2.2.1 Conceptual Models

One of the most known conceptual or qualitative models is the Dec model [8], developed by observations in a mono-cylinder engine with optical access at SANDIA National Labs. It shows an idealized spray with an average position and shape. It helps illustrate the temperature distribution along the spray and the location of pollutants (Figure 4).

Figure 4 : Dec’s model of combustion in the quasi-steady state of diffusion flame [8]

Dec describes the different phases of diesel combustion very similar to Heywood, related to the crank angle degrees after start of injection (ASI) (Figure 5):

 Initial spray development (0-4.5º ASI), where atomization, vaporization and mixing of fuel and air occurs.

 Auto-inflammation (3º-5º ASI), where the first visible incandescence appears.

 Pre-mixed combustion peak (4º-6.5º ASI), marked by the apparition of Polycyclic Aromatic Hydrocarbons (PAH) coming from a rich premixed zone. It has a strong chemiluminescence, and leads to the formation of soot particles later in the process.  Diffusion flame development (5.5º-6.5º ASI), where a diffusive flame surrounds the

spray, with the premixed combustion products (including unburned fuel) inside and the surrounding air outside.

 End of pre-mixed peak (7º-9º ASI), where the pre-mixed combustion ends and the jet continues to grow. There is a big concentration of particles at the end of the jet.

 Quasi-static diffusive combustion (9º ASI until the end of injection), where the combustion process is controlled by the mixing of incoming fuel and surrounding air.

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Figure 5 : Dec conceptual combustion model [8]

SANDIA also developed a conceptual model for LTC conditions, based on the previous Dec model (Figure 6). The model shows a way to create LTC conditions, which is using dilution to reduce the temperature and have a long premixing time of the fuel (the injection finishes before combustion starts). It also shows a more homogeneous combustion process (more premixed combustion than diffusion combustion), with less soot regions. It also shows a disadvantage, which is the formation of unburned hydrocarbons (UHC) near the injector late in the cycle [13] [14].

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Figure 6: LTC conceptual model (right) from SANDIA National labs, compared to the conventional Dec model (left) [14] Models can also be classified by their dimension (0D, quasi-1D, 1D, 3D). 0D models calculate average values for different parameters. 1D models take in consideration the variation in space. When complex calculations and equations are required to be integrated to the model, the qualitative model does not provide enough information to process this data.

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Experimentation and 3D CFD models can provide more detailed information on this process, but these are complex and expensive. Therefore, systematic 1D models (such as those developed in [15], [16], [9], [1], [17]) provide a good balance between simplicity and accuracy to help understand this complex phenomenon.

2.2.2 Systematic Models

Systematic models are those in which the fuel spray geometry is not fixed in advance. They can have a Lagrangian or Eulerian frame of reference, depending on the model approach. The most detailed models are 3D CFD models, but their implementation is costly in terms of memory requirements and computation time. There are also 0D models, which oversimplify the combustion process but are very practical for general engine calculations. That is why the use of 1D models is becoming widespread, with an acceptable tradeoff between accuracy and speed of calculations.

The most important parameter used in systematic 1D models is penetration. From it, other parameters can be inferred or calculated, such as the air entrainment, reaction rate, spray radius, among others. Early studies of inert sprays, such as those done by Abramovich [18] and Hiroyasu [15], show two regimes in the spray penetration: first, there is a constant speed region, characteristic of motion of solid and liquid particles; then, there is a decreasing speed region (penetration is proportional to the square root of time), characteristic of the motion of a submerged jet (in which the spray is mixing with surrounding fluid). Later studies done by Naber and Siebers [19] confirmed this behavior for the penetration of a spray (Figure 7).

Figure 7 : All the non-vaporizing penetration data plotted on top of the penetration correlation [19].

Later studies aimed to describe the penetration of a reacting spray, which approaches better the real phenomena happening inside a diesel engine. Using an Eulerian diesel spray model, Desantes [20] related the penetration and the ignition delay of a spray. It showed that after the ignition delay is reached, the penetration curve shifted from an inert penetration curve to a reactive penetration curve, which is greater than the latter one and approaches a curve whose ignition delay is zero. This behavior indicates an axial dilatation of the spray (in addition to the imposed radial dilatation) when the spray is burning. However, the ignition delay remains an input to the model and depends on calibration from the penetration curve.

To describe the reactive spray, Desantes [20] used the fuel fraction profile from inert models and applied it to the mixture fraction in the reactive model. Then, using an infinitely fast

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chemistry approach (Burke & Schumann, taken from [21]), a mapping between the mixture fraction and the mass fractions of the different species was created, to estimate the mass fractions radial distribution during the burning process. This mapping was calculated assuming the same radial distribution for the mixture fraction applies for the enthalpy and the velocity (assuming the Prandtl and Schmidt numbers are set to 1), as shown by Pastor [16]. Knowing the enthalpy distribution, a temperature distribution can also be calculated, assuming local equilibrium of liquid and vapor fuel (considering Raoult’s and Dalton’s laws), and the enthalpy of the other species present.

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2.3 WALL JET THEORY AND MODELS

2.3.1 Early Works

When a fluid jet impacts (or impinges on) a surface, the outward flow is termed a “wall jet”. This term was first introduced by Glauert in 1956 [22], and later used (with variations such as “partially open jet”, “surface jet” and “submerged jet) by Poreh [23] and others. Neglecting compressibility, Glauert divided the wall jet section profile in two overlapping parts: an inner part (in contact with the wall) and an outer part (in contact with the surrounding environment). The inner part is dominated by frictional resistance with the wall (like an ordinary boundary layer flow) and the outer part is dominated by free mixing with the surrounding media (like a free jet). The solutions for the velocity of both parts were matched at the position of the maximum velocity; this way an overall similarity was not achieved, but the solution of each part was self-similar. This result was confirmed experimentally by Bakke [24] and others.

Since both the velocity at the wall (z=0) and at the outer edge of the wall jet (z=∞) is zero (for static surrounding air), and the velocity profile must be continuous, there must be a maximum in between these points. And since the turbulent Prandtl number near the wall is approximately equal to unity, this maximum velocity (and temperature also) occur at the edge of the inner boundary layer.

Vlachopoulos [25] used a power law to model the inner jet:

7 1        e re r d z V V (1)

Where z is the coordinate perpendicular to the wall, de is the thickness of the inner boundary

layer (in this case it corresponds to the point of maximum velocity) and Vre is the radial

velocity at coordinate de. This correlation was used by Myers [26], but Vlachopoulos

observed that the experimental data was closer to a 1/14-power law profile. The outer jet is modelled with a Gaussian distribution, similar to the free jet:

2 5 . 1 max _ 1                   e bv e r r d d d z V V (2)

Where dbv is the thickness of the outer boundary layer (the coordinate where the jet velocity is

equal to the surrounding velocity). The exact position of this outer boundary layer isn’t critical to the solution, as long as it is sufficiently far from the inner boundary layer.

The inner boundary layer thickness obtained by correlation of the data was:

5 . 1 , , ,               r e i e i i e e R R R R d d (3)

Where de,i and Re,i are the inner boundary layer thickness and Reynolds number of an initial

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R will not be linear, but rather a power law. Therefore, since the half-width has a linear dependence with R, it is clear that the full velocity profiles are not self-similar, as seen in Figure 8 and Figure 9. However, the power in this power-law would be 6/5 (1.2), which is not too far from unity.

Figure 8 : Wall jet velocity and temperature profiles at R = 6 [25] Figure 9 : Wall jet velocity and temperature profiles at R = 10 [25]

2.3.2 Theoretical Deductions

Song and Abraham [27] presented theoretical deductions for round jets (free jets), radial jets (free jets propagating in radial direction) and wall-impinging jets (viewed as a special case of radial jet). However, the equations presented are valid only when the velocity profile is fully developed.

The profile of the wall-impinging jet is shown in Figure 10.

Figure 10 : Wall Impinging Jet [27]

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 

12               i a i i D x k m m x m      (4)

Where

m



 

x



m



i is the entrainment mass flow rate,

m

iis the injected mass flow rate, ρa is the ambient density, ρi is the injected fluid density, D is the orifice diameter. The term D(ρa / ρi)1/2

is also known as the effective diameter De. This means that the entrainment rate is

proportional to the axial penetration x. According to Abraham [28], k can vary from 0.2 to 0.457.

For the wall impinging jet, theoretical expressions that were proposed by Glauert [22]

(equations (5) and (6)) were fitted with empirical constants from measured data (Fm, Fn, m , n,

Table 1). m m m L y K F K L V             



(5) n n L y K F L x             



2 1 (6) Where L is the impinging distance (as seen in Figure 10), K is the momentum flux of the jet leaving the orifice, ν is the kinematic viscosity of the fluid. The maximum radial velocity Vm is proportional to ym and the jet half width X1/2 (place where the radial

velocity is half of the maximum) is proportional to yn. The constant “m” is close to -1

and the constant “n” is close to 1 (Table 1).

Table 1. Measured constants in wall-impinging jets

Experimental reference Fm Fn m n

Poreh et al [23] 1.32 0.098 -1.10 0.90

Witze and Dwyer [29] 1.11 0.0946 -1.12 1.01

Tanaka and Tanaka [30] 1.52 0.095 -1.09 0.97

The entrained mass (Me) obtained for the wall-impinging jet (equation (7) with respect to time) is proportional to t ((2+n) / (1-m)), which is close to t3/2 obtained for both the round and radial jet. However, there is a small dependence on L (the impinging distance).









       

_

_

 n  m a i m m n m n m n m f a n tip n n f a e t K F m L n F C y L n F C M                              1 2 2 1 1 2 3 1 1 1 2 1 1 2 092 . 1 2 2 092 . 1 2       (7)

Where ytip is the total tip penetration (L + distance along the wall), Cf is the fraction that defines the boundary for the jet tip (the tip velocity reduces to the fraction Cf of the initial velocity at the orifice). The tip penetration for a wall-impinging jet is defined as the summation of the impinging distance L and the radial distance from the tip of the wall jet to