A CRANK ANGLE RESOLVED CIDI ENGINE COMBUSTION MODEL WITH ARBITRARY FUEL INJECTION FOR CONTROL PURPOSE

DISSERTATION

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University

By

Chung-Gong Kim, B.S., M.S.

* * * * *

The Ohio State University

2004

Dissertation Committee: Approved by

Dr. Yann G. Guezennec, Adviser

Dr. Giorgio Rizzoni Adviser Dr. Andrea Serrani Department of Mechanical Engineering Dr. Ahmed Soliman

ABSTRACT

With the introduction of new generation common rail system Diesel engines capable of multiple injections per stroke, and in the context of ever more stringent pollutant emission standards, the optimization and calibration of modern compression ignition direct injection (CIDI) engines is more and more complex. On one hand, the additional degrees of freedom provide additional opportunities to optimize the engines.

On the other hand, the additional flexibility does not permit the exhaustive engine mapping approach used in the past any more, and necessitate the advent of new modeling tools for rapid optimization and calibration. Those tools must be sufficiently accurate to capture all the relevant physical phenomena, yet simple enough to be computationally cheap and permit the exhaustive exploration of a large multi-dimensional design and control space. In particular, one of the missing such model today is a simple and efficient tool for CIDI combustion simulation with arbitrary fuel injection profile. Thus in this study, a crank-angle resolved CIDI engine combustion model was developed and validated. This model uses a single-zone approach and is limited to the closed-valve part of cycle of a single cylinder for computational efficiency. All these sub-models were suitably parameterized in terms of externally controllable variables. To perform these ii parameterizations and sub-model validations, extensive experiments were conducted

using a fuel injection rig and a multi-cylinder engine on a dynamometer. With this

combustion model, the crank-angle resolved history of the in-cylinder parameters was

calculated. Based on these results, the NOx emissions were predicted using the extended

Zeldovich mechanism, and applying the concept of local equivalence ratio to calculate

the temperature of each burned gas element.

To validate the overall combustion and NOx estimation models, a series of engine tests were performed over a range of operating conditions. The calibrated models allow to accurately predict in-cylinder pressure, torque and NOx emissions and also allow to

perform a virtual dynamometer mapping, hence demonstrating the proposed

methodology. Furthermore, the results from these virtual engine mappings can be used to

calibrate the black-box models of the combustion process which are typically used in

control-oriented, dynamic Mean Value Models.

iii

Dedicated to my Parents in Heaven,

my precious family who supported and endured me,

and Cho.

iv ACKNOWLEDGMENTS

I would like to express my gratitude toward my advisor, Dr. Yann Guezennec for the assistance and advice throughout my research. I also would like to thank Dr. Giorgio Rizzoni for his guidance in my thesis work and for being on my candidacy examination committee member. I am very grateful that Hyundai Motor Company has given me a great opportunity in exploring the deeper world of automotive engineering. Both vice president Hyun-soon Lee and director Jung-kook Park were the most important individual who proposed and provided me another academic life. Also, I would like to thank all those students and staff members who have worked with me at CAR. Particularly I thank Avra Brahma, Shawn Midlam-Mohler, and Manik Narula for their cooperation during the CIDI engine and fuel injection rig tests. I also want to express my thanks to excellent Korean students, Byungho Lee and Ta-Young Gabriel Choi for their spiritual cheer-up and academic communication during my entire hard and long work. My small accomplishment would not be possible if it was not for the endless patience of my beloved family, Young-Ghil, Young-Sung, and my wife, Jung-Mi.

Thank you all whom I did not mentioned here.

v VITA

July 13, 1960 Born – Ulsan, South Korea

1980-1984 B.S. Mechanical Engineering, Seoul National University, Seoul, South Korea

1985-2004 Hyundai Motor Company, South Korea

1990-1992 Master of Science Mechanical Engineering, Korea Advanced Institute of Science and Technology, Daejon, South Korea

2001-2004 Graduate Research Assistant, Center for Automotive Research, OSU

FIELDS OF STUDY

Major Field: Mechanical Engineering

vi TABLE OF CONTENTS

Page

Abstract…………………….………..……………………………………………..……. ii

Dedication………………….………..…………………………………………………....iv

Acknowledgments………………………………………………………………….……...v

Vita ………………………………………………………………………………....…….vi

List of Figures ……………………………………………………………………..……..xi

List of Tables ……………………………………………………………………..……..xv

Nomenclature ……………………………………………………………………….…xxiv

Chapters:

1. Introduction ...... 1

1.1 The diesel engine and research background ...... 1 1.2 Mean value model in diesel engines...... 6 1.3 A crank angle resolved CIDI engine combustion model...... 9 1.3.1 Motivation of the research ...... 9 1.3.2 Crank-angle resolved combustion model by a single-zone approach...... 10 1.3.3 Research objective ...... 10

vii 2. Literature review ...... 12

2.1 CIDI engine combustion modeling...... 12 2.2 Single zone combustion model approach ...... 13 2.3 Fuel injection in diesel engines...... 16 2.4 Emission modeling ...... 22

2.5 Combustion and NOx modeling...... 24 2.6 A mean value engine model...... 27 2.7 After treatment system for diesel engines...... 27 2.8 Summary of literature review and research motivation...... 31

3. CIDI engine combustion model by a single-zone approach ...... 32

3.1 Introduction...... 32 3.1.1 Governing equation formulation...... 32 3.2 Sub models...... 34 3.2.1 Heat release rate model...... 34 3.2.2 Ignition model...... 37 3.2.3 Heat transfer model...... 40 3.2.4 Fuel injection rate model ...... 41 3.2.5 EGR gas mass estimation...... 43 3.2.6 Other sub models ...... 45 3.3 Numerical solver for the ordinary differential equations...... 46

3.4 NOx modeling ...... 47 3.4.1 Extended Zeldovich NO formation mechanism ...... 47 3.4.2 Temperature calculation for the rate constant...... 50 3.4.3 Total NO concentration calculation...... 52

viii 4. Validation test ...... 54

4.1 Introduction...... 54 4.2 Validation test set-up ...... 54 4.2.1 Test engine and dynamometer ...... 54 4.2.2 Fuel injection test rig ...... 56 4.3 Instrumentation ...... 57 4.3.1 Instrumentation of the fuel injection rig ...... 57 4.3.2 Instrumentation for the engine tests...... 63 4.4 Test result...... 70 4.4.1 Fuel injection rig test data treatment...... 70 4.4.2 Fuel injection rig test results...... 73 4.4.3 Engine test data treatment...... 75 4.4.4 Engine test results ...... 85 4.4.5 TDC offset treatment ...... 89 4.4.6 Estimation of the trapped fresh air...... 90 4.4.7 Determination of the auto-ignition point ...... 91 4.4.8 Test engine compression ratio ...... 92

5. Parameters identification for fuel injection rate estimation model and model validation ...... 95

5.1 Introduction...... 95 5.1.1 General trend of fuel flow rate...... 95 5.1.2 The effect of back pressure ...... 96 5.2 The dynamic fuel injection timing...... 98 5.3 Fuel injection flow rate modeling...... 101

ix 5.4 Coefficients modeling in flow rate model ...... 105

5.4.1 Coefficients modeling of A1 ...... 112

5.4.2 Coefficients modeling of A2 ...... 120

5.4.3 Coefficients modeling of A3 ...... 125

5.4.4 Fuel injection rate with model coefficients estimation Ai ...... 132

5.4.5 Validation of the injection flow rate estimation model ...... 133 5.4.6 Comparison of the model using the needle lift signal...... 136

6. Parameters identification for CIDI engine combustion and NOx molde and model validation ...... 141

6.1 Introduction...... 141 6.2 Ignition modeling...... 141 6.3 Watson combustion modeling ...... 152 6.3.1 Watson combustion model...... 152 6.3.2 Parameters in combustion model...... 154 6.3.3 Parameter identification in combustion model ...... 156 6.3.4 Watson combustion model result...... 191 6.3.5 Discussion of Watson combustion modeling result...... 197

6.4 Parameterization for NOx model...... 199 6.4.1 The local equivalence ratio estimation ...... 199

6.4.2 The NOx estimation...... 210

6.4.3 Discussion of NOx estimation result ...... 216

7. Virtual engine mapping test ...... 222

7.1 Review of the model development procedure ...... 222

x 7.2 Input data preparation ...... 224 7.2.1 The injector current profile estimation ...... 224 7.2.2 The other input variables estimations ...... 228

7.3 Summary for the combustion and NOx model...... 229 7.4 The final model validation on the other engine operating condition...... 232 7.5 Verification of the model by extrapolation...... 234 7.5.1 Discussion of the results for the extrapolated model ...... 241 7.6 The virtual engine mapping test (VEMT)...... 242

8. Conclusions, contributions, and recommendations ...... 250

8.1 Conclusions...... 250 8.2 Contributions ...... 251 8.3 Recommendations...... 257

REFERENCES...... 259

xi LIST OF FIGURES

Figure Page

Figure 1.1: A simplified schematic of the diesel engine system...... 2

Figure 1.2: The change in the engine control concept...... 4

Figure 1.3: The CIDI engine control model using a MVM approach in EGR/VGT system ...... 7

Figure 1.4. A sample result of EGR/VGT interaction modeling, Upadhyay [1]...... 8

Figure 2.1: An example of a multi-strike strategy with common rail system ...... 21

Figure 2.2: A conceptual image of the combustion flame in a diesel engine ...... 25

Figure 2.3: A various flow pattern in a wall-flow type DPF [75]...... 29

Figure 2.4: A possible diesel engine after-treatment system configuration...... 31

Figure 3.1: EGR ratio calculation in the test engine...... 44

Figure 3.2: NOx modeling procedure schematic...... 53

Figure 4.1: Test engine and engine dynamometer...... 55

Figure 4.2: Fuel injection test rig using the Bosch tube system ...... 56

Figure 4.3: A fuel injector on which a needle lift sensor is installed...... 58

xii Figure 4.4: The pressure wave inside a common rail system ...... 59

Figure 4.5: A detailed schematic around Bosch tube pressure sensor...... 60

Figure 4.6: An injector solenoid current probe...... 61

Figure 4.7: The dSpace system for injector drive...... 62

Figure 4.8: Fuel injection test rig using the Bosch tube system ...... 63

Figure 4.9: AVL amplifier rack (3066-A03/3076-A01)...... 65

Figure 4.10: IAV injector driver unit (Fi2re)...... 67

Figure 4.11: BEI Crank angle encoder ...... 68

Figure 4.12: Measurement system diagram of a CIDI engine test ...... 69

Figure 4.13: Principal measurement system for CIDI test engine...... 70

Figure 4.14: Typical raw data acquired in the fuel injection rig test and corresponding processed data ...... 71

Figure 4.15: A typical fuel injection behavior...... 72

Figure 4.16: The unfiltered raw Pcy and nHHR ...... 80

Figure 4.17: Pcy and nHHR : f r = 0.45 , order = 3 and 9 ...... 81

Figure 4.18: Pcy and nHHR : f r = 0.25 , order = 3 and 9 ...... 82

(a) The cylinder pressure and heat release rate...... 84

Figure 4.19: The final shape of the filtered cylinder pressure and heat release rate...... 84

xiii Figure 4.20: The. Effect of SOI of single injection at 1800 rpm with EGR on the net heat release rate curve( nHRR )...... 86

Figure 4.21: Effect of the SOI of pilot or main injection (pilot+main) fuel injection at 1500 rpm without EGR on the net heat release rate curve ( nHRR )...... 87

Figure 4.22: Effect of the SOI and PW of post and main fuel injection on the net heat release rate curve ( nHRR ) in 3-strike injection at 1800 rpm without EGR...... 88

Figure 4.23: The case when an encoder is installed incorrectly, retarded ...... 89

Figure 4.24: The definition of auto-ignition point: θign = 365(CA) ...... 91

Figure 4.25: Comparison of the pressure trace by modification of the compression ratio ...... 94

Figure 5.1: Total fuel injection quantity vs. (Pr- Pb ), PW, and Pb ...... 96

Figure 5.2: The back pressure effect...... 97

Figure 5.3: Injection delay time estimation ...... 100

Figure 5.4: Comparison of the fuel injection model...... 103

Figure 5.5: Coefficients vs. injection pressure, pulse width...... 106

Figure 5.6: The comparison of coefficients estimation models...... 110

Figure 5.7: Dependency of a1i on PW and Pb ...... 113

Figure 5.8: A1 evaluation by Eqn.(5.9)...... 115

Figure 5.9: b111 vs. Pb by Eqn. (5.9) ...... 115

Figure 5.10: Comparison A1 of Eqn. (5.10) with test data...... 117 xiv Figure 5.11: Coefficient A1 evaluation at short pulse width...... 118

Figure 5.12: Comparison of coefficient A2 by two estimation models...... 121

Figure 5.13: b211 vs. Pb by the revised model ...... 122

Figure 5.14: b221 vs. Pb with Eqn. (5.11)...... 123

Figure 5.15: Comparison of coefficient A2 ...... 124

Figure 5.16: Comparison of coefficient A3 ...... 126

Figure 5.17: Comparison of coefficient A3 by Eqn. (5.13) and (5.14) ...... 128

Figure 5.18: Model validation with test data for representative cases...... 134

Figure 5.19: Model validation with test data for representative cases...... 137

Figure 6.1: Locating the start of combustion point using the nHRR curve ...... 143

Figure 6.2: Parameter n in the ignition model from the test data ...... 144

Figure 6.3: Parameter Ta vs. SOI in ignition model from test data...... 146

Figure 6.4: Validation of ignition model by SOC...... 147

Figure 6.5: Validation of ignition model for each injection by SOC...... 150

Figure 6.6: Combustion duration in CIDI engine ...... 153

Figure 6.7: A typical combustion mode in CIDI engine...... 153

Figure 6.8: The trend of the burning mode factor, β ...... 159

Figure 6.9: The trend of the model shape factor, C p1 ...... 159

xv Figure 6.10: The trend of the model shape factor, C d1 ...... 160

Figure 6.11: The trend of the model shape factor, Cd 2 ...... 160

Figure 6.12: The relationship of the EGR % with variables MAF, AF, td andφig ...... 162

Figure 6.13: The trend of burning mode factor β ...... 163

Figure 6.14: The comparison of the estimated burning mode factor β by the untuned Watson model with test data...... 164

Figure 6.15: The comparison of the estimated burning mode factor β by the tuned Watson model with test data...... 165

Figure 6.16: The comparison of the burning mode factor β for each model ...... 168

Figure 6.17: The trend of shape factorC p1 ...... 170

Figure 6.18: The comparison of the estimated shape factor C p1 by the un-tuned Watson model with test data ...... 171

Figure 6.19: The comparison of the estimated shape factor C p1 by the tuned Watson model with test data ...... 172

Figure 6.20: The comparison of the estimated shape factor C p1 by the proposed model ...... 173

Figure 6.21: The comparison of the shape factor C p1 for each model ...... 175

Figure 6.22: The trend of shape factorCd1 ...... 177

xvi Figure 6.23: The comparison of the estimated shape factor Cd1 by the un-tuned Watson model with test data ...... 178

Figure 6.24: The comparison of the estimated shape factor Cd1 by the tuned Watson model with test data ...... 179

Figure 6.25: The extrapolation of shape factor Cd1 vs. φig ...... 180

Figure 6.26: The comparison of the estimated shape factor Cd1 by the proposed model with test data ...... 181

Figure 6.27: The comparison of the shape factor Cd1 for each model ...... 182

Figure 6.28: The trend of shape factorCd 2 ...... 183

Figure 6.29: The comparison of the estimated shape factor Cd 2 by the un-tuned Watson model with test data ...... 184

Figure 6.30: The comparison of the estimated shape factor Cd 2 by the tuned Watson model with test data ...... 185

Figure 6.31: The comparison of the estimated shape factor Cd 2 by the proposed model with test data ...... 187

Figure 6.32: The comparison of the shape factor Cd 2 for each model...... 188

Figure 6.33: The final combustion model result...... 193

Figure 6.34: The detailed combustion modeling result - Test Case #10 ...... 198

Figure 6.35: The local equivalence ratio calculation procedure...... 201

Figure 6.36: The local equivalence ratio as a function of various parameters ...... 204

xvii Figure 6.37: The comparison of the estimated φlocal by the proposed model with test data (RMS error % = 1.2 %)...... 207

Figure 6.38: The comparison of the estimated local equivalence ratio with the 17 ...... 209

Figure 6.39: The comparison of the estimated NOx with the 17 validation test data (RMS error % = 16 %)...... 210

Figure 6.40: The combustion model result of the validation test case #14 presenting the

best result of NOx prediction...... 212

Figure 6.41: The combustion model result of the validation test case #9 presenting the

worst result of NOx prediction ...... 213

Figure 6.42: The NOx model result of the validation test case #14 presenting the best

result of NOx prediction...... 214

Figure 6.43: The combustion model result of the validation test case #9 presenting the

worst result of NOx prediction ...... 215

Figure 6.44: The NOx emission and the start of fuel injection (SOI) ...... 217

Figure 6.45: The NOx emission and the start of combustion (SOC) ...... 218

Figure 6.46: The error analysis in NOx estimation model ...... 219

Figure 6.47: The error analysis in the local equivalence ratio model...... 220

Figure 6.48: The adiabatic burned gas temperature...... 221

Figure 7.1: The solenoid current profile estimation model...... 225

Figure 7.2: Estimated and test data injector current profile...... 227

Figure 7.3: Comparison of combustion modeling using the estimated current profile .. 228

xviii Figure 7.4: A crank angle resolved combustion model with NOx model ...... 231

Figure 7.5: Combustion and NOx estimation result...... 233

Figure 7.6: The trend of CIDI combustion vs. SOI ...... 236

Figure 7.7: The diagram of VEMT...... 244

Figure 7.8: Case 1: 1800 rpm, EGR 15%, single injection...... 245

Figure 7.9: Case 2: 1200 rpm, EGR 0%, single injection...... 246

Figure 7.10: Case 3: 2000 rpm, EGR 20%, single injection...... 247

Figure 7.11: Case 4: 2000 rpm, EGR 20%, 2-strike ...... 248

Figure 8.1: The final shape of the model structure ...... 251

Figure 8.2: The implementation of the model into mean value model...... 256

xix

LIST OF TABLES

Table Page

Table 1.1: A brief description of engine modeling techniques...... 5

Table 2.1: The model comparison between combustion and NOx model...... 26

Table 3.1: The typical values of Watson heat release model coefficients Eqn.(3.6) [43] ...... 37

Table 3.2: The coefficients in ignition model by the type of fuel used in Eqn. (3.7) [14] 39

Table 3.3: The Woschni heat transfer coefficients [21]...... 40

Table 3.4: The reaction rate constants in Zeldovich mechanism [17] ...... 49

Table 4.1: Test engine specifications...... 55

Table 4.2: Instrumentation list for the fuel injection rig...... 57

Table 4.3: Instrumentation list for the engine test ...... 64

Table 4.4: Summary of fuel injection rig test condition and results...... 74

Table 4.5: Range of engine test conditions...... 75

Table 4.6: Summary of engine test conditions...... 76

Table 4.7: Comparison of the trapped in-cylinder mass estimation ...... 90

xx Table 4.8: The result and effect of modification of an optimum compression ratio for the single fuel injection cases at 1800 rpm, pulse width 500 µ sec ...... 93

Table 5.1: Summary of the back pressure effect...... 98

Table 5.2: Fuel injection rate model evaluation: Model 1 and 2 ...... 102

Table 5.3: Coefficients comparison of model #1 and #2 used in Table 5.2 ...... 104

Table 5.4: Nomenclature for coefficients at corresponding layer in the model...... 107

Table 5.5: Coefficient model evaluation...... 108

Table 5.6: Coefficients set calculated by model #1 and model #2 ...... 109

Table 5.7: Comparison of each model by standard deviation % ...... 118

Table 5.8: Comparison of each model for coefficient A1 by std % ...... 119

Table 5.9: Comparison of each model for coefficient A2 by std % ...... 125

Table 5.10: Comparison of each model for coefficient A3 by std % ...... 129

Table 5.11: Summary of the final model for coefficient estimation...... 130

Table 5.12: Comparison of coefficients calculated by the final model ...... 131

Table 5.13: Model coefficients to be used in injection rate model...... 132

Table 5.14: Comparison of the model with test data by the total injection fuel quantity135

Table 5.15: Comparison of coefficient model by needle lift A1 ...... 138

Table 5.16: Comparison of coefficient model by needle lift ...... 139

xxi Table 5.17: Comparison of the model by the total injection fuel quantity: Current and needle lift ...... 140

Table 6.1: Start of combustion (SOC) and ignition delay time of test data at 1800 rpm 145

Table 6.2: Validation of ignition model...... 148

Table 6.3: Comparison of estimated SOC with test data for each fuel injection...... 149

Table 6.4: Statistical evaluation of ignition model for each fuel injection by the...... 151

Table 6.5: The summary table of combustion model parameters estimation model ..... 154

Table 6.6: Test condition and combustion model parameters calculated by the least.... 158

Table 6.7: The model evaluation by the RMS error ...... 167

Table 6.8: The comparison of the burning mode factor model...... 169

Table 6.9: The model evaluation by the RMS error ...... 174

Table 6.10: The detailed values of the shape factor C p1 estimated by each model...... 176

Table 6.11: The model expression and their evaluation by the RMS error ...... 182

Table 6.12: The model evaluation by the RMS error ...... 188

Table 6.13: The detailed values shape factor Cd 2 estimated by each model ...... 189

Table 6.14: The final estimation model of the combustion model parameter ...... 190

Table 6.15: Test data set for the combustion model validation ...... 191

Table 6.16: The comparison of the combustion model parameters of the test data and with estimated data...... 192

xxii Table 6.17: The comparison of the performance data of the validation test cases by the combustion model...... 196

Table 6.18: The NOx test data for parameters identification and the calculated local

equivalence ratioφlocal ...... 202

Table 6.19: The model evaluation by the RMS error ...... 206

Table 6.20: The estimated local equivalence ratio φlocal for the 20 parameters identification test cases by the proposed model...... 208

Table 6.21: The NOx estimation result for the 17 validation test cases...... 211

Table 7.1: An example of the virtual test run schedule for 5-strike fuel injection case . 223

Table 7.2: The current profile test data at various pulse widths at 1800rpm...... 226

Table 7.3: The additional estimation model ...... 229

Table 7.4: The summary of the models developed so far in the study ...... 230

Table 7.5: The engine operating condition, result of combustion and NOx estimation model...... 232

Table 7.6: The range of variables to be extrapolated...... 234

Table 7.7: Model verification test run by extrapolation ...... 235

Table 7.8: The operating conditions of virtual test run...... 243

xxiii

NOMENCLATURE

θ = crank angle [CA] h = enthalpy [kJ/kg]

SOI = start of injection [CA] PW = fuel injection pulse width [ µ sec]

SOC = start of combustion [CA] R = gas constant [kJ/kg/K]

3 ω = crank shaft angular speed [rad/sec] Vd = engine displacement [ m ]

3 ρ = density [kg/m ] m& f = fuel injection rate [g/sec] m& air = air flow rate [g/sec] m& egr = EGR gas rate [g/sec]

P1 = intake pressure [bar] Pr = common rail pressure [bar]

Pb = back pressure at SOI [bar] T1 = intake temperature [K]

T f = fuel temperature [°C ] N = engine revolution speed [rpm]

φ = equivalence ratio [-] J = rotational inertia [kg/m2] u = internal energy [kJ/kg] h = enthalpy [kJ/kg] q& w = heat transfer rate [kJ/kg] H u = low heating value of fuel [MJ/kg]

F1 = mass fraction of the burned gas in intake manifold [-]

IMEP = indicated mean effective pressure [bar]

Cv = specific heat [kJ/kg/K]

xxiv 1 CHAPTER 1

INTRODUCTION

1.1 The diesel engine and research background

In daily life, a vehicle is frequently said to be “a necessary evil.” This is because although it provides great convenience in our daily activity, there are also problems associated with it, such as air pollution. It is so natural, therefore, that a more efficient and less pollutant emitting engine is being sought by the automotive industry. With its high thermal efficiency and lean operation capability, the Diesel engine is a viable candidate, but inherent emission problems must be solved. The high thermal efficiency of the Diesel engine means less greenhouse gas emission, such as CO2, compared to the gasoline engine, which is currently becoming the most important and critical issue to be solved, especially in the European market. Moreover, emission problems have also been significantly improved owing to advanced technologies such as the common rail system, which is in recent production vehicles to comply with strict pollutant and noise standards. However, upcoming emission standards in 2007 or 2010 are going to be very difficult to meet. As a result of this trend, the penetration of Diesel engines into the European passenger car market has kept increasing, from 10% in the 1990’s to 30% in 2001 and approaching 60% in the same European countries..

Owing to the enormous endeavors of researchers to overcome the barriers associated with the Diesel engine, there have been significant advances in Diesel engine technology such as Variable Geometry Turbocharger (VGT) for intake air control, common rail system for precise fuel injection control, Direct Injection (CIDI) for efficient combustion, Exhaust

1 Gas Recirculation (EGR) control for NOx reduction, and the after-treatment system such as a diesel particulate filter. An example of a typical Diesel engine system applying these current technologies is illustrated in Figure 1.1.

Figure 1.1: A simplified schematic of the diesel engine system

2 The problem in applying these new technologies is that each component cannot be operated without affecting other components and reducing the performance. For example, increasing intake air boost pressure by changing the VGT vane angle reduces the EGR flow, consequently increasing NOx emission. In other words, since there are strong interactions among system components in a modern Diesel engine, taking into account these interactions and providing proper control is a requisite to maintaining optimum performance and reducing emission in the Diesel engine. Conventionally, look-up tables for the optimal operation control of each component are generated through extensive off- board dynamometer mapping tests over all operating conditions (engine speed, load, and environmental condition). Then, these tables are used on-board in the engine by interpolating operating points and employing adjusting parameters to consider other effects, such as temperature, etc. Thus, a significant amount of dynamometer tests are usually required for each control parameter. This has been the conventional approach so far and it can be more easily understood with the help of Figure 1.2 (a). However, due to computer performance upgrades in current vehicles in order to satisfy growing demands such as emission regulations and drivability, an on-board model-based control becomes required and possible. For this approach to be meaningful, appropriate and accurate models of the various engine processes need to be developed, validated and implemented. On one hand, such models need to accurately capture the effects of the growing number of actuators and sensors. But also, the models to be implemented on board fro real-time control need to be simple and computationally fast. This leads to a hierarchy of models with varying levels of details imbedded into each other, so that accurate, but fast controllers can be developed.

3 Model Off-board mapping test validated by a real on a real dynamometer dynamometer test

Off-board mapping test on a virtual dynamometer Motive for the Change: Generating the map Tighter emission and driveability requirement Developing the model

Engine control Engine control by map by the model embedded in control model (MVM)

(a) Conventional control concept (b) Current control concept

Figure 1.2: The change in the engine control concept

The kind of models which can be used for the engine control and modeling are classified as shown in Table 1.1. As far as the complexity, a black box model is the least complicated and CFD the most complicated one. A crank angle resolved model could be applied whenever there is a need for exploring the engine parameter as a function of the crank angle such as cylinder pressure and chemical compositions. This approach has also the advantage of the efficient prediction of the engine combustion when combined with a single-zone combustion modeling approach especially for the purpose of the virtual engine dynamometer calibration test.

4 Model Description Comment Black box • Spatially and temporally lumped. On-board • Relationship between input and output. applicable • Correlations obtained by static mapping of test engine. • No physics considered. Mean value • Spatially lumped but temporally resolved. (engine cycles) On-board (MVM) • Low frequency dynamics for control purpose of air and applicable EGR loop. with • Combustion is not resolved and can be modeled with a upgraded black box model. computer Crank- • Spatially lumped. (1 or multi-zone) Off-board angle modeling Resolved • Temporally resolved in a crank-angle domain. • Heat release and emissions are resolved explicitly. only • Possibility of studying, effect of fueling rate profile CFD and • Spatially and temporally resolved. Off-board Chemical modeling kinetics • Difficult to implement and computationally expensive. Usually, a few operating condition studied. only

Table 1.1: A brief description of various engine modeling techniques

Since the EGR-VGT interaction is one of the most important factors in diesel emissions, this interaction can be sufficiently modeled with a MVM during engine transient. However, MVM treat the combustion (and emissions) as a black box. This means that the other important factor, the fueling schedule, is either not explicitly captured or a more sophisticated black box model needs to be developed. Therefore, it would be the optimal

5 combination when MVM is used for the control modeling of VGT and EGR interaction, together with a black box model for combustion model [1], [47].

1.2 Mean value model in diesel engines

A mean value model is a combination of the quasi-steady models and filling- emptying models and consists of several non-linear algebraic equations and first order differential equations, which come from the thermodynamic analysis for each control volume with space-averaged values of variables. Using this MVM approach, Upadhyay [1] has developed an EGR-VGT control model of the intake and exhaust gas dynamic models. As can be seen in Figure 1.3, through the control of EGR valve position and turbine vane angle during the fuel injection process, the desired EGR and air flow rate, and intake charge composition can be calculated. With this information, engine torque or emissions are evaluated by a regression technique in a black box fashion using a modified Jensen’s correlation. Finally, this information is used in controlling the input variables to get the optimal performance from the engine. Thus, in this way, the high frequency combustion model and low frequency models such as air dynamics, turbo dynamics and crank shaft dynamics can be combined to provide useful information to be utilized in automotive control application. However, as stated before, this coupling is only as good as the black box models which describe the net effect of the fuel schedule and subsequent contribution on the torque generated on the crankshaft, pressure, temperature, composition and emissions of the exhaust flow.

6 m& f , SOI EGR valve position VGT vane angle

EGR/VGT Air Dynamics by Mean Value Model

Intake Intake Air EGR chemical pressure flow rate flow rate composition (temperature)

Engine combustion by black box model

Torque = f (P1 ,T1 , SOI,m& f ,m& air , m& egr )

Emissions = f ()P1 ,T1 , SOI,m& f ,m& air , m& egr

Temperauture rise = f ()F1 , SOI,m& f ,m& air , m& egr , N

Pollutant emissions: Torque, Exhaust Temperature NOx, Soot, CO, HC Engine dynamics: dN N ∑Torqi = J 2π i dt

Control for optimum performance

Figure 1.3: The CIDI engine control model using a MVM approach in EGR/VGT system

7 A representative result from the EGR/VGT control modeling with a mean value approach is shown in Figure 1.3, which shows the influence of EGR flow on the compressed air flow, and the interaction between the EGR and the intake air flow can be recognized. In this model, emissions and torque models were not developed and validated. But later on, a torque model was developed and validated with a black box approach by Hopka [48], in which the effect of the multiple fuel injections (which is currently the major motive in the Diesel engine research) was not studied.

w/o EGR flow

Figure 1.4. A sample result of EGR/VGT interaction modeling, Upadhyay [1]

Although a MVM does not explicitly describe the physical details of the system, particularly the combustion process, it does provide results on the dynamic interactions among the various systems, and can be an efficient tool for the purpose of control system design and diagnostic algorithm development [1], [8]. Consequently, MVM is an appropriate approach for the simulation of airflow in an engine where there is no complex mechanism such as chemical reactions. However, since only the total fuel flow rate is used in the current MVM [1], it is impossible to study the effects of multiple fuel 8 injections. This is a major drawback of the current MVM. In order to satisfy increasingly stringent emission standards, it is almost impossible to imagine a new generation of Diesel engines without the multiple fuel injections. Therefore, an improved and validated black box combustion model becomes necessary in order to take into consideration the effect of the multiple fuel injection profile, and use such a model to optimize and control recent and upcoming Diesel engines.

1.3 A crank angle resolved CIDI engine combustion model

As mentioned before, it needs to be emphasized again that this study is not concentrating on the detailed analysis of the CIDI engine combustion (as the KIVA code addresses), but on the development of a combustion model for model-based control of the CIDI engine to provide a tool for the virtual engine dynamometer test or to improve the black box type combustion model in the mean value engine model, especially for the case of the multiple fuel injections strategy.

1.3.1 Motivation of the research

As can be seen from the discussion so far, torque and emissions models considering the effect of multiple fuel injection profile have not been developed and validated in current MVMs. Moreover, instead of using a simple mathematical regression technique based on the extensive dynamometer mapping, the methodology to get correlations to be used in the black box combustion model needs to be improved.

In Diesel engines, the fuel injection timing plays a critical role in the phasing of the combustion, and hence the emissions and torque production. This is alike the spark timing in an SI engine. However, with the advent of the common rail technology and injectors capable of 3 to 5 injections per stroke ( 7 to 9 in future generations), there are multiple parameters defining the fuel injection schedule (and subsequent) combustion. Extensive experimental mapping of an engine by systematically varying all available parameters is an impossible task. Therefore, a simple but efficient diesel engine combustion model capable of modeling the effect of multiple fuel injections is required to

9 be developed. Then, using this model, a series of virtual dynamometer test data can be generated and used to get correlations for torque and emissions as functions of all available parameters. These correlations can then be imbedded in a MVM. Moreover,

NOx emission including the premixed combustion will be calculated, which is difficult to calculate by the current commercial codes such as BOOST, GT-POWER, and WAVE.

1.3.2 Crank-angle resolved combustion model by a single-zone approach

In order to get a more general and time-efficient combustion model in the Diesel engine for the purpose stated above, the following methodology was adopted by this study: A single-zone combustion modeling of a CIDI engine in a closed cycle for a single cylinder for the numerical simulation, to be validated with experimental data. The reason why a single-zone approach is chosen is that it is computationally efficient and a complex model is not desirable considering the extensive virtual dynamometer mapping. Moreover, so far there has been no attempt to model the combustion of multiple fuel injections in the CIDI engine with a single-zone approach. A closed cycle simulation is often adopted in the combustion modeling to reduce the computation time. This is consistent with the intended use in conjunction with a MVM, where the flow rate (intake and exhaust) are explicitly modeled. Since only the period from intake valve closing to exhaust valve opening is considered, there is no need to consider the effect of variation among cylinders. Thus, a single cylinder model is adopted. These combinations can provide an efficient and satisfactory tool of diesel engine combustion analysis for the purpose intended when there are lots of engine parameters such as the fuel injection schedule for the multi strike case.

1.3.3 Research objective

Thus, from the discussion so far, the research objective of this dissertation can be summarized as developing a combustion model for the virtual engine calibration test and improving the current black-box combustion model in a mean-value approach by developing a method for CIDI engine combustion analysis and providing more general

10 correlations for torque and emission prediction with arbitrary multi-strike fuel injection. A detailed description of the research objectives is as follows:

‰ developing a program to obtain in-cylinder pressure, temperature, and exhaust species composition as a function of crank-angle for arbitrary fuel injection schedule: - specifying the significance of parameters used in heat release sub-model

- analyzing the effects of the fuel injection schedule on the NO formation and engine performance

- investigating the CIDI engine combustion phenomenon with multiple fuel injections.

- providing a tool that can explore into the virtual engine test cases prior to the actual engine dynamometer test.

‰ validating the model with engine dynamometer test data

‰ demonstrating the feasibility of using the model to perform a “virtual engine mapping”.

Following this introduction, Chapter 2 describes the literature review, Chapter 3 the modeling and Chapter 4 the validation test set-ups. Chapter 5 presents parameters identification for fuel injection rate model and combustion and NOx model are discussed in Chapter 6. Chapter 7 describes the virtual engine mapping test, and finally conclusions and recommendations are presented in Chapter 8.

11 2 CHAPTER 2

LITERATURE REVIEW

2.1 CIDI engine combustion modeling

The reason why modeling is conducted in almost every research is that it can predict the result of not-yet-conducted experiment and modify design variables by analyzing the estimated data without substantial testing time, and cost. Thus, combustion modeling for the automotive diesel engine is always adopted in engine research and demonstrates its usefulness by providing combustion mechanism and design insights.

In 1963, for the first time Lyn [7] phenomenologically explained the heat release mechanism of diesel combustion and his work has been considered as a stepping-stone towards describing the diesel combustion phenomenon. Henein [2], [3] may be the first researcher to attempt to model the Diesel engine combustion. He phenomenologically analyzed diesel spray combustion including evaporation and ignition. Thus, he provided a basic starting point for succeeding researchers. Then, Shahed et al. [4] made a thermodynamic cycle simulation with an NO formation model assuming local stoichiometric combustion. They assumed spray combustion is negligible and that there is no interaction between combustion gas packages. Hiroyasu et al. [5] devised the first mathematical multi-zone approach in droplet evaporation assuming stoichiometric combustion. They provided a basis for a multi-zone approach to diesel fuel injection. In their study, the burned gas temperature, which can be calculated by considering the combustion a polytropic process, is used for NOx modeling [6].

12 2.2 Single zone combustion model approach

There are two categories of combustion model, the thermodynamic model and the dimensional model. One of the major advantages of the thermodynamic model is its computational efficiency, while the dimensional model considers spatial distribution of all parameters, and thus requires substantial computational time. The thermodynamic models include single and multi-zone models, and mean value models. As stated in the previous sections, a mean value model has been adopted by some researchers for control and diagnostic purposes [1], [8], [47]. But the purpose of MVM is not for analyzing the Diesel combustion itself, but for control purposes so that modeling can be oriented on the result only. When adopting a single zone approach for the Diesel engine combustion, the cylinder charge is assumed to be a homogeneous mixture of ideal gas at all times. The instantaneous state of the mixture can be described by the mixture pressure, temperature, and equivalence ratio. Fuel burns instantaneously as it is added to the cylinder [14]. On the contrary to this, in a multi-zone model [5], [6] the mixture in the combustion chamber is divided into more than two regions: the unburned, the burned zone or the quenching zone near the wall. In this model, a single computational zone is created at each fuel injection and has its own separate thermodynamic history throughout the calculation. Each zone is treated with the single zone approach, in which all the properties are uniform in its zone, and is assumed to be composed of fuel droplets of the same size. Although multi-dimensional model (CFD) using such as KIVA, STAR-CD etc. can not prove the preciseness in modeling the Diesel engine combustion because of complicated combustion mechanisms, some researchers has used commercial package due to its relatively high predictability over other models [9], [10], [11], [12], [13].

As can be inferred from the discussion so far, due to its efficient computational capability and simplicity of application, a single-zone approach for CIDI engine combustion is popular, such as in Ramos [14], Reitz [9], and Assanis [3], [12]. Even with CFD model such as the KIVA code [24], getting a satisfactory prediction for the pilot injection combustion and emissions is difficult, so a single zone approach seems not a bad choice. From now on, discussion will be concentrated on a single zone approach.

13 In a single-zone model approach, there are some heat release rate estimation models for diesel engines [43], [81], [82]. The famous Vibe function is useful and frequently applied in spark ignition engines as follows.

θ −θ ( − a[ o ]m +1 ) x(θ ) = 1 − e ∆θ where , x(θ ) is the burned gas fraction at θ crankangle ,

θ o is the start of combustion (SOC ), ∆θ is the burn duration, and a and m are the shape factors.

However, it is hardly expected that the heat release rate in diesel engine can be estimated with this burn rate model due to the heat release behavior which is different from that of SI engines. Therefore, some researchers have proposed different heat release rate models for diesel engines.

Since there are two distinctive modes in diesel engines combustion such as premixed and diffusion, heat release rate model utilizing double Vibe functions is also applied in diesel engine combustion model. Two combustion modes are assumed to be the same form of Vibe function except the shape factors involved. But, this approach is not consistent due to the unique combustion mode in diesel engines.

Chmela and Orthaber developed a diesel engine heat release model by considering the fuel injection kinetic energy called mixing controlled combustion (MCC) [82]. According to the model, the heat release rate is described as functions of the injected fuel quantity and inlet turbulence strength. As the model name implies, they consider the diffusion combustion mode only in diesel engines, which is not a reasonable assumption. The importance of premixed combustion is significant both in emission and performance aspect, and thus should not be neglected in diesel engine combustion.

Kreiger and Borman proposed a heat release rate model using a gamma function describing the asymptotic formula of the shape factor, which depends on the combustion chamber configuration [81].

14 n−1 . m fiω ⎛θ −θ s ⎞ ⎛ − ()θ −θ s ⎞ m fi = ⎜ ⎟ exp⎜ ⎟ Γ()n ⎝ θ d ⎠ ⎝ θ d ⎠

where θ s is the SOC,θ d is thecombustion duration, ln Γ()n is the polynomialfunction of n, and n is theshapefactor.

But, there is no consideration about auto-ignition delay in this heat release model. The shape factors need to be estimated with test data.

The Watson combustion model [43] is represented by the superposition of heat release rate by the unique function of two combustion mode and generally adopted in numerical modeling of Diesel engine combustion even in a commercial code such as WAVE and BOOST. Therefore, due to its reasonable approach, the Watson model for the heat release rate will be applied in this study too. Assanis et al. [10] used the Arrhenius type of combustion model, which was prepared by Hiroyasu et al. [15] and frequently used in the multi-zone approach. In the single-zone approach, the heat release rate may account for both premixed and diffusion combustion by means of the Wiebe function, so it can be expressed by one or more algebraic formulas. But model coefficients in these formulas, which may vary with engine design details and operating conditions, are determined empirically by fitting with data [17].

Since the auto-ignition is a starting point for combustion, this needs to be identified precisely in a CIDI engine combustion modeling. Ignition is a phenomenon in which heat is released rapidly as a result of chemical reaction of the fuel. Actually, ignition is initiated spontaneously when there are enough chain carriers to accelerate the chemical reaction. To identify this chain reaction step in the reaction system is a key point in auto-ignition mechanism. Therefore, the auto-ignition is an important sub-model in the CIDI engine combustion model. For example, the ignition models such as Henein [16], Heywood [17], and Hardenberg [18] could be applied due to their simplicity. When a more detailed chemical reaction is involved, some models like Westbrook [19], Minetti [20] using the CHEMKIN code need to be examined. There is a study in which the single-zone model using double Wiebe functions is used, and ignition delay is neglected

15 [25]. But, in Diesel engine combustion, auto-ignition determines all the subsequent processes, so ignition should not be disregarded in order to get a reasonable result.

For the heat transfer model, the Woschni correlation [21] can predict fairly well result in automotive engines. Due to its low computation cost and efficiency, a closed cycle simulation is often adopted in engine modeling by several researchers such as Assanis [12], Reitz [9], [23], and Hiroyasu [5]. A closed cycle is defined as the engine period from the intake valve closing (IVC) to the exhaust opening.

2.3 Fuel injection in diesel engines

It would not be overemphasized to say that the fuel injection system in modern diesel engines is the most important factor influencing the performance and emission. Since the fuel injection is a starting point in the diesel engine combustion, all the subsequent processes to occur in the combustion chamber are determined by this. Therefore, it is appropriate for this study to start from the consideration of the fuel injection system. Thus, both the understanding the fuel injection phenomenon itself and measuring the exact quantity and schedule of the injected fuel are important in diesel engine research.

The two representative methods developed so far in measuring the injection fuel rate are the Bosch method [54] and the Zeuch method [55]. The major difference of these two methods is the high frequency noise after the end of injection in the Bosch method [56]. The Zeuch method is based on the fact that the volumetric increment is measured by the rate of pressure change in the pressurized enclosure. On the other hand, Bosch developed a technology applying and analyzing the wave propagation phenomenon at high pressure flow system. The method states that the injection flow rate is proportional to the pressure in the propagated wave. Therefore, this method is appropriate only if the correct pressure measurement is guaranteed. With this reason, the Bosch method is widely used in modern diesel engine research and application. Another fuel injection method is based on the fuel electric charge which is generated when the fuel droplet hits a slant plate [59]. But, this method is not useful in modern multiple fuel injection system.

16 Anyway, estimation of the fuel injection rate in a running engine is done by applying the variable discharge coefficient estimated with information such as needle lift, injection pressure, and injector geometry [57], which is not easily done in actual engine applications. There are some studies on fuel injection rate applying the driver’s pedal (rack), fuel temperature, and engine speed. While Assanis et al. developed an injection estimation model for the total fuel injection [77], Gamo et al. developed and validated the estimation model as polynomial functions of the engine speed and rack position [78] :

2 m& f ()t = ω (t + 0.5 )(a0 + a1 x(t)+ a1 x(t) )

The fuel injection process is very complex one in diesel engine which is in high pressure environment. The fuel injection determines the fuel spray behavior. The spray mechanism is also composed of a series of process prior to the combustion such as the fuel droplet break-up, coalescence, atomization, penetration, evaporation, mixing, wall impingement, and air mixing. All these processes are influenced by the fuel injection. For example, the spray characteristic is good with a sharp-edged nozzle because the injection pressure becomes high by a reduced flow area with the nozzle edge, resulting in a long penetration and sufficient air mixing time [58]. After these spray process, an actual auto- ignition occurs with additional phenomenon of the chemical reaction during ignition delay. In other words, the fuel injection and spray are the determining factors in fuel ignition in the diesel engine combustion chamber. The simple spray parameters relating to diesel engine combustion is the Sauter Mean Diameter (SMD), which represents the degree of droplet break-up during fuel injection. Some researches have been done to get the physical correlation in terms of the engine operating conditions using CFD code. Hiroyasu proposed a useful correlation for the SMD estimation which can be applied in diesel engine combustion [60]. It is due to the common rail system that all these fuel spray process could be precisely realized in diesel engines without compromising the performance, resulting in the focus of the current vehicle application.

The common rail fuel system is widely used in modern diesel engines because of its precise and convenient control of fuel injection behavior. One example of the advantage is that the high fuel injection pressure is available at high load. Owing to the high

17 injection pressure, the injected fuel can travel deep into the combustion chamber overcoming the fluid resistance. As a result, sufficient time for mixing with surrounding air and fuel drop evaporation is available. There are lots of parameters to consider in the fuel injection phenomenon such as the start of fuel injection, injection pressure, fuel injection rate shaping, dwell time between injections, and injection pulse width. All these factors need to be carefully investigated to get the desired result in diesel engine combustion. Owing to the common rail system, a more flexible fuel injection strategy is possible such as the pilot fuel injection combustion, which will be covered in the next.

As early as 1937, the pilot fuel injection was experimented to reduce combustion noise and allow for poor ignition quality fuel use (low Cetane number). Now, the pilot injection is being used to shorten the ignition delay and to control the rapid pressure rise for emission reduction. When the portion of premixed combustion is relatively large, then the pressure gradient becomes large, and the temperature high. Therefore, premixed combustion needs to be controlled optimally. The method to reduce the pre-mixed combustion is to decrease the ignition delay in the diesel engine with the combustion heat of the pilot fuel injection. This is the basic background for applying the pilot fuel injection in the Diesel engine. So, whenever a long ignition delay is expected so that premixed combustion becomes large, pilot combustion presents an advantage over a long ignition delay. However, when premixed burning is small at high loads, the effect of pilot injection becomes relatively small [26]. The disadvantage of the pilot injection combustion is that since the injection timing of the pilot is generally significantly earlier than TDC, ignition delay becomes so long that the premixed combustion would prevail in the pilot injection. This premixed combustion enhances rapid pressure rise, so optimum control for the pilot is required for the merit of the pilot to dominate over the disadvantage. Minami et al. [27] proposed a mechanism of pilot injection in reducing

NOx emission such that the heat release rate of main injection slows down due to dilution by already burned gas from the pilot injection, which results in lacking of the necessary oxygen. Reitz et al. [28] experimentally investigated the effect of double pulse split injection on soot and NOx emissions. They found that as more fuel was injected in the first injection, NOx emissions increased, while soot decreased and suggested that an

18 optimum amount of fuel of the first injection was somewhere between 10 and 25%. Even with a commercial package such as KIVA, they concluded that some more improvements were needed to predict the premixed combustion more accurately with the case of 10% fuel in the first fuel injection pulse.

Another advantage of the pilot fuel injection is the combustion noise reduction. Since sound pressure level increases with the increase of the premixed portion of main combustion, pilot injection reduces the pressure gradient and lower peak pressure so that combustion noise and vibration are also reduced. Some test results show this trend well [29]. Beidl et al. [30] showed that noise level is reduced by 5.5 dB at idle condition with pilot injection combustion technology in their AVL test engine. Russell et al. reported the noise reduction of 8 dB at 2000 rpm at full load condition [31] and they also commented that combustion noise was related to the combination of peak pressure rise and peak pressure. Cylinder pressure acts as an excitation force, and is transmitted and attenuated as it passes through all engine components, then radiated from the cylinder, the head as sound and turns into combustion noise.

Many emission-reduction technologies developed so far tend to increase soot while reducing NOx, and vise versa. For example, although retarding fuel injection timing by decreasing temperature can be effective in reducing NO, this results in a soot increase. But, there is also optimum injection timing with single injection. In other words, when the injection timing is after the top dead center, as the injection timing retards, ignition delay increases, and NOx increases. This fact was validated in an experiment by Shundoh et al. [26]. Therefore, whenever injection timing retardation after TDC is needed, pilot injection would be the solution. However, if the injection timing with a single injection is delayed as much as about 10°ATDC , then misfire is induced. Therefore, it can be said that the NO reduction mechanism with multiple injections by retarding the fuel injection timing in the Diesel engine is similar to the spark timing retardation in the gasoline engine.

Besides the fuel injection timing, fuel injection quantity also needs to be optimized. When the first injected fuel is large (over 50%), the effect is the same as single injection

19 case. As the first injected fuel quantity decreases, the effect of NO formation becomes similar to that of single injection retarded by a dwell period [24]. Or, Minami et al. [27] showed that there is a restriction on the pilot injection quantity beyond which NOx begins to increase, and they recommended that the reference value of premixed fuel quantity be about 12%. The effect of split fuel injection on NOx reduction is well studied by Gao [32], who states that NO is reduced with split injection by retarding the main fuel injection timing.

As can be seen from the discussion so far, multiple fuel injections are, therefore, at the center of current diesel engine technology. All of these technologies are possible owing to the introduction of a high-pressure common rail fuel injection system and high speed electro-hydraulic injectors. The difficulty for multiple fuel injections strategy comes from the fact that the time for multi strike injections should finish in the very short period. However, this is quite difficult to achieve because there is the inertia of the injector system and the driving electric force is not easily recharged in a short period of time. In reality, it is currently known that the inertia of the injector system is the barrier to the flexibilities in fuel injection strategy. However, current production systems are capable of 3 to 5 fuel strikes, with 5 to 7 strike possible within a few years.

It is generally known that the reason why soot decreases by multiple injections is that soot is oxidized by oxygen which is supplied during the dwell time, that is to say, subsequent injections provide better mixing by entraining air into the combustion zone [12], [13], and [33]. In the single injection combustion, the injected fuel with high momentum penetrates to the rich, relatively low temperature region at the jet tip and continuously replenishes the rich region, producing soot. In a multi strike injection, however, the secondly injected fuel enters the relatively lean and high temperature region, which results from the first fuel injection. In addition, the soot cloud from the first injection is not replenished with fuel; instead, it continues to oxidize with the incoming oxygen. In this case, the dwell time between injections is important and needs to be optimized to sustain the oxygen supply and high temperature in the jet tip region [24]. When the dwell time is long, then there appears the premixed combustion in the

20 following combustion by subsequent injection, resulting in rapid rise of the heat release. The role of each fuel injection in multi strike injection could be explained as follows. • Pilot: increasing the in-cylinder temperature in order to enhance ignition, i.e. shortening the ignition delay and reducing the portion of pre-mixed combustion. It has been generally proposed that the pilot duration needs to be the same as that of the ignition delay period and that the objective of pilot injection be to have only a small fraction of the fuel take part in the rapid combustion period; • Pre-main: dividing the main fuel to reduce fuel quantity during main injection period and there is an optimum quantity for emission and performance; • Main: main power source with reduced peak pressure and temperature with nearly zero-portion of premixed combustion due to delayed fuel injection timing; • Post-main: nearly the same reason as the pre-main injection; • Post: increasing the exhaust gas temperature in order to facilitate after-treatment system such as DPF, DOC or accelerate the decomposition process of emissions.

1st Generation Common Rail Pilot Main Post

2nd Generation Common Rail

Pilot Pre-Main Main Post-Main Post

Noise control Performance control After-treatment at cold, low load

Figure 2.1: An example of a multi-strike strategy with common rail system 21 2.4 Emission modeling

A big and basic concern about the Diesel engine is the pollutant emissions and noise, which are the inherent problems of the Diesel engine combustion. It is the first priority and requisite, therefore, to reduce these emissions and noise in the Diesel engine.

NOx is composed of NO, N2O, and NO2, mostly NO. N2O is intermediately formed under the extremely lean atmosphere with EGR, and the effect on NO formation is found to be negligible [35]. Generally, there are 3 kinds of NO formation mechanisms: thermal NO, prompt NO, and fuel-bound NO. Most of NO is formed by highly temperature dependent reactions known as the Zeldovich mechanism, which is well established and whose predictiveness is validated so far. Moreover, almost all NO models can be explained by this Zeldovich mechanism. Some NO is formed in the combustion zone during combustion; it is ‘promptly’ formed, not formed in the post-flame zone. Fenimore [37] suggested that prompt NO is dominant at a low temperature, below 1,800 K, and in fuel rich environments. Its contribution to total NOx is only below 10% of the total NO. However, there has been little study to include prompt NO in the Diesel combustion model so far. Fuel-bound NO is formed from the nitrogen included in the fuel. Therefore, when the fuel considered is not nitrogen-bound, there is no need to consider it. However, other sources of nitrogen, such as from engine oil, could be considered in a real engine. NO is a strong function of local temperature so that the accuracy of temperature prediction determines that of NO formation. Residence time for chemical reaction of NO is another important factor. According to temperature and residence time, there are 3 approaches to NO modeling: mean cylinder gas temperature, fully mixed burned gas temperature, and adiabatic multi-layered burned gas temperature. NO formation is very highly temperature dependent and there is a large temperature gradient in the combustion chamber. We need, therefore, to take into account this fact in making NO model.

Heywood et al. implemented the first NOx model in 1970 [38] with constant specific heats for both the burned and unburned gases and an isentropic compression of the gas. But, the mean gas temperature, which is calculated from a single-zone approach, is too low for NO formation to be predicted and used for NO formation modeling. The fully mixed gas model is a homogeneous model whose temperature and composition are

22 assumed to be uniform in the burned gas. The temperature calculated from this model over-predicts NO by neglecting the effect of the residence time. In reality, the first element to burn has the highest temperature and longest residence time. The other model is a non-mixing (unmixed) model, where an adiabatic process is assumed among discrete elements in the burned gas and a one-dimensional temperature field is created as the combustion proceeds. The condition of the adiabatic process could only be justified by stating that most of NO formation takes place over a short time so that the error from neglecting the heat transfer is thereby minimized [35]. But this adiabatic assumption could introduce inaccuracy in NO modeling, particularly at a low speed and load condition. Several researchers such as Heywood [35], Hiroyasu et al. [5], [6], Blumberg [36], Lavoie et al. [39], and James [40] employed nonetheless this concept in NO modeling. Police et al. [41] used the polytropic process instead of isentropic process. To conclude, although the homogeneous model is still useful due to its simplicity, almost every researcher today believes that the non-mixing model is more accurate.

When preparing NOx formation modeling in an engine, most models need a calibration procedure to match the predicted data with experimental data. Although the calibration methods are different with each model, burned gas temperature is used to calibrate with its calculated data. But, considering the degree of dependency of NO formation on temperature, it would be hard to admit that this calibrated burned gas temperature is appropriate for NO modeling. Even with the KIVA code, Reitz et al. [24], [46] applied a calibration constant in NO formation rate calculation, which needs to be used in the final concentration. It would be better to consider the trade-off relationship with soot and NOx in preparing NOx formation modeling in an engine. The difference between soot and NO formation is that the soot concentration is governed by the formation and oxidation of soot during the engine cycle. No soot formation occurs after the end of heat release while soot oxidation continues even during expansion stroke. The best known modeling for soot formation would be that of Hiroyasu [5]. Soot oxidation (destruction) model is best described by the Nigel-Strickland-Constable model [24]. The net rate of soot formation can be estimated by the difference of formation and destruction rates [5].

23 One of the issues attracting the interest of researchers is to study the role of exhaust gas recirculation (EGR) in reducing NOx emission by lowering combustion temperature through increasing heat capacity, increasing intake air temperature, and diluting the oxygen concentration. The latter one can be eliminated considering the lean combustion of the diesel engine such that the net effect of EGR would be reducing the ignition delay, which is the same effect of pilot injection. EGR could be one solution for the Diesel engine, together with the pilot injection, if properly controlled. Moreover, it has nearly the same effect as pilot injection in that it reduces ignition delay and premixed combustion by increasing intake air temperature [34]. Anyway, since the exact prediction of EGR flow rate in diesel engine combustion is important, some models for EGR estimation have been developed applying an orifice flow equation and polynomial function of available variables [53].

2.5 Combustion and NOx modeling

Since the thermo-chemical state during combustion is negligible in overall energy balance, the thermal NO formation process can often be decoupled from the main combustion reaction mechanism and NO is calculated by assuming the equilibration of combustion reactions. This was originally suggested by Zeldovich. The definition of decoupling is that NO could not be considered in combustion calculation by assuming that there is no chemical species dissociation, which affect the heat balance equation.

While a single zone approach was used in combustion modeling, for NOx modeling the burn gas temperature is required by adopting a multi-layer approach. The connection between combustion and NOx modeling needs to be clarified. It is sure that there is the temperature gradient in the burned gas due to progressive burning of fuel as shown in Figure 2.2. Moreover, the temperature stratification such as this is a phenomenon where

NOx is formed, and thus needs to be considered for NOx formation mechanism. Actually, Hiroyasu developed a phenomenological spray combustion model which consists of two models – one for the heat release model and the other for the emission formation model of predicting NOx and smoke emissions. Decoupling between these two models is appropriate because NOx is formed at higher temperature in the post-burned zone.

24

Figure 2.2: A conceptual image of the combustion flame in a diesel engine

One assumption made in single-zone combustion model approach is that there is no temperature gradient in the chamber. However, since NO formation is a very strong local phenomenon of temperature, this assumption could not hold any longer in emission modeling. Therefore, a separate treatment of the combustion and emission modeling is required as done by other researchers. The differences between combustion and NOx modeling are compared as in Table 2.1 to catch the purpose and concept of the two types of models. In multi-zone combustion modeling, a zone is allocated based on the fuel spray history, not on the burned mixture element. All the energy balance equations including the mass continuity are to be solved in each zone. This is different from that used in the NOx model.

Even in the 2-zone model, an unmixed model is frequently used to calculate the fully mixed burned gas temperature. In many studies, for NOx emission estimation a hybrid modeling approach is adopted. [61], [62], [63], [35], [36]. Rizzo, Molina, and

Ishida adopted a single zone combustion model, whereas a two-zone model for NOx calculation is applied. Heywood and Blumberg used a two-zone approach for combustion and the multi-layer concept for NOx model. Ishida used a single-zone approach and extend the single-zone to a two-zone model with additional assumption [63].

25 Model Combustion NOx

Cylinder Mean Temperature Temperature Profile of Burned Element 2500 Simulation Motoring 1800 Test

2000

1600

1500 Example 1400

1200 1000 Temperature, (K) Temperature,(K)

Figure 1000 Mean Burn Gas Mean Cyl 500 Burn Ratio Heat Release 800

0

600 350 360 370 380 390 400 410 420 430 440 450 260 280 300 320 340 360 380 400 420 440 460 Crank Angle, (deg) Crank Angle,(deg)

Multi Zone (Unmixed) Approach Single Zone and Zeldovich • NO is a very strong function of • The effect of neglecting the x local temperature temperature stratification is

insignificant considering efficient • Heat transfer is neglected during short period of time, when an computational time. isentropic process is prevailing • Uniform temperature Important Assumption • Although the energy contribution • Although in the viewpoint of can be neglected, burned gas overall energy, this temperature temperature is of course a source of stratification could be neglected, it error, but it is negligible is needed in NOx formation

Combustion analysis including To calculate the local temperature Purpose of pressure, temperature, and others that is supposed to be higher than model mainly for engine performance the mean cylinder temperature

Local temperature is calculated in Mean cylinder gas temperature is each element. A higher temperature Comments calculated. But this is not appropriate needs to be considered for NO to for NO modeling x x form

Table 2.1: The model comparison between combustion and NOx model

26 2.6 A mean value engine model

Since a crank-angle resolved combustion model is too complicated to be practical in powertrain control, a mean-value modeling approach gives an appropriate flexibility to this end. Dobner [64] established a mathematical model of internal combustion engine for control purposes. Then, a mean-value engine modeling technique for compression ignition engine was proposed by several researchers [51], [65], [66], [67], [68]. A mean- value engine model is based on the intermediate complexity model between a CFD and a simple transfer function model. Therefore, this approach is frequently adopted in power- train control purpose such as a sliding mode control theory [68], [1]. The PTSIM developed at the Center for Automotive Research at The Ohio State University, is a powertrain simulator adopting a mean-value model approach to vehicle power-train. A mean-value model can also be applied to the VGT-EGR flow modeling in diesel engines application, leading to a 7-state control problem [1]. A mean-value modeling result was compared with that of a crank-angle resolved filling-emptying model in gas exchange process case using experimental data [67].

2.7 After treatment system for diesel engines

In the real engine emissions and performance aspects, ultimate goal could not be accomplished by the engine-side control alone. In other words, optimization of the engine side control strategy is just a trade-off process among different control parameters as discussed earlier. In order to achieve this goal, several after-treatment systems can be used without penalties of engine performances by operating the engine within optimum conditions. From previously stated literatures, some strategies about current issues such as reducing the diesel NOx emission have been outlined. Unfortunately, some of the diesel engine’s inherent advantages work in the opposite direction against the after- treatment systems: low exhaust temperature requires high activity catalysts and gives a long light-off characteristic, and lean-operated or low hydrocarbon content in exhaust gas inhibits NOx reduction. Alleviating these problems through engine-based methods comes at the expense of engine efficiency and added complexity. Typically, the thermo- chemical management of after-treatment systems requires temporary alteration of the 27 engine control strategy. After-treatment systems, such as diesel oxidation catalyst (DOC) and diesel particulate filter (DPF), could get their most efficient results only when linked with the upstream engine-side control and analysis as in current SI engine emission control technology [24]. Despite the system complexity, the SCR system utilizing urea as a reducing agent is receiving a lot of attention in after-treatment technologies. Takiguchi et.al [69] developed the onboard SCR system for automobile applying the fact that the ammonia reacts selectively with NOx on a catalyst as a reducing agent under the lean and low temperature ()250 − 500°C condition by one of the following chemical reaction paths.

NO + NH 3 + 1 4O2 → N 2 + 3 2 H 2O (standard) (2.1) 1 2 NO + NH 3 + 1 2 NO2 → N 2 + 3 2 H 2O (fast)

But, there are some problems to be solved in SCR system to be applied in vehicles. Ammonia is so toxic that storage problem on board is not feasible. Another issue is that at high temperature, ammonia is decomposed into nitrogen and water. Therefore, for the proper SCR operation, the precise control of the gas temperature is required for the maximum conversion efficiency of SCR system. In other words, when the engine operating condition reaches a point where the exhaust gas temperatures become high, the SCR operation needs to be blocked to reduce the chance of ammonia leak (over-slipped). If the fast chemical reaction path in Eqn.(2.1) could be applied in the SCR system, the overall conversion efficiency improves, especially at low temperature ()≤ 300°C . Therefore, if an oxidation catalyst (DOC) is placed in front of the SCR which produces

NO2 for the fast reaction, then the performance of the SCR at low temperatures will be significantly improved [70]. Moreover, NO2 also react actively with PM at low gas temperatures [71]. Currently, the cost of an SCR system is estimated to be around $1,000 for a production heavy-duty engine. If this cost issue could be resolved in the near future, SCR system could become a must in diesel engine emissions system by combining together with other components.

Lean NOx traps were developed for gasoline direct injection engines to reduce the inherently high NOx emission due to the stratified lean operation. The principle of NOx

28 traps is that NOx is stored during lean engine operation and released and reduced by reducing catalyst in a fuel rich atmosphere. The efficiency of the NOx trapping is known to be mostly dependent on the storage ratio and temperature. The efficiency is the maximum at the gas temperature of 600 K or so [72]. The gas temperature can be controlled by engine combustion such as the post injection of fuel or using a burner. For the maximum performance of NOx traps, controlling the regeneration duration and timing is important so that a modeling of NOx accumulation and control strategy is developed in this field using adaptive control [73]. Kim developed a lumped model of NOx traps applying NOx storage efficiency estimation by a Gaussian function [74]. The diesel particulate filter (DPF) is used to trap the diesel particulates and burn the particulate with methods such as burner, fuel injection into the passage when the pressure drop builds up in the exhaust system to reduce the engine performance deterioration. Therefore, predicting the particulate accumulation by a pressure drop across the filter with pressure sensors is the most important in operating the DPF system. Most studies have been done on estimating soot loading by pressure drop. The hydrodynamic consideration in the filter flow is analyzed and modeled by fluid dynamics to find out which parameters is the most dominating in pressure drop [75].

Figure 2.3: A various flow pattern in a wall-flow type DPF [75] 29 Since most DPFs are wall-flow type, consideration in pipe, porous, and wall flow is needed. The performance of the DPF will be better if the catalyst such as Pt is coated on the surface of the filter (CPF). This is because the catalyst has the effect of lowering the ignition temperature of soot. The role of NO2 in soot combustion to improve the performance of the DPF is the same SCR system as mentioned before. Therefore, the combination of DOC and DPF is ideal for the optimum conversion efficiency of the DPF. Because of the high temperature associated with the soot combustion at regeneration phase, the issue of DPF material is also an important factor to be considered in design and durability. With the advent of multiple fuel injections in CIDI engines, all these after treatment system can be controlled. Then, a more sophisticated engine control technology is required. With an appropriate CIDI engine combustion model with multiple fuel injections to get some information about exhaust gas properties, it would be possible to get the maximum efficiency out of after-treatment devices. It is also possible to employ an atomizer for fuel injection into the heater for expediting the catalytic converter light- off [42]. Of course, by using post–injection in a multiple injection strategy to increase the exhaust gas temperatures, the maximum after-treatment performance can be accomplished. With the discussion so far, the following system configuration for CIDI engine after treatment could be conceived as in Figure 2.4. As can be seen in the figure, a definite amount of NO is oxidized in order to produce NO2 in DOC, which then will be used at DPF for carbon oxidation, which is the fast and low temperature reaction. In other words, all emissions including HC, CO are oxidized by the DOC. By removing HC and CO, the conversion efficiency of the down stream system could be at its maximum. After all, the first priority in the diesel engines after-treatment system will be the configuration issue to get the maximum conversion efficiency and extended durability of the system by taking into consideration of all possible factors. EGR gas can also be drawn downstream of DPF when soot is removed.

30 Injection command P ECU 2

Urea HC,CO, Temp. P NO, PM 1 SCR/ Engine DOC DPF NH 3

2NO + O2 → C + 2NO2 → 4NH 3 + 2NO2 + 2NO →

2NO2 CO2 + 2NO 4N 2 + 6H 2O Oxidation of HC,CO

Figure 2.4: A possible diesel engine after-treatment system configuration

2.8 Summary of literature review and research motivation

By reviewing the literature related with the diesel engine research, in order to have the optimal result both in the engine-side and the after-treatment system, the multiple fuel injections strategy in current diesel engine combustion control is becoming common and one of solutions to meet tightening emission regulations. Moreover, the cycle time for engine and vehicle development is being reduced for cost and competitive advantage in the automotive industry. Therefore, a more time-efficient and simple-to-use tool is a prerequisite in this field. Unfortunately, there has been no study in combustion modeling with a single-zone approach for multiple injections. Through this study, a methodology will be presented to model the CIDI engine combustion with multiple fuel injections with a single –zone approach in the next chapter.

31 3 CHAPTER 3

CIDI ENGINE COMBUSTION MODELING BY THE SINGLE-ZONE APPROACH

3.1 Introduction

In this chapter, the major modeling such as the CIDI engine combustion and NOx emission model will be described with their mathematical background. The theory related with CIDI engine combustion model by a single-zone approach is described next. For

NOx calculation, it was post-processed with information acquired from the combustion calculation such as cylinder pressure, burning rate, and residual gas fraction to calculate the burned gas temperature. Since it is widely known that ignition is the most important parameter in CIDI engine combustion, it needs to be modeled and predicted as precisely as possible. The subsequent phenomenon in CIDI engine combustion could be mostly influenced by the ignition.

3.1.1 Governing equation formulation

By applying the thermodynamic first law to a combustion chamber as a control volume during a closed cycle, the following energy balance equation can be written.

Rate of change of internal energy = Work done + Net heat transfer + Enthalpy change across the boundary

Necessary physical assumptions used in deriving a governing equation from the energy balance relation are (1) at any instant, the cylinder charge is assumed to be a homogeneous mixture of ideal gas, which is always in thermodynamic equilibrium

32 without thermal or chemical gradient in the chamber; (2) fuel is evaporated as it is injected from an injector. (No spray combustion is considered in detail); (3) the crevice flow and blow-by gas are not considered; and (4) combustion is modeled as a uniformly distributed heat releasing phenomenon. Then, the previous description for the energy balance in the combustion chamber can be expressed in mathematical form as follows: d dV d dV ()mu = − p + q& + h j m& j ()mu + p = q& + h j m& j dt dt ∑ dt dt ∑

Recalling the ideal gas law and the caloric perfect gas equation for internal energy expression, u = CvT and pV = mRT , the left-hand side in the equation can be recast as d dV d ⎛ pV ⎞ dV ()mCvT + p = ⎜Cv ⎟ + p dt dt dt ⎝ R ⎠ dt

And the first term in the left-hand side in the equation can be rewritten by applying the chain rule of the differentiation.

d ⎛ pV ⎞ pV dCv p dV V dp pV dR ⎜Cv ⎟ = + Cv + Cv − Cv dt ⎝ R ⎠ R dt R dt R dt R 2 dt

R dC d ⎛ R ⎞ 1 dR R dγ But, since C = , v = ⎜ ⎟ = − v ⎜ ⎟ 2 γ −1 dt dt ⎝ γ −1⎠ γ −1 dt ()γ −1 dt

pV ⎛ 1 dR R dγ ⎞ p dV V dp pV dR dV = ⎜ − ⎟ + C + C − C + p ⎜ 2 ⎟ v v v 2 R ⎝ γ −1 dt ()γ −1 dt ⎠ R dt R dt R dt dt

pV ⎛ 1 C ⎞ dR R dγ ⎛ C ⎞ dV V dp = ⎜ − v ⎟ − + p v +1 + C ⎜ ⎟ 2 ⎜ ⎟ v R ⎝ γ −1 R ⎠ dt ()γ −1 dt ⎝ R ⎠ dt R dt

pV dγ ⎛ 1 ⎞⎛ dV dp ⎞ C 1 = − + ⎜ ⎟ pγ +V , v = 2 ⎜ ⎟⎜ ⎟ Q ()γ −1 dt ⎝ γ −1⎠⎝ dt dt ⎠ R 1− γ

Hence,

33 . d dV pV dγ ⎛ 1 ⎞⎛ dV dp ⎞ mu + p = q + h m = − + ⎜ ⎟ pγ +V . () & ∑ j j 2 ⎜ ⎟⎜ ⎟ dt dt ()γ −1 dt ⎝ γ −1⎠⎝ dt dt ⎠

Substituting the heat generation term, q& with q& = Q& + q&w and rearrangement for the

dQ ⎛ 1 ⎞⎛ dV dp ⎞ pV dγ dq equation gives = ⎜ ⎟ pγ +V − − w − h m ⎜ ⎟⎜ ⎟ 2 ∑ j & j dt ⎝ γ −1⎠⎝ dt dt ⎠ ()γ −1 dt dt

d d Using the relationships: θ = ωt,= ω , the combustion heat release rate in terms dt dθ of a crank angle can be cast as follows. dQ ⎛ 1 ⎞⎛ dV dp ⎞ pV dγ dq 1 = ⎜ ⎟ pγ +V − − w − h m (3.1) ⎜ ⎟⎜ ⎟ 2 ∑ j & j dθ ⎝ γ −1⎠⎝ dθ dθ ⎠ ()γ −1 dθ dθ ω

dp 1 ⎡ ⎛ dQ dqw 1 ⎞ pV dγ dV ⎤ = ⎢()γ −1 ⎜ + + ∑ h j m& j ⎟ + − pγ ⎥ (3.2) dθ V ⎣ ⎝ dθ dθ ω ⎠ ()γ −1 dθ dθ ⎦

dQ dQ pV dγ 1 ⎛ dV dp ⎞ Net_heat_releas_rate, comb + w + = ⎜ pγ +V ⎟ (3.3) dθ dθ ()γ −1 2 dθ γ −1⎝ dθ dθ ⎠

The combustion model is to solve the 1st order differential Equation (3.2) in terms of cylinder pressure or temperature, which are related to each other by the ideal gas law. Eqn. (3.3) is also applied to locate the point of start of combustion in the analysis of experimental pressure data.

3.2 Sub models

In order to solve this governing equation, Equation (3.2), several sub-models for each term in the equation need to be introduced as constitutive relations.

3.2.1 Heat release rate model

For a complete and lean combustion without dissociation of chemical species, the heat release rate from combustion is expressed as:

34 dQ dm = H b , ddθ u θ

where Hu is the lower heating value of diesel fuel (~ 42.5 MJ/kg).

This expression is valid for the case of diesel engine combustion, which equivalence ratio isφ ≤ 0.8 . In order to have an expression for burning rate, dmb dθ , Watson heat release model [44] is introduced as follows, which is the revision of semi-empirical Wiebe function.

In CIDI engine combustion, two modes of combustion, premixed (p) and diffusion (d) are assumed to proceed simultaneously from ignition for a short time period, dmdm dm so total burning rate can be expressed as bd=+p . If the burn ratio is dddθ θθ

mb introduced as, M b ≡ , where m fuel _ inj is a total injected fuel, then the burn rate m fuel_ inj dm dM is, bb= m . In this expression, we need to have an expression for rate of burn ddθ fuel_ inj θ ratio, dMb dθ as functions of available parameters such as engine operating conditions.

Since the diesel engine combustion is composed of premixed and diffusion combustion, the total burn ratio change could be expressed with a weighting factor of β as follows.

dMdM dM bd≡+−ββp (1 ) ddθ θθ d where the weighting factor, β , is the burning mode factor defined by a ratio of accumulated fuel burned by premixed combustion mode to total fuel injected and given by the following experimental correlation:

0.37− 0.26 βφ==−mmp fuel_ inj1 0.926 ig t d (3.4)

35 where td is the ignition delay time in msec and φig is the equivalence ratio at the time of ignition. There is, however, a different definition for φig , which is defined as the overall equivalence ratio [17], [76]. This is possible because the detailed fuel injection profile is available. But, it seems reasonable to define in the previous way.

Watson proposed the following expressions for each mode of combustion to have a shape in which is as representative as possible of the diesel engine combustion.

The dimensionless burn rate function for premixed mode is given as,

ccp12p M p =−1(1 −τ ) , and the burn rate function for diffusion mode combustion is given by,

cd 2 Mcdd=−1 exp( − 1τ ) (3.5)

θ −θig where τ is dimensionless time from ignition given by, τ = , and ∆=θbendigθθ − ∆θb is a combustion duration which is usually given as 125 (crank-angle), but needs to be given by experimental data and large enough to finish the complete combustion. Actually, this burn duration is a function of engine speed and load. And, model parameters used in these correlations could be estimated by actual engine test and statistical treatment of the test results. Watson proposed the following correlations for parameters in his study [44],

−8 2.4 For premixed combustion: crpmtpd1 =+21.2510 ×( ×) , cp2 = 5000

−b d For diffusion combustion: cadig1 = φ , cccdd21= () (3.6)

Here, cd1 ,cd 2 should be determined with the engine test result and ccpp12, are used as the constants in CIDI engine combustion model. The typical values of the constant that used in the Eqn. (3-6) are summarized in Table 3.1.

36 No. Engine Type a b c d Turbocharged, direct- 1 14.2 0.644 0.79 0.25 injection, 6 cyl. truck

Turbocharged, inter- 2 cooled, V-8, direct – 16.67 0.6 1.2 0.13 injection. 2*displacement of the 3 7.54 0.65 0.93 0.22 Engine #1.

Table 3.1: The typical values of Watson heat release model coefficients Eqn.(3.6) [43]

Finally, the Watson heat release model could be summarized as,

dQ dmbb dM⎡ dM p dM d⎤ ==HHmHmu u fuel__ inj = u fuel inj ⎢ββ +−(1 ) ⎥ ddθ θθ d⎣ d θθ d⎦

Although this heat release rate model can be applied for the case of the single fuel injection, it can also be extended to the multiple fuel injection cases by applying the principle of superposition to the heat release rate from each fuel injection. The idea that the superposition principle can be applied for the multiple fuel injections for CIDI engine combustion model is going to be investigated in this study for the first time.

3.2.2 Ignition model

The actual ignition mechanism involved in diesel engine combustion is very complex. The diesel fuel spray behavior needs to be considered for a detailed and exact description of ignition phenomenon in a diesel engine combustion chamber. All the processes for the fuel to be ignited in diesel condition could be expressed as a simple correlation by considering the major phenomenon only. Of course, there are mechanical, chemical and physical processes for the fuel droplet to be ignited. However, with the single-zone

37 combustion model which requires an efficient estimation of the ignition timing, it would be inappropriate to apply the detailed and complete ignition model. Therefore a simple and effective model for the diesel engine ignition model is already proposed and applied without significant prediction error.

Usually, the auto-ignition time for the diesel fuel at constant pressure p and temperature T can be estimated by Arrhenius-type correlation, which is established by considering chemical reaction in ignition phenomenon as follows.

−n ⎛⎞Ta tApd = exp⎜⎟ (3.7) ⎝⎠T

where the values of the coefficients A, n, Ta are proposed by the type of fuel used and could be found in a related study in Table 3.2 [14]. In this research, constants that are adopted in Watson model [44], Assanis [10] studies will be used as A =3.45, n =1.02, and Ta =2100 K for the starting estimation. These parameters are the empirical coefficients so that these should be modeled and identified from the extensive engine test over an extended operating condition in order to predict the precise point of auto-ignition timing in CIDI engine.

38 Fuel Type A n Ta (K) Diesel-1 3.45 1.02 2100 Diesel-2 53.5 1.23 676.5 Diesel-3 0.0405 0.757 5470 Diesel-4 2.43×10−6 2 20,915.3 n-Cetane 0.872 1.24 4050 n-Heptane 0.748 1.44 5270 Kerosene 1.68×10−5 2 19,008.7 Cetane 4.04×10−10 2 25,383

Table 3.2: The coefficients in ignition model by the type of fuel used in Eqn. (3.7) [14]

In a real engine, the cylinder pressure and temperature are changing constantly due to the piston movement, during the compression stroke. Therefore, the ignition delay needs to be calculated by considering these varying situations of the cylinder temperature and pressure by summing up the instantaneous ignition delay time at each time step.

Thus, the total ignition delay time, tig from the dynamic fuel injection time, tinj can be calculated when the following condition is encountered:

t [C] ig dt ==1, Ct∫ (3.8) []cdtinj

where [C] is the concentration of chain carriers such as H 2O2 and []Cc is the critical concentration of the species when the ignition is supposed to occur [16]. Then, the ignition delay can be calculated as a function of crank-angle by:

θ = ωt . ig ig 39 3.2.3 Heat transfer model

Woschni [21] linearized the convective and radiative heat transfer model in a diesel engine for non-premixed combustion (but can be extended to other type of combustion with calibrated constants), and proposed a well-accepted heat transfer relationship. The heat transfer rate is expressed as, when heat transfer coefficient h is given by

0.8 0.8 (vmot + vcomb ) q& w = hA()Tw − T ,h = 0.00326p , B 0.2T 0.53 " vmot = c1v pis

" Vd Tign vcomb = c2 ()p − pmot pignVign

where Vd is the displacement volume, A is the heat transfer area, Tw is the cylinder wall temperature, v pis is the mean piston speed, B is the cylinder bore diameter and constants,

" " c1 and c2 are to be determined for operating condition. The values of these constants are summarized in Table 3.3.

'' '' Stroke c1 c2 ,m ⋅sec/°C

Compression 2.28 0

Combustion and expansion 2.28 0.00324

Gas exchange 6.18 0

Table 3.3: The Woschni heat transfer coefficients [21]

40 3.2.4 Fuel injection rate model

The injection mass flow rate of the fuel is supposed to be used as an input to a combustion model. Usually, the actual fuel injection rate profile is not being used for the real engine control application in the automotive industry, instead a simple square shape of profile is assumed for modeling purpose. Only the total fuel injection quantity is calculated as functions of some parameters such as the injection pulse width, engine speed, and common rail pressure. However, this estimation is so rough that it would be difficult to say that it represents the real injection profile which is crucial in CIDI engine combustion model. The detailed fuel injection profile can provide some useful information such as fuel injection quantity and equivalence ratio during the ignition delay time, which is required in Watson combustion heat release rate model, the burning mode factor, β as in Eqn. (3.4). Therefore, this is the main reason why a fuel injection rate model is required in Watson combustion model applications. The fuel mass flow rate can be expressed by the following equation through the decomposition of the relevant parameters:

m& f = ρ Q& f = f [I()t ; Pr , Pb , PW ,T f ] (3.9)

In the fuel injection rig test, the volumetric injection flow rate is measured together with some parameters such as common rail pressure, back pressure, injector solenoid current, and pulse width. Then, this volumetric flow rate needs to be transformed to the mass flow rate by fuel density calculation at an engine operating condition. The volumetric fuel injection rate through an injector,Q& f , can be expressed in terms of injection pressure, fuel density, and injector nozzle area. This can be expressed as following equation:

2∆p 2∆p Q& = C A = A , A = C A ( 3.10) f d nozzle ρ eff ρ eff d nozzle

41 where Cd is the discharge coefficient, Anozzle is the flow area of nozzle, ∆p is the pressure difference across the injector. The fuel density is calculated as functions of fuel temperature and pressure, which is already found to be useful and widely used in the research by the following equation:

ρ = −0.686×T + 839.7 + 5171067.96×831.7 β , kg (3.11) f v m3

where T f is in degree Celsius and β v is the bulk modulus of the fuel. When the fuel density and pressure is constant, injection rate is proportional to opening area of nozzle. And this opening area is determined by hydraulic force and magnetic force exerted on the plunger. Actually, injection pressure force can be a direct force in opening the nozzle. Only the magnetic force generated by the current signal can move the nozzle. Therefore, as far as the flow area is concerned, the injector solenoid current is the only important parameter to be considered. In other studies, calculating the discharge coefficient is generally adopted to correct the geometrical flow area. If an effective flow area can be calculated correctly, then injection flow rate can be easily estimated. The effective area of nozzle can be expressed as a function of needle lift, which in turn are functions of current and hydraulic injection pressure. When considering the movement of needle, the magnetic force generated by current signal is dominant. Therefore, fuel injection rate can be thought as a function of current. Namely, flow rate can be expressed as:

Q& f ≈ f (Aeff ) ≈ f ()needlelift ≈ f (currrent) at the constant pressure and temperature.

Since the only available parameter that changes during the fuel injection for each test shot is the current signal, modeling by the current signal was tried. Moreover, the current signal is basically constant independent of test conditions such as injection pressure and pulse width. Therefore, the current can be used as a primitive variable in fuel flow rate modeling. However, it is generally known that the injection flow rate is related with other parameters such as injection pressure, pulse width, and fuel temperature. These parameters can be considered for the injection rate parameters

42 identification procedure in Chapter 5. In that procedure, a stochastic estimation technique could be applied in acquiring the model coefficient set in the correlation [80]. A linear and a quadratic equation with respect to the injector current will be proposed and identified for its parameters with validation test results:

2 Q& f ≈ f ()I = A1 + A2 × I or Q& f = A1 + A2 × I + A3 × I

Since a crank angle resolved fuel injection rate is required in the combustion model, the following conversion is needed.

dQf dQf dt dQf 1 dQf 1 = × = × = × dθ dt dθ dt ω dt 6×rpm

dθ where the angular speed of the crank shaft is given by ω = = 6× rpm . dt Therefore, the mass flow rate per crank angle can be calculated as:

dmf dQf dQf 1 =ρ =ρ × dθ dθ dt ω

3 where for example the fuel density, ρ ≈ 800[kg m ] at T f = 50°C, Pr = 800bar .

3.2.5 EGR gas mass estimation

It is necessary to estimate the burned gas mass at the intake valve closing to calculate the total trapped mass in the combustion chamber. The EGR mass can be estimated by measuring the CO2 concentration in the intake and exhaust manifold as shown in Figure 3.1.

43 [CO2 ]egr EGR

[]CO2 Intake [CO2 ] o i Engine manifold Fresh air

Figure 3.1: EGR ratio calculation in the test engine

The EGR mass ratio xegr in the intake manifold is defined and calculated as follows:

m m n M ⎛ M ⎞ egr egr egr egr ⎜ egr ⎟ xegr = = = = yegr ⎜ ⎟ ≈ yegr min mair + megr nM ⎝ M ⎠

where, M = M b yegr + M o ()1− yegr ≈ M egr recallingthat M o = 28.97, M egr = M b ≈ 28.86 0.1 ≤ φ ≤ 1.0, n the EGR molefraction is given by : y = egr egr n

The carbon dioxide concentration [CO2 ]i in the intake manifold can be calculated with the following equation by assuming a perfect mixing of the EGR gas and incoming fresh air.

[][]CO2 i = CO2 e yegr + []CO2 o (1− yegr ) from which

yegr {}[][]CO2 e − CO2 o = [][]CO2 i − CO2 o from which the EGR mole fraction can be written:

44 {[][]CO2 i − CO2 o } yegr = ≈ xegr (3.12) {}[][]CO2 e − CO2 o

Therefore, EGR ratio can be estimated by measuring the CO2 concentrations in the intake and exhaust manifold.

yegr The mass of EGR is then calculated by megr = mair . 1− yegr

3.2.6 Other sub models

In order to calculate the specific heat ratio of the mixture gas in a diesel engine,γ , a polynomial function of temperature (Tcy ) will be used due to the simplicity of the correlation, as Assanis proposed [10] :

−−582 γγ=−××+××0 610TTcy 110 cy .

Next, when the pressure data at IVC is available, the initial temperature at IVC is calculated by the ideal gas law. Otherwise, the initial temperature at IVC is calculated as follows. From the intake manifold energy balance:

EGR⎛⎞ EGR mTaf,, o+=+ m a T egr⎜⎟ m af m a T in 100⎝⎠ 100

where To is the temperature of the fresh air or ambient air, Tegr is the EGR gas temperature, ma, f and ma are the masses of fresh air and total mixture including the EGR gas, respectively. Thus, Tin can be calculated by this equation with as function of the mass flow rate of the fresh air and EGR gas as the measured test data. The mixture temperature at the intake valve closing can then be estimated by considering the energy balance in the combustion chamber as follows:

45 ⎛⎞EGR mTrr++⎜⎟ m af, m a T in 100 T = ⎝⎠ ivc EGR mm++ m af, a100 r

This temperature determines the prediction accuracy of the model. Therefore, every data needs to be given as input data for the calculation of temperature at IVC. With the ideal gas law, the mixture pressure at IVC is calculated as:

pivc= mRT cy ivc ivc V ivc

When there is cylinder pressure test data available, then the calculation presented so far is not required. Instead, the cylinder temperature can be directly calculated from the measured test data of the cylinder pressure. As can be seen in the equation, the trapped mass at the valve closing needs to be accurately estimated to get a correct initial condition for combustion model.

The same calculation procedure as Heywood suggested was adopted for the unburned or burn gas properties [17]. These include the thermodynamic properties such as the total number of mole of the burned and fresh gas, molecular weight and enthalpy of chemical species and so on can be calculated. A constant heat of vaporization, 270 kJ/kg, was used for instant evaporation of the light diesel fuel [17].

3.3 Numerical solver for the ordinary differential equations

To solve numerically a first order ordinary differential equation for the governing equation, Eqn. (3.2), the time marching, predictor-corrector scheme or 2nd order Runge- Kutta method is adopted as a solver. One degree of crank angle is chosen as the unit of the calculation step because it gives the computational efficiency.

46 3.4 NOx modeling

NO formation is known as a non-equilibrium process controlled by chemical kinetics and take place in the post flame region. NO modeling is well established, which is based on the extended Zeldovich mechanism as follows. The NOx model is divided into two portions: one is the part to calculate the temperature related with NOx formation, and the other is to solve the set of chemical reaction equations.

3.4.1 Extended Zeldovich NO formation mechanism

The extended Zeldovich mechanism for NOx is represented by the following chemical equation which is reduced from the original complete chemical reactions:

O + N2 = NO + N

N + O2 = NO + O

OH + N = NO + H

To solve these chemical equations, some supplementary chemical equations are also needed for the equation set to be determinate as follows:

OH + O = O2 + H

OO2 = 2

NO22+=2 NO

The numerical expressions for these chemical reactions can be solved with some assumptions as follows. The equilibrium state is assumed for the relevant species such as

H, O, OH, O2, and N2. Since N atom is a highly reactive species, its concentration can be assumed to be at a steady state. Thus the following relationship is possible:

d[]N ≈ 0. dt

47 Lastly, fuel-bound NO and prompt NO are neglected, as the thermal NO is responsible for the majority of NO formation in CIDI engines.

With the Zeldovich mechanism and assumptions, it can be easily shown that the net reaction rate of NO is given as follows [17]. Since the cylinder volume and burned gas volume are changing during reaction, it is convenient to use the expression of mole fraction instead of mole concentration because the mole fraction is independent of cylinder volume change during chemical reaction. It is worth noting that this net rate of

NO decreases or decomposes when [NO] is greater than [NO]e.

From the definition of mole concentration applying the ideal gas equation, net rate equation is:

dy RT dNO[] ( NO P) RT dy ==NO dt dt P dt

In this equation, temperature and pressure are constant during a time step, quasi-steady state condition. The rate change of mole fraction of NO in this equation is given by

2 dy P 2k1 f [O]e [N 2 ] (1− ([NO] [NO]e ) ) NO = e (3.13) dt RT ()1+ ()[][]NO NO e k1 f [][]N 2 e O e ()k2 f [][]N e O2 e + k3 f [OH ][]e N e

3 where [ ] is the mole concentration in mole/cm , ‘e’ denotes the equilibrium state, and kif is the reaction rate constant of forward reaction of chemical species ‘i’. This equation is written after expressing all the forward and backward rate equations for each species in all chemical reactions with assumptions described previously based on the law of mass action. The rate of change of the mole concentration as a function of crank angle is: dy 1 dy NO = NO , ω = 6× rpm dθ ω dt

48 The rate constants associated with these equations are those, which Heywood [17] used in his modeling he proposed an uncertainty factor of 2 in applying these rate constants in calculating NOx to match with test data [35]. The reaction rate constants of the forward and backward reaction which are involved in NOx calculation are summarized in Table 3.4.

Rate Constant Reaction Forward Reverse

14 ⎛⎞−38,000 14 O+ N2 = NO + N 15.2 ×10 × exp⎜⎟ 1.6 ×10 ⎝⎠T

8 ⎛⎞−3,150 10 ⎛⎞−19,500 N+ O2 = NO + O 6.4 ×10 ×T exp⎜⎟ 1.5 ×10 × T exp⎜⎟ ⎝⎠T ⎝⎠T

13 14 ⎛⎞−23,650 OH+N = NO+H 4.1 ×10 2.0 ×10 × exp⎜⎟ ⎝⎠T

3 ⎛⎞−31,090 O2 = 2O 3.6 ×10 × exp⎜⎟ ⎝⎠T

kk12ff N2 +O2 = 2NO kk12rr

Table 3.4: The reaction rate constants in Zeldovich mechanism [17]

For the diesel fuel, a light diesel fuel is assumed to be matched with test fuel, so the chemical formula of the diesel fuel used in this study is CH10.8 18.7 . The equilibrium concentrations of other species are calculated from previous reactions. Then, the mole concentration is converted from the mole fraction in order to be used in the chemical P reaction equations as; [ ] = yi Initial concentration of NO is that of residual gas or i RT

49 exhaust gas. So, an iteration procedure could be adopted with this concept. But, according to Heywood [32], initial condition of NO has little effect on NO formation, so the iteration for the initial concentration was not adopted in this study. The number of

NO mole at initial condition is given by, nmfmmNO=+ NO( egr residual) / M NO , where mfNO is the mass fraction of NO in exhaust gas and M NO molecular weight of NO.

3.4.2 Temperature calculation for the rate constant

From the result of combustion modeling, the mean cylinder gas temperature is calculated with the ideal gas law in order to get the mean gas properties. However, it is inappropriate to use the mean cylinder temperature in emission modeling. Moreover, it is a shortcoming of employing a single-zone approach for emission modeling to use this mean gas temperature, which generally is lower than the local temperature of burned gas. From ideal gas law, the mean cylinder temperature is simply given by

PVcy cy Tcy = mRcy cy

where Rcy is the gas constant, Pcy is the cylinder pressure, Vcy is the cylinder volume, and mcy is the mixture mass.

As discussed in the literature review chapter, the concept of multi-layer burned gas temperature is necessary for NOx calculation. According to this model, temperature stratification is formed every time when a new burned gas element is created from the start of combustion at each crank angle, then each burned gas experiences an isentropic process. The initial temperature of each layer is an adiabatic combustion temperature calculated by isenthalpic process. Each burned gas element has its own temperature history during compression and expansion without any heat transfer with adjacent elements. Without heat transfer and work output, the constant enthalpy process is described as hhub= . From this adiabatic combustion, the burned gas (adiabatic flame) temperature during compression and expansion is calculated as described in [17]. The

50 enthalpy for each species is calculated with the polynomial function of temperature only as described in sub-models section. In other words, the mixture enthalpies of the burned and unburned gas are calculated by summing the enthalpy of each species at each temperature, resulting in hnh= ∑ ii. It has been widely known by the experiments that u

NOx formation mechanism is a strong function of the local temperature in the burn gas element. The local temperature to be used in NOx modeling should be calculated by applying the concept of the burned element, not the mean cylinder temperature, which is too low to form NOx. The mole concentration of each chemical species will vary with different value of the local equivalence ratio. Thus, the burn gas temperature will also change because the enthalpy of the burn gas mixture also changes. The following description on the burned element temperature will help in understanding the NOx formation mechanism,

NOX = f ()T,O2 ,time T = f (φlocal , Pcy )

In this equation, the cylinder pressure is calculated from the combustion modeling. The local equivalence ration φlocal is defined as the average equivalence ratio of the burned gas element and is applied in calculating the adiabatic flame temperature of the burned gas element, which is used for the calculation of the initial temperature of the burned gas element during the adiabatic compression and expansion process. The following expression would be appropriate.

Pcy ≈ fuel schedule()pilot injection, SOI,etc from the combustion modeling result

Tadia. = f (EGR, φoverall , SOI, Tunburn, etc) = Tb,i After combustion, each burned gas element experiences an isentropic process. The temperature profile of burned gas element is calculated by

γ −1 γ −1 γ ⎛⎞PVid⎛⎞ TTibi==,,⎜⎟ T bi⎜⎟ ⎝⎠PVbi, ⎝⎠ cy

51 where γ is the specific heat ratio of the burned gas element, and TPbi,,, bi are the adiabatic flame temperature and pressure at the start of combustion, respectively.

3.4.3 Total NO concentration calculation

The NO concentration of each burned gas element NO is calculated by the net [ ]i reaction rate of NO, whose reaction temperature is given by an isentropic process during the compression and expansion stroke. In order to get the total NO concentration, NO concentration of each burned gas element is summed up by mass weighting (burn ratio increment), or mass averaging. Therefore, although the concentration of the first element to burn prior to mass correction is high, NOx contribution of this portion in total NOx concentration could be small.

Then, the total mole concentration of NO at a crank angle, θ is,

x=1 NO=∆ m NO ∆ m =∆ x NO []∑∑∑bi,, []ii bi i[] x=0

The experimental NOx data measured with emission measurement equipment such as

Horiba system is reported by the concentration of NO2, which is the rule of the

Environment Protection Agency. Therefore, the estimated NOx is corrected by multiplying the calculation data with an adjustment factor, 1.533. This adjustment factor is the ratio of the molecular weight of NO2 and NO. The whole procedure for estimating

NOx concentration in CIDI engine is summarized in Figure 3.2. As can be seen in this figure, there are 3 major models in this study: the common rail fuel injection rate estimation model, the CIDI engine combustion model, and the NOx calculation model. As in modeling work, there happen to be several model parameters in the various models. Especially when a single-zone approach is applied like in this study, these model parameters need to be identified through the model validation test. In the next chapter, the model validation test for fuel injection rate estimation, combustion model, and NOx model will be discussed.

52 Fuel Injection Rate Model Input Parameters: EGR, Pmain , MAF

dm f dθ

Local Equivalence Ratio Model: Combustion Model φlocal = f (EGR,SOC,β, Pmain ,MAF,C p1 )

Pcy

Adiabatic Flame Temperature Burn Gas Temperature γ −1 by isentropic process γ ⎛ Pcy ⎞ ⎜ ⎟ hunburn = hburn Tb,i = Tb,o ⎜ ⎟ ⎝ Punburn ⎠ Tb,o = f ()φlocal ,burn gas ratio,Tunburn

Extended Zeldovich Model

[]NO = ∑ []NO i ∆xb,i i

Figure 3.2: NOx modeling procedure schematic

53 4 CHAPTER 4

MODEL VALIDATION TEST

4.1 Introduction

Thus far, a numerical combustion modeling for the multiple fuel injection case of in CIDI engines was accomplished. To implement such models, validation tests for model parameters identification are required. Experimentation is essential in developing a reliable model by comparing with test data and then, calibrating and tuning the model before the model can be used with any degree of confidence if the rule of thumb for modeling is reminded at this time: all models are inherently incorrect to some degree. The overview of the experimental set-up, measurement system, and necessary sensors are described in the next few sections. Furthermore, the treatment of the raw test data for parameters identification will be discussed.

4.2 Validation test set-up

4.2.1 Test engine and dynamometer

The test engine used for model validation is a 2.5 liter, 4-cylinder, common rail, direct-injection, turbocharged engine with cooled EGR system. The detailed specifications of the engine are summarized in the Table 4.1. An engine dynamometer with a capacity of 200HP was used (direct current electric type dynamometer manufactured by General Electric). The control system for the dynamometer and throttle are provided by Dyne Systems. The dynamometer can be operated at two modes: one is constant speed and the other is constant torque. The validation test was done in the

54 constant speed mode. The test engine installed on the engine dynamometer is shown in Figure 4.1.

Model VM-DDC (VM R425) Configuration In-line 4, DOHC Displacement 2499 cc Bore × Stroke 92 mm x 94 mm Compression Ratio 17.5:1 Specific Power 41.2 kW/liter Min. BSFC 210 g/kW hr Rated Power 103 kW @ 4000 RPM Peak Torque 340 Nm @ 1800 RPM Intake system Waste-gate, inter-cooled turbocharger, Cooled EGR Fuel system Bosch common rail, Direct injection Emissions system EURO-IV emissions regulation certified

Table 4.1: Test engine specifications

Figure 4.1: Test engine and engine dynamometer

55 4.2.2 Fuel injection test rig

A Bosch tube type fuel injection rig was used to measure the fuel injection flow rate as Bosch proposed applying the wave propagation principle when high pressure fuel injected through a tube. With this injection rig, useful information was collected such as injection flow rate, dynamic behavior in the common rail system, and wave propagation phenomenon in the system. Through the test data analysis, a flow rate correlation as functions of available parameters could be acquired to be used in the combustion model as input. The original rig was made by the former graduate student at the Center for Automotive Research [83]. In Figure 4.2, a Bosch tube fuel injection rig is shown. This set-up was used in this study with minor modifications. Since the test engine is different with the original test engine used for the injection rig, the fuel injector was installed with an additional adaptor in the injector seat to seal the fuel leakage. Only one injector was used for the study. Every time when the injector was removed for inspection, the Bosch tube was filled with calibration diesel fuel.

Figure 4.2: Fuel injection test rig using the Bosch tube system 56 4.3 Instrumentation

4.3.1 Instrumentation of the fuel injection rig

There were several necessary sensors to measure the injection rate and other parameters as shown in Table 4.2. The detail information on each sensor including its usage in the test will follow:

Item Description Injector needle lift AVL, 426 inductive type Injection pressure SENSOTEC, S/1544-26G-06

Tube pressure PCB, 112A, piezoelectric

Fuel temperature OMEGA, K type thermocouple

Injector current AGILENT, 1146A AC/DC current probe

Injector driver dSpace, DS1003 processor, DS4002 I/O

Data acquisition NI, BNC2100, A/D converter, Labview

Table 4.2: Instrumentation list for the fuel injection rig

• Needle lift sensor: measuring the fuel injector needle lift. The exact point of fuel injection can be located by the need lift considering the transport delay time to the Bosch tube pressure sensor. The lift movement is detected by the inductance effect generated by a moving magnetic core. This sensor was installed inside a fuel injector body. Not only the positive movement but also the negative movement can be detected 57 when the injector plunger bounces on the nozzle during the injector closing stage. A fuel injector with a needle lift sensor is shown in Figure 4.3. The sensor installation was processed by the AVL. The sensor signal is then sent to a carrier amplifier (Model: 3076- A01) for signal processing.

Figure 4.3: A fuel injector on which a needle lift sensor is installed

• Fuel injection pressure sensor: measuring the static fuel pressure in a common rail pipe. This sensor was installed at the same location as a stock rail pressure sensor with some modification on the adaptor. The signal response was fast enough to detect the high frequency behavior of the pressure wave generated inside the rail. It would be more accurate to measure the injection pressure at the needle nozzle tip rather than in the common rail. But, it is hard to install a pressure sensor inside the nozzle tip without affecting injection flow due to very limited space. Therefore, the next candidate for injection pressure sensor installation location would be in the feed pipe. But, as can be seen in Figure 4.4, there are lots of pressure wave moving back and forth inside the pipe at a high frequency. So, it is difficult to pick up a correct signal corresponding to the 58 injection pressure at the time of injection. Therefore, it was determined that a static common rail pressure transducer would work for the purpose of the test.

Figure 4.4: The pressure wave inside a common rail system

• Bosch tube pressure: measuring the fuel injection rate by the pressure change in the tube filled with the same test fuel. A pressure transducer was installed 4.5 mm right after an injector tip in the Bosch tube on the rig in order to avoid excessive signal noise generated by the pressure wave. But transport delay time should be

59 considered when calculating the dynamic start of injection by the tube pressure signal. A direct measurement is not available because this device can not be installed in a running engine for the injection rate measurement. A detailed installation diagram around tube pressure sensor is shown in Figure 4.5.

Figure 4.5: A detailed schematic around Bosch tube pressure sensor

• Fuel temperature: measuring the test fuel temperature for calculation of the fuel density. A K-type thermocouple was installed at the return side of the fuel line where the fuel temperature is highest. This data was also used to prevent the fuel overheating for test condition consistency. When the temperature increased over 60°C , then the test was halted until the fuel cooled down.

60 • Injector current: Measuring the injector solenoid current. The AGILENT 1146A probe picks up the solenoid current at the injector lead wire. The current signal was used in preparing a fuel injection flow rate correlation as functions of available parameters and to calculate the dynamic start of injection, whose definition is a time from injection command to the actual fuel injection. The current probe used in the test is shown in Figure 4.6. The peak current when the fuel was injected was 20 A.

Figure 4.6: An injector solenoid current probe

• Injector driver: issuing the command to fuel injector through an injector circuit. It can control the injection parameters such as injection pulse width, and injection frequency. A ‘C’ language computer program was used to drive the dSpace 1003 and 4002 system. This system was replaced for the engine dynamometer test with commercial injector driver (FI2RE) manufactured by IAV. The dSpace system used in the test is shown in Figure 4.7.

61

Figure 4.7: The dSpace system for injector drive

• Data acquisition system: All signals from the rig are sent to an A/D converter through a BNC connector box. A charge amplification function is included inside the PCB transducers and connected to the BNC shielded box. All signals are then processed through A/D converter in the desk-top computer, where the data processing by Labview program was performed. At the fuel rig test, the fuel injection rate was measured by varying the operating conditions such as the injection pulse width, high pressure fuel pump speed, and injection pressure. The injection fuel flow rate was calculated by the Bosch tube [54]; dQ AP f = t dt ρc where c is the sound speed, A is the tube area, ρ is the fuel density, and Pt is the Bosch tube pressure. A detailed schematic of the instrumentation of the injection rig is summarized in Figure 4.8.

62

Figure 4.8: Fuel injection test rig using the Bosch tube system

4.3.2 Instrumentation for the engine tests

After the fuel injection rig tests were performed, the engine dynamometer validation tests were done using the same instrumentation as rig test except for the injection parameters and needle lift data. There are two kinds of signals acquired from engine tests: one is the slow one (time-base) and the other is the high frequency (crank angle-base) type of signal. Detail information of the engine test instrumentation is shown in Table 4.3.

63 Signal Description Pressure: SENSOTEC, strain gage type

• Intake manifold Range: 0-25 psig

• Exhaust manifold

• Intercooler out

Temperature: OMEGA, K type thermocouples

• Intake manifold

• Exhaust manifold

• Ambient

• Intercooler in

• Intercooler out

• Exhaust

Superflow, fan blade type Mass air flow Range: 0-240 g/s ETAS, LA4 with oxygen sensor Air to fuel ratio Range: 10.29 -327.67 NOx, CO, THC, CO2, O2 Horiba, MEXA -7500 Injector needle lift Same as the injection rig Injector current Same as the injection rig Rail pressure Stock sensor AVL, GU12P piezoelectric un-cooled. In-cylinder pressure Range: 0-200 bar Encoder BEI, H20DB pulse per crank angle with one index pulse per rev. Injector driver IAV, Fi2re system

Table 4.3: Instrumentation list for the engine test

64 1) Pressure

• In-cylinder pressure: measuring the combustion chamber pressure for each cylinder. Some variations between cylinders were expected. After checking the output signal from each cylinder, only one pressure was installed in the first cylinder. The pressure transducer was installed in the engine cylinder head using the glow plug installation holes without a water-cooling system. An AVL GU12P model was used because its thermal stability is better than others under un-cooled condition. The output signal was sent to a charge amplifier (AVL 3066-A03) through a BNC 2110 connector box as shown in Figure 4.9. The sensor output was converted to physical pressure by the following conversion equation.

P = C × (V −V0 ) + P0 [bar] whereC is the sensor sensitivity factor (bar/volt) which should be set before using the sensor V is the sensor signal, V0 is the reference signal, and P0 is the reference pressure. Atmospheric pressure is adopted for the reference condition with minimum error.

Figure 4.9: AVL amplifier rack (3066-A03/3076-A01) 65 • Fuel injection pressure: measuring the static pressure in the common rail. It was almost impossible to install the same SENSOTEC sensor as used in the rig test in the fuel pipe due to the high pressure and small size of the pipe. However, a calibration was possible to match the stock sensor signal with the SENSOTEC sensor output. The following calibration equation was used to calculate the rail pressure with the stock sensor.

Prail = −321.9 + 678.3×V [bar] where V is the output voltage from the stock sensor in volts. • Other pressure: strain gauge type pressure sensors were installed at some locations such as intake manifold, exhaust manifold, and compressor exit side. 2) Temperature • Intake charge temperature: A thermocouple was installed at the location where the mixing of the incoming air and the EGR gas is completed. • Others: Temperatures at other locations such as the exhaust manifold, ambient, intercooler in, intercooler out were also measured for reference. 3) Flow rate • Intake airflow rate: measuring the incoming fresh air flow rate with a sensor manufactured by SuperFlow, which is a fan-blade type volumetric flow meter.

• EGR gas flow rate: measuring CO2 concentrations in the intake and exhaust gas (this method is more desirable than the orifice type measurement due to accuracy) as described earlier. • Fuel injection flow rate: It is almost impossible to measure the fuel injection flow rate directly in a running engine, so that we need to measure the fuel injection rate indirectly using correlation as functions of available parameters such the injection pulse width, injector current, cylinder pressure, and fuel temperature. The injector current data was collected with the AGILENT current probe which was used in injection rig test. The injector needle lift signals were also measured for the purpose of the dynamic start of injection determination in the combustion mode. One important reason why a needle lift sensor is

66 used in engine test is that it is used to determine the dynamic start of injection (SOI), which is a major parameter in CIDI engine combustion. The fuel temperature was kept at around 55°C . The precise meaning of the fuel injection pressure might be the pressure at the injector nozzle tip. In other words, the pressure at the nozzle tip of a fuel injector should be used as actual injection pressure. However, it is very difficult to install a pressure sensor right at the tip, and the pressure difference between the rail and the tip can be considered negligibly small for modeling purposes. Thus, it is common to install a sensor near the fuel feed pipe instead of at the tip. During the extensive fuel injection rig test, it was found that there were lots of pressure wave reflecting in the small tube resulting in signal distortion. Therefore, the static rail pressure could be also used for the flow injection pressure.

4) Others • Injector driver: Issuing the command of the fuel injection schedule to the injector solenoid such as SOI, dwell times, number of injections. The command signal was sent to directly to a fuel injector, bypassing the stock ECU. All process was performed on the host PC providing a GUI environment to control multiple fuel injections. The system was manufactured by IAV and shown in Figure 4.10

Figure 4.10: IAV injector driver unit (Fi2re) 67 • Emission measurement: Horiba MEXA 7500-DEGR system was used for

NOx, CO2, CO, and O2 measurements in the exhaust system. The CO2 concentration in the intake manifold was also measured for the estimation of the EGR flow rate. • A/F meter: Checking the incoming air flow and the condition of the test engine. This is a universal, wide range, exhaust gas oxygen sensor which output is linearly proportional to the real time A/F. • TDC Encoder: Locating the top dead center of the firing cylinder to calculate crank angle and provide the trigger timing for DAQ system. This optical type encoder was aligned to the TDC by rotating the crank shaft by hand to match the signal with a real TDC mark. There are two types of signal available from the encoder: the TDC signal and the crank angle signal. Since one crank angle step was used for combustion model in this study, only the TDC was necessary and collected. As can be seen in Figure 4.11, it is relatively convenient to install in the test engine.

Figure 4.11: BEI Crank angle encoder

68 • Data acquisition system (DAQ): National Instrument hardware was used for all data acquisition components. LabView 6.2 software was used for the data collecting and post processing. Two SCXI signal conditioning boxes were used: one for the low frequency signals and one for the high frequency signals such as crank angle based cylinder pressure. These SCXI interface boxes protect the noise from ground problem, and amplify the signals. Then, all the signals come into the PC through the analog to digital converters. Test data was collected for 5-second duration for each condition.

The entire measurement system is shown in Figure 4.12, and the principal measurement system around the engine cylinder head is shown in Figure 4.13.

Figure 4.12: Measurement system diagram of a CIDI engine test

69

Figure 4.13: Principal measurement system for CIDI test engine

4.4 Test result

4.4.1 Fuel injection rig test data treatment

A brief process for handling the fuel injection rig test data at one of several test conditions is illustrated in Figure 4.14. The detailed test condition can be checked from Table 4.4. Test data set were analyzed to extract the physically appropriate form of data from the raw data set. Every sensor exhibits the offset and noise in the signal. Therefore, data filtering and offset treatment was needed during the data handling process. There are lots of fluctuations in the fuel injection rate as shown in the Bosch tube data in Figure 4.14 (b). A double filter function was used to get the filtered data of tube pressure, which is later used for fuel injection rate calculation.

70 (a) Raw current signal (b) Raw Bosch tube pressure

(c) Raw current signal-cycle averaged (d) Raw Bosch tube pressure-cycle averaged

(e) Filtered current signal (f) Calculated flow rate

Figure 4.14: Typical raw data acquired in the fuel injection rig test and corresponding processed data 71 After the data handling process, a typical fuel injection behavior for the same test condition is shown in Figure 4.15. As can be seen in the figure, there is a delay time after injector command signal is generated. After a constant delay time of about 0.55 msec, the fuel is injected and sensed by a pressure sensor installed at the nozzle tip in the Bosch tube. This delay time needs to be defined through estimation modeling for locating the exact timing of the dynamic fuel injection. During the entire fuel injection period, the rail pressure drop is about 20 bar. Hence, the injection pressure could be assumed as constant during injection.

Figure 4.15: A typical fuel injection behavior 72 4.4.2 Fuel injection rig test results

The test conditions for 45 test cases in terms of the common rail injection pressure, pulse width, and back pressure are summarized in Table 4.4. In the table, Pb is the back pressure which can be adjusted by an orifice which is installed at the end of the

Bosch tubing.Q f is the total fuel quantity injected per each injection cycle, which can be calculated by:

Q = Q& dt . (4.1) f ∫ f

The injection flow rate, Q& f is calculated from the Bosch tube pressure. T f is the average test fuel temperature measured at the exit side of high pressure pump. This fuel temperature was maintained as constant by a heat exchanger in the circuit. Pr is the nominal rail pressure during the test. The back pressure, Pb simulates the diesel condition in the actual combustion chamber during the compression stroke at the time of injection. As can be seen later, the order of magnitude of this back pressure is small compared to the injection pressure and can be assumed as constant at a certain reference value, say 30 bar. “# Inj.” is the number of injections considered as correct data by a validation procedure ( there are a few erroneous test results due to the noise problem). I thr is the threshold value of current signal to determine the start of injection by the current signal and is necessary to select the right point of start of injection instead of selecting false signal. The definition of two delay times can be checked in the previous figure (Figure

4.15). The delay td1 is the time delay from the onset of injector current command to the actual lifting of the injector needle and the delay, td 2 is the time delay from actual needle lifting to the time when flow is sensed by the pressure sensor. Hence, the total delay time is equal to td = td1 + td 2 . A more detail discussion on this injection delay time will follow later, including its meaning and importance in CIDI engine combustion. These injection rig test results were used to identify a useful correlation for the injection rate, which was then used in the combustion model as an input.

73 P T Test PW b f Pr Q f Delay1 Delay2 # Inj. I thr unit [ µ s] [bar] [°C ] [bar] 10−10 [ m3 ] [msec] [msec] - [A] 1 3000 75 52 1145 7.9507 0.32 0.21 49 2.8 2 3000 50 51 1142 7.5174 0.34 0.24 50 1.0 3 3000 30 52 1143 7.6431 0.34 0.23 50 1.0 4 2500 30 52 1151 6.3982 0.33 0.21 48 2.5 5 2500 50 52 1143 6.3884 0.32 0.21 50 2.1 6 2500 75 52 1144 6.3470 0.31 0.18 50 2.1 7 2000 75 53 1140 5.1203 0.32 0.21 46 1.9 8 2000 50 54 1139 5.0943 0.33 0.21 49 1.9 9 2000 30 54 1141 5.1642 0.33 0.21 50 1.5 10 1500 30 54 1134 3.7587 0.32 0.19 50 1.5 11 1500 50 55 1138 3.6518 0.31 0.18 45 2.3 12 1500 75 55 1130 3.8277 0.30 0.18 46 2.6 13 1000 75 56 1124 2.4751 0.31 0.20 49 2.3 14 1000 50 56 1134 2.4342 0.30 0.20 40 2.2 15 1000 30 56 1134 2.4138 0.32 0.20 48 1.9 16 3000 30 55 965 7.1714 0.36 0.21 50 1.3 17 3000 50 55 966 7.2863 0.35 0.22 50 2.1 18 3000 75 55 966 7.2749 0.35 0.21 50 2.1 19 2500 75 55 969 5.9206 0.33 0.22 50 2.1 20 2500 50 55 972 5.7731 0.34 0.22 47 2.0 21 2500 30 55 967 5.8956 0.35 0.20 50 2.0 22 2000 30 54 972 4.9261 0.35 0.20 50 2.0 23 2000 50 55 968 4.8407 0.33 0.19 48 2.0 24 2000 75 55 974 4.7832 0.33 0.19 50 2.0 25 1500 75 56 975 3.5486 0.34 0.18 48 2.0 26 1500 50 56 973 3.4241 0.35 0.20 49 0.5 27 1500 30 56 979 3.4065 0.34 0.19 48 2.0 28 1000 30 57 978 2.2549 0.33 0.20 47 2.0 29 1000 50 57 981 2.3217 0.32 0.19 47 2.0 30 1000 75 58 978 2.3568 0.34 0.20 50 1.8 31 1000 75 56 781 2.2198 0.34 0.22 50 1.0 32 1000 50 56 782 2.1309 0.37 0.18 47 1.8 33 1000 30 56 782 2.0458 0.36 0.20 49 1.8 34 1500 30 56 780 3.1711 0.36 0.19 47 1.6 35 1500 50 56 779 3.2424 0.36 0.19 50 1.6 36 1500 75 56 778 3.2962 0.36 0.18 50 1.6 37 2000 75 56 778 4.4804 0.36 0.18 49 1.6 38 2000 50 56 778 4.3157 0.37 0.20 49 1.6 39 2000 30 54 778 4.1620 0.38 0.18 49 1.6 40 2500 30 54 773 5.3608 0.36 0.21 49 1.6 41 2500 50 55 776 5.4031 0.36 0.21 50 1.5 42 2500 75 55 777 5.4810 0.38 0.18 50 1.5 43 3000 75 55 775 6.5860 0.37 0.18 50 1.5 44 3000 50 54 774 6.3367 0.39 0.17 50 1.5 45 3000 30 54 776 6.1954 0.39 0.19 6 2.5

Table 4.4: Summary of fuel injection rig test condition and results

74 4.4.3 Engine test data treatment

The range of engine test conditions is summarized in Table 4.5. Detail conditions for each test run are shown in Table 4.6. There are some issues with the data acquired which requires preprocessing such as the signal noise which needs to be filtered by applying an appropriate function, confirmation for the TDC synchronization, and test data interpretation. The test fuel was Diesel ECD-1 which is a product of Exxon. As can be seen in the table, test operating range were kept at low engine speeds and low load conditions due to unstable test engine during the validation tests. EGR percentage was not controllable, so that the EGR % was evaluated for the conditions that the stock ECU provided. More importantly, due to the stock fuel injector inertia problem of the current generation injector, multi strike fuel injections tests with more than 4 strikes were unavailable. The minimum pulse width for a pilot injection was around 100 µ sec . Below this value, actual fuel injection could not be achieved.

Range Variable Unit Lower Upper Engine Speed rpm 1500 1800 EGR % 0 18 Pulse width (PW) µ sec 100 600 Start of injection (SOI) CA 320 370 Number of injection - 1 3 Fuel temperature °C 50 60

Table 4.5: Range of engine test conditions

75 Test Engine PILOT MAIN POST EGR # INJ No. Speed SOI PW SOI PW SOI PW Unit rpm - - CA us CA us CA us 0 1800 w/o 3 340 200 355 400 366 100 1 1800 3 340 200 354 400 365 100 2 1800 3 340 200 354 400 370 100 3 1800 3 340 200 354 400 363 100 4 1800 3 340 200 351 400 370 100 5 1800 2 340 200 354 500 6 1800 2 340 200 351 500 7 1800 2 340 200 360 500 8 1800 2 340 200 354 400 9 1800 2 340 200 354 600 10 1800 1 354 500 11 1800 1 356 500 12 1800 2 340 200 360 500 13 1800 1 352 500 14 1800 1 350 500 15 1800 w/ 2 340 200 354 500 16 1800 2 330 200 354 500 17 1800 2 348 200 354 500 18 1800 2 340 200 351 500 19 1800 2 340 200 348 500 20 1800 2 340 200 360 500 21 1800 1 354 500 22 1800 1 351 500 23 1800 1 348 500 24 1800 1 357 500 25 1800 3 340 200 354 400 365 100 26 1800 3 330 200 354 400 365 100 27 1800 3 348 200 354 400 365 100 28 1800 3 340 200 354 400 362 100 29 1800 3 340 200 354 400 368 100 30 1500 w/o 2 340 100 354 400 31 1500 2 330 100 354 400 32 1500 2 345 100 354 400 33 1500 2 340 200 354 400 34 1500 2 340 200 360 400 35 1500 2 340 100 354 425 36 1500 2 340 100 360 425 37 1500 2 340 100 350 425 38 1500 2 340 100 354 375 39 1500 2 340 100 360 375 40 1500 2 340 100 350 375 41 1500 2 340 100 354 450 42 1500 2 340 100 360 450 43 1500 2 340 100 350 450 44 1500 2 330 100 354 450 45 1500 2 345 100 354 450 46 1500 2 340 200 354 450 47 1500 2 330 200 354 450 48 1500 2 345 200 354 450 49 1500 3 340 100 354 300 370 100 50 1500 3 340 100 354 200 370 200 51 1500 3 340 100 350 300 370 100 52 1500 3 340 100 354 300 365 100 53 1500 3 340 200 354 300 370 200 54 1500 3 340 200 354 300 367 200 55 1500 3 340 200 354 300 364 200 56 1500 3 340 200 354 300 360 200 57 1500 3 340 200 352 300 364 200 58 1500 3 340 200 350 300 364 200 59 1500 3 340 200 356 300 364 200 60 1500 3 340 200 360 300 367 200 61 1500 3 340 200 360 400 367 100 62 1500 3 340 200 358 400 367 100 63 1500 3 340 200 354 400 367 100 64 1500 3 340 200 354 400 365 100 65 1500 3 340 200 354 400 363 100 66 1500 3 340 200 354 400 67 1500 3 340 200 350 400 365 100

Table 4.6: Summary of engine test conditions

76 Above all, the engine in-cylinder pressure signal is important in analyzing combustion inside the test engine. The cylinder pressure signal is sometimes noisy. Therefore, this noisy signal needs to be rectified with appropriate methods such as filtering. One of many filters used in data processing is a double filter function. This filter performs the forward and backward filtering of the data. As a result of this double filtering, no phase distortion is expected and filter order is doubled. Butterworth filter design is normally used when there is no need for steeper roll-off characteristic. In this study, a double filter function in Matlab@ (“filt-filt”) was used for this purpose. It is also required that a suitable cutoff frequency and order of the filter in each test case be selected. The procedure to pre-process the raw test data is described for one sample case (single fuel injection and 1800 rpm) as follows: 1) Selecting an appropriate filter function is required in order to eliminate the undesired noise from the test data. When using a filter function, there are some facts that need to be taken care of. One is the possible magnitude change and another is the phase distortion of the original data. Thus, the double filter function is recommended because there is no phase distortion by using the forward and backward filtering.

2) Reduced frequency f r defined by the following needs to be calculated:

f data f r = f sampling 2

where f data is the frequency of noise which is determined on a case-by-case basis

and f sampling is the data sampling frequency (1-crank angle in this study) which depends on the engine speed. In the sample case in which the engine speed is 1800 rpm and the noise frequency is 4~5 crank angle, a reduced frequency is calculated as:

f data 1 5 ~ 1 4 ⎡CA⎤ f r = = ⎢ ⎥ = 0.4 ~ 0.5 . Then, a reduced frequency below f sampling 2 1 2 ⎣CA⎦ 0.4~0.5 should be selected when the low-pass filter is applied. A series of filtering were done by changing the reduced frequency and checking the cylinder

77 pressure and net heat release rate behavior. The net heat release rate ()nHRR can be calculated with equation (3.3) as follows: dQ dQ pV dγ 1 ⎛ dV dp ⎞ comb + w + = ⎜ pγ +V ⎟ dθ dθ ()γ −1 2 dθ γ −1⎝ dθ dθ ⎠ In this equation, it is known that the numerical differentiation of the cylinder pressure data is not desirable, as it is increase noise. To mitigate this effect, filtering the test data is required before numerical differentiation. In this work, a 4th order central difference scheme which is described by the following equation: dP P − 8P + 8P − P = i−2 i−1 i+1 i+2 . dθ ,i 12∆θ The effect of filtering with a Matlab function by several experimental reduced frequencies can be confirmed from Figure 4.16 to Figure 4.18. An optimal set of the reduced frequency and filter order will be chosen as follows. When the reduced frequency is equal to 0.45, there is virtually no filtering effect in test data and the peak value can be retained. This is because the cutoff frequency is 0.4~0.5. When the reduced frequency is high (0.45), although the peak value can be kept unchanged but filtering is not appropriate to eliminate the noise during compression stroke. In this case, the order of filtering is irrelevant. Contrary to this fact, when the reduced frequency is low (0.25), the filtering effect is enough at least for compression stroke. However, the peak value is significantly reduced and ignition point is phase-shifted by 3 crank angle degrees. Also, the order of filtering is not a dominant factor. Therefore, it is basically difficult to guarantee the two targets concurrently with an overall filtering approach. Considering these facts, it could be concluded that instead of applying overall filtering function to the entire engine cycle, a separate filtering of the forced phase of the process is more reasonable.

As a reduced frequency for the case of the compression stroke, 0.25 is finally selected in this study as an optimal value by considering the fore- mentioned trade-off of filtering. And 3rd order of filtering will be used for the compression stroke. 78 3) Using this reduced frequency, the raw cylinder pressure test data was filtered. With this filtered data, an ignition point was calculated by the heat release rate curve using equation (2-1). The ignition point is defined and explained in the subsequent section 4.4.7. 4) Then, using the reduced frequency that is calculated above (0.25) the raw test data ranging from the intake valve closing time to ignition, or start of combustion was filtered because most of noise is observed to be generated during this period only. Moreover, since this period is not as important for the combustion except determining the ignition point, the raw data could be filtered without significant loss of accuracy.

79 Cylinder Pressure Net Heat Release Rate 50 100

45

80 40

35 60

30

25 40 Pressure (bar) 20

Heat Release Rate (J/deg) 20 15

10 0

5

0 −20 250 300 350 400 450 250 300 350 400 450 Crank Angle (deg) Crank Angle (deg) (a) Entire plot

40 6

35 4

30 2

25 0

20

Pressure (bar) −2 15 Heat Release Rate (J/deg)

−4 10

−6 5

0 −8 250 300 350 250 300 350 Crank Angle (deg) Crank Angle (deg) (b) Compression stroke

50 100

45 80

40 60

35

40

Pressure (bar) 30

Heat Release Rate (J/deg) 20 25

0 20

15 −20 360 370 380 390 400 360 370 380 390 400 Crank Angle (deg) Crank Angle (deg) (c) Around SOC

18 8

16 6

14 4

12 2

Pressure (bar) 10 0 Heat Release Rate (J/deg)

8 −2

6 −4

4 −6 410 420 430 440 450 410 420 430 440 450 Crank Angle (deg) Crank Angle (deg) (d) Expansion stroke

Figure 4.16: The unfiltered raw Pcy and nHHR 80 Cylinder Pressure Net Heat Release Rate 50 100 Raw Raw Filtered Filtered 45

80 40

35 60

30

25 40 Pressure (bar) 20

Heat Release Rate (J/deg) 20 15

10 0

5

0 −20 250 300 350 400 450 250 300 350 400 450 Crank Angle (deg) Crank Angle (deg) (a) Entire plot

40 6 Raw Raw Filtered Filtered

35 4

30 2

25 0

20

Pressure (bar) −2 15 Heat Release Rate (J/deg)

−4 10

−6 5

0 −8 250 300 350 250 300 350 Crank Angle (deg) Crank Angle (deg)

(b) Compression stroke

50 100 Raw Raw Filtered Filtered

45 80

40 60

35

40

Pressure (bar) 30

Heat Release Rate (J/deg) 20 25 9−Order

0 20

15 −20 360 370 380 390 400 360 370 380 390 400 Crank Angle (deg) Crank Angle (deg)

(c) Around SOC

18 8 Raw Raw Filtered Filtered

16 6

14 4

12 2

Pressure (bar) 10 0 Heat Release Rate (J/deg) 9−Order 8 −2

6 −4

4 −6 410 420 430 440 450 410 420 430 440 450 Crank Angle (deg) Crank Angle (deg) (d) Expansion stroke

Figure 4.17: Pcy and nHHR : f r = 0.45 , order = 3 and 9

81

Cylinder Pressure Net Heat Release Rate 50 100 Raw Raw Filtered Filtered 45

80 40

35 60

30

25 40

Pressure (bar) 20

Heat Release Rate (J/deg) 20 15

10 0

5

0 −20 250 300 350 400 450 250 300 350 400 450 Crank Angle (deg) Crank Angle (deg)

(a) Entire plot

40 6 Raw Raw Filtered Filtered

35 4

30 2

25 0

20

−2 Pressure (bar) 15 Heat Release Rate (J/deg)

−4 10 9−Order

−6 5

0 −8 250 300 350 250 300 350 Crank Angle (deg) Crank Angle (deg)

(b) Compression stroke

50 100 Raw Raw Filtered Filtered

45 80

40 60

35

40

30 Pressure (bar)

9−Order

Heat Release Rate (J/deg) 20 25

0 20

15 −20 360 370 380 390 400 360 370 380 390 400 Crank Angle (deg) Crank Angle (deg)

(c) Around SOC

18 8 Raw Raw Filtered Filtered

16 6

14 4

12 2

10 0 Pressure (bar) Heat Release Rate (J/deg)

8 −2 9−Order

6 −4

4 −6 410 420 430 440 450 410 420 430 440 450 Crank Angle (deg) Crank Angle (deg)

(d) Expansion stroke

Figure 4.18: Pcy and nHHR : f r = 0.25 , order = 3 and 9 82 5) Finally, the net heat release rate itself is filtered with the smaller reduced frequency and filtering order. This action can keep the same peak value as the raw data and mitigate the noise at the same time, whose frequency is nearly the same as that of compression stroke. The filtering order of 2 will be used in this study because in CIDI engine combustion, there are two types of combustion for each fuel injection. Thus, diffusion combustion behavior is needed to be captured; the order of filtering needs to be lowered from the basic order that is used for the cylinder pressure during the compression stroke. 6) The advantage of this filtering methodology is as follows. Firstly and importantly, the auto ignition point is no longer distorted by filtering, which is very important in CIDI engine combustion. Secondly, the peak heat release rate can be kept close to its raw value. Thirdly, the noise generated during the compression stroke can be treated. The same methodology is expected to be applied for the pilot fuel injection cases.

The final results of filtering the cylinder pressure data are shown in Figure 4.19. As can be seen in the figure, the peak values of raw data are decreased by filtering. The peak net heat release rate is reduced by 10 % and the peak cylinder pressure remains the same. It is believed that this peak value is the real data, but the one resulting from numerical calculation including differentiation is slightly affected by the processing.

83 Cylinder Pressure Net Heat Release Rate 50 100 Raw Raw Filtered Filtered 45

80 40

35 60

30

25 40

Pressure (bar) 20

Heat Release Rate (J/deg) 20 15

10 0

5

0 −20 250 300 350 400 450 250 300 350 400 450 Crank Angle (deg) Crank Angle (deg)

(a) The cylinder pressure and heat release rate

Cylinder Pressure Net Heat Release Rate

Raw 25 Raw Filtered Filtered 48

20 46

44 15

42 10

40

5 Pressure (bar) 38 Heat Release Rate (J/deg)

36 0

34 −5 Ignition Point 32

30 −10 350 360 370 380 390 400 340 360 380 400 Crank Angle (deg) Crank Angle (deg)

(b) Blown figure around the ignition point

Figure 4.19: The final shape of the filtered cylinder pressure and heat release rate

84 4.4.4 Engine test results

To summarize the discussion so far, the cylinder pressure data is distorted by 1 crank angle degree and the peak pressure is the same. Therefore, filtering the cylinder pressure data could be done with the methods discussed so far. Especially the cylinder pressure data from IVC to SOC is greatly improved in its shape as can be seen in Figure 4.19. As can be seen in Figure 4.19, the ignition point seen in the raw data is exactly the same as the filtered data, which is the major advantage of this methodology. The methodology of filtering the cylinder pressure test data will be applied to get the net heat release rate curves for other test cases including the multiple fuel injections. The results of calculating the net heat release rate nHHR for some representative cases are shown in the following figures from Figure 4.20 to Figure 4.22. In these figures, the unit that are used for denoting the pulse width (PW) and start of injection (SOI) are µ sec and CA, respectively. The effect of SOI of main fuel injection for the single injection and without EGR case is shown in Figure 4.20. As the SOI changes, the ignition delay is constant at 11-12 crank angle degree, which means that the ignition delay time (duration) is independent of SOI.

Therefore, the activation temperature in the ignition model, Ta , is assumed to be a function of SOI.

Next is the case of pilot + main fuel injection without EGR As can be seen in Figure 4.21, the SOC of main injection is not related to either the SOI or the pulse width of the pilot injection. Therefore, the reason why the pilot injection is adopted in CIDI engines could be explained by saying that the ignition delay time of the main fuel injection decreases only if there is a pilot injection. Moreover, there is no need that the pulse width of the pilot injection should be large.

85 (a) Case 23. SOIm = 348 (b) Case 22. SOIm = 351

(c) Case 21. SOIm = 354 (d) Case 24. SOIm = 357

Figure 4.20: The. Effect of SOI of single injection at 1800 rpm with EGR on the net heat release rate curve( nHRR )

86 (a) Case 31. SOIp = 330 (d) Case 30.SOIm = 354, PWp=100

(b) Case 30. SOIp = 340 (e) Case 33.SOIm = 354, PWp=200

(c) Case 32. SOIp = 345 (f) Case34.SOIm= 360, PWp=200

Figure 4.21: Effect of the SOI of pilot or main injection (pilot+main) fuel injection at 1500 rpm without EGR on the net heat release rate curve ( nHRR ) 87

(a) Case 3. SOIpo=363, SOIm=354 (b) Case 4. SOIpo=370, SOIm=351

Figure 4.22: Effect of the SOI and PW of post and main fuel injection on the net heat release rate curve ( nHRR ) in 3-strike injection at 1800 rpm without EGR

The condition of the pilot injection is the same for both cases. SOIs for main and post injection are different. In case #4 where the SOI of post injection is later than case #3 by 7 (CA), there is a third distinct peak since the nHRR of main injection is on the decrease. THC of case #4 is smaller that that of case #3. The SOI is not affected by the nHRR from the precedent fuel injection when the dwell time is small. Although the SOI is retarded by 3 CA in case #3, the SOI of post injection is nearly the same as case #4. The maximum nHRR of both cases are the same. With this appropriate pre-processing, locating the precise ignition point consistently for each test case is possible. In the following chapter, using these filtered test data, some parameters such as those used in ignition model, combustion model, and NOx model for each test case will be identified. Before doing that, some other issues that need to be resolved in the data handling will be discussed in the next section.

88 4.4.5 TDC offset treatment

Some care must be concentrated when dealing with the cylinder pressure test data. One of them is to check whether a crank angle encoder is synchronously installed with engine crank shaft pulley without any phase shift. There is a method to ensure this issue by analyzing the pressure-volume diagram and correcting the crank angle coordinates with an offset crank angle. Actually this offset crank angle could be applied in the engine pressure code simulator. If the encoder is installed incorrectly in the clockwise or counter-clock wise direction, then the p-V diagram is distorted during the compression stroke [79]. In Figure 4.23 when the encoder is installed in a retarded direction, the p-V diagram is shown. As can be seen in the figure, the plot is crossed near the TDC. When correctly installed, there is no crossing point in the p-V plot. With this methodology, the location of the encoder was confirmed to be correct in the validation engine test.

P−V Diagram

48

46

44

42 Pressure (bar)

40

38

36

3.5 4 4.5 5 5.5 6 3 −5 Volume (m ) x 10

Figure 4.23: The case when an encoder is installed incorrectly, retarded

89 4.4.6 Estimation of the trapped fresh air

As described in Table 4.7, there are several methods to estimate a trapped air mass during the intake stroke. Since the first method in the table is difficult to be applied due to the sensor response time and 2nd one is inaccurate (possible over-estimating due to the neglected friction loss), the 3rd method in the table is usually applied in the engine research and will be used in this study. The trapped air mass per cylinder is again described as:

dm dt dm 1 720 dm 30 m = a × × ∆θ = a × × = a × a ,cyl dt dθ intake dt 6rpm 4 dt rpm

dm where a is the steady-state MAF test data. dt This trapped air estimation will be used throughout in this study as done in the automotive industry.

Method Equation Remarks 1 ivo Real time MAF 1 m = m θ dθ a ∫ & a () ω ivo 1 Flow loss neglected 2 m = ρS A ()θ −θ a ω p p ivc ivo 1 ⎡ sec ⎤ Average MAF ma = m& a × ×180[]deg ω ⎢deg⎥ 3 ⎣ ⎦ 180m = & a ω

Table 4.7: Comparison of the trapped in-cylinder mass estimation

90 4.4.7 Determination of the auto-ignition point

Since an actual starting point of combustion in CIDI engine so important, it is necessary to define the point of auto-ignition in order to apply the ignition model and get a reasonable result of combustion modeling. Moreover, its definition needs to be consistent in locating the auto-ignition point. In this study, the auto-ignition point is defined as the 1st point of positive net heat release. This definition can be translated as the same point as when the rate of pressure change becomes larger than that of motoring condition.

The auto ignition point is defined as a crank angle position when the following condition is met:

nHRR > 0 where, nHRR is the net heat release rate defined by Eqn. (3-3).

Figure 4.24: The definition of auto-ignition point: θign = 365(CA )

91 4.4.8 Test engine compression ratio

According to the VMR325 engine shop manual, the compression ratio of the test engine is 17 ± 0.5 . This is too broad a value to be used in the combustion model. Therefore, the specific compression ratio needs to be determined indirectly or measured directly. In order to determine the compression ratio indirectly, the cylinder pressure trace is used. The single fuel injection test cases are used for this purpose. The cylinder pressure calculated by the model at the ignition (SOC) location is compared with that of test data. The compression ratio is being sought iteratively until the difference between these two data reach within an error bound, say, 1.5 bar. As can be seen in , there are some variations in the optimum compression ratio (CRopt), especially in the case of EGR- inducted tests. From this method, the numerical compression ratio of this test engine is selected as 16.5, i.e. the low limit of specification data. The comparison when the compression ratios are 17.0 and 16.5 is performed on the cylinder pressure trace. The result can be shown in Figure 4.25. Also, the numerical comparison was carried out with the statistical method using the root mean square error and pressure differences at the SOC. To evaluate the accuracy of prediction with each compression ratio, the root mean square error technique was adopted as follows.

N 2 ∑()Pcy,est − Pcy,test error()∆P ≡ i=IVC cy N where N is the period (crank angle) from IVC to SOC.

The calculation results are also summarized in Table 4.8.

92 SOI MAF AF EGR SOC SOC CRopt ∆P , bar error(∆Pcy ) , bar Test t e SOC Case CA g/s - % CA CA - CR=17.0 CR=16.5 CR=17.0 CR=16.5

11 356 50.07 42.8 0.0 368 367 16.6 3.0 1.5 0.73 0.65

13 352 49.57 42.2 0.0 363 363 16.6 2.0 0.5 0.50 0.73

14 350 49.32 42.2 0.0 360 360 16.3 2.0 1.5 0.46 0.36

Table 4.8: The result and effect of modification of an optimum compression ratio for the single fuel injection cases at 1800 rpm, pulse width 500µ sec

In the table, ∆PSOC is the difference at the timing of ignition between test data and estimated cylinder pressure. SOCt and SOCe is the SOC of the test data and the estimated one with model, respectively. There could be some errors in the estimated cylinder pressure at the start of combustion. These errors are the result of the possible error of estimating the trapped mass in the cylinder at IVC, or the error in the engine compression ratio which the lower limit compression ratio is used in this study, or the reduced peak pressure with filtering process of the raw pressure data. As can be seen in the table, the cylinder pressure difference at the SOC is improved by optimizing the compression ratio from a nominal value. This is important because the heat release rate of the combustion model is affected in order to balance the pressure difference at SOC. Therefore, at least the pressure gap at SOC needs to be minimized to reduce the error of heat release rate estimation. The RMS error is reduced by an half with a modified compression ratio. This is because even though the pressure trace is nearly the same or worsened during the compression stroke, the pressure difference near the TDC is significantly improved. Again, as stated before, the effective compression ratio used in this study based on these various test was selected to be 16.5. This value was used consistently through the rest of the work.

93 Case 11

Case 13

Case 14 (a) C.R.=17.0 (b) C.R.=16.5

Figure 4.25: Comparison of the pressure trace by modification of the compression ratio 94 5 CHAPTER 5

PARAMETERS IDENTIFICATION FOR FUEL INJECTION RATE ESTIMATION MODEL AND MODEL VALIDATION

5.1 Introduction

Since the concept of fuel injection rate estimation was introduced in Chapter 3, the model parameters need to be identified with the rig data. Since this fuel injection model will be used in the combustion model as an input, the parameters identification procedure which is going to be discussed in this chapter has an important role in the overall model structure. Moreover, it could be said that the actual combustion phenomenon in a CIDI engine starts from the point of fuel injection into the combustion chamber. After the fuel is injected from an injector, the fuel will experience a series of process including such as break-up, atomization, droplet merge, wall impingement, and vaporization, mixing with surrounding air, and ignition when an appropriate condition is met. However, in this study, this detail process will not be considered. Instead, the apparent effect will be used for the combustion process by developing fuel injection estimation model. Before doing the main fuel injection modeling, some discussion on injection trend as functions of injection parameters such as injection and back pressure will follow. Then, the definition and modeling of the dynamic start of injection (SOI) will also be discussed and validated with the available test data.

5.1.1 General trend of fuel flow rate

It would be helpful to understand the fuel injection behavior by analyzing the test data in identifying the model parameters. It is easily found that the fuel injection flow rate 95 is related with the injection pressure, injection pulse width, and back pressure as shown in Figure 5.1. In other words, these parameters or operating conditions will be studied and used as independent variables in the fuel injection rate estimation model.

Figure 5.1: Total fuel injection quantity vs. (Pr- Pb ), PW, and Pb

5.1.2 The effect of back pressure

Verifying the reason why the back pressure has some effects on flow rate is required prior to the main model validation. The effect of back pressure on flow rate and needle lift at the test condition of nominal rail pressure=780 bar and pulse width=3 msec will be discussed here. In the fuel injection rig test, the back pressure has some effects on 96 the flow rate. It is necessary to find the cause of this phenomenon by investigating into the test graphs as shown in Figure 5.2. The analysis result of the test based on Figure 5.2 is summarized in Table 5.1. Although the magnitude of the back pressure is relative small compared to that of the fuel injection pressure, it could not be guaranteed that the effect of back pressure is still negligible in every operating case.

(a) The effect on fuel flow rate (b) The effect on needle opening speed at the initial stage

(c) The effect on rail pressure drop (d) The effect on the maximum needle lift and opening duration

Figure 5.2: The back pressure effect

97 Parameters Comparison Possible explanation

Max. Needle Lift P30 〉P50 〉P75 There is a limiting point in needle lift. Needle Lift Gradient P 〉P ≈ P In initial stage, opening rate of needle is ( dl dt ) 75 30 50 dependent on back pressure.

Opening Duration P75 〉P50 〉P30 Fast opening and late closing of needle

∆Pr P75 〉P30 〉P50 Combination of the preceding two Total Flow Rate P 〉P 〉P 75 50 30 factors

Table 5.1: Summary of the back pressure effect

Therefore, it could be concluded that the back pressure have some effect on the fuel flow rate through the effect of early opening of the needle lift and pressure difference when the rail pressure is relatively small.

5.2 The dynamic fuel injection timing

It would be obvious that instead of SOI which is the same as the ECU command, the dynamic SOI is actually required as the starting point in the CIDI engine combustion. In other words, there are some delay time between the SOI and the dynamic SOI. There are two kinds of delay time of fuel injection system in a CIDI engine as can be seen in

Figure 4.15. Thus, total delay time is td = td1 + td 2 . Here, delay td1 is the time delays from injector current command to actual lifting of the injector needle (This is decided by a value of needle lift signal.). Delay td 2 is the time delay from actual needle lifting to time

98 when the flow is sensed by the pressure sensor. The reason why these time delays are calculated is that these will be used in determining the crank angle position of actual fuel injection when current signal comes out. Therefore, modeling for these two delay times are necessary when there is no needle lift sensor in an actual engine. With available variables such as pulse width, rail pressure, back pressure, and current signal, it can be easily understood that delay time is related with the magnetic and hydraulic force exerted on the injector plunger. From this basic concept, the delay time modeling was done.

However, since delay td1 is a function of the fuel injection pressure, this delay time is modeled in terms of the rail pressure and back pressure. It can be easily understood that the needle lift movement is related with a force that is exerted on the needle plunger. And this force is related to some parameters such as the current to energize the solenoid, the pressure force (injection pressure), and the spring force. The rate of change of current is constant regardless of injection pressure and pulse width. (But, it could be considered when the strength of current is reduced.) It is obvious that this delay time is independent of pulse width. Therefore, we can assume that the delay time is a function of the injection pressure such that: td1 = f [(Pr − Pb )] = a1 + a2 Pr + a3 Pb

From this consideration together with the rig test data, the following simple regression function is obtained.

td1 = 0.4815 − 0.0001313× Pr − 0.00024× Pb (5.1)

The modeling result of delay time td1 is compared with actual test data in Figure 5.3. When applying this correlation in the real engine where a cylinder pressure sensor is not available, back-pressure could be assumed as fixed, say at 50 bar without significant loss of accuracy.

99

Figure 5.3: Injection delay time estimation

Another delay time to consider,td 2 , is the time delay between the time of needle lifting and the point of actual fuel injecting into a chamber. In a real engine, this time delay needs not to be considered. This time includes the transport delay time for fuel flow to the location of pressure sensor in this study as:

transport _ time = f injection _ velocity = Distance ()sound_speed

As shown in Figure 4.5, the distance between nozzle-tip and the sensor location is 4.5

β mm. When the sound_speed,c = v , the fluid bulk modulus, β is calculated by an ρ v experimental result [58] as follows:

β = 0.5208× P +1.3125 ×109 (5.2) v ( 100 )

100 where the pressure P is in MPa. The fuel density is calculated with Eqn. (3.11) as:

ρ = −0.686×T + 839.7 + 5171067.96×831.7 β , kg f v m3

9 When the injection pressure is 1000 bar, β v is about1.8333×10 Pa. The speed of sound is calculated to be 1500 m . Finally, we got the time delay due to transport as s 3.3×10−5 sec = 0.033msec , which is so small that it is negligible. However, as can be seen in Figure 5.3, the time delay td 2 is constant with about 0.2 msec. It can be thought that there is a delay time even after injector needle starts to open for fuel injection due to flow restriction. Moreover, this time delay is nearly constant independent of test condition. Therefore, total delay time can be estimated as:

t = t + t d d1 d 2 (5.3) = 0.4815 − 0.0001313× Pr − 0.00024× Pb + 0.2 [msec] Again, without loss of accuracy, the back pressure could be assumed to be a constant value of 50 bar, where a pressure sensor is not available in a running engine.

With the available parameters, the fuel injection rate modeling is carried out in the following section. The fuel injection rate will then be used in combustion model as input data.

5.3 Fuel injection flow rate modeling

Since the only available parameter that changes during the fuel injection for each test shot is the current signal, modeling with the current signal is tried. Moreover, the current signal is basically the same independent of two test conditions such as injection pressure and pulse width. Therefore, the current can be used as a primitive variable in fuel flow rate modeling. However, it is generally known that the flow rate is related to other parameters such as the injection pressure, the pulse width, and the fuel temperature. These parameters can be considered in the coefficient modeling. A stochastic estimation technique is applied in determining the coefficients set in the correlation. Linear and quadratic equations with current are first tried and summarized as follows.

101 Model Equation for flow rate ε % std % Q f Q& = A + A × I 1 f 1 2 -9.4 11.2

2 2 Q& f = A1 + A2 × I + A3 × I -3.4 9.4

Table 5.2: Fuel injection rate model evaluation: Model 1 and 2

The criteria for selecting an appropriate model are the error percentage in total flow calculation and average standard deviation percentage. Q f is the total fuel quantity

ε % ∑ Q f defined by Eqn.(4.1), and ε ,% = is the average value of ε of 45 test set. Q f N Q f N is the total number of test (45).

The standard deviation is defined by std % ≡ σ (Q& i,data − Q& i,est )/ max(Q& i,data )×100 [%]. And

std % the average standard deviation percentage is std %= ∑ N

Figure 5.4 shows the result of the flow rate modeling at one test condition. There is inaccurate prediction in flow rate estimation by model #1 during the initial stage of fuel injection. This can become an issue when the injection pulse width is short. Therefore, model #2 will be applied for fuel injection flow rate estimation in this research. But, there is still error in the closing stage, which is hard to be captured with stochastic estimation technique. And this is the reason why the flow rate model under-estimate. Since this stochastic function is related with current, signal flow rate becomes zero when there is no current. This is due to the fact that the estimation is static and does not contain dynamic terms.

102

Figure 5.4: Comparison of the fuel injection model

The coefficient sets calculated by model 1 and 2 are summarized in Table 5.3. As can be seen in the table, all coefficients are under-estimated. This is because flow rate is under-estimated due to the dynamic effect in the needle closing stage as mentioned before.

In the table, the error percentage in total flow is calculated as follows:

Q − Q ε = f ,est f ×100% Q f Q f It is clear that the prediction accuracy is high for long fuel pulse width, where the effects of needle closing stage are relatively small.

103 Test Model #1 Model #2 A1 A2 A1 A2 A3 unit −5 −3 ε std % −5 −3 −3 ε Q std % ×10 ×10 Q f ×10 ×10 ×10 f 1 0.1200 0.1604 -4.8 11.1 0.0789 0.3070 -0.8835 -3.1 9.5 2 0.0999 0.1563 -4.1 10.0 0.0586 0.3008 -0.8864 -2.4 7.2 3 0.0968 0.1605 -3.9 9.8 0.0612 0.2869 -0.7822 -2.4 7.6 4 0.1048 0.1607 -4.2 10.1 0.0612 0.2946 -0.8155 -2.5 8.7 5 0.1077 0.1609 -4.3 10.2 0.0607 0.3016 -0.8639 -2.4 8.7 6 0.1177 0.1585 -4.7 10.6 0.0682 0.2843 -0.7721 -2.7 9.5 7 0.1522 0.1534 -6.0 12.9 0.0957 0.2839 -0.7743 -3.7 11.8 8 0.1486 0.1570 -6.0 12.4 0.0933 0.2918 -0.8190 -3.7 11.2 9 0.1549 0.1580 -6.2 12.6 0.1026 0.2882 -0.7896 -4.0 11.5 10 0.1783 0.1549 -7.1 13.3 0.1040 0.2889 -0.8039 -4.0 11.9 11 0.1751 0.1490 -7.8 13.3 0.1084 0.2825 -0.8009 -4.7 11.9 12 0.1887 0.1541 -8.0 13.7 0.1229 0.2823 -0.7606 -5.1 11.4 13 0.2753 0.1543 -12.4 17.4 0.1992 0.2629 -0.6608 -8.7 16.6 14 0.2712 0.1512 -12.5 16.7 0.1839 0.2755 -0.7481 -8.2 15.4 15 0.2609 0.1506 -11.9 16.7 0.1688 0.2779 -0.7646 -7.4 15.2 16 0.0826 0.1488 -3.5 8.5 0.0278 0.2792 -0.7837 -1.2 6.1 17 0.0962 0.1456 -4.1 9.8 0.0383 0.2811 -0.7922 -1.6 7.6 18 0.0936 0.1473 -4.0 9.6 0.0393 0.2815 -0.7972 -1.7 7.4 19 0.0890 0.1457 -3.9 8.8 0.0475 0.2707 -0.7420 -2.3 7.1 20 0.0846 0.1433 -3.8 8.8 0.0433 0.2671 -0.7384 -1.9 7.0 21 0.0903 0.1447 -3.9 8.7 0.0461 0.2759 -0.7793 -2.0 6.8 22 0.1502 0.1419 -6.5 12.0 0.0921 0.2783 -0.7723 -3.9 10.4 23 0.1315 0.1422 -5.7 11.0 0.0760 0.2781 -0.7851 -3.2 9.2 24 0.1392 0.1423 -9.4 12.3 0.0624 0.2640 -0.7073 -2.7 10.4 25 0.1669 0.1417 -7.5 12.5 0.1055 0.2611 -0.6933 -4.6 11.1 26 0.1249 0.1398 -6.5 11.4 0.0809 0.2697 -0.7594 -4.2 9.5 27 0.1387 0.1389 -6.4 11.1 0.0691 0.2681 -0.7461 -3.1 9.0 28 0.2295 0.1370 -11.1 14.6 0.1365 0.2638 -0.7310 -6.3 12.8 29 0.2880 0.1375 -13.5 14.4 0.1151 0.2722 -0.7477 -5.2 12.6 30 0.3129 0.1373 -14.7 15.3 0.1187 0.2678 -0.7133 -5.4 13.3 31 0.2437 0.1259 -12.3 14.3 0.0923 0.2428 -0.6166 -4.5 11.3 32 0.2205 0.1247 -11.4 14.0 0.0983 0.2359 -0.5976 -4.9 11.5 33 0.1941 0.1238 -10.3 12.8 0.0915 0.2397 -0.6370 -4.6 11.4 34 0.1105 0.1253 -5.5 9.8 0.0637 0.2318 -0.5900 -3.1 7.9 35 0.1092 0.1288 -5.3 9.6 0.0669 0.2330 -0.5821 -3.2 7.9 36 0.1214 0.1306 -5.9 10.2 0.0739 0.2405 -0.6176 -3.4 8.4 37 0.1107 0.1322 -5.2 9.8 0.0509 0.2405 -0.6100 -2.3 8.0 38 0.1048 0.1291 -5.1 9.9 0.0454 0.2382 -0.6198 -2.1 8.0 39 0.0891 0.1297 -4.4 8.9 0.0406 0.2324 -0.6065 -2.0 7.2 40 0.0671 0.1318 -3.2 7.5 0.0321 0.2336 -0.5943 -1.5 5.8 41 0.0677 0.1335 -3.2 7.4 0.0324 0.2366 -0.6054 -1.5 5.6 42 0.0732 0.1356 -3.4 7.8 0.0393 0.2371 -0.6007 -1.8 6.3 43 0.0671 0.1373 -3.1 7.5 0.0280 0.2438 -0.6419 -1.3 5.8 44 0.0586 0.1342 -2.8 7.1 0.0262 0.2339 -0.6083 -1.2 5.5 45 0.0500 0.1341 -2.5 7.1 0.0217 0.2309 -0.5972 -1.1 5.7

Table 5.3: Coefficients comparison of model #1 and #2 used in Table 5.2

104 5.4 Coefficients modeling in flow rate model

Now we have a polynomial function for fuel injection flow rate estimation,

2 namely, Q& f = A1 + A2 × I + A3 × I (5.4) it is necessary to assess the dependency of individual coefficient on other variables in the model. There are 3 sets of coefficients in the flow rate model to calculate. Here, we want to express these coefficients as functions of other parameters such as the injection pressure, the pulse width, and possibly the back pressure. Therefore, it is possible that these coefficients are to be expressed as functions of these parameters. Calculating each coefficient in the flow rate equation and checking the dependency of these coefficients

( A1 , A2 , A3 ) on other parameters is done graphically. As can be seen in Figure 5.5, it is easily found that, first of all, there is a strong relationship between ∆P and each coefficient. Especially, for coefficient A1 , there are clear functional relationships with all available parameters. Therefore, each coefficient could be described in functional forms as follows:

A1 , A2 , A3 = f ()∆P, PW , Pb .

105 (a) Coefficient A1

(b) Coefficient A2

(c) Coefficient A3

Figure 5.5: Coefficients vs. injection pressure, pulse width 106 There will be lot of sets of coefficients in the full model, so that the notation of the subscripts for each coefficients need to be clarified as in Table 5.4:

1st Layer 2nd Layer 3rd Layer

= b ,b ,... = c ,c ,... , c ,c ,... A1 = {}a11,a12 ,... { 111 112 } { 1111 1112 } {}1121 1122

= {b121,b122 ,...} = {c1211,c1212 ,...}, {}c1221,c1222 ,... = b ,b ,... = c ,c ,... , c ,c ,... A2 = {}a21,a22 ,... { 211 212 } { 2111 2112 } {}2121 2122

= {b221,b222 ,...} = {c2211,c2212 ,...}, {}c2221,c2222 ,... = b ,b ,... = c ,c ,... , c ,c ,... A3 = {}a31,a32 ,... { 311 312 } { 3111 3112 } {}3121 3122

= {b321,b322 ,...} = {c3211,c3212 ,...}, {}c3221,c3222 ,...

Table 5.4: Nomenclature for coefficients at corresponding layer in the model

As can be seen in Figure 5.5, a linear or quadratic function of ∆P is enough to describe the functional relationship with relevant parameters. With this consideration, estimation of coefficients, Ai as a function of ∆P is carried out and the result are summarized in Table 5.5.

107 Coefficient Model Equation for Ai std % 2 1 A1 = a11 + a12 × ∆P + a13 × ∆P 18.1 A1 2 A1 = a11 + a12 × ∆P 18.1 2 1 A2 = a21 + a22 × ∆P + a23 × ∆P 2.7 A2 2 A2 = a21 + a22 × ∆P 2.9 2 1 A3 = a31 + a32 × ∆P + a33 × ∆P 4.5 A3 2 A3 = a31 + a32 × ∆P 4.8

Table 5.5: Coefficient model evaluation

In the table, “ std % ” is defined as standard deviation percentage of error in coefficient prediction divided by maximum coefficient of test data.

std % ≡ σ ()Ai,data − Ai,est / max( Ai )×100,[%] (5.5)

Although the model with a quadratic function form is slightly better than that with a linear function, there is no reason to adopt quadratic function when the difference between two models are negligible. Therefore, a linear function of ∆P is enough to represent the correlation for all coefficients, Ai . In other words, the model #2 in Table

5.5 is selected as a coefficient estimation function for all Ai with respect to ∆P . As can be inferred from the table, the accuracy of estimation of coefficients A2 and A3 as a function of ∆P only is already at a satisfactory level compared to that of coefficient A1 . In other words, while the coefficient A1 needs to be explored to find a more relevant correlation, coefficients A2 and A3 could be sufficiently expressed as a linear function of only ∆P . The coefficient set for the model #1 and #2 are calculated and summarized in Table 5.6. 108 Model #1: Model #2:

2 Ai = ai1 + ai2 × ∆P + ai3 × ∆P Ai = ai1 + ai2 × ∆P

−8 −7 a11 -4.165×10 a11 -4.551×10

−10 −10 A1 a12 4.060×10 a12 1.345×10

−13 a13 5.191×10

−6 −4 a21 7.770×10 a21 1.384×10

−7 −7 A2 a22 4.360×10 a22 1.393×10

−10 a23 -1.640×10

−4 −4 a31 5.350×10 a31 -2.434×10

−6 −7 A3 a32 -2.290×10 a32 -5.214×10

−10 a33 9.774×10

Table 5.6: Coefficients set calculated by model #1 and model #2

From the discussion so far, the following forms of correlation are proposed for the coefficients estimation in this study:

A1 = a11 + a12 × ∆P (5.6)

A2 = a21 + a22 × ∆P (5.7)

A3 = a31 + a32 × ∆P (5.8)

In Figure 5.6, the dependency of the coefficients upon the other remaining parameters such as the pulse width and the back pressure can be checked. There seems that other parameters have some relationship with the coefficient A1 . Coefficients A2 , A3 have also some weak relationship with the other parameters. The dependency of each

109 coefficient on pulse width is stronger than back pressure. So, relationship of these coefficients with pulse width needs to be checked in the followings until the dependency of these coefficients on variables is non-existent.

(a) A1 estimation by model #1 (b) A1 estimation by model #2

Continued

Figure 5.6: The comparison of coefficients estimation models

110 Figure 5.6 continued

(c) A2 estimation by model #1 (d) A2 estimation by model #2

(e) A3 estimation by model #1 (f) A3 estimation by model #2

First, a parameter analysis for the coefficient A1 will be carried out because of its strong dependency on the other two parameters, PW and Pb . The other coefficients then could be analyzed in the same way that coefficient A1 is estimated. Therefore, only the procedure for coefficient A1 estimation will be dealt with in detail and only the results of estimation for other two coefficients will be discussed instead of describing the detail process. 111 5.4.1 Coefficients modeling of A1

As can be seen in Figure 5.7, both coefficients a11 and a12 are strongly dependent on the pulse width, PW. Coefficient a11 can be estimated with a quadratic function of

PW, a12 as a linear function. A revised estimation form of coefficient for A1 is proposed as follows:

A1 = a11 + a12 × ∆P 2 = []b111 + b112 × PW + b113 × PW + []b121 + b122 × PW × ∆P

2 = b111 + b112 × PW + b113 × PW + b121 × ∆P + b122 × PW × ∆P (5.9)

Coefficient A1 is evaluated as follows.

⎡- 0.1189 ⎤ ⎢ ⎥ ⎢- 0.006722 ⎥ 2 −7 A1 = ⎢ 0.00000198 3 ⎥ []1 PW PW ∆P PW × ∆P ×10 ⎢ ⎥ ⎢ 0.025996 ⎥ ⎣⎢ - 0.00000622 4 ⎦⎥

Since the only remaining available parameter is the back pressure, it is needed to check whether coefficient A1 depends on back pressure or not. It would be reasonable only to look at the linear terms in Eqn. (5.9) for dependency on back pressure. As can be seen in Figure 5.7, A1 changes as the combination of PW, ∆P and the back pressure, Pb .

Namely, A1 increases as PW goes down and ∆P goes up. Therefore, it could be concluded that product terms of Pb with other variables needs to be considered in the forms as Pb ∆P, Pb PW , etc.

112 (a) a11 vs. PW (b) a12 vs. PW

−6 Coefficient a (Pr =1140 bar) x 10 11 1 Pb=75 bar 0.5 Pb=50 bar Pb=30 bar

11 0 a

−0.5

−1 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 −7 Coefficient a (Pr =970 bar) x 10 11 5

0 11 a −5

−10 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 −7 x 10 Coefficient a (Pr =780 bar) 0 11

−2

−411 a

−6

−8 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 PW (usec)

(c) a11 vs. PW and Pr

−9 Coefficient a (Pr =1140 bar) x 10 12 2.5 Pb=75 bar 2 Pb=50 bar Pb=30 bar

1.512 a

1

0.5 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 −9 Coefficient a (Pr =970 bar) x 10 12 2

1.5 12 a 1

0.5 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 −9 Coefficient a (Pr =780 bar) x 10 12 2

1.5 12 a 1

0.5 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 PW (usec)

(d) a12 vs. PW and Pr

Continued

Figure 5.7: Dependency of a1i on PW and Pb 113 Figure 5.7 continued

−6 Coefficient a (Pr =1140 bar) x 10 11 1 Pb=75 bar 0.5 Pb=50 bar Pb=30 bar

11 0 a

−0.5

−1 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 −7 Coefficient a (Pr =970 bar) x 10 11 5

0 11 a −5

−10 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 −7 x 10 Coefficient a (Pr =780 bar) 0 11

−2

−411 a

−6

−8 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 PW (usec)

(e) a11 vs. Pb

−9 Coefficient a (Pr =1140 bar) x 10 12 2.5 PW=3ms 2 PW=2.5ms PW=2ms

1.512 PW=1.5ms a PW=1ms 1

0.5 30 35 40 45 50 55 60 65 70 75 −9 Coefficient a (Pr =970 bar) x 10 12 2

1.5 12 a 1

0.5 30 35 40 45 50 55 60 65 70 75 −9 Coefficient a (Pr =780 bar) x 10 12 2

1.5 12 a 1

0.5 30 35 40 45 50 55 60 65 70 75 Pb (bar)

(f) a12 vs. Pb

The constant term in Eqn. (5.9), b111 needs to be calculated and checked if there is functional relationship. As can be seen in Figure 5.9, there is a linear functional

relationship with the back pressure, Pb .

114

Figure 5.8: A1 evaluation by Eqn.(5.9)

−7 Coefficient b (Pr =1140 bar) x 10 111 4 PW=3ms 2 PW=2.5ms PW=2ms PW=1.5ms 111 0 b PW=1ms −2

−4 30 35 40 45 50 55 60 65 70 75 −7 Coefficient b (Pr =970 bar) x 10 111 2

0 111 b −2

−4 30 35 40 45 50 55 60 65 70 75 −7 x 10 Coefficient b (Pr =780 bar) 2 111

1 111 b 0

−1 30 35 40 45 50 55 60 65 70 75 Pb (bar)

(a) b111 vs. Pb , Pr ,and PW (b) General trend of b111 vs. Pb

Figure 5.9: b111 vs. Pb by Eqn. (5.9) 115 From these considerations, the final form of coefficient A1 is as follows:

A1 = a11 + a12 × ∆P 2 = []b111 + b112 × PW + b113 × PW + []b121 + b122 × PW × ∆P

2 = b111 + b112 × PW + b113 × PW + b121 × ∆P + b122 × PW × ∆P .

With considering the function of Pb , coefficients can be proposed as

b111 = c1111 + c1112 × Pb , b112 = c1121 + c1122 × Pb , b113 = c1131 , b121 = c1211 + c1212 × Pb , b122 = c1221 .

Substituting these proposed coefficients into Eqn. (5.9) gives:

A = [][]c + c × P + c + c P × PW + c × PW 2 + [c + c × P ]× ∆P 1 1111 1112 b 1121 1122 b 1131 1211 1212 b + c1221 × PW × ∆P.

Rearranging this equation results in:

2 A1 = c1111 + c1112 × Pb + c1121 × PW + c1122 × Pb × PW + c1131 × PW + c1211 × ∆P (5.10) + c1212 × Pb × ∆P + c1221 × PW × ∆P.

There are 8 coefficients for the expression of A1 . The calculation result of coefficient A1 in Eqn. (5.10) is as follows:

⎡- 0.1606 ⎤ ⎢ ⎥ ⎢- 0.00061 ⎥ ⎢ 0.0000002 ⎥ ⎢ ⎥ 0.00249766 A = ⎢ ⎥[]1 P PW P × PW PW 2 ∆P P × ∆P PW × ∆P ×10 −6 1 ⎢- 0.0000006 ⎥ b b b ⎢ ⎥ ⎢ 0.0013706 ⎥ ⎢- 0.00000083 ⎥ ⎢ ⎥ ⎣⎢ 0.00000365 9 ⎦⎥

The comparison of coefficient A1 of Eqn. (5.10) with the test data is shown in Figure 5.10. 116

Figure 5.10: Comparison A1 of Eqn. (5.10) with test data

The effect of each model can be evaluated with Table 5.7. When only the effect of the back pressure term is considered, the result of the coefficient modeling is found to be good by improving the standard deviation percentage from 6.4% to 5.7%, which could be neglected. Moreover, in a real engine in which the cylinder pressure is hard to measure, the back pressure could be deemed as constant value say, at 50 bars. This portion of the error is assessed by assuming a constant value of back pressure at 50 bars. Calculation of std % gives 6.4% when Pb are set to constant pressure at 30 and 50 bar, 15.7% when Pb is set at 70 bar. Therefore, the effect of back pressure can be neglected without great loss of accuracy especially when the rail pressure is high and pulse width is long. But, the effect of back pressure is relatively great at short pulse width (low load). Therefore, whenever the issue of estimation at short pulse width is expected, this back pressure effect should be considered as the final model suggested. Additionally, the case for short pulse width needs to be checked as shown in Figure 5.11 while the rail and back pressure are held constant.

117 Equation Equation for coefficient A std % No. 1 A = a + a × ∆P (5.6) 1 11 12 18.1 A = b + b × PW + b × PW 2 + b × ∆P + b × PW × ∆P (5.9) 1 111 112 113 121 122 6.4

2 A1 = c1111 + c1112 × Pb + c1121 × PW + c1122 × Pb × PW + c1131 × PW (5.10) 5.7 + c1211 × ∆P + c1212 × Pb × ∆P + c1221 × PW × ∆P

Table 5.7: Comparison of each model by standard deviation %

Figure 5.11: Coefficient A1 evaluation at short pulse width

118 Since we made the best model for coefficient A1 estimation with available parameters, it would be helpful to find an optimal model from a point of view of efficiency and to avoid over-estimation possibility. We proposed 15 models and assessed their prediction accuracy by standard deviation percentage defined by Eqn.(5.5), std % . The result are summarized in Table 5.8.

std % Eqn. No. Equation for coefficient A1 A 18.1 (5.6) A1 = a1 + a2 × ∆P B 2 18.1 A1 = a1 + a2 × ∆P + a3 × ∆P C 8.4 A1 = a1 + a2 × PW + a3 × ∆P D 2 12.4 A1 = a1 + a2 × PW + a3 × PW E 2 8.3 A1 = a1 + a2 × PW + a3 × ∆P + a4 × ∆P F 2 7.2 A1 = a1 + a2 × PW + a3 × PW + a4 × ∆P G (5.9) 2 6.4 A1 = a1 + a2 × PW + a3 × PW + a4 × ∆P + a5 × PW × ∆P H 7.9 A1 = a1 + a2 × PW + a3 × ∆P + a4 × Pb I 9.5 A1 = a1 + a2 × PW + a3 × ∆P + a4 × Pb + a5 × PW × Pb A = a + a × PW + a × PW 2 + a × ∆P + a × P × PW J 1 1 2 3 4 5 b 6.8 + a6 × PW × ∆P K 2 6.7 A1 = a1 + a2 × PW + a3 × PW + a4 × ∆P + a5 × Pb × PW + a6 × Pb L 2 6.7 A1 = a1 + a2 × PW + a3 × PW + a4 × ∆P + a5 × PW × ∆P + a6 × Pb 2 M A1 = a1 + a2 × PW + a3 × PW + a4 × ∆P + a5 × PW × ∆P + a6 × Pb 7.3

+ a7 × Pb × ∆P 2 N (5.10) A1 = a1 + a2 × PW + a3 × PW + a4 × ∆P + a5 × PW × ∆P + a6 × Pb 5.7

+ a7 × Pb × ∆P + a8 × Pb × PW 2 O A1 = a1 + a2 × PW + a3 × PW + a4 × ∆P + a5 × PW × ∆P + a6 × Pb 5.8

+ a7 × Pb × PW

Table 5.8: Comparison of each model for coefficient A1 by std %

119 As can be seen in the table, when the ∆P 2 term is added or deleted, there is no significant effect on the std % . This can be also confirmed when Eqn. C and Eqn. E or F in the table

2 are compared. Thus, the ∆P term is not a major one in estimating coefficient A1 . Therefore, it is confirmed that the linear form of ∆P is enough and the ∆P 2 term is the possible source of over-estimation. Although a simple linear combination of all available parameters is also a good choice for estimation model as in Eqn. (5.9), it still needs a better model in this study. When the term Pb × PW in Eqn. M in Table 5.8 is added, std % is dropped from 7.3 % to 5.7 % as in Eqn. N in the table, from which the importance of the term, Pb × PW can be confirmed. It could be concluded that the effect of this term on A1 is insignificant when the term Pb × ∆P is eliminated. However, this term needs to be retained because it is apparent that it has some effect on the coefficient as explained previously with Figure 5.10. The Eqn. N in the table is selected as the final model of estimation for coefficient A1 in this study. The correlation for coefficient A1 is written together with the detail numerical values of model coefficients, ai as follows:

⎡- 0.1606 ⎤ ⎢ ⎥ ⎢- 0.00061 ⎥ ⎢ 0.0000002 ⎥ ⎢ ⎥ 0.00249766 A = ⎢ ⎥[]1 P PW P × PW PW 2 ∆P P × ∆P PW × ∆P ×10 −6 . 1 ⎢- 0.0000006 ⎥ b b b ⎢ ⎥ ⎢ 0.0013706 ⎥ ⎢- 0.00000083 ⎥ ⎢ ⎥ ⎣⎢ 0.00000365 9 ⎦⎥

5.4.2 Coefficients modeling of A2

As mentioned previously, coefficients A2 can also be estimated in the same way as done with coefficient A1 . Starting with Eqn. (5.7), both two coefficient terms a21 and a22 were found to have a linear relationship with PW and Pb .

120 Therefore, a revised form of the coefficient estimation function for A2 can be proposed as follows:

A = a + a × ∆P 2 21 22 = [][]b211 + b212 × PW + b221 + b222 × PW × ∆P

= b211 + b212 × PW + b221 × ∆P + b222 × PW × ∆P (5.11)

The benefit of the coefficient estimation of A2 is to improve the standard deviation from std % =2.9 to std % =2.3. But, the shape of the revised model is more reasonable. Coefficient A2 in Eqn. (5.11) is calculated and the result is as follow:

⎡ 0.1821 ⎤ ⎢- 0.000022 ⎥ A = ⎢ ⎥ []1 PW ∆P PW × ∆P ×10 −3 2 ⎢ 0.0000785 ⎥ ⎢ ⎥ ⎣ 0.00000003 0⎦

The estimation results by Eqn (5.11) are compared with estimation result by the original Eqn. (5.7) in Figure 5.12.

(a) Eqn.(5.10) (%std =2.3%) (b) Eqn. (5.7) ( std % =2.9%)

Figure 5.12: Comparison of coefficient A2 by two estimation models 121 However, there is still an incorrect trend which is related to the back pressure especially at the low rail pressure. Thus, a constant term in the coefficient model, b211 needs to be evaluated and checked if there is a functional relationship as shown in Figure 5.13.

−4 Coefficient b (Pr =1140 bar) x 10 211 2

1.9 PW=3ms 1.8 PW=2.5ms PW=2ms 211

b PW=1.5ms 1.7 PW=1ms 1.6 30 35 40 45 50 55 60 65 70 75 −4 Coefficient b (Pr =970 bar) x 10 211 2

1.9 211 b 1.8

1.7 30 35 40 45 50 55 60 65 70 75 −4 Coefficient b (Pr =780 bar) x 10 211 2

1.9 211 b 1.8

1.7

1.6 30 35 40 45 50 55 60 65 70 75 Pb (bar)

(a) Coefficient b211 vs. Pb (b) Global trend of b211 vs. Pb

Figure 5.13: b211 vs. Pb by the revised model

As for coefficientb211 , there is a functional relationship with the back-pressure,

Pb as can be seen in Figure 5.14. It is also recommended that the product terms of

Pb with the other variables need to be considered (such as Pb ∆P ). This is because the differences of A2 values become greater as functions of Pb , ∆P and PW.

122 −8 Coefficient b (Pr =1140 bar) x 10 221 10

9 PW=3ms 8 PW=2.5ms 221 PW=2ms b 7 PW=1.5ms PW=1ms 6 30 35 40 45 50 55 60 65 70 75 −8 x 10 Coefficient b (Pr =970 bar) 10 221

9 221

b 8

7 30 35 40 45 50 55 60 65 70 75 −8 Coefficient b (Pr =780 bar) x 10 221 10

9

221 8 b

7

6 30 35 40 45 50 55 60 65 70 75 Pb (bar)

(a) Coefficient b221 vs. Pb (b) Global trend of b221 vs. Pb

Figure 5.14: b221 vs. Pb with Eqn. (5.11)

Therefore, the following form of the correlation is appropriate for coefficient estimation A2 . Considering the function of Pb , coefficients in Eqn. (5.11) can be proposed as:

b211 = c2111 + c2112 × Pb , b212 = c2121 , b221 = c2211 + c2212 × Pb , b222 = c2221

Substituting the proposed coefficients into Eqn. (5.11) gives:

A2 = []c2111 + c2112 × Pb + c2121 × PW + [c2211 + c2212 × Pb ]× ∆P + c2221 × PW × ∆P .

Rearranging this equation results in:

A2 = c2111 + c2112 × Pb + c2121 × PW + c1211 × ∆P + c2212 × Pb × ∆P + c2221 × PW × ∆P (5.12)

There are 6 coefficients for the expression of A2 . The calculation result of coefficient A2 in Eqn (5.12) is as follows:

123 ⎡ 0.1438 ⎤ ⎢ ⎥ ⎢ - 0.00002 ⎥

⎢ 0.000112 ⎥ −3 A2 = ⎢ ⎥ []1 Pb PW ∆P Pb × ∆P PW × ∆P ×10 ⎢ 0.00000003 ⎥ ⎢ 0.00069232 ⎥ ⎢ ⎥ ⎣⎢ - 0.00000060 7 ⎦⎥

However, it should be checked whether Pb terms in Eqn. (5.12) needs to be included in the final model. The Figure 5.15 shows the effect of considering the back pressure in coefficient estimation. With final model to include the back pressure effect, the estimated data agree well with test data at low rail pressure. But the improvement in standard deviation is not so great (from 2.3 to 2.1 %). Moreover, the shape is not different from that of result calculated by Eqn. (5.11). Therefore, it would be better not to include Pb term in the A2 estimation model to avoid an overestimation problem in a real engine. Thus, the final estimation model for coefficient A2 is given by Eqn. (5.11).

(a) Eqn. (5.11) ( std % =2.1%) (b) Eqn. (5.10) ( std % =2.3%)

Figure 5.15: Comparison of coefficient A2 124 Since the final estimation model is prepared, it is necessary to find an optimal model starting with the final model. The result of this exploration is summarized in Table 5.9.

Parameter Pb will be eliminated because the effect of Pb is not so much as the case of coefficient A1 . Eqn (5.12) remains as an optimal model for coefficient A2 .

A2 = b211 + b212 × PW + b221 × ∆P + b222 × PW × ∆P .

Eqn. No. Equation for coefficient A2 std %

1 (5.7) A2 = a1 + a2 × ∆P 2.9

2 2 A2 = a1 + a2 × ∆P + a3 × ∆P 2.7

3 A2 = a1 + a2 × PW + a3 × ∆P + a4 × Pb 2.4

4 (5.10) A2 = a1 + a2 × PW + a3 × ∆P + a4 × PW × ∆P 2.3

5 A2 = a1 + a2 × PW + a3 × ∆P + a4 × PW × ∆P + a5 × Pb 2.2 A = a + a × PW + a × ∆P + a × P × ∆P + a × PW × ∆P 6 (5.11) 2 1 2 3 4 b 5 2.1 + a6 × Pb A = a + a × PW + a × ∆P + a × P × ∆P + a × PW × ∆P 7 2 1 2 3 4 b 5 2.0 + a6 × Pb + a7 × Pb × PW

2 8 A2 = a1 + a2 × PW + a3 × PW 7.3

Table 5.9: Comparison of each model for coefficient A2 by std %

5.4.3 Coefficients modeling of A3

Coefficients A3 can be estimated exactly the same way as coefficient A2 . 125 Starting with Eqn.(5.8), both coefficients a31 and a32 can be estimated with a linear function of PW. A revised form of coefficient estimation model for A3 is proposed as follows:

A3 = a31 + a32 × ∆P

= [][]b311 + b312 × PW + b321 + b322 × PW × ∆P (5.13)

= b311 + b312 × PW + b321 × ∆P + b322 × PW × ∆P

Coefficient A3 in Eqn. (5.13) is calculated as:

⎡ - 0.4049 ⎤ ⎢ 0.000079 ⎥ A = ⎢ ⎥ []1 PW ∆P PW × ∆P ×10 −3 3 ⎢ - 0.0002814 ⎥ ⎢ ⎥ ⎣ - 0.00000011 9⎦

The effect of including pulse width in estimation model can be confirmed in Figure 5.16.

(a) Eqn. (5.13): (std % = 4.0 %) (b) Eqn.(5.8): (std % = 4.8 %)

Figure 5.16: Comparison of coefficient A3

126 Introducing the same method as performed for coefficient A2 and rearranging Eqn. (5.13) results in Eqn. (5.14):

A3 = c3111 + c3112 × Pb + c3121 × PW + c3211 × ∆P + c3212 × Pb × ∆P + c3221 × PW × ∆P (5.14)

There are 6 coefficients for the expression of A3 . The calculation result of coefficient A3 in Eqn (5.14) is as follows:

⎡ - 0.3031 ⎤ ⎢ ⎥ ⎢ 0.00008 ⎥

⎢ - 0.000381 ⎥ −3 A3 = ⎢ ⎥ []1 Pb PW ∆P Pb × ∆P PW × ∆P ×10 ⎢ - 0.0000001 ⎥ ⎢ - 0.00189989 ⎥ ⎢ ⎥ ⎣⎢ 0.00000186 4 ⎦⎥

As can be seen in Figure 5.17, the improvement in standard deviation with this model is not so great (from 4.0 to 3.9 %). However, with the same reason as in the case for coefficient A2 , Eqn. (5.13) is chosen as the final estimation model for coefficient A3 :

A3 = b311 + b312 × PW + b321 × ∆P + b322 × PW × ∆P

Coefficient A3 in Eqn. (5.13) is evaluated as follows:

⎡ - 0.4049 ⎤ ⎢ 0.000079 ⎥ A = ⎢ ⎥ []1 PW ∆P PW × ∆P ×10 −3 3 ⎢ - 0.0002814 ⎥ ⎢ ⎥ ⎣ - 0.00000011 9⎦

127 (a) Eqn (5.14) ( std % = 3.9 %) (b) Eqn (5.13), ( std % = 4.0 %)

Figure 5.17: Comparison of coefficient A3 by Eqn. (5.13) and (5.14)

The next step is to explore the final estimation model to find an optimal model starting with the final model. The result of this exploration is summarized in Table 5.10 and Eqn

(5.13) remains as an optimal estimation model for coefficient A3 :

A3 = b311 + b312 × PW + b321 × ∆P + b322 × PW × ∆P .

128 Eqn. No. Equation for coefficient A3 std %

1 A = a + a × ∆P 4.8 3 1 2

2 2 A3 = a1 + a2 × ∆P + a3 × ∆P 4.5

3 A3 = a1 + a2 × PW + a3 × ∆P + a4 × Pb 4.2

4 (5.13) A3 = a1 + a2 × PW + a3 × ∆P + a4 × PW × ∆P 4.0

5 A3 = a1 + a2 × PW + a3 × ∆P + a4 × PW × ∆P + a5 × Pb 4.0 A = a + a × PW + a × ∆P + a × P × ∆P + a × PW × ∆P 6 (5.14) 3 1 2 3 4 b 5 3.9 + a6 × Pb A = a + a × PW + a × ∆P + a × P × ∆P + a × PW × ∆P 7 3 1 2 3 4 b 5 3.6 + a6 × Pb + a7 × Pb × PW

2 8 A3 = a1 + a2 × PW + a3 × PW 9.8

Table 5.10: Comparison of each model for coefficient A3 by std %

Table 5.11 shows the degree of improvement by each model for coefficient estimation in terms ofstd % . While the estimation for coefficient A1 is greatly improved, cases for

A2 and A3 remain the same.

In summary, the detailed coefficients can be found in Table 5.12 for each equation.

129 Original std % Final std %

A1 = c1111 + c1112 × Pb + c1121 × PW 2 A A = a + a × ∆P + c1122 × Pb × PW + c1131 × PW 1 1 11 12 18.1 5.7 + c1211 × ∆P + c1212 × Pb × ∆P

+ c1221 × PW × ∆P

A A = a + a × ∆P A2 = b211 + b212 × PW + b221 × ∆P 2 2 21 22 2.9 2.3 + b222 × PW × ∆P

A A = a + a × ∆P A3 = b311 + b312 × PW + b321 × ∆P 3 3 31 32 4.8 4.0 + b322 × PW × ∆P

Table 5.11: Summary of the final model for coefficient estimation

Table 5.12 shows the comparison of coefficients estimation by the final model and its original test data. In the table, the error percentage of coefficients estimation is defined as:

(A − A ) ε ()% ≡ i i,est ×100 . Ai

130 A1×10−5 A2×10−3 A3×10−3 No. Test Data (Eqn. 5-6,7,8) Final Model (Eqn. 5-9,11,13) A1 A2 A3 A1 ε (%) A2 ε (%) A3 ε (%) 1 0.0789 0.3070 -0.8835 0.0611 -22.6 0.2874 -6.4 -0.8014 -9.3 2 0.0586 0.3008 -0.8864 0.0558 -4.9 0.2905 -3.4 -0.8129 -8.3 3 0.0612 0.2869 -0.7822 0.0515 -16.0 0.2934 2.3 -0.8238 5.3 4 0.0612 0.2946 -0.8155 0.0653 6.7 0.2945 0.0 -0.8280 1.5 5 0.0607 0.3016 -0.8639 0.0691 13.8 0.2906 -3.7 -0.8134 -5.8 6 0.0682 0.2843 -0.7721 0.0745 9.2 0.2873 1.0 -0.8009 3.7 7 0.0957 0.2839 -0.7743 0.0973 1.6 0.2867 1.0 -0.7988 3.2 8 0.0933 0.2918 -0.8190 0.0916 -1.8 0.2901 -0.6 -0.8113 -0.9 9 0.1026 0.2882 -0.7896 0.0871 -15.1 0.2931 1.7 -0.8228 4.2 10 0.1040 0.2889 -0.8039 0.1188 14.2 0.2921 1.1 -0.8191 1.9 11 0.1084 0.2825 -0.8009 0.1243 14.7 0.2899 2.6 -0.8108 1.2 12 0.1229 0.2823 -0.7606 0.1286 4.6 0.2853 1.1 -0.7936 4.3 13 0.1992 0.2629 -0.6608 0.1701 -14.6 0.2845 8.2 -0.7905 19.6 14 0.1839 0.2755 -0.7481 0.1663 -9.5 0.2894 5.0 -0.8087 8.1 15 0.1688 0.2779 -0.7646 0.1612 -4.5 0.2921 5.1 -0.8191 7.1 16 0.0278 0.2792 -0.7837 0.0393 41.3 0.2686 -3.8 -0.7310 -6.7 17 0.0383 0.2811 -0.7922 0.0425 11.0 0.2660 -5.4 -0.7211 -9.0 18 0.0393 0.2815 -0.7972 0.0459 16.8 0.2625 -6.8 -0.7081 -11.2 19 0.0475 0.2707 -0.7420 0.0540 13.8 0.2629 -2.9 -0.7096 -4.4 20 0.0433 0.2671 -0.7384 0.0506 17.0 0.2668 -0.1 -0.7242 -1.9 21 0.0461 0.2759 -0.7793 0.0468 1.5 0.2689 -2.5 -0.7321 -6.1 22 0.0921 0.2783 -0.7723 0.0647 -29.7 0.2696 -3.1 -0.7347 -4.9 23 0.0760 0.2781 -0.7851 0.0677 -10.9 0.2662 -4.3 -0.7221 -8.0 24 0.0624 0.2640 -0.7073 0.0726 16.4 0.2636 -0.2 -0.7122 0.7 25 0.1055 0.2611 -0.6933 0.1006 -4.6 0.2637 1.0 -0.7128 2.8 26 0.0809 0.2697 -0.7594 0.0960 18.7 0.2669 -1.0 -0.7248 -4.6 27 0.0691 0.2681 -0.7461 0.0933 34.9 0.2706 0.9 -0.7383 -1.0 28 0.1365 0.2638 -0.7310 0.1306 -4.3 0.2704 2.5 -0.7378 0.9 29 0.1151 0.2722 -0.7477 0.1351 17.4 0.2680 -1.5 -0.7289 -2.5 30 0.1187 0.2678 -0.7133 0.1390 17.1 0.2641 -1.4 -0.7143 0.1 31 0.0923 0.2428 -0.6166 0.0970 5.2 0.2367 -2.5 -0.6116 -0.8 32 0.0983 0.2359 -0.5976 0.0945 -3.8 0.2403 1.9 -0.6252 4.6 33 0.0915 0.2397 -0.6370 0.0920 0.6 0.2431 1.4 -0.6356 -0.2 34 0.0637 0.2318 -0.5900 0.0605 -4.9 0.2428 4.7 -0.6345 7.5 35 0.0669 0.2330 -0.5821 0.0626 -6.3 0.2399 3.0 -0.6236 7.1 36 0.0739 0.2405 -0.6176 0.0649 -12.1 0.2363 -1.7 -0.6100 -1.2 37 0.0509 0.2405 -0.6100 0.0434 -14.8 0.2363 -1.8 -0.6100 -0.0 38 0.0454 0.2382 -0.6198 0.0411 -9.4 0.2398 0.7 -0.6231 0.5 39 0.0406 0.2324 -0.6065 0.0390 -3.8 0.2426 4.4 -0.6335 4.5 40 0.0321 0.2336 -0.5943 0.0273 -14.9 0.2419 3.5 -0.6309 6.1 41 0.0324 0.2366 -0.6054 0.0295 -8.8 0.2395 1.2 -0.6220 2.7 42 0.0393 0.2371 -0.6007 0.0316 -19.6 0.2362 -0.4 -0.6095 1.5 43 0.0280 0.2438 -0.6419 0.0297 6.3 0.2359 -3.3 -0.6085 -5.2 44 0.0262 0.2339 -0.6083 0.0279 -0.8 0.2392 2.3 -0.6210 2.1 45 0.0217 0.2309 -0.5972 0.0264 21.4 0.2423 4.9 -0.6325 5.9 std % 5.7 2.3 4.0

Table 5.12: Comparison of coefficients calculated by the final model

131 5.4.4 Fuel injection rate with model coefficients estimation Ai

The final set of model coefficients to be used in fuel injection flow rate model is summarized in Table 5.13.

Final equation for each coefficient 2 A1 = c1111 + c1112 × Pb + c1121 × PW + c1122 × Pb × PW + c1131 × PW A1 Eqn. (5.9) + c1211 × ∆P + c1212 × Pb × ∆P + c1221 × PW × ∆P

A2 Eqn. (5.10) A2 = b211 + b212 × PW + b221 × ∆P + b222 × PW × ∆P

A3 Eqn. (5.13) A3 = b311 + b312 × PW + b321 × ∆P + b322 × PW × ∆P

Table 5.13: Model coefficients to be used in injection rate model

The final form of fuel injection rate estimation is described in the following. This will be used in the injection rate estimation model as an input for the CIDI engine combustion model.

2 Q& f = A1 + A2 × I + A3 × I 2 = c1111 + c1112 × Pb + c1121 × PW + c1122 × Pb × PW + c1131 × PW

+ c1211 × ∆p + c1212 × Pb × ∆P + c1221 × PW × ∆P

+ []b211 + b212 × PW + b221 × ∆P + b222 × PW × ∆P × I 2 + []b311 + b312 × PW + b321 × ∆P + b322 × PW × ∆P × I

132 5.4.5 Validation of the injection flow rate estimation model

Generally, the total fuel injection quantity per cycle is linearly proportional to the injection pulse width when the injection pulse width is large. But, when the pulse width is short like as in case of the pilot injection, a linear relationship between the fuel quantity and pulse width no longer exists. In this study, since the current profile from the injector solenoid is used, the non-linearity is already reflected in the fuel injection model. Since a full polynomial function for the fuel injection flow rate estimation was prepared, it is necessary to validate this correlation with test data. The representative cases are plotted and compared with test data in Figure 5.18. The following two criteria will be applied in evaluating the performance of the model:

(1) std % ≡ σ (Q& i,data − Q& i,est )/ max(Q& i,data )×100 [%] Q − Q (2)ε = f ,est f ×100 []% Q f Q f where the total fuel quantity is calculated with Q = Q& dt . The average values of f ∫ f ε and std % for the 45 test data are -4.4% and 9.6%, respectively. This flow rate model Q f will be used in combustion model after being transformed to mass flow rate by multiplying the fuel density correlation in Eqn.(3.11) using the equation,

m& f ,est = ρQ& f ,est = f (current ()t ; Pr ,Pb ,PW,Tf )

As can be seen in Figure 5.18, every source of error in estimating the fuel injection flow rate originates from the period when the model disagrees with test data during needle closing portion. The final model evaluations of coefficients estimation for all cases are summarized in summarized in Table 5.14.

133 (a) The case of average ε (b) The case of average std % Q f

(c) The worst case of ε (d) The best case of ε Q f Q f

(e) The worst case of ε and std % (f) The best case of std % Q f

Figure 5.18: Model validation with test data for representative cases

134 Test PW Validation Result Pb Q f Pr unit [ µ s] [bar] −10 [bar] Q ε % 10 f Q f std % 1 3000 75 7.9507 1145 7.4078 -6.8 9.7 2 3000 50 7.5174 1142 7.4628 -0.7 8.7 3 3000 30 7.6431 1143 7.5111 -1.7 8.7 4 2500 30 6.3982 1151 6.2148 -2.9 8.7 5 2500 50 6.3884 1143 6.1487 -3.8 8.5 6 2500 75 6.3470 1144 6.1096 -3.7 9.3 7 2000 75 5.1203 1140 4.8475 -5.3 11.5 8 2000 50 5.0943 1139 4.8671 -4.5 11.0 9 2000 30 5.1642 1141 5.9007 14.3 11.4 10 1500 30 3.7587 1134 3.5839 -4.7 11.6 11 1500 50 3.6518 1138 3.5730 -2.2 12.1 12 1500 75 3.8277 1130 3.5325 -7.7 12.2 13 1000 75 2.4751 1124 2.2334 -9.8 16.4 14 1000 50 2.4342 1134 2.2587 -7.2 15.4 15 1000 30 2.4138 1134 2.2791 -5.6 15.3 16 3000 30 7.1714 965 6.9603 -2.9 6.9 17 3000 50 7.2863 966 6.9606 -4.5 8.2 18 3000 75 7.2749 966 6.8753 -5.5 8.0 19 2500 75 5.9206 969 5.7100 -3.6 7.1 20 2500 50 5.7731 972 5.7599 -0.2 7.1 21 2500 30 5.8956 967 5.7954 -1.7 6.7 22 2000 30 4.9261 972 4.5061 -8.5 10.2 23 2000 50 4.8407 968 4.5831 -5.3 9.1 24 2000 75 4.7832 974 4.5493 -4.9 11.2 25 1500 75 3.5486 975 3.3657 -5.2 11.0 26 1500 50 3.4241 973 3.2367 -5.5 9.6 27 1500 30 3.4065 979 3.4059 -0.0 9.2 28 1000 30 2.2549 978 2.1745 -3.6 13.0 29 1000 50 2.3217 981 2.1611 -6.9 12.7 30 1000 75 2.3568 978 2.1523 -8.7 13.5 31 1000 75 2.2198 781 2.0036 -9.7 12.9 32 1000 50 2.1309 782 2.0130 -5.5 12.5 33 1000 30 2.0458 782 2.0166 -1.4 10.9 34 1500 30 3.1711 780 3.1620 -0.3 8.0 35 1500 50 3.2424 779 3.1417 -3.1 7.9 36 1500 75 3.2962 778 3.1135 -5.5 8.3 37 2000 75 4.4804 778 4.1957 -6.4 8.4 38 2000 50 4.3157 778 4.2245 -2.1 8.4 39 2000 30 4.1620 778 4.2249 1.5 7.7 40 2500 30 5.3608 773 5.3307 -0.6 5.8 41 2500 50 5.4031 776 5.2820 -2.2 5.6 42 2500 75 5.4810 777 5.2255 -4.7 6.4 43 3000 75 6.5860 775 6.2424 -5.2 6.1 44 3000 50 6.3367 774 6.2995 -0.6 5.6 45 3000 30 6.1954 776 6.3337 2.2 5.9 Average -4.4 9.6

Table 5.14: Comparison of the model with test data by the total injection fuel quantity

135 5.4.6 Comparison of the model using the needle lift signal

Since the injector needle lift signal is available in the test engine, a model which used the lift signal is evaluated by comparing it with the model using the current signal. Exactly the same procedure was followed as the case for the current in order to get a fuel injection rate estimation model.

Starting with following equation for rate estimation model as a function of the lift, a set of model coefficients were identified with the test data:

2 Q& f = A1 + A2 × lift + A3 × lift

The results of model coefficients estimation, A1, A2 ,and A3 are summarized in Table 5.15 to Table 5.16.

Applying these estimated model coefficients, the injection rate profiles are also compared with the test data as shown in Figure 5.19. As can be seen in this figure, this is nearly the same as the model used the injector current profile.

The fuel injection rate estimation results are compared in detail with those of the test data in Table 5.17.

To conclude, the advantage of applying the needle lift signal for fuel injection rate estimation model is not significant compared with the model using the current. When the needle lift signal is not available in the test engine, the estimation model with the current could be applied except for calculating the dynamic start of injection with minimum error of prediction as in this study. Moreover, the bouncing behavior of the needle lift at the closing phase of needle could distract the estimation model. Therefore, the fuel injection estimation model as a function of the injector current profile will be applied in this research.

136 (a) The worst case of ε (b) The best case of ε Q f Q f

(c) The worst case of ε and std % Q f (d) The best case of std %

Figure 5.19: Model validation with test data for representative cases

137 std % Eqn. No. Equation for coefficient A1 A 12.3 A1 = a1 + a2 × ∆P B 2 12.3 A1 = a1 + a2 × ∆P + a3 × ∆P C 10.0 A1 = a1 + a2 × PW + a3 × ∆P D 2 10.0 A1 = a1 + a2 × PW + a3 × PW E 2 9.9 A1 = a1 + a2 × PW + a3 × ∆P + a4 × ∆P F 2 8.9 A1 = a1 + a2 × PW + a3 × PW + a4 × ∆P G 2 8.8 A1 = a1 + a2 × PW + a3 × PW + a4 × ∆P + a5 × PW × ∆P H 9.8 A1 = a1 + a2 × PW + a3 × ∆P + a4 × Pb I 9.5 A1 = a1 + a2 × PW + a3 × ∆P + a4 × Pb + a5 × PW × Pb A = a + a × PW + a × PW 2 + a × ∆P + a × P × PW J 1 1 2 3 4 5 b 8.7 + a6 × PW × ∆P K 2 8.3 A1 = a1 + a2 × PW + a3 × PW + a4 × ∆P + a5 × Pb × PW + a6 × Pb L 2 8.6 A1 = a1 + a2 × PW + a3 × PW + a4 × ∆P + a5 × PW × ∆P + a6 × Pb 2 M A1 = a1 + a2 × PW + a3 × PW + a4 × ∆P + a5 × PW × ∆P + a6 × Pb 8.5

+ a7 × Pb × ∆P 2 N A1 = a1 + a2 × PW + a3 × PW + a4 × ∆P + a5 × PW × ∆P + a6 × Pb 8.2

+ a7 × Pb × ∆P + a8 × Pb × PW

Table 5.15: Comparison of coefficient model by needle lift A1

138 Eqn. No. Equation for coefficient A2 std %

A A1 = a1 + a2 × ∆P 3.7 2 B A1 = a1 + a2 × ∆P + a3 × ∆P 3.7

C A1 = a1 + a2 × PW + a3 × ∆P 3.4 2 D A1 = a1 + a2 × PW + a3 × PW 3.0 E 2 3.4 A1 = a1 + a2 × PW + a3 × ∆P + a4 × ∆P 2 F A1 = a1 + a2 × PW + a3 × PW + a4 × ∆P 2.9 2 G A1 = a1 + a2 × PW + a3 × PW + a4 × ∆P + a5 × PW × ∆P 2.8

H A1 = a1 + a2 × PW + a3 × ∆P + a4 × Pb 3.3

I A1 = a1 + a2 × PW + a3 × ∆P + a4 × Pb + a5 × PW × Pb 3.3 J A = a + a × PW + a × PW 2 + a × ∆P + a × P × PW 2.7 1 1 2 3 4 5 b + a6 × PW × ∆P K 2 2.7 A1 = a1 + a2 × PW + a3 × PW + a4 × ∆P + a5 × Pb × PW + a6 × Pb L 2 2.9 A1 = a1 + a2 × PW + a3 × PW + a4 × ∆P + a5 × PW × ∆P + a6 × Pb M A = a + a × PW + a × PW 2 + a × ∆P + a × PW × ∆P + a × P 2.8 1 1 2 3 4 5 6 b + a7 × Pb × ∆P N A = a + a × PW + a × PW 2 + a × ∆P + a × PW × ∆P + a × P 2.7 1 1 2 3 4 5 6 b + a7 × Pb × ∆P + a8 × Pb × PW

(a) Coefficient A2

std % Eqn. No. Equation for coefficient A3

A A1 = a1 + a2 × ∆P 5.2 2 B A1 = a1 + a2 × ∆P + a3 × ∆P 5.2

C A1 = a1 + a2 × PW + a3 × ∆P 5.1

H A1 = a1 + a2 × PW + a3 × ∆P + a4 × Pb 5.1

I A1 = a1 + a2 × PW + a3 × ∆P + a4 × Pb + a5 × PW × Pb J A = a + a × PW + a × PW 2 + a × ∆P + a × P × PW 4.3 1 1 2 3 4 5 b + a6 × PW × ∆P K 2 4.3 A1 = a1 + a2 × PW + a3 × PW + a4 × ∆P + a5 × Pb × PW + a6 × Pb L 2 4.3 A1 = a1 + a2 × PW + a3 × PW + a4 × ∆P + a5 × PW × ∆P + a6 × Pb

(b) Coefficient A3

Table 5.16: Comparison of coefficient model by needle lift

139 Validation Result Test PW P Q P b f r Current (I) Needle Lift −10 unit [ µ s] [bar] 10 [bar] Q ε std % Q ε f Q f f Q f std % 1 3000 75 7.9507 1145 7.4078 -6.8 9.7 7.8524 -1.2 7.9 2 3000 50 7.5174 1142 7.4628 -0.7 8.7 7.8024 3.8 7.5 3 3000 30 7.6431 1143 7.5111 -1.7 8.7 7.8086 2.2 7.2 4 2500 30 6.3982 1151 6.2148 -2.9 8.7 6.5188 1.9 8.6 5 2500 50 6.3884 1143 6.1487 -3.8 8.5 6.4967 1.7 8.2 6 2500 75 6.3470 1144 6.1096 -3.7 9.3 6.4985 2.4 8.1 7 2000 75 5.1203 1140 4.8475 -5.3 11.5 5.2649 2.8 8.6 8 2000 50 5.0943 1139 4.8671 -4.5 11.0 5.2398 2.9 8.5 9 2000 30 5.1642 1141 5.9007 14.3 11.4 5.2421 1.5 8.8 10 1500 30 3.7587 1134 3.5839 -4.7 11.6 3.8501 2.4 9.2 11 1500 50 3.6518 1138 3.5730 -2.2 12.1 3.8620 5.8 9.3 12 1500 75 3.8277 1130 3.5325 -7.7 12.2 3.8626 0.9 9.4 13 1000 75 2.4751 1124 2.2334 -9.8 16.4 2.4869 0.5 12.2 14 1000 50 2.4342 1134 2.2587 -7.2 15.4 2.4972 2.6 12.2 15 1000 30 2.4138 1134 2.2791 -5.6 15.3 2.4895 3.1 12.6 16 3000 30 7.1714 965 6.9603 -2.9 6.9 7.0856 -1.2 7.2 17 3000 50 7.2863 966 6.9606 -4.5 8.2 7.1201 -2.3 8.1 18 3000 75 7.2749 966 6.8753 -5.5 8.0 7.1096 -2.3 7.7 19 2500 75 5.9206 969 5.7100 -3.6 7.1 6.0515 2.2 7.1 20 2500 50 5.7731 972 5.7599 -0.2 7.1 6.0421 4.7 7.1 21 2500 30 5.8956 967 5.7954 -1.7 6.7 6.0345 2.4 6.6 22 2000 30 4.9261 972 4.5061 -8.5 10.2 4.8808 -0.9 10.5 23 2000 50 4.8407 968 4.5831 -5.3 9.1 4.8591 0.4 9.5 24 2000 75 4.7832 974 4.5493 -4.9 11.2 4.8898 2.2 10.5 25 1500 75 3.5486 975 3.3657 -5.2 11.0 3.6871 3.9 9.0 26 1500 50 3.4241 973 3.2367 -5.5 9.6 3.6575 6.8 9.0 27 1500 30 3.4065 979 3.4059 -0.0 9.2 3.6284 6.5 8.8 28 1000 30 2.2549 978 2.1745 -3.6 13.0 2.3641 4.8 12.0 29 1000 50 2.3217 981 2.1611 -6.9 12.7 2.3780 2.4 12.0 30 1000 75 2.3568 978 2.1523 -8.7 13.5 2.3875 1.3 11.8 31 1000 75 2.2198 781 2.0036 -9.7 12.9 2.2798 2.7 12.0 32 1000 50 2.1309 782 2.0130 -5.5 12.5 2.2293 4.6 12.3 33 1000 30 2.0458 782 2.0166 -1.4 10.9 2.1788 6.5 12.3 34 1500 30 3.1711 780 3.1620 -0.3 8.0 3.3863 6.8 8.9 35 1500 50 3.2424 779 3.1417 -3.1 7.9 3.4040 5.0 8.5 36 1500 75 3.2962 778 3.1135 -5.5 8.3 3.4425 4.4 8.4 37 2000 75 4.4804 778 4.1957 -6.4 8.4 4.5134 0.7 10.5 38 2000 50 4.3157 778 4.2245 -2.1 8.4 4.4836 3.9 10.6 39 2000 30 4.1620 778 4.2249 1.5 7.7 4.5292 8.8 8.6 40 2500 30 5.3608 773 5.3307 -0.6 5.8 5.5127 2.8 6.8 41 2500 50 5.4031 776 5.2820 -2.2 5.6 5.5283 2.3 6.8 42 2500 75 5.4810 777 5.2255 -4.7 6.4 5.5586 1.4 6.9 43 3000 75 6.5860 775 6.2424 -5.2 6.1 6.4354 -2.3 7.0 44 3000 50 6.3367 774 6.2995 -0.6 5.6 6.4023 1.0 6.6 45 3000 30 6.1954 776 6.3337 2.2 5.9 6.3728 2.9 7.1 Average -4.4 9.6 Average 2.6 9.1

Table 5.17: Comparison of the model by the total injection fuel quantity: Current and needle lift

140 6 CHAPTER 6

PARAMETER IDENTIFICATION FOR CIDI ENGINE COMBUSTION AND NOx MODEL AND MODEL VALIDATION

6.1 Introduction

Models for the CIDI engine combustion and NOx have been developed so far and test for the model validation have been done, too. Then, the next step in this research will be to identify relevant parameters that were used in these models by validation tests.

Thus, in this chapter, parameters for the combustion and NOx model will be identified by adopting numerical techniques such as the stochastic estimation technique. For the combustion model, the parameters in the ignition model and the combustion heat release model will be identified, and parameters to be used in temperature calculation in NOx model will also be identified.

6.2 Ignition modeling

Since it is widely known that ignition is the most important parameter in CIDI engine combustion, it needs to be modeled and predicted as precisely as possible. The subsequent phenomenon in CIDI engine combustion could be determined by the ignition. There are two phenomena to be considered in the ignition process: one is the mechanical behavior such as fuel spray, evaporation and mixing with surrounding air and the other is the chemical reaction. In single zone combustion model approach, fuel is evaporated and completely mixed with necessary oxygen as it is injected. Therefore, only the chemical reaction side is usually considered in most ignition models when using a simple

141 combustion model. The ignition delay time model that will be used in this study is Eqn.

(3.7), at constant pressure, Pcy and temperature Tcy :

−n ⎛ T ⎞ τ = AP exp⎜ a ⎟ sec (3.7) cy ⎜ ⎟ [] ⎝ Tcy ⎠

The pre-exponential factor A is modeled by some research such as Watson and Assanis, and the activation temperature Ta is equivalent to the activation energy divided by gas constant, and n is a constant. It is known that Ta and n are functions of the cylinder pressure. These parameters will be modeled by analyzing the test data in this study as follows.

The ignition activation temperature in the ignition model, Ta , is calculated with a standard value of the parameter n (=1.02) by matching the calculated start of combustion (SOC) with that of test data of the first fuel injection. The reason why the first injection test cases are chosen for model parameter identification is that it is difficult to determine the ignition point for the other injection cases (2nd and 3rd injection). The SOC’s of the multiple fuel injections test are estimated graphically by examining the net heat release rate calculated by Eqn (3-3). The detailed plots can be found in Figure 4.20 to Figure 4.22. The method to locate the SOC in the test data is explained as follows with Figure 6.1. For the first SOC, find a crank angle which the heat release rate are larger than a nHRR criteria (the heat release rate from the pilot injection), say 5 (J/deg), then locate the SOC by decreasing the coordinate by 1 degree from that point until nHRR becomes negative. This method is possible since there is always a point where nHRR changes from negative to positive nHRR . Although this could be done numerically, but the other SOCs need to be found graphically by a nHRR curve with the same logic.

142 (a) Locating ignition timing (SOC) in a typical (pilot + main) fuel injection test

(b) Locating ignition timing (SOC) in a typical 3-strike fuel injection test

Figure 6.1: Locating the start of combustion point using the nHRR curve

There are lot of factors related with the actual ignition mechanism in CIDI engine such oxygen concentration, gas velocity, turbulence, gas temperature, and pressure. However, these factors could be dealt with in dimensional analysis such as CFD code. With the single zone approach for combustion model like this study, simple and controllable parameters need to be selected as independent variables for the curve fitting function. As can be seen in the test data, the start of injection timing (SOI) is selected as an appropriate parameter to represent ignition mechanism in CIDI engine combustion.

143 From this discussion, the 3rd order curve-fitting of the test data at the engine speed of 1800 rpm as a function of SOI gives the following result to be used in ignition model:

3 2 2 4 6 Ta = −0.089× SOI + 91.915×10 × SOI − 31.681×10 × SOI + 3.639×10 SOI in [CA]

(6.1)

Next, the parameter n is calculated with the same method as that used for Ta calculation, where Ta is calculated with the Eqn. (6.1). As can be seen in Figure 6.2, n could be assumed as constant, 1.01. All these calculation results are summarized in Table 6.1.

Figure 6.2: Parameter n in the ignition model from the test data

144 Fuel Injection Schedule Test Data Ignition First SOI Model Pilot Main Post Injection

SOI PW SOI PW SOI PW SOC Delay Ta (n=1.02) n Ta (n=1.01) CA us CA us CA us CA CA K - K

340 340 200 354 400 355 100 350 10 2600 1.01 2500 340 340 200 354 400 363 100 350 10 2500 1.02 2375 340 340 200 351 400 370 100 350 10 2700 1.00 2560

340 340 200 354 500 349 9 2550 1.02 2500 340 340 200 351 500 349 9 2550 1.02 2500 340 340 200 360 500 350 10 2550 1.02 2535 340 340 200 354 400 350 10 2600 0.99 2565

354 354 500 365 11 3000 1.02 2925 356 356 500 368 12 3000 1.02 2960 352 352 500 363 11 2950 1.02 2850 350 350 500 360 10 2950 1.02 2850

340 340 200 354 500 350 10 2650 0.98 2625 330 330 200 354 500 344 14 2500 1.04 2440 348 348 200 354 500 357 9 2600 1.02 2690 340 340 200 351 500 349 10 2600 0.98 2500 340 340 200 360 500 350 10 2600 0.98 2500

354 354 500 366 12 3000 1.00 3000 351 351 500 362 11 3050 1.00 2925 357 357 500 368 11 2950 1.00 2850

340 340 200 354 400 365 100 350 10 2600 1.00 2625 330 330 200 354 400 365 100 346 16 2600 1.00 2560 340 340 200 354 400 362 100 350 10 2500 1.03 2500 340 340 200 354 400 368 100 350 10 2400 1.05 2375

Table 6.1: Start of combustion (SOC) and ignition delay time of test data at 1800 rpm

145 With a constant n given by 1.01, the same procedure is repeated to get the expression of the activation temperature Ta as in Eqn. (6.2):

3 2 2 4 Ta = −0.112× SOI +1.157 ×10 × SOI − 3.986×10 × SOI (6.2) + 4.576×106 SOI in []CA

The result of this calculation can be seen in Table 6.1. This could be used at other engine speeds because ignition timing remains the same as the engine speed changes, which can be confirmed in test data that follows. Estimated values of Ta are shown in Figure 6.3, which are in good agreement with the test data. Even though there are wide variations of Ta and n value when the SOI is equal to 340 CA, the variation of SOC is still within 1 CA, which is a satisfactory result.

Figure 6.3: Parameter Ta vs. SOI in ignition model from test data

146 The final ignition model that will be used in this study is:

−1.01 ⎛ T ⎞ τ = 3.45P exp⎜ a ⎟ (6.3) cy ⎜ ⎟ ⎝Tcy ⎠ where Ta = f ()SOI and is given by Eqn (6-2):

T = −0.112× SOI 3 +1.157 ×102 × SOI 2 − 3.986×104 × SOI a + 4.576×106 SOI in []CA

Applying this ignition model, the predicted ignition timing (SOC) is tabulated and compared with test data in Figure 6.4 and Table 6.2.

The statistical evaluations of the modeling result are summarized in the Table 6.4. The error range of prediction for the first injection is about ± 2 [CA] . And the standard deviation of SOC difference σ [SOCmodel − SOCtest ] is 1.05. The mean value of

[]SOCmodel − SOCtest is -0.37, which means that the ignition model under-predict the SOC by a quarter crank angle.

Figure 6.4: Validation of ignition model by SOC

147 Fuel Injection Schedule Test Model Case PILOT MAIN POST Pilot Main Post Pilot Main Post No. Speed SOI PW SOI PW SOI PW SOC SOC SOC SOC SOC SOC Unit rpm CA us CA us CA us CA CA CA CA CA CA 0 340 200 355 400 366 100 350 362 368 350 361 369 1 340 200 354 400 365 100 350 361 368 350 361 369 3 340 200 354 400 363 100 350 362 368 351 362 368 4 340 200 351 400 370 100 350 359 376 349 357 374 5 340 200 354500 349 361 349 360 6 340 200 351500 349 358 349 357 7 340 200 360500 350 367 350 365 8 340 200 354400 350 361 349 360 9 340 200 354600 349 361 350 361 10 354 500 365 365 11 356 500 368 367 12 340 200 360 500 351 370 350 366 13 352 500 363 363 14 350 500 360 360 15 1800 340 200 354500 350 361 349 360 16 330 200 354500 344 363 345 360 17 348 200 354500 357 362 359 364 18 340 200 351500 350 359 349 357 19 340 200 348500 350 357 350 356 20 340 200 360500 350 368 350 366 21 354 500 366 365 22 351 500 362 362 23 348 500 359 359 24 357 500 368 369 25 340 200 354400 365 100 350 362 368 349 360 369 26 330 200 354400 365 100 346 363 370 346 360 369 27 348 200 354400 365 100 357 361 372 359 364 370 28 340 200 354400 362 100 350 362 369 351 361 367 29 340 200 354 400 368 100 350 362 368 352 362 371 41 340 200 354450 349 361 349 362 42 340 200 360 450 349 368 348 366 44 330 200 354 450 345 362 343 360 45 345 200 354 450 353 362 354 362 46 340 200 354 450 349 361 348 360 47 330 200 354 450 345 362 345 359 48 345 200 354 450 353 362 353 360 49 340 100 354 300 370 100 350 361 375 348 361 373 50 340 100 354 200 370 200 350 360 378 349 362 373 51 340 100 350 300 370 100 350 357 375 348 357 372 52 340 100 354 300 365 100 350 361 367 350 362 369 53 340 200 354 300 370 200 350 360 377 349 360 373 54 1500 340 200 354 300 367 200 349 360 373 349 360 370 55 340 200 354 300 364 200 350 360 370 349 360 368 56 340 200 354 300 360 200 350 360 366 349 360 364 57 340 200 352 300 364 200 350 364 370 348 357 367 58 340 200 350 300 364 200 350 357 370 348 356 367 59 340 200 356 300 364 200 350 363 369 348 361 368 60 340 200 360 300 367 200 350 367 374 348 365 370 61 340 200 360 400 367 100 350 368 375 349 365 370 62 340 200 358 400 367 100 350 366 375 348 363 370 63 340 200 354 400 367 100 349 361 374 349 360 369 64 340 200 354 400 365 100 349 361 367 349 360 368 65 340 200 354 400 364 100 349 361 366 349 360 367 67 340 200 350 400 365 100 349 357 371 348 356 368

Table 6.2: Validation of ignition model

148 1st Injection 2nd Injection 3rd Injection Test Model Test Model Test Model 350 350 362 361 368 369 350 350 361 361 368 369 350 351 362 362 368 368 350 349 359 357 376 374 349 349 361 360 368 369 349 349 358 357 370 369 350 350 367 365 372 370 350 349 361 360 369 367 349 349 361 361 368 371 365 365 370 366 375 373 368 367 361 360 378 373 351 350 363 360 375 372 363 363 362 364 367 369 360 360 359 357 377 373 350 349 357 356 373 370 344 345 368 366 370 368 357 359 362 360 366 364 350 349 363 360 370 367 350 350 361 364 370 367 350 350 362 361 369 368 366 365 362 362 374 370 362 362 361 362 375 370 359 359 368 366 375 370 368 369 362 360 374 369 350 349 362 362 367 368 346 346 361 360 366 367 357 359 362 359 371 368 350 351 362 360 350 352 361 361 349 349 360 352 349 348 357 357 345 343 361 362 353 354 360 360 349 348 360 360 345 345 360 360 353 353 360 360 350 349 364 357 350 349 357 356 350 348 363 361 350 350 367 365 350 349 368 365 349 349 366 363 350 349 361 360 350 350 361 360 350 348 361 360 350 348 357 356 350 348 350 348 350 349 350 348 349 349 349 349 349 349 349 348

Table 6.3: Comparison of estimated SOC with test data for each fuel injection

149 (a) Validation of ignition model for the 1st injection

(b) Validation of ignition model for the 2nd injection

(c) Validation of ignition model for the 3rd injection

Figure 6.5: Validation of ignition model for each injection by SOC 150 1st Injection 2nd Injection 3rd Injection Standard deviation,σ 1.05 1.91 2.31 [CA]

Mean value [CA] -0.37 -1.30 -1.74

Table 6.4: Statistical evaluation of ignition model for each fuel injection by the

difference of SOI (SOCest − SOCtest )

Here, σ = standarddeviation of (SOCest − SOCtest ).

The mean error of ignition prediction of the model for all fuel injection cases is about -1 CA, meaning that the model under-estimates 1 crank angle degree. The standard deviation of the error for the entire data set is 1.8 CA.

151 6.3 Watson combustion modeling

6.3.1 Watson combustion model

Total fuel can be calculated with the fuel injection rate model which was explained in the previous chapter. The fuel burn rate is given as the sum of two dimensionless burn modes weighted by the factor β :

⎡ dM p dM d ⎤ ⎢β + ()1− β ⎥ ⎣ dθ dθ ⎦

c p2 c p1 cd 2 where, M p = 1− (1−τ ) , M d = 1− exp(− cd1τ ) as given by Eqn. (3.5),

θ −θig τ is the dimensionless time from ignition given by, τ = , and ∆=θbendigθθ − is a ∆θb combustion duration and is given by 100 (CA) as a datum value, which needs to be large enough to complete combustion. In the relationship of the combustion duration with the fuel injection pulse width is shown and duration is known as a function of engine speed and load. Combustion durations when the injection pulse widths are 600 and 400 µ sec are 50 and 40 CA, respectively, as can be checked in the figure. And combustion duration in the model is usually used as twice as this actual duration, i.e. 100 CA. Moreover, there is no comment or modeling on this combustion duration in other study. Thus, in this study this burn duration will be correlated with the fuel injection pulse width. A typical behavior of CIDI engine combustion mode can be found in Figure 6.7.

152

Figure 6.6: Combustion duration in CIDI engine

Figure 6.7: A typical combustion mode in CIDI engine 153 6.3.2 Parameters in combustion model

The general form of model parameters that was adopted by Watson will be also used in this study. However, sub-parameters that are included in each model parameter need to be correlated with engine operating conditions such as EGR and SOI. In Watson heat release rate model, there are 5 shape factors to be identified: β,C p1 ,C p2 ,Cd1 ,Cd 2 . The effects of each shape factor on the combustion model and other approaches on these parameters modeling are summarized and explained in the Table 6.5.

β c p1 c p2 cd1 cd 2

Burn duration Timing of peak Timing of peak of Burn duration of Definition Weighting factor of diffusion of diffusion premixed burn premixed burn burn burn Function f (φig ,td ) f (φig ,td ) Constant f (φig ) f (φig )

Reason Fuel evaporated Timing of peak Watson’s during delay improving until time 5000 proposal Final β β a 5000 −b d 1− β φ 2 t 3 a + a × (rpm × t ) 3 c = aφ c = c(c ) 1 ig d 1 2 d d1 ig d 2 d1 form Constant, independent Constant, Constant, of engine independent of independent of engine engine

f ()Prail ,td ,rpm Arsie f (Prail ) 5000 f (φ,td , rpm) constant et al Reason Identification [80] No comment result Strategy ⎛φ ,t ,⎞ ig d To be To be To be in this f ⎜ ⎟ To be determined ⎜ ⎟ determined determined determined study ⎝ EGR ⎠

Table 6.5: The summary table of combustion model parameters estimation model

154 Watson discussed that, first of all, parameters cd1 and β are the major factors to be modeled in CIDI engine combustion model. In the following, the effect of each parameter on combustion behavior is briefly explained.

1) The burning mode factor

The burning mode factor determines the portion of fuel to be burned in premixed combustion mode out of total fuel injected. This factor strongly depends on the ignition delay and trapped equivalence ratio at ignition:

m p β2 β3 β = = 1− β1φig td m fuel _ inj

Typical parameters for the burning mode factor are as follows:

0.37 −0.26 β = 1− 0.926φig td

It is strange that a positive exponent is used for the φig in this expression. It would be reasonable that β is proportional to φig as well as td .

2) Premixed combustion mode

Large c p2 means a steep heat release rate curve and the timing of the peak is controlled by c p1 . A typical form of the parameters are

−8 2.4 c p1 = 2 +1.25×10 × (rpm × td ) and c p2 = 5000 .

3) Diffusion combustion mode

Parameter cd1 decreases with increasing trapped equivalence ratio. Thus, it can be used as means of relating the effective combustion duration to the equivalence ratio.

Parameter cd 2 determines the timing of peak value in diffusion combustion mode and is just a function of cd1 , namely the equivalence ratio.

155 A constant value will be used for the shape factor c p2 as other studies have suggested. From now on, the other 4 parameters, β,C p1 ,Cd1 ,Cd 2 need to be identified from the test data by using appropriate data regression techniques.

6.3.3 Parameter identification in combustion model

The cylinder pressure will be used for parameter identification of combustion model instead of the heat release rate profile because the heat release rate curve is intrinsically very sensitive to small pressure data variation due to the pressure derivative term in the equation. Another reason for this is that the cylinder pressure profile will be ultimately used in the evaluation of IMEP and NOx.

In this study, a Matlab function, 'fminsearch' is used to calculate the 4 shape factors (β,C p1 ,Cd1 ,Cd 2 ) from the test data. Since the main injection has the most important and dominant effect on the entire combustion, shape factors were calculated only for the main fuel injection combustion when the multiple fuel injections schedule is applied. As the criteria for the error evaluation, the prediction accuracy of the pressure profile is applied in the following way.

Prediction error(residual), ε = Pest (θ )− Ptest (θ )

∑ε 2 Root mean square error, rms[]ε = i N where N corresponds to the actual main burn duration excluding the tail burn period and equal to about 30 crank angle when the pulse width is 500 µ sec . A specific method is necessary to avoid ‘the local solution’ in minimizing the error when using Matlab fminsearch function. For a fuel pilot + main injection case, for example, the shape factors are evaluated by finding the coefficients to minimize the residual of cylinder pressure trace during the main fuel injection combustion period from the SOC. Only the main fuel injection combustion will be analyzed for combustion parameters. The result of the parameter identification for the main fuel injection case could be applied to the other fuel 156 injection cases such as pilot or post-main fuel injection where the fuel injection pulse width and start of injection are different from those of the main injection. For the combustion parameter identification, 20 test cases are selected out of 60 test cases by applying some criterion such as the normal test data and representative test case. Those test conditions are the engine speed, EGR, and fuel injection schedule. After optimizing the combustion parameters, these parameters estimation results will be validated by applying it to the other test cases which are different from the test data used for identification. Test data for the main fuel injection combustion and combustion model parameters calculated by using the fminsearch function are summarized in Table 6.6. In the table, the ignition delay time td and the trapped equivalence ratio during this time,φig are calculated with the test data, not with the model.

The graphical representations of these parameters at each test conditions (the fuel injection schedule, engine speed, and EGR) are shown in Figure 6.8. Although there is no distinct difference in the test data, a more thorough analysis of each parameter in terms of the engine operating variables will reveal some relationships between these parameters. From the information presented by these figures, the range and trend of each parameter could be captured.

157 PW SOC SOC SOI MAF t e AF EGR φig t β C p1 Cd1 Cd 2 rpm Main Total d CA us g/s - % CA CA - Ms - - - -

1800 356 500 500 50 42 0.0 368 368 0.21 0.74 0.7 2.6 30.0 2.5

1800 352 500 500 50 42 0.0 363 364 0.19 0.65 0.6 2.1 28.9 2.1

1800 350 500 500 49 42 0.0 360 360 0.16 0.56 0.6 2.6 28.9 2.6

1800 354 500 700 51 38 0.0 361 362 0.05 0.28 0.4 3.0 30.2 2.0

1800 354 400 600 49 51 0.0 361 361 0.06 0.28 0.4 3.5 28.1 3.4

1800 351 400 700 50 45 0.0 359 359 0.10 0.37 0.4 2.8 29.7 3.3

1800 348 500 500 42 36 15 359 359 0.23 0.65 0.6 2.5 41.9 2.9

1800 357 500 500 43 37 14 368 369 0.25 0.65 0.7 3.1 27.3 3.1

1800 351 500 700 44 32 12 359 358 0.10 0.37 0.4 3.6 30.3 3.0

1800 360 500 700 43 39 15 368 368 0.09 0.37 0.4 3.6 27.3 3.1

1800 354 400 700 40 52 19 361 362 0.09 0.28 0.4 4.0 28.1 3.4

1800 354 400 700 42 41 16 362 365 0.11 0.37 0.4 2.1 27.0 3.1

1500 360 450 550 39 47 0.0 368 368 0.14 0.56 0.4 3.0 26.7 3.3

1500 354 450 550 39 48 0.0 362 363 0.14 0.56 0.4 2.4 27.6 3.2

1500 354 450 550 39 46 0.0 362 362 0.15 0.56 0.4 2.8 27.3 3.1

1500 354 300 500 38 68 0.0 361 363 0.10 0.44 0.4 2.5 28.1 3.4

1500 352 300 700 38 60 0.0 364 358 0.07 0.33 0.4 4.3 27.8 3.2

1500 360 300 700 38 68 0.0 367 366 0.09 0.44 0.4 4.5 29.2 3.4

1500 354 400 700 38 47 0.0 361 361 0.10 0.44 0.4 3.0 28.1 3.2

1500 350 400 700 39 45 0.0 357 357 0.12 0.44 0.4 3.4 28.7 3.3

Table 6.6: Test condition and combustion model parameters calculated by the least square error estimation method with test data

158 Beta at 1800 rpm 0.8 Single 2−strike 0.7 3−strike Single EGR 0.6 2−strike EGR 3−strike EGR Beta 0.5

0.4

0.3 0 1 2 3 4

Beta at 1500 rpm 0.46 2−strike 0.44 3−strike

0.42

0.4 Beta

0.38

0.36

0.34 1 2 3 4 5 Data Point

Figure 6.8: The trend of the burning mode factor, β

C at 1800 rpm p1 4.5 Single 4 2−strike 3−strike Single EGR 3.5 2−strike EGR

p1 3−strike EGR C 3

2.5

2 0 0.5 1 1.5 2 2.5 3 3.5 4

C at 1500 rpm p1 4.5 2−strike 3−strike 4

3.5p1 C

3

2.5 0 1 2 Data3 Point 4 5 6

Figure 6.9: The trend of the model shape factor, C p1 159 C at 1800 rpm d1 45 Single 2−strike 40 3−strike Single EGR 2−strike EGR 3−strike EGR 35 d1 C 30

25 0 1 2 3 4

C at 1500 rpm d1 42 2−strike 40 3−strike 38 36 34 d1 C 32 30 28 26 0 1 2 3 4 5 6 Data Point

Figure 6.10: The trend of the model shape factor, C d1

C at 1800 rpm d2 3.5 Single 2−strike 3−strike 3 Single EGR 2−strike EGR 3−strike EGR d2 C

2.5

2 0 1 2 3 4

C at 1500 rpm d2 3.5 2−strike 3−strike

3 d2 C

2.5

2 0 1 2 3 4 5 6 Data Point

Figure 6.11: The trend of the model shape factor, Cd 2

160

Now, the functional correlations for each model parameter in terms of the available variables will be searched using a non-linear curve fitting technique. First, the model parameters calculated above from the test data will be analyzed by the physical reasoning. The original model developed by Watson will be tried and compared with test data, and then an appropriate model will be proposed and compared with others when some improvement are expected. Moreover, it would be helpful to find out if there is a relationship between the

EGR gas and operating variables such as MAF, AF, td andφig . As can be seen in Figure 6.12, it is obvious that there are relationships between EGR gas and MAF, AF due to the compressor dynamics and the reduced exhaust pressure. It is also easily inferred that when the EGR is induced, the ignition delay time could increase by the insufficient concentration of oxygen in the combustion chamber, but it is balanced with the increased intake temperature as the hot EGR gas is introduced. However, the trapped equivalence ratioφig could be related with the EGR gas, where the overall equivalence ratio (AF) increases due to EGR-VGT interaction as confirmed in Figure 6.12 (a). The close relationship between td andφig could be confirmed in the Figure 6.12 (c).

161

(a) MAF and AF vs. EGR %

(b)td andφig vs. EGR %

(c) φig vs. td

Figure 6.12: The relationship of the EGR % with variables MAF, AF, td andφig

162 First, the parameter identification procedure for the burning mode factor β is performed with test data which are shown in Table 6.6 and Figure 6.13 graphically. From that figure, it could be assumed that there are functional relationships between the burning mode factor and the operating parameters, that is to say, β = f (td ,φig ).

Burning Mode Factor vs. Delay Time 0.75 1800 rpm 1800 rpm w/ EGR 0.7 1500 rpm

0.65

0.6

0.55 Beta 0.5

0.45

0.4

0.35

0.3 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 t (ms) d

(a) β vs. EGR % (b) β vs. ignition delay, td

Burning Mode Factor vs. Engine Speed 0.75 Single Injection Multiple Injection 0.7

0.65

0.6

0.55 Beta 0.5

0.45

0.4

0.35

0.3 1300 1400 1500 1600 1700 1800 1900 2000 Engine Speed (rpm)

(c) β vs. trapped equivalence ratio, φig (d) β vs. engine speed

Figure 6.13: The trend of burning mode factor β

163 β2 β3 Watson originally proposed the burning mode factor as β = 1− β1φig td . First, the constants applied in this model will be identified from the test data using the RMS error analysis. The results are depicted in Figure 6.14 including the error estimation of the model. The original model was used in this estimation using the same un-tuned constants as developed by Watson.

Figure 6.14: The comparison of the estimated burning mode factor β by the untuned Watson model with test data

164 With this un-tuned Watson model, the RMS error is so large that this un-tuned model could not be used in the combustion model as it is. Next, the effect of the tuned model is tried to be checked.

Comparison of Beta by Tuned Watson

test 0.8 est

0.6 Beta 0.4

0.2 0 2 4 6 8 10 12 14 16 18 20 Data Point Evaluation of Beta by Tuned Watson

0.7 1800 rpm 1800 rpm w/ EGR 1500 rpm 0.6

0.5

Estimated Beta 0.4

0.3

0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 Test Beta

Figure 6.15: The comparison of the estimated burning mode factor β by the tuned Watson model with test data

165 It would be notable that the sign of the constant in the trapped equivalence ratio is not consistent with the physical meaning which was discussed with Figure 6.12.

However, the RMS error calculated with the tuned model, which is 16.4%, is still not acceptable. Therefore, a totally different model is tried with a stochastic estimation technique with respect to all available variables. But, the relevant variable should be kept as small as possible due to the unexpected estimation error under the extreme condition of the relevant parameters. The functional form of each model and the result of the root mean square error estimation are summarized in Table 6.7.

166 Model Equation Model RMS error (%)

0.37 −0.26 Un-tuned β = 1− 0.926φig td 35.0 Watson 16.4 −0.333 −0.0274 Tuned β = 1− 0.267φig td single injection: 25.0 ⎡ 1.786 ⎤ ⎢ ⎥ ⎢- 0.00186 ⎥ ⎢0.16 ⎥ ⎢ ⎥ 0.01 ⎢ ⎥⎡1 SOC EGR PW ⎤ ⎢ ⎥ main 1.21281 ⎢ ⎥ β = ⎢ ⎥⎢ φign td MAF ⎥ 4.3 ⎢ -.078 ⎥⎢ ⎥ PW PW2 SOC ×PW ⎢ 0.006 ⎥⎣ main main ⎦ ⎢ ⎥ ⎢0.0069 ⎥ ⎢ - 0.0000103 ⎥ Proposed Model ⎢ ⎥ ⎣⎢ 0.0000376 ⎦⎥ ⎡ 0.778 ⎤ ⎢ ⎥ ⎢ - 0.00984 ⎥ ⎢ 1.274 ⎥ ⎢ ⎥⎡1 PWmain φign MAF PW ⎤ β = 0.0067 ⎢ ⎥⎢ 2 ⎥ 5.2 ⎢ PW SOC × PW ⎥ ⎢ - 0.00491 ⎥⎣ main main ⎦ ⎢ ⎥ ⎢ 0.0000072⎥ ⎢ ⎥ ⎣- 0.0000275 ⎦

Table 6.7: The model evaluation by the RMS error

167 In the table, the percentage RMS error are defined as

N ()β − β 2 ∑ est test 1 RMS error = i ×100,[]% N β test

where, βtest are the average value of β by the test data. This expression for the error estimation will be adopted throughout the combustion parameter identification part in the research. The detailed values of the burning mode factors estimated by each model are summarized and compared with test data in Figure 6.16 and Table 6.8.

Figure 6.16: The comparison of the burning mode factor β for each model

168 Data Watson Model Watson Model Test Proposed Injection Point (Un-tuned) (Tuned)

1 0.7000 0.4410 0.5558 0.6839 Single 2 0.5850 0.4351 0.5444 0.6311 Single 3 0.5850 0.4466 0.5168 0.5725 Single 4 0.3970 0.5710 0.2716 0.3719 5 0.3606 0.5486 0.3042 0.3826 6 0.3775 0.4950 0.4165 0.4055 7 0.6000 0.3989 0.5692 0.5984 Single 8 0.7170 0.3830 0.5792 0.6853 Single 9 0.4034 0.4806 0.4313 0.3822 10 0.4190 0.5047 0.4063 0.4133 11 0.3606 0.4722 0.3957 0.3450 12 0.4150 0.4735 0.4380 0.3836 13 0.4400 0.4719 0.4958 0.4660 14 0.4225 0.4719 0.4958 0.4222 15 0.4044 0.4709 0.4968 0.4239 16 0.3606 0.5140 0.4242 0.3653 17 0.3700 0.5467 0.3390 0.3358 18 0.3475 0.5272 0.4097 0.3818 19 0.3606 0.5040 0.4346 0.3770 20 0.3738 0.4797 0.4584 0.3721

Table 6.8: The comparison of the burning mode factor model

169 Next, the shape factor C p1 data is analyzed with the test data shown in Figure 6.17.

Shape Factor C vs. EGR Shape Factor C vs.Delay Time p1 p1 4.5 4.5 1800 rpm 1800 rpm 1500 rpm 1800 rpm w/ EGR 1500 rpm

4 4

3.5 3.5 p1 p1 C C

3 3

2.5 2.5

2 2 0 2 4 6 8 10 12 14 16 18 20 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 EGR (%) t (ms) d

C p1 vs. EGR% C p1 vs. ignition delay, td

Shape Factor C vs.Equivalence Ratio Shape Factor C vs.Engine Speed p1 p1 4.5 4.5 1800 rpm 1800 rpm w/ EGR 1500 rpm

4 4

3.5 3.5 p1 p1 C C

3 3

2.5 2.5

2 2 0.05 0.1 0.15 0.2 0.25 1200 1400 1600 1800 2000 2200 phi Engine Speed (rpm) ig

C p1 vs. trapped equivalence ratio, φig C p1 vs. engine speed

Figure 6.17: The trend of shape factorC p1

170 From Figure 6.17, a functional relationship can be assumed asC p1 = f (td ,φig ). The exact same procedure will be followed as the one done in the case of burning mode factor estimation.

The original form of model developed by Watson is given by

−8 2.4 C p1 = 2 +1.25×10 × ()rpm × td . In this expression, instead of td , rpm × td is used in order to use the crank angle.

This model is evaluated without tuning the constants involved in the model. The results are shown in Figure 6.18.

Figure 6.18: The comparison of the estimated shape factor C p1 by the un-tuned Watson model with test data

171 The tuned model obtained by applying the least square error method is shown in Figure 6.19. The prediction is much improved compared to the result of the un-tuned model.

Figure 6.19: The comparison of the estimated shape factor C p1 by the tuned Watson model with test data

As can be seen in the test data figures, EGR gas is not relevant and in the final model, only the effect of the trapped equivalence ratio will be taken into consideration.

172 The following expression is obtained as the final form of the model for the shape factorC p1 using the least square error method as in the previous model.

−5 1.1615 −1.4277 C p1 = 2 + 2.1209×10 × ()rpm × td φig

However, the RMS error of this proposed function is still high (20%).

Therefore, another form using the stochastic estimation technique is tried and the evaluation result from the proposed model can be seen in Figure 6.20.

Figure 6.20: The comparison of the estimated shape factor C p1 by the proposed model

173 It is necessary to check that the model can be extrapolated to a reasonable range of parameters such as the equivalence ratio and delay time in order check if there is abnormal behavior under those conditions. With the proposed model, there is a possibility that C p1 could be over-estimated under a low equivalence ratio or a short ignition delay time. The results of the models tried in this research are summarized and compared in the Table 6.9 and Figure 6.21. It is notable to observe that the effect of EGR gas is included in the variable of φig implicitly, which is confirmed in the preceding figures. The detailed value of the shape factor C p1 can be checked in Table 6.10.

Model Equation Model RMS error (%)

−8 2.4 Un-tuned C p1 = 2 +1.25×10 × (rpm × td ) 37.9 Watson −2 0.6794 Tuned C p1 = 2 +1.0825×10 × (rpm × td ) 15.4

⎡ 4.2698 ⎤ ⎢ ⎥ ⎢ - 14.48 ⎥ ⎢ -15.158 ⎥ 2 ⎢ ⎥⎡1 φ ign φign td ⎤ Proposed Model C = - 6.932 ⎢ ⎥ 8.6 p1 ⎢ ⎥ t ×φ MAF SOC ⎢ 35.08 ⎥⎣⎢ d ign main ⎦⎥ ⎢ ⎥ ⎢ - 0.06771⎥ ⎢ ⎥ ⎣0.013533 ⎦

Table 6.9: The model evaluation by the RMS error

174

Figure 6.21: The comparison of the shape factor C p1 for each model

175 Data Watson Model Watson Model Proposed Test Point (Un-tuned) (Tuned) Model

1 2.6250 2.3951 3.4371 2.3321 2 2.0750 2.2868 3.3125 2.2580 3 2.5940 2.1981 3.1821 2.2715 4 3.0316 2.0375 2.7381 3.4806 5 3.5355 2.0375 2.7381 3.5697 6 2.8406 2.0747 2.8968 2.8740 7 2.4570 2.2868 3.3125 2.7774 8 3.0630 2.2868 3.3124 2.8573 9 3.5957 2.0749 2.8974 3.1653 10 3.5738 2.0749 2.8974 3.4815 11 4.0406 2.0376 2.7385 3.9203 12 3.0750 2.0747 2.8968 3.4236 13 2.9859 2.1276 3.0436 3.0968 14 2.7063 2.1276 3.0436 3.0508 15 2.8027 2.1276 3.0436 3.0306 16 3.5254 2.0747 2.8968 3.4267 17 4.2625 2.0374 2.7376 3.9345 18 3.8594 2.0747 2.8968 3.4832 19 3.0305 2.0747 2.8968 3.3597 20 3.3633 2.0747 2.8968 3.2494

Table 6.10: The detailed values of the shape factor C p1 estimated by each model

176 Next, Cd1 is analyzed with the test data as shown in Figure 6.22.

Shape Factor C vs. EGR Shape Factor C vs.Delay Time d1 d1 42 42 1800 rpm 1800 rpm 1500 rpm 1800 rpm w/ EGR 1500 rpm 40 40

38 38

36 36 d1 C 34 34 d1 C

32 32

30 30

28 28

26 26 0 2 4 6 8 10 12 14 16 18 20 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 EGR (%) t (ms) d

Cd1 vs. EGR% Cd1 vs. ignition delay, td

Shape Factor C vs.Equivalence Ratio Shape Factor C vs.Engine Speed d1 d1 42 42 1800 rpm 1800 rpm w/ EGR 1500 rpm 40 40

38 38

36 36 d1 d1 C C 34 34

32 32

30 30

28 28

26 26 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 1300 1400 1500 1600 1700 1800 1900 2000 phi ig Engine Speed (rpm)

Cd1 vs. ignition delay, φig Cd1 vs. engine speed

Figure 6.22: The trend of shape factorCd1

177 From the figure, no functional relationship can be found:Cd1 ≠ f (φig ,td ). The exact same procedure will be followed as the one done in the previous case.

−b The original form of the model developed by Watson iscd1 = aφig was tried and evaluated for its accuracy of the prediction without tuning the constants involved. The results are shown in Figure 6.23.

Comparison of C by Untuned Watson d1 100 test est 80

d1 60 C

40

20 0 2 4 6 8 10 12 14 16 18 20 Data Point Evaluation of C by Untuned Watson d1 100 1800 rpm 90 1800 rpm w/ EGR 1500 rpm 80 d1 70

60

Estimated C 50 40

30 30 40 50 60 70 80 90 100 Test C d1

Figure 6.23: The comparison of the estimated shape factor Cd1 by the un-tuned Watson model with test data

178 Since the original model without tuning the constants poorly predicts as shown in the figure, the tuned model is evaluated using the least square method. The result can be seen in Figure 6.24.

Comparison of C by Tuned Watson d1 45 test est 40

35 d1 C

30

25 0 2 4 6 8 10 12 14 16 18 20 Data Point Evaluation of C by Tuned Watson d1 42 1800 rpm 40 1800 rpm w/ EGR 38 1500 rpm d1 36 34 32 Estimated C 30 28 26 26 28 30 32 34 36 38 40 42 Test C d1

Figure 6.24: The comparison of the estimated shape factor Cd1 by the tuned Watson model with test data

In order to check whether there is a strange behavior with the tuned model, the tuned model is evaluated by extrapolation of Cd1 as shown in Figure 6.25. 179

Extrapolating the Trapped Equivalence Ratio 45 est test 40

35

30

25 d1 C 20

15

10

5

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 phi ig

Figure 6.25: The extrapolation of shape factor Cd1 vs. φig

However, as can be seen in Figure 6.22, it is obvious that there is no distinct functional relationship of this parameter with the trapped equivalence ratio. Therefore, the arithmetic average value (except the abnormally large value) will be used in this study as:

Cd1 =28.38

The result of the model evaluation can be seen in Figure 6.26.

180 Comparison of C by Propsoed Model d1 45 test est 40

35 d1 C

30

25 0 2 4 6 8 10 12 14 16 18 20 Data Point Evaluation of C by Proposed Model d1 42 1800 rpm 40 1800 rpm w/ EGR 38 1500 rpm d1 36 34 32 Estimated C 30 28 26 26 28 30 32 34 36 38 40 42 Test C d1

Figure 6.26: The comparison of the estimated shape factor Cd1 by the proposed model with test data

The models are summarized in Table 6.11 and results can be seen in Figure 6.27.

181 Model Equation Model RMS error (%)

−0.644 Un-tuned Cd1 = 14.2φig 118 Watson 0.0766 Tuned Cd1 = 34.23φig 10.3

Proposed Model Cd1 = 28.38 11.0

Table 6.11: The model expression and their evaluation by the RMS error

Model Comparison 100 test Untuned Tuned 90 proposed

80

70 d1 C 60

50

40

30

20 0 2 4 6 8 10 12 14 16 18 20 Data Point

Figure 6.27: The comparison of the shape factor Cd1 for each model

182 Next, the Cd 2 test data is analyzed with the test data in Figure 6.28.

Shape Factor C vs. EGR Shape Factor C vs.Delay Time d2 d2 3.5 3.5

1800 rpm 1500 rpm

3 3 d2 d2 C C

1800 rpm 1800 rpm w/ EGR 1500 rpm 2.5 2.5

2 2 0 2 4 6 8 10 12 14 16 18 20 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 EGR (%) t (ms) d

Cd 2 vs. EGR% Cd 2 vs. ignition delay, td

Shape Factor C vs.Equivalence Ratio Shape Factor C vs.Engine Speed d2 d2 3.5 3.5 1800 rpm 1800 rpm w/ EGR 1500 rpm

3 3 d2 d2 C C

2.5 2.5

2 2 0.05 0.1 0.15 0.2 0.25 1300 1400 1500 1600 1700 1800 1900 2000 phi ig Engine Speed (rpm)

Cd 2 vs. ignition delay, φig Cd 2 vs. engine speed

Figure 6.28: The trend of shape factorCd 2

183 As can be in the figure, the trend of C is nearly the same as the case of the shape d 2 factorCd1 . Therefore, an exact same procedure will be followed. The original form of

d model proposed by Watson is cd 2 = c(cd1 ) . This will be first evaluated for its accuracy without tuning the constants. The result can be seen in Figure 6.29.

Comparison of C by Untuned Watson d2 3.5 test est 3

2.5d2 C

2

1.5 0 2 4 6 8 10 12 14 16 18 20 Data Point Evaluation of C by Untuned Watson d2 3.5 1800 rpm 1800 rpm w/ EGR 1500 rpm 3 d2

2.5 Estimated C

2

1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 Test C d2

Figure 6.29: The comparison of the estimated shape factor Cd 2 by the un-tuned Watson model with test data

184 Since the original model without tuning the constants predicts poorly as in the figure, a tuned model is evaluated using the least square method. The result can be seen in Figure 6.30.

Comparison of C by Tuned Watson d2 3.5 test est

3 d2 C

2.5

2 0 2 4 6 8 10 12 14 16 18 20 Data Point Evaluation of C by Tuned Watson d2 3.5 1800 rpm 1800 rpm w/ EGR 1500 rpm

d2 3

2.5 Estimated C

2 2 2.5 3 3.5 Test C d2

Figure 6.30: The comparison of the estimated shape factor Cd 2 by the tuned Watson model with test data

185 Even though the result of the tuned Watson model is satisfactory, this model could not be used in this study. It is because the estimated values of Cd1 needs to be applied instead of test data. Moreover, the estimated mode is fixed at 28.38 so thatCd 2 would be constant, which is not reasonable. In other words,

−0.4212 −0.4212 Cd 2 = 12.513()cd1 = 12.513(28.38) = 3.0574 .

The RMS error when this estimation is applied is 13.6%. This estimation could not be applied in this study when there is clear indication of functional relationship of this parameter with the trapped equivalence ratioφig , as opposed to the case of Cd1 . The following expression is acquired as the final form of model for the shape factorCd 2 using the least square error method:

−0.1545 Cd 2 = 2.0 + 0.742()φig

As can be seen in Figure 6.31, the result is reasonable except for the lower value of Cd 2 .

These lower values of Cd 2 are the test cases of the single fuel injection. Therefore, the combustion model prediction is likely to worse for the single injection cases.

186

Figure 6.31: The comparison of the estimated shape factor Cd 2 by the proposed model with test data

The summary of each model can be found in Table 6.12 and the error estimation of each model is performed and summarized in the table. The shape factors calculated with each model are shown in Figure 6.32 for comparison, and the detailed values are tabulated in Table 6.13.

187 Model Equation Model RMS error (%)

0.25 Un-tuned Cd 2 = 0.79(cd1 ) 42.0 Watson −0.4212 Tuned Cd 2 = 12.513(cd1 ) 13.1

⎡ 1.8856 ⎤ ⎢ ⎥ ⎢ 6.659 ⎥ ⎢ -1.196 ⎥⎡1 φign td ⎤ Proposed Model Cd 2 = ⎢ ⎥⎢ ⎥ 8.7 ⎢- 6.97 ⎥⎣⎢ td ×φign MAF SOCmain ⎦⎥ ⎢ - 0.05491 ⎥ ⎢ ⎥ ⎣⎢ 0.010142⎦⎥

Table 6.12: The model evaluation by the RMS error

Figure 6.32: The comparison of the shape factor Cd 2 for each model 188 Data Watson Model Watson Model Test Proposed Point (Un-tuned) (Tuned)

1 2.5000 1.8489 2.9870 2.2826 2 2.0750 1.8313 3.0355 2.4855 3 2.5940 1.8313 3.0355 2.6229 4 2.0200 1.8519 2.9787 2.6669 5 3.4400 1.8189 3.0705 2.8179 6 3.2530 1.8445 2.9989 2.7667 7 2.9170 2.0098 2.5952 2.9443 8 3.1420 1.8058 3.1080 3.0275 9 2.9910 1.8529 2.9762 3.0673 10 3.0720 1.8058 3.1080 3.2128 11 3.4430 1.8189 3.0704 3.4345 12 3.1124 1.8008 3.1225 3.3022 13 3.3023 1.7957 3.1375 3.2286 14 3.1688 1.8101 3.0955 3.1955 15 3.0820 1.8059 3.1078 3.1821 16 3.4430 1.8189 3.0704 3.2991 17 3.1969 1.8147 3.0823 3.3216 18 3.4430 1.8368 3.0200 3.3037 19 3.2250 1.8189 3.0704 3.2779 20 3.2953 1.8291 3.0417 3.2761

Table 6.13: The detailed values shape factor Cd 2 estimated by each model

All the correlations for combustion model parameters are summarized and compared with the original model by RMS error in Table 6.14.

189 Parameter Model RMS error (%)

⎡ 0.778 ⎤ ⎢ ⎥ ⎢ - 0.00984 ⎥ ⎢ 1.274 ⎥ ⎢ ⎥⎡1 PWmain φign MAF PW ⎤ β = 0.0067 β ⎢ ⎥⎢ 2 ⎥ 5.2 ⎢ PW SOC × PW ⎥ ⎢ - 0.00491 ⎥⎣ main main ⎦ ⎢ ⎥ ⎢ 0.0000072⎥ ⎢ ⎥ ⎣- 0.0000275 ⎦ 0.37 −0.26 * β = 1− 0.926φig td 35.0 ⎡ 4.2698 ⎤ ⎢ ⎥ ⎢ - 14.48 ⎥ ⎢ -15.158 ⎥ 2 ⎢ ⎥⎡1 φ ign φign td ⎤ C = - 6.932 ⎢ ⎥ 8.6 C p1 ⎢ ⎥ t ×φ MAF SOC p1 ⎢ 35.08 ⎥⎣⎢ d ign main ⎦⎥ ⎢ ⎥ ⎢ - 0.06771⎥ ⎢ ⎥ ⎣0.013533 ⎦

−8 2.4 * C p1 = 2 +1.25×10 × (rpm × td ) 37.9 5000 N/A C p2 5000 N/A*

Cd1 = 28.38 11.0 C d1 −0.644 * Cd1 = 14.2φig 118.0 ⎡ 1.8856 ⎤ ⎢ ⎥ ⎢ 6.659 ⎥ ⎢ -1.196 ⎥⎡1 φign td ⎤ Cd 2 = ⎢ ⎥⎢ ⎥ 8.7 - 6.97 t ×φ MAF SOC Cd 2 ⎢ ⎥⎣⎢ d ign main ⎦⎥ ⎢ - 0.05491 ⎥ ⎢ ⎥ ⎣⎢ 0.010142⎦⎥

0.25 * Cd 2 = 0.79cd1 42.0 * Un-tuned original model by Watson

Table 6.14: The final estimation model of the combustion model parameter

190 6.3.4 Watson combustion model result

Now, the combustion modeling is ready for validation with the estimation model of the combustion parameters. These correlations for the combustion parameters are applied to the following test cases represented by in Table 6.15. These tests are different from those used for model development so far. One or two representative test case were selected from each test condition ( engine speed, EGR, and fuel injection schedule).

Fuel Injection Schedule Test Engine EGR MAF AF T1 Case Speed PILOT MAIN POST No. SOI PW SOI PW SOI PW

Unit rpm CA us CA us CA us % g/s - ‘C

10 1800 354 500 0.0 49.9 42.3 47

6 1800 340 200 351 500 0.0 50.7 37.6 46

3 1800 340 200 354 400 363 100 0.0 48.9 48.4 44

21 1800 354 500 14.4 42.6 36.0 58

15 1800 340 200 354 500 10.9 44.9 32.4 55

25 1800 340 200 354 400 365 100 16.5 41.3 41.3 56

46 1500 340 200 354 450 0 38.8 42.6 42

48 1500 345 200 354 450 0 38.6 44.5 42

58 1500 340 200 350 300 364 200 0 38.2 58.7 42

64 1500 340 200 354 400 365 100 0 38.5 47.9 42

Table 6.15: Test data set for the combustion model validation

191 Then, the tuned correlations for the combustion parameters were applied in the combustion sub-model to the selected test cases which are shown in Table 6.15. The combustion parameters are estimated and summarized in Table 6.16. The quality of the combustion model prediction capability was then analyzed by calculating the RMS error of the cylinder pressure residual.

Case Test Model error No. ∆P No. β β ()cy C p1 Cd1 Cd 2 C p1 Cd1 Cd 2

1 10 0.61 2.53 50.47 2.52 0.64 2.34 28.38 2.29 0.9

2 6 0.50 3.50 31.50 3.00 0.27 2.93 28.38 2.52 1.7

3 3 0.42 2.94 27.42 3.16 0.46 2.57 28.38 2.76 1.4

4 21 0.67 2.80 28.83 3.30 0.64 2.99 28.38 2.74 1.4

5 15 0.40 3.53 30.06 2.57 0.25 3.85 28.38 3.01 2.7

6 25 0.36 2.20 30.14 2.20 0.27 4.01 28.38 3.26 3.2

7 46 0.40 3.53 27.61 3.18 0.28 3.37 28.38 3.22 2.5

8 48 0.36 3.53 29.51 3.44 0.39 3.03 28.38 3.19 2.2

9 58 0.37 4.39 28.73 3.44 0.21 3.42 28.38 3.05 1.1

10 64 0.37 2.92 29.19 3.30 0.30 3.37 28.38 3.26 2.0

Table 6.16: The comparison of the combustion model parameters of the test data and with estimated data

192 In the table, error(∆Pcy ) is the root mean square error of the cylinder pressure during the combustion period. This is described by the following equation:

N 2 ∑()Pcy,est − Pcy,test error()∆P = i=SOC [bar] cy N where N corresponds to the main combustion duration (60 CA).

The arithmetic average prediction error of the cylinder pressure for the selected test cases is 1.9 bar, which means a relatively accurate estimation with the single-zone combustion model approach. The cylinder pressure is the principal output of the modeling that will be used in the next NOx modeling. Therefore, the results of the estimated cylinder pressure traces are compared with test data and shown in Figure 6.33.

(a) Test case 10 (b) Test case 6

Continued

Figure 6.33: The final combustion model result

193 Figure 6-33 continued

(c) Test case 3 (d) Test case 21

(e) Test case 15 (f) Test case 25

Continued

194 Figure 6-33 continued

(g) Test case 46 (h) Test case 48

(i) Test case 58 (j) Test case 64

195 Selected metrics estimated by the combustion model, such as IMEP, maximum cylinder pressure, and location of the maximum cylinder pressure, are compared with those from the test data in Table 6.17 . In the table, IMEP calculations are limited for the closed cycle duration only, which represent almost the whole IMEP. When the pressure resulting from combustion heat release is lower than that of compression pressure, there are large differences (about 10 CA) in the location of the peak pressure between the data and estimated result as in case number, 15 and 25. In other words, the estimated combustion heat is not under-estimated.

error Case IMEP Pmax θ P No. max No. ()∆Pcy test est. test est. test est. bar bar bar CA 1 10 0.9 3.4 3.7 49.3 51.0 371 371

2 6 1.7 4.0 4.4 54.9 54.2 368 366

3 3 1.4 3.1 3.9 46.9 50.5 368 368

4 21 1.4 3.4 3.6 47.1 45.2 371 374

5 15 2.7 4.2 3.9 47.1 47.6 370 361

6 25 3.2 2.9 3.8 48.7 46.9 371 361

7 46 2.5 3.2 3.7 48.0 44.3 369 369

8 48 2.2 3.0 3.9 47.1 48.6 368 369

9 58 1.1 2.4 2.5 46.1 45.6 363 363

10 64 2.0 3.0 3.7 46.3 44.9 366 368

Table 6.17: The comparison of the performance data of the validation test cases by the combustion model

196 6.3.5 Discussion of Watson combustion modeling result

As can be seen in the previous figures, the cylinder pressure estimated by the combustion model agrees well with the test data under the various engine operating conditions (engine speed, EGR %, and the fuel injection schedule). However, there are still some cylinder pressure residuals near SOC, which should be minimized as much as possible. These errors could affect the subsequent combustion prediction. In other words, it could be thought that the ignition phenomenon provides an initial condition for the rest of combustion. Then, subsequent combustion modeling could be affected. Two representative cases are emphasized (marked in bold): one is the worst result case and the other the best prediction case. In Figure 6.34, for the test case of engine speed 1800 rpm, without EGR, and single fuel injection, the modeling result for other variables such as heat release rate or mean cylinder temperature could be investigated. The normalized data of the injector current, needle lift to locate the dynamic SOI, and estimated injection flow rate are shown in the top. The prediction results of these variables are well agreed with test data even with a single-zone approach. The current profile is the test data measured with a current probe. However, in the modeling work, the current profile will also be estimated from the input parameters (the start of injection (SOI), pulse width, back (cylinder) pressure, and common rail pressure). This will be separately discussed later in this chapter.

Now that the combustion model has been done with quite good results, NOx emission modeling will be discussed using the combustion modeling result in the next section.

197

Figure 6.34: The detailed combustion modeling result - Test Case #10

198 6.4 Parameterization for NOx model

There are two major modes in diesel engines combustion namely premixed and diffusive combustion. The NOx contribution from the premixed combustion is insignificant compared to the total NOx emission which the major portion of NOx is the result of the main diffusion combustion. This is because the gas mixture during the premixed combustion is too rich. Thus, NOx formed during this period is negligible. In some research the NOx contribution of the premixed combustion was shown to be negligible and this fact is experimentally validated in some studies with laser based measurement [49], [50]. In other words, most NOx is formed in post-combustion zone. Therefore, whether the mode of combustion is premixed or diffusive is not important for

NOx formation. Only the result of combustion, which is the increased cylinder pressure and temperature are related with NOx formation. In parameters modeling in NOx estimation, there is no distinction between the kinds of combustion mode, premixed or diffusion. Therefore, the parameterization in NOx modeling will become a modeling of the temperature related with NOx formation. This is because, as mentioned in the previous modeling section, NOx is a strong function of the local temperature.

6.4.1 The local equivalence ratio estimation

Since the NOx formation is a phenomenon that is occurred locally in the post- flame region, the concept of the local equivalence ratio is necessary in NOx estimation.

Actually, since the NOx emission from the pilot fuel injection combustion is not so significant compared to the main combustion that the local equivalence ratio for NOx estimation will be applied throughout the entire combustion period regardless of the fuel injection schedule. Actually, the local equivalence ratio will change during the combustion period as the location of the flame changes from over-rich to lean condition in the chamber. However, in this study, this ratio is assumed to be constant. This assumption is usually adopted in the study even though there is a slight change of the ratio during combustion. The burn gas element temperature is calculated with this local equivalence ratio. Since the initial temperature is very important in the NOx calculation, a precise method to calculate the initial burn gas temperature is required in the NOx

199 modeling. This ratio can be extracted from the test data by applying the root mean square error method to the NOx data. The calculation procedure is as follows and described in a form of flow chart in the Figure 6.35. An initial local equivalence ratio is assumed and an adiabatic flame temperature is calculated with the definition of the adiabatic condition, which is defined as the enthalpy of the product element is equal to that of the reactant. This adiabatic temperature is also calculated by an iteration procedure. In other words, the initial temperature starting from the unburned gas temperature is increased by say, 5 degree, until the two enthalpies of the reactant and product are equal. Using this flame temperature as the initial temperature for the burned element, the burned gas element temperature is calculated assuming an adiabatic process. Then, NOx is calculated using this temperature profile and the estimated NOx is compared with test data. Again, the local equivalence ratio is corrected when the error is larger than a predetermined value.

This iteration continues until the calculated NOx is agreed with test data within a certain amount of error.

Basically, the NOx model of the single fuel injection could be applied to the multiple fuel injections without any modification. This is a reasonable approach as the cylinder pressure and temperature are the only major factors to be considered in this study. In other words, the source of the cylinder pressure change as a result of combustion is not important. The role of the pilot fuel injection is literally reducing the ignition delay time of the main fuel injection by increasing the cylinder temperature through the heat release. Moreover, the portion of NOx emission contribution from the pilot or post injection combustion is not available in this research. (Only the tail pipe emission was measured during the validation tests.) Therefore, a separate modeling of the local equivalence ratio for non-main fuel injection combustion in NOx estimation is not required. Instead, the ‘average’ local equivalence ratio was calculated for the entire combustion period regardless of the fuel injection schedule.

200 dm f Input Parameters: EGR , P main , MAF , ,... dθ

Combustion Model Local Equivalence Ratio Model: φlocal

Pcy

Adiabatic Flame Temperature Burn Gas Temperature Tb,o = f (φlocal ,burn gas ratio,Tunburn )

Extended Zeldovich Model

[]NO = ∑[NO]i ∆xb,i i

No NOest − NOtest ≤ ε Assume other φlocal

Yes

Optimal φ is determined. local

Figure 6.35: The local equivalence ratio calculation procedure

Applying the methodology described so far, the final optimum values of the local equivalence ratio for each test case have been calculated and the results are summarized in Table 6.18 along with the test conditions for the 20 test cases used in the parameters identification. The local equivalence ratios are calculated with all the prepared combustion parameters estimated from the validated combustion modeling. Therefore, it would be reasonable that when making a correlation for the local equivalence ratio, the estimated combustion parameters need to be used as independent variables instead of the parameters calculated with the parameters identification test data. As can be seen in Table 6.18, the local equivalence ratio for the test cases with no-zero EGR is higher than those of zero-EGR test cases. 201 PW SOC C φ SOI MAF EGR φ p1 C C NOx local ig td β d1 d 2 rpm Main Total test Est.

CA us g/s % CA CA - ms - - - - ppm -

1800 356 500 500 50.1 0.0 368 368 0.21 0.74 0.70 2.63 30.0 2.50 392 0.7547

1800 352 500 500 49.6 0.0 363 364 0.19 0.65 0.59 2.08 28.9 2.08 468 0.7547

1800 350 500 500 49.3 0.0 360 360 0.16 0.56 0.59 2.59 28.88 2.59 470 0.7500

1800 354 500 700 51.0 0.0 361 362 0.05 0.28 0.40 3.03 30.20 2.02 373 0.7547

1800 354 400 600 48.7 0.0 361 362 0.06 0.28 0.36 3.54 28.10 3.44 264 0.7219

1800 351 400 700 49.4 0.0 359 360 0.10 0.37 0.38 2.84 29.72 3.25 323 0.7263

1800 348 500 500 41.9 15.1 359 359 0.23 0.65 0.60 2.46 41.89 2.92 423 0.9000

1800 357 500 500 42.9 14.0 368 369 0.25 0.65 0.72 3.06 27.30 3.14 263 0.9056

1800 351 500 700 44.3 11.6 359 358 0.10 0.37 0.40 3.60 30.26 2.99 338 0.8381

1800 360 500 700 42.5 14.5 368 367 0.09 0.37 0.42 3.57 27.30 3.07 176 0.8888

1800 354 400 700 40.3 18.7 361 362 0.09 0.28 0.36 4.04 28.10 3.44 150 0.9000

1800 354 400 700 41.6 16.2 362 364 0.11 0.37 0.42 2.08 27.00 3.11 204 0.8944

1500 360 450 550 38.8 0.0 368 368 0.14 0.56 0.44 2.99 26.70 3.30 271 0.7594

1500 354 450 550 38.5 0.0 362 363 0.14 0.56 2.41 27.56 3.17 347 0.7263 0.42

1500 354 450 550 38.6 0.0 362 362 0.15 0.56 0.40 2.80 27.30 3.08 352 0.7594

1500 354 300 500 38.1 0.0 361 363 0.10 0.44 0.36 2.53 28.10 3.44 166 0.7175

1500 352 300 700 38.0 0.0 364 358 0.07 0.33 0.37 4.26 27.84 3.20 254 0.7131

1500 360 300 700 38.1 0.0 367 366 0.09 0.44 0.35 4.46 29.23 3.44 130 0.7044

1500 354 400 700 38.4 0.0 361 361 0.10 0.44 0.36 3.03 28.10 3.23 322 0.7406

1500 350 400 700 38.7 0.0 357 358 0.12 0.44 0.37 3.36 28.73 3.30 433 0.7219

Table 6.18: The NOx test data for parameters identification and the calculated local

equivalence ratioφlocal

202 Next, with these results, the local equivalence ratio modeling can be performed using the available variables such as the trapped equivalence ratio, the ignition delay time, EGR, pulse width, combustion parameters, and so forth. In order to capture the feasibility of each variable as the independent variables, plotting the calculated local equivalence ratio as functions of available variables is needed and is shown in Figure

6.36. Since NOx estimation was found to be very sensitive to the local equivalence ratio in the previous section, this local equivalence ratio modeling will be carried out by including all possible variables to reduce the estimation residuals to the minimum. This statement is easily understood as the local equivalence ratio is directly related with the burn gas temperature. However, as a rule of thumb, the number of terms that is used in the model should not exceed half the number of test applied for this identification process to avoid the over-estimation. Moreover, the order of polynomial should be also kept to a linear function if possible to be better believed in extrapolation cases.

203

Continued

Figure 6.36: The local equivalence ratio as a function of various parameters

204 Figure 6.36 continued

As can be found in Figure 6.36, the local equivalence ratio is the strong functions of EGR, β,C p1 × EGR , and PWmain × SOCmain . Starting from this relationship, the local equivalence ratio estimation modeling is performed using the stochastic estimation technique. The reason why the stochastic estimation technique is applied in the modeling is that there is no information on the range of relevant coefficients involved in the model to avoid the risk of a local minimum. Furthermore, a polynomial form is enough to

205 express the correlation. It would be worthwhile to point out that the local equivalence ratio of the test cases when the EGR gas is inducted into the cylinder becomes larger than for the non-EGR test cases. But there is no method to confirm this local equivalence ratio experimentally. An overall equivalence ratio could also provide the NOx emission trend. The result of the local equivalence ratio modeling applying the stochastic estimation technique is tabulated in Table 6.19.

Equation RMS error (%) 1 2 2 2 1 SOC EGR EGR PWmain β β C p1 Cd 2 PW PW φign 0.7 MAF SOCmain × PWmain β × SOCmain β × PWmain β × EGR

2 1 EGR PWmain SOCmain × PWmain C p1 × EGR 1.2

Table 6.19: The model evaluation by the RMS error

The second model will be adopted due to the complexity of the parameters involved in the first model regardless of the low RMS error. Since the estimation result is satisfactory, no more models are proposed and tried. The final model for the local equivalence ratio φlocal estimation and its coefficients are described as follows.

⎡ 0.668 ⎤ ⎢ 1.420 ⎥ ⎢ ⎥⎡1 EGR PW ⎤ main φlocal _ est = ⎢- 0.00142 ⎥⎢ ⎥ ⎢ ⎥⎣ SOC main × PWmain C p1 × EGR ⎦ ⎢ 0.0000044 ⎥ ⎣⎢ - 0.157 ⎦⎥ The RMS error of the estimated local equivalence ratio as defined below is about 1.2%.

206 N φ −φ 2 ∑()local,est local,test i i 1 RMS error()φlocal = ×100,[]% N φlocal,test

It is notable that the local equivalence ratio is a function of the combustion model shape factor, C p1 of the main fuel injection, which determines the magnitude of the combustion heat release rate. The estimation results are summarized in Table 6.20 and Figure 6.37. The overall estimation result is satisfactory except the test case #18 whose prediction error is 0.02.

Figure 6.37: The comparison of the estimated φlocal by the proposed model with test data (RMS error % = 1.2 %)

207

PW SOC φlocal SOI MAF EGR β C p1 NOx rpm Main Total test Est. test Est.

CA us g/s % CA CA - - ppm - -

1800 356 500 500 50.1 0.0 368 368 0.70 2.63 392 0.7547 0.7603

1800 352 500 500 49.6 0.0 363 364 0.59 2.08 468 0.7547 0.7515

1800 350 500 500 49.3 0.0 360 360 0.59 2.59 470 0.7500 0.7450

1800 354 500 700 51.0 0.0 361 362 0.40 3.03 373 0.7547 0.7494

1800 354 400 600 48.7 0.0 361 362 0.36 3.54 264 0.7219 0.7313

1800 351 400 700 49.4 0.0 359 360 0.38 2.84 323 0.7263 0.7296

1800 348 500 500 41.9 15.1 359 359 0.60 2.46 423 0.9000 0.8917

1800 357 500 500 42.9 14.0 368 369 0.72 3.06 263 0.9056 0.8925

1800 351 500 700 44.3 11.6 359 358 0.40 3.60 338 0.8381 0.8447

1800 360 500 700 42.5 14.5 368 367 0.42 3.57 176 0.8888 0.8730

1800 354 400 700 40.3 18.7 361 362 0.36 4.04 150 0.9000 0.9050

1800 354 400 700 41.6 16.2 362 364 0.42 2.08 204 0.8944 0.8907

1500 360 450 550 38.8 0.0 368 368 0.44 2.99 271 0.7594 0.7530

1500 354 450 550 38.5 0.0 362 363 0.42 2.41 347 0.7263 0.7432

1500 354 450 550 38.6 0.0 362 362 0.40 2.80 352 0.7594 0.7412

1500 354 300 500 38.1 0.0 361 363 0.36 2.53 166 0.7175 0.7181

1500 352 300 700 38.0 0.0 364 358 0.37 4.26 254 0.7131 0.7116

1500 360 300 700 38.1 0.0 367 366 0.35 4.46 130 0.7044 0.7220

1500 354 400 700 38.4 0.0 361 361 0.36 3.03 322 0.7406 0.7313

1500 350 400 700 38.7 0.0 357 358 0.37 3.36 433 0.7219 0.7261

Table 6.20: The estimated local equivalence ratio φlocal for the 20 parameters identification test cases by the proposed model

208 The prediction capability of the local equivalence ratio model is confirmed by applying final estimation model to the other validation test cases. The test conditions of this parameter validation are described in Table 6.21. The comparison results between the test data and estimated φlocal can be checked in Figure 6.38.

Figure 6.38: The comparison of the estimated local equivalence ratio with the 17 validation test cases (RMS error % = 1.7 %)

209 6.4.2 The NOx estimation

Now that the model for the local equivalence ratio is validated and prepared, the

NOx estimation can be done with the prepared NOx model by applying the extended

Zeldovich mechanism. In Figure 6.39, the result of the exhaust NOx concentration calculation is compared with the test data for the purpose of the final evaluation of the

NOx model. The detailed results of NOx estimation are summarized in Table 6.21. The error in the table is defined as the arithmetic error percentage of the estimated data with respect to the test data.

Figure 6.39: The comparison of the estimated NOx with the 17 validation test data (RMS error % = 16 %)

210 error φlocal NOx Engine No. PW PW SOI MAF EGR β ()∆Pcy Error Speed Inj. main total test est. test est.

rpm - CA us g/s % us - bar - - ppm %

1800 1 354 500 49.9 0.0 500 0.64 0.9 .75 .76 410 469 14

1800 2 351 500 50.7 0.0 700 0.34 1.7 .74 .74 446 454 2

1800 2 360 500 50.0 0.0 700 0.35 1.5 .75 .76 222 275 24

1800 2 354 600 53.5 0.0 800 0.43 2.9 .76 .77 443 479 8

1800 3 354 400 48.9 0.0 700 0.53 1.4 .74 .73 284 252 -11

1800 1 354 500 42.6 14 500 0.64 1.4 .90 .90 313 290 -7

1800 1 351 500 42.2 15 500 0.47 1.7 .90 .90 347 338 -3

1800 2 354 500 44.9 11 700 0.33 2.7 .84 .84 282 290 3

1800 3 354 400 41.3 17 700 0.35 3.2 .88 .86 208 139 -33

1500 2 354 450 38.8 0.0 650 0.28 2.5 .75 .74 362 266 -27

1500 2 354 450 38.6 0.0 650 0.39 2.2 .75 .74 369 309 -16

1500 3 354 300 38.1 0.0 700 0.26 1.2 .72 .72 205 167 -19

1500 3 354 300 38.2 0.0 700 0.27 1.3 .72 .72 230 181 -21

1500 3 350 300 38.2 0.0 700 0.24 1.1 .71 .71 260 266 2

1500 3 360 400 38.3 0.0 700 0.29 2.7 .74 .74 205 235 15

1500 3 354 400 38.5 0.0 700 0.39 2.0 .74 .73 325 264 -19

1500 3 354 400 38.5 0.0 700 0.30 2.4 .74 .73 323 264 -19

Table 6.21: The NOx estimation result for the 17 validation test cases

211 In order to analyze the source of NOx calculation error, the best (#14) and worst test (#9) combustion modeling results are illustrated in Figure 6.40 and Figure 6.41, in which a 3-strike fuel schedule is used. From these representative cases, it could be concluded that both the effective combustion modeling and the precise local equivalence ratio estimation are essential in acquiring the satisfactory result of NOx prediction.

Figure 6.40: The combustion model result of the validation test case #14 presenting the best result of NOx prediction

212

Figure 6.41: The combustion model result of the validation test case #9 presenting the worst result of NOx prediction

When both the local equivalence ratio and the combustion modeling are precisely predicted within a certain error boundary, NOx emission is also calculated correctly, and vice versa. A more detailed discussion on the NOx calculation result will follow in the next section.

213

Figure 6.42: The NOx model result of the validation test case #14 presenting the best result of NOx prediction

The NOx formation is finished within 30 crank angle after the start of combustion.

Although the temperature of the first element to burn is highest, the contribution to NOx emission of this element is not so great due to its small amount of burned gas. From

Figure 6.42, it is evident that the mean cylinder temperature is too low for NOx to form.

214

Figure 6.43: The combustion model result of the validation test case #9 presenting the worst result of NOx prediction

The error source in predicting NOx can be explained as follows. As can be seen in lower

–right plot in Figure 6.43, the NOx formation rate is decreased during the main combustion period (from 360 to 370 CA, circled portion in the plot). This phenomenon could be explained by investigating Figure 6.41, which shows a lowered heat release rate than the test data. Thus, the combustion modeling is affecting the NOx prediction result.

215 6.4.3 Discussion of NOx estimation result

As can be seen in Table 6.21, the RMS error of NOx prediction when the model is applied to the 17 validation test cases is 16 %, which is regarded as reasonable if the fact that a single-zone approach is adopted in this research and that possible error in the measurement of the test data such as for the NOx concentration and other data could exist.

The one reason why the NOx emission is overestimated or underestimated could be explained by the error in the estimated cylinder pressure acquired as a result of the combustion model. When the cylinder pressure is overestimated during combustion, NOx emission is also overestimated accordingly, and vise versa. For the test case #9, NOx is underestimated due to the large cylinder pressure prediction error. Another source for the

NOx prediction error could be explained by the incorrectly estimated value of the local equivalence ratio, whose estimation error should be limited within 0.02 for the correct

NOx prediction. It is a well-known fact that NOx emission is almost entirely determined by the start of injection (SOI) and EGR. At least, the trend of NOx formation as functions of SOI and EGR could be confirmed with this NOx modeling result as in Figure 6.44.

216

Figure 6.44: The NOx emission and the start of fuel injection (SOI)

One more thing to note is that the trend of the NOx prediction is also consistent with respect to the start of combustion (SOC), which can be shown in Figure 6.45. The fuel injection schedule such as the injection pulse width with or without pilot injection is not the same. Even with the same SOI, SOC is not the same due to the different history of the cylinder pressure for each condition. When the ignition delay time is different, then the shape of heat release is affected by the burning mode factor.

217

Figure 6.45: The NOx emission and the start of combustion (SOC)

If the prediction error of NOx estimation could be analyzed graphically in terms of other variables as in Figure 6.46 , the source of the error could be more obvious. First of all, the variation in NOx prediction error with the local equivalence ratio is clear compared to the other variables such as the burning mode factor and the shape factor. In order to have a

20 % error in the NOx prediction with the model, it is necessary to predict the local equivalence ratio with the accuracy of ± 0.01 from the correct test value. Moreover, the

NOx prediction error increases as the error in the cylinder pressure predicted by the combustion modeling increases. When the error of the cylinder pressure is around 2 bars, the NOx estimation error is 20 %. When the precise pressure during the main injection is expected even though the overall pressure prediction error is big like in the case 8, the

218 NOx emission is estimated closely. This fact illustrates the importance of accuracy of the cylinder pressure prediction in NOx estimation. And the NOx prediction also becomes worse by the error in estimating the burning mode factor.

Figure 6.46: The error analysis in NOx estimation model

Knowing that the local equivalence ratio estimation is a very significant factor on NOx modeling, the analysis on this factor is meaningful in order to minimize the error source 219 in NOx estimation. As explained in the previous modeling part ofφlocal , this fact can be confirmed along with Figure 6.47. In order to contain the prediction error of the local equivalence ratio within the desirable boundary of − 0.01 + 0.01 for the reasonable NOx estimation, the start of combustion (SOC) should be predicted by the 1-crank angle precision, which is the same as the encoder’s resolution. In addition to this factor, the burning mode factor and combustion model shape factor should be estimated as precisely as possible.

Figure 6.47: The error analysis in the local equivalence ratio model

220 The importance of estimating the adiabatic burn gas temperature by the local equivalence ratio, unburned gas temperature, and residual gas ratio can be verified with Figure 6.48. This figure is acquired by changing one parameter while others are fixed.

Moreover, NOx emission changes by an order of magnitude with a temperature change of

250 K in the Zeldovich mechanism. Thus, in this context, an accurate NOx prediction is very difficult and vulnerable to the variation of the relevant parameters.

Figure 6.48: The adiabatic burned gas temperature

Now that the model is prepared by the validation test and parameters identification process, it can be extended to other applications such as performing a virtual engine mapping test.

221 7 CHAPTER 7

VIRTUAL ENGINE MAPPING TEST

Since all the models such as the fuel injection rate, combustion, and NOx prediction model have been validated with the test data, the application of the validated models will be discussed in this chapter focusing on performing a virtual engine mapping test (VEMT). Indeed, one of the advantages of the modeling work is to run an engine model in the computer environment without spending the enormous time in actual engine testing and test equipment set-up (virtual engine mapping).

7.1 Review of the model development procedure

A brief review for model development procedure will follow in order to perform an effective virtual engine mapping.

(1) Model validation

• All the parameters and constants used in the models have been identified with test data. After that, the identified models have been validated with another set of test data to confirm the accuracy of modeling.

• In order to use the validated model for virtual mapping experiment, all the parameters and constants including the initial conditions should be prepared to simulate the actual engine input data. Therefore, some additional modeling for input data preparation will be performed in the next section.

(2) Virtual engine mapping test (VEMT)

222 Design of experiment (DOE) needs to be done before doing the virtual mapping test. The purpose of the design of experiment is to carry out the most effective and efficient tests in terms of the performance, time and cost saving. First, the level of each factor to be run in the virtual mapping experiments need to be determined. Usually, 3 levels for each factor are enough for the model to be non-linear [52]. The appropriate independent variables (factors) to be used in the experiment need to be defined. As shown in Table 7.1, for the 5-strike fuel injection case, there are 2 factors (Engine speed, EGR) as well as SOI and PW of each fuel injection. Even with this seemingly simple input parameters choice, the total number of factors reaches up to 12. Therefore, the total number of test run will be level factor = 312 = 531,441 (runs) at the least. With this simple test run, it seems impossible to run this type of test on a real dynamometer. The validated model developed in the previous chapter allows to explore virtually this design space.

Fuel injection Engine Factor EGR #1 #2 #3 #4 #5 Speed SOI PW SOI PW SOI PW SOI PW SOI PW Unit RPM % CA us CA us CA us CA us CA us Upper 4000 40 340 200 350 500 370 2000 390 500 410 200 Limit

High 2000 25 340 200 350 300 370 700 390 300 410 200

Level Med. 1600 15 330 150 345 200 360 550 380 200 400 150

Low 1200 0 320 100 340 100 350 400 370 100 390 100

Lower 500 0 320 100 340 100 350 300 370 100 390 100 Limit

Table 7.1: An example of the virtual test run schedule for the 5-strike fuel injection case

223 (3) The mean value model implementation of the model

• From the result of the previous virtual mapping experiment, the final model needs to be prepared for the mean value model implementation.

Pmax

IMEP = f ()Engine speed, EGR, SOI i , PWi ,i = 1,...,5 NOx • Finally, although this task will not be completed in this study, these models could be implemented in the mean value model for control purposes.

7.2 Input data preparation

In order to conduct a virtual engine mapping test using the validated model, it is necessary to prepare some estimation models of the engine operating condition variables. Although these input data were obtained and provided by actual engine test data during modeling development, they are to be given by any method such as an estimation model in a virtual test. The list of input data to be prepared by additional estimation model are the injector solenoid current profile, mass air flow rate, common rail pressure, and initial cylinder pressure and temperature. These data could be provided from a mean value modeling result in a complete model as shown in the Figure 1.3. For example, the air flow rate needs to be estimated in a mean value model by considering the complex interaction of EGR-VGT system. However, for this study, temporary models for these input data are going to be prepared for VEMT for demonstration purpose.

7.2.1 The injector current profile estimation

So far, as input to the fuel injection rate model, the solenoid current profiles which were acquired at the engine dynamometer test have been used. But, for the virtual mapping, the current profiles are no longer available. Therefore, a current profile estimation model is needed based on a digital pulse train (logic command). In a common rail system, the injector needle is forced to move with the hydraulics activated by the

224 solenoid. Thus, since the injector solenoid system can be explained by an inductor with a core, the following equation can describe the solenoid system [83].

di ⎛ dL ⎞ L + i⎜ + R⎟ = Vin dt ⎝ dt ⎠ where i is the coil current, L()x is the self inductance,

x is plungerdisplacement, Vin is theinput voltage, and Ris the coilresistance.

An analytic solution to this 1st order linear differential equation can not be obtained as L is a function of x, and the input voltage is still needed. Therefore, even a simple form mathematical estimation of the solenoid current could not be achieved with this equation. Based on experimental measurements it is observed that the current profile could simply be approximated by a triangle. Thus, as a good approximation of the current, a triangle shape profile could be generated as functions of SOI and pulse width as follows. It would be helpful to understand the idea with Figure 7.1.

I max (PWc )

SOIc I(t) Injector solenoid I(t) current PW profile c estimation

SOI PW t

Figure 7.1: The solenoid current profile estimation model

225 First, an estimation model of the injector current profile is going to be developed using some information from the typical injector current signal test data as shown in Table 7.2.

Command PW ( PW ) 100 200 300 400 500 600 c µ sec Time 460 560 650 740 835 930 Actual PW CA [CA] 5 6 7 8 9 10

Table 7.2: The current profile test data at various pulse widths at 1800 rpm

With this test data, the following correlation was acquired by a linear fitting. The actual pulse width is:

PW = 371.4 + 0.9274× PWc ,[µ sec]

The crank angle associated with the pulse width is calculated by the following:

PW _ CA = PW × 6× rpm,[CA]

And the peak current is estimated by the following expression:

−3 −6 2 I max = −0.023 + 0.71×10 × PWc − 0.55×10 × PWc

Since the typical shape of the injector solenoid current is a triangle, it can be described by the following equation:

226 I I = max t, t ≤ center _ pw PW c

I max I = − ()t − PW c , t ≥ center _ pw PW c − center _ pw

where, center _ pw = 0.5 × PW c

The actual and estimation results for the solenoid current profiles at different pulse widths are shown in Figure 7.2. As can be seen in the figure, the approximation of the current profile by a triangle shape agrees reasonably well with the actual test data. Even though, this can affect the injection flow rate estimation, there will be a small error with this estimated current profile, which will be confirmed by the combustion model using this estimated profile. As an example, the result of the cylinder pressure calculation using the estimated current profile is plotted in Figure 7.3. The agreement is quite reasonable. Therefore, in the case of the virtual engine mapping test, this solenoid current profile estimation model will be adopted to be used as an input to the fuel injection rate model.

Figure 7.2: Estimated and test data injector current profile 227

(a) The pressure calculated using the real(b) The pressure calculated using the current estimated current

Figure 7.3: Comparison of combustion modeling using the estimated current profile

7.2.2 The other input variables estimations

The other estimation models such as the mass air flow rate, rail pressure, temperature and pressure at IVC and intake obtained by applying the stochastic technique to the test data are summarized in Table 7.3. This can be done by applying some physical reasoning to the relationship of each variable with relevant parameters. These parameters that will be used for correlation are the independent variables such as the mass air flow, EGR, engine speed, and injection schedule. These estimation models are validated with the test set used in validation of the combustion and NOx model. Therefore, these models will be applied in virtual mapping test together with the current profile model previously obtained.

228

Variables Estimation Model RMS %

Mass air MAF = −20.331− 48.4343× EGR + 0.00422× PWm 0.68 flow rate + 0.00524× SOI + 0.036237 × rpm + 0.00121× PWt

Intake T1 = 51+146× EGR +1.57 × MAF − 0.0458× rpm 2.30 temperature

Intake 8314 m R = , m = m + m = air , pressure air 28.97 t air egr ()1− EGR

−3 3 mt RairT1 Vint = 2.25×10 (m ), P1 = Vint

Rail pressure Prail = 741− 0.059× PWt + 0.1878× rpm 0.75

Pressure and Pivc = 1.580 + 0.0196× MAF + 0.01× EGR P V 1.93 , T = ivc ivc temperature − 0.000692× rpm + 0.00499×T ivc m R at IVC 1 t ivc

Table 7.3: The additional estimation model

7.3 Summary for the combustion and NOx model

Before proceeding to the virtual mapping test, the final model to be applied in the test need to be summarized and reviewed. In Table 7.4, the principal models developed so far by this study are briefly summarized for the purpose of reviewing. A more detailed discussion on the model modification will follow. The schematic of all the related models used in this study are shown in Figure 7.4.

229 Model Input Output

1 Current profile Pulse width and SOI I(θ )

I(θ ) , pulse width, rail Fuel injection 2 Fuel injection model pressure, back pressure profile (m& f )

3 Ignition model SOI, Tcy ,Pcy Auto-ignition time (td )

4 Watson model EGR,φig ,td Heat release rate

5 Combustion model m& f , EGR, MAF,Tivc, Pivc Cylinder pressure (Pcy )

6 φlocal model EGR, SOC, PW Burn gas temperature

7 Zeldovich model Tb ,Pcy NOx

Table 7.4: The summary of the models developed so far in the study

230 EGR,Ti , Pi , MAF, N T SOI, PW f Prail , Pb Motoring

Pmot , Tmot

I()θ Dynamic SOI Activation temperature model

Fuel injection rate model Auto-ignition model

dm f SOC θ dθ ( ign ) dQcomb In-cylinder combustion model: dθ Combustion parameters model: dQcomb dQheat 1 ⎛ dV dp ⎞ pV dγ + = ⎜ pγ +V ⎟ − β,C p1,C p2 ,Cd1,Cd 2 dθ dθ γ −1⎝ dθ dθ ⎠ γ −1 dθ

Other models:Heat transfer,..

Pcy (Tcy ), Torque Local equivalence ratio model: φlocal

Adiabatic burn gas element temperature: Tb Initial burn gas temperature model: Tb,o

NO x model (Zeldovich)

Figure 7.4: A crank angle resolved combustion model with NOx model

231 7.4 The final model validation on the other engine operating condition

It would be meaningful if the overall model could be validated at another engine operating condition as described in Table 7.5. This is yet different from the test conditions at which the various models were developed for model parameters identification and validated. Only the current profile is estimated, which are not available at the test data. The results are summarized in the same table.

Fuel Injection Schedule Engine Rail PILOT MAIN EGR MAF AF T1 Speed pressure SOI PW SOI PW

Unit rpm CA us CA us % g/s bar - ‘C

2400 334 200 355 500 27.7 45 875 38 60

(a) Operating condition

error θ ign IMEP P θ NO max Pmax x (pilot/main) ()∆Pcy test est. test est. test est. Test est. test est.

Unit CA bar bar bar CA ppm

344/369 346/367 1.23 3.443.62 45.5 44 360 360 90 64

(b) Summary of the modeling result

Table 7.5: The engine operating condition, result of combustion and NOx estimation model

232

Figure 7.5: Combustion and NOx estimation result 233 7.5 Verification of the model by extrapolation

One of the methods to verify the prepared model is see if the trend as functions of available parameters predicted by the model is reasonable. The trends of the dependent variables such as IMEP, NOx, and maximum pressure as functions of the independent variable such as SOI, EGR, and PW are going to be shown in the following. When extrapolating the model with respect to one variable, the other independent variables (conditions) are fixed. The cases of the model extrapolation are summarized in Table 7.7. Basically, a model prepared through validation processing should not be extrapolated beyond 20% of the range of the variables which were used during model development. Beyond that point, the accuracy of the model prediction will deteriorate [52]. Therefore, in this context, the range of model extrapolation needs to be defined as in Table 7.6. The results of extrapolating the model are summarized in Figure 7.6 to confirm the trend of the CIDI engine combustion model prediction.

Model Extrapolation Variable Unit Lower Upper Lower Upper

Engine Speed rpm 1500 1800 1200 2000

EGR % 0 18 0 25

Pulse width (PW) µ sec 100 600 100 700

Start of Injection CA 320 360 320 370 (SOI)

Table 7.6: The range of variables to be extrapolated

234 # of Case # Variable Other conditions injections 1800 rpm, w/o EGR 1 1 SOI PWm = 500 1800 rpm, SOI = 354 2 EGR m PWm = 500 1800 rpm, w/o EGR PW SOI / PWpilot = 340 / 200 3 2 m SOI m = 354 1800 rpm, w/o EGR

SOI SOI / PWpilot = 340 / 200 4 m PWm = 500 1800 rpm, SOI / PW = 340 / 200 5 EGR pilot SOI / PWm = 354 / 500 SOI / PW = 340 / 200 pilot 6 rpm SOI / PWm = 354 / 400 w/o EGR

SOI / PW pilot = 340 / 200 SOI / PW = 354 / 400 7 3 rpm m SOI / PW post = 363/100 1800 rpm, w/o EGR

SOI / PW pilot = 340 / 200 SOI / PW = 354 / 400 8 EGR m SOI / PW post = 363/100 1800 rpm

SOI / PW pilot = 340 / 200

PWm = 300 9 SOI m SOI / PW post = 364 / 200 1500 rpm, w/o EGR 10 1~5 # Inj. 1800 rpm, w/o EGR

Table 7.7: Model verification test runs by extrapolation

235 (a) Case-1

(b) Case-2

Continued

Figure 7.6: The trend of CIDI combustion vs. SOI

236 Figure 7.6 continued

(c) Case-3

(d) Case-4

Continued

237 Figure 7.6 continued

(e) Case-5

(f) Case-6

Continued

238 Figure 7.6 continued

(g) Case-7

(h) Case-8

Continued

239 Figure 7.6 continued

(i) Case-9

(j) Case-10

240 7.5.1 Discussion of the results for the extrapolated model

As can be seen in Figure 7.6 (cases 1 through 10, subplot a through j), the extrapolated result of the model reasonably captures the trend of the CIDI engine combustion compared with the trend which the test data demonstrates. Even though only representative conditions of operating range of variables were selected due to the limited cases of validation test conditions, they represent nearly all operating engine points under normal driving conditions.

For the case #1, which shows the trend as function of SOI for a single (main) fuel injection, without EGR, and engine speed of 1800 rpm, all the output parameters decrease gradually as the SOI advances until the top dead center crank-angle. At low loads, when the SOC is ATDC with a retarded SOI, the peak pressure generated by the combustion heat is lower that that of the compression pressure at TDC. Therefore, the peak pressure after TDC is the same, (40 bar), which is compression pressure. As can be seen in the case #2, it can be easily found that EGR lowers the NOx emission except the point with an EGR of 8%. This might be explained by reminding the fact that the combustion model was validated based on a relatively high lower limit of EGR (10%, which is the stock ECU mapping data). However the other predicted data are consistent with the test data. In case #3, when the main injection PW is equal to 700 µ sec, performance data such as the peak pressure and IMEP is going to be out of the trend. But the NOx prediction is good. As can be seen in case #4, the trend is the same when there is only single fuel injection (case #1), which is reasonable. When there is EGR gas, the trend is the same as the case of single injection except that the NOx emission level is lowered (case #5). As engine speed increases, NOx emission decreases. This is because that the time for NOx to form is reduced when the speed increases. As a result, the residence time for NOx is reduced (case #6). For the pilot + main + post fuel injection cases (#7, #8, #9), it could be concluded that the model captures the physical trend without significant prediction error for all output variables. But it could be an issue that there is only two test data set like case #7 and #8. Even in those cases, the model predict the trend well where test data could present. Although there is no available test data for the 5-strike fuel injection cases,

241 the trend that the model predict is good enough to present the model applicability in CIDI engine research as shown in Figure 7.6 (j), (case 10). Literally, for the first time in the modeling work, this study developed a methodology to predict the CIDI engine combustion and NOx for multiple fuel injection cases by applying a single-zone combustion modeling approach. It is clear that the control strategy to apply the multiple fuel injections in terms of such parameters as SOI, pulse width, and dwell time of each individual injection is required to accomplish its goal of the reduced emissions without penalty on performance.

As can be inferred from the discussion so far, the trends predicted by the model are good. However, the exact trend or mathematical correlation could not be developed with this limited number of test case or extrapolated prediction results. Therefore, in order to acquire some meaningful correlations for major parameters such as the peak pressure, IMEP, peak pressure gradient, and NOx, an extensive mapping test need to be performed by the validated model using the design of experiment concept. However, it is generally known that over extrapolation of the model is not desirable [52]. Since the test conditions were limited in this study, the general trend of model prediction will be performed within the range covered by the validation test.

7.6 The virtual engine mapping test (VEMT)

Since the extrapolation of the model near the test range where the model was identified and validated showed physically reasonable trends, the validated model could be run for the purpose of performing a limited range virtual mapping engine test. However, the range of the extrapolation needs to be limited within the boundary of the test condition as shown in Table 7.8. The test case of the engine speed 2000 rpm and 20% EGR is a new condition that was not covered by the validation test. For the cases of multiple fuel injections test, only the main fuel injection data such as SOI and PW were varied. This is because the effect of pilot injection data is not significant on the entire combustion behavior as discussed in Chapter 4. The model structure for VEMT is shown in Figure 7.7. The results of the virtual engine mapping tests are shown from Figure 7.8 to Figure 7.11, which are the 3-D plots. 242 Case # of injections Other conditions Figure #

1800 rpm, 15% EGR 1 Figure 7.8 PWm = 500

1 2 1200 rpm, w/o EGR, Figure 7.9

3 2000 rpm, 20% EGR Figure 7.10

2000 rpm, 20% EGR 4 2 Figure 7.11 SOI / PWpilot = 340 / 200

Units: CA/µ sec

Table 7.8: The operating conditions for the virtual test run

The resolution for the pulse width step is limited by one crank angle.

For example, one step of pulse width at the engine speed of 1200 rpm is

1 1 ∆t = = []sec ≈140 µ sec , 6× rpm 7200 which is quite large so that the plots are not smooth at the pulse width axis.

243 SOI, PW Pb ,T f , EGR, N

Additional models: I()θ

Prail MAF,T1 , P1 ,Tivc

Fuel injection rate model

dm f (θ ) dθ

In-cylinder combustion model: Engine Ignition, heat transfer, heat release, and others geometry

Pcy (Tcy ), IMEP

NOx Model NOx φlocal , Zeldovich

Figure 7.7: The diagram of VEMT

244 (a) Peak pressure (b) IMEP

(c) Peak pressure change (d) Location of peak pressure

(e) Peak temperature (f) NOx

Figure 7.8: Case 1: 1800 rpm, EGR 15%, single injection

245 (a) Peak pressure (b) IMEP

(c) Peak pressure change (d) Location of peak pressure

(e) Peak temperature (f) NOx

Figure 7.9: Case 2: 1200 rpm, EGR 0%, single injection

246 (a) Peak Pressure (b) IMEP

(c) Peak pressure change (d) Location of peak pressure

(e) Peak temperature (f) NOx

Figure 7.10: Case 3: 2000 rpm, EGR 20%, single injection

247 (a) Peak Pressure (b) IMEP

(c) Peak pressure change (d) Location of peak pressure

(e) Peak temperature (f) NOx

Figure 7.11: Case 4: 2000 rpm, EGR 20%, 2-strike

248 The effects on 6 principal engine parameters for each run (peak pressure, IMEP, maximum pressure change, location of the peak pressure, peak mean temperature, and peak NOx) are shown in the figures as functions of SOI and PW.

As mentioned in the introductory part of this chapter, the result of the virtual engine mapping test (VEMT) could be used in deriving some correlations of the principal engine parameters such as IMEP and NOx. This could not be done today with a commercial code such as BOOST [22], as the multiple strike analysis especially for NOx estimation has not been done. With the methodology developed by this research, it would be possible to run an extensive range of the virtual engine mapping test and derive a useful correlation of IMEP and NOx to be used in a mean value model for control. Moreover, with a personal computer having a pentium-4 processor of 2.5 GHz clock speed, it takes only 45 seconds for a single fuel injection case and 62 seconds for a 2- strike case to run the code. This VEMT result could be used as a referencing data in an actual engine control by look-up tables or functional correlations such as a black box model.

249 8 CHAPTER 8

CONCLUSIONS AND RECOMMENDATION

8.1 Conclusions

The objective of this thesis was to develop a series of inter-related models to enable the rapid optimization and calibration of modern CIDI engines with multiple injection capabilities. Those tools had to be sufficiently accurate to capture all the relevant physical phenomena, yet simple enough to be computationally cheap and permit the exhaustive exploration of a large multi-dimensional design and control space. In particular, one of the missing such model today is a simple and efficient tool for CIDI combustion simulation with arbitrary fuel injection profile. Thus in this study, a crank- angle resolved CIDI engine combustion model was developed and validated. This model used a single-zone approach and was limited to the closed-valve part of cycle of a single cylinder for computational efficiency. This model was supplemented with many calibrated sub-models for the estimation of the fuel injection rate, auto-ignition delay, heat release rate, heat transfer, and NOx emissions. For the heat release model, Watson’s semi-empirical model form was used, albeit with suitably modified correlations. The total heat release rate in the case of multiple fuel injections was calculated by adopting a principle of “superposition” for the heat release of each fuel injection. For the prediction of the auto-ignition timing of each pulse, an Arrhenius type of ignition model was used, again with suitably identified parameters. All these sub-models were parameterized in terms of externally controllable variables, such as the start of fuel injection timing, pulse width, common rail pressure, back pressure, EGR, etc. A diagram schematically

250 representing the role of the various sub-models and their inputs and outputs is shown in Figure 8.1

Fuel injection rate model

SOI i PW i Pcy N T Combustion model cy Pb IMEP T f NOx EGR

NOx Model

Figure 8.1: The final shape of the model structure

To perform the parameterizations and sub-model validations, extensive experiments were conducted using a fuel injection rig (non-combusting) and a multi- cylinder engine (combusting) on a dynamometer. Both those rigs were extensively instrumented to properly identify the forms of the sub-models and to calibrate and validate them.

8.2 Contributions

Within the broad framework of the thesis presented above, the following specific contributions were made:

251 1) An algebraic sub-model to relate injector measured current profile to fuel flow

rate profile injected in the cylinder was developed. This sub-model was

parameterized with quantities such as rail pressure, back-pressure, fuel

temperature, etc. to capture all the relevant dependencies expected in an actual

engine. The profile was further decomposed into a delay and an actual profile

shape to best represent the physical phenomena. The agreement between the

model and the actual fuel flow rate profiles measured with a Bosch tube was quite

good, except for the closing event of the injector where the actual injector flow

rates persisted slightly beyond the interruption of the injector current.

2) An alternate algebraic model to relate the fuel flow rate to the injector needle lift

(when available) was also successfully developed. The usefulness of such model

is limited to the situations where the injector needle lift signal is available (a rare

occurrence in practice). However, due to the high correlation between the injector

current and needle lift, both sub-models perform equally well and future practical

such experiments can be limited to the easily measured injector current profile.

3) A third (highly simplified) model of the injection system was developed to bridge

the gap in an approximate algebraic fashion between the digital injector command

(logic pulse train) and the injector current. It was found that the current wave

forms were reasonably approximated by triangular wave forms in response to a

(rectangular) pulse train. The parameters of that triangle (height and width) were

appropriately parameterized as a function on controllable input parameters.

252 4) The composite use of the various and alternate injection sub-models described

above, lead to a good agreement of the fuel schedule (and hence the combustion

models) despite their simplified, non-physical basis.

5) An appropriate algebraic sub-model for the ignition delay was identified and

calibrated based on single injection experiments. It was further validated on a

larger data set showing good accuracy. The same model was then subsequently

used to model the ignition delay for each of the fuel pulses in the multiple

injection case.

6) The heat release process for the CIDI combustion corresponding to each fuel

injection was modeled using the Watson model, although with modified

correlations for all the parameters to best match the calibration data set. These

recalibrated parameters were further validated with additional data.

7) The heat release process for the CIDI engine combustion in the case of multiple

injections was developed using a “superposition principle” whereby the additional

heat release from the combustion of each fuel injection is additively modeled with

respect to the conditions present in the combustion chamber as a result of the

previous injections. To the author’s knowledge, it is the first time that such a

simple approach was successfully applied to model the heat release from multiple

injections using a single zone model.

8) The combined models (fuel injection, ignition delay, heat release) were used to

predict the heat release rate and in-cylinder pressure evolution as a function of

crank-angle for a large number of cases corresponding to single and multiple

injections, injection timings, EGR, etc. for which experimental data was available.

253 Overall, the agreement was very good in terms of resulting torque, peak pressure,

location of peak pressure, etc. despite the relative simplicity of the model (single-

zone, algebraic sub-models).

9) Using the in-cylinder pressure and temperature evolution as a function of crank-

angle as an input, the NOx emissions were predicted using the extended Zeldovich

mechanism. Since the model is a single zone, the concept of the local equivalence

ratio normally used in such calculation was modified and an “average local

equivalence ratio” concept was used. Its numerical value was obtained by

iteratively changing it and running the NOx model forward until the NOx level at

the end of the process agreed with the calibration data set. These values of the

“average local equivalence ratio” were then parameterized with respect to engine

operating conditions, so that it could be used to predict NOx for other cases.

10) This NOx model (and accompanying average local equivalence ratio model) were

used to predict emission levels over a significant range of engine operating

conditions representing single and multiple fuel injections, with various timing,

EGR dilution, etc. The overall agreement over the entire range was within less

than 50 ppm.

11) Finally, the feasibility of using such validated models to perform a “virtual engine

mapping” was demonstrated. The models are computationally cheap, requiring

only tens of seconds of computations on a personal computer per engine operating

point. This computational efficiency, combined with the reasonable accuracy of

the models and the ability to adequately capture the complexity of multiple

injection events in modern CIDI engines enables the possibility of completing

254 realistic, yet extensive virtual dynamometer engine mappings. Such mappings

can then be used for parameter optimization and engine calibration, without

requiring extensive and costly real dynamometer mappings. It is not advocated

that this process could replace real engine dynamometer tests altogether, but it

allows to perform only a limited number of suitably designed experiments to

calibrate to models and sub-models, followed by an extensive “virtual”

exploration of the parameter space.

12) A further outcome of this process is the ability of cheaply and conveniently

developed “calibrated” black-box models of the multiple injection combustion

process for use in Mean Value Models, and in turn for modern model-based

control. A possible implementation of this overall process is schematically

depicted in Figure 8.2.

255 m& f , EGR valve (α ) , VGT vane (β )

7-state mean value model

MAF,Intake composition, T1 (P),m& egr

Initial condition estimation at IVC ex. Pivc = f (MAF,m& egr ,T1 , N ) Tivc , Pivc

Fuel injection rate model Rail pressure

Combustion model

NOx Model

Pcy , Tcy , IMEP, NOx

Figure 8.2: The implementation of the model into mean value model

256 8.3 Recommendations

This research successfully demonstrated the feasibility of the overall approach. Recommendations for future work include the following:

1) Extending the emission modeling to not only include NOx but also to include

soot.

2) Performing calibration experiments over a wider range of engine operating

conditions. In this study, due to dynamometer limitations and other practical

factors, the majority of the experiments were confined to a limited range of RPM,

loads, EGR and no more than 3 injections per stroke. While this was sufficient to

demonstrate the feasibility of the methodology, all the parameterizations need to

be extended to a wider range of operating conditions.

3) Performing a more systematic “virtual engine mapping” and validating the

approach for engine operating conditions farther away (in the multi-dimensional

sense) from the calibration data points.

4) Automating many of the calibration and parameters extraction processes

described in this thesis, so that available experimental (limited) calibration points

can be automatically exploited.

5) Using the existing models developed in this thesis to guide the choice of future

calibration experimental data points. It is envision that the choice of calibration

points, automated calibration, and limited virtual mapping could be performed

iteratively until models are uniformly valid over a wide range of engine operating

conditions.

257 6) Using the results of the virtual mapping to develop suitable calibrated Mean-

Value Models of the dynamics of the CIDI engine plant and development of

appropriate model-base control, optimization and diagnostics.

In conclusion, this work is the first facet of a broad strategy at developing robust model-base calibration and control tool for modern CIDI engines. This work provided the necessary proof-of-concept to further continue this work based on the above recommendations.

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