REACTION-BASED MODELING AND CONTROL OF AN ELECTRICALLY

BOOSTED DIESEL ENGINE

By

Yifan Men

A DISSERTATION

Submitted to

Michigan State University

in partial fulfillment of the requirements

for the degree of

Mechanical Engineering – Doctor of Philosophy

2019

ABSTRACT

REACTION-BASED MODELING AND CONTROL OF AN ELECTRICALLY

BOOSTED DIESEL ENGINE

By

Yifan Men

This dissertation presents the reaction-based modeling of diesel combustion and model-based

control of diesel engine air path.

The dissertation first presents a control-oriented reaction-based diesel combustion model

that predicts the time-based rate of combustion, in-cylinder gas temperature and pressure

over one engine cycle. The model, based on the assumption of a homogeneous thermody-

namic combustion process, utilizes a two-step chemical reaction mechanism that consists of

six species: diesel fuel (C10.8H18.7), oxygen (O2), carbon dioxide (CO2), water (H2O), nitro-
gen (N2), and carbon monoxide (CO). The temperature variation rate is calculated based
on the rate of change of species concentrations, and the heat loss correlation is also used to

study the model performance. The accuracy of the model is evaluated using the test data

from a production GM 6.6 L, 8-cylinder, turbocharged engine. The model is calibrated over

large engine speed and load range as well as different injection timings and exhaust gas re-

circulation (EGR) rates by solving the optimization problem. The calibrated reaction-based

model accurately predicts the indicated mean effective pressure, while keeping the errors of

in-cylinder pressure and temperature small, and at the same time, significantly reduces the

calibration effort, especially when the engine is operated under multiple fuel injection opera-

tions, comparing to Wiebe-based combustion models. The calibrated model parameters have

a strong correlation to engine speed, load and injection timings, and as a result, a universal

parameter calibration structure is proposed for entire operational conditions.

The second part of the dissertation is to obtain a parametric understanding of diesel

combustion by developing a physics-based model that is able to predict the combustion met-

rics, such as in-cylinder pressure, burn rate, and indicated mean effective pressure (IMEP)

accurately, over a wide range of operating conditions, especially with multiple injections. In

the proposed model, it is assumed that the engine cylinder is divided into three zones: a

fuel zone, a reaction zone, and an unmixed zone. The formulation of reaction and unmixed

zones is based on the reaction-based modeling methodology, where the interaction between

them is governed by Fick’s law of diffusion. The fuel zone is formulated as a virtual zone,

which only accounts for mass and heat transfer associated with fuel injection and evapo-

ration. The model is validated using test data under different speed and load conditions,

with multiple fuel injections and EGR. It is shown that the three-zone model outperformed

the single-zone model in in-cylinder pressure prediction and calibration effort with a mild

penalty in computational time. One set of calibration parameters are used for all engine

operating conditions.

The third part of the dissertation is modeling and control of engine air path with an elec-

trically assisted boosting system. A physics-based control-oriented engine air path model

with electrical assistance has been developed. The model is validated with steady-state en-

gine test data and standard driving cycle data. Through one-dimensional simulation, it is

found that the electrically assisted boosting system is able to improve engine performance

under both steady-state and transient conditions. A model-based controller has been devel-

oped for the electric booster (eBoost) and bypass valve to improve the transient performance

of engine load response. Experiments have been performed on a Ford 6.7 L, 8-cylinder, tur-

bocharged diesel engine equipped with a prototype eBoost and a standard EGR valve as

the bypass valve. Steady-state test results have shown that eBoost is capable of improving

engine efficiency by reducing pumping loss, due to reduced turbine speed when eBoost is

providing additional boost energy. In the transient process, eBoost is able to significantly

reduce the response time of boost pressure tracking, as validated by load step tests.

Copyright by
YIFAN MEN
2019

ACKNOWLEDGEMENTS

This dissertation would not have been possible without the help from so many people who

provided me with guidance, support, and encouragement. I would like to express my sincere

appreciation to all of them.

Foremost, I would like to express my deepest gratitude to my advisor, Prof. Guoming

(George) Zhu. It is my great privilege to study and work under his persistent support and

extraordinary guidance. His comprehensive knowledge of control theory and extensive auto-

motive application experience continually and convincingly motivated a spirit of exploration

in regard to my Ph.D. research. As an advisor, his guidance is never limited to academic re-

quirements. He set an excellent example of how to better communicate with people, manage

time, and be a man of value.

I would like to express my most sincere appreciation to the committee members: Dr.

Harold Schock, Dr. Hassan Khalil, and Dr. Zhaojian Li, for their guidance and insightful

comments for my coursework and dissertation. Their excellent undergraduate and graduate

courses provided me with valuable knowledge and a solid foundation for my research work.

I would also like to send my heartfelt thanks to the graduate students, lab engineers

and visiting scholars, with whom I’m honored to have worked in our lab. My first gratitude

goes to Yingxu (Ocean) Wang, who is always there to help me out. I’d like to express my

appreciation to Dr. Tao Zeng who generously devoted his time guiding me through my

research project. My special gratitude goes to our electrical engineer, Kevin Moran, and

mechanical engineer, Tom Stuecken, without whose help it would be impossible for me to

complete the experiments. Many thanks to Dr. Shupeng Zhang, Dr. Jie Yang, Dr. Ruitao

Song, Dafa Yan, Mengyan Gu, Dr. Huan Li, Dr. Chengsheng Miao, Tianyi He, Ruixue Li,

Shen Qu, Yu He and Dawei Hu, for their kindly help and the time we spent together.

Lastly, I am overly grateful to my parents who have been a great source of support and

encouragement throughout my life.

v

TABLE OF CONTENTS

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

CHAPTER 1

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Research overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 Model-based calibration of reaction-based diesel combustion dynamics
1.2.2 Multi-zone reaction-based modeling of diesel combustion . . . . . . .
1.2.3 Modeling and control of an electrically assisted boosting system . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Dissertation contributions
1.4 Dissertation outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.1

CHAPTER 2 REACTION-BASED MODELING OF COMBUSTION DYNAMICS .
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 Engine combustion models . . . . . . . . . . . . . . . . . . . . . . . .
2.1.2 Wiebe function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.3 Reaction-based model
. . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Chemical kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Reaction-based modeling approach . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Overview of the modeled physics
. . . . . . . . . . . . . . . . . . . .
2.3.2 Molar concentration rate of species . . . . . . . . . . . . . . . . . . .
2.3.3
Instant cylinder volume and volume rate . . . . . . . . . . . . . . . .
2.3.4 Temperature rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.5 Rates of reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.6 Flow rate
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.7 Heat loss rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Reaction-Based model validation . . . . . . . . . . . . . . . . . . . . . . . .
2.4.1 Continuous-time model . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.2 GT-POWER DIPulse model . . . . . . . . . . . . . . . . . . . . . . .
2.4.3 Preliminary calibration results . . . . . . . . . . . . . . . . . . . . . .
2.4.4 Variable engine speed and load, fixed injection timing . . . . . . . . .
2.4.5 Variable injection timing, fixed engine speed and load . . . . . . . . .
2.4.6 EGR sweep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.7 Air-Fuel ratio sweep . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.8 Notes
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Model calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.1
Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.2 Overview of experimental data . . . . . . . . . . . . . . . . . . . . . .
2.5.3 Automated calibration algorithm . . . . . . . . . . . . . . . . . . . .
2.5.4
Individual calibration . . . . . . . . . . . . . . . . . . . . . . . . . . .

ix

xi

1
1
4
5
6
7
8
9

10
10
10
12
17
18
18
18
19
20
21
23
26
27
28
29
32
33
34
36
39
40
41
42
43
44
47
49

vi

2.5.5 Parameter correlations . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.6 Calibration structure . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.7 Calibration: engine map . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.8 Calibration: SOI sweep at constant speed and load . . . . . . . . . .
2.5.9 Calibration: SOI sweep at constant speed and fuel injection . . . . .
2.5.10 Model validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

CHAPTER 3 A THREE-ZONE COMBUSTION MODEL FOR DIESEL ENGINES
3.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Model description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Model structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 Volume and volume rate equations
. . . . . . . . . . . . . . . . . . .
3.2.3 Fuel zone
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.4 Unmixed zone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.5 Reaction zone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.6 Cylinder properties . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Test data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 Combustion characteristics . . . . . . . . . . . . . . . . . . . . . . . .
3.3.3 Parameter variability . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50
52
55
55
56
57
58

63
63
66
66
67
68
70
75
77
77
77
78
82
83

4.1
4.2 Engine air charge system model

85
CHAPTER 4 MODELING AND CONTROL OF AN EBOOST SYSTEM . . . . .
85
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
88
. . . . . . . . . . . . . . . . . . . . . . . . .
89
4.2.1 Engine intake and exhaust mass flow rate . . . . . . . . . . . . . . . .
91
4.2.2 EGR mass flow rate
. . . . . . . . . . . . . . . . . . . . . . . . . . .
92
4.2.3
Intake manifold temperature . . . . . . . . . . . . . . . . . . . . . . .
95
4.2.4 Exhaust manifold temperature . . . . . . . . . . . . . . . . . . . . . .
96
4.2.5 Turbine power and mass flow rate . . . . . . . . . . . . . . . . . . . .
98
4.2.6 Power loss model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.7 Compressor power and mass flow rate.
99
. . . . . . . . . . . . . . . . .
4.2.8 Model validation with transient data. . . . . . . . . . . . . . . . . . . 101
4.3 Extended air charge model with eBoost system . . . . . . . . . . . . . . . . 102
4.3.1 The eBoost compressor power and mass flow rate . . . . . . . . . . . 103
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.3.2 Motor drive power
4.3.3 Bypass mass flow rate
. . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.4 System analysis of the electrically boosted diesel engine . . . . . . . . . . . . 104
4.4.1
. . . . . . . . . . . . . . . . . . . . . . . . 105
4.4.2 Transient performance . . . . . . . . . . . . . . . . . . . . . . . . . . 110
4.5 Linear quadratic control of the VGT-EGR-eBoost system . . . . . . . . . . . 114
4.5.1 Control objective and problem formulation . . . . . . . . . . . . . . . 114
4.5.2 Linearization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
4.5.3 Linear quadratic regulator . . . . . . . . . . . . . . . . . . . . . . . . 117

Steady-state performance

vii

4.6 Experimental validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.6.1 Engine test setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.6.2 Test bench validation and engine baseline
. . . . . . . . . . . . . . . 122
Steady-state validation . . . . . . . . . . . . . . . . . . . . . . . . . . 124
4.6.3
4.6.4 Transient validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
4.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

CHAPTER 5 CONCLUSIONS AND FUTURE WORK . . . . . . . . . . . . . . . 134
5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
5.2 Recommendations for future work . . . . . . . . . . . . . . . . . . . . . . . . 135

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

viii

LIST OF TABLES

Table 2.1: Arrhenius rate parameters for single-step model . . . . . . . . . . . . . . .

Table 2.2: Arrhenius rate parameters for two-step model . . . . . . . . . . . . . . . .

Table 2.3: Arrhenius rate parameters for four-step model (propane) . . . . . . . . . .

Table 2.4: GT-POWER engine geometry and model parameters . . . . . . . . . . . .

Table 2.5: Relative error for IMEP from -132CA to 132CA (%) . . . . . . . . . . . .

Table 2.6: Relative error for output torque (%) . . . . . . . . . . . . . . . . . . . . .

Table 2.7:

IMEP (bar) from -132 CAD to 132 CAD . . . . . . . . . . . . . . . . . .

Table 2.8: Sensitivity coefficients of parameters . . . . . . . . . . . . . . . . . . . . .

Table 2.9: Engine specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Table 2.10: Summary of the experimental data . . . . . . . . . . . . . . . . . . . . . .

Table 3.1: Summary of test data . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Table 3.2: Optimized model parameters . . . . . . . . . . . . . . . . . . . . . . . . .

Table 3.3: Modeling error in in-cylinder pressure (%) . . . . . . . . . . . . . . . . . .

Table 4.1: Model calibration - engine intake mass flow rate

. . . . . . . . . . . . . .

Table 4.2: Model calibration - EGR mass flow rate . . . . . . . . . . . . . . . . . . .

Table 4.3: Model calibration - coolant temperature . . . . . . . . . . . . . . . . . . .

Table 4.4: Model calibration - compressor outlet temperature . . . . . . . . . . . . .

Table 4.5: Model calibration - exhaust manifold temperature . . . . . . . . . . . . .

Table 4.6: Model calibration - turbine power

. . . . . . . . . . . . . . . . . . . . . .

Table 4.7: Model calibration - turbine mass flow rate . . . . . . . . . . . . . . . . . .

Table 4.8: Model calibration - turbo shaft power loss . . . . . . . . . . . . . . . . . .

30

31

31

33

34

34

40

44

45

46

78

79

82

90

92

93

94

95

97

98

99

ix

Table 4.9: Model calibration - main compressor power . . . . . . . . . . . . . . . . . 100

Table 4.10: Model calibration - compressor mass flow rate . . . . . . . . . . . . . . . . 101

Table 4.11: Model calibration - eBoost compressor power . . . . . . . . . . . . . . . . 103

Table 4.12: GT-SUITE DOE simulation setup . . . . . . . . . . . . . . . . . . . . . . 106

Table 4.13: Specifications of Ford diesel engine . . . . . . . . . . . . . . . . . . . . . . 121

x

LIST OF FIGURES

Figure 2.1: Category of engine combustion models . . . . . . . . . . . . . . . . . . .

Figure 2.2: Schematic diagram of Wiebe’s approach . . . . . . . . . . . . . . . . . .

Figure 2.3: Full-cycle reaction-based modeling architecture

. . . . . . . . . . . . . .

Figure 2.4: Closed-cycle reaction-based modeling architecture . . . . . . . . . . . . .

Figure 2.5: Methods for in-cylinder temperature and pressure calculation . . . . . .

Figure 2.6: Model calibration approach . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.7: GT-POWER single-cylinder engine model with predictive combustion . .

Figure 2.8:

In-cylinder pressure for the two-step and GT-POWER models under
5×5 engine operation matrix . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.9: Calibration coefficients for the two-step model

. . . . . . . . . . . . . . .

Figure 2.10: In-cylinder temperature and pressure for the two-step and GT-POWER

models with different main injection timing

. . . . . . . . . . . . . . . .

Figure 2.11: In-cylinder temperature and pressure for the two-step and GT-POWER

models with late injection at 15 CAD ATDC . . . . . . . . . . . . . . . .

Figure 2.12: In-cylinder temperature and pressure for the two-step and GT-POWER

models with late injection at 20 CAD ATDC . . . . . . . . . . . . . . . .

Figure 2.13: In-cylinder temperature and pressure for the two-step and GT-POWER

models with late injection at 25 CAD ATDC . . . . . . . . . . . . . . . .

Figure 2.14: In-cylinder temperature and pressure for the two-step and GT-POWER

models with late injection at 30 CAD ATDC . . . . . . . . . . . . . . . .

Figure 2.15: In-cylinder temperature and pressure for the two-step and GT-POWER

models with late injection at 35 CAD ATDC . . . . . . . . . . . . . . . .

Figure 2.16: In-cylinder temperature and pressure for the two-step and GT-POWER

models with late injection at 40 CAD ATDC . . . . . . . . . . . . . . . .

xi

11

14

19

20

21

29

32

35

36

36

37

37

38

38

39

39

Figure 2.17: In-cylinder temperature and pressure for the two-step and GT-POWER

models with different EGR ratio . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.18: In-cylinder temperature and pressure for the two-step and GT-POWER

models with different air-fuel ratio

. . . . . . . . . . . . . . . . . . . . .

Figure 2.19: Sensitivity coefficients of most significant parameters

. . . . . . . . . . .

Figure 2.20: Pressure and temperature predictions at 1400 r/min, 2.5 bar . . . . . . .

Figure 2.21: MFB and HRR predictions at 1400 r/min, 2.5 bar . . . . . . . . . . . . .

Figure 2.22: Estimated vs. actual IMEP over the engine map . . . . . . . . . . . . . .

Figure 2.23: Estimated vs. actual IMEP for SOI sweep at 4 operating conditions . . .

40

41

45

48

49

50

50

Figure 2.24: Estimated vs. actual IMEP for SOI sweep at 1400 r/min with constant fuel 51

Figure 2.25: Calibrated EA,1 vs. SOI for different speed-load pairs . . . . . . . . . . .

Figure 2.26: Calibrated EA,2 vs. SOI for different speed-load pairs . . . . . . . . . . .

Figure 2.27: EA,1 vs. SOI for different EGR levels at 1400 r/min with constant fuel

Figure 2.28: EA,2 vs. SOI for different EGR levels at 1400 r/min with constant fuel

.

.

Figure 2.29: Calibration structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.30: Distribution of IMEP error with various smoothness . . . . . . . . . . . .

Figure 2.31: Calibration surfaces for EA,1 and EA,2 . . . . . . . . . . . . . . . . . . .

Figure 2.32: Predicted IMEP vs. actual IMEP for smoothed lookup table . . . . . . .

Figure 2.33: Predicted IMEP vs. actual IMEP for third order polynomial fit

. . . . .

Figure 2.34: Predicted IMEP vs. actual IMEP for second order polynomial fit

. . . .

Figure 2.35: Error distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.36: Predicted IMEP vs. actual IMEP for third order polynomial fit for EA,1

and second order polynomial fit for EA,2 . . . . . . . . . . . . . . . . . .

Figure 2.37: Predicted IMEP vs. actual IMEP for smoothed lookup table . . . . . . .

51

52

53

53

54

55

56

57

57

58

58

59

59

xii

Figure 2.38: Predicted IMEP vs. actual IMEP for second order polynomial fit

. . . .

Figure 2.39: Predicted IMEP vs. actual IMEP . . . . . . . . . . . . . . . . . . . . . .

Figure 3.1: Three-zone model schematic . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3.2: Fuel evaporation model . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3.3: Air entrainment model

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3.4: Pressure traces at different speed-load conditions with the same main

injection timing at 20◦ bTDC . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3.5: Pressure traces under different speed and load conditions with the same

main injection timing at 6◦ bTDC . . . . . . . . . . . . . . . . . . . . . .

Figure 3.6: Pressure traces at different speed-load conditions with the same main

injection timing at 5◦ aTDC . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3.7: Pressure traces at 1400 r/min, BMEP=2.5 bar, with different main

injection timings

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3.8: Heat release rate traces at 1400 r/min, BMEP=2.5 bar, with different

main injection timings . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3.9: Predicted IMEP vs actual IMEP for different operating conditions . . . .

Figure 4.1: System layout for engine air path with eBoost . . . . . . . . . . . . . . .

Figure 4.2: Model identification results for engine intake mass flow rate

. . . . . . .

Figure 4.3: EGR effective area vs. EGR valve position . . . . . . . . . . . . . . . . .

Figure 4.4: Model identification results for EGR mass flow rate . . . . . . . . . . . .

Figure 4.5: Model identification results for compressor outlet temperature . . . . . .

Figure 4.6: Model identification results for intake manifold temperature . . . . . . .

Figure 4.7: Model identification results for exhaust manifold temperature

. . . . . .

Figure 4.8: VGT control input vs. vane angle . . . . . . . . . . . . . . . . . . . . . .

Figure 4.9: Model identification results for turbine power

. . . . . . . . . . . . . . .

xiii

60

60

67

69

71

79

80

81

81

82

83

89

90

92

93

94

95

96

97

98

Figure 4.10: Model identification results for turbine mass flow rate . . . . . . . . . . .

99

Figure 4.11: Model identification results for main compressor power . . . . . . . . . . 100

Figure 4.12: Model identification results for main compressor mass flow rate

. . . . . 102

Figure 4.13: Model validation with FTP 75 driving cycle data . . . . . . . . . . . . . 102

Figure 4.14: Baseline engine maps for VGT, EGR, and BSFC (percentage of maxi-

mum value) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

Figure 4.15: DOE results for VGT and EGR . . . . . . . . . . . . . . . . . . . . . . . 107

Figure 4.16: DOE results for eBoost power (normalized percentage) and BSFC . . . . 107

Figure 4.17: System causality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

Figure 4.18: Percentage BSFC difference (upstream-downstream) . . . . . . . . . . . . 108

Figure 4.19: Compressor efficiency difference (downstream-upstream)

. . . . . . . . . 109

Figure 4.20: VGT position and exhaust manifold pressure difference (downstream-

upstream) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

Figure 4.21: Transient response for boost pressure stepped by 0.2 bar . . . . . . . . . 111

Figure 4.22: Transient response for boost pressure stepped by 0.4 bar . . . . . . . . . 111

Figure 4.23: Transient response for boost pressure stepped by 0.6 bar . . . . . . . . . 112

Figure 4.24: Open-loop transient response for load stepped from 100 to 500 N-m . . . 112

Figure 4.25: Closed-loop transient response for load stepped from 100 to 500 N-m . . 113

Figure 4.26: Error-based control signals for eBoost assist

. . . . . . . . . . . . . . . . 114

Figure 4.27: Set points for diesel engine air charge system control

. . . . . . . . . . . 115

Figure 4.28: Flow conditions with different pressure ratio . . . . . . . . . . . . . . . . 115

Figure 4.29: Set points for eBoost system . . . . . . . . . . . . . . . . . . . . . . . . . 116

Figure 4.30: Step load test profile for engine operated at 1500 r/min . . . . . . . . . . 118

Figure 4.31: Tracking performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

xiv

Figure 4.32: Control architecture for experimental implementation . . . . . . . . . . . 120

Figure 4.33: LQR for eBoost control

. . . . . . . . . . . . . . . . . . . . . . . . . . . 121

Figure 4.34: Engine test setup layout . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

Figure 4.35: Engine test matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

Figure 4.36: Exhaust restriction plate . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

Figure 4.37: Back pressure matching . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

Figure 4.38: BSFC improvement at 1000 r/min . . . . . . . . . . . . . . . . . . . . . 126

Figure 4.39: VGT and EGR operation with engine speed at 1000 r/min . . . . . . . . 127

Figure 4.40: Compressor inlet pressure and turbocharger speed with engine speed at

1000 r/min . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

Figure 4.41: Exhaust manifold pressure and fuel injection with engine speed at 1000

r/min . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

Figure 4.42: BSFC benefit from simulation and test results . . . . . . . . . . . . . . . 128

Figure 4.43: Test results over the entire matrix . . . . . . . . . . . . . . . . . . . . . . 129

Figure 4.44: Transient response at 700 r/min with air block . . . . . . . . . . . . . . . 130

Figure 4.45: Transient response at 1000 r/min with air block . . . . . . . . . . . . . . 130

Figure 4.46: Transient response at 1400 r/min with air block . . . . . . . . . . . . . . 131

Figure 4.47: Transient response at 700 r/min with bypass valve . . . . . . . . . . . . . 131

Figure 4.48: Transient response at 1000 r/min with bypass valve . . . . . . . . . . . . 132

Figure 4.49: Transient response at 1400 r/min with bypass valve . . . . . . . . . . . . 132

xv

CHAPTER 1

INTRODUCTION

1.1 Motivation

Internal combustion (IC) engines have been widely used in the automotive industry.

Both gasoline and diesel engines have been built in passenger and commercial cars, that

heavily affect in people’s everyday life. It has been shown that in many developed countries,

personal cars get very popular with about or even more than 0.5 cars per person [1]. The

huge market size of global car fleet and the increase in the access to cars lead to potentially

serious problems, such as world oil depletion [2], CO2 emissions and climate change [3], and
pollutant (NOx, HC and particulate matter) production [4]. In this scenario, changes in both

the market and regulatory policies have accelerated the development of new technologies for

the IC engines in the past decades. On the combustion concepts, spark-ignition (SI) engines

are being developed with lean-burn combustion, stratified gasoline combustion, etc. New

compression ignition (CI) combustion concepts include low-temperature combustion (LTC),

homogeneous charge compression ignition (HCCI), premixed charge compression ignition

(PCCI) and reactivity controlled compression ignition (RCCI). Regarding boosted engine

technologies, turbochargers with variable geometry turbines (VGT) have been widely used

with exhaust gas recirculation (EGR) for downsized engines. New boosting methods have

been developed by combining the existing technologies, either in series or parallel. The

resulting system introduces opportunities for improving efficiency and performance but also

becomes more complicated to control. As the new engine technologies are developed, it is

clear that the importance of engine control is growing for today and future IC engines [5].

Modern diesel engines are widely equipped with common rail direct fuel injection system,

variable geometry turbocharger (VGT) and exhaust gas recirculation (EGR). Control strate-

gies associated with these physical systems are designed to meet driver’s torque demand, with

1

the constraints on fuel economy and emissions. Multiple injections are commonly used to

control combustion phasing and duration and reduce noise, which may lead to desired output

torque, peak pressure, and exhaust temperature. VGT and EGR are able to provide diesel

engine with fresh air and required exhaust gas fraction, which makes it possible to meet the

requirement of the engine emission standard, fuel economy, and transient performance. The

control and optimization issue within this field is important and challenging. For example,

the widely used combustion model for diesel engines requires a tremendous amount of cal-

ibration effort, while the accuracy of such a model does not meet the requirement under

extreme operating conditions. To better control the diesel combustion under multiple injec-

tions and heavy EGR, a new modeling concept for diesel combustion dynamics is needed to

replace the traditional map-based model. On the other hand, VGT and EGR are naturally

coupled, leading to more challenges for robust and optimal control design of the diesel engine

air charge system [6].

Model-based control is very attractive in the engine research community. With this ap-

proach, the development cycle and effort can be significantly reduced by avoiding massive

engine tests. However, the key factor that determines the effectiveness of a model-based con-

troller is the quality of the control-oriented model. It is required that the control-oriented

model can reflect the plant behavior with an acceptable error while costing moderate com-

putational resources. Most of the current methods for engine combustion and air path use

manufacturer-based maps, leading to a large amount of calibration, non-physical extrap-

olation, and modeling errors. Physics-based modeling of engine combustion and air path

dynamics may mitigate the requirement of accurate representation of a complex physical

system and simply structured modeling. Considering the engine combustion with two injec-

tions, a single Wiebe function is not even able to represent the second peak of heat release

rate generated by the second injection. The physics-based combustion model, on the other

hand, is able to adapt to different injection events and predict the in-cylinder properties based

on instantaneous condition. Considering the VGT-EGR system with an extra compressor

2

driven by an electric motor at the upstream of the main compressor, the main compressor

may operate at a very low-pressure ratio where the map-based model could not work due to

significant error. A physics-based model for the compressor, in this case, is needed for both

normal operating conditions and conditions with an extremely low-pressure ratio.

A traditional calibration process for diesel combustion model can be described as follows.

First, the open-loop engine test is carried out over entire engine operating conditions, as func-

tions of engine speed, mass of fuel injection, injection timing and duration, EGR rate, etc.

Then the calibration process is essentially curve/surface-fitting, with predefined functions

and parameters. Each calibration parameter will result in at least one three-dimensional

(3-D) lookup table. The final combustion model will be a simple function but with multiple

3-D lookup tables. A physics-based combustion model is able to reduce the modeling error

at extreme conditions and eliminate the need for most lookup tables. A traditional engine

controller calibration process can be described as follows. First, a feedforward map that pro-

vides the desired fuel command as a function of engine speed and driver’s acceleration pedal

position is developed. The second step is to optimize the VGT vane position and EGR valve

position at each speed and torque condition, targeting the best performance/fuel economy

with the constraints on emissions. The third step is transient calibration. During transient

operations, the coupling between VGT and EGR is neglected, which indicates that the VGT

vane position is used to control boost pressure and EGR valve position is used to control

EGR rate separately. To achieve better tracking performance, coordinated control for VGT

and EGR is made possible by multi-input-multi-output (MIMO) control theory. Assisted

boosting technique has introduced more degree of freedom in control and opportunity in

improving transient performance. Based on the existing modeling and control structure of

VGT-EGR system, a new model and control design of the engine air charge system with an

assist device can be developed to achieve better performance and fuel economy.

3

1.2 Research overview

The research work is divided into two parts in this dissertation: reaction-based combus-

tion modeling, modeling and control of air charge system.

There are many types of engine combustion models. Multi-zone 3-D computational fluid

dynamics (CFD) models with detailed chemical kinetic mechanisms are capable of precisely

predicting the thermodynamics, flow, heat transfer, and pollutant formation during the

combustion process. However, these high-fidelity models are not suitable for model-based

control because they are too complicated to be used for real-time simulation. Traditionally,

zero-dimensional (0-D) mean-value models are widely used for engine control and hardware-

in-the-loop (HIL) simulation. The disadvantage of the mean-value model is that it does not

provide detailed information about the combustion on a crank-angle base, such as in-cylinder

pressure and temperature. A more widely used combustion model, called Wiebe function,

is popular because it is a simple function of the current crank angle. After calibration, the

Wiebe function can provide an acceptable prediction of burn rate for engine operating at

normal conditions. However, Wiebe function requires significant calibration effort, especially

when the operation is out of the normal range, e.g. multiple fuel injections and high EGR

rate. The scope of this dissertation is to adopt a new concept of combustion modeling so that

the current combustion model could be more physics-based. The adopted concept is called

reaction-based modeling, i.e. using chemical kinetics to describe combustion dynamics, but

maintain the model in zero dimension. The challenges of this study include: 1) implementa-

tion of thermochemistry and chemical kinetics in diesel combustion; 2) development of proper

calibration structure to extend the feasible range of conditions; 3) Reduction of calibration

effort by introducing key dynamics. Thus, combustion modeling work is further separated

into two parts. The first part mainly deals with the calibration of the existing reaction-based

model. The second part introduces the new modeling concept that completely eliminates

the need for lookup tables.

There have been studies on the assisted turbocharger systems, such as regenerative hy-

4

draulically assisted turbocharger (RHAT) and electrically assisted turbocharger (eTurbo). It

is shown that assisted devices improve engine steady-state and transient performance. The

numerical and experimental study on RHAT and eTurbo is extensive. However, the study

of the electrically assisted boosting system (eBoost) is not quite comprehensive. The system

analysis of eBoost has been carried out with very sparse operating conditions. Study on

transient performance is even rarer. The challenges of eBoost modeling and control include

modeling of the compressor under very low-pressure ratio and coordinated control of eBoost

compressor and bypass valve during transient operation.

1.2.1 Model-based calibration of reaction-based diesel combustion dynamics

Although crank-based Wiebe function filled the gap between mean-value model and 3-D

CFD model, the drawbacks, such as large calibration effort and extrapolation error limit

its application. To overcome these drawbacks, this dissertation proposes the adoption of

reaction-based approach to diesel combustion. The reaction-based approach is essentially

using chemical kinetics to model combustion process in zero dimension. It has already been

validated in homogeneous charge compression ignition (HCCI) engines, where the combustion

behavior is mainly controlled by chemical reactions. Diesel combustion, similar to HCCI,

is compression ignition, although the fuel-air mixing process is much more complicated.

Thus, it is promising to implement the reaction-based approach on the diesel combustion

model, with moderate modifications. In order to implement the reaction-based model, the

in-cylinder thermodynamics is transferred from macroscopic dimension to microscopic di-

mension. Every thermodynamic property is described on a molecular base. To determine

which chemical kinetic mechanism to adopt, a one-step mechanism, also called global mech-

anism, is tested first. Then a two-step and four-step mechanism is evaluated accordingly.

Considering the computational constraint and modeling error, a two-step mechanism is in-

tegrated in the model. Two parameters are identified through a sensitivity analysis of the

developed single-zone two-step reaction-based model. The two parameters are the activation

5

energy coefficients in the first and second reaction, respectively, which is quite intuitive. It

indicates that the diesel combustion is mostly dominated by chemical reactions. The model

is then calibrated and validated using engine test data. It is shown that the two rate co-

efficients vary as the engine operating condition changes. To reduce the requirement for

lookup tables, a calibration structure is developed so that the two coefficients can be fit

to polynomial as a function of injection timing and EGR rate. The calibration structure

has extend the applicable range of reaction-based model for diesel engines. It also improves

the in-cylinder pressure prediction accuracy and reduces number of calibration parameters,

compared to Wiebe function.

1.2.2 Multi-zone reaction-based modeling of diesel combustion

Multi-zone approach is widely used in diesel combustion models. Combining the reaction-

based method and multi-zone approach introduces a new opportunity to improved accuracy

and calibration efficiency.

Although the developed single-zone two-step reaction-based diesel combustion model has

shown potential for improving prediction accuracy and less calibration, there are two issues

that are not addressed yet: 1) the burn rate is overpredicted due to homogeneous assumption;

2) there are still lookup tables. To address the above issues, it is necessary to account for

in-cylinder inhomogeneity but still maintain the model in zero-dimensional. A multi-zone

approach is a natural option. There are many types of multi-zone approaches that are

applicable to diesel combustion, such as droplet breakup model, multiple identical reaction

zones, charge mixing model, turbulence model, etc. This dissertation proposes a three-zone

model significantly different than the above-mentioned models. In the proposed model, there

are three 0-D thermodynamic zones: fuel zone, reaction zone, and unmixed zone. Each zone

undergoes a unique physical process. The zone-to-zone interaction mitigates the sensitivity

in reaction coefficients and consequently eliminates the need for lookup tables. The burn rate

is less overpredicted due to relaxation of rate coefficients for the start of combustion. The

6

model has been validated with engine test data under multiple fuel injections and different

EGR rates. It is shown that the three-zone model is valid over a wide range of operating

conditions, which is a significant improvement compared to the single-zone model. The

developed reaction-based model cost only moderate computational resources and can be

used for model-based control. Furthermore, the calibration parameters can be fixed over the

entire engine operational map, which significantly simplifies the calibration process.

1.2.3 Modeling and control of an electrically assisted boosting system

To improve engine performance and fuel economy with eBoost, modeling and control of

engine air path with eBoost are essential. This dissertation adopts a standard 0-D engine air

path model with VGT and EGR. An eBoost model, which consists of an electric compressor

and a bypass valve, is added at the upstream of the main compressor. The physics-based

model has been validated with steady-state engine test data and driving cycle data. The

system behavior has been studied through 1-D simulations. It is shown that with eBoost

activated, engine steady-state performance (fuel economy) can be improved, mostly at low

speed and high load conditions. The corresponding optimal VGT and EGR positions change

as well. In addition, different configurations (upstream and downstream) have been studied

and compared over the entire engine map.

It is found that the downstream is preferred

in most engine speed and load conditions except the driving cycle range. In the transient

process, with a load step commanded, eBoost is able to track the target boost pressure much

faster than VGT alone. The reduction in boost pressure response directly leads to improved

engine torque response. A full-order multi-input-multi-output (MIMO) linear quadratic (LQ)

controller has been designed for set point regulation. With the weighting matrices well tuned,

the LQ controller outperformed the baseline decoupled PID controller. The improvement

in both steady-state and transient operation of the eBoost assist has been validated with

engine tests.

7

1.3 Dissertation contributions

The major contribution of this dissertation can be summarized as follows:

1. A reaction-based modeling methodology has been formulated and implemented in diesel

combustion model. The proposed model successfully predicts the in-cylinder pressure

with acceptable error. The sensitivity study shows that only two calibration parame-

ters are required to accurately calibrate the model. A calibration structure has been

developed so that the number of required lookup tables is reduced significantly. The

finalized combustion model can be a potential candidate to replace the existing Wiebe

function.

2. A three-zone modeling approach has been proposed specifically for diesel combustion.

The developed model improves the prediction accuracy and eliminates the lookup ta-

bles, which are the main drawbacks of the single-zone model, especially with multiple

injections. The three-zone reaction-based model has only a slight increase in com-

putational time and can still be implemented for model-based control and real-time

simulation. The calibration parameters are fixed over the entire engine operational

range, which eliminates the need for lookup tables. It is a promising model for future

combustion control.

3. A physics-based engine air path model with eBoost has been developed. The proposed

model has been validated with steady-state engine test data and standard cycle data.

The system behavior has been studied through 1-D simulations.

It is found that

eBoost improves steady-state and transient performance. Both an error-based and a

model-based controller has been developed to verify the capability of eBoost. It turned

out that the model-based controller, with well-tuned gain, has a better performance

than the error based controller. Experiments have been performed for validating the

simulation results.

8

1.4 Dissertation outline

The content of the dissertation is organized as follows. In Chapter 2, a comprehensive

review of the development and applications of engine combustion models is presented. The

mathematical formulation of the reaction-based model for engine combustion has been de-

rived. The construction of calibration of reaction-based diesel combustion model makes it

possible for the model to be feasible for diesel engines. The model and calibration approach

is validated with experimental data. In Chapter 3, a multi-zone approach is introduced to

account for inhomogeneities in the engine combustion chamber, which eliminates the mod-

eling error compared to the single-zone model.

It turned out that the three-zone model

significantly reduces the prediction error over a wider range of operating conditions and also

eliminates calibration parameter sensitivity, leading to fixed calibrations over the entire en-

gine operating range. In Chapter 4, modeling and control of an electrically assisted boosting

system will be presented. The eBoost system improves engine steady-state and transient

performance, which is validated both numerically and experimentally. Chapter 5 concludes

the dissertation and suggests some future work.

9

CHAPTER 2

REACTION-BASED MODELING OF COMBUSTION DYNAMICS

2.1

Introduction

Modern internal combustion engines are equipped with sophisticated systems to mon-

itor and control various aspects of engine performance during ongoing operations to meet

operator demands for performance (including torque and fuel economy) and to satisfy gov-

ernment regulations related to emissions, safety, and fuel economy. To enable model-based

engine control, physics-based control-oriented engine models were developed to simulate the

engine behavior in real-time.

In order to accurately predict the engine output torque, a

control-oriented in-cylinder pressure model is needed. Various combustion models have been

developed with different levels of accuracy and computational efficiency. Wiebe function was

widely used in real-time engine simulations for pressure modeling due to its simplicity. It

also has major limitations. More complicated combustion models are accurate but require

too much computational resource. In this section, a review of different combustion models is

presented. The reason why the reaction-based model is suitable for control is also addressed.

2.1.1 Engine combustion models

Engine combustion models are used for simulating in-cylinder dynamics of fuel-air reaction.

In addition to the variation of species concentrations, the combustion process is always asso-

ciated with temperature and pressure change. From a specific point of view, the combustion

model only deals with how the chemical energy is released and it is often a simple curve of

mass fraction burned (MFB). However, studying such type model alone is difficult because

the combustion process is the result of interaction between the reacting substances and the

environment. Therefore, a general point of view, where the combustion model consists of

chemical heat release, mass and energy conservation, heat transfer and even fluid mechanics,

10

is needed. Under this architecture, the number of dimension for a combustion model could

be 0, 1, 2 or 3. According to the published research on engine combustion models, the most

popular models that have been developed to date may be grouped into four categories, as

shown in Figure 2.1:

Figure 2.1: Category of engine combustion models

In the above classification, as the dimension of a model increases, both prediction accu-

racy and computational effort increase, leading to a trade-off between accuracy and com-

puting efficiency. Different application situation will result in different type of model. For

example, for accurate simulation of spatial flame characteristics, a 3-D computational fluid

dynamics (CFD) model is needed. If the model is used for control design where accuracy is

not strictly required, Wiebe function will work properly because it is easy to implement and

runs fast.

Zero-dimensional (0-D) models are the simplest and most suitable to observe the effects of

empirical variations in the engine operating parameters on overall heat release rates/cylinder

11

PredictivenessComputational effortWiebeNon-predictiveQuasi-D1-D FlameOperational range depends on model selectionPredictive within limited range3-D CFDToo much computationpressure schedules. These models are zero dimension in the sense that they do not involve

any consideration of the flow field dimensions. Thus, for the purpose of real-time simulation,

zero-dimensional models are most feasible.

Zero-dimensional models are further sub-divided into single zone models, two zone mod-

els, and multi-zone models. In single zone models, the working fluid in the engine is assumed

to be a thermodynamic system, which undergoes energy and/or mass exchange with the

surroundings and the energy released during the combustion process is obtained by applying

the first law of thermodynamics to the system.

In two-zone models, the working fluid is

imaginarily divided into two zones, unburned and burned zones. These zones are actually

two distinct thermodynamic systems with energy and mass interactions between themselves

and their common surroundings, the cylinder walls. The mass-burning rate (or the cylin-

der pressure), as a function of crank angle, is then numerically computed by solving the

simplified equations resulting from applying the first law to the two zones.

Most control-oriented models to date are implemented with so-called Wiebe function for

the calculation of heat release rate due to combustion. The Wiebe function generally has

(cid:34)

(cid:19)m+1(cid:35)

(cid:18) θ − θs

∆θb

the following format:

xb = 1 − exp

−a

(2.1)

where xb is the mass-fraction-burned of fuel; a and m are experimentally calibrated coeffi-
cients; θs is the start of combustion (SOC), ∆θb is the burning duration (BD), only these
two parameters could affect the combustion process during the simulation.

While the function itself is simple and easy to use, it can only be affected by specified

parameters during the combustion process, such as SOC, BD, etc., and experiment based

fitting coefficients, because of its empirical feature.

2.1.2 Wiebe function

Since Wiebe function is well-known, investigating its origins can be an interesting act, which

could provide insights in developing reaction-based combustion models.

12

In the mid-1950s, with Nikolay Semenov’s work in the area of chemical kinetics and chain

chemical reactions, engine researchers believed that a better model for internal combustion

engine combustion could be constructed based on the theory of radical chain reactions. Wiebe

linked chain chemical reactions with the fuel reaction rate in internal combustion engines

and his approach was based on the assumption that a single-step rate equation will not be

adequate to describe complex reacting systems such as those occurring in an internal com-

bustion engine. On the other hand, developing and solving rate equations which account for

the simultaneous and sequential interdependent chain and chain branching reactions would

be prohibitive. He reasoned that, for engineering purposes, the details of chemical kinetics of

all the reactions could be bypassed and a general macroscopic reaction rate expression could

be developed based on the concept of chain reactions. The details of his modeling approach

are described below [7].

In actual combustion systems such as in an internal combustion engine, chain reactions

may proceed sequentially and in parallel with the formation of intermediate species compris-

ing free atoms and radicals. Wiebe called these intermediate species active centers. Being

highly reactive, active centers play a pivotal role in chemical kinetics reactions and are cru-

cial to the reaction path. For the initiation of the reaction, a certain concentration of active

centers (initial centers) is required and these centers can be generated by heating the air-

fuel mixture or providing an electrical charge. During the combustion process, a very large

number of active centers will exist in close proximity to the molecules of the main reacting

substances. Combustion produces molecules of final products and more active centers that

are capable of starting new reaction cycles. Excluded from this scheme are chain inhibiting

centers resulting from radicals or free atoms colliding with a third body (any other radical,

atom, or molecule in the system or the walls). As combustion progresses, the concentration

of reactants decreases progressively, causing a corresponding decrease in the reaction rate.

In the oxidation of carbon monoxide, the global reaction is represented as

2 CO + O2 −−→ 2 CO2

(2.2)

13

A leading role is played by the elementary process

OH + CO

k1−−→ CO2 + H

(Reaction I)

The most probable reaction of atomic hydrogen is

H + O2

k2−−→ OH + O

(Reaction II)

which leads to the next reaction

O + CO

k3−−→ CO2

(Reaction III)

The three elementary processes (I, II, and III) make up an elementary reaction cycle which

is continuously repeated as the chain reactions propagate. The highly reactive radicals OH

produced by process (II) are the active centers.

Figure 2.2: Schematic diagram of Wiebe’s approach

These and other reactions may proceed in parallel or sequentially as shown schematically

in Figure 2.2. The reactions within the dashed-line boxes are the elementary reaction cycles,

whereas the reactions within the solid-line boxes are the effective reaction events. The latter

represent ensembles of simultaneously occurring elementary reactions at time t resulting in

14

CO2IIIIIIIIIIIIIIIdttTime, tthe formation of products of complete combustion (CO2) within a very short time interval
dt, and active centers (OH) capable of initiating subsequent effective reaction events unless

they are destroyed upon collision with the walls of the reaction vessel. The active centers

initiating the effective reaction events were referred by Wiebe as effective centers.

On the basis of this concept, Wiebe postulated that the incremental change in the number

of molecules of the main reactants dN participating in the effective reaction events in the

time interval t to t + dt is directly proportional to the change in the number of effective
centers dNe (i.e. −dN = ndNe), where n is the constant of proportionality. In differential
form

The relative density of the effective centers is defined as

−

(cid:19)

= n

(cid:19)
(cid:18) dN
(cid:18)dNe

dt

ρ =

dt

(cid:18)dNe
(cid:19)(cid:30)

dt

N

(2.3)

(2.4)

where N is the instantaneous number of molecules of the initial reactants. Equation (2.3)

can now be written as

from which

= nρdt

−dN
N

(cid:90) t
N = N0e−(cid:82) t

= −

N
N0

0

ln

nρdt

0 nρdt

(2.5)

(2.6)

where N0 is the number of moles of the main reactant in the combustion system at the start
of reactions.

If the burned fraction of the initial reactant at any moment in time t is defined as

then

x =

N0 − N

N0

x = 1 − e−(cid:82) t

0 nρdt

15

(2.7)

(2.8)

Wiebe assumed that the relative density of the effective centers can be expressed as ρ = ktm,

where k and m are constants, and if nk = K, equation (2.8) can be transformed into

x = 1 − e[K/(m+1)]tm+1

(2.9)

Wiebe named the parameter m “combustion characteristic exponent”.

From equation (2.9) it is apparent that the chemical reactions cease when the burned

fraction x tends to unity as time tends to infinity. However, in reality the combustion process
in an internal combustion engine is finite and if the combustion duration is denoted by td,
the burn fraction becomes

from which

Similarly at any time t

xd = 1 − e[K/(m+1)]tm+1

d

e[K/(m+1)]tm+1

d

= 1 − xd

e[K/(m+1)]tm+1

= 1 − x

(2.10)

(2.11)

(2.12)

Taking the logarithm of equations (2.11) and (2.12) and dividing one by the other yields

x = 1 − eC(t/td)m+1

(2.13)

where C = ln(1 − xd). Wiebe assumed that xd = 0.999 and rounded off the corresponding
value of C to 6.908.

The Wiebe function for the non-dimensional burned fraction x as a function of crank

(cid:19)m+1(cid:35)

(cid:34)

(cid:18) θ

θd

−6.908

angle degrees can be written as

x = 1 − exp

(2.14)

In deriving the burned fraction function, Wiebe made several assumptions that may not be

true in reality. For example, for reactions I, II, and III, at any instant of time, the ensemble

reaction is expressed as

(k1 + k3) CO + k2 O2 −−→ (k1 + k3) CO2 + (k1 − k2) H + (k2 − k3) O + (k2 − k1) OH

16

where dN = −(k1 + k2 + k3), dNe = k2 − k1. Wiebe assumed −dN = ndNe, which means

k1 + k2 + k3 = n(k2 − k1)

Note that this is not necessarily true.

In summary, Wiebe function is a good attempt to replace single-step global reaction

with ideal chemical kinetics. However, it is over-simplified such that it loses the physical

foundation behind the model.

2.1.3 Reaction-based model

Reaction-based combustion modeling technique has been used for off-line simulations in the

past. Autoignition behavior with different diesel blends was model in references [8] and

[9], where a reaction-based combustion model was used for predicting the autoignition. A

reduced chemical kinetic model was developed in [10] to simulate the IC (internal combustion)

engine combustion process with primary reference fuels and the model was fairly complicated

and cannot be used for real-time simulations. A multistage combustion model for diesel

engines is presented in [11], where three combustion stages, autoignition, premixed and

diffusion combustion are considered in the combustion process for a typical medium speed

diesel engine. Significant improvement in cylinder pressure and temperature prediction is

achieved. A control-oriented two-zone thermal kinetic model for a single cylinder HCCI

engine is presented in [12], where the combustion process was modeled using the first law of

thermodynamics and mixture concentration inhomogeneity.

As a summary, chemical kinetic mechanisms and thermal kinetic combustion models have

been developed in the past. However, the chemical kinetic mechanism is too complex to be

used for real-time simulations; and the simple thermal kinetic model may not provide the

accuracy needed for model-based control. For the proposed research, the chemical kinetic

mechanism will be simplified and combined with the thermal kinetic model to achieve real-

time simulations with desired modeling accuracy required for model-based control.

17

2.2 Chemical kinetics

In order to enable reaction-based models, a solid background in combustion chemistry

and chemical kinetics is necessary. Thermochemistry deals with stoichiometry for chemical

reactions and thus, information of reactants and products at the beginning and the end of

combustion process can be obtained, while chemical kinetics explains the rates of reactions,

which solves for the instantaneous concentration of each species. With such knowledge, one

can calculate the concentration of any one of the species involved in the combustion at any

instant of time. The detailed theory of combustion can be found in [13].

Chemical kinetics is a powerful tool to understand combustion. In many engine combus-

tion processes, chemical reaction rates control the overall rate of combustion. Also, ignition

and flame extinction are intimately related to chemical processes. Much progress has been

made to date since chemists have been able to define the detailed chemical pathways leading

from reactants to products and to measure or calculate their associated rates. It is hoped

that we could apply the basic chemical kinetics concepts to engine combustion models to

achieve reasonable precision but low computational complexity.

2.3 Reaction-based modeling approach

With all the background introduced in the previous section, the reaction-based model-

ing methodology can now be formulated. The developed model has been implemented for

continuous-time simulations.

2.3.1 Overview of the modeled physics

There are two cycle types for the engine combustion model: closed cycle and full cycle.

Closed cycle refers to the crank angle from intake valve closing (IVC) to exhaust valve

opening (EVO). In the closed cycle model, there is no flow model. The conditions at IVC

are the input to the model and can be estimated from experimental data. A full cycle model

is the closed cycle model combined with the flow model, extending the crank angle range to

18

0-720 CAD. Figure 2.3 shows the architecture of the full-cycle model. To enable the closed

cycle model we only need to turn off the flow feature in the full cycle model. The structure

of the closed cycle model is shown in Figure 2.4.

Figure 2.3: Full-cycle reaction-based modeling architecture

2.3.2 Molar concentration rate of species

The rate of change of concentration for species i,
i in the cylinder, Ni, by:

(cid:18) Ni

(cid:19)

˙[Xi], is related to number of moles of species

˙[Xi] =

d
dt

where

V

=

˙Ni
V

− ˙V Ni
V 2

= wi − ˙V

V

[Xi]

wi ≡ ˙Ni

V

The concentration production term wi can be further divided into two parts:

wi = wrxn,i + wf low,i

19

(2.15)

(2.16)

(2.17)

Temperature Model Concentration Model Heat Loss Model Flow Model QT, PMFR, hT, PMFRMWmix hmix[Xi], hi, cp,i, MWiTPmot, Tmot, VIVCvalve lift profileChemical ReactionsFigure 2.4: Closed-cycle reaction-based modeling architecture

where wrxn,i is the concentration production due to chemical reactions, which is determined
through the use of a combustion chemistry mechanism (Section 2.3.5); wf low,i is the con-
centration change due to mass flow into and out of the control volume (Section 2.3.6).

2.3.3

Instant cylinder volume and volume rate

The instant volume V is dependent on the current crank angle and geometry of the cylinder.

It is given by

V (t) = Vc +

πB2

4

(cid:20)

l + a − a cos

(cid:16) π

30

(cid:17) −

Ne · t

(cid:114)
l2 − a2 sin2(cid:16) π

30

(cid:17)(cid:21)

Ne · t

(2.18)

where Vc is the clearance volume; B is bore; l is connecting rod length; a is crank radius
(half stroke); Ne is engine speed in r/min; t is time.

The volume rate ˙V is given by

˙V =

aπ2B2

120

Ne · sin

Ne · t

(cid:16) π

30

30Ne · t(cid:1)
cos(cid:0) π
(cid:113)
l2 − a2 sin2(cid:0) π
30Ne · t(cid:1)



(cid:17)1 + a

20

(2.19)

Fuel InjectionChemical ReactionsHeat LossVolumeTemperatureConcentrationV,˙VInternal DynamicsExternal Input˙QT[Xi]T[Xi]wrxn,i˙minj2.3.4 Temperature rate

There are two different methods developed for calculation of in-cylinder temperature and

pressure. The first method, called heat release rate method (see Figure 2.5a), is similar to

that of Wiebe-based models.

In general, this method firstly calculates the mass fraction

burned (MFB) of fuel from either Wiebe function or chemical reactions. Noting that for

Wiebe function, the MFB is directly calculated. But for reaction-based models, we must

first get the concentration of fuel by solving the associated differential equation. Then we

will be able to calculate the MFB of the fuel. Next, the heat release rate is calculated

from the derivative of MFB. By the first law of thermodynamics, it is straightforward to get

the temperature of the in-cylinder mixture. The in-cylinder pressure is calculated by the

equation of state.

(a) Heat release rate method

(b) Temperature rate method

Figure 2.5: Methods for in-cylinder temperature and pressure calculation

The second method, called temperature rate method (see in Figure 2.5b), follows a slightly

different path, and note that is this method is not applicable for Wiebe function. Firstly, the

concentration of each species participating in the chemical reactions is solved. Secondly, it is

shown later that the temperature rate is a function of the concentration and concentration

rate of all the species as well as current temperature and pressure. At last, the temperature

for next time step is easily calculated numerically. The calculation of in-cylinder pressure is

21

(cid:88)

the same as before. To be more specific, the mathematical derivation is given as follows [14]:

The first law of thermodynamics for a closed system:

= ˙Q − ˙W +

dU
dt

˙mjhj

(2.20)

where U is the internal energy of the system;

˙W is the net rate of work done by the system; and(cid:80) ˙mjhj is the energy change due to mass

˙Q is the net heat transfer rate into the system;

flow.

For the case of the piston cylinder, the work output rate is:

˙W = P ˙V

where P is the pressure.

Now, given that the enthalpy is related to the internal energy as:

H = U + P V

Then the left hand side (LHS) of Equation (2.20) becomes

dU
dt

=

d(H − P V )

dt

=

dH
dt

− d(P V )

dt

=

dH
dt

− ˙P V − P ˙V

Equation (2.20) can be re-arranged as

dH
dt

= ˙Q + ˙P V +

(cid:88)

˙mjhj

(2.21)

(2.22)

(2.23)

(2.24)

The extensive property H can be expressed as a sum of weighted molar enthalpies of all

(cid:88)

species

H =

where ¯hi is the molar enthalpy of species i.
Thus LHS of Equation (2.24) becomes

d((cid:80) Ni

dt

¯hi)

=

dH
dt

=

d(V (cid:80)[Xi]¯hi)

dt

= ˙V

Ni

¯hi

(2.25)

(cid:88) ˙[Xi]¯hi + V

(cid:88)

[Xi] ˙¯hi

(2.26)

[Xi]¯hi + V

(cid:88)

22

where

˙¯hi = ¯cp,i

˙T

Note that ¯cp,i is the contant-pressure specific heat; T is the temperature;
rate. Thus,

˙T is the temperature

(cid:88)

(cid:88) ˙[Xi]¯hi + V ˙T

(cid:88)

LHS =

dH
dt

= ˙V

[Xi]¯hi + V

From the state equation of ideal gas, we have

[Xi]¯cp,i.

(2.27)

(2.28)

(2.29)

P =

[Xi]RuT

(cid:88)
(cid:88) ˙[Xi] + Ru

˙T V

(cid:88) ˙[Xi] + Ru
V (cid:80) [Xi](cid:0)¯cp,i − Ru

(cid:1)

and

(cid:88)
where Ru = 8314 (J/kmol · K) is the universal gas constant.
(cid:88)
The right hand side (RHS) of Equation (2.24) becomes

˙P = RuT

˙T

RHS = ˙Q + RuT V

[Xi],

(cid:88)

˙mjhj

(2.30)

[Xi] +

Re-arranging the equation, we have the expression to calculate temperature rate

˙Q + RuT V (cid:80) ˙[Xi] − V (cid:80)[ ˙Xi]¯hi − ˙V (cid:80)[Xi]¯hi +(cid:80) ˙mjhj

˙T =

.

(2.31)

Equations (2.15), (2.19) and (2.31) represent the set of nonlinear differential equations for

each of the states used in the model.

2.3.5 Rates of reactions

Three different modeling paths are studied: single-step reaction model [13], two-step reaction

model [15, 16] and four-step reaction model [17]. The single-step reaction is simple thus we

will start with this model to demonstrate our reaction-based modeling approach. Our final

objective is to develop a reaction model with reasonable accuracy and simplicity. Up to

this point, we attempted the two-step model with an additional reaction for CO oxidation,

and formulated a four-step model by further including two additional reactions. For each

23

model, the stoichiometric reaction of diesel fuel (with pseudo formula C10.8H18.7) and air is
assumed. The major products assumption is also made, such that the global reaction for

combustion can be written as:

C10.8H18.7 + 15.48 O2 + 58.19 N2 −−→ 10.8 CO2 + 9.35 H2O + 58.19 N2

(2.32)

The reaction rate for C10.8H18.7 oxidation in single step is given in the Arrhenius form

as:

wC10.8H18.7 = A exp

(cid:19)

(cid:18)

− EA
RuT

[C10.8H18.7]m[O2]n

(2.33)

where A, EA, m and n are the coefficients to be calibrated. There are also references for
these coefficients in [13]. By inspection of Equation (2.32) the rates of reactions of other
species can be calculated in terms of wC10.8H18.7 directly:

wO2 = 15.48wC10.8H18.7

wN2 = 0
wCO2 = −10.8wC10.8H18.7
wH2O = −9.35wC10.8H18.7

(2.34a)

(2.34b)

(2.34c)

(2.34d)

where the minus sign indicated that while C10.8H18.7 and O2 are being consumed, CO2 and
H2O are being created.

This single-step reaction rate model utilizes the idea of chemical reaction and the asso-

ciated rates. The advantages of this approach are obvious because only 4 are involved in

the formulation. Since it is a linear function of the amount of fuel reacted, the heat release

calculation is also quite simple. However, the time delay during the early stage caused by

the formation of intermediate hydrocarbons and CO is not described by the formulation,

which could not provide accurate information of hydrocarbon oxidation. In addition, the

in-cylinder mixture is assumed to be perfectly mixed before the start of combustion, which

is not the case for diesel engines. The rate of oxidation to CO2 is expected to proceed very
fast. One way to slow down the combustion is to add more reactions (steps) into the system,

24

such as breakdown of the fuel to the intermediate hydrocarbons, the oxidation of the inter-

mediate hydrocarbons to CO, and the oxidation of CO to CO2, so that the energy release is
distributed in each step.

Consider the two-step chemical kinetic mechanism:

C10.8H18.7 + 10.08 O2 + 58.19 N2 −−→ 10.8 CO + 9.35 H2O + 58.19 N2

CO + 0.5 O2 −−(cid:42)(cid:41)−− CO2

(2.35a)

(2.35b)

The reaction rates for C10.8H18.7 and CO oxidation are given as:

(cid:19)
(cid:19)

(cid:18)
(cid:18)

−EA,1
RuT
−EA,2
RuT

wC10.8H18.7 = A1 exp

wCOox = A2 exp

[C10.8H18.7]m1[O2]n1

[CO]m2[H2O]k1[O2]n2 − A3 exp

(cid:19)

(cid:18)

−EA,2
RuT

(2.36a)

[CO2]k2

(2.36b)

where A1, A2, A3, EA,1, EA,2, EA,3, m1, m2, n1, n2, k1 and k2 are the coefficients to be
calibrated (for reference, see [13]). By inspection of equations (2.35a) and (2.35b), the other

reaction rates follows as:

wO2 = 10.08wC10.8H18.7 + 0.5wCOox

wN2 = 0
wCO2 = −wCOox
wH2O = −9.35wC10.8H18.7
wCO = −10.8wC10.8H18.7 + wCOox

(2.37a)

(2.37b)

(2.37c)

(2.37d)

(2.37e)

The two-step model basically separates the highly exothermic oxidation of CO to CO2 from
the less exothermic oxidation of the fuel to CO:

1) C10.8H18.7

˙Q1−−→ CO

2) CO

˙Q2−−→ CO2

25

Since no prediction is made for the formation of intermediate hydrocarbons, this approach

does not account for the time delay in the initial release of a significant amount energy.

However, the two-step model is simple for implementation, thus the majority of the study

has been done using the two-step model.

Consider the four-step chemical kinetic mechanism for hydrocarbon oxidation [18]:

CnH2n+2 −−→ n
C2H4 + H2
2
C2H4 + O2 −−→ 2 CO + 2 H2

O2 −−→ CO2
O2 −−→ H2O
(cid:19)
(cid:19)
(cid:19)
(cid:19)

CO +

H2 +

1
2
1
2

(cid:18)
(cid:18)
(cid:18)
(cid:18)

− EA
RuT
− EA
RuT
− EA
RuT
− EA
RuT

(2.38a)

(2.38b)

(2.38c)

(2.38d)

(2.39a)

(2.39b)

(2.39c)

(2.39d)

where the reaction rates are expressed as

wCnH2n+2 = −10x exp

wC2H4 = −10x exp

wCO = −10x exp

wH2 = −10x exp

[CnH2n+2]a[O2]b[C2H4]c

[C2H4]a[O2]b[CnH2n+2]c

[CO]a[O2]b[H2O]c7.93 exp(−2.48φ)

[H2]a[O2]b[C2H4]c

where φ is the equivalence ratio. The exponents x, a, b and c are different for each reaction.

The reference value for these coefficients are available for propane (C3H8) in [13].

Note that by assigning negative values to CnH2n+2 and C2H4 exponents, the oxidation
of C2H4 and H2 could be inhibited. This indicates the potential of using the four-step model
to reduce the overall burn rate.

2.3.6 Flow rate

The term “flow rate” in this section is a generalized concept, which includes both gas flow rate

by valves and fuel injection rate. We will focus on development of the gas flow rate model

26

for the four cases during gas exchange. The fuel injection rate can be simply implemented

if the fuel injection profile is known.

For unchoked flow, meaning

we have

pT
p0

(cid:18) pT

p0

(cid:113) Ru

CDARp0
M W T0

˙m =

γ + 1

>

(cid:18) 2
 2γ
(cid:19) 1

γ

,

γ−1

(cid:19) γ
1 −

γ − 1

(cid:19) γ−1

γ

 1

2

,

(cid:18)pT

p0

(2.40)

where pT is the downstream pressure; p0 and T0 are the upstream stagnation pressure and
temperature, respectively; γ is the specific heat ratio; CD is the discharge coefficient; AR is
the reference open area for the valve.

(cid:18) 2

γ + 1

γ−1

,

(cid:19) γ
(cid:20) 2

γ + 1

(cid:21) γ+1

2(γ−1)

For choked flow, meaning

≤

pT
p0

we have

(cid:113) Ru

CDARp0
M W T0

√
γ

˙m =

where γ, CD and AR to be determined.

2.3.7 Heat loss rate

The heat transfer rate ˙Q can be expressed as

.

(2.41)

˙Q =

−Achc(T − Tw)

Ne

,

(2.42)

where Ac is the contact area between gas and cylinder wall; hc is the heat transfer coefficient;
T is the cylinder temperature; Tw is the cylinder wall temperature.

We can calculate the contact area by engine geometry and piston motion

Ac = Ach + Ap + πB(l + a − s),

(2.43)

27

where Ach is the cylinder head surface area; Ap is the piston crown surface area (Ap = πB2
for flat-topped pistons); s is the distance between crank axis and the piston pin axis and is

4

given as

s = a cos

(cid:16) π

30

+

(cid:17)
Ne · t
(cid:16) π

(cid:114)
l2 − a2 sin2(cid:16) π
(cid:17)
Ne · t
(cid:114)
(cid:17)
l2 − a2 sin2(cid:16) π
Ne · t

30

+

30

(cid:18)

Thus, the contact area can be written as

Ac = Ach +

πB2

4

+ πB

l + a − a cos

(cid:17)(cid:19)

Ne · t

,

(2.44)

30

(cid:21)0.8

,

(2.45)

where R = l

a is the ratio of connecting rod length to crank radius.

The heat transfer coefficient can be correlated as

(cid:20)

hc = αB−0.2P 0.8T−0.55

C1

¯Sp + C2

VdTr
PrVr

(P − Pmot)

where ¯Sp is the mean piston speed (m/s); Vd is the displaced volume; Tr, Pr and Vr are the
state properties at a reference point (e.g. IVC); Pmot is the motored in-cylinder pressure.

The mean piston speed is calculated as

¯Sp = 2LN,

where N is the rotational speed of crankshaft (rad/s); α, C1 and C2 are calibration param-
eters.

2.4 Reaction-Based model validation

A single-step and two-step models are developed in Simulink based on the reaction-

based modeling approach described in Section 2.3. To validate the modeling method, the

developed models are first compared to a simple GT-POWER model. The models are first

calibrated in an open-loop manner, which doesn’t account for temperature feedback. After

a set of reasonable parameters are obtained, the effect of temperature is considered. The

preliminary calibration and validation process has shown that the two-step model is capable

of accurately estimating combustion metrics under various engine operating conditions.

28

2.4.1 Continuous-time model

In the continuous-time simulation, it is convenient to run the simulation from IVC to EVO,

where a closed thermodynamic model can be formulated. For the specific engine that has

been simulated, the simulation duration is from 132CA BTDC to 132CA ATDC. The initial

conditions such as initial temperature, initial pressure, initial gas mixture and its properties

are coordinated with the data generated by the GT-POWER model. Instant volume and

its derivative are given as input signals derived from Sine functions, and also depend on the

engine geometry and engine speed. The fuel injection profile is given by the GT-POWER

model, which is determined in terms of total mass of fuel injected, mass flow rate, and pulse

width for each injection. This will ensure that the injection profiles for both reaction-based

model and GT-POWER model are identical.

The calibration approach is illustrated in Figure 2.6. The reaction-based model is a highly

coupled dynamic system. So the basic idea here is to decouple the whole system before we

actually calibrate it. To be more specific, we divide the closed-loop system into two parts:

1) the open-loop reaction rate calculation and 2) the open-loop temperature calculation.

Figure 2.6: Model calibration approach

For the first part, we use the temperature data from the GT-POWER model as the

29

Texpwi[Xi]HRRHRRexp[Xi]TOpen-loop reaction rate calculationOpen-loop temperature calculationinput signal and calculate the reaction rates. Then the heat release rate, which is a function

of the reaction rates, will be compared to the “ideal” heat release rate, which is also from

the GT-POWER model. In this way the coefficients in the reaction rate equations can be

calibrated. This part will be illustrated in detail in the following sections. For the latter part,

we can always perform the similar but reverse process to calibrate the temperature model.

However, a more convenient way is to compare the temperature under motoring condition,

so that the reaction rate won’t affect the temperature calculation. Once the temperature

model is calibrated for the motoring condition, no further calibration is necessary for models

with different reaction steps. However, the model might need to be re-calibrated if a different

engine is applied.

The single-step model has six states: the temperature, T , the concentrations of diesel

fuel, [C10.8H18.7], oxygen, [O2], nitrogen, [N2], carbon dioxide, [CO2], and water, [H2O].
The general rate equations are given in Section 2.3. The first step is to apply the parameters
from the references [13] to see if that works, and then to tune EA/Ru so that the start
of combustion coordinates with GT-POWER model. Finally A is tuned to maintain the

magnitude of the rate to be within a reasonable range. m and n are essentially fixed. The

calibrated coefficients in equation (2.33) are given in Table 2.1.

Table 2.1: Arrhenius rate parameters for single-step model

Parameters Values

A
EA/Ru
m
n

8000
17098
0.1
0.25

The single-step model verified that the reaction-based model is capable of estimating the

combustion metrics over a certain range. However, the single-step model is too simple and

doesn’t provide acceptable predictions even for individual case. The peak heat release rate

is always over-predicted if the combustion phasing is matched. Thus, our focus will be on

the two-step model.

30

The two-step model includes seven states: the temperature, T , the concentrations of

diesel fuel, [C10.8H18.7], oxygen, [O2], nitrogen, [N2], carbon dioxide, [CO2], water, [H2O],
and carbon monoxide, [CO]. The general differential equations are given in Section 2.3. The

calibration process is almost the same for the two-step model although there are two rate

equations and more coefficients to consider. Note that A1 and A2 are chosen to vary for
different engine operating conditions, such as engine speed, engine load and injection profile.

The calibrated coefficients in equation (2.36) are given in Table 2.2.

Table 2.2: Arrhenius rate parameters for two-step model

Parameters Values
varying
varying
5 × 108
15098
20130
0.1
1
1.65
0.25
0.5
1

A1
A2
A3
EA,1/Ru
EA,2/Ru
m1
m2
n1
n2
k1
k2

The four-step model includes eight states: the temperature, T , the concentrations of

diesel fuel, [CnH2n+2], oxygen, [O2], nitrogen, [N2], carbon dioxide, [CO2], water, [H2O],
carbon monoxide, [CO], and hydrogen, [H2]. The general differential equations are given in
Section 2.3. The calibrated coefficients in equation (2.39) are given in Table 2.3 [13].

Table 2.3: Arrhenius rate parameters for four-step model (propane)

Rate equations

2.39a

2.39b

2.39c

2.39d

x
EA/Ru
a
b
c

17.32
24962
0.50
1.07
0.40

14.7
25164
0.90
1.18
−0.37

14.6
20131
1.0
0.25
0.50

13.52
20634
0.85
1.42
−0.56

31

2.4.2 GT-POWER DIPulse model

A simple GT-POWER predictive diesel combustion model is developed and used for gen-

erating baseline simulation data for calibrating the developed model. The GT-POWER

engine model describes a single cylinder direct injection diesel engine with a reaction-based

combustion model (see Figure 2.7). The parameters are mostly set as default values.

Figure 2.7: GT-POWER single-cylinder engine model with predictive combustion

The GT-POWER model is used to generate the engine combustion data over the entire

engine operational map with different fuel injection properties, including injection timings

and quantities of pre-injection, main injection, and multiple after injections. There are 4

calibration parameters in GT-POWER DIPulse predictive combustion model:

1) Entrainment Rate Multiplier

2) Ignition Delay Multiplier

3) Premixed Combustion Rate Multiplier

4) Diffusion Combustion Rate Multiplier

32

The combustion rate is calculated in a similar way as the Arrhenius function-based model:

dmk
dt

= CM BM U LT ∗ φ ∗ (3 − φ)2 ∗ p2.5 ∗ exp(−4000
T

)

(2.46)

where mk is the mass of fuel in the mixed zone, CM BM U LT is the combustion rate multi-
plier, φ is the equivalence ratio, p is the pressure and T is the temperature.

Table 2.4 shows the engine geometry and parameters used in GT-POWER model, which

is coordinated with the experimental setup.

Table 2.4: GT-POWER engine geometry and model parameters

Parameters
Bore (mm)
Stroke (mm)
Connecting Rod Length (mm)
Compression Ratio
TDC Clearance Height (mm)
CA at IVC
Heat Loss Model
Combustion Model

Values
100
100
180
18
0.5
-132
WoschniGT
EngCylcombDIPulse

2.4.3 Preliminary calibration results

The reaction-based combustion model was validated in several steps. Firstly, we run simu-
lations under different engine speeds and loads following a 5×5 engine calibration matrix.
All the other control variables were fixed. Secondly, we studied the behavior of the model

under different injection timing, for both main injection and the late-injection, for fixed en-

gine speed and load. Thirdly, additional model validation were completed, including EGR

sweep and air-fuel ratio sweep.

In addition, the model was validated with experimental

data, although only for 3 engine operating conditions. The results showed that A1 and A2
are closely related to these engine operating conditions, with smooth variations. Thus, it is

possible to model A1 and A2 as functions of engine speed, engine load and injection timing.

33

2.4.4 Variable engine speed and load, fixed injection timing

This subsection studies the reaction-based model calibration over a given engine operational

map. The main purpose is to find out what is the key calibration parameters required for

calibrating the reaction-based model working over the engine map.

Figure 2.8 shows the calibration results for the 5×5 engine speed and engine load matrix.
Table 2.5 shows the IMEP error for each operating condition. Table 2.6 shows the output

torque error for each operating condition. All the errors are calibrated within 3%. Figure 2.9

shows the calibration coefficients to achieve this match.

Table 2.5: Relative error for IMEP from -132CA to 132CA (%)

50 mg

1000 r/min 2.75
1500 r/min 2.50
2000 r/min 1.11
2500 r/min 1.46
3000 r/min 0.49

60 mg
1.87
0.31
0.50
2.48
2.74

70 mg
1.85
2.70
2.06
1.46
2.93

80 mg
0.60
1.51
1.11
2.68
2.84

90 mg
0.75
2.50
2.42
2.37
2.50

Table 2.6: Relative error for output torque (%)

50 mg

1000 r/min 16.5
1500 r/min 15.5
2000 r/min 3.75
2500 r/min 3.12
3000 r/min 2.87

60 mg
9.67
6.39
1.22
1.83
2.52

70 mg
6.20
2.21
2.63
3.10
1.54

80 mg
7.55
5.22
1.87
2.86
1.69

90 mg
11.0
1.04
2.64
3.68
2.39

34

Figure 2.8: In-cylinder pressure for the two-step and GT-POWER models under 5×5 engine operation matrix

35

r/minr/minr/minr/minr/minFigure 2.9: Calibration coefficients for the two-step model

From this preliminary study, it is concluded that model parameters A1 (2.36a) and A2

(2.36b) need to be calibrated as the functions of engine speed and load.

2.4.5 Variable injection timing, fixed engine speed and load

Figure 2.10 shows the in-cylinder pressure curves from the reaction-based model and GT-

POWER model for main injection at 10 CAD BTDC, TDC and 5 CAD ATDC, respectively.

The late-injection timing was set to 25 CAD after main injection. The engine was running

at 1500 r/min with 50 mg of total injected fuel mass. The results showed that very little

re-calibration effort was needed for a fairly good match. The calibrated parameters are A1
and/or A2.

Figure 2.10: In-cylinder temperature and pressure for the two-step and GT-POWER models
with different main injection timing

Figure 2.11, 2.12, 2.13, 2.14, 2.15 and 2.16 are the in-cylinder temperature and pressure

36

010053000A1×10480Mass of Fuel Injected (mg)10RPM200060100001001230003A280Mass of Fuel Injected (mg)4RPM52000601000010050003000Heat Loss Coefficient80Mass of Fuel Injected (mg)RPM100002000601000r/minr/minr/min-150-100-50050100150Crank Angle Degree020406080100120140160180Pressure (bar)10BTDCReaction-Based ModelGT-POWERModel-150-100-50050100150Crank Angle Degree020406080100120140Pressure (bar)TDC-150-100-50050100150Crank Angle Degree020406080100120Pressure (bar)5ATDC5 aTDCTDC10 bTDCplots from the two-step model with different injection profiles, compared with that from GT-

POWER model at engine speed of 1500 r/min. There are two injections in this combustion

event: one main injection at 355 CAD and one late injection with various timings. For each

injection, the injected mass of fuel is 40 mg/hub.

Figure 2.11: In-cylinder temperature and pressure for the two-step and GT-POWER models
with late injection at 15 CAD ATDC

Figure 2.12: In-cylinder temperature and pressure for the two-step and GT-POWER models
with late injection at 20 CAD ATDC

The overall shape of the pressure curve from the two-step model matches well with GT-

Power simulation results. The effect of late injection to in-cylinder pressure is well predicted.

However, the over-predicted peak pressure indicates that there are still corrections to be

37

Crank Angle Degree200250300350400450500Temperature (K)400600800100012001400160018002000Temperature TracesTwo-step ModelGT-POWER ModelCrank Angle Degree200250300350400450500Pressure (bar)020406080100120140Pressure TracesTwo-step ModelGT-POWER ModelInjection RateCrank Angle Degree200250300350400450500Temperature (K)400600800100012001400160018002000Temperature TracesTwo-step ModelGT-POWER ModelCrank Angle Degree200250300350400450500Pressure (bar)020406080100120140Pressure TracesTwo-step ModelGT-POWER ModelInjection RateFigure 2.13: In-cylinder temperature and pressure for the two-step and GT-POWER models
with late injection at 25 CAD ATDC

Figure 2.14: In-cylinder temperature and pressure for the two-step and GT-POWER models
with late injection at 30 CAD ATDC

made. Note that the temperature after the second injection does not match well between

the reaction-based and GT-POWER models, especially when the second injection time is

heavily retarded. This could be due to the inaccuracy of GT-POWER DIPulse model. One

observation is that the ignition delay is extremely large for the GT-POWER simulations;

see Figure 2.15. The calculated indicated mean effective pressure (IMEP) and its error are

shown in Table 2.7. Note that we only need to correlate A2 with the injection timing to get

38

Crank Angle Degree200250300350400450500Temperature (K)400600800100012001400160018002000Temperature TracesTwo-step ModelGT-POWER ModelCrank Angle Degree200250300350400450500Pressure (bar)020406080100120140Pressure TracesTwo-step ModelGT-POWER ModelInjection RateCrank Angle Degree200250300350400450500Temperature (K)400600800100012001400160018002000Temperature TracesTwo-step ModelGT-POWER ModelCrank Angle Degree200250300350400450500Pressure (bar)020406080100120140Pressure TracesTwo-step ModelGT-POWER ModelInjection RateFigure 2.15: In-cylinder temperature and pressure for the two-step and GT-POWER models
with late injection at 35 CAD ATDC

Figure 2.16: In-cylinder temperature and pressure for the two-step and GT-POWER models
with late injection at 40 CAD ATDC

a good match.

2.4.6 EGR sweep

Figure 2.17 shows the in-cylinder pressure under different EGR ratios. The selected operating

points of EGR ratio are 15%, 20%, 25% and 30%.

39

Crank Angle Degree200250300350400450500Temperature (K)40060080010001200140016001800Temperature TracesTwo-step ModelGT-POWER ModelCrank Angle Degree200250300350400450500Pressure (bar)050100150Pressure TracesTwo-step ModelGT-POWER ModelInjection RateCrank Angle Degree200250300350400450500Temperature (K)400600800100012001400160018002000Temperature TracesTwo-step ModelGT-POWER ModelCrank Angle Degree200250300350400450500Pressure (bar)050100150Pressure TracesTwo-step ModelGT-POWER ModelInjection RateTable 2.7: IMEP (bar) from -132 CAD to 132 CAD

Injection Timing
15◦ ATDC
20◦ ATDC
25◦ ATDC
30◦ ATDC
35◦ ATDC
40◦ ATDC

IMEPRB IMEPGT Relative Error A2
16.2477
1.06
1.79
16.0589
2.68
15.1928
3.30
15.0783
15.0079
3.60
3.80
13.9484

16.2712
15.8008
15.3863
15.0184
14.6032
13.9833

0.14%
1.63%
1.26%
0.40%
2.77%
0.25%

Figure 2.17: In-cylinder temperature and pressure for the two-step and GT-POWER models
with different EGR ratio

2.4.7 Air-Fuel ratio sweep

The last validation step is to compare the model behavior under different air-fuel ratio (AFR)

conditions. The three cases are based on different boost pressure: 1.4 bar, 1.6 bar and 1.8

40

-150-100-50050100150Crank Angle Degree050100150Pressure (bar)15%Reaction-Based ModelGT-POWER Model-150-100-50050100150Crank Angle Degree020406080100120Pressure (bar)20%-150-100-50050100150Crank Angle Degree020406080100120Pressure (bar)25%-150-100-50050100150Crank Angle Degree020406080100120Pressure (bar)30%bar. The engine was running at 1500 r/min. There were two injections: one main injection

at -2 CAD and one late-injection at 25 CAD. The total mass of fuel injected was 50 mg/hub.

Figure 2.18: In-cylinder temperature and pressure for the two-step and GT-POWER models
with different air-fuel ratio

There was not much recalibration effort necessary to obtain the matched pressure curve

to achieve less than 3% relative error in IMEP. The calibrated parameters are A1 and/or
A2.

2.4.8 Notes

From the results of preliminary calibration of the reaction-based model, some general ideas

and insights of comprehensive calibrations are obtained:

1) For the fixed point calibration (that is, the model is set at fixed speed, load, injection

mass, injection timing and EGR rate) the model parameters can be calibrated to estimate

the combustion metrics.

2) To have a model that covers a wide range of engine operating conditions, some of the

parameters need to be function of engine control inputs.

41

-150-100-50050100150Crank Angle Degree010203040506070Pressure (bar)1.4 barReaction-Based ModelGT-POWER Model-150-100-50050100150Crank Angle Degree01020304050607080Pressure (bar)1.6 bar-150-100-50050100150Crank Angle Degree0102030405060708090100Pressure (bar)1.8 bar3) The engine speed, load, main injection timing and EGR rate are the most effective factors

that force the parameters to change, while multiple injections and air-fuel ratio do not

affect the parameters so much.

4) It is therefore necessary to first study the sensitivity of the model to all the parameters. By

eliminating the least sensitive parameters, the overall calibration effort can be significantly

reduced.

5) These parameters to be calibrated need to be formulated as functions of engine speed,

load, main injection timing, and EGR rate, either as lookup table or polynomials.

6) The fully calibrated model should be able to accurately predict engine output torque (or

IMEP) with any given engine control input.

2.5 Model calibration

The reaction-based model has been developed in MATLAB/Simulink and compared with

a GT-POWER model. The next step is to evaluate and further enhance the developed

reaction-based combustion model using engine test data set provided by GM. The evaluation

process is divided into two steps:

initial reduced data set evaluation and final full data

evaluation. The reduced data set evaluation results are used to guide the further model

enhancement and the enhanced model is used for final model evaluation.

The workflow of the model calibration is summarized as follows:

1) The model sensitivity with respect to each parameter is studied. The most sensitive

parameters are selected as candidates for calibration, while the rest are kept constant.

2) An automated optimization algorithm is implemented. The algorithm is able to handle

multiple parameters and objects. The cost function is defined and weightings are properly

selected.

42

3) The data set is used for fixed point calibration, and lookup tables are generated. The

smoothness of the calibration surface is also studied.

4) A calibration structure is developed.

5) For parameters with a smooth calibration surface, polynomial functions are generated

to match the calibration data. Multi-case algorithm is used to optimize the polynomial

coefficients.

6) The model is finalized by combining all the lookup tables and polynomial functions.

7) A final model evaluation is processed on the finalized model and conclusions are drawn

from the results.

2.5.1 Sensitivity analysis

The calibration process is essentially parameter estimation. Parameters that exert the most

influence on model responses are identified through a “sensitivity analysis” [19]. By calculat-

ing and comparing the sensitivity coefficients of all the parameters, a list, called “sensitivity

ranking”, can be obtained. For the same model, different sensitivity analysis methods will

result in different sensitivity rankings. However, the actual ranking is not as important as

these parameters consistently appear near the top of the list. Disagreement among rankings

by the various methods for variables of lesser importance is not of practical concern since

these variables have little or no influence on model outputs.

For the developed reaction-based model, the one-at-a-time method is used. Conceptually,

this method is to repeatedly vary one parameter at a time while holding the others fixed.

A sensitivity ranking can be obtained quickly by increasing each parameter by a given

percentage while leaving all others constant, and quantifying the change in model output.

To be more specific, suppose there are n parameters, the sensitivity coefficient of system

43

response ηi to parameter βj can be approximated as

∂ηi
∂βj
ηi

(cid:0)β1, ..., (1 + δ) βj, ..., βn
(cid:1)
(cid:0)(1 + δ) βj
(1 + δ) βj − βj

(cid:1) − ηi

(cid:1) − ηi

(cid:0)βj

(cid:0)β1, ..., βj, ..., βn

(cid:1)

(2.47)

si,j = βj

≈ βj

ηi

=

where δ is the relative perturbation and in this study δ = 0.001.

δ

The sensitivity coefficients of all the parameters are calculated for a variety of engine

operating conditions. It turns out that the most significant (sensitive) parameters remain

the same for all the tested points. As an example, the results of 680 r/min, 1 bar are shown

in Table 2.8. The system response chosen in this study is the cylinder pressure because it

is directly measured in test data. However, other system variables can also be studied. The

sensitivity in the table is the mean value over the entire tested cycle. The percentage of the

sensitivity coefficients with respect to the mean value of nominal cylinder pressure, which

is not perturbed, is calculated to evaluate the relative significance of each parameter. The
results show that EA,1, EA,2 and n1 are the parameters with percentage sensitivity greater
than 5%. Figure 2.19 shows the plots of crank-based sensitivity coefficients of EA,1, EA,2
and n1. The shape of EA,1 and n1 are very similar, which indicates that only one of the
two parameters needs to be calibrated. As a result, the parameters to be fully calibrated are
EA,1 and EA,2.

Table 2.8: Sensitivity coefficients of parameters

Parameters
Sensitivity
Percentage (%)

A1
0.18
1.63

A2
0.11
0.95

A3
0.00
0.01

EA,1 EA,2 m1
0.13
3.60
32.25
1.18

2.15
19.34

n1
0.83
7.43

m2
0.53
4.75

n2
0.08
0.68

k1
0.18
1.58

k2
0.01
0.05

2.5.2 Overview of experimental data

The experimental data to be used for calibration is from a GM 6.6 L, 8 cylinder, Dura-

max engine. The specifications of the engine is summarized in Table 2.9. The engine was

44

Figure 2.19: Sensitivity coefficients of most significant parameters

tested at steady-state under various speed and load conditions. The recorded test data in-

cludes in-cylinder pressure traces and other engine control inputs, along with post-processed

heat-release traces, air and EGR variables, pressure metrics such as IMEP (indicated mean

effective pressure) and NMEP (net mean effective pressure).

Table 2.9: Engine specifications

Model value
Parameter
103 mm
Bore
99.05 mm
Stroke
163 mm
Connecting rod length
16.4:1
Compression ratio
Intake valve duration
148 CAD
Exhaust valve duration 244 CAD

The available test data is summarized in Table 2.10 with three test data sets described

as follows.

Test Set #1: Engine map

• 16 operating points (OP) over the speed-load map.

45

-50-40-30-20-1001020304050Crank angle (°aTDC)020406080100120Sensitivity coefficients (bar)Pressures(EA,1)s(EA,2)s(n1)Table 2.10: Summary of the experimental data

Operating point

Engine map
680 × 9
1400 × 9
1400 × 10
2000 × 9
1400 × 45

BMEP qinj
kPa
mm3
48.0
Max 801.2
8.2
Min
57.1
Max 101.2
12.0
10.1
Min
98.7
23.5
Max 252.0
19.2
Min
248.4
Max 502.2
38.1
33.3
Min
496.4
41.6
Max 709.7
Min
690.9
30.7
19.2
Max 270.3
Min
131.8
18.7

SOImain EGR
◦bTDC %
19
TDC
25
TDC
25
2
25
-3
20
-3
12
-2

71.9
49.0
70.9
70.3
65.0
61.6
53.4
49.7
48.6
45.2
65.8
4.2

• Engine operated as calibrated at each OP with combustion inputs (fuel injection tim-

ings, EGR, air-fuel ratio, etc.) from speed-fuel maps and varied based on OP.

• main injection used for most key points and post injection used at certain high-load

OPs.

• An addition data set under the same conditions but with additional pilot injection for

comparison purpose.

Test Set #2: SOI sweeps at fixed speed and load

• 4 speed-load pairs: 680 r/min, 1 bar; 1400 r/min, 2.5 bar; 1400 r/min, 5 bar; 2000

r/min, 7 bar.

• Main injection only for 680 r/min and 1400 r/min and additional post injection included

at 2000 r/min.

• Fixed EGR level for each speed-load pair.

Test Set #3: SOI sweeps with constant fuel quantity

46

• Constant mass of fuel injected at 1400 r/min.

• Different EGR levels.

2.5.3 Automated calibration algorithm

The first step is to individually calibrate the whole data set, either manually or automat-

ically, in order to confirm the two selected parameters are sufficient to achieve acceptable

model performance. Test Set #1 is first used to manually calibrate the model. As a result,

the IMEP error can be made arbitrarily small while pressure and temperature traces are

kept close enough to those in test data. An automated optimization algorithm is devel-

oped to reduce the manual effort for individual calibration. The developed code is further

implemented for multi-case calibration, where the optimized parameters work for multiple

operating conditions. The algorithm is based on lsqnonlin, a MATLAB nonlinear optimiza-

tion function [20]. The function solves nonlinear Least-Squares curve fitting problems of the

form

min||f (x)||2

2 = min

(cid:104)

f1(x)2 + f2(x)2 + . . . + fn(x)2(cid:105)

where the cost function f (x) is in the following form

 =





f1(x)

f2(x)

...

fn(x)

W 0.5

P

W 0.5

T

P0

(cid:17)
(cid:16) P−Pexp
(cid:16) T−Texp
(cid:17)
(cid:16) IM EP−IM EPexp
(cid:0)M F B − M F Bexp

IM EP0

T0



(cid:17)
(cid:1)

W 0.5

IM EP

W 0.5

M F B

f (x) =

(2.48)

(2.49)

(2.50)

where Pexp, Texp, IM EPexp and M F Bexp are crank-based time series in column vector
from experimental data. P0, T0 and IM EP0 are normalizing factors. WP , WT , WIM EP
and WM F B are weighting factors.

For the individual calibration, x is the vector containing the parameters, i.e.

x =

EA,1

EA,2



47

As an example, Figure 2.20a shows the predicted in-cylinder pressure compared to experi-

mental data at 1400 r/min, 2.5 bar. The model successfully predicts the combustion phasing,

pressure rise, peak pressure and pressure drop. However, there is a difference in pressure near

the onset of combustion. Since the two-step mechanism does not account for the dissocia-

tion of large hydrocarbon molecules into small hydrocarbon molecules, the heat absorption

due to the dissociation was not modeled, resulting in higher pressure rise around the start

of combustion. The corresponding temperature (Figure 2.20b), mass-fraction-burned (Fig-

ure 2.21a) and heat release rate (Figure 2.21b) are shown in the following. The overall shape

of the predicted temperature is in good agreement with experimental data, although there

is a discrepancy in the compression stroke near top dead center, peak temperature and ex-

haust gas temperature. The large temperature drop at the end of combustion is due to the

over-estimated heat release rate as shown in Figure 2.21a and Figure 2.21b.

(a) In-cylinder pressure

(b) In-cylinder temperature

Figure 2.20: Pressure and temperature predictions at 1400 r/min, 2.5 bar

The first peak in the heat release rate refers to the first step of the chemical reaction.

The model predicted an earlier start of heat release but a delayed and steep rising. After a

short duration, the first step terminated and the second step initiated. The heat release rate

of the second step was also over-predicted since there is a peak in the predicted curve while

the experimental data shows a dip. In the mass-fraction-burned plot, it is worth noting that

48

-150-100-50050100150Crank angle (°aTDC)010203040506070In-cylinder Pressure (bar)Simulink ModelExperimental DataInjection Profile (scaled)-150-100-50050100150Crank angle (°aTDC)200400600800100012001400In-cylinder Temperature (K)Simulink ModelExperimental Datathe model accurately predicted the combustion incompleteness, where the MFB does not

reach 1 at the end of combustion. Note that a Wiebe-based combustion model is not able

to predict this phenomenon. It also shows an earlier completion of combustion compared to

the experimental data.

(a) Mass fraction burned

(b) Heat release rate

Figure 2.21: MFB and HRR predictions at 1400 r/min, 2.5 bar

The IMEP error was kept within 5% throughout the calibration process.

It can be

confirmed that a two-step model is capable of capturing the main combustion features but

is simple enough for real-time model-based control.

2.5.4

Individual calibration

The results of individual calibration is shown in Figure 2.22 over the engine map, Figure 2.23

for SOI sweep at 4 operational conditions, and Figure 2.24 for SOI sweep at 1400 r/min with

constant fuel. All the test points are within 5% error bound. In fact, the relative IMEP

error for each test point is kept within 1%.

49

-150-100-50050100150Crank angle (°aTDC)00.10.20.30.40.50.60.70.80.91Mass-Fraction-BurnedSimulink ModelExperimental Data-30-20-1001020304050Crank angle (°aTDC)-50005001000150020002500Heat Release Rate (kJ/s)Simulink ModelExperimental DataInjection Profile (scaled)Figure 2.22: Estimated vs. actual IMEP over the engine map

Figure 2.23: Estimated vs. actual IMEP for SOI sweep at 4 operating conditions

2.5.5 Parameter correlations

Cases of fixed speed-load pairs were studied by calibrating the same set of coefficients.

In spite of several outliers, the coefficients are shown to be correlated to SOI and engine

operating conditions.

As shown in Fig. 2.25, EA,1 is small for very advanced injection and rises as the injection

50

0246810Actual IMEP (bar)012345678910Estimated IMEP (bar)Data points45 degree line5% error bound0246810Actual IMEP (bar)01234567891011Estimated IMEP (bar)680 r/min, 1 bar1400 r/min, 2.5 bar1400 r/min, 5 bar2000 r/min, 7 bar45 degree line5% error boundFigure 2.24: Estimated vs. actual IMEP for SOI sweep at 1400 r/min with constant fuel

timing gets more retarded. For injections at 5 to 10 degree before TDC, EA,1 reaches its
peak. As the injection is further retarded, EA,1 decreases. Although the correlation between
EA,1 and SOI is not close to linear, a clear trend of EA,1 increasing as load getting higher is
shown. The maximum relative variation of EA,1 is 14.7%.

Figure 2.25: Calibrated EA,1 vs. SOI for different speed-load pairs

Fig. 2.26 shows the variation of EA,2 with respect to SOI. A close-to-linear correlation is

51

3.13.23.33.43.53.63.7Actual IMEP (bar)3.13.23.33.43.53.63.7Estimated IMEP (bar)5% EGR40% EGR50% EGR65% EGR45 degree line1% error bound-505101520253035SOI (°bTDC)1.61.651.71.751.81.851.91.95EA,1104680 r/min, 1 bar1400 r/min, 2.5 bar1400 r/min, 5 bar2000 r/min, 7 barobserved. However, at 1400 r/min with 5 bar load, EA,2 is lower than expected in general,
especially when the injection is extremely advanced.

Figure 2.26: Calibrated EA,2 vs. SOI for different speed-load pairs

The coefficients were also calibrated at the 1400 r/min with constant quantity of fuel

injection.

In this case, there were 4 EGR levels: 5%, 40%, 50% and 65%. Only main

injection was considered. The results are shown in Figure 2.27 and 2.28.

For EA,1, the 5% EGR level is away from its counterparts, where the data is fluctuating
around 1.69 × 104. However, the maximum variation is only 5%. For higher EGR levels the
trend is much more linear and no large variations are observed for different EGR levels.

For EA,2, an even better trend is observed. The coefficient is almost linearly correlated to
SOI for each EGR level. Although the trend with respect to EGR level is not clear because of

the lower values for 65% EGR case, The scattered points are generally close. The maximum

variation is 6%.

2.5.6 Calibration structure

The results of individual calibration indicate that the calibration parameters are strong

functions of engine speed, load and start of injection. Thus, lookup tables or functions are

52

-505101520253035SOI (°bTDC)22.22.42.62.833.2EA,2104680 r/min, 1 bar1400 r/min, 2.5 bar1400 r/min, 5 bar2000 r/min, 7 barFigure 2.27: EA,1 vs. SOI for different EGR levels at 1400 r/min with constant fuel

Figure 2.28: EA,2 vs. SOI for different EGR levels at 1400 r/min with constant fuel

needed for a universal set of parameters covering the entire engine test data set. Figure 2.29

shows the calibration structure of the parameters as lookup tables or functions of engine

control inputs.

The calibration structure is illustrated as follows:

• Individual calibration of the 16 key points over the engine operating map is performed,

53

-2024681012SOI (°bTDC)1.681.691.71.711.721.731.741.751.76EA,11045% EGR40% EGR50% EGR65% EGR-2024681012SOI (°bTDC)2.152.22.252.32.352.42.452.52.55EA,21045% EGR40% EGR50% EGR65% EGRFigure 2.29: Calibration structure

which has been completed in the previous subsection.

• Lookup tables are generated from the calibration results, which are denoted as EA,10

and EA,20.

• The automated calibration algorithm is implemented for multi-case calibration to op-

timize the coefficients of the second order polynomial for SOI sweep.

The second order polynomial fit structure expressed mathematically is in the form

EA,1 = a1 · (SOI − SOI0)2 + b1 · (SOI − SOI0) + EA,10

and

EA,2 = a2 · (SOI − SOI0)2 + b2 · (SOI − SOI0) + EA,20

(2.51)

(2.52)

where SOI0 is the injection timing of points on the engine map. a1, b1, a2 and b2 are initially
lookup tables, but can be reduced to numbers if error is not significantly increased.

The third order polynomial fit structure expressed mathematically is in the form

EA,1 = a1 · (SOI − SOI0)3 + b1 · (SOI − SOI0)2 + c1 · (SOI − SOI0) + EA,10

(2.53)

54

and

EA,2 = a2 · (SOI − SOI0)3 + b2 · (SOI − SOI0)2 + c2 · (SOI − SOI0) + EA,20

(2.54)

where SOI0 is the injection timing of points on the engine map. a1, b1, c1, a2, b2, c2 are
lookup tables of engine speed and load.

2.5.7 Calibration: engine map

The engine map calibration is used to obtain EA,10 and EA,20. The calibration surface is
generated by interpolation and extrapolation. A factor called “smoothness” can be tuned

with losing accuracy as shown in Figure 2.30. For the best accuracy, the smoothness is set

as 1. The calibration surface is shown in Figure 2.31.

Figure 2.30: Distribution of IMEP error with various smoothness

2.5.8 Calibration: SOI sweep at constant speed and load

The estimated IMEP is compared to actual one for different calibration strategies. The

smoothed lookup tables are first used and showed good agreement with test data in Fig-

ure 2.32. When the calibration structure is implemented, modeling errors are increased. A

third order polynomial fit is shown to achieve fairly good match, compared to test data as

shown in Figure 2.33. The error distribution is uniform. There are 8 outliers out of 37

55

Figure 2.31: Calibration surfaces for EA,1 and EA,2

points in this study, which means 78% of the points are within 5% error bound. A second

order polynomial structure simplified the expression of the parameters but also introduced

more error as shown in Figure 2.34. The error distribution for the two structures is shown

in Figure 2.35a and Figure 2.35b. The advantage in accuracy of 3rd order polynomial fit is
obvious. Alternatively, a mixed order polynomial fitting has been applied, where EA,1 is fit
with a third order polynomial and EA,2 is fit with a second order polynomial. The results,
as shown in Figure 2.36, showed slightly reduced accuracy but also less computational effort.

2.5.9 Calibration: SOI sweep at constant speed and fuel injection

Figure 2.37 and Figure 2.38 show the results for SOI sweep at constant speed and fuel for

smoothed lookup table with second order polynomial fit, respectively. It is shown that the

fitting is less accurate compared to cases with the constant speed and load. However, the

fitting captures most of the data points.

56

1.510001.61.725001041.8EA12000BMEP (bar)1.9500RPM21500100005002.210002.42.625001042.8EA22000BMEP (bar)3500RPM3.2150010000500Speed (r/min)Speed (r/min)Figure 2.32: Predicted IMEP vs. actual IMEP for smoothed lookup table

Figure 2.33: Predicted IMEP vs. actual IMEP for third order polynomial fit

2.5.10 Model validation

To validate the calibrated model, a reduced data set is used. The data are arbitrarily selected

from the full set. Half of the points are used to calibrate the model and the other half are

used to test the model’s performance. Figure 2.39 shows the predicted IMEPs vs. actual

ones for SOI sweep data. Most of the points are with the 10% bound although there are a

57

0246810Actual IMEP (bar)01234567891011Estimated IMEP (bar)680 r/min, 1 bar1400 r/min, 2.5 bar1400 r/min, 5 bar2000 r/min, 7 bar45 degree line3% error bound0246810Actual IMEP (bar)01234567891011Estimated IMEP (bar)680 r/min, 1 bar1400 r/min, 2.5 bar1400 r/min, 5 bar2000 r/min, 7 bar45 degree line5% error boundFigure 2.34: Predicted IMEP vs. actual IMEP for second order polynomial fit

(a) Third order polynomial fit

(b) Second order polynomial fit

Figure 2.35: Error distribution

few outliers.

2.6 Conclusions

Traditional Wiebe based combustion model needs to be pre-calibrated to simulate flame

propagation process and is not capable of predicting autoignition and heat release in diesel

combustion when combustion parameters change. Combustion model is required to predict

58

0246810Actual IMEP (bar)01234567891011Estimated IMEP (bar)680 r/min, 1 bar1400 r/min, 2.5 bar1400 r/min, 5 bar2000 r/min, 7 bar45 degree line5% error boundFigure 2.36: Predicted IMEP vs. actual IMEP for third order polynomial fit for EA,1 and
second order polynomial fit for EA,2

Figure 2.37: Predicted IMEP vs. actual IMEP for smoothed lookup table

the torque for diesel engines under different operating conditions, including multiple pulse

fuel injections, large range of AFR, EGR variations, etc. The key in-cylinder dynamics,

such as charge mixing, chemical reactions and heat transfer, need to be accounted for and

to do this a detailed crank-resolved model has been selected. The reaction-based modeling

59

0246810Actual IMEP (bar)01234567891011Estimated IMEP (bar)680 r/min, 1 bar1400 r/min, 2.5 bar1400 r/min, 5 bar2000 r/min, 7 bar45 degree line5% error bound22.533.544.55Actual IMEP (bar)22.533.544.55Estimated IMEP (bar)5% EGR40% EGR50% EGR65% EGR45 degree line3% error boundFigure 2.38: Predicted IMEP vs. actual IMEP for second order polynomial fit

Figure 2.39: Predicted IMEP vs. actual IMEP

approach is therefore chosen because autoignition and heat release rate are predicted based

on instant mixture composition and in-cylinder temperature and pressure.

In this chapter, a two-step reaction-based combustion model has been developed along

with the torque model. The model is based on first law of thermodynamics expressed in

species concentrations. The model has 9 state variables:

[C10.8H18.7], [O2], [CO], [CO2],

60

22.533.544.55Actual IMEP (bar)22.533.544.55Estimated IMEP (bar)5% EGR40% EGR50% EGR65% EGR45 degree line5% error bound024681012Actual IMEP024681012Estimated IMEPIMEP (bar)Data Points45 degree line10% error bound[H2O], [N2], V , T . The initial concentrations are calculated based on mass of fuel injected,
AFR, residual mass and EGR rate at IVC Each concentration is integrated independently

and temperature rate is calculated based on the effect of all the concentrations. The rate

of change of concentration is mainly controlled by a two-step chemical reaction, where the

rate is described by the Arrhenius function. The model has been developed and simulated

in MATLAB Simulink. The key findings are summarized as follows:

1. The model divides the combustion process into two stages: ignition, and first stage of

energy release and second stage of energy release.

2. At stage 1, the model predicts the autoignition accurately, followed by a fast heat

release process, producing major amount of CO, which is mostly accomplished by the

first chemical reaction step. This process coincides with the experimental observations.

3. At stage 2, [CO] reaches the limit that triggers the second stage chemical reaction.

Heat release rate is significantly lower than that in the first stage, however, it is still

based on the assumption of homogeneous combustion. The rate of rising is higher and

drops earlier compared to actual stratified combustion test results.

4. Unlike Wiebe-based model, for multi-injection conditions, the model is able to adapt

to any injection profile automatically.

5. The mathematical nature of Arrhenius function introduces a positive feedback of tem-

perature variation, i.e., once the reaction is initiated, temperature will grow faster and

faster. The only termination is when the fuel is almost completely consumed. This

characteristics allows the model to predict the ignition and early stage of combustion

accurately. But it also could over predict the heat release rate in middle and late com-

bustion stages. This could be also due to the homogeneous combustion assumption.

6. The model is able to predict incomplete combustion by calculating the species concen-

tration at the end of combustion. The residual [C10.8H18.7] and [CO] account for the

61

unburned mixture. This is important for very later injection case during regeneration

operation.

The model was calibrated in a comprehensive style. By sensitivity analysis, it is found
that the most sensitive parameters are activation energies in both steps: EA,1 and EA,2.
Since the two steps are independent in heat release, it is feasible to control the two stages
separately by changing EA,1 and EA,2. Individual calibration for single point gives precise
IMEP and good crank-based response. The parameters correlated well with SOI in linear

or second order polynomial sense at fixed speed and load condition. The polynomial fitting

is accurate for normal operating conditions but less accurate for very low and high load

conditions.

62

CHAPTER 3

A THREE-ZONE COMBUSTION MODEL FOR DIESEL ENGINES

3.1

Introduction

To meet the demands for performance (torque and fuel economy) and to satisfy the

government regulations for emissions and safety, modern diesel engines, typically operated

under lean air-fuel ratio (AFR), utilize control strategies such as multiple fuel injections

and exhaust gas recirculation (EGR). At low speed, a pilot injection is usually made 5 to 7

crank angle degrees before the main injection to increase the cylinder temperature so that

when the main injection occurs the fuel in the environment is at a higher temperature than

its autoignition point, uniform combustion.

It is shown that pilot injection also helps to

reduce combustion noise [21]. Under the regenerative operations of engine aftertreatment

subsystems (e.g., diesel particular filter and lean NOx trap), a post injection is often used to

maintain the engine exhaust AFR close to stoichiometry, and the injection timing is usually

significantly retarded. These strategies make control of diesel engine systems more difficult

than ever. To enable model-based control, physics-based models were developed to simulate

the engine behavior in real-time. Therefore, it is required that a control-oriented engine

combustion model gives accurate predictions while keeping itself computationally efficient.

Features of a combustion model include predicting burn rate, in-cylinder temperature

and pressure closely related to engine performance (e.g., torque and efficiency), which makes

it one of the most critical sub-models of an engine system model. Various types of combus-

tion models have been developed that can be categorized into four groups based on their

complexity: 1) zero-dimensional models; 2) quasi-dimensional models; 3) one-dimensional

models; 4) three-dimensional models.

Zero-dimensional models are also referred to as single-zone models due to the assumption

that the entire engine cylinder is a uniform thermodynamic control volume, which under-

63

goes energy and/or mass exchange with the surroundings and energy released during the

combustion process is governed by first law of thermodynamics. In most single-zone mod-

els [22] and some multi-zone models [23, 24], the well-known Wiebe function [7] is used to

model the fuel burn rate. The Wiebe function has advantages of low computational load and

easy implementation. However, when the control variables are out of the modeled opera-

tional range, for instance, when multiple injection strategy changes, Wiebe-based combustion

models are neither able to provide accurate predictions nor easy to calibrate. Moreover, a

separate ignition delay model [25] is needed to predict the start of combustion, which in

most cases is accomplished by the Arrhenius integral [26]. Empirical burn rate model [27] is

used alternatively by including cylinder state such as temperature, pressure, fuel and oxygen

concentrations, etc. The model predicts heat release rate, peak pressure and IMEP fairly

well for multiple injections while keeping computational load low. However, complementary

models such as fuel evaporation model, mixing model, and ignition delay model, crucial

to predicting combustion timing and limiting the burn rate, are required for such type of

models.

Reaction-based modeling approach [28] has been proposed and used for diesel combustion.

These models utilize thermochemistry and chemical kinetics [13] to describe the interactive

dynamics among in-cylinder species, which is quite different from the traditional macroscopic

thermodynamics-based models. The properties of the whole cylinder gas is assumed to be

the weighted sum of all the species properties, although temperature is uniform over the

entire control volume. The burn rate is calculated based on the species concentrations

and temperature, depending on which chemical kinetic mechanism is assumed.

Ideally,

the reaction-based models are able to adapt to any injection profile due to the consistent

formulation of the model structure. Moreover, because concentrations and temperature are

fed back to the burn rate calculation, the model has the potential to predict heat release

rate under various operating conditions such as multiple injections. The model in literature

[28] was tested to predict the in-cylinder pressure reasonably accurately under a wide range

64

of operating conditions, where it turned out that two combustion coefficients are functions

of engine speed and load, even injection timing. The functions can be modeled as second

order polynomials. The model is still under single-zone assumption without evaporation and

mixing mechanism leading to early start of combustion, over-predicted burn rate and peak

pressure, and fast burning during mixing-controlled combustion stage.

To compensate for the shortcomings of single-zone models, quasi-dimensional models (or

multi-zone models) are developed mainly to model the inhomogeneity of mixture in a diesel

engine cylinder. The models remain zero-dimensional but introduce interactions between

different zones. There are two types of quasi-dimensional diesel combustion models depend-

ing on the formulation. Phenomenological combustion models [29, 30, 31] are extension of

single-zone empirical models by expanding the fuel evaporation model into a spray model,

where a number of zones with different composition and temperature but the same pres-

sure are used and an air zone is used to account for air entrainment, leading to accurate

predictions of heat release rate, pressure, and NO emissions. However, the burn rate is still

calculated empirically; thus ignition delay models are required for these models. The other

type of models uses chemical kinetics to calculate combustion rate, in addition to using

detailed spray model [32, 33]. In these models, the inhomogeneity of composition and tem-

perature are accounted for by formulating a number of spray parcels that interact with each

other and with the surrounding air zone. There is no need for ignition delay model in this

case because the chemical kinetic mechanism predicts the start of combustion automatically.

Fewer calibration parameters are required for such models due to the absence of empirical

functions. The model is able to predict combustion metrics such as heat release rate and

in-cylinder pressure accurately over a wide range of engine operational map. However, the

computational load is significantly increased. Multi-zone modeling approaches have been

widely used for different combustion systems, such as HCCI [34, 35, 36] and PCCI [37] com-

bustion, and these models have been validated with rapid compression machine tests [38, 39].

For diesel combustion, the multi-zone approach used for handling fuel evaporation (spray

65

models [40, 41]) and mixing-controlled combustion [42]. More related work can be found in

[43] and [44].

In this chapter, a three-zone reaction-based model is developed with formulations [45]

significantly different from the models discussed above. The physical delay is accounted for

using fuel evaporation model, the chemical delay by a simplified chemical kinetic mechanism,

and air entrainment by Fick’s law of diffusion. The purpose of this work is to significantly

reduce the number of zones in the multi-zone model to decrease the computational load while

maintaining the critical physical significance and keeping the model prediction accurate with

minimal calibration parameters. The model’s capability of combustion metrics prediction

has been demonstrated. The model has been calibrated with test data from a GM 6.6 L

diesel engine. The improvement in both accuracy and parameter invariability compared to

the single-zone reaction-based model has been shown.

3.2 Model description

This section describes the main architecture of the proposed three-zone combustion

model. The structure of the model will be explained schematically, followed by mathematical

derivations of the dynamics in each zone.

3.2.1 Model structure

The structure of the three-zone model is shown in Figure 3.1a. The model is divided into

three zones: a fuel zone surrounded by a reaction zone that interacts with the unmixed

zone. It is assumed that fuel zone only contains diesel fuel molecules, while the unmixed

zone consists of fresh air and residual gas. During the simulation, liquid fuel is first injected

into the cylinder to form the fuel zone. Due to the lower temperature of the injected fuel

than gases in the reaction zone, the fuel is first heated as a whole until it reaches boiling

point. The fraction of fuel which is at boiling point begins to vaporize and mix with the

surrounding reaction zone gas. The vaporization process leads to two effects: transfer of fuel

66

molecules from the fuel zone to the reaction zone and heat absorption due to phase change.

On the other hand, the air and residual gas in the unmixed zone flow into the reaction zone,

driven by two types of forces: diffusion governed by Fick’s law and bulk mass transfer as

a result of the temperature difference between the two zones. The cross-sectional view of

modeled cylinder physics is shown in Figure 3.1b.

(a) Longitudinal view

(b) Cross-sectional view

Figure 3.1: Three-zone model schematic

3.2.2 Volume and volume rate equations

The zero-dimensional reaction-based modeling approach is based on the assumption that the

volume, where reactions take place, is predefined. Therefore, it is important to calculate the

volume and volume rate for each zone before calculating mass and thermal quantities.

The instant cylinder volume V and volume rate of change ˙V are dependent on current

crank angle and the cylinder geometry. Equation 2.18 and 2.19 demonstrate the calculation

of these two variables

For the fuel zone, the fuel is in liquid state, leading to the assumption that the density

of fuel is constant. Therefore, the volume rate can be calculated as

Vf =

mf
ρfuel

67

(3.1)

where mf is the mass in fuel zone and ρfuel is fuel density. In fact, the volume of fuel zone
is only 0.01% of cylinder volume, which makes it negligible in this study.

For unmixed zone, the volume Vu is calculated by ideal gas law:

Vu =

muRuTu
pM Wu

(3.2)

where mu is the total mass of unmixed zone; Ru is the universal gas constant; Tu is unmixed
zone temperature; p is the in-cylinder pressure; M Wu is the mixture molecular weight in
the unmixed zone. The rate of volume change of unmixed zone ˙Vu is calculated by taking
numerical derivative of Vu with respect to time.

The volume and its rate of change in the reaction zone can be calculated based on volumes

of cylinder and reaction zone:

Vr = V − Vu

˙Vr = ˙V − ˙Vu

(3.3)

(3.4)

and

3.2.3 Fuel zone

The objective of formulating fuel zone is to describe the physics of fuel evaporation during

and after injection events using a simplified droplet evaporation model [13], as shown in

Figure 3.2. Certain assumptions are made so that the model is computationally efficient

while still agrees reasonably well with experimental results:

1. The fuel is a single-component liquid.

2. Temperature is uniform and constant over the entire zone at any instant in time, and

it is assumed to be equal to the temperature when the fuel is initially injected. As the

fuel zone is heated by the reaction zone, the temperature will increase until it reaches

the boiling point of the fuel, Tboil. Only when the boiling point is reached does the
fuel begin to vaporize. The time duration between the start of injection and start of

fuel evaporation is defined as the physical delay of ignition.

68

3. The heat transfer between fuel zone and reaction zone begins as soon as fuel is injected

and ends when boiling point is reached.

4. The thermal-physical properties, such as thermal conductivity, density, and specific

heat, are assumed to be constant for solving the equations.

Figure 3.2: Fuel evaporation model

There are two states, the mass of fuel, mf , and temperature, Tf , in the fuel zone:

dmf
dt

= ˙minj − ˙mvap

˙mf =
− ˙Qvap + ˙minj(hinj − hf ) − ˙mvaphf g

mf cv,fuel

˙Tf =

(3.5)

(3.6)

where ˙minj is available through fuel injection profile or parameters; hinj is the specific en-
thalpy of fuel at injection temperature; hf is the specific enthalpy of the mass in fuel zone;
hf g is the specific heat for evaporation; cv,fuel is the constant-volume specific heat capacity
of fuel; and ˙mvap is the evaporation rate of fuel that can be derived by solving the energy
equation on the droplet surface:

˙Qvap = − ˙mvaphf g

(3.7)

69

Substituting Fourier’s law for ˙Qvap, the equation becomes

4πkgr2
f

dT
dr

= ˙mvaphf g

(3.8)

where kg is the conductivity and rf is the radius of the fuel zone. It is assumed that at any
time, the temperature in the reaction zone has a constant distribution gradient; thus, the
gradient term can be rewritten as 2(Tr − Tf )/lr, where Tr is the reaction zone temperature
and lr is the thickness of the reaction zone.

The evaporation rate and heat transfer can be calculated as follows

(3.9)

(3.10)



˙mvap =

8πkgr2

f (Tr−Tf )
lrhf g

0

if Tf = Tboil

if Tf < Tboil

˙Qvap = −8πkgr2

f (Tr − Tf )
lr

3.2.4 Unmixed zone

The unmixed zone contains fresh air and residual gas as a fraction of the whole cylinder gas.

It is assumed that the unmixed zone is a hollow cylinder with the reaction zone inside of it.

The mass transfer consists of bulk mass flow caused by temperature gradient and diffusion

caused by concentration gradient:

˙mtr = ˙mbulk + ˙mdiff

(3.11)

To physically account for bulk mass flow, a virtual interface zone (M) is assumed, as

shown in Figure 3.3. The mass of Zone M is assumed to be nonzero only within each step.

Temperature Tm is equal to the weighted averaged temperature of the reaction zone and
unmixed zone:

Tm =

mrTr + muTu

mr + mu

(3.12)

where mr and Tr are mass and temperature of reaction zone, respectively.

70

Figure 3.3: Air entrainment model

The total conductive heat transfer into reaction zone is calculated as

˙Qtr = −2kcAr(Tr − Tu)

lr

(3.13)

where kc is the conductivity of current interface. This heat transfer has two effects: moving
the mass from unmixed zone to reaction zone and heating up the rest of unmixed zone. It

can be expressed as

where

˙Qtr = ˙Qbulk + ˙Qheat

˙Qbulk = −2kcAr(Tr − Tm)

lr

(3.14)

(3.15)

Since the conductive heat transfer used to drive the bulk flow is from reaction zone and

only Zone M is contacted with reaction zone, the temperature difference in the calculation
should be Tr − Tm. As a result, the heat transfer for heating the unmixed zone is resulted:

˙Qheat = ˙Qtr − ˙Qbulk = −2kcAr(Tm − Tu)

lr
At this point, the bulk mass flow can be derived from ˙Qbulk:

˙mbulk = −

˙Qbulk

cm(Tr − Tu)

=

2kcAr(Tr − Tm)
lrcm(Tr − Tu)

71

(3.16)

(3.17)

where cm is specific heat capacity.
approaches 2kcAr
lrcm
0, 2kcAr
lrcm

˙mbulk ∈(cid:104)

. And when Tm approaches Tr,
.

(cid:105)

It is apparent that when Tm approaches Tu,

˙mbulk
˙mbulk approaches 0, which indicates

A simplified charge mixing model [24] is modified in this chapter to formulate the diffusive

mass flow rate of unburned gas from unmixed zone to reaction one, which is dominated by

turbulent diffusion. Under this assumption, Fick’s law is applied:

˙m(cid:48)(cid:48)
diff = −ρuDt

dY
dr

(3.18)

where ˙m(cid:48)(cid:48)
diff is the turbulent mass flux of the unmixed gas; ρu is the density of the unburned
gas; Dt is the turbulent diffusivity; and dY
dr is the mass fraction distribution in the reaction
zone in the direction of interest. In this case, it is calculated as the mass fraction difference

between reaction zone and unmixed zone:

dY
dr

≈ 2(Yr − Yu)

lr

(3.19)

where Yr and Yu are the mass fraction in reaction zone and unmixed zone, respectively.
The relationship between turbulent diffusivity and turbulent viscosity gives the following
equation that can be used to calculate Dt:

Sct =

νtDt

(3.20)

where Sct is the turbulent Schmidt number. Note that νt is the turbulent viscosity that can
be calculated by

νt = kd¯vlr

(3.21)

where ¯v is the averaged velocity of the gas flow in the reaction zone that can be approximated

by the mean piston speed; lr is the thickness of the reaction zone (the same as in the previous
calculation); and kd is the calibration parameter. The mass transfer rate from unmixed zone
to reaction zone can be expressed as

˙mdiff =

2kdρu¯vAr(Yu − Yr)

Sct

72

(3.22)

where Ar is the contact area of the surface between unmixed zone and reaction zone, which
is equal to the surface area of the reaction zone.

The reaction-based model of unmixed zone is based upon the first law thermodynamic

analysis of an open system. Six states are included in this zone and they are unmixed

zone volume (Vu), unmixed zone temperature (Tu), the concentrations of oxygen ([O2]),
carbon dioxide ([CO2]), water ([H2O]), and nitrogen ([N2]). In a chemical kinetic system,
the molecular concentration of species i is defined as

[Xu,i] =

Nu,i
Vu

(3.23)

is the number of moles of species i; mu,i is the mass; and M Wu,i is

mu,i
where Nu,i =
M Wu,i
the molecular weight.

The rate of change of molar concentration of species i is defined as

= wtr,i − ˙Vu
Vu
where wtr,i is the gas mixing rate, which can be calculated as

− ˙VuNu,i
V 2
u

[Xu,i]

[ ˙Xu,i] =

˙Nu,i
Vu

wtr,i = − ˙mtr

VuM Wu

From the first law of thermodynamics, we have

dUu
dt

= ˙Qu − ˙Wu − ˙mtrhu

(3.24)

(3.25)

(3.26)

where Uu is the internal energy of unmixed zone;
system;

˙Wu is the net rate of work done by the system;

˙Qu is the net heat transfer rate into the
˙mtrhu is the energy change due to

mass flow; and hu is the specific enthalpy of unmixed gases.

The rate of work done is defined as

The relation between internal energy Uu and enthalpy H is

˙Wu = p ˙Vu

Hu = Uu + pVu

73

(3.27)

(3.28)

Then by re-arranging and differentiating with respect to time the left hand side of (3.26)

becomes

dUu
dt

=

d(Hu − pVu)

dt

=

dHu
dt

− ˙pVu − p ˙Vu

By substitution, (3.26) can be re-arranged as

dHu
dt

= ˙Qu + ˙pVu − ˙mtrhu

(3.29)

(3.30)

The extensive property Hu can be expressed as a sum of weighted molar enthalpies of all
species

(cid:88)

Hu =

Ni

¯hi = Vu

[Xi]¯hi

(cid:88)
(cid:88) ˙[Xi]¯hi + Vu

Thus, LHS of (3.30) becomes

LHS = ˙Vu

(cid:88)

[Xi]¯hi + Vu

(cid:88)

[Xi] ˙¯hi

(3.31)

(3.32)

where ˙¯hi = ¯cp,i
equations of ideal gas in terms of concentrations are given as

˙Tu. Note that ¯cp,i is the constant-pressure molar heat of species i. The state

and

˙p = RuTu

By substitution, the right hand side (RHS) of (3.30) becomes (3.35).

RHS = ˙Qu + RuTuVu

˙TuVu

[Xi] + ˙mtrhu

(3.35)

Equating (3.32) and (3.35) and re-arranging the equation give the formula for the tempera-

ture rate in (3.36).

˙Qw − ˙Qheat + RuTuVu

˙Tu =

(cid:80) [ ˙Xu,i] − Vu
(cid:80) [Xu,i](cid:0)¯cp,i − Ru

(cid:80) [ ˙Xu,i]¯hi − ˙Vu

(cid:1)

Vu

(cid:80) [Xu,i]¯hi − ˙mtrhu

(3.36)

Heat transfer term ˙Qu consists of heat transfer from reaction zone and heat loss to cylinder
wall:

˙Qu = ˙Qw − ˙Qheat

74

(3.37)

p =

[Xi]RuTu

(cid:88)
(cid:88) ˙[Xi] + Ru
(cid:88) ˙[Xi] + Ru

˙Tu

[Xi]

(cid:88)
(cid:88)

(3.33)

(3.34)

The heat loss rate to cylinder wall

˙Qw can be expressed as

˙Qw = −Achc(Tu − Tw)

(3.38)

where Ac is the effective contact area between gas and cylinder wall; hc is the heat transfer
coefficient; and Tw is the cylinder wall temperature. The heat transfer coefficient is calculated
by Woschni’s correlation [46]

hc = αB−0.2p0.8T−0.55

u

(2.28Sp)0.8

(3.39)

where Sp is the mean piston speed and α is constant.

3.2.5 Reaction zone

The formulation of reaction zone is similar to that of unmixed zone, with gas-phase fuel and

mixed gas flowing into the reaction zone and chemical reaction mechanism integrated. There

are eight states included in this zone and they are reaction zone volume (Vr), reaction zone
temperature (Tr), concentrations of diesel fuel ([C10.8H18.7]), oxygen ([O2]), carbon dioxide
([CO2]), water ([H2O]), nitrogen ([N2]), and carbon monoxide ([CO]).

The rate of change of molar concentration of species i can be calculated as

[ ˙Xr,i] = wi − ˙Vr
Vr

[Xr,i]

(3.40)

where wi is the concentration production that can be further separated into two parts:

wi = wrxn,i + wflow,i

(3.41)

where wrxn,i is the concentration production due to chemical reactions and it is calculated
by the chemical kinetic mechanism, and wflow,i is the concentration change due to mass flow
into and out of the control volume. In the reaction zone, wflow,i consists of fuel evaporation
rate and gas mixing rate, i.e.

wflow,i = wvap,i + wtr,i =

1
Vr

75

(cid:32)

(cid:33)

˙mvap,i
M Wf,i

+

˙mtr,i
M Wu,i

(3.42)

where M Wf,i and M Wu,i are molecular weights of each species in fuel zone and unmixed
zone, respectively.

The formula for temperature rate is shown in (3.43).

˙Tr =

˙Qvap + ˙Qtr + RuTrVr
Vr

˙mvaphf + ˙mbulkhr + ˙mdiffhu

(cid:80) [Xr,i](cid:0)¯cp,i − Ru

+

Vr

(cid:80) [ ˙Xr,i] − Vr
(cid:80) [Xr,i](cid:0)¯cp,i − Ru
(cid:1)

(cid:1)

(cid:80) [ ˙Xr,i]¯hi − ˙Vr

(cid:80) [Xr,i]¯hi

where hr is the specific enthalpy of the mass in reaction zone.

The two-step chemical reaction [13] of C10.8H18.7 oxidation can be expressed as

C10.8H18.7 + 10.075 O2 −−→ 10.8 CO + 9.35 H2O

CO + 0.5 O2 ←−→ CO2

(3.43)

(3.44a)

(3.44b)

The reaction rates for C10.8H18.7 and CO oxidation are given by Arrhenius functions

(cid:19)
(cid:19)
(cid:19)

(cid:18)
(cid:18)
(cid:18)

−EA,1
RuT
−EA,2
RuT
−EA,3
RuT

w1 = − A1 exp
w2 = − A2 exp

+ A3 exp

[C10.8H18.7]m1[O2]n1

(3.45a)

[CO]m2[O2]n2[H2O]k1

[CO2]k2

(3.45b)

where A1, A2, A3, EA,1, EA,2, EA,3, m1, m2, n1, n2, k1 and k2 are constants.

By inspecting (3.44a) and (3.44b), the rest of the reaction rates are as follows

wO2 = 10.075w1 + 0.5w2
wCO2 = −w2
wH2O = −9.35w1
wCO = −10.8w1 + w2

(3.46a)

(3.46b)

(3.46c)

(3.46d)

Note that the second step is a reversible reaction, where the reverse reaction decomposes

CO2 molecules into CO and O2.

76

3.2.6 Cylinder properties

With the calculation of mixture properties of each zone, the averaged properties over the en-

tire cylinder can be obtained. In-cylinder temperature is defined as the mass-based averaged

temperature for all three zones:

T =

mf Tf + mrTr + muTu

mf + mr + mu

and in-cylinder pressure is calculated by ideal gas law:

p =

(mf + mr + mu)RuT

V M Wmix

where M Wmix is the molecular weight of the mixture over the whole cylinder.

(3.47)

(3.48)

3.3 Model Validation

3.3.1 Test data

The test data used for model validation are from the same GM 6.6 L, 8 cylinder Duramax

engine. The specifications of the engine are already summarized and can be found in Ta-

ble 2.9. The engine was tested at steady-state under various speed and load conditions. At

each operating condition, different start of injection (SOI) timings and EGR rates are used.

Brake mean effective pressure (BMEP) in bar is the measure of load. The recorded test data

include in-cylinder pressure traces and engine control inputs, along with post-processed heat

release rate traces, air and EGR variables, pressure metrics such as IMEP and net mean

effective pressure (NMEP) variables. The available test data are summarized in Table 3.1

as follows.

SOI of main injection sweeps at fixed speed and load conditions with pilot injection:

1) Four speed-load pairs: 680 r/min, 1 bar; 1400 r/min, 2.5 bar; 1400 r/min, 5 bar; and

2000 r/min, 7 bar.

2) An extra post injection at 2000 r/min.

77

Table 3.1: Summary of test data

Operating points

BMEP qinj
mm3
bar
680 r/min × 12 Max 1.01
10.6
8.9
0.99
1400 r/min × 11 Max 2.52
18.3
16.4
2.49
1400 r/min × 11 Max 5.02
31.3
27.6
4.98
2000 r/min × 10 Max 7.09
56.2
45.8
6.90

Min

Min

Min

Min

SOImain EGR
◦bTDC %
25
-10
25
-5
25
-5
20
-7

61.9
60.8
55.5
53.7
51.4
48.0
40.3
38.5

3) Fixed EGR rate for each speed-load pair.

In each of the four groups, half of the data points are randomly selected for model cali-

bration. The other half are used for model validation. To be more specific, 6 points from 680

r/min, 10 points from 1400 r/min and 5 points from 2000 r/min have been randomly selected

for calibration; and the remaining 23 data points are used to test the model performance.

3.3.2 Combustion characteristics

The accuracy of pressure prediction is of highest priority. Thus, a MATLAB function based

on nonlinear Least-Squares algorithm [20] is used to minimize the resulting pressure error.

The function solves nonlinear least-squares curve fitting problems of the form

(cid:104)

f1(x)2 + . . . + fn(x)2(cid:105)

||f (x)||2

2 = min
x

min

x

where the cost function f (x) in this study is in the following form

f (x) = p − pexp

(3.49)

(3.50)

(3.51)

Note that pexp is a crank-based vector from experimental data and x is a vector containing
the calibration parameters:

x =(cid:2)kg

(cid:3)T

kc

kd

78

Table 3.2: Optimized model parameters

kg
8.3 × 103

kc
1.1 × 104

kd
0.12

The parameter values for optimal performance are shown in Table 3.2.

The modeled pressure traces are first compared with test data for different speed and load

conditions under the same main injection timing; see Figure 3.4. Three operating conditions

are investigated: 680 r/min, 1 bar; 1400 r/min, 5 bar; 2000 r/min, 7 bar. The main injection
timing is fixed at 20◦ before top dead center (TDC). Under this advanced injection timing
condition, the model predictions are in good agreement with the measured values. The

start of combustion has been accurately predicted due to the fuel evaporation model. The

peak pressure prediction is fairly good, except for a slight mismatch with 2% relative error.

This error, which is a result of the premixed combustion stage, could be attributed to the

assumption of the two-step mechanism, which is an over-simplified model of the combustion

chemistry. The model predicts in-cylinder pressure accurately under different operating

conditions without re-calibrating model parameters. This demonstrates the advantages of

the physics-based model compared to calibration-based models.

(a) 680 r/min, BMEP=1 bar

(b) 1400 r/min, BMEP=5 bar

(c) 2000 r/min, BMEP=7 bar

Figure 3.4: Pressure traces at different speed-load conditions with the same main injection
timing at 20◦ bTDC

The second comparison is made under the same operational conditions except for chang-
ing the main injection timing being to 6◦ before TDC; see Figure 3.5. The overall pressure

79

-150-100-50050100150Crank angle degree0102030405060In-cylinder pressure (bar)Multi-zone modelTest dataInjection profile (scaled)-150-100-50050100150Crank angle degree020406080100120In-cylinder pressure (bar)Multi-zone modelTest dataInjection profile (scaled)-150-100-50050100150Crank angle degree020406080100120140In-cylinder pressure (bar)Multi-zone modelTest dataInjection profile (scaled)prediction is still accurate, although error increases near the peak pressure location at 2000

r/min. As discussed above, the two-step assumption results in modeling error during the

premixed combustion stage and in this case it is near TDC. On the other hand, the error in

fuel injection rate also increases the deviation during pressure rise.

(a) 680 r/min, BMEP=1 bar

(b) 1400 r/min, BMEP=5 bar

(c) 2000 r/min, BMEP=7 bar

Figure 3.5: Pressure traces under different speed and load conditions with the same main
injection timing at 6◦ bTDC

Another comparison is performed for the same operating conditions but with a retarded
injection timing at 5◦ after TDC; see Figure 3.6. While maintaining the calibration param-
eters unchanged, the model predictions are still within the acceptable range. At 680 r/min,

there is a larger error at the first peak, which could be due to the simplification of the fuel

evaporation model. Since the fuel zone is assumed to be one spherical volume, the contact

area is calculated based on the sphere radius, which could be different than the actual contact

area for heat transfer. Thus, temperature estimation of the fuel zone might not be perfect,

which would lead to inaccurate ignition delay for some extreme cases. At 1400 r/min and

2000 r/min, the error remains but becomes smaller and the model captures the trends fairly

well. Note that for different operational conditions, the EGR rate is different, which is not

explicitly included in the model. This factor could also account for the mismatch. With

the results shown in the above figures, it can be concluded that the model is capable of

predicting in-cylinder pressure under different speed, load, and injection timing.

The last comparison is mainly between the three-zone and single-zone models. The

operating conditions are restricted to 1400 r/min and 2.5 bar with retarded injection timings.

80

-150-100-50050100150Crank angle degree0102030405060In-cylinder pressure (bar)Multi-zone modelTest dataInjection profile (scaled)-150-100-50050100150Crank angle degree0102030405060708090In-cylinder pressure (bar)Multi-zone modelTest dataInjection profile (scaled)-150-100-50050100150Crank angle degree020406080100120In-cylinder pressure (bar)Multi-zone modelTest dataInjection profile (scaled)(a) 680 r/min, BMEP=1 bar

(b) 1400 r/min, BMEP=5 bar

(c) 2000 r/min, BMEP=7 bar

Figure 3.6: Pressure traces at different speed-load conditions with the same main injection
timing at 5◦ aTDC

However, similar results are obtained under other conditions. As shown in Figure 3.7, while

the three-zone model predicts the pressure traces with acceptable error, single-zone model

predicts a much earlier start of combustion, which leads to an over-predicted peak pressure.

This is due to the lack of physical delay in the single-zone model. The fuel is assumed to be

ready for combustion as soon as it enters the cylinder. However, in reality, it takes time for

the fuel to be prepared for combustion, which is well explained in the three-zone model.

(a) SOImain=2◦ aTDC

(b) SOImain=4◦ aTDC

(c) SOImain=5◦ aTDC

Figure 3.7: Pressure traces at 1400 r/min, BMEP=2.5 bar, with different main injection
timings

The under-estimated physical delay can be further observed in heat release rate traces in

Figure 3.8. The single-zone model predicts the start of combustion near the start of injection,

while the actual start of combustion is around 5 degrees after injection. The three-zone model

successfully matches the test results.

81

-150-100-50050100150Crank angle degree051015202530354045In-cylinder pressure (bar)Multi-zone modelTest dataInjection profile (scaled)-150-100-50050100150Crank angle degree01020304050607080In-cylinder pressure (bar)Multi-zone modelTest dataInjection profile (scaled)-150-100-50050100150Crank angle degree0102030405060708090100In-cylinder pressure (bar)Multi-zone modelTest dataInjection profile (scaled)-150-100-50050100150Crank angle degree010203040506070In-cylinder pressure (bar)Multi-zone modelSingle-zone modelTest dataInjection profile (scaled)-150-100-50050100150Crank angle degree010203040506070In-cylinder pressure (bar)Multi-zone modelSingle-zone modelTest dataInjection profile (scaled)-150-100-50050100150Crank angle degree010203040506070In-cylinder pressure (bar)Multi-zone modelSingle-zone modelTest dataInjection profile (scaled)(a) SOImain=2◦ aTDC

(b) SOImain=4◦ aTDC

(c) SOImain=5◦ aTDC

Figure 3.8: Heat release rate traces at 1400 r/min, BMEP=2.5 bar, with different main
injection timings

The corresponding numerical evaluation of the modeling error of both single-zone and

three-zone model is shown in Table 3.3. The modeling error in pressure is calculated as the
scaled root mean square of relative pressure error from intake valve closing (IVC) at 138◦
bTDC to exhaust valve opening (EVO) at 129◦ aTDC:

(cid:118)(cid:117)(cid:117)(cid:116) 1

N

error =

N(cid:88)

(cid:18) p(i)model − p(i)exp

(cid:19)2 × 100

i=1

p(i)exp

(3.52)

where p(i)model is the model predicted pressure; p(i)exp is the measured pressure; i is the
index of the sampling points within the investigated range of crank angle degrees; N is the

total number of sampling points.

Table 3.3: Modeling error in in-cylinder pressure (%)

Single-zone model Three-zone model

SOI
2◦ aTDC 6.3860
4◦ aTDC 5.9162
5◦ aTDC 5.8746

3.8778
3.1189
3.0215

3.3.3 Parameter variability

As the three-zone model outperforms the single-zone model in predicting the combustion

characteristics, it is worth noting that the three-zone model is also preferred when the models

82

-50050100Crank angle degree-20020406080100120140Heat release rate (J/CAD)Multi-zone modelSingle-zone modelTest dataInjection profile (scaled)-50050100Crank angle degree-20020406080100120140Heat release rate (J/CAD)Multi-zone modelSingle-zone modelTest dataInjection profile (scaled)-50050100Crank angle degree-20020406080100120140Heat release rate (J/CAD)Multi-zone modelSingle-zone modelTest dataInjection profile (scaled)are to be calibrated. To obtain the previous results, the single-zone model was calibrated

case-by-case [47], which indicates that the model is essentially a calibration-based model

with several lookup tables. Although polynomial fitting approach was applied to eliminate

part of the required calibration effort, the single-zone model still needs 5-6 parameters to be

calibrated with comprehensive test data.

On the other hand, the three-zone model is demonstrated to be table-free with a fixed

calibration. The resulting IMEP is shown in Figure 3.9. All the data points are within the

10% error bound, and this is the results with fixed model calibration parameters. Comparing

to single-zone model, which needs to change the parameters whenever the operating condition

changes, the three-zone model, once calibrated, is sufficient to keep all parameters constant.

Figure 3.9: Predicted IMEP vs actual IMEP for different operating conditions

3.4 Conclusions

The three-zone reaction-based modeling approach for diesel combustion is shown in this

chapter. The developed model is based on the single-zone reaction-based model, with ad-

dition of fuel evaporation model and air entrainment model. The model parameters are

83

02468101214Actual IMEP (bar)024681012Estimated IMEP (bar)680 r/min, 1 bar1400 r/min, 2.5 bar1400 r/min, 5 bar2000 r/min, 7 bar45° line10% error boundcalibrated using part of the test data from a GM 8-cylinder, turbocharged diesel engine.

The other part of the test data over a wide range of operating conditions are then used for

model validation. Comparisons between model predictions and measured data show good

agreement under different speed, load and injection timing. The model successfully predicts

in-cylinder pressure, heat release rate and IMEP without re-calibrating model parameters.

The three-zone model outperforms single-zone one for both accuracy and parameter invari-

ability. The current model can be used as a foundation to generate simplified control-oriented

linear models or nonlinear models for model-based control design.

84

CHAPTER 4

MODELING AND CONTROL OF AN EBOOST SYSTEM

4.1

Introduction

With increasingly stringent regulations on engine emissions and consumer requirements

for performance, modern turbocharged diesel engines are normally equipped with devices

such as variable geometry turbocharger (VGT) [48, 49] and exhaust gas recirculation (EGR)

[50]. Diesel engines with VGT and EGR not only gain additional power from the increased

injected mass of fuel due to boosted intake air mass but also reduce NOx and soot emissions

due to EGR [51]. The CO2 emission reduction can be achieved in terms of engine down-
sizing. Turbocharged engines have advantages compared to supercharged engines in boost

control, altitude performance, durability, packaging and noise [52]. However, the well-known

“turbo lag” is the most significant disadvantage of turbochargers (TC). Since the turbo lag is

usually perceptible as slow torque response during transient operations, it directly impacts

the drivability and limits engine transient performance. Coordinated VGT-EGR control is

able to mitigate the turbo-lag issue [53, 54, 55, 56], but the benefit (improved performance)

and cost (increased complexity) are significantly dependent on the control strategy.

Among all the techniques to eliminate turbo lag, such as transmission down-shifting,

EGR reduction, smoke limit relaxing, etc., one of the most promising approaches is to add

additional energy (so-called “assist energy”) to the air charge system. Depending on the type

of assist energy applied, there are hydraulically assisted and electrically assisted systems

that have been widely studied to improve the turbocharger performance. A conventional

hydraulically assisted system [57, 58] consists of a high-pressure oil pump driven from the

engine crankshaft and a hydraulic turbine which is driven by the high-velocity oil jet from

a simple nozzle. The more recently developed system, so-called “regenerative hydraulically

assisted turbocharger (RHAT)”, includes a hydraulic pump into the original system, which

85

has introduced additional freedom of control and the recovery ability that further improves

the performance and efficiency. The related studies can be found in [59, 60, 61, 62]. Electri-

cally assisted systems, on the other hand, comprise an electric motor that directly drives the

turbocharger shaft (electrically assisted turbocharger or eTurbo) or a separate compressor

(electrically assisted boosting system or eBoost). The main advantage of the hydraulically

assisted turbocharger, compared to the electrical turbocharger, is its higher power density.

Currently, most of the electrically assisted driving motors have the power output in the range

of 1.5 - 10 kilowatts. The desired power to assisted the acceleration of large turbocharg-

ers could be over 10 kilowatts, although applications of 48 volts electric motors on assisted

boosting has been validated, which could eliminate this shortcoming. The RHAT system also

works better for energy recovery. When the excessive exhaust energy is available to be har-

vested, it is usually within the range of 15 - 40 kilowatts, where the turbocharger is operating

at high speed with high kinetic energy. The current production electric motor does not pro-

vide energy recovery capability without a significant increase in inertia and mechanical stress

when operating at high speed. Although RHAT out-performs eTurbo due to lower inertia,

less cost, smaller packaging space and potentially better durability, it has certain challenges

such as improving its low efficiency, designing fast-response hydraulic control valves and

actuation systems with high-flow capacity with low losses, reducing parasitic and windage

losses, managing energy storage in a hydraulic tank, and optimizing hydraulic turbine and

turbo-pump that is able to deliver high efficiency over a wide operational range [61]. The

studies on eTurbo and the corresponding controls can be found in [63, 64, 65, 66, 67, 68, 69].

There have been extensive numerical studies on performance of eTurbo [68, 70] and

eBoost [71, 72]. In [73] a physics-based engine and vehicle model, consisting of a crank-angle-

resolved cylinder model and a mean-value (0-D) air path model, has been used to study the

improvement in engine performance with different assisted turbocharging topologies. Cases

studied include steady-state and tip-in operations and different driving cycles. It is shown

in the simulation results that both eTurbo and eBoost are able to improve steady-state and

86

transient engine performance.

In addition, eBoost has provided higher low-speed torque

output and faster transient response for transient operations starting at low engine speed,

since the boost pressure build-up is not limited by the surge line, while eTurbo possesses the

potential to increase high-speed torque output for a limited period of time. The improvement

in performance by different boost-assist options, such as pre-compressor assistance, intake

assistance, and exhaust assistance, have been investigated with 1-D simulations [74].

It

is concluded that the pre-compressor option gives the best performance by a considerable

margin as it avoids the compressor surge limit. A component-based model has been developed

to simulate engine air path dynamics in 0-D with the flexibility to implement different

assisting configurations and controls [75]. A 1-D simulation study of eTurbo and eBoost on

a gasoline engine and a diesel engine has shown that downstream configuration of eBoost

can significantly improve system efficiency at steady-state, compared to the upstream eBoost

configuration, due to the surge limit of main compressor [76]. It is also concluded that eTurbo

is not as ideal as eBoost because of the surge limit. An overview of the electrically assisted

devices can be found in [77]. An integrated framework on testing and control of the eTurbo

system has been developed in [78].

There is little existing literature in the area of the modeling and control of eBoost on

diesel engines in detail. The physics-based air-path model developed in [75] provides the

framework for a more comprehensive study of the control problems for eBoost systems. It is

pointed out in [79] that by increasing the system voltage from 12 to 48 volts, engine steady-

state fuel economy and transient response can be further improved. A dynamic pressure ratio

allocation method is used to separate the control reference to each actuator, considering the

relatively slow dynamics of turbocharger and fast response of eBoost [80]. The control design

was validated in a test vehicle equipped with a downsized turbocharged spark-ignition engine.

A distributed model predictive controller has been designed for an electrically boosted diesel

engine air charge system [81]. The developed controller coordinates the eBoost, VGT, and

EGR actuators to regulate the intake manifold pressure, exhaust manifold pressure, and

87

EGR rate to required set points.

In this chapter, the performance improvement is first studied through a GT-SUITE model

with added eBoost. Both steady-state and transient performance is shown to be improved

by properly controlling the eBoost speed. A control-oriented engine air-path model has been

developed for model-based eBoost control. The model is validated on a component base

with steady-state engine test data. Because the available data do not include the eBoost,

the eBoost compressor and motor model are not validated explicitly. The model has been

linearized about engine steady-state operating points and the linear quadratic controller

has been designed to regulate boost pressure and EGR rate to the desired levels. Engine

tests have been performed to validate the simulation results. According to steady-state

experimental data, the eBoost is able to improve the overall BSFC with the optimized speed

command value and the actual BSFC benefit is close to simulation results. It is also found

that the standard bypass valve is not suitable due to the leakage at closing position, which

significantly reduces the eBoost efficiency. Transient test results validated that the eBoost

is able to reduce the boost tracking response time.

4.2 Engine air charge system model

The air charge system layout is shown in Figure 4.1, where three parts are included in

this model: engine, turbocharger and eBoost.

In order to implement eBoost model to engine air charge system, a simplified three-

state engine air charge model is adopted first. The dynamic states of the model are intake

manifold pressure (p2), exhaust manifold pressure (p3) and turbocharger speed (ωtc). The
state equations can be found in (4.1).

(cid:0) ˙mc + ˙megr − ˙min
(cid:1)
(cid:0)− ˙mt − ˙megr + ˙mexh
(cid:16) ˙Wt − ˙Wc − ˙Wl
(cid:17)

88

˙p2 =

˙p3 =

˙ωtc =

RT2
V2
RT3
V3
1

Jcωtc

(cid:1)

(4.1a)

(4.1b)

(4.1c)

Figure 4.1: System layout for engine air path with eBoost

Each of the physical quantities in the equations is investigated and validated in the following

sections. The model for each component is identified using the steady-state engine test data.

There are totally 224 data points used for this model calibration. After the model is validated

component-by-component, it is further validated using transient engine test data.

4.2.1 Engine intake and exhaust mass flow rate

It is common to model the engine breathing process of four-stroke engines using the speed

density equation. The rate of mass flow from intake manifold to engine cylinder ˙min can be
modeled as:

˙min =

ηvolp2NeVd

120RT2

(4.2)

where ηvol is the volumetric efficiency of the engine; Ne is the engine speed in r/min; and
Vd is the displacement volume.

89

The volumetric efficiency is a function of engine speed and boost pressure, and can be

modeled as:

ηvol = kve,1

√
p2 + kve,2

(cid:112)

Ne + kve,3

(4.3)

where kve,1, kve,2 and kve,3 are parameters to be identified. With test data of engine intake
mass flow rate, intake manifold pressure and temperature, the volumetric efficiency can be

easily identified, leading to calibrated engine intake mass flow rate shown in Figure 4.2. The

calibrated values are listed in Table 4.1.

Figure 4.2: Model identification results for engine intake mass flow rate

Table 4.1: Model calibration - engine intake mass flow rate

Parameter Model value
1.09 × 10−5
0.0018
0.7703

kve,1
kve,2
kve,3

Engine exhaust mass flow rate can be modeled as the sum of engine intake mass flow rate

and fuel injection mass flow rate. This is based on the assumption that in-cylinder residual

gas fraction is negligible. Therefore:

˙mexh = ˙min + ˙mfuel

(4.4)

90

00.050.10.150.20.250.30.350.40.45Actual dmin (kg/s)00.050.10.150.20.250.30.350.40.45Estimated dmin (kg/s)Datax=ywhere fuel injection mass flow rate is calculated based on the commanded fueling rate in

each cylinder per cycle. For the target engine, which has eight cylinders, the fuel injection

mass flow rate can be expresses as in (4.5). The unit for fuel command ufuel is mg/stroke.

˙mfuel =

8 × 10−6

120

ufuelNe

(4.5)

4.2.2 EGR mass flow rate

EGR mass flow rate can be modeled using the standard throttle flow equation, which has

two inputs: effective area (Aeff) as a function of throttle position, and pressure ratio
Depending on the magnitude of pressure ratio, the calculation may be different. The standard

pus

.

(cid:16) pds

(cid:17)

(4.6)

(4.7)

(cid:19) γ+1

γ



form of throttle flow is shown below.

˙mth = Aeff

For unchoked flow, meaning

(cid:18) pds

(cid:19)

pus

ψ

=

For choked flow, meaning

>

pds
pus

(cid:118)(cid:117)(cid:117)(cid:117)(cid:116) 2γ

γ − 1

≤

pds
pus

(cid:18) pds

(cid:19)

(cid:19)

(cid:18) pds

pus

ψ

pus

γ + 1

γ−1

pus√
RTus

(cid:18) pds
(cid:19) γ
(cid:19) 2
(cid:19) γ
(cid:18) 2

(cid:18) 2
(cid:18) pds
(cid:18) 2
(cid:118)(cid:117)(cid:117)(cid:116)γ

γ −

γ−1

γ + 1

pus

(cid:19) γ+1

γ−1

(cid:18)p2

(cid:19)

p3

For EGR mass flow rate, effective area is a function of EGR valve opening(cid:0)uegr(cid:1), and

(4.8)

γ + 1

pus

=

ψ

pressure ratio is the ratio of exhaust manifold pressure to intake manifold pressure. Thus,

˙megr = Aegr

p3√
RT3

ψ

(4.9)

where Aegr can be modeled as a second order polynomial of uegr, as indicated by Figure 4.3.

Aegr = kea,1u2egr + kea,2uegr + kea,3

(4.10)

91

where the parameter values are given in Table 4.2. The identification results are shown in

Figure 4.4.

Figure 4.3: EGR effective area vs. EGR valve position

Table 4.2: Model calibration - EGR mass flow rate

Parameter Model value
−8.15 × 10−4
0.0011
−4.98 × 10−5

kea,1
kea,2
kea,3

4.2.3

Intake manifold temperature

Considering the charge air cooler (CAC) after the compressor and EGR cooler after EGR

valve, the temperature in the intake manifold is the mixed temperature from both intake

charge air cooler and EGR cooler. These components can be treated as standard heat

exchangers whose effectiveness is used to model the heat the heat transfer through the

coolers. The outlet temperature of the coolers can be written as:

Tcac = Tc(1 − εcac) + Tcool,cacεcac

(4.11)

92

0.10.20.30.40.50.60.7EGR valve position (fraction)0123EGR effective area (m2)10-4A_egr vs. u_egrFitFigure 4.4: Model identification results for EGR mass flow rate

for CAC, and

Tegr = T3(1 − εegr) + Tcool,egrεegr

(4.12)

for EGR cooler. Tcool,cac is the coolant temperature at CAC and Tcool,egr is the coolant tem-
perature at EGR cooler. The heat transfer efficiency coefficients εcac and εegr are assumed
to be constant, and their values are shown in Table 4.3.

Table 4.3: Model calibration - coolant temperature

Parameter Model value

εcac
εegr

0.98
0.97

Tc is the main compressor outlet temperature, which is estimated by a third order poly-

nomial equation with compressor mass flow rate and TC shaft speed as input:

Tc = kct,1 + kct,2 ˙mc + kct,3Ntc + kct,4 ˙m2

c + kct,5 ˙mcNtc + kct,6N 2

tc + kct,7 ˙m3
c

(4.13)

+ kct,8 ˙m2

cNtc + kct,9 ˙mcN 2

tc + kct,10N 3
tc

The model values for the parameters are given in Table 4.4. Model fitting results are given

in Figure 4.5.

93

00.010.020.030.040.050.06Actual dmegr (kg/s)00.010.020.030.040.050.06Estimated dmegr (kg/s)Datax=yTable 4.4: Model calibration - compressor outlet temperature

Parameter Model value

kct,1
kct,2
kct,3
kct,4
kct,5
kct,6
kct,7
kct,8
kct,9
kct,10

356.81
235.79
4.38 × 10−4
3.53 × 103
−0.0254
1.82 × 10−9
1.55 × 104
−0.1837
6.76 × 10−7
−3.71 × 10−13

Figure 4.5: Model identification results for compressor outlet temperature

Assuming that the mixture temperature in the intake manifold is based on each mass

flow rate, thus

T2 =

˙mcTcac + ˙megrTegr

˙mc + ˙megr

(4.14)

The identification results are shown in Figure 4.6.

94

340360380400420440460480500520Actual Tc (K)350400450500Estimated Tc (K)Datax=yFigure 4.6: Model identification results for intake manifold temperature

4.2.4 Exhaust manifold temperature

The calculation of exhaust manifold temperature is based on engine exhaust temperature

and heat exchange between the engine exhaust flow and exhaust pipe. The exhaust manifold

temperature is modeled as a result of heat exchange process:

(cid:18)

(cid:19)

T3 = T0 + (Texh − T0) exp

− ket,1
˙mexhcp

The engine exhaust temperature is modeled based on the Seliger cycle [82].

(cid:19)1− 1

γ

(cid:18)p3

p2

(cid:20) ˙mfuel · LHV

˙mexhcp

r1−γ

c

·

Texh = ket,2

(4.15)

(4.16)

(cid:21)

(1 − xr) + T2rγ−1

c

where rc is the engine compression ratio; and xr is cylinder residual gas fraction. The model
parameters are calibrated as shown in Table 4.5 and Figure 4.7

Table 4.5: Model calibration - exhaust manifold temperature

Parameter Model value

ket,1
ket,2

28.3286
1.0158

95

290300310320330340350360370380390Actual T2 (K)300310320330340350360370Estimated T2 (K)Datax=yFigure 4.7: Model identification results for exhaust manifold temperature

4.2.5 Turbine power and mass flow rate

The physics-based control-oriented turbine power model can be found in the open literature.

The turbine operation depends on turbine inlet condition and TC shaft speed:

˙Wt =

1
60

Ntc ˙m2
t

1
B

RT3
p3

tan α1

(4.17)

˙mt is the mass flow rate through turbine; B is
where Ntc is the TC shaft speed in r/min;
turbine inlet clearance, which can be a tuning parameter; and α1 is the gas entry angle to
the rotor and is determined by the vane guide blade angular position controlled by VGT

position actuator. Their relation can be shown in Figure 4.8. In this study, the vane angle

is modeled as a polynomial function of VGT command and TC shaft speed:

α1 = kα,1 + kα,2uvgt + kα,3Ntc + kα,4u2vgt + kα,5uvgtNtc + kα,6N 2

tc + kα,7u3vgt

(4.18)

+ kα,8u2vgtNtc + kα,9uvgtN 2

tc + kα,10N 3
tc

where uvgt is the VGT control input. The identified parameters are shown in Table 4.6.
Model calibration results are shown in Figure 4.9.

The mass flow rate through a turbine can be modeled as a similar function to throttle

96

500600700800900100011001200Actual T3 (K)600650700750800850900950100010501100Estimated T3 (K)Datax=yFigure 4.8: VGT control input vs. vane angle

Table 4.6: Model calibration - turbine power

Parameter Model value

kα,1
kα,2
kα,3
kα,4
kα,5
kα,6
kα,7
kα,8
kα,9
kα,10

1.6517
−2.6254
−3.60 × 10−5
5.4184
2.54 × 10−5
4.20 × 10−10
−2.7310
−1.46 × 10−5
−7.56 × 10−10
−1.68 × 10−15

(cid:18) p4

(cid:19)

p3

˙mvgt = Avgt

p3√
RT3

ψ

(4.19)

flow:

where the coefficients are calibrated as shown in Table 4.6 and the model fit results are

shown in Figure 4.10. Calculation of ψ is defined in equation (4.7) and (4.8).

97

00.10.20.30.40.50.60.70.80.9VGT control (fraction)0.60.70.80.911.11.21.31.41.51.6Vane angle (rad)DataFittingFigure 4.9: Model identification results for turbine power

Table 4.7: Model calibration - turbine mass flow rate

Parameter Model value
5.30 × 10−4
1.96 × 10−4
3.99 × 10−9
−7.42 × 10−4
−4.57 × 10−9

kva,1
kva,2
kva,3
kva,4
kva,5

4.2.6 Power loss model.

The mechanical loss to the turbocharger shaft is a combination of both heat transfer and

friction losses. In this study, only friction loss is considered. According to [83], power loss

can be modeled as a polynomial function of rotational speed:

˙Wl = kpl,1N 2

tc + kpl,2Ntc + kpl,3

(4.20)

Since there is no direct measurement of power loss, the identification for turbine power and

power loss should be carried out together. Table 4.8 gives the values of calibrated parameters.

98

0123456789Actual dWt (W)1040123456789Estimated dWt (W)104Datax=yFigure 4.10: Model identification results for turbine mass flow rate

Table 4.8: Model calibration - turbo shaft power loss

Parameter Model value
6.96 × 10−7
2.36 × 10−11
7.50 × 10−9

kpl,1
kpl,2
kpl,3

4.2.7 Compressor power and mass flow rate.

Although map-based empirical models for a centrifugal compressor have been widely used

[84], they have poor extrapolation outside the mapped operating conditions. A physics-based

compressor model is able to provide good predictions and relatively low computational cost.

A reduced complexity model of compressor power is adopted in this study to efficiently

simulate the compressor behavior. The model is generalized such that only two variables are

used as inputs: mass flow rate and rotational speed.

˙Wc = kcp,1 ˙mcN 2

tc + kcp,2 ˙m2

cNtc + kcp,3 ˙m3
c

(4.21)

where kcp,1, kcp,2 and kcp,1 are parameters to be identified and their values are listed in
Table 4.9. The model identification results can be found in Figure 4.11.

99

00.050.10.150.20.250.30.350.40.450.5Actual dmvgt (kg/s)00.050.10.150.20.250.30.350.40.450.5Estimated dmvgt (kg/s)Datax=yTable 4.9: Model calibration - main compressor power

Parameter Model value
2.24 × 10−5
−2.7366
1.68 × 105

kcp,1
kcp,2
kcp,3

Figure 4.11: Model identification results for main compressor power

Compressor mass flow rate can be modeled as a De Laval nozzle [85] based on the tur-

bocharger geometry with external work input from the compressor wheel:

(cid:19)

, ωtc

(cid:18) p2

p1

˙mc =

Acp1√
RT1

Φ

The critical pressure ratio rcrit is defined as

rcrit = 1 +

µr2

If

Then

p2
p1

<

(cid:19)

, ωtc

(cid:18) p2

p1

Φ

exitω2
tc
cpT1

γ−1

(cid:19) γ
(cid:18)2rcrit

γ + 1

(cid:18) 2rcrit
(cid:118)(cid:117)(cid:117)(cid:116)γ

γ + 1

=

100

(cid:19) γ+1

γ−1

(4.22)

(4.23)

(4.24)

012345678Actual dWc (W)104012345678Estimated dWc (W)104Datax=yIf

Then

(cid:18) p2

p1

Φ

(cid:19)

, ωtc

≥

(cid:18)2rcrit
(cid:118)(cid:117)(cid:117)(cid:117)(cid:116) 2γ
(cid:19) 1

γ + 1

γ

γ−1

(cid:19) γ
rcrit −

γ − 1

(cid:19) γ−1

γ



(cid:18) p2

p1

where rexit is the radius at the outlet of compressor.

p2
p1

=

(cid:18) p2
(cid:18)

p1

(cid:20)

µ = 0.8

σ0 + ∆σ0 + tan β2B,0

(cid:18)

1 − exp

σ0 = 1 − 1
−2π
(cid:104)
2
Z
Cd,max − Cd,cor

Ac = 2πrdifBdif

Cr,exit,c
Uexit

(cid:19)
(cid:19)(cid:21)
(cid:0)Uexit − Uexit,opt

cos β2B,0

(cid:1)2(cid:105)

(4.25)

(4.26)

(4.27)

(4.28)

The identification results for compressor mass flow rate are shown in Table 4.10 and Fig-

ure 4.12.

Table 4.10: Model calibration - compressor mass flow rate

Parameter Model value
7.95 × 10−4
1.9673
1.23 × 10−5
334.44

Bdif
Cd,max
Cd,cor
Uexit,opt

4.2.8 Model validation with transient data.

Up to this point, all the components in the VGT-EGR system model, shown in Figure 4.1,

have been calibrated using steady-state test data. The third-order nonlinear model of engine

air charge system is further validated using the FTP 75 driving cycle data. The results are

shown in Figure 4.13.

101

Figure 4.12: Model identification results for main compressor mass flow rate

Figure 4.13: Model validation with FTP 75 driving cycle data

4.3 Extended air charge model with eBoost system

By integrating electrically driven compressor (e-compressor) and motor shaft dynamics

to the developed 3-state air charge system model, the system becomes a fifth-order nonlinear

model. The additional two states are upstream pressure of main compressor (downstream

pressure of e-compressor) and electric motor shaft speed, respectively. State equations of the

102

00.050.10.150.20.250.30.350.40.45Actual dmc (kg/s)00.050.10.150.20.250.30.350.40.45Estimated dmc (kg/s)Datax=y400450500550600650700750800Time (s)11.21.41.6Boost pressure (bar)SimulationTest Dataextended air charge system model are shown below.

(cid:1)
(cid:0) ˙me + ˙mbp − ˙mc
(cid:1)
(cid:0) ˙mc + ˙megr − ˙min
(cid:0)− ˙mt − ˙megr + ˙mexh
(cid:16) ˙Wt − ˙Wc − ˙Wl
(cid:17)
(cid:16) ˙Wm − ˙We − ˙Wl
(cid:17)

˙p1 =

˙p2 =

˙p3 =

˙ωtc =

˙ωe =

RT1
V1
RT2
V2
RT3
V3
1

Jcωtc

1

Jeωe

(cid:1)

(4.29a)

(4.29b)

(4.29c)

(4.29d)

(4.29e)

4.3.1 The eBoost compressor power and mass flow rate

The model for eBoost compressor power and mass flow rate is adopted from main compressor.

Thus,

˙We = kep,1 ˙meω2

e + kep,2 ˙m2

eωe + kep,3 ˙m3
e

(4.30)

where kep,1, kep,2 and kep,1 are calibration parameters whose values are shown in Table 4.11.

Table 4.11: Model calibration - eBoost compressor power

Parameter Model value
2.21 × 10−3
−37.25
3.47 × 105

kep,1
kep,2
kep,3

The eBoost compressor mass flow rate can be modeled similarly:

(cid:19)

, ωe

(cid:18) p1

p0

˙me =

Aep0√
RT0

Φ

(4.31)

where Φ is the same function as defined in equation (4.23), (4.24) and (4.25). Ae is calculated
in the same way as Ac defined in equation (4.28).

103

4.3.2 Motor drive power

The motor power output is modeled as a function of motor drive torque and motor speed.

Thus,

The characteristics of motor is integrated using the efficiency map provided by the manu-

˙Wm = τd · ωe

(4.32)

facturer.

4.3.3 Bypass mass flow rate

Let ˙mbp be the mass flow rate passing through the bypass valve, which can be modeled as
the standard throttle flow:

(cid:18) p1

(cid:19)

˙mbp = Abp

p0√
RT0

ψ

p0

where Abp can be simplified as a proportional function of ubp,

Abp = 6 × 10−4ubp

(4.33)

(4.34)

and ψ is calculated based on the standard flow equations as defined in (4.7) and (4.8).

4.4 System analysis of the electrically boosted diesel engine

To perform a preliminary evaluation of benefit of eBoost on engine performance, a com-

prehensive study, which is carried out in GT-SUITE simulation environment, has been com-

pleted through 1-D simulations, using both design of experiment and optimization. The

GT-SUITE model is developed based on the existing Ford 6.7 L, 8-cylinder diesel engine

model equipped with VGT and EGR. The eBoost compressor and electric motor compo-

nents are added, and the corresponding manufacturer supplied maps are implemented. The

model has been validated with engine test data.

104

4.4.1 Steady-state performance

First, the baseline lookup tables for VGT rack position, EGR valve position and brake specific

fuel consumption (BSFC) have been generated based on manufacturer mapped target boost

pressure and EGR rate. These maps are useful to evaluate the effect of eBoost to the system

performance. The generated maps are shown in Figure 4.14.

(a) VGT position

(b) EGR position

Figure 4.14: Baseline engine maps for VGT, EGR, and BSFC (percentage of maximum
value)

(c) BSFC

Next step is to construct a design-of-experiment (DOE) simulation and let the eBoost

power sweep within a reasonable range. The designed operating conditions are summarized

in Table 4.12.

105

100015002000250030003500Engine Speed (r/min)100200300400500600700800900100011001200Torque (Nm)2030304040505060607070808090901001000102030405060708090100100015002000250030003500Engine Speed (r/min)100200300400500600700800900100011001200Torque (Nm)0010101020202030303040404050505060606070708080900102030405060708090100100015002000250030003500Engine Speed (r/min)100200300400500600700800900100011001200Torque (Nm)03691215182124273033363942454848484851515154545454575757606060636363666669697275780102030405060708090100Table 4.12: GT-SUITE DOE simulation setup

Simulation label
Parameter
Engine speed (r/min)
Fuel injection (mg/stroke)
eBoost power (kW)
Bypass valve (degree)

Simulation setup

Minimum Maximum
600
10
0
0

3600
120
9
90

# of level
6
12
10
2

VGT and EGR are controlled in the same way as in the baseline simulation: VGT is

controlled to track target boost pressure and EGR is controller to track target EGR rate.

eBoost power is maintained constant for each simulation. Bypass valve is on-off controlled so

that the bypass valve is wide open when eBoost power is zero and fully closed when eBoost

power is not zero.

At each engine speed and load condition, the operating point with the best BSFC has

been selected as “optima” operating condition. The optimal points form a new map, leading

to the best eBoost power with the lowest BSFC. Note that the BSFC in this case considers

the eBoost power used as loss. Thus, the new BSFC, called effective BSFC, is calculated as

BSFCeff =

BSFC ·
˙Wb − 1

ηeηm

˙Wb
˙Wm

(4.35)

where BSFCeff is the effective BSFC;
efficiency; and ηm is the motor characteristic efficiency.

˙Wb is brake power; ηe is the battery energy conversion

The results of DOE simulations are shown in Figure 4.15 and 4.16. The results indicate

that under low speed low load condition, eBoost power improves the steady-state fuel econ-

omy, leading to increased steady-state output torque for the same BSFC. The corresponding

VGT and EGR controls also change. VGT increases its opening when eBoost is engaged

because additional power is added to maintain the same boost pressure, leading to reduced

required power from turbine. EGR increases its opening in this situation because when tur-

bine power is reduced, exhaust pressure decreases. As a result, to maintain the same EGR

rate, EGR valve opening should be increased.

106

(a) DOE VGT opening increase (%)

(b) DOE EGR opening increase (%)

Figure 4.15: DOE results for VGT and EGR

(a) DOE optimal eBoost power (%)

(b) DOE BSFC reduction (%)

Figure 4.16: DOE results for eBoost power (normalized percentage) and BSFC

A comparison between the upstream and downstream configuration of eBoost is of great

interest. The causality of system input and output is shown in Figure 4.17 and summarized

as follows. There are two paths for eBoost to affect BSFC. The first path, which is the direct

path, explicitly increases BSFC due to additional power consumption. The second path also

called the indirect path, decreases turbine power so that exhaust pressure is lowered, leading

to improved combustion efficiency. In this process, turbocharger efficiency (ηtc) and eBoost
efficiency (ηeboost) are competing and this shifts the optimal operational point.

107

100015002000250030003500Engine Speed (r/min)100200300400500600700800900100011001200Torque (Nm)1010101020202020203030304040405050506060707080900102030405060708090100Figure 4.17: System causality

The results of two configurations are shown below.

Figure 4.18: Percentage BSFC difference (upstream-downstream)

108

(a) eBoost compressor efficiency difference (%)

(b) Main compressor efficiency difference (%)

Figure 4.19: Compressor efficiency difference (downstream-upstream)

(a) VGT position difference (%)

(b) Exhaust manifold pressure difference (%)

Figure 4.20: VGT position and exhaust manifold pressure difference (downstream-upstream)

As shown in Figure 4.18, Region A is where the upstream configuration is preferred and

Region B is where downstream is preferred. At 1800 r/min, downstream is preferred in low

and high load conditions while upstream is preferred at mid load conditions. As shown in

Figure 4.19a, eBoost efficiency is decreased by up to 7% for downstream configuration at

mid load. At high load conditions, eBoost efficiency is increased by up to 40%. As shown

in Figure 4.19b and Figure 4.20a, Compressor efficiency is decreased by 1%, which is much

109

less than decrement in eBoost. VGT opening is reduced by 10% at 1800 r/min, mid load.

Considering the change in exhaust manifold pressure, as shown in Figure 4.20b, increased

exhaust pressure indicates decreased combustion efficiency. This explains the increase in

BSFC for the downstream configuration.

In summary, upstream configuration is only preferred when engine is operating at mid

speed and load conditions (Region A). To maintain the same boost pressure and minimal

BSFC, eBoost and TC are competing based on their operational efficiencies. If eBoost is

relatively more efficient than TC, more electric power is applied and VGT opening reduces;

and if eBoost is relatively less efficient than TC, less electric power is applied and VGT

opening increases.

In the two configurations, eBoost is operating at different conditions,

such as compressor speed, pressure ratio, temperature, etc. Difference in eBoost and TC

efficiencies (thus operations) is the key in the cause of the difference in BSFC. This indicates

that there is room for co-optimization of eBoost and TC maps.

4.4.2 Transient performance

To study the transient performance change due to eBoost, various scenarios have been con-

sidered, such as open-loop responses to boost pressure step and to engine load step, and

closed-loop response to load step.

The open-loop response to boost pressure step reveals the different response time of VGT

turbine and eBoost. The simulation has been performed at 1500 r/min, where load torque

is assumed to be 250 N-m. As shown in Figure 4.21, to raise the boost pressure to the

same level (0.2 bar up from baseline pressure 1.119 bar), the rise time and settling time

with eBoost and bypass valve activation are less than these when VGT is activated. This is

consistent with the assumption that electrically driven compressor has much faster response

than exhaust gas turbine. The control input for VGT and eBoost is a step function.

As the stepped pressure is increased, the difference in response time becomes larger, as

shown in Figure 4.22 for 0.4 bar stepped boost and Figure 4.23 for 0.6 bar stepped boost.

110

Figure 4.21: Transient response for boost pressure stepped by 0.2 bar

Note that a higher level of eBoost energy required to achieve the higher target boost pressure,

is expected.

Figure 4.22: Transient response for boost pressure stepped by 0.4 bar

It can be concluded that eBoost has a much faster response than the VGT turbine. To

achieve the same boost level, the settling time reduction can be expected to be up to 50%

depending on the boost requirement.

111

Figure 4.23: Transient response for boost pressure stepped by 0.6 bar

Because the turbo-lag is mainly caused by slow response of available energy at turbine

inlet, a more realistic scenario is to include the engine load step by assuming a reasonable dy-

namics from fuel injection to available energy at exhaust manifold. As shown in Figure 4.24,

for a load step from 100 to 500 N-m at 1500 r/min, with a relatively fast response of the ex-

haust energy, the difference between VGT and eBoost responses are significantly reduced. In

this case, the fuel injection is also considered, where the exhaust energy is greatly increased,

leading to much larger power to drive the main compressor. A non-minimal phase behavior

of eBoost response is also observed in Figure 4.24.

Figure 4.24: Open-loop transient response for load stepped from 100 to 500 N-m

112

4550556065Time (s)11.11.21.31.4Intake manifold pressure (bar)VGT-EGReBoost-BypassReference4550556065Time (s)0.020.0250.030.0350.04EGR mass flow rate (kg/s)VGT-EGReBoost-BypassReferenceTo conclude on the potential of the eBoost system’s capability of improving diesel engine

torque response, a comparison is made between the case where only VGT is activating to

track target boost pressure and the case where both VGT and eBoost are activated. This is

accomplished by integrating error-based controllers for VGT, EGR, eBoost and bypass valve

in the simulations. VGT is controlled by a PI controller to eliminate both steady-state and

transient errors of boost pressure. eBoost and bypass valve are controlled so that they are

only active in transient and restore the original state when the error is zero. This ensures

that eBoost does not compensate for steady-state boost tracking, which is more realistic for

vehicle electric energy management.

In Figure 4.25, where the engine speed is 1500 r/min and load torque is stepped from 100

to 500 N-m, boost pressure and EGR mass flow rate are compared among target level, VGT

only, and eBoost assist. The rising time for eBoost assist is significantly reduced. However,

due to the drop right after the rise, the overall settling time for both cases are similar. From

Figure 4.26, it is clear that spinning of eBoost and closing of bypass valve effectively increase

the compressor inlet pressure (p2) and could lead to fast rising of boost pressure.

Figure 4.25: Closed-loop transient response for load stepped from 100 to 500 N-m

113

4949.55050.55151.552Time (s)11.11.21.31.4Intake manifold pressure (bar)VGT-EGReBoost-BypassReference4949.55050.55151.552Time (s)0.020.030.040.05EGR mass flow rate (kg/s)VGT-EGReBoost-BypassReferenceFigure 4.26: Error-based control signals for eBoost assist

4.5 Linear quadratic control of the VGT-EGR-eBoost system

4.5.1 Control objective and problem formulation

The control objective for the diesel engine air charge system is to regulate the amount of

fresh air and oxygen concentration in the intake manifold to the desired values provided by

the optimized engine calibration process. These calibration maps are generated based on

an optimized trade-off between fuel economy and NOx emissions with the constraints on

soot formation. The desired fresh air and oxygen concentration can be transferred to target

values for air-fuel ratio and EGR fraction. If the fueling rate is known from driver’s pedal

position, the desired air-fuel ratio and EGR fraction can be converted to set points for boost

pressure (p2) and EGR mass flow rate ( ˙megr), as shown in Figure 4.27.

Adding the eBoost and bypass valve to the VGT-EGR system changes the overall system

characteristics. If eBoost compressor is running at low speed (p1 < p0), the flow through
bypass valve is in the forward direction (see Figure 4.28a); if eBoost compressor is running

at high speed (p1 > p0), the flow through bypass valve reverses (see Figure 4.28b). The
pressure condition at compressor inlet separate the system behavior into two different dy-

namics. Therefore, it is suggested to design separated controllers for different scenarios (see

114

4949.55050.55151.552Time (s)11.5Boost pressure (bar)p2Referencep14949.55050.55151.552Time (s)0.60.70.8Control signalVGT controlReference4949.55050.55151.552Time (s)0510eBoost power (kW)4949.55050.55151.552Time (s)00.51Bypass controlFigure 4.27: Set points for diesel engine air charge system control

Figure 4.29). In this study, only the feedback control for p1 > p0 is discussed.

(a) Flow condition with p1 < p0

(b) Flow condition with p1 > p0

Figure 4.28: Flow conditions with different pressure ratio

115

0p1p0p1pFigure 4.29: Set points for eBoost system

4.5.2 Linearization

Linearization of the full-order nonlinear model follows the standard process [86]. In summary,

system states can be expressed as

and input vector is

x = [p3

p2 ωtc ωe

p1]T

u = [uvgt uegr ueb ubp]T

(4.36)

(4.37)

Linearize the model about the equilibrium point x0 and define the error vectors δx, δu, and
δy as:

δx = x − x0
δu = u − u0

Then the linearized state-space model can be written as

δ ˙x = Aδx + Bδu

116

(4.38)

(4.39)




−45.10
2.78 −66.60

22.36 −161.92 −3.95
1099.94 −42.87
−5.73

0.28

A =

0.07

0

0

0.21
−2.97

0

0

131.73 −2462.61 920.29 −233.87

B =

7571446.13 −7868122.06

0

557.87

1719996.04
−6.38 × 10−9

0

0

0

0

1612.56

0



7.68

83.32
−0.40

0.04



−11080.59
−120213.39

577.28

−549703.39

(cid:105)

dt

0

0

0

0

95.746



0

0

0

0

0

0

0

(4.40)

(4.41)

(4.42)

(4.43)

For instance, the linearized system matrices with engine speed of 1500 r/min, brake
torque τe = 500 N-m, eBoost power ueb = 2 kW, and bypass valve opening ubp = 0.01 are

4.5.3 Linear quadratic regulator

A linear quadratic regulator (LQR) is designed to regulate the system near the equilibrium

point with the cost function below.

(cid:90) ∞

0

J =

(cid:104)

xT (t)Qx(t) + uT (t)Ru(t)

where

Q =

6.5078

0

5082.4

0

0



0

0

0

0

0

0

0

3457.5

0

0

9337.9

0

117



5

0

0 10

0

0

0

0

0

0

0.01

0

R =



0

0

0

10

The control gain K is calculated by solving algebraic Riccati equation

0 = P A + AT P + Q − P BR−1BT P

A state feedback controller is considered in this case

u(t) = Kx(t) = −R−1BT P x(t)

(4.44)

(4.45)

(4.46)

(a) Engine fuel injection

(b) Target boost pressure

Figure 4.30: Step load test profile for engine operated at 1500 r/min

The designed LQR control has been implemented to the nonlinear model to study its

performance. The set point is initially at 1500 r/min with 450 N-m. After 5 seconds, a load

step with a new target torque of 550 N-m is applied (see Figure 4.30). The tracking results

are shown in Figure 4.31. A separate PID control system (including 4 PID controller for

all the actuators) has been developed for comparison. The objective is to demonstrate the

capability of eBoost to improve transient boost tracking. With LQR controller, the VGT

118

4.555.566.5Time (s)4.24.34.44.54.64.74.84.955.1Fuel injection (kg/s)10-34.555.566.5Time (s)1.251.31.351.41.451.5Boost pressure (bar)105(a) Boost pressure tracking

(b) EGR mass flow rate tracking

(c) VGT control

(d) EGR control

(e) eBoost power

(f) Bypass valve control

Figure 4.31: Tracking performance

119

4.555.566.5Time (s)1.251.31.351.41.451.51.55Boost pressure (bar)105LQRPIDTarget4.555.566.5Time (s)0.0150.020.0250.030.0350.040.0450.050.0550.060.065EGR mass flow rate (kg/s)LQRPIDTarget4.555.566.5Time (s)0.50.550.60.650.70.750.80.85VGT controlLQRPID4.555.566.5Time (s)0.10.20.30.40.50.60.70.80.91EGR controlLQRPID4.555.566.5Time (s)12345678910eBoost power (kW)LQRPID4.555.566.5Time (s)00.0050.010.0150.020.0250.030.035Bypass valve controlLQRPIDcontrol is less aggressive and eBoost control is more aggressive, leading to much faster boost

pressure response. The overshoot is also greatly reduced.

Due to the limitation of experimental setup, a full-order LQR controller is not possible

because VGT and EGR valves are controlled by engine control module (ECM) while eBoost

and bypass valve are controlled by the MotoTron module. Therefore, an alternative LQR

controller is designed explicitly for eBoost (see Figure 4.32 for the control system archi-

tecture). The eBoost controller is designed based on the extended system including VGT

and EGR controllers. A simulation of the eBoost controller at 2000 r/min with 250 N-m is

performed and the results are shown in Figure 4.33. The fast rising of boost pressure with

eBoost control is expected due to fast response of the electric motor.

Figure 4.32: Control architecture for experimental implementation

120

Figure 4.33: LQR for eBoost control

4.6 Experimental validation

4.6.1 Engine test setup

To validate the numerical study and control design, engine test has been performed at MSU

Energy and Automotive Research Laboratory. The tested engine is provided by Ford Motor

Company and the specifications are given in Table 4.13.

Table 4.13: Specifications of Ford diesel engine

Item
Engine Type
Configuration
Displacement
Bore
Stroke
Compression Ratio
Combustion System High Pressure Common Rail Direct Injection

Value
Diesel, 4-Cycle
V8
6.7 L
99 mm
108 mm
15.7:1

The experiments are made possible by comprehensive instrumentation of the engine in-

121

stalled onto the MSU dynamometer. An alternating current (AC) dynamometer (dyno),

coupled with engine crankshaft through a 1:2.75 gearbox, is used to supply and absorb en-

gine power and maintain the engine speed. The dyno is capable of holding engine speed

up to 3200 r/min. On the measurement side, Cylinder pressure is measured by 8 pressure

transducers installed in each cylinder head. The signals pass through AVL charge ampli-

fiers and are fed to an A&D Combustion Analysis System (CAS) for data visualization and

recording. Regular pressure signals such as manifold absolute pressure (MAP), compressor

inlet pressure, turbine outlet pressure, etc., are measured by Druck pressure sensors and

fed into CAS. All the temperature signals such as ambient temperature, intake manifold

temperature, coolant temperature, exhaust temperature, etc., are measured by thermal cou-

ples and the data are recorded by the dyno NI Data Acquisition (DAQ) system. On the

control side, the engine comes with a production ECM whose calibration can be accessed

and modified using ETAS INCA software through ES600.1 interface. The ECM outputs the

control signals such as fuel injection quantity, injection timing, VGT position, EGR valve

position based on current engine speed and pedal position. An open engine control unit

(ECU), MotoTron, is used to sending control signals to peripheral devices, such as cooling

tower, fuel pump, eBoost motor, and bypass valve. MotoTron module is also responsible

to send the commanded pedal position signal to the ECM for the desired engine load. The

control algorithm for the eBoost and bypass valve is programmed in MotoTron. To sync

the recorded data across multiple devices, CAN communication is implemented among Mo-

toTron module, NI DAQ, and INCA computer. In this way, data can be shared on the CAN

bus and INCA software can be used for data recording. The layout of the engine test setup

is shown in Figure 4.34.

4.6.2 Test bench validation and engine baseline

It is important to make sure all the sensors, actuators, controllers and communications work

properly before performing any test. A testing matrix, shown in Figure 4.35, has been

122

Figure 4.34: Engine test setup layout

generated based on simulation results. The selected range of engine speed and load is where

eBoost activation is most desired. At each operational condition, the engine was run for 5

minutes after it reaches steady-state.

An important goal for the engine baseline test is to match the back pressure. Back

pressure is the pressure at the turbine outlet, before the aftertreatment system. Back pressure

is generally higher than ambient pressure due to the hydraulic resistance from the exhaust

system (exhaust manifold, catalytic converter, muffler, and connecting pipes). Back pressure

has a negative effect on engine efficiency, leading to decrement of engine power output. Since

there is no production aftertreatment system in the current engine setup, the back pressure

has to be simulated using a restriction plate. As shown in Figure 4.36, two plates with 15

0.5 inch holes are fixed to the exhaust pipe. By rotating the outer plate, the effective area

123

Figure 4.35: Engine test matrix

can be changed to match back pressure at different engine operating conditions. As shown

in Figure 4.37, the back pressure is matched for all tested points, with less than 2% error.

Figure 4.36: Exhaust restriction plate

4.6.3 Steady-state validation

It has been shown that for mid speed and load conditions, eBoost is able to achieve up

to 9% fuel efficiency improvement at steady state. This number could be overestimated

124

6008001000120014001600180020002200Engine speed0100200300400500600700800Brake torqueFigure 4.37: Back pressure matching

due to unmodeled losses in the physical system.

In the engine test, eBoost speed was

commanded through MotoTron and was controlled in a closed-loop by the eBoost controller.

The commanded eBoost motor speed is based on simulation results with the best engine

efficiency.

As expected, the activation of eBoost increases the boost energy. As the boost pressure

is maintained at the same level, VGT position opening increases to reduce the turbocharger

speed. This change leads to decreased exhaust manifold pressure. With the same engine

boost pressure, decreased exhaust pressure reduces the pumping loss, which improves engine

efficiency, as reflected by reduced fuel injection amount. Since the pressure drop is decreased

from exhaust to intake manifold, EGR valve position is increased to maintain the EGR rate.

It can be concluded that the general trend of all the parameters are reasonably validated.

However, the improvement in fuel efficiency is not as high as predicted by the model. This

could be due to three reasons. First, the model may not completely match the physical

system because, eBoost, bypass and the connecting pipes models are not validated due to

lack of data. Second, even if the model is accurate, fine tuning of the eBoost speed is still

required to find the optimal operating conditions. Finally, the leakage of the bypass valve

125

051015Case number0.70.80.91Back pressure (normalized)MSU 2019Ford 20170246810121416Case number-1-0.500.51Relative error (%)could reduce the eBoost efficiency.

Tests have been performed for the entire engine test matrix. Detailed results with engine

speed at 1000 r/min are presented as an example. Three load conditions are investigated:

113 N-m, 261.3 N-m, and 445.1 N-m. At each load condition, eBoost is maintained at

different speed (20000 r/min to 55000 r/min) to provide different boost level. Note that for

all conditions, the bypass air path is blocked with a solid scaled pipe to prevent any leakage

caused by the bypass valve. At each engine load condition, the effective BSFC changes with

eBoost speed effectively (see Figure 4.38a). There is an optimal eBoost speed for best BSFC.

With properly tuned eBoost speed, the overall BSFC benefit can be improved compared to

the baseline system (see Figure 4.38b)

(a) Effective BSFC

(b) BSFC benefit

Figure 4.38: BSFC improvement at 1000 r/min

The VGT and EGR valve positions are significantly changed with different eBoost speed

(see Figure 4.39). With higher eBoost speed, VGT opening is increased to maintain the

same boost pressure. EGR increased opening to maintain the same EGR mass flow rate.

This observation is consistent with simulation results.

Considering the direct effect of eBoost, the compressor inlet pressure is investigated. As

expected, the compressor inlet pressure is almost linear to eBoost speed (see Figure 4.40a).

126

1.522.533.544.555.56eBoost speed (r/min)1040.70.750.80.850.90.951Effective BSFC (normalized)113 N-m261.3 N-m455.1 N-m1.522.533.544.555.56eBoost speed (r/min)104-2-1012345BSFC benefit (%)113 N-m261.3 N-m455.1 N-m(a) VGT position

(b) EGR valve position

Figure 4.39: VGT and EGR operation with engine speed at 1000 r/min

The increase in compressor inlet pressure leads to increased VGT position and reduced

turbocharger speed, as shown in Figure 4.40b.

(a) Compressor inlet pressure

(b) Turbocharger speed

Figure 4.40: Compressor inlet pressure and turbocharger speed with engine speed at 1000
r/min

The reduction in exhaust manifold pressure is significant due to increased opening of

VGT (see Figure 4.41a). The decreased exhaust manifold pressure is beneficial because of

reduced pumping loss, leading to the reduced fuel consumption (see Figure 4.41b)

The BSFC benefits, predicted from simulation results, have been validated with test

127

1.522.533.544.555.56eBoost speed (r/min)1040.10.20.30.40.50.60.70.80.91VGT position (normalized)113 N-m261.3 N-m455.1 N-m1.522.533.544.555.56eBoost speed (r/min)1040.10.20.30.40.50.60.70.80.91EGR valve position (normalized)113 N-m261.3 N-m455.1 N-m1.522.533.544.555.56eBoost speed (r/min)10411.051.11.15Compressor inlet pressure (bar)113 N-m261.3 N-m455.1 N-m1.522.533.544.555.56eBoost speed (r/min)1041.522.533.54Turbocharger speed (r/min)104113 N-m261.3 N-m455.1 N-m(a) Exhaust manifold pressure

(b) Turbocharger speed

Figure 4.41: Exhaust manifold pressure and fuel injection with engine speed at 1000 r/min

results for three engine load conditions at 1000 r/min. Major engine parameters have been

investigated and the trend is consistent with simulation results. In addition, the test results

indicate that the standard EGR valve may not be suitable for bypass valve due to undesired

leakage (see Figure 4.42).

Figure 4.42: BSFC benefit from simulation and test results

Test results for the entire engine test matrix are shown in Figure 4.43. From the BSFC

benefit map (Figure 4.43a) it is confirmed that steady-state fuel economy can be improved

128

1.522.533.544.555.56eBoost speed (r/min)1041.051.11.151.21.251.31.351.4Exhaust manifold pressure (bar)113 N-m261.3 N-m455.1 N-m1.522.533.544.555.56eBoost speed (r/min)1041015202530354045Fuel injection (mg/hub)113 N-m261.3 N-m455.1 N-m113 N-m261.3 N-m455.1 N-mEngine load (N-m)-15-10-50510BSFC benefit (%)SimulationWith bypass valveBlockedby applying eBoost power. Greater improvement is achieved at lower speed conditions. The

test results also provides guidelines for eBoost operation (see Figure 4.43b).

(a) BSFC benefit (%)

(b) eBoost speed (r/min)

Figure 4.43: Test results over the entire matrix

4.6.4 Transient validation

Transient tests were conducted for step load inputs at constant engine speed. The dyno

maintained engine speed at 700 r/min, 1000 r/min, and 1400 r/min. With closed-loop

control of pedal position, the torque can be maintained at the target initial level (100 N-m).

Under the transient tests, the pedal position is stepped up to 100% for maximum brake

torque. A step speed command is applied to the eBoost controller to enhance the boost

pressure tracking. As a result, improvement in engine torque response is expected. Different

levels of eBoost speed are commanded to investigate the effectiveness of eBoost. Baseline

results (without eBoost) are included for comparison. The study is carried out with air block

and with bypass valve to evaluate the loss of efficiency due to valve leakage.

As shown in Figure 4.44, with engine speed of 700 r/min, eBoost is able to slightly

reduce response time, but significantly increase maximum torque. With engine speed of

1000 r/min, eBoost slightly increases maximum brake torque, but greatly reduces response

129

80010001200140016001800Engine Speed150200250300350400450500550600650700Brake torque1.07711.07711.07712.15422.15422.15422.15423.23143.23144.30855.385600.511.522.533.544.5580010001200140016001800Engine Speed150200250300350400450500550600650700Brake torque6582.64016582.640113165.280113165.280119747.920219747.920226330.560226330.560232913.200300.511.522.53104time (see Figure 4.45). With engine speed of 1400 r/min, eBoost reduces torque response

time moderately, with no improvement in maximum torque (see Figure 4.46).

(a) Brake torque

(b) Boost pressure

Figure 4.44: Transient response at 700 r/min with air block

(a) Brake torque

(b) Boost pressure

Figure 4.45: Transient response at 1000 r/min with air block

Testing results with bypass valve are shown in Figure 4.47, 4.48, and 4.49. Due to the fact

that the bypass valve is not able to be fully closed, the loss of torque increase and response

reduction is significant.

130

024681012Time (s)50100150200250300350400450500Brake torqueBaselineNe=30000 r/minNe=40000 r/minNe=50000 r/minNe=60000 r/minNe=70000 r/minNe=80000 r/min024681012Time (s)0.911.11.21.31.41.5Boost pressure (bar)BaselineNe=30000 r/minNe=40000 r/minNe=50000 r/minNe=60000 r/minNe=70000 r/minNe=80000 r/min024681012Time (s)0100200300400500600700Brake torqueBaselineNe=40000 r/minNe=60000 r/minNe=70000 r/minNe=80000 r/minNe=90000 r/min024681012Time (s)0.911.11.21.31.41.51.6Boost pressure (bar)BaselineNe=40000 r/minNe=60000 r/minNe=70000 r/minNe=80000 r/minNe=90000 r/min(a) Brake torque

(b) Boost pressure

Figure 4.46: Transient response at 1400 r/min with air block

(a) Brake torque

(b) Boost pressure

Figure 4.47: Transient response at 700 r/min with bypass valve

131

024681012Time (s)0100200300400500600700800900Brake torqueBaselineNe=60000 r/minNe=70000 r/minNe=73000 r/min024681012Time (s)11.11.21.31.41.51.61.71.81.9Brake torque (N-m)BaselineNe=60000 r/minNe=70000 r/minNe=73000 r/min024681012Time (s)50100150200250300350400450500Brake torqueBaselineNe=30000 r/minNe=40000 r/minNe=50000 r/minNe=60000 r/minNe=70000 r/minNe=80000 r/min024681012Time (s)0.911.11.21.31.41.5Boost pressure (bar)BaselineNe=30000 r/minNe=40000 r/minNe=50000 r/minNe=60000 r/minNe=70000 r/minNe=80000 r/min(a) Brake torque

(b) Boost pressure

Figure 4.48: Transient response at 1000 r/min with bypass valve

(a) Brake torque

(b) Boost pressure

Figure 4.49: Transient response at 1400 r/min with bypass valve

132

024681012Time (s)0100200300400500600700Brake torqueBaselineNe=40000 r/minNe=50000 r/minNe=60000 r/minNe=70000 r/min024681012Time (s)0.911.11.21.31.41.51.6Boost pressure (bar)BaselineNe=40000 r/minNe=50000 r/minNe=60000 r/minNe=70000 r/min024681012Time (s)0100200300400500600700800900Brake torqueBaselineNe=60000 r/minNe=70000 r/minNe=73000 r/min024681012Time (s)11.11.21.31.41.51.61.71.81.9Boost pressure (bar)BaselineNe=60000 r/minNe=70000 r/minNe=73000 r/min4.7 Conclusions

The research on electrically assisted boosting system is still in early stage. In this chapter,

the eBoost system was studied both numerically and experimentally. Some conclusions are

summarized as follows:

1) A control-oriented engine air-path model has been developed for eBoost control. The

model is validated on a component base with steady-state engine test data.

2) The performance improvement is first studied based on a GT-SUITE model with added

eBoost. Both steady-state and transient performance is shown to be improved by properly

controlling the eBoost speed.

3) Steady-state tests were performed to validate the simulation results. According to steady-

state experimental data, the eBoost is able to improve the overall BSFC with the opti-

mized eBoost speed command. The actual BSFC benefit is close to simulation results.

4) Transient test results confirm that the eBoost is able to reduce the response time of boost

tracking.

5) To improve eBoost efficiency, the bypass valve cannot have any leak. As a result, a special

bypass valve is needed.

133

CHAPTER 5

CONCLUSIONS AND FUTURE WORK

5.1 Conclusions

The conclusions of this dissertation can be summarized as follows:

1. A reaction-based modeling methodology has been formulated and implemented in diesel

combustion model. The proposed model successfully predicts the in-cylinder pressure

with acceptable error. The sensitivity study shows that only two calibration parame-

ters are required to accurately calibrate the model. A calibration structure has been

developed so that the number of required lookup tables is reduced significantly. The

finalized model can be a potential candidate to replace the current Wiebe function.

2. A multi-zone modeling approach has been proposed specifically for diesel combustion.

The developed model improves the prediction accuracy and eliminates the lookup ta-

bles, which are the main drawbacks of the single-zone model, especially with multiple

fuel injections. The three-zone reaction-based model increases in computational time

slightly but still can be implemented for model-based control and real-time simulations.

It is a promising model for future combustion control.

3. A physics-based engine air charge system model with eBoost has been developed. The

proposed model has been validated with steady-state engine test data and standard

cycle data. The system behavior has been studied through 1-D simulations. It is found

that eBoost improves both steady-state and transient performance. A complete test

bench for turbocharged diesel engine has been set up. Baseline tests have been per-

formed to validate the instrumentation and generate baseline parameters. Tests have

been performed under different operating conditions to validate the eBoost’s capability

of improving steady-state fuel economy and transient response.

134

5.2 Recommendations for future work

The following future work is recommended for the reaction-based modeling and study on

the eBoost system:

1. Future work for reaction-based modeling includes replacing the two-step mechanism

with a more detailed mechanism that improves chemical delay model. A systematic

method, that determines the optimal number of zones and/or reaction steps depending

on the application, is an open problem to be solved.

2. For eBoost operations, it is possible for the eBoost to create too much boost, causing

the main compressor to operate as a turbine (upstream pressure greater than down-

stream pressure). This could happen at the beginning of each tip-in process. An

accurate model for this process is important to understand the behavior of eBoost

under transient operations as well as improve eBoost control.

3. Model predictive control is a promising method for eBoost system because it handles

control constraints very well. The challenge is to develop an accurate system model

and develop the controller implementable for real-time control.

135

BIBLIOGRAPHY

136

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