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THESIS

2004- ‘
gfﬂg'oi a? 4/ 5

This is to certify that the
dissertation entitled

DEVELOPMENT OF A BASIS FOR CONTROL OF
COMBUSTION IN AN INTERNAL COMBUSTION ENGINE

presented by

YUAN SHEN

has been accepted towards fulﬁllment
of the requirements for the

Doctoral degree in Mechanical Engineering

 

 

Major Professor’s Signature
’ ‘ji

Date

MS U is an Afﬁrmative Action/Equal Opportunity Institution

_ -.-.--o-o---a-o-o-n-o-n-.-.-.-.- —- — — 4

 

LIBRARY
Mlchigan State
Unlverslty

 

 

 

PLACE IN RETURN BOX to remove this checkout from your record.
To AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6/01 c:/ClRC/DateDue.p65vp. 15

 

DEVELII

DEVELOPMENT OF A BASIS FOR CONTROL OF COMBUSTION IN AN
INTERNAL COMBUSTION ENGINE

By

Yuan Shen

A DISSERTATION

Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Mechanical Engineering

2003

DEVEL‘

 

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ABSTRACT

DEVELOPMENT OF A BASIS FOR CONTROL OF COMBUSTION IN AN
INTERNAL COMBUSTION ENGINE

By

Yuan Shen

This work is composed of several distinct sections however the focus is to effect
engine control. The ﬁrst effort represents quantiﬁcation of ﬂow during individual
cycles and the development of a method which can be used to deﬁne the cycle-to-cycle
variability in pre—combustion phase of a four stroke cycle. It was determined that one
could uniquely describe this phase of the airﬂow or fuel-air mixing by evaluating the
probability density function of normalized circulation. Of particular signiﬁcance was
the identiﬁcation that cycle-resolved measurements are needed to accurately describe
pre—combustion air motion and fuel-air mixing phenomena and that simulations which
rely on ensemble-averaged Navier-Stokes equations cannot provide reliable indications
necessary for combustion control in an internal combustion piston engine. It was the
result of these experiments that inspired development of theoretically based methods
which would provide insight into an algorithm for an engine control for the governor
system.

This effort led to the two new concepts related to the events which occur during the
conversion of reactants to products before and during the work producing segments of
the four stroke cycle. We term these segments the dynamic stage of combustion and
the exothermic stage of combustion. Mathematical analysis are constructed which
uniquely deﬁne the bounds of these stages of combustion and provide a rational
basis for developing future engine controls. The majority of the effort described in
this dissertation is orientated to developing these potential control algorithms and
of a description of what is termed the effectiveness of combustion. Based on these

continuously differentiable algorithms, the rate of conversion of reactants to products

and the rat ‘
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and the rate of change of the conversion of reactants to products can be obtained.
Results of this analysis have been applied to a stratiﬁed charge methanol fuelled
engine. In the future, these methods can be integrated in microprocessor controls
and will provide the feedback necessary to control the next generation of internal

combustion engines.

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ACKNOWLEDGEMENT

I would like to thank the following people who make this work reality.

First, I would like to thank Dr. Harold Schock, my academic advisor, for giving me
the opportunity to work in the MSU Engine Research Lab (ERL). I would not have
been able to complete this dissertation without his guidance and ﬁnancial support.

Second, I would like to thank Dr. Antoni K. Oppenheim, my advisory committee,
for his help and patient guidance throughout my work. Without his support, I would
not make much progress in my studies.

Third, I would like to extend my sincere thanks to Dr. Tom Shih, Dr. Ahmed
Naguid, and Dr. Mark Dykman for being my committees and their helpful comments
and thought-provoking questions; Dr. Indrek Wichman for his help on Chapter 5;
Andy Fedewa, Tom Stuechen, Edward Timm for their help to make me understand
experimental details; Jan Chappell for her assistance on a daily basis. I would also
like to thank rest of students and research associates at MSU ERL for their wonderful
company: Boon-Keat Chui, Anthony Christie, Andy Sasak, Mohmood Rahi, Mark
Novak, Kyle Judd, and Bin Zhu.

Finally, I would like to thank my parents and my wife, for their love.

Cont

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1.2.

 

Contents

Introduction

1.1 Background ................................

1.2 Literature review .............................
1.2.1 Pre-combustion analysis .....................
1.2.2 Combustion analysis .......................
1.2.3 Cycle-to-cycle variation reduction ................

1.3 Motivation and objectives ........................

Pre-combustion ﬂow analysis

2.1 Introduction ................................
2.2 Experimental setup ............................
2.3 Normalized circulation ..........................
2.4 PDF method ...............................
2.5 Cyclic variations of the flow with different port. blockers ........

2.5.1 Tumble plane ...........................

2.5.2 Swirl plane ............................
2.6 The inﬂuence of the shape of port blockers ...............

Dynamic stage of combustion in an IC engine

3.1 Introduction ................................
3.2 The polytropic process ..........................
3.3 Dynamic stage of combustion ......................
3.4 Bounds ...................................
3.5 Life function ................................
3.6 Discussion .................................
3.6.1 Life function and W'iebe function ................
3.6.2 Derivatives of life function ....................
3.7 Procedure .................................
3.8 Implementation ..............................
3.8.1 Engine ...............................
3.8.2 Results ...............................
Exothermic stage of combustion in an IC engine
4.1 Introduction ................................
4.2 State space ................................
4.2.1 Component fractions .......................

vi

oar—iii

3
12
16
19

21
21
22
22

27
29
32

37
37
38
41
42
44
46
46
50
51
52
52
54

69
69
70
70

4.3

 

4.2.2 Component states ......................... 71

4.3 Combustion processes ........................... 76
4.3.1 Mixing ............................... 76
4.3.2 Exothermic center ........................ 76

4.4 Exothermic system ............................ 79
4.4.1 Balances .............................. 79
4.4.2 Coordinates ............................ 80
4.4.3 Progress parameter ........................ 81
4.4.4 Combustion in a piston engine .................. 82
4.4.5 Correlation ............................ 84

4.5 Closed system ............................... 85
4.5.1 Thermodynamic relationship ................... 85
4.5.2 Thermodynamic properties .................... 87

4.6 Procedure ................................. 89

4.7 Implementation .............................. 90
4.7.1 Engine ............................... 90
4.7.2 Exothermic stage of combustion ................. 90
4.7.3 Closed system ........................... 96

Thermodynamic analysis in an IC engine 105

5.1 Introduction ................................ 105

5.2 Thermodynamic analysis ......................... 106

5.3 Heat release function ........................... 110

5.4 Results ................................... 111

Conclusions and recommendations 115

6.1 Conclusions ................................ 115

6.2 Recommendations ............................. 117

Evaluation of state transformations of reactants and products with

STAN J AN 120
A1 Introduction ................................ 120
A2 Procedure ................................. 121
A.3 Results ................................... 131

vii

List

3.1
3.2
3.3
3.4
3.5

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List of Tables

3.1
3.2
3.3
3.4
3.5

4.1
4.2

A1
A2
A.3
A.4

Comparison of ﬁrst derivatives of life function and Wiebe function . . 50
Engine speciﬁcations ........................... 52
Engine operating conditions ....................... 55
The indices of polytropic compression and expansion of four cases . . 55
Life function parameters ......................... 56
Equations of state ............................. 72
Parameters to evaluate the mass fraction of products ......... 91
Thermodynamic properties of air, fuel, reactants, and products in case 1132

Thermodynamic properties of air, fuel, reactants, and products in case 2133
Thermodynamic properties of air, fuel, reactants, and products in case 3134
Thermodynamic properties of air, fuel, reactants, and products in case 4135

viii

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List of Figures

1.1
1.2

1.3

1.4
1.5

2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
2.12
2.13

2.14
2.15

Schematic of MTV optical setup .....................
Velocities and vorticities of the ﬂow in the tumble plane, CAD 180,
tumble port blocker (70%) ........................
Velocities and vorticities of the ﬂow in the swirl plane, CAD 270, tum-
ble port blocker (90%) ..........................
The schematic of a controlled combustion engine ............
Prototype of a controlled combustion engine system: 1 - the air-blast
atomizer; 2 - the ﬂame jet generator; 3 - turbulence jet plumes; 4 - the
electronic control modulator; and 5 - the pressure transducer and shaft
decoder records expressed in terms of an indicator diagram. .....

3.5-liter DaimlerChrysler engine .....................
Tumble port blocker ...........................
Swirl port blocker .............................
The PDF for the circulation over a unit area on the tumble plane at
CAD 180, tumble plate blocker. .....................
The PDF for the circulation over a unit area on the tumble plane with
different port blockers at CAD 270. ...................
Inﬂuences of different port blockers on the cycle—to-cycle variations of
the ﬂow on the tumble plane at CAD 270. ...............
The PDF for the circulation over a unit area on the tumble plane with
different port blockers at CAD 300. ...................
Inﬂuences of different port blockers on the cycle-to-cycle variations of
the ﬂow on the tumble plane at CAD 300. ...............
The PDF for the circulation over a unit area on the swirl plane with
different port blockers at CAD 270. ...................
Inﬂuence of different port blockers on the cycle-to-cycle variations of
the ﬂow on the swirl plane at CAD 270. ................
The PDF for the circulation over a unit area on the swirl plane with
different port blockers at CAD 300. ...................
Inﬂuences of different port blockers on the cycle-to-cycle variations of
the ﬂow on the swirl plane at CAD 300. ................
Tumble port blocker B ..........................
Swirl port blocker B ...........................
Inﬂuences of port blockers B on the cycle-to-cycle variations of the ﬂow
on the tumble plane at CAD 270. ....................

ix

19
23

24
24
26
28
29
30
30
31

31

32

34

2.16 Inﬂuences of port blockers B on the cycle-to-cycle variations of the ﬂow
on the tumble plane at CAD 300. ....................
2.17 Inﬂuences of port blockers B on the cycle-to-cycle variations of the ﬂow
on the swirl plane at CAD 270. .....................
2.18 Inﬂuences of port blockers B on the cycle-to-cycle variations of the ﬂow
on the swirl plane at CAD 300. .....................

3.1 Pressure records for ten cycles in single-cylinder spark-ignition engine
operating at 1500rev/min, a) = 1.0, pink, 2 0.7atm, MBT timing
25 ° BTC. (From Heywood [1]) ......................
3.2 The polytropic pressure model of ideal processes in an IC engine . . .
3.3 The polytropic pressure model of real processes in an IC engine
3.4 The Wiebe function and its derivatives for a = 3 and x = 0.5, 1, 2.5,
5 and 10 ...................................
3.5 The life function of the dynamic stage of combustion and its derivatives
for a = 3 and X = 0.5, 1, 2.5, 5 and 10 ..................
3.6 Bottom view of the engine head .....................
3.7 Illustration of combustion chamber ...................
3.8 Pressure trace of case 1 ..........................
3.9 Pressure trace of case 2 ..........................
3.10 Pressure trace of case 3 ..........................
3.11 Pressure trace of case 4 ..........................
3.12 Logarithmic indicator of the pressure trace of case 1 ..........
3.13 Logarithmic indicator of the pressure trace of case 2 ..........
3.14 Logarithmic indicator of the pressure trace of case 3 ..........
3.15 Logarithmic indicator of the pressure trace of case 4 ..........
3.16 Polytropic pressure model of case 1 ...................
3.17 Polytropic pressure model of case 2 ...................
3.18 Polytropic pressure model of case 3 ...................
3.19 Polytropic pressure model of case 4 ...................
3.20 Life function of DSC and its ﬁrst derivative of case 1 .........
3.21 Life function of DSC and its ﬁrst derivative of case 2 .........
3.22 Life function of DSC and its ﬁrst derivative of case 3 .........
3.23 Life function of DSC and its ﬁrst derivative of case 4 .........
3.24 Second derivative of life function of DSC of case 1 ...........
3.25 Second derivative of life function of DSC of case 2 ...........
3.26 Second derivative of life function of DSC of case 3 ...........
3.27 Second derivative of life function of DSC of case 4 ...........
3.28 Analytical and measured cylinder pressure of case 1 ..........
3.29 Analytical and measured cylinder pressure of case 2 ..........
3.30 Analytical and measured cylinder pressure of case 3 ..........
3.31 Analytical and measured cylinder pressure of case 4 ..........

4.1 Diagram of component fractions .....................
4.2 3-D illustration of the state space ....................

35

38
40
40

48

49
53
54
57
57
58
58
59
59
60
60
61
61
62
62
63
63
64
64
65
65
66
66
67
67
68
68

71
73

4.3

4.13

4.14

4.13
4.16
4.17
4.18
4.19

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4.4

4.5

4.6

4.7

4.8

4.9

4.10
4.11
4.12
4.13
4.14
4.15
4.16
4.17
4.18
4.19
4.20
4.21
4.22
4.23
4.24
4.25
4.26
4.27
4.28
4.29

4.30

Diagram of component states with an illustration of the processes of
mixing and adiabatic exothermic center, EC, and exothermic system,

ES ...................................... 74
Diagram of component states for an adiabatic exothermic center in
w-eandw-hspace ........................... 78
Diagram of component states for a non-adiabatic exothermic system
in w — 6 space. .............................. 80
Correlation between mass fractions of products. ............ 85
State diagram of the exothermic stage of combustion for case 1 . . . . 92
State diagram of the exothermic stage of combustion for case 2 . . . . 92
State diagram of the exothermic stage of combustion for case 3 . . . . 93
State diagram of the exothermic stage of combustion for case 4 . . . . 93
Proﬁles of the mass fraction of products and its effective component of
case 1 ................................... 94
Proﬁles of the mass fraction of products and its effective component of
case 2 ................................... 94
Proﬁles of the mass fraction of products and its effective component of
case 3 ................................... 95
Proﬁles of the mass fraction of products and its effective component of
case 4 ................................... 95
State diagram of a closed system for case 1 ............... 97
State diagram of a closed system for case 2 ............... 97
State diagram of a closed system for case 3 ............... 98
State diagram of a closed system for case 4 ............... 98
Proﬁles of the mass fraction of products and its components in the
closed system of case 1 .......................... 99
Proﬁles of the mass fraction of products and its components in the
closed system of case 2 .......................... 99
Proﬁles of the mass fraction of products and its components in the
closed system of case 3 .......................... 100
Proﬁles of the mass fraction of products and its components in the
closed system of case 4 .......................... 100

Proﬁles of the temperature of reactants, products, and system of case 1 101
Proﬁles of the temperature of reactants, products, and system of case 2 101
Proﬁles of the temperature of reactants, products, and system of case 3 102
Proﬁles of the temperature of reactants, products, and system of case 4 102

Proﬁles of the speciﬁc volume of reactants, products, and system of
case 1 ................................... 103
Proﬁles of the speciﬁc volume of reactants, products, and system of
case 2 ................................... 103
Proﬁles of the speciﬁc volume of reactants, products, and system of
case 3 ................................... 104
Proﬁles of the speciﬁc volume of reactants, products, and system of
case 4 ................................... 104

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5.1 Schematic of the mixture in a cylinder of a four-stroke IC engine.

5.2 Heat release function ............................

5.3 Comparison of measured cylinder pressure and analytical cylinder pres-
sure for case 1 ...............................

5.4 Comparison of measured cylinder pressure and analytical cylinder pres-
sure for case 2 ...............................

5.5 Comparison of measured cylinder pressure and analytical cylinder pres-
sure for case 3 ...............................

5.6 Comparison of measured cylinder pressure and analytical cylinder pres-
sure for case 4 ...............................

A.1 Diagram of component states with an illustration of the processes of
mixing and adiabatic exothermic center, EC, and exothermic system,
ES ......................................
A.2 Flowchart of evaluating thermodynamic states of reactants and prod-
ucts during the exothermic stage of combustion. ............
A.3 Step 1a —— Specify the data ﬁle .....................
A.4 Step 1b —- The species in the data ﬁle COMB.SUD ..........
A.5 Step 2 — Specify the mole number of each species in the reactants . .
A.6 Step 3a —— Specify the temperature and pressure of reactants at the
initial state of DSC ............................
A.7 Step 3b — Thermodynamic properties of reactants at the initial state
of DSC ...................................
A.8 Step 4a — Specify the temperature and pressure of reactants at the
ﬁnal state of DSC .............................
A.9 Step 4b —— Thermodynamic properties of reactants at the ﬁnal state
of DSC ...................................
A.10 Step 5 — Specify the species of products ................
A.11 Step 6a — Specify the pressure and enthalpy of products at the initial
state of DSC ................................
A.12 Step 6b —— Thermodynamic properties of products at the initial state
of DSC ...................................
A.13 Step 7a — Specify the temperature and pressure of products at the
ﬁnal state of DSC .............................
A.14 Step 7b -—— Thermodynamic properties of products at the ﬁnal state of
DSC ....................................
A.15 Step 8 — Quit STANJAN ........................
A.16 State transformations of air, fuel, reactants, and products in case 1
A.17 State transformations of air, fuel, reactants, and products in case 2
A.18 State transformations of air, fuel, reactants, and products in case 3
A.19 State transformations of air, fuel, reactants, and products in case 4

xii

107
109

113

113

114

114

121
123
125
125
126
126
127
127

128
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Chapter 1

Introduction

1 . 1 Background

With the development of the automotive industry, energy and environment problems
are increasingly concerned. For production internal combustion (IC) engines, the
engine power, fuel economy, and emission have been considered as the most important
issues. In principle, the aim of most engine research is to achieve a high work output
engine with high efﬁciency and low pollution.

In a premix four-stroke internal combustion engine, which dominates personal
transportation in the United States, an operating cycle is composed of four strokes,

which are intake stroke, compression stroke, power stroke, and exhaust stroke.

1. During the intake stroke, the fuel and air mixture is induced through the intake

valve into the cylinder;

2. During the compression stroke, both intake and exhaust valves are closed and

the mixture inside the cylinder is compressed by the piston;

3. During the power stroke, the mixture inside the cylinder is ignited and the
combustion propagates throughout the charge, raising the mixture pressure and

temperature and forcing the piston to do mechanical work;

4. During the exhaust stroke, the exhaust valve is open and the burned gases exit

the cylinder.

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To increase the work output of a four-stroke IC engine with high efﬁciency and low
pollution, each stroke should be well understood and optimized. It has been studied
that each stroke in a engine operation cycle is affected by several factors [1][2]. For
the intake and compression stroke, the ﬂow in the cylinder is turbulent, subjective to
factors including compression ratio, engine speed, intake valve timing, and intake port
shape. For the power stroke, the combustion is mainly affected by the ﬂow around
the spark plug, the location of the spark plug, the air-to-fuel (A/ F ) ratio, ignition
timing, etc. For the exhaust stroke, the A / F ratio, exhaust valve timing, and exhaust
manifold pressure strongly affect the residual mass fraction (RMF) and exhaust gas
recirculation (EGR), which further affect the next engine operation cycle.

Since an operating cycle of a four-stroke SI engine is affected by numerous factors
and some of them are different from each cycle, there exist cycle-to-cycle variations
on the pressure and emission output. The existence of cycle-to-cycle variations will
inevitably affect the performance of an IC engine.

In nature, cycle-to-cycle variations are superposition of a non-chaotic deterministic
process on a stochastic process [3][4]. The deterministic effects on the combustion
process in an IC engine are from intake system geometry, A/ F ratio, combustion
chamber geometry, etc. The randomly changed parameters would be the in-cylinder
turbulence, exhaust gas recirculation (EGR), valve leakage, etc. Since these stochastic
effects exist, cycle-to-cycle variations in a four-stroke SI engine cannot be eliminated,
but they can be minimized.

Reducing the cycle-to-cycle variations in an IC engine would improve the engine
performance and increase the engine power. Studies have shown that the reduction
of the cycle-to-cycle variations would increase the engine power output at the same
fuel consumption [5]. It is also believed that the reduction of cycle-to-cycle variations
would help control the emission. Speciﬁcally, a reduction of cycle-to.cycle variability

of the fuel-air mixture motion in the cylinder allows knock-limit timing to be more

 

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1 .2 Literature review

Cycle-to—cycle variations exist in every stroke of an operating cycle of a four—stroke IC
engine. To minimize the cycle-to—cycle variations, each stroke of an operating cycle
should be studied. Based on the time sequence of a four-stroke cycle, the analysis
on the cycle-to—cycle variations in an IC engine can be classiﬁed into pro-combustion
analysis (intake and compression strokes), combustion analysis (power stroke), and
exhaust analysis (exhaust stroke). So far, most of the efforts to minimize the cycle-
to-cycle variations have been focused on the pre-combustion analysis and combustion

analysis.

1.2.1 Pre—combustion analysis

For the pre-combustion ﬂow in the cylinder, Molecular Tagging Velocimetry (MTV)
was used to examine the ﬂow pattern in a motored four-stroke spark-ignition (SI)
engine in the Engine Research Lab at Michigan State University. MTV [6][7] [8] is an
advanced optical diagnostic technique for making non-intrusive instantaneous velocity
measurements at multiple locations over a plane simultaneously. A tracer chemical
(in the MSU case biacetyl) combined with nitrogen gas is ”tagged” by a pulse of
UV laser light (A2308). Two sets of intersecting lines form a grid inside the engine
cylinder, and an image is taken of the ﬂuorescing biacetyl with an intensiﬁed CCD
camera. This is done approximately 200 times and the images are averaged to obtain
a reference image. Next, the excitation process is repeated. This time the image
is recorded after the laser pulse, but still within the phosphorescence lifetime of the
molecules. The time between these images and the reference image is known and the
distance each line intersection has traveled can be measured giving a velocity vector

for each intersection point. Traditional scattering methods require the ﬂow to be

seeded wit
advantage
IhP ﬂtHV it
in Figure ]

IIH‘Iuty
Figures 13
Illllnhle all
lites' WI'IUII

The results
et. al. .‘I
geometries ‘

The enst
ﬂow. Howex
tecycle \‘ari
field is an at
It NIHI‘SI’IIIS
strong, TIM
the CNile-to“
Tfigui. 1\' .

[(IIIFSImke I(

examining ﬂt

 

r
We well ..

and IIII‘IF ax,

 

ZI‘aHs. I‘.
("“‘HIIJIIstion (.I
tttjtt'tion (DI .

In -
IIIIN’II Ill'U a

 

 

seeded with light-scattering particles that may have difﬁculty following the ﬂow. The
advantage of this measurement technique is that the tracer is molecularly mixed with
the ﬂow and follows it perfectly. The schematic of the MTV optical setup is shown
in Figure 1.1.

The ensemble-averaged ﬂow patterns in the cylinder recorded MTV are present in
Figures 1.2 and Figure 1.3, which show typical ensemble averaged rotational motions
(tumble and swirl) of the ﬂow on the tumble and swirl planes, respectively. In ﬁg-
ures, vectors represent ﬂow velocities, and the shading represents the ﬂow vorticity.
The results are generally consistent with the visualization results obtained by Trigui,
et. a1. [9], Choi and Guezennec [10], Reuss [11] and Khalighi [12], though intake
geometries were different.

The ensemble-averaged ﬂow pattern in the cylinder is of help to characterize the
ﬂow. However, it neglects detailed features in the real individual ﬂow ﬁeld and cycle-
to-cycle variations on the ﬂow pattern. In other words, the ensemble-averaged ﬂow
ﬁeld is an artiﬁcial ﬁeld containing common features of the real individual ﬂow ﬁelds.
It represents none of the real individual ﬂow ﬁelds if cycle-to-cycle variations are
strong. Therefore, the individual ﬂow ﬁeld has to be studied in order to understand
the cycle-to-cycle variations on the pre-combustion ﬂowpattern in the cylinder.

Trigui, Kent, et. al. [9] implemented a visualization of the pre—combustion ﬂowin a
four-stroke IC engine by 3-D particle tracking velocimetry (3-D PTV). After carefully
examining ﬂow patterns for several consecutive cycles, they found that even in the case
of very well organized swirl or tumble, the vortices are rarely centered in the volume
and their axes are usually inclined in some complex way inside the 3D volume.

Zhang, Ueda, et. a1. [13] visualized the two-dimensional bulk ﬂow ﬁelds inside the
combustion chamber around top dead center (TDC) in a motored four-stroke direct
injection (DI) diesel engine. By comparing the continuous cycle-resolved ﬂow ﬁelds

between two arbitrary cycles from BTDC 3 to TDC on the swirl plane, they found

   

Beam Blocker

 

Engine Cylinder

Mirror

 
 
 

 

Beam Blocker

Horizontal
Laser Beams

 

  
  

    

Mirror

 

It:

CCD
Camera

  
  

Engine Cylinder

 
 

Vertical Laser Beams
Beam Blocker

 
   
    

4— 50mm Cylindrical Lens

 

Cylindrical

    

<— 1

   
   

Splitter

 

Mirror

4

50mm Cylindrical Lens

 

Incoming Laser Beam

 

 

Figure 1.1: Schematic of MTV optical setup

 

 

   

 

 

 

 

 

 

 

Tumble Plane Average VelocityNortlcity Field
for CAD 180,1550 rpm, 15 in Hg Vort
T with Tumble Port Blocker and 70% Blockage E 3000
1 -. 20 m/s 5 2700
__ - E 2400
-. E 2100
0 __ g 1000
1 __ g 1500
- , 5 1200
‘ E 900
'2 1' g 600
A " E 300
5'3 " E o
v _ g -300
>' -4 - E -600
— E -900
-5 -- g: -1200
4 :15 -1500
-5 -l- E 4800
__ -2100
-7 -. -2400
__ -2700
-8 A . . :1 . t t t . : . . f: : '30”
0 1 2 5 7 8 10
X (cm)

 

 

 

 

Figure 1.2: Velocities and vorticities of the ﬂow in the tumble plane, CAD 180, tumble
port blocker (70%)

—'Lo

ttt'ttﬁ—rrtrttrrvv

    

Y(cm)
cbo'chnc'nJE-oorb

o'ITII'TjTI'IIII'IIT

 

I

Flgllrp 1.3_ t
[)1th ”UPI“?

 

Swln Plane Average Veloclty/Vortlclty Fleld
for CAD 270, 1550 m, 15 in H9
Swirl Plate Blocker, 0% Blockage

 

20 m/s

I
—L
11’ Illlllllllllfilllll'

    
 

 

 

 

I
\l
ﬂllIFlllrllllTlllI ll I

1J_lll|llll1|llllllllllIllllll1l|lllllllllllllllll

12345678910

 

O

 

 

 

Figure 1.3: Velocities and vorticities of the ﬂow in the swirl plane, CAD 270, tumble
port blocker (90%)

that for t1
the swirl (

The (5‘
011-5 factor:
leading to
sient in st
geometry 1

Haschet
four-stroke
and load.
intensities 1
different en
motions lit-t
at idle ('ond
pattern at t

Lee and
pialf’d a Si};
stages of tilt

Khalighi
180“~Il‘}_;{rttt1 \
(tit-mm, it it
during early

dead center

 

drtfirninates tht

shrouded int ‘-

. . I
Irttshihar

at w
the. IIpsII't‘r

 

 

that for the in-cylinder flow during the intake and compression strokes, the center of
the swirl changed its location from one cycle to the next.

The cycle-to-cycle variations on the pre—combustion ﬂoware introduced by numer-
ous factors. These include ﬂuctuations of pressure in the intake and exhaust system,
leading to boundary conditions variations at the intake and exhaust valves and tran-
sient in speed and throttle position. It is believed that the engine speed and the
geometry of the intake system are the most important factors.

Hascher, Novak, et. a1. [14] measured the in-cylinder pre-combustion ﬂowin a
four-stroke SI engine with the same intake port geometry but variable stroke, speed,
and load. They found that the maximum mean ﬂow velocities and the turbulent
intensities inside the cylinder sealed with the engine speed, but the ﬂow patterns at
different engine speeds exhibit strong similarities. They also found that the tumbling
motions break down into two equally strong downward flows along the cylinder liner
at idle conditions. In another word, the throttle condition affects the in-cylinder ﬂow
pattern at the speciﬁc intake port geometry.

Lee and Yoo’s studies [15] showed that the different intake port conﬁgurations
played a signiﬁcant role in the generation of the initial tumbling motion in the early
stages of the intake stroke.

Khalighi [12] generated a well-deﬁned tumble motion in the cylinder by using
180-degree shrouds on both intake valves in a four-valve engine. With this inlet
conﬁguration, a small (less than half-cylinder-diameter in size) vortex is generated
during early induction and it becomes larger as the piston moves down. At bottom
dead center (BDC), the vortex becomes as large as the cylinder bore diameter and
dominates the in-cylinder flow. This suggests that the tumbling motion generated by
shrouded intake valves would continue into the compression stroke.

Urushihara, Murayama, et. a1. [16] used 13 types of swirl control valves installed

at the upstream of the intake port. to generate different combinations of swirl ﬂow

and 1111“}
that tntll
swirl ﬁlm.

mean \‘f‘l‘

Basvtl
oral t'hara
variations

Since 1‘!
truss-t nn ll)
were freqntl
BU}. The (l
the integrn
and normal
body rotati

For a lit

\‘Plot'itt' ,3

Then. the t.

is t‘falt‘ulr‘ttml

 

Or

 

and tumble flow in the cylinder. Their studies on these combinations of ﬂow showed
that tumble ﬂow generates turbulence in combustion chamber more effectively than
swirl ﬂow does. In addition, swirling motion reduces the cycle-to-cycle variation of
mean velocity in the combustion chamber, while tumbling motion tends to increase
it.

Based on the qualitative understanding on the in-cylinder ﬂow is important, sev—
eral characteristic quantitative parameters were introduced to reduce cycle-to-cycle
variations of the ﬂow in the cylinder.

Since rotational motion is a signiﬁcant characteristic of the cold ﬂow, tumble ratio,
cross—tumble (perpendicular to both tumble and swirl planes) ratio, and swirl ratio
were frequently used to quantify the pre-combustion ﬂow in the cylinder [9, 17, 18, 19,
20]. The deﬁnition of the tumble, cross-tumble and swirl ratios involves computing
the integral of the angular momentum about a speciﬁc axis over the entire volume
and normalizing it with the angular momentum of a similar volume of ﬂuid in solid
body rotation at crankshaft speed.

For a flow particle at f" (with respect to the origin) having velocity 27 and angular

velocity d3 , the angular momentum of the particle is
Ezrxazrx(axinzmnhyj—thzk (1.1)

Then, the total angular momentum of mass in the cylinder with respect to the origin

is calculated by the integral,

If : [ﬁdm 2 /(FX ”(7') dm : [(f’x (J) x 8))(1711 (1.2)

I? = /ffdm = [bridm + fill/30,771 + fhjcdm 2 HI; + Hy} + Hzfc (1.3)

wllt‘l") H.
arignlHr lzl
with ”My

If Ill“

mtnnt‘“I ”7
Hs

Similarlf-

 

\t’llt’ff) 1:1
Partit‘lt‘ “ll
crankshaft

Tliercft ii

the cross—t H

and the suit

Since [in

t ' '
l“) affect (

where H, is the total angular momentum with respect to the x-axis, Hy is the total
angular momentum with respect to the y-axis, and Hz the total angular momentum
with respect to the z-axis.

If the ﬂow is imagined to rotate as a solid at crankshaft speed, the total angular

momentum with respect to x-axis is

H53, = /hI dm 2 /(FX 17),,(1711 : tag/(77x 1‘“), dm 2 tag/In dm (1.4)
Similarly,

Hgy : wO/Iyy dm (1.5)

H52 2 (do/[22 (1771 (1.6)

where I“, Iyy, and 122 are three components of the momentum inertia of a ﬂow
particle with respect to the x-axis, y-axis, and z-axis, respectively. And tag is the
crankshaft angular velocity.

Therefore, according to the deﬁnition, the tumble ratio is

 

 

Hi f hm dm
TR 2 = —— 1.7
H53, wo flu dm ( )
the cross-tumble ratio is
Hz f 122 dm
, R z : __ 1.8
C HSz w0f122d7n' ( )
and the swirl ratio is
TR _ Hy = M (1.9)

— H53, woflyy dm
Since the tumbling, cross-tumbling and swirling motions coexist in the cylinder,
they affect each other. At the end of compression, the tumbling motion and cross-

tumbling motion break. The break of tumbling/cross-tumbling motion not only dis-

10

turllﬁ t
(“tirrt’lill

introdtl

where 1‘:
the mud
In Eq
turbulent
kinetic on
of these It
Althou
pre-umilm
ratio. Aet‘t
tumble or 5.:
located acct
[including t
Circular

the velocity

 

Af‘t‘urdin

 

turbs the swirl motion but also strengthens and stabilizes the swirl motion. To
correlate such complicated interactions, a model based on the heuristic reasoning was

introduced by Trigui, Kent, et. al. [9], which is

E = (TR2 + CR2 + SR?) — a(|TR||CR| + |TR||SR| + |SR||CR|) (1.10)

where E is a quantitative parameter characterizing the ﬂow in the cylinder, TR is
the tumble ratio, CR is the cross-tumble ratio, and SR the swirl ratio.

In Equation (1.10), the ﬁrst three quadratic terms have a favorable inﬂuence of the
turbulence, while the mixed terms represent an unfavorable inﬂuence (destruction of
kinetic energy through interaction). The constant 0 represents the relative inﬂuence
of these two effects.

Although the tumble ratio and swirl ratio were often used to characterize the
pre-combustion ﬂowin the cylinder, it is hard to obtain the accurate tumble or swirl
ratio. According to the deﬁnition of the tumble and swirl ratio, the calculation of the
tumble or swirl ratio depends on the ﬂow rotation center, which is very difﬁcult to be
located accurately. To overcome this disadvantage, J affri, et. a1. [19] used circulations
(including total, average, and root-mean-square) to describe the ﬂow in a cylinder.

Circulation F [21] is deﬁned as the line integral of the tangential component of

the velocity taken around a closed curve C in the ﬂow ﬁeld, i.e.,

r 2 ad; (1.11)

According to the deﬁnition, vorticity C is

5: 6 x z? (1.12)

11

The}

where .-l
SUHW’
process t.
Reuss [ll
at 5111110 (
the in-cyl
aWTaged l

the standa

1.2.2 (

Combustiol
Principal (‘1'
air. The)‘ e
an exotliert
is conventio
observed as
t'omlmstion.
characterize

Daw and
Variable of it.
applied ("haw
Stroke SI en;

\vrir '
dttdtmus Uf'
l

 

 

Therefore,

rzﬁa. a§=//A(vx U)-f1dA=//Af-f1d.~t (1.13)

where A is the area enclosed by the curve C and ft is the normal of A.

Since the cycle-to-cycle variation is superposition of a non-chaotic deterministic
process on a stochastic process, a statistical method is preferred to characterize it.
Reuss [11] introduced the probability density function (PDF) of the ﬂow velocity
at some characteristic points in the cylinder to characterize the cyclic variations of
the in-cylinder ﬂow. By using the PDF method, Reuss obtained both ensemble-
averaged (represented by the mean of velocities) and cycle-resolved (represented by

the standard deviation of velocities) quantities of the ﬂow at characteristic points.

1.2.2 Combustion analysis

Combustion is a necessary process for an internal combustion engine to generate work.
Principal components of an engine combustion system are the hydrocarbon fuel and
air. They are ﬁrst combined into a molecular aggregate, and then transformed by
an exothermic reaction to form products. The process of the exothermic reaction
is conventionally referred to as heat release. In an IC engine, the transformation is
observed as a measurable cylinder pressure rise manifesting the essential outcome of
combustion. Thus, cylinder pressure is frequently utilized as a direct parameter to
characterize the combustion and cycle-to-cycle variations in IC engines.

Daw and Kahl [22] employed the peak cylinder pressure in each power stroke as a
variable of interest to study cycle-to-cycle variations in a four-stroke SI engine. They
applied chaotic time series analysis (CTSA) method to the cylinder pressure in a four-
stroke SI engine fueled with methanol and iso-octane and found that cycle-to—cycle

variations of peak pressure exhibit some of the characteristic features of deterministic

12

 

chaos-
Ludw
sure curV'
their stutl
obtained l
{01‘ (”de‘.
the eyele-1
Basetl
istic proce
estalilisliet
ries to clia
a four—stro

The I)!“

 

t-liaractel'ie
as. rate of l
record.

The niil
the percent
pressure t'li.
motion and
the cylintlel'
established.
the value of
P‘JNVE‘nt pres

of this result

chaos.

Ludwig, Leonhardt, et. al. [23] selected the gravity center of the difference pres-
sure curve as a characteristic parameter to study combustion in a diesel engine. In
their studies, a difference pressure curve containing information of the combustion is
obtained by subtracting the pressure samples of a ﬁring motor from the non-ﬁring mo-
tor case. The gravity center of the difference pressure curve was used to characterize
the cycle-to-cycle variations of the combustion in the engine.

Based on the fact that cycle-to-cycle variations are superposition of a determin-
istic process on a stochastic process, Roberts, Peyton Jones, and Landsborough [24]
established a stochastic process model for the entire ensemble of pressure-time histo-
ries to characterize the cycle-to-cycle variation throughout the combustion period in
a four-stroke SI engine.

The pressure in the cylinder is important not only for itself as a quantitative
characteristic parameter, but also because some combustion related parameters, such
as rate of heat release and rate of mass burned, can be derived from the pressure
record.

The milestone was set by Rassweiler and Withrow [25]. After failing to correlate
the percent mass burned with the measured pressure data, they divided the measured
pressure change in a speciﬁc interval into two parts: pressure change due to piston
motion and pressure change due to combustion. In this way, a relationship between
the cylinder pressure rise during the combustion and the fraction of mass burned was
established. They concluded that throughout the entire period of the combustion,
the value of percent mass burned at any given crank angle is very nearly equal to the
percent pressure rise due to combustion at the same crank angle. The signiﬁcance
of this result is that information about the fraction of mass of charge burned at any

instant during the combustion may be obtained by ﬁnding the percent of the pressure

13

rise due I

where .11
total ma>
reduced ]
t'onihust it

With 1|
therniodt:
to the ('1‘]=

The 11; =
from inlet

lor an inciu.

where th.
dime b." th.
internal 0“,,

lithe 1%),

pressure. er

 

rise due to combustion using measured pressure data, i.e.,

ill’lz—ILR' (114)
A1 B-B '

wllere Mb is the mass of inﬂamed section of the charge at the given time, M is the
total mass of charge, H is the measured pressure at the time of ignition, P is the

red uced pressure at. the given time, and Pf the reduced pressure at the end of the

combustion.
With the cylinder pressure data, a heat release model based on the ﬁrst law of

thermodynamics was proposed by Homsy and Atreya [26] for the study of heat transfer

to the cylinder wall during the combustion.
The ﬁrst law equation for the in-cylinder mass in a closed system, which starts

from inlet valve close (IVC) and ends at exhaust valve open (EVC), can be written

for an incremental crank angle interval as

thr : dW + dUS + dQu, (1.15)

where thr is the gross heat energy released during the combustion, dW is the work

done by the piston and expressed as (ll-V = p - dV , dUS is the change in sensible

internal energy, and de the heat transfer to cylinder wall.

If the gas in the cylinder is assumed the ideal gas, three equations relating cylinder

pressure, cylinder volume, and gas temperature are obtained.

In - CU - (1T 2 dUg (1.16)
(1(p- l") ..
—— = (IT 1.1

m - R ( I)
(in

14

 

“her? I”
at const 1‘
By “I

Thpff‘l
from Ill" l
gas and Il

SiniiléiI

 

 

for direct-i

PM 111”
aeterizing
with with
However. I

sure is not

re. ignitit;

burn rat e I

flame burn

to tilt‘iscrilie

t'onibust it it
The cyl

Inflepenr leIi

little \‘ariai
[rttslilli

(it"ft‘l

“Perl ff

1“ The t‘vlii
’. H

where m is the mass in the cylinder, T is the gas temperature, Cu is the speciﬁc heat
at constant volume, R is the gas constant, and '7 the ratio of speciﬁc heats.

By applying the above ideal gas relationships to the ﬁrst law equation (1.15), the
heat transfer model is reduced to

, 1
de = thr — —3— -p-dV — —— - V - (11) (1.19)
7 — 1 7 —1

Therefore, the heat transfer to the wall during the combustion can be calculated
from the pressure data based on the assumptions that gas in the cylinder is the ideal
gas and that there is no blow-by or valve leakage.

Similar heat transfer models were described by Heywood [1] and Brunt, et. al. [27]
for direct—injection engines.

For most cases, the cylinder pressure is a preferable quantitative parameter char-
acterizing the combustion process, since it is easily measured and when combined
with with piston position is the macroscopic manifestation of the four stroke cycle.
However, the combustion in an IC engine is such a complex process that cylinder pres-
sure is not able to characterize it completely. The combustion-related parameters,
i.e., ignition delay, crank angle location at 50% mass fraction burned (MFB), early
burn rate (crank angle duration corresponding to 0-10% MFB), and fully developed
ﬂame burn rate (crank angle duration corresponding to 10-90% MFB), are of help
to describe and have been implemented to provide more detailed information about
combustion process in an IC engine.

The cylinder pressure and the above combustion-related parameters could be used
independently or simultaneously to characterize the combustion process and cycle-to-
cycle variations on the combustion in an IC engine.

Urushihara, Murayama, et. al. [28] used early burn rate (040% MP B) and fully
developed ﬂame burn rate ( 10-90% MFB) to determine the inﬂuence of the turbulence

in the cylinder on the combustion process. They found that the fully developed ﬂame

burn rat
that incl"
John!
on the co
burn rate
comlmst i
comlnisti
Steve
effective
study tlit
They {”11
work out
rE’tlnce (:5
Dai. f.
0f ('B't'le-t
rallt‘), in-
rate. and
111) El (‘1)11
ignition (
Dt‘sm
adaDteti

next 80,,

1.2.3

l .
._ [111]] th"
Uta » .

“F 111‘“

Itis}

burn rate is directly proportional to the early burn rate. In addition, they observed
that increasing turbulence intensity would shorten the combustion duration.

Johansson and Olsson [29] studied the effects of the shape of combustion chamber
on the combustion process by early burn rate (0-10% MF B) and fully developed ﬂame
burn rate (IO-90% MF B). They also found that fully developed ﬂame burn rate of the
combustion has a strong correlation to the average turbulence in the cylinder during
combustion.

Stevens, Shayler and Ma [30] calculated cross-correlation of gross indicated mean
effective pressure (IMEP) and crank angle location at 50% mass fraction burned to
study the effect of the spark timing and fuelling level on the cycle-to-cycle variations.
They found that modifying A/ F ratio or spark timing has a signiﬁcant effect on the
work output of that cycle, and thereby can be used as an eﬂective control variable to
reduce cycle-to-cycle variations.

Dai, Trigui, and Lu [3] identiﬁed seven physical parameters to represent the sources
of cycle-to—cycle variations in a SI engine, which are engine speed, engine load, A/ F
ratio, in-cylinder residual mass fraction, early burn rate, fully developed ﬂame burn
rate, and crank angle location at 50% MF B. By correlating these parameters, they set
up a complex nonlinear model to characterize the cycle-to-cycle variations in spark
ignition engines.

Despite efforts of nearly 100 years, no satisfactory method have been universally
adapted to quantify and control cycle-to—cycle variabilities in piston engines. In the

next section, we begin to outline a strategy with this problem.

1.2.3 Cycle-to—cycle variation reduction

Upon the understanding of the pre-combustion ﬂow and combustion in an IC engine,
many methods have been presented to reduce cycle-to-cycle variation.

It is believed that the main source of cycle—to-cycle variation is the turbulent

16

nature
was to
at the f
The
der hah
35]. shrt.
how to st
motion 1'
kernel (‘1‘)
and prod
Ohsn:
uniform -3
optiniizati
wall is uni.
obtain a n
C'oiiiliu

ratio in the

 

that when
lence gener
the charge

The alﬂi
ing the eye;
S}'L\i‘tertl.\j Ht)"

th

e engine
information

he '
lIttrotluct

 

nature of charge motion at the time of ignition [31, 32, 33, 34]. Therefore, most effort
was to obtain the consistent ﬂow pattern and stable A / F ratio around the spark plug
at the end of compression.

The rotational motion (tumble, cross-tumble and swirl) of the charge in the cylin-
der has been investigated widely. Swirl control valves [28], port blockers [19, 20, 17,
35], shrouded intake valves [12] and masked cylinder head [9] were used to investigate
how to stabilize the ﬂow at the end of the compression. And it was found that swirling
motion can generate a more stabilized ﬂow field at the time of ignition, cause ﬂame
kernel convection in the tangential direction, especially with an off-center spark plug,
and produce high levels of small-scale turbulence in the cylinder.

Ohsuga, Yamguchi, et. al. [36] studied three fuel-supply systems and achieved a
uniform A/ F ratio in the cylinder by optimizing the fuel supply system. With the
optimization of the fuel-supply system, fuel vapor distribution around the cylinder
wall is uniform and this uniform fuel vapor is transported by the tumbling motion to
obtain a uniform A/ F ratio around the spark plug at the time of ignition.

Combustion chamber geometry, which has strong inﬂuences on the ﬂow and A / F
ratio in the cylinder, was extensively studied by Johansson, et. al. [29, 37]. It is found
that when the standard disc-shaped combustion chamber was replaced with a turbu-
lence generating geometry, such as cross combustion chamber, the inhomogeneity of
the charge in the cylinder became very low.

The above ﬂow control techniques have been successful in a limited manner reduc-
ing the cycle-to-cycle variation in work in a SI engine. However, they are open-loop
systems not able to implement the real-time control on the combustion process in
the engine. Other techniques, having the ability to extract real-time characteristic
information for each cycle and effectively reduce the cycle-to-cycle variations, have to
be introduced.

Two researches suggested that the fundamental source of cycle-to—cycle variations

17

is Illf’ H

on this ‘
aetiW’l."
the fnel -‘
ititrtitliit‘t

In a 1'
are the St:
a gt‘ivet‘ttt .
strategiw
actuators
reacting [it

is a rnicrt >-

 

to niodtila

The scheti

is the non-linear nature of the chemical reactions in combustion [33, 38]. Based
on this viewpoint and the experimental evidence that combustion instability can be
actively controlled by coupling pressure variation in the combustion chamber with
the fuel supply system [45], the concept of controlled combustion engines (CCE) was
introduced [39, 42, 43, 44].

In a controlled combustion engine, principal elements of the engine control system
are the same as those in general feedback control systems, i.e., sensors, actuators, and
a governor. In this application, the sensor measures cylinder pressure. In other control
strategies [39], the emission sensors (e.g. oxygen concentration sensor) are used. The
actuators for the CCE could be fuel jet injectors and jet igniters producing turbulent
reacting jet plumes where combustion takes place away from the walls. The governor
is a micro-electronic processor incorporating a sufﬁciently fast data reduction facility
to modulate the execution of the exothermic process in real time of the engine cycle.

The schematic of a controlled combustion engine is shown in Figure 1.4.

 

 

    

 

Actuators T Output

     
 
 

 

Sensors

 
 
 

 

  

Governor

Figure 1.4: The schematic of a controlled combustion engine

A prototype [43, 44] of a controlled combustion engine is shown in Figure 1.5.
In this prototype, the electronic control modulator generates the control information
from cylinder pressure, which is measured by pressure sensors. The feedback control
information is then sent to the air-blast. atomizer and ﬂame jet. generator to control

the combustion in the cylinder.

18

 

Figure 1.5.

ornizer 2

modtila t 1)
terms of z-

1.3 I

There cm
which are
contrt'il iii.
to have a1
“01 able t
In this (lib

Variations

1 ,
Dingkprs U1

 

 

 

 

 

 

  

 

 

 

 

tr

Figure 1.5: Prototype of a controlled combustion engine system: 1 - the air-blast at-
omizer; 2 - the ﬂame jet generator; 3 - turbulence jet plumes; 4 - the electronic control
modulator; and 5 - the pressure transducer and shaft decoder records expressed in
terms of an indicator diagram.

 

 

 

 

1.3 Motivation and objectives

There currently exist two ways to reduce cycle-to-cycle variations in an IC engine,
which are pre—combustion ﬂow control and combustion control. Pre—combustion ﬂow
control means that one changes the ﬂow ﬁeld characteristics in such a manner so as
to have an inﬂuence on the subsequent combustion events. It is an open-loop system
not able to implement real-time control on cycle-to-cycle variations in the cylinder.
In this dissertation, a statistical method is improved to quantify the cycle-to-cycle
variations of the pre—combustion ﬂow ﬁeld and the inﬂuence of 3 different port plate
blockers on the ﬂow ﬁeld is investigated.

Combustion control means that based on analysis of the combustion process one
alters some type of input actuator to change the nature of the subsequent combustion
event. The combustion control, realized by controlled combustion engines (CCE), is a

close-loop system having a perspective to reduce cycle-to-cycle variations effectively.

19

 

Thp ("(tll.
(Ft-104‘ "
[llt' [mill
charL’,P ('
(-(')1111'Hll‘
taut [W
the ('Yt'l
ln a
a key it
in an I(
the nip)
cycle.
nature
sensors.
Tilt“ (1111
cont rt )1
in a cor
inform;-
ln 1'
int I‘t‘itlll
(Tile v;
(‘Valiiat
kph“ l
fluamjf
taint-«1
(hintillif

flit.J ('\-(

The combustion control has the advantage over pre-combustion ﬂow control to reduce
cycle-to—cycle variations in an IC engine as this method can provide an input based on
the nature of the previous event. In addition, with the emerging of the homogeneous
charge compression ignition (HCCI) engine in which the combustion process can be
controlled by adjusting the initial temperature and species concentrations of reac-
tant [40] [41], combustion control becomes a practical technique to effectively reduce
the cycle-to-cycle variations in the engine.

In a controlled combustion engine, the data reduction algorithm in the governor is
a key to implementing the correct and accurate real-time control on the combustion
in an IC engine. There are two requirements for the data reduction algorithm. First,
the input data should be measured conveniently and accurately for each operating
cycle. The cylinder pressure is an ideal choice as input because of its descriptive
nature with respect to the desired output and the availability of reliable pressure
sensors. Second, the algorithm for data reduction should not be complicated so that
the control information can be quickly generated by a micro-electronic combustion
control unit (CCU). Current data reduction algorithms are not readily implemented
in a control algorithm [42]. Little effort has been expanded to date to obtain control
information from the cylinder pressure.

In this dissertation, a new data-reduction method based on the cylinder pressure is
introduced to pave the way for controlling the combustion and reducing the cycle-to-
cycle variation in an IC engine. The pressure diagnostics is an inverse process, which
evaluates the mechanism of the combustion in the cylinder from its measured output.
Upon pressure diagnostics, the development of the dynamic stage of combustion is
quantiﬁed and the effectiveness of combustion during the exothermic process is ob-
tained. Therefore, a concept for the controlled combustion engine, which controls the
dynamic stage of combustion to improve the effectiveness of combustion and reduce

the cycle-to-cycle variations on combustion, is present.

20

 

 

Chel

q

lg!

Pre-

 

2.1 i

The pre—t
engine 3.3
have diff.
The (-y(-1
TU l)? I‘t'r
(’Stltn‘dtt’
the 3211111
"lf‘t‘mle. '
Variabih
functitm
C’h‘dl‘ar-n:

In t1J

+1..
1.19 tllrll

UT chow“
ittstmnd
Sdzlll-llf‘g

Elie ,

d “'f.) It ,(

;\ -..
, (‘

Chapter 2

Pre-combustion ﬂow analysis

2. 1 Introduction

The pre—combustion ﬂow in the engine cylinder is affected by many factors including
engine geometry, speed, valve timing, and valve lift. From cycle to cycle, these factors
have different inﬂuences on the in-cylinder ﬂow, and thus a cyclic variation is created.
The cycle-to-cycle variation of the pre-combustion ﬂow inside the cylinder is known
to be responsible for various aspects of the combustion characteristics. It has been
estimated that there would be a 10% increase in power output of premix engines for
the same fuel consumption if cyclic variability could be eliminated [5] . In the last
decade, various methods were developed to characterize in-cylinder ﬂow and the cyclic
variability of this flow. Speciﬁcally, Reuss [11] introduced the probability density
function (PDF) of the ﬂow velocity at some characteristic points in the cylinder to
characterize the cyclic variations of the in-cylinder ﬂow.

In this chapter, an improved PDF method is introduced to quantify the effects of
the tumble and swirl port blockers on cyclic variability of in-cylinder ﬂow. In stead
of choosing the velocities at a local point as samples, the author employ normalized
instantaneous circulation of the ﬂow on a tumble or swirl plane. The PDFS of such
samples are generated to characterize the cycle-to—cycle variations. Besides PDFS,
the averaged turbulent kinetic energy (TKE) of the flow on the tumble or swirl plane

is calculated and compared to the PDF results.

21

 

2.2

.\lule('ul.

 

ine passi
Figure 12
IP-Sfrul'ir
as well a~

and the I

 

insert. ii
lll>l(i(' (if ‘
intake rm
to accept

Three
“0 Dun l.
and a sw
three (as.
The two 1
O” The fit.
“‘iliC‘l] [h‘

“'85 run a

2.3 I

the ﬂ‘ﬁv 0
LUV ‘ ~ ‘

J“ 13 r( ’I‘

Equatihll

\l‘

2.2 Experimental setup

Molecular Tagging Velocimetry (MTV), described in Section 1.2.1, was used to exam-
ine passive control of the ﬂow to a 3.5-liter DaimlerChrysler engine, which is shown in
Figure 2.1. The head is mounted on top of a single cylinder Hatz engine that has been
re—stroked to 81 mm to match the crankshaft geometry of the DaimlerChrysler engine
as well as use the original connecting rod. Located between the DaimlerChrysler head
and the Hatz reciprocating assembly are the quartz cylinder and piston with a quartz
insert. Both the cylinder and piston are designed to provide optical access to the
inside of the engine cylinder while retaining the original engine bore of 96 mm. The
intake runner of the standard DaimlerChrysler intake manifold is used and modiﬁed
to accept the port blockers for studying passive flow control.

Three different intake port conﬁgurations were considered for these experiments:
no port blocker or open port, a tumble port blocker with 70% blockage (Figure 2.2)
and a swirl port blocker with 90% blockage (Figure 2.3). Data was acquired for all
three cases at the tumble plane and a swirl plane for crank angles 270 ° and 300 ° .
The two speciﬁc crank angles are chosen for studies on the inﬂuence of port blockers
on the ﬂow ﬁeld near the end of compression. The latter crank angle is the limit at
which there is still optical access to the tumble plane flow. In all cases, the engine

was run at 1550 rpm and throttled to 15 inches Hg.

2.3 Normalized circulation

Shown in Figure 1.2 and 1.3 are typical rotational motions (tumble and swirl) of
the ﬂow on the tumble and swirl planes inside the cylinder, respectively. Since the
flow is rotational, the circulation of the ﬂow on the tumble or swirl plane, deﬁned by
Equation (1.11) and (1.13), is used to characterize the motion of the flow.

When the flow on the tumble or swirl plane was studied at different CADs. the

22

 

Figure 2.1: 3.5-liter DaimlerChrysler engine

23

 

Figure 2.2: Tumble port blocker

 

Figure 2.3: Swirl port blocker

24

 

  
  

area of

“liere .4

2.4

The pa
Act t‘l‘i [t
(.iiSMryt ;
Ilit" VF)
FINN“;
\‘f‘ltu-‘l
Ifi
IIIII)()
(‘ulat
()f 114'
57 am

and

(em-(5,]

[1\ \Y

area of each plane is not the same. To make the results comparable, the circulations

of ﬂow on different planes have to be normalized by the area of the plane, which is

 

 

1 1 -
13,, = ’ fa ds": ff q-MA (2.1)
147‘ (s‘ 14’1“ fl

where AT is the studied area of the tumble or swirl plane.

2.4 PDF method

The probability density function (PDF) of a local ﬂow velocity is introduced to char-
acterize the cyclic variations of the ﬂow inside the cylinder by Reuss [11]. In this
dissertation, the PDFs of the normalized circulation over a tumble or swirl plane in
the cylinder are generated. This method has an advantage over Reuss’s method, since
circulation over a plane is a better parameter characterizing the ﬂow ﬁeld than local
velocities [17].

Figure 2.4 shows a PDF of the normalized circulation on the tumble plane. Three
important quantities are calculated based on the PDF: mean value of normalized cir-
culations, the range of change of normalized circulations, and the standard deviation
of normalized circulations. In this work, a Gaussian curve with the same mean and
standard deviation was superimposed on the measured probability density function
and used to display the experimental results.

Suppose there are 1le sample cycles. For each cycle, the normalized circulation
over a tumble or swirl plane PM is computed by Equation (1.13). The mean of the

normalized circulation is the ensemble-averaged NC deﬁned by Equation (2.2).

M
izl FAN

T :
111

(2.2)

The range of change of normalized circulations, which represents the range of

25

 

Probability

FIRM;
131x

(You

 

0.16
---"" Tumble Plate (RG = 670.6, Mean = -1 274.6, STDEV = 127.1)
0.14-
0.12-

0.10-

 

0.08-

Probability

0.06; / \
0.04-

0.02- I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.00 .

4300-
4200
-1 100‘

Circulation/Area (l/s)

Figure 2.4: The PDF for the circulation over a unit area on the tumble plane at CAD
180, tumble plate blocker.

cyclic variation of the ﬂow inside the cylinder, is formulated as

RC = n1ax{F,\r,} — min{I"N,-} (2.3)

The standard deviation of normalized circulations is

 

M 2: FNi2 — (Z FNi)2

M(M - 1) (2'4)

 

STDEV = \J

The mean value of normalized circulations gives the ensemble-averaged informa-
tion of the ﬂow inside the cylinder, generally characterizing the rotational motion

inside the cylinder. The range of change of normalized circulations could quantify

26

 

the eye

 

range it
rant (in
data ca
ryrlir \'
(firtiuln
inately
rirrula

shown

2.5

2.5.

The

mali
that
Shut
(ST
the

fitil

(ﬁsl7

the cycle-to-cycle variability of the flow inside the cylinder. A higher value of the
range indicates more cyclic variations. However, the range is not statistically signiﬁ-
cant parameter to quantify the cyclic variations because extraordinary experimental
data can contaminate the results. A more representative quantity characterizing the
cyclic variation of the ﬂow inside the cylinder is the standard deviation of normalized
circulations. In general, the range of change of the normalized circulation is approxi-
mately 6 times equal to the standard deviation, which indicates that the normalized
circulation of the ﬂow on a tumble or swirl plane is normally distributed. This is

shown clearly by the shape of the PDF in Figure 2.4.

2.5 Cyclic variations of the ﬂow with different port
blockers

2.5. 1 Tumble plane

The results shown in Figure 2.5 show that the standard deviations (STDEV) of nor-
malized circulation (NC) increases when port blockers are applied, which indicates
that cycle-to-cycle variations of the flow are strengthened by port blockers. It is also
shown that the tumble port blocker (STDEV = 112.123“) and swirl port blocker
(STDEV = 117.08“) have the same effect on strengthening the cyclic variations of
the ﬂow, though tumble port blocker has stronger effect on strengthening the rota-
tional motion of the ﬂow (lMEANl = 1354.23‘1 for the tumble port blocker, while
IMEANI = 609.73‘1 for the swirl port blocker).

To further evaluate this conclusion, the turbulent kinetic energy (TKE) [81][82] is
calculated for the same ﬂow ﬁeld. The ﬂow in the cylinder is known to be turbulent
and thus the turbulent kinetic energy is a eligible parameter characterizing cycle-
to-cycle variations of the flow. Higher turbulent kinetic energy indicates stronger
turbulence and more cyclic variations.

Similar to normalizing the circulation, the averaged TKE over the studied plane

27

 

 

Figur
diffen
‘5 ('Hlt
are I‘-

TliE

‘ti‘lx‘ur‘

0“” ai
.‘p‘( .3-
i} i 0]) (4).;
fund)

@-

0.16

 

 

 

 

; ..—--— TP Blocker (RG = 651.0; MEAN: -13542; STDEV = 112.12)
0 14a -— " SP Blocker (RG = 658.6; MEAN = -6097; STDEV = 117.0)
d ------ No Blocker (R6 = 429.4; MEAN = -2455; STDEV = 70.3)
0.12-
% 0.10- A
E .
to 0.08— / \
‘3 \
9 1 /
‘L 0.06— / \
0.04— / \ ,-
. / \"l
0.02- / A
' / \
0,00o lléllléIIIéITl‘r-‘ﬁrrj IﬁIIII:IIIIITTT-$-lllo
a e s a e e § § a, a

Circulation/Area (1/s)

Figure 2.5: The PDF for the circulation over a unit area. on the tumble plane with
different port blockers at CAD 270.

is calculated by normalizing the TKE by the area of the studied plane. Suppose there
are P vectors on the plane, and the local TKE at point z' is E,, then the averaged
TKE is

1 N
EN : — E Eifli (2.5)
AT i=1

where AT is the total area of the studied plane and A,- the area containing point 2'.
Figure 2.6 shows the comparison of the cyclic variability characterized by the
STDEV of normalized circulation and by the averaged TKE. It is shown that results
obtained with both methods are consistent, i.e., port blockers strengthen the cycle-
to-cycle variations of the ﬂow. However, the averaged TKE of ﬂow with tumble port
blocker is about 1.5 times greater than that with swirl port blocker, indicating the
tumble port blocker has stronger inﬂuence on the cyclic variations of the ﬂow.

Similar results and conclusions are found for the tumble plane at 300 , as shown

28

ﬁt I“. ()1

in PM

2.53

3111 m
1315111
The 1
l)l()(
Ch i1

hi

 

 

 

 

 

 

 

140 7
l-I—PDF +T_K@

120 - - 6
100 7" )— 5 NA
3
A E
m L . v
3 8° ‘ t 4 u,
a P5
D .0— l— u
5 60 1 3 g
S
3
40 e- 1» 2 <

20 «l- ‘_1

0 0

Tumble Open Swirl

Figure 2.6: Inﬂuences of different port blockers on the cycle-to-cycle variations of the
ﬂow on the tumble plane at CAD 270.

in Figure 2.7 and 2.8.

2.5.2 Swirl plane

Shown in Figure 2.9 are the PDFs of normalized circulation of the ﬂow on the swirl
plane with different port blockers. It is shown that the swirl plate blocker strengthens
the rotational motion on the swirl plane (|MEAN| = 865.7 3“), while the tumble plate
blocker slightly weakens it (|MEAN| = 18.53”). In addition, both port blockers
change the rotational direction of the ﬂow from the clockwise to counter-clockwise.
It is also indicated by the STDEV that both port blockers has the same effects on
strengthening cycle-to-cycle variations of the ﬂow (STDEV = 116.83“1 for the tumble
port blocker and STDEV : 113.45“1 for the swirl port blocker). Figure 2.10 shown
the comparison of the cyclic variability characterized by the STDEV of normalized
circulation and by the averaged TKE. It is shown that results obtained by both
methods are consistent.

Similar results and conclusions are found for the ﬂow on the swirl plane at 300 i

29

HST-Jr,

It)“. (’1

 

 

 

 

 

0.16
; / TP Blocker (R6 = 1061.6; MEAN = -1536.5; STDEV = 179.1)
014_ .. «r SP Blocker (RC3 = 1255.3; MEAN = -822.3; STDEV = 181.2)
. ------ No Blocker (R6 = 659.6; MEAN = -3074; STDEV = 117.2)
0.12-
1
0.10—
3*
IE 1 / \ 1
8 008— / \ '
0 ° '0'
2 1 \ .
0' .’
0.06- \ .-
\ .-"
0.04— \:'
0.02- ;"\ ‘
, \\
0,00 ﬂ III III III’I—II III III rI'T'III II.—I_r-IIT
oéééééééégééo
55555555555 5
Circulation/Area (1/s)

Figure 2.7: The PDF for the circulation over a. unit area on the tumble plane with
different port blockers at CAD 300.

 

 

 

 

 

200 7
p671 E
180 __ l-I— + K?
~- 6
160 ._
14o -- ‘7 5 «f;
g 120 1- ﬂ 4 g
> 1001- 5
U] D
«e o
a 80 1- 3 g»
0
60 -- -~ 2 5
40 1-
+ 1
20 ‘-
0 0
Tumble Open Swirl

Figure 2.8: Inﬂuences of different port blockers on the cycle-to—cycle variations of the
ﬂow on the tumble plane at CAD 300.

30

 

Figm

diff“!

Fir;

SI}

4 .i 1‘ J ‘1‘.

 

‘ —--"" TP Blocker (RG = 727.9; MEAN = 18.5; STDEV = 116.8)
_ - --" SP Blocker (RG = 727.2; MEAN = 865.7; STDEV = 113.4)
‘ ----- No Blocker (RG = 366.3; MEAN = -62.9; STDEV = 64.9)

Probability

 

 

 

§ §

Circulation/Area (1/s)

 

Figure 2.9: The PDF for the circulation over a unit area on the swirl plane with
different port blockers at CAD 270.

 

 

 

 

 

140 8
FEE—347E]

12o ~~ " 7

4- 6
100 -- N;
.. 5 "F
A E
5‘”. 8° .. .1:
1— 5° ‘* g,
(D ... 3 8
9
40 .. <

1- 2

20 ‘” ._ 1

0 0

Tumble Open Swirl

Figure 2.10: Inﬂuence of different port blockers on the cycle-to—cycle variations of the
ﬂow on the swirl plane at CAD 270.

31

 

Flg’llr

dlflt‘l‘t

PXt‘eI

alloy)

 

0.16
l .-—-' TP Blocker (RG = 1261.7; MEAN = 0.2; STDEV = 204.7)

0 14- 7' " SP Blocker (RG = 652.2; MEAN = 532.4; STDEV = 117.1 )
. ..... NO BlOCkef (RG = 3680; MEAN : -233, STDEV : 632)

0.125

0.10-

-l

0.08~

q

0.06-

Probability

0.04-

0.02-

 

 

0.00 1

 

 

Circulation/Area (1/s)

Figure 2.11: The PDF for the circulation over a unit area on the swirl plane with
different port blockers at CAD 300.

except that the tumble port blocker has stronger inﬂuence on the cycle-torycle vari-

ations of the ﬂow than swirl port blocker, which are shown in Figure 2.11 and 2.12.

2.6 The inﬂuence of the shape of port blockers

The inﬂuence of the shape of port blocker is also studied in the dissertation. Shown in
Figure 2.13 and 2.14 are tumble and swirl port blockers with different shape from those
shown in Figure 2.2 and 2.3. In the context, port blockers shown in Figure 2.2 and
2.3 are called blockers A, while port blockers shown in Figure 2.13 and 2.14 are called
blockers B. It is shown in Figure 2.15 2.18 that the shape of the port blocker has
the strong inﬂuence on the ﬂow. Both tumble and swirl port blockers B have weaker
inﬂuence on the rotational motion of the ﬂow on the tumble plane than blockers

A. However, blockers B and blockers A have a similar inﬂuence on cyclic variations

32

Flgur
the {1

Hi th
him-1,
him)
in-q-
111111)
the i

t‘fficj

(if '1‘

 

 

 

240 16
@790? 17k?)
~~ 14
200 ~-
r- 12
160 J- :5
E ""10 g
5 LL!
L>u 120 4- -- 8 PE
0 3
l- a:
a) 4- 6
E
80 7- g
<
.p 4
40 «-
4— 2
0 0

 

 

Tumble Open Swirl

Figure 2.12: Inﬂuences of different port blockers on the cycle-to-cycle variations of
the ﬂow on the swirl plane at CAD 300.

of the ﬂow on the tumble plane. For the ﬂow on the swirl plane, the inﬂuences of
blockers A and blockers B are similar. It is apparent that geometric nature of port
blockers have a signiﬁcant inﬂuence on the rotational motion and cyclic variations of
in-cylinder ﬂow. Experiment has shown that the level of variation produced by port
blockers A had a strong inﬂuence on the combustion rate and engine eﬂiciency, while
the inﬂuence of blockers B was ineffective in changing the combustion rate or engine
efﬁciency.

This leads us to believe that in order to further evaluate the nature of the inﬂuence
of in-cylinder ﬂow motion on combustion, we must develop a realistic measure of rate

of conversion of reactants to products. This development is discussed in next chapters.

33

 

Figure 2.13: Tumble port blocker B

 

Figure 2.14: Swirl port blocker B

34

 

Figut
UH ti]

1’} [l

0.16

 

 

 

 

 

/ TP Blocker (RG=513.9; MEANa-209.7; STDEV-98.2)
0 my .. —— SP Blocker (RG=522.3; MEAN=-353.4; STDEV=94.2)
' ----- N0 Blocker (RG=594.7; MEAN=-177.0; STDEV-104.8)
0.125
4 Q
0.10—
E . :' i.
F3 :' '.
n 0.08— .- z.
9
a.
0.06—
0.04— /
. /
0.02~ /
/ .
o 00 / "
' 0 cl: '6' 5*f‘a’ﬁa”‘€"5”'a HEEFIO
O O O O C O C O C O
29 :2 :5 a! :2 “2 <9 5 e N
Circulation/Area (1/s)

Figure 2.15: Inﬂuences of port blockers B on the cycle-to-cycle variations of the ﬂow
on the tumble plane at CAD 270.

 

 

 

 

 

0.13
4 / re Blocker (RG=978.6; MEAN=-138.5; STDEV=177.2)
, , se Blocker (RG=1493.1; MEAN=-504.0; STDEV=253.8)
0-14‘ ------ No Blocker (RG=912.9; MEAN=-442.3; STDEV=152.8)
0.121
0.10—
(“-3 :' '1
n 0.034 ..
9 t
D.
0.06—
t
0.04—
0.02~
0.000..-$.--$ .6“ a) - g -.
O O O O O
5 :2 z 9: e
Circulation/Area (1/s)

Figure 2.16: Inﬂuences of port blockers B on the cycle-to-cycle variations of the ﬂow
on the tumble plane at CAD 300.

35

Flgur
en ti)

0.16

 

 

 

 

 

.———— TP Blocker (ae=534.4; MEAN=31.4; STDEV=90.0)
0,14- ,, SP Blocker (RG=659.9; MEAN=429.4; STDEV=105.5)
------ No Blocker (RG=692.2; MEAN=-24.5; STDEV=103.2)
0.12“
0.10“
g: .
*3 1
n 0.03
e
D.
0.06“
0.04“
0.024
\.
0‘00 1IV I' l Ylv erﬁrl YI'flr
O O O O O o O O O O
O O O o o O O O o

Circulation/Area (1/5)

Figure 2.17: Inﬂuences of port blockers B on the cycle-to-cycle variations of the ﬂow
on the swirl plane at CAD 270.

 

 

 

 

 

0.16
/ TP Blocker (RG=672.9; MEAN=46.0; STDEV=113.7)
0,4- ,’ SP Blocker(RG=575.0;MEAN=526.8;STDEV=100.7)
----- No Blocker (RG=554.6; MEAN=-3.8; STDEV=92.5)
0.12~
0.103
5“
E
.o 0.08—
9 .
m
0.06—
0.04—
J
0.02~
\\
0.0011 rmrt“tr"t"'r'rr"t"
O O O O O O O O O
O O O O O O O O
CO v 0.] N v CO (D e
Circulation/Area (1 /s)

Figure 2.18: Inﬂuences of port blockers B on the cycle-to-cycle variations of the ﬂow
on the swirl plane at CAD 300.

36

Chapter 3

Dynamic stage of combustion in an
IC engine

3. 1 Introduction

The sole purpose of combustion in a piston engine is to generate pressure in order to
push the piston and produce work. In a work-production cycle, the air/fuel mixture
is ﬁrst induced into the cylinder, then experiences the polytropic compression from
the piston. The compression increases the pressure and temperature in the cylinder,
and a heat-release chemical reaction is activated by a spark or other means. Finally,
gases in the cylinder experience an expansion process and push the piston to produce
work.

The cylinder pressure is the most signiﬁcant parameter characterizing the engine
operation. The processes of compression, chemical reaction, and expansion during an
engine operation cycle are all recorded by the cylinder pressure.

Because of the existence of cycle-to-cycle variations in chemical reaction rates, the
cylinder pressure records are different from cycle to cycle. The pressure records for ten
cycles in a single-cylinder spark-ignition engine are shown in Figure 3.1. It is shown
in the ﬁgure that cycle-to-cycle variations of the pressure records are macroscopic
manifestation of the exothermic chemical reaction process. Therefore, studies on the
pressure records during the chemical reaction process in a piston engine are of help to

reduce the cycle-to—cycle variations in the engine. In this chapter, the dynamic stage

37

 

0f ct

('}'('l1

Figu
Lq)(kr;

Hm

3.2

ill 1)
Elite
1111).}

;)&[)I

“I l M

of combustion in a SI engine is deﬁned and analyzed to characterize and control the

cycle-to-cycle variations in the combustion.

 

 

 

 

w '1'— T I f I
35'- ..
30’ .i

g 25* d

a

a?

5 20- -

5‘

5 1.1L 1
10b -1
5t- ..
o L J L l l
-150 -1m --50 0 50 It!) ,150

Figure 31: Pressure records for ten cycles in single-cylinder spark-ignition engine
operating at 1500rev/min, (13 = 1.0, pin)“ 2 0.7atm, MBT timing 25 ° BTC. (From
Heywood [1])

3.2 The polytropic process

In principle, the compression and expansion processes in an internal combustion en-
gine are considered to be polytropic processes. By introducing the polytropic pressure
model 70,, the two polytropic processes are represented by two horizontal lines in the

plot of the polytropic model. The polytropic pressure model is deﬁned as
7U; E PU?“ (3.1)

where vs denotes the volume of the system normalized with respect to the clearance

volume, and nk, the polytropic index of expansion for Is.- : e, or of compression when

38

(”95?
the I
(if St.

In th

\Vliert
cranl

rewrj

k = c.

It has been proposed that the exponent 77. in the polytropic relationship of the
pressure and the volume during the combustion varies approximately 71C to 11,, with
the mass fraction burned, 33b. Since the evaluation of an, requires the priori knowledge
of start and end of combustion, a simple evaluation of the exponent n. is proposed.

In the simple evaluation, the exponent it varies linearly from me to ne with time, i.e.,

(3.2)

77;, = 71C + (72,. -— nc) x

where G,- is the crank angle at which the polytropic compression ends and 9; is the
crank angle at which the polytropic expansion starts. Therefore, Equation 3.1 can be

rewritten as

n), = 71C for compression
_ 4n); , . _. ‘
M = PM; W here "I: — nk : n for combustion (3-3)

71,, = 72,. for expansion

Shown in Figure 3.2 is a plot of polytropic pressure model of ideal processes in
an internal combustion engine. However, because of the heat transfer to the wall and
gas leakage during and after the exothermic process of combustion, the plot of the
polytropic model of real processes in a direct-injection spark-ignition engine is shown
in Figure 3.3.

Examination of Figure 3.3 reveals that the compression process can be reasonably
approximated by a polytrOpic process, while the expansion process can only be ap-
proximated by a polytropic process in a short range since the heat transfer to the wall
and gas leakage decreases the polytropic pressure model. It is also shown in the ﬁgure
that the polytropic pressure mode] increases during the combustion process. At the
end of the compression, the polytrope increases due to the exothermic process of corn-

bustion. Before the engine piston reaches the top dead center (TDC), the heat release

39

 

 

 

 

 

it
“e
“C
180 240 300 360 420 480 G 540

Figure 3.2: The polytropic pressure mode] of ideal processes in an IC engine

 

 

 

l l l l l

180 240 300 360 420 480 0 540

 

Figure 3.3: The polytropic. pressure model of real processes in an IC engine

40

from t
hign‘t’l

nnnlcl

   
   
    
 

thetﬂt
heat t1
inaxitn

heat tr

3.3

The (l3.
shifts tl.
pnnluch
lutstiun
lsrecord

The
Nﬂ‘pfntt

Thrill-”51011

 

[hunt (1f ,
anT§5 (
lllt’,‘ pup”;
(ll‘ll'dmjp
3 (“N-"Jim
Tt‘achml E-
a “'55,,1 (
Iﬁﬂylrhlu

Th“ e

from combustion slows down the piston movement, making the combustion chamber
bigger than that without the combustion process, therefore the polytropic pressure
model increases. After the TDC, the heat release accelerates the piston and increases
the polytropic model. When the heat release from the combustion is balanced by the
heat transfer to the wall near the end of the combustion, the polytrope reaches the
maximum point, after which the polytrope decreases because of the domination of

heat transfer to the wall.

3.3 Dynamic stage of combustion

The dynamic stage of combustion constitutes a part of the exothermic process that
shifts the expansion polytrope away from the compression polytrope to create a work-
producing cycle. It expresses the essential function of the exothermic process of com-
bustion and provides the sole reason for the use of fuel. Its evolution, or management,
is recorded by the measured pressure proﬁle.

The initial state of the dynamic stage of combustion, i, takes place at the end of
the process of polytropic compression, following ignition dominated by the effects of
diffusion associated with heat and mass transfer. Its ﬁnal state, f, occurs at a balance
point of the system when the positive effect of pressure generation by the exothermic
process of combustion reaches its maximum imposed by the negative inﬂuence of
the energy lost by heat transfer to the walls of the cylinder-piston enclosure. The
dynamic stage of combustion is identiﬁed by its bounds with their singular nature:
a discontinuity in the rate of pressure signal at the initial state, i, and its maximum
reached at the ﬁnal state, f. The signal is provided by the measured pressure, p, in
a vessel of constant volume, or by its equivalent in a cylinder-piston enclosure, the
polytropic pressure model 77),.

The evolution of pressure, or its model, is expressed in terms of a progress param-

41

etc!

111 f.

and

whet
cranl
3.4 t

E‘Xlt’ll

furmr
c1 uup
S“hit.
Fur at
TllP ;]

3.4

T1
‘1" 8.1,
’3 I117

lftlu.

vii, r}

if

eter, which is the normalized polytropic pressure model.

 

(3.4)

In Equation 3.4, 7*,r is the normalized life time of the dynamic stage of combustion
and it is deﬁned as
9 — (9,

7,. E —@f _ 92: (3.5)

where (9,- is the crank angle of the start of dynamic stage of combustion and 9f the
crank angle of the end of dynamic stage of combustion. It is shown in Equation
3.4 that the evolution of dynamic stage of combustion is depicted as a time proﬁle
extending from the intersection of the polytropic pressure model with the baseline of
77,- = const to the maximum point of the polytropic pressure model.

In the course of the dynamic stage of combustion, most of the reactants are trans-
formed into products, which is a process associated with changes of state of all the
components of the system. The essential features of this process are revealed by
solving an inverse problem: deduction of information on an action from its outcome.
For an internal combustion engine, this task is accomplished by pressure diagnostics.
The analytical technique for it has been developed over the last decade [41—56] and

is presented here in a reﬁned version.

3.4 Bounds

The solution of the inverse problem, :r,,(r,,) , is expressed by an integral curve bounded
by two singularities. Thus, it is actually a solution of a double-boundary-value prob-
lem.

The initial state, i, is an essential singularity of the dynamic stage of combustion.

At the initial state, speciﬁc volume of products is e, = l-='}/M,- :2 0/0(!). Thus,

42

depending on the round-off error, calculations of the initial state of products tend to
approach either inﬁnity or that of reactants.

The ﬁnal state, f, is also a singularity because of the balance reached then between
the positive effects of the pressure generated in the course of the exothermic process of
combustion and the negative inﬂuence of heat transfer to the walls and exhaustion of
reactants. Thus, in contrast to the intrinsically discontinuous nature of initiation, the
ﬁnal state of the dynamic stage is approached smoothly at the maximum of polytropic
pressure model, 77.

The trajectory of the dynamic stage of combustion in an IC engine is, then, an
integral curve bounded by two singularities. It starts at a saddle point singularity
of the initial point, i, speciﬁed by the intersection between the proﬁle of polytropic
pressure model with that of the preceding process of compression with 7rc = const.
In order to determine the coordinates of point f, a nodal singularity of the polytropic
pressure model is identiﬁed by its maximum.

The initial point, i, is obviated by experimental data. However, this state is piv-
otal for expressing the dynamic features of the exothermic process. Its identiﬁcation
has to be treated, therefore, with special care —- a task that implies disregarding a
certain number of experimental data (quite small in practice) in its immediate vicin-
ity, associated with ignition. The analysis is, thus, focused on the dynamics of the
exothermic process, irrespective of the mechanism by which it is initiated, or of the
particular form in which it takes place. In particular, it is independent of the type
of ignition or of the kind of ﬂame by which it is executed, and is thus applicable to
turbulent, as well as ﬂameless combustion.

It is thus evident that, in order to obtain a solution accommodating the require-
ments of the two singularities within which it is bounded, :rn(r,,) has to be expressed
in terms of a sufﬁciently smooth analytic function. This is accomplished by means of

the life function introduced in the next section.

43

3.5 Life function

The life function of the dynamic stage of combustion is an analytical function 1",,( r")
ﬁtting the discrete value calculated by Equation (3.4). According to the nature of the
dynamic stage of combustion, the analytic function has to comply with the require-
ments of the singularities at its two bounds. Their particular features can be expressed
succinctly as follows. To simplify the expression, all subscripts 7r are omitted in the

derivation.

1. Atr=0and;r,-:0,

(dz/d7”),- > 0, marking the start of initiation (or birth);

2. At0<r<1a.nd0<:r<1,

dr/dr > 0, commensurate with propagation (or life);

3. AtTfZI,

(dz/d7” = 0, identifying the termination (or death).

The above conditions are satisﬁed by an ordinary differential equation

(1:17 _ (1(6 + 1,)(1_ T)x (y > 0) (3-6)

(17 __
with all its parameters positive, so that at initial state i, where 7' = 0 and :r = 0,

(1.1?

(—)i Z (If > 0 (3.7)
dT
while at ﬁnal state f,
(Ir
— = 3.8
((17)! 0 ( )

44

For convenience, Equation (3.6) is split into two parts by the introduction of an

explicit function of time, C, so that

and
gig _

(1T

By quadrature, Equation (3.9) yields

m
+
H

 

111(

01'

Solving Equation (3.10), one gets

(I x+l
<=X+,u—u—r)l

 

(3.10)

(3.11)

(3.12)

(3.13)

at. the ﬁnal state of dynamic stage of combustion, T = 1, .17 = 1, and C = Cf: then

 

 

0
Cf _ x + 1
and according to Equation (3.12)
1
6 : eCf — 1

45

(3.14)

Therefore, with the ﬁnal conditions of the dynamic stage of combustion speciﬁed,

Equation (3.12) yields the integral expression for the life function

6‘ — 1
(IT I eCI—_T (3.16)

where C and Cf are speciﬁed by Equation (3.13) and (3.14), respectively.

3.6 Discussion

3.6.1 Life function and Wiebe function

In studies of combustion in an internal combustion engine, several heat-release func-

tions have been introduced. A famous function is the Wiebe function [1, 62, 63, 64].

(I: ’ Z ‘— ,X '—

 

)’<+‘J (3.17)

where Q is the crank angle, 9,, is the crank angle at which the combustion starts, 9,,
is the crank angle at which the combustion ends, a and X are adjustable parameters.

The life function of the dynamic stage of combustion is a power function of time.
By combining Equation (3.6), (3.13) and (3.14), the life function of the dynamic stage

of combustion is reformatted as

eﬁll—(l—Tlxﬂl _1

 

(3.18)

x: a
ex+l —1

Comparing the Wiebe function and life function, it is found that these two func-
tions have a relationship if 6), = G),- and 6),. 2 9f. The life function is in effect a
reverse of the W iebe function, i.e., the start of the Wiebe function is the end of the

life function and the end of the Wiebe function is the start of the life function.

46

For 8,, = G,- and (9,, 2 9f, the Wiebe function is reduced to

;1Tu.v'(7') : 1 — €Xp[—ﬁTX+l] (3.19)

and the reverse of the W iebe function is

 

 

 

grﬁ-(T) = 1 -:ru'(1— 7') = {Sim-TV“ (3.20)
From Equation (3.18),
a ‘ 31(1-7)‘+‘_--—
1;: e [P ‘ L e l (3.21)
m“ —-1

usually, if; > 5, then 6177 z (em — 1) and 6.1? x 0. Therefore, the life function

of the dynamic stage of combustion is reduced to

J‘ : €-_\:1(1_T)\+l

(3.22)

which is the same as the reverse of the Wiebe function.

The reverse relationship between these two functions is illustrated by Figure 3.4
and Figure 3.5. In ﬁgures, the Wiebe function and life function, together with their
derivatives expressing the “rate of burn,” are illustrated for the same parameters of
a : 3 and X = 0.5, 1, 2.5, 5 and 10.

A comparison of first derivatives of the life function and Wiebe function is shown
in Table 3.1. It is shown that the ﬁrst derivative of the Wiebe function is greater
than zero at the ﬁnal state, indicating that the combustion is continuing. According
to the definition of heat—release functions, the combustion is ended at the ﬁnal state,

therefore W iebe function loses the physical meaning at the ﬁnal state.

47

 

 

 

 

 

 

 

 

 

 

1

x a=5
0.8 ' x

0.1
0.5
0.6 ' l
1.
2.5
0.4 - 5
10

0.2

0 .

0 02 04 0.6 08 t 1
10 W- , — 1 — —— _n__
5‘ 01:5
8
6 1* x 0.10.5125 5 10
4 .

2 F , 4,1,1
’34..
0 M

Figure 3.4: The Wiebe function and its derivatives for a = 3 and X = 0.5, l, 2.5, 5
and 10.

 

 

 

 

 

 

 

 

 

 

mN

 

x 105 2510.5

1
-\\‘.c.__, /‘*
0 1’1

0 0.2 0.4 0.6 0.8 T 1

 

 

 

 

Figure 3.5: The life function of the dynamic stage of combustion and its derivatives
for a = 3 and X = 0.5, 1, 2.5, 5 and 10.

n40.

Ul‘;

 

Table 3.1: Comparison of ﬁrst derivatives of life function and Wiebe function

 

life function Weibe function

 

9:9,- dJI/d9>0 dI/d9=0
Gi<9<®f d;l‘/d9>0 (113/(19>0
9:9, (II/(16:0 (tr/(19 >0

 

3.6.2 Derivatives of life function

By setting three conditions at the initial and ﬁnal states of the dynamic stage of com-
bustion as well as during the stage, an continuous analytical function describing the
evolution of the dynamic stage of combustion is obtained, which is the life function.
Since life function is continuous, its derivatives are available.

From Equation (3.6) and (3.15), the ﬁrst derivative of life function is

d, 1
i — —I : (1(17 + —..—)(1 — m (3.23)

(17' ex+l — 1
and the second derivative of life function is

(12.10
:L‘ = —.
de

=e+wxc+5) (3%)

p—

where C is obtained from Equation (3.10), C is obtained from Equation (3.13), C is

obtained from Equation (3.10), and

€=—au1—n**=— X C w2m

l—T

 

Similar to the principle that the distance of a vehicle approaches can be controlled
by its speed and acceleration, the evolution of the dynamic stage of combustion

can be controlled by the first and second derivatives of the life function. In this

50

control mechanism, the life function of the dynamic stage of combustion is akin to

the distance, its ﬁrst derivative is akin to the velocity, and its second derivative to

the acceleration.

3.7 Procedure

The procedure for identifying the dynamic stage of combustion and obtaining its life

function is as follows.

1.

The measured pressure profile with respect to time, p(9), is used together with
the proﬁle of the volume of the cylinder-piston enclosure normalized with respect
to the clearance volume, 05(9), to obtain the indicator diagram, expressing the

functional relationship p(223).

From the indicator diagram in logarithmic scales, the slopes of the compression

polytrope, 72,, the expansion polytrope, me, are obtained by linear regression.

. The proﬁle of the polytropic pressure model, 7rk(9), to determine the dynamic

stage of the combustion, is then obtained on the basis of step 2, according to

Equation (3.1), together with the base line of 75(9) 2 const.

The initial state i and the ﬁnal state f of the dynamic stage are identiﬁed on the
basis of step 3: the initial state is the ﬁrst point deviating from the compression

polytrope, while the ﬁnal state is the maximum of the expansion polytrope.

. Based on the identiﬁcation of initial state and final state, the discrete values

of life function and life time of dynamic stage of combustion are obtained by

Equation (3.4) and (3.5), respectively.

. The proﬁle of the polytropic pressure model expressed in terms of the analytical

life function is obtained by Equation (3.16), (3.13) and (3.14), whereby its

parameters, (1: and X, are. established by regression.

51

7. The ﬁrst and second derivatives of life function of the dynamic stage of com-

bustion are evaluated by Equation (3.23) and (3.24).

3.8 Implementation

3.8.1 Engine

The technique of pressure diagnostics to evaluate the performance of a dynamic stage
of combustion was carried out for a single cylinder, dual overhead-cam, four-valve,
direct injection, spark ignition, AVL model 503 engine connected to a 200 hp General

Electric DC dynamometer [65]. The engine speciﬁcations are listed in Table 3.2.

Table 3.2: Engine specifications
Bore 7.95 cm

 

Stroke 9.99 cm

Connecting Rod Length 19.8 cm

Compression Ratio 193:1
Intake Valve Open 12 i BTDC
Intake Valve Close 8 ABDC

Exhaust Valve Open 38 ° BBDC
Exhaust Valve Close 20 O ATDC

 

The front of the engine block was modified to allow access to shafts operating
at half-crank-angle speed for the overhead cams and the fuel pump. The engine
contained a Mahle piston with a hemispherical bowl machined into the center of
its face. The cylinder head and the camshaft were, in effect, separate units, allowing
changes in combustion chamber geometry to be made without any modification of the

engine head. Towards this end, the top of the cylinder was ﬁtted with a removable

52

l
/,

 
 
 

 

' f , Direct
Injector

.
.//
/
/

I. i

Pressure
Transducer .1

.1'“ ,

   

Figure 3.6: Bottom view of the engine head

block accommodating the direct injector, a 10mm spark plug, and an optical pressure
transducer. A facility for changing the location of these units was furnished, as well
as means to modify the shape and volume of the cylinder-piston enclosure without
affecting the compression ratio. The block was connected to the cylinder head by six
cap screws, and sealed by a CNC machined copper crush washer. A set of removable
blocks was machined with hemispherical bowls of different shapes.

A photograph of the cylinder head, viewed from the bottom, is presented in Figure
3.6, showing the bowl with the spark plug and the direct injector located close to the
center between the valve seats, as well as the tapped hole for the pressure transducer.
The geometrical conﬁguration of the combustion bowl in the piston and in the block,
forming the cylinder head, is depicted in Figure 3.7. The hemispherical bowl in
the piston is 2.258 cm (1.125 inch) in diameter, accommodating 23.25% of total
compression volume. The bowl in the head is 3.28 cm3 (0.2 inch3) in volume, providing

12.45% of total compression volume. The squish volume takes up the rest.

53

mks Port—\ n J {—Exhaust Port
\   /

/.Exhaust Valve

 

ﬂake Valve—

 

 

    

 

 

 

     

Boleolume r/ v ‘
hHead / A////
I Cylndﬂcal
Baas” / 44 .1...

v
\\
\\
,\\\\\\\
\\\\\\\\\\\\<\<\\\\\\\\\\

\\\\‘\‘\\\\\\\\\\\\\\\\\\\\\‘\

\

 

.\\

I

Figure 3.7: Illustration of combustion chamber

All engine tests were run at an operating speed of 1500 rpm. The experiments
conducted in this engine assembly examined several hundred operating conditions.
The objective of the experiments was to evaluate the mechanical integrity and per-
formance of a stratiﬁed charge engine assembly which can accommodate the variable
geometry inserts described earlier in this section. For the current work, the operating
conditions for a sample of four, selected for pressure diagnostics, are listed in Table
3.3. The air/ fuel ratios are expressed by the relative air/fuel ratio, A(with respect to
the stoichiometric ratio of 6.435 for methanol). The selection was made to cover a
full scope of measured indicated mean effective pressure (IMEP), represented by the

maximum and the minimum of two relative air/fuel ratios, A 2 1.5 and A = 1.75.

3.8.2 Results

Measured pressure data for the four selected cases are displayed in Figures 3.8~-- 3.11
(step 1). The corresponding indicator diagrams in logarithmic scales are displayed in

Figures 3.12-3.15. In the logarithmic scales, the slopes of the compression polytrope,

54

Table 3.3: Engine Operating conditions

 

 

 

 

 

L Case /\ IMEP Injection (° BTDC) Ignition (° BTDC)
1 1.5 max 60 10
2 1.5 min 50 20
3 1.75 max 50 10
4 1.75 min 70 12.5

 

 

 

 

 

 

 

no, and the expansion polytrOpe, ne, are evaluated by linear regression (step 2). The
values of 71C and me for four cases are shown in Table 3.4. Figures 3.16—3.19 display
the polytropic pressure models; the solid horizontal lines in the ﬁgures represent the

polytropic compressions (step 3).

Table 3.4: The indices of polytropic compression and expansion of four cases

1 2 3 4

 

 

 

 

nC 1.2451 1.2672 1.2679 1.2348

 

11,, 1.2864 1.2842 1.299 1.2502

 

 

 

 

 

 

 

The initial state of the dynamic stage of combustion, i, is then determined by
the ﬁrst point of the polytrope deviating from the base line of 7rC = const. Its ﬁnal
state, f, is established at the maximum of the polytrope (step 4). Then, proﬁles of
the polytropic pressure models, speciﬁed by Equation (3.1) and (3.4), are expressed
by regression in terms of life functions, yielding their parameters, or and X (steps 5
and 6).The parameters of the life functions are listed in Table 3.5

In Figures 3.8-~3.19, the experimental data are represented by open circles. The
initial and ﬁnal points of the dynamic stage of combustion, i and f, are identiﬁed
there by large open circles and large open squares, respectively, according to their
identiﬁcation in step 4.

Shown in Figures 3.20—3.23 are the life functions of the dynamic stage of com-

55

Table 3.5: Life function parameters

1 2 3 4

 

 

 

9, 355 347 355 360

 

9f 381 379 379 399

 

0 28.8583 33.476 24.4691 16.5622

 

 

 

 

 

 

 

X 3.16596 6.13036 2.50746 2.22327

 

bustion with their ﬁrst derivatives. The second derivatives are shown in Figures
3.24—3.27 (step 7).

In Figures 3.28-~~3.31, the analytical pressure traces (solid lines) obtained from
the polytropic compression process and life function of dynamic stage of combustion
are shown. Compared with the measured pressure data (open circles), it is shown that
the life function of the dynamic stage of combustion is a good method to characterize

the combustion process in an IC engine.

100 ~

p/atm

50
0

 

240 300 360 420 480 9 540

180

Figure 3.8: Pressure trace of case 1

100 ~'

platm

50

l

300

 

420 480 9 540

360

240

180

Figure 3.9: Pressure trace of case 2

57

100 -

 

 

 

 

 

platm
a;
50 ~ i, 1},
° is
0 1 1 1 i
180 240 300 360 420 480 9 540
Figure 3.10: Pressure trace of case 3
100 —
platm
l
50 L
1 1 1 J
180 240 300 360 420 480 9 540

Figure 3.11: Pressure trace of case 4

M... f 1
log (p)i

1.5

0.5

 

 

 

0 0.5 l 108 (Vs) 1.5

Figure 3.12: Logarithmic indicator of the pressure trace of case 1

 

 

0 0.5 1 log (Vs) 1.5

Figure 3.13: Logarithmic indicator of the pressure trace of case 2

59

log (P) ‘

1.5

0.5

 

 

0 0.5 1 log (Vs) 1.5

Figure 3.14: Logarithmic indicator of the pressure trace of case 3

 

l

0 0.5 1 log (Vs) 1.5

 

Figure 3.15: Logarithmic indicator of the pressure trace of case 4

60

120 -'

 

 

 

1

1t/atm 3
Z 1

o 1

80 — o 1
° 1

° ‘.

f,’ l

,M j "c
40 -

l
0 1 1 1 1 1 1

 

180 240 300 360 420 480 9 540

Figure 3.16: Polytropic pressure model of case 1

120 r

l
R! atm ll

30-

00000000

WM

40

l l l

 

0 1 1
180 240 300 360 420 480 9 540

Figure 3.17: Polytropic pressure mode] of case 2

61

 

 

 

120 —
n/atm o
80 r o
8 15¢ i
40 3'" 1
1
0 l l l L l i
300 360 420 480 9 540

180 240

Figure 3.18: Polytropic pressure model of case 3

120 -
1

1d atm
80 L
.3
M “c
40

360 420 480 9 540

1
_J

 

180 240

Figure 3.19: Polytropic pressure model of case 4

62

 

 

 

 

11"““"" —~—— e-——~~— 3
X X
2
0.5
1
0 0
355 360 365 370 375 o 380

Figure 3.20: Life function of DSC and its ﬁrst derivative of case 1

 

1 F" ~~~~~~ 4 ea 4

X X
3

0.5 2
1

0 - — 0

 

 

 

345 350 355 360 365 370 375 8 380

Figure 3.21: Life function of DSC and its ﬁrst derivative of case 2

63

 

 

 

11‘ ——— “ ———~———~e —3
X X
2

0.5
1
0 0
355 360 365 370 375 e 380

Figure 3.22: Life function of DSC and its ﬁrst derivative of case 3

1 3
x 1'1
2

0.5
1
0 —— 0

 

 

 

355 360 365 370 375 380 385 390 395 9 400

Figure 3.23: Life function of DSC and its ﬁrst derivative of case 4

64

 

 

 

355 360 365 370 375 8 380

Figure 3.24: Second derivative of life function of DSC of case 1

 

 

1
-25 l ,

345 350 355 360 365 370 375 8 380

 

Figure 3.25: Second derivative of life function of DSC of case 2

 

 

 

355 360 365 370 375 0 380

Figure 3.26: Second derivative of life function of DSC of case 3

25 2 -— . in, ,, . . i 7 ,L,, i. - ...._ .m— 7. . .27 -

15

 

 

 

355 360 365 370 375 380 385 390 395 9 400

Figure 3.27: Second derivative of life function of DSC of case 4

66

100 -* ,

platm

50-

 

0 1 1
180 240 300 360 420

l J

480 9 540

Figure 3.28: Analytical and measured cylinder pressure of case 1

100 -

platm ‘

50~

 

 

0 1 1
180 240 300 360 420

’ 1
1
1
1

1
1

1

1

1

1

480 9 540

Figure 3.29: Analytical and measured cylinder pressure of case 2

67

100 —

platm

50

 

 

0
180 240 300 360 420 480 6 540

Figure 3.30: Analytical and measured cylinder pressure of case 3

100— » ~ —

platm

50—

 

 

03—. 1 1 1 J

180 240 300 360 420 480 9 540

 

Figure 3.31: Analytical and measured cylinder pressure of case 4

68

Chapter 4

Exothermic stage of combustion in
an IC engine

4.1 Introduction

In chapter 3, the dynamic stage of combustion is introduced to characterize the corn-
bustion process in an IC engine and the analytical life function of its evolution is
derived, which paves the way for controlling the combustion in the engine. The ob-
jectives of combustion control in an IC engine are high output with high efﬁciency
and low pollution as well as reducing cycle-to—cycle variations. In order to achieve
the goals, the understanding of the combustion process in an IC engine is necessary.

In an internal combustion engine, the exothermic process of combustion is ex-
ecuted by an oxidation reaction between a. hydrocarbon fuel, F, and air, A, upon
their mixing to form a molecular aggregate. During the exothermic process of com-
bustion, the mixture of reactants (fuel and air) is transformed to the products. At
the end of the exothermic process, all reactants are transformed to the products.
In this chapter, the exothermic process of combustion in an IC engine is deﬁned as
the exothermic stage of combustion, then a thermodynamic study on the exothermic

stage of combustion is presented and the effectiveness of combustion is quantified.

69

4.2 State space

A combustion system can be viewed as a set of thermodynamically identiﬁed compo-
nents forming a substance enclosed within an impermeable boundary. The identiﬁca-
tion of the system is speciﬁed by two vector sets: the vectors of component fractions
and the vectors of component states. Then, any process of mixing and/or chemical
reaction is expressed by an inner product of a selected intersection between the two

sets.

4.2.1 Component fractions

Changes in the composition of a system, taking place in the course of its exothermic
stage of combustion, are illustrated by a diagram of components, Figure 4.1. It
represents an example of a fuel-lean system that consists initially of fuel, F, and air,
A, forming the reactants, R. The diagram displays a transformation of their mass
fractions, Yp and YA, into products, P, so that Yp + YA 2 YR : Yp. The rest of the
system’s mass, YB : 1 — Yp, is taken up by the fraction of cylinder charge that does
not participate in this transformation and remains, therefore, invariant throughout
the exothermic stage of combustion.

The variation of the component mass fractions, yK (K = F, A, P), taking place
in the course of the exothermic stage of combustion, is expressed in terms of the
product generation progress parameter (equal to total mass fraction of products), :17 p,
the degree of transformation from the initial state,i, to the terminal state, t. While
the progress parameter of the dynamic stage of combustion is In , the degree of
transformation from the initial state, i, to the ﬁnal state, f.

According to the deﬁnition of the dynamic stage and exothermic stage of combus-
tion, the terminal state, t, can only be located at or after the ﬁnal state, f. It can

not be located before the ﬁnal state.

70

 

 

 

 

 

 

 

 

 

 

 

 

 

1
YB
1
1 1
YA
YA Y
YR YF P
YF Y
0 __1 1 1 .
0 Y9 1
0 x 1
1C
0 xp 1

Figure 4.1: Diagram of component fractions

During the exothermic stage of combustion, the variable mass fraction of the

generated products is

yp I \fpl'p (4.1)

while for the air or fuel (K : A, F)

3111' = YKU — 17p) (4.2)

4.2.2 Component states

The thermodynamic state of a component is ﬁxed by three parameters in a three-
dimensional state space. Adopted usually for this purpose are pressure, p, speciﬁc
volume, v, and temperature, T. However, this is not a complete speciﬁcation, because

the knowledge of speciﬁc heats is required to evaluate the internal energy, 6. If

71

the internal energy is adopted as one of the parameters of state, a point in such a
coordinate system provides a complete speciﬁcation of the state. It is, in fact, the
signiﬁcance of internal energy in this respect, that was brought up by Gibbs [66].

In accordance with this principle, the internal energy, 6, is adopted here as a
primary parameter of state to form, together with the mechanical parameter, w =-
h — e = pv = p/ p, and pressure, p, the coordinate system of a three-dimensional state
space. The temperature, T, is thus relegated to the secondary role of a dependent
variable. This concept is by no means new, having been recognized de facto by most
classical equations of state, as illustrated by Table 4.1. Of particular signiﬁcance
in this respect is the fact that the mechanical energy, 11}, as well as the internal
energy, 6, are readily obtainable from thermodynamic tables, such as JANAF [67],
and calculable by the use of computational programs, such as STANJAN [68] and
CEA [69][70].

Table 4.1: Equations of state

 

 

 

Van der Walls w = ﬁTﬁ .. %

DICtI‘iCh (u) : ﬁTﬁe—a/URT
Beattle—Bridgeman w = $7" + g + 572. + 1%
Becker-Kistakowsky-Wilson (BKW) w : %T[1 + rear] :1: = 60:11)“
JOHCS-‘VilkInS-Lee (-J\1VL) ’11} : A[1 — U ]ve-Rlv/vc

Cl' 1 UC

+B[1—— ” ]ve_R2”/”C + £6

(‘pzllc Cl.‘

 

 

Principal components of a conventional combustion system are a hydrocarbon fuel
and air. They are ﬁrst combined into a molecular aggregate, and then transformed
by an exothermic reaction to form products P ——-— a process referred to conventionally
as “heat release.” In an enclosure, the transformation is observed as a measurable

pressure rise manifesting the essential outcome of the exothermic stage of combustion.

For implementation of these principles, the thermodynamic state of a system or
of any of its components is expressed in terms of a polar state vector, zK(w, e, p), or
zK(-w, h, p), where K = A, F, R, P, S respectively for air, fuel, reactants, products
and system, in a three-dimensional state (or phase) space, portrayed as a diagram
of component states in Figure 4.2. A polar vector is one stemming from the origin
of the coordinate system. The locus of states for a component is then de facto a
vector hodograph, which can be referred to as a state polar ~— a surface in the three-
dimensional state space. The intersection of such a surface with a plane of constant
pressure, or a projection of its polar on this plane, is identiﬁed by its Cartesian
coordinates 2K = 1111,30,», or 2K 2 'wK, hK.

A

p Reactant

 

 

 

 

 

 

 

 

 

 

Figure 4.2: 3-D illustration of the state space

The state diagram of Figure 4.3 can be, therefore, visualized as the projection
of state vectors on a pressure platform at p 2 pi, introducing thereby distortions
to the shape of the locus of states speciﬁed at the initial pressure. This feature
is of particular signiﬁcance for the products P since, in order to comply with the
condition of thermodynamic equilibrium, their composition and, hence, molar masses

are variable along the locus of states. The reactants R, on the other hand, are usually

73

treated as a perfect gas, because their components, A and F, are assumed to behave
as perfect gases, as they are according to JANAF tables [67], while its composition

is ﬁxed by their deﬁnition.

 

 

 

 

 

 

 

 

 

 

. 1 t
'1?-
0
“”1 °‘/ . P
l
P@Pi
:9.
0 3:12“ 1 W
|——
0xPEsl

Figure 4.3: Diagram of component states with an illustration of the processes of
mixing and adiabatic exothermic center, EC, and exothermic system, ES.

In the case of a perfect gas, the surface of the loci of states is the same at all
pressure levels, and is represented by a curved wall parallel to the pressure axis, while
that for a perfect gas with constant speciﬁc heats the wall is plane. On the diagram
of component states, the projection of the latter at any pressure level is, therefore, a
straight line. An exothermic process is then a transformation from state i to state t ,
expressed by a vector difference between two polar vectors, represented by the vector

of transformation, .‘:,,_2 (a-z = R-P, i-f). Such vectors delineating the four changes of

74

state taking place at the bounds of an exothermic stage of combustion are as follows:

1. From i on R to i on P, both at 1),, representing the process of exothermic
reaction from 1:50 2 0 to 2:50 .—_-_ 1 where 1:195 = 0, subscript EC denoting an

exothermic center, while ES the exothermic system.

2. From i on R to t on R, representing the compression of reactants as pressure

increases from p,- to 1),.

3. From t on R to t on P, both at p, > 1),, representing the exothermic reaction

at $35 =1.

4. From i on P at p, to t at pt, representing the compression of products as pressure
increases from p,- to pt, while the progress parameter changes from $55 = 0 to

(17155 =1.

The coordinates of reactants R are evaluated on the basis of their composition
speciﬁed in the formulation of the problem, while the coordinates of their products P
are determined by the condition of thermodynamic equilibrium that, according to the
Gibbs phase rule, is speciﬁed in terms of two parameters of state. For a given initial
state, of particular interest states are: (1) pT for constant pressure and temperature,
(2) hp for constant enthalpy and pressure, and (3) ev for constant internal energy and
speciﬁc volume. The latter lies beyond the locus of states, P@p,, as demonstrated
in Figure 4.3, being of interest only when the whole ﬁeld is composed of a single
exothermic center. In fact, the segment from hp to ev on P and that from i to t on
R, represent the ideal case of an isochoric and adiabatic system, which consumes all

the charge to execute the exothermic process of combustion.

4.3 Combustion processes

4.3.1 Mixing

For a chemical reaction to take place, components in the system must be ﬁrst mixed
to form a molecular aggregate. If, initially, the thermodynamic coordinates of fuel
and air are different, they have to be brought to the same state i on R —- a task
accomplished physically by transport processes of molecular mass diffusion and ther-
mal conduction, assisted by viscosity. In Figure 4.3, the concomitant changes of state
taking place in the course of molecular mixing are expressed by shifts along the state
polars of A and F from their original state points, 0, to points i, of the same pressure
and temperature.

The direction of this shift is indicated by arrows between these points. Thus, the
effect of mixing is manifested by vector rotation around point i on R. Irrespective of
the influence of molecular diffusion, which, as a rule, must be involved in forming the
reacting aggregate, its outcome is identiﬁed right from the outset by the intersection

of the straight line between points 0 on A and F with R.

4.3.2 Exothermic center

An exothermic center is a site of the exothermic reaction — the source of the exother-
mic stage of combustion. In combustion literature, exothermic centers have been
known for a long time, more or less vaguely, as ”hot spots.” Their non-steady behav-
ior under the inﬂuence of diffusion phenomena has been studied extensively as a site
of ignition [71]. Their diffusion-dominated steady state behavior is, in effect, that
of a laminar ﬂame. Their non-steady version in a turbulent ﬁeld is referred to as a
”ﬂamelet model” [72].

The fluid mechanical features of exothermic centers have been investigated experi-

mentally and theoretically for their relevance to detonation and explosion phenomena,

76

leading, among others, to the identiﬁcation of mild and strong ignition centers [60][74].

As pointed out above in the section on component states, the coordinates of states
for the system at any pressure level, 25 = 015,65, or 25 = 105,113, are given by the
scalar product of the vector of components and the vector of states. Thus, with

reference to Figure 4.1 and 4.3,
ZS = Q" 5 = yFZF + 37.1% + yPZP + 318213 (4-3)
whence, in view of Equation (4.1) and (4.2)
33 = YFZF + YAZA + YBZB + (YPZP — YFZF — Y.43A)$P (4-4)

For the charge, whose composition is ﬁxed by its initial conditions, the state
parameters are

20 E YFZF + XIAZA + XIBZB (4.5)

The ﬁrst two parts of Equation (4.5) identify the state parameters of the reactants,

23, 1.9.,

YFZF '1' YAZA E (YF + Yslza 14-6)

then,

2 _ Y'1221.‘ +YAZA _ ZF +0334

R — 7 — —
\rp‘i'yA 1+0};

 

(4.7)

where the state coordinates of F and A are prescribed by their initial chemical spec-
iﬁcation and 03 is the air-fuel ratio deﬁned as 03 = YA/Yp.

Thus, by virtue of Equation (4.5) and (4.7),Equation (4.4) yields

3 — 2(7 1' Y'p(Zp — ZR).L‘p (4.8)

A change of state taking place in the course of an adiabatic exothermic reaction

77

proceeds along a constant enthalpy path —— a diagonal on the e—w plane, expressed
by e = h,- — w, or just a change of the reference parameter, Aw, on the h-w plane, as
depicted in Figure 4.4. Displayed there also is the conventional way of identifying the
coordinates of a state vector 2 = w, e, or z = w, h. It utilizes variable speciﬁc heats
associated with the drop of internal energy at a reference temperature, referred to as
the heat of reaction or “heat release.” As reﬂected in the geometry of the diagram,
the slope D K = C K + 1. If the reactants are considered as perfect gases, C K 2 cv / R,
while D K 2 c,,/ R, where cw, express speciﬁc heats at constant volume or constant

pressure, while R is the gas constant.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

e R R P h
. ° : / f,
P
i / 0
C DR
r.
xEC
/ f 1
(Ir fhp
CPDP
1 w

 

0 xEC I

Figure 4.4: Diagram of component states for an adiabatic exothermic center in w — e
and w — [1 space.

Exothermic centers are, in effect, kernels of exothermic ﬁelds. Since they take
place at discrete sites, for a gasdynamic interpretation disregarding the effects of

molecular diffusion, i.e. at the Peclet numbers Fe 2 oo , they form singularities.

78

Each of them is then, in effect, a constant pressure deﬂagration point, rather than
front in the classical version of this term. In the ﬁeld, it acts as a point discontinuity,
across which a ﬁnite change of state takes place, corresponding to a jump from i,
where $1: = 0 and 20 = 23,-, to t, where 1'}? = 1. Its amplitude is then, according to
Equation (4.8)

251 — 23. = YP(ZP — ZR) (4.9)

4.4 Exothermic system

4.4. 1 Balances

By deﬁnition, a thermodynamic system is conﬁned within an impermeable boundary.
The effects of the exothermic reaction it undergoes are expressed by Equation (4.8),
while the corresponding change of state is depicted in Figure 4.5.

As evident there, the process progresses along the loci of states on R and P,
rather than across them as in the case of an exothermic center. Hence, the progress
parameter, .rp, for the system is different from that for the center, as is apparent from
Figure 4.5, in contrast to Figure 4.4. The state transformations associated with the
exothermic stage of combustion in a closed system are determined by the balances of
volume and energy.

The volume balance is obtained from Equation (4.8) for 2 = w, whence
1113 — 11X; 2 Yp(wp — 1113);rp (4.10)

Concomitantly, the energy balance is derived from Equation (4.8) for z = 6
es — cc 2 Yp(ep — eR);1:p (4.11)

Upon taking into account. the energy expenditure, e8, the internal energy of the

79

 

 

 

 

 

,t
l
r
11 CR
HR hp
t
(1P -
rpT l

 

 

 

Ce P@Pi

 

 

 

 

 

 

 

0,1,1

Figure 4.5: Diagram of component states for a non-adiabatic exothermic system in
w — 6 space.

system is

85' = 652' - 8e (4.12)

then, Equation (4.11) is rewritten as

hrp(€p — 83)."L'p Z 851— 8C — 88 (4.13)

4.4.2 Coordinates

In Figure 4.5, the coordinates of the four pivotal points, i and t on R and their equiv—
alents on P, are identiﬁed as follows. First, their directions are expressed in terms of
the slopes, CK = (e, - e,)K/(w, — 11.1,)K (K = R, P), and, secondly, the separation

between them is established by the difference between intersections of their linear

80

extensions with the e axis, qp = 630 — epo. The latter furnishes a rational geometric
entity that replaces the conventional concept of “heat release” (HR). The awkward
role of this concept is displayed in Figure 4.5, let alone the confusion associated with
its “apparent” version, as well as with the related notions of higher and lower “heating
value”, “heat of reaction”, or “heat of combustion.”

Then, according to the diagram of Figure 4.5,
GR 2 C310}; (4.14)

while

813 Z Cp'wp — ([p (4.15)

Since the initial state of the system is de facto the initial state of the charge,
80 — 851‘ = CC(w(; — 1.05,) (4.16)

whereas

83 - (’p I CRIUR — prp + (1}) (4.17)

4.4.3 Progress parameter

With Equations (4.14) (4.17) taken into account, the energy balance of Equation

(4.13) becomes
(CRZUR - Cp'lb‘p + (1p)\fp.17p I dec — "(1951) '1' Be (4.18)

which, upon eliminating (Up by using the volume balance of Equation (4.11), yields

1 C p( 1115 — 111(7) + dec — 1113,) + e8
.Tp I , (4.19)
X p (1P — (CP - Calms

 

 

81

It is an expression relating the total mass fraction of products :1: p with time t via the
prescribed functional relationships of w5(t) and ee(t), furnishing thus a fundamental

relationship for the inverse problem of an exothermic process —- pressure diagnostics.

4.4.4 Combustion in a piston engine

For a closed system, such as the cylinder of an internal combustion engine or an
explosion test vessel, Equation (4.19) provides the basis for pressure diagnostics: the
deduction of information on the evolution of the exothemic stage of combustion from

the measured pressure transducer record. In this case, the energy expenditure is

6,, E 11.1w + e; (4.20)

In terms of Us denoting the ratio of cylinder to clearance volume 110, the work

performed by the system is

11.1w E 11C / 5(1) — pb)dv (4.21)

’51

where pb is the back pressure on the outer side of the piston. The second term, 61,
expresses the energy unmanifested by the measured pressure proﬁle. It is made up
primarily of the energy loss incurred by heat transfer to the walls and secondarily of
energy associated with mass lost by leakage.

For a piston engine, the process of compression is represented by a polytrope,

according to which
(UK

— _. PM (K = R, o) (4.22)

11151

where P = Mp,- and ma 2 1 — 'nc‘l, with nC denoting the polytropic index of
the process of compression. If the process is isentropic. then no : 1 + C571 and

771C = (I '1' C(f)—l.

82

 

Upon combining Equation (4.19) and (4.20) and normalizing the equation with
respect to the initial state of exothermic stage of combustion, Equation (4.19) becomes
Cp(Pl — 1) '1' (Cp — (30“an — 1) +11”): '1‘ Q]

.T = , 4.23
P \ Pl-QP — (Ce — Cnlpmil ( )

 

where V : 03/115,, 1113/1113,- 2 PV, tum/1115, = I'Vk, .0;: = qp / 11.15,, and .Q, = (”I/1113,.
The mass fraction of products, actual and/or total, is considered, in accord with

the meaning of e], as a sum of two components, so that
17p ZiL‘E-i-l‘] (4.24)

where subscript E denotes its effective part, manifested by the effects of the generated

pressure, while I marks its ineffective part. Then, Equation (4.23) is divided into

.1' ~ — CP(PV ‘1)+(CP — Cc)(P’"<‘ -1)+I'Vk
[4, \,'p[Qp- (CF—CR)PmR]

 

(4.25)

and
Yp[.(2p — (Cp -— CR)P’"R]

 

(4.26)

(171

In Equation (4.23), Yp is not known unless the composition of products is identi-
ﬁed from the exhaust gas. Thus, 27;) cannot be calculated directly from the equation.
However, upon the combination of Equation (4.1) and (4.23), the mass fraction of

products during the combustion is obtained as

l _ _ Cp(Pl" — 1) + (Cp — C(7)(Pm€ — 1) ‘1'le '1' .0]
JP — [2P _ (CP _ CR)PmR

 

Similarly,
1 ._ C,-.(p1r_ 1) + (Cp — C(a)(P’"s — 1) +113. (4 28)
J}: — 0P _ (CP __ CR)1’)mR .

 

83

 

12p — (cp — C,,)Pm-R

 

yr (4.29)

4.4.5 Correlation

The heat transfer to the wall, 621, is not determined. Thus the mass fraction of
products, yp, as well as its ineffective component, y], cannot be calculated from
Equation (4.27) and (4.29), respectively.

Thermodynamic properties of the system during its exothermic stage of combus-
tion have been established by a study of heat transfer from combustion in a vessel of
constant volume, equipped with transfer gauges and pressure transducers [56][74]. In
this case, 71,. = 0, so that He 2 1), while the independent variable, 9, is expressed by
time, t. The program of experimental investigations covered a broad range of turbu-
lent conditions. It was found then that the following conditions should be satisﬁed,

whether combustion was propagated in a laminar or turbulent manner.

1. At yp : 0: yE/ygmOI 2 0, while dyE/dyp : 1'3, i.e., (1(yE/yEmaI)/(Iyp =

113/yEmax;
2- at yP : 1: yE/yEnmr : 11 while dyE/dyP : 01 1.9., d(yE/yEmar)/dyp : O

The above conditions are satisﬁed by a simple power function

yE/yEmar : 1 — (1 — .I/P)3/yEm”I (4.30)

which is plotted in Figure 4.6.

It was then established, moreover, that 1‘3 : yj/iax. In view of this, the correla-

1

tion function for evaluating the mass fraction of generated products, yp(9), from its

effective part, yE(Q), is obtained by the inverse of Equation (4.30), yielding

1/2

HP : 1 — (1 — yE/yErrlaI)yE"'“ (“l-31)

84

O
n-

 

yE/yEmax , 1

 

 

 

‘B/yEmax y I w
0 . 1
0 y P I

 

Figure 4.6: Correlation between mass fractions of products.

Application of Equation (4.31) to the enclosure of a variable cylinder volume
during the exothermic stage of combustion is based on the postulate that the piston
movement does not signiﬁcantly affect the relationship between the mass fraction of

generated products, 3115(9), and its effective component, y,;(9).

4. 5 Closed system

4. 5. 1 Thermodynamic relationship

Upon the recognition that the mixture in the cylinder can be considered as a closed
system during the period starting from the intake valve close (IVC, denoted by a)
and ending at the exhaust valve open (EV O, denoted by z), the method extended
to analyze the exothermic stage of combustion can be used to analyze such a closed

system.

Because of the change of the analysis system. Equations (4.27). (4.28) and (4.29)

85

 

should be changed accordingly for the analysis of such closed system. The system
is changed from the cylinder mixture during the exothermic stage of combustion to
that in the closed system (from IVC to EVO), the normalization base in Equation
(4.27), (4.28) and (4.29) should be changed from the initial state, i, to the IVC, a.

Thus, the mass fraction of products in the closed system is

I _ Cp(PV — 1) + (cp — CC)(P"'C — 1) +11". + (2,
JP "' {2P _ ((31J _ CR)PmR

 

(4.32)

Where P : p/pa: [)1 : pi/pae 1 Z vii/(75a: 11' Z ”Si/v.90) 'U-‘w/wSa = ”ilk, ww :

1

21C f5: (p — pb)dv, {2p 2 qp/zuga, {21 = eI/wSG and 171C = 1 — 77.C_ , with 71.0 denoting

the polytropic index of the process of compression.

Similarly,
1 _ CP(P[" _ 1) + (Cp — CC)(Pm(1_1)+n,k
yr. — .Qp — (CP - CR)P'"R

01
I Z
J’ (2,. — (cp — enema

 

(4.33)

(4.34)

 

By observing effective part of the mass fraction of products, it is found the 3115
consists of the contribution to the change in internal energy of the system and to the

production of piston work, i.e.,

 

.115 = y. + y“, 14-35)

where
2 GP<egg:(gt-.3315": - .1 n.
1th (4.37)

 

1.1 :
J (2,. — (cp — (3,.)an
From Equation (4.11), the fundamental thermodynamic reference parameter of

products, the mechanical energy. is

1113 — “’6‘

.I/ P

U‘p : Rpr Z (13R + (4.38)

86

 

 

In terms of the normalized variables and the polytropic relationship formulated

by Equation (4.22), the normalized mechanical energy of products is

W. — W PV — Pmc
WP =.— 11",. + —5———9 = PM + ——-———-— (4.39)
ZIP UP

All these relations apply well to the process of expansion where yp = 1 and to
the exothermic stage of combustion where 0 < yp < 1. However, for the process of

compression, where yp = 0 and 1113 = mg, Equation (4.32) becomes

_ CC(P’"C — 1) + Wk + {2,

 

 

4.40
0p — (c. — caema 1 1
Accordingly, Equation (4.33) and (4.36) become

Cc(PmC — 1) + I/Vk
’ 1 = 4.41
”5 r2.» — (cp - enema ( )

PW" — 1

Cd ) (4.42)

 

5" Z (2,. — (c. — enema

4.5.2 Thermodynamic properties

For the reactants, which composed of air and fuel, its composition is almost ﬁxed,
thus the reactants behave as the ideal gas. The temperature of the reactants can be

obtained from the equation of state and Equation (4.22).

U711

 

 

 

11
TR = p R Ta 2 Ta = PM (4.43)
Davao w Ra
The speciﬁc volume of the reactants is
w 1 V )
UR = R I—a'vh’a = Pmc'lﬂvaa (4'44)
wRa p I)

where the speciﬁc volume of reactants at IVC, 1.11,“, is obtained by STAN JAN .

87

 

As a matter of principle, the products do not behave as an ideal gas, since its
composition and molar masses are variable in order to comply with the condition
of thermodynamic equilibrium. However, if the gas constant of products is assumed
to change linearly during the exothermic stage of combustion, it is reasonable to

calculate the temperature and speciﬁc volume of the products from the equation of

state and Equation (4.39), i.e.

l? R 111 R Pl” — P mC R
TP: pPlj-‘z: P—f-EZ(PmC+ ) P
Pivpi RP, 'U-lPi RP,- yp R p.

1

 

 

 

T,- (4.45)

where the gas constant of products HP 2 Rp, + (RP, — Rp,)(9 — O,)/(Ot — (9,). The

speciﬁc volume of the reactants is

w , ,- PV — Pmc’ ),
”Up = P P—‘L’pi Z (Pm—C '1' ———)I—'Upi (4.46)
szi P 3119 P

 

where the speciﬁc volume of products at the initial state, Up,‘, is obtained by STAN-
JAN.

For the system, which is the mixture in the closed system, its temperature and
speciﬁc volume are the same as those of the reactants during the compression process
1111) = 0). During the expansion process (Up = 1), they are the same as those of
products. During the exothermic stage of combustion (0 < yp < 1), the temperature

and speciﬁc volume of the system can be reasonably evaluated from the equation
of state with the assumption that the gas constant of the mixture changes linearly.

Thus, the temperature of the system is

 

TS : 1. ‘_ ___—T (447)
P111317 Rs.- Pz‘ 1’6 vs,- RS. 1

where the gas constant of system R3 = R5, + (RS, — R5, )(9 — O,)/((—), — (9,) and the

volume ratio 115/op, :2 1 + 1/2('rc — 1)[R + 1 — cosﬂ — (R2 — si112)1/2] [1].

88

 

The speciﬁc volume of the system is
Us = 4031' = 44+“sr (4-48)

where the speciﬁc volume of the system at the initial state, 115,, is obtained by STAN-

JAN.

4.6 Procedure

The procedure for analyzing the exothermic stage of combustion and the closed system

is as follows.

1. Identify the initial state i and ﬁnal state f of the dynamic state of combustion

analyzed in Chapter 2.

2. Use STANJAN to evaluate the internal energy 6 and mechanical parameter,

to : [111, of the reactants at the initial state i and ﬁnal state f respectively.

3. Plot point i and point f of reactants in the e — 111 plane of the state space to

evaluate the slope of the state change of reactants, C R.

4. Since the initial state, i, is a singular point for the products, it is impossible to
evaluate the internal energy and mechanical parameter of products at the initial
state. Therefore one more state is required to evaluate the slope of the state
change of products, Cp. As mentioned in Section 4.2.2, point hp (constant
enthalpy and constant pressure) can be used to evaluate Cp. Therefore, use
STANJAN to evaluate the internal energy 6 and mechanical energy 10 of the

products at point hp and point f, respectively.

5. Plot point hp and point f of products in the e — to plane of the state space to

evaluate the slope of the state change of products. Cp.

89

6. Evaluate the heat release, qp, from the plot in the e — w plane of the state space.

7. Use Equations (4.28) and (4.31) to evaluate the effective component of the mass
fraction of products and mass fraction of products itself during the exothermic
stage of combustion, respectively. Use Equation (4.24) to evaluate the ineffective

component of the mass fraction of products.

8. Identify the terminal state of the exothermic stage of combustion, t, which is

the maximum of the effective component of mass fraction of products.

9. For the closed system, evaluate the mass fraction of products and its components

by Equations (4.33), (4.36), (4.37), (4.31) and (4.24).

10. Determine the temperature and speciﬁc volume of the reactants, products, and

system by Equations (4.43) — (4.48).

4.7 Implementation

4.7.1 Engine

The technique of pressure diagnostics to reveal the performance of a exothermic stage
of combustion and a closed system was carried out for the same engine mentioned in

section 3.8.1. The engine operation conditions are shown in Table 3.3.

4.7.2 Exothermic stage of combustion

State diagrams of the exothermic stage of combustion for four cases are shown in
Figures 4.7—4.10. From these diagrams, the slopes of state changes of reactants and
products as well as the heat release during the combustion are evaluated and shown

in Table 4.2.

90

Shown in Figures 4.11—~4.14 are the mass fractions of the products and their
effective parts during the exothermic stage of combustion. When the effective com-
ponent of the mass fraction of products reaches its maximum, the terminal state of
the exothermic stage of combustion is reached and the combustion is ended. The
crank angles of initial state and terminal state of the exothermic stage of combustion

for four cases are shown in Table 4.2.

Table 4.2: Parameters to evaluate the mass fraction of products

 

 

 

 

 

 

 

 

 

 

 

 

1 2 3 4

e. 355 347 355 360
e, 383 380 380 400
CR 3.0568 3.3242 3.0479 2.8439
c. 3.6224 3.5834 3.5258 3.5032
qR(KJ/g) 2.1137 2.0498 1.8351 1.8647

 

91

 

 

 

 

 

 

0 1
e (kJ/g)
-1 -
-2 -
-3 J l I
0.1 0.2 0.3 0.4 W (kJ/g) 3.5

Figure 4.7: State diagram of the exothermic stage of combustion for case 1

 

 

 

 

 

0
e (Idle)
-1 -
-2 -
-3 l 1 l
0.1 0.2 0.3 0.4 W (kJ/g) 0.5

Figure 4.8: State diagram of the exothermic stage of combustion for case 2

92

 

 

 

 

0 Rt
1
e (kJ/g)
-1 -
P
i
-2 b
-3 L I I
0.1 0.2 0.3 0.4 W (kl/g) 0.5

Figure 4.9: State diagram of the exothermic stage of combustion for case 3

 

 

 

 

 

0
e(kJ/g)
-1 -
-2 -
-3 I I I
0.1 0.2 0.3 0.4 W(kJ/g) 0.5

Figure 4.10: State diagram of the exothermic. stage of combustion for case 4

93

 

 

 

 

 

 

 

1 .__--.____T_____ *4 eeeeeee ~———
1 Yr
0.5 . I ’
: 1:
0 1 l I
340 360 380 400 9 420

Figure 4.11: Proﬁles of the mass fraction of products and its effective component of
case 1

 

 

 

 

 

 

 

 

 

1 1 1 a It
] e
0.5 -
g y!
0 1 L
340 360 380 400 6 420

Figure 4.12: Proﬁles of the mass fraction of products and its effective component of
case 2

94

 

 

 

 

 

 

 

 

340 360 380 400 G 420

Figure 4.13: Proﬁles of the mass fraction of products and its effective component of
case 3

 

 

 

 

 

 

 

340 360 380 400 9 420

Figure 4.14: Proﬁles of the mass fraction of products and its effective component of
case 4

95

4.7.3 Closed system

For the closed system, the state diagrams are shown in Figures 4.15—4.18. In ﬁgures,
the states of system at the crank angle of intake valve close and exhaust valve open
are included and denoted by point a and z.

The mass fraction of products and its components are shown in Figure 4.19——
4.22. In ﬁgures, point Ij indicates the crank angle at which the fuel is injected and
point Ig indicates the crank angle at which the spark discharges for ignition. Upon
the observation of y6 and yw, respectively reﬂecting the change of internal energy
and work in the closed system, the fuel consumption in the engine cylinder is well
understood. The energy is stored in the system by the piston work in the course
of compression, with more energy added during the exothermic stage of combustion.
The energy is released during the expansion process to produce piston work. Thus,
it is a two-step, laser-like, sequence, in which a short process of charging is followed
by a long process of discharging.

Shown in Figures 4.23—4.26 are the temperature proﬁles of reactants, products,
and the system. The speciﬁc volumes of reactants, products, and the system are

shown in Figures 4.27#—4.30.

96

 

 

 

 

 

-1 -
.2 -
-3 '

0 0.25 w (kJ/g)

Figure 4.15: State diagram of a closed system for case 1

 

 

 

 

 

0
e (kJ/g)
-1 -
-2 -
-3 l
0 0.25 W (kJ/g)

Figure 4.16: State diagram of a closed system for case 2

97

 

 

 

 

 

0
e (kJ/g)
-l r
-2 -
-3 '
0 0.25 W (kJ/g)

Figure 4.17: State diagram of a closed system for case 3

 

 

0
e (kJ/g)
-1 b
-2 -
-3 '

 

 

 

0 0.25 w (kJ/g)

Figure 4.18: State diagram of a. closed system for case. 4

98

 

 

 

 

 

 

 

 

 

 

 

 

 

-0.5 1 l l
180 240 300 360 420 480 8 540

Figure 4.19: Proﬁles of the mass fraction of products and its components in the closed
system of case 1

 

 

 

 

 

 

 

 

 

 

 

1 a i i t Zr
4
3’? g
\i 3 yE
0.5 ' \
1g 3 ¥
‘3' . 3 ° <-—:
‘A. o E
.3. E y;
P i
_0.5 1 J i 1 n

180 240 300 360 420 480 6 540

Figure 4.20: Proﬁles of the mass fraction of products and its components in the closed
system of case 2

99

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

l a II +
g 4.
Y? i
" y E
0.5 - ‘
0 ‘3
_0.5 1 l l I
180 240 300 360 420 480 9 540

Figure 4.21: Proﬁles of the mass fraction of products and its components in the closed
system of case 3

 

 

 

 

 

 

 

 

 

 

 

 

 

a
l
0.5 -
0
_0.5 n i 1 n
180 240 300 360 420 480 9 540

Figure 4.22: Proﬁles of the mass fraction of products and its components in the closed
system of case 4

100

 

2000 ;
T/K
1500 -

1000 '

 

500b

 

 

 

 

 

 

 

 

 

I l

180 240 300 360 420 480 0 540

 

Figure 4.23: Proﬁles of the temperature of reactants, products, and system of case 1

 

2000
T/K

1500 b

1000 "

 

500 '

 

 

 

 

 

 

 

 

 

 

 

0
180 240 300 360 420 480 8 540

Figure 4.24: Proﬁles of the temperature of reactants, products, and system of case 2

101

 

 

2000 ‘i"
T/K

1500

1000

500 '

 

 

 

 

 

 

 

 

 

 

0
180 240 300 360 420 480 6 540

Figure 4.25: Proﬁles of the temperature of reactants, products, and system of case 3

 

  

 

 

 

 

 

 

 

 

 

a I t z

2000 i
1D!( 5
1500 -’ c!
1000 - 3

lg l
500 " Ts /(1K/

0 If I ii I I
180 240 300 360 420 480 (2 540

Figure 4.26: Proﬁles of the temperature of reactants, products, and system of case 4

102

 

 

v(m3/kg)

0.75

0.5

0.25

 

 

 

 

 

 

 

 

0 I
180 240 300 360 420 480 6 540

Figure 427: Proﬁles of the speciﬁc volume of reactants, products, and system of case

 

0.5

0.25

 

 

 

 

 

 

 

 

0
180 240 300 360 420 480 8 540

Figure 4.28: Proﬁles of the speciﬁc volume of reactants, products, and system of case
2

103

v(m3/kg)
0.75

0.5

0.25

 

 

 

 

 

 

 

 

0 l
180 240 300 360 420 480 G 540

Figure 4.29: Proﬁles of the speciﬁc volume of reactants, products, and system of case

 

 

 

 

0.5

0.25

 

 

 

 

 

 

 

 

 

0 I I
180 240 300 360 420 480 9 540

Figure 4.30: Proﬁles of the speciﬁc volume of reactants, products, and system of case
4

104

Chapter 5

Thermodynamic analysis in an IC
engine

5. 1 Introduction

In chapter 4, the exothermic stage of combustion is analyzed to understand the com-
bustion process in an IC engine and the effectiveness of combustion is calculated. In
the analysis, several assumptions were made in deducing the mass fraction of products

and its effective components, which are shown as following:

1. The state changes of reactants and products from initial state, i, to terminal

state, t, are linear as shown in Figure 4.5.

2. The heat release evaluated from the state diagram is a reasonable approxima-

tion.

3. The ﬁnal state of dynamic stage of combustion, f, is employed to approximate
the terminal state of exothermic state of combusiton, t, for the evaluating the

slope of state change of products.

4. In the state diagram, point hp of products falls on the straight line connecting

point i and point t of products.

5. During the exothermic stage of combustion, the process of compression for the

reactants is poly-'tropic and the. polytropic exponent is the same as that during

105

the compression process.

Because of these approximations, the mass fraction of products and its effective
component may be artiﬁcial results. It is necessary to study their credibility for the
well understanding of the combustion process. In this chapter, a simple thermody-
namic model is proposed to calculate the cylinder pressure from the heat release func-
tion. The calculated cylinder pressure is then compared with the measured pressure

and the effectiveness of analysis on the exothermic stage of combustion is studied.

5.2 Thermodynamic analysis

Thermodynamic analysis for the mixture in the cylinder has been carried out exten-
sively [1][75][76]. By taking different assumptions for the heat addition (combustion)
to the system in the cylinder, different models have been proposed. In this chapter, a
model based on heat release function is present, which is proposed by Ferguson [77]
and improved by the author.

A thermodynamic analysis is applied to the control volume enclosed by the dashed
line shown in Figure 5.1. In this thermodynamic analysis, the mixture inside the
cylinder is assumed to be the ideal gas. Then the relationship among the pressure
(P), speciﬁc volume (v), and temperature (T) can be expressed by the equation of

state

pi) 2 RT (5.1)
lnp + luv 2 In R + In T (5.2)

During the combustion process, the intake valve and exhaust valve are both closed,
therefore the mass of the mixture, m, is constant. By assuming the gas constant B

is not changing with temperature during the combustion, Equation (5.3) is obtained

106

 

VT

mPl

 

 

 

Figure 5.1: Schematic of the mixture in a cylinder of a four-stroke IC engine.

by differentiating Equation (5.2).

d' d- dT
p v T

According to the ﬁrst law of thermodynamics, the differential form of the energy

conservation in the control volume shown in Figure 5.1 can be expressed as

du = dq — (111) (5.4)

Since du : cvdT and cite = pdv, then

cvdT = dq - pd'v (5.5)

It is assumed that the mixture in the cylinder is the ideal gas, then the relation-

107

ships among constants of ideal gas are shown in Equation (5.6) and (5.7).
R 2 cp - c,, (5.6)
CP
~ 2 — 5.7
I % ( )

Dividing Equation (5.5) by Equation (5.1) and combining Equation (5.6) and

(5.7), the ﬁrst law of thermodynamics is transformed to

H _ a _ (12 (. ,,
(v—UT—pv v a
By differentiating Equation (5.8) with respect to the crank angle degree or CAD,

9, an ordinary differential equation (ODE) is obtained.

(7—1)Td8 ’ pv de me °°

Similarly, differentiating Equation (5.3) with respect to the CAD Q, the differen—
tial form of the equation of state is obtained.

idp 1dv_1dT

pE+;E_TE (5.10)

Upon the combination of Equations (5.9) and (5.10), the change of pressure with

respect to the change of the crank angle is shown as follows:

dp 7 — 1 dq 7]) (112
— = —— — —— 5.11
d(-) 2) d9 1) d9 ( )

To evaluate Equation (5.11), the heat release Q during the combustion should be

known. Physically, heat release in an IC engine is a function of the CAD, i.e., Q :
Q(9). Therefore, heat release, Q, can be expressed as q = q,,,;r(9) and Q = f: qd(-),

where 1(9) is the heat release function shown in Figure 5.2.

108

 

 

 

Q
Cb

Figure 5.2: Heat release function.

Then,
(11) __ (7 - 00.7.1.3 712g
d(-) — 1) d9 v d9

CAD

a

(5.12)

It is known that at the initial state of the exothermic stage of combustion, the

cylinder pressure is p, and the cylinder volume is If}. Then, a normalized ordinary

differential equation of pressure change is

ﬂf _ (7 — 005.51g _ ﬁdV
d9 — piviV (19 V (19

 

where P = p/pz- and V = v / 11,. Then,

dP _ £31; _ 113W
d9 ‘ V d(-) V d(—)

 

where K = (7 — 1>q.-..(p.v.).

Equation (5.14) can be simpliﬁed in the form

(119 ,
E + 0(9)P — 43(9)

109

(5.13)

(5.14)

(5.15)

where (1(9) = (’7/I"’)dl«"/d9 and [3(9) 2 V‘IKdI/d9.

The solution to Equation (5.15) is

d) 05
91
P: C+/ )’3(¢) exp /a'(w)dw dd) exp —/a(w)dw (5.16)
9:
since
¢ 6 1 (11"
[d(tu) dw : 71/ —— (1w : 7111 1(9) 2 ln l“'(9)7 (5.17)
V dw
then
P _ C 1 9‘ 3 ‘ A, I 1' l8
_W+Wme(am o.)

By imposing the boundary condition that p =2 p, and v = v,- at the initial state of

the exothermic stage of combustion, the normalized pressure is

p,- K 9t (1:1: ,
P I — — ——I I 7 d 7.1

The complete solution is obtained by specifying the heat release function, 13(9). Then

the integral can be numerically integrated and the cylinder pressure is obtained by

p :— Pp, (5.20)

5.3 Heat release function

In Chapter 4, the mass fraction ()f products during the exothermic stage of combustion
is introduced. At the initial state i, there is no product, thus the mass fraction of
products yp :— 0. At the terminal state t, no more product is generated, thus the mass
fraction of products yp = 1. With the assumption that. there is no inert components
in the mixture, i.e., Yp : 1, the progress parameter is equal to the mass fraction

of products, .rp(9) = 1],:(9). Therefore, the initial state and terminal state of the

110

exothermic stage of combustion mark the start and end of the combustion respectively,
and the progress parameter of the exothermic stage of combustion, .Tp, is the heat
release function of combustion.

By using the heat release function and the effectiveness of combustion obtained
in Chapter 3, the analytical cylinder pressure can be obtained by Equations (5.19)

and (5.20).

5.4 Results

The engine studied here is the same as that in Chapter 3 and Chapter 4. Engine ge-
ometry and operating conditions are shown in and Table 3.2 and Table 3.3. In studies,
the engine is fuelled with methanol, and the heat release during the exothermic stage
of combustion is obtained from STANJAN and shown in Table 4.2.

Shown in Figures 5.3 —— 5.6 are comparisons of the measured cylinder pressure
and analytical cylinder pressure obtained from the simple thermodynamic model.
It is shown that the simple thermodynamic analysis gives good qualitative results.
Both the measured pressure and analytical pressure in the cylinder increase after the
ignition, rising to the maximum, then decreasing. Quantitatively, the relative errors
of the simple thermodynamic analyses are 8.3%, 21.0%, 12.8%, and 23.7% respectively

for the four cases. The errors exist. because of the following:

1. Several approximations were made to obtain the mass fraction of products and

some of them are rough ones.

2. In the thermodynamic analysis, it is assumed that there is no inert components
in the mixture. However, because of the existence of the residual gas in the

cylinder, the inert. components are ineﬁtable.

3. Leakage, blowby and friction are ignored in the thermodynamic analysis.

111

4. In the analysis of the exothermic stage of combustion and the thermodynamic
model, the mixture in the cylinder is assumed to be perfect gas. The gas con-
stant and speciﬁc heat. are assumed constant. However, the mixture in the
cylinder is high-pressure, high-temperature gas, whose composition is deter-
mined by chemical equilibrium, the gas constant and speciﬁc heat are changing

with temperature.

Noting that the model used in thermodynamic analysis is simple, it is admitted
that the discrepancies between the analytical and measured cylinder pressure are
acceptable, though they are over 20% in case 2 and case 4. Thus, assumptions made

to calculate mass fraction of products and its components are reasonable.

112

 

100

 

 

 

Nam)
50 /
—Experiment *Calculation
0
355 363 371 379 CAD

Figure 5.3: Comparison of measured cylinder pressure and analytical cylinder pressure
for case 1

 

 

 

100 .— ~

I

p(atm)‘i
i

50 ;
I ,./
i / /
|
( —Experiment *Calculation
0 __ _- m _.__-______n, _

347 355 363 371 CAD 379

Figure 5.4: Comparison of measured cylinder pressure and analytical cylinder pressure
for case 2

113

l
l
l
l
l
l
I
l

100

p(atm)

 

50 .
’

1
0 1._ __

355 363 371 CAD 379

— Experiment * Calculation

 

 

 

Figure 5.5: Comparison of measured cylinder pressure and analytical cylinder pressure
for case 3

 

 

 

 

 

100 rmw— —~-
—Experiment *Calculation
p(atm)
50
0 __ _ _____________ 1

355 363 371 379 387 CAD 395

Figure 5.6: Comparison of measured cylinder pressure and analytical cylinder pressure
for case 4

114

Chapter 6

Conclusions and recommendations

6. 1 Conclusions

In this dissertation, cycle-to—cycle variations in internal combustion (IC) engines were
quantiﬁed and strategies to control the cyclic variability were proposed. According
to the operation sequence of a four-stroke 1C engine, the studies were divided into
two phases: pre-combustion phase and combustion phase.

For studies on the pre-combustion phase, a statistical method was employed to
study cycle-to-cycle variations of the pre-combustion ﬂow. By generating the proba-
bility density function of the normalized circulation of the flow on the tumble or swirl
plane, the rotational motion and cycle-to-cycle variations of the flow were quantiﬁed.
The inﬂuences of different port blockers on the rotational motion and cycle-to-cycle
variations of the ﬂow in a DaimlerChrysler four-stroke engine were investigated. It
was determined that the rotational motion and cyclic variability of the pre-combustion
ﬂow can be controlled by changing the shape of the port blocker.

For controlling the cycle-to—cycle variations during the combustion phase, a method
of pressure diagnostics for an internal combustion engine and its application to a di-
rect injection methanol engine was presented. In an internal combustion engine, the
compression and expansion are polytropic processes, between which is the combustion
process. By introducing a polytropic pressure model, 7n, 2 pen", the end of the poly—

tropic compression and the beginning of polytropic expansion were identiﬁed, which

115

are two bounds of dynamic stage of combustion (DSC). Three boundary conditions
were set for the dynamic stage of combustion and an ordinary differential equation
satisfying the boundary conditions was solved to obtain an analytical life function of
the dynamic stage of combustion. Since the life function is analytical and continuous,
its ﬁrst and second derivatives were obtained. Similar to using the speed and accel-
eration to control the distance, the ﬁrst and second derivatives of the life function of
DSC can be used to control the progress of the dynamic stage of combustion.

Controlling the progress of dynamic stage of combustion is only a method to con-
trol the combustion process, it is not a control goal. For an internal combustion
engine, the stability and effectiveness of combustion are desired. To achieve this, the
exothermic stage of combustion was investigated. In this study, the product of cylin-
der pressure and speciﬁc volume of the system in the cylinder, 11) -.: p1), expressing
the mechanical properties of force and displacement, was adopted as a principal ther-
modynamic reference parameter. Together with the mechanical parameter, w, the
internal energy, e, was adOpted as another thermodynamic parameter to construct
the state space. With STAN JAN , a computational program for chemical equilibrium
analysis, the state transformations of reactants and products during the exothermic
stage of combustion were evaluated and two relationships between the mechanical pa-
rameter and internal energy were obtained. Combining these two relationships with
the volume balance and energy balance equations, the effectiveness of combustion was
calculated. Upon evaluating the effectiveness of combustion, a control strategy was
reached for a controlled combustion engine, which is to maximize the effectiveness of
combustion by controlling the progress of dynamic stage of combustion.

The thermodynamic analysis for the exothermic stage of combustion was extended
to investigate the closed system in the cylinder, from the moment when the intake
valve is closed to that when the exhaust valve is opened. By analyzing the change

of internal energy and work of the system, the manner of engine operation was ther-

116

modynamically well understood. Upon deposition of a relatively minor amount of
internal energy into the working substance by piston compression, the major amount
of internal energy was acquired by the substance during the exothermic stage of com-
bustion. And this is followed by the process of expansion, when piston work is derived
entirely by expenditure of the previously acquired internal energy. Therefore, it is a
two-step, laser-like, sequence of events: a short process of charging succeeded by a
long process of discharging.

When using the exothermic stage of combustion to study the effectiveness of com-
bustion, several assumptions were made to simplify the analysis. In the dissertation,
a simple thermodynamic model was proposed to calculate the cylinder pressure from
the heat release function. The calculated cylinder pressure was then compared with
the measured pressure and it was found that the calculated cylinder pressure trace
matches the measured cylinder pressure, indicating the assumptions made for pressure

diagnostics are reasonable.

6.2 Recommendations

In this dissertation, the quantiﬁcation and control of cycle-to—cycle variations during
the pre-combustion phase and combustion phase were studied separately. It is be-
lieved that the identiﬁcation of the interaction between these two phases would be of
help to improve the control strategy for reducing cyclic variability of the engine.

For the study of cycle-to—cycle variations during the combustion phase, a new
method of pressure diagnostics was introduced and applied to a direct injection spark
ignition engine fuelled with methanol. In principle, the combustion mechanism in a
spark ignition engine is quite different from that in a diesel engine or a homogeneous
charge compression ignition (HCCI) engine. Thus, a study of the applicability of the
new pressure diagnostics to a diesel or HCCI engine is necessary.

For the quantiﬁcation of the effectiveness of combustion, thermodynamic prOper-

117

ties of air, fuel, reactants, and products at the initial and terminal state of exothermic
stage of combustion were evaluated with STANJAN. However, STANJAN is not ca-
pable of evaluating thermodynamic properties and concentrations of intermediate
species during the combustion. The author believes that the evaluation of thermo—
dynamic properties and concentrations of intermediate species will give a better un-
derstanding of the combustion process in an internal combustion engine and suggests

employing CHE-.VIKIN for this task.

118

APPENDIX

119

Appendix A

Evaluation of state transformations
of reactants and products With

STANJ AN

A. 1 Introduction

The state space has been introduced in Chapter 3. In the state space, the thermody-
namic state transformations of reactants and products during the exothermic stage of
combustion are well illustrated. Figure A.1 showes a general state space illustrating
four thermodynamic state transformations during the exothermic state of combus-
tion, which are i) from i on R to i on P, ii) from i on R to t on R, iii) from t on R to
t on P, and iiv) from i on P at p, to t at 19,. Also shown in Figure A.1 are the air/ fuel
mixing process and three states of products under special combustion conditions.

In Figure A.1, the slopes of state change of reactants and products from the initial
state i to the terminal state t of the exothermic state of combustion are important
to the evaluation of the effectiveness of combustion. Therefore, the determination of
thermodynamic states of reactants and products at the initial and terminal states is
critical.

The combustion process is a chemical reaction during which the thermodynamic
properties of reactants and products can be obtained from thermodynamic tables such
as JANAF [67] or calculated by the computational program, such as STAN JAN [68]
and CEA [69] [70]. In this analysis, STANJ AN is used to evaluate the thermodynamic

120

 

 

 

 

 

 

 

 

 

 

o /
.4" CV
i\ t
l 0
/’/°/0 . p
i
We
:9.
0 xpEC 1 W
}———
0xPESI

Figure A.1: Diagram of component states with an illustration of the processes of
mixing and adiabatic exothermic center, EC, and exothermic system, ES.

properties of air, fuel, reactants, and products at the states of interest.

A.2 “Procedure

STANJAN is a powerful and easy-to-use program for analysis of chemical equilib-
rium in single- or multi-phase systems based on the method of element potentials and
.1 AN AF tables [78]. To evaluate thermodynamic properties of the system with STAN-
JAN, two thermodynamic parameters of the system are required. In this analysis,

two sets of thermodynamic parameters are used:

1. temperature and pressure;

121

2. enthalpy and pressure same as last run.

Two stages of combustion, sharing the same initial state, were deﬁned in Chapter
3 and 4, respectively. The dynamic stage of combustion (DSC) starts from the initial
state and ends at the ﬁnal state, which is the maximum of the polytrOpic pressure
model. The exothermic stage of combustion (ESC) starts from the initial state and
ends at the terminal state, which is the maximum of effectiveness of combustion.

The determination of terminal state of ESC requires prior knowledge of the ther-
modynamic properties of reactants/ products at the terminal state of ESC. However,
the evaluation of thermodynamic properties at the terminal state of ESC cannot
be implemented without determining the terminal state of ESC. According to stud-
ies [79][80], the terminal state of ESC is located after the ﬁnal state of DSC, but
they are close to each other. Therefore, the ﬁnal state of DSC can be utilized to
to approximate the terminal state of ESC. After employing thermodynamic prop-
erties of reactants/products at ﬁnal state of DSC to determine the location of the
terminal state of ESC, the thermodynamic properties of reactants/products at the
terminal state of ESC were evaluated. By comparing thermodynamic properties of
reactants/ products at the ﬁnal state of DSC to those at the terminal state of ESC,
it was concluded that the ﬁnal state of DSC is a good approximation to the terminal
state of ESC when evaluating thermodynamic properties.

The ﬂowchart of evaluating thermodynamic states of reactants and products is
shown in Figure A.2. By assuming that the mixture in the cylinder the ideal gas,
the temperature of reactants and products can be calculated from the ideal gas equa—
tion. At the initial state of ESC, the temperature of the system, which contains only
reactants, can be calculated with knowledge of inlet temperature. Then the thermo-
dynamic state of reactants at initial state of ESC can be obtained from STANJAN

by inputting the temperature and pressure of reactants.

122

 

 

 

 

 

TRU) perfect gas TR“) Tp(f)
PR(i) PRU) P P“)

 

V

 

 

 

 

 

 

 

 

 

 

 

 

STANJAN

 

 

 

 

 

 

 

e[{(i) ep(hp) 6R“) 31)“)
WR(i) wp(hp) WR(f) WP“)

 

 

 

 

 

 

 

 

 

 

 

 

Figure A.2: Flowchart of evaluating thermodynamic states of reactants and products
during the exothermic stage of combustion.

As previously discussed in Chapters 3 and 4, it is impossible to obtain the tem-
perature of products from the ideal gas equation, since the initial state of ESC is a
singular point. However, it is reasonable to assume that the combustion process at
the initial state of ESC is under constant enthalpy and pressure conditions. Thus,
the thermodynamic state of products at initial state of ESC can be obtained from
STANJAN by specifying that the enthalpy and pressure of products are the same as
those of reactants at the initial state of ESC.

After evaluating the temperatures of reactants and products at the ﬁnal state
of DSC with Equations (4.43) and (4.47) respectively, the thermodynamic states of
reactants and products at ﬁnal state of DSC can be obtained from STANJAN by

inputting the temperature and pressure of reactants and products.

123

Steps for evaluating thermodynamic properties of reactants and products with
STANJ AN are following. Figures illustrating the evaluation of thermodynamic prop-
erties of reactants/products in the methanol engine described in Chapters 3 and 4

are shown with each step.

1. Specify the data ﬁle including reactants and products species (Figures A.3 and
A.4);
2. Enter the mole number of each species in the reactants (Figure A5);

3. Enter the temperature and pressure of reactants at the initial state of ESC and

obtain the thermodynamic properties at this state (Figures A.6 and A.7);

4. Enter the temperature and pressure of reactants at the ﬁnal state of ESC and

obtain the thermodynamic properties at this state (Figures A8 and A9);

5. Change to the products analysis and choose all the species in the data ﬁle as

the components of products (Figure A10);

6. Enter the pressure and enthalpy of products at the initial state of DSC, which
are the same as those of reactants at the initial state of DSC respectively, and
obtain the thermodynamic properties of products at this state (Figures All

and A.12);

7. Enter the temperature and pressure of products at the ﬁnal state of DSC and

obtain the thermodynamic properties at this state (Figures A13 and A.14);

8. Return to step 2 to evaluate thermodynamic properties of reactants/ products

of another case or quit STANJAN (Figure A15).

124

' STANJAN - 11:1 I:

  

 

Figure A.3: Step 1a » — Specify the data ﬁle

' - STANJAN

 

 

Figure A4: Step II) 7 The species in the data ﬁle COMB.SUD

Select STANJAN

 

 

Figure A.5: Step 2 7 Specify the mole number of each species in the reactants

Select STANJAN -11: x

‘ (

  

 

 

Figure A.6: Step 3a Specify the temperature and pressure of reactants at the initial
state of DSC

126

Select STANJAN

.w;
‘ _"~.I.IJL \le 'c

. (llih'llu i 1.1' "I flit'uf'llrl 1 la:

 

DSC

. Select STANJAN

Inter P (ant): (G.
l

FIIII'I' T ‘5'.) 7711.8

 

 

Figure A8: Step 4a Specify the temperature and pressure of reactants at the ﬁnal
state of DSC

127

.. Select STANJAN

. 2) ,q
3 OHIHt 03 T*

W ‘ ’.l198r‘06 j kg

 

 

DSC

~ Select STANJAN

1 .

 

Figure A.10: Step 5 *7 Specify the, species of products

Select STANJAN $1.: 1“

  

 

 

Figure A.11: Step 6a _,. Specify the pressure and enthalpy of products at the initial
state of DSC

- Select STANJAN

, 211)”! kg Inma.
l “combos . “ " I “first ()1 nus l.
,;(1111E~05 j ; .b-Jliul.“ 01 J 1.9, l

 

 

Figure A.12: Step 6b Thermodynamic properties of products at the initial state
of DSC

129

- Select STANJAN

 

 

Figure A.13: Step 7a W Specify the temperature and pressure of products at the ﬁnal
state of DSC

' Select STANJAN

111.111.E0_ "
..‘JIJL ()1

 

Figure A.14: Step 7b ,, Thermodynamic properties of products at the final state of

DSC

130

Select STANJAN

 

 

Figure A.15: Step 8 -—- Quit STANJAN

A.3 Results

The thermodynamic properties of air, fuel, reactants, and products in the methanol
engine under 4 operating conditions listed in Table 3.3 are shown in Tables A.1 —
A.2. The state transformations of air, fuel, reactants, and products during the ESC

are shown in Figures A.16 —— A.19.

131

Table A.1: Thermodynamic properties of air, fuel, reactants, and products in case 1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

States p(atm) T(K) v(m3/kg) u(kJ/g) h(kJ/g) w(kJ/g) M(g/mol)
a 1.1 300.0 0.80495 -0.0846 0.0019 0.0865
1 42.3 649.3 0.043657 0.1761 0.3630 0.1869
A 28.581
f 66.0 724.8 0.031234 0.2359 0.4448 0.2089
t 51.5 681.8 0.037653 0.2017 0.3982 0.1965
a 1.1 300.0 0.72478 -6.3580 -6.2800 0.0780
1 42.3 649.3 0.039309 —5.8650 -5.6960 0.1690
F 32.042
f 66.0 724.8 0.028123 -5.7530 -5.5650 0.1880
t 51.5 681.8 0.033903 -5.8160 -5.6400 0.1760
a 1.1 300.0 0.79742 -0.6740 -0.5883 0.0857
1 42.3 649.3 0.043249 —0.3914 -0.2061 0.1853
R 29.123
f 66.0 724.8 0.030942 -0.3268 -0.1198 0.2070
t 51.5 681.8 0.037301 -0.3637 -0.1691 0.1946
hp=i 42.3 2084.9 0.14486 -0.8270 —0.2061 0.6209 27.92
P f 66.0 1492.1 0.066415 -1.5200 -1.0760 0.4440
27.931
t 51.5 1383.2 0.078907 -1.6390 -1.2270 0.4120

 

 

132

 

 

Table A.2: Thermodynamic properties of air, fuel, reactants, and products in case 2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

States p(atm) T(K) v(m3/kg) u(kJ/g) h(kJ/g) w(kJ/g) M(g/mol)

a 1 300.0 0.85325 -0.0846 0.0019 0.0865

1 31.9 648.7 0.057837 0.1757 0.3626 0.1869
28.581

f 91.2 827.0 0.025791 0.3189 0.55728 0.2383

1‘. 51.4 724.3 0.04008 0.2355 0.4442 0.2087

a 1 300.0 0.76826 -6.3580 -6.2800 0.0780

1 31.9 648.7 0.05208 -5.8660 -5.6970 0.1690
32.042

f 91.2 827.0 0.02322 -5.6010 -5.3870 0.2140

1'. 51.4 724.3 0.03609 —5.7530 -5.5660 0.1870

a 1 300.0 0.84526 -0.6740 -0.5883 0.0857

1 31.9 648.7 0.057296 -0.3919 -0.2067 0.1852
29.123

f 91.2 827.0 0.025549 -0.2373 -0.0012 0.2361

t 51.4 724.3 0.039703 -0.3272 -0.1204 0.2068
hp=i 31.9 2084.0 0.19201 -0.8273 -0.2067 0.6206 27.919

f 91.2 1628.4 0.052457 -1.3680 -0.8829 0.4851
27.931

1: 51.4 1308.0 0.07476 -1.7200 -1.3300 0.3900

 

 

 

 

 

 

 

 

133

 

Table A.3: Thermodynamic properties of air, fuel, reactants, and products in case 3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

States p(atm) T(K) v(m3/kg) u(kJ/g) h(kJ/g) w(kJ/g) M(g/mol)
a 1 300.0 0.85325 -0.0846 0.0019 0.0865
1 42.6 673.0 0.044932 0.1948 0.3887 0.1939
A 28.581
f 58.6 728.1 0.035338 0.2386 0.4484 0.2098
t 50.2 700.8 0.039705 0.2168 0.4187 0.2019
a 1 300.0 0.76826 -6.3580 -6.2800 0.0780
1 42.6 673.0 0.040457 -5.8300 -5.6550 0.1750
F 32.042
f 58.6 728.1 0.031819 -5.7480 -5.5590 0.1890
t 50.2 700.8 0.03575 -5.7880 -5.6060 0.1820
a 1 300.0 0.82166 —0.5966 -0.5109 0.0857
1 42.6 673.0 0.044567 -0.2970 -0.1046 0.1924
R 29.087
f 58.6 728.1 0.035051 -0.2501 -0.0420 0.2081
1’. 50.2 700.8 0.039382 -0.2734 -0.0731 0.2003
hp=i 42.6 1949.7 0.13392 -0.6826 -0.1046 0.5870 28.043
P f 58.6 1400.6 0.069925 -1.2990 -0.8440 0.4150
28.048
13 50.2 1340.0 0.078091 -1.3640 -0.9663 0.3977

 

 

 

134

 

 

 

Table A.4: Thermodynamic properties of air, fuel, reactants, and products in case 4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

States p(atm) T(K) v(m3/kg) u(kJ/g) h(kJ/g) w(kJ/g) M(g/mol)
a 1 300.0 0.85325 -0.0846 0.0019 0.0865
1 39.3 638.9 0.046237 0.1680 0.3521 0.1841
A 28.581
f 21.8 548.0 0.071495 0.0982 0.2561 0.1579
t 15.4 500.9 0.092509 0.0628 0.2071 0.1443
3 1 300.0 0.76826 -6.3580 -6.2800 0.0780
1 39.3 638.9 0.041632 -5.8800 -5.7140 0.1660
F 32042
f 21.8 548.0 0.064374 -6.0150 -5.8730 0.1420
t 15.4 500.9 0.083295 -6.0850 -5.9550 0.1300
a 1 300.0 0.84631 -0.5966 -0.5109 0.0857
1 39.3 638.9 0.045861 -0.3257 -0.1431 0.1826
R 29.087
f 21.8 548.0 0.070914 -0.4008 -0.2442 0.1566
t 15.4 500.9 0.091757 —0.4390 -0.2958 0.1432
hp=i 39.3 1923.6 0.14322 -0.7134 -0.1431 0.5703 28.044
P f 21.8 1017.3 0.136524 -1.6920 -1.3900 0.3020
28.048
1: 15.4 925.1 0.175737 -1.7810 -1.5070 0.2740

 

 

 

 

 

 

 

 

 

 

 

 

 

2
e (kJ/g)

 

 

 

 

 

.3 1
O 0.25 w (kJ/g) 0.5

Figure A.16: State transformations of air, fuel, reactants, and products in case 1

 

 

 

 

 

 

 

 

 

 

.8 l
0 0.25 w (kJ/g) 0.5

Figure A.17: State transformations of air, fuel, reactants, and products in case 2

136

 

 

 

 

 

 

 

 

o 0.25 w (kJ/g) 0.5

Figure A.18: State transformations of air, fuel, reactants, and products in case 3

 

2
e (kJ/g)

o .-

 

 

 

 

 

 

 

0 0.25 W (kJ/Q) 0.5

Figure A.19: State transformations of air, fuel, reactants, and products in case 4

137

BIBLIOGRAPHY

138

Bibliography

[1] Heywood, J.B., Internal Combustion Engine Fundamentals, McGraw-Hill Pub-
lishing Company,1988.

[2] Stone, R, Introduction to Internal Combustion Engines, SAE International,
2000.

[3] Dai, W., Trigui, N., and Lu, Y., “Modeling of Cyclic Variations in Spark-
Ignition Engines,” SAE Paper 2000-01-2036, 2000.

[4] Letellier, C., Meunier-Guttin-Cluzel, S., et. al., “Use of the Nonlinear Dynami-
cal System Theory to Study Cycle-to-Cycle Variations from Spark Igntion En-
gine Pressure Data,” SAE Paper 971640.

[5] Ozdor, N., Dulger, M., and Sher, E., “An Experimental Study of the Cyclic
Variability in Spark Ignition Engines,” SAE Paper 960611, 1996.

[6] Koochesfahani, M.M., “Molecular Tagging Velocimetry (MTV): Progress and
Applications,” AIAA Paper AIAA-99-3786, 1999.

[7] Stier, B. and Koochesfahani, M.M., “Molecular Tagging Velocimetry (MTV)
Measurements in Gas Phase Flows,” Experiments in Fluids, Vol. 26, pp. 297—
304, 1999.

[8] Gendrich, GP. and Koochesfahani, M.M., “A Spatial Correlation Technique for
Estimating Velocity Fields Using Molecular Tagging Velocimetry (MTV),” Vol.
22, pp. 67—77, 1996.

[9] Trigui, N., Kent, J.C., et al., “Characterization of Intake Generated Fluid Flow
Fields in IC Engines Using 3-D Particle Tracking Velocimetry (3—D PTV),”
SAE Paper 940279, 1994.

[10] Choi, WC. and Guezennec, Y.G., “Measurement of Cycle-to-Cycle Variations
and Cycle-Resolved Turbulence in an IC Engine Using a 3—D Particle Tracking
Velocimetry,” JSME International Journal, Series B, Vol. 41, No. 4, pp. 991—
1003, 1998, 1998.

[11] Reuss, D.L., “Cyclic Variability of Large-Scale Turbulent Structures in Directed
and Undirected IC Engine Flows,” SAE Technical Paper 200001-0246, 2000.

139

[12]

[13]

[14]

[15]

[16]

[17]

[18]

WI

[20]

[21]

[22]

1231

[24]

Khalighi, 8., “Study of the Intake Tumble Motion by Flow Visualization and
Particle Tracking Velocimetry,” Experiments in Fluids, Vol. 10, pp. 230—236,
1991.

Zhang, L., Ueda, T., et al., “Cycle-to-Cycle Variation of In-Cylinder Flow in
a Motored Engine,” JSME International Journal, Series B, Vol. 38, No. 3, pp.
426431, 1995.

Hascher, H.G., Novak, M., et al., “The 3—D In—Cylinder Charge Motion of a
Four-Valve SI Engine under Stroke, Speed, and Load Variation,” SAE Technical
Paper 200001-2789, 2000.

Lee, K., Yoo, SC, et al., “An Experimental Study of In—Cylinder Air Flow
in a 3.5L Four Valve SI Engine by High Speed Flow Visualization and Two—
Component LDV Measurement,” SAE Technical Paper 930478, 1993.

Urushihara, T., Murayama, T, et al., “Turbulence and Cycle-by-cycle Variations
of Mean Velocity Generated by Swirl and Tumble Flow and Their Effects on
Combustion,” SAE paper 950813, 1995.

Schock, H., Shen, Y., et. al., “The Measurement and Control of Cyclic Varia-
tions of Flow in a Piston Cylinder Assembly,” SAE Technical Paper 2003-01-
1357, 2003.

Tomonori, U., Taichi, M., et al., “Turbulence and Cycle-by-Cycle Variation
of Mean Velocity Generated by Swirl and 'Ihmble Flow and Their Effects on
Combustion,” SAE Technical Paper 950813, 1995.

Jaffri, K., Hascher, H.G., et al., “Tumble and Swirl Quantiﬁcation within a
Motored Four-Valve SI Engine Cylinder Based on 3-D LDV Measurements,”
SAE Technical Paper 970792, 1997.

F loch, A., Frank, J.V, and Ahmed, A., “Comparison of the Effects of Intake-
Generated Swirl and Tumble on Turbulence Characteristics in a 4-Valve En-
gine,” SAE Technical Paper 952457, 1995.

Munson, B.R., Young, DE, and Okiishi, T.H., Fundamentals of Fluid Mechan-
ics, John Wiley & Sons, Inc., 1998.

Daw, CS. and Kahl, W.K., “Interpretation of Engine Cycle-to-cycle Variation
by Chaotic Time Series Analysis,” SAE Technical Paper 902103, 1990.

Ludwig, C., Leonhardt, S., et al., “Measurement and Monitoring of Pressure
Curves in Diesel Engines,” Proceedings of the American Control Conference,
San Francisco, California, June 1993.

Roberts, J .B., Peyton Jones, J .C., and Landsborough, K.J., “Cylinder Pressure
Variations as a Stochastic Process,” ” SAE Technical Paper 970059, 1997.

140

[25] Rassweiler, GM. and Withrow, L., “Motion Pictures of Engine Flames Corre-
lated with Pressure Cards,” SAE Technical Paper 800131, 1980.

[26] Homsy, SC. and Atreya, A., “An Experimental Heat Release Rate Analysis
of a Diesel Engine Operating Under Steady State Conditions,” SAE Technical
Paper 970889, 1997.

[27] Brunt, M.F.J., Rai, H., and Emtage, AL, “The Calculation of Heat Release
Energy from Engine Cylinder Pressure Data,” SAE Technical Paper 981052,
1998.

[28] Urushihara, T., Murayama, T, et al., “Turbulence and Cycle-by-cycle Variations
of Mean Velocity Generated by Swirl and Tumble Flow and Their Effects on
Combustion,” SAE paper 950813, 1995.

[29] Johansson, B. and Olsson, K., “Combustion Chambers for Natural Gas SI En-
gines Part I: Fluid Flow and Combustion,” SAE Technical Paper 950469, 1995.

[30] Stevens, S.P., Shayler, P.J., and Ma, T.H., “The Impact of Combustion Phasing
on Cycle-by-cycle Performance of a Spark Ignition Engine,” SAE Technical
Paper 950687, 1995.

[31] Young, M.B., “Cyclic Dispersion in the Homogeneous-Charge Spark-Ignition
Engine — A Literature Survey,” SAE Technical Paper 810020, 1980.

[32] Hill, PG. and Kapil, A., “The Relationship between Cyclic Variations in Spark-
Ignition Engines and the Small Structure of Turbulence,” Combustion and
Flame, Vol. 78, pp. 237—247, 1989.

[33] Foakes, AP. and Pollard, D.G., “Investigation of a Chaotic Mechanism for
Cycle—to—cycle Variations,” Combustion Science and Technology, Vol. 90, pp.
281—287, 1993.

[34] Kantor, J .C., “A Dynamical Instability of Spark—Ignited Engines,” Science, Vol.
224, pp. 1233—1235, 1984.

[35] Russ, S., Peet, G., and Stockhausen, W., “Measurements of the Effect of In-
Cylinder Motion on Flame Development and Cycle-to-Cycle Variations Using
an Ionization Probe Head Gasket,” SAE Technical Paper 970507, 1997.

[36] Ohsuga, M., Yamaguchi, J ., et al., “In-Cylinder Air Fuel Ratio and Combustion
Control for Spark Ignition Engines,” SAE Technical Paper 950076, 1995.

[37] Johansson, 8., Neij, H., et al., “Investigations of the Inﬂuence of Mixture Prepa-
ration on Cyclic Variations in a SI-Engine, Using Laser Induced Fluorescence,”
SAE Technical Paper 950108, 1995.

[38] Daily, J .W., ”Cycle-to-Cycle Variations: A Chaotic Process?” Combustion Sci-
ence and Technology, Vol. 57, pp. 149—162, 1988.

141

l39l Docquier, N- and Candel, 3, “Combustion Control and Sensors: a Review,”
Progress in Energy and Combustion Science, Vol. 28, pp. 107— 150, 2002.

[40] Najt, PM. and Foster, D.E., “Compression-Ignited Homogeneous Charge Com-
bustion,” SAE Technical Paper 830264, 1983.

[41] Flynn, P., Hunter, G., et al. “Premixed Charge Compression Ignition Engine
with Optimal Combustion Control,” US Patent 6276334 BI.

[42] Kamei, E., Namba, H., et al., “Application of Reduced Order Model to Auto-
motive Engine Control System,” Journal of Dynamic Systems, Measurement,
and Control, Transaction of the ASME, Vol. 109, pp. 232—237, 1987.

[43] Wolanski, P. and Oppenheim, A.K., “Controlled Combustion Engines (CCE),”
SAE Technical Paper 1999—01-0324, 1999.

[44] Oppenheim, A.K., “Prospects for Combustion in Piston Engines,” SAE Tech-
nical Paper 2002-01-0999, 2002.

[45] Neumeier, Y. and Zinn, B.T., “Active Control of Combustion Instabilities with
Real Time Observation of Unstable Combustor Modes,” AIAA-96—0758, 34th
Aerospace Sciences Meeting 82 Exhibit, Reno, NV, 1996.

[46] Gavillet, G.G., Maxson, J.A. and Oppenheim, A.K., “Thermodynamic and
Thermochemical Aspects of Combustion in Premixed Charge Engines Revis-
ited,” SAE Technical Paper 930432, 1993.

[47] Maxson, J.A., Hensinger, D. M., Hom, K., and Oppenheim, A. K., “Perfor-
mance of Multiple Stream Pulsed Jet Combustion Systems,” SAE Technical
Paper 910565, 1991.

[48] Maxson, J .A. and Oppenheim, A. K., “Pulsed Jet Combustion —— Key to a Re-
ﬁnement of the Stratiﬁed Charge Concept,” Twenty- Third Symposium (Interna-
tional) on Combustion, Pittsburgh, The Combustion Institute, pp. 1041—1046,
1991.

[49] Oppenheim, A.K., “The Knock Syndrome -——- Its Cures and Its Victims,” SAE
Technical Paper 841339, 1984.

[50] Oppenheim, A.K., “The Beauty of Combustion Fields and Their Aero—Thermo—
Dynamic Signiﬁcance,” Dynamics of Reactive Systems Part 1: Flames, Progress
in Astronautics and Aerodynamics, Washington DC, AIAA pp.25l—265, 1985.

[51] Oppenheim, A.K., “Quest for Controlled Combustion Engines,” SAE T ransac-
tions, The Journal of Engines, Vol. 97(6), pp.1033—1039, 1988.

[52] Oppenheim, A.K., “Life on Earth at the Point of Inﬂection & The Future of
Combustion in Engines,” Proceedings of the Institution of Mechanical Engi-
neers, C448/076 & 022, ImechE, pp. 215— 220 & 187—192, 1992.

142

[53] Oppenheim, A.K., “Aerodynamic Control of Combustion,” Journal of Fluids
Engineering, Vol. 115(4), pp. 561—567, 1993.

[54] Oppenheim, A.K., “Turbulent Combustion in Contrast to Flames,” Modern De-
velopments in Energy, Combustion and Spectroscopy, Oxford, Pergamon Press,
pp. 1—13, 1993.

[55] Oppenheim, AK. and Maxson, J .A., “Thermodynamics of Combustion in an
Enclosure,” Progress in Astronautics and Aeronautics, American Institute of
Aeronautics and Astronautics, New York, pp. 365—382, 1991.

[56] Oppenheim, AK. and Maxson, J .A., “A Thermochemical Phase Space for Com-
bustion in Engines,” Twenty-Fifth Symposium (International) on Combustion,
The Combustion Institute, Pittsburgh, Pennsylvania, pp. 157—165, 1994.

[57] Oppenheim, A.K., Barton, J.E., Kuhl, AL. and Johnson, W.P., “Reﬁnement
of Heat Release Analysis,” SAE Technical Paper 970538, 1997.

[58] Oppenheim, A. K., Beltramo, J. et al., “Combustion by Pulsed Jet Plumes-
Key to Controlled Combustion Engines,” SAE Transactions, The Journal of
Engines, Vol. 98, pp. 175—182, 1989.

[59] Oppenheim A.K., Kuhl A.L., et al., “Model and Control of Heat Release in
Engines,” Engine Combustion and Flow Diagnostics, SP-1157, SAE Technical
Paper 960601, pp. 15—23, 1996.

[60] Oppenheim, A.K., Maxson, J.A., et al., “Fireball Mode of Combustion and
Its Adaptive Control,” Twenty-Sixth International Symposium on Automotive
Technology and Automation, Aachen, Germany, 1993.

[61] Oppenheim, A.K., Maxson, J .A., and Shahed S.M., “Can the Maximization of
Fuel Economy be Compatible with the Minimization of Pollutant Emissions?”
SAE Technical Paper 940479, 1994.

[62] Gutowski, J .A., Balles, E.N. et al., “Heat Release Analysis of Engine Pressure
Data,” SAE Technical Paper 841359, 1984.

[63] Heywood, J .B., Higgins, J .M., et al. “Development and Use 0 a Cycle Simulation
to Predict SI Engine Efﬁciency and NOx Emissions,” SAE Technical Paper
790291, 1979.

[64] Benson, R.A., The Thermodynamics and Gas Dynamics of Internal-Combustion
Engines, Vol. 1, Clarendon Press, Oxford, 1962.

[65] George, R.S., Schock, H.J., et al. “Design of a High Compression Direct Injec-
tion Spark-Ignition Methanol Fuelled Research Engine with an Integral Injector
Ignition Source Insert,” SAE Technical Paper 2001-01-3651, 2001.

[66] Gibbs, J .W., “On the Equilibrium of Heterogeneous Substances,” Transactions
of the Connecticut Academy, III 1875-76: pp. 108-248.

143

[67]

[58]

[691

[70]

[71]

[72]
[73]

[76]

[77]

[78]

[79]

[80]

Stull, DR. and Prophet H. “J ANAF Thermochemical Tables,” National Bureau
of Standards (currently NIST for National Institute of Standards and Technol-
ogy), US. Department of Commerce, Report NSRDS-NBS 37, 1971.

Reynolds, W.C., “STANJAN Interactive Computer Programs for Chemical
Equilibrium Analysis”, Department of Mechanical Engineering, Stanford Uni-
versity, Stanford, California, 1986.

Gordon, S. and McBride, B.J., “Computer Program for Calculation of Com-
plex Chemical Equilibrium Compositions and Applications, 1. Analysis”, NASA
Reference Publication 1311, 1994.

McBride, B.J. and Gordon, S., “Computer Program for Calculation of Complex
Chemical Equilibrium Compositions and Applications, II. Users Manual and
Program Description”, NASA Reference Publication 1311, 1996

Boddington, T., Gray, P. and Harvey, D.L., “Thermal Theory of Spontaneous
Ignition: Criticality in Bodies of Arbitrary Shape,” Philosophical Transactions
of the Royal Society of London, Series A, Mathematical and Physical Sciences,
Vol. 270, No. 1207, pp. 467-506, 1971.

Peters, N ., Turbulent Combustion, Cambridge University Press, 2000.

Oppenheim, A.K., “Dynamic Features of Combustion,” Philosophical Trans-
actions of the Royal Society of London, Series A, Mathematical and Physical
Sciences, Vol. 315, No. 1534, pp. 471-508, 1985.

Oppenheim, AK. and Kuhl, A.L., “Energy Loss from Closed Combustion Sys-
tems,” Proceedings of the Combustion Institute, Vol. 28, 2000.

Ferguson, GR. and Kirkpatrick, A.T., Internal Combustion Engines : Applied
T hermosciences, 2nd Edition, John Wiley & Sons, 2001.

Van Wylen, G.J. and Sonntag, R.E., Fundamentals of Classical Thermodynam-
ics, 3rd Edition, John Wiley & Sons, 1985.

Ferguson, C.R., Internal Combustion Engines : Applied Thermosciences, lst
Edition, John Wiley & Sons, 1986.

Reynolds, W.C., “The Element Potential Method for Chemical Equilibrium
Analysis: Implementation in the Interactive Program STANJAN,” Version 3,
Department of Mechanical Engineering, Stanford University, Stanford, Califor-
nia, 1986.

Shen, Y., Schock, H., et al., “Dynamic Stage of Combustion in a Direct. Injection
Methanol Fueled Engine,” SAE Technical Paper 2002—01-0998, 2002.

Shen, Y., Schock, H. and Oppenheim, A., “Pressure Diagnostics of Closed Sys-
tem in a Direct Injection Spark Ignition Engine,” SAE Technical Paper 2003-
01-0723, 2003.

144

[81] Pope, S.B., Turbulent Flows, Cambridge University Press, 2000.
[82] Hinze, J.O., Turbulence, McGraw-Hill Book Company, 1959.

   

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