minimising cold start fuel consumption and emissions from

Minimising Cold Start Fuel Consumption and

Emissions from a Gasoline Fuelled Engine

Denis Andrianov

Submitted in total fulfilment of the requirements of the degree of

Doctor of Philosophy

November 2011

Department of Mechanical Engineering,

The University of Melbourne,

Victoria, Australia

Produced on archival quality paper

Abstract

The catalytic converter, which is in the exhaust of most vehicles on road today, has led to a

dramatic improvement in the quality of the air in industrialised cities despite a large growth in

traffic. As a result, almost all of the gaseous pollutant emissions from cars are now released in the

first minutes of driving while the catalyst warms to its operating temperature. Current emissions

control approaches therefore mostly aim at reducing this warm up time, and are developed during

extensive testing by experienced engineers. This involves significant time and cost, and may not

guarantee an optimal outcome.

In this thesis, a novel approach to this warm-up problem is proposed. Dynamic optimisation

procedures are applied to a mathematically compact model of an engine and its exhaust system

to identify new engine control strategies and trends for prescribed driving conditions. The order

of the model, which can be calibrated from steady state engine maps and a single transient

engine test, is high enough to capture most of the major phenomenon involved, but is of low

enough order to permit dynamic optimisation studies. Both the model itself and some of the

optimised strategies found are validated using a transient engine dynamometer and emissions

facility.

Several constrained optimisation problems are considered, in which different tailpipe emis-

sions regulations are the constraints under which the fuel consumption is minimised. The so-

lutions of these optimisation problems indicate that optimised spark advance is always charac-

terised by retarded timing during cold start, followed by a transition to near maximum brake

torque (MBT) timing. These results suggest that a bang-bang type of approach might apply.

To test this, an ignition policy, defined initially by retarded spark timing limited by drivability

considerations and MBT timing afterwards, is prescribed. It is demonstrated that provided the

switching time is optimised, overall fuel consumption and tailpipe emissions approach the re-

sults of the dynamic optimisation. Further, higher degree of freedom optimisation, particularly

incorporating air-fuel ratio and cam timing, suggest that additional gains may be achievable.

iii

Declaration

This is to certify that

1. the thesis comprises only my original work towards the PhD except where indicated,

2. due acknowledgement has been made in the text to all other material used,

3. the thesis is less than 100000 words in length, exclusive of tables, maps, bibliographies and

appendices.

v

Acknowledgements

I would like to express my gratitude to a number of people who have supported me over the

course of this project.

• Michael Brear and Chris Manzie (my supervisors)

Their guidance was invaluable. The enlightening discussions at our regular meetings and

their enthusiasm have inspired me throughout the four years of my PhD. Furthermore,

the transient dynamometer ACART facility made available to me enabled numerous useful

experimental results to be produced. Thank you!

• Farzad Keynejad

Our occasional but long lasting discussions and debates over cold start engine modelling and

dynamic optimisation have contributed to my understanding of the topic. Furthermore,

the engine model presented in this thesis is based on some of Farzad’s work.

• Peter Dennis

Peter’s in-house built software for sampling and post-processing of in-cylinder pressure

data was used extensively throughout my experiments. Without this tool calibration of

parts of my model would not have been possible.

• Martin Thurkettle

Martin had kindly provided all of the technical support required for the commissioning of

the Horiba emissions bench in our test cell.

• Robert Dingli

Rob’s vast experience in the automotive industry and his willingness to assist have enabled

me to perform good quality experiments and to learn a lot about the state-of-the-art in

engine development and testing.

vii

• Don Halpin and Ted Grange

The assistance from Don and Ted, who helped to instrument the engine and the exhaust

system, was invaluable.

• Eileen Shea

Many thanks to Eileen for ordering all that hardware required for my experimental work.

• Harry Watson

Harry is known as “the walking encyclopaedia” in our department. Consequently, none of

my numerous engine related questions have remained unanswered. Thank you, Harry.

• Mohsen Talei

Mohsen is famous for his great sense of humour. As his laughter could often be heard far

from the source of sound, the dynamics of which he studied, it made writing of this thesis

very entertaining.

• Kai Morganti

Kai was one of the first to appreciate my hydrogen filled balloon floating about the office

after too many experiments. His “wall of shame”, which helped turn Mohsen into a local

celebrity, shall expose that historical moment for many years to come and thus inspire

future generations of postgraduate students.

• Peter Hield, Ashley Wiese, Pouria Mehrani, Payman Abbasi, Matthew Blom, Pedro Or-

baiz, Tien Mun Foong, Lucas Esclapez, Bishoy Alfons and Qaiser Zakka

These people (and those already mentioned) have contributed to a friendly, comfortable

and enjoyable environment in our offices. It has been a pleasure to work among you guys!

• Mariya (my wife), Alisa (my daughter) and the rest of my family

A big thank you to my family for their support and my wife for her patience, especially

during the last phases of this project.

viii

Contents

Abstract iii

Declaration v

Acknowledgements vii

Nomenclature xiii

1 Introduction 1

1.1 Research objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2 Thesis layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Literature review 7

2.1 Prior use of optimisation tools in engine calibration . . . . . . . . . . . . . . . . . 7

2.1.1 Optimisation of engine maps . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1.2 Dynamic optimisation of engine control variables . . . . . . . . . . . . . . 8

2.2 Dynamic optimisation theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3 Spark ignition engine models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.3.1 Cold start friction and engine warm-up models . . . . . . . . . . . . . . . 16

2.3.2 Modelling of air and fuel dynamics . . . . . . . . . . . . . . . . . . . . . . 17

2.3.3 Exhaust gas heat loss models . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.4 Engine-out emissions models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.5 Three-way catalyst models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.6 Integrated models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3 Experimental methods 27

3.1 Dynamometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.2 Engine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.3 Fuel conditioning system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

ix

3.4 Exhaust system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.5 Fast response thermocouples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.6 Indicated work measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.6.1 In-cylinder pressure measurements . . . . . . . . . . . . . . . . . . . . . . 36

3.6.2 Calculation of the indicated work . . . . . . . . . . . . . . . . . . . . . . . 38

3.7 Exhaust gas analysers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.7.1 Cambustion HFR400 fast flame ionisation detector . . . . . . . . . . . . . 40

3.7.2 Horiba 200 series emissions bench . . . . . . . . . . . . . . . . . . . . . . 42

3.7.3 Autodiagnostics ADS9000 . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.7.4 Steady state comparison of analysers . . . . . . . . . . . . . . . . . . . . . 50

3.7.5 Calculating wet molar fractions from dry gas composition . . . . . . . . . 51

3.8 Measurement of the air-fuel ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.8.1 Bosch LSU 4.9 wide-band sensor . . . . . . . . . . . . . . . . . . . . . . . 55

3.8.2 Calculation of λ from the exhaust composition . . . . . . . . . . . . . . . 56

3.8.3 Comparison of λ measurement techniques . . . . . . . . . . . . . . . . . . 58

3.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

4 Cold start fuel consumption and tailpipe emissions model 61

4.1 Transient dynamometer control system . . . . . . . . . . . . . . . . . . . . . . . . 62

4.2 The engine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

4.2.1 Flow past the throttle plate . . . . . . . . . . . . . . . . . . . . . . . . . . 63

4.2.2 Intake manifold pressure dynamics . . . . . . . . . . . . . . . . . . . . . . 65

4.2.3 Air and fuel consumption . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4.2.4 Exhaust gas temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

4.2.5 Torque production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

4.2.6 Friction and engine warm-up . . . . . . . . . . . . . . . . . . . . . . . . . 69

4.3 Engine-out emissions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

4.3.1 CO, HC and NOX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.3.2 CO2, H2O, O2 and H2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

4.4 Exhaust manifold and connecting pipe . . . . . . . . . . . . . . . . . . . . . . . 73

4.4.1 Energy conservation in the gas phase . . . . . . . . . . . . . . . . . . . . . 73

4.4.2 Energy conservation in the solid phase . . . . . . . . . . . . . . . . . . . . 75

4.4.3 Heat transfer coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

4.5 The three-way catalyst . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

x

4.5.1 Energy and mass conservation equations . . . . . . . . . . . . . . . . . . 79

4.5.2 Chemical kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

4.5.3 Heat and mass transfer coefficients . . . . . . . . . . . . . . . . . . . . . 84

4.5.4 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

4.5.5 Model discretisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5 Model calibration and validation 89

5.1 Engine and dynamometer control system models . . . . . . . . . . . . . . . . . . 91

5.1.1 Calibration of the engine model . . . . . . . . . . . . . . . . . . . . . . . . 92

5.1.2 Calibration of the dynamometer control system model . . . . . . . . . . . 101

5.1.3 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

5.2 Engine-out emissions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

5.2.1 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

5.2.2 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

5.3 Exhaust manifold and connecting pipe models . . . . . . . . . . . . . . . . . . . . 122

5.3.1 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

5.3.2 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

5.4 Three-way catalyst . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

5.4.1 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

5.4.2 Model reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

5.4.3 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

5.5 The integrated engine, exhaust system and catalyst model . . . . . . . . . . . . . 146

5.6 Error analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

5.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

6 Minimising fuel consumption under tailpipe emissions constraints 159

6.1 Optimal control problem formulation . . . . . . . . . . . . . . . . . . . . . . . . . 159

6.2 Modified optimal control problem formulation . . . . . . . . . . . . . . . . . . . . 161

6.3 Spark timing solution for an under-floor catalyst with Euro-3 limits . . . . . . . 166

6.3.1 ∆t = 20 second grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

6.3.2 ∆t = 10 second grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

6.3.3 Sensitivity of the results of optimisation using ∆t = 10 second grid to

modelling uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

6.3.4 Switching result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

xi

6.3.5 Validation of local optimality . . . . . . . . . . . . . . . . . . . . . . . . . 174

6.4 Spark timing solution for a close-coupled catalyst with Euro-3 limits . . . . . . . 175

6.4.1 ∆t = 20 second grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175


6.5 Spark timing and λ solution for an under-floor catalyst with Euro-3 limits . . . . 182

6.5.1 ∆t = 20 second grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182


6.6 Spark timing and λ solution for a close-coupled catalyst with Euro-3 and Euro-4

limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186

6.6.1 ∆t = 20 second grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186


6.7 Spark and cam timing solution for a close-coupled catalyst with Euro-3 limits . . 187

6.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

7 Conclusions 199

7.1 Recommendations for further work . . . . . . . . . . . . . . . . . . . . . . . . . . 202

A Derivation of the catalyst model equations 207

A.1 Energy conservation in the gas phase . . . . . . . . . . . . . . . . . . . . . . . . 207

A.2 Energy conservation in the solid phase . . . . . . . . . . . . . . . . . . . . . . . . 210

A.3 Mass conservation in the gas phase . . . . . . . . . . . . . . . . . . . . . . . . . 211

A.4 Mass conservation in the washcoat . . . . . . . . . . . . . . . . . . . . . . . . . . 213

B Volumetric and indicated efficiency parameters 215

xii

Nomenclature

V ariables :

A area [m2]

AFRS stoichiometric air-fuel ratio

Ac substrate cross-sectional area [m2]

ae cylinder wall heat transfer parameter

af engine friction calibration parameters

at throttle body calibration parameter

At throttle open area [m2]

Acyl total combustion chamber surface area [m2]

Ae,i pre-exponential factor of reaction i [mol K/m3 s]

Aec cross-sectional area of the gas in the monolith [m2]

aex,1 exhaust system heat transfer parameter

aex,2 exhaust system heat transfer parameter

aind,j,k,l,m,n,o net indicated efficiency calibration parameters

aMBT,i,j,k MBT spark timing calibration parameters

avol,j,k,l,m,n volumetric efficiency calibration parameters

aX,j,k,l,m,n,o engine-out X emissions calibration parameters

B cylinder bore diameter [m]

be cylinder wall heat transfer parameter

bt throttle body calibration parameter

bex,1 exhaust system heat transfer parameter

c specific heat capacity [J/kg K]

CD discharge coefficient

Ci molar fraction of species i [mol/mol]

cp specific heat at constant pressure [J/kg K]

xiii

ct throttle body calibration parameter

cv specific heat at constant volume [J/kg K]

CV,i molar concentration of species i [mol/m3]

d total distance covered by a vehicle [km]

Dc hydraulic diameter of a channel [m]

Di,j binary diffusion coefficients for species i and j [m2/s]

e specific internal energy [J/kg]

E total internal energy [J ]

eX normalised emissions [mol X/kg fuel]

Ea,i activation energy of reaction i [J ]

F extensive property

F continuous vector field

f intensive property

h specific enthalpy [J/kg]

hcyl in-cylinder heat transfer coefficient [W/m2 K]

hgs heat transfer coefficient at gas-solid boundary [W/m2 K]

hm,gs,i mass transfer coefficient for species i [m/s]

hsa heat transfer coefficient at solid-ambient boundary [W/m2 K]

∆hf,i standard enthalpy of formation for species i [J/mol]

∆hr,i enthalpy of reaction i [J/mol]

ID intake duration [CAD]

J cost function

Jcrank moment of inertia of the crankshaft [kg m2]

k thermal conductivity [W/mK]

kI integrator gain

kP proportional gain

Kwg equilibrium constant for the water-gas shift reaction

l length [m]

L reactor length [m]

lC crank throw [m]

lP cylinder pin offset [m]

lR piston rod length [m]

lw washcoat thickness [m]

xiv

m mass [kg]

mair air mass flow rate [kg/s]

mcyl exhaust mass flow rate [kg/s]

mfuel fuel mass flow rate [kg/s]

mport air mass flow rate towards intake ports [kg/s]

Mi molar mass of species i [kg/mol]

Mfuel molar mass of fuel on C1 basis [kg/mol CHrHC]

N engine speed [rad/s]

NRMSE normalised root mean squared error

NuD Nusselt number based on characteristic length D

nc number of cylinders

ni amount of species i [mol]

ni molar transport rate of species i [mol/s]

Nr total number of reactions

n normal unit vector

ncat number of nodes in the catalyst model

nfuel amount of fuel on C1 basis [mol C1]

nss total number of steady state experiments

Nst number of time stages

p pressure [Pa]

Peh,D heat Peclet number based on characteristic length D

Pem,D,i mass Peclet number for species i based on characteristic length D

Pr Prandtl number

Pe wetted perimeter [m]

pbme brake mean effective pressure [Pa]

pfme frictional mean effective pressure [Pa]

pime indicated mean effective pressure [Pa]

q arbitrary quantity

Q heat [J ]

QLHV lower heating value of the fuel [J/kg]

R gas constant [J/kg K]

ReD Reynolds number based on characteristic length D

RMSE root mean squared error

xv

Ru universal gas constant, 8.31 J/mol K

rX proportion of compound X

Rc,i consumption rate of species i [mol/m3 s]

rHC hydrogen to carbon ratio

rO2 molar fraction of O2 in air [mol/mol]

Rr,i reaction rate of reaction i [mol/m3 s]

S geometric surface area per unit reactor volume [m2/m3]

S surface

Sci Schmidt number for species i

ShD,i Sherwood number for species i based on characteristic length D

Si legislated emissions limits [g/km]

Sp average piston velocity [m/s]

T temperature [K]

tf final time constant [s]

tcyc drive cycle duration [s]

tsw switching time [s]

u velocity [m/s]

u input vector

uc vector of engine control inputs

uco vector of engine control inputs subject to optimisation

ucu vector of engine control inputs excluded from optimisation

v kinematic viscosity [m2/s]

v velocity vector

V volume [m3]

Vg,cyl volumetric consumption at intake manifold conditions [m3/s]

Vi diffusion volume of species i

VS cylinder swept volume [m3]

w proportion of the washcoat that is catalytically active

W work output [J ]

wcon flexibility of soft constraints

x state vector

xI integrator state

Xfilm fraction of the injected fuel condensed

xvi

z vector with algebraic variables

α catalytic surface area per unit reactor volume [m2/m3]

α throttle angle [◦]

ǫ reactor void fraction

ηind,net net indicated efficiency

ηvol volumetric efficiency

γ cp/cv ratio

λ normalised air-fuel ratio

µ dynamic viscosity [Ns/m2]

ψ extent of oxygen storage

Ψ oxygen storage capacity [mol/m3]

ρ density [kg/m3]

τ time constant [s]

τbrake brake engine torque [N m]

τcrank indicated engine torque [N m]

τfric frictional engine torque [N m]

θ crankshaft position [CAD]

θ spark timing [CAD BTDC]

Θ vector with tuning parameters

ϕi addition rate of species i [mol/m3 s]

ϑexh exhaust valve closing angle [CAD ABDC]

ϑint intake valve closing angle [CAD ABDC]

ϑovlp valve overlap [CAD]

Subscripts :

ADS9000 taken using the ADS9000 gas analyser

amb ambient, atmospheric

bore cylinder bore

c consumption

c.s. control surface

c.v. control volume

cat catalyst

cl clearance

xvii

cor corrected

cp connecting pipe

cs engine control strategy

css engine control strategy simplified

cyl exhaust port gas conditions

em exhaust manifold

eng lumped engine conditions

EUDC Extra Urban Drive Cycle

ex exhaust system component

film liquid

g gaseous phase

gen generation

h convection

i inner

im intake manifold

in inlet gas

inj injection

k conduction

max maximum value

MBT maximum brake torque

min minimum value

NEDC New European Drive Cycle

o outer

off offset

out outlet gas

r generation

s solid phase or near solid phase

tp tailpipe

vap vapourised, evaporation

Superscripts :

(d) dry basis

(j) at node j

xviii

(m) measured, based on measurements

∗ excited state

off offset

ref reference

⋆ optimal

xix

Chapter 1

Introduction

Road vehicles with internal combustion engines are a significant source of air pollution (Seinfeld,

2004) and are responsible for roughly 12% of overall CO2 emissions in Australia (ABS, 2006).

The major pollutants found in the exhaust include carbon monoxide (CO), nitrogen oxides

(NO and NO2, also referred to as NOX) and unburned hydrocarbons (HC). These substances

present significant environmental and health risks. For example, carbon monoxide can combine

with haemoglobin, contained in blood, preventing the delivery of oxygen to bodily tissues, whilst

some of the emitted hydrocarbons are poisonous and carcinogenic (Heywood, 1988). Apart from

contributing to the formation of acid rains (Pitts et al., 1983), NOX emissions, under the

influence of sun-light and certain types of hydrocarbons, can react with oxygen in air to produce

ozone in the lower layers of the atmosphere. This often results in photochemical smog formation,

which is linked to respiratory health problems.

Carbon monoxide, hydrocarbon and NOX emissions from cars are consequently controlled in

many countries by legislation. To improve the air quality and account for the increasing number

of road vehicles, the allowable emissions limits are being continually tightened. The compliance

of vehicles to emissions standards is tested over drive cycles, which define fixed vehicle speed

profiles. Drive cycles identify the periods of acceleration, braking, idling and sometimes gear

shifting events. Consequently, this enables repeatability of the emissions measurements and

allows the performance of different vehicles to be compared if the cycle is followed closely.

Figure 1.1 shows a typical vehicle speed trace following the New European Drive Cycle (NEDC),

which is used throughout Europe and Australia.

The emissions limits imposed by legislation now require catalytic converters. Three-way

catalysts, illustrated in Figure 1.2, are used in the exhaust systems of many modern spark ignition

engines to simultaneously convert most of the CO, NOX and HC engine-out emissions to much

1

0

20

40

60

80

100

120

0 200 400 600 800 1000 1200

Ve

hic

le s

pe

ed

(km

/h)

Time (s)

Figure 1.1: New European Drive Cycle (NEDC)

less harmful CO2, H2O and N2. However, the chemical processes involved depend strongly on

the catalyst temperature. Whilst the conversion efficiency of a hot catalyst is generally high, a

cool catalyst is typically characterised by a very low conversion efficiency. After a cold engine

start, the catalyst is brought up to its operating temperature primarily by the hot exhaust

gases. Consequently, a significant amount of pollution is typically released prior to the so called

“catalyst light-off”. As cold start emissions usually now play a critical role in meeting a specific

emissions standard, several approaches to minimising emissions using the catalyst have been

developed.

One commonly used approach involves repositioning the catalyst closer to the engine (Pfalz-

graf et al., 1996, Henein and Tagomori, 1999), thus increasing its inlet gas temperature. Many

other, more complex approaches have also been studied. For example, Engler et al. (1993),

Henein and Tagomori (1999) used traps, designed to adsorb hydrocarbons at cool temperatures

and release them after light-off. Lafyatis et al. (1998) implemented a secondary air injection

system, taking advantage of the highly exothermic carbon monoxide oxidation reaction. Ma

et al. (1992), Kanada et al. (1996) studied ways of burning pre-catalyst exhaust gas, whilst Oh

et al. (1993), Kirchner and Eigenberger (1996) examined the use of electrically heated catalysts.

However, all of these strategies have their shortcomings. Close coupling of the catalyst requires

2

Figure 1.2: Exhaust system with three-way catalysts

greater catalyst robustness, whilst the other approaches discussed have additional component

and/or energy costs.

Engine control can be viewed as a cost effective alternative, with which additional hardware

can be avoided. Engine control inputs in a typical spark ignition engine include spark timing,

air-fuel ratio (or injection duration) and cam (or valve) timing. A common strategy is to retard

the spark timing to reduce the thermal efficiency of the engine. This enables more heat to be

rejected with the exhaust, which affects the catalyst light-off time. Another approach is to raise

the idle speed to produce an increased number of combustion events, and thus higher enthalpy

input to the catalyst. Both of these approaches, however, result in increased fuel consumption,

which ideally should be minimised.

A vehicle that uses less fuel, whilst meeting the required emissions standard, can potentially

give the manufacturer a competitive advantage. Furthermore, improved fuel economy results

in lower CO2 emissions, which contribute significantly to global warming. Thus, minimising

fuel consumption by means of improved engine control is highly attractive to the automotive

industry, especially as this comes at almost no additional hardware cost.

The state of the art in cold start engine control development involves extensive engine testing.

However, the number of cold start runs is limited by the time needed for the engine and the

exhaust system to cool after each test. As a rough guide, up to two cold start tests can be

performed in a day on a single engine, which makes current cold start engine calibration processes

3

time consuming, and consequently, expensive. Furthermore, due to the large search space that

needs to be considered, it is unclear whether the resulting control strategies are optimal with

respect to the fuel economy. Therefore, tools that could help to reduce the number of experiments

and guide engine calibrators towards better fuel economy are of great value to the car industry.

1.1 Research objectives

The minimisation of fuel consumption under tailpipe emissions constraints can be viewed as

a dynamic optimisation problem. Solving this problem experimentally is a challenge for rea-

sons already discussed. Alternatively, the problem can be examined mathematically using an

accurate, computationally practical and validated cold start model of the engine and exhaust

system. This approach will therefore be investigated in this thesis, where the overall goal is to

develop a methodology which allows identification of engine control strategies that minimise fuel

consumption under tailpipe emissions constraints.

This study examines a gasoline fuelled spark ignition engine with a three-way catalyst. To

achieve the overall goal, the following specific objectives have been formulated.

1. To develop and validate a physics-based integrated engine, exhaust system and three-way

catalyst model

As there is significant interest in minimising fuel consumption under tailpipe emissions

limits, a low order cold start model that can simulate fuel consumption, as well as the

legislated CO, NOX and HC tailpipe emissions after a cold start is required. The model

inputs need to include typical engine control variables such as spark timing, cam timing

and the air-fuel ratio. Driving conditions are to be prescribed via engine speed and torque

setpoints to avoid modelling of the complete power-train. The model should be based on

physical principles when practical to enhance its portability, reduce the calibration effort

required and enable accurate simulation of all relevant phenomenon under a wide range of

conditions.

2. To develop, validate and understand the trends in engine control policies that minimise

fuel consumption under tailpipe emissions constraints

The integrated model shall be included in off-line dynamic optimisation studies, where

the overall fuel consumption is minimised under specified cumulative tailpipe emissions

limits and exhaust system configurations. Selected combinations of engine control inputs

are to be optimised under prescribed driving conditions. To examine the trends in the

4

optimal control strategies, different tailpipe emissions constraints and catalyst positions

in the exhaust system shall be considered. Local optimality of the proposed strategies is

to be verified experimentally when possible by implementing perturbed solutions to the

optimisation problem on an engine.

1.2 Thesis layout

This thesis is organised as follows. In Chapter 2 current engine calibration techniques and some

of the existing research-oriented engine optimisation tools are summarised. Their limitations are

carefully assessed, and the need for optimal cold start engine control strategies, developed using a

physics-based integrated model approach, is highlighted. A brief review of dynamic optimisation

procedures is presented to facilitate the selection of an appropriate algorithm. Advantages and

disadvantages of the existing engine, engine-out emissions, aftertreatment and combined models

are then discussed, emphasising lack of mathematically compact validated physics-based three-

way catalyst and integrated models required by the optimisation. The need for a new catalyst

model formulation and an integrated model is thus justified.

Chapter 3 describes the equipment, experimental procedures and software used to facilitate

model identification and validation, and validation of the engine control strategies. The topics

covered include control of the engine and the transient dynamometer, fuel flow measurement,

fast measurement of the exhaust gas temperature, in-cylinder pressure measurement and data

post-processing, exhaust composition analysis and air-fuel ratio estimation.

An integrated model capable of simulating cold start fuel consumption, as well as CO, NO

and HC tailpipe emissions under transient driving conditions, is formulated in Chapter 4. The

inputs to the model are spark timing, cam timing, normalised air-fuel ratio, as well as engine

speed and torque references. The model possesses a modular structure, is relatively portable

and is easy to calibrate, whilst being based on the physical principles where practical. Variation

in engine friction during warm-up; exhaust port gas temperature and exhaust flow rate; gas

temperature drop from the exhaust port to the catalyst inlet; engine-out emissions; warm-up

dynamics of the engine and exhaust system components; and simplified chemistry inside the

catalyst are all modelled.

In Chapter 5 the integrated model is calibrated based on fully warm steady state engine

data and the results from a single transient engine test. The integrated model is then validated

experimentally and the accuracy of the model is assessed.

In Chapter 6 the constrained optimal control problem is formulated. It is then simplified to

5

enable dynamic optimisation to become computationally practical. Iterative dynamic program-

ming is used to solve this problem under tailpipe emissions constraints, based on Euro-3 and

Euro-4 for under-floor and close-coupled catalysts. The trends in the resulting control policies

and the benefits of multi-variable optimisation are noted. The results are validated whenever

possible and the local optimality of a proposed spark timing strategy is verified experimentally.

The major contributions are summarised in Chapter 7, where some of the ideas for further

work are additionally included.

6

Chapter 2

Literature review

This chapter discusses the state-of-the-art in engine calibration and control, and reviews some

of tools available for improving the engine performance within the current control architecture,

as well as some of the proposed academic approaches for minimising cold start fuel consumption

and cumulative CO, NOX and HC tailpipe emissions. Limitations of the existing methodologies

are highlighted, thus justifying the goal of this thesis, identified earlier in Chapter 1. This is

followed by a brief summary of dynamic optimisation procedures to aid the selection of an

efficient algorithm for solving the proposed emissions constrained minimum fuel problem. A

large variety of engine, engine-out emissions, three-way catalyst and combined models are then

critically reviewed to help select an accurate, portable and easily calibratable set of models to

use as a basis in the proposed optimisation.

2.1 Prior use of optimisation tools in engine calibration

There are two primary directions of control related research, targeting vehicle fuel economy and

emissions problems. One focuses mainly on improving calibration maps used within the current

control architecture, whilst the other is aimed at developing new control algorithms.

2.1.1 Optimisation of engine maps

The control systems of most current production engines use static maps to determine what engine

control parameters to apply at certain engine operating conditions. These maps are tradition-

ally calibrated based on steady state experiments, where many combinations of engine control

setpoints are tested. With the growing number of control parameters in newer engines, main-

taining optimal map-based calibration presents a challenge, due to the exponentially growing

search space that needs to be considered.

7

To reduce the number of experiments, the industry standard is to use the Design of Ex-

periment (DoE) approaches, which assume certain engine characteristic behaviour. Regression

fitting of black-box models to the acquired data is then typically performed for subsequent off-line

searching of the optima. These black-box models generally neglect the physics of the problem

and can be in the form of polynomials or neural networks. Model-based Calibration Toolbox

(MathWorks, 2011) and AVL CAMEO (AVL, 2011) are examples of commercially available and

widely used static optimisation tools in the automotive industry.

Whilst the DoE methods tend to reduce the calibration burden, the resulting search for the

optimal set of engine control inputs is not exhaustive, which often yields sub-optimal calibration.

Thus, some of the research effort is currently aimed at developing more accurate and less time

consuming methods for tuning of the engine maps. For example, Hafner and Isermann (2003)

proposed using engine models in the form of neural networks, calibrated based on relatively

small dynamic data sets, for the required point-wise optimisation. However, the model’s ability

to accurately reproduce the engine’s behaviour remains an open topic. Alternatively, Jankovic

and Magner (2004) and Popovic et al. (2006) investigated use of the on-line extremum seeking

algorithms, where engine control variables are perturbed and the changes in the objective func-

tion are measured to identify the direction of the search. Although these approaches can be

helpful in calibrating the engine maps, current implementations of extremum seeking are still

too slow to be directly applicable in real-time engine control. For example, Jankovic and Magner

(2004) reported that roughly 15-20 minutes was required to determine the optimal set of spark

timing, as well as inlet and exhaust cam timing for a fixed engine speed and torque condition.

2.1.2 Dynamic optimisation of engine control variables

Even when the engine maps are optimally calibrated, it remains unclear whether such point-

wise calibration can yield an optimal control policy during transient engine operation (at least in

terms of fuel economy and tailpipe emissions). Furthermore, optimal control of slow dynamics,

such as engine and catalyst warm-up, can be difficult to achieve within the current engine control

architecture. To counter these issues, other engine control research has been geared towards the

development of new control algorithms for transient and cold start operation.

The conversion efficiency of a catalytic converter is generally very low at low substrate tem-

peratures. Cold start is therefore of special interest, as it is during this period that the fuel

economy is significantly penalised and large fractions of emissions are released into the atmo-

sphere. This review will thus be limited mostly by work focusing on cold start related engine

8

control with emphasis on reducing fuel consumption and emissions.

Dohner (1978) was among the first to develop optimised open-loop engine control strategies

over the FTP drive cycle, initiated from a cold start. The air-fuel ratio and spark timing

were optimised dynamically, minimising fuel consumption under cumulative CO, NOX and HC

tailpipe emissions constraints, and then correlated with some of the measurable states, including

coolant temperature. Due to the absence of relevant warm-up models, a real engine with an

oxidation catalyst were employed. However, oxidation catalysts have long been replaced with

three-way catalysts in modern gasoline fuelled vehicles, which limits the results of this study to

older vehicles. Moreover, optimisation using hardware-in-the-loop can be very time demanding,

and therefore expensive, whereas model-based approaches can have the benefits of speed and

low cost.

Cohen et al. (1984) attempted the same optimisation problem over the FTP cycle using black-

box models, based on the work by Tennant et al. (1979). The original correlations of Tennant

et al. (1979) were modified to include engine and oxidation catalyst temperatures, thus enabling

warm-up conditions to be simulated. Validation results have not been presented. Again, the

methodology is time consuming and expensive, as black-box models are not portable and require

a considerable calibration effort. Furthermore, such models may be oversimplified and may fail

to accurately simulate some of the key system dynamics.

In a slightly different approach Sun and Sivashankar (1997) used a cold start engine model to

minimise cumulative engine-out HC emissions subject to fuel consumption and exhaust enthalpy

constraints, thus indirectly minimising tailpipe emissions. Air-fuel ratio, spark timing and ex-

haust gas recirculation were optimised over a fraction of a drive cycle. Similarly, Sanketi et al.

(2006a) minimised engine-out HC emissions and maximised the exhaust port gas temperature

using a physics-based model for a fully warm engine. Spark timing and the air-fuel ratio were

used as the engine control parameters. In both cases, however, no validation results were pre-

sented. Other work, which considered only engine-out emissions in the optimisation include Sun

and Sivashankar (1998) and Benz et al. (2011). Neglecting the aftertreatment system dynamics,

however, may not necessarily yield globally optimal control solutions with respect to the fuel

economy and tailpipe emissions.

Other studies (Kang et al., 2001, Kolmanovsky et al., 2002) have used integrated models of

spark ignition engines and aftertreatment systems to minimise fuel consumption and cumulative

NOX emissions (Kang et al., 2001) and fuel consumption under cumulative tailpipe emissions

constraints (Kolmanovsky et al., 2002). However, only fully warm operating conditions were

9

considered and phenomenological catalyst models, which may be oversimplified, were employed.

Shaw and Hedrick (2003) proposed an alternative approach, where predetermined air-fuel

ratio and exhaust gas temperature profiles were tracked using a spark timing and fuel flow con-

troller. These profiles were subsequently based on previous testing of the catalyst performance.

Such separation of engine and catalyst dynamics, however, does not guarantee global optimality

in terms of the resulting cumulative tailpipe emissions and fuel economy.

It appears that much of the previous work has either been limited by use of black-box or

phenomenological models, which require a significant calibration effort and may be oversimplified;

fully warm operating conditions assumptions; indirect consideration of tailpipe emissions; or

purely experimental approaches, which can be very time demanding. Furthermore, validated

results are only occasionally presented, and very little work appears to have considered modern

gasoline fuelled engines with three-way catalysts. Thus, the goal of this thesis, presented in

Chapter 1, is well justified.

To fulfil this goal, dynamic optimisation procedures should be applied to a validated inte-

grated model of the engine, the exhaust system and the catalyst, developed based on physical

principles. The performance of the model using the resulting optimised engine control tra-

jectories should be validated and the optimality of these solutions confirmed experimentally.

Additionally, case studies involving different combinations of tailpipe emissions constraints and

exhaust system configurations could enable trends in the control policies to be observed, which

may potentially help reduce engine calibration time or lead to better engine calibration.

2.2 Dynamic optimisation theory

To identify engine control variables that minimise fuel consumption under cumulative tailpipe

emissions constraints, a dynamic optimisation procedure must be applied to the integrated

model, describing cold start fuel consumption and tailpipe emissions dynamics. The existing

procedures should thus be reviewed to help choose an effective algorithm.

For a general model described by a set of differential algebraic equations (DAE),

x(t) = F (x(t), z(t),u(t), t), (2.1a)

0 = G(x(t), z(t),u(t), t), (2.1b)

10

Figure 2.1: Dynamic optimisation methods

the dynamic optimisation problem can be formulated as

u⋆(t) = arg minu(t)

J(u(t)), (2.2)

J(u(t)) = h(x(tf ), tf ) +

∫ tf

0

g(x(t),u(t), t) dt, (2.3)

where u⋆(t) is the optimal control policy, u(t) and x(t) are the input and state vectors and

tf is the final time constant. Vector z(t) contains algebraic variables, which are free of time

derivatives. Functions h and g in the performance index J are specified depending on the desired

outcome of the optimisation. A number of techniques can be used for solving this optimisation

problem, some of which are presented in Figure 2.1. Note that many of these algorithms can

produce sub-optimal solutions.

Solving optimal control problems using indirect methods (calculus of variations or Pontrya-

gin’s minimum principle) involves transforming the original problem into the so called two point

boundary value problem, where the boundary conditions are specified at initial and final time

instances. More details on this topic can be found, for example, in Kirk (2004). The resulting set

of differential equations, which are often non-linear, can either be solved analytically or numer-

ically to yield optimal control policies. Analytic solutions can generally be produced only when

very simple models are considered. In many other cases two-point boundary value problems can

11

be difficult to solve, due to the nature of the boundary conditions, and the solutions are normally

obtained with iterative procedures, such as steepest descent, quasilinearisation and variation of

extremals Kirk (2004). The integrated model of the engine, the exhaust and the catalyst is ex-

pected to be relatively complex, whilst containing a number of non-linear differential equations.

Thus, this approach appears to be impractical.

The application of direct methods involves discretising and converting (2.1)–(2.3) into a non-

linear programming (NLP) problem, which can then be solved using iterative procedures, such

as the Newton’s method or Sequential Quadratic Programming (Pedregal, 2004, Nocedal and

Wright, 2006). The discretisation methods could be split into sequential and simultaneous broad

categories. Sequential discretisation involves parameterising only the control variables, whilst the

states are calculated numerically and are not included in the resulting NLP (Vassiliadis et al.,

1994, Diehl, 2001, Leineweber et al., 2003). Conversely, simultaneous methods parameterise

both input and state variables, whilst both the dynamic model equations and the optimisation

problem are integrated and solved as a single NLP (Diehl, 2001). Although the resulting NLP’s

are generally larger than those arising from the sequential methods, these NLP’s may possess

a favourable sparse structure. Collocation (Tsang et al., 1975, Kurtanjek, 1991) and multiple

shooting (Diehl, 2001, Leineweber et al., 2003) are common examples of simultaneous strategies.

The integrated model is expected to include several input variables, and due to its physics-based

nature, a reasonably large number of states. Furthermore, if highly transient drive cycle condi-

tions are to be considered in the optimisation, time would need to be discretised using a large

number of intervals. The resulting NLP’s can be very large and very difficult to solve. Hence,

direct methods will not be used here.

Another alternative optimisation technique is dynamic programming, described in many

textbooks (Luus, 2000, Pedregal, 2004, Kirk, 2004). It is based on the principle of optimality,

originally formulated by Bellman (1954):

“An optimal policy has the property that whatever the initial state and initial

decision are, the remaining decisions must constitute an optimal policy with regard

to the state resulting from the first decision.”

With dynamic programming all state and input variables, as well as time are discretised. Typ-

ically, the final time tf , which is fixed, is divided into Nst equal intervals or stages ∆t, such

that

∆t =tfNst

(2.4)

12

and

t = k∆t. (2.5)

The recurrence relation of dynamic programming is then

J⋆k,Nst

(x[k]) = minu[k]

{∆t g(x[k],u[k], k∆t) + J⋆k+1,Nst

(x[k + 1])}, (2.6)

J⋆Nst,Nst

(x[Nst]) = h(x(tf ), tf ), (2.7)

where the state x[k] and input u[k] vectors are sampled at time k∆t, and J⋆k,Nst

(x[k]) is the

minimum achievable value of the cost function (2.3) between time instances k∆t and tf .

The optimisation procedure begins by evaluating h(x(tf ), tf ) for all discretised values of the

states x(tf ). The recurrence equation (2.6) is then evaluated by traversing backwards in time

from k = Nst − 1 to k = 0, while computing the function g(x[k],u[k], k∆t) for all combinations

of the discretised states x[k] and inputs u[k]. This calculation results in a table of the minimum

cost values J⋆k,Nst

(x[k]) and the associated optimal controls u⋆[k] across all time stages and

combinations of the states considered. Traversing the table forwards in time from some initial

condition x[0], while solving the model equations using the stored values of u⋆[k], an optimal

control policy u⋆ can be found.

Computational problems of dynamic programming closely resemble those of the indirect and

direct optimisation procedures. It suffers from the so called “curse of dimensionality”, where the

computational effort and storage requirements increase exponentially with increasing numbers of

states and inputs or finer discretisation in these variables. This limits the application of dynamic

programming to lower order models and coarse grids, making it impractical for the proposed

optimisation.

However, in contrast to the other optimisation methods, dynamic programming can be easily

modified to give a significant reduction in the computational requirements. Such methods (Lar-

son, 1965, 1967, Luus, 2000) typically attempt to eliminate large amounts of state-time search

space by considering only the regions believed to enclose the optimal trajectory. Of course,

these approaches can only guarantee local optimality. Nevertheless, they overcome the “curse of

dimensionality” and will be adapted in this thesis.

Iterative dynamic programming (Luus, 2000) is a computationally fast variation of dynamic

programming, which is well suited to convex problems and problems, where the initial guesses of

the optimal control policy, which need to be specified, are near optimal. It has several advantages

over other flavours of dynamics programming in terms of speed, flexibility and convergence

13

properties. Each iteration of this algorithm is a pass of dynamic programming with a few

peculiarities.

Firstly, the discretisation of the state vector x[k] is limited, which can greatly reduce the

numerical intensity of the optimisation procedure. An attempt is made to discretise the state

space only in “accessible” areas by testing various combinations of the inputs and observing

the state transitions in each iteration of the algorithm. Such dynamic state grid allocation can

eliminate a large portion of the state-time space, which otherwise needs to be considered if the

classic dynamic programming is used.

Secondly, with each iteration of the algorithm, the inputs to be tested at each of the discretised

values of the state vector x[k] are chosen to lie in the proximity of the recorded best control

policy from the previous iteration. The range of values tried is reduced with each iteration,

making the discretisation of the inputs more refined. After many iterations the optimised input

trajectory is expected to converge to the optimal control policy in many optimisation problems.

Whilst these modifications to dynamic programming can significantly reduce its computa-

tional requirements, further improvement in the speed of the optimisation procedure may be

limited by the discretisation of the time domain. Use of finely resolved time grids increases the

number of solutions to the model equations required, and consequently, can be time demanding.

Use of rough grids, however, limits the frequency at which the optimised control inputs can be

varied. Thus, depending on the time-scale behaviour of the system dynamics and the optimal

control problem considered, some higher frequency characteristics of the optimal trajectories

might be missed. If possible, time grids of varying resolutions should be tested to ensure that

the solutions developed are grid independent.

2.3 Spark ignition engine models

To permit dynamic optimisation of engine control variables, where cold start fuel consumption

is minimised under cumulative tailpipe emissions constraints, an integrated model of the engine,

the exhaust system and the catalyst, capable of simulating cold start fuel consumption and

tailpipe emissions is required. A large variety of engine models of varying complexity have been

proposed. Many of them can be categorised as zero-dimensional, event-based, black-box and

mean value models.

Zero-dimensional models (Patterson and Van Wylen, 1963, Arsie et al., 1998, 2003, Hoffmann

et al., 2009) divide the working fluid into zones, which enclose burned and unburned mixtures in

the combustion chamber. The naming originates from the fact that the shape and the location

14

of these zones can be abstract. Energy and mass conservation equations with simplified chemical

kinetics are generally applied to the zones and solved over a range of crankshaft positions. Whilst

these models take on a physics-based approach, they operate on a relatively short time scale,

which makes them computationally demanding and not suitable for dynamic optimisation studies

over drive cycles, such as those considered in this thesis.

Hybrid models (Balluchi et al., 2000, Sanketi et al., 2006a) contain a mixture of time-based

and event-based modelling. Engine operation is split into several operating regimes, triggered by

particular events, such as ignition, fuel injection or valve opening and closing. The time-based

component can be any of the existing continuous or discrete time engine models. As most of the

events occur very quickly with respect to the dynamic response of the catalyst, individual events

are not expected to significantly affect its dynamics. Thus, the introduction of the additional

complexity by hybrid modelling appears to be unnecessary and is not considered in this work.

On the other extremity are black-box models (Tennant et al., 1979, Berard et al., 2000), which

establish fixed relationships between the engine inputs and outputs. They are largely of empirical

nature, and consequently do not port easily between engine designs. The models are typically

calibrated based on a large set of experiments, which can take a significant amount of time and

effort. Adaptation of the model to a different engine requires a complete recalibration. Black-box

models, however, are computationally inexpensive and can be relatively easily integrated into

engine control systems.

Mean value engine models (MVEM) are a step forward from black-box models towards the

physics-based approach. Some history behind these models and typical mathematical formula-

tions can be found in Aquino (1981), Moskwa (1988), Cho and Hedrick (1989), Hendricks (1997)

and Guzzella and Onder (2004). The MVEM’s simulate the mean values of engine variables,

whilst operating on a time scale of longer than a single cycle. The release of heat during com-

bustion and any other fast dynamics, dominating on a time scale of less than a single cycle, are

approximated by algebraic relationships. Slower dynamics, such as the rotation of the crankshaft

and pressure fluctuations in the intake manifold, are typically modelled using differential equa-

tions. The order of MVEM’s is generally low. For example, Hendricks and Sorenson (1990)

showed that for a given throttle-torque-injected fuel input trajectory, intake manifold pressure,

air mass flow rate, air-fuel ratio and engine speed could all be accurately estimated using only

a 3 state model.

Mean value models are also distinguished by their modular structure and include a number

of sub-models, most of which can be calibrated independently. Many of the model equations

15

are based on the physical principles, such as conservation of energy and mass, and the ideal

gas assumptions. Thus, the MVEM’s are generally more portable than the black-box models

described above, while being of sufficiently low order to be useful in off-line optimisation and

even on-line control. Therefore, this class of models appears to be the most sensible to consider

in this thesis.

There is a wide variety of MVEM models in the literature, each with its own set of features.

However, the MVEM’s described above do not consider engine warm-up dynamics. As the ulti-

mate goal of this work is to minimise cold start fuel consumption, a model capable of simulating

this parameter is required. Furthermore, the dynamics of the catalyst, and subsequently those

of tailpipe emissions, are expected to be functions of the exhaust gas flow rate, temperature and

composition. Hence, the exhaust mass flow rate and the exhaust port gas temperature need to

be additionally included in the engine model. The modular structure of the MVEM’s allows

these features to be integrated in the form of sub-models. To identify what approaches could be

used to model these dynamics, some of the existing engine models need to be examined.

2.3.1 Cold start friction and engine warm-up models

Engine friction in a cold engine can be significantly higher than in a hot engine at the same engine

speed, primarily due to the higher viscosity of the lubricating oil. Consequently, to simulate fuel

consumption after a cold start with a reasonable degree of accuracy, modelling of friction and

engine warm-up behaviour is essential.

Sandoval and Heywood (2003), Leong et al. (2007), Shayler et al. (2007) have examined

the effects of oil viscosity (and subsequently oil temperature) on the motoring friction of a

reciprocating engine. To enable friction measurement in engine components, motoring tests

are typically performed on stripped down engines. Sandoval and Heywood (2003) presented a

comprehensive cold start friction model, based on the work of Patton et al. (1989), where friction

in the bearings of the crankshaft, valve-train mechanism and the cylinder-piston assembly have

been correlated to engine speed and oil viscosity at these locations. The oil viscosity can be

specified by the oil temperature in relevant parts of the engine. Simulation of these temperatures,

however, requires a relatively complex thermal model, which can be difficult to calibrate.

Whilst these models can successfully describe friction in certain engines, they are highly

empirical, and it is not clear how well they can be adapted to other engines in their current

form. Verifying modelled friction in various mechanical components is exceedingly difficult and

time consuming, as this generally requires a disassembly of the engine. Furthermore, firing

16

friction can be differ considerably from motoring friction (Heywood, 1988), primarily due to

in-cylinder temperature and gas pressure loading differences. Consequently, the possibility of

using simplified models, that could be calibrated more easily, to describe firing friction should

be investigated.

Modelling of cold start friction requires identification of engine component temperatures,

which can be used to specify the oil viscosity in various parts of the engine. A well known model

(Kaplan and Heywood, 1991) consists of several lumped parameter thermal models. Average

temperatures of the pistons, cylinder block, cylinder head, the oil sump and other engine com-

ponents are calculated. Surprisingly, model predictions and experimental results used in the

validation show that the temperatures of the block, the head and the coolant in two different

reservoirs agree closely during warm-up. The modelled results are within roughly 5◦C of each

other. As this is only a small fraction of the temperature range covered during engine warm-

up, model reduction may be possible without significantly compromising the accuracy of the

component temperatures modelled. Whilst model reduction may lead to a simplified model cali-

bration process, it can also benefit the proposed dynamic optimisation in terms of computational

requirements.

Many low order cold start engine models (Shayler et al., 1997, Farrant et al., 2005, Kunze

et al., 2006, Manzie et al., 2009) are based on engine warm-up models of similar complexity to

Kaplan and Heywood (1991) and friction models such as Sandoval and Heywood (2003). Whilst

these models may be adequate for this work, their calibration is difficult. Thus, an approach

similar to that of Keynejad and Manzie (2011) shall be adopted here, which bases engine friction

on a representative lumped engine temperature.

2.3.2 Modelling of air and fuel dynamics

To model air dynamics in an engine, MVEM’s generally employ volumetric efficiency maps

(Moskwa, 1988, Cho and Hedrick, 1989, Hendricks, 1997, Manzie et al., 2009), calibrated based

on steady state test data. These maps are used for calculating the amount of air entering the

cylinders through the intake port, subject to an engine operating condition.

To attain a good modularity of the engine model, air dynamics across the throttle are com-

monly separated from those inside the combustion chamber. This requires air dynamics in the

intake manifold to be modelled, in order to simulate the conditions at the intake port. A common

approach is to combine the continuity equation with the ideal gas law to calculate the pressure in

the manifold, which appears as a state in the resulting equation (Hendricks, 1997). Temperature

17

dynamics are often neglected, as temperature fluctuations are expected to be small.

The flow across the throttle can be approximated by a steady flow through a nozzle (Heywood,

1988). Thus, it is usually modelled using a static function of the pressure drop and the throttle

angle (Heywood, 1988, Hendricks, 1997, Manzie et al., 2009), taking one of two forms, depending

on whether or not the flow is choked.

The fuel flow into the combustion chamber mfuel can be calculated using the well known

fuel puddle equations (Aquino, 1981), if the mass flow rate of injected fuel mfuel,inj is used as

a control input,

τvap mfuel,film = Xfilm mfuel,inj − mfuel,film, (2.8)

mfuel,vap = (1 −Xfilm) mfuel,inj , (2.9)

mfuel = mfuel,vap + mfuel,film, (2.10)

where τvap is the fuel puddle evaporation time constant, mfuel,film and mfuel,vap are the mass

flow rates of liquid and vapourised fuel through the intake port, and Xfilm is the fraction of

the injected fuel condensed to form a puddle. Alternatively, mfuel can be prescribed based on

calculated air flow mair and some reference normalised air-fuel ratio λ input (Manzie et al.,

2009),

mfuel =1

λ AFRSmair. (2.11)

The latter approach allows the effects of controller independent air-fuel ratio setpoints to be

examined, whilst the former approach is necessary for development of model-based air-fuel ratio

controllers, which deliver the setpoints.

2.3.3 Exhaust gas heat loss models

To model the exhaust gas port temperature using a physics-based approach, one must consider

the heat generated within the cylinders from the combustion of fuel, indicated work output and

heat losses to the surrounding surfaces. The amount of heat rejected from the engine with the

exhaust, and thus, the exhaust gas temperature can then be estimated from energy conservation.

In MVEM’s fast dynamics, such as combustion and torque production are based on static maps.

The charge cooling effects, however, can be modelled using physical principles.

Two widely cited correlations for in-cylinder heat transfer coefficients are those of Annand

(1963) and Woschni (1967). The latter is based on instantaneous in-cylinder temperature and

pressure, so can not be used with MVEM’s, as only the mean quantities of these variables can

18

be calculated. The other expression, given by

hcyl = α1k

B

(

Sp B

v

)α2

, (2.12)

is based on the average piston velocity Sp. Variables B, k and v are the bore diameter, thermal

conductivity and kinematic viscosity respectively, whilst the parameters α1 and α2 are tunable.

A similar approach is used in this thesis.

2.4 Engine-out emissions models

The regulated pollutants found in the exhaust include carbon monoxide (CO), unburned hydro-

carbons (HC) and nitrogen oxides (NO and NO2), also referred to as NOX . Modelling of these

emissions requires knowledge of their formation mechanisms, which are briefly described below.

One of the primary sources of CO is incomplete combustion (Guzzella and Onder, 2004).

Hence, the air-fuel ratio is a major variable affecting these emissions (Harrington and Shishu,

1973). Under rich conditions, the combustion is incomplete and large amounts of CO appear

to form. Despite the abundance of oxygen during lean operation, the CO emissions continue to

be produced in quantities, significantly higher than the equilibrium levels at exhaust conditions.

This is partially due to the non-ideal mixture uniformity, which can cause locally rich pockets

of mixture to form, leading to incomplete combustion. Quenching of the flame at the metal

surfaces and rapid cooling of the charge during expansion can additionally increase CO emissions

(Heywood, 1988, Guzzella and Onder, 2004).

One of the most significant sources of hydrocarbon emissions are considered to be in-cylinder

crevices (Adamczyk et al., 1983, Heywood, 1988, Alkidas, 1999, Dober, 2002), in which the

trapped mixture escapes primary combustion due to its low temperature, resulting from the close

proximity of the cool walls. Adsorption of fuel in engine oil at high pressures and subsequent

desorption after the main ignition event is another significant HC retention mechanism (Kaiser

et al., 1982, Heywood, 1988). Poor mixture preparation, especially during cold start (Alkidas,

1999) can result in droplets impinging upon the cylinder walls, causing maldistribution of fuel

within the cylinder and leading to incomplete combustion and higher HC emissions. Carbon

deposits in the cylinders can either increase or decrease HC emissions, depending on the engine

design (Shayler and Belton, 1999). Furthermore, during combustion, the low temperature metal

surfaces act as heat sinks, conducting heat away from the flame and preventing oxidation of fuel

in a thin region around walls and inside crevices. This is known as flame quenching. Whilst

its contribution to the total HC emissions is usually small under fully warm conditions, it

19

can be more significant during cold start (Alkidas, 1999). Hydrocarbons that escape primary

combustion are mostly oxidised in the hot bulk gases during expansion and exhaust strokes

(Dober, 2002), which reduces engine-out HC emissions to roughly 1% of the fuel consumed.

Nitrogen oxide emissions are generally formed in high temperature zones from nitrogen con-

tained in air. There is evidence suggesting that a significant portion of NOX originates from

the mixture, burned early in the combustion process. As the pressure in the cylinders rises

during combustion, this part of the working fluid is heated to temperatures significantly higher

than those experienced immediately after its burn-up. Consequently, higher NOX concentra-

tions have been observed near spark plugs (Lavoie, 1970). As the maximum flame temperatures

are strongly dependent on the air-fuel ratio, the formation of NOX is directly affected by the

mixture composition.

The models for estimating these emissions can be roughly divided into physics-based and

black-box categories. Without doubt the dynamics of engine-out emissions are highly complex,

thus many assumptions are generally embedded in the physics-based models. Consequently, the

accuracy of calculated emissions is usually limited. Many physics-based models, such as those

of Lavoie and Blumberg (1980), Arsie et al. (1998), take on a multi-zone approach, where the

working fluid in the combustion chamber is divided into unburned and burned regions to cap-

ture compositional and thermal dynamics, which can be important for the reaction mechanisms

considered. Conservation equations are generally solved for each of the zones at various parts of

the cycle. These models operate on a crank-angle basis, which is incompatible with the mean

value engine model approach to be used.

A physics-based model that can potentially be used for this application is the low order cold

startHC model developed by Shayler and Belton (1999). It operates on a time-scale of more than

1 cycle and takes advantage of similar approaches to those used in mean value engine models.

Empirical correlations and mass conservation equations are used to model intake port fuel puddle

dynamics, fuel deposition and storage on the in-cylinder walls, retention of hydrocarbons in

crevices and partial oxidation of the hydrocarbons escaping primary combustion. The model

parameters are either constants or tunable functions of the coolant temperature. Although,

the modelled emissions appear to agree reasonably well with the experimental data presented,

the model performance over a drive cycle has not been demonstrated. Furthermore, direct

identification of some of the calibration parameters can be difficult, as many of the model states

are not easily measurable.

Other control-oriented emissions models for fully warm (Lumsden, 2004, Benz et al., 2010)

20

and cold start (Shayler et al., 1997, Shayler and Belton, 1999, Hirsch et al., 2008) conditions are

of the black-box type. They disregard the physics behind the emissions formation mechanisms

and map some of the engine control inputs and states to engine-out emissions. Warm-up models

tend to additionally consider reference temperatures in their maps, such as those of the coolant

or oil. As expected, the models are calibrated based on relatively large data sets. Consequently,

whilst being computationally fast, they do not port easily between engines and a substantially

larger effort is usually required for their calibration, as opposed to most physics-based models.

Nevertheless, despite these drawbacks, modelling of CO, NOX and HC engine-out emissions

using black-box models appears to be the only feasible approach for the purposes of this work.

2.5 Three-way catalyst models

Physics-based catalyst models include a reaction mechanism and a description of substrate dy-

namics. Voltz et al. (1973) was one of the first to formulate the rates of carbon monoxide and

propylene oxidation reactions,

2 CO +O2 −→ 2 CO2, (2.13)

2 C3H6 + 9O2 −→ 6 CO2 + 6H2O, (2.14)

in an automotive platinum catalyst. Being of the Langmuir-Hinshelwood type, the rate expres-

sions took into account the inhibition of these reactions due to the presence of CO, NO and

C3H6. The work of Voltz et al. (1973) appears to have formed the basis for almost all physics-

based future developments in this area of research. Their basic model has since been extended

by other researchers with updated kinetics and more comprehensive reaction mechanisms. For

example, Oh and Cavendish (1982) developed oxidation rate expressions for hydrocarbons char-

acterised as easily and not so easily oxidising, while Subramaniam and Varma (1985) were one

of the first to consider nitric oxide reduction by carbon monoxide,

2 CO + 2NO −→ 2 CO2 +N2. (2.15)

Oxygen storage by ceria was later incorporated into many kinetic schemes (Pattas et al., 1994,

Pontikakis and Stamatelos, 2004, Auckenthaler, 2005, Holder et al., 2006), which usually consider

the oxygen rich (CeO2) and oxygen depleted (Ce2O3) states of ceria. Pontikakis and Stamatelos

21

(2004), for example, have used the following oxygen storage mechanism:

Ce2O3 + 0.5O2 −→ 2 CeO2, (2.16)

Ce2O3 +NO −→ 2 CeO2 + 0.5N2, (2.17)

2 CeO2 + CO −→ Ce2O3 + CO2, (2.18)

CHfast1.8 + 3.8 CeO2 −→ 1.9 Ce2O3 + CO2 + 0.9H2O, (2.19)

CHslow1.8 + 3.8 CeO2 −→ 1.9 Ce2O3 + CO2 + 0.9H2O. (2.20)

Steam reforming reactions (Koltsakis et al., 1997, Dubien et al., 1998, Holder et al., 2006),

CxHy + x H2O −→ x CO +(y

2+ x

)

H2, (2.21)

and the water-gas shift reaction (Holder et al., 2006),

CO2 +H2 → CO +H2O, (2.22)

have been additionally included in some of the more recent reaction schemes. While most of

the reaction mechanisms reported appear to be of a single step kind, some multi-step schemes

have been proposed as well (Balenovic, 2002, Auckenthaler, 2005), which can potentially provide

more insight into the dynamics of the catalyst.

Two-dimensional substrate models view the monoliths or channels axisymmetrically and

can be roughly divided into 2 categories. One type of models consider the properties and

composition of the exhaust gas across the entire cross-section of the substrate as well as in the

longitudinal direction, taking into consideration the effects of uneven flow distribution at the inlet

(Zygourakis, 1989, Koltsakis et al., 1997, McCullough et al., 2001). The other models simulate

temperature and concentration gradients in the radial direction of a single channel (Hayes and

Kolaczkowski, 1994, Wanker et al., 2000), which enables them to avoid use of questionable

Nusselt and Sherwood number correlations for modelling heat and mass transport between the

gas and solid phases. Three-dimensional models have also been developed (Groppi et al., 1995)

and allow to consider channels of any shape. Despite the more realistic assumptions, two and

three-dimensional models are currently computationally impractical for dynamic optimisation

and control.

One-dimensional substrate models (Heck et al., 1976, Oh and Cavendish, 1982, Groppi et al.,

1995, Kirchner and Eigenberger, 1996, Siemund et al., 1996, Balenovic, 2002, Pontikakis and

Stamatelos, 2004, Auckenthaler, 2005, Holder et al., 2006) typically separate the bulk fluid

conditions inside the channels from those inside the washcoat layer and the substrate. Energy and

22

mass conservation equations, which are closely linked with chemical kinetic schemes of various

complexities, are generally solved. The models can simulate temporal and spatial distribution

of temperature and concentrations of species along the length of the monolith.

Laminar flow inside the channels and an even distribution of the velocity field across the

face of the substrate are commonly assumed. Heat release from the exothermic reactions in the

washcoat, heat transfer by forced convection and mass transfer between the gas and the walls

are usually modelled. The modelling of the latter phenomena typically relies on Nusselt and

Sherwood number correlations, such as those found in Hawthorn (1974), Votruba et al. (1975)

and Hayes and Kolaczkowski (1994), originally developed for non-reacting flows. However, a

large share of these expressions has received criticism (Hayes and Kolaczkowski, 1994) for failing

to predict heat and mass transfer accurately under the conditions of the reacting flows found

inside catalysts. Axial thermal conduction in the substrate and heat losses to the environment

by means of radiation and convection are sometimes additionally considered.

One-dimensional catalyst models are commonly represented by partial differential equations.

The solutions are developed numerically, usually after discretisation of the spatial coordinate

and subsequent conversion of the equations to a set of ordinary differential equations. The

number of nodes used in the discretisation determines the numerical complexity of the problem.

Consequently, the simulation speed can be increased by compromising some of the spatial reso-

lution and accuracy of the modelled tailpipe emissions. As these types of models are typically

employed in applications that do not consider dynamic optimisation and control, the spatial

resolution used is generally high.

Phenomenological models (Brandt et al., 2000, Fiengo et al., 2002, Shaw et al., 2002, Sanketi

et al., 2006b) are designed for potential integration into real-time control systems. They typically

comprise of a lumped parameter catalyst warm-up sub-model and a conversion efficiency map,

which is generally a function of the catalyst temperature, the exhaust gas composition and the

mass flow rate. Oxygen storage dynamics, if modelled, are highly empirical. No chemical kinetics

are considered. The simulation speed of the models is often fast, but the calibration usually

requires extensive experiments. Consequently, the models do not port easily between catalysts

of different geometry, substrate properties, precious metal loading, and may be oversimplified.

In this study we seek a mathematically compact physics-based catalyst model in an attempt

to reduce the calibration effort and enhance the portability of the model. At first glance, a one

dimensional approach with a low order kinetic scheme and oxygen storage reactions may appear

to be feasible. Of course, the appropriate number of nodes to be used in the discretisation of

23

the spatial coordinate, and thus the order of the model, is yet to be determined. The effect of

grid resolution on the accuracy of the simulated tailpipe emissions is unclear and needs to be

investigated. Also, how do the typical mean value engine model assumptions, such as the single

cycle time-scale, impact on the simulated tailpipe emissions?

2.6 Integrated models

So far stand-alone engine, engine-out emissions and catalyst models have been covered in this

review. However, to consider cold start fuel consumption and CO, NOX and HC tailpipe

emissions in the dynamic optimisation of the engine control inputs, an integrated physics-based

model of the engine, engine-out emissions, the exhaust system and the catalyst is required.

Cohen et al. (1984) was one of the first to develop an integrated cold start model with an

oxidation catalyst, but no physics were included and no validation results presented. Berard

et al. (2000) presented an integrated model, which additionally included vehicle, driver and

transmission dynamics. The model, however, also relied heavily on look-up tables and little

physics-based modelling was employed. For example, fuel consumption and engine-out CO,

NOX and HC emissions were correlated by static maps of engine speed and torque for a fully

warm engine. The effect of engine controls, such as the air-fuel ratio and spark timing, on these

variables was not included. Tailpipe emissions were modelled using static surfaces of the catalyst

efficiency based on the exhaust gas temperature. During warm-up calculated fuel consumption

and emissions were corrected by pre-calibrated functions of time. It is clear that the black-

box approach requires a significant calibration effort, and if the mentioned engine control inputs

were additionally considered, model calibration may have been very difficult. Furthermore, these

models are not portable between engines and catalysts, and due to their highly empirical nature,

may not accurately capture many of the dynamics.

Later Fussey et al. (2001) extended the power-train model of Berard et al. (2000) with a

physics-based exhaust and aftertreatment system. However, the black-box engine model was

retained, and validation results were not demonstrated.

Balenovic (2002) considered a mean value engine model and a single state phenomenological

catalyst model in the development of an air-fuel ratio controller for a hot catalyst. As this model

was limited to fully warm operating conditions, it can not be directly applied here.

Fiengo et al. (2002) developed highly empirical models of the engine, the exhaust temperature

and HC engine-out emissions. The control inputs included the air-fuel ratio and spark timing.

However, engine warm-up dynamics, such as friction, were not modelled. Thus, only indicated

24

torque could be calculated, which is not sufficient for the desired objective. Exhaust gas heat

losses in the exhaust system were also not considered and a phenomenological model described

the dynamics of the catalyst. As the model lacks some of the required functionality and is largely

of empirical nature, it is not considered in this investigation.

The integrated model of Sanketi et al. (2006b) is in many ways similar to that of Fiengo et al.

(2002). The engine dynamics, however, were implemented in a more physics-oriented hybrid

model, based on an MVEM, with spark timing and air-fuel ratio control inputs. Nevertheless,

engine warm-up dynamics were not modelled, onlyHC emissions were considered and no exhaust

system dynamics were included. The catalyst was described by a phenomenological model, with

static maps approximating its conversion efficiency. As previously, the functionality of this model

is inadequate for the problem being considered in this thesis.

Physics-based low order models capable of simulating cold start fuel consumption, as well as

CO, NOX and HC tailpipe emissions over drive cycles as a function of engine control inputs,

such as the air-fuel ratio, spark advance and valve timing, do not appear to exist. Thus, a new

combined control-oriented model based on the physical principles must be developed.

2.7 Summary

Existing methodologies for minimising cold start fuel consumption subject to cumulative tailpipe

emissions constraints are mostly limited by purely experimental approaches, use of black-box

or phenomenological models, or models that indirectly consider tailpipe emissions. Whilst the

experimental approach is currently the industry standard, it can be time consuming and therefore

costly. Black-box and phenomenological models require a significant calibration effort and may

be oversimplified. Indirect consideration of tailpipe emissions in the optimisation can yield

inaccurate or misleading results.

To identify optimal engine control strategies, an integrated low order model of the engine,

the exhaust system and the three-way catalyst needs to be identified and included in a dynamic

optimisation study. Iterative dynamic programming is one optimisation procedure that is well

suited to the problem. Whilst it does not guarantee global optimality, it can be used to overcome

the “curse of dimensionality”. Furthermore, it possesses favourable speed, flexibility and con-

vergence properties. However, it should be noted that when the time domain is resolved using

coarse grids, some of the higher frequency characteristics of the optimal trajectories may not be

captured and certain types of trajectories, such as bang-bang, could be missed.

For the integrated model to be accurate, portable and easily calibratable, it should be based

25

on physical principles where practical. Whilst many physics-based models have been proposed

for various engine sub-systems and catalytic converters, these models appear to have never been

unified. Therefore, a new integrated model needs to be developed. A mean value approach

appears to be a reasonable candidate for approximating some of the engine dynamics. Whilst

the MVEM’s are based partially on black-box approaches, these models are nonetheless modular,

relatively portable and are of low enough order to make dynamic optimisation studies feasible.

Modelling of engine-out emissions, however, necessitates use of black-box approaches, as the

emissions formation mechanisms are highly complex. Catalyst dynamics can be approximated

reasonably well using one dimensional models with low order kinetic schemes and oxygen storage

reactions. However, as these models have traditionally been of high order, the effect of model

reduction on the accuracy of simulated tailpipe emissions needs to be investigated.

26

Chapter 3

Experimental methods

Unless otherwise stated, all experimental data presented in this thesis was collected in the

Thermodynamics laboratory at the University of Melbourne. The test cell, shown in Figure 3.1,

was equipped with a floating test bench bed (1 ) to dampen the mechanical vibrations induced

by the test rig. The bed sat on cushions, each filled with compressed air by the compressor (2 ),

while the Horiba–Schenck TITAN T 460 transient dynamometer (3 ) and the 4L Ford Falcon BF

engine (4 ) were mounted on top of the bed. The air intake (5 ) and the air filter were positioned

above the engine. Both the engine and the dynamometer could be controlled remotely from an

adjacent control room.

The coolant conditioning module (6 ) was connected to the engine’s outer coolant loop, re-

placing the radiator and allowing the engine’s inlet coolant temperature to be controlled. The

engine thermostat was removed to enable rapid cooling of the engine. If the coolant needed to be

circulated exclusively through the engine’s internal cooling loop, as required during some engine

warm up tests, the flow through the outer circuit was eliminated with the aid of mechanical

valves.

The engine’s oil circuit was split at the oil filter (between the oil pump and the oil gallery)

and connected in series with the oil conditioning system (7 ), controlling the temperature of the

oil entering the oil gallery. If the oil conditioning system was not required, it could be bypassed,

allowing the oil to circulate almost as in an unmodified engine. The control system (8 ) provided

power for the heaters, pumps and variable flow valves in the water and oil conditioning modules,

and enabled tracking of water and oil temperature setpoints. The parameters of the system

could be manipulated remotely.

The AVL KMA 4000 fuel conditioning system (9 ) delivered fuel from the fuel tank (10 ) to

the engine’s fuel rail and measured the instantaneous engine fuel consumption. The optional

27

Figure 3.1: Test cell layout

fuel chiller (11 ) could be utilised for fuel cooling.

A Kistler pressure transducer was inserted into the engine’s 6th cylinder. Its output was

preconditioned using a Kistler charge amplifier before being read by the LabVIEW data ac-

quisition card along with the crankshaft rotary encoder signal. A software package developed

in-house by Peter Dennis was run on the computer (12 ) for sampling in-cylinder pressure. Given

pressure transducer calibration data, the program can generate files containing pressure traces

as functions of the crankshaft position relative to the piston’s top dead centre. A cylinder

pressure analysis tool CYLPRES was developed to calculate indicated mean effective pressure

(IMEP), pumping mean effective pressure (PMEP), as well as some statistics with respect to

these quantities from the pressure trace files.

Three sets of exhaust gas analysers were used throughout the experimental work. The Horiba

200 Series bench served as the primary instrument for most steady state and transient work.

Its feedgas (pre-catalyst) and tailpipe (post-catalyst) sample tubes, (13 ) and (14 ), are shown in

Figure 3.1.

The Cambustion Fast Flame Ionisation Detector (FFID) (15 ) has a very fast response and

28

a very short gas transit time compared to all other analysers used. The instrument enabled

accurate estimates of transit delays of other analysers, making synchronisation of the emissions

data with the rig’s operating parameters possible. The FFID was also used to observe catalyst

oxygen storage dynamics. Bottles (16 ) contained hydrogen and air (fuel and oxidant for the

FFID flame) and a HC calibration gas.

Autodiagnostics ADS9000 gas analysers (17 ) were used mainly for steady state engine-out

emissions mapping to supplement the Horiba bench measurements. Occasionally the ranges

of the Horiba HC and NOX analysers were exceeded and the ADS9000 measurements were

used instead. An emissions data logger software package ADS9000 was developed to link the

ADS9000 to a PC (18 ) with a serial cable to facilitate logging of the emissions.

The cooling fans (19 ) were directed at the instrumentation on the engine and the exhaust

system to avoid possible damage to the equipment from the heat released. Ventilation fans

(20 ) provided a continuous flow of fresh air from the bottom of the test cell towards window

extraction fans near the ceiling. This helped to maintain a roughly constant room temperature

during tests and avoided any accumulation of the exhaust gases in the room.

3.1 Dynamometer

The Horiba–Schenck TITAN T 460, shown in Figure 3.2, is a transient dynamometer capable of

motoring the engine. When used as a brake, it generates electricity, directing it back into the

electrical grid. The specifications of the dynamometer are given in Table 3.1.

Manufacturer Horiba–SchenckModel Titan T 460Rated Power 460 kWSpeed Range 0 – 8000 RPMMaximum Torque 1484 Nm

Table 3.1: Dynamometer specifications

The dynamometer was controlled by the STARS Automation Software Platform of SRH Sys-

tems Ltd. from the control room. The same software was also linked to the engine management

system, taking over some of the engine’s control inputs, including the accelerator pedal position.

The dynamometer supports a number of control modes. In idle mode the engine is instructed

to idle, while no torque is applied on the crankshaft. The throttle–speed mode sets the desired

pedal position, while a specified engine speed is maintained. The speed–torque and torque–speed

modes run the engine at predefined power settings and are important for the implementation

29

Figure 3.2: Horiba–Schenck TITAN T 460 transient dynamometer

of drive cycles. Targeted torque and speed are achieved by adjusting the pedal position. If the

engine is unable to produce the required power and the particular combination of engine torque

and speed can not be maintained, preference is given to maintaining speed in the speed–torque

mode and torque in the torque–speed mode.

Many of the results presented in this thesis are based on the New European Drive Cycle

(NEDC) tests. These were implemented on the transient dynamometer using the STARS soft-

ware as a sequence of speed–torque and idle modes. Running the engine in speed–torque mode

guaranteed that its power output was representative of the drive cycle conditions, irrespective

of the applied engine control inputs, such as spark timing, valve timing or the air-fuel ratio. To

obtain torque and speed trajectories, a vehicle chassis dynamometer test was first conducted

at Ford with the same engine and engine calibration. The pedal position, engine speed and

idle events were recorded. This trajectory was then run on the transient dynamometer with a

standard engine calibration in a sequence of throttle–speed and idle modes. The engine torque

was measured and both the engine speed and torque trajectories were then available.

30

Figure 3.3: Ford Falcon BF engine

3.2 Engine

The engine was a current production 4L Ford Falcon BF engine, shown in Figure 3.3 with

specifications in Table 3.2. The engine could be controlled using ATI Vision software by Accurate

Technologies INC from the control room. ATI mapped fragments of the engine control unit

(ECU) memory to symbolic names, which could be read or written to during engine operation

as required. For example, by manipulating some of the ECU’s internal variables one could

command a throttle position, spark timing, inlet and exhaust cam timing or read the outputs

from the switching oxygen and MAP sensors. ATI was also connected to various data acquisition

boards, enabling the logging of external sensor outputs.

The tool TRAJECT was developed in ATI’s script language to control throttle, idle speed,

spark timing, cam timing, air-fuel ratio and intake manifold pressure. Air-fuel ratio control was

implemented as a PI controller by adjusting the injection duration with feedback from a wide-

band λ sensor. Intake manifold pressure could be tracked by another PI controller by adjusting

the throttle angle with feedback from a MAP sensor. The program accepted a file containing

reference values of engine control variables as a function of time. TRAJECT was extensively

31

General Parameters:

Manufacturer Ford of AustraliaCylinders In line 6Firing Order 1-5-3-6-2-4Capacity 3984 cm3

Bore 92.25 mmStroke 99.31 mmConrod length 153.85 mmPin offset 1.00 mmCompression Ratio 10.3:1

Valve Train:

Configuration DOHC Dual Independent VCTValve Lift 11.00 mmValve Head Diameter (intake) 35 mmValve Head Diameter (exhaust) 32 mmVCT Range 60 CADIntake Valve Open 27.5 CAD BTDC – 32.5 CAD ATDCIntake Valve Close 48.5 CAD ABDC – 108.5 CAD ABDCExhaust Valve Open 78.5 CAD BBDC – 18.5 CAD BBDCExhaust Valve Close 2.5 CAD BTDC – 57.5 CAD ATDCIntake Centre-Line 99.5 CAD ATDC – 159.5 CAD ATDCExhaust Centre-Line 131.5 CAD BTDC – 71.5 CAD BTDC

Engine Management:

Powertrain Control Module Ford BF Falcon-InstrumentedProcessor Freescale Spanish OakCalibration Ford BF Falcon

Other:

Intake System StandardOil Ford 5W30

Table 3.2: Engine specifications

used for engine mapping work and implementation of open-loop engine control schemes.

3.3 Fuel conditioning system

The primary roles of the AVL KMA 4000 fuel conditioning system were to circulate gasoline in

the engine’s fuel rail while adding new fuel and to measure instantaneous fuel consumption by

the engine. The fuel mass flow measurement system consists of an AVL PLU 121 volumetric

flow meter positioned directly downstream of the L-DENS liquid density sensor.

AVL PLU 121 uses a gear displacement pump, driven by an electric motor, and a differential

pressure device. The speed of the motor is controlled to achieve zero pressure difference across

32

the pump. Under these conditions there is negligible leakage of fuel past the gear teeth and

the volumetric flow rate is closely proportional to the angular velocity of the gear meter. The

working principle of the L-DENS module is based on the measurement of temperature and

resonant frequencies of a U-shaped mechanical oscillator through which the sample is fed. The

density of the fluid is calculated as a function of these variables. When the outputs from both

of these sensors are available, they are multiplied together by the AVL KMA 4000 to give the

fuel mass flow rate. The relative error of this measurement is ±0.1% (Horiba, 2006).

3.4 Exhaust system

The exhaust system was comprised of a cast iron exhaust manifold, front pipe, an adaptor joining

the front pipe to the exhaust manifold and slightly modified inter and rear pipes to suit the test

cell’s spatial constraints. The front, inter and rear pipes were standard Ford components. The

set up and the location of various sensors is shown in Figure 3.4. Physical parameters are listed

in Table 3.3.

Figure 3.4: Exhaust system

An exposed junction fast response K-type thermocouple was inserted near one of the exhaust

ports and at the outlet of the exhaust manifold to measure gas temperature. A 3 mm pad

type thermocouple was welded to the manifold for measuring its surface temperature. The mass

of the exhaust manifold was determined with digital scales after disassembly from the engine,

while the geometric parameters were calculated from measurements made using a calliper and a

measuring tape.

The pipe section joining the exhaust manifold to the catalyst will be referred here to as the

connecting pipe. Its surface temperature was measured with a pad type thermocouple welded

roughly half-way along the pipe.

The catalyst, shown in Figure 3.5, was aged on a 75 hour Ford 4-mode schedule, equivalent

to roughly 80000 km of road driving. Three holes were carefully drilled half way into the

33

Exhaust Manifold:

Type 6 into 1Material cast ironMass 9.0 kgInner radius at inlet 0.019 mInner radius at outlet 0.029 mInner surface area 0.181 m2

Outer surface area 0.199 m2

Connecting Pipe:

Material stainless steelMass 3.0 kgInner radius 0.030 mOuter radius 0.032 mLength 0.440 m

Three-Way Catalyst:

Material cordieriteChannel shape squareNumber of bricks 1Length 143.5 mmChannel hydraulic diameter 1.105 mmThickness of channel walls 0.165 mmCross-sectional area 0.0119 m2

Pt : Pd : Rh composition 12:0:5

Table 3.3: Parameters of the exhaust system

ceramic substrate towards the brick’s centre at equally spaced locations, where 3 mm closed

junction thermocouples were inserted. Fast response thermocouples were not required here

as the transient dynamics of the substrate are much slower than those of the thermocouples.

However, two fast response thermocouples were placed directly before and after the brick to

measure the inlet and exit gas temperatures.

A standard Ford switching type oxygen sensor was installed at its dedicated location near the

outlet of the exhaust manifold. Data from this sensor was acquired by the engine management

system to control the stoichiometric air/fuel ratio. Normalised air-fuel ratio measurements were

taken using Bosch LSU 4.9 wide-band sensor. If the engine was required to operate at a non-

stoichiometric air-fuel ratio, the sensor was utilised in the feedback loop of a PI controller,

adjusting the injection duration. The wide-band sensor output together with the fuel flow

measurement were used to calculate the exhaust gas mass flow rate.

The Horiba analysers, Autodiagnostics ADS9000 and Cambustion Fast Flame Ionisation

Detectors measured the pre-catalyst and post-catalyst exhaust emissions and are described in

34

Figure 3.5: Three-way catalyst converter

subsequent sections.

3.5 Fast response thermocouples

The exposed junction fast response thermocouples, shown in Figure 3.6, were hand built using

a welding procedure similar to Hart and Elkin (1946). A portion of a K-type thermocouple

extension cable was stripped of insulation. Two fine wires were inserted into 3 mm ceramic

tubing containing two isolated channels, while the unused wires were cut. The wires extruding

from the ceramic were twisted by several turns and trimmed. For a successful weld the ends

of the twisted pair had to be sharp and touching each other. The wires between the ceramic

and the extension lead were isolated using Teflon tape to prevent a possible circuit shortage. To

protect them from twisting and breaking, a rigid plastic tube was slid over the thermocouple

assembly, restricting the relative movement of the ceramic and the extension cable.

A 1 cm long, 0.5 mm diameter HB pencil lead was connected to the negative terminal of a

20 V DC power supply. This polarity had to be observed in order to achieve a reliable weld. The

positive terminal was connected to the thermocouple cables themselves. The twisted ends and

35

Figure 3.6: Fast response thermocouple

the carbon rod were brought together while keeping them parallel with respect to each other,

allowing the tip of the lead to brightly glow momentarily. This melted the thermocouple wires,

producing tiny ball-shaped welds as in Figure 3.6.

The ceramic tubing could be slid through a stainless steel fitting mounted on the exhaust

system. Several layers of aluminium tape were applied on the ceramic, enabling it to rigidly sit

inside the fitting and preventing ambient air from entering the exhaust system.

3.6 Indicated work measurements

3.6.1 In-cylinder pressure measurements

In-cylinder pressure measurements were taken from a single cylinder using a Kistler type 603B1

pressure transducer mounted in the pent-roof of the combustion chamber. The sensor consists

of a stainless steel case with a diaphragm on one end and a coaxial connector on the other. The

gas pressure being measured acts on the diaphragm, pushing it against a stack of quartz plates,

separated by gold electrodes. Such arrangement of piezoelectric sensing elements enables the

charge output from the individual plates to be added and a relatively large overall charge to be

produced. During transient measurements the acceleration of the diaphragm and the sensing

element components can cause a redundant signal to be added to the output. To eliminate this

problem, another piezoelectric crystal is embodied in the transducer, connected with an inverted

polarity to the sensing element. The output from this accelerometer cancels the erroneous

components of the sensing element output.

The pressure transducer comes with a calibration certificate, specifying the sensor’s sensitivity

36

in terms of pC/bar for a set of pressure ranges. In this study the 0–103.42 bar range was used.

The operating temperature range is between -268 and 260◦ C, and the measurement error is

expected to be no greater than 0.3% of the full scale deflection under these conditions. To enable

measurements beyond 260◦ C, a 1 mm layer of high temperature silicon paste was applied to

the sensing end of the transducer, thermally insulating the diaphragm.

The coaxial cable attached to the sensor had a very high insulation resistance. This helped to

prevent charge leakage and is a requirement for good quality data acquisition using this type of

sensors. To ensure that the high resistance was maintained, the cable connectors were thoroughly

cleaned using a contact cleaning solution.

The output from the pressure sensor was conditioned using the Kistler type 5064A1Y51

charge amplifier, converting the pressure signal to a potential difference in the range from -10

to 10 volts. This voltage was then sampled using a LabVIEW card and a desktop PC, running

the Combustion Analysis Tool (CAT) developed in-house by Mr Peter Dennis.

To synchronise pressure measurements with the instantaneous volume of the combustion

chamber, a high precision British Encoder 755HS rotary incremental encoder, mounted on the

engine’s crankshaft, was used. The angular position of the sensor at the piston’s top dead centre

was taken to be the angle of maximum pressure in a motoring engine with a wide open throttle

plus 1 crank-angle degree to compensate for charge cooling effects (Randolph, 1994). Such top

dead centre calibration was performed each time prior to engine testing.

The encoder generates a square output pulse with a period of 1 crank angle degree. By

distinguishing between the rising and the falling edges of this output, a resolution of 0.5 crank

angle degrees was attained. In theory, counting the pulses allows to accurately track the position

of the encoder. In practise, however, noise generated by the spark events and various electrical

equipment sometimes interfered with this signal, and the true crankshaft position could be lost.

The encoder can trigger a secondary output pulse once per revolution. To correct for the possible

position drift, the encoder position was reset based on the secondary pulse every few dozen cycles.

Fortunately the errors in the primary pulse were not frequently encountered and should not effect

the acquired data significantly.

To test for the possible gas leakages, the engine was motored with the throttle fully open

to maximise the pressure in the combustion chamber during compression, and pressure mea-

surements were taken. It can be verified from the resulting p–V diagram in Figure 3.7 that the

pressure during compression and expansion strokes agrees closely, as one would expect from a

leak-proof combustion chamber. The small difference between the two curves can be attributed

37

0

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

0 100 200 300 400 500 600 700 800

Pre

ssure

(kP

a)

Volume (cm3)

100

1000

100 1000

Pre

ssure

(kP

a)

Volume (cm3)

Figure 3.7: p–V diagram of a motoring cylinder with the throttle fully open

Figure 3.8: Piston position as a function of crankshaft position

to the combination of charge cooling and exhaust blowdown effects, and is not necessarily an

indication of a leak through the pressure sensor fitting. Unfortunately, leak testing fluids could

not be applied directly onto the fitting to avoid the risk of contaminating the pressure sensor’s

sensitive electrical connections.

3.6.2 Calculation of the indicated work

In-cylinder pressure measurements can be used to calculate the work delivered to a piston. This

quantity, also known as the indicated work, is used in the model calibration described in the

subsequent chapters. Indicated work is obtained using

W =

∫

p dV. (3.1)

38

However, because the instantaneous combustion chamber volume V is not measured, the changes

in V must be related to the changes in the crankshaft position θ, obtained using a rotary encoder.

Hence, the integral (3.1) can be rewritten as

W =

∫

p(θ)dV

dθdθ. (3.2)

To determine dVdθ , consider the description of the piston’s motion in Figure 3.8. The origin of

the stationary X–Y coordinate system O coincides with the crankshaft point of rotation. Points

C and P are at the centres of the crankpin and the piston pin respectively. Point M lies on the

piston’s centreline and possesses the same Y -coordinate as point P . Line segments OC, CP and

PM describe the position of the crank throw, the conrod and the pin offset. The position of the

piston is uniquely identified by the variable y. If the largest value of y is taken to be ymax then

the in-cylinder volume becomes

V (θ) = Vcl +Abore(ymax − y(θ)). (3.3)

Differentiation with respect to θ gives

dV

dθ= −Abore

dy

dθ. (3.4)

The derivative dydθ is identified from the geometry of the problem. Consider the vector diagram

in Figure 3.8. It is clear that the relationship

rC + rR + rP = y J (3.5)

always holds. Vectors rC, rR and rP can be expressed in terms of their absolute lengths and

the angles θ and φ as

rC = lC sin θ I + lC cos θ J, (3.6)

rR = −lR sinφ I + lR cosφ J, (3.7)

rP = lP I. (3.8)

Substituting (3.6)–(3.8) into (3.5) and equating X and Y components yields

lC sin θ − lR sinφ+ lP = 0, (3.9)

lC cos θ + lR cosφ = y. (3.10)

Equation (3.9) is rearranged for φ in terms of θ,

φ = arcsin

(

lC sin θ + lPlR

)

, (3.11)

39

and is substituted into (3.10) producing

y = lC cos θ + lR cos

[

arcsin

(

lC sin θ + lPlR

)]

. (3.12)

Differentiation using the chain rule results in

dy

dθ= −lC sin θ −

lPlClR

cos θ(

lClP

sin θ + 1)

√

1 − l2Cl2R

(

sin θ + lPlC

)2. (3.13)

Finally, substitution of this expression into (3.4) and then (3.4) into (3.2) gives

W = Abore

∫

p(θ)

lC sin θ +lP

lClR

cos θ(

lClP

sin θ + 1)

√

1 − l2Cl2R

(

sin θ + lPlC

)2

dθ. (3.14)

The program CYLPRES was developed to numerically evaluate the expression (3.14) for the

relevant part of the cycle. This software was used extensively to calculate the indicated mean

effective pressure (IMEP) and the pumping mean effective pressure (PMEP), along with the

standard deviation, coefficient of variance (CoV) and the extremities of these quantities from

the raw pressure data.

3.7 Exhaust gas analysers

3.7.1 Cambustion HFR400 fast flame ionisation detector

Cambustion HFR400 Fast Flame Ionisation Detector (FFID) measured pre and post-catalyst

HC emissions (see Figure 3.16). This device has a very fast transient response with a time

constant of less than 2 ms and is specifically designed for taking measurements in the exhaust,

where pressure fluctuations can be large (Cambustion, 1997).

Two heated sample lines were inserted at appropriate locations in the exhaust system. The

sample line is a thin stainless steel tube with a built-in electric heater, controlled by the LHC500

heated sampling system. The temperature of the sample tube is maintained roughly at 150◦C

to vapourise any liquid entering the tube. Failure to do so can impact the calibration of the

FFID or extinguish the flame in the hydrocarbon sensing module.

The structure of the hydrocarbon sensing module is described in Figure 3.9. It contains a

constant pressure and a flame chamber, joined by a FID capillary. A vacuum pump is used to

drop the pressure inside these volumes to well below atmospheric. The pressures are fine tuned

by the main control unit, which bleeds off appropriate amounts of air into the chambers. A

40

constant pressure difference is maintained across the FID tube to achieve a fixed sample flow

into the flame, even when pressure fluctuations exist in the exhaust. The sample is drawn into

the constant pressure chamber and into the flame chamber, where it is burned. The flame is

produced by burning hydrogen in air, which are supplied from the control unit. The burning

of the exhaust gas is accompanied by the release of positively charged ions and electrons, the

number of which is roughly proportional to the carbon atoms contained in the burnt sample

(Cambustion, 1997). A small current is induced as the electrons hit the surface of an electrode

plate. This signal is converted into an output voltage between -10 and 10 volts subject to

calibration parameters. The output can then be sampled by a data acquisition board and logged

using ATI Vision.

Figure 3.9: FFID hydrocarbon sensing module

Both of the sample tubes used in the experiments were 280 mm in length. The hydrocarbon

sensing modules were fitted with 0.008 in FID tubes and recommendations from Cambustion

(1997) were considered for specifying constant pressure and flame chamber pressures. The pres-

sure in the constant pressure chamber was set to 350 mm Hg below atmospheric, while the

pressure in the flame chamber to 100 mm Hg below that of the constant pressure chamber.

The extent of sample ionisation is a function of the FID flame temperature, dependent on the

hydrogen and air line pressures. To determine the combination of the pressures, maximising the

sensitivity of the instrument (suggested by Cambustion (1997)), the sample tubes were flooded

with calibration gas at atmospheric conditions, as shown in Figure 3.10. A sample tube was

Figure 3.10: Flooding of the FFID sample tube with calibration gas

inserted into a PVC hose connected to the regulator of the span gas bottle. A small amount of

41

propane was allowed to leak past the sample line and out into the ambient. The sample flow rate

was slowly increased until the output voltage no longer changed. By this stage atmospheric air

could no longer dilute the calibration gas at the inlet of the sample tube. Fuel and air pressures

were then adjusted to obtain the highest output voltage, resulting in 2.1 bar fuel and 4.5 bar

air pressure for both hydrocarbon sensing modules. This setting was used in all subsequent

experiments.

To minimise calibration drift, the sample lines and FID tubes had to be cleaned prior to every

experiment due to the accumulation of carbon deposits. Sample tubes were cleaned using a steel

guitar string, while the FID tubes using a special cleaning wire denoted by a yellow marker

(suitable for 0.008 in tubes). After lighting the FFID flame, the device was allowed to warm up

until the indicated flame temperature and the output voltage reached a steady state. An unlit

lighter was used to test for leaks by directing the butane jet at various seals and connectors and

monitoring the FFID output. The instrument was calibrated using laboratory air and a propane

span gas prior to each test. At the end of the tests calibration was verified using the same gases.

3.7.2 Horiba 200 series emissions bench

The Horiba 200 Series Emissions Bench is a vehicle certification grade bench, designed to measure

feedgas and tailpipe O2, CO, CO2, NO and HC emissions. Several concentration ranges are

supported on most analysers to facilitate accurate measurement under various engine operating

conditions. The time constants associated with the gas analysis are on the order of 2 seconds.

The bench operates by drawing the exhaust into a pair of flexible sample lines (for feedgas

and tailpipe measurements) towards a sample conditioning unit (SCU). The sample tubes are

maintained at a constant temperature of approximately 110◦C to avoid any water condensation

and blockage in the lines. In the SCU the exhaust gases are cleaned, dehydrated and pumped

through to gas analysers. A variety of techniques are then applied for determining the gas

composition. Exhaust O2 is measured by magneto-pneumatic methods, CO and CO2 by non-

dispersive infrared (NDIR) absorption, NO by chemiluminescence and HC by flame ionisation

detection (FID).

Oxygen molecules exhibit paramagnetic properties and are attracted into externally applied

magnetic fields. In magneto-pneumatic analysers, shown in Figure 3.11(a), a constant flow of

nitrogen gas is maintained into the chamber split by a microphone. The gas is discharged through

a pair of passages beside the two electromagnets. The sample gas flows at a constant rate past

the outlets of these capillaries. When an electromagnet is excited, the O2 molecules in the sample

42

(a) Magneto-pneumatic detector

(b) Non-dispersiveinfrared detector

(c) Chemilumines-cent detector

(d) Flame ionisationdetector

Figure 3.11: Measurement principle of Horiba gas analysers

gas are diverted towards one of the outlets, restricting the flow of nitrogen through one channel

and increasing the flow of nitrogen through the other. This difference in flow rates results

in a pressure difference across the microphone’s diaphragm. The electromagnets are excited

alternately, producing continuous pressure fluctuations across the microphone. The electrical

output from the microphone is detected and related to the O2 concentration in the sample gas.

Oxygen is not the only component in the exhaust gas affected by a magnetic field. Some of the

other paramagnetic gases which can potentially interfere with the O2 measurement include NO,

NO2, CO, CO2 and some types of hydrocarbons. The relative interferences of some of these gases

are repeated from Horiba (1990b) in Table 3.4. From the table it can be seen that the sensitivity

of the analyser to NOX is high. However, the concentrations of these compounds in an engine’s

exhaust are typically several orders of magnitude smaller than those of O2. Concentrations

of order 5000 ppm are considered large. Under such conditions errors in O2 measurements of

roughly +0.002 mol/mol are expected and in many cases can be tolerated. The magnitude of dry

CO2 concentrations in the exhaust are of order 0.13 mol/mol, which can give an error of roughly

−0.00035 mol/mol in O2 measurement. These error estimates were confirmed experimentally

using calibration gases. Interference caused by the other species is very small due to their low

presence and the low sensitivity of the analyser.

In NDIR analysers (see Figure 3.11(b)) the exhaust gases are pumped through a sample

cell. A reference cell is positioned beside and is completely sealed. It contains zero gas, usually

nitrogen. The two cells are exposed to light produced by a lamp. Depending on the concentration

of the gas being measured, the extent of light absorption of certain wavelengths is affected.

Higher concentrations result in more absorbed light. The difference in light intensity from the

two beams entering the detector cell causes the sensor membrane to deflect. This deflection is

43

Gas Sensitivity [output / (mol/mol)]O2 1NO 0.43NO2 0.28CO 0.0001N2 0CO2 -0.0027C3H8 -0.0086

Table 3.4: Relative sensitivity of the magneto-pneumatic detector to various exhaust gases

directly related to the concentration of the compound being measured. To reduce the sensitivity

of the instrument to other compounds, a filter, which transmits wavelengths absorbed only by

the species of interest, is placed between the cells and the detector. The chopper is used to

alternately block the light entering one of the cells. This causes the detector membrane to

vibrate, generating an electric output.

Some of the compounds present in the exhaust including H2O, CO2 and CO have overlap-

ping absorption spectra and may introduce errors to CO and CO2 measurements. Most of the

water is removed from the gas sample in the chiller of the SCU prior to the analysers, and its

effect on the measurements is small. The effect of CO2 on CO measurements can be signifi-

cant when considering low CO concentrations (Horiba, 1991). However, it has been confirmed

experimentally that for the large range of CO concentrations considered in this thesis this inter-

ference is minimal. Figure 3.12(a) presents results from an experiment, where the CO analyser

was first zeroed with N2 and then spanned using a high concentration CO2 gas. The steady

state outputs coincide, indicating no detectable interference. The observed peak in the output

is the analyser’s response to a small amount of CO calibration gas left over in the lines from the

previous spanning of the instrument.

The effect of CO on the CO2 measurement was studied in similar experiment, where N2

zero gas was introduced into the CO2 analyser, followed by a high concentration CO span gas.

The results are presented in Figure 3.12(b) and show an absolute error of 0.03% mol/mol in the

analyser’s output. For the purposes of this work, errors of this magnitude can be tolerated and

such interference effects will be unaccounted for.

Chemiluminescent analysers (see Figure 3.11(c)) measure the intensity of light produced in

the following chemical reactions:

NO +O3 → (1 − rNO∗

2) NO2 + rNO∗

2NO∗

2 +O2,

NO∗2 → NO2 + hv,

44

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 5 10 15 20 25 30 35 40 45

CO

(%

mol/m

ol)

Time (s)

(a) CO analyser spanned with N2 (first 4 seconds),then with 20.6% mol/mol CO2

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 5 10 15 20

CO

2 (

% m

ol/m

ol)

Time (s)

(b) CO2 analyser spanned with N2 (first 4 sec-onds), then with 8.98% mol/mol CO

Figure 3.12: Interference of NDIR measurements

where rNO∗

2is the proportion of NO2 in the excited state NO∗

2 , roughly equal to 0.1 (Horiba,

1990a). Excess ozone (O3) is produced inside the UV lamp by exposing air to ultraviolet radi-

ation, guaranteeing complete oxidation of NO irrespective of the amount entering the reaction

chamber. The exited NO∗2 is unstable and is quickly reverted to the non-excited state, accompa-

nied by the emission of light. Silicon photodiodes are used to measure the light intensity, which

is related to the NO concentration in the sample gas. The process of measuring both NO and

NO2 involves routing the exhaust gas through an NO2 converter prior to the reaction chamber,

where NO2 is decomposed into NO in the following reaction:

NO2 + C → NO + CO.

The analyser response is then related to the total NO in the sample gas entering the reaction

chamber. To remove excess O3 from the analyser’s exhaust, it is passed through a de-ozonator.

FID analysers (see Figure 3.11(d)) premix H2 with the exhaust gas and burn the mixture in

air. The heat released from the flame ionises the hydrocarbons in the sample. When a poten-

tial difference between the electrode and the flame holder is applied, a small current develops

across the flame. This current is measured and amplified, producing an analyser output roughly

proportional to the total number of carbon atoms in the sample gas.

A comprehensive study of the FID sensitivity to various types of hydrocarbons can be found in

Dietz (1967). It has been shown that the sensitivity to a variety of alkanes, alkenes, alkynes and

aromatics varies by several percent, while the sensitivity to compounds containing oxygen and

nitrogen is substantially less. Because the exhaust of a gasoline spark-ignition engine contains

45

limited amounts of such substances (Heywood, 1988), the FID was expected to provide an

accurate measure of the total hydrocarbons based on the carbon count.

From steady state tests using calibration gases and a gas divider it has been demonstrated

that the outputs of magneto-pneumatic and FID analysers are linear with respect to the con-

centrations measured, while those from NDIR and to a lesser degree chemiluminescent analysers

are non-linear. To account for these non-linearities, the analyser outputs were sampled and

post-processed in real time on ATI using calibration curves, functions that translate these out-

puts to real concentrations. Figure 3.13 shows several examples of calibration curves for some of

the analysers and measurement ranges. The crosses represent experimentally obtained analyser

outputs for a number of known gas compositions. Calibration curves were approximated by 4th

order polynomials and identified using a least squares approach.

All analysers were routinely zeroed and spanned before and after every experiment. Nitrogen

was used as the zero gas. For the spanning of NDIR and chemiluminescent analysers a special

software tool CALGAS was developed. Based on the appropriate calibration curve and concen-

tration of the span gas used, CALGAS calculates the reference value of the analyser output to

tune to while spanning. CALGAS achieves this by applying the Newton method to solve the

equation of the form

ax4 + bx3 + cx2 + dx+ e = Cg, (3.15)

where Cg is the concentration of the component of interest in the span gas, a, b, c, d and e

are constants identifying the calibration curve and x is the analyser output to be identified as a

fraction of the full scale deflection.

To characterise the transient dynamics of the Horiba analysers, their response to a step change

in the sample gas concentrations was studied. The step input was produced by allowing nitrogen

to flow through the analysers until a steady reading of 0 was observed, then by immediately

introducing a calibration gas. The zero gas was reintroduced again after the outputs settled.

Figure 3.14 shows the response of the FID analyser. If the analyser dynamics can be ap-

proximated by a first order linear time-invariant system then the time constant for the FID is

roughly equal to 1.0 second. Time constants τ , estimated for all of the analysers based on their

step response, are presented in Table 3.5.

To evaluate the effects of long sample tubes and volumes in the sample gas path (such as water

traps, filters and pumps) on the transport delay and the response of the analysers, 1020 ppm

propane was injected through a T-fitting at slightly positive pressure with one end connected to

a Horiba sample tube and the other to Cambustion FFID. After a steady reading was obtained,

46

0

5

10

15

20

25

0 0.2 0.4 0.6 0.8 1

O2 (

% m

ol/m

ol)

Analyser output as fraction of full scale deflection

(a) 25% O2 range

0

2

4

6

8

10

12

0 0.2 0.4 0.6 0.8 1

CO

(%

mol/m

ol)


(b) 10% CO range

0

5

10

15

20

25

0 0.2 0.4 0.6 0.8 1

CO

2 (

% m

ol/m

ol)


(c) 20% CO2 range

0

200

400

600

800

1000

0 0.2 0.4 0.6 0.8 1

NO

(ppm

)


(d) 1000 ppm NO range

0

200

400

600

800

1000

1200

0 0.2 0.4 0.6 0.8 1

HC

(ppm

C3)


(e) 1000 ppm HC range

Figure 3.13: Calibration curves

47

0

200

400

600

800

1000

1200

0 0.5 1 1.5 2 2.5 3 3.5 4

HC

(ppm

C3)

Time (s)

0

200

400

600

800

1000

1200

0 0.5 1 1.5 2 2.5 3 3.5 4

HC

(ppm

C3)

Time (s)

Figure 3.14: Horiba FID response to a step change in the gas concentration close to the analyser’sinlet port

Analyser τ based on rising output (s) τ based on falling output (s)O2 1.2 1.1CO 2.0 1.6NO 1.0 1.1HC 1.0 1.1CO2 1.8 1.2

Table 3.5: Estimated time constants τ of Horiba gas analysers

the source of propane was removed, allowing atmospheric air to be sampled. Measurements

from the Horiba bench and the FFID were simultaneously logged by a PC and are presented

in Figure 3.15. Because the FFID has a very fast response, it allows to accurately identify the

instant of the ambient air exposure.

The transport delay can be affected by the gas pressure supplied. When propane is injected,

the positive pressure at the tube’s inlet is not representative of the exhaust system conditions.

Hence, the response time of the Horiba bench is evaluated based on the fallingHC concentration,

after the sample tube becomes exposed to the ambient air. The transport delay (based on a

10% change of the output) was estimated to be roughly 9.5 seconds, while the time constant for

the FID measurement increased from 1.1 to 2.2 seconds. It was ensured by tuning the sample

mass flow rates that both the feedgas and tailpipe benches produced in-phase measurements.

The slight offset in the steady state readings of the FFID and the FID can be attributed to the

use of different span gases for calibrating the instruments. The FID’s were calibrated using 200

ppm propane, while the FFID using 1020 ppm gas. Hence, the small error between the readings

is not surprising.

48

0

200

400

600

800

1000

1200

0 5 10 15 20 25 30 35 40

HC

(p

pm

C3)

Time (s)

Cambustion FFIDHoriba feedgas FID

Figure 3.15: FID and FFID response to a step change in the gas concentration at the sampletube end

3.7.3 Autodiagnostics ADS9000

Autodiagnostics ADS9000 are compact gas analysers embedded in a rectangular steel case (see

Figure 3.16). They sample at a rate of roughly 1.4 Hz and have time constants on the order of

a few seconds. Their specifications are provided in Table 3.6. The analysers have a small panel

at the back with zero, span and sample line fittings, a power connector, a serial communications

port and a small water trap filter. Both of the emission benches measure O2, CO, CO2 and

HC, while only one measures NO concentrations. The analysers use NDIR to detect CO, CO2

and HC, and the electro-chemical cell method for O2 and NO. HC concentrations reported by

NDIR techniques are usually not very precise due to the large variety of hydrocarbons in the

exhaust, all possessing different light absorption characteristics. In fact the sensitivity of NDIR

to the total HC can vary greatly depending on the exhaust gas composition. It is common

practice to correct these measurements with a multiplier depending on the type of fuel used

(Heywood, 1988, Dober, 2002).

The connection to the exhaust system was implemented via a 1/4 in, 3 m PVC hose and a

short 50 cm stainless steel tubing fitted to the exhaust pipe to prevent the PVC tubing from

melting.

ADS9000 were calibrated with the help of a dedicated computer program from Autodiagnos-

tics. High range CO, CO2, NO and C3H8 span gases were fed into the analyser’s span port at

low pressure to satisfy the required sample flow rate. Laboratory air was used for the calibration

49

Figure 3.16: Cambustion FFID and Autodiagnostics ADS9000

of the O2 sensor. New calibrations were saved to the device’s on-board memory and checked

periodically using the same span gases.

The official software for the ADS9000 lacked the ability to record the emissions data to text

files, making it awkward to obtain steady state and transient measurements. In order to overcome

this problem a software package ADS9000 was developed, implementing the communications

protocol used by the analysers’ hardware. Apart from logging the emissions to text files and the

screen, the program can estimate wet emissions and the air-fuel ratio on-the-fly for hydrogen

and various hydrocarbon fuels based on the measured dry exhaust gas composition.

3.7.4 Steady state comparison of analysers

Excellent agreement was observed between the feedgas and tailpipe Horiba analysers while sam-

pling the same location in the exhaust system. The outputs from the two ADS9000 benches

agreed closely as well. This was indicative of a consistent calibration of the instruments and a

reduced possibility of leaks in the sampling systems. To further test the emissions measurements

for consistency, the Horiba analysers and the ADS9000 benches were compared. Figure 3.17 cor-

50

Gas Output Units Measurement Range Data ResolutionO2 % vol 0–25 0.01CO % vol 0–10 0.01CO2 % vol 0–20 0.01NO ppm 0–10000 1HC ppm C6 0–10000 1

Table 3.6: ADS9000 Ranges and Data Resolution

relates the emissions from the Horiba feedgas analysers with one of the ADS9000.

The agreement between the benches is good. Note, however, that the ADS9000 uses NDIR

for detecting HC and a chemical cell method for measuring NO, unlike the Horiba analysers

that take advantage of more precise techniques. Hence, the observed disagreement for these

quantities is not surprising.

Traditionally NDIR HC measurements are corrected by a multiplier, dependent on the type

of fuel employed (Heywood, 1988). By fitting the ADS9000 NDIR to the Horiba FID data using

a least squares approach, this constant turns out to be 2.284 and agrees well with 2.29 reported

by Dober (2002) for gasoline.

The ADS9000 appears to overestimate NO concentration. To compensate for this error,

the measurements were corrected with a gain and an offset. The following relation has been

identified from the least squares fit of the ADS9000 NO data to the Horiba chemiluminescent

analyser output:

NOcor = 0.916 NOADS9000 − 44.0, (3.16)

where NOcor is the corrected and NOADS9000 is the concentration obtained from the ADS9000

in ppm. Figure 3.18 demonstrates the agreement of the corrected HC and NO measurements

using the ADS9000 with the Horiba bench.

3.7.5 Calculating wet molar fractions from dry gas composition

As was mentioned previously, most of the water is removed from the exhaust gas in the sample

lines of the Horiba and ADS9000 emissions benches. Under normal operation, almost no water

vapour reaches the exhaust analysers. Hence, the concentrations reported are not representative

of the real concentrations in the exhaust system. This section explains how the true “wet”

concentrations are calculated based on the measured “dry” exhaust gas composition. Note that

the Cambustion FFID directly measures wet hydrocarbons and does not require any further

post-processing of its output.

51

0

1

2

3

4

5

0 1 2 3 4 5

AD

S9000 O

2 (

% v

ol)

Horiba emissions bench O2 (% vol)

(a) ADS9000 chemical cell vs. Horiba magneto-pneumatic analyser for O2

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

AD

S9000 C

O (

% v

ol)

Horiba emissions bench CO (% vol)

(b) ADS9000 NDIR vs. Horiba NDIR for CO

10

11

12

13

14

15

10 11 12 13 14 15

AD

S9000 C

O2 (

% v

ol)

Horiba emissions bench CO2 (% vol)

(c) ADS9000 NDIR vs. Horiba NDIR for CO2

0

1000

2000

3000

4000

5000

0 1000 2000 3000 4000 5000

AD

S9000 N

O (

ppm

)

Horiba emissions bench NO (ppm)

(d) ADS9000 chemical cell vs. Horiba chemilumi-nescence for NO

0

1000

2000

3000

4000

5000

6000

7000

8000

0 1000 2000 3000 4000 5000 6000 7000 8000

AD

S9000 H

C (

ppm

C1)

Horiba emissions bench HC (ppm C1)

(e) ADS9000 NDIR vs. Horiba FID for HC

Figure 3.17: Comparison of the Horiba and ADS9000 analysers at various steady state engineoperating conditions

52

0

1000

2000

3000

4000

5000

0 1000 2000 3000 4000 5000

Corr

ecte

d A

DS

9000 N

O (

ppm

)

Horiba emissions bench NO (ppm)

(a) ADS9000 chemical cell vs. Horiba chemilumi-nescence for NO

0

1000

2000

3000

4000

5000

6000

7000

8000

0 1000 2000 3000 4000 5000 6000 7000 8000

Corr

ecte

d A

DS

9000 H

C (

ppm

C1)

Horiba emissions bench HC (ppm C1)

(b) ADS9000 NDIR vs. Horiba FID for HC

Figure 3.18: Comparison of the Horiba and the corrected ADS9000 output at various steadystate engine operating conditions

Wet and dry molar fractions of species i, Ci and C(d)i respectively, are defined by

Ci =ni

∑

j njfor all i, (3.17)

C(d)i =

ni∑

j,j 6=H2O njfor i 6= H2O. (3.18)

Combining these equations gives

Ci

∑

j

nj = C(d)i

∑

j,j 6=H2O

nj . (3.19)

Simple manipulation reveals

Ci = C(d)i

∑

j,j 6=H2O nj∑

j nj

= C(d)i

∑

j nj − nH2O∑

j nj

= C(d)i (1 − CH2O). (3.20)

Unfortunately, CH2O is not measured, and hence, must be estimated. To develop an expres-

sion for CH2O in terms of the measured emissions, consider the overall reaction describing the

combustion of gasoline in a spark ignition engine,

nfuel CHrHC+ nair(rO2O2 + [1 − rO2 ]N2) → nC CHrHC

+ nCO CO + nNO NO+

nCO2 CO2 + nO2 O2 + nN2 N2 + nH2 H2 + nH2O H2O. (3.21)

53

In this reaction air is represented by a mixture of O2 and N2. The molar fraction of O2 in air

is specified by the constant rO2 , equal to 0.2095. Petrol is approximated by hydrocarbons with

a fixed hydrogen to carbon ratio rHC . In Australia this ratio is specified by AS2877 (1986) as

1.85. Despite the fact that the hydrocarbon molecules in the engine’s exhaust are quite different

to those in the fuel, their hydrogen to carbon ratio is assumed to be the same as of the fuel

(AS2877, 1986).

Nitrogen dioxide is excluded from the reaction (3.21) as its concentration in the exhaust of a

petrol fuelled engine is generally less than 2% of NO (Heywood, 1988). Hydrogen, on the other

hand, can be produced in significant quantities (Heywood, 1988, Holder et al., 2006) and should

be considered. As the H2 concentration could not be measured with the gas analysers used in

this work, it is calculated from the water-gas shift reaction

CO2 +H2 → CO +H2O, (3.22)

which is assumed to be at a chemical equilibrium under the exhaust conditions. A commonly

accepted equilibrium constant for this reaction is 3.5 (Spindt, 1965).

By balancing the amount of C, H and O on both sides of the reaction (3.21), the following

equalities can be stated:

nfuel = nC + nCO + nCO2 , (3.23)

nfuel rHC = nC rHC + 2 nH2 + 2 nH2O, (3.24)

2 nair rO2 = nCO + nNO + 2 nCO2 + 2 nO2 + nH2O. (3.25)

An additional equation is included based on the definition of the equilibrium constant for the

reaction (3.22),

Kwg =nCO nH2O

nCO2 nH2

. (3.26)

Rearranging (3.26) as

nH2 =nCO nH2O

Kwg nCO2

(3.27)

and substituting (3.23) and (3.27) into (3.24) gives

(nC + nCO + nCO2) rHC = nC rHC + 2 nH2O + 2nCO nH2O

Kwg nCO2

. (3.28)

Rearranging for nH2O produces

nH2O = 0.5 rHC(nCO + nCO2) Kwg nCO2

Kwg nCO2 + nCO. (3.29)

54

By multiplying both sides of the equation byP

j nj

(P

j nj)2 , it can be rewritten in terms of the

component molar fractions as

CH2O = 0.5 rHC(CCO + CCO2)Kwg CCO2

Kwg CCO2 + CCO. (3.30)

Molar fractions CCO and CCO2 can be related to the measured dry composition C(d)CO and C

(d)CO2

using (3.20) as

CH2O = 0.5 rHC

(C(d)CO + C

(d)CO2

)KwgC(d)CO2

(1 − CH2O)

KwgC(d)CO2

+ C(d)CO

. (3.31)

If C(d)H2O is defined as

C(d)H2O = 0.5 rHC

(C(d)CO + C

(d)CO2

)KwgC(d)CO2

KwgC(d)CO2

+ C(d)CO

(3.32)

then (3.31) can be rewritten as

CH2O = C(d)H2O(1 − CH2O). (3.33)

Rearranging this equation yields the final expression for CH2O in terms of the dry composition,

CH2O =C

(d)H2O

1 + C(d)H2O

. (3.34)

This enables the wet molar fractions Ci to be calculated using (3.20) from the dry exhaust gas

measurements.

3.8 Measurement of the air-fuel ratio

3.8.1 Bosch LSU 4.9 wide-band sensor

The Bosch LSU 4.9 is a heated wide-band sensor, also called the universal exhaust gas oxygen

sensor (UEGO), that measures λ based on the exhaust gas composition in the range between

0.65 and infinity. Some studies (Auckenthaler, 2005) have reported its time constant to lie well

below 40 ms. The response time of the available gas analysers from which λ could be accurately

estimated was almost 2 orders of magnitudes slower, making the sensor an attractive alternative.

The details of the sensor’s working principle can be found in Bosch (2010) and Regitz and Collings

(2008). Only a brief description will be provided here.

The UEGO was positioned directly downstream of the exhaust manifold to reduce transport

delays. A MOTEC PLM powered and operated the device, while providing a programmable

output voltage, which was sampled and interpreted by ATI. For the purposes of engine mapping

55

and validation of dynamic optimisation results presented later in the thesis, a PI controller with

feedback from the λ sensor was implemented in ATI to control the air-fuel ratio beyond the

stoichiometric value.

Some of the internal components of the UEGO sensor are outlined in Figure 3.19. The sensor

Figure 3.19: Wide-band λ sensor

contains a Nernst sensing cell and a pump cell composed from zirconia (ZrO2) electrolyte with

two platinum electrodes on either side. The diffusion gap allows the exhaust gases to enter

into the internal cavity. The electrodes are heated to roughly 700◦C and behave as catalytic

converters, bringing the exhaust gas to a chemical equilibrium. The electrostatic potential that

forms across the sensing cell is a non-linear function of the exhaust air-fuel ratio. The largest

changes in this voltage can be observed around stoichiometry. The Nernst cell is effectively a

switching λ sensor, which can accurately predict when the mixture is rich or lean. If the mixture

appears to be rich, the pump cell current is controlled to achieve a sufficient inflow of oxygen

from the exhaust gas, so that to bring the exhaust in the internal chamber to a stoichiometric

state. If the mixture appears lean, the direction of the current is inverted and excess oxygen is

pumped back into the exhaust stream. The output from the UEGO sensor becomes a function

of the pumping current.

3.8.2 Calculation of λ from the exhaust composition

Consider the overall reaction for the combustion of gasoline in a spark ignition engine (3.21),

described above. For convenience, the equalities (3.23)–(3.25), arising from the balance of C, H

and O atoms on either side of the reaction are repeated below:

nfuel = nC + nCO + nCO2 , (3.35)

nfuel rHC = nC rHC + 2 nH2 + 2 nH2O, (3.36)

2 nair rO2 = nCO + nNO + 2 nCO2 + 2 nO2 + nH2O. (3.37)

56

From the definition of the normalised air-fuel ratio λ,

λ =1

AFRS

mair

mfuel

=1

AFRS

nairMair

nfuelMfuel. (3.38)

Therefore,

nair = λ AFRSnfuelMfuel

Mair. (3.39)

Substituting (3.39) into (3.37) produces

2 rO2 λ AFRSnfuelMfuel

Mair= nCO + nNO + 2 nCO2 + 2 nO2 + nH2O. (3.40)

Replacing nfuel using (3.35) gives

2 rO2 λ AFRSMfuel

Mair(nC + nCO + nCO2) = nCO + nNO + 2 nCO2 + 2 nO2 + nH2O. (3.41)

By dividing both sides by∑

i ni and rearranging the equation, an expression in terms of the wet

molar fractions is obtained,

λ =1

2 rO2 AFRS

Mair

Mfuel

CCO + 2 CCO2 + 2 CO2 + CNO + CH2O

CC + CCO + CCO2

. (3.42)

Alternatively, λ can be written in terms of the dry exhaust composition by substituting (3.20)

into (3.42),

λ =1

2 rO2 AFRS

Mair

Mfuel

(C(d)CO + 2 C

(d)CO2

+ 2 C(d)O2

+ C(d)NO)(1 − CH2O) + CH2O

(C(d)C + C

(d)CO + C

(d)CO2

)(1 − CH2O)

=1

2 rO2 AFRS

Mair

Mfuel

C(d)CO + 2 C

(d)CO2

+ 2 C(d)O2

+ C(d)NO +

CH2O

1−CH2O

C(d)C + C

(d)CO + C

(d)CO2

, (3.43)

and replacing CH2O in this equation with (3.34), giving

λ =1

2 rO2 AFRS

Mair

Mfuel

C(d)CO + 2 C

(d)CO2

+ 2 C(d)O2

+ C(d)NO + C

(d)H2O

C(d)C + C

(d)CO + C

(d)CO2

. (3.44)

The stoichiometric air-fuel ratio AFRS is found by considering the complete combustion of fuel

in air

nfuel CHrHC+ nair(rO2O2 + [1 − rO2 ]N2) → nCO2 CO2 + nH2O H2O + nN2 N2. (3.45)

The equalities arising from the balance of C, H and O atoms are

nfuel = nCO2 , (3.46)

rHCnfuel = 2 nH2O, (3.47)

2 rO2 nair = 2 nCO2 + nH2O. (3.48)

57

Substitution of (3.46) and (3.47) into (3.48) produces

2 rO2 nair = 2 nfuel +1

2rHCnfuel (3.49)

ornair

nfuel=

1 + 14 rHC

rO2

. (3.50)

The stoichiometric air-fuel ratio is therefore equal to

AFRS =mair

mfuel=

nair

nfuel

Mair

Mfuel=

1 + 14 rHC

rO2

Mair

Mfuel. (3.51)

Substitution of (3.51) into (3.44) yields the final expression for λ in terms of the dry exhaust

composition,

λ =1

1 + 14 rHC

12 C

(d)CO + C

(d)CO2

+ C(d)O2

+ 12 C

(d)NO + 1

2 C(d)H2O

C(d)C + C

(d)CO + C

(d)CO2

. (3.52)

This equation was used extensively for calculating λ throughout the engine mapping work.

3.8.3 Comparison of λ measurement techniques

Although the UEGO sensors benefit from a fast response, their outputs may be distorted when

certain exhaust compositions are encountered. Auckenthaler (2005) suggests that the ratio be-

tween H2, CO and HC in the exhaust can affect the accuracy of the λ measurement. These

distortions have also been observed in the current work. To illustrate this, consider Figure 3.20,

where results from a single experiment for 2 steady state engine operating conditions are pre-

sented. The normalised air-fuel ratio had been measured using the UEGO sensor and calculated

based on the emissions data collected from the Autodiagnostics ADS9000 and the Horiba emis-

sions benches. Figure 3.20(a) shows one operating point, where all λ measurements agree well,

while Figure 3.20(b) demonstrates a noticeable error between the measurements for the other

condition. The fact that λ values based on emissions compare well in almost all cases, including

those presented in Figure 3.20, suggests that the error is in the UEGO measurement. Nev-

ertheless, the UEGO measurements were found to be sufficiently accurate under most engine

operating conditions.

3.9 Summary

The experimental work was carried out on a Horiba-Schenck transient dynamometer, capable of

simulating driving conditions using reference torque and speed trajectories. The engine was a

current production 4L Ford Falcon BF engine, equipped with a Kistler pressure transducer for

58

0.85

0.86

0.87

0.88

0.89

0.9

0.91

0.92

0.93

0.94

0.95

0 5 10 15 20

λ

Time (s)

UEGOHoriba emissions

ADS9000 emissions

0.95

0.96

0.97

0.98

0.99

1

1.01

1.02

1.03

1.04

1.05

0 5 10 15 20

λ

Time (s)

UEGOHoriba emissions

ADS9000 emissions

Figure 3.20: λ measurements at steady state operating conditions

measuring indicated and pumping mean effective pressures. Fuel mass flow rate was measured

using an AVL fuel conditioning system.

The exhaust system comprised of a cast iron exhaust manifold, an aged three-way catalyst and

a pipe section connecting these components. Open junction thermocouples measured the exhaust

gas temperature in various part of the exhaust system, whilst pad type thermocouples, welded

to the exhaust manifold and the connecting pipe, measured the respective surface temperatures.

Three sets of emissions benches were used throughout engine testing. The Horiba vehicle

certification grade bench served as the primary instrument for most steady state and transient

work. Laboratory grade Autodiagnostics gas analysers were used mainly for steady state engine-

out emissions mapping to supplement the Horiba bench measurements. Cambustion FFID was

used to observe catalyst oxygen storage dynamics. It also enabled accurate estimates of tran-

sit delays of the other analysers, making synchronisation of the emissions data with the rig’s

operating parameters possible.

The normalised air-fuel ratio λ was evaluated based on dry exhaust gas composition mea-

surements during steady state experiments and was based on the output of a fast response Bosch

UEGO sensor during transient tests to retain high frequency information.

The test rig was utilised extensively during model calibration and validation work presented

in later chapters. It additionally enabled some of the optimised engine control strategies, also

developed later in this thesis, to be implemented and validated.

59

Chapter 4

Cold start fuel consumption and

tailpipe emissions model

To simulate cold start engine control strategies over drive cycles and to aid the development of

optimal control strategies, a warm-up model, describing thermodynamic processes in a gasoline

fuelled spark ignition engine, an exhaust system and a catalyst is required. The model should

calculate instantaneous fuel consumption and CO, NO and HC tailpipe emissions during a drive

cycle, thus enabling to quantitatively compare a given set of engine control policies. Whilst this

model must be of relatively low order to permit dynamic optimisation, it should take advantage

of physics-based approaches to improve its portability and reduce the calibration effort. This

could additionally provide insight into some of the internal dynamics that are otherwise difficult

to measure.

The structure of the proposed model is shown in Figure 4.1. The dynamometer control

system model is implemented as a PI controller, adjusting the engine’s throttle angle α to track

the reference torque τrefbrake for some prescribed engine speed N ref .

The engine model belongs to the well established class of mean value engine models with the

addition of cold start friction and warm-up dynamics. While being mathematically compact,

it operates on a time scale of roughly one cycle and is heavily based on empirical correlations.

The model calculates instantaneous fuel consumption mfuel, mass flow rate of the exhaust mcyl,

exhaust port gas temperature Tcyl and intake manifold pressure pim as a function of the throttle

angle α, engine speed N , the commanded normalised air-fuel ratio λ, spark timing θ, and cam

timing ϑint and ϑovlp.

As the heat losses in the exhaust system can considerably affect the catalyst dynamics, the

lumped thermal models of the exhaust system are used to calculate the gas temperature drop

61

Figure 4.1: Structure of the combined engine, emissions, exhaust and aftertreatment systemmodel

from the exhaust port to the catalyst inlet.

Concentrations of the major species emitted from the engine are based on static maps and

chemical equilibrium calculations. These maps are functions of several measurable engine vari-

ables. As the catalyst dynamics after light-off can be especially sensitive to the air-fuel ratio in

the exhaust gas, its composition is kept consistent with the commanded λ.

The catalyst is represented by a physical one-dimensional model, incorporating a reduced

order chemical kinetic scheme from Pontikakis and Stamatelos (2004) with oxygen storage. The

model can determine temporal and spatial distribution of substrate temperature, pollutant con-

centrations, stored oxygen, reaction and consumption rates as well as many other parameters.

4.1 Transient dynamometer control system

Engine torque and speed trajectories can be used on transient dynamometers to simulate drive

cycles (see Chapter 3.1). When the trajectories are implemented in speed-torque mode, the

dynamometer accurately maintains the reference speed of the engine, while the desired torque

is achieved by controlling the throttle using the accelerator pedal position. Irrespective of the

engine state, the air-fuel ratio, spark timing and cam timing, the control system attempts to run

the engine at the prescribed power output reference.

In this study the dynamometer control system is modelled by a PI controller. It is integrated

with the engine model as shown in Figure 4.1. The throttle angle α is adjusted to minimise the

62

error between the reference and the estimated torque, while the engine speed is prescribed. The

equations describing this system are

xI = τrefbrake − τbrake, (4.1)

α = kP (τrefbrake − τbrake) + kI xI , (4.2)

N = N ref . (4.3)

The gains kP and kI are selected to achieve acceptable tracking of the reference torque.

4.2 The engine

Catalyst dynamics can be sensitive to the exhaust mass flow rate and temperature. Consequently,

the engine model should reasonably simulate these variables under cold start and fully warm

conditions. Engine operation after a cold start is usually characterised by higher friction, arising

from the low oil viscosity in the rubbing components. To overcome this friction, the engine

consumes more fuel, and consequently, the exhaust mass flow rate is increased. To capture these

effects, the engine’s warm-up behaviour must be modelled.

A cold start mean value engine model (MVEM) for a spark ignition engine is considered

here. It is a 2 state model that predicts mean quantities of engine variables and operates

on a time scale of order 1 cycle. Fast dynamics, such as heat release inside the cylinders,

are approximated by algebraic relationships, while slow dynamics, such as engine temperature,

are modelled using differential equations. The resulting set of differential-algebraic equations

(DAE) is solved numerically. One of the advantages of MVEM over the models attempting to

mathematically describe the fast phenomenon is the computational speed. The approach, of

course, compromises generality and increases calibration effort, but is nevertheless necessary for

dynamic optimisation studies to be feasible.

This MVEM is based on the work of Manzie et al. (2009). The inputs and outputs are

summarised in Figure 4.1, while the mass transport and heat transfer considered are described

in Figure 4.2. The complete set of parameters defining the model are given in Table 4.1.

4.2.1 Flow past the throttle plate

The flow of air past a throttle plate can be approximated by the flow through a nozzle (Heywood,

1988). Consider Figure 4.3. By treating air as an ideal gas, assuming no entropy generation

and applying the steady flow energy equation across the nozzle, one can arrive at the following

63

Figure 4.2: Mass transport and heat transfer in the mean value engine model

Fixed parameters

Acyl total combustion chamber surface area [m2]B cylinder bore diameter [m]Jcrank moment of inertia of the crankshaft [kg m2]nc number of cylindersQLHV lower heating value of the fuel [J/kg]VS cylinder swept volume [m3]Vim intake manifold volume [m3]

Tuned parameters

ae cylinder wall heat transfer parameterbe cylinder wall heat transfer parametermeng ceng thermal mass of the engine [J/K]

Calibrated functions

(At CD)(α) product of the throttle open area and discharge coefficientpfme(N,Teng) frictional mean effective pressure [Pa]ηind,net(λ, θ, ϑint, ϑovlp, N, pim) net indicated efficiencyηvol(λ, ϑint, ϑovlp, N, pim) volumetric efficiency

Table 4.1: Parameters defining the engine model

equations

mair =CDAt(α)pamb√

RTamb

(

pim

pamb

)1γ

(

2γ

γ − 1

[

1 −(

pim

pamb

(γ−1)/γ)])

12

(4.4a)

for pressure ratios pim/pamb greater than the critical value γ(

2γ+1

)(γ+1)/2(γ−1)

and

mair =CDAt(α)pamb√

RTamb

√γ

(

2

γ + 1

)

γ+12(γ−1)

(4.4b)

for choked flow, when the pressure ratio is less than the critical value. Pressure pamb is upstream

of the throttle plate, while the pressure at the minimum area in the throttle body is equal to

the pressure inside the intake manifold pim. Any pressure recovery effects due to air expansion

downstream of the throttle plate are lumped into the discharge coefficient CD. The derivation

of these equations can be found in Heywood (1988).

64

Figure 4.3: Gas flow through a nozzle approximating a throttle body

The throttle open area At is a function of the throttle angle α, while the discharge coefficient

CD is a function of many variables, including At, pim/pamb ratio and the Reynolds number

(Heywood, 1988). For simplicity the product AtCD is treated as a function of α only and is

identified experimentally.

4.2.2 Intake manifold pressure dynamics

Let the moving air inside the intake manifold be the system, encapsulated in a control volume

(c.v.) and a control surface (c.s.). For some extensive property F and intensive property f = dFdm

of the fluid, the conservation law, sometimes referred to as the Reynolds or Leibnitz’s theorem

(White, 1991, Panton, 2005), requires

DF

Dt=

∂

∂t

∫

c.v.

fρg dV +

∫

c.s.

(fρg)v · n dS, (4.5)

The total internal energy of a moving fluid element of mass m is

E = m(eg +1

2|v|2), (4.6)

where e is the specific internal energy and 12 |v|2 is the specific kinetic energy. By considering E

as the extensive property and substituting (4.6) into (4.5), the substantial derivative of the total

internal energy could be split into volume and surface integrals,

Ec.v. =DE

Dt

=∂

∂t

∫

c.v.

dE

dmρg dV +

∫

c.s.

(

dE

dmρg

)

v · n dS

=∂

∂t

∫

c.v.

ρgeg +1

2ρg|v|2 dV +

∫

c.s.

(ρgeg +1

2ρg|v|2)v · n dS. (4.7)

Under the assumption of inviscid flow, the rate of work done by the fluid within the control

volume is

Wc.v. =

∫

c.s.

pim v · n dS. (4.8)

The conduction of heat in the axial direction is ignored and no heat addition is assumed, as the

temperature difference between the gas and the manifold walls is small. Hence, the first law of

65

thermodynamics requires

Ec.v. = −Wc.v.. (4.9)

Substituting (4.7) and (4.8) into (4.9) and merging the two surface integrals produces

∂

∂t

∫

c.v.

ρgeg +1

2ρg|v|2 dV +

∫

c.s.

(ρgeg + pim +1

2ρg|v|2)v · n dS = 0. (4.10)

As the Mach number in the manifold is small (typically on the order of 0.01), the contribution

of the velocity terms to the energy balance is expected to be negligible. Therefore, these terms

are not considered in this model. Substituting eg = cvTg and introducing the specific enthalpy

hg = eg + pim

ρggives

∂

∂t

∫

c.v.

ρgcvTg dV +

∫

c.s.

(ρghg)v · n dS = 0. (4.11)

Expressing the left integral in terms of pressure by using the gas law ρgTg = pim/R produces

∂

∂t

∫

c.v.

pimcvRdV +

∫

c.s.

(ρghg)v · n dS = 0. (4.12)

By assuming evenly distributed pressure within the control volume and ambient air temperature,

the equation becomes

VimcvR

dpim

dt= maircpTamb − mportcpTamb (4.13)

and can be simplified to

dpim

dt=γ R Tamb

Vim(mair − mport). (4.14)

Constants γ and R are evaluated under ambient conditions.

4.2.3 Air and fuel consumption

A calibratable volumetric efficiency is defined as

ηvol(λ, ϑint, ϑovlp, N, pim) =Vg,cyl

ncylVS

, (4.15)

where Vg,cyl is the volumetric consumption of the fluid at intake manifold conditions and VS

is the cylinder volume swept during intake strokes per unit time. Its dependence on λ, ϑint,

ϑovlp, N and pim is justified empirically in later chapters. The volumetric efficiency is used for

calculating the mass flow rate of air into the cylinders. Since the mixture is comprised largely

of air, ηvol is calibrated based on air intake only to take advantage of the ideal gas arguments.

66

By applying the ideal gas law and expressing VS in terms of the engine speed, the volumetric

efficiency becomes

ηvol(λ, ϑint, ϑovlp, N, pim) =mportRTamb

pim· 4π

ncylVSN. (4.16)

Note that it has been assumed that the air temperature inside the intake manifold is equal to

the ambient temperature. The mass flow rate of air into the cylinders can then be calculated by

rearranging the equation as

mport =pimncylVSN

4πRTambηvol(λ, ϑint, ϑovlp, N, pim). (4.17)

Under the assumption that the engine’s air-fuel ratio control is accurate, the fuel mass flow rate

mfuel is specified by mport and the commanded λ as

mfuel =mport

λ AFRS. (4.18)

If this assumption does not hold, a fuel puddle equation can be added. The total mass flow rate

of the mixture drawn into the cylinders is calculated as

mcyl = mport + mfuel. (4.19)

4.2.4 Exhaust gas temperature

The net indicated efficiency ηind,net(λ, θ, ϑint, ϑovlp, N, pim) is a static calibratable surface used

in the estimation of the engine torque and the exhaust port gas temperature. This efficiency is

defined as the ratio of work delivered to a piston over the entire four-stroke cycle and the heat

generated inside the cylinder within that time. Its dependence on λ, θ, ϑint, ϑovlp, N and pim

is justified empirically in later chapters.

As previously mentioned, individual valve opening and closing events are not considered,

nor is the movement of the piston. Instead, the cylinders are modelled as an open combustion

chamber with a continuous flow of fluid. The modelled heat release from combustion instantly

affects the temperature of the fluid inside the cylinders. To develop an expression for the gas

temperature, consider the steady flow energy equation applied to the fluid inside the control

volume, encapsulated by the combustion chamber,

Qc.v. − Wc.v. = mcyl ∆hg, (4.20)

where kinetic energy terms have been neglected. Heat addition is due to combustion and heat

exchange with the surrounding walls. If their temperature is approximated by the lumped engine

67

temperature Teng, then

Qc.v. = mfuelQLHV +Acylhgs(Teng − Tcyl). (4.21)

The work output is calculated from the net indicated efficiency map as

Wc.v. = mfuel QLHV ηind,net(λ, θ, ϑint, ϑovlp, N, pim). (4.22)

By substituting (4.21) and (4.22) into (4.20) and expressing the enthalpy hg in terms of temper-

atures, the energy equation can be rewritten as

mfuel QLHV (1 − ηind,net(λ, θ, ϑint, ϑovlp, N, pim)) +Acyl hgs (Teng − Tcyl) =

mcyl (cp(Tcyl) Tcyl − cp(Tamb) Tamb). (4.23)

and solved for the exhaust temperature Tcyl.

Similar to Annand (1963) and Heywood (1988), the heat transfer coefficient between the gas

and the walls of the combustion chamber hgs is evaluated from a Nusselt number correlation of

the form

NuB = ae Rebe

B (4.24)

Parameters ae and be are constants and are determined experimentally for a particular engine.

The Nusselt number NuB = hgsB/kcyl is based on the cylinder bore diameter B. The Reynolds

number ReB = ρcylucylB/µcyl is a function of the mean velocity of the flow inside the cylinder

ucyl, gas density ρcyl and dynamic viscosity µcyl. It can be shown that by expressing the velocity

in terms of the fluid mass flow rate,

ucyl =4mcyl

ncylπB2ρcyl, (4.25)

the Reynolds number becomes

ReB =4mcyl

ncylπBµcyl. (4.26)

Introduction of the Nusselt number definition and the Reynold’s number equation into (4.24)

gives

hcyl = aekcyl

B

(

4 mcyl

π B µcyl ncyl

)be

, (4.27)

where conductivity kcyl and dynamic viscosity µcyl can be calculated from

kcyl = 3.4288 · 10−11 T 3cyl − 9.1803 · 10−8 T 2

cyl + 1.294 · 10−4 Tcyl − 5.2076 · 10−3, (4.28)

µcyl = 1.066 · 10−14 T 3cyl − 3.6432 · 10−11 T 2

cyl + 6.6706 · 10−8 Tcyl + 1.433 · 10−6. (4.29)

These correlations are based on the data published in Turns (1996) for air at atmospheric pressure

and are valid for temperatures in the range between 250 and 1600 K.

68

4.2.5 Torque production

An expression for the brake torque τbrake is obtained by applying Newton’s second law to the

crankshaft. This yields

τbrake = τcrank − τfric − JcrankdN

dt. (4.30)

From the definition of ηind,net in Chapter 4.2.4 we can write

τcrank =mfuelQLHV

Nηind,net. (4.31)

Substitution of (4.31) into (4.30) produces

τbrake =mfuelQLHV

Nηind,net − τfric − Jcrank

dN

dt. (4.32)

4.2.6 Friction and engine warm-up

Engine speed, oil viscosity in mechanically interacting components and gas pressure loading are

some of the variables that affect engine friction (Heywood, 1988, Leong et al., 2007, Manzie

et al., 2009). Oil viscosity in the engine is dependent on the temperatures of various engine

components. The contribution of local friction from isolated rubbing of components to the

overall engine friction is difficult to quantify. This often requires motoring tests to be conducted

on a partially disassembled engine. An example of a model attempting to capture motoring

friction can be found in Sandoval and Heywood (2003). Motoring friction, however, can differ

from firing friction due to the differences in cylinder gas pressures, piston and cylinder liner

temperatures (Sandoval and Heywood, 2003). The model presented here attempts to describe

firing friction using a lumped thermal model of the engine. As will be demonstrated in later

chapters, this low order approach appears to perform sufficiently well, and the complexity of the

experimental work needed for calibration of the model is greatly reduced.

Let the system boundary encapsulate the engine body, excluding the exhaust manifold and

the contained fuel and air. The first law of thermodynamics requires

Eeng = Qeng − Weng . (4.33)

If the system possesses a uniform temperature Teng, the rate of change of the total internal

energy based on the lumped thermal representation of the engine is

Eeng = mengceng∂Teng

dt. (4.34)

69

Most of the heat is added to the system as a result of heat transfer from the exhaust gases to

the cylinder walls, the temperature of which is approximated by Teng. Hence,

Qeng = Acylhgs(Tcyl − Teng). (4.35)

As a result of combustion, the fluid in the cylinders performs work on the engine equal to the

indicated engine work. Consequently, the engine produces brake work. Therefore, the total work

output from the system is

Weng = N(τbrake − τcrank). (4.36)

The difference between the indicated and the brake torques under quasi-steady assumptions is

the frictional torque. Hence,

Weng = −N τfric. (4.37)

Substitution of (4.34), (4.35) and (4.37) into (4.33) yields

mengceng∂Teng

dt= Acylhgs(Tcyl − Teng) +N τfric. (4.38)

The frictional torque is evaluated from

τfric =ncylVS

4πpfme(N,Teng), (4.39)

where the static frictional effective pressure function pfme(N,Teng) is calibrated based on tran-

sient cold start testing. Later chapters will demonstrate that pfme can be reasonably approxi-

mated by a function of N and Teng.

4.3 Engine-out emissions

Physics based cold start models for predicting engine-out emissions are presently computationally

too intensive for optimisation and control studies, as they typically operate on a crank-angle

basis. The approach taken here is an extension of Keynejad and Manzie (2011). It follows the

philosophy of mean value engine modelling, where dynamics with a time-scale behaviour of less

than a single cycle are approximated by static functions. Carbon monoxide, HC and NOX

engine-out emissions are therefore correlated with some of the key measurable engine operating

parameters, shown in Figure 4.1, based on the existing steady state experimental data for a

fully warm engine. These parameters include intake manifold pressure pim, normalised air-fuel

ratio λ, spark timing θ, cam timing ϑ and engine speed N . Other emissions are evaluated

from a chemical equilibrium based on the correlated CO, HC and NOX pollutants and the

70

Fixed parameters

AFRS stoichiometric air-fuel ratioKwg water-gas shift reaction equilibrium constantMair molar mass of air [kg/mol]Mfuel molar mass of gasoline [kg C1/mol]rHC fuel H to C ratiorO2 proportion of O2 in air [mol/mol]

Tuned functions

eCO CO emissions [mol/kg fuel]eNO NO emissions [mol/kg fuel]eHC HC emissions [mol C1/kg fuel]

Table 4.2: Parameters defining the engine-out emissions model

commanded λ. Because the dynamics of the three-way catalyst can be very sensitive to the

λ-value in the exhaust, the model is formulated to guarantee the consistency of the exhaust

composition modelled and the air-fuel ratio. The parameters defining the model are given in

Table 4.2.

The outputs from the emissions model are normalised quantities eX , defined by the number

of mol of the chemical compound X produced from combusting one kg of fuel.

4.3.1 CO, HC and NOX

It is well known that λ is a parameter that strongly influences engine-out emissions. Intake

manifold pressure and spark timing influence the peak and post-combustion temperatures, while

the engine speed affects the time for the reactions to take place, before ‘freezing’ of the reaction

mechanisms (Guzzella and Onder, 2004, Heywood, 1988). Both the intake manifold pressure,

valve timing, and to a lesser degree, λ and engine speed affect the residual gas fraction in the

cylinders (Heywood, 1988). Hence, all of these factors influence the reactions in one way or

another and thus affect the formation of pollutants. The emission fits are, therefore, considered

to be possible functions of all these variables. The engine-out CO, HC and NOX emissions

model consists of the following polynomial surfaces:

eCO(pim, λ, θ, ϑint, ϑovlp, N), (4.40)

eNO(pim, λ, θ, ϑint, ϑovlp, N), (4.41)

eHC(pim, λ, θ, ϑint, ϑovlp, N). (4.42)

Note that NOX emissions are modelled entirely as NO, as the amount of NO2 produced by a

gasoline fuelled engine is expected to be small (Heywood, 1988).

71

4.3.2 CO2, H2O, O2 and H2

The knowledge of normalised CO and HC emissions, obtained from static functions, is suffi-

cient for estimating the normalised CO2 emissions. Consider the overall reaction describing the

combustion of gasoline

nfuel CHrHC+ nair(rO2O2 + [1 − rO2 ]N2) → nHC CHrHC

+ nCO CO + nNO NO+

nCO2 CO2 + nO2 O2 + nN2 N2 + nH2 H2 + nH2O H2O (4.43)

and the water-gas shift reaction

CO2 +H2 → CO +H2O, (4.44)

which are close to chemical equilibrium under the exhaust conditions. The equalities (3.35),

(3.36) and (3.40), arising from the balance of C, H and O atoms in (4.43) and the definition of

λ, were described in Chapter 3.7.5 and are repeated here for convenience:

nfuel = nHC + nCO + nCO2 , (4.45)

rHC nfuel = rHC nHC + 2 nH2 + 2 nH2O, (4.46)

2 rO2 λ AFRSMfuel

Mairnfuel = nCO + nNO + 2 nCO2 + 2 nO2 + nH2O. (4.47)

A commonly accepted equilibrium constant for the water-gas shift reaction under the exhaust

conditions is equal to 3.5 (Spindt, 1965). Expressing this constant in terms of the amounts of

reactants and products results in the additional equation

Kwg =nCO nH2O

nCO2 nH2

. (4.48)

By dividing both sides of the equations by mfuel, (4.45)–(4.48) can be written in terms of the

normalised emissions eX as

1

Mfuel= eHC + eCO + eCO2 , (4.49)

rHC

Mfuel= rHC eHC + 2 eH2 + 2 eH2O, (4.50)

2 rO2 λ AFRS1

Mair= eCO + eNO + 2 eCO2 + 2 eO2 + eH2O, (4.51)

Kwg =eCO eH2O

eCO2 eH2

. (4.52)

From (4.49) the normalised CO2 emissions are therefore

eCO2 =1

Mfuel− eHC − eCO. (4.53)

72

The amount of water vapour produced can be calculated from (4.50) and (4.52). Rearranging

(4.52) as

eH2 =eCO eH2O

Kwg eCO2

(4.54)

and substituting into (4.50) gives

rHC

Mfuel= rHC eHC + 2 eH2O + 2

eCO eH2O

Kwg eCO2

. (4.55)

Rearranging the equation produces the final expression for the normalised water vapour,

eH2O =1

2rHC

1Mfuel

− eHC

1 + eCO

Kwg eCO2

. (4.56)

Normalised oxygen emissions can be calculated directly from (4.51). Rearranging that equa-

tion gives

eO2 =rO2

MairAFRS λ− 1

2eCO − 1

2eNO − eCO2 −

1

2eH2O. (4.57)

Normalised hydrogen emissions can be calculated using (4.54).

4.4 Exhaust manifold and connecting pipe

As mentioned previously, the dynamics of the catalyst can depend strongly on the inlet gas

conditions. The exhaust system model is therefore required to reasonably estimate the drop in

gas temperature between the exhaust port and the catalyst inlet following a cold start.

This model calculates the gas temperature at the outlet of the exhaust manifold (or the

connecting pipe) Tg,out as a function of the inlet gas temperature Tg,in and the exhaust mass

flow rate mcyl, as shown in Figure 4.1. The manifold and the connecting pipe are modelled as

lumped bodies of temperature Ts. The walls are considered thin and the temperatures of interior

and exterior surfaces are assumed equal. Convective heat exchange at the gas-solid boundary

is considered, while heat transfer to the bodies via conduction and radiation is ignored. The

parameters defining the model are given in Table 4.3.

To distinguish the exhaust manifold conditions from those of the connecting pipe, variables

Tem, Tem,in and Tem,out, and Tcp, Tcp,in and Tcp,out will be adapted. Each set refers to the

respective body temperature, and inlet and outlet gas temperatures.

4.4.1 Energy conservation in the gas phase

Let the exhaust gas inside the exhaust manifold or the connecting pipe be the system, contained

in a control volume (c.v.) and surrounded by a control surface (c.s.). By following the same

73

Fixed parameters

Aex,i inner surface area [m2]Aex,o outer surface area [m2]mex cex thermal mass [J/K]

Tuned parameters

aex,1 Nusselt number correlation parameterbex,1 Nusselt number correlation parameteraex,2 Nusselt number correlation parameter

Table 4.3: Parameters defining the exhaust system model

argument as described in Section 4.2.2, the rate of change of the system’s total internal energy

is

Ec.v. =∂

∂t

∫

c.v.

ρgeg +1

2ρg|v|2 dV +

∫

c.s.

(ρgeg +1

2ρg|v|2)v · n dS, (4.58)

while the rate of work done by the fluid within the control volume is

Wc.v. =

∫

c.s.

p v · n dS. (4.59)

The conduction of heat in the axial direction can be ignored as convective heat transfer dominates

for the flow speeds generally encountered in exhaust systems. Thus, the rate of heat addition to

the control volume is

Qc.v. =

∫

c.v.

hgsPe (Ts − Tg) dx, (4.60)

The first law of thermodynamics requires

Ec.v. = Qc.v. − Wc.v.. (4.61)

By substituting (4.58)–(4.60) into (4.61) the following equation is obtained:

∂

∂t

∫

c.v.

ρge+1

2ρg|v|2 dV +

∫

c.s.

(ρge+1

2ρg|v|2)v · n dS

= −∫

c.s.

p v · n dS +

∫

c.v.

hgsPe (Ts − Tg) dx. (4.62)

After the surface integrals are merged and the ideal gas law p = ρgRTg is substituted, the

equation becomes

∂

∂t

∫

c.v.

ρge+1

2ρg|v|2 dV +

∫

c.s.

(ρge+ ρgRTg +1

2ρg|v|2)v · n dS =

∫

c.v.


74

Substitution of e = cvTg and the specific heat relation cv +R = cp produces

∂

∂t

∫

c.v.

ρgcvTg +1

2ρg|v|2 dV +

∫

c.s.

ρg(cpTg +1

2|v|2)v · n dS =

∫

c.v.


The magnitude of the velocity terms are significantly smaller than the internal energy terms and

can be neglected. Under the assumption that the thermodynamic properties of the gas and the

solid body are not spatially variable, the equation can be simplified to

Vc.v.∂(ρgcvTg)

∂t+ mg,outhg,out − mg,inhg,in = hgsAex,i(Ts − Tg), (4.65)

where Tg and Ts are lumped gas and surface temperatures respectively, and hgs is a mean

convection coefficient for the gas-solid boundary.

The gas temperature dynamics inside an exhaust system are substantially faster than the

transient dynamics of a three-way catalyst. Hence, a quasi-steady approximation can be used

and the time derivative can be eliminated from the equation. Under steady state conditions

continuity requires mg,in = mg,out. With these assumptions the energy equation reduces to

mcyl [cp(Tg,out) Tg,out − cp(Tg,in) Tg,in] = hgsAex,i (Ts − Tg). (4.66)

If the lumped gas temperature Tg is approximated by

Tg ≈ Tg,out + Tg,in

2, (4.67)

then (4.66) becomes

mcyl [cp(Tg,out) Tg,out − cp(Tg,in) Tg,in] = hgsAex,i (Ts −1

2[Tg,out + Tg,in]), (4.68)

which can be solved for the exhaust gas outlet temperature Tg,out.

4.4.2 Energy conservation in the solid phase

Let the the body of the exhaust manifold or the connecting pipe be the system. The rate of

change of the system’s total internal energy is

Ec.v. =∂

∂t

∫

c.v.

ρses dV, (4.69)

It is assumed that most of the heat transfer occurs via a convective mechanism at the boundaries

between the exhaust gas and the manifold’s internal walls, and between the ambient environment

and the outer walls. Heat conduction through the solid is small compared to the convective heat

75

exchange and is ignored. The temperatures of the exhaust manifold and the connecting pipe are

relatively low during the cold start period, and so radiation losses are also not considered. With

these assumptions the rate of heat addition becomes

Qc.v. =

∫

c.v.

hgsPe,i (Tg − Ts) dx+

∫

c.v.

hsaPe,o (Tamb − Ts) dx. (4.70)

Since there is no work performed on the system, the first law of thermodynamics requires

Ec.v. = Qc.v.. (4.71)

Substituting (4.69) and (4.70) into (4.71) and assuming constant ρs results in

ρscex∂

∂t

∫

c.v.

Ts dV =

∫

c.v.

hgsPe,i (Tg − Ts) dx+

∫

c.v.

hsaPe,o (Tamb − Ts) dx. (4.72)

For a lumped parameter model this reduces to

mex cexdTs

dt= hgs Aex,i (Tg − Ts) + hsa Aex,o (Tamb − Ts), (4.73)

where Tg is specified by 4.67. Thus,

mex cexdTs

dt= hgs Aex,i (

1

2[Tg,out + Tg,in] − Ts) + hsa Aex,o (Tamb − Ts). (4.74)

4.4.3 Heat transfer coefficients

The flow in the exhaust manifold is turbulent and is not fully developed. In addition, the

manifold possesses a complex geometry with multiple bends and varying hydraulic diameter.

Therefore, published Nusselt Nu number correlations for fully developed turbulent pipe flow,

such as Gnielinski (1976), are inappropriate for estimating the heat transfer coefficients. Instead,

correlations of the form

NuDi= aex,1 Re

bex,1

Di, (4.75)

NuDo= aex,2 (4.76)

are used, where parameters aex,1, bex,1 and aex,2 are calibrated. Heat transfer coefficients are

then calculated as

hgs =kg(Tg, Pamb)

DiNuDi

, (4.77)

hsa =kg(Tamb, Pamb)

DoNuDo

. (4.78)

Conductivity kg and dynamic viscosity µg are evaluated from (4.28) and (4.29) respectively.

76

4.5 The three-way catalyst

The highly complex washcoat chemistry in catalysts, the dynamics of which can be sensitive

to the exhaust mass flow rate and composition, temperature distribution in the substrate, the

amount of stored oxygen and many other parameters, makes this problem difficult to model.

Capturing many of the important dynamics using lumped parameter models, which neglect

much of the physics and rely on maps, calibrated from a large set of experiments, can be dif-

ficult, time consuming and may result in a model that does not port well between catalysts.

In contrast, models with extensive kinetic schemes or those that resolve the fluid and substrate

properties in two or three directions are generally computationally too slow to be useful in

dynamic optimisation.

The model presented here is based on the work of Pontikakis and Stamatelos (2004). It is

one-dimensional and the spatial coordinate is taken as the offset in the longitudinal direction

from the front face of the monolith. A low order chemical kinetic scheme is included, which along

with the unknown model parameters, can be calibrated on a single set of transient engine test

results. Temporal and spatial distribution of pollutant concentrations, their consumption rates,

temperature, stored oxygen and many other variables can be evaluated with a reasonable degree

of accuracy and computational cost. The boundary conditions are set by the other sub-models

as indicated in Figure 4.1. The major differences from the model developed by Pontikakis and

Stamatelos (2004) can be characterised as follows.

• The current model includes transient terms in all of the heat and mass conservation equa-

tions, while Pontikakis and Stamatelos (2004) take advantage of quasi-steady assumptions

and consider only one transient term in the energy equation for the substrate. Of course,

the dynamic behaviour of the exhaust gas is significantly faster than of the monolith, and

such assumptions can be well justified. However, it was found that solutions could be

produced quicker using the DASSL solver from Petzold (1982), if the transient terms were

included.

• The equations for heat and mass transfer were derived from first principles, but possibly

under other assumptions to Pontikakis and Stamatelos (2004). Hence, some of the param-

eters describing the geometry of the catalyst appear differently in the new equations.

• Heat losses to ambient surroundings were not considered in this model.

The problem layout and the physical processes considered are shown in Figure 4.4, while the

parameters defining the model are given in Table 4.4. The monolith contains a large number of

77

Figure 4.4: Mass transport and heat transfer in the catalyst model

channels, the walls of which are assumed to be uniformly coated with a thin layer of catalytically

active material, referred to as the washcoat. The washcoat is expected to be significantly thinner

than the walls of the channels. Thus, the physical properties of the solid phase are approximated

by those of the substrate.

The model separates the bulk fluid conditions inside the channels from those inside the

washcoat layer and the solid phase. Furthermore, for a given distance from the front face of

the brick, these conditions are assumed to be equivalent in all of the channels, leading to the

assumption of a uniform flow distribution across the face of the monolith. Although this may

not be verified in most real TWC systems, it is nonetheless required by the one-dimensional

modelling approach, where temperatures and concentrations are resolved only in the stream-

wise direction.

Pressure fluctuations in catalysts should be small. Hence, constant pressure is assumed along

the monolith and the density of the exhaust is a function of only the gas temperature, calculated

using the ideal gas law at atmospheric pressure.

The Reynolds number based on the hydraulic diameter of the channels ranges from about

20 to 400, depending on the engine operating conditions. According to Holder et al. (2006) and

78

Fixed parameters

Ac cross-sectional area of the substrate [m2]cs specific heat capacity of the substrate [J/(kg ·K)]Dc hydraulic diameter of a channel [m]ks thermal conductivity of the substrate [W/(m ·K)]L reactor length [m]S geometric surface area per unit reactor volume [m2/m3]ǫ reactor void fractionρs density of the substrate [kg/m3]Ea,i activation energies [J ]

Tuned parameters

Ae,i 9 pre-exponential factors [mol K/m3 s]lw washcoat thickness [m]α catalytic surface area per unit reactor volume [m2/m3]Ψ oxygen storage capacity [mol/m3]

Table 4.4: Parameters defining the catalyst model

Wanker et al. (2000), a laminar flow occurs in the channels. This allows use of correlations for

modelling heat and mass transfer between the gas and the solid phases, which are governed by

forced convection and diffusion. Heat transfer between the catalyst and the surroundings is not

modelled, as catalysts are normally well insulated.

Axial thermal conduction in the substrate is considered, as it can considerably affect catalyst

dynamics (Oh and Cavendish, 1982). Thermal conduction in the gas phase is ignored, as con-

vective heat transfer dominates in the stream-wise direction under mean velocity flow. Similarly,

diffusion of the species in the axial direction is not considered as the diffusion velocities of all

species are expected to be much smaller than the average velocity of the flow in the monolith.

This model takes advantage of a reduced order chemical kinetic scheme developed by Pon-

tikakis and Stamatelos (2004), comprising of 10 reactions and including an oxygen storage mech-

anism. It is assumed that these reactions take place inside the washcoat layer. Consequently,

exothermic reactions cause heat to be generated in the solid phase.

4.5.1 Energy and mass conservation equations

The catalyst model consists of four principal equations, governing heat transfer in the gas and

solid phases, and mass transport in the gas phase and in the washcoat layer. These equations

79

are

ǫpamb cpR Tg

∂Tg

∂t= −mcyl cp

Ac

∂Tg

∂x+ S hgs (Ts − Tg), (4.79)

ρs cs (1 − ǫ)∂Ts

∂t= S hgs (Tg − Ts) + ks (1 − ǫ)

∂2Ts

∂x2− lw α

Nr∑

i=1

Rr,i ∆hr,i, (4.80)

ǫ ρg∂Cg,i

∂t= −mcyl

Ac

∂Cg,i

∂x+ S ρg hm,gs,i (Cs,i − Cg,i) , (4.81)

S ρg∂Cs,i

∂t=

S

lwρg hm,gs,i (Cg,i − Cs,i) − αMg Rc,i. (4.82)

Their derivation from first principles is provided in Appendix A.

Parameters ǫ, S, α and lw specify the geometry of the catalyst. The void fraction ǫ is defined

by the ratio Aec

Ac, where Aec and Ac are the cross-sectional areas of the gas in the brick, and the

gas and solid phases in the monolith respectively. The geometric surface area per unit reactor

volume S is defined by Pe

Ac, where Pe is the total perimeter of the channels. Similarly, the catalytic

surface area per unit reactor volume α is given by w Pe

Ac, with w specifying the proportion of the

washcoat that is catalytically active. The parameter lw is the washcoat thickness. While ǫ and

S can be readily calculated from the dimensions of the monolith, α and lw can not be measured

easily and are calibrated from experiments.

The transient energy equation (4.79) for the gas phase describes the temperature distribution

in time and space. The source terms on the right hand side of the equation reflect convective

heat transfer in the axial and orthogonal directions respectively. Similarly, the transient energy

conservation equation (4.80) determines the temperature distribution in the solid phase. Whilst

the first term governs the change in the internal energy, the following terms describe the con-

vective heat exchange with the gas phase, conduction in the axial direction and heat generated

from the exothermic reactions.

In this model transport of O2, CO, H2, NO, as well as easily and not so easily oxidising

hydrocarbons (HCfast and HCslow) is considered. For each of the species two mass transport

equations need to be solved. The transport of species i in the gas phase is modelled using (4.81).

The first term in the equation is related to the accumulation of the species in the gas phase.

The following terms reflect convective mass transport in the axial and orthogonal directions.

Conservation of species i in the washcoat is handled by (4.82). Again, the first term is related

to the accumulation of the species, whilst the remaining terms govern the convective mass

exchange with the gas phase and the consumption of the species from the reactions occurring in

the washcoat.

The outputs of the catalyst model are the mass flow rates of the legislated tailpipe emissions,

80

given by

mCO,out = mcylMCO

MgCg,CO(L, t), (4.83)

mNO,out = mcylMNO

MgCg,NO(L, t), (4.84)

mHC,out = mcyl

(

MHCfast

MgCg,HCfast

(L, t) +MHCslow

MgCg,HCslow

(L, t)

)

. (4.85)

4.5.2 Chemical kinetics

The reaction mechanism used is presented in Table 4.5. It is based on the work of Pontikakis

and Stamatelos (2004), featuring 10 single step reactions with Langmuir–Hinshelwood and Ar-

rhenius rate expressions, modified with empirical terms. It has been previously demonstrated

(Pontikakis, 2003, Pontikakis and Stamatelos, 2004, Andrianov et al., 2009, 2010) that this re-

duced order kinetic scheme can be used to simulate tailpipe emissions accurately under highly

transient conditions. The reaction mechanism can be easily adapted to suit many kinds of

washcoats and Pt:Pd:Rh ratios.

The kinetic scheme, however, does not capture the chemical processes on the surfaces of the

individual Pt, Rh and Pd components of the washcoat. Instead, the overall chemical behaviour

of a particular washcoat is lumped into the reaction rate expressions. The pre-exponential factors

Ae,i are considered as the fitting parameters and are identified for each washcoat formulation.

The apparent activation energies Ea,i are approximately known (Pontikakis, 2003) and for the

purposes of this work are fixed. The values were taken directly from Pontikakis and Stamatelos

(2004) and are reproduced in Table 4.5. The inhibition term G is defined as

G = Ts(1 + 3.98 e96534/(RuTs) C2s,CO C2

s,HC) (1 + 4.79 × 105 e−31036/(RuTs) C0.7s,NO)×

(1 + 65.5 e7990/(RuTs) Cs,CO + 2080 e3000/(RuTs) Cs,HC )2, (4.86)

where Cs,HC = Cs,HCfast+ Cs,HCslow

. It has been successfully used in this form to model

oxidation reactions on very different catalysts (Pontikakis, 2003). Hence, its parameters are

retained in this work.

Significant quantities of H2 exist in the exhaust of gasoline fuelled engines (Heywood, 1988).

Its oxidation can lead to significant heat dissipation in catalytic converters and can affect their

dynamic behaviour (Pontikakis, 2003). Hence, hydrogen oxidation is considered by many mod-

ellers, including Oh and Cavendish (1982), Siemund et al. (1996), Balenovic (2002), Holder et al.

(2006). The oxidation dynamics of H2 are similar to that of CO (Oh and Cavendish, 1982,

81

iR

eactio

nA

ctivatio

nen

ergy

[J]

Rea

ction

rate

[mol/

s·m

3]

Oxid

atio

nrea

ctions

1CO

+0.5O

2 →CO

2E

a,1

=90000

Rr,1

=A

e,1

exp(−

Ea

,1/R

uT

s)

Cs

,CO

Cs

,O2

G

2H

2+

0.5O

2 →H

2 OE

a,2

=90000

Rr,2

=A

e,2

exp(−

Ea

,2/R

uT

s)

Cs

,H2

Cs

,O2

G

3CH

fast

1.8

+1.4

5O

2 →CO

2+

0.9H

2 OE

a,3

=95000

Rr,3

=A

e,3

exp(−

Ea

,3/R

uT

s)C

s,H

Cf

as

tC

s,O

2

G

4CH

slo

w1.8

+1.4

5O

2 →CO

2+

0.9H

2 OE

a,4

=120000

Rr,4

=A

e,4

exp(−

Ea

,4/R

uT

s)C

s,H

Cs

lo

wC

s,O

2

G

NO

reductio

nrea

ction

52NO

+2CO

→2CO

2+N

2E

a,5

=90000

Rr,5

=A

e,5

exp(−E

a,5 /R

uT

s )C

s,C

OC

s,N

O

Oxygen

stora

gerea

ctions

6Ce2 O

3+

0.5O

2 →2CeO

2E

a,6

=90000

Rr,6

=A

e,6

exp(−E

a,6 /R

uT

s )C

s,O

2(1−

ψ)

7Ce2 O

3+NO

→2CeO

2+

0.5N

2E

a,7

=90000

Rr,7

=A

e,7

exp(−E

a,7 /R

uT

s )C

s,N

O(1−

ψ)

82CeO

2+CO

→Ce2 O

3+CO

2E

a,8

=85000

Rr,8

=A

e,8

exp(−E

a,8 /R

uT

s )C

s,C

Oψ

9CH

fast

1.8

+3.8CeO

2 →1.9Ce2 O

3+CO

2+

0.9H

2 OE

a,9

=85000

Rr,9

=A

e,9

exp(−E

a,9 /R

uT

s )C

s,H

Cψ

10

CH

slo

w1.8

+3.8CeO

2 →1.9Ce2 O

3+CO

2+

0.9H

2 OE

a,1

0=

85000

Rr,1

0=A

e,1

0ex

p(−E

a,1

0 /R

uT

s )C

s,H

Cψ

Table

4.5

:R

eactio

nm

echanism

and

rate

expressio

ns

(Pontika

kis

and

Sta

matelo

s,2004)

82

Pontikakis and Stamatelos, 2004) and because H2 concentrations could not be measured in the

present work, the pre-exponential factor Ae,2 was assumed to equal Ae,1.

There is a range of hydrocarbons in the exhaust, each with its own oxidation dynamics.

Hence, in this kinetic scheme and many others (Oh and Cavendish, 1982, Zygourakis and Aris,

1983, Koltsakis et al., 1997, Holder et al., 2006) hydrocarbons are lumped into “fast-oxidising”

and “slow-oxidising” categories. Because only the total amount of hydrocarbons could be mea-

sured in the current work (based on carbon count), the exhaust hydrocarbons were assumed to

consist of 85% fast-oxidising and 15% of slow-oxidising HC, as in Pontikakis and Stamatelos

(2004).

The first four reactions in Table 4.5 describe the oxidation of CO, H2 and HC using O2

adsorbed directly from the exhaust stream, while reaction 5 represents NO reduction using

CO. Oxygen storage in catalysts is commonly enabled by ceria compounds, contained in the

washcoat. Reactions 6 and 7 model the storage of oxygen in ceria from the influx of O2 and

NO, while reactions 8–10 model the oxidation of CO and HC using stored oxygen. Note that

ceria in the form of CeO2 is considered to be in the oxygen enriched state, while Ce2O3 is in the

oxygen depleted state. The extent of oxygen stored ψ is therefore defined as the instantaneous

proportion of CeO2 in the total ceria, i.e.

ψ =nCeO2

nCeO2 + 2 nCe2O3

. (4.87)

The time derivative of ψ is proportional to the rate of CeO2 production and inversely proportional

to the rate of its depletion. Therefore, ψ can be expressed in terms of the reaction rates Rr,i as

ψ =1

Ψ(2Rr,6 + 2Rr,7 − 2Rr,8 − 3.8Rr,9 − 3.8Rr,10) , (4.88)

where Ψ is the total amount of ceria per unit washcoat volume or the total oxygen storage

capacity.

Consumptions rates Rc,i for each of the species i are calculated based on the reaction rates

and the associated stoichiometric coefficients as

Rc,O2 = 0.5Rr,1 + 0.5Rr,2 + 1.45Rr,3 + 1.45Rr,4 + 0.5Rr,6, (4.89)

Rc,CO = Rr,1 + 2Rr,5 +Rr,8, (4.90)

Rc,H2 = Rr,2, (4.91)

Rc,NO = 2Rr,5 +Rr,7, (4.92)

Rc,CHfast1.8

= Rr,3 +Rr,9, (4.93)

Rc,CHslow1.8

= Rr,4 +Rr,10. (4.94)

83

Heats of reaction ∆hr,i in (4.80) are based on the standard enthalpies of formation ∆hf,i specified

in Table 4.6.

i ∆hf,i [J/mol]CO -110500CO2 -393500NO 91300H2O -241800CH4 -74600C3H6 20000Ce2O3 -1796200CeO2 -1088700

Table 4.6: Standard enthalpies of formation (Lide, 2007)

4.5.3 Heat and mass transfer coefficients

Heat (hgs) and mass (hm,gs) transfer coefficients are obtained from

hgs =kg

DcNuDc

, (4.95)

hm,gs,i =Di,N2

DcShDc,i. (4.96)

The model makes use of the Nusselt (Nu) and Sherwood (Sh) number correlations proposed by

Hawthorn (1974) for non-reacting flows,

NuDc= 3.66

(

1 + 0.095Dc

LPeh,Dc

)0.45

, (4.97)

ShDc,i = 3.66

(

1 + 0.095Dc

LPem,Dc,i

)0.45

. (4.98)

Alternative correlations also exist in literature (Votruba et al., 1975, Gnielinski, 1976, Hayes

and Kolaczkowski, 1994). Peclet (Pe) numbers can be expressed in terms of the Prandtl (Pr),

Schmidt (Sc) and Reynolds (Re) numbers as follows,

Peh,Dc= ReDc

Pr, (4.99)

Pem,Dc,i = ReDcSci, (4.100)

where

Pr =cp µg

kg, (4.101)

Sci =µg

ρg Di,N2

, (4.102)

ReDc=

mcyl Dc

ǫ Ac µg. (4.103)

84

The thermal conductivity of the exhaust mixture kg and the dynamic viscosity µg are approxi-

mated by (4.28) and (4.29). Gas phase diffusion coefficients Di,N2 are adapted from Fuller et al.

(1966), while treating the exhaust gas as a binary mixture of nitrogen and the compound i under

consideration. Under atmospheric pressure,

Di,N2 =10−7 T 1.75

g (1/Mi + 1/MN2)1/2

(V1/3i + V

1/3N2

)2. (4.104)

Diffusion volumes Vi are provided in Table 4.7. Note that the diffusion coefficients for fast and

slow oxidising hydrocarbons are approximated by those of representative compounds: propene

(C3H6) and methane (CH4) respectively.

i Vi [–]O2 16.6CO 18.9H2 7.07NO 11.17C3H6 61.38CH4 24.42N2 17.9

Table 4.7: Diffusion volumes

4.5.4 Boundary conditions

The gas temperature and the species concentrations inlet boundary conditions are the model

inputs,

Tg(0, t) = Tg,in, (4.105)

Cg,i(0, t) = Cg,i,in. (4.106)

The outlet boundary conditions for the gas phase are

∂Tg(L, t)

∂x= 0 (4.107)

∂Cg,i(L, t)

∂x= 0. (4.108)

Non-conducting boundary conditions are specified for the solid phase at the front and the back

of the monolith,

∂Ts(0, t)

∂x= 0, (4.109)

∂Ts(L, t)

∂x= 0. (4.110)

85

4.5.5 Model discretisation

To develop solutions to the set of partial differential equations (4.79), (4.80), (4.81) and (4.82),

the spatial coordinate was discretised using a uniformly spaced grid. Spatial derivatives were

then approximated using central differencing,

[

∂2Ts

∂x2

]

x(j)

≈ T(j+1)s − 2 T

(j)s + T

(j−1)s

(∆x)2, (4.111)

[

∂Tg

∂x

]

x(j)

≈ T(j+1)g − T

(j−1)g

2 ∆x, (4.112)

[

∂Cg,i

∂x

]

x(j)

≈C

(j+1)g,i − C

(j−1)g,i

2 ∆x, (4.113)

where ∆x is the distance between the nodes and the superscripts (j− 1) and (j+1) refer to the

nodes neighbouring node j. Thus, for each of the nodes the following set of ordinary differential

equations needs to be considered,

T (j)g = f1 (T (j−1)

g , T (j)g , T (j+1)

g , T (j)s , mcyl), (4.114)

T (j)s = f2 (T (j)

g , T (j−1)s , T (j)

s , T (j+1)s ,Cs

(j), ψ(j), mcyl), (4.115)

C(j)g = f3 (T (j)

g ,Cg(j−1),Cg

(j),Cg(j+1),Cs

(j), mcyl), (4.116)

C(j)s = f4 (T (j)

g ,Cg(j),Cs

(j), ψ(j), mcyl), (4.117)

ψ(j) = f5 (T (j)s ,Cs

(j), ψ(j)), (4.118)

where

Cg(j) = [C

(j)g,O2

, C(j)g,CO, C

(j)g,H2

, C(j)g,NO, C

(j)g,HCfast

, C(j)g,HCslow

]T , (4.119)

Cs(j) = [C

(j)s,O2

, C(j)s,CO, C

(j)s,H2

, C(j)s,NO, C

(j)s,HCfast

, C(j)s,HCslow

]T . (4.120)

The model equations (4.83)–(4.85) and (4.114)–(4.118) can be summarised in a more compact

form,

x(t) = Fcat (x(t),u(t)), (4.121a)

[mCO,out, mNO,out, mHC,out]T = Hcat (x(t),u(t)), (4.121b)

where functions Fcat and Hcat enclose the model equations, and x and u are vectors, containing

state and input variables. These vectors are specified by

x(t) = [Tg,Ts,Cg,Cs, ψ]T, (4.122a)

u(t) = [mcyl, Tg,in,Cg,in]T , (4.122b)

86

where Tg,in is the inlet gas temperature and Cg,in is the feedgas composition vector. For a

catalyst discretised using ncat nodes x(t) ∈ ℜ15ncat and u(t) ∈ ℜ8.

4.6 Summary

A physics-based model for a gasoline fuelled engine, capable of calculating cold start fuel con-

sumption, as well as CO, NO and HC tailpipe emissions under transient driving conditions

has been proposed. This model integrates the dynamics of a spark ignition engine, engine-out

emissions, an exhaust system and a three-way catalyst. The model is relatively portable, as it

is based on physical principles where practical. The driving conditions can be simulated using

brake torque and engine speed trajectories, whilst spark timing, cam timing and reference λ

inputs serve as engine control variables.

The dynamometer control system model, defined by (4.1)–(4.3), enables driving conditions

to be simulated using engine speed and torque setpoints. It prescribes the engine speed and

regulates the throttle to track the demanded torque.

The mean value engine model, defined by (4.4), (4.14), (4.17)–(4.19), (4.23), (4.27)–(4.29),

(4.32), (4.38) and (4.39), includes transient friction and engine warm-up dynamics, allowing cold

start fuel consumption and exhaust flow rate to be simulated. The exhaust port gas temperature

and intake manifold pressure are required by other models, so are additionally modelled.

The composition of the exhaust gas, given by (4.40)–(4.42), (4.53), (4.54), (4.56) and (4.57), is

determined partly from the static engine maps and partly from chemical equilibrium calculations.

It is ensured that the λ-value of the exhaust is consistent with the λ control input. That way

the three-way catalyst dynamics can be more tolerable to errors introduced by the engine-out

emissions model.

The exhaust system model, specified by (4.68), (4.74) and (4.75)–(4.78), calculates the gas

temperature drop between the exhaust port and the catalyst. The exhaust manifold and the

downstream pipe are treated as lumped bodies with convective heat exchange between their inner

surfaces and the exhaust gas. The warm-up dynamics of the exhaust system are considered.

The catalyst is modelled using (4.121) in one dimension with a reduced order chemical kinetic

scheme which can be adapted to a wide range of washcoats. Oxygen storage effects are captured.

Consequently, temporal and spatial distribution of pollutant concentrations, and thus, tailpipe

emissions can be calculated.

The integrated model can be represented by a system of differential algebraic equations

87

(DAE),

x(t) = Finteg (x(t), z(t),u(t)), (4.123a)

0 = Ginteg (x(t), z(t),u(t)), (4.123b)

where functions Finteg and Ginteg enclose the model equations, and x, z and u are vectors,

containing state, algebraic (variables without time derivatives) and input variables respectively.

These vectors are identified below,

x(t) = [xI , pim, Teng, Tem, Tcp,Tg,Ts,Cg,Cs, ψ]T , (4.124a)

z(t) = [Tcyl, Tem,out, Tcp,out]T , (4.124b)

u(t) = [τrefbrake, N

ref , λ, θ, ϑint, ϑovlp]T , (4.124c)

where x(t) ∈ ℜ5+15ncat , z(t) ∈ ℜ3 and u(t) ∈ ℜ6 for a catalyst discretised using ncat nodes. The

outputs are given by

[mfuel, mCO,out, mNO,out, mHC,out]T = Hinteg (x(t),u(t)). (4.125)

In the following chapter this integrated model will be calibrated and then validated.

88

Chapter 5

Model calibration and validation

In this chapter the integrated model components presented in the last chapter are first calibrated

based on steady state and transient data. These sub-models and the integrated model are

then validated experimentally under various transient conditions. Most of the tunable model

parameters are determined by solving the following optimisation problems using gradient descent

methods:

Θ⋆ = argminΘ

nss∑

i=1

[qi(Θ) − q(m)i ]2, (5.1)

Θ⋆ = argminΘ

∫ tf

0

[q(Θ, t) − q(m)(t)]2 dt, (5.2)

where Θ is a set of tuning parameters, Θ⋆ is the optimal set of these parameters, and q and

q(m) are modelled and experimentally obtained quantities respectively. Equation (5.1) considers

nss steady state data points, each identified by a unique index i. The steady-state data used

for the calibration of the model included roughly nss ≈ 1000 operating points for a fully warm

engine, where many combinations of engine speed, intake manifold pressure, λ, spark timing and

cam timing have been tested. Projections of this data set are shown in Figure 5.1. Equation

(5.2) was solved over transient conditions, where q and q(m) were based on the first 400 seconds

(tf = 400) of the NEDC drive cycle. This was roughly the time required for the engine to reach

a fully warm state and substantially longer than the time until catalyst light-off. The engine

was controlled using the ECU’s built-in engine control strategy.

The tuning parameters of the integrated model are summarised in Table 5.1, where pa-

rameters kI and kP are the gains of the dynamometer control system PI controller, ae and be

determine the heat transfer coefficient between the in-cylinder gas and the walls, mengceng is

the thermal mass of the engine, AtCD is the product of the throttle open area and the discharge

coefficient, ηind,net and ηvol are the net indicated efficiency and the volumetric efficiency of the

89

700

1300

1900

Speed (rev/min)

-10

10

30

50

Spark (CAD BTDC)

0.8

0.9 1

1.1

1.2

λ

40

60

80

100

IVC (CAD ABDC)

0

20

40

25

50

75

Overlap (CAD)

MA

P (

kP

a)

700

1300

1900

Speed (

rev/m

in)

-10

10

30

50

Spark

(C

AD

BT

DC

)

0.8

0.9

1 1

.1 1

.2

λ

40

60

80

100

IVC

(C

AD

AB

DC

)

Figure 5.1: Projections of the fully warm engine mapping data used in calibration of the enginemodel

90

engine, pfme is the frictional mean effective pressure, eCO, eNO and eHC are the legislated nor-

malised engine-out emissions, aex, bex and cex define the heat transfer coefficient between the

gas and the exhaust manifold or connecting pipe walls, Ae,i are pre-exponential factors for the

reaction rates in the catalyst, lw is the washcoat thickness, α is the catalytic surface area per

unit reactor volume and Ψ is the catalyst oxygen storage capacity.

Sub-model Tunable constants Calibratable functionsDynamometer control system kI , kP

Engine ae, be, (meng CP,eng) (At CD), ηind,net, ηvol, Pfme

Engine-out emissions eCO, eNO, eHC

Exhaust manifold aex,em, bex,em, cex,em

Connecting pipe aex,cp, bex,cp, cex,cp

Three-way catalyst Ae,i, lw, α, Ψ

Table 5.1: Integrated model tuning parameters

5.1 Engine and dynamometer control system models

The engine model was partly calibrated based on the steady state data for a fully warm engine

and partly on the transient NEDC data. The values of the known model parameters used in

simulations are provided in Table 5.2.

Parameter ValueAcyl 0.04215 m2

B 0.09225 mJcrank 0.15 kg m2

nc 6QLHV 44 × 106 J/kgVS 6.637× 10−4 m3

Vim 0.004 m3

Table 5.2: Engine model fixed parameter values

The transient validation cases considered were based on the following.

1. The first 400 seconds of the NEDC drive cycle,

This served as the calibration case for only some of the engine model parameters. Hence,

it was nevertheless suitable for validating many of the modelled dynamics. The input

variables simulating the NEDC conditions are included in Figure 5.2.

2. The first 250 seconds of the EUDC drive cycle initiated from a cold start,

91

0

20

40

60

Ve

hic

le(k

m/h

)

0 500

1000 1500 2000

0 50 100 150 200

En

g. sp

ee

d(r

ev/m

in)

Bra

ke t

orq

ue

(Nm

)speedtorque

0 2 4 6 8

10

Th

rott

le(d

eg

)

0.9

1

1.1

λ

0 10 20 30 40 50

Sp

ark

(CA

D B

TD

C)

0 20 40 60 80

100

0 50 100 150 200 250 300 350 400 0 10 20 30 40 50

IVC

(CA

D A

BD

C)

Ove

rla

p(C

AD

)

Time (s)

intake camoverlap

Figure 5.2: Engine and dynamometer control system model inputs for simulating NEDC condi-tions

The test includes a wide variety of low to high power transient engine operation. The rate

of engine warm-up was significantly faster than during the NEDC test, and the cold engine

was brought up to its fully warm state in roughly 250 seconds. That makes this a good

alternative case for validating friction and engine warm-up dynamics, while justifying the

low order modelling approach. The inputs to the model used in simulations are presented

in Figure 5.3.

3. 500 seconds of idle initiated from a cold start for a range of speeds.

The test case is used to verify that friction, and consequently, fuel consumption are mod-

elled correctly under the slow engine warm-up conditions. Figure 5.4 shows the inputs to

the model used in simulations.

5.1.1 Calibration of the engine model

Throttle

The product of the discharge coefficient and the throttle open area was approximated by

At CD = at α2 + bt α+ ct, (5.3)

92

0

40

80

120

Vehic

le(k

m/h

)

0

500

1000

1500

2000

0

50

100

150

200

Eng.

speed

(rev/m

in)

Bra

ke t

orq

ue

(Nm

)

speedtorque

0.9

1

1.1

λ

0 10 20 30 40 50

Spark

(CA

D B

TD

C)

0 20 40 60 80

100

0 50 100 150 200 250 0 10 20 30 40 50

IVC

(CA

D A

BD

C)

Ove

rlap

(CA

D)

Time (s)

intake camoverlap

Figure 5.3: Engine and dynamometer control system model inputs for simulating cold startEUDC conditions

0

500

1000

1500

2000

0

50

100

150

200

Eng. speed

(rev/m

in)

Bra

ke torq

ue

(Nm

)

speedtorque

0.9

1

1.1

λ

0 10 20 30 40 50

Spark

(CA

D B

TD

C)

0

20

40

60

80

100

0 100 200 300 400 500 0

10

20

30

40

50

IVC

(CA

D A

BD

C)

Overlap

(CA

D)

Time (s)

intake camoverlap

Figure 5.4: Engine and dynamometer control system model inputs for simulating cold start idleconditions

93

where at, bt and ct were determined from (5.1) with

qi = mair(p(m)im,i, α

(m)i , at, bt, ct), (5.4)

q(m)i = m

(m)air,i. (5.5)

The function mair(p(m)im,i, α

(m)i , at, bt, ct) is evaluated from (4.4) at some measured steady state

intake manifold pressure p(m)im,i and throttle angle α

(m)i . The mass flow rate m

(m)air,i was obtained

from the steady-state measurements of the fuel flow rate m(m)fuel,i and λ

(m)i . The optimised values

of the coefficients in (5.3) were identified as

at = 1.3381× 10−3, (5.6)

bt = 4.6367× 10−4, (5.7)

ct = 9.5868× 10−6. (5.8)

The resulting function mair is shown in Figure 5.5. Its high degree of correlation with the

measured mass flow rate for all nss experiments is demonstrated in Figure 5.6.

Volumetric efficiency

The volumetric efficiency ηvol was approximated by the polynomial

ηvol =

2∑

j=0

2∑

k=0

2∑

l=0

2∑

m=0

2∑

n=0

avol,j,k,l,m,n pjim λk ϑl

int ϑmovlp N

n, (5.9)

subject to the constraints j + k + l +m + n ≤ 2. A second order polynomial was selected, as

it is of the lowest order that results in a reasonable quality fit. The 21 parameters avol,j,k,l,m,n

were identified (see Appendix B) by solving (5.1) with

qi = ηvol(p(m)im,i, λ

(m)i , ϑ

(m)int,i, ϑ

(m)ovlp,i, N

(m)i , avol,j,k,l,m,n), (5.10)

q(m)i = η

(m)vol,i, (5.11)

where η(m)vol,i was calculated from the steady state measurements m

(m)fuel,i, λ

(m)i , p

(m)im,i and N

(m)i as

η(m)vol,i =

4π m(m)fuel,i(1 +AFRSλ

(m)i ) RTamb

p(m)im,i VS ncyl N

(m)i

. (5.12)

The volumetric efficiency map ηvol(p(m)im,i, λ

(m)i , ϑ

(m)int,i, ϑ

(m)ovlp,i, N

(m)i ) is correlated against η

(m)vol,i in

Figure 5.7 for all nss experiments.

94

0 2

4 6

8 10

12 14

30

40

50

60

70

80

0 0.01 0.02 0.03 0.04 0.05 0.06

Flow(kg/s)

0.05 0.04 0.03 0.02 0.01

Throttle angle relative to theclosed position (deg)

MAP (kPa)

Flow(kg/s)

Figure 5.5: Calculated mass flow rate past the throttle

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Measure

d m

ass f

low

rate

(kg/s

)

Calculated mass flow rate (kg/s)

Figure 5.6: Measured and calculated mass flow rate past the throttle

95

Indicated efficiency

The indicated efficiency ηind,net was approximated by the polynomial

ηind,net =

2∑

j=0

2∑

k=0

2∑

l=0

2∑

m=0

2∑

n=0

2∑

o=0

aind,j,k,l,m,n,o pjim λk θl ϑm

int,i ϑnovlp,i N

o, (5.13)

subject to j + k + l + m + n + o ≤ 2. Regardless of the engine temperature, the indicated

efficiency was expected to be roughly constant for the given set of engine parameters. Thus,

no temperature dependence was included. The 28 parameters aind,j,k,l,m,n,o were estimated by

solving (5.1) with

qi = ηind,net(p(m)im,i, λ

(m)i , θ

(m)i , ϑ

(m)int,i, ϑ

(m)ovlp,i, N

(m)i , aind,j,k,l,m,n,o), (5.14)

q(m)i = η

(m)ind,net,i. (5.15)

The values for these parameters are listed in Appendix B. The indicated efficiency η(m)ind,net,i was

determined from the measurements p(m)ime,i, N

(m)i and m

(m)fuel,i as follows,

η(m)ind,net,i =

p(m)ime,i VS ncyl N

(m)i

4π m(m)fuel,i QLHV

. (5.16)

It is correlated with ηind,net,i in Figure 5.8 for all nss experiments. Whilst fitting of higher order

polynomials can reduce the mean error between ηind,net,i and η(m)ind,net,i, the low order polynomial

considered here prevents overfitting of the data and avoids large errors during extrapolation of

ηind,net,i.

Combustion chamber heat transfer coefficient

The optimisation problem (5.2) was solved for the Nusselt number correlation coefficients ae and

be with

q(t) = Tcyl(ae, be, t), (5.17)

q(m)(t) = T(m)cyl (t). (5.18)

96

0.4

0.5

0.6

0.7

0.8

0.9

0.4 0.5 0.6 0.7 0.8 0.9

Me

asu

red

vo

lum

etr

ic e

ffic

ien

cy

Calculated volumetric efficiency

Figure 5.7: Measured and calculated volumetric efficiency

0

0.1

0.2

0.3

0.4

0.5

0 0.1 0.2 0.3 0.4 0.5

Measure

d indic

ate

d e

ffic

iency

Calculated indicated efficiency

Figure 5.8: Measured and calculated indicated efficiency

97

The exhaust port gas temperature Tcyl(ae, be, t) was simulated using equations (4.4), (4.14),

(4.17)–(4.19), (4.23), (4.27)–(4.29) and

α(t) = α(m)(t), (5.19a)

N(t) = N (m)(t), (5.19b)

λ(t) = λ(m)(t), (5.19c)

θ(t) = θ(m)(t), (5.19d)

ϑint(t) = ϑ(m)int (t), (5.19e)

ϑovlp(t) = ϑ(m)ovlp(t), (5.19f)

where trajectories (5.19) are shown in Figure 5.2. Engine temperature Teng in (4.23) was ap-

proximated by the measured cylinder head temperature T(m)ch , thus allowing ae and be to be

tuned independently of the model parameters describing the engine warm-up behaviour. The

parameters were identified as

ae = 69, (5.20)

be = 0.2. (5.21)

As seen from Figure 5.9, this places the convection coefficient hcyl, specified by (4.27), within

a physically reasonable range, between 120 and 220 W/(m2 K). Figure 5.10 illustrates close

agreement of simulated and measured gas temperatures.

Cold start friction and engine temperature

According to (4.30),

τfric = τcrank − τbrake − JcrankdN

dt. (5.22)

By multiplying both sides of the equation by 4πncylVS

, the torques are converted to the respective

mean effective pressures,

pfme = pime − pbme −4π Jcrank

ncylVS

dN

dt. (5.23)

One way of measuring cold-start engine friction is to take advantage of this equation. The brake

mean effective pressure pbme can be calculated from the brake torque measurements, while the

indicated mean effective pressure pime can be estimated from the calibrated static net indicated

efficiency surface ηind,net and the measured engine operating parameters. Alternatively, pime

could be calculated from dynamic in-cylinder pressure measurements. In this work, however,

98

100

120

140

160

180

200

220

240

0 50 100 150 200 250 300 350 400

He

at

tra

nsfe

r co

eff

icie

nt

(W /

(m

2 K

))

Time (s)

Figure 5.9: Simulated combustion chamber heat transfer coefficient using only the engine model(NEDC conditions)

0

100

200

300

400

500

600

700

800

0 50 100 150 200 250 300 350 400

Exhaust

port

gas t

em

pera

ture

(˚C

)

Time (s)

measuredmodelled

Figure 5.10: Measured and simulated exhaust port gas temperature using only the engine model(NEDC conditions)

99

the latter approach was not used, since its measurement during transient engine operation is

more complex experimentally.

Engine friction is a function of many variables, including engine speed and oil viscosity in

the rubbing components. The lumped parameter approach adopted here correlates friction with

engine speed N and some bulk engine temperature Teng, which reflects the state of the oil in

various parts of the engine during warm-up. The frictional mean effective pressure pfme is

approximated by

pfme(N,Teng) = af1 Teng + af2 T2eng + af3 N + af4. (5.24)

As will be demonstrated later in the chapter, the polynomial gives a reasonable estimate of

friction.

To calibrate the parameters af,i, the optimisation problem (5.2) was solved with

q(t) = pfme(N(m), Teng), (5.25)

q(m)(t) = p(m)ime − p

(m)bme −

4π Jcrank

ncylVSN (m)

=4π m

(m)fuelQLHV

ncyl VS N (m)ηind,net(λ

(m), θ(m), ϑ(m)int , ϑ

(m)ovlp, N

(m), p(m)im )−

4π

ncyl VSτ

(m)brake −

4π Jcrank

ncylVSN (m).

For pfme expressed in Pa, Teng in ◦C and N in rev/min, the parameters were identified as

af1 = −7881, (5.26)

af2 = 50.596, (5.27)

af3 = 39.107, (5.28)

af4 = 324910.6. (5.29)

The frictional mean effective pressure pfme is visualised in Figure 5.11.

It has been determined empirically that the engine cylinder head temperature T(m)ch can

provide a good indication of the engine’s warm-up state. Hence, in the subsequent discussion

T(m)ch is used as a measurable reference for the lumped engine temperature Teng. The engine’s

thermal mass meng ceng was therefore tuned to match the rate of change of the modelled engine

temperature Teng with that of the measured cylinder head temperature T(m)ch . The resulting

thermal mass was

meng ceng = 115000 J/K. (5.30)

100

800 1000

1200 1400

1600 1800

20

30

40

50

60

70

80

0 50

100 150 200 250 300

FMEP(kPa)

200 120 80 60

Engine speed(rev/min)

Cylinder headtemperature (˚C)

FMEP(kPa)

Figure 5.11: Modelled frictional mean effective pressure (FMEP)

5.1.2 Calibration of the dynamometer control system model

The parameters of the dynamometer control system model were calibrated using simulations

of the coupled dynamometer control system and engine models, specified by (4.1)–(4.3), (4.4),

(4.14), (4.17)–(4.19), (4.23), (4.27)–(4.29), (4.32), (4.38), (4.39) and

τrefbrake = τ

(m)brake(t), (5.31a)

N ref (t) = N (m)(t), (5.31b)

λ(t) = λ(m)(t), (5.31c)

θ(t) = θ(m)(t), (5.31d)



where trajectories (5.31) are shown in Figure 5.2. The coefficients of the PI controller were tuned

to enable τbrake(t) accurately track τrefbrake(t). It was ensured that the commanded throttle angle

α(t) was within reasonable bounds of α(m)(t) for the prescribed operating conditions. The set

101

of controller gains

kP = 0.02, (5.32)

kI = 0.2 (5.33)

give excellent tracking performance. This is demonstrated in Figure 5.12. The throttle angles

α(t) and α(t)(m) are shown in Figure 5.13 for the transient test and are in close agreement.

5.1.3 Validation

Validation results presented in this section apply to the combined engine and the dynamome-

ter control system models, defined by equations (4.1)–(4.3), (4.4), (4.14), (4.17)–(4.19), (4.23),

(4.27)–(4.29), (4.32), (4.38) and (4.39). The solutions were produced by feeding measured inputs

τrefbrake, N

ref , λ(m), θ(m), ϑ(m)int and ϑ

(m)ovlp according to (5.31). These input trajectories are shown

in Figures 5.2–5.4.

NEDC test case

The model is validated by comparing the controlled input α, internal states pim and Teng and

the outputs mfuel and Tcyl to those measured. Being a known function of the input λ and mfuel,

the output mcyl is indirectly verified by validating mfuel.

Time traces of α, pim and Teng are compared to experimental data in Figures 5.13, 5.14 and

5.15. During the first part of the drive cycle, the observable error in the intake manifold pressure

is the result of small errors in the calculated volumetric efficiency ηvol at parked cam positions

and highly retarded spark timing, resulting from limitations in the available engine mapping

data used in the calibration of the polynomial. Nevertheless, the observed errors appear to be of

small enough magnitude to have only a limited effect on the fuel consumption dynamics. This is

demonstrated in Figures 5.16 and 5.17, which show excellent agreement between simulated and

measured fuel consumption. Over the 400 second period the cumulative error is only 1.56% of

the total fuel consumed.

The heat transfer coefficient parameters were calibrated based on the open-loop engine simu-

lations (without the dynamometer control system model). The close agreement of the calculated

and measured exhaust port gas temperatures is verified in Figure 5.18 for the closed-loop simu-

lation.

Figure 5.19 shows the modelled distribution of energy released from fuel inside the combus-

tion chamber. It can be seen, especially during low power operation, that the indicated work

required to produce the same brake output work gradually decreases with time. Such behaviour

102

-20

0

20

40

60

80

100

120

140

160

180

0 50 100 150 200 250 300 350 400

To

rqu

e (

N m

)

Time (s)

referencemodelled

Figure 5.12: Brake torque tracking performance of the dynamometer control system model(NEDC conditions)

0

1

2

3

4

5

6

7

8

9

10

11

0 50 100 150 200 250 300 350 400

Thro

ttle

angle

(deg)

Time (s)

measuredmodelled

Figure 5.13: Measured and modelled throttle angle (NEDC conditions)

103

0

20

40

60

80

100

0 50 100 150 200 250 300 350 400

Inta

ke

ma

nifo

ld p

ressu

re (

kP

a)

Time (s)

measuredmodelled

Figure 5.14: Measured and calculated intake manifold pressure (NEDC conditions)

0

20

40

60

80

100

0 50 100 150 200 250 300 350 400

Tem

pera

ture

(˚C

)

Time (s)

measured cylinder head temperaturemodelled lumped engine temperature

Figure 5.15: Measured cylinder head temperature and calculated engine temperature (NEDCconditions)

104

0

0.5

1

1.5

2

2.5

0 50 100 150 200 250 300 350 400

Fu

el m

ass f

low

ra

te (

g/s

)

Time (s)

measuredmodelled

Figure 5.16: Measured and calculated fuel mass flow rate (NEDC conditions)

0

50

100

150

200

250

300

0 50 100 150 200 250 300 350 400

Fuel consum

ed (

g)

Time (s)

measuredmodelled

Figure 5.17: Measured and calculated cumulative fuel consumption (NEDC conditions)

105

is expected from a real engine, as frictional losses are reduced with the increasing oil tempera-

ture, and less indicated power is required from a warm engine to produce the same brake power

output as a cold engine. The reduction in indicated power at higher engine loads (for example

at 130 and 330 seconds) can be significantly less, as the frictional losses become smaller relative

to the indicated power output produced (see Figure 5.20).

Additionally, the energy balance in Figure 5.19 shows that between roughly 15% (low indi-

cated power) and 25% (higher indicated power) of the fuel energy is lost in the exhaust and

between roughly 40% (higher indicated power) and 75% (low indicated power) is transferred

as heat to the walls of the combustion chamber. The relative magnitudes of parasitic losses

contributing to the engine’s warm-up behaviour are presented in Figure 5.21, where it can be

seen that its temperature is largely affected by the heat transfer to the walls of the combustion

chamber, while frictional losses appear to contribute only a small amount.

EUDC test case

The brake torque tracking performance of the dynamometer control system model is demon-

strated in Figure 5.22, which shows very close agreement between the reference and the calcu-

lated torque. The commanded and measured throttle angles are compared in Figure 5.23 and

appear to agree well. The small differences observed in the first part of the cycle can be at-

tributed to the errors in the volumetric efficiency modelled, as in the case of the NEDC drive

cycle results (see Figure 5.13). These errors are also reflected in the modelled intake manifold

pressure in Figure 5.24. Nevertheless, the agreement between simulated and measured results is

good.

From Figure 5.25 the lumped engine temperature modelled agrees reasonably with the mea-

sured cylinder head temperature. As seen previously, the impact of the volumetric efficiency

modelling errors on the fuel flow rate is small. This can be observed from Figures 5.26 and 5.27,

which demonstrate a high degree of agreement between the modelled and measured fuel con-

sumption. The error in the consumed fuel modelled over the 250 second period is approximately

3.3%.

The theoretical heat transfer coefficient for the convective heat exchange between the working

fluid and the combustion chamber walls hgs is shown in Figure 5.28. Its magnitude falls roughly

in the same range as for the NEDC test case, between 130 and 230 W/(m2K). The coefficient is

strongly dependent on the power output of the engine. A larger brake power output is associated

with a higher magnitude of hgs. The exhaust gas temperature, shown in Figure 5.29, is modelled

106

0

100

200

300

400

500

600

700

800

0 50 100 150 200 250 300 350 400

Exh

au

st

po

rt g

as t

em

pe

ratu

re (

˚C)

Time (s)

measuredmodelled

Figure 5.18: Measured and calculated exhaust port gas temperature (NEDC conditions)

0

0.2

0.4

0.6

0.8

1

0 50 100 150 200 250 300 350 400

Fra

ction o

f th

e h

eat

pro

duced in t

he c

om

bus.

cham

ber

Time (s)

indicated worklosses to combustion chamber walls

exhaust enthalpy increase

Figure 5.19: Modelled distribution of energy released from fuel (NEDC conditions)

107

0

20

40

60

80

100

120

140

160

180

200

220

0 50 100 150 200 250 300 350 400

To

rqu

e (

N m

)

Time (s)

indicatedfrictional

Figure 5.20: Calculated indicated engine torque and the opposing frictional torque (NEDCconditions)

0

0.2

0.4

0.6

0.8

1

0 50 100 150 200 250 300 350 400

Fra

ction o

f th

e h

eat

pro

duced in t

he c

om

bus.

cham

ber

Time (s)

losses to combustion chamber wallsfrictional losses

Figure 5.21: Frictional and heat losses as a fraction of the heat produced in the combustionchamber (NEDC conditions)

108

reasonably accurately. The largest modelling errors of order 100 ◦C occur during the first 25

seconds of the cycle, but become less significant shortly after.

The distribution of heat energy released from the fuel is presented in Figure 5.30, where it

can be seen that between roughly 40% and 60% of the energy is lost to the combustion chamber

walls, while between roughly 20% and 30% escapes with the exhaust. Figure 5.31 demonstrates

variation of the frictional torque τfric as the engine is warmed up. It can be seen that in the

case of a cold engine, around 70 Nm of indicated torque is required to overcome friction, while

approximately only 20 Nm is needed when the engine is warm. Engine warm up appears to

occur primarily as a result of the heat losses to combustion chamber walls as opposed to the

frictional losses, which contribute 3 to 6 times less energy. This is evident from Figure 5.32.

Results for an idling engine

The goal of the cold start idle test is to further verify the lumped parameter approach used with

the friction correlation (5.24). It can be seen from Figure 5.33 that the modelled engine and the

measured cylinder head temperatures agree reasonably well throughout most of the 500 second

period. The agreement between the modelled and measured fuel consumption is excellent (see

Figures 5.34 and 5.35), which justifies the low order modelling strategy taken in this study.

109

-40

-20

0

20

40

60

80

100

120

140

160

180

0 50 100 150 200 250

To

rqu

e (

N m

)

Time (s)

referencemodelled

Figure 5.22: Brake torque tracking performance of the dynamometer control system model(EUDC conditions)

0

2

4

6

8

10

12

0 50 100 150 200 250

Thro

ttle

angle

(deg)

Time (s)

measuredmodelled

Figure 5.23: Measured and modelled throttle angle (EUDC conditions)

110

0

20

40

60

80

100

0 50 100 150 200 250

Inta

ke

ma

nifo

ld p

ressu

re (

kP

a)

Time (s)

measuredmodelled

Figure 5.24: Measured and calculated intake manifold pressure (EUDC conditions)

0

20

40

60

80

100

0 50 100 150 200 250

Tem

pera

ture

(˚C

)

Time (s)


Figure 5.25: Measured cylinder head temperature and calculated engine temperature (EUDCconditions)

111

0

0.5

1

1.5

2

2.5

0 50 100 150 200 250

Fu

el m

ass f

low

ra

te (

g/s

)

Time (s)

measuredmodelled

Figure 5.26: Measured and calculated fuel mass flow rate (EUDC conditions)

0

50

100

150

200

250

300

0 50 100 150 200 250

Fuel consum

ed (

g)

Time (s)

measuredmodelled

Figure 5.27: Measured and calculated cumulative fuel consumption (EUDC conditions)

112

130

140

150

160

170

180

190

200

210

220

230

0 50 100 150 200 250

He

at

tra

nsfe

r co

eff

icie

nt

(W /

(m

2 K

))

Time (s)

Figure 5.28: Calculated combustion chamber heat transfer coefficient (EUDC conditions)

0

100

200

300

400

500

600

700

800

0 50 100 150 200 250

Exhaust

port

gas t

em

pera

ture

(˚C

)

Time (s)

measuredmodelled

Figure 5.29: Measured and calculated exhaust port gas temperature (EUDC conditions)

113

0

0.2

0.4

0.6

0.8

1

0 50 100 150 200 250

Fra

ctio

n o

f th

e h

ea

t p

rod

uce

d in

th

e c

om

bu

s.

ch

am

be

r

Time (s)

indicated worklosses to combustion chamber walls

exhaust enthalpy increase

Figure 5.30: Modelled distribution of energy released from fuel (EUDC conditions)

0

50

100

150

200

250

0 50 100 150 200 250

Torq

ue (

N m

)

Time (s)

indicatedfrictional

Figure 5.31: Calculated indicated engine torque and the opposing frictional torque (EUDCconditions)

114

0

0.2

0.4

0.6

0.8

1

0 50 100 150 200 250

Fra

ctio

n o

f th

e h

ea

t p

rod

uce

d in

th

e c

om

bu

s.

ch

am

be

r

Time (s)

losses to combustion chamber wallsfrictional losses

Figure 5.32: Frictional and heat losses as a fraction of the heat produced in the combustionchamber (EUDC conditions)

0

20

40

60

80

100

0 100 200 300 400 500

Tem

pera

ture

(˚C

)

Time (s)


Figure 5.33: Measured and calculated cylinder head temperature (idle conditions)

115

0

0.5

1

1.5

2

2.5

0 100 200 300 400 500

Fu

el m

ass f

low

ra

te (

g/s

)

Time (s)

measuredmodelled

Figure 5.34: Measured and calculated fuel mass flow rate (idle conditions)

0

20

40

60

80

100

120

140

160

180

200

0 100 200 300 400 500

Fuel consum

ed (

g)

Time (s)

measuredmodelled

Figure 5.35: Measured and calculated cumulative fuel consumption (idle conditions)

116

5.2 Engine-out emissions

The engine-out emissions model was calibrated based on the steady state data for a fully warm

engine. Initially, the CO, NO and HC static surfaces were fit to the independent variables pim,

λ, θ, ϑint, ϑovlp and N . The significance of these parameters was examined statistically for each

of the fits and least important variables were removed from the functions to avoid overfitting of

the data. The calibrated model was then validated under transient NEDC conditions by using

the time traces of the measured engine operating parameters as the inputs and comparing the

measured instantaneous and cumulative emissions with those modelled.

5.2.1 Calibration

With X denoting either CO, NO or HC, the normalised emissions surfaces eX [mol X/kg fuel]

were approximated by polynomials of the form

eX =

OX∑

j=0

OX∑

k=0

OX∑

l=0

OX∑

m=0

OX∑

n=0

OX∑

o=0

aX,j,k,l,m,n,o pjim λk θl ϑm

intϑnovlp N

o, (5.34)

subject to the constraints j+k+l+m+n+o ≤ OX , where OX is the order of the the polynomial.

The emission fits were developed by solving (5.1) with

qi = eX(P(m)im,i, λ

(m)i , θ

(m)i , ϑ

(m)int,i, ϑ

(m)ovlp,i, N

(m)i ), (5.35)

q(m)i =

C(m)X,i (1 +AFRS λ

(m)i )

M(m)g

. (5.36)

Some statistics that reflect upon the quality of the fits are the root mean squared error

(RMSE) and normalised root mean squared error (NRMSE), defined by

RMSE =

√

√

√

√

1

nss

nss∑

i=1

[eX,i − e(m)X,i ]2, (5.37)

NRMSE =RMSE

max(e(m)X,i ) − min(e

(m)X,i )

. (5.38)

By removing independent variables from eX one at a time and observing RMSE after re-fitting of

the surfaces, it was discovered that CO emissions were weakly dependent on all of the indepen-

dent parameters other than λ, NO emissions were strongly dependent on all of these variables

and HC emissions were strongly dependent on all of the variables except ϑint and ϑovlp. The

degree of significance is summarised in Table 5.3 for each of the independent parameters. As a

consequence, statistically less important variables were eliminated from the surfaces eX , making

117

Variable removed ∆NRMSEeCO

pim 8.1%λ 941.2%θ 3.9%ϑint 0.6%ϑovlp 0.3%N 2.6%

eNO


eHC


Table 5.3: Change in NRMSE after removal of a single independent variable in eX

it easier to examine the trends in these functions. The resulting functions are

eCO(λ),

eNO(pim, λ, θ, ϑint, ϑovlp, N),

eHC(pim, λ, θ,N).

The dependence of the measured CO emissions on λ at steady state is demonstrated in

Figure 5.36. A 5th order polynomial was chosen for approximating eCO(λ) in order to accurately

represent the sharp change of slope in emissions at λ ≈ 1, while maintaining the almost constant

slopes on the rich and the lean sides of the graph. The resulting least squares fit is shown in the

same figure.

Whilst increasing the order of eNO and eHC polynomials tends to reduce RMSE and increase

R2 (see Table 5.4), polynomials of low order were sought. This can help to prevent overfitting

of the data and avoid large errors during extrapolation. The order of the selected polynomials

and the quality of the fits are summarised in Table 5.5.

Figures 5.36–5.39 show the calibrated eCO, eNO and eHC polynomials for a range of their

domain variables. The contour plots in Figures 5.37–5.39 are associated with the surfaces in solid

118

eX / OX 2 3 4eNO

Terms 28 84 210R2 0.8492 0.9542 0.9846RMSE 0.2057 0.1134 0.0658NRMSE 0.0808 0.0442 0.0257

eHC

Terms 15 35 70R2 0.8224 0.8886 0.9259RMSE 0.3361 0.2662 0.2171NRMSE 0.0372 0.0295 0.0240

Table 5.4: Effect of polynomial order on the quality of eNO(pim, λ, θ, ϑint, ϑovlp, N) andeHC(pim, λ, θ,N) fits

eX OX Terms R2 NRMSEeCO 5 6 0.9961 0.0203eNO 3 84 0.9542 0.0442eHC 2 15 0.8224 0.0372

Table 5.5: Properties of the polynomials eX used in the engine-out emissions model

colour. Surfaces in grey provide an indication of the change with respect to a third independent

variable. The trends in all of these figures appear to be sensible. For example, the strong

dependence of CO emissions on λ in Figure 5.36, the maximum value of NO emissions occurring

at λ ≈ 1.1 in Figure 5.37 and the decreasing HC emissions with increasing λ (for the range

considered) in Figure 5.39 are all well known trends observed in many spark-ignition engines

(e.g. Heywood (1988)).

5.2.2 Validation

In this section the performance of the engine-out emissions model is demonstrated over the

transient NEDC conditions. The time traces p(m)im , λ(m), θ(m), ϑ

(m)int , ϑ

(m)ovlp and N (m) were first

used as the inputs to the static functions eX . The estimated normalised emissions eX(t) were

then converted to the exhaust concentrations according to

CX =eX m

(m)fuel M

(m)g

m(m)fuel(1 +AFRS λ(m))

=eX M

(m)g

1 +AFRS λ(m), (5.39)

filtered using low pass filters with cut-off frequencies corresponding to those of the gas analysers

(see Chapter 3) and compared to the measured concentrations.

Figures (5.40)–(5.47) compare measured and modelled engine-out emissions. It can be seen

119

0

5

10

15

20

25

30

35

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2

CO

(m

ol/kg

fu

el)

λ

Figure 5.36: Measured and modelled CO emissions as a function of λ for a wide range of steadystate conditions

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2

0 5

10 15

20 25

30 35

40

0

0.5

1

1.5

2

2.5

3

NO(mol/kg fuel)

MAP = 50 kPa 0.3 0.9 1.5 2

λ

Spark timing(CAD BTDC)

NO(mol/kg fuel)

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2

0 5

10 15

20 25

30 35

40

0

0.5

1

1.5

2

2.5

3

MAP = 45 kPa

Figure 5.37: Modelled NO emissions as a function of λ, spark timing and intake manifoldpressure (17.5 CAD BTDC intake valve opening, 25 CAD valve overlap, 1000 rev/min enginespeed)

120

-10-5

0 5

10 15

20

15

20

25

30

35

0

0.5

1

1.5

2

NO(mol/kg fuel)

MAP = 50 kPa 0.2 0.6 1.1 1.4

Intake valve opening(CAD BTDC)

Valve overlap (CAD)

NO(mol/kg fuel)

-10-5

0 5

10 15

20

15

20

25

30

35

0

0.5

1

1.5

2

MAP = 45 kPa

Figure 5.38: Modelled NO emissions as a function of intake valve opening, valve overlap andintake manifold pressure (stoich. AFR, 45 CAD BTDC spark timing, 1300 rev/min engine speed)

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2

0 5

10 15

20 25

30 35

40

0

0.5

1

1.5

2

2.5

3

HC(mol C1/kg fuel)

MAP = 30 kPa 0.5 1

1.6 2

λ

Spark timing(CAD BTDC)

HC(mol C1/kg fuel)

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2

0 5

10 15

20 25

30 35

40

0

0.5

1

1.5

2

2.5

3

MAP = 50 kPa

Figure 5.39: Modelled HC emissions as a function of λ, spark timing and intake manifoldpressure (1300 rev/min engine speed)

121

that instantaneous concentrations do not always agree closely. However, the magnitude of these

emissions is comparable and the most significant trends are successfully captured by the model.

Cumulative emissions, which are of greater importance for the optimal control problem con-

sidered in this thesis, agree well. By the end of the 400 second period modelled cumulative

engine-out CO, NO and HC emissions are within 3%, 12% and 1% of those measured.

The disagreement in cumulative NO emissions is the most noticeable. Figure 5.42 indicates

that significant errors in simulated NO emissions occur early in the cycle. This appears to be

the result of using a warm engine emissions model to predict cold start emissions. The amount

of NOX produced in a cold engine is generally less than in a hot engine. This is a consequence of

increased charge cooling inside the combustion chamber and lower in-cylinder peak temperatures,

which inhibit the formation of NOX . The over-exaggerated modelled emissions are therefore not

surprising.

In Figure 5.44 instantaneous HC emissions peak roughly at 160, 270 and 350 seconds. Due

to limitations in the engine control system, these parts of the cycle were characterised by misfire

during rapid throttle closing events. However, as the fuel flow rate was relatively low under such

conditions, cumulative emissions were not significantly affected.

Instantaneous H2 emissions are shown in Figure 5.47. Whilst H2 could not be measured

directly using the available gas analysers, its concentration was estimated based on the other

measured species. From Figures 5.40 and 5.47 it is evident that H2 concentrations are roughly

a third of the CO, which is consistent with literature (Heywood, 1988, Balenovic, 2002, Holder

et al., 2006).

5.3 Exhaust manifold and connecting pipe models

The exhaust manifold and connecting pipe models were calibrated over the first 400 seconds of

NEDC and validated over 250 seconds of cold start EUDC conditions. The values of the fixed

model parameters used in simulations are listed in Table 5.6. The exhaust mass flow rate m(m)cyl

and inlet gas temperature T(m)g,in , previously measured in an experiment, were used as inputs to

simulate the transient conditions. The time traces of the inputs used in calibration are given in

Figure 5.48, while those used in validation are shown in Figure 5.49.

122

0

0.5

1

1.5

2

2.5

3

0 50 100 150 200 250 300 350 400

CO

(%

mo

l/m

ol)

Time (s)

measuredmodelled

Figure 5.40: Measured and modelled instantaneous engine-out CO emissions (NEDC conditions)

0

5

10

15

20

25

30

0 50 100 150 200 250 300 350 400

CO

(g)

Time (s)

measuredmodelled

Figure 5.41: Measured and modelled cumulative engine-out CO emissions (NEDC conditions)

123

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 50 100 150 200 250 300 350 400

NO

(p

pm

)

Time (s)

measuredmodelled

Figure 5.42: Measured and modelled instantaneous engine-outNO emissions (NEDC conditions)

0

0.5

1

1.5

2

2.5

3

3.5

0 50 100 150 200 250 300 350 400

NO

(g)

Time (s)

measuredmodelled

Figure 5.43: Measured and modelled cumulative engine-out NO emissions (NEDC conditions)

124

0

2000

4000

6000

8000

10000

0 50 100 150 200 250 300 350 400

HC

(p

pm

C1)

Time (s)

measuredmodelled

Figure 5.44: Measured and modelled instantaneous engine-outHC emissions (NEDC conditions)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 50 100 150 200 250 300 350 400

HC

(g)

Time (s)

measuredmodelled

Figure 5.45: Measured and modelled cumulative engine-out HC emissions (NEDC conditions)

125

0

1

2

3

4

5

0 50 100 150 200 250 300 350 400

O2 (

% m

ol/m

ol)

Time (s)

measuredmodelled

Figure 5.46: Measured and modelled instantaneous engine-out O2 emissions (NEDC conditions)

0

0.2

0.4

0.6

0.8

1

0 50 100 150 200 250 300 350 400

H2 (

% m

ol/m

ol)

Time (s)

calculated from other measured emissionsmodelled

Figure 5.47: Instantaneous engine-out H2 emissions modelled and calculated based on othermeasured emissions (NEDC conditions)

126

0

5

10

15

20

25

30

35

40

45

Exh

au

st

flow

ra

te (

g/s

)

0

100

200

300

400

500

600

700

800

0 50 100 150 200 250 300 350 400

Gas t

em

pe

ratu

re (

˚C)

Time (s)

measured at exhaust manifold inletmeasured at connecting pipe inlet

Figure 5.48: Exhaust manifold and connecting pipe model inputs simulating NEDC conditions,used in calibration

0

5

10

15

20

25

30

35

40

45

Exhaust

flow

rate

(g/s

)

0

100

200

300

400

500

600

700

800

0 50 100 150 200 250

Inle

t gas tem

pera

ture

(˚C

)

Time (s)

exhaust manifold model inputconnecting pipe model input

Figure 5.49: Exhaust manifold and connecting pipe model inputs simulating cold start EUDCconditions, used in validation

127

Parameter ValueExhaust manifoldAex,i 0.181 [m2]Aex,o 0.199 [m2]mex cex 4140 [J/K]

Connecting pipeAex,i 0.0826 [m2]Aex,o 0.0882 [m2]mex cex 1380 [J/K]

Table 5.6: Exhaust system model fixed parameter values

5.3.1 Calibration

The heat transfer coefficient parameters aex,1, bex,1 and aex,2 were tuned by solving

{aex,1, bex,1, aex,2}⋆ = arg minaex,1,bex,1,aex,2

∫ tf

0

[

Tg,out(t) − T(m)g,out(t)

]2

+[

Ts(t) − T (m)s (t)

]2

dt.

(5.40)

This places more emphasis on matching the higher in magnitude exhaust gas temperatures rather

than the substantially cooler exhaust manifold and connecting pipe body temperatures during

the warm-up period. Such weighting is desirable as modelling errors in the body temperatures

can be tolerated to a greater degree compared to those in the gas temperatures. The latter can

propagate directly to the catalyst model, introducing errors in the calculated tailpipe emissions.

Solutions to (5.40) were produced using a gradient descent method with several initial guesses

for aex,1, bex,1 and aex,2.

The outlet exhaust temperature Tg,out and the surface temperature Ts were simulated using

(4.68), (4.74) and (4.75)–(4.78) over prescribed m(m)cyl and T

(m)g,in input trajectories, such that

mcyl(t) = m(m)cyl (t), (5.41a)

Tg,in(t) = T(m)g,in . (5.41b)

Optimised values of the exhaust manifold tuning parameters are

aex,1,em = 0.0179, (5.42)

bex,1,em = 0.95, (5.43)

aex,2,em = 0, (5.44)

128

0

20

40

60

80

100

120

140

160

180

0 50 100 150 200 250 300 350 400

He

at

tra

nsfe

r co

eff

icie

nt

(W /

(m

2 K

))

Time (s)

exhaust manifoldconnecting pipe

Figure 5.50: Modelled heat transfer coefficients hgs (NEDC conditions)

while those of the connecting pipe are

aex,1,cp = 0.0641, (5.45)

bex,1,cp = 0.789, (5.46)

aex,2,cp = 529. (5.47)

The modelled exhaust manifold and the connecting pipe heat transfer coefficient hgs for the

exhaust gas–solid phase boundary are shown in Figure 5.50.

Consider the exhaust manifold results. The lower bound of hgs is roughly 15 W/(m2 K),

occurring during an idle event. This value appears to be suspiciously low for a convective heat

exchange involving turbulent flow and is likely to be the result of the high complexity of the

exhaust manifold dynamics, which can not be captured well by the lumped parameter model.

The heat transfer coefficient hsa, calculated from (4.78), is 0, which is reasonable, as the manifold

was covered by a protective thermal shield and convective losses to the ambient air were expected

to be small.

In the case of the connecting pipe, hgs falls into a more reasonable range. However, the

heat transfer coefficient hsa, roughly equal to 219 W/(m2 K), appears to be surprisingly large,

especially when compared to hgs. This can be explained by the powerful stream of laboratory

129

air directed at the connecting pipe (and the engine) at the time of the experiment and the

complexity of the dynamics in the relatively long pipe section, experiencing significantly large

spatial temperature gradients. Also, since only convective heat transfer is modelled between the

ambient surroundings and the solid body, other losses, such as conduction towards the catalyst

casing are all lumped into hsa.

Despite these quite significant simplifications in the models for hgs and hsa, it is evident

from Figures 5.51 and 5.52 that measured and simulated temperatures of the exhaust gas at the

outlet of the exhaust manifold and the connecting pipe agree closely, as do the measured and

calculated temperatures of the bodies.

5.3.2 Validation

Exhaust manifold and connecting pipe model validation results are based on the cold start EUDC

conditions, which differ from the conditions used in calibration. Simulated and measured gas

temperatures at the exit of the exhaust manifold and the connecting pipe section are presented

in Figures 5.53 and 5.54. In both cases the modelled results are on average within 5% of those

measured. The same figures demonstrate a reasonable agreement of modelled and measured

body temperatures.

5.4 Three-way catalyst

The catalyst model is first calibrated under the NEDC drive cycle conditions. Then the sensi-

tivity of the modelled outputs to the number of grid points used in the approximation of the

spatial domain is examined. Based on the results of this analysis, the order of the model is

reduced to the extent that its integration into dynamic optimisation studies becomes feasible,

whilst the accuracy of the solutions produced is not greatly compromised. The reduced order

model is then validated by considering its steady state behaviour, oxygen storage dynamics and

calculated tailpipe emissions under cold start EUDC conditions.

To simulate the various transient conditions, the quantities m(m)cyl , T

(m)g,in , C

(m)g,O2,in, C

(m)g,CO,in,

C(m)g,NO,in and C

(m)g,HC,in were measured experimentally, while C

(m)g,H2,in was calculated based on

the water-gas shift reaction equilibrium and the emissions measurements. These variables were

then used as the inputs to the catalyst model (4.121). Note that the exhaust mass flow rate

m(m)cyl was not measured directly, but was calculated based on the fuel mass flow rate and the

UEGO sensor λ output. The fixed model parameters used in simulations are listed in Table 5.7.

130

0

100

200

300

400

500

600

700

800

0 50 100 150 200 250 300 350 400

Te

mp

era

ture

(˚C

)

Time (s)

outlet gas temperature measuredoutlet gas temperature modelled

exhaust manifold temperature measuredexhaust manifold temperature modelled

Figure 5.51: Measured and modelled exhaust manifold body temperature and outlet gas tem-perature (NEDC conditions)

0

100

200

300

400

500

600

700

800

0 50 100 150 200 250 300 350 400

Tem

pera

ture

(˚C

)

Time (s)


connecting pipe temperature measuredconnecting pipe temperature modelled

Figure 5.52: Measured and modelled connecting pipe body temperature and outlet gas temper-ature (NEDC conditions)

131

0

100

200

300

400

500

600

700

800

0 50 100 150 200 250

Te

mp

era

ture

(˚C

)

Time (s)


exhaust manifold temperature measuredexhaust manifold temperature modelled

Figure 5.53: Measured and modelled exhaust manifold body temperature and outlet gas tem-perature (EUDC conditions)

0

100

200

300

400

500

600

700

800

0 50 100 150 200 250

Tem

pera

ture

(˚C

)

Time (s)


connecting pipe temperature measuredconnecting pipe temperature modelled

Figure 5.54: Measured and modelled connecting pipe body temperature and outlet gas temper-ature (EUDC conditions)

132

Parameter ValueAc 0.0119 m2

cs 1500 J/(kg ·K)Dc 0.001105 mks 3.0 W/(m ·K)L 0.1435 mS 2740 m2/m3

ǫ 0.757ρs 2240 kg/m3

Ea,i see Table 4.5

Table 5.7: Catalyst model fixed parameter values

5.4.1 Calibration

There are significant differences in the amounts of CO, NO and HC tailpipe emissions emitted

over a drive cycle. Hence, the model tuning procedure should take advantage of a cost function

that scales the errors in the modelled emissions appropriately. Let the cost function Jcat,0 be

defined in terms of the normalised cumulative errors in the flow rates ni,out of each of the

pollutants i leaving the catalyst as

Jcat,0 =1

nCO,out(tf )(m)

∫ tf

0

|nCO,out − n(m)CO,out| dt+

1

nNO,out(tf )(m)

∫ tf

0

|nNO,out − n(m)NO,out| dt+

1

nHC,out(tf )(m)

∫ tf

0

|nHC,out − n(m)HC,out| dt, (5.48)

where

ni,out = Cg,i,out

m(m)cyl

Mg, (5.49)

m(m)i,out = C

(m)g,i,out

m(m)cyl

M(m)g

, (5.50)

n(m)i,out(tf ) =

∫ tf

0

n(m)i,out dt. (5.51)

By multiplying Jcat,0 by the constant nCO,out(tf )(m) and rewriting the expression under a single

integral, an equivalent cost function is obtained,

Jcat =

∫ tf

0

|nCO,out − n(m)CO,out| +

nCO,out(tf )(m)

nNO,out(tf )(m)|nNO,out − n

(m)NO,out|+

nCO,out(tf )(m)

nHC,out(tf )(m)|nHC,out − n

(m)HC,out| dt. (5.52)

133

The catalyst model tuning parameters Ae,i, lw and α were determined by solving

{Ae,i, lw, α}⋆ = arg minAe,i,lw,α

Jcat (5.53)

using a gradient descent procedure with a large number of various initial guesses for the tuning

parameters. Tailpipe emissions mCO,out, mNO,out and mHC,out were simulated by solving the

catalyst model equations (4.121) with 4 uniformly spaced nodes discretising the axial direction

(ncat = 4) and

mcyl = m(m)cyl , (5.54a)

Tg,in = T(m)g,in , (5.54b)

Cg,in = C(m)g,in. (5.54c)

The oxygen storage capacity Ψ was fixed and later verified by observing the emptying behaviour

of stored oxygen during lean-rich transitions in the exhaust λ. Model calibration was carried out

under the NEDC drive cycle conditions using 4 equally spaced nodes to approximate the spatial

coordinate in the model. The use of a large number of nodes was impractical due to the high

computational effort required. As will be shown later, the tailpipe emissions modelled using only

4 nodes compare very well with those modelled using a large number of nodes, justifying this

tuning process. The resulting set of optimised parameters is given in Table 5.8.

Parameter ValueAe,1 1.064380× 1020

Ae,2 1.064380× 1020

Ae,3 5.687341× 1018

Ae,4 1.625393× 1017

Ae,5 5.610389× 1012

Ae,6 1.819701× 1013

Ae,7 5.175123× 1013

Ae,8 2.610655× 1011

Ae,9 2.972991× 1011

Ae,10 2.009992× 1013

lw 1.98 × 10−5 mα 273 m2/m3

Ψ 600 mol/m3

Table 5.8: Optimised values of catalyst model parameters

Figures 5.55–5.60 demonstrate the performance of the calibrated model under the NEDC

conditions used in the calibration. The figures compare modelled and measured instantaneous

and cumulative tailpipe emissions, from which it is evident that the catalyst light-off and emis-

sions breakthroughs are modelled reasonably well. The observed saturation of the measured NO

134

tailpipe emissions in Figure 5.57 was the result of exceeding the maximum range of the NO gas

analyser. The disagreement between the measured and modelled cumulative NO emissions in

Figure 5.58 is largely owed to this saturation and the true modelling errors are expected to be

significantly less than observed in this plot.

5.4.2 Model reduction

The resolution of the grid approximating the spatial direction in the catalyst model determines

the order of the model. A fine grid leads to a more precise development of solutions to the

model equations at the expense of the increasing computational effort. On the contrary, a sparse

grid results in a mathematically more compact representation of the model, but often leads

to increased modelling errors in the catalyst light-off time and overall tailpipe emissions. To

identify the lowest order of the model that can calculate tailpipe emissions with a reasonable

degree of accuracy, the sensitivity of tailpipe emissions to the number of nodes ncat was therefore

examined.

Figures 5.61–5.66 present simulated using (4.121) instantaneous and cumulative tailpipe emis-

sions results based on ncat = 1, 2, 4 and 51 nodes with NEDC boundary conditions, as used in the

calibration. These nodes are uniformly spaced and positioned at distances(

i+ 12

)

Lncat

from the

front face of the catalyst, where i is the node index beginning from 0. For example, in the case

of ncat = 1, the node is positioned at the centre of the monolith. From the figures it is clear that

while the performance of the lumped parameter (single node) model is unacceptable, the results

from the 2, 4 and 51 node models are comparable. The time to catalyst light-off, as calculated

by the latter 3 models, is almost the same and cumulative emissions are within several percent

of each other. This observation was at first surprising, but the distribution of the consumption

rates Rc,i in the 2 node model under many conditions appear to sensibly approximate those in

the 51 node model. For example, in Figure 5.67 HC consumption rates are plotted as a function

of the displacement from the catalyst inlet in a catalyst discretised using 2 and 51 nodes. The

snapshot of this distribution was taken some time after light-off with NEDC boundary condi-

tions. The areas under the curves, representing instantaneous species consumption rates in the

monolith, are comparable in both cases. The 2 node representation was therefore selected for

the purposes of this work. As will be shown later, this low order model can perform well under

many different transient conditions.

135

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 50 100 150 200 250 300 350 400

CO

(%

mo

l/m

ol)

Time (s)

measured pre-catalystmeasured post-catalystmodelled post-catalyst

Figure 5.55: Measured and calculated instantaneous tailpipe CO emissions using a 4 node cat-alyst model (NEDC conditions)

0

5

10

15

20

25

0 50 100 150 200 250 300 350 400

CO

(g)

Time (s)


Figure 5.56: Measured and calculated cumulative tailpipe CO emissions using a 4 node catalystmodel (NEDC conditions)

136

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 50 100 150 200 250 300 350 400

NO

(p

pm

)

Time (s)


Figure 5.57: Measured and calculated instantaneous tailpipe NO emissions using a 4 nodecatalyst model (NEDC conditions)

0

0.5

1

1.5

2

2.5

3

3.5

0 50 100 150 200 250 300 350 400

NO

(g)

Time (s)


Figure 5.58: Measured and calculated cumulative tailpipe NO emissions using a 4 node catalystmodel (NEDC conditions)

137

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

0 50 100 150 200 250 300 350 400

HC

(p

pm

C1)

Time (s)


Figure 5.59: Measured and calculated instantaneous tailpipe HC emissions using a 4 nodecatalyst model (NEDC conditions)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 50 100 150 200 250 300 350 400

HC

(g)

Time (s)


Figure 5.60: Measured and calculated cumulative tailpipe HC emissions using a 4 node catalystmodel (NEDC conditions)

138

0

0.5

1

1.5

2

2.5

0 50 100 150 200 250 300 350 400

CO

(%

mo

l/m

ol)

Time (s)

51 nodes4 nodes2 nodes1 node

Figure 5.61: Calculated instantaneous tailpipe CO concentration as a function of the number ofgrid points used (NEDC conditions)

0

5

10

15

20

25

0 50 100 150 200 250 300 350 400

CO

(g)

Time (s)


Figure 5.62: Calculated cumulative tailpipe CO emissions as a function of the number of gridpoints used (NEDC conditions)

139

0

500

1000

1500

2000

0 50 100 150 200 250 300 350 400

NO

(p

pm

)

Time (s)


Figure 5.63: Calculated instantaneous tailpipe NO concentration as a function of the numberof grid points used (NEDC conditions)

0

0.5

1

1.5

2

2.5

3

0 50 100 150 200 250 300 350 400

NO

(g)

Time (s)


Figure 5.64: Calculated cumulative tailpipe NO emissions as a function of the number of gridpoints used (NEDC conditions)

140

0

2000

4000

6000

8000

10000

0 50 100 150 200 250 300 350 400

HC

(p

pm

C1)

Time (s)


Figure 5.65: Calculated instantaneous tailpipe HC concentration as a function of the numberof grid points used (NEDC conditions)

0

1

2

3

4

5

0 50 100 150 200 250 300 350 400

HC

(g)

Time (s)


Figure 5.66: Calculated cumulative tailpipe HC emissions as a function of the number of gridpoints used (NEDC conditions)

141

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

No

rma

lise

d H

C c

on

su

mp

tio

n r

ate

Normalised distance from the inlet

51 nodes2 nodes

Figure 5.67: Calculated instantaneous distribution of HC consumption rate in a catalyst discre-tised using 2 and 51 nodes

5.4.3 Validation

Steady state conversion efficiency

Three-way catalysts operate at their peak efficiency roughly at stoichiometric conditions and

their steady state performance can be strongly affected by the λ-value of the exhaust. Even

under slightly lean steady state conditions, the conversion efficiency of NO can be reduced

significantly. This is partly due to the limited availability of CO after its oxidation with excess

oxygen for NO reduction. Similarly, under rich conditions there are limited amounts of oxidants

to react with CO and HC compounds. Consequently, the conversion of CO and HC is usually

impaired. It is typical for the range of λ, where the steady state conversion efficiency of CO,

NO and HC remains above 80%, to be on the order of 0.01 (Heywood, 1988, Twigg et al., 2002,

Auckenthaler, 2005).

To verify that the catalyst model can sensibly reproduce such steady state behaviour, the

engine-out emissions model was used to calculate an exhaust gas composition corresponding to

the particular set of λ values tested. These gas compositions were then fed as the inputs to the

2 node catalyst model. The resulting modelled conversion efficiency as a function of λ is shown

in Figure 5.68. It can be seen that while the maximum conversion efficiency occurs at λ = 1.00,

142

0

0.2

0.4

0.6

0.8

1

0.96 0.97 0.98 0.99 1 1.01 1.02 1.03 1.04

Co

nve

rsio

n e

ffic

ien

cy

λ

COHCNO

Figure 5.68: Calculated steady state CO, NO and HC conversion efficiency as a function of λ

as expected, the λ “window” for the 80% conversion efficiency is roughly 0.01, which agrees well

with the literature.

Oxygen storage dynamics

To validate the modelled oxygen storage dynamics, consider the experiments, in which both

the engine and the catalyst are at a steady state, operating under lean conditions. By quickly

transitioning λ towards the rich side, it is possible to observe the emptying dynamics of the

stored oxygen.

The time needed to consume most of the stored oxygen is of order 1 second. However, this

can vary, depending on the state of the catalyst and the operating conditions, such as λ and

the mass flow rate of the exhaust. Unfortunately, most of the exhaust gas analysers used in this

work possessed time constants on the order of a few seconds, making it difficult to observe the

oxygen storage behaviour. In an attempt to resolve this issue, both the feedgas and tailpipe HC

emissions were measured using the fast response Cambustion FFID. The results are presented

in Figure 5.69. Good HC conversion efficiency shortly after the lean–rich transition is indicative

of sufficiently large quantities of stored oxygen to continue the oxidation reactions. Conversely,

poor HC conversion a few seconds later is related to the limited amount of oxygen remaining in

143

the washcoat.

To simulate tailpipe emissions, feedgas HC concentrations obtained using the FFID were

used as the inputs to the model, along with the other pre-catalyst emissions measured by the

Horiba bench. The normalised air-fuel ratio, calculated primarily based on the measurements

from the slow response exhaust gas analysers, was therefore the λ-value as seen by the catalyst

model. The UEGO sensor provided a significantly faster measurement of λ, and consequently,

a more precise estimate of the instance the conditions became rich. For the catalyst model

boundary conditions to be consistent with the lean–rich λ switch, it was ensured that the λ = 1

cross-over of the two λ measurements occurred at roughly the same time. This was achieved by

shifting the Horiba measurements in time relative to all other measurements.

Figure 5.69 compares the measured and simulated tailpipe HC emissions. It is evident that

under the conditions of this test, the oxygen storage emptying behaviour is simulated reasonably

well. Figure 5.70 presents results for the rich–lean transition of λ, from which it can be seen that

the HC conversion efficiency is almost instantly restored, as soon as the air-fuel ratio reaches

stoichiometry. The modelled results closely capture this behaviour.

Catalyst dynamics under EUDC conditions

The transient dynamics of the 2 node catalyst model are validated on the first 250 seconds of the

EUDC drive cycle conditions initiated from a cold start. On average the power output from the

engine during EUDC is substantially higher relative to NEDC. This gives rise to the exhaust mass

flow rates, increasing the total enthalpy input into the catalyst and reducing the light-off time

from roughly 150 seconds during the NEDC to approximately 60 seconds. A physically sound

and a well calibrated model is therefore expected to replicate this behaviour, as well as calculate

tailpipe emissions with a reasonable degree of accuracy during the hot catalyst operation.

Figure 5.71 shows the measured and modelled instantaneous tailpipe emissions results. The

time to CO light-off modelled is within a few seconds of that measured. The diminishing tailpipe

concentrations immediately after the light-off through to roughly 120 seconds are modelled

closely. The minor CO breakthrough at 200 seconds is also predicted well. The high level

of agreement between the modelled and experimental results is reflected in the cumulative emis-

sions plots in Figure 5.72. The total modelling error in the mass of CO leaving the tailpipe

relative to the mass of CO produced by the engine is below 2.5%.

Measured and modelled tailpipe NO concentrations are presented in Figure 5.73. As men-

tioned previously, the observed saturation of the measured emissions is the result of exceeding

144

0.9

0.95

1

1.05

1.1

λ

UEGObased on emissions

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Norm

alis

ed

HC

co

nce

ntr

atio

n

Time (s)


Figure 5.69: Feedgas and tailpipe HC measured using the FFID and tailpipe HC modelledduring a lean–rich switch (roughly 11 g/s flow rate, 330◦C gas inlet temperature)

0.9

0.95

1

1.05

1.1

λ

UEGObased on emissions

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Norm

alis

ed H

C c

oncentr

ation

Time (s)


Figure 5.70: Feedgas and tailpipe HC measured using the FFID and tailpipe HC modelledduring a rich–lean switch (roughly 11 g/s flow rate, 330◦C gas inlet temperature)

145

the maximum range of the gas analyser used. The NO light-off occurs by the end of this sat-

uration period, roughly at 60 seconds. The time to light-off and tailpipe emissions during the

warm catalyst operation appear to be simulated adequately. The measured tailpipe cumulative

emissions shown in Figure 5.74 underestimate the true emissions due to the saturation of the

analyser output. Hence, the total modelling error in the cumulative tailpipe NO is exaggerated

and is expected to be significantly less.

Instantaneous and cumulative HC emissions results are provided in Figures 5.75 and 5.76.

Again, the time to light-off is accurately estimated, while the measured and simulated tailpipe

emissions agree closely. The total error in the cumulative emissions modelled is less than 3% of

the HC emitted from the engine.

5.5 The integrated engine, exhaust system and catalyst

model

In this section the performance of the integrated model, defined by (4.123) and (4.125) with

ncat = 2, is tested under the NEDC conditions, specified by the ECU built-in engine control

strategy shown in Figure 5.2. Thus,

τrefbrake(t) = τ


N ref (t) = N (m)(t), (5.55b)

λ(t) = λ(m)(t), (5.55c)

θ(t) = θ(m)(t), (5.55d)


ϑovlp(t) = ϑ(m)ovlp(t). (5.55f)

These inputs contain high frequency information, which propagates to the tailpipe concentrations

calculated. To enable easier interpretation and comparison of the modelled and measured results,

the simulated instantaneous emissions have been processed using low pass filters with cut-off

frequencies corresponding to those of the gas analysers. Note that engine model performance

results for this set of inputs have been presented in Section 5.1.3 and will not be discussed here.

Figures 5.77 and 5.78 compare measured and calculated instantaneous and cumulative CO

tailpipe emissions. Feedgas emissions, also included in the figures, give an indication of the

errors involved relative to engine-out emissions. The results demonstrate that the time until CO

light-off is predicted well, while the overall modelling error in the cumulative CO emissions is

146

0

0.5

1

1.5

2

2.5

3

3.5

0 50 100 150 200 250

CO

(%

mo

l/m

ol)

Time (s)


Figure 5.71: Measured and calculated instantaneous tailpipe CO emissions using a 2 node cat-alyst model (EUDC conditions)

0

5

10

15

20

25

30

0 50 100 150 200 250

CO

(g)

Time (s)


Figure 5.72: Measured and calculated cumulative tailpipe CO emissions using a 2 node catalystmodel (EUDC conditions)

147

0

500

1000

1500

2000

2500

0 50 100 150 200 250

NO

(p

pm

)

Time (s)


Figure 5.73: Measured and calculated instantaneous tailpipe NO emissions using a 2 nodecatalyst model (EUDC conditions)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 50 100 150 200 250

NO

(g)

Time (s)


Figure 5.74: Measured and calculated cumulative tailpipe NO emissions using a 2 node catalystmodel (EUDC conditions)

148

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

0 50 100 150 200 250

HC

(p

pm

C1)

Time (s)


Figure 5.75: Measured and calculated instantaneous tailpipe HC emissions using a 2 nodecatalyst model (EUDC conditions)

0

1

2

3

4

5

6

0 50 100 150 200 250

HC

(g)

Time (s)


Figure 5.76: Measured and calculated cumulative tailpipe HC emissions using a 2 node catalystmodel (EUDC conditions)

149

less than 14% of the total CO emitted from the engine. The observed disagreement between

the modelled and simulated emissions is primarily caused by the errors in the estimated catalyst

model inputs, particularly the feedgas emissions. This is evident from the cumulative emissions

plots, where the measured and modelled quantities begin to diverge prior to the catalyst light-

off. Nonetheless, the agreement between the model and the experiments is reasonable and most

trends are reproduced.

Similarly, NO results are presented in Figures 5.79 and 5.80. As noted previously, the

saturation of the measured tailpipe NO concentration is the result of exceeding the maximum

range of the gas analyser. This makes the measured cumulative emissions appear less than

the true quantities. The differences between the modelled and measured cumulative plots are

hence exaggerated. Apart from this measurement error, the discrepancies are also caused by the

engine-out NO modelling errors shortly after the cold start. The calculated emissions are higher

than expected for two reasons. Firstly, the engine-out NO model was calibrated based on fully

warm engine data, and hence, the effects of cold combustion chamber walls were not taken into

consideration. This can have a significant impact on the engine-out NO (Shayler et al., 1997).

Secondly, as seen from Table 5.3, engine-out NO is a strong function of the intake manifold

pressure. Consequently, the errors in the estimate of intake manifold pressure (see Figure 5.14)

additionally affect the calculated emissions. Nevertheless, the time to NO light-off is calculated

well and simulated tailpipe emissions, especially after catalyst light-off, agree reasonably closely

with the measurements.

Simulated and measured tailpipe HC emissions are shown in Figures 5.81 and 5.82. The

observed discrepancies in instantaneous emissions are largely caused by errors introduced in the

engine-out emissions model. Most of the trends, however, are nonetheless successfully reproduced

in the simulation, and calculated and measured cumulative emissions compare well.

5.6 Error analysis

To quantify the effects of error in the engine, engine-out emissions, exhaust system and the three-

way catalyst sub-models, a sensitivity analysis of tailpipe emissions to modelling error in several

of the key sub-model outputs was performed. Errors in each of the outputs were eliminated by

substitution of corresponding experimental results, such that

mcyl = m(m)cyl or (5.56)

Tcyl = T(m)cyl or (5.57)

150

0

0.5

1

1.5

2

2.5

3

3.5

4

0 50 100 150 200 250 300 350 400

CO

(%

mo

l/m

ol)

Time (s)


Figure 5.77: Measured and calculated instantaneous tailpipe CO emissions using the integratedmodel with a 2 node catalyst model (NEDC conditions)

0

5

10

15

20

25

0 50 100 150 200 250 300 350 400

CO

(g)

Time (s)


Figure 5.78: Measured and calculated cumulative tailpipe CO emissions using the integratedmodel with a 2 node catalyst model (NEDC conditions)

151

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 50 100 150 200 250 300 350 400

NO

(p

pm

)

Time (s)


Figure 5.79: Measured and calculated instantaneous tailpipe NO emissions using the integratedmodel with a 2 node catalyst model (NEDC conditions)

0

0.5

1

1.5

2

2.5

3

0 50 100 150 200 250 300 350 400

NO

(g)

Time (s)


Figure 5.80: Measured and calculated cumulative tailpipe NO emissions using the integratedmodel with a 2 node catalyst model (NEDC conditions)

152

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

0 50 100 150 200 250 300 350 400

HC

(p

pm

C1)

Time (s)


Figure 5.81: Measured and calculated instantaneous tailpipe HC emissions using the integratedmodel with a 2 node catalyst model (NEDC conditions)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 50 100 150 200 250 300 350 400

HC

(g)

Time (s)


Figure 5.82: Measured and calculated cumulative tailpipe HC emissions using the integratedmodel with a 2 node catalyst model (NEDC conditions)

153

Tem,out = T(m)em,out or (5.58)

Tcp,out = T(m)cp,out or (5.59)

eCO = e(m)CO or (5.60)

eNO = e(m)NO or (5.61)

eHC = e(m)HC (5.62)

at any one time. The integrated model specified by (4.123), (4.125) and ncat = 2 (excluding the

equations describing the dynamics of the variable subject to substitution) was then simulated

given the inputs

τrefbrake(t) = τ


N ref (t) = N (m)(t), (5.63b)

λ(t) = λ(m)(t), (5.63c)

θ(t) = θ(m)(t), (5.63d)



describing cold start NEDC and EUDC driving conditions. The errors obtained between mea-

sured and modelled cumulative tailpipe emissions are presented in Tables 5.9 and 5.10 for both

of these test cases. Note that the modelling uncertainties specified are with respect to measured

cumulative feedgas emissions.

The most significant improvement in the accuracy of simulated tailpipe CO emissions occurs

when measured exhaust mass flow rate mcyl or normalised engine-out CO emissions eCO are

substituted. Consequently, the largest errors appear to be introduced in the engine and engine-

out emissions models. As the accuracy in simulating mcyl and eCO is highly dependent on

the warm engine maps used in calibration, use of steady-state data covering a wider range of

operating conditions for calibrating the model is likely to reduce the errors observed.

When simulated engine-outNO emissions eNO are substituted by experimental results, errors

in the respective tailpipe emissions are almost eliminated in both of the test cases considered.

These errors, therefore, are mostly the result of the discrepancies in modelling eNO, which

is not surprising, as engine-out NO emissions are approximated by fully warm engine maps,

despite these emissions being considerably affected by engine temperatures during warm-up.

To minimise the modelling uncertainty, the static function describing eNO can be extended to

154

Var. replaced by

experimental data

Errors in overall cumulative

tailpipe emissions modelled

CO NO HC

– 13.9% 21.0% 1.3%

mcyl 9.0% 20.0% 2.1%Tcyl 17.9% 26.3% 4.7%Tem,out 14.3% 21.7% 0.0%Tcp,out 14.4% 22.0% 0.8%eCO 6.0% 21.3% 3.0%eNO 13.5% 2.7% 1.5%eHC 14.2% 20.7% 2.1%

Table 5.9: Sensitivity of tailpipe emissions to modelling error in 7 sub-model outputs for 400seconds of NEDC conditions, modelling error removed by replacing modelled output with mea-sured

Var. replaced by

experimental data

Errors in overall cumulative

tailpipe emissions modelled

CO NO HC

– 16.2% 14.8% 7.3%

mcyl 10.8% 17.4% 8.4%Tcyl 20.7% 23.0% 3.9%Tem,out 16.9% 17.2% 7.5%Tcp,out 16.4% 17.4% 8.2%eCO 15.9% 15.1% 7.3%eNO 15.6% 0.4% 7.3%eHC 14.9% 13.1% 4.9%

Table 5.10: Sensitivity of tailpipe emissions to modelling error in 7 sub-model outputs for 250seconds of cold start EUDC conditions, modelling error removed by replacing modelled outputwith measured

include an appropriate temperature dependence. This, however, may require other thermal

dynamics to be modelled and the complexity of the engine model to be increased.

In contrast to CO and NO, cumulative tailpipe HC emissions are simulated much more

accurately. Errors in these emissions appear to be affected by discrepancies in the engine,

engine-out emissions and exhaust system sub-models to a similar degree, suggesting that the

performance of several sub-models may need to be improved before considerable benefits in the

accuracy can be obtained.

155

5.7 Summary

The integrated cold start model of a spark ignition engine, an exhaust system and a three-way

catalyst, developed in the previous chapter, possesses a modular structure, which simplifies the

calibration process. In this chapter the components of this model were calibrated independently

of each other based on fully warm engine maps and the results from a single cold start transient

engine test.

The engine model was validated based on 3 transient tests. The results indicated that the

lumped parameter approximation of engine temperature was sufficient for accurately specifying

friction during engine warm-up. The largest error in cumulative fuel consumption attained after

a cold start test was 3.3%.

Using steady state data for a fully warm engine, it was empirically shown that feedgas

CO emissions were primarily a function of only λ, which agrees with the literature (Heywood,

1988). Nitric oxide emissions were found to be a strong function of many variables, including

intake manifold pressure, λ, spark timing, intake valve closing angle, valve overlap and to a lesser

extent the engine speed. Hydrocarbon emissions were shown to scale mainly with intake manifold

pressure, λ, spark timing and engine speed, whilst being relatively unaffected by cam timing.

Many of these trends, however, have previously been observed on other engines (Heywood, 1988,

Lumsden, 2004). Validation of the engine-out emissions model showed that whilst measured

and simulated instantaneous emissions did not always agree closely, cumulative emissions, which

are of greater importance for the optimal control problem considered in this thesis, agreed well.

Errors in cumulative CO, NO andHC emissions modelled were on the order of 3%, 12% and 1%.

The noticeably larger errors in NO emissions appear to be the result of using a warm engine

emissions model to predict cold start emissions. Surprisingly, HC emissions were relatively

unaffected by engine temperature.

The performance of catalyst models discretised using different numbers of nodes was com-

pared. It was found that the 2 node and 51 node models agreed reasonably well. By using

2 nodes the order of the model, and hence, the computational requirements could be greatly

reduced. For example, whilst it took on the order of a day to simulate the first 400 seconds of

NEDC on a desktop PC using the integrated model with a 51 node catalyst, roughly a minute

was required when a 2 node catalyst was used. The resulting integrated model can thus be of

low enough order to permit dynamic optimisation studies.

The performance of the combined model was verified, demonstrating for the first time that

an integrated physics-based model of an engine, an exhaust system and a three-way catalyst can

156

be used in real-time to simulate cold start tailpipe emissions and fuel consumption reasonably.

For the NEDC test case, the differences between modelled and measured cumulative tailpipe

emissions were on the order of 14% for CO and 2% for HC with respect to the measured

cumulative feedgas emissions. Differences in cumulative NO emissions appeared to be more

significant, but were exaggerated due to saturation of the gas analyser range. The overall fuel

consumption modelled was within 1.6% of that measured. Similar levels of accuracy were also

attained for the cold start EUDC test case.

157

Chapter 6

Minimising fuel consumption

under tailpipe emissions

constraints

A spark ignition engine control problem, where cold start fuel consumption is minimised under

cumulative tailpipe emissions constraints, has never been solved using an integrated physics-

based model of the engine, the exhaust system and the three-way catalyst. Having developed

and validated such model in previous chapters, it can now be included in dynamic optimisation

studies over a drive cycle. In this chapter, first, a general dynamic optimisation problem is

formulated. It is then simplified to suit the optimisation procedure and to reduce the compu-

tational requirements. The simplified problem is solved using iterative dynamic programming,

subject to two exhaust system configurations, to identify optimised engine control trajectories

and trends. The results are explicitly validated whenever possible.

6.1 Optimal control problem formulation

The dynamic optimisation problem is formulated as

u⋆c(t) = arg min

uc(t)Jcs(uc(t)), (6.1)

Jcs(uc(t)) =

∫ tcyc

0

mfuel(uc(t), t) dt, (6.2)

where constant tcyc corresponds to the duration of the drive cycle. The engine control vector uc,

uc = [λ, θ, ϑint, ϑovlp]T , (6.3)

159

is a subset of the integrated model input vector u from (4.124c), such that

u = [τrefbrake, N

ref ,uc]T . (6.4)

The brake torque τrefbrake and engine speed N ref define the driving conditions and are prescribed

previously measured trajectories,

τrefbrake(t) = τ

(m)brake(t), (6.5)

N ref (t) = N (m)(t). (6.6)

Vector u⋆c(t) refers to the optimal trajectory of the engine control setpoints, whilst variables in

uc are subject to optimisation and are constrained within physically reasonable ranges, such

that

λmin ≤ λ(t) ≤ λmax, (6.7)

θMBT (t) + θadv,min ≤ θ(t) ≤ θMBT (t) + θadv,max, (6.8)

ϑint,min ≤ ϑint(t) ≤ ϑint,max, (6.9)

ϑovlp,min ≤ ϑovlp(t) ≤ ϑovlp,max (6.10)

for some known function of spark advance θMBT (t), corresponding to the maximum brake torque

timing, and constants λmin, λmax, θadv,min, θadv,max, ϑint,min, ϑint,max, ϑovlp,min and ϑovlp,max.

To consider the dynamics of the integrated model, problem (6.1) must be constrained by model

equations (4.123) and (4.125), developed in Chapter 4. They are repeated here for convenience

in a compact form,

x(t) = Finteg (x(t), z(t),u(t)), (6.11a)

0 = Ginteg (x(t), z(t),u(t)), (6.11b)

[mfuel, mtp]T = Hinteg (x(t),u(t)), (6.11c)

where mtp = [mCO,out, mNO,out, mHC,out]T . For a catalyst discretised using ncat nodes, x(t) ∈

ℜ5+15ncat , z(t) ∈ ℜ3 and u(t) ∈ ℜ6.

To enable trends in optimal control trajectories to be identified for different exhaust systems,

an alternative formulation of the model is additionally required. To simulate a closely coupled

catalyst, the connecting pipe sub-model was removed, and the outlet boundary conditions of

the exhaust manifold were used to specify the inlet conditions for the catalyst. Consequently,

equations (4.68) and (4.74) for the connecting pipe were eliminated. The integrated model with

160

the new exhaust system can thus be specified by

x(t) = Finteg,ccc (x(t), z(t),u(t)), (6.12a)

0 = Ginteg,ccc (x(t), z(t),u(t)), (6.12b)

[mfuel, mtp]T = Hinteg (x(t),u(t)), (6.12c)

where x(t) ∈ ℜ4+15ncat , z(t) ∈ ℜ2 and u(t) ∈ ℜ6. Depending on whether an under-floor or a

closely-coupled catalyst configuration is required, either (6.11) or (6.12) will be substituted.

Tailpipe emissions are limited by

∫ tcyc

0

mtp(uc(t), t) dt < mtp,max, (6.13)

where vector mtp,max = [mCO,out,max,mNO,out,max,mHC,out,max]T specifies the maximum per-

missible cumulative tailpipe emissions.

The development of solutions to this optimisation problem over the full duration of the NEDC

cycle (tcyc = 1180 seconds) can be computationally very intensive. Furthermore, inequality

constraints (6.13) can be difficult to handle explicitly using iterative dynamic programming.

Thus, an approximation for this optimisation problem is considered.

6.2 Modified optimal control problem formulation

To reduce the computational requirements and improve the time resolution of the optimised

control policies, the cycle was limited to the first 400 seconds. This time frame included catalyst

light-off and covered engine warm-up from cold to almost fully warm operating conditions.

Furthermore, the number of control input variables in uc considered for optimisation was reduced

to make the optimisation feasible. Let uc be partitioned into vectors uco and ucu, containing

engine control setpoints that are subject and not subject to optimisation respectively,

uc = [ucu,uco]T . (6.14)

To handle (6.13) using iterative dynamic programming, these hard constraints were replaced

with barrier functions

bi(uco(t), t) =

0 for∫ t

0mi,out(uco(t), t) dt < mi,out,max,

1mi,out,max

∫ t

0 mi,out(uco(t), t) dt for∫ t

0 mi,out(uco(t), t) dt ≥ mi,out,max.

(6.15)

161

These functions are 0, if the constraints are satisfied, and greater than or equal to 1, when they

are violated. The cost Jcs was therefore modified to

Jcss(uco(t)) =

∫ tf

0

mfuel(uco(t), t)dt+wcon [bCO(uco(t), tf )+ bNO(uco(t), tf )+ bHC(uco(t), tf )],

(6.16)

where tf = 400 seconds. The parameter wcon determines the flexibility of the constraints. In

order to simulate hard constraints, the value for wcon selected was several orders of magnitude

larger than the overall fuel consumption.

Problem (6.1) can then be approximated by

u⋆co(t) = arg min

uco(t)Jcss(uco(t)). (6.17)

Alternatively, if uco(t) is specified by the offset uoffco (t) from some known trajectory uref

co (t), so

that

uco(t) = urefco (t) + uoff

co (t), (6.18)

then (6.17) can be rewritten as

u⋆co(t) = uref

co (t) + arg minu

offco (t)

Jcss(uco(uoffco (t))). (6.19)

Problems (6.17) and (6.19) are equivalent. However, (6.19) is better suited to implementations

in real ECU’s, where, for example, offsets from MBT can be used for specifying spark timing.

Iterative dynamic programming requires time to be discretised, and the time intervals consid-

ered in this optimisation are large with respect to some of the engine dynamics. From experience,

the solutions developed to (6.19) are often associated with lower values of Jcss, when some of

the variables in urefco (t) are prescribed time trajectories measured during a test with the built-in

ECU engine control strategy. Thus, solutions to (6.19) will be considered in this chapter. Due

to the course time discretisation used, however, certain types of trajectories, such as bang-bang,

could be missed. In another study (Keynejad, 2009), where a simpler cold start fuel consumption

minimisation problem was solved, the optimal engine control policy was predicted to be of the

switching type. Whilst such trajectories may not necessarily be optimal with respect to (6.19),

this possibility should nevertheless be investigated. The use of finer time grids in iterative dy-

namic programming will also be considered to test whether the solutions produced are time grid

independent.

The equality constraints are specified either by (6.11) or (6.12) with the catalyst model

discretised using ncat = 2. The input vector u is given by

u = [τrefbrake, N

ref ,ucu,uco]T . (6.20)

162

Euro-3 Euro-4mCO,out,max (g) 22.8 9.9mNO,out,max (g) 1.29 0.69mHC,out,max (g) 1.58 0.79

Table 6.1: Tailpipe emissions constraints for the first 400 seconds of the NEDC drive cycle

The brake torque τrefbrake, engine speed N ref and the unoptimised control variables ucu are pre-

scribed trajectories previously obtained from an NEDC test with the ECU engine control strat-

egy, such that

τrefbrake = τ

(m)brake, (6.21)

N ref = N (m), (6.22)

ucu = u(m)cu . (6.23)

Tailpipe emission limits mtp,max were based on Euro-3 and Euro-4, and approximated by

mtp,max =

∫ tf

0m

(m)tp dt

∫ tcyc

0m

(m)tp dt

dNEDC Si,NEDC , (6.24)

where m(m)tp are the mass flow rates of the pollutants measured over the NEDC using the built-in

ECU engine control strategy. The constants dNEDC and Si,NEDC are the total distance covered

by the vehicle, roughly equal to 11 km, and the legislated emissions limits in terms of the mass

of the pollutants per km travelled. The resulting constraints are provided in Table 6.1.

Several compositions of uco (and consequently urefco and uoff

co ), two sets of constraints on

uco and uoffco , and two integrated models, (6.11) and (6.12) were considered. These cases are

formulated below.

1. Optimal spark timing strategy for an under-floor catalyst with Euro-3 constraints

In this study integrated model equations were specified by (6.11), whilst tailpipe emissions

limits mtp,max were assigned values as indicated in Table 6.1 for Euro-3. Spark timing was

considered as the only optimisation variable. Hence,

uco = [θ(t)], (6.25)

urefco = [θ(m)(t)], (6.26)

uoffco = [θoff (t)], (6.27)

where θ(m)(t) was obtained from an NEDC test with a built-in engine control strategy.

The advantage of such formulation is that a zero uoffco vector could then be used as a

163

reasonable initial guess of the optimal control strategy in the first iteration of iterative

dynamic programming. To ensure that the engine operating conditions remained within

the range of data used in the calibration of the engine model, spark timing was constrained

according to

−10◦ ≤ θ(t) ≤ 50◦, (6.28)

θMBT (t) − 30◦ ≤ θ(t) ≤ θMBT (t) + 5◦ and (6.29)

θoff = 0◦ during the last 4 idle events. (6.30)

Violation of (6.28) or (6.29) resulted in saturation of θ(t) at the limiting value. The

maximum brake torque spark timing θMBT was specified by a static function of the form

θMBT =

2∑

i=0

2∑

j=0

2∑

k=0

aMBT,i,j,k piim λj Nk (6.31)

for pim ∈ x, λ ∈ uc, N = N ref and i + j + k ≤ 2, where parameters aMBT,i,j,k were

calibrated based on steady state data with spark timing sweeps for a fully warm engine.

The dependence of θMBT on other variables was not included due limitations of the data

set.

2. Optimal spark timing strategy for a close-coupled catalyst with Euro-3 constraints

To observe the trends in the optimised spark timing when switching to a close-coupled

catalyst, the integrated model used in the previous case formulation was replaced by (6.12),

whilst tailpipe emissions limits mtp,max and variables in uco, urefco and uoff

co remained

unchanged.

In case 1, constraints (6.28)–(6.30) were conservative, with θ specified by θ(m) during the

last 4 idle segments. Whilst relaxation of these constraints could lead to extrapolation

of the static surfaces used in the integrated model from the range of the steady state

calibration data (see Figure 5.1), this may, however, allow some additional trends in the

optimised strategies to be observed. In this study these constraints were relaxed, so that

−10◦ ≤θ(t) ≤ 50◦, (6.32)

θMBT (t) − 35◦ ≤θ(t) ≤ θMBT (t) + 10◦ and (6.33)

θoff ≤ 10◦ during the last 4 idle events. (6.34)

As shall be demonstrated, the trends in the optimised control policy due to the shift in the

catalyst position and relaxation of the spark timing constraints can be clearly distinguished.

Furthermore, the effect of only the catalyst position shift is considered in a separate case.

164

3. Optimal spark timing and λ strategy for an under-floor catalyst with Euro-3 constraints

This case considers the same model as in case 1, but the optimisation variables were

modified to include λ, i.e.

uco = [θ(t), λ(t)]T , (6.35)

urefco = [θ(m)(t), 0]T , (6.36)

uoffco = [θoff (t), λoff (t)]T . (6.37)

The constraints on these variables are specified by (6.32)–(6.34) and

0.9 ≤ λoff (t) ≤ 1.1. (6.38)

4. Optimal spark timing and λ strategy for a close-coupled catalyst with Euro-3 constraints

The formulation of the optimisation problem was identical to that of case 3, with the

exception that integrated model (6.12) was used in place of (6.11).

5. Optimal spark timing and λ strategy for a close-coupled catalyst with Euro-4 constraints

Similarly, the formulation of the optimisation problem was identical to that of case 4, with

the exception that Euro-4 constraints were assigned to mtp,max from Table 6.1.

6. Optimal spark and cam timing strategy for a close-coupled catalyst with Euro-3 constraints

This study considered integrated model (6.12) and tailpipe emissions limits mtp,max for

Euro-3 in Table 6.1. Spark timing and cam timing were simultaneously optimised, so that

uco = [θ(t), ϑint(t)]T , (6.39)

urefco = [θ(m)(t), ϑ

(m)int (t)]T , (6.40)

uoffco = [θoff (t), ϑint,off (t)]T . (6.41)

The constraints on spark timing variables were specified by (6.32)–(6.34) and inlet cam

timing was limited by

46.5◦ABDC ≤ ϑint,off ≤ 98.5◦ABDC. (6.42)

However, if the valve overlap control input ϑovlp was prescribed using (6.23), the available

range for the intake valve closing angle ϑint could be limited by the physical constraints

in the cam timing mechanism. For example, for some fixed amounts of valve overlap, it

165

may not be possible to advance the inlet cam-shaft to its limit, if the exhaust cam-shaft

is in the fully advanced position. Thus, to consider a wider range of possible ϑint in the

optimisation, the valve overlap should be specified in terms of ϑint, when the exhaust

cam-shaft is in the fully advanced state. In this study, (6.23) is therefore replaced with

λ = λ(m)(t), (6.43)

ϑovlp =

ϑ(m)ovlp(t) for ϑint(t) − ID + ϑ

(m)ovlp(t) > ϑexh,min

ϑexh,min − (ϑint(t) − ID) for ϑint(t) − ID + ϑ(m)ovlp(t) ≤ ϑexh,min,

(6.44)

where ID is the intake duration and ϑexh,min is the most advanced exhaust valve closing

angle. For this engine

ϑexh,min = −4.5◦ATDC. (6.45)

Solutions to (6.19) were produced using iterative dynamic programming (see Section 2.2).

The time period [0, tf ] was divided into 20 (and sometimes 40) stages of equal length. In studies

where dim(uco) = 2, variables in uco were discretised using 3 points, whilst for dim(uco) = 1, 5

points were used. The computational time needed to converge to a local optima on a modern

desktop PC was on the order of 3 days for dim(uco) = 2 and 1 day for dim(uco) = 1. Significantly

longer time was required if 40 time stages were considered.

6.3 Spark timing solution for an under-floor catalyst with

Euro-3 limits

6.3.1 ∆t = 20 second grid

Application of iterative dynamic programming to (6.19) for problem case 1, with time domain

discretised using evenly distributed intervals ∆t of 20 seconds, results in a spark timing strategy

as shown in Figure 6.1, where limits (6.29) are also indicated. The spark timing policy is

characterised by a period of initially high retard, where it is in close proximity of the lower limit

in (6.29). This is followed by a transition to near MBT spark timing, and finally, by near MBT

operation in later parts of the cycle, excluding idle. Recall that during warm engine idle, spark

timing was effectively excluded from the optimisation due to (6.30).

As the maximum indicated thermal efficiency is observed near MBT spark advance, retarding

the spark from that setpoint can lead to a reduction in the indicated efficiency. Under such

conditions, more heat is rejected with the exhaust, which causes the exhaust enthalpy at the

catalyst inlet to increase and enables the catalyst warm-up time to be reduced. The amount of

166

heat rejected is related to the exhaust gas temperature and fuel consumption, which are shown

in Figures 6.2 and 6.3. According to Figures 6.4–6.6 catalyst light-off occurs roughly 60 seconds

after engine start. Surprisingly, the optimised spark timing remains retarded from MBT until

approximately 130 seconds. The additional influx of heat appears to be required to raise the

catalyst temperature further, in order to achieve higher pollutant conversion efficiencies during

the acceleration event at roughly 120 seconds.

In later parts of the cycle, the optimised control strategy is expected to approach MBT spark

timing during non-idle periods. There are, however, noticeable differences between the two spark

timing. For example, roughly from 260 to 280 seconds the engine operating conditions are such

that the brake thermal efficiency is relatively insensitive to spark advance near the MBT setpoint.

Consequently, the optimised strategy is characterised by retarded ignition, allowingHC and NO

tailpipe emissions to be reduced considerably at the expense of a small fuel consumption penalty.

By the end of 400 seconds, cumulative HC emissions are almost at the Euro-3 limit, suggest-

ing that further reduction in fuel consumption may be limited by the emissions constraints. This

tradeoff between fuel consumption and tailpipe emissions, therefore, emphasises the opportunity

to improve fuel economy if the emissions are below the limits.

The optimised spark timing strategy was implemented on an engine. The performance of

the model can thus be assessed by comparing modelled and measured results. The observed

differences, however, additionally include the effects of imprecise control policy implementation,

caused primarily by phasing errors between the spark timing strategy and the prescribed en-

gine torque and speed trajectories, specifying the driving conditions. However, as seen from

Figures 6.2 and 6.3, these errors do not appear to be significant, and the exhaust port gas

temperature and fuel consumption results agree very well, while the emissions results in Fig-

ures 6.4–6.6 compare reasonably. The largest errors observed are related to the NO emissions,

which depend most strongly upon the combustion chamber temperatures. As discussed in Chap-

ter 5, one of the causes of the discrepancy is the neglect of this temperature dependence in the

engine-out emissions model. During engine warm-up the cylinder walls are relatively cool and

the peak temperatures during combustion are lower than in a warm engine. Consequently, NO

emissions, the formation of which is stimulated by the higher temperatures, are lower in a cold

engine, and the emissions are overestimated in the simulation.

In this study, errors in the simulated cumulative CO and NO tailpipe emissions were not

expected to affect the optimality of the control strategy produced. Both measured and modelled

quantities are well within the emission limits, and the respective constraints are inactive. As

167

both cumulativeHC tailpipe emissions and fuel consumption, the reduction of which was limited

primarily by these emissions, were accurately simulated by the model, the optimality of the engine

control policy produced was expected to be near the optimum.


To test whether the solution developed in Section 6.3.1 was time grid independent, the spark

timing strategy was reproduced on a grid with intervals ∆t fixed at 10 seconds. The resulting

spark timing policy, demonstrated in Figure 6.7, is characterised by a more significant retard in

the initial phase of the cycle, and a much sharper and earlier transition from highly retarded to

near MBT spark advance. The benefit in terms of the overall fuel consumption is roughly 1.4%

with respect to the strategy with ∆t = 20 seconds. Given the significant differences between

the two strategies, this improvement may at first appear unrealistically small. However, closer

examination reveals that much of the slower transition in the original spark timing strategy

occurs during idle, when the fuel flow rate is low. This makes cumulative fuel consumption and

tailpipe emissions relatively insensitive the shape of the transition in this case study.

6.3.3 Sensitivity of the results of optimisation using ∆t = 10 second

grid to modelling uncertainties

In Chapter 5.6 it was demonstrated that whilst errors in simulated fuel consumption tend to

be reasonably small, errors in calculated cumulative tailpipe emissions are generally much more

significant. As minimisation of fuel consumption after a cold start appears to be limited by

tailpipe emissions, the consequences of modelling uncertainties in these quantities on the results

of optimisation need to be examined.

Modelling uncertainties in tailpipe emissions depend strongly upon the assumptions embed-

ded in the catalyst model, as well as the accuracy of the calculated pre-catalyst exhaust gas

composition, temperature and mass flow rate. Chapter 5.6 revealed that much of the observed

disagreement between calculated and measured tailpipe emissions can be attributed to errors

arising in the engine-out emissions model. Consequently, for the purposes of this analysis the

engine-out emissions model will be viewed as the dominant source of error with respect to the

tailpipe emissions.

The results of optimisation in Section 6.3.1 indicate that minimisation of fuel consumption is

limited by HC tailpipe emissions, as their cumulative quantity closely approaches the emissions

constraints by 400 seconds. Errors in tailpipe, and consequently, engine-out HC emissions are

therefore expected to have the most significant effect on the solution to the optimal control

168

-10

0

10

20

30

40

50

Sp

ark

tim

ing

(C

AD

BT

DC

)

optimised Euro-3 strategylimits

0

30

60

0 50 100 150 200 250 300 350 400

Vehic

le (

km

/h)

Time (s)

Figure 6.1: Spark timing strategy optimised using ∆t = 20 sec grid under Euro-3 constraints forthe under-floor catalyst

0

200

400

600

800

1000

0 50 100 150 200 250 300 350 400

Exhaust

port

gas t

em

pera

ture

(˚C

)

Time (s)

measuredmodelled

Figure 6.2: Measured and modelled exhaust port gas temperature for the Euro-3/under-floorcatalyst spark timing strategy

169

0

50

100

150

200

250

300

0 50 100 150 200 250 300 350 400

Fu

el co

nsu

me

d (

g)

Time (s)

measuredmodelled

Figure 6.3: Measured and modelled fuel consumption for the Euro-3/under-floor catalyst sparktiming strategy

0

5

10

15

20

25

30

35

0 50 100 150 200 250 300 350 400

CO

(g)

Time (s)

Euro-3 constraint

feedgas, measuredfeedgas, modelledtailpipe, measuredtailpipe, modelled

Figure 6.4: Measured and modelled cumulative CO emissions for the Euro-3/under-floor catalystspark timing strategy

170

0

0.5

1

1.5

2

2.5

3

3.5

0 50 100 150 200 250 300 350 400

NO

(g

)

Time (s)

Euro-3 constraint


Figure 6.5: Measured and modelled cumulativeNO emissions for the Euro-3/under-floor catalystspark timing strategy

0

1

2

3

4

5

0 50 100 150 200 250 300 350 400

HC

(g)

Time (s)

Euro-3 constraint


Figure 6.6: Measured and modelled cumulativeHC emissions for the Euro-3/under-floor catalystspark timing strategy

171

-10

0

10

20

30

40

50S

pa

rk t

imin

g (

CA

D B

TD

C)

∆t = 10 sec∆t = 20 sec

limits for ∆t = 10 sec strategy

0

30

60

0 50 100 150 200 250 300 350 400

Vehic

le (

km

/h)

Time (s)

Figure 6.7: Spark timing strategy optimised using ∆t = 10 sec and ∆t = 20 sec grids underEuro-3 constraints for the under-floor catalyst

problem. To quantify the impact of these uncertainties, optimisation results of Section 6.3.2

were reproduced using a modified integrated model, where engine-out HC emissions eHC had

been scaled by -15% and +15% from the original calibration. The resulting optimised spark

timing strategies are shown in Figure 6.8. Their relative performance in terms of the overall fuel

consumption and cumulative tailpipe emissions achieved is summarised in Table 6.2.

Change with respect to re-sults of optimisation ob-tained using original modelcalibration

Engine-out HC emissionsscaled by -15%

Engine-out HC emissionsscaled by +15%

∆m⋆fuel -1.0% 0.9%

∆m⋆CO,out 8.3% -6.6%

∆m⋆NO,out 2.8% 2.6%

∆m⋆HC,out 0.0% 0.0%

Table 6.2: Sensitivity of optimised cumulative fuel consumption and tailpipe emissions to errorsin simulated engine-out HC emissions

As expected, the effect of underestimating engine-out HC emissions is an improvement in

the optimised fuel economy. Conversely, the effect of overestimating these emissions is a degra-

172

-10

0

10

20

30

40

50

Sp

ark

tim

ing

(C

AD

BT

DC

)

original model calibrationengine-out HC scaled by +15%engine-out HC scaled by -15%

0

30

60

0 50 100 150 200 250 300 350 400

Vehic

le (

km

/h)

Time (s)

Figure 6.8: Effect of errors in simulated engine-out HC emissions on the optimised spark timingstrategy (optimised using ∆t = 10 sec grids, Euro-3 constraints and the under-floor catalyst)

dation of this parameter. However, the impact of varying engine-out emissions by as much as

15% is surprisingly small, and the optimised fuel consumption falls within 1% of the results

obtained using an integrated model with the original calibration. Time traces of the spark tim-

ing strategies produced are also similar, with major differences characterised by the extent of

spark timing retard immediately after engine start and the timing of the transition to near MBT

spark advance. When engine-out HC emissions are overestimated, the optimised spark timing is

initially more significantly retarded (10◦ ATDC for the first 30 seconds) and transitions to MBT

timing earlier than in the original results or those with underestimated HC emissions. The more

significant spark timing retard contributes to faster catalyst warm-up at the cost of increased

fuel consumption, whilst earlier transition towards MBT timing helps to minimise that penalty.

6.3.4 Switching result

The results of the finer time grid in Section 6.3.2 suggest that the optimal spark advance strat-

egy might be of the bang–bang (switching) type, with the lower limit specified by the largest

acceptable retard and the upper limit by MBT spark timing, as similar strategies have been

previously predicted on simpler related problems (Keynejad, 2009). However, due to the high

173

complexity of the model, no rigorous proof can be provided at this stage.

To test if a switching strategy could yield an improved fuel economy, the spark timing policy

θsw(t) was prescribed the following form,

θsw(tsw, t) =

max(−10◦, θMBT (t) − 30◦) for t < tsw,

min(50◦, θMBT (t)) for t ≥ tsw,(6.46)

except during the last 4 idle events, when θsw(tsw, t) was set to the optimised trajectory of

Section 6.3.2. Note that such spark timing automatically satisfied (6.28)–(6.30). Prior to time

tsw, the strategy was specified by the most retarded spark timing possible under these constraints.

It was then switched to approach MBT timing, estimated using (6.31). The optimisation problem

was reformulated as

uco = [θsw(tsw, t)], (6.47)

t⋆sw = argmintsw

Jcss(uco), (6.48)

and solved using a line search procedure, yielding

t⋆sw = 61.3 sec. (6.49)

Figure 6.9 shows the effect of the switching time tsw on the overall fuel economy and tailpipe

emissions as simulated by the model. Whilst earlier switching tended to improve the fuel econ-

omy, it also appeared to violate cumulative tailpipe emissions limits, as less heat was made

available for the catalyst. Later switching caused more heat to be rejected into the exhaust,

which generally reduced overall tailpipe emissions, but increased fuel consumption. Surprisingly,

very late switching resulted in higher overall CO emissions. This was due to a significant rise

in engine-out CO emissions, some of which propagated through the hot catalyst. The switching

time t⋆sw was therefore a balanced compromise between cumulative tailpipe emissions and fuel

economy.

The performance of the switching strategy appears to approach that of the policy from

Section 6.3.2. The minimum value of the cost function Jcss was within 0.4% of the result

produced using iterative dynamic programming. However, further improvement may have been

limited by use of (6.31), which was only an approximation of MBT spark advance.

6.3.5 Validation of local optimality

Due to the tight schedule of the transient dynamometer facility at the University of Melbourne,

only the control policy of Section 6.3.1 was validated. This was not considered a problem, as

the associated cost function was reasonably close to those of Sections 6.3.2 and 6.3.4.

174

250

270

290

310

Fuel (g

)

0 5

10 15 20 25

Tailp

ipe C

O(g

)

Euro-3 constraint

0

1

2

3

Tailp

ipe N

O(g

)

Euro-3 constraint

0

1

2

3

4

0 20 40 60 80 100 120 140

Tailp

ipe H

C(g

)

Time of spark timing switch (s)

Euro-3 constraint

Figure 6.9: The effect of spark timing switching time on the overall fuel consumption and tailpipeemissions for the under-floor catalyst

To validate the solution to (6.19), the optimised spark timing was offset by −10◦, −5◦, 5◦

and 10◦. The perturbed control strategies were implemented on an engine and the results are

shown in Figures 6.10–6.13, where the offset of 0◦ corresponds to the optimised trajectory.

While the trajectories with retarded spark timing appear to satisfy the emissions constraints,

they result in an overall fuel consumption increase. Conversely, trajectories with more advanced

spark timing improve the fuel economy, but violate the hydrocarbon limits. The minimum

achievable fuel consumption, that allows the emissions constraints to be satisfied, corresponds

roughly to offset 0◦. Therefore, the experiments confirm the local optimality of the control

policy. Of course, this is not an exhaustive evaluation of the optimality. However, such would

require an impractically large number of experiments.

6.4 Spark timing solution for a close-coupled catalyst with

Euro-3 limits


In Section 6.3 it was demonstrated that as far as the cost function Jcss was concerned, there

were small differences between the results of optimisation using ∆t = 20 sec and ∆t = 10 sec

175

250

260

270

280

290

300

310

-15 -10 -5 0 5 10 15

Fu

el co

nsu

me

d (

g)

Constant spark timing advance from optimal (CAD)

Figure 6.10: Measured fuel consumption for perturbed spark timing trajectories

0

5

10

15

20

25

-15 -10 -5 0 5 10 15

Cum

ula

tive t

ailp

ipe C

O (

g)


Euro-3 constraint

Figure 6.11: Measured tailpipe CO emissions for perturbed spark timing trajectories

176

0

0.2

0.4

0.6

0.8

1

1.2

1.4

-15 -10 -5 0 5 10 15

Cu

mu

lative

ta

ilpip

e N

O (

g)


Euro-3 constraint

Figure 6.12: Measured tailpipe NO emissions for perturbed spark timing trajectories

0

0.4

0.8

1.2

1.6

2

2.4

2.8

-15 -10 -5 0 5 10 15

Cum

ula

tive t

ailp

ipe H

C (

g)


Euro-3 constraint

Figure 6.13: Measured tailpipe HC emissions for perturbed spark timing trajectories

177

time discretisation. Therefore, to reduce excessive computational requirements and to ensure

consistency between all of the results, all further studies were limited to ∆t = 20 sec grids.

Figure 6.14 illustrates the solution to (6.19) for problem case 2. The duration of the initial

spark timing retard appears to have been significantly reduced relative to the optimised control

policy for the under-floor catalyst. The additional enthalpy, available in the exhaust after the

elimination of the connecting pipe, stimulates the heating of the catalyst. The elevated catalyst

inlet temperatures are shown in Figure 6.15. The control policy is thus aimed more at improving

the fuel economy, rather than the conversion efficiency of the catalyst.

At the cost of slightly increased fuel consumption (see Figure 6.16), the spark timing is

heavily retarded during the first idle event. This increases the mass flow rate of the exhaust and

the catalyst inlet gas temperature, which helps to bring the catalyst to its operating temperature

quicker. Conversely, during the idle events in the later parts of the cycle, the spark timing is

advanced to the limit set by (6.34), which improves the fuel economy and also appears to favour

the slower cooling of the catalyst.

On average the optimised spark timing strategy is closer to MBT timing than the control

policy for the under-floor catalyst, enabling the engine to operate more efficiently, and thus, as

demonstrated in Figure 6.16, to consume less fuel. Figures 6.17–6.19 indicate that while this

additionally results in lower overall engine-out CO emissions, engine-out NO and HC emissions

are significantly increased. However, as the catalyst is exposed to higher inlet gas temperatures,

its conversion efficiency is enhanced, which results in very similar cumulative tailpipe emissions

to the case study with the under-floor catalyst. The time to catalyst light-off remains almost

fixed at 60 seconds for the two exhaust systems.


The aim of the following numerical experiment was to verify that a switching control policy was

capable of matching or improving upon the performance of the strategy identified in Section 6.4.1.

The procedure used here is analogous to that presented in Section 6.3.4. The spark timing

strategy was defined by

θsw(tsw, t) =

max(−10◦, θMBT (t) − 35◦) for t < tsw,

min(50◦, θMBT (t)) for t ≥ tsw,(6.50)

except during the last 4 idle events, when θsw(tsw, t) was set to the optimised trajectory of

Section 6.4.1. The static optimisation problem defined by (6.47) and (6.48) was then solved,

178

-10

0

10

20

30

40

50

Sp

ark

tim

ing

(C

AD

BT

DC

)

close-coupled catalyst strategyunder-floor catalyst strategyclose-coupled strategy limits

0

30

60

0 50 100 150 200 250 300 350 400

Vehic

le (

km

/h)

Time (s)

Figure 6.14: Spark timing strategies optimised under Euro-3 constraints for the under-floor andclose-coupled catalysts

0

200

400

600

800

1000

0 50 100 150 200 250 300 350 400

Cata

lyst

inle

t gas t

em

pera

ture

(˚C

)

Time (s)

under-floor catalyst strategyclose-coupled catalyst strategy

Figure 6.15: Modelled catalyst inlet gas temperature for the Euro-3/under-floor catalyst andEuro-3/close-coupled catalyst spark timing strategies

179

0

50

100

150

200

250

300

0 50 100 150 200 250 300 350 400

Fu

el co

nsu

me

d (

g)

Time (s)

under-floor catalyst strategyclose-coupled catalyst strategy

Figure 6.16: Modelled fuel consumption for the Euro-3/under-floor catalyst and Euro-3/close-coupled catalyst spark timing strategies

0

5

10

15

20

25

30

35

0 50 100 150 200 250 300 350 400

CO

(g)

Time (s)

Euro-3 constraint

under-floor catalyst strategy, feedgasclose-coupled catalyst strategy, feedgas

under-floor catalyst strategy, tailpipeclose-coupled catalyst strategy, tailpipe

Figure 6.17: Modelled cumulative CO emissions for the Euro-3/under-floor catalyst and Euro-3/close-coupled catalyst spark timing strategies

180

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 50 100 150 200 250 300 350 400

NO

(g

)

Time (s)

Euro-3 constraint



Figure 6.18: Modelled cumulative NO emissions for the Euro-3/under-floor catalyst and Euro-3/close-coupled catalyst spark timing strategies

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 50 100 150 200 250 300 350 400

HC

(g)

Time (s)

Euro-3 constraint



Figure 6.19: Modelled cumulative HC emissions for the Euro-3/under-floor catalyst and Euro-3/close-coupled catalyst spark timing strategies

181

producing

t⋆sw = 32.5 sec. (6.51)

The minimum value of the cost function Jcss agreed closely with the result of Section 6.4.1. The

performance of the switching control policy, therefore, closely approximates that of the strategy

produced using iterative dynamic programming, which is consistent with earlier findings from

Section 6.3.4.

6.5 Spark timing and λ solution for an under-floor catalyst

with Euro-3 limits


The solution to (6.19) for problem case 3, developed using ∆t = 20 sec time discretisation, is

presented in Figure 6.20. The strategy was implemented on an engine, and the output of a UEGO

sensor, positioned upstream of the catalyst, is included in the figure. Despite the difficulties in

tracking of the λ trajectory, simulated and measured exhaust gas temperature, fuel consumption

and emissions results in Figures 6.21–6.25 are in reasonable agreement.

The λ control policy was initially lean to help reduce engine-out, and consequently, cold

start tailpipe CO and HC emissions. In later parts of the cycle, however, it was transitioned to

near stoichiometric or slightly lean setpoints. The latter strategy compromised NO conversion

efficiency in the hot catalyst in favour of the fuel economy and lower tailpipe CO and HC

emissions. The conversion efficiency of these pollutants remained high due to the abundance of

oxygen under lean conditions. Whilst the engine-outNO emissions were generally low at idle (see

Figure 6.24), they were much more significant during some of the higher brake power operation,

which resulted in increased tailpipeNO emissions, causing both NO andHC cumulative tailpipe

emissions to fall onto the Euro-3 limits by the end of 400 seconds.

The trends in the spark timing strategy closely resembled those of problem cases 1 and 2

for ∆t = 20 sec, characterised by an initial period of high retard, transition towards MBT, and

then near MBT operation. With this strategy catalyst light-off occurred roughly at 60 seconds.

However, the spark timing was retarded significantly from the MBT setpoint for another 70

seconds. This provided additional heat for the catalyst, increasing its conversion efficiency

during some of the later higher power events, marked by the increased inflow of pollutants.

During idling periods with a hot catalyst, the spark timing was advanced to the limit specified

by (6.34). As previously, this helped to reduce the exhaust mass flow rate, and consequently,

slow down the cooling and deactivation of the catalyst.

182

-10

0

10

20

30

40

50

Sp

ark

tim

ing

(C

AD

BT

DC

)

Euro-3 strategylimits

0.9

1

1.1

λ

Euro-3 strategyimplementation

limits

0

30

60

0 50 100 150 200 250 300 350 400Vehic

le (

km

/h)

Time (s)

Figure 6.20: Spark timing and λ control strategies optimised under Euro-3 constraints for theunder-floor catalyst

0

200

400

600

800

1000

0 50 100 150 200 250 300 350 400

Exhaust

port

gas t

em

pera

ture

(˚C

)

Time (s)

measuredmodelled

Figure 6.21: Measured and modelled exhaust port gas temperature for the Euro-3/under-floorcatalyst spark timing and λ strategy

183

0

50

100

150

200

250

300

0 50 100 150 200 250 300 350 400

Fu

el co

nsu

me

d (

g)

Time (s)

measuredmodelled

Figure 6.22: Measured and modelled fuel consumption for the Euro-3/under-floor catalyst sparktiming and λ strategy

0

5

10

15

20

25

30

35

0 50 100 150 200 250 300 350 400

CO

(g)

Time (s)

Euro-3 constraint


Figure 6.23: Measured and modelled cumulative CO emissions for the Euro-3/under-floor cata-lyst spark timing and λ strategy

184

0

0.5

1

1.5

2

2.5

3

3.5

4

0 50 100 150 200 250 300 350 400

NO

(g

)

Time (s)

Euro-3 constraint


Figure 6.24: Measured and modelled cumulative NO emissions for the Euro-3/under-floor cat-alyst spark timing and λ strategy

0

1

2

3

4

5

0 50 100 150 200 250 300 350 400

HC

(g)

Time (s)

Euro-3 constraint


Figure 6.25: Measured and modelled cumulative HC emissions for the Euro-3/under-floor cat-alyst spark timing and λ strategy

185

The overall fuel consumption saving relative to the single parameter spark timing optimisation

results of problem case 1, developed using a ∆t = 20 sec grid was approximately 5.7%. This

was achieved at the cost of increased cumulative NO tailpipe emissions.


If spark timing is prescribed the switching form (6.50) then the dynamic optimisation problem

(6.19) and vectors uco and ucu can be replaced with the following,

uco =[θsw(tsw , t)], (6.52)

ucu =[λidp(t), ϑ(m)int , ϑ

(m)ovlp]

T , (6.53)

t⋆sw = argmintsw

Jcss(uco), (6.54)

where λidp(t) is the result of optimisation from Section 6.5.1. Solving (6.54) yielded

t⋆sw = 58.3 sec. (6.55)

The minimum value for the cost function Jcss was well within 1% of the result in Section 6.5.1.

Despite not having reoptimised the λ trajectory to suit the new spark timing, the performance

of the control strategy with the switching spark advance appears to approach the results of

iterative dynamic programming, which is consistent with previous observations.

6.6 Spark timing and λ solution for a close-coupled cata-

lyst with Euro-3 and Euro-4 limits


Solutions to problem (6.19), developed using ∆t = 20 sec time discretisation, for case studies

4 and 5 are presented in Figures 6.26 and 6.27, and compared in Figure 6.28. It appears that

to meet Euro-4 optimally, the ignition needs to be delayed by almost a constant crank-angle

from the optimised Euro-3 control policy during the first 100 seconds. This is expected to

increase the catalyst inlet gas temperature by up to 100◦ C, while penalising the overall fuel

consumption by roughly 4.2%, as indicated in Figures 6.29 and 6.30. Increasing the exhaust

mass flow rate and temperature at the catalyst inlet reduces the time to light-off and improves

the catalyst performance afterwards. For the remainder of the drive cycle, the two spark timing

strategies almost coincide, and neither the simulated fuel consumption nor the catalyst inlet gas

temperature are significantly affected by the small differences in the λ trajectories.

186

Figures 6.31–6.33 demonstrate modelled cumulative emissions. As previously, whilst all of

the cumulative tailpipe emissions constraints were fulfilled, both NO and HC emissions appear

to lie on the respective limits by the end of 400 seconds. Apart from the reduced catalyst warm-

up time and its slightly enhanced conversion efficiency, one of the major contributions towards

meeting the Euro-4 constraints comes from the significant reduction of engine-out emissions,

partly caused by a more significant spark retard and partly by the appropriate choice of λ at

various points in the cycle.

It appears that the primary role of the λ control policy is not to affect the catalyst inlet

enthalpy, but to offset the composition of engine-out emissions and control the conversion effi-

ciency of the catalyst. Relative proportions of tailpipe emissions can be redistributed to suit the

constraints, and thus allow use of more favourable spark timing strategies.


To test whether a switching spark timing strategy could match or outperform the results of

iterative dynamic programming, the spark advance trajectory was prescribed (6.50), vectors uco

and ucu were redefined using (6.52) and (6.53), with λidp(t) specified by the result of optimisation

from Section 6.6.1, and (6.54) was then solved. The results indicated that

t⋆sw = 13.7 sec (6.56)

for Euro-3 emissions constraints and

t⋆sw = 42.0 sec (6.57)

for Euro-4. As previously, in both of these cases the minimum values of cost functions Jcss were

within 1% of the results from Section 6.6.1, and thus, the performance of the switching policies

closely approximates iterative dynamic programming results.

6.7 Spark and cam timing solution for a close-coupled cat-

alyst with Euro-3 limits

The study examines the benefits of including cam timing in the dynamic optimisation. The

solution to problem (6.19) for case study 6 is visualised in Figure 6.34 along with the optimised

spark timing and measured ECU cam timing trajectories from case study 2.

The optimised spark timing strategies from the single and two parameter optimisation stud-

ies agreed closely during most of the drive cycle. Some of the most significant differences in the

187

-10

0

10

20

30

40

50S

pa

rk t

imin

g (

CA

D B

TD

C)


0.9

1

1.1

λ


0

30

60

0 50 100 150 200 250 300 350 400Vehic

le (

km

/h)

Time (s)

Figure 6.26: Spark timing and λ optimised under Euro-3 constraints for the close-coupled catalyst

-10

0

10

20

30

40

50

Spark

tim

ing (

CA

D B

TD

C)


0.9

1

1.1

λ


0

30

60

0 50 100 150 200 250 300 350 400Vehic

le (

km

/h)

Time (s)

Figure 6.27: Spark timing and λ optimised under Euro-4 constraints for the close-coupled catalyst

188

-10

0

10

20

30

40

50

Sp

ark

tim

ing

(C

AD

BT

DC

)

Euro-3 strategyEuro-4 strategy

0.9

1

1.1

λ


0

30

60

0 50 100 150 200 250 300 350 400Vehic

le (

km

/h)

Time (s)

Figure 6.28: Spark timing and λ optimised under Euro-3 and Euro-4 constraints for the close-coupled catalyst

0

200

400

600

800

1000

0 50 100 150 200 250 300 350 400

Cata

lyst

inle

t gas t

em

pera

ture

(˚C

)

Time (s)


Figure 6.29: Modelled catalyst inlet gas temperature for the spark timing and λ control policiesand the close-coupled catalyst

189

0

50

100

150

200

250

300

0 50 100 150 200 250 300 350 400

Fu

el co

nsu

me

d (

g)

Time (s)


Figure 6.30: Modelled fuel consumption for the spark timing and λ control policies and theclose-coupled catalyst

0

5

10

15

20

25

0 50 100 150 200 250 300 350 400

CO

(g)

Time (s)

Euro-3 constraint

Euro-4 constraint

Euro-3 strategy, feedgasEuro-4 strategy, feedgasEuro-3 strategy, tailpipeEuro-4 strategy, tailpipe

Figure 6.31: Modelled cumulative CO emissions for the spark timing and λ control policies andthe close-coupled catalyst

190

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 50 100 150 200 250 300 350 400

NO

(g

)

Time (s)

Euro-3 constraint

Euro-4 constraint


Figure 6.32: Modelled cumulative NO emissions for the spark timing and λ control policies andthe close-coupled catalyst

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 50 100 150 200 250 300 350 400

HC

(g)

Time (s)

Euro-3 constraint

Euro-4 constraint


Figure 6.33: Modelled cumulative HC emissions for the spark timing and λ control policies andthe close-coupled catalyst

191

spark timing (and cam timing) were observed between 80 and 120 seconds. However, neither fuel

economy nor emissions were greatly affected, as this time was characterised by a low fuel flow.

Figures 6.35 and 6.36 demonstrate that the modelled fuel consumption and exhaust port gas tem-

perature were not strongly affected by these differences. Consequently, the dynamic behaviour

of the catalyst was expected to be comparable to the single parameter optimisation result from

case study 2. Figures 6.37–6.39 confirm this by demonstrating very similar tailpipe emissions

for the two cases. Simulated cumulative tailpipe NO emissions increase only slightly due to the

increase in the respective engine-out emissions, but remain below the specified emissions limits.

There are several notable differences between the measured ECU and the optimised cam

timing. Firstly, under the ECU strategy, the inlet cam remains roughly in the fully advanced

(parked) state until approximately 120 seconds into the drive cycle. This was the result of low

oil pressure, which was inadequate for the cam timing actuators to function effectively. The

optimised inlet cam position is retarded during the first and the second “hill” in the NEDC

cycle, resembling the behaviour of the optimised and ECU strategies after 200 seconds, when

the driving conditions were repeated. This was expected to improve the fuel economy (see

Figure 6.35), and appears to be physically reasonable, as the engine cycle then approaches a

more efficient Atkinson cycle. Secondly, whilst the ECU strategy tends to retard the inlet cam

timing during later idle events, the optimised policy advances the cam to the limit and increases

the valve overlap. This is expected to reduce the fuel flow rate by approximately 2.3% during

these periods. Whilst this observation has not been backed up by experiments, it is nevertheless

not surprising, as the ECU idle management typically considers additional constraints, related

to engine noise and vibration.

The improvement in overall fuel economy of only 1.4% over the single parameter spark timing

optimisation result and reasonable agreement of the optimised and ECU cam timing trajectories

suggest that the ECU cam control strategy in this engine may already be near the expected

optimum.

6.8 Summary

In this chapter a cold start optimal engine control problem was studied, where fuel consumption

was minimised over the first 400 seconds of the NEDC under cumulative CO, NO and HC

tailpipe emissions constraints. The results indicated that tightening of these constraints led

to increased fuel consumption. This suggests that the energy contained in the additional fuel

can be effectively utilised to increase the catalyst temperature, and consequently, improve its

192

-10

0

10

20

30

40

50

Sp

ark

tim

ing

(CA

D B

TD

C)

40

60

80

100

IVC

(CA

D A

BD

C)

0

10

20

30

40

50

Ove

rla

p(C

AD

)

spark and cam strategyspark strategy

limits

0

30

60

0 50 100 150 200 250 300 350 400

Vehic

le(k

m/h

)

Time (s)

Figure 6.34: Optimised spark and cam timing trajectories for the close-coupled catalyst andEuro-3 constraints

0

50

100

150

200

250

300

0 50 100 150 200 250 300 350 400

Fuel consum

ed (

g)

Time (s)

Euro-3 spark and cam strategyEuro-3 spark strategy

Figure 6.35: Fuel consumption modelled using the optimised spark and cam timing for theclose-coupled catalyst and Euro-3 constraints

193

0

200

400

600

800

1000

0 50 100 150 200 250 300 350 400

Exh

au

st

po

rt g

as t

em

pe

ratu

re (

˚C)

Time (s)

Euro-3 spark and cam strategyEuro-3 spark strategy

Figure 6.36: Exhaust port gas temperature modelled using the optimised spark and cam timingfor the close-coupled catalyst and Euro-3 constraints

0

5

10

15

20

25

30

35

0 50 100 150 200 250 300 350 400

CO

(g)

Time (s)

Euro-3 constraint

Euro-3 spark and cam strategy, feedgasEuro-3 spark strategy, feedgas

Euro-3 spark and cam strategy, tailpipeEuro-3 spark strategy, tailpipe

Figure 6.37: CO emissions modelled using the optimised spark and cam timing for the close-coupled catalyst and Euro-3 constraints

194

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 50 100 150 200 250 300 350 400

NO

(g

)

Time (s)

Euro-3 constraint



Figure 6.38: NO emissions modelled using the optimised spark and cam timing for the close-coupled catalyst and Euro-3 constraints

0

1

2

3

4

5

0 50 100 150 200 250 300 350 400

HC

(g)

Time (s)

Euro-3 constraint



Figure 6.39: HC emissions modelled using the optimised spark and cam timing for the close-coupled catalyst and Euro-3 constraints

195

conversion efficiency. The performance of various control policies, developed using iterative

dynamic programming with ∆t = 20 sec time discretisation, are compared in Table 6.3 in terms

of the fuel consumption saving.

Optimisation variablesθoff θoff and λref θoff and ϑoff

Under-floor catalyst, Euro-3 0% 5.4%⋆

Close-coupled catalyst, Euro-3 7.4%⋆ 10.9%⋆ 8.7%⋆

Close-coupled catalyst, Euro-4 6.8%⋆

⋆ optimised with relaxed spark timing constraints

Table 6.3: Estimated fuel consumption saving for strategies developed using iterative dynamicprogramming with ∆t = 20 sec, relative to the single parameter spark timing optimisationresults for an under-floor catalyst and Euro-3 limits

Consequences of modelling uncertainties on the outcome of optimisation were studied briefly.

In the simplified analysis calculated engine-out emissions were taken as the dominant source

of error with respect to the tailpipe emissions. It was shown that scaling of engine-out HC

emissions by -15% and +15% affects the optimised cumulative fuel consumption by no more than

1%. Consequently, errors in simulated engine-out HC emissions are not expected to significantly

affect the performance of the engine control strategies developed.

The optimised spark timing was validated experimentally. It is characterised by a significant

ignition retard early in the drive cycle, followed by near MBT operation during later stages

(except idle). By using an accurately resolved time domain, a rapid transition between these

setpoints was demonstrated, resembling a bang-bang strategy. By artificially assigning a switch-

ing control policy from the most retarded spark timing possible under current model calibration

to MBT timing and optimising the switching time, the performance of the strategies developed

using iterative dynamic programming could be approached. Furthermore, due to uncertainties

in the specification of the MBT spark advance, it is likely that the performance of the switching

strategies could be improved. If the switching time is indeed the only parameter that needs to be

determined in the development of optimal spark timing policies, this could lead to a significant

simplification of cold start engine calibration.

The consequences of operating near MBT spark timing during some of the later idle events

have not been studied due to limitations in the model maps. However, it has been demonstrated

that advancing the spark timing towards the MBT setpoint could be beneficial, as far as the

optimal control strategy is concerned.

Close-coupled catalyst results showed that the duration of the initial spark timing retard was

196

expected to be shorter than for the case with the under-floor catalyst. Such strategy enabled

the engine to consume less fuel. Despite the substantial predicted increase in HC and NO

cumulative engine-out emissions, tailpipe emissions were expected to remain below the specified

limits, due to the improved conversion efficiency of the catalyst, which was exposed to higher

inlet gas temperatures. The optimal time to catalyst light-off appeared to be roughly fixed for

a given set of cumulative tailpipe emissions limits, irrespective of the catalyst position in the

exhaust system.

Iterative dynamic programming results additionally indicated that while the optimised Euro-

3 and Euro-4 ignition timing strategies for a close-coupled catalyst almost coincided in later parts

of the drive cycle, their timing differed by almost a constant crank-angle immediately after a cold

start. This observation is inconsistent with earlier switching strategy arguments, which assumed

switching to be initiated from the most retarded spark timing possible under current model

calibration. However, these results may be the consequence of using a coarse time discretisation

in the optimisation. Furthermore, as far as fuel economy is concerned, the performance of the

switching strategy was very similar.

Optimally scheduling both spark timing and λ provided additional benefits towards reducing

the fuel consumption. The trends in spark timing resembled those of the single parameter

optimisation. The λ trajectory was characterised by multiple switches and appeared to control

primarily the relative proportions of engine-out emissions and the conversion efficiency of the

catalyst. This was done is such a way, so that at least two of the overall cumulative tailpipe

emissions were at the specified limits. The redistribution of emissions was achieved with an

overall lean mixture, which was favourable to fuel economy.

The inclusion of cam timing in the optimisation problem did not yield a significant reduction

in the overall fuel consumption under the cumulative tailpipe emissions constraints considered.

This may suggest that the ECU cam control strategy, which was used for comparison, was already

near the expected optimum. If an exhaustive calibration is assumed to have been performed by

the engine manufacturer, the fact that the proposed and the ECU cam control strategies agreed

reasonably, especially during the higher power events, adds confidence to the results of the

optimisation.

197

Chapter 7

Conclusions

A new methodology for identifying optimal cold start engine control strategies was developed

and applied to a spark ignition engine with a three-way catalyst. The problem of minimising

cold start fuel consumption under cumulative tailpipe emissions constraints was studied for the

first time using a physics-based integrated model of an engine, an exhaust system and a catalyst.

The major contributions of this thesis are as follows.

1. Validated physics-based integrated model of an engine, an exhaust system and a three-way

catalyst

An integrated model of a spark ignition engine, the exhaust system and a three-way cat-

alyst was developed, and extends previous work. The model can calculate instantaneous

fuel consumption, as well as CO, NO and HC tailpipe emissions under transient driving

conditions, enabling quantitative comparison of different engine control policies. Whilst

existing models of similar functionality have been developed using mostly black-box ap-

proaches, this model is based on physical principles where practical, making it reasonably

accurate, modular, portable, more easily calibratable, and nonetheless, of low enough or-

der to permit integration into dynamic optimisation studies or real-time simulation. Only

warm engine maps and the results from a single transient engine and exhaust test are

required for complete model calibration.

The integrated model includes the following sub-models.

• A mean value engine model

This second order model considers engine warm-up and temperature dependent firing

friction. It calculates intake manifold pressure, exhaust port gas temperature and fuel

consumption as a function of engine control setpoints, based on the mass and energy

199

conservation equations, and a minimum set of empirical equations. The physics-based

approach used results in a modular and portable structure with a minimum number

of parameters to be calibrated.

Firing engine friction can differ considerably from motoring friction (Heywood, 1988),

primarily due to in-cylinder temperature and gas pressure loading differences. To the

author’s knowledge, this is the first engine model to explicitly consider cold start

firing friction, whilst other related models (Shayler et al., 1997, Manzie et al., 2009,

Keynejad and Manzie, 2011) have traditionally considered motoring friction correla-

tions similar to those of Sandoval and Heywood (2003) to approximate firing friction.

Furthermore, due to the highly empirical nature of those correlations, they may not

port easily between engines and may require recalibration based on stripped down

engine tests. The friction model introduced in this thesis does not require engine

disassembly and is expected to fit many engine designs using a simple calibration

procedure.

Whilst validated low order engine models simulating the exhaust port gas temperature

have previously been proposed (Fiengo et al., 2002, Manzie et al., 2009, Keynejad and

Manzie, 2011), they have been limited by slow temperature measurements. As this

temperature can have a significant influence on the catalyst response, fast response

thermocouples were used in this thesis to calibrate in-cylinder heat transfer coefficient

parameters and to demonstrate that the high frequency temperature dynamics can

be accurately modelled using the mean value approach.

• Engine-out emissions model

Due to the complexity of the emissions formation mechanisms, engine-out CO, NO

and HC emissions are approximated by static functions of the engine state and con-

trol setpoints. To simulate O2 and H2 emissions, which are additionally required by

the catalyst model, a new approach was developed. It is based on chemical equilib-

rium calculations and ensures consistency between the exhaust gas composition and

the commanded λ. Consequently, the need for calibratable O2 and H2 surfaces was

avoided.

• Exhaust manifold and connecting pipe models

The exhaust manifold and the connecting pipe are both modelled using a lumped

parameter approach. Warm-up behaviour and heat transfer between the exhaust gas

and inner surfaces, and between outer surfaces and the ambient air are considered.

200

These models estimate the gas temperature drop from the exhaust port to the catalyst

inlet.

• Three-way catalyst model

A one dimensional physics-based three-way catalyst model, integrating a chemical

kinetic scheme from Pontikakis and Stamatelos (2004), was formulated. The model

takes the exhaust mass flow rate, inlet gas temperature and molar fractions of the

major species as inputs, and calculates the respective molar fractions at the tailpipe.

The effect of grid resolution used to approximate fluid and substrate properties in

the axial direction was investigated to provide insight into the minimum modelling

requirements to capture key phenomena, such as light-off time and conversion ef-

ficiency. It was found that a 2 node approximation was sufficient to ensure close

agreement of simulated and measured tailpipe emissions under many operating con-

ditions. This resulted in a new validated physics-based model formulation of low

enough order to be useful in dynamic optimisation studies or real-time simulation.

Whilst this model can successfully capture catalyst warm-up, CO, NO and HC

light-off, oxygen storage and many other dynamics, only the results from a single

transient engine test are required for its calibration. Furthermore, the model is rel-

atively portable. Thus, for example, adaptation to another substrate geometry may

be possible without recalibration.

This integrated model was validated over the first 400 seconds of the NEDC drive cycle.

Differences between simulated and measured cumulative tailpipe emissions were on the

order of 14% for CO and 2% for HC with respect to the measured cumulative feedgas

emissions. Differences in cumulative tailpipeNO emissions appeared to be more significant,

but could not be quantified due to saturation of the NO gas analyser. The overall fuel

consumption modelled was within 1.6% of that measured.

2. Identification of optimised spark ignition engine control strategies and trends

Cold start fuel consumption from a spark ignition engine was minimised under cumula-

tive CO, NO and HC tailpipe emissions constraints over NEDC driving conditions. For

the first time physics-based models of the engine, the exhaust system and the catalyst,

described earlier, were included in the optimisation. To examine the trends in the engine

control policies produced, tailpipe emissions constraints based on Euro-3 and Euro-4, as

well as under-floor and close-coupled catalysts were considered.

201

The results showed that the reduction in fuel consumption was limited by the cumulative

tailpipe emissions constraints, i.e. more fuel was needed to satisfy Euro-4 limits as opposed

to Euro-3. This, therefore, indicates an opportunity to improve fuel economy, if cumulative

tailpipe emissions are below the limits.

An optimised spark timing strategy was developed and validated experimentally. It is

characterised by retarded timing during cold start, followed by a transition to near MBT

timing. These results suggested that a bang-bang type of approach might apply. To test

this, an ignition policy, defined initially by the most retarded spark timing possible under

current model calibration and MBT timing afterwards, was prescribed. It was demon-

strated that the overall fuel consumption approached the results of iterative dynamic pro-

gramming. The timing of the switch determined the tradeoff between cumulative tailpipe

emissions and fuel consumption. By switching early emphasis was placed on improving

the fuel economy at the expense of higher cumulative tailpipe emissions. Conversely, late

switching resulted in poorer fuel economy but tended to lower emissions.

The effect of additionally including a λ setpoint in the optimisation was to redistribute the

proportions of cumulative CO, NO and HC tailpipe emissions to better suit the emissions

constraints. The optimised λ trajectory was characterised by multiple switches and an

overall lean mixture, thus favouring the fuel economy.

The inclusion of cam timing in the optimisation problem did not yield a significant reduc-

tion in the overall fuel consumption under the cumulative tailpipe emissions constraints

considered. This may suggest that the ECU cam control strategy, which was used for

comparison, was already near the expected optimum.

7.1 Recommendations for further work

Recommendations for further work are summarised below.

1. Development of drive cycle-independent engine control strategies

If the key features of the deduced engine control trajectories, such as the spark timing

switching time, can be correlated to some of the measurable states, on-line implementation

of optimised control strategies could then be easily achieved. To investigate whether this is

possible, the current work needs to be extended to consider a variety of cold start driving

conditions, exhaust system configurations and tailpipe emissions limits.

202

2. Cold start engine-out emissions model

Whilst CO and HC emissions in the current work appeared to be weakly dependent on the

engine temperature, the sensitivity of NO emissions was much more significant. However,

as the related cold start effects could not be correlated well with any of the measured

temperatures for a wide range of driving conditions, engine-out emissions, specified by

(4.40)–(4.42), were calibrated based on fully warm engine data. To allow NOX emissions

to be simulated more accurately, the model should be extended to include, for example,

dependence on cylinder wall temperature, which has a direct effect on NOX production.

However, such measurements can be challenging to perform.

3. Particulate matter emissions

Euro-5 and the proposed future European standards require particulate matter (PM) emis-

sions from gasoline fuelled passenger cars to be controlled. To consider these emissions

in the dynamic optimisation, the integrated model needs to be supplemented by a PM

engine-out emissions model, and possibly, by aftertreatment models, which can addition-

ally consider PM removal if necessary.

4. Development of a transmission model

The integrated model of an engine, an exhaust system and a three-way catalyst developed

in this thesis can be extended with the model of a transmission. Thus, depending on the

type of transmission considered, either a reference gear (for a gearbox with a finite number

of gear ratios) or a continuous gear ratio (for a continuously variable transmission) could

be used as an additional control input. This would enable to quantify the effects of gear

shifting strategies on cold start fuel consumption and tailpipe emissions. The effects of

cold starting the transmission can also be included in the model and studied.

5. Optimisation of the gear shifting schedule and gear ratios

The proposed integrated model of a transmission, an engine, an exhaust system and a

three-way catalyst can then be included in optimisation studies over drive cycles, where

the gear shifting schedule and engine control setpoints are optimised to minimise cold start

fuel consumption under cumulative tailpipe emissions constraints. The results may be

useful in the development of control strategies for automated transmissions. Optimisation

of gearbox parameters, such as gear ratios, can be additionally performed to help choose

the most suitable transmission for a given vehicle.

203

6. Optimisation of inter-cylinder air-fuel ratios for low temperature catalyst light-off

Under lean exhaust conditions catalytic oxidation of carbon monoxide is possible at tem-

peratures significantly lower than typical light-off temperatures (Lafyatis et al., 1998). As

this reaction is highly exothermic, it can be used to accelerate catalyst light-off. However,

under lean engine operating conditions, engine-out CO emissions are generally low. One

way of significantly increasing the amount of CO (and H2, which is also easily oxidised)

in the exhaust, whilst maintaining an overall lean mixture, is to run some cylinders rich

and others lean. Optimisation of the inter-cylinder air-fuel ratios during cold start and

assessment of the possible benefits of this approach can be the subject of another inves-

tigation. The integrated model presented in this thesis can be easily extended to permit

such a study.

7. Development of a complete power-train model

The integrated model can be extended further to include driver and vehicle dynamics,

permitting cold start tailpipe emissions and fuel consumption to be calculated as a function

of vehicle speed profiles, as well as gear shifting and engine control strategies. Not only

would that allow to explicitly consider certain driving conditions, but also to perform

sensitivity analyses based on vehicle and driver characteristics.

8. Adaptation of the integrated model to Diesel engines, hybrids and related aftertreatment

systems

The physics-based integrated model concept introduced in this thesis can be adapted to

other types of engines and aftertreatment systems. Diesel engines fitted with oxidation

catalysts, particulate filters, NOX traps or selective catalytic reduction catalysts might be

good candidates, as would be hybrid vehicles and vehicles with so called “start-stop”.

9. Amendments to the reaction chemistry in the catalyst model to quantify the effects of cat-

alyst ageing, precious metal loading and washcoat composition

The chemical kinetic scheme used in this thesis does not explicitly consider washcoat com-

position, precious metal loading and the extent of ageing. Consequently, adaptation of the

model to a catalyst with a different washcoat formulation currently requires recalibration

of the model parameters. Whilst some attempts to quantify the effects of Pt : Rh : Pd

ratios and precious metal loading have been made (Pontikakis, 2003, Konstantas, 2006),

there is a great scope for further research in this field.

204

10. Monte Carlo analysis of the integrated model

Sensitivity of the integrated model outputs to the model parameters can be examined

using the Monte Carlo approach to help quantify how errors in these parameters affect the

overall modelling uncertainty.

205

Appendix A

Derivation of the catalyst model

equations

A.1 Energy conservation in the gas phase

For a system contained in a control volume (c.v.) and surrounded by a control surface (c.s.) the

first law of thermodynamics requires that the changes in the total energy Ec.v. are equal to the

sum of the work Wc.v. and the heat Qc.v. inputs,

Ec.v. = Wc.v. + Qc.v.. (A.1)

When considering the exhaust gas as the system, it can be shown using the Reynold’s transport

theorem (see Chapter 4.2.2) that

Ec.v. =∂

∂t

∫

c.v.

ρg(eg +1

2|v|2) dV +

∫

c.s.

ρg(eg +1

2|v|2)v · n dS. (A.2)

There is no mechanical work performed on the gas. Under the assumption of inviscid flow, the

rate of work input becomes

Wc.v. = −∫

c.s.

p v · n dS. (A.3)

Heat is added to the control volume by means of the convective heat transfer from the solid

phase Qh,s→g. Hence,

Qc.v. = Qh,s→g. (A.4)

Substitution of (A.2)–(A.4) into (A.1) gives

∂

∂t

∫

c.v.

ρg(eg +1

2|v|2) dV +

∫

c.s.

ρg(eg +1

2|v|2)v · n dS = −

∫

c.s.

p v · n dS + Qh,s→g. (A.5)

This can be rewritten in terms of only the volume integrals by converting the surface integrals

using the Gauss’s theorem,∫

c.s.

F · n dS =

∫

c.v.

∇ · F dV. (A.6)

207

By considering the continuous vector field F to be [ρg(eg + 12 |v|2) + p] v, equation (A.5) is

transformed into

∂

∂t

∫

c.v.

ρg(eg +1

2|v|2) dV +

∫

c.v.

∇ · ([ρg(eg +1

2|v|2) + p] v) dV = Qh,s→g. (A.7)

In one dimension Qh,s→g can be based on the heat transfer coefficient hgs and the temperature

difference between the solid (Ts) and the gas (Tg) phases,

Qh,s→g =

∫

c.v.

Pe hgs (Ts − Tg) dx. (A.8)

Equation (A.7) can then be rewritten as

∂

∂t

∫

c.v.

ρg(eg +1

2u2)Aec dx+

∫

c.v.

∂

∂x

(

ρg u (eg +1

2u2) + u p

)

Aec dx =

∫

c.v.

Pehgs (Ts−Tg) dx.

(A.9)

Because the effective cross-sectional area of the gas phase Aec and the effective channel perimeter

Pe are constant, (A.9) can be simplified to

∂

∂t

∫

c.v.

ρg(eg +1

2u2) dx+

∫

c.v.

∂

∂x

(

ρg u (eg +1

2u2) + u p

)

dx =Pe

Aec

∫

c.v.

hgs (Ts − Tg) dx.

(A.10)

Differentiation using the chain rule gives

∫

c.v.

(

eg +1

2u2

)

∂ρg

∂t+ ρg

(

∂eg

∂t+ u

∂u

∂t

)

+

(

eg +1

2u2

)

∂(ρgu)

∂x+ ρgu

(

∂eg

∂x+ u

∂u

∂x

)

(A.11)

+p∂u

∂x+ u

∂p

∂xdx =

Pe

Aec

∫

c.v.

hgs (Ts − Tg) dx

or

(

eg +1

2u2

) (

∂ρg

∂t+∂(ρgu)

∂x

)

+ ρg

(

∂eg

∂t+ u

∂u

∂t

)

+ ρgu

(

∂eg

∂x+ u

∂u

∂x

)

+ p∂u

∂x+ u

∂p

∂x(A.12)

=Pe

Aechgs (Ts − Tg).

However, continuity requires∂ρg

∂t +∂(ρgu)

∂x = 0. Hence,

ρg

(

∂eg

∂t+ u

∂eg

∂x

)

+ ρgu

(

∂u

∂t+ u

∂u

∂x

)

+ p∂u

∂x+ u

∂p

∂x=

Pe

Aechgs (Ts − Tg). (A.13)

Equation (A.13) can be simplified further without additional assumptions. Consider the momen-

tum equation arising from the Reynold’s transport theorem (4.5) with the extensive property

being the momentum in the stream-wise direction mu of a moving fluid particle,

∂

∂t

∫

c.v.

ρgu dV +

∫

c.s.

(ρgu) v · n dS = −∫

c.s.

p i · n dS, (A.14)

208

where i is a unit vector in the stream-wise direction and −∫

c.s. p i · n dS is the net force, acting

on the control surface (viscous forces are excluded). By converting the surface integrals into the

volume integrals using the Gauss’s theorem (A.6), the following equation is obtained,

∂

∂t

∫

c.v.

ρgu dV +

∫

c.v.

∇ · (ρguv) dV = −∫

c.v.

∇ · (p i) dV. (A.15)

For the one-dimensional case considered here, the equation reduces to

∂p

∂x= −∂(ρgu)

∂t− ∂(ρgu

2)

∂x. (A.16)

By expanding the derivatives using the chain rule, it follows that

∂p

∂x= −ρg

∂u

∂t− u

∂ρg

∂t− 2ρgu

∂u

∂x− u2∂ρg

∂x

= −ρg

(

∂u

∂t+ u

∂u

∂x

)

− ρgu∂u

∂x− u

∂ρg

∂t− u2 ∂ρg

∂x(A.17)

Substituting the continuity equation∂ρg

∂t = −∂(ρgu)∂x gives

∂p

∂x= −ρg

(

∂u

∂t+ u

∂u

∂x

)

− ρgu∂u

∂x+ u

∂(ρgu)

∂x− u2 ∂ρg

∂x

= −ρg

(

∂u

∂t+ u

∂u

∂x

)

− ρgu∂u

∂x+ ρgu

∂u

∂x+ u2 ∂ρg

∂x− u2 ∂ρg

∂x

= −ρg

(

∂u

∂t+ u

∂u

∂x

)

. (A.18)

According to (A.18) the terms ρgu(

∂u∂t + u∂u

∂x

)

and u ∂p∂x in (A.13) cancel. Hence,

ρg

(

∂eg

∂t+ u

∂eg

∂x

)

+ p∂u

∂x=

Pe

Aechgs (Ts − Tg), (A.19)

or in a more compact form,

ρgDeg

Dt+ p

∂u

∂x=

Pe


If the internal energy is expressed as eg = hg − pρg

, the equation becomes

ρgDhg

Dt− Dp

Dt+

p

ρg

Dρg

Dt+ p

∂u

∂x=

Pe


By taking advantage of the continuity equation∂ρg

∂t = −∂(ρgu)∂x the derivative

Dρg

Dt can be rewrit-

ten as

Dρg

Dt=

∂ρg

∂t+ u

∂ρg

∂x

= −∂(ρgu)

∂x+ u

∂ρg

∂x

= −ρg∂u

∂x− u

∂ρg

∂x+ u

∂ρg

∂x

= −ρg∂u

∂x. (A.22)

209

It follows that the terms pρg

Dρg

Dt and p∂u∂x in (A.21) cancel, producing

ρgDhg

Dt− Dp

Dt=

Pe


It has been demonstrated (Panton, 2005) using dimensionless analysis that for low Mach number

flows, such as those observed in three-way catalysts, DpDt is small. The equation can therefore be

approximated by

ρgDhg

Dt=

Pe


Rearranging, expanding the substantial derivative and expressing enthalpy hg in terms of the

gas temperature Tg gives

Aec ρg cp

(

∂Tg

∂t+ u

∂Tg

∂x

)

= Pe hgs (Ts − Tg). (A.25)

The gas velocity u can be written in terms of the mass flow rate input mcyl as

u =mcyl

Aec ρg. (A.26)

Equation (A.25) then becomes

Aec ρg cp∂Tg

∂t+ mcyl cp

∂Tg

∂x= Pe hgs (Ts − Tg). (A.27)

By dividing both sides of the equation by the substrate cross-sectional area Ac and evaluating

gas density ρg at atmospheric pressure pamb using the ideal gas law ρg = pamb

R Tg, the final form of

the energy equation is obtained,

ǫpamb cpR Tg

∂Tg

∂t+mcyl cpAc

∂Tg

∂x= S hgs (Ts − Tg), (A.28)

where ǫ = Aec

Acis the void fraction and S = Pe

Acis the geometric surface area per unit reactor

volume.

A.2 Energy conservation in the solid phase

Let a fragment of the monolith including the washcoat layer be the system enclosed by a control

surface (c.s.) and contained in a control volume (c.v.). The first law of thermodynamics requires

Ec.v. = Qc.v.. (A.29)

Note that the mechanical work induced on the system is expected to be small and is neglected.

The total energy of the system is

Ec.v. =∂

∂t

∫

c.v.

ρs es dV. (A.30)

210

Heat is added to the control volume by means of forced convection Qh,g→s, conduction Qk in

the solid phase and heat generation from the reactions Qr. Losses to the ambient environment

are not considered, as modern catalysts are normally well insulated. The total heat added is

thus

Qc.v. = Qh,g→s + Qk + Qr. (A.31)

Substituting (A.30) and (A.31) into (A.29) gives

∂

∂t

∫

c.v.

ρs es dV = Qh,g→s + Qk + Qr. (A.32)

For the one-dimensional case (A.32) becomes

∂

∂t

∫

c.v.

ρs es (Ac −Aec) dx =

∫

c.v.

Pe hgs (Tg − Ts) dx+

∫

c.s.

ks∂Ts

∂xi · n dS

−∫

c.v.

Nr∑

i=1

(Rr,i ∆hr,i) w lw Pe dx, (A.33)

where the integrals on the right hand side of the equation correspond to Qh,g→s, Qk and Qr

respectively. Converting the surface integral to a volume integral using the Gauss’s theorem

(A.6) and differentiating both sides of the equation with respect to x produces

(Ac −Aec)∂(ρs es)

∂t= Pe hgs (Tg − Ts) + (Ac −Aec) ks

∂2Ts

∂x2− w lw Pe

Nr∑

i=1

Rr,i ∆hr,i. (A.34)

By expressing the internal energy es in terms of temperature Ts and assuming constant solid

phase density ρs and specific heat cs, it follows that

(Ac −Aec) ρs cs∂Ts

∂t= Pe hgs (Tg − Ts) + (Ac −Aec) ks

∂2Ts

∂x2− w lw Pe

Nr∑

i=1

Rr,i ∆hr,i. (A.35)

Finally, dividing both sides of the equation by Ac gives

ρs cs (1 − ǫ)∂Ts

∂t= S hgs (Tg − Ts) + ks (1 − ǫ)

∂2Ts

∂x2− lw α

Nr∑

i=1

Rr,i ∆hr,i. (A.36)

A.3 Mass conservation in the gas phase

Consider the exhaust gas in the channels of the monolith, contained in a control volume (c.v.)

and surrounded by a control surface (c.s.). If ni is the amount of species i contained in the

moving gas of mass m, then according to the Reynold’s transport theorem (4.5)

Dni

Dt=D

(

Cg,i

Mgm

)

Dt=

∂

∂t

∫

c.v.

ρgCg,i

MgdV +

∫

c.s.

(

ρgCg,i

Mg

)

v · n dS. (A.37)

211

Molecules can leave or enter the exhaust gas by means of diffusion away or towards the washcoat

layer. Diffusion of the species in the axial direction is can be neglected as the diffusion velocities

of all species are expected to be much smaller than the average velocity of the flow in the

monolith. To account for the mass transport in the orthogonal direction to the flow, (A.37) is

balanced by a source term,

∂

∂t

∫

c.v.

ρgCg,i

MgdV +

∫

c.s.

(

ρgCg,i

Mg

)

v · n dS =

∫

c.v.

ϕi dV, (A.38)

where ϕs→g,i is the addition rate of species i per unit volume. Using the Gauss’s theorem (A.6)

to convert the surface integral into a volume integral produces

∂

∂t

∫

c.v.

ρgCg,i

MgdV +

∫

c.v.

∇ ·(

ρgCg,i

Mgv

)

dV =

∫

c.v.

ϕs→g,i dV. (A.39)

Assuming constant Mg, differentiating both sides of the equation with respect to V and rear-

ranging gives∂(ρg Cg,i)

∂t+ ∇ · (ρg Cg,i v) = Mg ϕs→g,i. (A.40)

Expanding the terms using the chain rule results in

ρg∂Cg,i

∂t+ Cg,i

∂ρg

∂t+ ρg v · ∇Cg,i + Cg,i∇ · (ρg v) = Mg ϕs→g,i. (A.41)

With the substitution of the continuity equationdρg

dt = −∇ · (ρgv), (A.41) is simplified to

ρg∂Cg,i

∂t+ ρg v · ∇Cg,i = Mg ϕs→g,i. (A.42)

For a one-dimensional problem this reduces to

ρg∂Cg,i

∂t+ ρg u

∂Cg,i

∂x= Mg ϕs→g,i. (A.43)

The diffusion of species away from the washcoat can be modelled with a mass transfer coefficient

defined as

hm,gs,i =ns→g,i

A ∆CV,i, (A.44)

where ns→g,i is the transfer rate of species i in mol/s, A is the effective mass transfer area in

m2 and ∆CV,i is the concentration difference in mol/m3. Therefore, for a small change along

the spatial coordinate δx,

ns→g,i = hm,gs,i Pe δx (Cs,i − Cg,i)ρg

Mg. (A.45)

It follows that

ϕs→g,i =ns→g,i

Aec δx= hm,gs,i

Pe

Aec

ρg

Mg(Cs,i − Cg,i) . (A.46)

212

Substitution of (A.46) into (A.43) yields

Aec ρg∂Cg,i

∂t+Aec ρg u

∂Cg,i

∂x= hm,gs,i Pe ρg (Cs,i − Cg,i) . (A.47)

The velocity u can be expressed in terms of the mass flow rate input mcyl as in (A.26), giving

Aec ρg∂Cg,i

∂t+ mcyl

∂Cg,i

∂x= hm,gs,i Pe ρg (Cs,i − Cg,i) . (A.48)

Finally, dividing both sides of the equation by Ac produces

ǫ ρg∂Cg,i

∂t+mcyl

Ac

∂Cg,i

∂x= S ρg hm,gs,i (Cs,i − Cg,i) . (A.49)

A.4 Mass conservation in the washcoat

The mass balance equations for the species in the washcoat layer are derived using a similar

procedure to that described in Chapter A.3, with the exception that the volume and the surface

integrals are evaluated under the washcoat exhaust gas conditions and two source terms are

considered. With these differences in mind, the mass balance equation (A.43) is rewritten as

ρg∂Cs,i

∂t+ ρg u

∂Cs,i

∂x= Mg ϕg→s,i −Mg ϕc,i, (A.50)

where ϕg→s,i is the rate of migration of species i from the bulk stream and ϕc,i is the consumption

rate of the species per unit washcoat volume. These terms can be evaluated as

ϕg→s,i =−ns→g,i

Pe lw δx

= hm,gs,i1

lw(Cg,i − Cs,i)

ρg

Mg, (A.51)

ϕc,i =Rc,i Pe lw w δx

Pe lw δx

= Rc,i w, (A.52)

where δx is a small displacement in the stream-wise direction. The velocity of the exhaust gas u

is expected to be small due to the large degree of obstruction inside the washcoat layer. Hence,

the term ρg u∂Cs,i

∂x can be eliminated from (A.50). Substituting (A.51) and (A.52) into (A.50)

then gives

ρg∂Cs,i

∂t=

1

lwρg hm,gs,i (Cg,i − Cs,i) − wMg Rc,i. (A.53)

Multiplying both sides of the equation by S produces

S ρg∂Cs,i

∂t=

S

lwρg hm,gs,i (Cg,i − Cs,i) − αMg Rc,i. (A.54)

213

Appendix B

Volumetric and indicated

efficiency parameters

The parameters for the volumetric and net indicated efficiency, specified by (5.9) and (5.13) are

presented in Table B.1 for pim expressed in terms of kPa, θ in terms of CAD BTDC, ϑint in

terms of CAD relative to 58.5 CAD ABDC and ϑovlp in terms of CAD of valve overlap.

ηind,net parameters ηvol parameters

aind,0,0,0,0,0,0 −8.4001× 10−1 avol,0,0,0,0,0 3.5689× 10−1

aind,0,0,0,0,0,1 3.4125× 10−5 avol,0,0,0,0,1 1.8431× 10−4

aind,0,0,0,0,0,2 −6.2929× 10−9 avol,0,0,0,0,2 −3.6965× 10−8

aind,0,0,0,0,1,0 1.536× 10−3 avol,0,0,0,1,0 1.6316× 10−3

aind,0,0,0,0,1,1 6.8762× 10−7 avol,0,0,0,1,1 1.7808× 10−6

aind,0,0,0,0,2,0 −5.1696× 10−5 avol,0,0,0,2,0 −9.6684× 10−5

aind,0,0,0,1,0,0 1.211× 10−3 avol,0,0,1,0,0 −2.7419× 10−4

aind,0,0,0,1,0,1 5.2989× 10−7 avol,0,0,1,0,1 3.4818× 10−7

aind,0,0,0,1,1,0 −8.6462× 10−5 avol,0,0,1,1,0 −1.3453× 10−4

aind,0,0,0,2,0,0 −6.1361× 10−5 avol,0,0,2,0,0 −1.1835× 10−4

aind,0,0,1,0,0,0 8.6231× 10−4 avol,0,1,0,0,0 −2.0586× 10−1

aind,0,0,1,0,0,1 1.2589× 10−6 avol,0,1,0,0,1 −1.6754× 10−5

aind,0,0,1,0,1,0 4.4078× 10−5 avol,0,1,0,1,0 −9.5532× 10−4

aind,0,0,1,1,0,0 5.3959× 10−5 avol,0,1,1,0,0 1.1206× 10−3

aind,0,0,2,0,0,0 −1.2642× 10−4 avol,0,2,0,0,0 1.1292× 10−1

aind,0,1,0,0,0,0 1.4883 avol,1,0,0,0,0 8.8101× 10−3

aind,0,1,0,0,0,1 −4.1641× 10−5 avol,1,0,0,0,1 −8.2443× 10−7

215

aind,0,1,0,0,1,0 −2.7417× 10−3 avol,1,0,0,1,0 2.9296× 10−5

aind,0,1,0,1,0,0 −3.6511× 10−3 avol,1,0,1,0,0 1.4431× 10−5

aind,0,1,1,0,0,0 8.8654× 10−3 avol,1,1,0,0,0 1.5496× 10−4

aind,0,2,0,0,0,0 −9.4752× 10−1 avol,2,0,0,0,0 −5.2594× 10−5

aind,1,0,0,0,0,0 8.2314× 10−3

aind,1,0,0,0,0,1 −4.9836× 10−7

aind,1,0,0,0,1,0 4.4968× 10−5

aind,1,0,0,1,0,0 6.3069× 10−5

aind,1,0,1,0,0,0 −8.5707× 10−5

aind,1,1,0,0,0,0 8.5054× 10−3

aind,2,0,0,0,0,0 −1.1767× 10−4

Table B.1: Indicated and volumetric efficiency parameters

216

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Minerva Access is the Institutional Repository of The University of Melbourne

Author/s:ANDRIANOV, DENIS

Title:Minimising cold start fuel consumption and emissions from a gasoline fuelled engine

Date:2011

Citation:Andrianov, D. (2011). Minimising cold start fuel consumption and emissions from a gasolinefuelled engine. PhD thesis, Engineering, Mechanical Engineering, The University ofMelbourne.

Persistent Link:http://hdl.handle.net/11343/36827

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