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Detailed Modelling of CO2 Addition Effects on the Evolution ofParticle Size Distribution Functions in Premixed Ethylene Flames

by

Ali Naseri

A thesis submitted in conformity with the requirementsfor the degree of Master of Applied Science

Graduate Department of Mechanical and Industrial EngineeringUniversity of Toronto

c© Copyright 2016 by Ali Naseri

Abstract

Detailed Modelling of CO2 Addition Effects on the Evolution of Particle Size Distribution Functions in

Premixed Ethylene Flames

Ali Naseri

Master of Applied Science

Graduate Department of Mechanical and Industrial Engineering

University of Toronto

2016

This study investigates computationally the influence of CO2 addition on the sooting behavior in pre-

mixed ethylene/ oxygen/ argon burner stabilized stagnation flames at the atmospheric pressure. The

discrete sectional approach combined with a reversible nucleation model and a novel model of reversible

polycyclic aromatic hydrocarbon (PAH) condensation were employed to solve the size evolution of the

particle size distribution function (PSDF). The predicted temperature profiles and PSDFs are in rea-

sonably good agreement with the experimental data for nascent soot measured in the burner stabilized

stagnation configuration. The evolution of the PSDFs shows that CO2 addition reduces the soot nucle-

ation and mass growth rates, consequently lowering the soot yield. The addition of CO2 reduces the

concentrations of H, C2H2, and C6H6, which all suppress the soot formation process through a chemical

effect, while its thermal effect is negligible.

ii

Dedication

To my family and my friends,

for their love, support, and encouragement.

iii

Acknowledgements

Firstly, I am so grateful to almighty God, who led me in this path. When I was leaving my country

to start this journey he was the one whom I have been trusting and pacified me in the tough situations.

I hope that he will not forget me and forgive me for my mistakes, so that I can receive his guidance to

continue my path and succeed.

I Would like to thank my lovely supervisor Professor Murray J. Thomson from the bottom my heart

for his constant support and guidance during my master’s study. Not only has he been a wise advisor

and a passionate leader, but also he has been a real friend to me. When I visited Professor Thomson on

the U of T campus for the first time, I discussed my concerns with him, and after a short talk I found

myself relaxed and hopeful for the future. Beside the knowledge, I have learned many valuable things

such as ethics and patience from him.

Moreover, I want to express my deepest gratitude to my dear family for their incessant love, support,

and passion even from thousands of miles away from me. Much appreciation to my lovely parent who

have spent their whole life for my progress and success, and sacrificed, so that I can make my dreams.

I thank my darling sister who has always been helpful and considerate to me. My family is my main

motivation to continue graduate studies.

Finally, I would like to thank Combustion Research Laboratory members and staff, specifically, Dr.

Armin Veshkini for sharing his knowledge and expertise with me, Dr. Mohammad Reza Kholghy for his

support and friendship, Dr. Yashar Afarin, Dr. Nick Eaves, Anton Sediako, Sina Zadmajid, Tongfeng

Zhang, and Tirthankar Mitra.

iv

Contents

1 Introduction 1

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.1 Soot Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.2 Soot Formation Pathways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2.3 CO2 Addition Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.2.4 Soot Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.3 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2 Methodology 11

2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2 Burner Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.3 Gas-Phase Governing Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.3.1 Conservation of Mass and Momentum . . . . . . . . . . . . . . . . . . . . . . . . . 13

The 2D Cylindrical Coordinates and Similarity Solution . . . . . . . . . . . . . . . 13

2.3.2 Conservation of Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Radiation Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Optically Thin Approximation (OTA) . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.3.3 Conservation of Species . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Chemical Kinetics Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

KAUST Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

CRECK Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.4 Soot Aerosol Dynamics Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.4.1 The Sectional Aerosol Dynamics Model . . . . . . . . . . . . . . . . . . . . . . . . 22

Nucleation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Condensation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Chemical Surface Growth and Oxidation Models . . . . . . . . . . . . . . . . . . . 28

Coagulation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Fragmentation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.4.2 Numerical Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Premixed Stagnation Flame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Boundary Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

v

3 Results and Discussion 34

3.1 Model Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.1.1 Temperature Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.1.2 Soot Volume Fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.1.3 Particle Size Distribution (PSD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.1.4 Stagnation Wall Temperature Sensitivity Analysis . . . . . . . . . . . . . . . . . . 38

3.1.5 HACA Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.2 CO2 Addition Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.2.1 Soot Volume Fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.2.2 Particle Size Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.2.3 PAH Condensation Reversibility Effect . . . . . . . . . . . . . . . . . . . . . . . . 46

3.2.4 Wall Temperature Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.2.5 Thermal Effect of CO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.2.6 Chemical Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

Species Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.3 Nucleation - Condensation Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.4 Chemical Kinetic File Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4 Concluding Remarks and Future Work 67

4.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

4.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

4.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

Appendices 70

A 71

B 73

Bibliography 79

vi

List of Tables

2.1 summary of flame conditions[1] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2 HACA–based soot surface growth and oxidation reactions[2], k = AT be−Ea/RT . . . . . . 28

vii

List of Figures

1.1 TEM images of soot for 5-decene, 1-decene, n-decane, and biofuel surrogate as a function

of height above burner (Source: Reprinted from ref.[3]). . . . . . . . . . . . . . . . . . . . 3

1.2 Example of the obtained HR-TEM images. Laboratory soot sample formed in the pyrolysis

of acetylene-ethanol mixture containing 40% of ethanol in volume at 1375 K and 10% of

ethanol in volume at 1475 K (Source: Reprinted from ref.[4]). . . . . . . . . . . . . . . . . 4

1.3 Schematic of soot morphology(Source: Reprinted from ref.[5]). . . . . . . . . . . . . . . . 6

1.4 Conceptual mechanisms of soot particle nucleatoin (Source: Reprinted from ref.[6]). . . . 7

2.1 Schematic representation of a burner stabilized stagnation flame, including coordinate

orientation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2 2D visualization of a BSS flame including the 1D grid for the numerical solution. The

variable j represents the nodes’ index, and JJ is the total number of nodes. . . . . . . . . 15

2.3 Schematic representation of the major reaction pathways for the formation of large PAHs

considered by the KAUST chemical kinetic mechanism (source: picture taken from ref.[2]). 19

2.4 Schematic representation of the major reaction pathways for the formation of BIN1B

considered by the CRECK chemical kinetic mechanism (source: picture taken from ref.[7]). 20

2.5 Processes shaping the particle size distribution function in a small volume element of gas.

Diffusion and sedimentation involve transport across the walls of the element. Coagula-

tion, nucleation, and growth take place within the element (source: picture taken from

ref.[8]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.6 Soot morphology in a burner stabilized stagnation flame. . . . . . . . . . . . . . . . . . . . 23

2.7 Nucleating species chemical structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.8 Illustration of armchair sites on the surface of a soot particle. . . . . . . . . . . . . . . . . 28

3.1 Schematic of different burner-to-stagnation surface separations. . . . . . . . . . . . . . . . 35

3.2 Comparison between modelled (solid lines) and measured (symbols) axial temperature

profiles of the BSS ethylene flame for a series of HP values. . . . . . . . . . . . . . . . . . 36

3.3 Comparison of the measured soot volume fraction (triangles) and model predictions (cir-

cles) as a function of burner-to-stagnation surface separation. . . . . . . . . . . . . . . . . 37

3.4 Comparison of the computed (solid lines) and measured (symbols) PSDs. The experimen-

tal data is adopted from [9]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.5 Wall Temperature Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.6 Comparison of the different surface reactivity parameters. . . . . . . . . . . . . . . . . . . 40

3.7 Comparison of the H radical concentration and fv for the spacings 0.6 and 0.8 cm. . . . . 40

viii

3.8 Comparison of the flames C3 (φ = 2.07) and A1 (φ = 2.00) for the burner–to–stagnation

surfaces of 0.55 and 0.80 cm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.9 Comparison of the computed (circles) and measured (triangles) soot volume fraction for

the addition of 0.0%, 12%, and 18% of CO2, respectively (see Tab. 2.1). . . . . . . . . . 43

3.10 Comparison of the computed (solid lines) and measured (symbols) PSDs. The experimen-

tal data is adopted from [1]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.11 Comparison of the constant (column a) and reversible (column b) condensation model. . . 46

3.12 Stagnation wall temperature sensitivity analysis for the measured boundary condition,

470 K; the flame C3 boundary condition, 497 K; and the flame C3 boundary condition

plus the measurement uncertainty, 530 K. The comparisons has been made for the spacing

0.6 cm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.13 Comparison of the effect of CO2 (frame (a)) and chemically inert specie FCO2 (frame (b))

on the PSDs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.14 Comparison of the effect of CO2 and chemically inert specie FCO2 on the temperature

profiles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.15 Comparison of the effect of CO2 (frame (a)) and chemically inert specie FCO2 (frame (b))

on the concentration of C2H2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.16 Comparison of the specific heat capacity of CO2 and Ar. The value CP /Ru is dimensionless. 50

3.17 Effect of CO2 addition on the major species including hydrogen radical, hydroxyl, acety-

lene, and benzene for the spacing 0.6 cm. . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.18 Effect of CO2 addition on the nucleating species concentrations for the spacing 0.6 cm.

Frame (b) represents the normalized PAH summation at the stagnation plane over a range

of burner-to-stagnation surface separations. . . . . . . . . . . . . . . . . . . . . . . . . . . 52

3.19 Normalized sensitivity analysis of anthanthrene, compared at x = 0.2 cm for flames A1,

A2, and A3 on the spacing of 0.6 cm. Reactions include CO2 and CH∗2 are marked by

green and red, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.20 Normalized sensitivity analysis of benzene, compared at x = 0.04 cm for flames A1, A2,

and A3 on the spacing of 0.6 cm. Reactions include CO2 and CH∗2 are marked by green

and red, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.21 Absolute rate of production for acetylene, compared at x = 0.04 cm for flames A1, A2,

and A3 on the spacing of 0.6 cm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.22 Normalized sensitivity analysis of acetylene, compared at x = 0.04 cm for flames A1, A2,

and A3 on the spacing of 0.6 cm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

3.23 Comparison of soot mass generated by HACA, nucleation, and condensation for the spac-

ing 0.6 cm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.24 Soot total mass fraction for the flames A1, A2, and A3 over a range of burner-to-stagnation

surface separations including 0.5, 0.6, and 0.8 cm. . . . . . . . . . . . . . . . . . . . . . . . 58

3.25 Soot condensation mass fraction for the flames A1, A2, and A3 over a range of burner-

to-stagnation surface separations including 0.5, 0.6, and 0.8 cm. . . . . . . . . . . . . . . . 58

3.26 Soot nucleation mass fraction for the flames A1, A2, and A3 over a range of burner-to-

stagnation surface separations including 0.5, 0.6, and 0.8 cm. . . . . . . . . . . . . . . . . 59

3.27 Normalized soot nucleation and condensation mass fraction for the flames A1, A2, and

A3 over a range of burner-to-stagnation surface separations including 0.5, 0.6, and 0.8 cm. 60

ix

3.28 Comparison of the nucleation mass, condensation mass, and total mass of soot for the

spacing 0.6 cm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

3.29 Particle size distribution function for (a) KAUST mechanism and (b) CRECK mechanism. 62

3.30 PSD comparison for the constant condensation, frame (a); reversible condensation model

with the original temperature boundary condition, frame (b); and reversible condensation

model with another reported temperature, frame (c). . . . . . . . . . . . . . . . . . . . . . 63

3.31 Condensation efficiency comparison for the original wall temperature, frame (a), and

another reported temperature, frame (b). . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

3.32 Boundary temperature effects on the fv prediction. frame (a) shows the computed fv

compared with measurements for the original temperature boundary condition; frame (b)

represents a similar concept to frame (a) but the computed values for the spacing 0.8 cm

has been replaced with new ones calculated at new temperature. . . . . . . . . . . . . . . 64

3.33 Condensation efficiency comparison for the original wall temperature and four condensable

species including: (a)anthantherene, (b) benzo(ghi)fluoranthene, (c)benzo[ghi]perylene,

and (d)pyrene. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

A.1 Carbon monoxide and propargyl concentrations compared for flames A1, A2, and A3. . . 71

A.2 Hydrogen radical and Hydroxyl concentrations compared for flames A1, A2, and A3. . . . 72

A.3 Oxygen radical and CH2* concentrations compared for flames A1, A2, and A3. . . . . . . 72

B.1 Comparison of the different chemical kinetic mechanisms for the CO2 addition effects on

the concentration of acetylene. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74


the concentration of hydrogen radical. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75


the concentration of hydroxyl. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76


the concentration of benzene. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77


the concentration of pyrene. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

x

Nomenclature

Roman Symbols

Vk Diffusion velocities, cm/s

Q′′′ Heat loss

C Particles’ velocity vector

cP Specific Heat of mixture under the constant pressure condition

Df Fractal dimension

f Net body force

fs Section spacing factor

fv Soot volume fraction

G Gibbs energy

gz Axial gravitational force

H Enthalpy

h◦ Species specific enthalpy

k Reaction rate

nv Particle number density, cm−3

P Pressure, pa

r Radial coordinate, cm

Ru Universal gas constant

S Entropy

T Temperature, K

u Axial velocity, m/s

ui Velocity tensor

V Diffusion velocity

v Radial velocity, m/s

W Molecular weight,g/mol

x Height above burner, cm

Y Mass fraction

xi

z Axial coordinate, cm

Acronyms

BSS Burner Stabilized Stagnation

EGR Exhaust Gas Recirculation

GC/MS Gas Chromatography/Mass Spectrometry

GDE General Dynamics Equation

GHG Green House Gas

HACA Hydrogen Abstraction Carbon Addition

HRTEM High Resolution Transmission Electron Microscope

KAUST King Abdullah University of Science and Technology

LMMS Laser Microprobe Mass Spectrometry

LTE Local Thermodynamics Equilibrium

MD Molecular Dynamics

NOC Nano-particles of Organic Carbon

OTA Optically Thin Approximation

PAH Polycyclic Aromatic Hydrocarbon

PM Particulate Matter

PNP Precursor Nano-Particle

PSD Particle Size Distribution

RTE Radiative Transfer Equation

TEM Transmission Electron Microscope

Greek Symbols

χ Species mole fraction

ω Chemical reaction rate

κP Plank mean absorption coefficient.

λ Second viscosity coefficient, Eq. 2.2

λ Thermal conductivity of the mixture, Eq. 2.11

µ Dynamic viscosity, pa·s

ψ Stream function

ρ density, g/cm3

σ Stephen Boltzman constant

θ Angular coordinate

Subscripts

i Reaction index

j Grid index

xii

k Species index

r Radiation

s Soot

xiii

Chapter 1

Introduction

1.1 Motivation

Energy is one of the necessary requirements for the humans’ life, and a reliable and accessible supply

of energy is crucial for the sustainability of modern societies. Currently, fossil fuels supply about 80%

of the global energy consumption [10]. It is estimated that the entire demand for energy will grow

constantly all through the world with especially large rises in the demands from emerging economies.

The overall liquid fuels consumption of the world, as an example of the world’s hydrocarbon consumption,

is predicted to expand by 33 million barrels per day for the duration of thirty years, starting from 2010,

which is equivalent to 30% of the current consumption [11]. Energy use has adverse environmental and

health consequences that have led to considerable restrictive regulations. The generation of energy from

fossil fuels is mostly produced by combustion which is a source of atmospheric emissions such as NOX,

green house gases (GHGs), and particulate matter (PM). PM is a known pollutant and its health and

environmental consequences are linked directly to its size [6].

Combustion derived nano-particles known as soot are a significant part of the ambient fine partic-

ulate matter (PM2.5) [12]. The adverse influences of PM2.5 on public health have been well recorded

by epidemiological researches. Time-series studies of the short-term effects of air pollutants, conducted

around the world, have steadily described noticeable connection between daily mortality and daily expo-

sure to PM2.5. Two large-scale group studies organized in the United States reported increased mortality

associated with an increase in annual average PM2.5 levels. According to some other studies, traffic-

generated fine particulate air pollution, indicated by soot, may constitute greater risk on the human

health than PM2.5 from other sources [12]. The World Health Organization Regional Office for Europe

performed a recent systematic review on the health effects of black carbon and found that threatening

effects from both short and long-term studies are much higher for soot compared to PM10 and PM2.5

when the particulate measures are expressed per µg/m3.

Soot particle aerosols have significant impacts on climate change through several mechanisms: ab-

sorption of solar radiation; influence on cloud formation; and deposition on the snow and ice [12, 13].

Black carbon in soot is the dominant absorber of visible solar radiation in the atmosphere. Black carbon

is often transported over long distances, mixing with other aerosols along the way. The aerosol mix can

form transcontinental plumes of atmospheric brown clouds, with vertical extents of 3 to 5 km. Because

of the combination of high absorption; a regional distribution roughly aligned with solar irradiance; and

1

Chapter 1. Introduction 2

the capacity to form widespread atmospheric brown clouds in a mixture with other aerosols, emissions

of black carbon are the second strongest contribution to current global warming, after carbon dioxide

emissions. In the Himalayan region, solar heating from black carbon at high elevations may be just as

important as carbon dioxide in the melting of snowpacks and glaciers. The interception of solar radiation

by atmospheric brown clouds leads to dimming at the Earth’s surface with important implications for

the hydrological cycle, and the deposition of black carbon darkens snow and ice surfaces, which can

contribute to melting, in particular of Arctic sea ice [14].

For these reasons, governments are setting stricter particulate emission regulations like EURO 6 and

ICAO in both automotive and aviation engines, respectively. Most of these regulations limits the total

particulate mass emissions over different periods of time. However, there are increasing considerations

that possible effects of other particulate characteristics, such as particle number, particle morphology,

molecular structure , and detailed chemical speciation on the environment and health should be taken

into account [6]. In this way, a comprehensive understanding of the risks associate with PMs may be

achieved. Thus, understanding the soot mass growth pathways as well as evolution of particle size

distributions has received considerable attention [15].

Formation of condensed-phase materials is present in many flames. These materials form generally as

nanoparticles suspended in combustion products [6]. Soot particles are emitted from various combustion

processes, mostly the incomplete rich combustion of fossil fuels, biofuels, and biomass[12]. Improvement

of effective technologies to reduce soot emissions from combustion applications has been an attractive

research area over the past years [16]. The dilution of the fuel and/or oxidizer mixture stream is an

established method (e.g., exhaust gas recirculation (EGR)) to develop low temperature combustion in

order to prevent both soot and NOX formation. CO2 is one of the major components of combustion

products; understanding how addition of CO2 affects the flame properties and soot formation requires

attention.

The big picture of the soot modelling research is to come up with a detailed generic soot model

which can be applicable for different flame conditions. After such a reliable model is developed the

main features can be extracted and implemented into CFD softwares for design purposes. Predictive

models would enable engine, furnace, and other practical device designers to tune various design and

operating parameters without the necessity for highly priced experimentation and prototype building.

Although this idea is worthy, it is very challenging. The detailed modelling of soot formation for

laboratory scale burners has been started recently. Therefore, based on the viewpoint that has been

forecast for the environmental and industrial researches, the present work seeks the further validation

and improvement of a recently developed soot model which is capable of predicting soot volume fraction,

particle nanostructure and size distribution. Addition of CO2 could be a perturbing factor for the flame

simulations to see how robustly the code performs in capturing the effects of different disturbing elements.

Soot formation process is highly reversible [6]; the concept of reversibility in terms of modelling has

been introduced by Eaves et al. [17, 18] and Veshkini et al. [15]. Although the existence of reversibility

in soot models is necessary based on the physical characteristics of the process, this feature needs to be

studied with details in order to find the probable defects that the reversible model may possess.


1.2 Literature Review

1.2.1 Soot Characteristics

Soot particles are the product of fuel rich combustion and mostly form in high temperature zones.

Particles generated in different conditions including laminar premixed and diffusion flames show universal

structures [19]. However, the nanostructure and aggregation features of the soot nuclei depend on the

flame type, locations within a flame, and other factors like residence time. Fig. 1.1 depicts the structure

evolution of soot samples as observed by transmission electronic microscope (TEM) for four different

fuels of a coflow burner along the flame axis and wing.

Figure 1.1: TEM images of soot for 5-decene, 1-decene, n-decane, and biofuel surrogate as a function ofheight above burner (Source: Reprinted from ref.[3]).

At low heights above the burner, the number of particles is high but the size of them is small. It is also

observed that there are many liquid like particles available along the center line close to the fuel tube tip

as shown in lower frames of Fig. 1.1. As the height above burner increases, the aggregates solidify and

become more apparent due to the growth and carbonization process which results in dehydrogenation

and higher C/H ratio.

The nascent soot particles, also referred to as precursor nanoparticles (PNP) and nanoparticles

of organic carbon (NOC), are assumed spherical particles which their size ranges from 1 to 5 nm in

diameter. Their spherical appearence and absence of aggregation are indications of liquid-like behaviour

and supposition of coalesce upon collision [20]. Laser microprobe mass spectrometry (LMMS) [21], gas

chromatography/mass spectrometry (GC/MS) [22] and high-resolution transmission electron microscopy

(HRTEM) [23] measurements indicated that the nascent particles can be thought of as polymer-like


structures containing polycyclic aromatic hydrocarbon (PAH) molecules ranging in molecular masses

from 152 to 302 amu. Elemental analysis of nascent soot particles shows that these particles have a

relatively low atomic C/H ratio of ∼ 1.6 - 4 which can also be associated with their high chemical

reactivity [23].

Simultaneous coagulation of the 1 - 5 nm particles, addition of compounds from the gas-phase, and

loss of H atoms direct particles towards gaining a graphitic structure, and eventually transforms nascent

soot particles to aggregate carbonaceous and hardened primary particles [24, 25]. The nascent particles

may also be absorbed onto the surface of the aggregates upon collision [25].

Mature soot particles, as illustrated in Fig. 1.2, consist of small spherical units that are referred to as

primary particles. Primary particle diameters generally range from 20 to 60 nm, with standard deviations

of 15% - 25% [26]. The primary particles within an aggregate have nearly identical diameters, and form

chain-like aggregated structures that have broad distributions of the number of primary particles per

aggregate ranging from a few up to several thousands [26]. The long chain soot aggregates and a

comprehensive assortment of particles set the probable complexity in the characterization, and more

importantly in soot formation modelling. This complication is addressed by experimental evidence that

soot aggregates show a fractal-like structure [27]; these aggregates have a universal fractal dimension

around Df = 1.8, even when an aggregate is composed of two or three primary particles[28]. Fractal

dimension is used to calculate the surface area and rate of size change of the aggregates. The fact

that aggregates resemble fractals enables us to implement the theory of fractal aerosol in both laser

measurements and simulations [25].

Figure 1.2: Example of the obtained HR-TEM images. Laboratory soot sample formed in the pyrolysisof acetylene-ethanol mixture containing 40% of ethanol in volume at 1375 K and 10% of ethanol involume at 1475 K (Source: Reprinted from ref.[4]).

GC/MS measurements [22] and liquid chromatography [29] substantiate the availability of 2 to 10

ring PAHs as the components of mature soot particles. The transition from nascent soot particles to

mature soot aggregates is accompanied by an increase of carbon to hydrogen ratio (C/H) which results

in higher density for aggregates (ρs = 1.77 − 2.00 g/cm3 [30]) compared to the nascent soot particles

(ρs = 1.20− 1.50 g/cm3 [31]).

The coexistence of the singlet spheroids and the carbonaceous aggregates also has been observed in

particle size distribution (PSD) measurements in laminar premixed flames [1, 9, 32]. In the later flames

the bimodal PSD evolves from a unimodal PSD as a function of time and height. The bimodal particle


size distribution is an indication of coexistence of nascent and mature soot particles. Comparison of

the measured PSD with the TEM results [3] and electrical mobility measurements [33] indicates that

the particles < 5 nm in diameter are associated with the nascent soot particles (nucleation mode)

which exhibit a distinctive behavior from the 10–50 nm particles (the accumulation mode). Particles

belonging to the accumulation mode, display the expected soot properties that are characterized by light

scattering and TEM: they gain mass and increase their size due to surface growth and reduce in number

due to coagulation as a function of residence time. Meanwhile, the mean size and number density of

the nucleation mode remains nearly constant everywhere in the flame. Since the nascent particles grow

and coagulate with other particles, the consistent presence of the nucleation mode implies a continuous

nucleation. These observations link the shape of the particle size distribution to the morphology and

mode of particles.

1.2.2 Soot Formation Pathways

According to the aerosol dynamics, the transition of gas-phase molecular structures to the condensed-

phase is known as nucleation. The freshly formed fine particles grow in size and mass by means of joining

to together, surface reactions, and condensation of large gas-phase species. Grown single particles stick

to each other and form fractal-shape structures (soot) through aggregation. It is worth to mention that

all these steps are highly reversible due to the thermodynamics properties that soot particles have [6].

At the end, oxidation leads soot particles to lose mass. These processes take place mainly concurrently

in short periods of time as shown in Fig. 2.6. Most of these fundamental processes that govern soot

formation are not well understood; in order to include them in simulations, a mathematical model that

can capture the underlying physics of each step must be developed.


Figure 1.3: Schematic of soot morphology(Source: Reprinted from ref.[5]).

Fuel pyrolysis and oxidation is the first stage of the soot formation from pure hydrocarbon flames.

Generally, the simple fuel combustion chemistry is relatively well known, and fairly precise chemical

kinetic mechanisms exist for the desired fuels [34, 35]. The next step includes the formation of light

cyclic aromatic hydrocarbons from the gas-phase species of the fuel decomposition. Propargyl (C3H3)

recombination or chemically activated isomerization is the main rout toward the formation of the first

aromatic ring [36]. There are different routes after the first aromatic ring to form larger multicyclic

aromatic compounds (i.e. PAHs); among them, the the hydrogen-abstraction-carbon-addition (HACA)

reaction sequence [37] is one of the most effective pathways. The combination of fuel pyrolysis/oxidation

and PAH formation and growth routes have been used to produce chemical kinetic mechanisms to

describe the formation of PAH species [38, 39].

Emergence of condenced-phase materials in combustion products comes after the appearance of large

PAH species in the gas phase. Three conceptual pathways may be hypothesized for soot nucleation from

large PAHs, e.g. anthanthrene. As shown in Fig. 1.4, path A shows the growth of planar PAHs into

curved, fullerene-like structures; paths B and C involve the physical coalescence and chemical coalescence

of PAHs into crosslinked three-dimensional structures, respectively [6]. Indirect experimental evidence

supports PAH dimerization (paths B and C) as the initial nucleation step [6]. Further growth of these

structures in this manner leads to emergence of nascent soot particles. Additional mass growth as well


as dehydrogenation of the nascent particles is marked as the beginging of the solid state [40].

Figure 1.4: Conceptual mechanisms of soot particle nucleatoin (Source: Reprinted from ref.[6]).

Addition of small hydrocarbon species can contribute to the soot particles growth. Acetylene is the

dominant mass growth species which plays its role in the HACA process [41]. Mass growth on soot

surface requires H-abstraction to form an aryl radical site, followed by acetylene attack in a manner

similar to the gas-phase mechanism. There is conclusive evidence that young soot particles formed in

premixed flames have a coreshell structure, with the core being aromatic in nature and the shell being

aliphatic. Again, the nature of binding between aromatic and aliphatic constituents remains unclear.

The mass growth of soot can proceed without the presence of gas-phase H atom, indicating that the

HACA mechanism may be incomplete to describe the entire process of soot formation [6].

The condensation of the gas-phase PAHs on the surface of the soot particles is also a feasible soot

growth pathway, which is referred to as PAH-soot surface condensation [42]. Although the experiments

posit that PAH clusters are the building block of soot[43], molecular dynamics (MD) studies show that

the adsorbed PAH species are not stable[44]; thus, a better comprehension of such processes is required.

The last step in the soot formation and growth process is aggregation. Aggregation involves two

types of soot structural growth: coagulation and coalescence. The formation of fractal-like aggregates

as a result of particle collisions is called coagulation which affects the evolution of PSD, number density,

and morphology. After the collision, soot particles may undergo structural evolution which is a function

of particle state, surface reactivity, temperature, residence time, etc. [8]. Coalescence leads the collision

of liquid-like nascent soot particles to complete merging of the colliding particles [45]. The soot particles

restructuring mechanisms are not well understood. New models are needed to estimate the maturity of

the particles as well as comprehensive coagulation models that describe the coalescence process, neck

formation, and aggregation.

The amount of soot emissions depends on the oxidation of the soot. There are three possible oxidation

pathways: reactions with O, OH and O2. Oxidation by OH radical prevails in near stoichiometric and

fuel-rich flame conditions [46]. Eventhough under the mentioned conditions some oxidation can occur

through collisions with O, contribution from OH outruns the O radical’s involvement [47]. The OH

oxidation efficiency is a function of OH collisions with soot particles that result in the removal of a

carbon atom; this efficiency is reported to be 0.13 [46, 47]. In fuel lean conditions, oxygen plays a

crucial role in soot oxidation due to abundance of O2. Research has indicated that changes of both

initial structure of soot [23] and structure of soot during oxidation [47] complicates defining a universal

oxidation rate.


1.2.3 CO2 Addition Effect

In this section there will be a discussion on the CO2 addition influences on the soot formation process.

Several experimental studies, specially for coflow diffusion flames, have been performed to investigate

the effect. According to the literature [1, 16], CO2 addition suppresses soot formation in most of the

flame conditions; however, there are unanswered questions regarding the role of CO2 in the process.

There is evidence which suggests the suppression of soot is due to the thermal effects [48, 49], while the

majority of the literature posits that the observed phenomenon is mostly due to chemical effects.

Schug et al. [48] and Abhinavam et al. [49] concluded that the soot formation suppression is due to

thermal effects. Abhinavam et al. [49] measured the concentrations of soot precursor species including

C2H2 and C6H6 for different diluents such as argon, helium, and carbon dioxide. The different levels

of soot precursors produced in the diluted flames are attributed to the differences in the transport

properties of the diluents, where the thermal diffusivities cause the temperature difference between the

helium flame (hottest flame) and the carbon dioxide-diluted flame (coolest flame). This feature makes

carbon dioxide a better suppressant among the diluents tested.

Du et al. and Zhang et al. [50, 51] found that CO2 hinders the soot formation chemically; they

measured concentrations of species to investigate the dilution effect. Liu et al. [52] took advantage of

a numerical model, and determined that CO2 addition suppresses the soot nucleation by lowering the

acetylene and enhancing the concentration of OH radicals; reactions CO2+H → CO+OH and CO2+CH

→ HCO+CO were found to be responsible for the chemical effects of CO2 addition.

In a more recent paper, Liu et al. [16] studied the effects of fuel dilution by CO2 and N2 on soot

formation and the flame structure in laminar coflow C2H4/air diffusion flames both experimentally

and numerically including soot simulation; according to their study, CO2’s role in the soot suppression

process is mainly due to its chemical effects. According to Guo et al. [53], CO2 addition reduces the

H radical formation which consequently results in lower pyrene concentrations. Less PAH reduces the

inception rate.

The chemical effects of CO2 on soot formation are more complex in premixed flames[16], and tech-

nically the soot formation process totally differs between premixed and diffusion combustion. In the

premixed flames soot starts to form after passing the flame front and in the post flame region, while in

the diffusion flames soot forms in a fuel rich heated zone before reaching the flame front. Zhang et al.

[54], in a numerical simulation of soot precursors in a plug flow reactor, insisted on the chemical effect of

CO2 addition. They determined that the reaction CO2+H ←→ CO+OH is pretty fast at intermediate

temperature; the mentioned reaction competes with the reaction O2+H ←→ O+OH in depleting the H

radicals. Tang et al. [1] did a thorough experimental investigation and a chemistry simulation of species

to understand how CO2 addition affects the PSD function evolution. They concluded that that CO2 ad-

dition hinders particle inception, and thermal effect plays a minor role. Tang et al. took advantage of a

burner stabilized stagnation (BSS), which minimizes the problem of probe perturbation in experiments.

This burner was used earlier by Abid et al. and Camacho et al. [9, 32] to follow the evolution of PSD

function of nascent soot.

Up to here, there is a consensus among different researches about chemical effects of CO2 addition

on soot formation; however, disagreement still exists on how the added CO2 affects the soot formation

chemically, even via inception or surface growth. In addition,some studies suggest CO2 addition does

not always suppress soot formation[55, 56]; however, inclusion of CO2 in the combustion reactants seems

a pragmatic solution to prevent soot formation in the contemporary devices. Utilizing this capability


requires a better understanding of the morphology in different conditions. A numerical study for a

premixed case accompanied with a soot model could be helpful to find out the reasons which accounts

for the phenomenon.

1.2.4 Soot Modelling

Soot modelling is a multiscale problem because it includes a variety of time and length scales such as

angstroms for atomic level scales (10−10m), nanometers for dimers and soot particles (10−9m), milimeters

for flow scales (10−3m), and centimeters for burner geometry (10−2m). In order to address the multiscale

problems the smallest/shortest length/time scales should be taken into account to model the processes

based on the understanding. One of obstacles in these sort of problems is to set up a balance between

the accuracy and simplicity of the model.

Kennedy [57] has reported the early achievements of developments of soot models. According to the

time/length scales and the model complication, soot models can be classified into three categories:

• empirical soot models;

• semi-empirical soot models;

• detailed soot models.

Empirical soot models have their origins in correlations that have been derived experimentally. The

correlations usually reflect the influence of variation of different flame parameters, e.g., pressure, tem-

perature, and equivalence ratio on the sooting behaviour. These correlations are coupled with flame

models to relate the amount of soot produced with the operating conditions. The empirical models are

fairly fast, compared to other types, which make them suitable for industrial purposes. The purpose of

semi-empirical models is to increase the accuracy and keep the simplicity by including the elementary

soot formation/oxidation routes in the model. Fairweather et al. [58] have developed one of the most

widely used semi-empirical models. The model solves two transport equations, one for the soot mass

fraction and one for the soot primary particles. The Fairweather model includes soot particle inception,

surface growth, oxidation, and coagulation which are estimated empirically. The major disadvantage of

the empirical correlation implementation is the limited validity of the model, i.e., the model functions

properly for the calibration cases.

The final classification is made up of the detailed soot models. These are complicated and com-

putationally intensive models. The detailed soot models take advantage of the cutting edge aerosol

dynamics prediction tools which make them reliable of finding a proper solution for a wide range of

aggregate structures. The most recent chemical and physical kinetic mechanisms describing PAH and

soot formation/oxidation are embodied into the detailed models. These models can yield comprehensive

information about the factors influencing particles for a broad range of conditions. This characteristic

enables them to investigate the fundamentals of soot formation.

The simulation of the combustion and soot particles in flames comprises the following steps:

• modelling the flow field (solving the Navier-Stokes equations);

• predicting the temperature (solving the energy equation);

• calculating the gas-phase composition (solving the gas-phase chemistry);


• and finally, calculating the soot variables (solving the aerosol dynamics equations);

which all of these steps are intimately coupled.

Detailed models require a detailed chemical kinetic mechanism which simultaneously describes the

pyrolysis and oxidation of fuels as well as the formation and growth of PAH species. PAH formation and

growth involve broad range of species and pathways which makes the chemical mechanisms to include

hundreds of species and thousands of reaction, even for simple fuels [38, 39, 59, 60]; this adds a noticeable

computational burden to the simulations.

The proper aerosol dynamics models for studying soot comprises sectional methods [7, 15, 61–64],

Galerkin methods [65, 66], stochastic methods [67], and moment methods [68, 69]. These capable

algorithms can capture the majority of the particle properties with moderate computational resources;

however, modifications to these models to extract additional information, dramatically increase their

complexity and computational cost.

An advanced sectional aerosol dynamics model [15, 70] is used in this thesis that can provide soot

morphology in addition to mean soot properties and the size distribution of particles. Two equations,

number densities of aggregates and primary particles, are solved per section which allows resolving the

formation and coagulation of the fractal-like soot aggregates as well as soot polydispersity. Abilities

of the sectional soot model to successfully simulate soot formation has been demonstrated in plug flow

reactors [70], shock tubes [71], and coflow diffusion flames [18, 72, 73]. The sectional soot aerosol dynamic

model is described in detail in Chapter 2.

1.3 Objectives

In the current work, a comprehensive soot model will be used to calculate the PSD functions for BSS

flames. The base ethylene/oxygen flame along with three different composition of argon and CO2 will

be studied to investigate the effect of CO2 inclusion. The simulation results will be validated against

experimental measurements performed by Tang et al. [1]; the plots of PSD functions for different burner-

to-stagnation-surface separations and soot volume fractions (fv) will be compared to experimental data

to find a better insight into the effect of CO2 on the soot inception and growth. When the model is

proved to capture the trends and values fairly good, it will be used to answer the following questions

regarding the influence of CO2 addition qualitatively:

• Is the suppression effect of CO2 due to thermal or chemical factors;

• What are the chemical reactions involved in this soot reduction process;

• Between the nucleation and condensation, which step is affected more.

Moreover, there will be a discussion on the temperature effect on the condensation model. The influence

of the chemical kinetic file on the evolution of PSDs will be studied as well. This study is the first work

which takes advantage of a BSS flame soot model to investigate the CO2 addition effect; thus, we are

able to see the influence of dilution on the HACA surface and other factors in the soot morphology.

Chapter 2

Methodology

2.1 Overview

The scope of this chapter is the demonstration of the governing equations and variables that are funda-

mental for the chemically-reacting flow simulations in this work. Firstly, there will be a discussion about

the experimental setup that has been used to compare the modelling results with. The similarity solu-

tion of the generalized governing equation are employed in modelling different flames considered in the

current work. This method forms the governing equations as one-dimensional boundary value problem

valid along the center line of a stagnation flow. The aforementioned approach has been used to model the

premixed burner stabilized flames. It also includes an explanation on a sectional approach for modelling

combustion-derived particulate matter (soot) formation. In the upcoming sections, the burner descrip-

tion, gas-phase governing equations, soot aerosol dynamics model, and finally the numerical method

used to solve the governing equations will be discussed.

2.2 Burner Description

Fig. 2.1 shows the schematic of a burner stabilized stagnation (BSS) flame. Laminar premixed flat

ethylene flames with an unburned composition of 16%(mol) ethylene, 24% (mol) oxygen and 60% (mol)

argon were generated by a commercial McKenna burner with a stainless outer layer and a 6 cm-diameter-

bronze water-cooled porous sintered plug. The unburned fuel and oxidizer mixture leaves the plug with

an equivalence ratio, ϕ, of 2 and a cold gas velocity of 8 cm/s (298 K and 1 atm). The McKenna burner

has a water cooling system, embedded within the porous plug, which prevents the burner damage.

A shroud of nitrogen, at 25–30 cm/s, isolates the flame from the surrounding air to keep the flame

stabilized. An S-type Pt-Pt-10%Rh thermocouple coated with a Y/Be/O mixture to hinder surface

catalytic reaction was used to measure the flame temperature[1].

A flat plate, which is called stagnation plate, is located at a distance to the burner and parallel to it

to form the stagnation flame. A tubular probe made up of stainless steel with a bore size of 6.1 mm and

wall thickness of 0.125 mm was embedded in the stagnation plate to take samples. A sample orifice with

a diameter of 0.16 mm was drilled in the middle of the tubular probe by laser. A type-K thermocouple

embedded in the stagnation plate to measure the orifice temperature. The orifice temperature was

about 465 ± 30 K during sampling. The burner to stagnation plate distance Hp was determined by

11

Chapter 2. Methodology 12

a Vernier height gauge with an accuracy of ±0.02 cm. The particle size distribution was measured by

Scan Mobility Particle Sizer (SMPS, Model 3936)[1].

Table 2.1: summary of flame conditions[1]

Flame 0.0% CO2: A1 12.0% CO2: A2 18.0% CO2:A3

C2H4 0.16 0.16 0.16

O2 0.24 0.24 0.24

Ar 0.60 0.48 0.42

CO2 0.00 0.12 0.18

Three flames with different fuel composition were examined thoroughly (see, Table 2.1). Flame A1

has no CO2 content in the unburned fuel mixture and has been studied by Abid et al.[32] and Camacho

et al.[9]; this flame can be noticed as a reference sooting flame for comparison. In flames A2 and A3,

20% and 30% of argon were replaced by CO2, respectively[1].

z

r

Premixed Fuel and Oxidizer

Orifice

Flame Front

Figure 2.1: Schematic representation of a burner stabilized stagnation flame, including coordinate ori-entation.

The work by Tang et al. [1] has been selected for this study because it contains rich measurements

of the soot properties of interest. Soot volume fraction (fv), particle number density, and particle

diameters are the important properties in soot research. Most of the experimental data in the literate


provide only soot volume fraction. Models can be easily tweaked to predict soot volume fraction with a

good agreement. However, a model can be accounted reliable if it functions properly in terms of capturing

all three mentioned properties. The modelling tool that will be explained in the coming sections will be

validated against fv, soot number density, and particle diameters measured by Tang et al. [1].

2.3 Gas-Phase Governing Equations

Conservation of mass and momentum (Navier-Stokes), conservation of energy, and conservation of species

compose the gas-phase governing equations. The solution of these equations describes the flow field,

pressure, temperature, and gas mixture compounds. In order to to solve all the equations, species

production rate, transport properties, and thermodynamics properties have to be evaluated to calculate

the source terms. In the following sections all the conservation equations and evaluation method of

thermo-chemical properties will be explained.

2.3.1 Conservation of Mass and Momentum

The mass conservation equation (continuity) in tensor form is depicted in Eq. 2.1.

∂ρ

∂t=

∂

∂xk(ρuk) (2.1)

In Eq. 2.1 the ρ is the density of the mixture, t refers to the time, and uk is the velocity component in

the xk direction. Eq. 2.2 presents the general form of the Navier-Stokes equations in tensor form.

ρ∂uj∂t

+ ρuk∂uj∂xk

= − ∂p

∂xj+

∂

∂xj

(λ∂uk∂xk

)+

∂

∂xi

[µ

(∂ui∂xj

+∂uj∂xi

)]+ ρfi (2.2)

where λ is the second viscosity coefficient, µ is the dynamic viscosity and fi is the net body force.

The 2D Cylindrical Coordinates and Similarity Solution

The flame configuration used in this study is the BSS premixed flame which consists of a cylindrical

tube with an axisymmetric flow field (Fig. 2.1). The tube carries the fuel and oxidizer mixture toward

the plate, and the flow velocity reaches zero close to the plate. Since the flow is axisymmetric, the

governing equations become 2D when they are expressed in cylindrical coordinates. Assuming ∂∂θ = 0

for axisymmetric flow, the cylindrical form of Eqs. 2.1 and 2.2 is as follows:

1

r

∂

∂r(rρv) +

∂ρu

∂z= 0 (2.3)

ρv∂u

∂r+ ρu

∂u

∂z= −∂p

∂z+

1

r

∂

∂r

(rµ∂u

∂r

)+ 2

∂

∂z

(µ∂u

∂z

)− 2

3

∂

∂z

[u

r

∂

∂r(rv)

]−

2

3

∂

∂z

(µ∂u

∂z)

)+

1

r

∂

∂r

(rµ∂v

∂z

)+ ρgz

(2.4)


ρv∂v

∂r+ ρu

∂v

∂z= −∂p

∂r+

∂

∂z

(µ∂v

∂z

)+

2

r

∂

∂r

(rµ∂v

∂r

)− 2

3

1

r

∂

∂r

[µ

r

∂

∂r(rv)

]− 2

3

1

r

∂

∂r

(rµ∂u

∂z

)+

∂

∂z

(µ∂u

∂r

)− 2uv

r2+

2

3

u

r2

∂

∂r(rv) +

2

3

u

r

∂u

∂z

(2.5)

In Eqs. 2.4 and 2.5, r and z are the radial and axial coordinates; v and u are the radial and axial

velocities; p is the pressure, and gz is the axial gravitational acceleration. The Eqs. 2.2 and 2.3 can be

simplified to a 1D boundary value problem by inserting a stream function in the form ψ(z, r) = r2U(z)

into the mentioned equations. When such a stream function is introduced v/r and other variables become

free of r [74]. Kee et al. [75] have suggested the following variables:

G(z) =−ρvr

(2.6)

F (z) =ρu

2(2.7)

Implementing Eqs. 2.6 and 2.7 in the continuity, Eq. 2.3, yields

G(z) =dF (z)

dz(2.8)

Likewise, the radial momentum equation satisfies when

H =1

r

∂p

∂r= constant (2.9)

Consequently, the axial momentum equation becomes

H − 2d

dz

(FG

ρ

)+ 3

G2

ρ+

d

dz

[µd

dz

(G

ρ

)]= 0 (2.10)

The approach used above to simplify 2D Navier-Stokes equation into a 1D momentum equation, Eq.

2.10, is called similarity solution. The 1D grid that used for the solution of Eq. 2.10 is depicted in

Fig. 2.2. In this figure j represents the index of grid nodes, and JJ is the total number of grid points.

Although Eq. 2.10 have been formulated with respect to z, the simulation code uses the variable X for

the height above burner.


Premixed

Fuel-Air

Mixture

j = 1

j = 2

j = 3

j = 4

j = JJ

j = JJ - 1

j = JJ - 2

j = JJ - 3

X

dir

ecti

on

Flame

Figure 2.2: 2D visualization of a BSS flame including the 1D grid for the numerical solution. Thevariable j represents the nodes’ index, and JJ is the total number of nodes.

2.3.2 Conservation of Energy

The conservation energy equation is depicted in Eq. 2.11 as a function of temperature [76].

ρcp∂T

∂t+ ρcpv.∇T = ∇.(λ∇T )− ρ

∑cp,kYkvk.∇T −

∑h0kωkWk + Q′′′r (2.11)

where, from left to right, the first term is temporal rate of change of temperature, the second term stands

for the convective heat transfer, and cp represents the specific heat of mixture under constant pressure.

On the other side of Eq. 2.11, the first term shows the conductive heat transfer and λ is the thermal

conductivity of the mixture; the second term represents the heat flux rate due to species diffusion, and

vk is the diffusion velocity of the kth species. h0k in the third term is the kth species specific enthalpy,

and the whole term is total rate of enthalpy generation by chemical reactions. finally, Q′′′r represents the

heat loss due to radiation of soot and other gaseous species. In Eq. 2.11 the effect of soot and gas-phase

species can be separated in the right hand side. As a result, the energy equation for a 1D axisymmetric


burner (BSS configuration) is as follows:

ρcpu∂T

∂z− ∂

∂z

(λ∂T

∂z

)+ ρ

KK∑k=1

cp,kYkvk,z∂T

∂z+

KK∑k=1

h0kωkWk + ρcp,sYsvs,z

∂T

∂z+

h0sωsWs − Q′′′r = 0

(2.12)

Here, subscript k refers to parameters pertaining to species k and subscript s denotes soot related

parameters; KK is the total number of species in the gas phase.

Radiation Heat Transfer

In laminar flame simulations, radiation heat transfer has been identified as one of the major heat loss

sources. Radiation heat transfer plays a role in temperature prediction, as well as soot and flame

structure. Although many processes involved in soot formation process are endothermic, since soot is

the prominent source of radiation, it affects the temperature noticeably. The heat loss due to radiation

decreases the soot formation rate which , consequently, reduces heat loss. Thus, there is a feedback

loop between soot and temperature and vice versa which combines the soot formation and radiation

heat transfer. Eq. 2.13 expresses the radiative transfer equation (RTE) for an axisymmetric cylindrical

system, assuming the medium stays in local thermodynamic equilibrium (LTE)[77].

µ∂Iv∂r− η

r

∂Iv∂φ

+ ξ∂Iv∂z

= −κvIv + κvIbv (2.13)

where, parameters Iv, Ibv and κv represent spectral intensity, spectral black-body intensity, and the

spectral absorption coefficient, respectively; µ, η, and ξ are directional cosines. The left hand side

calculates the rate of change of spectral intensity. On the other side of Eq. 2.13, the first term is

responsible for the reduction of radiant energy leaving an element of volume of the medium. The second

one represents the emission rate of the matter. Integrating the RTE along all solid angles and over the

entire spectrum yields the overall radiation heat transfer rate.

There is no explicit solution for the radiation heat transfer equation because it is an integro-differential

equation. Thus, the solution to such equations requires a few simplifying assumptions. The method that

has been adopted for the current work is called optically thin approximation (OTA) which helps to

calculate the term Q′′′r in Eq. 2.12.

Optically Thin Approximation (OTA)

Optical thickness is a measure of the ability of a path length of a medium to attenuate the radiation of

a given wavelength. This dimension-less parameter, τ0v, for a matter with homogeneous composition,

temperature, and pressure is defined as:

τ0v = κvL (2.14)

where L is a characteristic length. In the condition of optically thin limit (τ0v � 1), the radiation by a

fluid element will go directly to the bounding surfaces and any absorption by the fluid will be negligible.

As a result, the radiation transfer equation turns to [78]:

Q′′′r = −4σκP (T 4 − T 4∞) (2.15)


Here, σ is the Stefan-Boltzman constant; κp is the Plank mean absorption coefficient of the mixture;

T and T∞ are the local and the ambient temperatures, respectively. Liu et al. [79] compared different

radiation models and concluded that OTA can predict the temperature of low sooting laminar premixed

flames fairly well. Therefore, in this study the OTA method has been used to consider the radiation

heat transfer from three species including CO, CO2, and H2O, as well as soot particles.

κP = PH2OκH2O + PCO2κCO2

+ PCOκCO (2.16)

In Eq. 2.16, Pi and κi denote the partial pressure and the Plank mean absorption coefficient of species

i, respectively. The plank mean absorption coefficient for each species is calculated using Eq. 2.17.

κi =

5∑j=0

AijTj , i = H2O, CO2, and CO (2.17)

Here, Aij is the polynomial coefficient of a species expressed in terms of temperature [80]. Soot particles

are supposed to act as Rayleigh absorber-emitters [81]. The Plank mean absorption coefficient can be

calculated using the following equation [82]:

κPs = 3.83CfvT (2.18)

where fv represents soot volume fraction, and C is a constant [82] as follows:

C = 36πnk

(n2 − k2 + 2)2

+ 4(nk)2(2.19)

in which, 1n+ ik which denotes the complex refractive index of soot, is set to be 1.57 +0.56i [83].

2.3.3 Conservation of Species

Determination of the gas chemical composition in a reacting flow, where there are several chemical

species available, requires a conservation equation for each of the available chemical species. This mass

transfer equation in axisymmetric cylindrical coordinates comes as follows:

ρv∂Yk∂r

+ ρu∂Yk∂z

= −1

r

∂

∂r(rρYkVk,r)−

∂

∂z(ρYkVk,z) +Wkωk

k = 1, 2, ...,KK

(2.20)

where Yk is the mass fraction of the kth species; Vk,r and Vk,z are the species radial and axial diffusion

velocities for the kth species, respectively; Wk denotes the molecular weight of the kth species; KK is

the total number of gaseous species. The kth species molar production rate, ωk, per unit volume and for

non-third body reactions can expressed by Eq. 2.21.

ωk =

NR∑i=1

vki

(kfi

KK∏k=1

[Xk]v′ki − kri

KK∏k=1

[Xk]v′′ki

)(2.21)

Here,

vki = v′′ki − v′ki (2.22)


NR represents the total number of reactions; The forward and reverse reaction rates of the ith reaction

are shown by kfi and kri, respectively; v′ki and v′′ki are the stoichiometric coefficients of the reactants

and products, respectively; Xk denotes the molar concentration of the kth species. Chemical reaction

source term, ωk, contains the link between soot formation/oxidation and gas-phase chemistry.

The Eq. 2.20 expresses the conservation of species for a 2D cylindrical domain. Considering the

assumptions for the premixed 1D flame, the conservation equation takes the following form:

ρu∂Yk∂z

+∂

∂z(ρYkVk)−Wkωk = 0 k = 1, 2, ...,KK (2.23)

Chemical Kinetics Mechanism

Two chemical kinetics mechanisms, which both take advantage of recently advanced PAH formation

pathways, have been utilized in this work to describe the gas-phase reaction kinetics. The first chemical

mechanism have developed by the Clean Combustion Research Centre at King Abdullah University of

Science and Technology (KAUST) and this mechanism will be referred to as the KAUST mechanism

hereafter. The other chemical kinetic mechanism used in this work has been developed by CRECK

Modelling Group at Polytechnic University of Milan, and it will be referred as CRECK mechanism

hereafter. In the following sections, there will be a brief explanation for each mechanism with an

emphasis on the PAH formation pathways.

KAUST Mechanism

The KAUST mechanism includes the pyrolysis and oxidation of fairly light fuels, C1–C4 [39]. This

mechanism comprises of 202 species and 1351 reactions. The KAUST mechanism is capable of describing

the PAH growth up to the formation of coronene (A7). According to this mechanism, A1 can form via


Figure 2.3: Schematic representation of the major reaction pathways for the formation of large PAHsconsidered by the KAUST chemical kinetic mechanism (source: picture taken from ref.[2]).

three pathways including propargyl (C3H3) recombination, addition of C2Hx on C4Hy molecules, and

addition of CH3 on cyclopentadienyl (C5H5) radicals. PAHs larger than A1 can also grow through three

routes involving HACA; reactions containing species with odd-carbon number such as indenyl (C9H7),

C5H5, and C3H3; and the addition of C4H4 to large PAH radicals.

The reactions included in this chemical mechanism are fundamental reactions which contain detailed

species. In fundamental reactions the stoichiometric coefficients of the reactants and products, v′ki and

v′′ki in Eq. 2.21, are integer numbers which require less memory from the computational point of view.

The open source CHEMKIN 2.0 library which is a package to calculate chemical generation rates and

thermodynamics properties can easily handle these sort of chemical kinetic files.

In order to calculate the reaction rates of unavailable reactions in the literature, quantum calculations

were utilized. Since PAH molecules are large in size and their reactions are relatively independent of

pressure, the rate constants for PAH reactions were estimated in the high pressure limits. A reason-

able agreement between measured and simulated PAH concentrations were obtained in several laminar

premixed and counterflow flames which verifies the model reliability to predict PAH concentrations [39].

CRECK Mechanism

The CRECK mechanism is a detailed chemical kinetic model for the pyrolysis and combustion of a

large variety of fuels at high temperature conditions. The review and assessment of the mechanism were

hierarchically conducted, in the sequence of the foundational C0–C4 species; the reference fuels of alkanes

(n–heptane, iso–octane, n–decane, n–dodecane), cyclo–alkanes (cyclohexane and methyl–cyclo–hexane)

and the aromatics (benzene, toluene, xylene and ethylbenzene); and the oxygenated fuels of alcohols,


C3H6O isomers, ethers (dimethyl ether and ethyl tertiary butyl ether), and methyl esters up to methyl

decanoate [38].

This mechanism contains 249 species and 8153 reactions. There are also PAH formation and growth

reactions from the single aromatic ring, A1, to two artificial PAH species known as BIN1A and BIN1B

which their chemical formulas are C20H16 and C20H10, respectively. In rich conditions, benzyl radicals

are important precursors of PAH components, via the radical recombination reactions as well as C2H2

addition (HACA) [38].

Figure 2.4: Schematic representation of the major reaction pathways for the formation of BIN1B con-sidered by the CRECK chemical kinetic mechanism (source: picture taken from ref.[7]).

Contrary to KAUST mechanism, CRECK involves lumped species which results in reactions with real

stoichiometric coefficients. Although this is not an issue in terms of the combustion theory, in practice,

the codes should be able to handle this type of reactions. The open source CHEMKIN package that has

been used in this study seems to be capable of dealing with such reactions; however, the code could not

calculate the ωk using Eq. 2.21 for the reactions which include real stoichiometric coefficients. After

further development and modification the problem was fixed and the CRECK mechanism was used in

this work.

2.4 Soot Aerosol Dynamics Model

In the soot study, the interesting properties are usually soot particle size, concentration, and interaction

with gas phase. Fig. 2.5 summarizes the physical and chemical processes that evolve the soot particle

size distribution for a soot particle trapped in a microscopic volume of gas. All these processes can be

classified into two groups: internal interactions which includes gas-to-particle conversion and coagulation;

and external processes involving diffusion and thermophoresis which transports the particles across the

boundary of the volume. The Smoluchowski equation [84] provides detailed information to derive a

general dynamic equation (GDE) for the particle number density , n(v, r, t), along with all the mentioned

processes. Sufficiently small surface-to-volume ratio has been assumed in order to prevent deposition


on the walls and sedimentation. The GDE for the tracking of the particle number density, nv, in the

volume range between v and v + dv is as follows [8]:

∂nv∂t

+∇.nvV = ∇.D∇nv +

[∂nv∂t

]growth

+

[∂nv∂t

]coag.

+

[∂nv∂t

]frag.

−∇.cnv (2.24)

where the diffusion coefficient, D, is a function of particle size, and c is the particle velocity vector

resulting from the external force field; the second term on the right hand side, is the summation of

the growth rates; the third term refers to the collisions of the particles; the fourth term represents the

influence of fragmentation on the number density changes.

Figure 2.5: Processes shaping the particle size distribution function in a small volume element of gas.Diffusion and sedimentation involve transport across the walls of the element. Coagulation, nucleation,and growth take place within the element (source: picture taken from ref.[8]).

The explicit solution to the GDE is very complicated, i.e., impossible for a couple of reasons. Firstly,

the GDE is a nonlinear, partial integro-differential equation; moreover, a boundless number of discrete

particle sizes exists in an aerosol-containing environment. As a result, the solution to the GDE requires

numerical modelling. One of the proposed numerical schemes to handle this equation is finite sectional

approximation [85]. The suggested method is utilized to quantify the continuous size/mass spectrum

using a set of sections, or bins, in which all the particles are supposed to have the same size, or they have

a defined size distribution within the section. The discretization of the entire size domain into the size

classes reduces the number of conservation equations required from infinity to the number of sections.

This possibility permits the tracking of the multiple integral quantities per section. As an example,

beside the particles number density, surface area of the particles, aggregate structure, and composition

of the particles can be followed. In the coming section, the sectional approach that has been used in

this thesis will be explained, and there will be a discussion on the mathematical models representing

different soot formation stages.


2.4.1 The Sectional Aerosol Dynamics Model

The sectional aerosol model that has been incorporated in this work is derived from the fixed pivot

approach in the classical sectional description of the particle population balance equation [86]. The

fractal-like solid soot aggregates’ mass spectrum is distributed into a number of quantified classes, i.e.,

particle mass bins. A fixed defined mass is assigned for each section which contains a collection of

aggregates. The typical mass of each section follows a geometric progression with a common ratio fs,

known as spacing factor, and a scale factor equal to the mass of a dimer, UDIM . The correlation among

the mass of section i, Ui, the common ratio, and the scalar is expressed in the following equation.

Ui = UDIM × f i−1s (2.25)

All soot aggregates in a section are assumed to be of similar enough characters that they can be

modelled using mean characteristics. The criteria for distributing soot aggregates into sections is their

mass. A transport equation is considered for the number density of soot aggregates and solved for each

section. In the nucleation step the dimers form from gas-phase incipient species. The soot dimers are

assumed to be spherical, and they occupy the first section. Soot particles move from lower sections to

the higher ones via processes which increase their mass, e.g., coagulation and surface growth. conversely,

oxidation or fragmentation pushes the higher section particles to lower sections.

Beside the aggregate number density equation, another transport equation is required to track the

primary particle number density per section. The introduced transport equation lets the model to

estimate the soot nano-structure by conserving the primary particles for the aggregates [87–89]. A few

assumptions have been made to simplify the primary particle number density equation. Firstly, primary

particles are treated as solid spheres. Secondly, the primary particles inside the aggregates of the same

section share similar enough features, so that they can be modelled using mean characteristics, and

they connect together by point contact, i.e., particle necking is neglected. Particle coalescence is also

neglected. Finally, a universal fractal dimension, Df , of 1.8 is assumed for the agglomorates larger than

the primary nuclei; while smaller particles are supposed to behave like dense spheres (Df = 3.0) [26, 27,

89]. Fixed fractal dimension supposition is usual in aerosol dynamic models when simultaneous particle

nucleation, coagulation, and surface growth processes are taking place. Using the fractal dimension,

the mass of a single aggregate, the primary particle number density, and the aggregate number density,

the aggregates nano-structure can be completely specified. The following soot properties can be derived

from an aerosol dynamic model: particle size distribution (PSD), soot volume fraction (fv), primary

particle diameter, aggregate surface area, and number of primary particles per aggregate.

According to the above-mentioned explanations, the transport equations for aggregate and primary

particle number densities in an axisymmetric cylindrical coordinate for each section are expressed in the

following relations.

ρv∂Na

i

∂r+ ρu

∂Nai

∂z= −1

r

∂

∂r

(rρNa

i Vai,r

)− ∂

∂z

(ρNa

i Vai,z

)+ ρSai (2.26)

ρv∂Np

i

∂r+ ρu

∂Npi

∂z= −1

r

∂

∂r

(rρNp

i Vpi,r

)− ∂

∂z

(ρNp

i Vpi,z

)+ ρSpi

(i = 1, 2, ...,MS)

(2.27)


The 1D assumptions convert the Eqs. 2.26 and 2.27 to:

ρu∂Na

i

∂z= − ∂

∂z(rρNa

i Vai ) + ρSai (2.28)

ρu∂Np

i

∂z= − ∂

∂z(rρNp

i Vpi ) + ρSpi

(i = 1, 2, ...,MS)

(2.29)

In Eqs. 2.28 and 2.29, superscripts a and p represent the parameters related to aggregates and

primary particles, respectively; Ni denotes the number of the ith sectional soot aggregates per unit mass

of the gaseous mixture; Vi is diffusive velocity of soot particles; MS expresses the total number of soot

sections, and Si is the total summation of the source and sink terms correlated with the mass change

within each section. The mentioned term can be described in terms of the soot processes using the

following equation:

Si =

(∂Ni∂t

)nu

+

(∂Ni∂t

)cond

+

(∂Ni∂t

)sg

+

(∂Ni∂t

)ox

+

(∂Ni∂t

)coag

+

(∂Ni∂t

)fr

(2.30)

where, the processes considered are inception (nu), surface condensation (cond), chemical surface growth

(sg), oxidation (ox), coagulation (coag) and fragmentation (fr). The soot nucleation is only considered

for the first section. Fig. 2.6 depicts all above mentioned processes along the axis of the flame.

z

r

Premixed Fuel and Oxidizer

OH O2OH

OH

OHOH

O2

O2

O2

O2

Fuel Pyrolysis

PAH Formation

Nucleation

Growth

Oxidation

Figure 2.6: Soot morphology in a burner stabilized stagnation flame.


Nucleation Model

In the PAH-based soot formation models, the generation and growth of aromatic species connects the

combustion gas-phase chemistry and soot formation zone. Evidence shows the formation of small soot

particles depends on the existence of PAH species [90]. Thus, the dimerization of a pair of PAH molecules

is considered as the nucleation model. The dimer formation rate is proportional to the rate of collision

of PAH species [59].

According to Sabbah et al. [44], Wang [6], Eaves et al. [17, 18], and Veshkini et al. [15], the pair of

PAH molecules constructing a dimer can separate due to the thermodynamics condition which is very

routine in the flame temperature; thus, the presence of efficiencies in the nucleation models is necessary

to account for the dimer dismantling. In order to avoid dealing with arbitrary or tuned efficiencies and

to improve the nucleation model based on a fundamental understanding of the dimerization process, the

nucleation process has been allowed to be reversible.

PAH + PAH←→ Dimer (2.31)

The forward rate of dimerization is determined by the rate of physical collision of the nucleating PAH

molecules in the free-molecular regime, similar to the non-reversible nucleation model. The forward rate

of dimerization and the forward rate coefficient (kFWD) for a dimer composed of PAHj and PAHk are

calculated according to Eqs. 2.32 and 2.33, respectively:(∂NDIM∂t

)FWD

= kFWD [PAHj ] [PAHk] (2.32)

kFWD =2.2

ρ

√8π(NC,PAHj

+NC,PAHk

)kBT

CmassNC,PAHjNC,PAHk

(dPAHj + dPAHk

)2A2v (2.33)

where kB is the Boltzmann constant; Cmass is the mass of a carbon atom; NC,PAH is the number of

carbon atoms in the incipient PAH species; dPAH is the diameter of the incipient PAH species; Av is

Avogadro’s number; and [PAHi]denotes the molar concentration of the incipient PAH species.

Following the work by Eaves et al. [17, 18], the reverse rate coefficient (kREV ) is calculated from the

relationship between the dimerization equilibrium constant and rate coefficients, Eq. 2.34.

kFWD

kREV= Kp,D(RT )∆n[17, 18] (2.34)

The assumption of gaseous species for the dimers leads ∆n to be equal to 1. In order to calculate the

equilibrium constant of dimerization, Eq. 2.35, the Gibbs free energy of dimerization has to be evaluated,

which is related to enthalpy and entropy through the following relation: ∆G◦D = ∆H◦D − T∆S◦D. The

following equations can be derived using statistical mechanics [91] considering the assumptions described

in [17, 18] to estimate the change in enthalpy and entropy of the nucleation processes for any arbitrary

PAH–PAH collision:

Kp,D = exp

(−∆G◦D

RT

)(2.35)

∆HD∼= −E0 − 4kBT +

6∑i=1

(1

2+

1

ehcvi/kBT − 1

)hcvi (2.36)


∆SDRu

∼= ln

[(m3hcB1B2

2m1m2B3

)3/2h3P

π2(e1kBT )4

σ1σ2

σ3

]+

6∑i=1

{hvi/kBT

exphvi/kBT −1− ln

(1− e−hvi/kBT

)} (2.37)

Here, ∆HD is the enthalpy change due to dimerization, ∆SD is the entropy change due to dimerization,

Ru is the universal gas constant, kB is the Boltzman constant, T is the gas temperature, h is Plank’s

constant, c is the speed of light, m1 and m2 are the masses of the two colliding entities, m3 is the

combined mass of the two entities, σi are the symmetry numbers, with dimers assumed to have no

symmetry (σi = 1), and Bi are the rotational constants. Two remaining parameters, E0 and vi, influence

both enthalpy and entropy change. E0 is the binding energy, and vi is the ith (out of 6 in total) vibration

mode frequency created when nucleation process takes place. It is assumed that the frequencies of the

colliding objects remain constant during the nucleation processes, which indicates PAHs stick to each

other via physical coalescence [6].

According to the literature review performed by Veshkini et al. [15] and Eaves et al. [17, 18] on

the importance of reversibility in soot formation and its associated parameters, the binding energy of

coronene dimer, 69.2 KJ/mol, has been picked to be incorporated into the Eq. 2.36. The study of Eaves

et al. [17, 18] also provides information about the vibrational frequencies; based on the equilibrium

constant proposed for pyrene dimerization, an effective vibration frequency of 18 cm−1 can be inferred.

Due to the limited computational resources, the nucleation model cannot consider all the possible

PAHs as nucleating species. According to Veshkini et al. [15] , the species anthanthrene, benzo[ghi]perylene,

and benzo(ghi)fluoranthene have the features of the PAH molecules. These three species are available

in KAUST II mechanism. For the CRECK mechanism, the largest PAHs available in the species are

pyrene, BIN1A, and BIN1B, which the last two have 20 carbon atoms. The molecular structure of the

mentioned species is shown in Fig. 2.7.

Figure 2.7: Nucleating species chemical structure.


Condensation Model

The absorption of large gas-phase species to the particle’s surface is one of the heterogeneous gas-to-

particle conversions known as condensation. Similar to nucleation, the collision of condensing species

and the surface of the particles builds the base of the condensation model [92]. The PAHs that are

allowed to condensate are the same as those were introduced to the nucleation process. The code has

the ability to consider other PAHs as well.

In previously developed soot models, a 100 % sticking probability upon collision is a common as-

sumption [15]; however, based on the flame thermodynamics condition the freshly attached PAHs can

easily evaporate from the surface of the soot particles due to high reversibility [6] which requires the

condensation model to be reversible. Neither a single condensation efficiency nor a functional form

can satisfactorily reproduce all soot morphological parameters [15]. Therefore, a condensation model

is required to calculate the reverse rate of condensation process based on the flame conditions. Eaves

et al. [17, 18] developed an efficiency based reversible model to study soot formation in the Santoro

coflow diffusion flame. According to the work by Eaves [17, 18] the combination of fully reversible nu-

cleation model and an efficiency based reversible condensation model can reasonably predict all the soot

morphological properties. However,

The condensation model that has been used in the current work has been adopted from Veshkini et

al. work [15]. This novel model is based on an equilibrium stand point of view. In their study soot

particles in each section are assumed to be a unique species with properties of a large PAH molecule

with the same mass. The mass growth via PAH addition will transform a soot particle to a particle with

higher mass which is described by the reaction as follows:

Sooti + nPAH ←→ Sooti+1 (2.38)

Here, n in the Eq. 2.38 denotes the total number of PAHs needed to push a particle from section i to

i+ 1, and can be calculated with:

n =WTPAH

Ui(fs − 1)Av(2.39)

Here, WTPAH is the molecular weight of the PAH; Ui is the mass of section i; fs is the sectional factor,

and Av is the Avogadro’s number. The equilibrium constant of the mentioned reaction can be calculated

with Eq. 2.40.

Kp,C = exp

(−∆G◦CRT

)= exp

(−∆H◦C − T∆S◦C

RT

)=

Ni+1

Niχneq,PAH(2.40)

where Ni is the number density of soot particles in the ith section. In order to calculate the equilibrium

constant and Gibbs free energy, very similar to nucleation model, the following equations can be derived

using statistical mechanic principles to determine the enthalpy and entropy change for the addition of n

PAH molecules to a soot particle:

∆HD∼= −nE0 − 4nkBT +

6n∑i=1

(1

2+

1

ehcvi/kBT − 1

)hcvi[15] (2.41)


∆SDRu

∼= ln

[(m3(hcB1)nB2

2nmn1m2B3

)3/2(h3P

π2(e1kBT )4

)nσn1 σ2

σ3

]+

6n∑i=1

{hvi/kBT

exphvi/kBT −1− ln

(1− e−hvi/kBT

)} (2.42)

where n is the number of PAH molecules, ∆HD is the enthalpy change due to dimerization, ∆SD is the

entropy change due to dimerization, Ru is the universal gas constant, kB is the Boltzman constant, T

is the gas temperature, h is Plank’s constant, c is the speed of light, m1 and m2 are the masses of the

two colliding entities, m3 is the combined mass of the two entities, σi are the symmetry numbers, and

Bi are the rotational constants.

The estimated equilibrium constant is substituted into Eq. 2.40 to calculate the mole fraction of the

PAH. The equilibrium concentration of condensing PAH species is incorporated in a Heaviside function

to form a condensation efficiency function which is shown in Eq. 2.43

γik =1

1 + exp

[−2

[4χPAHk

(Kp,Ck

Ni

Ni+1

) 1n − 2

]] (2.43)

Here, n is the PAH coefficient in reaction 2.38 and determined by Eq. 2.39; χPAHkis the mole fraction

of the kth condensing PAH species and Kp,Ckis the corresponding species equilibrium constant for

condensation. Similar to the nucleation process, the binding energy of coronene dimer, 69.2KJ/mol,

has been picked to be incorporated into the Eq. 2.41. It has also been found that the collision vibration

frequency of 17 cm−1 can satisfactorily reproduce all morphological soot properties. The condensation

efficiency, γCond., is the sticking probability which takes into account the probability of the molecules

bouncing off the surface after collision. Using the condensation efficiency and other parameters the

condensation rate can be calculated using the following equation:

Icond,i =

KPAH∑k=1

γikβikNC,kCmass [PAH]kNai (2.44)

where Icond,i is the mass growth rate of the ith section soot agglomerate due to condensation in the unit

of gs/gmix/sec, and is non-negative value; βik is the collision kernel of the kth condensing species and

the ith section soot aggregate.

According to the sectional scheme the mass growth must be distributed among all mass sections.

The mass of aggregates in each section is fixed; therefore, the mass growth of an aggregate in section i

is reflected by transferring the equivalent amount of mass in terms of number of aggregates from section

i to section i+ 1. In the primary particle transport equation, Eq. 2.29, the growth term is multiplied by

the number of primary particles per aggregate in order to conserve the primary particle numbers. The

above stated descriptions are presented mathematically in following relations:

(∂Na

i

∂t

)cond

=

− Icond,l

m2−m1if i = 1

Icond,i−1

mi−mi−1− Icond,i

mi+1−miif i = 2, ...,MS − 1

Icond,MS−1

mMS−mMS−1, if i = MS

(2.45)


(∂Np

i

∂t

)cond

=

− Icond,l

m2−m1if i = 1

Icond,i−1

mi−mi−1np,i−1 − Icond,i

mi+1−minp,i if i = 2, ...,MS − 1

Icond,MS−1

mMS−mMS−1np,i−1 if i = MS

(2.46)

Here, mi is the aggregate mass of the section i; np,i is the number of primary particles per aggregate of

the section i which is equal toNp

i

Nai

. It should be emphasized that for the first and last section the sum

of all growth terms must equal zero to make sure that no new particles are numerically formed due to

growth processes.MS∑i=1

(∂Na

i

∂t

)cond

=

MS∑i=1

(∂Np

i

∂t

)cond

= 0 (2.47)

Chemical Surface Growth and Oxidation Models

The soot surface heterogeneous reactions with the gas-phase species used in this work are expressed

in Tab. 2.2. The renowned hydrogen-abstraction-carbon-addition (HACA) is responsible for the mass

growth and oxidation by oxygen [59, 92]. The kinetics of the surface reactions in HACA scheme is a

function of surface sites, the arm chair sites depicted in Fig. 2.8 which contains four carbon atoms.

These carbon atoms could be saturated, Csoot–H, or dehydrogenated, Csoot◦ , on the particle surface.

Figure 2.8: Illustration of armchair sites on the surface of a soot particle.

Table 2.2: HACA–based soot surface growth and oxidation reactions[2], k = AT be−Ea/RT

No. Reaction A(cm3

mol.s

)b Ea

(kcalmol

)S1 Csoot–H+H ↔ Csoot◦ + H2 4.2× 1013 0.0 13.0

S2 Csoot–H+OH ↔ Csoot◦ + H2O 1.0× 1010 0.73 1.43

S3 Csoot◦+H → Csoot–H 2.0× 1013 0.0 0.0

S4 Csoot◦+C2H2 → Csoot–H + H 8.0× 107 1.56 3.8

S5 Csoot◦+O2 → 2CO + product 2.2× 1012 0.0 7.0

S6 Csoot–H+OH → CO + product γOH = 0.13

The following equation is useful to calculate the concentration of the saturated sites on the particle’s

surface.


[Csoot − (H)] =AsAv

χCsoot−(H) (2.48)

Here, As(cm2/cc) is soot surface density; Av is the Avogadro’s number; and χCsoot−(H) is the number

of the sites per unit surface area of the soot particles and estimated to be 0.23 [59]. The concentration

of dehydrogenated sites, [(C)soot◦ ], is calculated with χCsoot◦ in similar way. The following equation

calculates χCsoot◦ using as steady state assumption.

χCsoot◦ =(k1 [H] + k2 [OH])χCsoot−(H)

k−1 [H2] + k−2 [H2O] + k3 [H] + k4 [C2H2] + k5 [O2](2.49)

As a result, the mass increase rate due to HACA (S4), and the mass reduction rate caused by O2

oxidation (S5) are:

IC2H2,i = 2αCmassAs,iAv

(k1 [H] + k2 [OH])χCsoot−Hk4 [C2H2]Npi

k−1 [H2] + k−2 [H2O] + k3 [H] + k4 [C2H2] + k5 [O2](2.50)

IO2H2,i = 2αCmassAs,iAv

(k1 [H] + k2 [OH])χCsoot−Hk5 [O2]Npi

k−1 [H2] + k−2 [H2O] + k3 [H] + k4 [C2H2] + k5 [O2](2.51)

In Eqs. 2.50 and 2.51, As,i is the primary particle surface area in the section i, and α is the surface

reactivity parameter. According to Tab. 2.2, the reaction S6 is another source for soot oxidation. This

oxidation rate can be estimated based on kinetic theory with a probability γOH as follows:

IOH,i = γOHβOH,iCmass [OH]Nai (2.52)

The surface growth source term,(∂Ni

∂t

)sg

, is evaluated by substituting Icond,i with IC2H2,i using Eqs.

2.45 and 2.46. The surface oxidation source terms are calculated using the following relations:

(∂Na

i

∂t

)ox

=

Iox,2

m2−m1− Iox,1

m1 if i = 1

Iox,i+1

mi+1−mi− Iox,i

mi−mi−1if i = 2, ...,MS − 1

Iox,MS

mMS−1−mMSif i = MS

(2.53)

(∂Np

i

∂t

)ox

=

Iox,2

m2−m1np,2 − Iox,1

m1if i = 1

Iox,i+1

mi+1−minp,i+1 − Iox,i

mi−mi−1np,i if i = 2, ...,MS − 1

Icond,MS

mMS−1−mMSnp,MS if i = MS

(2.54)

The reason that different relations are used for the growth and oxidation stems from the fact that

oxidation moves particles from high sections to low sections while the growth processes do the opposite.

Coagulation Model

Coagulation is the sticking of the two soot particles when they collide. The role of this process is to

increase the soot aggregate size. Coagulation adds to the number density of aggregates in higher mass

sections, while decreases soot aggregate concentration in lower mass sections. Thus, coagulation keeps

the number of primary particles constant, while reduces the number of aggregates. The coagulation

rate is calculated using binary collision rate of soot particles estimated in the entire Knudsen numer


regime [70, 93] using a sticking probablity [63]. The coagulation rate in the ith section for aggregates

and primary particles are calculated as

(∂Na

i

∂t

)coag

=∑j

∑k

(1− δjk

2

)ηijkβjkξjkN

aj N

ak −Na

i

MS∑m=1

βimξimNam (2.55)

(∂Np

i

∂t

)coag

=∑j

∑k

(1− δjk

2

)ηp,ijkβjkξjkN

pjN

pk −N

pi

MS∑m=1

βimξimNam (2.56)

{∀k ∈ [1, i] ∧ j ∈ [k, i] | mi−1 < mj +mk < mi+1}

In equations 2.55 and 2.56, δjk is the Kronecker delta; βjk is the Boltzman collision kernel of two

aggregates from the sections j and k; and ξjk represents the coagulation collision coefficient. The mass

and number of aggregates have to be kept constant during the coagulation step; therefore, the freshly

formed aggregates are transferred to two consecutive sections. This division has been accomplished using

parameter ηijk which is defined as follows:

ηijk =

mi+1−(mj+mk)

mi+1−miifmi ≤ mj +mk ≤ mi+1

mi−1−(mj+mk)

mi−1−miifmi−1 ≤ mj +mk ≤ mi

0 else

(2.57)

Moreover, the parameter ηp,ijk in Eq. 2.56 is defined according to the following expression:

ηp,ijk =mi

mj +mk(np,j + np,k) (2.58)

Fragmentation Model

The cracking of the fractal-shape aggregate chain into smaller aggregates is known as fragmentation. In

the current work, only the oxidation-driven fragmentation has been incorporated into the model. The

model considers the aggregates breakage into two children aggregates with identical mass; moreover, no

fragmentation takes place for an aggregate containing fewer than two primary particles. According to

the assumptions, the fragmentation rate of the aggregates in the section i is expressed by

(∂Na

i

∂t

)fr

=

Γ+S2N

a2 if i = 1

(Γ− 1)SiNai + Γ+Si+1N

ai+1 if i = 2, ...,MS − 1

(Γ− 1)SMSNaMS if i = MS

(2.59)

(∂Np

i

∂t

)fr

=

Γ+S2N

a2 np,2

fsif i = 1

(Γ− 1)SiNai np,i +

Γ+Si+1Nai+1np,i

fsif i = 2, ...,MS − 1

(Γ− 1)SMSNaMSnp,MS if i = MS

(2.60)

where Γ and Γ+ denote breackage distribution functions which moves the newly formed children aggre-

gates int two neighbor sections in order to conserve the mass and number of aggregates. The breakage

distribution functions are estimated as [94]:


Γ =fs − 2

fs − 1(2.61)

Γ+ =fs

fs − 1(2.62)

The term Si in Eq. 2.59 is the fragmentation rate per aggregate and is adopted from [94]:

Si = 1.0× 105rox,i (np,i)1/Df (2.63)

where rox,i represents the oxidation rate on a mass basis of soot aggregates in the ith section per unit

surface area; Df is the aggregate fractal dimension.

2.4.2 Numerical Method

The main differential equations described in previous sections do not have explicit solutions; therefore, a

numerical approach is required to find a very close estimation to the real solution with an error tolerance

of 10−6. The premixed boundary value problem is solved numerically based on the finite difference

framework. In the following sections, the details for the numerical method that was utilized for the

premixed stagnation flame will be presented.

Premixed Stagnation Flame

The OPPDIF code has been designed to simulate a premixed/diffusion counter-flow flame in a 1D domain

[95]. This code can be modified to a burner stabilized stagnation using the non-slip boundary condition

at the oxidizer boundary. The described soot aerosol dynamics model has been coupled with OPPDIF

code to predict the soot desired properties in premixed stagnation flames. The differential equations

in OPPDIF code are discretized using the finite difference approximation. The discretization of the

sectional aggregate number density and primary particle number density has been carried out similar to

the species conservation equation discretization. The code has the capability to switch between second

order central difference and first order windward difference methods for the convective terms.

The terms that are not differentiated, such as the chemical production rate terms, are calculated at

the mesh points j. Other parameters that do not come within the derivatives are also evaluated at the

mesh points.

Discretization of the governing equations forms a nonlinear system of equations. The Newton’s

method has been implemented to find the solution to this system of equations which is cast in residual

form as follows:

F (v) = 0 (2.64)

where v is the vector of all unknowns and F (v) is the vector of all equations. If v◦, an approximated

solution vector, is guessed for the unknowns, the equations F likely will not tend to zero; rather,

evaluating the functions F by the v◦ as an input will form the residual vectors:

F (v◦) = RES (2.65)

The final goal is to find values for the unknowns vector, v∗, with zero residuals, F (v∗) = 0. OPPDIF


takes advantage of the modular solver subroutine TWOPNT to address the boundary value problem.

TWOPNT uses a hybrid method to find the solution. This subroutine utilizes the modified damped

Newton’s method to attempt solution of the steady state, and when the newton iteration is diverging it

turns to time integration [96]. After the time evolution performed on the solution, TWOPNT restarts

the Newton’s method to converge the solution to the steady state. The Newton’s method produces a

series of intermediate unknown vectors,{v(n)

}, that converges to the solution of nonlinear equations:

v(n+1) = vn +

(∂F

∂v

)−1

v(n)

F (v(n)) (2.66)

The Newton’s method is not computationally efficient and is afflicted by lack of robustness. The

calculation of ∂F∂v , Jacobian matrices, is highly time consuming, and the convergence to the solution

depends on a very good initial guess v0. The modified Newton’s method imposes the following modifi-

cations to the primary method. Firstly, since the linear system changes minimally from one iteration to

the next, the Jacobian matrix updates after a few number of iterations. Second, a damping factor λ(n)

has been defined for the evaluation of v(n+1) from v(n) in order to adjust the solution in each iteration

and reduce the chance of divergence. As a result, the Eq. 2.66 changes to:

v(n+1) = vn + λ(n)(J (n)

)−1

F (v(n)) (2.67)

Here, the damping factor reduces according to a geometric progression.

λ(n) = 2−0.5, 2−1.0, ..., 2−2.5 (2.68)

In order to form the elements of the Jacobian matrix, a finite difference perturbation method is suggested

by [97]. References [73, 95, 96, 98] provide detailed information regarding the OPPDIF code, numerical

method, and modified Newton’s method.

Boundary Condition

The boundary conditions at the inlet nozzle are express below:

F =ρIuI

2(2.69)

G =−ρvr

= 0 (2.70)(dH

dz

)I

= 0 (2.71)

T = TI (2.72)

ρuYk + ρVkYk = (ρuYK)I (2.73)

ρuNi + ρViNi = (ρuNi)I (2.74)

where, the index I refers to the input value of parameters which can be derived from the experimental

setup information; Vk and Vi represent the diffusion velocity of the kth specie and soot aggregate of the

section i, respectively. The inflow boundary condition specifies the total mass flux, including diffusion

and convection. If there would be a gradient at the boundary, the conditions would allow diffusion to


the upstream.

The boundary condition at the stagnation plane is listed below:

F = 0 (2.75)

G =−ρvr

= 0 (2.76)(dH

dz

)W

= 0 (2.77)

T = TW (2.78)

ρ

(dVkYzdz

)W

= Wkωk (2.79)

(DNidz

)W

= 0 (2.80)

Since the nonslip boundary condition assumption has been made, u, v, and Vk are all zero at the

stagnation wall. The wall temperature, TW , equals the measured temperature. The axial convective

velocity reduces to zero in the proximity of the wall which produces a diffusive flux equal to the chemical

source term of each specie at the stagnation wall.

Chapter 3

Results and Discussion

The results on the contribution of CO2 addition to the soot formation in burner stabilized stagnation

(BSS) premixed flames are presented in the following order. The first section will discuss the model

validation against benchmark ethylene flames. Within the mentioned section, computed temperature

profiles, soot volume fraction (fv), and particle size distributions (PSDs) are compared with measure-

ments from [9], respectively. Then a wall temperature sensitivity analysis will reveal how dependent

the code is on the boundary temperature. After validation, the model was used to see to effect of CO2

addition on the PSDs. In the second section, the computed fv and PSDs for the CO2-diluted flames will

be compared with experimental results from [1]. Then, the reversibility of the soot model and boundary

temperature effect on the morphology will be expressed. At the end of this section, the role of CO2 in

the soot formation process will be explained. Finally, the influence of the chemical kinetic file on the

evolution of PSDs and capturing the CO2 addition effect will be presented.

3.1 Model Verification

The model that has been utilized in this thesis was adopted from the work by Veshkini et. al. [15].

This model couples the OPPDIF code, which calculates the flame temperature and gas-phase species

composition, with a sectional aerosol dynamics model, which is a bridge between gas-phase chemistry

and solid-phase particulates. Soot volume fraction, particle nanostructure, and size distribution are soot

properties of interest. The simulation tool used in the current work can predict the mentioned properties

considering flame temperature, mixing effects, and residence time. A radiation heat transfer model was

also incorporated into the model to account for the radiation heat loss emitted from CO2, H2O, and

soot particles.

The soot nucleation and condensation models incorporated in this work use different parameters than

what is suggested by Veshkini et al. [15]. This fact necessitates the revalidation of the model using a

similar test case before moving toward the main problem.

34

Chapter 3. Results and Discussion 35

HP =

0.5

cm

z

r

Premixed

Fuel and

Oxidizer

z

r

Premixed

Fuel and

Oxidizer

HP =

0.6

cm

z

r

Premixed

Fuel and

Oxidizer

HP =

0.7

cm

Figure 3.1: Schematic of different burner-to-stagnation surface separations.

Properties of soot measured in flame C3 [9] were chosen as the validation test for the model discussed

above. This flame was also used by Veshkini et al. [15] and Saggese et al. [7] for a similar purpose.

Camacho et al. [9] generated soot in a 16.3% ethylene–23.7% oxygen– 60%argon BSS flame at atmo-

spheric pressure. The cold gas velocity was 8 cm/s (298 K and 1 atm). The soot was sampled along

the centerline of the flame through an orifice which is drilled into the stagnation surface. A scanning

mobility particle sizer was used to analyze the gas sample over a range of burner-to-stagnation surface

separations, Fig. 3.1, to measure the PSDs. The volume fractions of the particles, fv, were calculated

via the detailed PSDs.

In the BSS flame setup, each burner-to-stagnation surface represents a distinct flame although the

inlet conditions are the same. This difference stems from the temperature and velocity profile changes due

to the different burner-to-stagnation surface separations. Since each spacing forms a unique boundary

condition, all the probe sampling techniques should consider each spacing as a unique flame [7]. The

experimental measurements over the separation range of 0.55 to 0.8 cm have been used for the model

verification.

3.1.1 Temperature Profiles

Soot formation process is a strong function of temperature; as a result, accurate prediction of the flame

temperature is a necessary requirement for predicting the properties related to soot. Soot mostly forms

in the post flame region, i.e., the region after the peak temperature. The inclusion of radiation heat

transfer model prevents temperature overprediction in the post flame region.

Fig. 3.2 compares the computed and measured temperature profiles for a series of burner-to-

stagnation surface separations, HP. The peak temperature is all around 1830 K; however, the burnt

gas cools off at different rates depending on the HP. In general, the computed temperature profiles cap-

ture the experimental results within their uncertainties. This means the model solves the energy equation

correctly and provides a reliable temperature profile to calculate other thermodynamics properties for

the next steps.


400

800

1200

1600

2000

0 0.2 0.4 0.6 0.8

T(K

)

X(cm)

HP = 0.7 cm

400

800

1200

1600

2000

0 0.2 0.4 0.6 0.8

T(K

)

X(cm)

HP = 0.55 cm

X(cm)

400

800

1200

1600

2000

0 0.2 0.4 0.6 0.8

T(K

)

HP = 0.8 cm

Simulation

Experiment

400

800

1200

1600

2000

0 0.2 0.4 0.6 0.8

T(K

)

X(cm)

HP = 0.6 cm

T(K

)

Figure 3.2: Comparison between modelled (solid lines) and measured (symbols) axial temperature pro-files of the BSS ethylene flame for a series of HP values.

3.1.2 Soot Volume Fraction

Soot volume fraction, fv, is a global measure of a flame’s sooting behaviour. The numerical prediction

of fv values satisfies many industrial purposes. In the experiment, soot volume fraction is derived using

the integration of the PSD with respect to the particle diameter, while in the modelling, fv is calculated

using the mass fraction and density of soot particles. Comparison of the calculated and experimental

soot volume fraction as a function of burner-to-stagnation surface separation is presented in Fig. 3.3.

The agreement between the measurements and the simulations is reasonably good.


0.000

0.005

0.010

0.015

0.020

0.025

0.5 0.6 0.7 0.8 0.9

f v(p

pm

)

Height Above Burner, HP

Experiment

Simulation

Figure 3.3: Comparison of the measured soot volume fraction (triangles) and model predictions (circles)as a function of burner-to-stagnation surface separation.

Although soot volume fraction is an important parameter of interest and can provide enough infor-

mation about the total soot formed in a flame, it does not present other useful information about the

soot aggregate structures. Current emission regulations, e.g. PM2.5, are based solely on the mass of

particles emitted. However, according to Wang [6], soot models have to be able to predict the chemical

composition of nascent soot and its size distribution since the environmental and human health effects

of soot emission are more directly related to the PSD and chemical composition than particle mass.

3.1.3 Particle Size Distribution (PSD)

At a detailed level, the model generates the evolution of the PSDs reasonably well from nucleation level

to later stages of mass/size growth, as shown in Fig. 3.4. PSDs show detailed information about the

size of the particles and their population; more importantly, they can depict different stages of the

soot morphology. The PSDs are computed at the stagnation surface. The model predicts the overall

progression of the PSDs; all the computed lines are in a qualitative agreement with the measurements.


Experiment Simulation

Particle Diameter, DP (nm)

Pa

rtic

le D

iam

eter

, D

P(n

m)


fdsafaf

1.0E+06

1.0E+07

1.0E+08

1.0E+09

1.0E+10

1.0E+11

1.0E+12

1 10 100

HP = 0.7 cm

1.0E+06

1.0E+07

1.0E+08

1.0E+09

1.0E+10

1.0E+11

1.0E+12

1 10 100

HP = 0.8 cm

16

17

18

19

110

111

112

1 10 100

HP = 0.55 cm

16

17

18

19

110

111

112

1 10 100

HP = 0.60 cm

Pa

rtic

le S

ize

Dis

trib

uti

on

, D

N/D

log

DP

(c

m-3

)

Figure 3.4: Comparison of the computed (solid lines) and measured (symbols) PSDs. The experimentaldata is adopted from [9].

Studying the PSD functions can help identifying the roles of different processes in forming aggregates.

In lower spacings such as 0.55 cm the size distribution is unimodal. By moving from HP 0.6 cm to

HP 0.7 cm, the unimodal distribution becomes bimodal due to the growth, e.g. condensation, and

coagulation processes as the height increases. Meanwhile, the curve widens, indicating large aggregates

are formed.

3.1.4 Stagnation Wall Temperature Sensitivity Analysis

As mentioned in the section 3.1.3, the PSD function is computed at the stagnation surface location.

Moreover, the wall temperature is used as the temperature boundary condition. Soot formation is

a strong function of temperature. In this work, the temperature that has been assigned to the wall

boundary was derived from the experimental measurements [9]. According to Camacho et al. [9], Tang


et al. [1], and Abid et al. [32], the embedded thermocouple into the stagnation surface measures the

temperature within the uncertainty range of ±30 K. This fact necessitates a wall temperature sensitivity

analysis to see how temperature changes affect the PSDs.

1 10 100

HP = 0.8 cm

Experiment

Tw = 470

Tw = 485

Tw = 55016

17

18

19

110

111

112

1 10 100

HP = 0.55 cm

Experiment

Tw = 460

Tw = 497

Tw = 510

Tw = 520

Tw = 550PS

D,

DN

/Dlo

gD

P (c

m-3

)


Figure 3.5: Wall Temperature Sensitivity Analysis

The comparison between measurements (symbols) and modelled (solid lines) PSDs over a range of

wall temperatures is depicted in Fig. 3.5 for the spacings 0.55 and 0.8 cm. The left frame shows even 10

K difference in wall temperature represents a noticeable effect on the PSDs. The right frame investigates

the similar influence in a larger spacing. The analysis shown in Fig. 3.5 expresses how sensitive the

model is to the stagnation wall boundary temperature. As a result, the ±30 K temperature uncertainty

should be considered in determining the proper temperature boundary condition.

3.1.5 HACA Effect

The very popular hydrogen–abstraction–carbon–addition (HACA) process is one of the pathways for the

formation of polycyclic aromatic hydrocarbons (PAHs). There are evidences in coflow diffusion flames

which show that HACA mechanism is important in soot mass/surface growth [16, 17, 79]. Moreover, in

premixed BSS flames, Tang et al. [1] suggests that HACA plays a role in the soot growth; Saggese et

al. [7] also incorporated this pathway into their BSS flame soot model, and based on their sensitivity

analyses, this process is important. Wang [6] provides evidence that most of the soot growth in BSS

flames occur in a region which the temperature drops to 1450 K and the concentration of the H atoms

is too small to account for the radical formation on the soot surface; thus, the observed growth is

unexpected in terms of the HACA mechanism. Veshkini et al. [15] showed that HACA plays a minor

role in the growth process using a thorough sensitivity analysis. The model that was used in this work

includes the HACA surface growth, in which alpha is the efficiency of the process. The comparison of

the two extreme cases is depicted in Fig. 3.6. Solid black line shows fully-disabled surface reactivity,

and dashed blue line represents 100% surface reactivity. The soot model generates very similar PSDs

for the abovementioned extreme cases which means the HACA mechanism in BSS flames might not be


as active as it is in the coflow diffusion flames.

16

17

18

19

110

111

112

1 10 100

HP = 0.60 cm

Experiment

Alpha = 0.0

Alpha = 1.0


PS

D,

dN

/ d

Lo

gD

P(c

m-3

)

Figure 3.6: Comparison of the different surface reactivity parameters.

0.0E+004.0E-038.0E-031.2E-021.6E-022.0E-02

0.0E+001.2E-042.4E-043.6E-044.8E-046.0E-04

0.00.20.40.60.8

HP = 0.8 cm

H radical fvS

oot

Volu

me

Fra

ctio

n (

pp

m)

0.0E+00

4.0E-03

8.0E-03

1.2E-02

1.6E-02

2.0E-02

0.0E+00

1.2E-04

2.4E-04

3.6E-04

4.8E-04

6.0E-04

0.0 0.2 0.4 0.6 0.8

HP = 0.8 cm

H radical

fv

0.0E+00

1.0E-03

2.0E-03

3.0E-03

4.0E-03

5.0E-03

0.0E+00

1.2E-04

2.4E-04

3.6E-04

4.8E-04

6.0E-04

0.0 0.2 0.4 0.6

HP = 0.6 cm

H radical

fv

X(cm)

Mole

Fra

ctio

n

Figure 3.7: Comparison of the H radical concentration and fv for the spacings 0.6 and 0.8 cm.

The reactions that are taken into account for the HACA surface growth model are listed in table

2.2. H radical exists in the majority of the reactions introduced in table 2.2. According to Wang [6],

successful HACA surface growth requires H radicals to activate a position on the surface of the soot for

addition of an acetylene molecule. The H radical concentration along with fv has been depicted with

respect to the height above burner in Fig. 3.7. fv is a soot global parameter which shows the mass

growth trend. Based on Fig. 3.2, the flame front is located at 0.1 cm above the burner tip. Fig. 3.7

shows that most of the soot growth occurs in the post flame region and very close to the stagnation wall.

Moreover, the concentration of H radical is almost zero in the region that most of the soot mass growth

occurs. As a result, the species generation term of the reactions involved in the HACA soot surface

growth would be negligible, which means ineffective HACA growth. This conclusion is consistent with


the study by Saggese et al. [7]. In their work, they have shown that by decreasing the HACA reactions’

rates by a factor of ten, the change that happens to the PSD is insignificant. This means weakening the

HACA process does not affect the evolution of PSDs and growth process.

Up to here, the model was validated against the experimental measurements for different parameters

of interest. The modelling tool is now ready to study other BSS flames. The dilution of the fuel and/or

oxidizer mixture stream is an established method to develop low temperature combustion in order to

prevent both soot and NOx formation. CO2 is one of the major components of combustion products,

and there is experimental evidence that diluting the unburnt fuel mixture with CO2 would suppress the

soot formation [1, 12]; however, there are unanswered questions in this field. Here after, the scope of the

work is about the CO2 addition effects on premixed BSS ethylene flame sooting behaviour.


3.2 CO2 Addition Effects

The soot properties that are studied in this section were chosen from the work by Tang et al. [1]. They

measured the PSD functions for three different ethylene BSS flames over a range of burner-to-stagnation

surface separations. Tang et al. [1] generated soot in a 16% ethylene–24% oxygen–60% argon BSS flame

at atmospheric pressure for the first flame, A1. For the second and third flames, 20% and 30% of Ar

has been replaced with CO2, respectively. The summary of the flame compositions is available in table

2.1. The cold gas velocity was 8 cm/s (298 K and 1 atm) for all cases. The soot was sampled along

the centerline of the flame through an orifice which is drilled into the stagnation surface. A scanning

mobility particle sizer was used to analyze the gas sample to produce the PSDs.

The flame C3 discussed in section 3.1 on the page 35 is very similar to flame A1 in terms of the mea-

surement technique and boundary condition; however, there is a minor difference among their equivalence

ratios, φ. The equivalence ratios for the flames C3 and A1 are 2.07 and 2.00, respectively. As a result, it

is worth to compare both experimental and computed PSDs for a few spacings to see what is the effect

of equivalence ratio and how the model captures the effect. Fig. 3.8 shows the comparison between

computed and measured PSDs for the flames C3 and A1. According Fig. 3.8, the model captures the

trend of experimental data; however, it does not show the noticeable diameter reduction observed in

measured PSDs. This discrepancy could be attributable to the chemical kinetic file, imprecise stagna-

tion wall temperature, or measurement data scatter. The experimental PSDs for flames C3 and A1 have

been measured at different locations, and the particle sizer apparatus is highly sensitive to the ambient

pressure and temperature.

171819

110111112

1 100

C3 Exp. C3 Num.

A1 Exp. A1 Num.

1 10 100

HP = 0.80 cm

107

108

109

1010

1011

1012

1 10 100

HP = 0.55 cm

PS

D,

dN

/dL

og

DP

(cm

-3)

(a) (b)


Figure 3.8: Comparison of the flames C3 (φ = 2.07) and A1 (φ = 2.00) for the burner–to–stagnationsurfaces of 0.55 and 0.80 cm.

The measurements in [1] show addition of CO2 drastically reduces both soot particle sizes and volume

fraction. There are hypotheses on the role of CO2 in the soot formation suppression; however, a detailed


soot model is required to check all the suppositions to become more certain about the phenomenon.

According to the literature review performed in the section 1.2.3, the introduced model was used to

answer the following questions in the upcoming sections:

• Is the suppression effect of CO2 due to thermal or chemical factors;

• What are the chemical reactions involved in this process;

• Between the nucleation and condensation, which one is affected more.

3.2.1 Soot Volume Fraction

In this section the influence of the CO2 addition on the soot volume fraction, fv, is studied. The

comparison between computed (circle-solid line) and measured (triangle-dashed line) is shown in Fig.

3.9. For the flame A1, 0.0% CO2, the agreement between the modelling and experimental result is good.

Addition of CO2 reduces the soot volume fraction. The frames (b) and (c) of Fig. 3.9 show the model

can capture the reduction, but it does not predict the correct value for all the burner-to-stagnation

surface separations.

1-14

1-13

1-12

1-11

1-10

1-9

1-8

0.45 0.55 0.65 0.75 0.85

12.0 % CO2

Exp.

Num.

10-14

10-13

10-12

10-11

10-10

10-9

10-8

0.45 0.55 0.65 0.75 0.85

00.0 % CO2

Exp.

Num.

0.45 0.55 0.65 0.75 0.85

0.00 % Exp. 0.00 % Num.

12.0 % Exp. 12.0 % Num.

18.0 % Exp. 18.0 % Num.

(a)

10-14

10-13

10-12

10-11

10-10

10-9

10-8

0.45 0.55 0.65 0.75 0.85

X(cm)

18.0 % CO2

Exp.

Num.(c)

(b)

(d)

So

ot

Vo

lum

e F

ra

ctio

n, F

V

Height Above Burner, HP (cm)

Figure 3.9: Comparison of the computed (circles) and measured (triangles) soot volume fraction for theaddition of 0.0%, 12%, and 18% of CO2, respectively (see Tab. 2.1).


The frame (d) summarizes the calculated and measured fv for all three flames; the simulation results

are in a qualitative agreement with the experimental data in capturing the CO2 suppression effect.

Although the model may not work properly for the 18% CO2 dilution, capturing the reduction trend

could be adequate for the purpose of this study.

3.2.2 Particle Size Distribution

The PSDs which depict information about the particle sizes and population are discussed in this section.

The measured PSDs over 5 burner-to-stagnation surface separations derived from the work by Tang et

al. [1] show the addition of CO2 reduces both the particle sizes and numbers (Fig. 3.10). The reduction

of the numbers could be attributable to the lower nucleation rates due to the CO2 inhibition effects. The

smaller diameter size might stem from the lower agglomeration rates due to less availability of particles

or less active PAH condensation.

The introduced soot model was used to reproduce the PSDs. For each of the 5 spacings of interest,

three flames had to be simulated which resulted in 15 simulations. 60 sections have been selected to

capture the evolution of PSDs. The spacing factor, fs, discussed in section 2.4.1, has been chosen to be

1.2 for the spacings 0.5 and 0.55 cm; 1.3 was used for other larger spacings.

The computed and measured PSDs are compared in Fig. 3.10, and they show a qualitative agreement.

The numerical results also support that having CO2 as a diluent in the fuel and oxidizer mixture reduces

the soot formation and growth. For the flame A1, 0.0% CO2, the agreement of the particle sizes seems

fairly good; however, for the flames A2 and A3 as the burner-to-stagnation surface separation increases

the simulation is not able to capture the spread between the points which representing the increasing

amounts of CO2.

The modelling tool used in this work consists of different modules including flame simulator (the

OPPDIF code), chemical reactions and thermodynamics libraries, and the soot model. Any defect or

lack of accuracy in each segment could account for this discrepancy. In the following sections there will

be a discussion about the possible sources of error.


17

18

19

110

111

112

1 100

0.00 % Exp. 0.00 % Num.

12.0 % Exp. 12.0 % Num.

18.0 % Exp. 18.0 % Num.

17

18

19

110

111

112

HP = 0.70 cm

1 10 100

HP = 0.80 cm

107

108

109

1010

1011

1012

HP = 0.50 cm

107

108

109

1010

1011

1012

1 10 100

HP = 0.55 cm

107

108

109

1010

1011

1012

1 10 100

HP = 0.60 cm


Pa

rtic

le S

ize

Dis

trib

uti

on

, d

NP/d

log

DP

(c

m-3

)

Figure 3.10: Comparison of the computed (solid lines) and measured (symbols) PSDs. The experimentaldata is adopted from [1].


3.2.3 PAH Condensation Reversibility Effect

The reversible PAH condensation model used in this work has been adopted from the work by Veshkini

et al. [15]. Many soot models take advantage of constant condensation models. The model in this work

can also be switched to constant condensation. The advantage of reversible condensation is to calculate

the rate of PAH desorption from the surface of the soot based on the flame condition rather than a tuned

constant value. Fig. 3.11 shows the importance of reversibility in capturing the CO2 addition influence

on the particle sizes. Similar tests for higher spacings have been performed by Veshkini et al. [15] show

the constant condensation model cannot capture even the bimodality of the PSD function.

171819

110111112

1 10 100

0.00 % Exp. 0.00 % Num.

12.0 % Exp. 12.0 % Num.

18.0 % Exp. 18.0 % Num.

HP = 0.50 cm

1 10 100

HP = 0.60 cm

107

108

109

1010

1011

1012

HP = 0.50 cm

107

108

109

1010

1011

1012

1 10 100

HP = 0.60 cm

Pa

rtic

le S

ize

Dis

trib

uti

on

, D

N/D

log

DP

(c

m-3

)


(a) (b)

Figure 3.11: Comparison of the constant (column a) and reversible (column b) condensation model.


3.2.4 Wall Temperature Effect

In section 3.1.4 a stagnation wall temperature sensitivity analysis have been performed, and the modelling

result showed that the PSD functions are highly sensitive to the boundary temperature. The PSDs for

different stagnation wall temperature have been compared for the spacing 0.6 cm in Fig. 3.12. The

purpose of this section is to investigate the effect of wall temperature on the capturing the CO2 addition

effect. Three possible boundary temperatures including the measured temperature and uncertainty

limits are studied here for the spacing 0.6 cm. The model overpredicts the diameter at 470 K; at 530 K,

the diameters of particles are underpredicted; the middle temperature, 497 K, shows the best agreement

among the possible boundary conditions. The stagnation wall temperature has been determined using

an embeded thermocouple. The mentioned thermocouple reports the average temperature of the gas

and the water cooled wall. however, the code only considers the domain inside the gas. These facts

suggest that the reported measured temperature could be slightly lower than the real gas temperature,

i.e., a wall temperature of 510 K can capture the exact diameter.

17

18

19

110

111

112

1 100

00.0 % Exp. 00.0 % Num.

12.0 % Exp. 12.0 % Num.

18.0 % Exp. 18.0 % Num.

1 10 100

TWall = 530 K

17

18

19

110

111

112

1 10 100

TWall = 470 K

17

18

19

110

111

112

1 10 100

TWall = 497 K

Pa

rtic

le S

ize

Dis

trib

uti

on

, d

N/d

log

DP

(cm

-3)


Figure 3.12: Stagnation wall temperature sensitivity analysis for the measured boundary condition, 470K; the flame C3 boundary condition, 497 K; and the flame C3 boundary condition plus the measurementuncertainty, 530 K. The comparisons has been made for the spacing 0.6 cm.


3.2.5 Thermal Effect of CO2

Preliminary results have been presented in previous sections. This part seeks the answer to the first

question of interest regarding the thermal or chemical influence of CO2 addition. The answer to this

question cannot be found from experimental investigation since it is not possible to conduct experiments

in which the thermal and dilution effects of CO2 could be separated from its chemical effects. The thermal

influence can be isolated by defining a fictitious CO2 specie, named FCO2. FCO2 is a chemically inert

specie that does not react, but possesses the identical thermal properties, transport characteristics, and

the third body collision efficiencies as CO2. This method have been successfully used in [1, 16] to study

the CO2 addition effects on the soot precursors and volume fraction. Liu et al. [16] took advantage of

the mentioned approach to calculate soot volume fraction for a coflow diffusion flame. Tang et al. [1]

used the fictitious specie approach to study the soot precursors for a few BSS flames; they only simulated

the flame chemistry without a soot model.

17

18

19

110

111

112

1 100

00.0 % Exp. 00.0 % Num.

12.0 % Exp. 12.0 % Num.

18.0 % Exp. 18.0 % Num.

17

18

19

110

111

112

1 10 100

HP = 0.60 cm FCO2

17

18

19

110

111

112

1 10 100

HP = 0.60 cm CO2


PS

D,

dN

/dL

og

DP

(cm

-3)

(a) (b)

Figure 3.13: Comparison of the effect of CO2 (frame (a)) and chemically inert specie FCO2 (frame (b))on the PSDs.

In the current work the specie FCO2 was used to imitate CO2 thermal effects on the evolution of

PSD function. For the addition of 0.0% CO2 or FCO2, the model generates similar PSDs, solid navy

blue lines in Fig. 3.13. Replacing 12.0% and 18.0% of argon with CO2 shows a significant diameter

reduction in frame (a) of Fig. 3.13; frame (b), which only reflects the thermal effect, shows a slight

size reduction compared to frame (a). Since the axes are in log-scale, the figure may not reflect the

extent of reduction. The size reduction observed in frame (b) is attributable to higher specific heat

of CO2 compared to argon. In order to elaborate the thermal effects of CO2, similar comparisons for

temperature and acetylene have been performed and are presented next.


00.0 %12.0 %18.0 %

X(cm)

300

700

1100

1500

1900

0 0.1 0.2 0.3 0.4 0.5

FCO2

00.0 %

12.0 %

18.0 %

300

700

1100

1500

1900

0 0.1 0.2 0.3 0.4 0.5

CO2

00.0 %

12.0 %

18.0 %

T(K

)

(a) (b)

Figure 3.14: Comparison of the effect of CO2 and chemically inert specie FCO2 on the temperatureprofiles.

Comparison of the computed temperature profiles of the flames diluted with CO2 and FCO2 is

depicted in Fig. 3.14. In both frames, the peak temperature are almost the same; however, the higher

heat capacity of CO2 and FCO2 accounts for the slight difference in peak temperatures. It is interesting

that the temperature profiles of both diluents are identical which means the thermal properties of the

CO2 are more important in terms of the temperature prediction, and its chemical role does not seem to

have an effect.

00.0 %12.0 %18.0 %

X(cm)

0

0.01

0.02

0.03

0.04

0 0.1 0.2 0.3 0.4 0.5

FCO2

0

0.01

0.02

0.03

0.04

0 0.1 0.2 0.3 0.4 0.5

CO2

C2H

2M

ole

Fra

cti

on

(b)(a)

Figure 3.15: Comparison of the effect of CO2 (frame (a)) and chemically inert specie FCO2 (frame (b))on the concentration of C2H2.


Acetylene is one of the most important species in terms of PAH formation and growth. Any changes

in acetylene concentration affects the PAH formation and result in noticeable variations in soot. As

expected, the frame (b) of Fig. 3.15 shows that addition of FCO2 does not change the equilibrium

concentration of acetylene in the post flame region. The flame front is located at 0.1 cm, and the slight

difference in acetylene concentration seen in preflame zone is due to the tiny temperature differences;

however, the frame (a) clearly illustrates the chemical role of CO2 in acetylene suppression.

0.0

2.0

4.0

6.0

8.0

500 1000 1500 2000

CP/R

u

T(K)

CO2 Ar

Figure 3.16: Comparison of the specific heat capacity of CO2 and Ar. The value CP /Ru is dimensionless.

In order to compare the thermal properties of CO2 and Ar, specific heat capacities are plotted in

Fig. 3.16. The dimensionless value CP /Ru has been calculated using the following relation:

CPRu

= a1 + a2 × T + a3 × T 2 + a4 × T 3 + a5 × T 4 (3.1)

where CP is the specific heat capacity, Ru is the universal gas constant, T is the temperature, and ai

are the polynomial coefficients of the curve fitting process. The values for ai have been derived from the

thermochemical data accompanied by KAUST chemical mechanism files [39]. Fig. 3.16 clearly shows

that CO2 has larger CP which means it can take away more heat from the flame through the exhaust

gas. That is why a slight temperature decrease is observed in Fig. 3.14 after addition of CO2. In terms

of the Ar chemical role, if the reactions in the KAUST mechanism are investigated, it can be seen that

Ar do not play any role in none of the reactions while there are 18 reactions which contain CO2 in their

reactants.

In sum, the first question out of three discussed in section 3.2 on page 43 could be answered in

the following way: CO2 dilution suppresses the soot formation both chemically and thermally, but the

chemical effect is more evident, and the thermal effect seems weaker compared to chemical influence.

This result shows that the thermal effect is not negligible. The modelling tool can be used to go deep

into the chemistry side to track the reactions that are behind the phenomenon.


3.2.6 Chemical Effect

Based on the discussion in section 2.4, it can be inferred that CO2 addition might not have a direct

effect in soot formation process. Section 3.2.5 explains that soot is suppressed due to CO2 chemical

role in the reactions. Moreover, the nucleating species are of great importance since they are the bridge

between the gas-phase chemistry and condensed-phase particles. As a result, the current section tries to

investigate the chemical reactions in order to find the exact role of CO2 in the observed phenomenon.

0.0E+0

2.0E-4

4.0E-4

6.0E-4

8.0E-4

-0.4 0.1 0.6

A1 0.0 % CO2 A2 12.0% CO2 A3 18.0% CO2

X(cm)

0.E+00

2.E-05

4.E-05

6.E-05

8.E-05

1.E-04

0.0 0.2 0.4 0.6

OH

0.E+00

2.E-04

4.E-04

6.E-04

8.E-04

0.0 0.2 0.4 0.6

H

Mole

Fra

ctio

n

0.E+00

1.E-04

2.E-04

3.E-04

4.E-04

5.E-04

0.0 0.2 0.4 0.6

Benzene C6H6

0.0E+0

5.0E-3

1.0E-2

1.5E-2

2.0E-2

2.5E-2

0.0 0.2 0.4 0.6

C2H2

Figure 3.17: Effect of CO2 addition on the major species including hydrogen radical, hydroxyl, acetylene,and benzene for the spacing 0.6 cm.

The computed mole fractions of H radical, hydroxyl, acetylene and benzene, four major species, have

been depicted for the spacing 0.6 cm in Fig. 3.17. These concentrations have been computed using

CHEMKIN Pro software without considering soot formation. Acetylene is the precursor to formation

of the first aromatic ring, benzene, and the building block of the growth of larger PAHs. Benzene is

the base molecule that larger PAHs form from this species through different pathways; thus, differences

in the mole fraction of benzene due to addition of CO2 will result in a difference in nucleating species,

PAHs with 6 or 7 rings, and soot yield. Fig. 3.17 shows that replacing 12% and 18% of Ar with CO2

causes the concentration of acetylene to reduce 15.6% and 21.5%, respectively; the reduction for benzene

is 20.1% and 29.2%, respectively.


0.00E+002.00E-064.00E-066.00E-068.00E-06

-0.4 0.6

00.0 % 12.0 % 18.0 %

0.0E+00

1.0E-07

2.0E-07

3.0E-07

0.0 0.2 0.4 0.6

Benzo[ghi]perylene

0.0E+00

2.0E-06

4.0E-06

6.0E-06

8.0E-06

0.0 0.2 0.4 0.6

Anthanthrene

0.0E+00

2.0E-06

4.0E-06

6.0E-06

8.0E-06

0.0 0.2 0.4 0.6

A4R5 benzo(ghi)fluoranthene

X(cm)

Mo

le F

ract

ion

0.0

0.1

0.2

0.3

0.4

0.5

0.5 0.6 0.8

HP (cm)

Normalized PAH Level

(b)(a)

(c) (d)

Figure 3.18: Effect of CO2 addition on the nucleating species concentrations for the spacing 0.6 cm.Frame (b) represents the normalized PAH summation at the stagnation plane over a range of burner-to-stagnation surface separations.

In this study, dimers are assumed to form via physical coalescence of large PAHs including an-

thanthrene, benzo[ghi]perylene, and benzo(ghi)fluoranthene. These species, known as nucleating species,

are the feed stock to the soot model; moreover, the same species are allowed to condensate on the surface

of soot particles in the condensation growth model. Fig. 3.18 compares the nucleating species concen-

trations for different CO2 contents for the spacing 0.6 cm. The summation of 3 PAHs at the stagnation

surface location have been normalized for the flames A1, A2, and A3 over a range of burner-to-stagnation

surface separations in frame (b) of Fig. 3.18. This figure shows, addition of 12% and 18% CO2 results

in 38.2% and 51.2 % PAH suppression for the flames A2 and A3, respectively. This reduction caused

by addition of CO2 in the concentration of PAHs will result in a reduction in both soot nucleation and

condensation as shown in Fig. 3.10. The effect of CO2 addition on other important species including O,

CO, etc. is presented in Appendix A. In order to understand the role of CO2 in this process and answer

the second question, a thorough species sensitivity analysis is required.


Species Sensitivity Analysis

In the previous section the concentration plots of PAH species showed that addition of CO2 would reduce

the concentration of acetylene and nucleating PAH species. According to the literature [16], the reaction

CO2+H↔ CO+OH, which is called water shift reactoin, plays an important role in soot suppression by

depleting H radical [1, 16]. H radical is an important specie to HACA mechanism which is one of the

major PAH growth pathways. The comparison of H radical concentration for the flames A1, A2, and

A3 has been depicted in Fig. 3.17. This figure shows addition of CO2 affects the content of H radical

at its peak value. Although the observed difference seems insignificant, it seems to have a noticable

effect on species like benzene which are in their formation zone. Appendix A contains the comparison

of numerous species regarding the effect of CO2 addition. This section tries to dig out other reactions

which are involved in this process in order to answer the second question of the section 3.2.

The reaction pathway analysis tool of CHEMKIN pro software has been used to perform a sensitivity

analysis on the species of interest including anthanthrene, acetylene, benzene, carbon monoxide, carbon

dioxide, hydroxyl radical, and hydrogen radical without considering soot. The mentioned tool is capa-

ble of drawing reaction pathways and calculating the reaction sensitivity to track the most influential

reactions for a specific specie.

Figure 3.19: Normalized sensitivity analysis of anthanthrene, compared at x = 0.2 cm for flames A1,A2, and A3 on the spacing of 0.6 cm. Reactions include CO2 and CH∗2 are marked by green and red,respectively.

Since nucleating species are the bridge between gas-phase chemistry and solid particles, at the first

step, the sensitivity analysis was performed on them. Fig. 3.19 shows the sensitivity analysis of an-

thanthrene. The analysis has been performed at 0.2 cm which looks to have the fastest growth of this

specie. The first three important reactions affect the formation and consumption of anthanthrene contain


H radical; this fact can show how difference in H radical content can cause anthanthrene suppression.

CO2 addition changes the hierarchy of the reactions involved in the flame chemistry, which consequently

causes the concentration change in important species.

As mentioned earlier, sensitivity analysis is tool which finds the most influential reactions for the

formation of a specific specie. Contrarily to what is claimed about the water shift reaction, the sensitivity

analysis results shown in Fig. 3.19 do not include water shift reaction which means it is not important.

Moreover, regarding the role of CO2+H ↔ CO+OH effects on soot suppression [1, 16], there is no

experimental evidence to support this hypothesis. Instead, a reaction appears after addition of CO2

which does not exist in the base flame, A1. The sensitivity analysis reveals the mentioned reaction as

follows:

CH∗2 + CO2 ↔ CH2O + CO (3.2)

where CH∗2 is called activated methylene and CH2O is formaldehyde. Interestingly, reaction 3.2 contains

CO2 and CO. It was tried to find a direct relation between the participant species of the mentioned

reaction and anthanthrene to account for the suppression effect. However, the effort was unsuccessful

which means the role of reaction 3.2 should be investigated in the precursors species.

Figure 3.20: Normalized sensitivity analysis of benzene, compared at x = 0.04 cm for flames A1, A2, andA3 on the spacing of 0.6 cm. Reactions include CO2 and CH∗2 are marked by green and red, respectively.

All the large PAHs form from benzene which necessitates to perform sensitivity analysis for benzene

as well. Fig. 3.20 shows the normalized benzene sensitivity for the flames A1 (0.0% CO2), A2 (12.0%

CO2), and A3 (18.0% CO2), receptively. The positive sensitivity means that the reaction promotes the

production rate of the specie of study. According to Fig. 3.20, the reaction 3.2 does not exist in flame

A1, and it appears in flame A2; Finally, in flame A3 reaction 3.2 goes to higher priority. The negative

sensitivity value of the reaction 3.2 also shows that this reaction reduces the formation of A1. The


sensitivity analysis reveals another important reaction, which is marked by red in Fig. 3.20, as follows:

C2H2 + CH∗2 ↔ C3H3 + H (3.3)

As mentioned in section 2.3.3, the propargyl, C3H3, recombination is one the major pathways to form

the first aromatic ring, Benzene, via the following reaction:

2C3H3 → C6H6 (3.4)

Reaction 3.4 is marked by blue in Fig. 3.20. Considering reactions 3.2,3.3, and 3.4, it can be inferred

that addition of CO2 depletes the CH∗2 radical; less acetylene and CH∗2 form less propargyl, C3H3; and

finally, less propargyl suppresses the formation of benzene. The reduction in the formation of benzene

propagates throughout larger PAHs, and decreases the soot formation.

Figure 3.21: Absolute rate of production for acetylene, compared at x = 0.04 cm for flames A1, A2, andA3 on the spacing of 0.6 cm.

In the next step, the acetylene which is the building block of PAHs will be studied using the reaction

pathway analysis tool. The absolute rate of production and sensitivity analysis of acetylene are depicted

in Figs. 3.21 and 3.22, respectively. According to Fig. 3.22, the reaction 3.2 does not exist in flame

A1; however, flames A2 and A3 include this reaction, and it has a higher priority in flame A3 which

is consistent with the initial CO2 concentration. In order to find out the relation between CO2 and

acetylene, reactants and products of reaction 3.2 has been tracked which disclosed the following sequence

of reactions:

CH∗2 + CO2 ↔ CH2O + CO

CH∗2 + C2H4 ↔ H2CC + CH4 (3.5)

H2CC(+M)↔ C2H2(+M) (3.6)

Based on Fig. 3.21, the reaction 3.6 represents one of the reactions responsible for the production of

acetylene, and addition of CO2 makes this reaction less effective. As a result, CO2 addition depletes

CH∗2 radical via reaction 3.2; consequently, less CH∗2 produces less H2CC in reaction 3.5. Finally, the

reaction 3.6 becomes less effective due to smaller concentration of H2CC.


Figure 3.22: Normalized sensitivity analysis of acetylene, compared at x = 0.04 cm for flames A1, A2,and A3 on the spacing of 0.6 cm.

In summary, the second question discussed in section 3.2 can be answered as follows: the chemical

effect of CO2 addition on the soot formation process is partly attributable to the reaction CH∗2 +CO2 ↔CH2O + COIt seems that this reaction is not the only one which reflects the CO2 addition effect.

Since many of reactions are interrelated, recognizing a single reaction as the cause of this observation is

complicated; thus, more effort is required to clarify this issue.


3.3 Nucleation - Condensation Effects

This section seeks the answer to the third question discussed in section 3.2.1 on page 43. In addition to

condensation, there is another surface growth mechanism included in the model which is called HACA

surface growth and it has been explained in section 2.4.1. Before comparing the influence of CO2 on the

condensation and nucleation, it is worthwhile to discuss the effect of CO2 on HACA process.

-80%

-52%

1.E-13

1.E-11

1.E-09

1.E-07

1.E-05

1.E-03

HACA Nucleation Condensation Total

00.0% CO212.0% CO218.0% CO2

Mass of Soot (g soot / cm3 gas)

Figure 3.23: Comparison of soot mass generated by HACA, nucleation, and condensation for the spacing0.6 cm.

According to Tang et al.[1], CO2 reduces soot growth through HACA. In order to investigate this

hypothesis, Fig. 3.23 compares the mass of soot generated by HACA, Nucleation, and Condensation

separately for each percentage of CO2. The vertical axis of the figure is in log scale. This figure

shows addition of 12% and 18% co2 reduces the HACA surface growth by 80% and 52% respectively.

However, HACA mass is significantly smaller than nucleation and condensation which means the HACA

is negligible.

Most of the mass forms during soot formation comes from the nucleation and condensation processes

according to the assumptions made in section 2.4. The comparison of the soot total mass for flames

A1, A2, and A3 over a range of burner-to-stagnation surface separations is depicted in Fig. 3.24. By

increasing the spacing, mass grows more, and the difference between the mass of A1, A2, and A3 becomes

less. This result is consistent with the computed PSDs presented in Fig. 3.10; however, the experimental

measurement shows a drastic suppression trend at higher spacings similar to lower spacings.


0.0E+00

5.0E-06

1.0E-05

1.5E-05

2.0E-05

2.5E-05

A1 A2 A3

HP = 0.8 cm

0.0E+00

5.0E-07

1.0E-06

1.5E-06

2.0E-06

2.5E-06

A1 A2 A3

HP = 0.6 cm

0.0E+00

2.0E-07

4.0E-07

6.0E-07

8.0E-07

A1 A2 A3

HP = 0.5 cm

Flame type: 0.0% CO2 (A1), 12.0% CO2 (A2), 18.0% CO2 (A3)

So

ot

To

tal

Ma

ss F

ra

ctio

n

Figure 3.24: Soot total mass fraction for the flames A1, A2, and A3 over a range of burner-to-stagnationsurface separations including 0.5, 0.6, and 0.8 cm.

Since the code tracks the number of primary particles all through the flame, the number of particles

formed by nucleation can be easily calculated by the summation of primary particle numbers. The

assumption of having no coalescence makes the tracking of primary particle numbers possible. The mass

produced via nucleation can be derived by multiplying the total number of primary particles by the

average mass of dimers, 6.768 × 10−22 g. Subtracting the nucleation mass from the total mass yields

the produced mass due to PAH condensation, i.e., HACA and other growth processes are ineffective.

The soot condensation and nucleation mass fraction graphs over a range of burner-to-stagnation surface

separations are presented in Figs. 3.25 and 3.26, respectively.


0.0E+00

5.0E-06

1.0E-05

1.5E-05

2.0E-05

2.5E-05

A1 A2 A3

HP = 0.8 cm

0.0E+00

5.0E-07

1.0E-06

1.5E-06

2.0E-06

2.5E-06

A1 A2 A3

HP = 0.6 cm

0.0E+00

2.0E-07

4.0E-07

6.0E-07

8.0E-07

A1 A2 A3

HP = 0.5 cm

Soo

t C

on

den

sati

on

Mass

Fra

cti

on

Figure 3.25: Soot condensation mass fraction for the flames A1, A2, and A3 over a range of burner-to-stagnation surface separations including 0.5, 0.6, and 0.8 cm.

Comparison of Figs. 3.24 and 3.25 shows that these graphs are very similar to each other which

means most of the mass forms during soot formation process comes from the condensation as well as

other growth processes. The nucleation mass fractions, Fig. 3.26, are comparable for all three spacings

due to the similar vertical axis bounds. The nucleation rate is increasing with respect to the spacing

which makes sense because by increasing the spacing the residence time increases and more primary


particles form. But the faster increase rate of nucleation for flames A2 and A3 is strange.

Considering only nucleation with the condensation model turned off, the produced mass should be

proportional to the nucleating PAH mass ratios. Since all the cases studied in this work were run with

reversible condensation model, the PAH trend is not evident in the nucleation mass graph, Fig. 3.26.

This means that nucleation cannot work independent of the condensation model and the reversible

condensation model affects the nucleation rates as well.

0.0E+00

2.0E-08

4.0E-08

6.0E-08

8.0E-08

1.0E-07

A1 A2 A3

HP = 0.8 cm

0.0E+00

2.0E-08

4.0E-08

6.0E-08

8.0E-08

1.0E-07

A1 A2 A3

HP = 0.6 cm

0.0E+00

2.0E-08

4.0E-08

6.0E-08

8.0E-08

1.0E-07

A1 A2 A3

HP = 0.5 cm


Soot

Nu

clea

tion

Mass

Fra

cti

on

Figure 3.26: Soot nucleation mass fraction for the flames A1, A2, and A3 over a range of burner-to-stagnation surface separations including 0.5, 0.6, and 0.8 cm.

The normalized nucleation and condensation mass fractions over a range of spacings are depicted in

Fig. 3.27. This figure shows by increasing the separation distance both nucleation and condensation

become stronger for the flames A2 and A3 relative to A1. The stronger condensation is a feature of

larger spacing as experimental measurements verifies that by showing a bimodal behaviour in PSDs

(Fig. 3.10). This question might come into mind how stronger condensation causes more nucleation.

The reversible nucleation establishes a bridge between the gas-phase molecules and dimers. If dimers

stay in the first bin and do not grow they have the possibility to decompose to nucleating gas-phase

PAHs which reduces the nucleation rate. However, if they grow through condensation or other growth

mechanisms, they move to upper sections. What the code recognizes as nucleation is the number of

primary particles. If a particle wants to decompose to its constituent PAHs, the particle should be

in the first section. The growth process through condensation pushes the particles to upper sections

which consequently reduces the chance of reverse nucleation. In order to capture the CO2 suppression

reasonably good for all spacings, the normalized masses in Fig. 3.27 should have a similar trend among

spacings, while the results show lack of it.


0.00.10.20.30.40.50.60.70.80.91.0

0.5 0.6 0.8

A1 A2 A3

0.0

0.2

0.4

0.6

0.8

1.0

0.5 0.6 0.8

Condensation

0.0

0.2

0.4

0.6

0.8

1.0

0.5 0.6 0.8

Nucleation

Burner-to-stagnation surface distance (cm)

Norm

ali

zed

Mass

Fra

cti

on

Figure 3.27: Normalized soot nucleation and condensation mass fraction for the flames A1, A2, and A3over a range of burner-to-stagnation surface separations including 0.5, 0.6, and 0.8 cm.

1.E-07

1.E-06

1.E-05

1.E-04

Nucleation Condenstaion Total

Soot Mass Comparison for HP = 0.6 cm

-84%

-95%

-55%

-37%

Figure 3.28: Comparison of the nucleation mass, condensation mass, and total mass of soot for thespacing 0.6 cm.

In conclusion, in order to compare the effect of CO2 on nucleation and condensation the spacing

0.6 cm has been selected because the model captures the reduction in diameter fairly good and both

nucleation and condensation are present in this spacing. Fig. 3.28 compares the mass of soot derived

from nucleation and condensation for each percentage of CO2 separately. The vertical axis is in log

scale. If we calculate the reduction of nucleation mass for 12% and 18% CO2 we get 55% and 37%

reduction, respectively. Similar calculations for condensation show 95% and 84% reduction, respectively.


The greater reductions observed in the condensation mass compared to the nucleation indicates addition

of CO2 reduces soot formation mostly via suppressing condensation step.


3.4 Chemical Kinetic File Sensitivity Analysis

In the previous sections the code was analyzed against different conditions and parameters. Moreover,

the code did not predict the size reduction due to the CO2 addition at the spacing 0.8 cm, e.g. Fig.

3.29. This observation could be attributable to the chemical kinetic file, temperature boundary, or soot

model. This section tries to identify the major cause of PSD misprediction for larger spacings.

In the first step the effect of chemical kinetic file is studied. The burner-to-stagnation surface sep-

aration investigated here is 0.8 cm. The comparison of KAUST and CRECK chemical kinetic files is

presented in Fig. 3.29. These two mechanisms have been introduced in section 2.3.3. A soot model with

similar parameters were used to generate the PSDs of Fig. 3.29; the differences between frames (a) and

(b) are the chemistry mechanism and thermodynamics data. Fig. 3.29 shows both mechanisms under-

predict the CO2 addition effect, but KAUST mechanism produces slightly better results than CRECK

kinetic file. The effect of CO2 addition on the gas-phase chemistry of CRECK mechanism and many

other kinetic files are presented in Appendix B.

171819

110111112

1 100

00.0 % Exp. 00.0 % Num.12.0 % Exp. 12.0 % Num.18.0 % Exp. 18.0 % Num.

(a)

107

108

109

1010

1011

1012

1 10 100

CRECK, HP = 0.80 cm

107

108

109

1010

1011

1012

1 10 100

KAUST, HP = 0.80 cm

(b)


PS

D,

dN

/dL

og

DP

(cm

-3)

Figure 3.29: Particle size distribution function for (a) KAUST mechanism and (b) CRECK mechanism.

In the second step, the effect of stagnation surface temperature is studied. The temperature used

for the original run was derived from [1]; In order to check the role of temperature, the value that has

been reported in [32] for a similar flame was replaced with the original boundary temperature. The

comparison of the two temperatures is depicted in Fig. 3.30. Fig. 3.30 shows an increase of 37 K in

wall temperature (frames (b) and (c)) would cause a significant change in the CO2 addition effects on

the size reduction. The PSDs were both measured and computed close to the stagnation surface.


17

18

19

110

111

112

1 100

00.0 % Exp. 00.0 % Num.

12.0 % Exp. 12.0 % Num.

18.0 % Exp. 18.0 % Num.

17

18

19

110

111

112

1 10 100

HP = 0.80 cm Twall = 523 K

107

108

109

1010

1011

1012

1 10 100

HP = 0.80 cm

107

108

109

1010

1011

1012

1 10 100

HP = 0.80 cm Twall = 486 K

PS

D,

dN

/dL

og

DP

(cm

-3)

(b) (c)


Twall = 486 K

(a)

Constant Condensation

Reversible Condensation Reversible Condensation

Figure 3.30: PSD comparison for the constant condensation, frame (a); reversible condensation modelwith the original temperature boundary condition, frame (b); and reversible condensation model withanother reported temperature, frame (c).

0.0

0.2

0.4

0.6

0.8

1.0

0.78

A1 A2 A3

0.0

0.2

0.4

0.6

0.8

1.0

0.780 0.785 0.790 0.795 0.800

HP = 0.8 cmTwall = 523

0.0

0.2

0.4

0.6

0.8

1.0

0.780 0.785 0.790 0.795 0.800

HP = 0.8 cm

Twall = 486

(a) (b)

X(cm)

Co

nd

ensa

tio

n E

ffic

ien

cy

Figure 3.31: Condensation efficiency comparison for the original wall temperature, frame (a), and anotherreported temperature, frame (b).


A constant condensation case has also been plotted in frame (a) of Fig. 3.30. This figure shows

although the constant condensation model can capture the particle diameter for the flame A1, its per-

formance in capturing the other flames’ PSDs is poor. Moreover, since nucleation is related to the

condensation process, the frame (a) of Fig. 3.30 shows an overprediction in number density of smaller

particles which means stronger nucleation. This figure shows the necessity of the reversible condensation

model to capture the correct trend of diameter reduction due to CO2 addition.

In order to find a clear understanding of what is exactly going on, the condensation efficiency relation,

Eq. 2.43, has been plotted for three flames A1, A2, and A3 and compared for two boundary temperatures

in Fig. 3.31. This figure represents the condensation efficiency of the anthantherene, which is the most

effective condensable specie among the species allowed for the condensation process. Frame (a) of Fig.

3.31 shows that a 100% condensation efficiency for all three flames; this maximum efficiency causes the

greatest possible mass growth which seems unphysical. However, frame (b) of Fig. 3.31 shows a distinct

difference between all three flames which is in accordance with the PAH concentration differences in Fig.

3.18. This behaviour will be explained at the end of this section. The correct prediction of condensation

efficiency could lead to capture the effect of CO2 on the size reduction.

1-141-131-121-111-101-91-8

0.450.95

0.00 % Exp. 0.00 % Num.12.0 % Exp. 12.0 % Num.18.0 % Exp. 18.0 % Num.

1-14

1-13

1-12

1-11

1-10

1-9

1-8

0.45 0.55 0.65 0.75 0.85

Soot

Volu

me

Fra

ctio

n,

Fv

10-14

10-13

10-12

10-11

10-10

10-9

10-8

0.45 0.55 0.65 0.75 0.85

(a) (b)

HP (cm)

Soot

Volu

me

Fra

ctio

n, F

v

Figure 3.32: Boundary temperature effects on the fv prediction. frame (a) shows the computed fvcompared with measurements for the original temperature boundary condition; frame (b) represents asimilar concept to frame (a) but the computed values for the spacing 0.8 cm has been replaced with newones calculated at new temperature.

According to Fig. 3.32, the new boundary temperature also shows a noticeable improvement in terms

of fv predictions. In Fig. 3.32, frames (a) and (b) are basically the same, but in frame (b), the fv values

for the spacing 0.8 cm has been replaced with the ones calculated at the newly adopted temperature.

The condensation model used in this work looks very sensitive to temperature. This fact stems from the

nature of Eq. 2.43 implemented to calculate the condensation efficiency. Eq. 2.43 can be rearranged in

the following format:

γCond. =1

1 + exp(−8×

[YPAH

Yeq− 0.5

]) (3.7)

where γCond. is the condensation efficiency, YPAH is the mass fraction of each nucleating specie, and

Yeq is the equilibrium mass fraction of the condensable species which can be calculated via the relations

discussed in section 2.4.1. YPAH is a function of both chemical kinetic mechanism file and temperature,


but the effect of chemical reactions is stronger. Yeq is a strong function of temperature, selected PAH

species; the differences for condensation efficiencies observed in Fig. 3.31 is attributable to this variable.

0.0

0.2

0.4

0.6

0.8

1.0

0.78

A1 A2 A3

0.0

0.2

0.4

0.6

0.8

1.0

0.780 0.785 0.790 0.795 0.800

A4R5 benzo(ghi)fluorantheneTwall = 486 K

(b)

0.0

0.2

0.4

0.6

0.8

1.0

0.780 0.785 0.790 0.795 0.800

anthanthreneTwall = 486 K

(a)

Co

nd

ensa

tio

n E

ffic

ien

cy

0.0

0.2

0.4

0.6

0.8

1.0

0.780 0.785 0.790 0.795 0.800

pyreneTwall = 486 K

X(cm)

0.0

0.2

0.4

0.6

0.8

1.0

0.780 0.785 0.790 0.795 0.800

benzo[ghi]peryleneTwall = 486 K

(c) (d)

Figure 3.33: Condensation efficiency comparison for the original wall temperature and four condensablespecies including: (a)anthantherene, (b) benzo(ghi)fluoranthene, (c)benzo[ghi]perylene, and (d)pyrene.

According to Eaves et al. [18], in reality, a wide range of PAHs can condensate on the surface of

soot particles but with different rates. In the modelling of this process, due to the lack of computational

resources, only a few of these PAHs are assumed to condensate. Fig. 3.30 shows the wall temperature

increase creates a distinct spread among the condensation efficiencies which consequently results in a

better prediction of particle sizes. It could be hypothesized that using a lighter PAH would have the

same effect as temperature increase. As a result, pyrene was also considered as one of the condensable

species, and its condensation efficiency has been depicted along with the other three condensable species

at 486 K in Fig. 3.33. It is worthwhile to mention that Yeq in Eq. 3.7 is a function of both temper-

ature and the PAH structure; smaller PAHs has larger Yeq. The condensation efficiency is a function

of PAH concentration, PAH structure, and temperature. Fig. 3.18 shows the concentrations of A4R5

and anthantherene are in the same order; however, since A4R5 has smaller structure, it has lager Yeq

which makes the ratio Yeq/YPAH less than one. Thus, the condensation efficiency for A4R5 becomes

unsaturated (frame (b) of Fig. 3.33). Benzo[ghi]perylene has a similar Yeq to anthantherene, but, based

on Fig. 3.18, its concentration is smaller with an order of magnitude. This results in smaller Yeq/YPAH

values and smaller condensation efficiencies compared to the A4R5. By switching to pyrene, the con-

densation efficiency turns to be constant with a value of 0.0189. In general, Fig. 3.33 explains selection

of condsable species affects the PSD profiles significantly. However, at a constant wall temperature,


switching to lighter PAHs does not create the spread, which is necessary to capture the CO2 effect,

among the condensation efficiencies.

In conclusion, since the influence of chemical mechanism file, boundary temperature, and soot model

on PSDs and other soot properties are intimately entangled, it requires more effort and specific techniques

to clearly identify the role and importance of each factor. Based on the results shown in this section,

the temperature seems a prominent variable which can cause noticeable changes.

Chapter 4

Concluding Remarks and Future

Work

4.1 Summary

Combustion derived particulate matter, soot particles, have adverse influences on human health and

climate change. The research for reducing the formation of soot particles have been of great interest

during the past decade. In internal combustion engines, CO2 addition occurs when EGR used to reduce

NOX formation. Experimental evidences show that CO2 addition suppresses soot formation in many

flames. The fact that CO2 is one of the major components of the combustion products makes this

species an interesting case to study. There are experimental research regarding the effect of CO2 on

the evolution of soot particles in laminar premixed and diffusion flames. Although experimental studies

provide evidence of the CO2 suppression effect, they are not able to isolate the influence of different

factors and present detailed information throughout the measurement field. Since soot morphology

consists of complicated steps, a detailed soot model is required to study each step separately and track

the effect of interest down in the chemistry level.

In this work, beside the gas phase governing equations, a detailed sectional aerosol dynamics model

is coupled with the OPPDIF code to solve soot particle size distribution (PSD) functions. The spacing

between the sections has been set with regard to the sampling bins adopted in the measurement of PSDs.

The soot particle mass ranges from 50 to 65 discrete sections which covers a condensed phase particle

diameter range of 1 to 3300 nm. For the cases with larger separation distances, the number of sections

have been increased to such an extent that soot volume fraction (Fv) in the last section remains less

than 1 ppb. The aerosol dynamics model which includes reversible nucleation and condensation solves

the conservation equations of soot aggregate number densities, and primary particle number densities

for each soot section. The model with the above-mentioned features was used to study the suppression

effect of CO2 on the soot formation in a burner stabilized stagnation (BSS) flame.

In the first step, the model was verified against an ethylene benchmark flame (flame C3). Then, the

model was used to study the effect of CO2 addition on the evolution of PSDs. The atmospheric pressure

base flame, A1, has the following properties: 16% C2H4, 24% O2, and 60% with cold gas velocity of 8

cm/s at 300 K. In flames A2 and A3, 20% and 30% of Ar were replaced with CO2, respectively. The

simulations were performed for three flames over five burner-to-stagnation surface separations which

67

Chapter 4. Concluding Remarks and Future Work 68

means fifteen cases in total.

4.2 Conclusions

In terms of the model verification, the temperature profile was predicted reasonably good within the

uncertainty limit. This result shows the correct solution to the energy equation and implementation of

radiation heat transfer. The reproduced soot volume fraction and PSDs are in a reasonable agreement

with measurements. A stagnation wall temperature analysis performed shows the code is highly sensitive

to boundary temperature; ±30 K, which is the measurement uncertainty, change in the wall boundary

temperature would cause 30% change in particle diameter prediction. The renowned HACA process,

which is important to polycyclic aromatic hydrocarbon (PAH) growth and soot surface reactivity, seems

to be ineffective in mass growth process due to lack of H radicals in the region that is suitable for

probable HACA growth.

In general, the model captures the effect of CO2 addition on the PSDs and Fv, qualitatively. The

prediction of size and Fv for flame A1 is in reasonable agreement with measurements, while for A2 is

acceptable; for flame A3 neither the size nor Fv agrees well with the experimental results. Predictions

in size for lower spacings, e.g. 0.5 cm, is fine; however, as the distance between burner and stagnation

surface increases the code fails to capture the spread between the diameters compared to the exper-

iment. By increase of burner-to-stagnation surface separation the condensation grows stronger. The

condensation efficiency equation used in the reversible model is a strong function of temperature and

PAH concentration; thus, the misprediction of particle sizes could be attributable to either temperature

boundary condition or chemical kinetic mechanism. Since code captures the effect of CO2 addition to

some extent, it can be helpful to elaborate the role of CO2.

Both thermal and chemical factors affect the soot formation process. In order to separate the chemical

and thermal effects a fictitious species, FCO2, which only has thermal properties of CO2 has been

introduced into the chemical mechanism. Running simulations with FCO2 rather than CO2 reduces the

average diameter of the particles from A1 to A2 and A3 by 18% and 27%, respectively; however, similar

simulation with CO2 reveals that average particle sizes from A1 to A2 and A3 would reduce by 60% and

71%, respectively. This shows that chemical characteristics of CO2 seem stronger than thermal features.

In order to find out the chemical reaction that is behind this suppression capability of CO2, an

intensive sensitivity analysis has been performed. Sensitivity analysis revealed CO2 addition does not

have a direct effect on large PAHs; it affects the formation of acetylene and benzene which are the

building block of PAHs and the base aromatic molecule, respectively. The differences observed in the

concentration of acetylene and benzene stem from the reaction CH∗2 + CO2 ↔ CH2O + CO. Addition

of CO2 depletes CH∗2 radical which is a precursor to the formation of H2CC; this specie forms acetylene

through the reaction H2CC(+M) ↔ C2H2(+M). In terms of benzene formation, CH∗2 is a precursor to

propargyl, C3H3; the recombination of propargyl has been recognized as one of the major pathways to

form benzene. In conclusion, CO2 reduces the concentration of acetylene and benzene by depleting the

CH∗2 radicals.

A thorough mass analysis has been performed to separate the effect of CO2 addition on the nucleation

and condensation. The simulation results show that most of the mass formed during the soot formation

process comes from condensation, and the role of PAH condensation in capturing the CO2 effects is more

important than nucleation. Nucleation only takes place in the first section, but PAH condensation occurs

Chapter 4. Concluding Remarks and Future Work 69

in all sections. CO2 addition reduces the concentration of large PAHs; as a result, the condensation also

grows weaker. The experimental results show that addition of CO2 cancels the bimodality of the PSDs

which indicates lack of strong condensation.

This paragraph is dedicated to the original contributions of this work. The model used in this thesis

had been tested for only a few premixed ethylene flames. As the first contribution, the model was vali-

dated against three different fuel mixtures (different contents of CO2) and five burner-to-stagnation sur-

face separations which compose fifteen distinct new flames in total. The model had been used only with

KAUST chemical kinetic file, but in the current work the effect of changing the chemical kinetic file and

thermochemical data was also tested. The code used to be compatible with usual chemical mechanisms.

In usual mechanisms the stoichiometric coefficients of the reactions are integers (2H2+O2 ↔ H2O).

In many other chemical mechanisms the reactions may have non-integer stoichiometric coefficients due

to the existence of lumped species (O+C2H5 →.35CH3CHO+.35H+.35CH2O+.35CH3+.3C2H4+.3OH).

The code was improved to be able to handle the reactions with non-integer stoichiometric coefficients

and it was tested with CRECK mechanism. The condensation model did not work properly with the

values reported in the literature for the vibrational frequencies and binding energy of PAHs. A new

vibrational frequency has been found within the range suggested by literature in order to get a fairly

good agreement for all the cases. Finally a method has been developed to explicitly separate the thermal

and chemical effects of CO2 on the soot formation process which makes the quantitative comparisons

possible.

4.3 Future Work

There are studies in the literature which have investigated the effect of different diluents including CO2

on the soot formation process in coflow diffusion flames. The soot model has been used in this work can

be incorporated into a coflow diffusion flame code. Using a similar soot model for diffusion and premixed

flames could yield interesting results. It is worthwhile to implement the soot model in the coflow flame

code to see how the model functions in diffusion flames.

In order to investigate the influence of the chemical kinetic file on capturing the CO2 dilution effects,

the usage of reversible condensation models that are less temperature dependent could be helpful. The

reversible model used in this work is based on the equilibrium concentrations of the condensable PAHs;

however, there are models in the literature which function differently. These models can be used to

isolate the effect of temperature and look at the chemistry influence on the PSDs separately.

The PAH production section of the chemical kinetic file used in this work has been validated against a

premixed ethylene flame with equivalence ratio of 3.06; however, this mechanism file and other mechanism

files have not been tested and validated for the effect of CO2. Thus, conducting experiments to measure

CO2 addition effects on PAH concentrations using popular burners, which can be easily modelled, would

be useful.

Appendices

70

Appendix A

Addition of CO2 changes the concentration of quite a few species. The major species that are important

to the soot formation process have been presented in the main body of the thesis. A group of other

species including carbon monoxide, propargyl, hydrogen radical, hydroxyl, oxygen radical, and CH∗2 is

presented here.

0.0E+0

4.0E-5

8.0E-5

1.2E-4

1.6E-4

-0.40.6

A1 0.0 % CO2 A2 12.0% CO2 A3 18.0% CO2

0.00

0.10

0.20

0.30

0.0 0.2 0.4 0.6

CO

0.0E+0

4.0E-5

8.0E-5

1.2E-4

1.6E-4

0.0 0.2 0.4 0.6

C3H3

X (cm)

Mole

Fracti

on

Figure A.1: Carbon monoxide and propargyl concentrations compared for flames A1, A2, and A3.

71

Appendix A. 72

0.0E+0

4.0E-5

8.0E-5

1.2E-4

1.6E-4

-0.40.6

A1 0.0 % CO2 A2 12.0% CO2 A3 18.0% CO2

X (cm)

0.0E+0

2.0E-4

4.0E-4

6.0E-4

8.0E-4

0.0 0.2 0.4 0.6

H

Mole

Fracti

on

0.0E+0

2.0E-5

4.0E-5

6.0E-5

8.0E-5

1.0E-4

0.0 0.2 0.4 0.6

OH

Figure A.2: Hydrogen radical and Hydroxyl concentrations compared for flames A1, A2, and A3.

0.0E+0

4.0E-5

8.0E-5

1.2E-4

1.6E-4

-0.40.6

A1 0.0 % CO2 A2 12.0% CO2 A3 18.0% CO2

X (cm)

0.0E+0

4.0E-6

8.0E-6

1.2E-5

0.0 0.2 0.4 0.6

O

Mole

Fracti

on

0.0E+0

1.0E-7

2.0E-7

3.0E-7

0.0 0.2 0.4 0.6

CH2*

Figure A.3: Oxygen radical and CH2* concentrations compared for flames A1, A2, and A3.

Appendix B

The simulation of soot particles is a strong function of chemical kinetic mechanism file since chemistry

mechanisms predict the formation of species which are part of the soot formation process. In this section

five chemical mechanisms are compared to see how they reflect the CO2 addition effects. The kinetic

files are as follows:

• CRECK [38];

• Lawrence Livermore National Laboratory [99];

• ABF [59];

• KAUST II [39];

• DLR [60].

The above-mentioned chemical mechanisms have been used to compare the concentration of species

including acetylene, hydrogen radical, hydroxyl, benzene, and pyrene which are common among the

mechanism files.

73

Appendix B. 74

0.0E+01.0E-42.0E-43.0E-44.0E-45.0E-46.0E-47.0E-4

-0.2 0.8 A1 0.0%

A2 12.0%

A3 18.0%

X (cm)

0.0E+0

1.0E-2

2.0E-2

3.0E-2

4.0E-2

0.0 0.2 0.4 0.6 0.8

CRECK

0.0E+0

1.0E-2

2.0E-2

3.0E-2

4.0E-2

0.0 0.2 0.4 0.6 0.8

ABF

0.0E+0

1.0E-2

2.0E-2

3.0E-2

4.0E-2

0.0 0.2 0.4 0.6 0.8

Sandia National Lab

Mo

le F

ract

ion

0.0E+0

1.0E-2

2.0E-2

3.0E-2

4.0E-2

0.0 0.2 0.4 0.6 0.8

DLR

0.0E+0

1.0E-2

2.0E-2

3.0E-2

4.0E-2

0.0 0.2 0.4 0.6 0.8

KAUST II

C2H2 - Acetylene

Figure B.1: Comparison of the different chemical kinetic mechanisms for the CO2 addition effects onthe concentration of acetylene.

Appendix B. 75

0.0E+01.0E-42.0E-43.0E-44.0E-45.0E-46.0E-47.0E-4

-0.2 0.8 A1 0.0%

A2 12.0%

A3 18.0%

X (cm)

Mo

le F

ract

ion

H - Hydrogen

0.0E+0

4.0E-4

8.0E-4

1.2E-3

0.0 0.2 0.4 0.6 0.8

CRECK

0.0E+0

4.0E-4

8.0E-4

1.2E-3

0.0 0.2 0.4 0.6 0.8

ABF

0.0E+0

4.0E-4

8.0E-4

1.2E-3

0.0 0.2 0.4 0.6 0.8

Sandia National Lab

0.0E+0

4.0E-4

8.0E-4

1.2E-3

0.0 0.2 0.4 0.6 0.8

DLR

0.0E+0

4.0E-4

8.0E-4

1.2E-3

0.0 0.2 0.4 0.6 0.8

KAUST II

Figure B.2: Comparison of the different chemical kinetic mechanisms for the CO2 addition effects onthe concentration of hydrogen radical.

Appendix B. 76

0.0E+01.0E-42.0E-43.0E-44.0E-45.0E-46.0E-47.0E-4

-0.2 0.8 A1 0.0%

A2 12.0%

A3 18.0%

X (cm)

Mo

le F

ract

ion

0.0E+0

5.0E-5

1.0E-4

1.5E-4

2.0E-4

0.0 0.2 0.4 0.6 0.8

CRECKOH - Hydroxyl

0.0E+0

5.0E-5

1.0E-4

1.5E-4

2.0E-4

0.0 0.2 0.4 0.6 0.8

ABF

0.0E+0

5.0E-5

1.0E-4

1.5E-4

2.0E-4

0.0 0.2 0.4 0.6 0.8

Sandia National Lab

0.0E+0

5.0E-5

1.0E-4

1.5E-4

2.0E-4

0.0 0.2 0.4 0.6 0.8

DLR

0.0E+0

5.0E-5

1.0E-4

1.5E-4

2.0E-4

0.0 0.2 0.4 0.6 0.8

KAUST II

Figure B.3: Comparison of the different chemical kinetic mechanisms for the CO2 addition effects onthe concentration of hydroxyl.

Appendix B. 77

0.0E+01.0E-42.0E-43.0E-44.0E-45.0E-46.0E-47.0E-4

-0.2 0.8 A1 0.0%

A2 12.0%

A3 18.0%

X (cm)

Mo

le F

ract

ion

0.0E+0

1.0E-4

2.0E-4

3.0E-4

4.0E-4

5.0E-4

6.0E-4

0.0 0.2 0.4 0.6 0.8

CRECKC6H6 - Benzene

0.0E+0

1.0E-4

2.0E-4

3.0E-4

4.0E-4

5.0E-4

6.0E-4

0.0 0.2 0.4 0.6 0.8

ABF

0.0E+0

1.0E-4

2.0E-4

3.0E-4

4.0E-4

5.0E-4

6.0E-4

0.0 0.2 0.4 0.6 0.8

Sandia National Lab

0.0E+0

1.0E-4

2.0E-4

3.0E-4

4.0E-4

5.0E-4

6.0E-4

0.0 0.2 0.4 0.6 0.8

DLR

0.0E+0

1.0E-4

2.0E-4

3.0E-4

4.0E-4

5.0E-4

6.0E-4

0.0 0.2 0.4 0.6 0.8

KASUT II

Figure B.4: Comparison of the different chemical kinetic mechanisms for the CO2 addition effects onthe concentration of benzene.

Appendix B. 78

0.0E+01.0E-42.0E-43.0E-44.0E-45.0E-46.0E-47.0E-4

-0.2 0.8 A1 0.0%

A2 12.0%

A3 18.0%

X (cm)

Mo

le F

ract

ion

1.0E-12

1.0E-11

1.0E-10

1.0E-9

1.0E-8

1.0E-7

1.0E-6

1.0E-5

0.0 0.2 0.4 0.6 0.8

CRECKA4 - Pyrene

1.0E-12

1.0E-11

1.0E-10

1.0E-9

1.0E-8

1.0E-7

1.0E-6

1.0E-5

0.0 0.2 0.4 0.6 0.8

ABF

1.0E-12

1.0E-11

1.0E-10

1.0E-9

1.0E-8

1.0E-7

1.0E-6

1.0E-5

0.0 0.2 0.4 0.6 0.8

Sandia National Lab

1.0E-12

1.0E-11

1.0E-10

1.0E-9

1.0E-8

1.0E-7

1.0E-6

1.0E-5

0.0 0.2 0.4 0.6 0.8

DLR

1.0E-12

1.0E-11

1.0E-10

1.0E-9

1.0E-8

1.0E-7

1.0E-6

1.0E-5

0.0 0.2 0.4 0.6 0.8

KAUST II

Figure B.5: Comparison of the different chemical kinetic mechanisms for the CO2 addition effects onthe concentration of pyrene.

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