Measurements of the Structure of
Turbulent Premixed and Stratified
Methane/Air Flames
M. S. Sweeney
Magdalene College
University of Cambridge
A dissertation submitted to the University of Cambridge
for the degree of Doctor of Philosophy
May 2011
Measurements of the Structure of Turbulent Premixed and
Stratified Methane/Air Flames
M. S. Sweeney
The influence of stratification on the structure of turbulent methane/air combustion is
investigated using experimental data from laboratory scale burners: a weakly turbulent
slot burner, and a higher turbulence co-annular swirl burner. The degree of stratification
can be controlled independently of the overall fuel/air flow rate. The resulting measure-
ments of scalar and velocity fields provide detailed test cases for existing and emerging
turbulent flame models, covering a range of u′/SL from 1 to 10, turbulence intensities
from 5 to 60%, and stratification ratios from 1 to 3.
Simultaneous Rayleigh/Raman/CO-LIF measurements of temperature and major
species concentrations — CH4, CO2, CO, H2, H2O and O2 — along a line are used
to investigate the structure of a series of flames in both the slot and swirl burners.
Concurrent cross-planar OH-PLIF allows thermal gradients to be angle corrected to their
three-dimensional values. Finally, non-reacting and reacting velocity fields complete the
flame database.
The behavior of major species concentrations in the slot and swirl burner with re-
spect to temperature is found to agree well on the mean with unstrained premixed
laminar flame calculations. Scalar means conditioned on stoichiometry also show good
agreement, aside from hydrogen which is enhanced under stratified conditions. Surface
density function and scalar dissipation are lower than calculated values in all cases,
suggesting that turbulence-induced thickening dominates the effect of increased strain.
Metrics commonly used to derive flame surface density (FSD) were investigated. FSD
may be determined using a statistical method based on measurements of temperature
and its gradient, or a geometric method based on 2D temperature or LIF imaging. A
third metric, an extension of the geometric method, is proposed. Good agreement is
observed between the three metrics.
The current database provides the first detailed high resolution scalar measurements
for premixed and stratified flames. The data analysis provides insight into the physics
of stratification: for the flames considered, the effects of stratification appear to be
surprisingly small compared to those of turbulence, even at significant stratification
ratios. The datasets provide a means of validating current and future computational
turbulent combustion models.
Declaration
This dissertation is the result of my own work and includes nothing which is the outcome
of work done in collaboration except where specifically indicated in the text. It has not
been submitted for another qualification to this or any other university. The full length
of this thesis is 51 926 words and includes 89 figures.
M. S. Sweeney
October 12, 2011
Keywords: Turbulent Combustion, Stratified Combustion, Premixed Combustion, Laser
Diagnostics, OH-PLIF, Flame Surface Density, V-Flame, Swirl, Methane/Air, Curva-
ture, Equivalence Ratio, PIV.
i
Acknowledgements
I would like to thank Professor Simone Hochgreb, my supervisor, for taking a chance
on someone without any prior exposure to the field of combustion, and for carefully
curating my project from inception to finish. She has been patient when I have been
confused, supportive when I have been lost, and congratulatory when I have succeeded!
I would also like to acknowledge the contribution of Dr. Robert Barlow of Sandia
National Laboratories, USA. In addition to enabling me to take detailed multi-scalar
measurements of the highest caliber at his laboratorya, he has been a constant source
of wisdom on aspects of research both experimental and theoretical. Similar gratitude
is owed to Bob Harmon, Rob’s technologist, and Matt Dunn, his current post-doc, and
Guanghua Wang, his previous post-doc.
I thank the Department of Engineering, EPSRC and Rolls Royce for their financial
contributions to this work, the Leverhulme Trust for an International Network Grant,
and Magdalene College for keeping a roof over my head. Without the help of these
institutions I could never have remained in higher education, nor traveled the world to
demonstrate my research.
Thanks is also due to everyone in the Heat Gallery for providing both education and
entertainment, often in equal measure; Chong, Hemanth, Inkyu, Isil, James, Jim, Ray,
Isil. To Tristan, thank you for pointing me towards this project, putting in a good word
for me with Simone, and being good banter throughout.
Above all else I’d like to thank Oli for always being there for me, both as a colleague
and as a friend. The experiences we have shared over the past few years, from turbulence
to tea-breaks, are among my fondest memories of Cambridge.
aWork at Sandia was supported by the United States Department of Energy, Office of Basic Energy
Sciences, Division of Chemical Sciences, Geosciences and Biosciences. Sandia National Laboratories
is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the
United States Department of Energy under contract DE-AC04-94-AL85000.
ii
To Jim Scott, who always wanted to be an engineer
iii
Contents
Nomenclature viii
1 Introduction 1
1.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Thesis Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Background 5
2.1 Modes of Combustion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Laminar Premixed Combustion . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Turbulent Premixed Combustion . . . . . . . . . . . . . . . . . . . . . . 9
2.4 Stratified Combustion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4.1 Experimental Studies on Stratification . . . . . . . . . . . . . . . 13
2.4.2 Numerical Studies on Stratified Combustion . . . . . . . . . . . . 16
2.5 Laser Diagnostics of Combustion . . . . . . . . . . . . . . . . . . . . . . 19
2.5.1 Rayleigh Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.5.2 Raman Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.5.3 Laser Induced Fluorescence . . . . . . . . . . . . . . . . . . . . . 22
2.5.4 Particle Image Velocimetry . . . . . . . . . . . . . . . . . . . . . . 22
2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3 Experimental Details 25
3.1 Cambridge Stratified Slot Burner . . . . . . . . . . . . . . . . . . . . . . 26
3.1.1 Burner Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.1.2 Operating Conditions . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.1.3 Multi-scalar Laser Diagnostics . . . . . . . . . . . . . . . . . . . . 29
3.1.4 Velocity Characterization . . . . . . . . . . . . . . . . . . . . . . 33
iv
3.2 Cambridge Stratified Swirl Burner . . . . . . . . . . . . . . . . . . . . . . 35
3.2.1 Burner Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2.2 Operating Conditions . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2.3 Multi-scalar Laser Diagnostics . . . . . . . . . . . . . . . . . . . . 41
3.2.4 Velocity Characterization . . . . . . . . . . . . . . . . . . . . . . 43
3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4 Data Processing Methodology 49
4.1 OH Image Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.1.1 Pre-processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.1.2 Flame Front Extraction . . . . . . . . . . . . . . . . . . . . . . . 52
4.1.3 Flame Normal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.1.4 Curvature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.1.5 2D OH Progress Variable . . . . . . . . . . . . . . . . . . . . . . . 58
4.2 Scalar Data Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.2.1 Mixture fraction and Equivalence Ratio . . . . . . . . . . . . . . . 60
4.2.2 Progress Variable . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.2.3 Differential Diffusion Correction . . . . . . . . . . . . . . . . . . . 64
4.2.4 Scalar Gradients . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.2.5 Error analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.3 Flame Surface Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.3.1 Σ1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.3.2 Σ2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.3.3 Σ3 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5 Slot Burner Results 84
5.1 Flow Field Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.2 Instantaneous Flame Structure . . . . . . . . . . . . . . . . . . . . . . . 87
5.3 Favre-Averaged Flame Structure . . . . . . . . . . . . . . . . . . . . . . . 89
5.4 Extent of Stratification . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.5 Influence of Stratification on Species Evolution . . . . . . . . . . . . . . . 94
5.6 Curvature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.7 Influence of Stratification on Scalar Gradients . . . . . . . . . . . . . . . 102
5.7.1 Unconditioned . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
v
5.7.2 Conditioned on local stoichiometry . . . . . . . . . . . . . . . . . 104
5.7.3 Conditioned on local curvature . . . . . . . . . . . . . . . . . . . 106
5.8 Flame Surface Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
6 Cambridge Stratified
Swirl Burner Results 110
6.1 Flame Visual Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
6.2 Flow Field Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 112
6.2.1 Non-Reacting Cases . . . . . . . . . . . . . . . . . . . . . . . . . 115
6.2.2 Reacting Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
6.2.3 Near-exit Conditions . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.2.4 Summary of Turbulence Parameters . . . . . . . . . . . . . . . . . 124
6.3 Instantaneous Flame Structure . . . . . . . . . . . . . . . . . . . . . . . 130
6.4 Flame Structure and Selection of Long Record Locations . . . . . . . . . 134
6.4.1 Thermal Structure . . . . . . . . . . . . . . . . . . . . . . . . . . 135
6.4.2 Compositional Structure . . . . . . . . . . . . . . . . . . . . . . . 137
6.4.3 Long Record Locations . . . . . . . . . . . . . . . . . . . . . . . . 139
6.5 Extent of Stratification . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
6.6 Favre-Averaged Flame Structure . . . . . . . . . . . . . . . . . . . . . . . 143
6.6.1 Non-Swirling Lean Cases . . . . . . . . . . . . . . . . . . . . . . . 144
6.6.2 Moderately Swirling Lean Cases . . . . . . . . . . . . . . . . . . . 148
6.6.3 Highly Swirling Lean Cases . . . . . . . . . . . . . . . . . . . . . 151
6.6.4 Stoichiometric Cases . . . . . . . . . . . . . . . . . . . . . . . . . 155
6.7 Influence of Stratification on Species Evolution . . . . . . . . . . . . . . . 158
6.7.1 Unconditioned Results . . . . . . . . . . . . . . . . . . . . . . . . 159
6.7.2 Results Conditioned on Local Equivalence Ratio . . . . . . . . . . 169
6.8 Curvature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
6.9 Progress Variable PDFs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
6.10 Influence of Stratification on Scalar Gradients . . . . . . . . . . . . . . . 182
6.10.1 Surface Density Function & Scalar Dissipation Rate . . . . . . . . 182
6.10.2 Turbulent Flame Thickness . . . . . . . . . . . . . . . . . . . . . 188
6.10.3 Flame Surface Density . . . . . . . . . . . . . . . . . . . . . . . . 191
6.11 Summary of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
vi
7 Flame Surface Density Metrics 196
7.1 Slot Burner Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
7.2 Swirl Burner Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
7.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
8 Conclusions 204
A List of Publications 208
A.1 Journal Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
A.2 Conference Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
B Error propagation formulas 210
List of References 212
List of Figures 220
List of Tables 224
Author Index 225
Colophon 227
vii
Nomenclature
The page number indicates the first mention of each symbol/acronym. All units are SI
unless stated otherwise.
Roman Symbols
Ae Exit area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
c Progress variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
cOH OH progress variable . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
Da Damköhler number . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
F Finite difference coefficient . . . . . . . . . . . . . . . . . . . . . . . . 75
h Enthalpy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
i, j and k Orthogonal coordinate system . . . . . . . . . . . . . . . . . . . . . . 54
I Signal intensity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
I Turbulence intensity . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
Ka Karlovitz number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
L Length scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
Lturb Turbulent length scale . . . . . . . . . . . . . . . . . . . . . . . . . . 11
n Flame normal vector . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
|∇c| Progress variable gradient, surface density function . . . . . . . . . . 63
P Probability density function . . . . . . . . . . . . . . . . . . . . . . . 63
Pw Wetted perimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
R Radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
r Radal location in swirl burner . . . . . . . . . . . . . . . . . . . . . . 42
Re Reynolds number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
s Distance along the flame front . . . . . . . . . . . . . . . . . . . . . . 56
SL Laminar flame speed . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
t Flame tangent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
viii
T Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
U Mean velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
u′ Velocity fluctuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
u′/SL Turbulence intensity . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
U Mean absolute velocity . . . . . . . . . . . . . . . . . . . . . . . . . . 115
x Line measurement axis . . . . . . . . . . . . . . . . . . . . . . . . . . 54
x Distance from centreline in slot burner . . . . . . . . . . . . . . . . . 42
Y Mass fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Z Mixture fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
z Axial location in slot burner and swirl burner . . . . . . . . . . . . . 42
Greek Symbols
α Thermal diffusivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
χc Scalar dissipation rate . . . . . . . . . . . . . . . . . . . . . . . . . . 77
∆ Full width half maximum . . . . . . . . . . . . . . . . . . . . . . . . 139
δ Flame thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
δt Turbulent flame thickness . . . . . . . . . . . . . . . . . . . . . . . . 188
ηK Kolmogorov length scale . . . . . . . . . . . . . . . . . . . . . . . . . 124
κd Discrete two-dimensional local curvature . . . . . . . . . . . . . . . . 56
κc Continuous two-dimensional local curvature . . . . . . . . . . . . . . 57
∇ Gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
νK Kolmogorov velocity scale . . . . . . . . . . . . . . . . . . . . . . . . 124
Ω Inter-plane angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
φ Equivalence ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
ψ Arbitrary scalar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
φ Lookup table corrected equivalence ratio . . . . . . . . . . . . . . . . 66
Φ Linear bridged equivalence ratio . . . . . . . . . . . . . . . . . . . . . 69
τK Kolmogorov time scale . . . . . . . . . . . . . . . . . . . . . . . . . . 124
θ Solid angle between line measurement axis and 3D flame normal . . . 54
ζ Number of thinning operations . . . . . . . . . . . . . . . . . . . . . 59
Subscripts
1 Inner wall of annulus . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
1 Fuel stream . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
2 Outer wall of annulus . . . . . . . . . . . . . . . . . . . . . . . . . . 122
2 Oxidizer stream . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
ix
3 Location of peak axial velocity . . . . . . . . . . . . . . . . . . . . . 122
b Burned . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
s Bilger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
e Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
F Fuel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
g Global . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
K Kolmogorov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
L Laminar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
n Nominal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
O Oxidizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
P Product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
s Stoichiometric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
T Turbulent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
t Turbulent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
u Unburned . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
x Two-dimensional projection (of gradient) . . . . . . . . . . . . . . . . 63
Chemical Species
Al2O3 Aluminum Oxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
CH4 Methane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
CO2 Carbon dioxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
CO Carbon monoxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
H2O Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
N2 Nitrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Nd:YaG Neodymium-doped yttrium aluminum garnet . . . . . . . . . . . . . 44
O2 Oxygen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Acronyms
BML Bray-Moss-Libby flamelet model . . . . . . . . . . . . . . . . . . . . 12
CFM Coherent flame model . . . . . . . . . . . . . . . . . . . . . . . . . . 12
CMC Conditional moment closure . . . . . . . . . . . . . . . . . . . . . . . 12
CTA Constant temperature anemometry . . . . . . . . . . . . . . . . . . . 33
FSD Flame surface density . . . . . . . . . . . . . . . . . . . . . . . . . . 12
FWHM Full Width Half Maximum . . . . . . . . . . . . . . . . . . . . . . . . 31
HWA Hot wire anemometry . . . . . . . . . . . . . . . . . . . . . . . . . . 33
LDV Laser Doppler velocimetry . . . . . . . . . . . . . . . . . . . . . . . . 16
x
LIF Laser induced fluorescence . . . . . . . . . . . . . . . . . . . . . . . . 22
LES Large eddy simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 12
MFC Mass flow controller . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
PIV Particle image velocimetry . . . . . . . . . . . . . . . . . . . . . . . . 14
PLIF Planar laser induced fluorescence . . . . . . . . . . . . . . . . . . . . 14
Pdf Probability density function . . . . . . . . . . . . . . . . . . . . . . . 12
RMS Root mean squared . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
RANS Reynolds-averaged Navier Stokes . . . . . . . . . . . . . . . . . . . . 12
SB Cambridge Stratified Slot Burner . . . . . . . . . . . . . . . . . . . . 27
SNR Signal to noise ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
SwB Cambridge Stratified Swirl Burner . . . . . . . . . . . . . . . . . . . 39
xi
“I tried, didn’t I? Goddammit, at least I did that!”
— R. P. McMurphy, in One Flew Over The Cuckoo’s Nest by Ken Kesey
xii
Chapter 1
Introduction
Worldwide energy consumption is approximately 16.5TW based on recent figuresa, and
is steadily increasing due to the rapid advancement of newly industrialized countries such
as China, India and Brazil. Combustion of fossil fuels accounts for the vast majority
of energy production (67%), with natural gas combustion contributing approximately
22% of total energy production.
Combustion of fossil fuels is primarily used in power generation (e.g. coal power
stations and gas turbine power stations) and transportation (e.g. motor vehicles and jet
engine aviation), and as such plays an important role in modern life. The combustion
of energy-dense hydrocarbon fuels is required to meet the high power requirements of
these applications. The combustion process is intrinsically linked with the production of
undesirable byproducts, whether in the form of ozone-damaging nitrous oxides (NOx),
unburned hydrocarbons and other combustion-related pollutants. Scientific concern and
public awareness of the environmental impact of human activity has risen substantially
over the past half century, with the result that many governments have implemented
aEnergy consumption figures based on the most recent (2008) figures released by the U.S. Energy
Information Administration (http://tonto.eia.doe.gov/).
1
Introduction 2
increasingly stringent emissions limits for combustion applications. Combustion sys-
tems now aim to have stable combustion with low levels of the previously mentioned
pollutants, without compromising fuel efficiency to a serious degree.
Achieving these often ambitious goals is one of the key challenges facing energy
production, prompting significant research endeavors from both industry and academia.
Though it has been an area of active investigation since the 19th century, it is only
relatively recently that experimental diagnostics have been able to probe the internal
structure of the flame and that computational power has advanced to the point that
combustion may be simulated. Theoretical combustion modeling has made great strides
in the past three decades, with a number progressing to computational models with
industrial applications. However, there remain many areas in combustion where the
understanding of the underlying physics is not yet fully closed.
Practical combustion applications, whether by accident or design, commonly feature
reactant mixture fields that exhibit spatial variation in composition. Such conditions are
defined as stratified in the present work. However, the fundamental science underpinning
stratified combustion remains poorly characterized and understood relative to other
combustion regimes. There is a paucity of high quality stratified combustion datasets to
assist model validation and development. This lack of validation hinders the emergence
of future computational models from current theoretical models. It also imposes a
penalty on the development of novel stratified devices, as current physical models have
unknown accuracy.
1.1 Objectives
The overall objective of this project is to provide further insight into the fundamental
physics governing stratified combustion. Stratification may influence the evolution of
Introduction 3
chemical species within the flame, and also chemical-turbulence interactions. These po-
tential effects can be investigated through detailed analysis of key combustion quantities
derived from experimental measurements.
The specific objectives of the present work are:
i) To design and test a turbulent stratified swirl burner with characteristics suitable
for model validation.
ii) To generate experimental datasets suitable for identifying the effect of stratification
on combustion.
iii) To develop a suite of validated data processing algorithms enabling the extraction
of key combustion quantities from experimental data.
iv) To derive insight into the fundamentals of stratified combustion through detailed
comparison of comparable premixed and stratified results.
v) To package experimental data into open-access datasets for use in validation of
emerging combustion models.
1.2 Thesis Overview
Chapter 2 provides a concise review of the main concepts relevant to the study of turbu-
lent stratified combustion. The literature is discussed where relevant to highlight both
consensus and discord within the combustion community in these areas.
Chapter 3 describes the two turbulent burners (a V-flame slot burner and a co-
annular swirl burner) used in the present work, the operating conditions surveyed in
Introduction 4
each, and the experimental methodologies employed. Measurement uncertainties are
detailed to quantify any systematic errors.
Chapter 4 covers the data processing used to calculate various derived quantities
relevant to the study of combustion (e.g. curvature) from the raw experimental data.
Background is supplied for non-standard and novel algorithms, implementation details
are discussed, and thorough error analysis applied where feasible to calculate propagated
uncertainties for the derived quantities.
The influence of stratification on combustion is investigated using data from a weakly
turbulent V-flame in Chapter 5. The interaction between turbulence and the effect of
stratification is also examined. Similar analysis is provided in Chapter 6 for data from
the swirl burner.
An investigation of the congruence of three metrics which can be used to calculate
flame surface densities from experimental data is presented in Chapter 7. As this chapter
makes use of data from both the slot and swirl burners, it is presented after the data
used to calculate the flame surface densities have been shown (Chapter 5, Chapter 6).
Finally, the primary findings of the present work are presented in Chapter 8. Sug-
gestions on the potential avenues for future work are also detailed.
Chapter 2
Background
Combustion has been an area of active research for many decades, resulting in a large
body of available literature. In general the research has focused on premixed flames,
where the fuel and oxidizer are fully mixed prior to ignition, and non-premixed flames,
where combustion takes place at the interface between separate fields of fuel and oxi-
dizer. Stratified combustion, a subset of premixed combustion where the fully mixed
fuel/oxidizer field exhibits a spatial composition gradient, has been the subject of rel-
atively few studies, despite the practical relevance of stratification in real world com-
bustion systems [1–5]. This stratification may be intentional, giving acceptable flame
stability in overall lean combustion. It may be due to physical design constraints, which
may impose limits on the mixing length for the fuel and oxidizer. There is a pressing need
to advance the understanding of stratified combustion and its underlying physics, and
this thesis focuses on a series of experiments which aim to further this understanding.
The following section provides the necessary background material to put this research
and subsequent discussion of results in context.
A brief overview of the various modes of combustion is provided in the following
section to expand on the brief descriptions given previously. The state of premixed and
5
Background 6
stratified turbulent combustion research is then assessed, providing a framework against
which the merits of the current work can be evaluated. Key studies and findings in
both the experimental and modeling domains are presented. Finally, a concise review of
material pertaining to the laser diagnostics techniques used in the present work is given.
2.1 Modes of Combustion
Combustion is defined as an exothermic chemical reaction between fuel and oxidizer. The
process may be subdivided into a number of different modes. The most basic division
is between premixed or non-premixed combustion. The strict definition of premixed
combustion states that fuel and oxidizer must be completely mixed on a molecular level;
in practice, flows in which there is no significant variation in composition are said to be
premixed. An example of this is a premixed Bunsen burner flame. This may be obtained
by fully opening the air inlet at the base of the Bunsen burner, allowing complete mixing
of air and fuel before flow reaches the burner exit. In non-premixed combustion, the fuel
and oxidizer are separate and the flame stabilizes at the stoichiometric interface that
arises due to molecular diffusion between the two fields. A classic example of this is
the yellow flame generated by a candle as evaporated fuel (typically paraffin in modern
candles) diffuses into ambient air.
The next level of classification is into either fuel-lean, stoichiometric, or fuel-rich
combustion. Stoichiometric combustion occurs when fuel and oxidizer are present in
the correct ratio for complete reaction to take place between them, with no shortage of
either fuel or oxidizer. In lean combustion there is an excess of oxidizer relative to the
amount of fuel, and vice-versa for rich combustion.
Between the extrema of premixed and non-premixed combustion, one can find situa-
tions in which the fuel stream is partially mixed with oxidizer, either intentionally (e.g.,
Background 7
to suppress soot), or by the natural evaporation and turbulent mixing processes taking
place prior to reaching a zone of flame stabilization. In this work, the term stratified
combustion is considered to be a subset of premixed combustion provided the mixture
is entirely fuel-rich or fuel-lean. Flames propagate through fuel/oxidizer fields which
though fully premixed exhibit significant spatial variation in air/fuel ratio. This form of
combustion is referred to by a number of terms in the literature — “stratified”, “partially
premixed”, “stratified premixed”, “imperfectly premixed” — but to avoid confusion and
to aid brevity will be referred to as stratified combustion throughout this thesis.
The present work is primarily concerned with identifying the effects of stratification
on turbulent CH4/air combustion. Turbulent premixed combustion at comparable oper-
ating conditions (flow rates, global and local stoichiometry etc) provides reference cases
against which the extent of these effects may be evaluated. Both modes of combustion
are examined in more detail in the following sections, with a particular focus on the cur-
rent state of the literature on stratified combustion in the experimental and modeling
domains.
2.2 Laminar Premixed Combustion
A basic understanding of the structure of laminar premixed flames is useful in the study
of their turbulent counterparts, and also of turbulent stratified flames. A laminar pre-
mixed flame may be considered to comprise three parts: unburned reactants, burned
products, and a thin layer separating the two. An idealized thermal profile across a lam-
inar flame front is shown in Figure 2.1. The layer separating the burned and unburned
gases may be subdivided into three regions; the preheat zone, the reaction zone and the
equilibration zone.
The bulk of the chemical reactions occur in the reaction zone, which is typically
Background 8
Figure 2.1: Schematic showing the structure of a laminar premixed flame, adapted
from Cant et al [6]. T is temperature, Y is mass fraction, and the subscripts u, b, O, F
and P refer to unburned, burned, oxidizer, fuel and product quantities respectively.
sub-millimeter in thickness. The conversion of unburned to burned gases takes place
via a number of intermediary reactions. The region between the unburned reactants
and the reaction zone is known as the preheat zone. The temperature is raised by the
conduction of heat and radicals from the reaction zone, but not to a level sufficient to
overcome the activation energy of most combustion reactions. Therefore there is little
chemical activity in this region. The equilibration zone is where much of the net heat
release in laminar premixed combustion occurs, via the formation of products by the
recombination of intermediate species, and it is in this region that most species achieve
chemical equilibrium.
When describing the evolution of various quantities within a flame, laminar or oth-
erwise, it is often easier to work in terms of a progress variable c. The progress variable
is a scalar, defined such that it has a value of zero in unburned reactants (cu = 0) and
unity in the burned products (cb = 1). Various measures of progress variable have been
defined, with the majority using a normalization of temperature or chemical species
Background 9
concentration to define c. Some commonly used progress variables are listed below:
c (h) =
h− hu
hb − hu
(2.1)
c (T ) =
T − Tu
Tb − Tu
(2.2)
c (YO) = 1−
YO − YO
b
YO
u
− YO
b
(2.3)
c (YF) = 1−
YF − YF
b
YF
u
− YF
b
(2.4)
c (YP) =
YP − YP
u
YP
b
− YP
u
(2.5)
where YP is often taken to be Y[CO+CO2]. Equation 2.1 is often approximated by Equa-
tion 2.2. The thermal progress variable c (T ) is often used where temperature measure-
ments are available. Strictly speaking it is only valid in adiabatic, incompressible flows
with near-unity Lewis number, as otherwise the relationship between c and T is not
unique [6]. However it is often applied in the experimental literature to cases outside
of this narrow definition. The choice of scalar basis has an influence on the behavior of
progress variable and its gradient, as shown in Figure 2.2. When comparing results in
c-space from other sources care should be taken to ensure that the same basis is used.
The current work uses a modified form of Equation 2.2 which allows c to be applied to
stratified flows where the fuel/oxidizer composition is not constant. This is detailed in
Chapter 4.
2.3 Turbulent Premixed Combustion
In turbulent premixed combustion, the fuel and oxidizer streams are mixed prior to any
combustion events such that the stoichiometry of the combined fluid is homogeneous in
Background 10
Figure 2.2: Comparison of progress variable c using a variety of scalar basis. Data
is obtained from unstrained laminar premixed flame calculations in a methane/air field
where φ = 0.73.
Background 11
space. In practice however a certain degree of inhomogeneity is permissible before the
system may no longer be classified as premixed. This form of combustion is common in
real world applications, and will be familiar to anyone who has ever used a gas cooking
stove, or a Bunsen burner with a fully open air supply.
A reacting front (flame front) propagates towards unburned mixture at a speed de-
termined by the local temperature, pressure, and stoichiometry. In order to stabilize
the flame in a stationary burner, it is desirable to balance this propagation with a bulk
motion of the premixed field. In this case the shape of the mean flame brush is governed
by the laminar burning velocity relative to the bulk velocity of the flow.
The addition of turbulence to the laminar premixed flame has a number of potential
effects, which may act in concert or against each other. For example, the flame front will
typically become convoluted, which has the effect of increasing flame surface area and
hence propagation due to increased reaction rates. However, if turbulent eddies penetrate
the preheat zone, the interplay between reactive and diffusive processes within the flame
may be locally altered, which can lead to a reduction in propagation rate.
The characteristics of turbulent premixed flames may be broadly classified based on
the relationship between the turbulence intensity u′/SL and the turbulent length scale
(normalized by the corresponding laminar flame thickness) Lturb/δL, as shown by the
modified Borghi diagram in Figure 2.3.
Numerous models have been proposed and applied to the simulation of turbulent
premixed combustion. These include, in order of increasing complexity: Bray-Moss-
Libby (BML) flamelet modeling [7]; Flame Surface Density (FSD) modeling [8, 9]; G-
equation modeling [10]. BML modeling is centered on the probability density function of
the progress variable, P (c), and its behavior in the limit of infinitely thin flamelets. FSD
modeling quantifies the surface-to-volume ratio at a specific value of progress variable
within the flamelet. It assumes that the flamelet is controlled by local stoichiometry and
Background 12
Figure 2.3: Modified Borghi diagram for classifying turbulent flames: A, laminar flames;
B, wrinkled flamelets; C, corrugated flamelets; D, thin reaction zones; E, broken reaction
zones.
strain, and that the area is governed by turbulence. The G-equation approach shows
some similarities to FSD modeling, but offers a greater degree of flexibility. It is based on
a non-reacting scalar variable G, which is used to define the flame surface via a level-set
approach.
Premixed turbulent combustion modeling has typically been expressed in a Reynolds-
Averaged Navier Stokes (RANS) framework, though Large Eddy Simulation (LES) ap-
proaches have become more common recently. It is beyond the scope of the present work
to describe each of these methods in detail; a good review can be found in [6]. Veynante
et al [11] give an excellent synopsis of turbulent combustion modeling at the turn of the
millennium, while Echekki et al [12] provide a more recent and extensive treatment.
Note that in comparison to diffusion flames, there is still a paucity of high quality
experimental datasets available for turbulent premixed model validation. This is in
part due to practical difficulties, as it is only in recent years that the optical resolution
of temperature and species measurements has become sufficiently refined to allow the
Background 13
structure of thin, premixed turbulent flame fronts to be probed. This has hindered
premixed model validation in the past, though the situation is continually improving.
2.4 Stratified Combustion
As mentioned earlier in the present chapter, practical combustion applications and model
combustors designed to study relevant phenomena at atmospheric pressure typically
operate in a stratified regime [1–5, 13–15]. This stratification may be intentional, giving
acceptable flame stability in overall lean combustion, or it may be due to physical design
constraints, which may impose limits on the mixing length for the fuel and oxidizer. It
may also occur simply by accident of design. Advancing the understanding of stratified
combustion is important due to this practical relevance. This section provides a brief
overview of the key experimental and numerical findings on stratification to date.
2.4.1 Experimental Studies on Stratification
2.4.1.1 Laminar Stratified Combustion
Various studies support the idea that stratification increases the lean flammability lim-
its in comparison to equivalent premixed cases. Kang and Kyritsis [16] measured the
laminar displacement speed of a flame front through a lean stratified mixture and found
that depending on the degree of stratification imposed, the lean flammability limit could
be lowered to φ = 0.4, significantly below the established value of φ = 0.5 [17]. As the
flame propagates towards and below the conventional flammability limit, combustion is
supported by heat released when the flame burned through mixture closer in composi-
tion to stoichiometric. The extension of the lean flammability limit where a stratified
mixture field has been induced has also been reported for spark-ignition engines [18, 19].
Background 14
Furthermore, both Kang and Kyritsis [16] and Gallizzi and Escudié [20] (in laminar
V-flame experiments) found that laminar flame speeds are increased beyond the expected
values based on local stoichiometry, which they attributed to the presence of a nearby
stoichiometric zone.
2.4.1.2 Turbulent Stratified Combustion
The effect of stratification on low turbulence (u′/SL ∼ O (1)), low Reynolds number
lean flames has been investigated recently in a small number of studies. Renou et al [21]
studied the behavior of unsteady flame kernels propagating through carefully tailored
equivalence ratio gradients in overall lean flames, and found that stratification increased
the flame propagation rate. The local variation in burning velocity was accompanied by
an increase in flame front wrinkling relative to premixed flames, with a corresponding
broadening of curvature distributions. Pasquier et al [22] studied the propagation of
flames through stratified lean turbulent propane mixtures in a combustion bomb. These
studies followed the fuel concentration ahead of the flame and the local velocity in 2D
planar laser induced fluorescence (PLIF) and particle image velocimetry (PIV) measure-
ments in premixed and stratified mixtures. The results showed that flame propagation
was influenced by the stoichiometry history of the mixture, whereby locally lean mix-
tures burn faster if pockets of richer mixtures were burned through earlier in the flame’s
propagation history.
Robin et al [23] studied a rod-stabilized V-flame supplied with a Gaussian distribu-
tion of mean equivalence ratio. Each branch of the flame propagates across the stratified
mixture field, which decreases in fuel/air ratio from a central peak to air at the edges.
Rayleigh scattering was used to obtain the temperature field, and the flow was seeded
with acetone to obtain the mixture fraction using PLIF. The analysis of flame thickness
Background 15
and curvature indicates that the presence of stratification in lean flames leads to a de-
crease in flame thickness, which is attributed to an additional stretch component arising
from differential flame propagation speeds. Anselmo-Filho et al [24] used a low turbu-
lence, rod-stabilized slot burner flame (as in the present work) to investigate the effect
of stratification on geometric flame properties. Analysis of curvature data from a large
interrogation window indicates that probability density functions (pdfs) of curvature are
broadened by stratification, and that the flame surface density is increased relative to
the premixed case across a wide region of the flame.
The combustion research community has begun to look at the behavior of stratified
flames at more practically relevant turbulence levels, with a number of recent experi-
mental studies examining results from novel turbulent stratified burners [25–29].
Seffrin et al [25] introduced an axisymmetric concentric-tube burner designed to allow
the investigation of flames at high Reynolds numbers (Re ∼ O (104)). Laser Doppler
velocimetry (LDV) and particle image velocimetry were used to characterize the ve-
locity field for a number of operating conditions. The structure of these flames were
investigated by Böhm et al [26] using Rayleigh scattering, and the resulting mean and
RMS profiles of temperature indicated a lower turbulent burning speed in the stratified
case relative to the corresponding premixed case. However it is worth noting that the
equivalence ratio at the intersection of the mixing layer and the mean flame brush was
significantly lower in the stratified case (0.6 < φ < 0.9) than in the premixed (φ = 0.9),
and hence this result may be solely due to the premixed flame burning through lean mix-
ture of higher equivalence ratio than the stratified case. This makes it difficult to draw
any solid conclusions as to the influence of stratification on the turbulent burning veloc-
ity in this experiment. Examining instantaneous temperature profiles and corresponding
OH-PLIF images, Böhm et al conclude that the effect of stratification on temperature
profiles is secondary to that of the actual three-dimensional flame front geometry due to
Background 16
turbulence. Additionally they found that curvature distributions trended similarly with
stratification to those reported by Anselmo-Filho et al [24].
Flame surface density measurements obtained from the axisymmetric co-annular
burner used in the current work (see Chapter 3) were presented in [27]. Though the
study investigated methods of deriving FSD rather than the effects of stratification on
said quantity, the result shown indicated that stratification attenuated FSD in non-
swirling flows; similar reductions were not evident in the swirling results. Galizzi et
al [28] studied a stratified turbulent rod-stabilized V-flame, carrying on from their pre-
vious work on laminar stratified flames [20]. The main effects of stratification observed
were changes to the velocity field, with burned gases being accelerated towards the flame
front opposite the stratified zone. Vena et al [29] examined the effects of equivalence
ratio gradients on the topology of flame fronts in a turbulent iso-octane/air V-flame.
They observed variations in curvature distributions that were less significant than those
reported elsewhere in the methane/air literature. Their main conclusion was that while
stratification may effect the overall structure and instantaneous behavior of globally
stoichiometric flames, the effects on curvature may be limited in locally stoichiometric
flames.
2.4.2 Numerical Studies on Stratified Combustion
A number of numerical studies have examined the behavior of partially premixed and
stratified flames, from 1D laminar to 3D turbulent flows. Pires da Cruz et al [30]
originally investigated the behavior of freely-propagating methane flames through step
changes in stoichiometry. The findings are in agreement with experimental results from
laminar flames below the stoichiometric point: lean flames traveling from a richer mix-
ture to a leaner mixture (back-supported) travel faster than expected based on their
Background 17
local mixture fraction. Flame propagation is enhanced by diffusion of additional heat
and radicals from higher enthalpy regions to lower enthalpy regions. Thus, the flame
speeds of flames propagating away from the stoichiometric point are faster than those
propagating towards it. This acceleration allows back-supported lean flames to propa-
gate below the lower flammability limit. When burning towards stoichiometric in rich
cases, flames are also influenced by the diffusion of molecular and atomic hydrogen from
the rich to the stoichiometric side of the flame. This further accelerates flame propaga-
tion, despite the lower temperatures of the rich flame. In general, the acceleration effect
due to enrichment was found to be on the order of 10-20% of the local flame speed.
Marzouk et al [31] investigated the role of stratification by calculating laminar op-
posed flow propane/air flames subjected to a gradient in equivalence ratio and strain.
Similarly to Pires da Cruz et al [30], they observed that lean flames can be supported by
richer flames via diffusion of heat and radicals to burn beyond the premixed flammabil-
ity limit, and that the rate of heat release is correspondingly higher than expected from
the local equivalence ratio. Furthermore, their investigation of the dynamic behavior of
back-supported flames showed that greater equivalence ratio gradients allow the flame
to propagate through increasingly lean mixtures, again by virtue of the diffusion of heat
and radicals. Richardson et al [32] systematically investigated the behavior of steady,
stabilized strained flames with fresh reactants on one side and burned products on the
other, where the opposed streams have different equivalence ratios. They conclude that
the effect of equivalence ratio gradients on steady flames is primarily due to the modified
radical pool flux rather than heat. Further, they conclude that the unsteady behavior
of stratified flames is different from that of premixed flames, and that the response to
variable strain is a function of the relative response of diffusion and reaction times, which
are affected by the equivalence ratio gradient.
The effect of stratification in turbulent combustion has been considered using direct
Background 18
numerical simulations (DNS) in several studies. Hèlie and Trouvé [33] have performed
3D, single-step chemistry DNS of mean stoichiometric propane/air stratified flames with
various initial mixture fraction distributions and length scales. They found that the
flame surface density was unaffected by stratification, and that the lowering of the
overall reaction rate relative to the homogeneous case was entirely due to deviation
from stoichiometry and the corresponding reduction in local reaction rate. Poinsot et
al [34] performed three-dimensional reduced chemistry simulations of turbulent strat-
ified propane/air flames with a Gaussian distribution of mixture fraction centered at
Z = 0.049 (φ = 0.8). They concluded that the main effect of stratification is to enhance
heat release via the production of flame surface area via flame stretch. The difference
between the findings in [33] and [34] is primarily due to the assumed mean stoichiometry.
Poinsot et al [34] also notes that the induced stretch by partial premixing is small, and
that this effect should be overwhelmed by flow stretch at high turbulence levels.
Haworth et al [35] performed two-dimensional complex chemistry simulations of tur-
bulent propane stratified flames for a stoichiometric mean equivalence ratio. The study
demonstrated the two-stage spatial structure of stratified flames, and concluded that
there was no difference in overall heat release rate between homogeneous and stratified
conditions. Jimenez et al [36] extended that work, by varying the length scale and the
mean equivalence ratio of stratification. The study showed that both the global and the
local rates of heat release are affected by the scale and distribution of mixture fraction
fluctuation, the effect depending on the mean equivalence ratio.
Computational models that are simple extensions of premixed modeling approaches
have been applied to stratified systems with some success [14, 15, 23, 37–39], and more
extensive approaches bridging regimes have also been proposed [40, 41]. Still, the avail-
ability of detailed experimental data for model development and validation is very lim-
ited, and the state of modeling for stratified combustion is less advanced than that for
Background 19
non-premixed or fully premixed combustion. Furthermore, fundamental questions re-
garding the structure and dynamics of turbulent stratified flames remain unanswered.
In particular, issues of whether the flame structure is affected by local equivalence ra-
tio gradients commensurate with flame or turbulence structures have yet to be fully
understood.
2.5 Laser Diagnostics of Combustion
The measurement capabilities of experimental combustion research have advanced rapidly
over the past thirty years as ever more refined laser diagnostics systems became tech-
nologically and commercially viable. Early experiments were constrained by the power
and repetition rate of lasers, the optical resolution of light collection devices, and the
data storage available. The result of this was that many early surveys were by neces-
sity limited to single species measurements at a point, which were laboriously traversed
across radial and axial locations in order to develop profiles of the mean and fluctuation.
Modern systems allow for high speed stereoscopic velocity characterization, for planar
or line imaging of major species and temperature, and much more. Crucially such meth-
ods allow for temporally and spatially resolved measurements to be made in turbulent
reacting flows without perturbing the flow field.
The principles underlying the main diagnostic techniques used in this work are pre-
sented in the following subsections. More detailed accounts of each of the techniques are
available in the literature, and the treatment by Eckbreth [42] is recommended for the
interested reader.
Background 20
2.5.1 Rayleigh Scattering
Rayleigh scattering is the elastic scattering of light by particles whose major dimension is
an order of magnitude smaller than the wavelength of the incident light. Mie scattering
will occur if the particles are larger than this cut-off value. A dipole moment is induced
in an atom or molecule when it is hit by a laser beam of suitable wavelength. This
moment is strongly aligned with the polarization of the particle’s electric field. When
the dipole moment relaxes, light at the same wavelength as the incident light is emitted
(elastic scattering).
In a single species measurement volume, the probability of light being scattered by
a particle is given by its Rayleigh cross-section. In combustion experiments, where mul-
tiple species are present simultaneously, the effective Rayleigh cross-section must be
calculated before any quantitative results can be obtained from Rayleigh scattering ex-
periments. The effective cross-section is the mole fraction weighted sum of the Rayleigh
cross-sections of each species in the measurement volume. The intensity of the light
emitted from a gaseous sample is directly proportional to the product of the intensity
of the incident light, the effective Rayleigh cross-section of the impinged gas, and the
summation of the number densities of species in the gas.
Provided sufficient knowledge of the local composition is available, it is possible to
determine the local temperature or density from Rayleigh measurements. Where detailed
knowledge of the local composition is not feasible due to experimental constraints, it is
possible to overcome this issue by choosing a fuel mixture such that the effective cross
section is close to unity. In the current work local measurements of major species are
used to determine the effective Rayleigh cross-section, and hence the temperature.
Rayleigh measurements have been applied with increasing frequency to both pre-
mixed [27, 43–48] and stratified systems [23, 26, 27, 47, 49].
Background 21
2.5.2 Raman Scattering
Raman scattering is an inelastic process, as the incident and emitted radiation are of
different wavelengths. Incident light may cause a change in the vibrational, rotational or
electronic energy levels of an impinged atom or molecule. Light of a different (typically
lower) frequency is emitted when the atom or molecule relaxes to either an elevated
energy level (Stokes scattering) or a lower energy level (anti-Stokes scattering) relative
to the original energy state. In combustion diagnostics we are primarily concerned with
changes in the vibrational modes.
The signal obtained from Raman scattering is typically much smaller than that from
other forms of scattering, as the vibrational Raman scattering cross-sections are less than
0.1% of those for Rayleigh scattering. This requires very large laser energies, spread out
over wider pulses than those provided by conventional commercial grade lasers, thus
limiting its widespread use. The Raman cross-section is a function of the incident light,
and the Raman signal from each species is directly proportional to the product of this
cross-section and the number density of the species.
A further complication to Raman scattering measurements is that measurements
from a specific species are prone to interference from other species. An example of
interference in species relevant to combustion diagnostics is that of CH4 on O2. Many
combustion relevant interferences are detailed in [50]. Fluorescence from soot precursors
is another source of interference in Raman measurements. Fortunately this can be
avoided by selecting operating conditions which minimize sooting (i.e. operating in
globally lean conditions).
Despite the difficulties associated with Raman scattering measurements, they have
been successfully applied to a range of turbulent combustion systems including pre-
mixed [47], partially premixed [51, 52], and stratified [47] flames. The current work
Background 22
makes extensive use of species measurements obtained from Raman scattering diagnos-
tics.
2.5.3 Laser Induced Fluorescence
Laser induced fluorescence, or LIF, is a commonly applied technique in the field of
experimental combustion. Molecules are induced into an excited energy state by the
application of laser light at a particular frequency. Provided the excited atom or molecule
does not undergo a quenching collision first, after a specific period the particle will
fluoresce isotropically. This isotropy enables planar imaging of species (PLIF) to be
performed. There are few species that can fluoresce at practically accessible wavelengths,
which limits the application of this technique.
Quenching collisions significantly decrease the LIF signal, which complicates the
quantification of LIF measurements. In order to correct for signal degradation due to
quenching it is necessary to have simultaneous measurements of temperature and the
colliding molecules relevant to the flow under investigation. The present work makes
use of OH-PLIF and two-photon CO-LIF, qualitatively in the case of the former and
semi-quantitatively in the latter.
2.5.4 Particle Image Velocimetry
Particle image velocimetry, or PIV, is a non-intrusive laser diagnostic which allows a
flow field to be characterized through the sequential imaging of seed particles in the
flow illuminated by laser light. The flow field is seeded with particles whose size and
properties are chosen to allow them to follow the motion of the fluid under investigation
without perturbing it. The particles should be roughly uniform in diameter, as the signal
obtained scales with the square of their major dimension. The current work makes use
Background 23
of sub-micrometer diameter alumina particles (Al2O3).
Two images of the particles in the flow field are obtained in quick succession, by
illuminating the seeded field using a sheet of laser light, imaging the reflected light using
an optical collection system, and repeating the process after a suitable separation time.
This separation time is tuned such that the average displacement of the particles is only
a few pixels (∼ 3−5) between the two images. Interrogation windows are then traversed
over the image pairs, and correlation algorithms are used to determine the velocities in
the field. The use of interrogation windows limits the resolution of PIV measurements,
as typically a minimum window size of 32× 32 pixels is required for accurate results.
Single camera PIV can only provide the components of velocity in the imaging plane
(i.e. Ux, Uy). This is reasonable for applications where the out-of-plane component is
small, such as in radially symmetric non-swirling flames. It is necessary to use stereo-
scopic PIV (SPIV) in cases where this is not true.
2.6 Summary
The present chapter has given a brief overview of the topics in order to put the current
work in context. First, an overview of the various modes of combustion was given. This
provided definitions of premixed and stratified combustion, which form the focus of the
present work. The key findings in the stratified literature, experimental and numerical,
were presented to assist interpretation of the results and discussion shown later on in
Chapter 5 and Chapter 6 by the reader, regardless of their field of specialization.
Chapter 3 presents the two burners surveyed experimentally in the present work.
Their geometry and the operating conditions surveyed are described in full. The exper-
imental methods used to obtain data from the flames in these burners are also detailed.
The following chapter (Chapter 4) is closely linked to Chapter 3, focusing on the data
Background 24
analysis techniques applied to the experimental data to derive quantities such as curva-
ture, flame surface density, and scalar dissipation rate.
Chapter 3
Experimental Details
This chapter provides an overview of the burners and experimental methods used to
generate the premixed and stratified flame data studied in subsequent chapters. The
chapter is divided into two main sections, each focusing on a particular burner. These
sections outline the design, operating conditions, and experimental methods applied to
each burner. The first burner (Section 3.1) is a stratified slot burner that generates a
weakly turbulent rod-stabilized V-flame with variable stratification. This burner was
designed and fabricated as part of a previous PhD programme. The second burner
(Section 3.2) is a co-annular swirl burner that allows turbulent bluff-body stabilized
flames of variable stratification and swirl to be investigated.
The experiments performed on the burners may be broken down into multi-scalar
measurements and velocity characterization. There is considerable overlap in the experi-
mental details of the multi-scalar measurements as they were performed in the Turbulent
Combustion Laboratorya using broadly similar equipment and techniques. As such the
methods are described in depth for the slot burner experiments (Section 3.1.3), while
only major differences are detailed for the swirl burner (Section 3.2.3). Note that the
aSandia National Laboratories, Livermore, CA, USA
25
Experimental Details 26
velocity characterization in the slot burner was performed during a previous PhD pro-
gram, and is included to put the analysis of scalar measurements presented in Chapter 5
in context.
3.1 Cambridge Stratified Slot Burner
3.1.1 Burner Design
The Cambridge Stratified Slot Burner is a rectangular slot burner, similar in geometry
to others used elsewhere in the premixed [53, 54] and stratified [21, 49] literature. The
attraction of this design is that it is one of the simplest geometries for investigating
turbulent stratified combustion; the flow field can be considered to be approximately
two-dimensional, with the mixing layer between streams of different stoichiometry gen-
erating a spatial gradient in equivalence ratio. The flame is stabilized on a rod, which
results in an open-air turbulent V-flame that intersects the mixing layer mentioned pre-
viously. The lack of a combustion chamber allows complete optical access to the areas of
interest. The geometry of the burner and the turbulence generating grid are simplified
to ensure that it is attractive to simulate using either modeling or DNS methods.
Burner Geometry: The apparatus, originally described in [47, 55], consists of a pla-
nar slot burner comprising 6 parallel slots; each slot is a channel 5mm wide and 50mm
deep separated by 0.3mm metal slits, through which fuel/oxidizer mixtures can flow
(Figure 3.1 and Figure 3.2). The outer slots are used to carry an air co-flow to prevent
entrainment of ambient air. One pair of inner slots carries a richer mixture, φr, and the
remaining inner pair carries a controlled leaner mixture, φl. Premixed or stratified flow
fields are achieved by distributing a constant volumetric flow rate of air equally across
Experimental Details 27
Figure 3.1: Schematic of the stratified slot burner (SB) showing internal structure,
reproduced from Anselmo Filho et al [55]. All dimensions in mm and to scale.
the inner four slots and adjusting two methane flow rates to give the desired operating
conditions.
Grid & Flame Stabilizing Rod: A wire mesh grid with a 1.02mm square pattern and
79% open area is attached to the burner mouth to generate turbulence in the reactant
streams. A Ø1.5mm flame stabilizing rod is placed downstream of the burner mouth
(z = 10mm), offset from the burner center-line (x = 2mm). The rod ensures that
intersection of the mixing layer and the flame brush occurs before the entrainment of co-
flow air into the region of interest, far enough downstream of the rod to avoid interference
with the laser sheets.
The slot burner is referred to as SB in the rest of this work.
Experimental Details 28
Figure 3.2: Schematic of the exit geometry of the stratified slot burner (SB) showing
location of flame stabilization rod •, V-flame , mixing layer , and turbulence
generating grid at exit. CH4/air slots are marked with open arrows, and co-flow air
slots with closed arrows. φl is the lean flow and φr the rich flow in stratified cases. All
dimensions in mm and to scale.
3.1.2 Operating Conditions
The burner was run in premixed and stratified regimes for a range of flow rates at a
nominal global equivalence ratio φg = 0.73. Three cases are investigated in this thesis; a
premixed case, fs1, a moderately stratified case, fs4, and a highly stratified case, fs6.
The heat load was kept fixed at 7.1 kW, and stratification was achieved by keeping air
flow rates constant and varying the split of methane to the reactant flows. The operat-
ing conditions are summarized in Table 3.1. Before moving on it is worth noting that
lean stratified combustion can be further broken down into back- and front-supported
regimes. Back-supported combustion occurs when the products are closer to stoichio-
metric than the reactants, and vice-versa for front-support. The current work deals
exclusively with back-supported flames, and all stratified cases described subsequently
Experimental Details 29
Table 3.1: Operating conditions and bulk flow rates at 1 atm, 294 K. Volumetric flow
rate of air includes co-flow air supply.
Flame Combustion φl φr φr/φl
CH4 Flow 1 CH4 Flow 2 Air Flows
Regime (l/min) (l/min) (l/min)
fs1 Premixed 0.73 0.73 1.00 6.58 6.58 85.0
fs4 Stratified 0.51 0.95 1.86 4.61 8.55 85.0
fs6 Stratified 0.37 1.10 3.00 3.29 9.87 85.0
will be assumed to be back-supported except where otherwise stated.
Flow control: The gas flows for the multi-scalar measurements (Section 3.1.3) were
metered using mass flow controllers. These mass flow controllers were calibrated against
laminar flow elements to within 1% of reading. The velocity measurements (Sec-
tion 3.1.4) used Roxspur NGX series glass variable area rotameters. These rotame-
ters have a specified accuracy of ±3.0% of reading scale. Each rotameter was factory-
calibrated for appropriate gas and flow rate. The rotameters were recalibrated against
Bronkhorst EL-Flow F-203AC series thermal mass flow controllers (MFCs) to correct
for back-pressure in the system. The MFCs have an accuracy of ±0.5% of reading and
±0.1% of full scale.
3.1.3 Multi-scalar Laser Diagnostics
Multi-scalar laser diagnostics in the slot burner were carried out at Sandia National
Laboratories by R. S. Barlow. The diagnostics setup allows for the line measurement of
temperature (Rayleigh scattering) and major species (Raman scattering) with simulta-
neous cross planar OH-PLIF. The experimental setup is illustrated in Figure 3.3. This
setup has previously been described in [47, 56, 57].
Experimental Details 30
Figure 3.3: Illustration demonstrating the optical system at Sandia National Labo-
ratories for combined Raman/Rayleigh/CO-LIF line measurements with simultaneous
cross-planar OH-PLIF imaging.
Line Imaging of Temperature and Major Species: Beams from four frequency
doubled Nd:YAG lasers were used for Raman and Rayleigh line imaging, yielding a total
energy of 1.8 J/pulse in the probe volume. The focus had a diameter of∼ 0.22mm (1/e2).
The beam diameter was ∼ 0.24mm at the ends of the 6mm length of the measured
segment. CO was excited at 230.1 nm (two photons), with the UV laser beam aligned
on the same axis as the Nd:YAG laser beams.
A single detection unit housed CCD cameras for Raman, Rayleigh, and CO-LIF. A
pair of 150mm diameter achromats (Linos Photonics, f/2 and f/4) imaged a portion of
the laser beam into the apparatus. The main internal components included two custom-
built motor-driven chopper wheels, six commercial camera lenses, and a transmission
grating. The two chopper wheels were locked in frequency and phase to a master con-
troller, which also generated timing signals for the lasers and cameras. The “slow” wheel
(3 000RPM, 300 µs FWHM gate) was located at the focus of the collection lens pair
Experimental Details 31
to provide gating for the Rayleigh camera. A 1-inch diameter leaf shutter (35ms) at
the entrance to the detection unit allowed just one laser exposure during each camera
cycle. The image acquisition rate was 5Hz, while lasers fired at 10Hz. Relay lenses and
beam splitters separated the wavelengths of interest and refocused the respective images
onto the Rayleigh detector, the intensified CO-LIF detector, and the stationary slit of
the “fast” wheel (21 000RPM, 3.9 µs FWHM gate) for the Raman spectrometer. The
CCD cameras were the same as those used in [47], with the non-intensified, low-noise,
cryogenically-cooled Raman detection array (Princeton Instruments VersArray 1300B,
with CryoTiger Cooling Unit operated at −110 ◦C) being most critical for the overall
system performance.
The four camera lenses in the optical train between the slow wheel and the Raman
CCD array were 85mm f/1.8, 50mm f/1.4, 85mm f/1.4, and 135mm f/2. The lenses
in front of the Rayleigh and CO cameras were 85mm f/1.8 and 50mm f/1.4, respec-
tively. Nikon lenses were used throughout, with the exception of the 135mm Canon
lens. A long-pass filter separated the wavelength range monitored by the Raman cam-
era (∼ 550 nm to 700 nm) from the Rayleigh scattering (532 nm) and CO fluorescence
(∼ 480 nm to 488 nm). A second long-pass filter split the CO and Rayleigh signals, and
10 nm bandpass filters centered at 484 nm and 532 nm were used in front of the respective
camera lenses.
The custom transmission grating (Kaiser Optical) for the Raman spectrometer was
76mm square, with anti-reflection coating and design specifications of 1 200 lines/mm,
625mm center wavelength, and 22◦ incident and refracted angles. Efficiency specifica-
tions were approximately 0.78, 0.90 and 0.78 for wavelengths of 565 nm, 625 nm and
685 nm, respectively.
The optical resolution was determined primarily by the pair of achromatic lenses at
the front end of the collection system. The measured line-spread function at best focus
Experimental Details 32
was ∼ 40 µm FWHM for each system at fixed wavelength, using a knife edge method [58].
Final focusing of each camera was accomplished using a laser-drilled target with a linear
pattern of 50 µm holes on 200 µm centers, located on the plane bisecting the laser align-
ment aperture. For the Raman system, a neon lamp was used to back-illuminate the
target, producing an array of dots in the detected image and allowing convenient opti-
mization of focus across the array. The effective resolution is influenced by the presence
of a flame in the collection path, and it is reduced when the flame normal is not aligned
with the beam due to the finite beam diameter. The spacing of binned pixels along
the laser axis was 105 µm, 20 µm and 101 µm for the Raman, Rayleigh, and CO-LIF
measurements respectively.
Cross-planar OH-PLIF: The instantaneous 3D orientation of the flame was deter-
mined using planar imaging of OH fluorescence from two crossed laser sheets that inter-
sected along the multi-scalar line measurement axis [24, 56]. A dye laser was pumped us-
ing a frequency-doubled Nd:YaG laser, the frequency of which was doubled to 283.5 nm.
The output beam was split into two separate 1mJ beams, and one beam was optically
delayed by 40 ns to ensure the fluorescence from each would not interfere with the other.
The beams were reshaped using sheet-forming optics and crossed such that the inter-
plane angle was 60◦ and their intersection axis was coincident with the line measurement
window. 10-element UV lenses (CERCO 45mm f/1.8) were combined with intensified
CCD cameras (Andor) to image the fluorescence obtain by the excitation of the Q1 (8)
line of the OH molecules. The imaged region for each plane was 10mm by 8mm, with
a resolution of 0.15mm/pixel.
Experimental Error: Calibrations for the line-imaged measurements were based on
cold flows, heated flows, laminar jet diffusion flames, and flat CH4/air flames of known
Experimental Details 33
stoichiometry. Estimates of accuracy were based on uncertainties in calibration flow
conditions and repeatability of measurement. Table 3.2 lists uncertainties based on
estimated accuracy and the standard deviation (precision) of averaged measurements.
Table 3.2: Uncertainties in scalar measurements based on measurements in calibration
flows, arranged in order of descending accuracy.
Scalar Accuracy, ∆ (%) Precision, σ (%) Calibration Flow
T 2 0.75
 φ = 0.97, T = 2 185K
N2 2 0.7
H2O 3 2.4
CO2 4 3.2
φ 5 2.2
CO 10 4.5
}
φ = 1.28, T = 20 450KH2 10 7.5
3.1.4 Velocity Characterization
Velocity characterization in the slot burner was performed by P. Anselmo-Filho, and is
detailed in full in [55]. A brief synopsis will be given in order to assure the reader as to
the reliability of the velocity data presented later on. Axial velocities in the cold flow
were characterized by hot wire anemometry (HWA) operating in constant temperature
anemometry (CTA) mode. The main disadvantages of HWA are that it is by definition
an intrusive procedure (unlike laser diagnostic methods), that it can only be used in
cold flow conditions, and that it is significantly more difficult to measure two or three
component velocities than single component velocities due to the increased complexity
in accurately calibrating measurements. Only one-dimensional velocity measurements
were made in the slot burner.
Experimental Details 34
Principles of Operation: The basic principle of HWA is that the probe is cooled by
the flow of the fluid about it, which reduces its resistance. In CTA mode, the applied
voltage is varied with the changing resistance to ensure the probe maintains a constant
temperature. This voltage is measured and may be converted to a velocity measure-
ment. The technique requires calibration procedures to be followed prior to making any
measurements.
HWA Setup: The velocity characterization used a single normal probe (Dantec Dy-
namics 55P16), 5 µm in diameter and 1.25 mm in length. The operating range for this
probe was 0.05m/s to 500m/s, making it a suitable choice for the velocities expected in
the flow. The probe was connected to a Dantec Dynamics 56C01 CTA unit with a 56C17
CTA bridge and a 56N20 signal conditioner using a standard BNC cable. The voltage
signal from the CTA system was recorded using a digital acquisition board (National
Instruments PCI 6035E).
HWA Calibration: The calibration rig was based on that used by Johnstone et al [59],
and comprised a low angle diffuser, a cylindrical settling chamber with two flow stabiliza-
tion screens, and a nozzle with exit diameter 25.58mm and contraction ratio of 25 : 1.
The laboratory temperature was kept constant at 20±1 ◦C, while the calibration airflow
was maintained at 20± 2 ◦C. The air flow was metered using a Bronkhurst El-Flow F-
203AC thermal mass flow controller (MFC), which had a factory calibration of ±0.5% of
reading plus ±0.1% full scale. The calibration methodology detailed in [59] was iterated
until the calibration error was within 0.5%. This procedure generated a polynomial fit
between the measured voltage and velocity.
Experimental Details 35
HWA Measurements: The sampling frequency was chosen to be 100 kHz to ensure
the flow was temporally resolved, as the cutoff frequency was measured to be 50 kHz.
The sample time was 40 s, giving a sample size of 4× 106. These values were chosen
to ensure statistically independent samples. The experimental error in the mean ve-
locity measurements due to the effects of spatial resolution was estimated to be about
1.0%, assuming isotropic turbulence. When combined with probe calibration error, the
combined error was determined to be roughly 3.0%.
Velocity profiles were taken by traversing the probe in increments of 0.5mm along
a line parallel to the burner exit and z = 15mm downstream of it. Note that hot flow
properties for the slot burner are currently unavailable. A systematic PIV measurement
campaign is planned for the future.
3.2 Cambridge Stratified Swirl Burner
3.2.1 Burner Design
The slot burner provided a good introduction to the behavior of stratified flames, and at
conditions which could be reasonably simulated by DNS. It has also attracted interest
from RANS modelers [60]. However, the turbulence intensity of the flames surveyed
(Re ∼ 2 000) are not really comparable with those seen in practical combustion systems.
The simulation of flames in burners at more realistic turbulence levels have become ever
more viable with the advance of computational power, the refinement of existing models
and the emergence of newer models. A burner with substantially higher flow rates (and
Reynolds numbers) was designed to investigate the effect of stratification in a more
representative flow. The burner was designed to provide flows with a variable degree of
swirl to allow the turbulence levels to be varied for a given level of stratification; this was
Experimental Details 36
to allow any potential turbulence dependences of stratification in this geometry to be
identified. It has the potential to assist flame stabilization, as in practical combustors,
allowing more extreme stratified conditions to be investigated than would otherwise be
possible. This latter avenue of research was not pursued in the current work.
The swirl burner is shown in plan view in Figure 3.4; key components are labeled and
will be referenced in braces, {}, in the following discussion. It consists of two annular
channels through which fuel/oxidizer mixtures can flow, and a large (382 mm diameter)
co-flow of filtered air to prevent the entrainment of ambient air. Air flow in the co-flow
is conditioned in the following way. First, it is passed through 3 perforated disks {M},
the first of which has 3 mm diameter holes with 40% open area, while the subsequent
pair has 1.5 mm diameter holes with 25% open area. The flow is then straightened by
passing it through a 38.1 mm deep honeycomb section {L} with 3 mm holes and 75%
open area. Finally any clustered particles are filtered using two mesh gauze {K}, the
first of which has 1.2 mm square holes and 70% open area, while the second has 1 mm
square holes with 40% open area.
The annuli are formed by three concentric tubes {E-G}. The exit geometry is shown
in Figure 3.5. The innermost tube {G} is terminated in a ceramic cap {J}. This acts as
a central bluff body which aids flame stabilization. The use of ceramic material ensures
that heat losses to the bluff body are minimized, and the conditions are assumed to be
close to adiabatic.
A locating collar {D} is used to ensure that the major axes of the tubes are coincident.
The outer tube {E} is aligned relative to the middle tube {F} using a set of three 60 µm
diameter pins arranged at 120◦. The diameter of the pins was selected as a compromise
between structural strength and the desire to minimize disturbance to the flow. The
perturbation of the flow was further reduced by placing the locating collar a number of
hydraulic diameters upstream of the burner exit.
Experimental Details 37
Figure 3.4: Elevation of the stratified swirl burner (SwB). A: inner annulus plenum; B:
outer annulus axial flow plenum; C: outer annulus swirl flow plenum; D: locating collar;
E: outer tube; F: middle tube; G: inner tube; H: flow straighteners; I: swirl generating
collar; J: ceramic cap; K: wire mesh; L: honeycomb section; M: perforated disk. Flow
fittings are omitted for clarity. All dimensions are to scale and in mm.
The pins are slotted through holes in the locating collar and the outer tube, and
the relative position of the middle tube is controlled by varying the depth to which the
pins are screwed into the locating collar. A transparent cap with concentric markings
corresponding to the desired positions of the various tubes was placed on the outer tube
to assist location. Another set of three pins, offset by 30◦ to the previously mentioned set,
are used to locate the inner tube relative to the outer one following a similar procedure.
Flow to the inner annulus is supplied via a plenum {A} at the base of the burner.
Experimental Details 38
Figure 3.5: Plan view of the exit geometry in the stratified swirl burner (SwB), showing
a plan view and a cross section through the burner axis. The curved vectors in the plan
view show the direction of swirling flows in the outer annulus, while the out of page
vectors show the axial flow in the inner annulus. All dimensions are to scale and in mm
Though plenum’s primary purpose is to channel flow from the supply lines to the inner
annulus, it also quietens the flow structures in the lines on entrance to the burner. The
plenum also ensures that any fuel/oxidizer that is incompletely mixed before exiting the
supply lines is fully mixing prior to entering the annulus. The outer annulus is fed by
the middle and upper plenums {B, C} in the burner. If the middle plenum {B} is used
in isolation, then the resulting outer annulus flow is axial. A variable degree of swirl
Experimental Details 39
can be introduced to the outer flow by passing a percentage of the overall outer annulus
flow through upper plenum {C}. Gas from the upper plenum joins the outer annulus
through a swirl collar {I}, via a radially symmetric pattern of inlets angled at 30◦ to
the annulus. These angled jets induce a tangential component to the axial flow from the
middle plenum, generating a swirling flow at the burner mouth.
Flow straightening plates {H} are fitted to the inner and outer annulus close to
the plenums supplying axial flow. The plates have a number of small through-holes
arranged in a radially symmetric pattern, with major axes parallel to those of the annuli.
Turbulence is generated by the changes in sectional area as flow passes through the plates,
and the pressure drop across them is sufficient that the downstream flow is more uniform
than in the absence of the plates.
The distance between the flow straighteners and the burner exit was a compromise
between the need for a long axial length to ensure that turbulence is fully developed,
the practical challenges long burner geometries pose for laser diagnostics, and the decay
of swirl and turbulence intensity with distance. The development length is over 25
diameters in both annuli, which is sufficient to give fully developed turbulent flow with
greater hydraulic Reynolds numbers than the slot burner at exit in a moderately compact
geometry, with significant levels of swirl achievable.
The swirl burner is referred to as SwB in the rest of this work. This should not be
confused with SB, which refers to the slot burner detailed in Section 3.1.1.
3.2.2 Operating Conditions
A matrix of operating conditions was created for experiments using the swirl burner, as
shown in Table 3.3. These conditions were chosen to allow the investigation of flames
in premixed and stratified regimes, with or without swirl. Bulk velocities were chosen
Experimental Details 40
to maximize the Reynolds numbers in the flows given the physical constraints imposed
by the mass flow controllers available and the maximum throughput of the laboratory
air supply. The total power load is 33.6 kW, with the fractional load being 0.25 for the
inner fuel/air stream and 0.75 for the outer fuel/air stream.
The bulk velocity in the outer annulus, Uo , was held at twice the value of the velocity
in the inner annulus, Ui , in order to generate substantial levels of shear between the two
flows and ensure thorough mixing of the flows near to the burner mouth (Ui = 8.31m/s,
Uo = 18.7m/s). Co-flow air was supplied around the outer annulus with a bulk velocity
Uco-flow = 0.4m/s to prevent the entrainment of ambient air. The Reynolds numbers
(Re = ρUL/µ) derived from the bulk velocities and the exit geometry are Rei = 5 960
for the inner annulus and Reo = 11 500 for the outer annulus.
The stratification ratio φi/φo was varied from 1 for premixed cases to 3 for highly
Table 3.3: Operating conditions for Cambridge Stratified Swirl Burner. In all cases
Ui is 8.31m/s and Uo is 18.7m/s, and the Uco-flow is 0.4m/s.
Flame Qtg/Qt φi/φo φi φo φg
SwB1 0.0
 1 0.75 0.75

0.75
SwB2 0.25
SwB3 0.33
SwB4 0.4
SwB5 0.0
 2 1.0 0.5SwB6 0.25SwB7 0.33
SwB8 0.4
SwB9 0.0
 3 1.125 0.375SwB10 0.25SwB11 0.33
SwB12 0.4
SwB13 0.0
 1 1.0 1.0
 1.0SwB14 0.25SwB15 0.33
SwB16 0.40
Experimental Details 41
stratified cases. The swirl ratio Qtg/Qt was varied between 0 for non-swirling flow to
0.4 for highly swirling flow. The 0.4 swirl ratio cases were found not to stabilize reliably
in the stratified cases and so are not considered in the remainder of the present work.
The gas flows in all experiments were metered using mass flow controllers. In the
case of the multi-scalar measurements (Section 3.2.3), the MFCs were calibrated against
laminar flow elements to within 1% of reading. All the controllers used for the velocity
characterization were Alicatb mass flow controllers, with factory calibration specifying
accuracies within ±0.8% of reading and ±0.2% of full scale.
3.2.3 Multi-scalar Laser Diagnostics
The basic operation of the multi-scalar laser diagnostic system for the SwB experiments
was similar to that detailed in Section 3.1.3, with the main difference being an improve-
ment to the OH-PLIF imaging setup. A pair of UV aplanat lenses with AR-coating
(CVI APMQ-500-100) were used with the Andor CCD cameras detailed in Section 3.1.3
to image OH fluorescence from the flame. The imaged area was smaller than in the
previous experiments, with each plane being 8mm by 4mm, but the resolution was ap-
proximately three times finer at 48 µm/pixel. The spacings of the binned temperature
and species measurements along the laser axis were marginally different to the previous
experiment; 103 µm, 20 µm and 101 µm for the Raman, Rayleigh, and CO-LIF mea-
surements respectively. The uncertainties in the revised diagnostics system are similar
to those in the slot burner experiments, and are given in Table 3.4. The multi-scalar
experiments were carried out with the additional assistance of M. J. Dunn.
Multi-scalar data were taken in two separate campaigns. First, the temperature,
equivalence ratio and species profiles were mapped out in space by taking measurements
bFor further details on the Alicat MFCs please refer to http://www.alicatscientific.com/
products/gas-flow-controller.php
Experimental Details 42
in overlapping windows along the radial direction for various heights above the burner
mouth (z = 10mm, z = 20mm, . . .). These measurements were downsampled to a
uniform pixel resolution of 103 µm. 300 shots were taken in each measurement window,
with an additional 1 200 shots taken at the mean flame front position for each axial
location. The measurement locations for both campaigns are shown schematically in
Figure 3.6.
Preliminary analysis of these images identified the axial and radial locations at which
the mixing layer intersected the mean flame bush. Further data was taken at these lo-
cations; 5 000 and 30 000 shots were taken for premixed and stratified cases respectively.
More data was taken for stratified cases than for premixed cases to improve results
conditioned on local equivalence ratio in Chapter 6. This data was recorded by over-
sampling at a sampling resolution of approximately 20 µm. The data was then processed
Figure 3.6: Illustration of measurement locations for multi-scalar diagnostics campaigns
in swirl burner (SwB). A: 103 µm measurement window (300 shots); B: 103 µm mea-
surement window (1 500 shots); C: 20 µm measurement window (5 000 shots in premixed
cases, 30 000 shots in stratified cases). Note that the line measurement window C lies
at the intersection of the mixing layer and the mean flame brush. All line measurement
windows approximately 6mm in length and overlap slightly (overlap omitted for clarity).
All dimensions are to scale and in mm.
Experimental Details 43
Table 3.4: Uncertainties in scalar measurements in SwB based on measurements in
calibration flows, arranged in order of descending accuracy. Uncertainties are determined
from measurements in premixed CH4/air flat flame where φ = 1.28 and T = 2 050K.
Precision in the wavelet denoised data is shown in parentheses.
Scalar Accuracy, ∆ (%) Precision, σ (%) SNR
T 2 0.7 (0.5) 150 (200)
N2 2 0.8 (0.5) 130 (190)
H2O 3 2.0 (1.1) 50 (88)
CO2 4 3.5 (2.2) 29 (45)
φ 5 1.5 (1.2) 65 (86)
CO 10 5.9 (4.2) 16 (23)
H2 10 6.3 (4.3) 17 (24)
using wavelet filtering to remove the noise caused by the oversampling. Details on this
technique will be published in [61]. Note that effective spatial resolution of the measure-
ments is roughly 60 µm and is limited by the optical resolution of the imaging system,
the laser beam diameter, and blurring effect of the flame itself, which is difficult to eval-
uate. However the wavelet filtered 20 µm data allows smooth gradients to be obtained
at the 60 µm spacing. The precision of these wavelet filtered data is improved relative
to the downsampled 103 µm data (the accuracy is unchanged), as shown in Table 3.4.
3.2.4 Velocity Characterization
Velocity characterization in SwB was performed using two-dimensional particle image
velocimetry (PIV), giving the velocity components in the axial and radial directions.
Three-dimensional stereo PIV measurements were performed but results from these ex-
periments are omitted due to concerns over the accuracy of the results obtained. There
were issues with obtaining high quality images of the seed particles in both cameras which
were not surmountable due to the time constraints on the use of the stereo equipment.
As such only results from the two-dimensional PIV measurements will be presented in
Experimental Details 44
the current work; this should be borne in mind when considering results from the swirling
cases, which have a substantial component of velocity in the tangential direction.
3.2.4.1 2D velocity surveys
Preliminary velocity characterization was carried out by M. S. Sweeney using particle
image velocimetry. The inner annulus, outer annulus, and co-flow were each seeded with
1 µm calcined aluminum oxide particles. The seeding was achieved by passing a portion
of each air flow through simple turbulent jet seeders (see Figure 3.7). The seeders were
based on a design by M. J. Dunn which had proven successful in previous experiments.
It had the advantages of being suitable for relatively high flow rates, easily reloaded with
seed particles, and simple and cheap to fabricate. Air enters through a 12.7mm inlet at
the base of the seeder. It is then forced through a number of small diameter holes near
the wall of the main body. This creates a number of turbulent jets, which aerosolize
the seed powder in the main body. This seeded flow passes through a perforated plate
before exiting through a 12.7mm outlet.
These particles were illuminated using a double-pulsed Nd:YaG laser (Litron Nano
PIV) operating at 532 nm. The vertical laser sheets had sub-millimeter thickness at the
burner centerline. Each pulse was separated by a dt of 16 µs. The dt value was chosen
using an iterative parameter optimization process to ensure that the typical displacement
of particles within the flow between each pulse was 3 pixel to 5 pixel. This is a standard
procedure in PIV experiments, and it is necessary for sensible velocities to be derived
from the data using correlation algorithms.
The light scattered by the seed particles was imaged using a CCD camera (LaVision
Imager Pro X 4M) fitted with a Nikon AF Micro Nikkor 60mm lens (f/4) and a 50mm
interference filter centred about 532 nm (0.5 nm FWHM). The imaged field was 69.3mm
wide by 69.3mm tall, with a pixel resolution of 34.1 µm. Sample shots (both non-reacting
Experimental Details 45
Figure 3.7: Illustration of seeder design. Dimensions are not to scale, and were varied
based on the capacity required by the flow rates in the corresponding air supply. The
perforated disks shown in plan view have a blockage ratio of 50% and hole diameters of
1mm; the hole patterns shown are for illustrative purposes.
and non-reacting) are shown for SwB1 in Figure 3.8. The sample shots also highlight
potential issues with the reacting measurements. The signal intensity is significantly
lower than in the non-reacting case, while the expansion of hot gas results in low seed
density within the hot products. The results from the non-reacting cases are expected
to be of higher accuracy than those from the reacting cases for these reasons.
Note that data below z = 5mm was found to be unusable due to the high amounts
of light reflected from seed particles that accumulate on the central bluff-body due to
its associated recirculation zone. To prevent this interference, and any possible damage
Experimental Details 46
Table 3.5: Number of instantaneous velocity fields recorded in PIV measurements of
the reacting swirl burner cases.
SwB 1 2 3 5 6 7 9 10 11 13 14 15
# 5 000 2 000 1 000 5 000 2 000 2 000 5 000 1 000 2 000 5 000 2 000 1 000
to the imaging equipment, a light block was attached to the outside of the co-flow. This
shielded the central bluff body from any incident laser light, and accounts for the absence
of signal in the sample shots near to z = 0mm.
The PIV system was run at 7.5Hz, and the raw images were processed using LaVision
software (DaVis 7.4). Algorithmic mask generation was used to constrain calculations
to relevant areas in each image, and vectors were calculated using single-pass cross-
correlation with a 32×32 window size and 50% overlap. This gives vector field resolution
of 0.55mmc. Muli-pass cross-correlation was not performed due to time constraints on
the use of the LaVision-licensed workstation. 2 000 shots were taken in each of the
non-reacting cases. 1 000 to 5 000 shots (Table 3.5) were taken in the reacting cases
depending on the quality of signal obtained in the PIV images, and the time constraints
mentioned previously.
3.3 Summary
The present chapter has detailed two separate stratified burners and the experimental
campaigns applied to them. The first, SB, is a weakly turbulent rod-stabilized V-flame
slot burner. The second, SwB, is a much more turbulent co-annular swirl burner. Op-
erating matrices varying the stratification level (and the swirl level in the case of SwB)
cThe resolution of the PIV measurements in terms of the smallest velocities it can resolve with
adequate accuracy could be determined by investigating the frequency spectra obtained from the in-
stantaneous velocity fields. However this analysis is non-trivial and due to time constraints has not
been attempted in the present work.
Experimental Details 47
have been detailed. Advanced multi-scalar laser diagnostics were applied to flames in
both burners to measure temperature, equivalence ratio, and major species. Velocity
characterization was performed using hot wire anemometry in the case of SB (experi-
ments carried out by P. Anselmo-Filho) and two-dimension particle image velocimetry
in the case of the swirl burner. These data require further processing to calculate the
quantities which will be examined in later chapters (such as flame surface density, scalar
dissipation rate and local curvature); details of the data analysis are given in Chapter 4.
E
xperim
entalD
etails
48
Figure 3.8: Randomly selected PIV shots from the non-reacting (left) and reacting (right) premixed non-swirling SwB1
case in the swirl burner.
Chapter 4
Data Processing Methodology
The data generated by the multi-scalar laser diagnostics detailed in the previous chapter
provide a great deal of information on the instantaneous and mean structure of the
CH4/air flames surveyed. However, further processing is required to obtain many of
the quantities relevant to combustion from the multi-scalar data. It is important to
have a clear explanation of all data processing used, as the method of determining
certain quantities (e.g., curvature) can affect the derived values to a non-trivial degree.
Furthermore the details are necessary in the interests of reproducibility, enabling any
future experimental and modeling investigations to make like-for-like comparisons with
the results in the present work if so desired.
The data processing has been divided into three broad sections: OH image processing,
scalar data processing, and flame surface density methods. The OH images obtained
during the multi-scalar laser diagnostics provide information on the local topology of
the flame. They can also be converted into two-dimensional progress variable images.
A description of the image processing methods applied to the OH-PLIF data is given in
Section 4.1.
The species data is used to calculate the equivalence ratio using a mole balance
49
Data Processing Methodology 50
between hydrocarbon and oxygen mole fractions. The mixture fraction may be calculated
using similar methods. These quantities as defined in the present work show substantial
deviations through the flame front due to the effects of differential diffusion. This poses
issues for conditioning results on local equivalence ratio, particularly in the stratified
cases. Section 4.2 provides the definitions used in the present work for Z and φ, as well
as the methodology employed to mitigate the differential diffusion effects mentioned
previously. The progress variable, c, is defined and the methods used to derive scalar
gradient terms such as scalar dissipation rate are also given.
Finally, three different metrics used to obtain flame surface density results from the
experimental data are presented in Section 4.3. This data processing makes use of both
the OH-PLIF images and the multi-scalar measurements. These metrics are compared
and contrasted in Chapter 7.
4.1 OH Image Processing
The OH-PLIF images obtained during the experimental campaigns detailed in Chapter 3
are useful in their own right as they provide a qualitative impression of the regime the
flame is operating in. The degree of wrinkling or convolution is easily observed, and
any evidence of local extinction can be identified. As much of the OH production takes
place within the reaction zone of the flame, the concentration of OH correlates reasonably
well with the progress of reaction, and hence can provide a visual measure of the flame
thickness. Although these are all qualitative uses of the OH-PLIF images, significant
amounts of quantitative information may also be obtained from them. Various image
processing techniques are employed to derive quantitative values for curvature, three-
dimensional flame normal, and OH-based progress variable from the raw images, and
these are detailed in the following subsections.
Data Processing Methodology 51
4.1.1 Pre-processing
The OH-PLIF images as recorded need a certain degree of pre-processing to obtain nor-
malized images which allow subsequent processing (e.g., the extraction of OH contours)
to be performed robustly. A sample unprocessed image is shown in Figure 4.1a. Note
that the background level is significantly greater than zero counts.
The following steps, common in processing OH-PLIF images in the literature [27, 47,
62, 63], are applied to the raw images:
i) Background correction
ii) Laser power profile correction
iii) Normalization
Background correction is performed by taking a number of dark images (recorded
with the laser shuttered) and averaging to get a mean dark image (Figure 4.1b) which
is subtracted from the raw images.
There is a clear attenuation of signal in the top and bottom quarters of the raw image,
due to the non-uniform distribution of power in the laser sheet. The sheet typically has
a Gaussian power profile, for which corrections must be made.
To correct for these intensity variations, images are taken above a premixed stoichio-
metric CH4/air flat flame at near adiabatic conditions in the product region (∼ 30mm
downstream of the burner exit). The imaged region has an approximately constant OH
concentration, and hence the intensity profile of the beam can be obtained. A sample
mean sheet correction image is shown in Figure 4.1c. By dividing the raw OH image by
the mean sheet it is possible to correct for the intensity variation seen in the raw image
(Figure 4.1d). Finally the OH images are normalized between 0 and 1.
Data Processing Methodology 52
(a) (b)
(c) (d)
Figure 4.1: (a) Raw OH-PLIF image, (b) dark image, (c) sheet correction image, and
(d) corrected OH-PLIF image.
4.1.2 Flame Front Extraction
OH-PLIF images are commonly used to derive flame fronts from experiments [24, 27,
56, 57, 63]. The flame front is defined as the contour of maximum OH gradient. This
approach was taken to process the slot burner images, using an augmented Canny edge
detection algorithm with autonomous parameter selection [62]. This method gives the
optimal gradient-derived flame front in OH-PLIF images without a priori parameter
selection, though it incurs significant computational cost.
Data Processing Methodology 53
This algorithm was deemed too computationally intensive relative to the accuracy
benefits for processing the larger swirl burner image sets. A simpler threshold-based
methodology was employed instead. Preliminary flame fronts were obtained in each
image using a basic Canny edge detection algorithm with pre-determined parameters.
The median OH value along the preliminary fronts was then used to threshold the
image, and the final flame fronts were derived from the thresholded images. Flame
fronts generated using the thresholding method on a sample set of 100 OH images
from the premixed SwB130 case gave similar curvature values (κ = 0.05 mm
−1, σκ =
0.74 mm−1) to those obtained using the augmented Canny method (κ = 0.02 mm−1,
σκ = 0.83 mm
−1), and were processed two orders of magnitude faster.
4.1.3 Flame Normal
Flame front geometry and the angle between the crossed planes were used to extract
the three-dimensional flame normal, n, at the line measurement axis [56, 57]. The
normal was determined by resolving the two-dimensional flame tangents (t1, t2) in each
plane from the 2D image coordinate system into the 3D laboratory coordinate system
(Figure 4.2), and taking their cross product:
n = t1 × t2
=
t1︷ ︸︸ ︷
(x˙1 i + y˙1 sin Ω j + y˙1 cos Ω k)×
t2︷ ︸︸ ︷
(x˙2 i− y˙2 sin Ω j + y˙2 cos Ω k) (4.1)
where 2Ω is the angle subtended by the crossed planes (here Ω = 30◦), the subscripts
1 and 2 correspond to the two OH-PLIF planes, and the coordinates i, j and k are as
shown in Figure 4.2. The normal vector, n, is orientated such that it points from the
products into the reactants. The angle θ between n and the line measurement axis,
Data Processing Methodology 54
Figure 4.2: Planar coordinate system (left) and laboratory coordinate system (right).
Note that ip = i and jp = sin Ωj+ cos Ωk.
x = (1 i + 0 j + 0 k), may be evaluated using the dot product rule:
θ = arccos
(
n · x
|n||x|
)
= arccos (n · x) (4.2)
4.1.4 Curvature
Two methods of obtaining local 2D measurements of curvature from the OH-PLIF data
are detailed in the following sections. These comprise a discrete method, which defines
the curvature along the flame fronts defined in Section 4.1.2, and a continuous method
which gives curvature throughout the imaged area. Note that these methods only provide
two-dimensional analogues of the true three-dimensional curvature, and give neither
the principal components of curvature nor related quantities. A potential avenue for
determining the three-dimensional principal curvatures is described briefly in Chapter 8.
Data Processing Methodology 55
Figure 4.3: Curvature calibration images consisting of single pixel flame fronts with
radii of between 2 and 200 pixel.
However the implementation of this technique is incomplete at the time of writing, and
a more complete discussion of the methodology is beyond the scope of the present work.
4.1.4.1 Discrete Curvature
Each flame front contour was indexed using a simple 8-directional search algorithm,
and the resulting x and y coordinates were indexed using the distance along the front,
s. Third order polynomials were fitted to each x and y data point with respect to s
using 14 neighboring points. The order of the fit and the number of points used were
selected based on a sensitivity analysis using images of curves with known curvaturea.
The calibration images used are shown in Figure 4.3. The curves vary systematically
from radii of curvature of 2 pixel to 200 pixel, which correspond to ranges of curvatures of
0.017mm−1 ≤ |κ| ≤ 3.3mm−1 (0.05mm−1 ≤ |κ| ≤ 10mm−1) at the OH-PLIF resolution
aThe calibration images were generated by hand using GNU Image Manipulation Program [64].
Data Processing Methodology 56
of the slot (swirl) burner experiments.b
Indexing with respect to s prevents issues in polynomial fitting due to the fact that
y is not in general a mono-valued function of x, y 6= f (x). These polynomials are
differentiated to determine x˙ = dx/ds, x¨ = d2x/ds2, y˙ = dy/ds, and y¨ = d2y/ds2 in
the image coordinate system (Figure 4.2).
The discrete two-dimensional local curvature, κd, at any point on the flame front is
given by the following expression using the quantities derived previously:
κd =
x˙y¨ − y˙x¨(
x˙2 + y˙2
) 3
2
(4.3)
where κd is taken as positive if the flame front is convex towards the reactants. The
major limitation of this method is that it is only defined at the flame front itself, and
hence line measurement data can only be curvature-conditioned at a single point, greatly
reducing the size of potential datasets for such analysis.
4.1.4.2 Continuous Curvature
The discrete curvature described in the previous section is not well suited to conditioning
other quantities as it is only defined along the single pixel flame front. A continuous
measure of local 2D curvature along the line measurement window is necessary for sen-
sible conditioning of the scalar data. Kass et al [65] give a definition applicable to the
entire image using a formula that resembles Equation 4.3:
κc =
dI
dx
2 d
2
I
dy
2 − 2 dIdx dIdy d
2
I
dxdy
+ dI
dy
2 d
2
I
dx
2(
dI
dx
2
+ dI
dy
2
) 3
2
(4.4)
bThe OH-PLIF resolution is approximately 150 µm/pixel and 50 µm/pixel in the slot and swirl burner
data respectively.
Data Processing Methodology 57
Figure 4.4: Left to right: Continuous curvature obtained from a sample OH-PLIF image
(see inset) randomly selected from SwB3 at z = 30mm; corresponding distribution of
continuous curvature using all data within 0.5mm of the flame front. 50 evenly spaced
bins between −15mm−1 to 15mm−1 were used to generate the PDF.
where I is taken to be the signal intensity of the OH-PLIF image. This gives a local
measure of two-dimensional curvature at every point in each OH-PLIF plane, as shown
in Figure 4.4. Note that in the present work the experimental images and their gradients
are smoothed using a two-dimensional median filter with a 5 × 5 pixel window size to
prevent erroneous curvature values arising due to noise; this method is particularly
noise-sensitive due to the presence of both first- and second-order differential terms.
The curvature values calculated using Equation 4.4 are within the range expected for
the turbulence intensities seen in the slot and swirl burner flames provided the signal
to noise ratio (SNR) of the signal intensity is sufficiently high. The curvature values
are interpolated to the line-based multi-scalar measurement resolution so that the scalar
data can be conditioned on κc.
The continuous curvature values given by Equation 4.4 are not identical to the dis-
crete measure given by Equation 4.3 even when assessed at the same location. However,
the agreement is very good, as demonstrated by the sample case shown in Figure 4.5; fur-
thermore, the correlation coefficient between κc and κd is R = 0.914 2 when considering
a 300 image dataset from the highly swirling premixed SwB3 case at z = 30mm.
Data Processing Methodology 58
Figure 4.5: Comparison of discrete and continuous curvature methods applied to the
same OH-PLIF image (see inset) from SwB3 30mm downstream of the burner exit.
4.1.5 2D OH Progress Variable
OH-PLIF images are used to calculate flame surface density, as described further on in
Section 4.3. However, the pre-processed images generated in Section 4.1.1 must first
be converted into two-dimensional progress variable maps before they can be used to
determine the flame surface density. Here the progress variable, cOH, is defined as a
normalization of the OH signal such that cOH is zero valued in the unburned reactants,
and unity valued in the products.
The level of OH in the flames surveyed is near-zero in the reactants, rises sharply
in the reaction zone to a super-equilibrium peak, and decays towards final equilibrium
relatively slowly in the products. Using OH as a scalar progress variable is complicated
by the fact that normalization of OH by the final equilibrium value would permit cOH ≥ 1
over a large area of the image. Thresholding images to identify flame regions at high OH
gives poor results as the OH value may dip below the threshold on the product side due
to the decay. An adjustment to the pre-processed OH images (Section 4.1.1) is necessary
Data Processing Methodology 59
to produce an OH progress variable suitable for use in calculations, as follows.
The OH images are thresholded between product (foreground, cOH = 1) and reactant
(background, cOH = 0) regions using the median OH signal value in pixels of high OH
gradient (found using a simple Canny edge detection algorithm [66]) to determine the
threshold value. This threshold value is below the minimum OH value in the equilib-
rium zone for the majority of cases. The perimeters of foreground regions are taken
to be flame fronts. This methodology is employed over more rigorous gradient-based
methods [62] to reduce computational costs. A thinning morphological operation [67]
is applied iteratively to the foreground regions, eliminating a one-pixel thick perimeter
from each foreground region with every iteration, until the perimeter with the max-
imum mean value of IOH is identified; essentially defining the contour describing the
super-equilibrium condition. Note that images are padded by replication at the edges
to prevent problems arising where foreground regions cross the edges of the image.
The number of thinning operations, ζ, was increased until the mean OH value along
foreground perimeters showed a global maximum (OH = OHg at ζ = N), as shown
in Figure 4.6. The maximum OH value along the perimeters for ζ = N , OHmax, was
noted. The enclosed foreground areas are taken to be product regions, and are set to
OHmax (plateaued). OH values between the perimeter of the plateaued region (ζ = N)
and the original product perimeter (ζ = 0) were smoothed to avoid sudden jumps in
signal by scaling the difference between the original data and OHmax. A Gaussian scaling
function was used in the results presented in later sections. Values greater than OHmax
were set to 1. This operation preserves islands of products in the reactants and pockets
of reactants in the products. This process defines a progress variable whereby complete
reaction (cOH = 1) is strongly correlated with the location of maximum OH, which may
result in discrepancies in comparisons with other progress variable definitions.
Data Processing Methodology 60
Figure 4.6: Demonstration of plateau technique applied to an OH image from SwB11.
Clockwise from top left; pre-processed OH image; plateaued OH image; initial OH flame
front (ζ = 0) - - - -, perimeter at the global maximum (ζ = N) ; mean OH level
along the contour associated with each degree of thinning ζ
4.2 Scalar Data Processing
The multi-scalar line measurements also require additional processing to obtain both
a sensible form of equivalence ratio and also derived gradient-based quantities such as
scalar dissipation rate. This section outlines the methodologies employed in the interests
of reproducibility and transparency.
4.2.1 Mixture fraction and Equivalence Ratio
The mixture fraction, Z, is defined as a scalar which is conserved through a premixed
flame, and is crucial to the formulation of a variety of modeling methods. In the present
work mixture fraction is defined using the mass balance suggested by Bilger [68] for
Data Processing Methodology 61
hydrocarbon fuels:
Z =
2YC/MC + 0.5YH/MH +
(
YO,2 − YO
)
/MO
2YC,1/MC + 0.5YH,1/MH + YO,2/MO
(4.5)
where Ya is the mass fraction of the sum of all measured species containing the element
a, Ma is the atomic weight of element a, and the subscripts 1 and 2 refer to values in
fuel and air respectively. This definition allows the mixture fraction to be approximately
conserved across the reaction zone.
The present work also makes use of an equivalence ratio derived from an atomic
balance as follows:
φ =
XCO2 + 2XCH4 +XCO + 0.5
(
XH2O +XH2
)
XCO2 +XO2 + 0.5
(
XCO +XH2O
) (4.6)
The equivalence ratio detailed in Equation 4.6 is the ratio of the demand for oxygen based
on the local mass fractions of hydrogen and carbon to the locally available oxygen. This
definition of equivalence ratio yields values that are close to those calculated using the
scaled Bilger mixture fraction Z [68]:
φB =
Z
1− Z
1− Zs
1− Z (4.7)
≈ φ
where the subscripts B and s refer to the Bilger definition and the stoichiometric value
respectively. The relationship between Z and φB is approximately linear for the range of
mixture fractions typically experienced within flammable methane/air flames (0.0339 <
Z < 0.0756). This is due to Z and Zs being small relative to unity, with the result that
φB ≈ Z/Zs.
Data Processing Methodology 62
4.2.1.1 The Effect of Differential Diffusion
Both the equivalence ratio in Equation 4.6 and the mixture fraction Z (and the derived
φB) are constructed to be conserved scalars across a reaction zone, as carbon, hydrogen
and oxygen are conserved elements across a flame. However, carbon- and hydrogen-
containing species may have different molecular weights and diffuse at different rates.
Hydrogen and water are smaller molecules than carbon monoxide and carbon dioxide,
with the result that they may diffuse faster. This creates local imbalances in the carbon
and hydrogen mass fractions at any position in the thermal ramp of a flame, such that
the equivalence ratio as defined in Equation 4.6 is only approximately conserved in
temperature space.
Figure 4.7: Demonstration of the effects of differential diffusion on equivalence ratio
across an unstrained premixed laminar flame front. Data is taken from flame calculations
with a nominal equivalence ratio of φn = 0.7.
Figure 4.7 demonstrates this behavior using an unstrained premixed laminar flame
calculation. In the case shown the maximum deviation in equivalence ratio between
the nominal and the observed value is 6.5%; depending on the value of φn this peak
deviation ranges from 6.0% to 7.7%. This is particularly relevant in the context of
defining a local stoichiometry for a stratified flame, where the fuel/oxidizer ratio is by
Data Processing Methodology 63
definition expected to exhibit spatial variation. Given the deviations in φ expected in
a premixed flame, when the flame is stratified it is not possible to clearly separate the
variation in φ due to differential diffusion effects from the spatial gradients in φ induced
by the stratification itself.
Therefore, when comparing experimental premixed and stratified results, a correc-
tion process is required to allow for like-for-like comparisons to be made. This process
should be robust, and create a framework within which rigorous comparisons condi-
tioned on local equivalence ratio can be made. The approach employed in the present
work is detailed in Section 4.2.3 after the concept of the progress variable is introduced
(Section 4.2.2), which is required for some of the methodology discussed.
4.2.2 Progress Variable
The progress variable is a scalar c defined such that it has a value of zero in unburned
reactants (cu = 0) and unity in the burned products (cb = 1). Typically this quantity
is a normalization of temperature or chemical species concentration with respect to
its values in both the burned and unburned gases. The definition of a suitable progress
variable simplifies the description of the overall reaction, which involves multiple species,
to a single variable which is uniquely related to the others. However the behavior of
the progress variable is dependent on the choice of basis, as mentioned in Section 2.2
of Chapter 2, and hence care must be taken when comparing results in c-space from
various studies.
The progress variable has many applications in premixed flame modeling. Important
examples include its probability density function (pdf), a key component of Bray-Moss-
Libby flamelet modeling [7], and its gradient |∇c|, which is integral to flame surface
density (FSD) modeling [8, 69].
Data Processing Methodology 64
The present work makes use of a thermal progress variable, c (T ). In a purely pre-
mixed flame this is simply a normalization of the local flame temperature by the maxi-
mum temperature attained in the burned products and the temperature of the unburned
reactants, as given in Equation 2.2 in Section 2.2 of Chapter 2c. However, if this is
applied to a flame in which the equivalence ratio field is varying spatially, errors are
introduced. Hence, the equilibrium temperature used in the calculation of the thermal
progress variable must be allowed to vary with local equivalence ratio:
cT (x, φ) =
T (x)− Tu
Te (φ)− Tu
(4.8)
where T (x) is the local temperature, Tu is the temperature in the unburned reactants,
and Te (φ) is the equilibrium flame temperature as a function of φ (determined from
premixed unstrained laminar flame calculationsd). This form of thermal progress variable
is much more suitable for flames with a significant degree of stratification than a basic
temperature normalization.
Figure 4.8 demonstrates that while there may not be substantial deviations between
c (T ) and c (T, φ) in the pre-heat and reaction zones, there are clear differences between
the two measures in the equilibration zone. In the present work the progress variable de-
fined in Equation 4.8 is used throughout. Results presented in Chapter 5 and Chapter 6
use the differential-diffusion corrected φ to determine c (T, φ).
4.2.3 Differential Diffusion Correction
The effects of differential diffusion detailed in Section 4.2.1.1 require the equivalence
ratio calculated from the species measurements to be corrected in order for sensible con-
cStrictly speaking, thermal enthalpy should be used; however, deviations from this definition due to
the use of temperature are small.
dLaminar flame calculations were generated using CHEMKIN [70] and GRI-Mech 3.0 [71]
Data Processing Methodology 65
Figure 4.8: Variation in progress variable c where the equilibrium flame temperature Te
is based on T in the reactants (c (T )) or is taken to be a function of the local stoichiometry
(c (T, φ)). Sample data is randomly selected from the highly stratified fs625 case in the
slot burner.
ditioning and comparison of other measured quantities to be made. Two such correction
methods have been considered during the course of this research; a lookup table of cor-
rection factors based on the deviations observed in premixed laminar flame calculations,
and a linear bridging function between the pre-heat zone and the equilibration zone.
The methodologies are detailed in Section 4.2.3.1 and Section 4.2.3.2 respectively.
Premixed data from both the slot (fs1) and swirl burner (SwB1) are corrected using
each of these methods. The lookup table method is shown to alter but not correct for
the deviations in local equivalence ratio in experimental data as it fails to take into
account the turbulence dependence of the differential diffusion effect; the linear bridging
method is deemed more suitable in light of this and is applied to all data presented in
subsequent sections.
Data Processing Methodology 66
Figure 4.9: Demonstration of the differential diffusion correction using data from un-
strained premixed laminar flame calculations where φn = 0.7. Clockwise from top left:
high resolution (8 µm), smooth values from calculations; high resolution values with
added noise; values downsampled to the slot burner experimental resolution (105.2 µm)
with added noise; experimental resolution, smooth values.
4.2.3.1 Lookup Table Approach
A lookup table of correction factors to adjust for the effect of differential diffusion
on equivalence ratio was derived from premixed unstrained laminar flame calculations.
Equivalence ratio corrected using the lookup table approach is denoted in the present
work by φ. The result of applying these correction factors to laminar flame calculations
at high resolution and at the resolution of the multi-scalar experiments is shown in Fig-
ure 4.9. The equivalence ratio is reconstructed to the nominal values whether the original
data is smooth or noisy. The noise applied has a Gaussian distribution, zero mean, and
a standard deviation of 1.5× 10−3, which results in similar levels of point-to-point noise
as that seen in the experimental data.
It is worth noting that the effects of differential diffusion on equivalence ratio are
not the same across different flame conditions or types. This can be seen in Figure 4.10,
which shows the effect of the correction on experimental data from: a vertical premixed
Data Processing Methodology 67
Figure 4.10: Scatter plots and mean fits of equivalence ratio from experiments on
a laminar vertical premixed flame (vf), a weakly turbulent premixed flame (fs125),
and a more turbulent premixed flame (SwB130), demonstrating the varying influence
of differential diffusion. Calculated values from laminar unstrained flame calculations
at the corresponding stoichiometry are also shown. Values of φ are determined using a
lookup table derived from calculations.
laminar methane/air flame, denoted vf in the figure; the fs1 case from the slot burner;
and the SwB1 case from the swirl burner. The data in the vertical burner vf was
obtained by R. S. Barlow using the same methodology as that for the swirl burner,
described in Section 3.2.3 of Chapter 3. The vertical flame burner is shown for reference
in Figure 4.11, and further details are given in a publication by Barlow et al [72] (in
submission at the time of writing). The three cases listed are premixed, non-swirling
flames, and are arranged in order of increasing turbulence.
Applying the correction factors obtained from flame calculations to the experimental
data allows like-for-like comparisons, but still results in equivalence ratio values which
vary with temperature, albeit in a different manner. It should be noted that the SwB1
case shows significantly elevated equivalence ratio on the product side (7.5% greater than
the mean reactant value). This is due to the effect of the recirculation zone above the
central bluff-body in the swirl burner, and is discussed in depth in Chapter 6. The results
Data Processing Methodology 68
Figure 4.11: Vertical flame burner vf with multi-scalar line measurement axis shown
schematically. Figure adapted from [72].
from the vertical burner and the slot burner are considered in the ensuing discussion as
the influence of the elevated product-side equivalence ratio makes it difficult to evaluate
the correction in the swirl burner case.
The differences between the uncorrected calculated and experimental mean values
are small in the laminar case compared with the others, indicating that the differential
diffusion effect may be coupled to local turbulence levels. This observation is corrobo-
rated by the analysis of differential diffusion effects by Barlow et al [72]. However even
in the laminar flame the φ data exhibits non-trivial variation with temperature (up to
3% relative to φn). Without a more complete knowledge of the variables governing the
differential diffusion effects, and their relative importance, the lookup table method does
not appear to be a viable route for processing the equivalence ratio data, and as such is
Data Processing Methodology 69
Figure 4.12: Diagram illustrating the location of the pre- and post-flame regions, where
the equivalence ratio dips below its nominal value φn = 0.7. Normalized temperature
and its gradient are also plotted.
not used further in this work.
4.2.3.2 Linear Bridging Function Approach
Figure 4.12 shows the variation of equivalence ratio in space in a premixed laminar flame
calculation due to differential diffusion, as well as the normalized temperature T̂ and
the normalized temperature gradient |̂∇T |. At the beginning of the pre-heat zone (T̂ ,
|̂∇T | << 1) and near the end of the equilibrium zone (T̂ ∼ 1, |̂∇T | << 1) the equiva-
lence ratio derived using Equation 4.6 is close to the nominal value. A possible approach
to correct the equivalence ratio data as measured is therefore to linearly interpolate be-
tween the pre- and post-flame regions, where differential diffusion effects are significant.
The resulting linear bridged equivalence ratio is denoted by Φ. This approach is rea-
sonable provided the length scales associated with equivalence ratio variations due to
stratification are larger than the thermal length scales of the flame.
The algorithm used to apply this linear bridging function to the experimental data
is summarized in the flow chart in Figure 4.13. The temperature data is normalized
using the maximum and minimum values to give T̂ . The normalized gradient |̂∇T | is
obtained in a similar manner after applying a second order central-differencing scheme to
Data Processing Methodology 70
the temperature data. These normalized quantities are thresholded to obtain estimates
of the location of the pre- and post-flame regions. Figure 4.14 shows the values of the
normalized quantities in premixed laminar flame calculations (taken at the locations
where the equivalence ratio first dips below the nominal value on both the reactant and
product side of the differential diffusion deviation) for a range of compositions.
The initial values of T̂1 = 0.025, |̂∇T |1 = 0.1 and T̂2 = 0.95, |̂∇T |2 = 0.1 were
chosen empirically to determine the pre- and post-flame regions respectively. These
values were selected as a compromise between the intermediary values of the thresholds,
and the desire to minimize jitter in the thresholded regions due to noise in the burned
and unburned gases.
After the normalized quantities are thresholded, spurious signals are removed. Iso-
lated peaks and dips in the thresholded profiles are removed by convolution with suitable
kernels, while broader troughs and peaks (up to a maximum width of three times the
experimental resolution) are either eliminated or filled after being identified.
Using the thresholded profiles, the mean equivalence ratio in the pre- and post-
flame regions is obtained from a three point average of the equivalence ratio data at
the respective locations. These mean equivalence ratio values are used to refine the
estimates of the thresholds T̂1, |̂∇T |, T̂2, and |̂∇T |2 by interpolating the calculated
parameters (Figure 4.14) in equivalence ratio space.
The thresholding process is then repeated using the new threshold values. The new
mean equivalence ratio in the pre- and post-flame regions is compared with the old
values, and the process is iterated until the mean difference between the old and new
values is less than 0.5%. Once this criterion has been fulfilled the equivalence ratio
data is linearly interpolated between the two regions using the final mean equivalence
ratio values. Note that the criterion was selected empirically, and a rigorous sensitivity
Data Processing Methodology 71
Figure 4.13: Flow chart illustrating the process flow involved in applying a linear
bridging function to equivalence ratio data. Note that T̂ and |̂∇T | are shown as Tn and
dTn respectively.
Data Processing Methodology 72
Figure 4.14: Values of normalized temperature and temperature gradient marking the
locations of the pre- and post-flame regions for a range of compositions. The data are
taken from laminar premixed calculations at the points where the equivalence ratio first
dips below the nominal equivalence ratio (LHS) and 99% of the nominal equivalence
ratio (RHS).
analysis remains to be performed.
The algorithm as described typically takes two iterations to converge for the premixed
fs125 case and six iterations for the highly stratified fs625 case, with computation times
of 2.74ms and 11.14ms per shot respectively. It was found that by using the calculated
threshold parameters at the locations where the equivalence ratio dipped below 99% of
the nominal value (RHS in Figure 4.14), the mean equivalence ratios in the pre- and
post-flame regions converged to the same values and locations as when the previously
described thresholds were used, but with less iterations required for the stratified cases
(two instead of six). As a result the present work uses these threshold values due to the
reduction in computational expense. Examples of instantaneous data from the fs125,
fs425, and fs625 cases are shown in Figure 4.15, both raw and after the application of
the linear bridging function.
The effect of the linear bridging function when considered on the mean is shown
in Figure 4.16 for both the vertical flame case vf and the premixed slot burner case
Data Processing Methodology 73
Figure 4.15: Demonstration of linear bridging function applied to equivalence ratio
profiles from fs125, fs425, and fs625 cases (left to right). Raw equivalence ratio data is
plotted with filled markers (gray within the linear bridging region, blue without), while
the linear bridged data is plotted in red. Normalized temperature is plotted in cyan, and
pre- and post-flame regions are shaded dark and light gray respectively.
fs125. The vf case yields mean values very close to the nominal equivalence ratio
value Φn following the application of the linear bridging function. The fs125 case shows
significantly less variation through intermediate temperature values than the uncorrected
data, with the mild slope seen attributable to the uncorrected equivalence ratio data in
the product region being biased high by approximately 2%. It may be possible to correct
for this discrepancy by determining the degree of bias — by comparing mean equivalence
ratio at c ≈ 0 and c ≈ 1 — and multiplying the equivalence ratio values in the post
flame region by a suitable correction factor. The robustness of such a correction has
yet to be evaluated, and so the present work does not attempt to modify the post-flame
equivalence ratio values.
4.2.4 Scalar Gradients
The rate of change of scalars is often of interest in combustion. The present work is
only concerned with spatial gradients, as the time resolution of the multi-scalar mea-
Data Processing Methodology 74
Figure 4.16: Scatter plots and mean fits of equivalence ratio from experiments on a
laminar vertical premixed flame (vf) and a weakly turbulent premixed flame (fs125),
demonstrating the effect of linear bridging the local equivalence ratio data to give the
bridged equivalence ratio, Φ. The gray scatter data are instantaneous uncorrected equiv-
alence ratio values, φ.
surements does not allow the calculation of valid time derivatives. The methods used to
obtain these gradients are detailed in this section.
Discrete Differentiation: Scalar gradients are obtained by applying finite differenc-
ing schemes to discrete experimental data, rather than explicitly differentiating known
mathematical functions. A variety of finite difference schemes are available to the ex-
perimentalist (See Table 4.1), though in the present work all gradients are obtained
using a simple second order central-differencing scheme, with forward- and backward-
differencing schemes applied at the edges of the line measurement data. The main
motivation for using such a simple scheme is to reduce spatial averaging which increases
in magnitude with differentiation scheme order due to the relatively coarse resolution
of the 103 µm experimental data. The use of a second order scheme also minimizes the
propagated error (higher order schemes require more points) and helps to avoid very
noisy gradients in measurements from the equilibration zone, where typically the scalar
Data Processing Methodology 75
data exhibits point-to-point jitter.
Order F−5 F−4 F−3 F−2 F−1 F−0 F1 F2 F3 F4 F5
2nd 1
2
0 −1
2
4th − 1
12
2
3
0 −2
3
1
12
6th 1
60
− 3
20
3
4
0 −3
4
3
20
− 1
60
8th − 1
280
4
105
−1
5
4
5
0 −4
5
1
5
− 4
105
− 1
280
10th 1
1260
− 5
504
5
84
− 5
21
5
6
0 −5
6
5
21
− 5
84
5
504
− 1
1260
Table 4.1: Central finite difference coefficients for the first derivative to varying orders
of accuracy.
Angle Correction: The 3D flame normal is rarely coincident with the line measurement
axis, n · x 6= 1, as seen in Figure 4.2. Therefore, the gradient of any given scalar with
respect to x, or x, is expected to be smaller that the 3D value in most realizations as
it is a projection of the true gradient. A first order correction is obtained by dividing
gradients by the cosine of the solid angle θ between the flame normal and the line
measurement axis. However, the uncertainties in the measurement are amplified by the
correction as the solid angle increases, to the extent that the accuracy of the gradient
values deteriorates substantially [56]. The angle-corrected gradient of any scalar ψ is
thus given as dψ/dn = (dψ/dx) / cos θ, θ ≤ θm.
Note that for this correction to be strictly valid, the angle θ should be obtained
as in Equation 4.2 using the same scalar field as the scalar whose gradient is being
corrected. It is assumed in the present work that the OH field is well correlated with
the temperature field in three-dimensional space. Hence the solid angle θ derived from
the OH-PLIF measurements can be used to correct temperature gradients in the present
work.
Data Processing Methodology 76
Resolution correction: Differentiation of discrete scalar data introduces errors in the
calculation of gradients which are a function of the experimental resolution, the most
notable effect of which is the systematic reduction of peak gradient values. These errors
can be reduced by the use of higher order differentiation schemes, but such methods
increase the propagated uncertainty in the derived gradients substantially in compari-
son to simple second order central-differencing, due to the increased number of sampled
points. In the present work a basic resolution correction factor has been used to com-
pensate for the effects of measuring scalars at the experimental resolution. This is not
applied to the 20 µm wavelet filtered data as the attenuation is negligible.
Laminar calculations for premixed unstrained CH4/air flames were used to gener-
ate noise-free spatial profiles of temperature, T , and another scalar, ψ, at much finer
resolutions than is feasible in experiments, for a range of discrete equivalence ratios,
0.6 ≤ φ ≤ 1.4. The calculated equivalence ratios were corrected for differential diffusion
effects. The scalar profiles were differentiated using a tenth order accurate scheme (See
Table 4.1) to give the fine resolution gradient dψ/dx|f . The profiles were then resampled
at the experimental resolution before once differentiating using a second order scheme to
calculate gradients at this resolution, dψ/dx|e. A look-up table of φ, T and the resolu-
tion correction-factor R = (dψ/dx|e) / (dψ/dx|f) was created, and bilinear interpolation
in local temperature and equivalence ratio is performed to estimate the local resolution
correction factor R (T, φ).
This correction brings the accuracy of second order differentiation schemes in line
with higher order schema. This approximation is only valid where the scalar is strongly
correlated with T and φ, which is the case for the progress variable c considered in
this study. Additionally, it is assumed that correction factors obtained in laminar un-
strained flames will be similar to the experimental turbulent flames for a given φ and
T . The correction factors obtained may be biased slightly high, as turbulence has been
Data Processing Methodology 77
reported to increase flame thickness relative to equivalent laminar cases [73, 74]. The
final expression for the gradient of the scalar is thus:
|∇ψ| =
∣∣∣∣dψ/dxR cos θ
∣∣∣∣ (4.9)
The change in progress variable gradient ∇c due to this correction factor is small rela-
tive to the peak values attained through the flame (1mm−1 to 2.26mm−1 in the current
work); the mean magnitude of the correction is approximately 30 µm−1, with a maxi-
mum correction on the order of 100 µm−1.
Scalar Dissipation Rate: The scalar dissipation rate, χc, determines how quickly
fluctuations in progress variable decay within the flame. Furthermore it is a measure
of the mixing rate of reactants and products, and is proportional to the mean burning
rate (assuming fast chemistry and mixing limited combustion). It appears directly or
indirectly in both premixed [10, 11, 38, 75, 76] and nonpremixed [76–79] combustion
models. It also appears as a sink term in the scalar variance equation. The mixture
fraction dissipation rate, χZ , and the cross dissipation rate, χZ,c, are also important
quantities (particularly in non-premixed combustion), but are not considered further
as they cannot be derived from the current experimental datasets due to the lack of
information on the three-dimensional mixture fraction field. The scalar dissipation rate
is given by the following expression:
χc = α|∇c|2 (4.10)
where the thermal diffusivity, α, is obtained by interpolating a lookup table of calculated
values in temperature and equivalence ratio. The calculated thermal diffusivity values
Data Processing Methodology 78
were taken from unstrained premixed laminar flame calculations.
4.2.5 Error analysis
The uncertainties introduced in the evaluation of the quantities detailed previously are
quantified so as to understand which effects may be due to physical factors, such as flame
straining and curvature, and which may be artifacts of the data analysis itself. The
precision of these derived quantities, σ, are determined through the application of error
propagation in conjunction with the experimental uncertainties listed in Table 3.4 and
Table 3.4. The equations used are lengthy and so are detailed separately in Appendix B.
Table 4.2: Table of propagated uncertainties for derived quantities in the slot burner
and the swirl burner. Uncertainties for each quantity are expressed as a percentage of
the mean value of the scalar at the location of peak |∇c|.
Flame y σTeq σc σα σ|∇c| σχc
(mm) (%) (%) (%) (%) (%)
fs1
25 0.13 1.01 1.22 2.63 5.38
30 0.13 1.01 1.22 2.65 5.43
fs4
25 0.13 1.03 1.22 2.15 4.47
30 0.14 1.03 1.22 2.65 5.39
fs6
25 0.13 1.03 1.23 2.06 4.30
30 0.14 1.02 1.25 2.84 5.91
SwB1 10 0.89 1.40 1.16 3.84 7.75
SwB2 10 0.87 1.38 1.17 3.89 7.83
SwB3 10 0.91 1.43 1.16 5.57 9.86
SwB5 10 0.55 1.12 1.17 2.36 4.84
SwB6 10 0.52 1.09 1.18 2.41 4.91
SwB7 10 0.61 1.14 1.17 2.73 5.41
SwB9 10 0.13 0.90 1.23 3.20 6.48
SwB10 10 0.14 0.92 1.22 2.75 5.57
SwB11 10 0.38 0.98 1.21 2.89 5.67
SwB13 10 0.49 1.08 1.18 2.34 4.79
SwB14 10 0.51 1.09 1.18 2.41 4.94
SwB15 10 0.53 1.13 1.17 2.10 4.34
Data Processing Methodology 79
The resulting uncertainties for both the slot and swirl burner datasets are listed in
Table 4.2. Uncertainties are presented at z = 10mm for the sake of brevity; these values
are indicative of the propagated uncertainties at other axial locations. Uncertainties are
presented for the approximately 100 µm pixel resolution data only.
4.3 Flame Surface Density
Flame surface density (FSD) is defined as the ratio of flame surface area to volume for
an iso-surface of a relevant scalar. FSD plays an important role in combustion modeling.
It shows up in coherent flamelet models; if the combustion device is operating in the
flamelet regime, then the reaction rate in such models may be expressed in terms of the
FSD. Flame surface density measurements have typically been derived from experimental
data using two significantly different methods.
FSD is generally obtained from the product of the conditional progress variable
probability and the conditionally-averaged progress variable gradient [8] provided that
the progress variable, c, has been derived from measurements of temperature [45, 80].
This quantity, defined further on in Equation 4.11, is referred to as Σ1 in the present
section. It is referred to simply as Σ later on in Chapter 5 and Chapter 6 unless otherwise
stated.
A geometric method for determining flame surface density from Rayleigh (tempera-
ture), Mie, or suitable PLIF images was proposed by Shepherd [81] and used in a number
of studies [24, 81–83]. In this method, FSD is defined as the ratio of average flame front
crossing length to mean flame brush area for a given mean progress variable c. This
quantity, henceforth referred to as Σ2, is analogous to Σ1, but is defined in previous
studies for c = 0.5 only. Σ2 can be extracted from any scalar progress variable image;
OH measurements predominate [24, 81, 82], though CH has also been used [83]. Here
Data Processing Methodology 80
Σ2 is based on OH-LIF measurements.
A third measure of flame surface density, Σ3, is proposed further on. This is an
extension of Σ2, modified to enable direct comparison with Σ1. These flame surface
density metrics are compared in Chapter 7, and the extent to which the values they
report are self-similar is investigated.
Further classes of geometric FSD measurement have been proposed by Cohé et al [84]
and Veynante et al [85]. These forms are not considered in the present work due to
constraints on time; however, the description of the latter in [85] implies that it is very
similar in implementation to Σ2.
To avoid any confusion in the subsequent sections, it is reiterated that three distinct
definitions of flame surface density will be used in the present work. When discussing the
quantity Σ, the subscript 1 (or the absense of a subscript) refers to the exact definition
of flame surface density provided by Pope [8], the subscript 2 refers to the geometric
definition supplied by Shepherd [81], and the subscript 3 refers to the extended geo-
metric method. Two forms of progress variable are used: a thermal progress variable
(Section 4.2.2) and an OH progress variable (Section 4.1.5). The subscripts T and OH
refer to the thermal and OH progress variables respectively when discussing the quantity
c.
4.3.1 Σ1 Methodology
The statistical flame surface density, Σ1, is defined using the exact expression derived
by Pope [8]:
Σ1 (c; c) = P (c; c) 〈|∇c||c〉 |c (4.11)
Data Processing Methodology 81
For the evaluation of the line temperature based FSD, Σ1,T , the conditional progress
variable pdf P (cT ; cT ) was calculated by binning the cT data by cT (centers at cT =
0.05, 0.15, ..., 0.95), and calculating the conditional probability of finding a data point
within each instantaneous cT bin (centers at cT = 0.05, 0.15, ..., 0.95). The conditionally
averaged progress variable gradient
〈|∇cT ||cT 〉 |cT was found by binning the ∇cT data in
cT and cT as per P (cT ; cT ).
Another variant of Σ1 may be derived using the progress of reaction cOH, defined
using the values of the OH progress images (Section 4.1.5) along the line measurement
axis, in conjunction with Equation 4.11 to give Σ1,OH. Σ1,OH is then derived from the
angle- and resolution-corrected OH gradient, ∇cOH, and the conditional pdf of cOH,
P (cOH; cOH).
4.3.2 Σ2 Methodology
Shepherd [81] defined geometric flame surface density as:
Σ2 (c) = L (c) /A (c) (4.12)
where L (c) is the flame crossing length at the specified value of mean progress variable,
and A (c) is the corresponding area. The plateaued OH images (Section 4.1.5) are thresh-
olded at cOH = 0.5 to produce binary images of products and reactants. Flame fronts
are extracted from these images using the method detailed in Section 4.1.2. Product-
reactant images are then averaged to give a mean OH image, which is thresholded at
cOH = 0.1, 0.2, . . . , 0.9. The area A (cOH) is determined for each threshold level. In-
stantaneous flame fronts are analyzed to determine the length of their intersection with
each cOH region of the mean image, and these lengths are averaged for all images to give
L (cOH). Σ2,OH is then given by Equation 4.12.
Data Processing Methodology 82
4.3.3 Σ3 Methodology
Σ3 is an extension to the method proposed by Shepherd [81] and detailed in Section 4.3.2,
but with a few key differences. Note that in the present work the OH progress variable
is used to give Σ3,OH; however if Rayleigh temperature images were available it would
be possible to calculate Σ3,T .
The mean OH image is generated from the plateaued OH images rather than the bi-
narized OH-PLIF images (thresholded at cOH = 0.5) to remove the influence of threshold
choice. The area A (cOH) is determined at each cOH level as before. Instead of computing
L at a single cOH level, the crossing lengths for each instantaneous cOH are found for
each cOH, and averaged to give L (cOH, cOH). The flame surface density Σ3 is then given
by:
Σ3 (c, c) = L (c, c) /A (c) (4.13)
Equation 4.13 allows results to be compared for a range of instantaneous cOH as well as
cOH in a similar vein to Σ1,T , which is not possible for Σ2,OH. It should be noted that
Σ2 (cOH) ≈ Σ3 (cOH = 0.5, cOH), with the differences in determining the mean OH image
in each method accounting for any observed deviations.
4.4 Summary
The present chapter has detailed the data processing methods used to calculate derived
quantities from the experimental data measured in the slot and swirl burners. The
image processing required to calculate geometric quantities such as curvature, flame
normal angle have been detailed, as well as a method of creating OH progress variable
images (Section 4.1). The methods of processing the scalar data have also been shown,
Data Processing Methodology 83
with a particular focus on the correction of the effect of differential diffusion on local
equivalence ratio in the flame (Section 4.2) and the derivation of propagated uncertainties
in the derived quantities. Finally, three flame surface density metrics have been presented
(Section 4.3).
Chapter 5 focuses on the analysis of results from the slot burner, while Chapter 6 pro-
vides a similar investigation for the swirl burner. The three flame surface density metrics
described in Section 4.3 are compared in Chapter 7 to evaluate their congruence.
Chapter 5
Slot Burner Results
The results for the slot burner detailed in Section 3.1.1 of Chapter 3 are organized as
follows. First, non-reacting velocity measurements and derived quantities are presented.
Next, the instantaneous structure of the cases investigated are illustrated with sample
scalar data and associated OH-PLIF images. The overall behavior of each condition
is examined using Favre-averaged profiles of temperature and species. The extent of
stratification is quantified using the two-dimensional projection of the equivalence ra-
tio gradient on the line measurement axis. State space species-temperature behavior
in the turbulent flames is compared with that of premixed unstrained laminar flame
calculations.
The influence of stratification on flame curvature distributions is also examined.
Measured surface density function and scalar dissipation rate are compared with laminar
flame calculations, for both unconditioned data and data conditioned on local equiva-
lence ratio. Similar analyses are performed conditioned on the local curvature. Finally
measurements of flame surface density derived using the Pope definition (Section 4.3.1
of Chapter 4) are presented conditioned on mean and instantaneous progress variable.
84
Slot Burner Results 85
5.1 Flow Field Measurements
Velocity profiles were taken with a spatial resolution of 0.5mm at z = 15mm downstream
of the burner exit. Mean axial velocity U and turbulence intensity u′/U are shown
in Figure 5.1 [55]. As mentioned previously, the data presented in this section were
obtained from experiments performed by P. Anselmo-Filho, and are included for the
sake of completeness. The mean velocity is reasonably uniform, with variations due to
wakes from the splitter plates.
The turbulent integral length scale (Lturb) was calculated from the autocorrelation
function of the time series of velocity. The Kolmogorov length scale (η) was estimated
using Taylor’s hypothesis of homogeneous isotropic turbulence. The ratio of turbulence
intensity to laminar flame speed u′/SL was calculated using data for methane from [86]
for a mean Φg = 0.73. The integral scale of turbulence in the cold flow is around 2mm
Figure 5.1: Hot wire measurements of mean vertical velocity U (top row) and turbulence
intensity u′/U (bottom row) in the slot burner at z = 15mm downstream of the burner
exit. The burner centerline is located at x = 0mm.
Slot Burner Results 86
Table 5.1: Mean cold flow properties derived from measurements taken at z = 15mm
downstream of the burner exit. Raw data was averaged over a cross stream region
0 < x < 16.05mm.
U u′ u′/SL Lturb η δL Re ReT
(m/s) (m/s) (mm) (mm) (mm)
3.05 0.32 1.33 1.93 0.09 0.62 2 316 38
in the measurement region, and u′/SL is of the order unity in the flames (Table 5.1).
The Damköhler number is Da = 2.35 and the Karlovitz number is Ka = 0.59, placing
the flames surveyed marginally within the corrugated flamelet regime in the modified
Borghi diagram (Figure 5.2).
Figure 5.2: Modified Borghi diagram illustrating the main regimes of premixed combus-
tion: A, laminar flames; B, wrinkled flamelets; C, corrugated flamelets; D, thin reaction
zones; E, broken reaction zones. The flames surveyed in the slot burner operate in the
corrugated flamelet regime and are shown by a red circle.
Slot Burner Results 87
5.2 Instantaneous Flame Structure
Instantaneous sample shots of temperature, T , and linearly bridged equivalence ratio, Φ,
are shown in Figure 5.3, and the corresponding images of OH-PLIF in Figure 5.4. Note
that the temperature data are plotted with markers at the experimental resolution; all
other quantities are plotted with lines only save for cases where overlapping data require
markers for clarity. It is clear that significant gradients of Φ may arise within the reaction
zone for the stratified cases.
Analysis of the data within the flame brush demonstrates that the instantaneous
equivalence ratio gradients in the flame brush (∇xΦfs425 = 277m−1 and ∇xΦfs625 =
399m−1) can be significantly higher than the mean gradients (∇Φfs425 = 81m−1 and
∇xΦfs625 = 132m−1). Further discussion of the extent of stratification is given in Sec-
tion 5.4. These steep gradients are commensurate with the thermal and reaction zone
length scales within the flame, and raise the question of whether reaction in such flames
can be considered quasi-steady based on local mixture fraction, or whether their imme-
diate environment must also be taken into account. Laminar calculations of flames with
Figure 5.3: Single-shot profiles of temperature (left) and equivalence ratio (right) at
25 mm downstream of the burner exit for premixed fs1, , moderately stratified fs4,
, and highly stratified fs6, , cases.
Slot Burner Results 88
Figure 5.4: Top and middle rows: Single-shot OH-PLIF image pairs (randomly selected)
for the premixed (left), moderately stratified (middle), and highly stratified (right) slot
burner flames, corresponding to the instantaneous profiles shown in Figure 5.3. Bottom
row: Continuous curvature along the line measurement axis (z = 25mm). Data from the
second plane are plotted with dashed lines, and instantaneous flame brushes are marked
in gray.
positive or negative mixture fraction gradients seem to indicate that non-local effects
should be evident, particularly for very lean flames [30–32], with the behaviour exhibited
being influenced by the history of equivalence ratios experienced by the flame.
The OH-PLIF images shown in Figure 5.4 are typical, and demonstrate the weakly
turbulent nature of the flame; no pockets or examples of local flame extinction are
evident. This is true of all the cases considered. The values of κc along the line measure-
ment axis demonstrate the potential pitfalls of using the continuous form of curvature to
Slot Burner Results 89
condition experimental data, as substantial deviations from the methane/air curvature
levels seen in other weakly turbulent flows (−2.5mm−1 < κ < −2.5mm−1) are observed
for each case. These sudden jumps in curvature tend to occur either before the preheat
zone, in which case they are attributed to the weak gradients resulting in the denomina-
tor of Equation 4.4 being much smaller than the numerator, or due to noisy OH signal
in the equilibrium zone.
5.3 Favre-Averaged Flame Structure
Radial profiles of Favre-averaged temperature, species mole fractions and equivalence
ratio measurements are plotted at two axial distances above the burner exit in Figure 5.5.
The flat Φ˜ profile for the premixed fs1 flame demonstrates that there is little to no
entrainment of co-flow air within the measurement window, while the moderate mean
equivalence ratio gradients for the stratified cases show the structure of the mixing layer
between the leaner and richer flows upstream of these axial locations.
The center of the flame brush, taken as the peak in T ′′ (Figure 5.6), is located
significantly farther from the burner centerline in the stratified cases compared to the
premixed case. Examination of the Φ˜ profiles shows that the position of the flame brush
in the stratified flame is dominated by burning through higher equivalence ratios in the
upstream portion of the V-flame. The difference in the degree of stratification seen be-
tween the fs4 and fs6 cases is small relative to the premixed fs1; this is corroborated
by the results in Section 5.4 further on in the present chapter. This suggests that the
main effect of stratification on the mean flame position is the balance between the mean
heat release rate (which leads to the expansion of the inner V-shape), the mean flame
speed at the mean equivalence ratio, and the incoming velocity. Burning mixtures near
the stoichiometric point leads to high rates of heat release and greater expansion of the
Slot Burner Results 90
Figure 5.5: Radial profiles of Favre-averaged temperature, equivalence ratio, and mole
fractions of major chemical species for premixed, , moderately stratified, , and
highly stratified, , cases at z = 25mm (bottom halves) and z = 30mm (top halves).
Open circles show the locations of the flame brush as defined by the T ′′ FWHM positions.
Slot Burner Results 91
Figure 5.6: Radial profiles of Favre-averaged RMS fluctuation of temperature, equiva-
lence ratio, and mole fractions of major chemical species. Line types and symbols as in
Figure 5.5.
Slot Burner Results 92
V, but by the same token a higher flame speed and thus a larger mean flame brush angle
relative to the axial direction.
The values of Φ˜ at the center of the flame brush in the stratified cases are fairly close
to the premixed value at the z = 25mm location (within 4%). Further downstream at
z = 30mm, Favre-averaged equivalence ratios at peak T ′′ are lower for the stratified cases
than the premixed case (9% lower for fs430, 15% lower for fs630). The differences in Φ˜
at z = 25mm and z = 30mm indicate that results seen in data at the upstream location
which have not been conditioned on local equivalence ratio should generally reflect those
conditioned on local equivalence ratio at the same location. It may not be possible to
draw valid comparisons between the premixed and stratified cases at z = 30mm without
applying such conditioning.
Favre-average mole fractions for CO2 largely mirror the Favre-averaged temperature
profiles, as expected for product species and X˜H2O. X˜O2 is antisymmetric to the profiles
of the product species and the temperature. The Favre-averaged X˜CH4 profiles follow
the equivalence ratio in the non-reacting region and peak just ahead of the flame brush.
Finally the intermediates H2 and CO appear in smaller concentrations, peaking around
the center of the flame brush. Interestingly both of these quantities are substantially
higher in the equilibrium zone for fs6 than fs4 at the upstream z = 25mm location,
but these differences are almost completely eliminated just 5mm farther downstream.
Discussion of the correlation of the species and temperature appears in Section 5.5.
5.4 Extent of Stratification
It is not possible to measure the three-dimensional equivalence ratio gradient using
the experimental dataset for the slot burner, as there is no information on the three-
Slot Burner Results 93
Figure 5.7: Probability density functions of two-dimensional equivalence ratio gradient,
∇xΦ, for the slot burner cases at z = 25mm (left plot) and z = 30mm (right plot). Data
taken from within the linear bridged region of the flame. Line types as in Figure 5.5.
dimensional equivalence ratio field. However, the two-dimensional projection of the true
three-dimensional gradient is given by the gradient of Φ along the line measurement axis.
This quantity is denoted as ∇xΦ in the present work. Figure 5.7 shows the probability
distributions for ∇xΦ at both axial locations, while Table 5.2 shows some basic statistics
for the distributions.
The mean two-dimensional equivalence ratio gradient increases significantly between
the fs4 and fs6 case (63% and 54% for z = 25mm and z = 30mm respectively),
Table 5.2: Statistics for equivalence ratio gradients in the slot burner. Equivalence
ratio data is linearly bridged (Φ).
Flame
y ∇xΦrms ∇xΦ γ1 γ2
(mm)
(
m−1
) (
m−1
)
(−) (−)
fs1
25 9.0 11.8 -0.83 14.7
30 8.2 12.5 -0.06 0.1
fs4
25 80.9 49.3 0.15 -0.1
30 69.1 39.6 0.12 0.2
fs6
25 132.0 80.4 -0.07 -0.2
30 106.7 55.8 0.13 0.5
Slot Burner Results 94
though these increases are small in comparison to those relative to the premixed case
(743% to 1 367%). The near-zero positive gradients exhibited by the premixed case are
due to the equivalence ratio being biased slightly high in the product sides in the current
experimental data.
5.5 Influence of Stratification on Species Evolution
Scatter plots of major species against temperature are shown in Figs. 5.8-5.10, along
with values from laminar flame calculations for unstrained premixed flames at the mean
Φ. The local Φ for each data point is shown using the color scale in Figure 5.8. Note that
the data are downsampled by a factor of ten to aid clarity. All species in the premixed
case (Figure 5.8) are in good agreement on the mean with laminar flame calculations.
In each scatter plot the data are binned in T space, with centers at 100K intervals
starting at T = 300K, and the mean equivalence ratio is found within each bin. A multi-
dimensional lookup table of unstrained premixed methane/air laminar flame calculations
is interpolated in T and Φ to find the corresponding premixed value for each species. It
is clear that the premixed calculations give good agreement in the thermal domain with
the mean of the experimental scatters with the exception of hydrogen. This is important
as it indicates that models whose chemistry is based around the laminar flamelet concept
are unlikely to be able to capture the behavior of hydrogen in simulations of stratified
flames.
Slot Burner Results 95
Figure 5.8: Plots of temperature against key scalars for fs125 (bottom row) and fs130
(top row), colored by Φ, as shown in the colorbar. Mean fits are plotted in red. Laminar
flame calculations are shown by gray horizontal (value at local mean Φ) and vertical
(range of maximum and minimum local Φ) lines.
Slot Burner Results 96
Figure 5.9: Plots of temperature against key scalars for fs425 (bottom row) and fs430
(top row). Symbols as in Figure 5.8
Slot Burner Results 97
Figure 5.10: Plots of temperature against key scalars for fs625 (bottom row) and fs630
(top row). Symbols as in Figure 5.8
Slot Burner Results 98
5.6 Curvature
Flame curvature can be obtained from the OH-PLIF images in discrete or continu-
ous two-dimensional forms as described in Section 4.1.4 of Chapter 4. Results for pre-
mixed flames have been reported by Shepherd [81], and for stratified flames by Anselmo-
Filho [24]. The slot burner used in the current work is the same as that used in the
latter study, but the curvature measurements reported previously were obtained from a
much larger OH-PLIF measurement window. The work by Shepherd showed that the
mean curvature in a turbulent premixed methane/air V-flame is skewed towards positive
values. The work in [24] on the current burner as well as that by Renou et al. in [21]
showed that flame curvature distributions are broadened and shifted closer to a zero
mean as stratification increases. Curvature results in the present work are given in both
continuous (Section 4.1.4.2 in Chapter 4) and discrete (Section 4.1.4.1 in Chapter 4)
forms.
The results of the present work, however, show only partial agreement with previous
Figure 5.11: Distributions of discrete curvature, κd, binned in steps of κd = 0.05mm
−1.
κd = 0mm
−1 is marked with a gray vertical line to aid clarity. Data from planes one
and two are shown by solid lines and crosses respectively.
Slot Burner Results 99
Table 5.3: RMS and excess kurtosis values for discrete and continuous measures of local
curvature in the slot burner at 25 and 30mm downstream of the burner exit. Continuous
data is taken from the region 0.1 < c < 0.9. All curvature data filtered to remove outliers(
|κ| > 3mm−1
)
. Data from the second plane is given in parentheses in each case.
Flame y |κd| |κc| γ2,d γ2,c
(mm)
(
mm−1
) (
mm−1
)
(−) (−)
fs1
25
0.241 (0.250) 0.349 (0.394) 0.151 (0.342) 5.018 (4.132)
fs4 0.304 (0.318) 0.425 (0.485) 0.320 (0.256) 3.830 (2.638)
fs6 0.284 (0.298) 0.406 (0.451) 1.424 (1.243) 4.385 (3.417)
fs1
30
0.272 (0.285) 0.362 (0.393) 0.104 (0.082) 5.036 (4.188)
fs4 0.335 (0.343) 0.375 (0.459) 0.146 (0.202) 4.002 (3.103)
fs6 0.325 (0.333) 0.348 (0.437) 0.104 (0.404) 4.352 (3.567)
findings. The pdfs of discrete curvature κd shown in Figure 5.11 are similar to the
normal distribution in both planes. The discrete distributions are marginally leptokurtic,
indicating a slightly peakier distribution than a normal one, with the exception of the
highly stratified case at z = 25mm downstream, which exhibits significantly higher
levels of kurtosis, as shown in Table 5.3. The reason for the anomalous result in the
latter case is uncertain.
The continuous distributions plotted in Figure 5.12 are significantly more leptokurtic
than their discrete counterparts, as seen in Table 5.3. One speculative explanation of
this behavior is that the continuous data is obtained for a range of locations within the
instantaneous thermal ramp of the flame (0.1 < c < 0.9), while the discrete data is
taken at the location of maximum OH gradient. However limiting the continuous data
to smaller intervals of progress variable fails to bring the kurtosis in line with the discrete
results, indicating that this alone does not explain the differences.
As the distributions are symmetric and centered close to zero curvature, it seems that
the flames undulate such that positive and negative curvatures of similar magnitude
Slot Burner Results 100
Figure 5.12: Distributions of continuous curvature, κc, binned in steps of κc =
0.05mm−1. κc = 0mm
−1 is marked with a gray vertical line to aid clarity. Data from
planes one and two are shown by solid lines and crosses respectively.
are almost equally distributed within the measurement window. Broadening of the
distribution with stratification is observed, in line with the results highlighted earlier.
The RMS curvature values (Table 5.3) increase with stratification compared to the
premixed case, aside from in the continuous fs630 data. Note that this broadening
is not monotonic; while both stratified cases typically have larger RMS values than the
premixed case, the fs4 case shows higher RMS curvature than the more stratified fs6
case.
However, increased stratification appears to shift the mean in the positive direction
rather than towards zero. This trend is corroborated by the work of Bonaldo [87], who
found that increasing stratification resulted in an increase in the probability of small
positive radii of curvature (high positive curvature). The difference between the results
presented here and those from [24], which used the same burner, is attributed to the
significantly smaller cross planar LIF window size in the present work (10 × 8 mm vs
38× 25 mm); the previous results may have been affected by a wider variation in local
mean Φ.
Slot Burner Results 101
Figure 5.13: Joint pdf of progress variable, c, and continuous curvature, κc, taken from
plane one for premixed (left column), moderately (middle column) and highly (right col-
umn) stratified slot burner cases, at z = 25mm (bottom row) and z = 30mm downstream
of the burner exit. κc = 0mm
−1 is shown by dashed white lines, and the probability
P (c; κc) is expressed on a log10 scale.
It is interesting to note that the continuous curvature is typically smaller in magni-
tude in the intermediate region of the flame (0.2 < c < 0.8), as shown in the joint pdfs
of κc and c in Figure 5.13, with higher curvature values being more predominant near
the progress variable extrema. One possible explanation for this is that the continuous
curvature definition (Equation 4.4 in Chapter 4) includes OH signal gradients of first and
second order; away from the reaction zone, these quantities will have near-zero values
and may result in very high curvatures due to the small value of the denominator of
Equation 4.4 in Chapter 4. However, a look at the contour plot of a randomly selected
OH-PLIF image from the premixed case shown in Figure 5.14 demonstrates qualitatively
that the high curvature values may not be an artifact of near-zero gradients; while similar
levels of wrinkling are seen throughout the reaction zone, the contours are significantly
more convoluted near the unburned reactants and the burned products.
Slot Burner Results 102
Figure 5.14: Contour plot of IOH from the premixed OH-PLIF image shown in Fig-
ure 5.4. The image itself is shown inset for reference.
5.7 Influence of Stratification on Scalar Gradients
5.7.1 Unconditioned
Thermal progress variable, surface density function, and the scalar dissipation rate were
calculated using the measured temperature and local equivalence ratio. The resulting
unconditioned scatter plots of |∇c| and χc as a function of progress variable are shown
in Figures 5.15 and 5.16 respectively. The data are downsampled by a factor of ten
to aid clarity, but are used in full to determine conditional means in progress variable
space. Significant levels of scatter are observed, particularly for the fs6 case. The
mean values are substantially smaller than the calculated unstrained laminar values
throughout progress variable space; Sankaran et al [73] and more recently Moureau et
al [74] have reported similar trends in simulations of premixed turbulent flames and
their laminar counterparts. In the latter study the turbulent flame was found to be
thickened relative to laminar equivalents on both an instantaneous and mean basis, as
in the present work. It is interesting that thermal gradients are significantly attenuated
even at the low levels of turbulence found in the slot burner.
Slot Burner Results 103
Figure 5.15: Relationship between progress variable c and three-dimensional surface
density function |∇c| for the premixed (left column), moderately stratified (middle
column) and highly stratified (right column) cases at z = 25mm (bottom row) and
z = 30mm (top row). Symbols are as in Figure 5.8.
Figure 5.16: Relationship between progress variable c and three-dimensional scalar
dissipation rate χc for the premixed (left), moderately stratified (middle column) and
highly stratified (right column) cases at z = 25mm (bottom row) and z = 30mm (top
row). Symbols as in Figure 5.8.
Slot Burner Results 104
The conditional means of |∇c| and χc in the premixed case give good agreement with
the behavior seen in laminar flame calculations, albeit at significantly reduced values
(37% lower peak 〈|∇c||c〉, 56% lower peak 〈χc|c〉). This may be due to turbulence
thickening the flame relative to unstrained laminar values, as suggested by the DNS
simulations in [73, 74]. At each value of instantaneous progress variable c, a broadly
positive correlation between gradient terms and equivalence ratio is exhibited by the
stratified cases, with higher values of Φ tending to result in thinner flames and higher
thermal diffusivities. At the z = 25mm location it appears that both 〈|∇c||c〉 and 〈χc|c〉
are enhanced due to stratification; the former is 9% (14%) greater in the fs4 (fs6) case
than the premixed case, and the latter is increased by 17% (24%). Further downstream
in the flame, no such change is discernible. However as discussed in Section 5.3, only the
upstream z = 25mm location is viable for qualitative comparisons between the premixed
and stratified cases without further conditioning the data.
5.7.2 Conditioned on local stoichiometry
In order to isolate the effect of stratification from the effects of local equivalence ratio, it
is necessary to condition the data on the local Φ. The conditional mean equivalence ratio
in progress variable space 〈Φ|c〉 is determined for the premixed case at both locations.
The |∇c| and χc data in all cases, premixed and stratified, are then conditioned such
that Φ is within ±1% of 〈Φ|c〉 within each progress variable bin. This ensures that
any comparisons made between the premixed and stratified cases are unlikely to be
influenced by the effect of local equivalence ratio to any significant degree. However this
reduces the size of the datasets substantially, with the result that the number of points
within each c bin ranges from 50 to 60 in the mean thermal ramp (0.2 ≤ c ≤ 0.8). This
highlights the need to take very large datasets in stratified flows if multiple levels of
Slot Burner Results 105
Figure 5.17: Comparison between premixed and stratified cases when conditioned in
c-space on local Φ to within ±1% of the mean values in the unconditioned premixed
data, for premixed, , moderately stratified, , and highly stratified, , cases
at z = 25mm (bottom row) and z = 30mm (top row).
conditioning are to be performed.
The doubly conditioned means of surface density function
〈|∇c||c,Φ〉 and scalar dis-
sipation rate
〈
χc|c,Φ
〉
are plotted in Figure 5.17, and the differences in peak amplitudes
between the premixed and stratified cases are summarized in Table 5.4. The data show
that both surface density function and scalar dissipation rate are enhanced due to strat-
ification relative to the premixed case. The enhancement is modest, but more significant
in the upstream location, which may indicate that the effect of stratification on these
Table 5.4: Difference in peak values of doubly conditioned surface density function〈|∇c||c,Φ〉 and scalar dissipation rate 〈χc|c,Φ〉 conditioned on local equivalence ratio Φ
for stratified cases expressed relative to equivalent premixed values.
Flame y
〈|∇c||c,Φ〉〈χc|c,Φ〉
fs4
25 +15% +31%
30 + 7% + 12%
fs6
25 +20% +43%
30 + 7% +13%
Slot Burner Results 106
quantities is strain sensitive.
5.7.3 Conditioned on local curvature
As both curvature and the thermal gradients within the flame are related to strain, it
is interesting to condition the surface density function data on the curvature to see if
high positive or negative values of local curvature result in elevated or suppressed levels
of |∇c|. The progress variable and surface density function data were filtered by their
continuous curvature values into near zero (|κc| < 0.01mm−1), positive (κc > 0.5mm−1)
and negative (κc < 0.5mm
−1) sets. Mean fits to these data were obtained and are shown
in Figure 5.18.
Local continuous curvature appears to have no significant effect on the surface density
function in the cases surveyed. It is possible that this is due to the limits chosen for the
positive and negative curvature datasets; correlation between elevated curvature and
surface density function may only become apparent at substantially higher curvature
Figure 5.18: Mean fits of surface density function |∇c| in progress variable space condi-
tioned on continuous curvature κc for fs125, fs425 and fs625 (bottom row); and fs130,
fs430 and fs630 (top row). Low curvature data are shown in by full lines, highly positive
data by crosses, and highly negative by circles.
Slot Burner Results 107
levels. It is not possible to condition the surface density function at larger curvature
values in the present datasets given the paucity of data where κc > 0.5 in the majority
of the flame (0.2 < c < 0.8). However it is still possible to definitively say that surface
density function in the cases under consideration is independent of local continuous
curvature to at least |κc| = 0.5mm.
5.8 Flame Surface Density
Flame surface densities calculated using the Pope formulation [8] (detailed in Sec-
tion 4.3.1 of Chapter 4) are presented in Figure 5.19, demonstrating the trends in Σ
across both mean and instantaneous c space. The general behavior is as expected from
previous investigations, trending from a positive to negative skew as c increases. Note
that the values for high c = 0.95 are unphysical, and are due to the noise in the thermal
data in the products.
Flame surface density shows similar trends for all cases, with the premixed case
appearing elevated relative to the stratified cases at most values of the instantaneous
thermal progress variable. This contrasts the behavior expected from the curvature
Figure 5.19: Behavior of flame surface density in terms of mean and instantaneous
progress variable for fs125, fs425 and fs625 (bottom row); and fs130, fs430 and fs630
(top row). Symbols as in Figure 5.5.
Slot Burner Results 108
distributions seen in Section 5.6; broader curvature pdfs are associated with thinner
flames (due to strain effects), which should result in higher flame surface densities.
There appears to be little difference between the results from the fs4 and fs6 cases.
These are tentative conclusions as the data is rather jittery due to the sample sizes. It
is not possible to further condition this data on local equivalence ratio in the slot burner
datasets as they are not large enough for such triple conditioning.
5.9 Summary
Line imaging of Raman-Rayleigh scattering and CO-LIF with simultaneous cross-planar
OH-PLIF were used to create detailed datasets in premixed and stratified low-turbulence
methane/air V-flames. The dataa have been investigated to determine the effect of
stratification on the behavior of species in thermal state space, curvature, surface density
function |∇c|, scalar dissipation rate χc, and flame surface density Σ. Specific conclusions
are as follows:
i) The distribution of discrete curvature in stratified flames is broader than for pre-
mixed flames, in agreement with previous findings, although the mean peak becomes
more positive (convex towards the reactants) with stratification, in contrast to prior
work.
ii) The curvature distributions obtained using the continuous methodology are signifi-
cantly more leptokurtic or peaky than the equivalent discrete distributions.
iii) The spread of continuous curvature values within the bulk of the flame (0.1 < c <
0.8) is significantly narrower than it is near the unburned reactants and the burned
products.
aThe data are available for comparison with model calculations or direct simulations [88].
Slot Burner Results 109
iv) Turbulent flames are substantially thicker (37%) than premixed unstrained laminar
flames at the same equivalence ratio both instantaneously and on the mean. This is
perhaps a surprising experimental result, but is substantiated by DNS simulations.
v) Laminar flame calculations of hydrogen mole fraction give poor agreement with the
experimental means under stratified conditions. The overall state-space structure
of the other measured species is well captured by laminar flamelets on the mean
regardless of stratification.
vi) Both the flame surface density function |∇c| and scalar dissipation rate χc are
enhanced relative to the premixed case by stratification.
vii) Curvature shows no significant correlation with the magnitude of surface density
function in slot burner data.
Chapter 6
Cambridge Stratified
Swirl Burner Results
The stratified swirl burner, SwB, introduced in Section 3.2.1 of Chapter 3 enables the
investigation of a range of interesting combustion behaviors. SwB is a more practically
relevant burner as it operates at substantially higher levels of turbulence intensity than
the slot burner investigated in Chapter 5. The central bluff body induces a recirculation
zone above the burner, which produces some interesting deviations from the general
behavior seen in the slot burner. The effects of the recirculation zone, in addition to the
aforementioned higher turbulence levels, also make this a much more challenging and
interesting case for simulations.
A qualitative visual overview of the flames surveyed is given by a series of short-
and long-exposure photographs. The flow fields in these cases are explored using the
results from the two-dimensional PIV campaign. Key turbulence parameters are given
at the locations considered further on when examining the scalar data. The velocity
data explain some of the behavior seen in the flame visual survey.
The instantaneous flame structure is examined using profiles of temperature and
110
Cambridge Stratified
Swirl Burner Results 111
equivalence ratio, providing a snapshot of the flames surveyed and demonstrating the
resolution of the measurements. The thermal and compositional structure of the various
cases are considered for various axial distances downstream of the burner exit, enabling
the intersection of the mixing layer and the mean flame brush to be identified; signifi-
cantly larger datasets were taken at these locations to enable the data to be multiply
conditioned. The extent of stratification is investigated using the probability distribu-
tions of the two-dimensional equivalence ratio gradient.
Representative Favre-averages and fluctuations of temperature, major combustion
species and equivalence ratio are presented for each of the cases, and the profiles are
compared and contrasted. The influence of stratification on the evolution of these species
is examined in temperature space, using both the full datasets and data conditioned on
local equivalence ratio. The flame topology is investigated using curvature distributions
and statistics for each of the main cases. Progress variable distributions are presented
to demonstrate the thickness of the flames. Finally the influence of stratification on
the surface density function, turbulent flame thickness and the scalar dissipation rate is
considered using both unconditioned data and data conditioned on the local equivalence
ratio.
6.1 Flame Visual Survey
Figure 6.1 and Figure 6.2 show photographs of the flames studied in the present work (for
long- and short-exposures respectively). The long-exposure photographs in Figure 6.1
demonstrate the mean shape of the flames surveyed through their visible spectrum
chemiluminescence. The non-swirling flow cases (top row) demonstrate a non-monotonic
broadening of flame angle with increasing stratification. This broadening is attributed
to a combination of greater expansion of burnt products and increased flame speeds as
Cambridge Stratified
Swirl Burner Results 112
the stratified flames burn through higher equivalence ratios than in the premixed cases.
The variation in flame angle with stratification is less obvious in cases where the flow
is swirling (middle and bottom rows). In all cases the chemiluminescence in the visible
spectrum (integrated along the axis perpendicular to the focal plane) shows an increase
with stratification. The breadth of the flame increases and the height decreases as swirl
is increased (moving down columns).
The turbulent nature of the flames studied is demonstrated by the short-exposure
photographs in Figure 6.2. The chemiluminescence indicates that although significant
levels of wrinkling are present, the flame fronts are continuous and there is no evidence
of local extinction. Again, the distance downstream of the burner exit where high CH
excitation is exhibited decreases with increasing swirl for all stratification levels.
6.2 Flow Field Measurements
The velocity fields in the conditions listed in Table 3.3 of Chapter 3 were investigated
using two-dimensional particle image velocimetry, as described in Section 3.2.4.
Data is presented for both mean absolute velocity, U , and velocity fluctuation, u′, in
a measurement window 25mm wide and 40mm tall, starting at z = 5mm downstream
of the burner exit. U and u′ are calculated from the instantaneous two-dimensional
velocity fields, with spurious outliers removed. A light shield was used to prevent the
illumination of seed particles adhering to the central bluff body; the intensity of light
reflected by the bluff body in its absence was sufficient to cause damage to the imaging
equipment. The use of the light shield prevented high quality vectors being obtained
closer to the burner exit than z = 5mm.
C
am
bridge
Stratified
Sw
irlB
urner
R
esults
113
Figure 6.1: Long exposure photos of flame conditions in the swirl burner. Cases are marked by their corresponding
numbers; 1→ SwB1.
C
am
bridge
Stratified
Sw
irlB
urner
R
esults
114
Figure 6.2: Short exposure photos of flame conditions in the swirl burner. Cases are marked by their corresponding
numbers; 1→ SwB1.
Cambridge Stratified
Swirl Burner Results 115
Mean and fluctuating components of velocity are plotted side by side to give an
overall field 50mm wide, 40mm tall. Note that both U and u′ are derived from the
same side of the centerline of the experimental images. Under the assumption of radial
symmetry, U is shown (mirrored) for r < 0mm and u′ is shown for r > 0mm, with
white streak lines to highlight the flow patterns.
6.2.1 Non-Reacting Cases
Non-reacting results are presented in Figure 6.3 for the three flow field patterns; non-
swirling, moderately swirling and highly swirling. These velocity fields are presented to
illustrate the velocity characteristics due solely to the flows in the burner. The flow near
the upstream limit of the measurement window (z ≈ 5mm) resembles fully developed
annular channel flow, with dips between the peak values of U corresponding to the
inner and outer flows due to the tube wall separating the flows. This can be seen more
clearly in the near-exit profiles presented for the reacting cases in Section 6.2.3. These
Figure 6.3: Mean absolute (r < 0mm) and fluctuating (r > 0mm) velocity maps for
non-swirling (A), moderately swirling (B), and highly swirling (C) non-reacting swirl
burner cases. Streamlines are shown by solid white lines.
Cambridge Stratified
Swirl Burner Results 116
peak velocities decay with downstream distance, and the decreases observed increase
monotonically with the addition of swirl.
A recirculation zone is seen above the central bluff body, extending from the mouth of
the burner to 18.5mm downstream in each case. The length appears to be independent
of the degree of swirl. The width of the recirculation zone is approximately 12.7mm in
diameter, as governed by the size of the central bluff body. The recirculation zones draw
the radial position of the peak mean flow from both the inner and outer annuli towards
the centerline, and this effect is accentuated as the downstream distance z increases.
The presence of such recirculation zones is important as it affects the results from
the multi-scalar measurements presented later. Fully- and partially-reacted combustion
products may be transported into the recirculation zone and then back into the reactants
from the inner annulus, resulting in deviations from values that would be expected from
the nominal stoichiometry detailed in Table 3.3 of Chapter 3.
The plots of u′ demonstrate clearly defined shear layers between the recirculation
zone, the inner flow, the outer flow, and the co-flow. The breadth and magnitude of these
zones indicate that significant turbulent mixing takes place between the streams in all
cases. The velocity fluctuations between the co-flow and the outer flow are substantially
broadened by the introduction of swirl. It is tempting to assume that the high levels
of u′ seen in the moderately swirling case for z > 35mm arise from experimental error.
However the absence of similar results in either the non-swirling or the highly swirling
data implies that this is a real effect.
Significantly higher levels of audible noise experienced when running the burner in the
moderately swirling condition than in either the non-swirling or highly swirling condi-
tions. This indicates that the burner operates in an unstable mode under the moderately
swirling conditions, and is corroborated by the u′ data. The raised levels of turbulence
within the recirculation zone can be interpreted as supporting this postulation.
Cambridge Stratified
Swirl Burner Results 117
Two additional shear layers form at the middle and outer tube walls, and are visible
in the u′ profiles (particularly for the non-swirling case). These shear layers generate the
mixing layers between the inner annulus, outer annulus, and co-flow streams, resulting
in smooth gradients in Φ for the stratified cases.
6.2.2 Reacting Cases
Mean and fluctuating components of velocity are shown for the reacting swirl burner
cases in Figure 6.4. The cases are plotted such that the degree of swirl increases along the
columns from non-swirling (left column) through moderately swirling (middle column)
to highly swirling (right column). The stratification ratios increase moving down the
rows from lean premixed (top row) through moderately stratified (2nd row) to highly
stratified (3rd row); the bottom row shows the stoichiometric premixed cases. The mean
velocity demonstrates peaks in mean absolute velocity U corresponding to the inner and
outer annulus flows, with u′ illustrating the shear layers between the various flows. The
shear layer between the inner- and outer-flow and the outer- and co-flow merge in most
cases by z = 30mm, indicating substantial levels of turbulent mixing take place between
the fuel/oxidizer streams from the inner and outer annuli by this location.
The radial location of peak U is roughly constant in the premixed non-swirling case
SwB1 for all axial distances in the measurement window, in contrast to the behavior
exhibited by the non-reacting non-swirling case (Figure 6.3). This is attributed primarily
to the expansion of burnt products in the reacting case.
Considering the other non-swirling cases (SwB5, SwB9, SwB13), the radial position
of peak U moves progressively farther away from the burner centerline with increasing
axial distance (moving down the rows of the left hand column). This is due to the
effects of burning through fuel at a higher equivalence ratio than in the lean premixed
Cambridge Stratified
Swirl Burner Results 118
Figure 6.4: Mean absolute (r < 0mm) and fluctuating (r > 0mm) velocity maps for
reacting swirl burner cases. Cases are marked with their corresponding numbers (i.e.,
1→ SwB1). Streamlines are shown by solid white lines.
non-swirling case (SwB1), resulting in greater temperature changes through the flame
and consequently larger changes in density. The greater equivalence ratio also results in
an increased flame speed, shifting the radial location of the peak U slightly farther out.
The radial location of peak U at the downstream limit of the measurement window is
the same for both levels of stratification.
Again moving down the left column of Figure 6.4, the length of the recirculation zone
decreases from roughly 29mm for the premixed SwB1 case to 18mm to 20mm in the
other cases (SwB5, SwB9, SwB13). The reason for this is not immediately clear. The
Cambridge Stratified
Swirl Burner Results 119
magnitude of the velocities within the recirculation zones is considerably higher than in
the corresponding non-reacting case (35% to 70% greater).
In the moderately swirling cases (middle column; SwB2, SwB6, SwB10, SwB14),
the mean velocity field due to the outer and inner annulus flows are reasonably similar to
those in the equivalent non-swirling cases, though the effects of the swirl flow cause the
mean flow to diverge outwards significantly more from the axial locations corresponding
to the end of the recirculation zone. This effect is more pronounced in the highly swirling
cases (right column; SwB3, SwB7, SwB11, SwB15), and occurs closer to the burner
exit (z ≈ 10mm).
Examining the mean velocity plot for the premixed moderately swirling SwB2, it
is clear that the addition of swirl has significantly extended (30%) the recirculation
zone relative to the corresponding non-swirling case, SwB1. However the recirculation
zones for the other moderately swirling cases (middle column; SwB6, SwB10, SwB14)
exhibit recirculation zones which are slightly shorter than their non-swirling equivalents
(left column). The reasons for this are unclear, and merit further investigation.
The flow fields of the reacting highly swirling cases (right column; SwB3, SwB7,
SwB11, SwB15) highlight an interesting phenomenon; the recirculation zone in the pre-
mixed SwB3 extends farther downstream than the measurement window, and appears
to follow the shape of the shear layers within it. This is very different to the behavior
seen in the non-swirling (left column) and moderately swirling (middle column) cases,
as well as the other highly swirling cases (SwB7, SwB11, SwB15), all of which exhibit
more conventional recirculation zones above the central bluff body. This may be due to
the balance between the heat release in the reacting case and the degree of swirl causing
the recirculation zone interface to move further downstream.
Figure 6.5 provides qualitative visual evidence of this behavior. The photograph
was taken during the short exposure flame survey shown in Figure 6.2 while the burner
Cambridge Stratified
Swirl Burner Results 120
Figure 6.5: Short exposure photograph of very highly swirling stoichiometric case
SwB16 demonstrating extended recirculation zone.
was operating in the very highly swirling stoichiometric case SwB16 (results for this
condition are not presented due to difficulties in stabilizing these flames under stratified
conditions). The card used to record the current case being recorded is in contact with
the flame brush at z ≈ 65mm above the burner exit, and is burning, resulting in a
yellow/orange sooty flame.
This fortuitous accident demonstrates that the extended recirculation zone proposed
earlier is in action, as the cone of yellow/orange chemiluminescence within the blue
chemiluminescence of the swirling flame demonstrates that it has entrained products
from the card flame down to the bluff body. The yellow/orange cone subtends an angle
of 25◦ to the vertical, which is similar to that subtended by the recirculation zone
interface for SwB3 (15◦). This slight discrepancy is attributed to the different level of
swirl between the highly and very highly swirling cases.
The recirculation zones in the non-swirling cases (left column) exhibit a region of high
Cambridge Stratified
Swirl Burner Results 121
u′ near the edge of the recirculation zone (i.e. above the walls of the central bluff body),
with lower levels of u′ observed in the interior of the recirculation zone. The moderately
swirling cases (middle column) show similar peaks in u′, which do not decay to lower
levels in the inner region of the recirculation zone. In contrast, the highly swirling case
demonstrates substantially lower turbulence in the recirculation zone, echoing the results
seen for the non-reacting cases in Section 6.2.1. This apparent decrease in turbulence at
high swirl is attributed to the combination of an underestimation of u′ in the swirling
cases due to the two-dimensional nature of the PIV measurements, as well as a shift
back to a stable mode brought about by the further addition of swirl. This latter effect
is believed to dominate the former, and is as mentioned previously is corroborated by
the noise levels observed when running the burner; significantly lower volumes were
experienced when operating the burner for highly swirling cases.
Interestingly, the effect of stratification on the mean flow fields for the swirling cases
(middle and right columns) is less pronounced than in the non-swirling cases (left col-
umn).
6.2.3 Near-exit Conditions
Profiles of near-exit (z ≈ 5mm) mean and RMS velocities are presented in Figure 6.6.
These profiles are extracted from the data (U , u′) used to produce Figure 6.4. As
mentioned in Section 6.2.1, the need to use a light shield to avoid illuminating the
central bluff body prevented high quality vectors being obtained nearer to the burner
exit than z = 5mm. These profiles are presented as they allow the velocities recorded
to be separated into their radial and axial components and clearly visualized.
The exit profiles for the reacting cases demonstrate behavior consistent with fully
developed annular channel flow, with peaks in U z (much larger than those for the radial
Cambridge Stratified
Swirl Burner Results 122
Figure 6.6: Mean and fluctuating velocity profiles near at z ≈ 5mm downstream of the
burner exit for all reacting cases.
velocity U r) corresponding to flow from the inner and outer annuli . The peak of the
outer flow stream is approximately twice that of the inner flow, as expected from the bulk
velocities calculated for the annuli. Kaneda et al [89] provide a formula for determining
the location of peak U z in a fully developed turbulent annular flow:
R3 =
R2 (R1/R2)
0.343 +R1
1 + (R1/R2)
0.343 (6.1)
where R refers to a radius and the subscripts 1, 2, and 3 refer to the inner wall of
the annulus, the outer wall of the annulus and the location of the peak axial velocity
respectively. The exit profiles show good agreement in the non-swirling cases with the
Cambridge Stratified
Swirl Burner Results 123
values obtained using the geometry detailed in Figure 3.5 of Chapter 3; the peak in U z
is expected to lie near R3 = 8.8mm for the inner stream and near R3 = 14.9mm for the
outer stream.
All cases except for SwB6 exhibit negative U z for r < 5mm corresponding to the
recirculation zones above the burner’s ceramic cap, which acts as a central bluff body. A
decrease in the magnitude of the positive and negative U z peaks is seen with increasing
swirl, which is expected due to the split between the swirling and non-swirling compo-
nents of the flow. It should again be noted that the tangential component of velocity is
not available in the current datasets.
The extent and strength of the turbulent mixing layers between the inner- and outer-
flows and the outer-flow and the co-flow air are shown by u′z. In the non-swirling cases
(left column) there are pronounced peaks in u′z at the interface between the inner-flow
and the recirculation zone, which decay to a reasonably uniform level in the center of
the recirculation zone. The magnitude of u′z is elevated in the bulk of the recirculation
zone in the moderate swirl cases (middle column). Again this increase with swirl is non-
monotonic; the moderate swirl level appears to result in an unstable mode of operation,
while the high swirl cases operate in a stable flow field, as mentioned previously in
Section 6.2.2.
The measured radial velocities U r are small in comparison to the axial velocities
at this axial location. The radial fluctuations u′r are similar to their axial counterparts,
albeit reduced by a factor of approximately 2, and show peaks in the shear layers between
the inner- and outer-flows and also the outer- and co-flow. Increasing the stratification
results in greater levels of radial fluctuation at the interface between the recirculation
zone and the inner-flow for the non-swirling cases (left column). This effect is not
observed to any significant degree for the swirling cases.
Near to the burner exit it is appears that stoichiometry has limited impact on either
Cambridge Stratified
Swirl Burner Results 124
the mean or fluctuating components of velocity.
6.2.4 Summary of Turbulence Parameters
The turbulence parameters were calculated using Equation 6.3 through Equation 6.9.
The turbulent length scale, Lt, is approximated by the hydraulic diameter of the burner
as the PIV records were insufficiently long to calculate the autocorrelation coefficient to
a satisfactory standard.
I =
u′
U
(6.2)
Lt = 4
Ae
Pw
(6.3)
Ret =
uLt
ν
(6.4)
ηK = LtRe
−3/4
t (6.5)
νK = uRe
−1/4
t (6.6)
τK =
ηK
νK
(6.7)
Da =
SLLt
u′δL
(6.8)
Ka =
δ2L
η2K
(6.9)
where I is the turbulence intensity, Lt is the turbulent length scale, Ae is the exit area of
the burner, Pw is the wetted perimeter of the burner exit, ηK is the Kolmogorov length
scale, νK is the Kolmogorov time scale, τK is the Kolmogorov velocity scale, and all other
symbols have their usual meanings. The kinematic viscosity, ν, and laminar flame speed,
SL, are calculated for the measured (or in the case of z = 5mm, interpolated) values of
mean temperature and equivalence ratio.
These turbulence parameters have been calculated for three locations within the
Cambridge Stratified
Swirl Burner Results 125
flow field, and are listed in Table 6.1 through Table 6.3. The axial positions chosen
are: near-exit (z = 5mm), the line measurement location closest to the burner exit
(z = 10mm), and at the intersection of the mixing layer with the mean flame brush
(z = 20mm to 50mm, see Table 6.5 for details). The positions of peak Favre-averaged
temperature variation, T˜ , (detailed later on in Section 6.4.1) were used to choose the
radial locations considered.
The near-exit case (z = 5mm) is included as it is as close to the exit conditions as can
be characterized with the current velocity data. As line measurement data is unavailable
in this case, the radial position is taken as the linear interpolation between the edge of
the bluff body and the center of the flame brush at z = 10mm, while relevant quantities
such as temperature are approximated by the values at z = 10mm. Parameters for
z = 10mm are also presented in this section as discussion further on will look at scalar
data from these locations. Lastly, the turbulence parameters at the intersection of the
mixing layer and the mean flame brush are parametrized as analyses of these data form
the crux of the current chapter.
The turbulent parameters are used to plot the region mapped out by the swirl burner
cases onto a modified Borghi diagram in Figure 6.7. The swirl burner cases, whether
considering data from z = 5mm, z = 10mm or the intersection of the mixing layer
and the mean flame brush, lie squarely within the thin reaction zone regime, in contrast
to the weakly turbulent slot burner cases which were marginally within the wrinkled
flamelet regime. It should be noted that the u′ used to characterize the flows is obtained
from measurements in the axial and radial directions only; the swirl cases, which feature
substantial tangential velocity fluctuations, will be lower than their true position on the
modified Borghi diagram.
Cambridge Stratified
Swirl Burner Results 126
Figure 6.7: Modified Borghi diagram showing both the slot and swirl burner cases: A,
laminar flames; B, wrinkled flamelets; C, corrugated flamelets; D, thin reaction zones; E,
broken reaction zones. The slot burner condition is marked with a solid red dot, while
the swirl burner cases at z = 5mm (z = 10mm) [long record locations] are plotted with
magenta (cyan) [yellow] full circles, and are enclosed by a red (blue) [orange] ellipse.
C
am
bridge
Stratified
Sw
irlB
urner
R
esults
127
Table 6.1: Key turbulence parameters calculated at z = 5mm for the swirl burner cases.
Flame U u
′ I Ret Lt ηK τK νK Da Ka
(m/s) (m/s) (%) (−) (mm) (µm) (µs) (m/s) (−) (−)
SwB1 5.66 3.19 56 401 9.97 111 156 0.71 1.18 40
SwB2 7.06 3.67 52 496 9.97 95 122 0.78 1.44 51
SwB3 6.92 3.14 45 433 9.97 105 153 0.69 1.82 41
SwB5 5.71 3.16 55 397 9.97 112 158 0.71 1.98 25
SwB6 8.15 3.58 44 568 9.97 86 117 0.73 1.94 46
SwB7 6.35 2.74 43 424 9.97 107 177 0.60 2.78 26
SwB9 5.36 3.40 63 363 9.97 120 154 0.78 1.48 41
SwB10 6.07 3.87 64 525 9.97 91 113 0.81 1.49 62
SwB11 7.18 3.75 52 444 9.97 103 126 0.82 1.83 33
SwB13 6.17 3.33 54 433 9.97 105 144 0.73 2.12 30
SwB14 6.33 3.11 49 536 9.97 90 138 0.65 2.28 40
SwB15 5.28 2.84 54 371 9.97 118 182 0.65 2.54 22
C
am
bridge
Stratified
Sw
irlB
urner
R
esults
128
Table 6.2: Key turbulence parameters calculated at z = 10mm for the swirl burner cases.
Flame U u
′ I Ret Lt ηK τK νK Da Ka
(m/s) (m/s) (%) (−) (mm) (µm) (µs) (m/s) (−) (−)
SwB1 6.33 2.46 39 309 9.97 135 231 0.59 1.62 27
SwB2 8.23 2.73 33 369 9.97 118 190 0.62 1.58 33
SwB3 8.13 2.53 31 351 9.97 123 210 0.58 1.53 30
SwB5 6.38 2.68 42 334 9.97 128 204 0.63 2.71 19
SwB6 9.44 2.63 28 418 9.97 108 185 0.58 2.67 29
SwB7 7.82 2.18 28 338 9.97 126 249 0.51 3.36 18
SwB9 6.49 2.91 45 308 9.97 135 195 0.70 1.76 32
SwB10 6.83 3.20 47 432 9.97 105 150 0.70 1.71 46
SwB11 8.64 3.01 35 356 9.97 122 176 0.69 2.30 24
SwB13 8.19 2.68 33 348 9.97 124 199 0.62 2.66 22
SwB14 7.58 2.25 30 387 9.97 114 225 0.51 3.20 25
SwB15 6.83 2.28 33 298 9.97 139 253 0.55 3.19 16
C
am
bridge
Stratified
Sw
irlB
urner
R
esults
129
Table 6.3: Key turbulence parameters calculated at the intersection of the mixing layer and the mean flame brush for the
swirl burner cases.
Flame z U u
′ I Ret Lt ηK τK νK Da Ka
(mm) (m/s) (m/s) (%) (−) (mm) (µm) (µs) (m/s) (−) (−)
SwB1 30 9.15 2.19 24 332 9.97 128 250 0.51 1.63 30
SwB2 30 12.57 2.87 23 377 9.97 117 179 0.65 1.32 34
SwB3 30 15.43 3.65 24 541 9.97 89 117 0.76 0.96 57
SwB5 50 12.07 7.87 65 985 9.97 57 40 1.41 0.48 98
SwB6 40 13.21 4.47 34 557 9.97 87 95 0.92 0.98 44
SwB7 30 14.05 3.67 26 383 9.97 115 139 0.83 1.48 22
SwB9 50 12.46 7.58 61 762 9.97 69 48 1.44 0.45 123
SwB10 40 12.31 4.07 33 486 9.97 96 111 0.87 0.89 55
SwB11 30 14.55 3.66 25 417 9.97 108 133 0.81 0.99 30
SwB13 30 10.80 2.36 22 332 9.97 128 232 0.55 2.98 20
SwB14 30 10.95 2.67 24 327 9.97 130 206 0.63 2.70 19
SwB15 20 9.34 2.21 24 269 9.97 150 275 0.54 3.29 14
Cambridge Stratified
Swirl Burner Results 130
6.3 Instantaneous Flame Structure
Before beginning any in-depth analysis of the various quantities obtained directly or
derived from the multi-scalar line measurements, it is important to give at least a cursory
examination of sample instantaneous profiles of these scalars. This allows the general
behaviors exhibited by each operating condition to be shown, as well as giving the
reader a measure of confidence that the raw data used to calculate derived quantities
and conditional means further on in this chapter is sensible. In the interests of brevity,
given the volume of material to be covered in the current chapter, instantaneous data
presented will be limited to temperature, equivalence ratio (linearly bridged), and OH-
PLIF images as these form the basis of the majority of the analysis in the following
sections.
Figure 6.8 show instantaneous profiles of temperature and equivalence ratio in the
swirl burner cases, using data taken from shots at z = 30mm. These data were taken
Figure 6.8: Single-shot profiles of temperature (top row) and equivalence ratio (bottom
row) at z = 30mm downstream of the burner exit for swirl burner cases.
Cambridge Stratified
Swirl Burner Results 131
in initial surveys of the flames detailed in Table 3.3 of Chapter 3, the results of which
are presented later on in Section 6.1. These records were relatively short (300 shots at
each location, with an additional 1 200 shots at location where the mean flame front is
located), at 103 µm resolution, and were taken to establish the locations at which the
mixing layer intersected the flame brush. These locations are referred to throughout
the present chapter as the long record locations, as larger datasets were subsequently
taken at these locations (5 000 shots for premixed cases, 30 000 shots for stratified), using
wavelet filtering and oversampling to give 20 µm resolution.
The format of Figure 6.8 merits brief discussion, as it is used extensively from Sec-
tion 6.7 onwards. The data are presented such that the lean cases (SwB1 through
SwB11) are grouped by flow condition. Hence the first column shows the non-swirling
cases (SwB1, SwB5 and SwB9), the second the moderately swirling cases (SwB2,
SwB6, SwB10), and the third the highly swirling cases (SwB3, SwB7 and SwB11).
The stoichiometric cases (SwB13, SwB14 and SwB15) are grouped in the fourth col-
umn. This format allows the effect of stratification at each flow condition to be assessed
visually with the minimum of difficulty, as well as highlighting the effects of swirl on the
stoichiometric cases, which do not have stratified equivalents.
The instantaneous profiles show some interesting behavior, such as the raised values
of equivalence ratio near to the centerline of the burner in the premixed cases. The
elevated values result in mild gradients in equivalence ratio along the line measurement
axis, ∇xΦa, as seen in Table 6.4. This curious result is explained in the discussion of the
Favre-averaged results later on in Section 6.6.
The profile of equivalence ratio for SwB9 demonstrates the necessity of taking data
at the intersection of the mixing layer and the flame brush, as the flame in this highly
a∇xΦ is the two-dimensional projection of the true three-dimensional equivalence ratio gradient
projected onto the line measurement axis.
Cambridge Stratified
Swirl Burner Results 132
Table 6.4: Two-dimensional equivalence ratio gradients from instantaneous profiles
shown in Figure 6.8.
SwB 1 2 3 5 6 7 9 10 11 13 14 15
∇xΦ
(
mm−1
)
73 39 26 159 76 205 −1 340 282 98 67 66
stratified case stabilizes in the rich reactants from the inner annulus, which are not yet
well mixed with the leaner reactants from the outer annulus. The equivalence ratio pro-
files in those stratified cases where this condition has been fulfilled (SwB10, SwB11)
demonstrate large degrees of fluctuation in Φ. This highlights the importance of con-
ditioning on local rather than on mean or global equivalence ratios when considering
scalar data later on in this chapter.
The temperature valley seen in the SwB11 profile in the third column shows a case
where a pocket of lean mixture has penetrated richer flow, causing the flame to stabilize
at the interface between the two. This illustrates the need for image processing of the
OH-PLIF images to be able to cope robustly with the presence of pockets of unburned
mixture in the flame as well as islands or peninsulas of flame.
Figure 6.9 shows profiles of temperature and equivalence ratio in the moderately
stratified, highly swirling SwB730 case, using both the 103 µm resolution super-binned
data and the 20 µm resolution wavelet filtered data. The data are plotted with markers
at each point to demonstrate the increase in fidelity achieved in the wavelet filtered data.
It is clear that the wavelet filtered data is substantially smoother than the super-binned
data, as well as higher resolution. The implication of this is that gradients obtained
from the wavelet filtered data are significantly smoother on a shot to shot basis than the
super-binned data. All data at the intersection of the mixing layer with the flame brush
(the long record locations mentioned previously) are recorded and processed using the
wavelet filtering.
Cambridge Stratified
Swirl Burner Results 133
Figure 6.9: Single-shot profiles of temperature (top) and equivalence ratio (bottom) at
z = 30mm downstream of the burner exit for SwB730 at both super-binned resolution
(103 µm/pixel) and wavelet filtered resolution (20 µm/pixel). The flame brush is mapped
from the temperature to the equivalence ratio profiles using gray dashed lines.
Sample OH-PLIF images for SwB130, SwB630, SwB1130 and SwB1330 are shown in
Figure 6.10, along with the continuous curvature along their centerline. The resolution
of these images is 48 µm/pixel, which is roughly three times finer than in the slot burner
data. These images correspond to the profiles plotted in Figure 6.8; for brevity only four
conditions are shown. As in the slot burner data, the continuous curvature results are
erratic in both the low (reactants) and high (products) regions of OH due to the effect of
small gradients on the denominator of Equation 4.4 (see Section 4.1.4.2 of Chapter 4).
The gray regions in Figure 6.10, which mark the instantaneous flame brush, indicate
that some caution should be taken when conditioning data on curvature, as there is
some disparity between the location of the thermal ramp and the OH reaction zone.
Cambridge Stratified
Swirl Burner Results 134
Figure 6.10: Single-shot OH-PLIF images (top row) for SwB1, SwB6, SwB11 and
SwB13, corresponding to the instantaneous profiles shown in Figure 6.8. Continuous
curvature along the line measurement axis (shown by solid white lines in the top row) is
shown in the bottom row. Regions corresponding to the instantaneous flame brush are
marked in gray.
6.4 Flame Structure and Selection of Long Record Lo-
cations
In light of the sparsity of data in the slot burner after conditioning on local equivalence
ratio, it was decided that substantially larger datasets would be recorded in the swirl
burner cases to allow for multiple conditioning of data without reducing the data by too
great an amount. It was not feasible to record large datasets at multiple axial locations
in each flame condition due to the time constraints on the use of facilities at Sandia
National Laboratories. The intersection of the mixing layer and the mean flame brush
was deemed to be the most sensible location to record the large datasets, as the mean
equivalence ratio at these locations would be comparable across the relevant cases (i.e.
Φ ≈ 0.75 for the lean cases, Φ ≈ 1 for the stoichiometric cases). This minimizes data
reduction when conditioning on local equivalence ratio is performed. The locations of
Cambridge Stratified
Swirl Burner Results 135
the intersection of the mixing layer and the mean flame brush are referred to throughout
the remainder of the present work as the long record locations. In order to identify these
long record locations, it was necessary to determine the radial location of the center
of the flame brush for various downstream distances (thermal structure), and also the
mean equivalence ratio at these locations (compositional structure).
6.4.1 Thermal Structure
The center of the flame brush was taken to be the location of peak variation of the
Favre-averaged temperature, T˜ , and was obtained from the short recordb temperature
and density measurements detailed in Chapter 3. The resulting thermal flame structure
for each case is shown in Figure 6.11. The format is as follows: swirl increases from left
to right, moving from non-swirling cases (left column) through moderately swirling cases
(middle column) to highly swirling cases (right column); stratification increases down
the first three rows from lean premixed cases (top row) through moderately stratified
cases (2nd row) to highly stratified cases (3rd row), with the stoichiometric premixed
cases lying in the bottom row. This format is used extensively throughout the present
work. The full width half maximum (FWHM) locations obtained from the T ′′ profiles
are used to quantify the width of the flame brush at each location.
These plots shed more light on the flame structure than the mean and instantaneous
shots shown in Section 6.1. In the non-swirling cases, the flame brush angle increases
with the addition of stratification (from 5◦ to 9◦), though the difference between the two
levels of stratification is minor (∼ 1◦). The addition of swirl reduces the change in flame
angle between the premixed and stratified cases to the point that it is negligible (less
bThe short records consist of 300 to 1 500 shots of data, which were taken to allow complete radial
profiles through the flame to be recorded quickly at multiple axial locations. Further details are provided
in Figure 3.6 of Chapter 3.
Cambridge Stratified
Swirl Burner Results 136
Figure 6.11: Flame brushes in the swirl burner cases. Center of flame brush as defined
by peak Favre averaged temperature variation denoted by open circular markers, ◦ ,
with the shaded region showing the associated FWHM.
than 1◦).
As swirl is added, the flame brushes shift from being slightly concave towards the
reactants in the non-swirling cases, regardless of the fuel/oxidizer composition, straighten
out (moderately swirling cases) and eventually become convex towards the reactants
(highly swirling cases). This explains the visual differences seen in the flame surveys.
Considering only the lean premixed and stratified cases, the mean flame angle increases
to ∼ 12◦ for the moderately swirling condition, and increases to ∼ 20◦ for high swirling.
The corresponding increases in the stoichiometric premixed cases are to ∼ 17◦ and ∼ 26◦
respectively.
The width of the flame brush also increases regularly with increasing axial distance,
Cambridge Stratified
Swirl Burner Results 137
in agreement with the broadening of the turbulent mixing layers seen in Figure 6.4.
In the non-swirling cases the width is influenced by stratification, with the moderately
and highly stratified cases being on average 13% and 4% greater than the premixed
SwB1 case respectively. However the standard deviation of these differences is such
that it is difficult to state conclusively that the differences seen between the two levels
of stratification are significant; the most salient conclusion from the data is simply that
stratification results in a thicker flame brush in non-swirling flow conditions. The effect
of stratification on the swirling cases is the opposite to that seen in the non-swirling cases;
the addition of stratification results in a reduction in FWHM of ∼ 5% on average, with
little difference between the moderate and high levels of stratification.
When the composition is held constant and the degree of swirl is varied the flame
brush is significantly enlarged. Moving from the non-swirling to moderately swirling
cases, increases in FWHM of 17% to 34% are seen; the corresponding increases between
the non-swirling and highly swirling cases are 74% to 105%. Again, this behavior tallies
with the velocity fluctuations seen in Figure 6.4.
6.4.2 Compositional Structure
The compositional structure of the flames surveyed is shown in Figure 6.12, using the
same layout as the thermal structure plots shown in Figure 6.11. Note that the quantity
plotted is the raw unprocessed equivalence ratio, φ, and not the linearly bridged equiv-
alent, Φ, as the latter form was not used in the determination of the intersection of the
mixing layer with the mean flame brush.
The mean equivalence ratio at the center of the flame brush, defined as for Fig-
ure 6.11, decreases with increasing axial distance in all cases. This is due to a combina-
tion of the flame stabilizing at wider radial positions further downstream of the exit due
Cambridge Stratified
Swirl Burner Results 138
Figure 6.12: Compositional structure of the flames surveyed in the swirl burner. The
equivalence ratio at the center of flame brush is denoted by open circular markers, ◦ ,
with the shaded region showing the equivalence ratio values at the associated FWHM
points. The nominal stoichiometry is marked by - - - -. Equivalence ratio data is not
linear bridged.
to decreasing axial velocity and the increasing width of the turbulent mixing layers. The
premixed mean equivalence ratio also decreases with axial distance, albeit significantly
less; this is attributed to the dilution of the fuel/oxidizer mix with co-flow air, which
becomes more significant as z increases due to the growing mixing layer between the
outer- and co-flow streams.
The addition of swirl reduces the mean equivalence ratio as a function of downstream
distance. The effect is relatively slight for the lean premixed case, but is substantial in
the stratified and stoichiometric cases. The range of mean equivalence ratio encompassed
Cambridge Stratified
Swirl Burner Results 139
by the FWHM locations at each downstream position show moderate increases with both
the degree of stratification and swirl.
6.4.3 Long Record Locations
The nominal mean equivalence ratio φn was used in conjunction with plots of the com-
positional structure to determine the radial and axial locations at which to take the long
record datasets. The values chosen are listed in Table 6.5. The radial locations are the
positions of the peak Favre-averaged temperature variance as in Figure 6.11. The axial
locations were selected to ensure the mean equivalence ratio at the center of the flame
brush was as close as possible to the nominal value while ensuring that a significant
range of equivalence ratio values were experienced within the FWHM window.
Note that in certain cases, such as SwB11, it appears from Figure 6.12 that the
location listed in Table 6.5 is suboptimal. This is due to slight changes in equivalence
ratio resulting from modifications to the processing of the Rayleigh/Raman/CO-LIF line
measurement data, altering the ideal axial locations relative to those determined from
the initial analysis of the short record data. However the differences are still relatively
small, with the mean equivalence ratio being 12% greater than the nominal value at
worst, and on average being within 6%.
It is worth noting that the spread of Reynolds-averaged equivalence ratio between
the FWHM positions, ∆φ, is generally an order of magnitude higher in the stratified
cases than in the premixed cases, and that the FWHM flame brush thickness, ∆T ,
is small enough that the line measurement window (∼ 6mm) should encompass most
of the temperature variance in all cases. Values for the mean equivalence ratio and
corresponding FWHM are also given in the linear bridged form in Table 6.5 for reference,
though they were not used in the determination of the long record locations.
Cambridge Stratified
Swirl Burner Results 140
Table 6.5: Radial and axial locations of the intersection of the mixing layer and the
mean flame brush (long record locations) in the swirl burner, with corresponding FWHM
flame brush thickness, ∆T , Reynolds-averaged equivalence ratio, φ, FWHM range of
Reynolds-averaged equivalence ratio, ∆φ. Nominal values of equivalence ratio based on
the fuel/air flows are φn = 0.75 for the lean cases and φn = 1 for the stoichiometric cases.
Corresponding values using linear bridged phi, Φ, are shown in parentheses for reference.
Flame z r ∆T φ (Φ) ∆φ (∆Φ)
(mm) (mm) (mm) (−) (−)
SwB1 30 9.1 2.8 0.77 (0.78) 0.04 (0.04)
SwB2 30 13.3 4.0 0.76 (0.76) 0.01 (0.01)
SwB3 30 18.9 5.4 0.77 (0.77) 0.10 (0.10)
SwB5 50 13.6 5.7 0.78 (0.79) 0.35 (0.35)
SwB6 40 16.1 5.3 0.80 (0.81) 0.36 (0.36)
SwB7 30 19.0 5.4 0.83 (0.85) 0.41 (0.41)
SwB9 50 12.6 5.3 0.82 (0.82) 0.41 (0.42)
SwB10 40 14.9 4.9 0.84 (0.84) 0.44 (0.45)
SwB11 30 19.5 5.3 0.81 (0.83) 0.50 (0.51)
SwB13 30 10.9 3.4 1.03 (1.03) 0.03 (0.04)
SwB14 30 13.8 3.5 1.04 (1.04) 0.04 (0.04)
SwB15 20 13.1 3.2 1.03 (1.05) 0.02 (0.01)
6.5 Extent of Stratification
The Favre-averaged profiles of equivalence ratio shown in Section 6.6 demonstrate that
significant degrees of stratification are achieved within the flame brush in the nominally
stratified cases at the long record locations. However they also reveal non-negligible
spatial gradients of equivalence ratio in the nominally premixed cases, due mainly to the
effect of the recirculation zone but also to the measurements of Φ which are known to
be biased slightly high in the products.
In order to quantify the extent of stratification at the long record locations, this brief
section presents and discusses probability density functions and basic statistics for the
cases surveyed at the long record locations. Pdfs of equivalence ratio gradients derived
Cambridge Stratified
Swirl Burner Results 141
Figure 6.13: Probability density functions of two-dimensional equivalence ratio gradi-
ents at the long record locations in the swirl burner. Pdfs of gradients obtained using the
raw equivalence ratio data, ∇xφ, are shown in the top row, while pdfs generated using
linear bridged equivalence ratio gradients, ∇xΦ, are shown in the bottom row.
from both raw and linearly bridged equivalence ratio data are presented in Figure 6.13.
A word of caution is advised here; the gradients presented are two-dimensional projec-
tions of the true equivalence ratio gradient. It is not currently feasible to measure the
instantaneous orientation of the equivalence ratio field simultaneous with the other data
taking, and hence only the two-dimensional analogue ∇xΦ along the line measurement
axis can be presented.
A cursory examination of the top row of this figure reveals the issue with using the
raw equivalence ratio data to determine the level of stratification, as even the premixed
cases exhibit large positive and negative gradients of φ due to the effects of preferen-
tial differential diffusion detailed previously in Section 4.2.1.1 of Chapter 4. When the
equivalence ratio is linearly bridged to give Φ, more physically sensible results are ob-
Cambridge Stratified
Swirl Burner Results 142
Table 6.6: Statistics for two-dimensional equivalence ratio gradients in the swirl burner
at long record locations. Equivalence ratio data is linearly bridged.
Flame
z |∇xΦ| ∇xΦ γ1 γ2
(mm)
(
m−1
) (
m−1
)
(−) (−)
SwB1 30 24 14 0.85 1.26
SwB2 30 27 16 1.81 27.10
SwB3 30 50 19 4.40 41.12
SwB5 50 116 92 1.74 6.26
SwB6 40 126 96 1.73 6.94
SwB7 30 160 125 2.25 23.09
SwB9 50 152 118 1.58 5.08
SwB10 40 171 129 1.58 5.38
SwB11 30 212 169 1.81 11.42
SwB13 30 43 22 0.51 2.49
SwB14 30 39 17 1.44 9.61
SwB15 20 46 27 0.81 2.89
tained (bottom row of Figure 6.13), as the absolute mean gradients are near-zero for the
premixed cases.
The main point to note is that the gradient distributions appear similar for both
nominal degrees of stratification. This is perhaps a surprising result, given the nominal
stoichiometries of the richer inner flow and the lean outer flow are varied symmetrically
about Φg = 0.75 while the respective flow rates are kept constant. However an examina-
tion of Table 6.6, which summarizes the main statistical moments for ∇xΦ, reveals that
both the mean and absolute mean gradients are substantially increased moving from the
moderate to high stratification levels (28% to 35%).
However, these changes are small in comparison to the increases experienced relative
to the premixed cases (222% to 535%). As such analyses of any given quantity of inter-
est at the two stratification levels are unlikely to exhibit large differences in comparison
Cambridge Stratified
Swirl Burner Results 143
to those for the premixed equivalent. It is worth noting that the absolute mean gradient,
|∇xΦ|, for the moderate stratification level is similar to that in the most stratified slot
burner case (|∇xΦ| ∼ 123m−1 in fs630).
The level of swirl also plays a role as it increases the gradients seen in the stratified
cases by between 9% to 39%. Though these changes in gradient are small relative to
those moving from the premixed cases to the stratified ones, they should still be borne
in mind when considering figures and discussion in the subsequent sections.
Note that the mean and RMS gradients for the premixed linear bridged equivalence
ratio data, while small, are non-negligible and positive. This is also seen in the pdfs
in the bottom row of Figure 6.13, which deviate from the expected zero-centered delta
functions. These small positive gradients are caused by the elevated levels of Φ seen
towards the center of the flow field due to the effects of the recirculation zone, and are
not an artifact of the linear bridging function.
To conclude, significant spatial gradients of equivalence ratio are observed in the
stratified swirl burner cases. The change in RMS gradient between the two stratification
levels is small relative to the change from the premixed cases, but is large enough to
justify examining data from both. The premixed data has small positive gradients in
equivalence ratio on average due to the elevated Φ in the center of the flow field.
6.6 Favre-Averaged Flame Structure
Radial profiles of Favre-averaged temperature, equivalence ratio and major species at
z = 10mm and at the intersection of the mixing layer and the mean flame brush (the long
record locations identified in Section 6.4.3) are shown in Figure 6.14 through Figure 6.21.
The corresponding fluctuations are plotted in Figure 6.15. Plots at z = 10mm as well as
the farther downstream long record locations give a locally resolved picture of the spatial
Cambridge Stratified
Swirl Burner Results 144
evolution of the measured quantities in the flame. Data are given for radial locations
from 0mm to 25mm as in the velocity plots in Section 6.2; the behavior of the measured
scalars in the flames surveyed is assumed to be radially symmetric.
6.6.1 Non-Swirling Lean Cases
Results from the lean non-swirling cases (SwB1, SwB5, SwB9) are given in Figure 6.14
and Figure 6.15, demonstrating structural differences brought about due to stratification
of the inlet flows. The thermal ramps in T˜ are almost coincident in the z = 10mm cases,
despite the substantial differences in Φ˜ within the flame brush. This indicates that the
effects of burning through higher equivalence ratio are insubstantial at this proximity to
the burner exit. As the flame reaches the intersection of the mixing layer and the mean
flame brush, the stratified flame brushes have moved radially outwards substantially
due to the combined effects of higher flame speed and gaseous expansion inside the
flame resulting from the higher levels of Φ˜ experienced. At both locations the stratified
cases achieve higher temperature in the equilibrium zone, as expected for the higher
equivalence ratios.
Interestingly the flame position in the highly stratified SwB950 case stabilizes inside
that for the SwB550 case at the long record locations, even though both are measured
at the same downstream distance (z = 50mm) and SwB9 has a higher peak equivalence
ratio. One plausible explanation for this discrepancy is provided by the equivalence ratio
burned through by the two cases farther upstream, near the burner exit. Examining the
profiles of Φ˜ at z = 10mm reveals that the flame brush in the SwB510 spans the range
1 to 1.1 while the more stratified SwB910 spans 1.1 to 1.2; the mean laminar burning
velocity in the former is approximately 5% greater than in the latter. While differences
will be observed due to turbulence, the effects should be commensurate due to the similar
Cambridge Stratified
Swirl Burner Results 145
Figure 6.14: Radial profiles of Favre-averaged measurements for the lean non-swirling
cases in the swirl burner at z = 10mm (bottom halves) and at the long record locations
(top halves). The premixed SwB1 case is shown by , the moderately stratified SwB5
case by , and the highly stratified SwB9 case by . Locations corresponding
to FWHM in T ′′ are plotted as open circles of the appropriate color. Favre-averaged
temperature is in K.
Cambridge Stratified
Swirl Burner Results 146
Figure 6.15: Radial profiles of Favre-averaged fluctuations for the lean non-swirling
cases in the swirl burner at z = 10mm (bottom halves) and at the long record locations
(top halves). Symbols as in Figure 6.14.
Cambridge Stratified
Swirl Burner Results 147
turbulence levels experienced by both cases (both have non-swirling flow patterns) and
hence the mean equivalence ratios may partially account for the flame brush locations
for SwB550 and SwB950 at the long record locations.
The plots of Φ˜ show that the central recirculation zones influence the hydrogen-
carbon-oxygen balance significantly, resulting in elevated equivalence ratio levels in these
regions. The shear layer between the recirculation zones and the inner annulus flow
results in a mixing layer between the elevated and nominal inner annulus equivalence
ratios, which generates significant equivalence ratio gradients in the flame brushes for all
three cases at z = 10mm. This is true even in the premixed SwB130 case, despite the
inner and outer annulus fuel/air streams being at a constant nominal stoichiometry. The
elevated equivalence ratios are attributed to the effect of the central recirculation zone
on the hydrogen-carbon balance near the burner exit. This behavior is examined in more
detail in a forthcoming (at the time of writing) publication by Barlow et al [72]. The
Φ′′ profiles demonstrate that the flame brushes in the stratified cases do not intersect
the mixing layers between the inner- and outer-flows at this location, whereas this is the
case at the long record location (by definition).
The Favre-averaged profiles of CO2, O2 and H2O behave similarly to T˜ (albeit mir-
rored in the case of O2), as is expected. Some notable behavior is observed in these
species. It is clear at both z = 10mm and the long record locations that for the strati-
fied cases all oxygen is consumed in reactions in the equilibrium zone, in marked contrast
to the behavior in the premixed case. This is attributed to the combination of higher T˜
and Φ˜; the behavior of Y˜O2 exhibited by all three cases is very similar within the actual
flame brush at the long record locations, where T˜ and Φ˜ are much the same for SwB1,
SwB5 and SwB9.
The peak values of Y˜CO2 attained in the premixed case vary significantly relative
to those in the stratified cases moving from the upstream to the long record locations.
Cambridge Stratified
Swirl Burner Results 148
Near the burner exit, the premixed value lies between the moderately (higher) and highly
(lower) stratified values. Looking further downstream, the difference between the two
stratified cases remains consistent but the premixed Y˜CO2 is much closer to the SwB9
value.
There is a sharp ramp in the level of CO through the stratified flame brushes at
z = 10mm, with the peak level in SwB510 (SwB910) being 202% (323%) higher than
in the premixed SwB110. This decreases rapidly in the premixed case, and declines at
a more gradual rate in the stratified cases. Farther downstream at long record locations
similar values of Y˜CO are observed within the flame brush for all cases, at much lower
magnitudes than the stratified cases at z = 10mm. The profile for SwB130 is similar
to that at z = 10mm, though the peak is smeared out. In contrast, the moderately
stratified SwB550 shows a gentle increase towards the centerline of the burner on the
product side of the flame brush, while SwB950 increases substantially in the post-flame
region. The behavior seen in the stratified cases tracks the stoichiometry of the products.
Y˜H2 is seen to trend similarly to Y˜CO. The low levels of Y˜H2 in SwB1 are due to the
lean stoichiometry of the flow. The higher levels of H2 seen in the post-flame region
for the stratified cases may be attributed to the lack of additional O2 in these regions,
preventing the formation of additional H2O in addition to the effects of stoichiometry.
Y˜CH4 and Y˜N2 are relatively unremarkable, with the former following Φ˜ in the pre-
flame region before dropping to zero through the flame, and the latter being relatively
invariant in the flame brush.
6.6.2 Moderately Swirling Lean Cases
Favre-averaged and fluctuating components of temperature, equivalence ratio and major
species are plotted for SwB2, SwB6 and SwB10 in Figure 6.16 and Figure 6.17. The
Cambridge Stratified
Swirl Burner Results 149
Figure 6.16: Radial profiles of Favre-averaged measurements for the lean moderately
swirling cases in the swirl burner at z = 10mm (bottom halves) and at the long record
locations (top halves). Symbols as in Figure 6.14.
Cambridge Stratified
Swirl Burner Results 150
Figure 6.17: Radial profiles of Favre-averaged fluctuations for the lean moderately
swirling cases in the swirl burner at z = 10mm (bottom halves) and at the long record
locations (top halves). Symbols as in Figure 6.14.
Cambridge Stratified
Swirl Burner Results 151
addition of moderate swirl to the lean non-swirling cases has little effect on the shape or
magnitude of the profiles of the averaged quantities. The most notable change is that
both the average and fluctuating profiles are shifted radially outwards, as expected from
the thermal flame structure shown in Figure 6.11. The profiles of the fluctuations are
also similar to those seen in the non-swirling cases, though shifted radially outwards,
with slightly elevated levels at the z = 10mm location for most species.
Outside of this, some slight differences are observed in the profiles of Φ˜, Y˜O2 , and
Y˜CH4 for the premixed SwB2 case. The higher degree of mixing between the recirculation
zone and the inner annulus flow eliminates the Φ˜ ramp seen between these two regions
at z = 10mm by the time the flow reaches the intersection of the mixing layer with the
mean flame brush (long record locations). This gives a much flatter Φ˜ profile across the
flame brush of SwB230 than was seen in SwB130 at the same axial location (z = 30mm).
The post-flame region of the Y˜O2 profile at the long record location for the premixed
SwB230 is elevated by 25% compared to the non-swirling SwB130 case. The reasons
for this relatively large change are unclear as alterations of a similar magnitude are not
seen in any single other species; it is assumed that the variation is balanced by slight
alterations in all oxygen-based reactions, rather than any specific mechanism.
Lastly, the Favre-averaged CH4 profile at the downstream location is substantially
smoothed out by the addition of swirl, with the plateau evident in the SwB130 case
being absent for SwB230.
6.6.3 Highly Swirling Lean Cases
The behavior exhibited by the Favre-averaged quantities in the highly swirling lean
cases (SwB3, SwB7, SwB11) are markedly different to those seen in the non- and
moderately-swirling cases, as shown in Figure 6.18 and Figure 6.19. These differences
Cambridge Stratified
Swirl Burner Results 152
Figure 6.18: Radial profiles of Favre-averaged measurements for the lean highly swirling
cases in the swirl burner at z = 10mm (bottom halves) and at the long record locations
(top halves). Symbols as in Figure 6.14.
Cambridge Stratified
Swirl Burner Results 153
Figure 6.19: Radial profiles of Favre-averaged fluctuations for the lean highly swirling
cases in the swirl burner at z = 10mm (bottom halves) and at the long record locations
(top halves). Symbols as in Figure 6.14.
Cambridge Stratified
Swirl Burner Results 154
are attributed to the entrainment of co-flow air into the recirculation zone, which does
not take place for the other flow fields.
The Favre-averaged profiles show dips in T˜ in the post-flame region at both z =
10mm and the long record locations, with the effect in the latter being more significant.
These changes are particularly pronounced for the stratified cases, which attain higher
peak T˜ due to the higher values of Φ˜. Similar dips are not seen for the non-swirling or
the moderately swirling lean cases in Figure 6.14 and Figure 6.16 respectively. It appears
that the recirculation zone for the highly swirling cases entrains co-flow air, whereas the
recirculation zones in the other cases consists solely of hot products. The oxygen levels
in the premixed SwB3 case are substantially (200%) raised in comparison to those in
SwB1, while the values in the stratified highly swirling cases show a minimum and then
steadily increase moving towards the centerline instead of bottoming out to zero as for
the other flow patterns. Combined with the zero levels of Y˜CH4 in the post-flame region,
this indicates that the entrained fluid is air from the co-flow and not fuel/oxidizer from
the pre-flame region.
The mean Φ˜ gradients seen at the z = 10mm location are slightly negative in the
premixed and stratified cases due to the reduced Φ˜ in the recirculation zone caused by
the entrainment of co-flow air described previously. Further downstream at the long
record locations the premixed Φ˜ shows a positive slope in the flame brush as the flame
is stabilizing in the shear layer between the outer annulus flow and the co-flow air. The
gradients in SwB7 and SwB11 are similar to those in the corresponding non-swirling
and moderately swirling cases.
Relative to the non-swirling cases, the production of Y˜H2 through the flame front
is enhanced for the premixed SwB3 and significantly attenuated for both SwB7 and
SwB11.
The behavior of Y˜CO is changed significantly relative to the previously examined flow
Cambridge Stratified
Swirl Burner Results 155
conditions by the addition of high swirl. The profiles all resemble the premixed behavior,
following an approximately Gaussian profile, with the result that the Y˜CO rapidly decays
to zero in the post flame region.
Y˜CO2 and Y˜H2O trend similarly to the profiles seen for the non-swirling and moderately
swirling cases, but with dips in the post-flame region which as with the plots of T˜ are
more pronounced for the stratified cases. The profiles of Y˜CH4 in the highly swirling
cases resemble those in the moderately swirling configuration.
The fluctuating components of the measured quantities behave similarly to the cases
associated with the other flow conditions, but with significant levels of fluctuation in the
post flame regions for T ′′, Φ′′, Y ′′O2 , Y
′′
CO2
and Y ′′H2O.
6.6.4 Stoichiometric Cases
The effects of the addition of swirl to a stoichiometric flame are shown in Figure 6.20
and Figure 6.21. The differences between SwB13, SwB14 and SwB15 are negligible at
the upstream z = 10mm location. The profiles of Φ˜ at this axial position are elevated
in the recirculation zone, indicating that there is no significant entrainment of air from
the co-flow the data shown.
Looking at the long record profiles (z = 20mm for SwB15, z = 30mm otherwise), the
behavior exhibited is generally very similar, with the major differences being the radial
shift outwards associated with increasing swirl. However, some interesting deviations are
seen in the highly swirling SwB15 case. Firstly, the T˜ profile shows a gradual decline
in the post-flame region, akin to that seen in the highly swirling lean premixed SwB3
case in Section 6.6.3. A similar trend is observed in Φ˜, indicating that there is some
entrainment of air from the co-flow at this point. Oddly the levels of Y˜O2 in the SwB15
post-flame region are only slightly elevated, in contrast to the behavior seen in SwB3.
Cambridge Stratified
Swirl Burner Results 156
Figure 6.20: Radial profiles of Favre-averaged measurements for the stoichiometric
cases in the swirl burner at z = 10mm (bottom halves) and at the long record locations
(top halves). Symbols as in Figure 6.14.
Cambridge Stratified
Swirl Burner Results 157
Figure 6.21: Radial profiles of Favre-averaged fluctuations for the stoichiometric cases
in the swirl burner at z = 10mm (bottom halves) and at the long record locations (top
halves). Symbols as in Figure 6.14.
Cambridge Stratified
Swirl Burner Results 158
Both SwB1330 and SwB1430 stabilize at a flat near-stoichiometric Φ˜, with low levels
of fluctuation. The flame brush in the highly swirling SwB1520 stabilizes in the gently
sloping Φ˜ region generated by the shear layer between the stoichiometric flows and the
co-flow air. As a result the Φ′′ is significantly higher for this highly swirling case than
for SwB1330 or SwB1430. Stabilization of the flame in the mixing layer also explains
the attenuation of the Y˜CH4 and Y˜N2 profiles seen for the highly swirling case at the long
record location.
The values of Y˜CO plateau in the post-flame region for both the non-swirling and
moderately swirling cases at the long record location. In contrast Y˜CO in the highly
swirling case tapers to near zero after peaking on the product side of the flame brush.
Similar behavior is also seen in the profiles of Y˜H2 , though rather than tapering to zero
the SwB1520 case decays to approximately half the value of SwB1330 or SwB1430.
The Favre-averaged fluctuations are very similar for these three cases, with the ex-
ception of those for Φ′′ and Y ′′N2 . These discrepancies are explained by the reasons given
in the discussion of the averaged quantities for the differences observed there.
6.7 Influence of Stratification on Species Evolution
Section 6.6 highlighted significant differences in the behavior of the mass fractions of
certain species when considering Favre averages and fluctuations. The evolution of the
major species involved in combustion reactions is intrinsically temperature dependent.
This section examines the trends exhibited by the various species mass fractions in
temperature space, with the intent of identifying the influence of stratification. First, in
Section 6.7.1, unconditioned data are used to investigate the mean behavior of the key
combustion species in the swirl burner. These results are compared with laminar flame
calculations at the local mean equivalence ratio to highlight differences between cases,
Cambridge Stratified
Swirl Burner Results 159
and also to demonstrate the ability of ensembles of laminar unstrained calculations to
capture the behavior of the turbulent flames surveyed. Data is then conditioned on
local equivalence ratio in Section 6.7.2 to facilitate a more quantitative assessment of
the influence of stratification and swirl on the thermal response of these species.
6.7.1 Unconditioned Results
The instantaneous data from the swirl burner is used to generate mean fits of T and
the scalar under consideration, at both the z = 10mm and the long record locations.
The data is not conditioned on equivalence ratio, and so there is a spread in the values
of local equivalence ratio. The range of Φ values are shown in Figure 6.12, and the
magnitude of the ranges in the long record locations are summarized in Table 6.5.
Data at z = 10mm is binned in temperature space in steps of 50K, while the long
record data is binned in steps of 20K. The bin sizes were empirically chosen to give
smooth mean fits in the unconditioned data, and differ due to the variation in the amount
of data available. In addition to determining the mean species mass fraction within
each temperature bin, the mean equivalence ratio is also calculated. The probability
distribution of Φ within each bin is used to determine the 10th and 90th percentiles
of equivalence ratio, which are taken as a measure of the minimum and maximum Φ
respectively. Laminar flame calculations corresponding to these Φ values are plotted for
comparison with the experimental data.
The experimental data sets are too large to plot all points in a scatter plot without
introducing a large degree of redundancy and obfuscation due to points overlapping each
other. To counteract this, 100 points were randomly selected from each temperature bin,
and only these are plotted in the scatter plots in this section. Note that the mean values
within each bin are derived using the full dataset. The points selected are recorded to
Cambridge Stratified
Swirl Burner Results 160
ensure the scatter plots show the same data points for each species. The scatter data is
also colored by the local equivalence ratio to give a qualitative impression of both the
composition and the degree of stratification. All data points below the lean flammability
limitc for laminar methane/air flames (Φ = 0.47) are plotted in black to highlight these
data.
The figures are arranged such that subplots in the left, middle and right columns
correspond to non-swirling, moderately swirling and highly swirl cases respectively. Sim-
ilarly the top, second and third rows of subplots show the lean premixed, moderately
stratified and highly stratified cases, while the stoichiometric cases are shown on the
bottom row. This format is used throughout the current section, though where data is
subject to conditioning (for example on local equivalence ratio) only data from the long
record locations are presented as the datasets at z = 10mm are insufficiently large to
produce satisfactory multiply conditioned results.
Figure 6.22 shows the evolution of YCO2 in the various swirl burner flames. The
uniformity of color in the scatter data for z = 10mm demonstrates that there is little
variation in equivalence ratio in any of the cases surveyed, regardless of the degree of
stratification. As mentioned in Section 6.6, this is due to the flame brush stabilizing at
this axial location such that the majority of it lies within the inner annulus flow, before
it has mixed to any large degree with the outer annulus flow. This is also shown by
the differences between the YCO2 values obtained from the laminar flame calculations;
in general the difference between values corresponding to the local mean, 10th and 90th
percentile Φ are negligible.
While the general trend observed in the mean fit to YCO2 at z = 10mm is similar to
that in the laminar flame calculations — showing a steady increase with temperature
cThe lean flammability limit is taken to be Φ = 0.47 based on the experimental findings of Shoshin
et al [90]. There is a degree of variation in the lean limit found, depending on the experimental
configuration used, but typically it has been found to be in the range 0.45 < Φ < 0.51 [90–93].
Cambridge Stratified
Swirl Burner Results 161
Figure 6.22: Plots of temperature against YCO2 for the swirl burner at both z = 10mm
(bottom halves) and long record (top halves) locations, colored by Φ, as shown in the
colorbar. Data below the lean flammability limit (Φ = 0.47) are plotted in black. Mean
fits are shown by solid blue lines. Laminar flame calculations are shown by gray horizontal
(value at local mean Φ) and vertical (range of maximum and minimum local Φ) lines.
Cambridge Stratified
Swirl Burner Results 162
before a sharp ramp near the beginning of the equilibrium zone — the magnitudes in the
experimental data are substantially higher than the laminar values. Looking across the
columns, no consistent trend with swirl is observed. Looking down the rows however, the
effect appears more pronounced in the stratified cases and in the stoichiometric cases.
This effect decreases with axial distance, as shown by the long record data which are
much closer to their calculated values, though still slightly elevated. The raised YCO2
at z = 10mm is attributed to preferential molecular transport, which is exacerbated by
the presence of the recirculation zone. This effect is investigated in detail by Barlow et
al [72] using data from a single annulus bluff-body burner of similar dimensions to the
swirl burner. They observed that this effect is highly dependent on the bulk velocity, Ub,
in the annulus; species mass fractions were in good agreement with laminar calculations
for Ub < 2.6, while similarly elevated YCO2 was seen for Ub = 7.7m/s (Ub = 7.5m/s
in the inner annulus of the swirl burner). They propose that the primary hydrogen-
containing species (H2 and H2O) are preferentially diffused ahead of carbon-containing
species (CO2 and CO) away from the products, and are subsequently carried away from
the flame flame front as the flow moves downstream. The recirculation zone results in
increased residence time for the hydrogen-depleted products, amplifying the elevated
CO2 levels. These findings will be referred back to in the analysis of relevant species
later on in this section.
It is worth noting that the behavior exhibited by both SwB510 and SwB1310 is
virtually identical (both are stabilized in streams with a nominal equivalence ratio of
Φn = 1). As both are subject to similar mean velocities (see Table 6.2) this indicates that
the increasingly raised YCO2 seen with increasing stratification in the lean cases is due
to the magnitude of the upstream equivalence ratio, and not the degree of stratification.
This dependence was not observed in [72] as the swirl burner data was taken exclusively
from the lean premixed SwB110 and SwB210 cases.
Cambridge Stratified
Swirl Burner Results 163
Further downstream, at the long record locations, the agreement between the ex-
perimental means and the laminar calculations is substantially better, with the com-
putational values underestimating the experimental data slightly but lying within the
bounds of the scatter data. The spread of values expected based on the 10th and 90th
percentiles of equivalence ratio are also in good agreement with the spread seen in the
stratified experimental data.
The preferential molecular transport detailed previously is also evident in the pro-
files of YCO, though the difference relative to comparable calculated laminar values is
significantly less. In general, with the exception of SwB310, the agreement between
the mean experimental YCO and the calculated values at the mean Φ is very good be-
low T = 1 500K for z = 10mm. Past this point the mean experimental values typically
undershoot the peak laminar YCO by up to 20%, though the SwB1410 shows good agree-
ment with the calculated values. In the premixed lean highly swirling SwB310 case this
undershoot is exhibited throughout the flame brush.
Interestingly in the highly stratified cases (third row down), very different behavior
is observed for the non- and moderate-swirl cases (first and second column from left)
than in the high swirl case (third column). The laminar values of YCO in the former
continue to rise in the equilibrium zone, whereas they dip in the latter. The scatter data
indicates that the equivalence ratio in SwB910 and SwB1010 is higher than in SwB1110,
which may account for this discrepancy.
The lower equivalence ratio values in the equilibrium regions of the highly swirling
lean cases (top three rows, third column) as seen qualitatively in Figure 6.23 and more
explicitly in the Favre averages in Figure 6.18 attenuates the magnitude of the mean
YCO for high temperatures, indicating the importance of conditioning the data on the
local Φ before drawing hard conclusions from the data.
Further downstream at the long record locations the agreement seen between the ex-
Cambridge Stratified
Swirl Burner Results 164
Figure 6.23: Plots of temperature against YCO for the swirl burner. Symbols and
format as in Figure 6.22.
Cambridge Stratified
Swirl Burner Results 165
perimental means and the corresponding laminar calculated values is excellent through-
out the entire temperature space. This indicates that the effect of the preferential
molecular transport, which was already lower than for CO2 at z = 10mm, is virtually
negligible for CO by the time the mixing layer intersects with the flame brush. Addition-
ally, the range of values spanned by the scatter data in the stratified cases is matched
almost exactly by the spread of the 10th and 90th percentile calculated values. It ap-
pears at this point that mean behavior of CO in the turbulent flame is well captured by
laminar flamelet calculations, regardless of the level of stratification or swirl.
The experimental YH2 data shown in Figure 6.24 is reasonably well modeled on the
mean by the laminar calculations, with the latter falling within the limits of the scatter
data in the majority of the temperature space of the cases surveyed.
The main differences seen at the upstream location across the various cases is that the
rate of production of H2 in the experimental data is less than expected from the laminar
values in the premixed zone up to T ∼ 600K. This is attributed to the preferential
transport of the H2 away from the reactants as detailed by Barlow et al [72]. This
relationship is then inverted in the reaction zone, with the experimental YH2 trending
above the anticipated values, before again dipping below them in the equilibrium zone.
SwB310 again provides an exception, with the measured data trending significantly
above the laminar calculated values for all T .
Considering the long record locations, the lean premixed cases (top row) are ob-
served to trend almost exactly in line with the laminar values. This is also true of the
stoichiometric premixed cases (bottom row), though to a lesser degree. The stratified
cases (middle rows) trend higher than the laminar values throughout temperature space.
The extent of this difference appears magnified by the stratification, being up to 66%
higher for the highly stratified cases compared to 33% higher for the moderately strat-
ified cases. The spread of values in the stratified cases is reasonably well captured by
Cambridge Stratified
Swirl Burner Results 166
Figure 6.24: Plots of temperature against YH2 for the swirl burner. Symbols and format
as in Figure 6.22.
Cambridge Stratified
Swirl Burner Results 167
Figure 6.25: Plots of temperature against YH2O for the swirl burner. Symbols and
format as in Figure 6.22.
Cambridge Stratified
Swirl Burner Results 168
Figure 6.26: Plots of temperature against YO2 for the swirl burner. Symbols and format
as in Figure 6.22.
Cambridge Stratified
Swirl Burner Results 169
the laminar calculations, though not to the same degree as for YCO.
Excellent agreement is seen between the laminar calculations and experimental means
for YH2O (Figure 6.25) and YO2 (Figure 6.26) at both z = 10mm and the long record
locations.
Figure 6.22 through Figure 6.26 indicate that in general the thermal evolution of the
key combustion species a short distance downstream of the burner exit is well captured
on the mean by laminar flame values at the mean local equivalence ratio. The agreement
seen is relatively insensitive to the degree of stratification or swirl.
6.7.2 Results Conditioned on Local Equivalence Ratio
The results observed in Section 6.7.1 pose the question as to whether the stratification in
the swirl burner has a noticeable influence on the relationship between temperature and
species. In order to better assess this issue it is necessary to condition the data on the
local equivalence ratio in order to insulate the results from the influence of composition.
The present section focuses solely on the long record location data as the datasets are
much larger than at z = 10mm, and thus the means and deviations obtained from the
conditioned data are more accurate than would be the case for the z = 10mm datasets.
Figure 6.27 shows mean fits for species data conditioned on the local equivalence ratio
such that Φ = 0.79 for the lean cases and Φ = 1 for the stoichiometric cases (±1%).
YCO2 shows negligible influence of stratification under non-swirling flow conditions. The
influence of stratification shows a slight swirl dependency, with both stratified cases
trending slightly below the corresponding premixed case. The effect of stratification on
YCO2 increases moving from the moderate to high swirl level. The addition of swirl has
no noticeable impact on the behavior of the premixed cases. In all cases the experimental
means are elevated relative to the equivalent laminar values through the majority of the
Cambridge Stratified
Swirl Burner Results 170
Figure 6.27: Plots of temperature against key combustion species for the swirl burner
at the long record locations. Data is conditioned on local equivalence ratio to be within
±1% of the nominal stoichiometry. Corresponding laminar flame calculations are shown
by solid black lines.
temperature range. The maximum differences are seen for the premixed cases, which are
up to 8% greater in the middle of the flame than the corresponding values from laminar
flame calculations.
Laminar flame calculations capture the behavior of the conditioned premixed SwB1
Cambridge Stratified
Swirl Burner Results 171
YCO data very well, but as swirl is introduced the production of carbon monoxide is
increased relative to the non-swirling case in the middle of the flame (∼ 14%). Inter-
estingly while both the premixed and moderately stratified lean cases peak at similar
magnitudes to the laminar calculations, the highly stratified cases show reduced peaks
(−12% for SwB9, −15% for SwB10) for the non-swirling and moderate swirl flows.
This effect is not as pronounced in the highly swirling SwB11 case. The stoichiometric
cases appear relatively insensitive to the degree of swirl, and are all relatively well mod-
eled by laminar calculations for Φ = 1, though the calculated peak is in excess of the
experimental means.
The hydrogen profiles in Figure 6.27 show the largest deviations from the correspond-
ing laminar values. The lean premixed cases are reasonably well captured by the laminar
calculations, but both levels of stratification exhibit markedly different behavior in the
reaction zone; whereas the calculated YH2 increases at a constant rate with increasing
temperature in this region, the stratified cases show an elevated and parabolic profile.
This is true regardless of the degree of swirl. A speculative explanation for this is that
the preferential transport of hydrogen away from the flame front near the burner exit
results in elevated levels of YH2 further downstream at the long record location. As the
long record locations are further downstream for the stratified cases than the premixed,
there may be a larger accumulation of YH2 resulting in the differences seen in the plots.
The stoichiometric cases trend much higher than the corresponding calculations, and
show no evidence of being influenced by swirl.
Excellent agreement is seen in YH2O and YO2 , both between the premixed and strati-
fied experimental means, and between the experimental means and laminar calculations
(all flow conditions). The conclusions taken from this are that the consumption of oxy-
gen and the production of water in the current burner are insensitive to the degree of
stratification or swirl, and hence may be accurately modeled using ensembles of laminar
Cambridge Stratified
Swirl Burner Results 172
flame calculations.
The main conclusions of this section are that on the mean the production and con-
sumption of key species is well captured by ensembles of laminar flame calculations,
particularly at the intersection of the mixing layer and the mean flame brush, despite
the obvious differences in turbulence characteristics and stratification levels between the
various cases. When conditioned on local equivalence ratio, stratification appears to
have negligible effect on the behavior of YO2 or YH2O, and only a minor effect on YCO
and YCO2 . The mass fractions of hydrogen appear to be enhanced significantly in the
stratified cases relative to the premixed; however, it is unclear as to whether this effect
is due to the spatial gradients of equivalence ratio in and of themselves or instead is an
artifact of preferential differential molecular transport of H2 away from the flame front
into the reactants near to the burner exit.
6.8 Curvature
Stratification has typically been found to broaden the curvature distributions of turbu-
lent methane/air flames, as detailed in Section 5.6 of Chapter 5. The mean of these
distributions also tends to shift towards zero as the stratification increases. A broad-
ening effect was observed in the slot burner, though the mean shifted away from zero.
The present section will investigate the effect of stratification on curvature in the more
turbulent swirl burner. The initial analysis will make use of both discrete and continuous
forms of curvature, κd and κc respectively. Subsequent analysis is based upon continuous
data only, as it can be multiply conditioned without becoming too sparse for sensible
conclusions to be drawn.
Based on the findings in the slot burner, which showed only minor differences in the
Cambridge Stratified
Swirl Burner Results 173
distributions of curvature for the two OH-PLIF planes (Figure 5.11), the data investi-
gated in this section is taken from the first plane only.
Figure 6.28 demonstrates the spatial evolution of curvature in the swirl burner cases.
Mean absolute discrete curvatured, |κd| is plotted against axial distance z using data
taken from the short records used to show thermal and compositional flame structure in
Section 6.4. The general trends exhibited are the same regardless of the composition or
degree of swirl; mean absolute curvature rises steeply near the burner exit before reach-
ing a plateau at |κd| ∼ 1.25mm−1, and decays gradually with increasing downstream
distance. In the initial region of quasi-linear increase, the curvature increases rapidly as
the annular jets at the burner exit interact with their surroundings and become more
wrinkled. Surface generation attains a maximal value before gradually decaying as both
velocities and turbulence levels decrease further downstream.
Figure 6.28: Relationship between mean absolute discrete curvature, |κd|, and axial
distance for the swirl burner cases. Data is taken from the short data records used in
Section 6.4, and is conditioned to remove outliers such that |κd| < 6mm−1.
The influence of stratification is not immediately apparent from these plots as they
are not conditioned on local equivalence ratio, and also are effectively premixed close to
dContinuous curvature is omitted from Figure 6.28 to improve the clarity of the figure, but similar
behavior is observed.
Cambridge Stratified
Swirl Burner Results 174
the burner exit as seen in Figure 6.14. However, considering the behavior of the stratified
systems as a whole, rather than data conditioned at a specific equivalence ratio gradient,
the effect of stratification appears mild, perhaps resulting in the mean absolute curvature
peak to be reached further upstream than in the corresponding premixed cases.
Some tentative conclusions about the influence of swirl may be drawn from this figure;
the addition of swirl results in additional surface generation (as would be expected due
to the increased turbulence), leading to increased values of mean absolute curvature.
This is best illustrated by the rightmost column of Figure 6.28, which shows consistent
increases in the mean absolute curvature of the stoichiometric cases with increasing swirl
for all distances.
Similar trends are observed scanning the other columns from left to right, though
this is less immediately clear. Considering the discrete mean absolute curvature values
at z = 30mm the addition of moderate swirl increases |κd| by 20% to 27.5% relative to
the non-swirling cases, while the high swirl level results in an increase of 40% to 70%.
Pdfs of curvature at the long record locations (where the mixing layer intersects the
flame brush) are shown in Figure 6.29, and basic statistics are summarized in Table 6.7.
The most noticeable aspect of the continuous curvature distributions is how little effect
stratification appears to have, regardless of whether flow is non-swirling or swirling.
This is in contrast to the discrete distributions, where stratification clearly results in
slightly broader distributions of curvature. The latter result is in line with the findings
of Anselmo-Filho et al [24] and Renou et al [21]. It is speculated that the insensitivity
of the continuous distributions to stratification is due to the fact that the results are
not conditioned on a specific progress variable value, whereas the discrete curvature is
located at a progress variable close to the peak gradient in OH in each instantaneous
shot.
Looking at the mean absolute values of discrete curvature listed in Table 6.7, it ap-
Cambridge Stratified
Swirl Burner Results 175
Figure 6.29: Local curvature probability density functions for continuous curvature κc
(top row) and discrete curvature κd (bottom row) from the long record locations in the
swirl burner cases.
pears that the addition of swirl increases |κd|, though the increase seen is not monotonic
in the stoichiometric case. However caution is advised in interpreting these curvature
results as the long record locations are at various axial distances from the burner exit;
thermal iso-surfaces are liable to exhibit different degrees of wrinkling and by extension
curvature depending on the downstream distance. A more considered analysis follows.
The lean premixed cases (all at z = 30mm) demonstrate sizable increases in mean
curvature modulus with increasing swirl, with SwB230 and SwB330 being 20% and
49% greater than the SwB130 case respectively. The intersection of the mixing layer
and the flame brush moves steadily towards the burner exit with increasing swirl in the
lean stratified cases, with the result that it is not possible to make a similar compari-
son conditioned on a single level of stratification. The stoichiometric non-swirling and
Cambridge Stratified
Swirl Burner Results 176
moderately swirling premixed cases are both measured at z = 30mm, and an increase
of 15% is seen with the addition of swirl, which is comparable to the increase seen be-
tween the corresponding lean cases. Note that the highly swirling stoichiometric case
SwB1520, which shows an increase in |κd| (15%), is located closer to the burner exit
(z = 20mm). Flames become more convoluted with downstream distance as the bulk
velocities decay and interaction with the environment increases, and hence the highly
swirling lean premixed case is expected to show a greater difference in mean absolute
curvature at z = 30mm.
Comparing SwB550 to SwB950, as well as SwB640 to SwB1040 and SwB330 to both
SwB730 and SwB1130, enables tentative conclusions to be drawn as to the effect of
stratification on mean absolute curvatures. Negligible differences are observed between
the two levels of stratification at the long record locations for either discrete or contin-
uous mean absolute values, regardless of flow type. This is to be expected given the
similar levels of stratification found between the cases. In the highly swirling lean cases,
increases of 9% relative to the premixed SwB130 are demonstrated for both stratifica-
tion levels. The marginal differences seen between the two stratification levels regardless
of the degree of swirl again indicates that the relative difference in spatial gradients
of equivalence ratio is insufficient to generate significant differences in curvature. The
results in the highly swirling case quantitatively show the broadening of the curvature
distribution with stratification, in line with the findings in the literature. The influence
of stratification (at the levels found in the current work) is significantly weaker than
that of swirl.
The continuous statistics are based on local curvature values throughout the flame
front, rather than simply at the location of the peak OH gradient (as is the case for the
discrete curvature). This will naturally have an effect on the values reported, so caution
is advised in the interpretation of the values shown in Table 6.7.
C
am
bridge
Stratified
Sw
irlB
urner
R
esults
177
Table 6.7: Statistics for discrete and continuous measures of local curvature in the swirl burner at long record locations.
Continuous data is taken from data within the thermal ramp across the flame front. Data in parentheses is taken from short
record locations to aid discussion of results.
Flame
z |κd| |κc| κd κc γ1,d γ1,c γ2,d γ2,c
(mm)
(
mm−1
) (
mm−1
) (
mm−1
) (
mm−1
)
(−) (−) (−) (−)
SwB1 30 0.74 1.08 0.02 0.02 −0.39 −0.56 2.68 7.56
SwB2 30 0.89 1.17 0.05 0.06 −0.50 −0.29 3.29 5.79
SwB3 30 1.10 1.45 0.10 −0.06 −0.36 −0.24 2.84 3.74
SwB5 50 (30) 1.09 (0.81) 1.45 (1.03) 0.07 0.03 −0.39 −0.10 2.25 4.03
SwB6 40 (30) 1.13 (0.99) 1.44 (0.92) 0.10 −0.01 −0.32 −0.10 2.01 3.92
SwB7 30 1.19 1.57 0.11 −0.13 −0.32 −0.19 2.05 3.19
SwB9 50 (30) 1.09 (0.70) 1.43 (0.80) 0.07 0.01 −0.39 −0.15 2.27 4.02
SwB10 40 (30) 1.12 (0.89) 1.44 (1.03) 0.08 0.01 −0.34 −0.14 2.06 3.83
SwB11 30 1.19 1.57 0.10 −0.02 −0.32 −0.06 2.07 3.12
SwB13 30 0.83 1.10 0.04 0.05 −0.37 −0.55 2.42 6.16
SwB14 30 0.96 1.20 0.07 −0.01 −0.38 −0.32 2.58 5.10
SwB15 20 (30) 0.95 (1.15) 1.21 (1.54) 0.06 0.04 −0.31 −0.37 3.07 5.09
Cambridge Stratified
Swirl Burner Results 178
The investigation of local curvature in the slot burner revealed that high values of
continuous curvature were more likely to be found outside of the intermediate region of
the flame (0.2 < c < 0.8). Figure 6.30 shows the bivariate pdf of progress variable c
and continuous curvature κc for the swirl burner cases at the long record locations. The
data is conditioned on local equivalence ratio to within ±1% of the nominal values —
Φ = 0.79 for lean cases, Φ = 1 for stoichiometric — to isolate any differences due to
stratification from the effects of local stoichiometry.
Figure 6.30: Bivariate pdfs of continuous curvature κc and progress variable c for
the swirl burner cases at the long record locations. κc = 0mm
−1 is plotted with a
dashed white line to highlight asymmetries in the distributions with respect to c. Data
is conditioned such that Φ = 0.79 and Φ = 1 for the lean and stoichiometric cases
respectively (±1%).
Cambridge Stratified
Swirl Burner Results 179
The reduction in data points due to this conditioning accounts for the relative rough-
ness of the probability contours. It is readily apparent from the bivariate pdfs that in
the intermediate regions the continuous curvature values exhibit similar behavior to the
discrete pdfs seen in Figure 6.29, with the distributions at any given progress variable
0.2 < c < 0.8 showing peaks at near-zero (negative) curvature and negligible probability
past |κc| = 2.5mm−1. Stratification broadens these distributions in all cases, though the
effect is most pronounced in the non-swirling flow cases.
The addition of swirl also typically has a broadening effect. Interestingly the high
swirl premixed lean case SwB330 appears to show a trend towards increasingly negative
values of continuous curvature moving towards the products, with a weak negative cor-
relation R2 = −0.22 (c < 0.7). An explanation for this behavior in light of its absence
both in the stratified and stoichiometric highly swirling cases is not immediately appar-
ent. Note that the lack of contours for high c values in the lean cases is due to the high
positive correlation between Φ and c in the stoichiometric cases resulting in a lack of
data for c > 0.9 following equivalence ratio conditioning.
In conclusion, it is clear that discrete mean absolute curvature is substantially in-
creased by the addition of swirl in both the lean and stoichiometric premixed cases.
Stratification also influences |κd|, though the increases seen relative to the premixed
cases are similar for both levels of stratification.
6.9 Progress Variable PDFs
PDFs of progress variable provide useful information as they allow the similarity between
the flames under investigation and an ideal laminar flame to be quickly assessed; the
latter is characterized by a double delta function, with peaks at c = 0 and c = 1. PDFs
of progress variable for the swirl burner cases are presented in Figure 6.31. It is clear
Cambridge Stratified
Swirl Burner Results 180
Figure 6.31: Probability density function of progress variable c for the swirl burner
cases at the long record locations. Nominal equivalence ratio for lean (Φ = 0.79) and
stoichiometric (Φ = 1) are shown by dashed white lines.
that the studied flames deviate substantially from the idealized behavior, as expected
from their turbulent nature.
The addition of stratification shifts the near-unity progress variable peak back to-
wards the zero peak. This effect is observed for all conditions; lean or stoichiometric,
non-swirling or swirling.
Interestingly the addition of swirl only reduces the near-unity peak of the premixed
lean cases when moving from non-swirling flow to moderate swirl; the shift to high swirl
has little further effect. The implication of this is that the addition of swirl increases
the instantaneous flame thickness of premixed flames but that above a certain level
the further addition of swirl fails to increase the thickness of the flame. One possible
explanation is that the production of small eddies — which may penetrate and thicken
the reaction zone — either plateaus at/below the moderate swirl level or does not increase
monotonically with swirl.
Note that none of the distributions shows a peak at c = 1, with only the SwB330
showing any significant percentage of flames attaining said value. This can be further
Cambridge Stratified
Swirl Burner Results 181
elucidated by looking at the bivariate pdf of progress variable and equivalence ratio,
shown in Figure 6.32. The probability density function for SwB330 shows a distinct
hook towards lower equivalence ratios as the progress variable approaches unity. This is
attributed to the effect of co-flow air being entrained by the recirculation zone, reducing
the local equivalence ratio, as seen in the Favre-averages in Figure 6.18. Although the
entrained air also reduces the local temperature, again evident in Figure 6.18, the balance
between that effect and the reduction of the local equivalence ratio is such that higher
values of local progress variable are attained.
Figure 6.32: Bivariate probability density function of progress variable c and equiv-
alence ratio Φ for the swirl burner cases at the long record locations. Vertical dashed
white lines are plotted at the mean lean and stoichiometric Φ values (0.79 and 1).
Cambridge Stratified
Swirl Burner Results 182
In contrast, the equivalence ratio tends towards higher values in the equilibrium zone
for the other cases. This is expected in the stratified cases as they are back-supported
(the spatial gradient of equivalence ratio is positive moving from reactants to products),
and hence the flames do not attain temperatures sufficient for the local progress variable
to reach unity. In the stoichiometric cases the equivalence ratio is slightly higher than
unity near the burner centerline, as detailed in Section 6.6.4, again accounting for the
failure to attain unity progress variable. It should also be noted that the local equilibrium
temperature Te is obtained from calculations which are unstrained and adiabatic. The
effect of strain in the experimental data will reduce the true value of Te, and while efforts
have been made to ensure the experiments are close to adiabatic, deviations from this
will account in part for the attenuated peak progress variable values seen in the data.
6.10 Influence of Stratification on Scalar Gradients
This section will consider the following quantities, all of which are highly dependent on
temperature gradients: surface density function, |∇c|; thermal scalar dissipation rate,
χc; turbulent flame thickness, δt; and flame surface density Σ. The general approach will
be first to consider the unconditioned data, to show the behavior on the mean, and then
to condition the data on local equivalence ratio to isolate the effects of stratification (i.e.
local equivalence ratio gradients) from those due to local stoichiometry.
6.10.1 Surface Density Function & Scalar Dissipation Rate
Surface density function, |∇c|, and scalar dissipation rate, χc, are very closely related
(χc ∝ |∇c|2) Scatter plots of surface density function, |∇c|, against progress variable
c are provided in Figure 6.33. The data is colored by the local equivalence ratio to
highlight any composition dependent effects. Points below the lean flammability limit
Cambridge Stratified
Swirl Burner Results 183
Figure 6.33: Plots of progress variable c against surface density function |∇c| for the
swirl burner at both z = 10mm (bottom halves) and long record (top halves) locations,
colored by Φ, as shown in the colorbar. Data below the lean flammability limit (Φ = 0.47)
are plotted in black. Mean fits are shown by solid blue lines. Laminar flame calculations
are shown by gray horizontal (value at local mean Φ) and vertical (range of maximum
and minimum local Φ) lines.
Cambridge Stratified
Swirl Burner Results 184
(Φ = 0.47) are plotted in black to illustrate any extension of the lean limit. Note that few
such points are visible even in the highly stratified case due to the fact that the scatter
data has been downsampled such that a hundred points are plotted within each progress
variable bin. The aim of this down-sampling is to reduce the degree of redundancy in
plotting and also to highlight the range of equivalence ratios experienced, and not to
provide an approximation to the bivariate pdf by virtue of point density.
The conditional mean fits are significantly lower than laminar unstrained values at
the corresponding nominal stoichiometries. Comparable turbulence-induced thickening
has been reported in the modeling literature by Sankaran et al [73] and more recently
by Moureau et al [74]. The magnitude of the disparities seen in the swirl burner results
appear to have a fairly strong equivalence ratio dependence; Φ values are nearly constant
at the z = 10mm locations, and the differences are much larger in the richer cases. The
agreement is better in the stratified cases at the long record locations, but large differ-
ences are still seen for the premixed cases. This indicates that the use of ensembles of
unstrained laminar flame calculations is unsuitable for capturing the behavior of surface
density function on the mean, particularly for premixed cases; an unsurprising result as
such a method fails to take into account any potential thickening of the flame front (and
hence attenuation of |∇c|) by the entrainment of small eddies into the preheat zone.
Evidence of such eddies penetrating the flame front are provided by the instantaneous
temperature profiles, where small local peaks and troughs are regularly observed within
the overall thermal ramp.
The peak |∇c| in the experimental data typically occurs closer to the equilibrium
zone (high c) than in the numerical values. The rapid evolution of |∇c| seen in the
laminar flame calculations is attenuated in the regions preceding the |∇c| peak, and
the experimental means exhibit quasi-linear slopes for much of this progress variable
space. This slope, observed in many of the mean fits, is attributed to the effect of eddies
Cambridge Stratified
Swirl Burner Results 185
Figure 6.34: Plots of progress variable c against scalar dissipation rate χc for the swirl
burner at both z = 10mm (bottom halves) and long record (top halves) locations, colored
by Φ, as shown in the colorbar. Data below the lean flammability limit (Φ = 0.47) are
plotted in black. Mean fits are shown by solid blue lines. Laminar flame calculations are
shown by gray horizontal (value at local mean Φ) and vertical (range of maximum and
minimum local Φ) lines.
Cambridge Stratified
Swirl Burner Results 186
penetrating the preheat zone; the flame may be locally thickened, reducing the rate at
which |∇c| increases in c space, and leading to a near-linear slope of |∇c| against c.
The |∇c|mean fits all return to zero for progress variable values that are substantially
below unity. This indicates that the shift of the second delta in the progress variable
pdfs towards the reactants seen in Figure 6.31 is not due to the flames failing to reach
equilibrium within the line measurement window, and may be attributed to the effects
of elevated equivalence ratios (due to stratification or preferential molecular transport)
and non-idealities (i.e. non-adiabatic conditions).
Figure 6.34 shows conditional mean fits of scalar dissipation rate in progress variable
space, using the same conventions as Figure 6.33. Again, the data is not conditioned
on equivalence ratio as the objective is to examine the behavior on the mean. As χc is
closely related to |∇c|, detailed analysis will be reserved for conditioned data. Unsur-
prisingly, the squared term in the formula for χc results in the differences seen for the
quasi-premixed conditions at z = 10mm being amplified; agreement with corresponding
laminar calculations is very poor in all cases.
The long record locations show somewhat more interesting behavior. The differences
seen in the premixed cases remain relatively large, particularly for the stoichiometric
case. However the conditional means in the stratified cases trend closely with their
laminar unstrained values, and the spread of the scatter data is well captured by the
laminar values at the 10th and 90th percentiles of local equivalence ratio within each
progress variable bin.
Figure 6.35 shows the behavior of |∇c| and χc in progress variable space when data is
conditioned such that the local equivalence ratio is within ±1% of the mean equivalence
ratio (Φ = 0.79 for the lean cases, Φ = 1 for the stoichiometric). This ensures that
any trends observed are unlikely to be influenced unduly by stoichiometry effects. The
profiles of |∇c| again trend below their laminar unstrained calculated equivalents, with
Cambridge Stratified
Swirl Burner Results 187
Figure 6.35: Conditional mean fits of surface density function (top row) and scalar
dissipation rate (bottom row) in progress variable space for the swirl burner cases at the
long record locations. Data is conditioned such that Φ = 0.79 and Φ = 1 (±1%) in
the lean and stoichiometric cases respectively. Vertical lines show standard deviations at
that location. Laminar flame calculations at the specified equivalence ratio are shown by
solid black lines.
the latter lying approximately one standard deviation above the experimental conditional
means.
Given the degree of variance seen within the experimental data it is difficult to know
whether differences seen between the means are significant. However it does appear that
stratification shifts the location of peak surface density function towards the products
for the lean cases. The stoichiometric cases show decreases in peak amplitudes with
increasing swirl, which is not noticeable in the lean cases save for SwB3. It appears
that the flame structure is more sensitive to turbulence at the stoichiometric point than
at the leaner conditions experienced for the other conditions.
The scalar dissipation rate shows a more convincing trend with increasing stratifi-
cation, with the premixed lean cases consistently undershooting the peak levels seen in
their stratified equivalents. Interestingly the locations of peak χc are less sensitive to the
degree of stratification than for the surface density function. In all cases the peaks at-
Cambridge Stratified
Swirl Burner Results 188
tained are substantially lower than the laminar calculations. The heightened turbulence
sensitivity noted for |∇c| in the stoichiometric cases is also observed in the χc profiles.
6.10.2 Turbulent Flame Thickness
The turbulent flame thickness is of interest in stratified flames as the presence of equiv-
alence ratio gradients is expected to result in fluctuations in local propagation speed,
with an associated change in flame area. Any such changes effect the degree of stretch
in the flame, and subsequently the turbulent flame thickness δt. The definition of turbu-
lent flame thickness used in the following analysis is based on the Rayleigh temperature
measurements, specifically the ratio of the magnitude of the thermal ramp across the
flame front to the maximum thermal gradient within the flame:
δt =
Tb − Tu
|∇T |max
(6.10)
where subscripts have their usual meanings.
Figure 6.36: Probability density functions of turbulent flame thickness δt for the swirl
burner cases at the long record locations. Data is conditioned such that Φ = 0.79 and
Φ = 1 in the lean and stoichiometric cases respectively (±2.5%). The corresponding
laminar flame thicknesses δL are marked with a vertical dashed line, - - - -.
Cambridge Stratified
Swirl Burner Results 189
Table 6.8: Statistics for turbulent flame thickness δt in the swirl burner at long record
locations. Data is conditioned such that Φ = 0.79 and Φ = 1 in the lean and stoichio-
metric cases respectively (±2.5%) at the location of peak temperature gradient. Values
in parentheses are taken from short records.
Flame
z δt σδt γ1 γ2
(mm) (mm) (mm) (−) (−)
SwB1 30 0.62 0.08 1.05 3.53
SwB2 30 0.59 0.12 0.80 2.69
SwB3 30 0.55 0.15 0.80 1.09
SwB5 50 (30) 0.56 (0.53) 0.14 1.23 3.17
SwB6 40 (30) 0.54 (0.51) 0.14 1.17 3.05
SwB7 30 0.52 0.15 1.27 3.32
SwB9 50 (30) 0.54 (0.42) 0.14 1.13 2.50
SwB10 40 (30) 0.52 (0.50) 0.14 1.21 2.85
SwB11 30 0.50 0.15 1.26 3.04
SwB13 30 0.47 0.09 1.89 8.77
SwB14 30 0.47 0.09 1.73 7.01
SwB15 20 (30) 0.47 (0.52) 0.11 2.01 7.65
Probability density functions for the swirl burner cases at the long record locations
are presented in Figure 6.36, and the corresponding principle moments are given in
Table 6.8 for reference. The flame thickness distributions highlight some interesting
behavior. Firstly, the premixed cases are consistently thicker than the stratified, in
agreement with the results in the slot burner data and also the findings of Robin et
al [23]. Note that flame thickness in the latter is derived using the temperature difference
between Tu and the temperature at the location of peak temperature gradient, which
is analogous to the thickness of the preheat zone [94]. However, the trends observed
are expected to be similar to those seen for the turbulent flame thickness defined in
Equation 6.10.
Cambridge Stratified
Swirl Burner Results 190
The influence of swirl is quite interesting, as it only appears to have a significant
effect on the lean premixed flames. The distributions of δt progressively broaden and
shift to lower mean values moving from SwB1 to SwB3, yet no significant difference
is observed with flow type for either the stratified or the stoichiometric distributions.
Figure 6.36. The mean turbulent flame thickness in the premixed cases decreases moving
from the lean Φn = 0.79 to the stoichiometric Φn = 1, which is in line with the behavior
of laminar flame calculations for Φ < 1.1.
Finally, the lean stratified cases appear to have values of δt which are equal to or lower
than the equivalent laminar flame value. This is interesting as it seems contrary to the
surface density results seen in Figure 6.35 of Section 6.10.1, which showed attenuated
values of mean |∇c| relative to laminar calculations, implying thickened flame fronts
in agreement with the modeling literature [73, 74]. This disparity is attributed to the
definition of δt given by Equation 6.10; as the formula is dependent on the temperature
range spanned by the flame, and the peak thermal gradient, it fails to take into account
any broadening of the physical flame front which may arise if there are local peaks and
troughs inside the overall thermal ramp (e.g. due to eddy penetration).
Figure 6.37: Conditional mean fit of turbulent flame thickness against continuous
curvature for the swirl burner cases at the long record locations. Data is conditioned
such that Φ = 0.79 and Φ = 1 in the lean and stoichiometric cases respectively (±2.5%).
Cambridge Stratified
Swirl Burner Results 191
Figure 6.37 illustrates the variation of mean turbulent flame thickness with mean
continuous curvature. Note that the data (particularly for the highly swirling cases)
is relatively sparse after conditioning on local equivalence ratio, with the result that
the conditional means are somewhat noisy. However, the general behavior exhibited
indicates that there is a weak positive correlation between curvature and flame thickness
in the swirl burner cases (0.08 < R < 0.22). The noted correlation for positive values
of mean curvature is significantly less than that reported by Robin et al [23], and it is
reasonable to say that continuous curvature is for all practical purposes decoupled from
the turbulent flame thickness in the swirl burner. Note that the trends exhibited in
similar analyses in the literature [23, 95] show substantial differences both within and
across the studies. This is particularly well highlighted by the results seen in [23], where
the relationship between curvature and turbulent flame thickness is heavily modified
by the type of turbulent grid used, the nominal equivalence ratio, and the degree of
stratification.
6.10.3 Flame Surface Density
Flame surface densities calculated using the Pope formulation [8] (detailed in Sec-
tion 4.3.1 of Chapter 4) are presented in Figure 6.38, demonstrating the trends in Σ
across both mean and instantaneous c space in the swirl burner cases at the long record
locations. The profiles trend similarly to those in the slot burner data in Section 5.8 of
Chapter 5, exhibiting a shift from positive to negative skew as c increases. The values
for high c = 0.95 are again unphysical, but are attributed to the shift of the unity peak
in the progress variable pdfs towards the reactants (Section 6.9 of Section 6.9) rather
than noise in the product temperature data, as the latter is essentially eliminated by
the wavelet filtering.
C
am
bridge
Stratified
Sw
irlB
urner
R
esults
192
Figure 6.38: Behavior of flame surface density in terms of mean and instantaneous progress variable for lean non-swirling
(top row), moderately swirling (2nd row), highly swirling (3rd row) and stoichiometric cases (bottom row) in the swirl burner
at the long record locations.
Cambridge Stratified
Swirl Burner Results 193
Flame surface density appears quite sensitive to whether or not the conditions are
premixed or stratified in the non-swirling cases, more so than the equivalent data in
the slot burner. This may indicate that the effect of stratification on flame topology
has a degree of turbulence dependence. The premixed SwB130 profiles peak at values
between 8% to 51% greater than the corresponding stratified cases. This is a peculiar
result given the broader curvature pdfs seen for the stratified cases in Figure 6.29; the
expectation would be that the higher frequency of large curvature, more wrinkled flames
in these cases would result in a greater surface area and a corresponding larger flame
surface density. The differences between the two levels of stratification in SwB550 and
SwB950 are comparatively tiny, between −1% to 2%.
Interestingly the addition of swirl decreases the differences seen between the pre-
mixed and stratified cases, indicating that the effects of stratification on flame surface
density have a turbulence dependency. The stratified cases trend higher for low instan-
taneous values of progress variable (−9% to −2% for c ≤ 0.25) and increasingly lower
for higher values of progress variable (5% to 26% for 0.35 ≤ c ≤ 0.85). These differ-
ences are almost eliminated moving to the high swirl conditions, with the stratified cases
peaking between −8% to 4% relative to the premixed values. The effect of swirl on the
stratified cases themselves small compared to that seen for the premixed cases, with
peak amplitudes in stratified conditions being increased (contrast with the behavior in
the premixed cases) by 0% to 15%.
6.11 Summary of Results
This chapter has presented results from a new turbulent swirling stratified methane/air
burner. An experimental matrix encompassing three degrees of stratification and swirl
in lean cases and three levels of swirl in stoichiometric premixed cases were investigated
Cambridge Stratified
Swirl Burner Results 194
using a variety of techniques. Axial and radial flow fields were revealed using two-
dimensional PIV, while the thermo-chemical structure was probed within the flame front
using high resolution Rayleigh/Raman/CO-LIF line measurements with simultaneous
cross-planar OH-LIF. The main results of these analyses are summarized as follows:
• The turbulence levels are substantially greater than those seen in the slot burner
in Chapter 5, and the flames surveyed fall within the thin reaction zone regime on
the modified Borghi diagram.
• The addition of swirl influences the stability of the flow field. The moderate swirl
cases appears to generate instabilities and operate in an unstable mode, resulting
in higher u′ relative to equivalent non-swirling and highly swirling cases.
• The flames surveyed feature large recirculation zones above the central bluff body,
which has significant impact on the species concentrations within the flame.
• Significant levels of stratification are achieved within the flame front, as shown
in Section 6.5, with the moderately stratified cases showing RMS gradients of Φ
comparable to the most highly stratified slot burner cases.
• Favre averaged results in Section 6.6 reveal elevated equivalence ratio levels within
the recirculation zone, which is attributed to the effects of preferential molecular
transport of hydrogen away from the flame front near to the burner exit.
• The mean behavior of key combustion species in the swirl burner flames at the
intersection of the mixing layer with the flame brush is well captured by the use
of ensembles of unstrained laminar flame calculations, with the exception of H2.
Significant differences are seen further upstream in H2 and CO2 due to the effects
of preferential molecular transport.
Cambridge Stratified
Swirl Burner Results 195
• When conditioned on local equivalence ratio, H2 is well modeled in the lean pre-
mixed cases by laminar calculations but is under-predicted through much of the
temperature space for the stratified and stoichiometric conditions. This has im-
portant implications for models attempting to capture the behaviour of stratified
flames using simple laminar flame models in their chemistry.
• Discrete curvature pdfs are broadened by the addition of stratification, in line with
results seen elsewhere in the literature.
• Surface density function and scalar dissipation rate are significantly attenuated
relative to their corresponding laminar unstrained values, which is reflected in the
mean turbulent flame thicknesses. The peak surface density function values are
similar between stratified and premixed cases when conditioned on local equiva-
lence ratio, but are shifted towards the products under stratified conditions. Scalar
dissipation rate is enhanced by stratification in all cases.
• Flame surface density appears to show a strong turbulence dependence in the lean
cases, which seems to be moderated under stratified conditions. The premixed
lean case SwB1 peaks significantly higher than all other cases through mean and
instantaneous progress variable space.
Chapter 7
Flame Surface Density Metrics
This aim of this chapter is slightly different from from the previous two in that it is the
underlying methodology of deriving flame surface density that is under investigation,
rather than the behavior of the data itself. Over course of this chapter the values
obtained using the three FSD metrics described in Section 4.3 of Chapter 4 are compared
and contrasted. The metrics considered are the statistical expression derived by Pope [8]
(Equation 4.11 of Chapter 4), Σ1, the geometric method proposed by Shepherd [81]
(Equation 4.12 of Chapter 4), Σ2, and a geometric method which extends the Shepherd
method to the entirety of c space [27] (Equation 4.13 of Chapter 4), Σ3. Raw data from
the slot burner (Chapter 5) and the swirl burner (Chapter 6) are used to ensure that
any conclusions drawn are robust, and not simply an artifact of considering data from
a single (perhaps fortuitous) condition.
7.1 Slot Burner Results
The purpose of the present chapter is to provide a systematic comparison of the relative
behavior of various flame surface density measures, rather than to comment on the
196
Flame Surface Density Metrics 197
behavior of FSD itself in CH4/air flames at different operating conditions. Stratification,
turbulence intensity, curvature and swirl level may have an influence on the behavior of
Σ. Variations in local flame speed and density due to spatial gradients in φ might be
expected to affect FSD. The use of a large number of experimental cases allows robust
comparison of the various FSD measures across a range of conditions.
True values of FSD for each experimental case are not known a priori. However, the
general behaviour of Σ in both c and c space is known from results presented in both
the experimental and modeling combustion literature [80, 81, 85, 96, 97]. For example,
FSD should show a positive skew against c for low values of c. Hence a given measure
is deemed to perform better than another if the measured behavior follows the expected
physical behavior to a greater degree than the other.
Figure 7.1 shows the various flame surface density measures derived from the slot
Figure 7.1: Flame surface density measurements from fs1 (top row), fs4 (middle row)
and fs6 (bottom row). Σ1 (cT , cT ) is shown by , Σ2 (cOH = 0.5, cOH) by ◦ , and
Σ3 (cOH, cOH) by +. Colors (and rows) delineate premixed, moderately stratified and
highly stratified cases.
Flame Surface Density Metrics 198
burner data. The data are plotted using absolute values rather than relative differences
in order to show the trends in Σ with c and c. The statistical Σ1,T and the geometric
Σ3,OH show good agreement at intermediary values of progress variable, but very poor
at the extremes. In general Σ3,OH reaches slightly lower values than Σ1,T . The coarse
resolution of the OH measurements compared to the thermal measurements in the slot
burner data (Section 3.1.3 in Chapter 3) may account for part of this attenuation: the
calculation of areas and contour lengths from the cOH data is inherently sensitive to the
experimental resolution. Resolution effects (spatial averaging) in Σ1,T are expected to
be small due to the corrections applied (Section 4.2.4).
At high c, the geometric method gives more physically realistic results than those
for Σ1,T , which tends to explode as high c values are reached. This is attributed to two
factors: the presence of non-zero gradients of cT in the high cT regions as the investigation
window fails to encapsulate burnout and noise in the cT measurements in this region,
giving non-zero gradients. For low c, Σ1,T gives much better results than the geometric
Σ3,OH. The Shepherd measure, Σ2,OH, is in good agreement with Σ3 (cOH = 0.45, cOH),
which is expected as Σ3,OH is analogous to Σ2,OH near cOH = 0.5.
7.2 Swirl Burner Results
Σ1,T , Σ2,OH and Σ3,OH are similarly compared for the swirl burner data in Figure 7.2.
Moderately swirling cases are omitted for brevity but exhibit similar behavior to highly
swirling cases. The agreement between the surveyed metrics is substantially better
for the premixed swirl burner data than that seen for the slot burner. Additionally
the stratified cases show excellent agreement between Σ1,T , Σ2,OH and Σ3,OH. This is
attributed primarily to the refinement of the OH image resolution by a factor of three
for the swirl burner datasets relative to those for the slot burner experiments (due to
Flame Surface Density Metrics 199
improvements in the laser diagnostics described in Chapter 3). Again, Σ1,T is found to
increase rapidly with cT for high cT , with similar explanations as for the slot burner.
The behavior of Σ3,OH for low cOH is markedly improved in comparison to that in the
slot burner datasets. Σ2,OH and Σ3,OH are almost identical for cOH = 0.45, again as
expected.
The behavior of Σ3 (cOH = 0.95, cOH) is significant, as it shows substantially more
realistic behavior than Σ1 (cT = 0.95, cT ) in Figure 7.2. This may be attributed to the
lack of noise at high cOH due to the use of the OH progress images (Section 4.1.5 of
Chapter 4). This contrasts with the high cT gradients experienced at high cT due to
noise in the Rayleigh measurement in the products. This indicates that smoothing or
denoising is necessary in high cT data if sensible results for FSD are to be obtained in
said data.
A note of caution in these comparisons is that c in Figure 7.1 and Figure 7.2 is defined
using a different scalar depending on the FSD measure. It is perhaps surprising that such
good agreement is seen despite the use of two different scalars. It is necessary to use the
same scalar to derive Σ1 and Σ3 in order to isolate disparities due to methodology alone.
Σ1,OH and Σ3,OH are compared for a selection of SwB operating conditions in Figure 7.3.
A subset of conditions is shown for brevity; similar trends are observed throughout.
Very good agreement is found between Σ1,OH and Σ3,OH for cOH > 0.1, demonstrating
that the two measures of FSD behave in a near-identical manner when using the same
scalar. Σ1,OH and Σ3,OH tend to diverge at the low extreme of cOH for cOH < 0.5, with
Σ1,OH being significantly higher than the geometric measure. This is attributable to
the fact that while ∇cOH is small for low cOH, it is still non-zero. This means that the
product of the scalar gradient with the P (cOH; cOH) (high when both cOH and cOH are
low) fails to decay towards zero as cOH decreases.
Flame Surface Density Metrics 200
Figure 7.2: Flame surface density measurements from the swirl burner. Σ1 (cT , cT ) is
shown by , Σ2 (cOH = 0.5, cOH) by ◦ , and Σ3 (cOH, cOH) by +. Colors delineate
premixed, moderately stratified and highly stratified cases.
Flame Surface Density Metrics 201
Figure 7.4 demonstrates the sensitivity of Σ1 to the choice of scalar using data from
SwB1. The ratio of the conditional progress variable probability in terms of cOH to
cT is compared to corresponding ratio for the conditionally-averaged progress variable
gradient from Equation 4.11. If Σ1 is independent of the choice of scalar, then the data
should collapse the dashed reciprocal curve in Figure 7.4. The data lie close to this curve
for cT , cOH < 0.9, demonstrating that Σ1 shows little dependence on whether c is defined
using temperature or OH. The data for c > 0.9 deviate substantially from the curve,
showing Σ1,OH to trend substantially higher and lower than Σ1,T . This corresponds to
the differences seen in Figure 7.2 for c = 0.95. It is difficult to determine whether
probability or gradient ratios dominate this effect.
7.3 Conclusions
A quantitative comparison has been made between measures of flame surface density
based on the statistical method proposed by Pope (Σ1), the geometric method derived by
Figure 7.3: Flame surface density measurements from the swirl burner for cases SwB1
(uniformly premixed, non-swirling), SwB3 (uniformly premixed, highly swirling), and
SwB7 (moderately stratified, highly swirling). Σ1 (cOH, cOH) is shown by and
Σ3 (cOH, cOH) by +. Colors delineate premixed and highly stratified cases.
Flame Surface Density Metrics 202
〈|∇cOH ||cOH 〉 |cOH / 〈|∇cT ||cT 〉 |cT
P
(c
O
H
;
c O
H
)
/
P
(c
T
;
c T
)
B
A
0 1 2 3
0
1
2
3
Figure 7.4: Ratio of mean progress variable gradients against ratio of conditional
progress variable probabilities (OH:T) for SwB1. Low values c < 0.1 are shown by
•, intermediate c points where 0.1 ≤ c ≤ 0.9 are shown by •, and points where c > 0.9
are shown by ◦ . The dashed curve corresponds to Σ1,OH = Σ1,T . Σ1,OH < Σ1,T on the
side of the dashed curve marked A, and vice-versa on the side marked B.
Shepherd (Σ2), and a novel extension of the latter (Σ3) in both premixed and stratified
turbulent CH4/air flames, using both T and OH as measurands of progress of reaction.
Two different burners were used in separate experiments in order to obtain robust results
that are insensitive to geometry or Reynolds number. A slot burner provided weakly
turbulent V-flames, varying from uniformly premixed to highly stratified. A swirl burner
provided 12 turbulent flames with varying stratification, swirl strength and global equiv-
alence ratio. Measurements of local temperature, equivalence ratio flame orientation and
flame tomography were made using simultaneous multi-scalar line diagnostics and cross
plane OH-PLIF imaging.
The results demonstrate that geometric methods (Σ2, Σ3) and statistical methods
(Σ1) give virtually identical results at intermediate values of c for the swirl burner data,
Flame Surface Density Metrics 203
and demonstrate negligible dependence on stratification levels. Poorer agreement is
seen in the slot burner data, and this is attributed to OH-LIF resolution being three
times coarser in these experiments (150 µm/pixel) than in the swirl burner experiments
(48 µm/pixel). Geometric methods are more sensitive to experimental resolution than
the statistical method, for which a simple correction can partially compensate for spatial
averaging effects.
Deriving Σ1 requires simultaneous dual-plane Rayleigh (temperature), Mie or LIF
imaging in order to determine the true three-dimensional gradients of progress variable
instead of their projection on the line measurement axis, while Σ3 achieves comparable
results using experimentally simpler single sheet imaging, provided the resolution is
sufficiently fine. Flame surface density values derived using these two methods appear
to agree regardless of whether or not they are calculated using the same scalar, though
suitable smoothing or filtering of data is required for Σ1 due to the gradient terms
involved.
Chapter 8
Conclusions
The goals of this project were as follows:
• to develop a burner to enable the investigation of stratified flames under more
turbulent conditions than seen in the slot burner.
• to investigate the effects of stratification on combustion.
• to acquire and develop the experimental, data processing, and analytical skills
required to accomplish these goals.
These objectives have been met over the last three and a half years, and have been de-
tailed in the previous chapters. The effects of stratification on key combustion species,
scalar gradients, and curvature have been investigated through the analysis of multi-
scalar data from both the weakly turbulent slot burner (Chapter 5) and the more turbu-
lent swirl burner (Chapter 6). The data processing skills acquired during the course of
the project also enabled a detailed comparison of some of the key metrics used to mea-
sure flame surface density in experimental data (Chapter 7). The primary conclusions
drawn from the work are given in the following section, with potential avenues of future
work presented in the subsequent section.
204
Conclusions 205
Primary Conclusions:
• The equivalence ratio (derived from a mass fraction balance of hydrocarbons to
oxygen in Chapter 4) is not viable for conditioning data within the flame front as
substantial deviations from nominal stoichiometry is observed even in premixed
flame calculations due to differential diffusion effects. This issue is exacerbated
in stratified flows, as it also becomes impossible to separate instantaneous spatial
gradients of equivalence ratio due to the stratification from those due to the dif-
ferential diffusion effects. In the present work this issue is overcome by the use
of a linear bridging function within the flame front (Section 4.2.3.2 of Chapter 4),
providing a robust first-order solution to the problem.
• The evolution of the major combustion species in thermal space is well captured
on the mean by ensembles of unstrained laminar flame calculations in both the
slot and swirl burner datasets, with the exception of hydrogen.
• Stratification influences the surface density function (conditioned on local equiva-
lence ratio), though this effect varies depending on the burner and flow conditions.
|∇c| is consistently elevated in the slot burner data under stratified conditions,
while the swirl burner shows only a shift in the c values associated with peak |∇c|
towards the products for stratified cases.
• Scalar dissipation rate is consistently increased in stratified cases relative to equiv-
alent premixed conditions. This is seen in both the slot and swirl burner data.
• The swirl burner is significantly more turbulent than the slot burner and displays
some interesting behavior in terms of thermo-chemistry near the burner exit due
to the combined effects of the recirculation zone above the central bluff body
and preferential transport of species away from the flame front. The extensive
Conclusions 206
experimental datasets already available on this burner mark it as a potentially
interesting candidate for numerical modeling.
• The geometric flame surface density formula provided by Shepherd has been shown
to be consistent with the formal derivation of Pope, and an extension to the Shep-
herd method has been proposed and validated which enables the comparison of
the methods across both mean and instantaneous progress variable space.
Future Work:
• One interesting avenue of future work is to investigate the feasibility of extracting
three-dimensional curvature data from cross-planar images. This is of practical
relevance to the experimental combustion field as there are numerous existing cross-
planar datasets, as well as labs where such measurements are likely to be taken in
the future. Some preliminary work has been done on this, with early indications
being that it may be possible to calculate the three-dimensional curvature through
careful application of coordinate system transforms and the least squares solution
of a Taylor series expansion for the temperature field. However, further work on
the implementation of this technique is required before any concrete conclusions
are drawn.
• The use of a linear bridging function to overcome the effects of differential diffusion
on equivalence ratio within the flame front provides a robust basis for the analysis
of stratified flames, but may not be an optimal strategy. It is suggested that both
linear bridging and other potential methods to correct for differential diffusions
effects be investigated further.
• The flow field in the swirl burner has been characterized in the axial and radial
directions using PIV, as shown in Section 6.2 of Chapter 6. The absence of velocity
Conclusions 207
data in the tangential direction is unsatisfactory, and it is proposed that a high
speed stereo PIV campaign be undertaken with the current burner to ensure full
three-dimensional characterization of these flames.
• High temporal resolution velocity measurements such as laser Doppler velocimetry
(LDV) could be performed to improve calculations of the turbulent length scale.
• Qualitative imaging of the equivalence ratio field using acetone PLIF would provide
useful information on the mixture fraction field, and allow the investigation of the
effect of local pockets of high/low equivalence ratio on curvature on a larger scale
than in the multi-scalar laser diagnostics.
• One major issue experienced during the experimental work was the difficulty in
achieving consistent seeding. Commercial grade seeding chambers are not finan-
cially viable when multiple seeders are required in a single experiment. Addition-
ally there appears to be a lack of consensus on good seed chamber design within
the department. This could potentially be an interesting avenue of research dur-
ing an experimental PhD student’s first year; the goal would be the design and
implementation of a seed chamber capable of giving consistent seeding at a range
of flow rates. It may also be a promising candidate project for 4th year engineering
students, as the work could be built on over successive years until a sufficiently
good design (and set of design parameters and underlying physics) is established.
Appendix A
List of Publications
A.1 Journal Publications
• Sweeney, M. S., Hochgreb, S., and Barlow, R. S. (2011) The Structure of Premixed and
Stratified Low Turbulence Flames, Combustion and Flame, 158, 5, 935–948
• Barlow, R. S., Dunn, M. J., Sweeney, M. S., Hochgreb, S. (2011) Effects of preferential
transport in turbulent bluff-body-stabilized lean premixed CH4/air flames, Combustion
and Flame, In Press
• Sweeney, M. S., Hochgreb, S., Dunn, M. J., and Barlow, R. S. (2010) A Comparative
Analysis of Flame Surface Density Metrics in Premixed and Stratified Flames, Proceedings
of the Combustion Institute, 33, 1, 1419–1427
• Sweeney, M. S. and Hochgreb, S. (2009) Autonomous extraction of optimal flame fronts
in OH planar laser-induced fluorescence images, Applied Optics, 48, 19, 3866–3877
• Barlow, R. S., Wang, G. H., Anselmo-Filho, P., Sweeney M. S., and Hochgreb, S. (2008)
Application of Raman/Rayleigh/LIF diagnostics in turbulent stratified flames, Proceed-
ings of the Combustion Institute, 32
208
List of Publications 209
A.2 Conference Publications
• Sweeney, M. S., Hochgreb, S., Dunn, M. J., and Barlow, R. S. (2011) A New Series
Of Turbulent Stratified Flames: Preliminary Findings, Proceedings of the Meditteranean
Combustion Symposium
• Barlow, R. S., Dunn, M. J., Sweeney, M. S., and Hochgreb, S. (2010) Multiscalar Measure-
ments on a Variable Swirl Burner Operating in Premixed and Stratified Modes, AFRC
Pacific Rim Combustion Symposium
• Sweeney, M. S., Darbyshire, O. R., Hochgreb, S., and Barlow, R. S. (2009) Premixed and
Stratified Flame Diagnostics Based on 3D Flame Orientation, 4th European Combustion
Meeting
• Barlow, R. S., Wang, G. H., Anselmo-Filho, P., Sweeney M. S., and Hochgreb, S.
(2008) Application of Multiscalar Laser Diagnostics to Turbulent Stratified Methane/Air
Flames, 46th AIAA Aerospace Sciences Meeting and Exhibit
Appendix B
Error propagation formulas
The error formulae used to calculate the propagated error in the derived quantities (e.g.
|∇c| and χc) in the slot and swirl burner datasets are detailed in this appendix in the
interests of transparency. The calculated propagated errors are shown in Table 4.2 of
Chapter 4 for the slot and swirl burner datasets.
The precision in the equilibrium temperature conditioned on local equivalence ratio,
T (φ) is given by:
σTe =
∂Te
∂φ
σφ (B.1)
For the progress variable, c:
σc =
[(
∂c
∂T
σT
)2
+
(
∂c
∂φ
σφ
)2] 12
(B.2)
210
Error propagation formulas 211
For the thermal diffusivity conditioned on local temperature and equivalence ratio,
αc (T, φ):
σαc =
[(
∂αc
∂T
σT
)2
+
(
∂αc
∂φ
σφ
)2] 12
(B.3)
(B.4)
For the gradient of c it is necessary to consider the temperature and equivalence ratio
to be independent variables at the local point k, the preceding point k − 1 and the
subsequent point k + 1:
σ|∇c|k =
[(
∂|∇c|k
∂φk−1
σφk−1
)2
+
(
∂|∇c|k
∂Tk−1
σTk−1
)2
+
(
∂|∇c|k
∂φk
σφk
)2
+
(
∂|∇c|k
∂Tk
σTk
)2
+
(
∂|∇c|k
∂φk+1
σφk+1
)2
+
(
∂|∇c|k
∂Tk+1
σTk+1
)2] 12
(B.5)
Similar considerations apply to the uncertainties in thermal scalar dissipation χc:
σχc =
[(
∂χc
∂φk−1
σφk−1
)2
+
(
∂χc
∂Tk−1
σTk−1
)2
+
(
∂χc
∂φk
σφk
)2
+
(
∂χc
∂Tk
σTk
)2
+
(
∂χc
∂φk+1
σφk+1
)2
+
(
∂χc
∂Tk+1
σTk+1
)2] 12
(B.6)
List of References
[1] A. Mansour. Gas turbine fuel injection technology. Proceedings ASME Turbo Expo,
2:141–149, 2005.
[2] D. A. Nickolaus, D. S. Crocker, D. L. Black, and C. E. Smith. Development of
a lean direct fuel injector for low emission aero gas turbines. International Gas
Turbine Initiative, 2002.
[3] H. J. Bauer. New low emission strategies and combustor designs for civil aeroengine
applications. Progress in Computational Fluid Dynamics, 4(3-5):130–142, 2004.
[4] A. C. Alkidas. Combustion advancements in gasoline engines. Energy Conservation
and Management, 48(11):2751–2761, 2007.
[5] M. C. Drake and D. C. Haworth. Advanced gasoline engine development using op-
tical diagnostics and numerical modeling. Proceedings of the Combustion Institute,
31:99–124, 2007.
[6] R. S. Cant and E. Mastorakos. An introduction to turbulent reacting flows. Imperial
College Press, 2008.
[7] K. N. C. Bray, P. A. Libby, and J. B. Moss. Unified modelling approach for premixed
turbulent combustion part 1 — general formulation. Combustion and Flame, 61:
143–172, 1985.
[8] S. B. Pope. The evolution of surfaces in turbulence. International Journal of
Engineering Science, 26(5):445–469, 1988.
[9] S. M. Candel and T. J. Poinsot. Flame stretch and the balance equation for the
flame area. Combustion Science and Technology, 70(1-3):1–15, 1990.
[10] N. Peters. The turbulent burning velocity for large-scale and small-scale turbulence.
Journal of Fluid Mechanics, 384(1):107–132, 1999.
[11] D. Veynante and L. Vervisch. Turbulent combustion modeling. Progress in Energy
and Combustion Science, 28(3):193–266, 2002.
212
List of References 213
[12] T. Echekki and E. Mastorakos. Turbulent combustion modeling: Advances, new
trends and perspectives. Springer Verlag, 2010.
[13] W. Meier, P. Weigand, X. R. Duan, and R. Giezendanner-Thoben. Detailed char-
acterization of the dynamics of thermoacoustic pulsations in a lean premixed swirl
flame. Combustion and Flame, 150(1-2):2–26, 2007.
[14] A. X. Sengissen, J. F. Van Kampen, R. A. Huls, G. G. M. Stoffels, J. B. W. Kok,
and T. J. Poinsot. LES and experimental studies of cold and reacting flow in a
swirled partially premixed burner with and without fuel modulation. Combustion
and Flame, 150(1-2):40–53, 2007.
[15] C. Duwig and C. Fureby. Large eddy simulation of unsteady lean stratified premixed
combustion. Combustion and Flame, 151(1-2):85–103, 2007.
[16] T. Kang and D. C. Kyritsis. Methane flame propagation in compositionally strati-
fied gases. Combustion Science and Technology, 177:2191–2210, 2005.
[17] S. R. Turns. An introduction to combustion. McGraw-Hill, 2000.
[18] R. K. Green and C. C. Zavier. Charge stratification in a spark ignition engine.
Proceedings of the IMechE, Part A: Journal of Power and Energy, 206(11):59–64,
1992.
[19] C. Arcoumanis, M. R. Gold, J. H. Whitelaw, and H. M. Xu. Local mixture injection
to extend the lean limit of spark-ignition engines. Experiments in Fluids, 26(1):126–
135, 1999.
[20] C. Galizzi and D. Escudié. Experimental analysis of an oblique laminar flame front
propagating in a stratified flow. Combustion and Flame, 145(3):621–634, 5 2006.
[21] B. Renou, E. Samson, and A. Boukhalfa. An experimental study of freely propagat-
ing turbulent propane/air flames in stratified inhomogeneous mixtures. Combustion
Science and Technology, 176:1867–1890, 2004.
[22] N. Pasquier, B. Lecordier, M. Trinité, and A. Cessou. An experimental investigation
of flame propagation through a turbulent stratified mixture. Proceedings of the
Combustion Institute, 31(1):1567–1574, 2007.
[23] V. Robin, A. Mura, M. Champion, O. Degardin, B. Renou, and M. Boukhalfa.
Experimental and numerical analysis of stratified turbulent v-shaped flames. Com-
bustion and Flame, 153(1–2):288–315, 2008.
[24] P. Anselmo-Filho, S. Hochgreb, R. S. Barlow, and R. S. Cant. Experimental mea-
surements of geometric properties of turbulent stratified flames. Proceedings of the
Combustion Institute, 32(2):1763–1770, 2009.
List of References 214
[25] F. Seffrin, F. Fuest, D. Geyer, and A. Dreizler. Flow field studies of a new series
of turbulent premixed stratified flames. Combustion and Flame, 157(2):384–396,
2010.
[26] B. Böhm, J. H. Frank, and A. Dreizler. Temperature and mixing field measure-
ments in stratified lean premixed turbulent flames. Proceedings of the Combustion
Institute, 33(1):1583–1590, 2011.
[27] M. S. Sweeney, S. Hochgreb, M. J. Dunn, and R. S. Barlow. A comparative analysis
of flame surface density metrics in premixed and stratified flames. Proceedings of
the Combustion Institute, 33(1):1419–1427, 2011.
[28] C. Galizzi and D. Escudié. Experimental analysis of an oblique turbulent flame
front propagating in a stratified flow. Combustion and Flame, 157(12):2277–2285,
2010.
[29] P. C. Vena, B. Deschamps, G. J. Smallwood, and M. R. Johnson. Equivalence
ratio gradient effects on flame front topology in a stratified iso-octane/air turbulent
v-flame. Proceedings of the Combustion Institute, 33(1):1551–1558, 2011.
[30] A. P. da Cruz, A. M. Dean, and J. M. Grenda. A numerical study of the lami-
nar flame speed of stratified methane/air flames. Proceedings of the Combustion
Institute, 28(2):1925–1932, 2000.
[31] Y M Marzouk. Dynamic response of strained premixed flames to equivalence ratio
gradients. Proceedings of the Combustion Institute, 28(2):1859–1866, 2000.
[32] E. S. Richardson, V. E. Granet, A. Eyssartier, and J. H. Chen. Effects of equiv-
alence ratio variation on lean, stratified methane-air laminar counterflow flames.
Combustion Theory and Modeling, 14(6):775–792, 2010.
[33] J. Hélie and A. Trouvé. Turbulent flame propagation in partially premixed com-
bustion. Proceedings of the Combustion Institute, 27(1):891–898, 1998. Sysposium
(International) on Combustion.
[34] T. Poinsot, D. Veynante, A. Trouve, and G. Ruetsch. Turbulent flame propagation
in partially premixed flames. Proceedings of the CTR Summer Program, 1996.
[35] D. C. Haworth, R. J. Blint, B. Cuenot, and T. J. Poinsot. Numerical simulation
of turbulent propane-air combustion with nonhomogeneous reactants. Combustion
and Flame, 121(3):395–417, 2000.
[36] C. Jiménez, B. Cuenot, T. Poinsot, and D. C. Haworth. Numerical simulation and
modeling for lean stratified propane-air flames. Combustion and Flame, 128(1–2):
1–21, 2002.
List of References 215
[37] V. Robin, A. Mura, M. Champion, and P. Plion. A multi-Dirac presumed pdf model
for turbulent reactive flows with variable equivalence ratio. Combustion Science and
Technology, 178:1843–1870, 2006.
[38] K. N. C. Bray, P. Domingo, and L. Vervisch. Role of the progress variable in models
for partially premixed turbulent combustion. Combustion and Flame, 141:431–437,
2005.
[39] Z. Tan and R. D. Reitz. An ignition and combustion model based on the level-
set method for spark ignition engine multidimensional modeling. Combustion and
Flame, 145(1-2):1–15, 2006.
[40] E. Knudsen and H. Pitsch. A general flamelet transformation useful for distin-
guishing between premixed and non-premixed modes of combustion. Combustion
and Flame, 156(3):678–696, 3 2009.
[41] P. D. Nguyen, L. Vervisch, V. Subramanian, and P. Domingo. Multidimensional
flamelet-generated manifolds for partially premixed combustion. Combustion and
Flame, 157(1):43–61, 1 2010.
[42] A. C. Eckbreth. Laser diagnostics for combustion temperature and species. CRC,
1996.
[43] A. Buschmann, F. Dinkelacker, T. Schäfer, M. Schäfer, and J. Wolfrum. Measure-
ment of the instantaneous detailed flame structure in turbulent premixed combus-
tion. In Symposium (International) on Combustion, volume 26, pages 437–445.
Elsevier, 1996.
[44] F. O’Young and R. W. Bilger. Scalar gradient and related quantities in turbulent
premixed flames. Combustion and Flame, 109(4):682–700, 1997.
[45] Y. C. Chen and R. W. Bilger. Experimental investigation of three-dimensional
flame-front structure in premixed turbulent combustion I: hydrocarbon/air bunsen
flames. Combustion and Flame, 131(4):400–435, 2002.
[46] M. J. Dunn, A. R. Masri, and R. W. Bilger. A new piloted premixed jet burner to
study strong finite-rate chemistry effects. Combustion and Flame, 151(1-2):46–60,
2007.
[47] R. S. Barlow, G. H. Wang, P. Anselmo-Filho, M. S. Sweeney, and S. Hochgreb.
Application of Raman/Rayleigh/LIF diagnostics in turbulent stratified flames. Pro-
ceedings of the Combustion Institute, 32(1):945–953, 2009.
[48] M. A. Gregor, F. Seffrin, F. Fuest, D. Geyer, and A. Dreizler. Multi-scalar measure-
List of References 216
ments in a premixed swirl burner using 1D Raman/Rayleigh scattering. Proceedings
of the Combustion Institute, 32(2):1739–1746, 2009.
[49] O. Degardin, B. Renou, and A. Boukhalfa. Simultaneous measurements of temper-
ature and fuel mole fraction using acetone planar induced fluorescence and Rayleigh
scattering in stratified flames. Experiments in Fluids, 40:452–463, 2006.
[50] A. C. Eckbreth, P. A. Bonczyk, and J. F. Verdieck. Combustion diagnostics by laser
Raman and fluorescence techniques. Progress in Energy and Combustion Science,
5(4):253–322, 1979.
[51] A. R. Masri, R. W. Dibble, and R. S. Barlow. The structure of turbulent non-
premixed flames revealed by Raman-Rayleigh-LIF measurements. Progress in En-
ergy and Combustion Science, 22(4):307–362, 1996.
[52] D. Geyer, A. Kempf, A. Dreizler, and J. Janicka. Turbulent opposed-jet flames: A
critical benchmark experiment for combustion LES. Combustion and Flame, 143
(4):524–548, 2005.
[53] T. W. Lee, G. L. North, and D. A. Santavicca. Surface properties of turbulent
premixed propane/air flames at various Lewis numbers. Combustion and Flame, 93
(4):445–456, 1993.
[54] S. A. Filatyev, J. F. Driscoll, C. D. Carter, and J. M. Donbar. Measured properties
of turbulent premixed flames for model assessment, including burning velocities,
stretch rates, and surface densities. Combustion and Flame, 141(1-2):1–21, 2005.
[55] P. Anselmo-Filho. Experimental investigations of turbulent stratified V-flames using
laser diagnostics. PhD thesis, University of Cambridge, Cambridge, UK, 2008.
[56] A. N. Karpetis, T. B. Settersten, R. W. Schefer, and R. S. Barlow. Laser imaging
system for determination of three-dimensional scalar gradients in turbulent flames.
Optics Letters, 29(4):355–357, 2004.
[57] A. N. Karpetis and R. S. Barlow. Measurements of flame orientation and scalar
dissipation in partially premixed methane flames. Proceedings of the Combustion
Institute, 30(1):665–672, 2005.
[58] G. H. Wang and N.T. Clemens. Effects of imaging system blur on measurements
of flow scalars and scalar gradients. Experiments in Fluids, 37(2):194–205, 2004.
[59] A. Johnstone, M. Uddin, and A. Pollard. Calibration of hot-wire probes using
non-uniform mean velocity profiles. Experiments in Fluids, 39(3):527–534, 2005.
[60] O. R. Darbyshire, N. Swaminathan, and S. Hochgreb. The effects of small-scale
List of References 217
mixing models on the prediction of turbulent premixed and stratified combustion.
Combustion Science and Technology, 182(9):1141–1170, 2010.
[61] M. J. Dunn and R. S. Barlow. A wavelet based denoising algorithm optimized for
high resolution line imaging in fluid mechanics. Experiments in Fluids, 2011. Paper
in preparation.
[62] M. S. Sweeney and S. Hochgreb. Autonomous extraction of optimal flame fronts
in OH planar laser-induced fluorescence images. Applied Optics, 48(19):3866–3877,
2009.
[63] M. S. Sweeney, S. Hochgreb, and R. S. Barlow. The structure of premixed and
stratified low turbulence flames. Combustion and Flame, 158(5):935–948, 2011.
[64] Open Source. GNU Image Manipulation Program. Online, 2011.
http://www.gimp.org/.
[65] M. Kass, A. Witkin, and D. Terzopoulos. Snakes: Active contour models. Interna-
tional Journal of Computer Vision, 1(4):321–331, 1988.
[66] F. J. Canny. A computational approach to edge detection. IEEE Transactions on
Pattern Analysis and Machine Intelligence, 8(6):679–698, 1986.
[67] L. Lam, S. W. Lee, and C. Y. Suen. Thinning methodologies — a comprehensive
survey. IEEE Transactions on Pattern Analysis and Machine Intelligence, pages
869–885, 1992.
[68] R. W. Bilger, S. H. Stårner, and R. J. Kee. On reduced mechanisms for methane/air
combustion in nonpremixed flames. Combustion and Flame, 80(2):135–149, 1990.
[69] R. S. Cant, S. B. Pope, and K. N. C. Bray. Modelling of flamelet surface-to-volume
ratio in turbulent premixed combustion. Proceedings of the Combustion Institute,
23(1):809–815, 1991.
[70] Sandia National Laboratories. Chemkin. Online, 2011.
http://www.ca.sandia.gov/chemkin/.
[71] G. P. Smith and D. M. Golden. GRI-Mech 3.0. Online, 2010. URL http://www.
me.berkeley.edu/gri_mech/.
[72] R. S. Barlow, M. J. Dunn, M. S. Sweeney, and S. Hochgreb. Effects of prefer-
ential transport in turbulent bluff-body-stabilized lean premixed CH4/air flames.
Combustion and Flame, Submitted, 2011.
[73] R. Sankaran, E. R. Hawkes, J. H. Chen, T. Lu, and C. K. Law. Structure of a
spatially developing turbulent lean methane-air Bunsen flame. Proceedings of the
Combustion Institute, 31(1):1291–1298, 2007.
List of References 218
[74] V. Moureau, P. Domingo, and L. Vervisch. From large-eddy simulation to direct
numerical simulation of a lean premixed swirl flame: filtered laminar flame-pdf
modeling. Combustion and Flame, 158(7):1340–1357, 2011.
[75] S. M. Martin, J. C. Kramlich, G. Kosály, and J. J. Riley. The premixed conditional
moment closure method applied to idealized lean premixed gas turbine combustors.
Journal of Engineering for Gas Turbines and Power, 125:895, 2003.
[76] A. Y. Klimenko and R. W. Bilger. Conditional moment closure for turbulent com-
bustion. Progress in Energy and Combustion Science, 25(6):595–688, 1999.
[77] R. W. Bilger. The structure of diffusion flames. Combustion Science and Technology,
13(1):155–170, 1976.
[78] N. Peters. Laminar diffusion flamelet models in non-premixed turbulent combustion.
Progress in Energy and Combustion Science, 10(3):319–339, 1984.
[79] R. W. Bilger. Conditional moment closure for turbulent reacting flow. Physics of
Fluids A: Fluid Dynamics, 5:436, 1993.
[80] M. S. Sweeney, O. R. Darbyshire, S. Hochgreb, and R. S. Barlow. Premixed and
stratified flame diagnostics based on 3D flame orientation. 4th European Combustion
Meeting, 2009.
[81] I. G. Shepherd. Flame surface density and burning rate in premixed turbulent
flames. Proceedings of the Combustion Institute, 26(1):373–379, 1996.
[82] I. G. Shepherd and R. K. Cheng. The burning rate of premixed flames in moderate
and intense turbulence. Combustion and Flame, 127(3):2066–2075, 2001.
[83] J. Kiefer, Z. S. Li, J. Zetterberg, X. S. Bai, and M. Aldén. Investigation of lo-
cal flame structures and statistics in partially premixed turbulent jet flames using
simultaneous single-shot CH and OH planar laser-induced fluorescence imaging.
Combustion and Flame, 154(4):802–818, 2008.
[84] C. Cohé, F. Halter, C. Chauveau, I. Gokalp, and O. L. Gulder. Fractal characteri-
zation of high-pressure and hydrogen-enriched CH4-air turbulent premixed flames.
Proceedings of the Combustion Institute, 31(1):1345–1352, 2007.
[85] D. Veynante, J. M. Duclos, and J. Piana. Experimental analysis of flamelet models
for premixed turbulent combustion. Proceedings of the Combustion Institute, 25(1):
1249–1256, 1994.
[86] Y. Dong, C. M. Vagelopoulos, G. R. Spedding, and F. N. Egolfopoulos. Measure-
ment of laminar flame speeds through digital particle image velocimetry: Mixtures
List of References 219
of methane and ethane with hydrogen, oxygen, nitrogen, and helium. Proceedings
of the Combustion Institute, 29(2):1419–1426, 2002.
[87] A. Bonaldo and J. B. Kelman. Experimental annular stratified flames characteri-
sation stabilised by weak swirl. Combustion and Flame, 156(4):750–762, 2009.
[88] M. S. Sweeney, S. Hochgreb, and R. S. Barlow. Cambridge stratified slot burner
dataset. Online, 2010. URL http://www.dspace.cam.ac.uk/handle/1810/
226470.
[89] M. Kaneda, B. Yu, H. Ozoe, and S. W. Churchill. The characteristics of turbulent
flow and convection in concentric circular annuli part I: Flow. International Journal
of Heat and Mass Transfer, 46(26):5045–5057, 2003.
[90] Y. Shoshin, L. Tecce, and J. Jarosinski. Experimental and computational study
of lean limit methane-air flame propagating upward in a 24 mm diameter tube.
Combustion Science and Technology, 10(11):1812–1828, 2008.
[91] Y. Shoshin, G. Gorecki, J. Jarosinski, and T. Fodemski. Experimental study of
limit lean methane/air flame in a standard flammability tube using particle image
velocimetry method. Combustion and Flame, 157(5):884–892, 2010.
[92] A. Levy. An optical study of flammability limits. Proceedings of the Royal Society
of London. Series A. Mathematical and Physical Sciences, 283(1392):134, 1965.
[93] E. von Lavante and R. A. Strehlow. The mechanism of lean limit flame extinction.
Combustion and Flame, 49(1–3):123–140, 1983.
[94] J. Gottgens, F. Mauss, and N. Peters. Analytic approximations of burning velocities
and flame thicknesses of lean hydrogen, methane, ethylene, ethane, acetylene, and
propane flames. Symposium (International) on Combustion, 24(1):129–135, 1992.
[95] D. Thévenin. Three-dimensional direct simulations and structure of expanding
turbulent methane flames. Proceedings of the Combustion Institute, 30:629–637,
2005.
[96] I. G. Shepherd and W. T. Ashurst. Flame front geometry in premixed turbulent
flames. Proceedings of the Combustion Institute, 24(1):485–491, 1992.
[97] F. C. Gouldin and P. C. Miles. Chemical closure and burning rates in premixed
turbulent flames,. Combustion and Flame, 100(1–2):202–210, 1995.
List of Figures
2.1 Schematic showing the structure of a laminar premixed flame. . . . . . . 8
2.2 Comparison of various progress variables. . . . . . . . . . . . . . . . . . . 10
2.3 Modified Borghi diagram for classifying turbulent flames. . . . . . . . . . 12
3.1 Schematic of the stratified slot burner. . . . . . . . . . . . . . . . . . . . 27
3.2 Schematic of the exit geometry of the stratified slot burner. . . . . . . . . 28
3.3 Illustration of multi-scalar laser diagnostics system. . . . . . . . . . . . . 30
3.4 Elevation of the stratified slot burner . . . . . . . . . . . . . . . . . . . . 37
3.5 Stratified swirl burner exit geometry. . . . . . . . . . . . . . . . . . . . . 38
3.6 Swirl burner multi-scalar measurement locations. . . . . . . . . . . . . . 42
3.7 PIV seeder design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.8 Sample PIV images for the swirl burner. . . . . . . . . . . . . . . . . . . 48
4.1 OH-PLIF image pre-processing. . . . . . . . . . . . . . . . . . . . . . . . 52
4.2 Coordinate systems for cross-planar OH-PLIF. . . . . . . . . . . . . . . . 54
4.3 Curvature calibration images. . . . . . . . . . . . . . . . . . . . . . . . . 55
4.4 Demonstration of continuous curvature results. . . . . . . . . . . . . . . . 57
4.5 Comparison of discrete and continuous measures of curvature. . . . . . . 58
4.6 Derivation of OH progress variable images. . . . . . . . . . . . . . . . . . 60
4.7 Demonstration of differential diffusion effects in laminar flame calculations. 62
4.8 Variation in progress variables due to stratification. . . . . . . . . . . . . 65
4.9 Demonstration of lookup table correction of differential diffusion effects
in laminar flame calculations. . . . . . . . . . . . . . . . . . . . . . . . . 66
4.10 Effect of lookup table correction for differential diffusion in experimental
data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.11 Photographs of vertical flame burner. . . . . . . . . . . . . . . . . . . . . 68
220
List of Figures 221
4.12 Schematic characterizing location of differential diffusion effect using nor-
malized temperature and temperature gradient. . . . . . . . . . . . . . . 69
4.13 Flow chart for linear bridging function for correction of differential diffu-
sion effects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.14 Linear bridging function parameters. . . . . . . . . . . . . . . . . . . . . 72
4.15 Demonstration of linear bridging function to correct differential diffusion
effects in instantaneous experimental data. . . . . . . . . . . . . . . . . . 73
4.16 Demonstration of mean effect of applying linear bridging function to ex-
perimental data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.1 Slot burner hot wire velocity measurements. . . . . . . . . . . . . . . . . 85
5.2 Modified Borghi diagram showing slot burner. . . . . . . . . . . . . . . . 86
5.3 Instantaneous profiles of temperature and equivalence ratio for slot burner. 87
5.4 Sample OH images and curvatures for slot burner. . . . . . . . . . . . . . 88
5.5 Favre averages for slot burner cases. . . . . . . . . . . . . . . . . . . . . . 90
5.6 Favre-averaged RMS fluctuations for slot burner cases. . . . . . . . . . . 91
5.7 Pdfs of 2D equivalence ratio gradient for the slot burner. . . . . . . . . . 93
5.8 Plots of temperature against scalars for premixed slot burner cases. . . . 95
5.9 Plots of temperature against scalars for moderately stratified slot burner
cases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.10 Plots of temperature against scalars for highly stratified slot burner cases. 97
5.11 Pdfs of discrete curvature for the slot burner. . . . . . . . . . . . . . . . 98
5.12 Pdfs of continuous curvature for the slot burner. . . . . . . . . . . . . . . 100
5.13 Joint pdfs of progress variable and continuous curvature for the slot burner.101
5.14 Instantaneous OH-PLIF contour plot for premixed slot burner case. . . . 102
5.15 Relationship between progress variable and surface density function for
slot burner cases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.16 Relationship between progress variable and scalar dissipation rate for slot
burner cases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.17 Behavior of scalar gradients in progress variable space conditioned on
equivalence ratio for slot burner cases. . . . . . . . . . . . . . . . . . . . 105
5.18 Curvature conditioned mean fits of surface density function against progress
variable for the slot burner cases. . . . . . . . . . . . . . . . . . . . . . . 106
5.19 Flame surface density in the slot burner cases. . . . . . . . . . . . . . . . 107
List of Figures 222
6.1 Photographic survey of swirl burner cases (long exposure). . . . . . . . . 113
6.2 Photographic survey of swirl burner cases (short exposure). . . . . . . . . 114
6.3 Non-reacting velocity fields for swirl burner cases. . . . . . . . . . . . . . 115
6.4 Reacting velocity fields for swirl burner cases. . . . . . . . . . . . . . . . 118
6.5 Extended recirculation zone in swirl burner case with very high swirl. . . 120
6.6 Near-exit velocity profiles for the swirl burner cases. . . . . . . . . . . . . 122
6.7 Modified Borghi diagram showing both slot and swirl burner cases. . . . 126
6.8 Instantaneous profiles of temperature and equivalence ratio for the swirl
burner cases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
6.9 Demonstration of multi-scalar measurement resolution in swirl burner data.133
6.10 Sample OH-PLIF images and corresponding continuous curvature in the
swirl burner. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
6.11 Thermal flame structure in the swirl burner. . . . . . . . . . . . . . . . . 136
6.12 Compositional flame structure in the swirl burner. . . . . . . . . . . . . . 138
6.13 Pdfs of two-dimensional equivalence ratio gradients for the swirl burner
cases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
6.14 Favre averages for the lean non-swirling cases in the swirl burner. . . . . 145
6.15 Favre-averaged fluctuations for the lean non-swirling cases in the swirl
burner. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
6.16 Favre averages for the lean moderately swirling cases in the swirl burner. 149
6.17 Favre-averaged fluctuations for the lean moderately swirling cases in the
swirl burner. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
6.18 Favre averages for the lean highly swirling cases in the swirl burner. . . . 152
6.19 Favre-averaged fluctuations for the lean highly swirling cases in the swirl
burner. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
6.20 Favre averages for the stoichiometric cases in the swirl burner. . . . . . . 156
6.21 Favre-averaged fluctuations for the stoichiometric cases in the swirl burner.157
6.22 Behavior of YCO2 in temperature space for swirl burner cases. . . . . . . . 161
6.23 Behavior of YCO in temperature space for swirl burner cases. . . . . . . . 164
6.24 Behavior of YH2 in temperature space for swirl burner cases. . . . . . . . 166
6.25 Behavior of YH2O in temperature space for swirl burner cases. . . . . . . . 167
6.26 Behavior of YO2 in temperature space for swirl burner cases. . . . . . . . 168
6.27 Behavior of species in temperature space conditioned on equivalence ratio
for swirl burner cases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
List of Figures 223
6.28 Behavior of discrete curvature with axial distance for the swirl burner cases.173
6.29 Pdfs of curvature for the swirl burner cases. . . . . . . . . . . . . . . . . 175
6.30 Bivariate pdfs of continuous curvature and progress variable for the swirl
burner cases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
6.31 Pdfs of progress variable for the swirl burner cases. . . . . . . . . . . . . 180
6.32 Bivariate pdfs of progress variable and equivalence ratio for the swirl
burner cases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
6.33 Behavior of surface density function with progress variable for the swirl
burner cases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
6.34 Behavior of scalar dissipation rate with progress variable for the swirl
burner cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
6.35 Equivalence ratio conditioned mean fits of scalar gradients against progress
variable for the swirl burner cases. . . . . . . . . . . . . . . . . . . . . . . 187
6.36 Pdfs of turbulent flame thickness for the swirl burner cases. . . . . . . . . 188
6.37 Curvature conditioned mean fits of turbulent flame thickness for the swirl
burner cases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
6.38 Flame surface density for swirl burner cases. . . . . . . . . . . . . . . . . 192
7.1 Comparison of FSD metrics using slot burner data. . . . . . . . . . . . . 197
7.2 Comparison of FSD metrics using swirl burner data. . . . . . . . . . . . . 200
7.3 Comparison of FSD metrics derived from OH using swirl burner data. . . 201
7.4 Effect of scalar choice on statistical FSD metric. . . . . . . . . . . . . . . 202
List of Tables
3.1 Slot burner operating conditions and flow rates. . . . . . . . . . . . . . . 29
3.2 Slot burner measurement uncertainties. . . . . . . . . . . . . . . . . . . . 33
3.3 Swirl burner operating conditions. . . . . . . . . . . . . . . . . . . . . . . 40
3.4 Swirl burner measurement uncertainties. . . . . . . . . . . . . . . . . . . 43
3.5 Size of PIV datasets in swirl burner. . . . . . . . . . . . . . . . . . . . . 46
4.1 Finite difference coefficients. . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.2 Slot burner propagated uncertainties. . . . . . . . . . . . . . . . . . . . . 78
5.1 Slot burner cold flow properties. . . . . . . . . . . . . . . . . . . . . . . . 86
5.2 2D equivalence ratio gradient statistics for the slot burner. . . . . . . . . 93
5.3 Curvature statistics for the slot burner. . . . . . . . . . . . . . . . . . . . 99
5.4 Effect of stratification on doubly conditioned scalar gradients for the slot
burner cases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.1 Swirl burner turbulence parameters at z = 10mm. . . . . . . . . . . . . . 127
6.2 Swirl burner turbulence parameters at z = 10mm. . . . . . . . . . . . . . 128
6.3 Swirl burner turbulence parameters at the intersection of the mixing layer
and the mean flame brush. . . . . . . . . . . . . . . . . . . . . . . . . . . 129
6.4 Two-dimensional equivalence ratio gradients for sample instantaneous swirl
burner data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
6.5 Radial and axial locations of the intersection of the mixing layer with the
mean flame brush in the swirl burner cases. . . . . . . . . . . . . . . . . 140
6.6 Statistics for 2D equivalence ratio gradients in the swirl burner cases. . . 142
6.7 Curvature statistics for the swirl burner cases. . . . . . . . . . . . . . . . 177
6.8 Turbulent flame thickness statistics for the swirl burner cases. . . . . . . 189
224
Author Index
Alkidas [4], 5, 13
Anselmo-Filho et al. [21], 15, 16, 31, 77, 94,
96, 170
Anselmo-Filho [52], 25, 26, 32, 82
Arcoumanis et al. [16], 13
Böhm et al. [23], 15, 20
Barlow et al. [44], 20, 21, 25, 29, 30
Barlow et al. [69], 65, 66, 143, 158, 161
Bauer [3], 5, 13
Bilger et al. [64], 58
Bilger [73], 75
Bilger [75], 75
Bonaldo and Kelman [83], 96
Bray et al. [35], 18, 75
Bray et al. [7], 11, 61
Buschmann et al. [40], 20
Canny [62], 57
Cant and Mastorakos [6], 8, 9, 12
Cant et al. [66], 61
Chen and Bilger [42], 20, 77
Cohé et al. [80], 77
Darbyshire et al. [57], 34
Da Cruz et al. [27], 16, 17, 85
Degardin et al. [46], 20, 25
Dong et al. [82], 82
Drake and Haworth [5], 5, 13
Dunn and Barlow [58], 42
Dunn et al. [43], 20
Duwig and Fureby [12], 13, 18
Echekki and Mastorakos [9], 12
Eckbreth et al. [47], 21
Eckbreth [39], 19
Filatyev et al. [51], 25
Galizzi and Escudié [25], 15, 16
Galizzi and Escudié [17], 14, 16
Geyer et al. [49], 21
Gottgens et al. [92], 185
Gouldin and Miles [95], 193
Green and Zavier [15], 13
Gregor et al. [45], 20
Hélie and Trouvé [30], 17, 18
Haworth et al. [32], 18
Jiménez et al. [33], 18
Johnstone et al. [56], 33
Kaneda et al. [87], 118
Kang and Kyritsis [13], 13, 14
Karpetis and Barlow [54], 29, 51
Karpetis et al. [53], 29, 31, 51, 73
Kass et al. [61], 54
Kiefer et al. [79], 77
Klimenko and Bilger [72], 75
Knudsen and Pitsch [37], 18
Laboratories [67], 62
Lam et al. [63], 57
225
Author Index 226
Lee et al. [50], 25
Levy [90], 156
Mansour [1], 5, 13
Martin et al. [71], 75
Marzouk [28], 17, 85
Masri et al. [48], 21
Meier et al. [10], 13
Moureau et al. [85], 98, 100, 180, 186
Nguyen et al. [38], 18
Nickolaus et al. [2], 5, 13
Pasquier et al. [19], 14
Peters [70], 75
Peters [74], 75
Poinsot et al. [31], 18
Pope [65], 61, 77, 78, 103, 187, 192
Renou et al. [18], 14, 25, 94, 170
Richardson et al. [29], 17, 85
Robin et al. [20], 14, 18, 20, 185, 187
Robin et al. [34], 18
Sankaran et al. [84], 98, 100, 180, 186
Seffrin et al. [22], 15
Sengissen et al. [11], 13, 18
Shepherd and Ashurst [94], 193
Shepherd and Cheng [78], 77
Shepherd [77], 77–79, 94, 192, 193
Shoshin et al. [88], 156
Shoshin et al. [89], 156
Smith and Golden [68], 62
Source [60], 53
Sweeney and Hochgreb [59], 50, 57
Sweeney et al. [24], 15, 16, 20, 192
Sweeney et al. [76], 77, 193
Sweeney et al. [86], 104
Tan and Reitz [36], 18
Thévenin [93], 187
Turns [14], 13
Vena et al. [26], 15, 16
Veynante and Vervisch [8], 12, 75
Veynante et al. [81], 77, 78, 193
Wang and Clemens [55], 31
von Lavante and Strehlow [91], 156
O’Young and Bilger [41], 20
Colophon
This thesis is typeset in Computer Moderna using LATEX2ε with the hepthesis
b class
with modifications made by the author. American English is used throughout. Figures
are generated using Matlabc, GNU Image Manipulation Programd, Pro/ENGINEERe,
and Xfigf.
ahttp://www.tug.dk/FontCatalogue/cmr/
bhttp://www.ctan.org/tex-archive/help/Catalogue/entries/hepthesis.html
chttp://www.matlab.com/
dhttp://www.gimp.org
ehttp://www.ptc.com/products/creo-elements-pro/
fhttp://www.xfig.org/
227