Simulations of turbulent swirl
combustors
Simon Ayache
Department of Engineering
University of Cambridge
Selwyn College
A thesis submitted for the degree of
Doctor of Philosophy
Tuesday, 20th of December, 2011
A` mes parents Laurent et Re´gine, et mes grands-parents Henri et
Simonne.
Dla mojej ukochanej z˙ony, Urszuli.
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. The dissertation contains approximately 63,500 words, 138 figures and 5
tables.
Signature :
Name : Simon Ayache
Date : Tuesday, 20th of December, 2011
ii
Acknowledgements
I am very grateful to many people for their support and their help throughout
the duration of my PhD.
First and foremost, I would like to thank my supervisor, Prof. Epaminondas
Mastorakos, for his guidance throughout my PhD. His continuous availability and
insight have contributed towards making my PhD years at Cambridge go very
smoothly and pleasantly.
I also express my sincere thanks to Mr Peter Benie (Cambridge) for his help
and expertise in Computing Science. Little would be possible in Hopkinson Lab-
oratory without his support. I would also like to thank Dr. Marco Zedda (Rolls-
Royce UK) for welcoming me in his CFD team in Derby and for making my
stay in Derby a fruitful one, even though the work I conducted there could not
be included in this thesis. I also wish to express my gratitude to the European
Commission for its financial support granted through the Marie Curie Project
MYPLANET.
I would like to thank my friends from Selwyn College as well as my colleagues
from the MYPLANET project and the University of Cambridge who created a
pleasant atmosphere that lasted all the way through my PhD. In particular, I
wish to thank Andrea Maffioli, Alexandre and Carole Neophytou, Camille Letty,
Ivan Bahena-Ledezma, Robert Gordon, Theresa Leung, Thibault Pringuey, Frank
Yuen, Davide Cavaliere, Peter Schroll, Andrea Pastore and Cheng Tung Chong.
I hope to preserve our friendship in the future.
Thanks to my parents who have always believed in me and supported me
during my studies.
My final thanks go to Ula, a former Selwyn College mate who recently decided
to take my last name. You have been with me all the way through this PhD, and
iii
I am so grateful for that. This thesis would not have been possible without you.
iv
Publications
Journal publications
1. S. Ayache, J.R. Dawson, A. Triantafyllidis, R. Balachandran, E. Mas-
torakos, Experiments and large-eddy simulations of acoustically-forced bluff-
body flows. International Journal of Heat and Fluid Flow, 31 (5), pp. 754-
766. ISSN 0142-727X, 2010.
2. S. Ayache, E. Mastorakos, Conditional Moment Closure/Large Eddy Simu-
lation of the Delft-III natural gas non-premixed jet flame. Flow, Turbulence
and Combustion, 88, pp. 207-231. ISSN 1386-6184, 2012.
3. S. Ayache, E. Mastorakos, Investigation of the “TECFLAM” non-premixed
flame using Large Eddy Simulation and Proper Orthogonal Decomposition.
Flow, Turbulence and Combustion, submitted.
Conference publications
1. S. Ayache, J.R. Dawson, A. Triantafyllidis, R. Balachandran, E. Mas-
torakos, Experiments and large-eddy simulations of acoustically-forced bluff-
body flows. Proceedings of Sixth International Symposium on Turbulence,
Heat and Mass Transfer, Rome, Italy, 14-18 September 2009.
2. S. Ayache, E. Mastorakos, Conditional Moment Closure/Large Eddy Sim-
ulation of the Delft-III natural gas non-premixed jet flame. Proceedings of
the Eighth International Symposium on Engineering Turbulence Modelling
and Measurements, Marseille, France, 9-11 June 2010.
v
3. S. Ayache, E. Mastorakos. LES of the confined swirling non-premixed
TECFLAM S09c flame using Conditional Moment Closure, Proceedings of
the Fifth European Combustion Meeting, Cardiff, Wales, UK, 28 June-1
July 2011.
4. S. Ayache, E. Mastorakos, Investigation of the TECFLAM non-premixed
flame using Large Eddy Simulation and Proper Orthogonal Decomposition,
Proceedings of the Seventh Mediterranean Combustion Symposium, Chia
Laguna, Cagliari, Sardinia, Italy, 11-15 September 2011.
vi
Abstract
This thesis aims at improving our knowledge on swirl combustors. The work
presented here is based on Large Eddy Simulations (LES) coupled to an ad-
vanced combustion model: the Conditional Moment Closure (CMC). Numerical
predictions have been systematically compared and validated with detailed ex-
perimental datasets. In order to analyze further the physics underlying the large
numerical datasets, Proper Orthogonal Decomposition (POD) has also been used
throughout the thesis. Various aspects of the aerodynamics of swirling flames are
investigated, such as precession or vortex formation caused by flow oscillations, as
well as various combustion aspects such as localized extinctions and flame lift-off.
All the above affect flame stabilization in different ways and are explored through
focused simulations.
The first study investigates isothermal air flows behind an enclosed bluff body,
with the incoming flow being pulsated. These flows have strong similarities to
flows found in combustors experiencing self-excited oscillations and can therefore
be considered as canonical problems. At high enough forcing frequencies, double
ring vortices are shed from the air pipe exit. Various harmonics of the pulsating
frequency are observed in the spectra and their relation with the vortex shedding
is investigated through POD.
The second study explores the structure of the Delft III piloted turbulent
non-premixed flame. The simple configuration allows to analyze further key com-
bustion aspects of combustors, with further insights provided on the dynamics of
localized extinctions and re-ignition, as well as the pollutants emissions.
The third study presents a comprehensive analysis of the aerodynamics of
swirl flows based on the TECFLAM confined non-premixed S09c configuration.
A periodic component inside the air inlet pipe and around the central bluff body
vii
is observed, for both the inert and reactive flows. POD shows that these flow
oscillations are due to single and double helical vortices, similar to Precessing
Vortex Cores (PVC), that develop inside the air inlet pipe and whose axes rotate
around the burner. The combustion process is found to affect the swirl flow
aerodynamics.
Finally, the fourth study investigates the TECFLAM configuration again, but
here attention is given to the flame lift-off evident in experiments and reproduced
by the LES-CMC formulation. The stabilization process and the pollutants emis-
sion of the flame are investigated in detail.
viii
Contents
Contents ix
List of Figures xiv
List of Tables xxviii
1 Introduction 1
1.1 Swirl flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Motivation of studying swirl flows . . . . . . . . . . . . . . . . . . 1
1.3 Methods of investigation . . . . . . . . . . . . . . . . . . . . . . . 2
1.4 Scope of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Literature review 5
2.1 The problem of flame stabilization: localized extinction, lift-off and
blow-off . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Aerodynamics and stabilization of flames without swirl . . . . . . 7
2.2.1 Canonical problem for flame stabilization . . . . . . . . . . 7
2.2.2 Bluff body flows . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.3 Flows behind a sudden expansion . . . . . . . . . . . . . . 9
2.2.4 Sudden expansion and bluff body flows . . . . . . . . . . . 10
2.3 Aerodynamics and stabilization of swirl flames . . . . . . . . . . . 10
2.3.1 Swirl flow characterization . . . . . . . . . . . . . . . . . . 10
2.3.2 Vortex breakdown and recirculation zone . . . . . . . . . . 11
2.3.3 Precessing Vortex Core . . . . . . . . . . . . . . . . . . . . 13
2.3.4 Stabilization of swirl flames . . . . . . . . . . . . . . . . . 14
ix
CONTENTS
2.4 Combustion instabilities . . . . . . . . . . . . . . . . . . . . . . . 16
2.4.1 Acoustic instabilities . . . . . . . . . . . . . . . . . . . . . 16
2.4.2 Hydrodynamic instabilities . . . . . . . . . . . . . . . . . . 17
2.4.3 Pulsating flows . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4.3.1 Bluff body flows . . . . . . . . . . . . . . . . . . 19
2.4.3.2 Flows behind a sudden expansion . . . . . . . . . 19
2.4.3.3 Sudden expansion and bluff body flows . . . . . . 19
2.5 Pollutants emissions . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.5.1 Pollutants formation . . . . . . . . . . . . . . . . . . . . . 20
2.5.2 Reduction of emissions . . . . . . . . . . . . . . . . . . . . 21
2.6 Simulations of swirl flames . . . . . . . . . . . . . . . . . . . . . . 23
2.6.1 Examples of simulations . . . . . . . . . . . . . . . . . . . 24
2.6.2 Prediction of emissions . . . . . . . . . . . . . . . . . . . . 25
2.7 Context of the work and its objectives . . . . . . . . . . . . . . . 26
3 Models and codes 28
3.1 Large Eddy Simulations . . . . . . . . . . . . . . . . . . . . . . . 28
3.2 Combustion modelling . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2.1 Mixture fraction . . . . . . . . . . . . . . . . . . . . . . . 31
3.2.2 3D-CMC . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2.3 0D-CMC . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2.4 Coupling LES-CMC . . . . . . . . . . . . . . . . . . . . . 34
3.3 Proper Orthogonal Decomposition . . . . . . . . . . . . . . . . . . 36
3.3.1 Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4 Large-eddy simulations of forced bluff body flows 40
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.1.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.2.1 Flow conditions . . . . . . . . . . . . . . . . . . . . . . . . 43
4.2.2 Mesh and modelling . . . . . . . . . . . . . . . . . . . . . 46
x
CONTENTS
4.2.3 Data processing and comparison with experiments . . . . . 47
4.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . 48
4.3.1 The unforced flow . . . . . . . . . . . . . . . . . . . . . . . 48
4.3.2 Phase-averaged velocities and turbulent intensities . . . . . 50
4.3.3 Spectra and vortex formation . . . . . . . . . . . . . . . . 59
4.4 Proper Orthogonal Decomposition analysis of the 160Hz forced flow 66
4.4.1 Mode 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.4.2 Modes 1 and 2 . . . . . . . . . . . . . . . . . . . . . . . . 68
4.4.3 Modes 3 and 4 . . . . . . . . . . . . . . . . . . . . . . . . 75
4.4.4 Modes 6 and 7 . . . . . . . . . . . . . . . . . . . . . . . . 76
4.4.5 Mode 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.4.6 Mode 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.4.7 Conclusions from the POD analysis of the 160 Hz case . . 84
4.5 Summary of main findings . . . . . . . . . . . . . . . . . . . . . . 87
5 Conditional Moment Closure/Large Eddy Simulation of the Delft-
III natural gas non-premixed jet flame 88
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.1.2 Background works . . . . . . . . . . . . . . . . . . . . . . 89
5.1.3 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.2.1 Model and codes . . . . . . . . . . . . . . . . . . . . . . . 90
5.2.2 Flow considered, boundary conditions and numerical methods 90
5.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . 96
5.3.1 Instantaneous distributions . . . . . . . . . . . . . . . . . . 96
5.3.2 Velocity and mixture fraction fields . . . . . . . . . . . . . 97
5.3.3 Reaction zone and localised extinctions . . . . . . . . . . . 101
5.3.4 Temperature prediction and pollutants emissions . . . . . 113
5.4 Summary of main findings . . . . . . . . . . . . . . . . . . . . . . 114
6 Investigation of the aerodynamics of a non-premixed swirl flame
using LES 126
xi
CONTENTS
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
6.1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
6.1.2 Background works . . . . . . . . . . . . . . . . . . . . . . 127
6.1.3 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6.2.1 Flow computed . . . . . . . . . . . . . . . . . . . . . . . . 128
6.2.2 Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6.2.3 Large Eddy Simulation and combustion modelling . . . . . 129
6.2.4 Boundary conditions . . . . . . . . . . . . . . . . . . . . . 130
6.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . 130
6.3.1 Analysis of the steady flame . . . . . . . . . . . . . . . . . 130
6.3.2 Mean and instantaneous flow fields . . . . . . . . . . . . . 131
6.3.3 Mean radial profiles . . . . . . . . . . . . . . . . . . . . . . 133
6.3.4 Inert simulation . . . . . . . . . . . . . . . . . . . . . . . . 134
6.3.5 Autocorrelation and spectra . . . . . . . . . . . . . . . . . 135
6.3.6 Swirl-induced separation inside the burner . . . . . . . . . 136
6.3.7 Proper Orthogonal Decomposition . . . . . . . . . . . . . . 137
6.3.7.1 2D POD . . . . . . . . . . . . . . . . . . . . . . . 137
6.3.7.2 3D POD . . . . . . . . . . . . . . . . . . . . . . . 142
6.3.7.3 Inert versus reactive rotating vortices . . . . . . . 146
6.4 Summary of main findings . . . . . . . . . . . . . . . . . . . . . . 147
7 Conditional Moment Closure/Large Eddy Simulation of a lifted
non-premixed swirl flame 186
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
7.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
7.2.1 Models and codes . . . . . . . . . . . . . . . . . . . . . . . 187
7.2.2 Boundary conditions and numerical methods . . . . . . . . 188
7.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . 189
7.3.1 Instantaneous distributions . . . . . . . . . . . . . . . . . . 189
7.3.2 Velocity and mixture fraction fields . . . . . . . . . . . . . 191
7.3.3 Reaction zone and lift-off . . . . . . . . . . . . . . . . . . . 197
7.3.4 Flame dynamics and lift-off . . . . . . . . . . . . . . . . . 202
xii
CONTENTS
7.3.5 Temperature, species and pollutants prediction . . . . . . 210
7.4 Summary of main findings . . . . . . . . . . . . . . . . . . . . . . 216
8 Conclusions 228
8.1 Overview of the PhD work . . . . . . . . . . . . . . . . . . . . . . 228
8.2 LES of forced bluff body flows . . . . . . . . . . . . . . . . . . . . 229
8.3 CMC/LES of the Delft-III natural gas non-premixed jet flame . . 230
8.4 Investigation of the aerodynamics of a non-premixed swirl flame
using LES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
8.5 CMC/LES of a lifted non-premixed swirl flame . . . . . . . . . . 233
8.6 Guidelines for further studies . . . . . . . . . . . . . . . . . . . . 233
References 236
xiii
List of Figures
2.1 Schematic of a bluff-body flow. . . . . . . . . . . . . . . . . . . . 7
2.2 Schematic diagram of processes leading to CRZ formation. From
Ref. [112]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3 (a) Visualization of a PVC structure as predicted by LES at the
exit of the swirler using an isosurface of low pressure. From Ref.
[96]. (b) A sketch of a PVC. From Ref. [21]. . . . . . . . . . . . . 14
2.4 Effect of combustion upon the PVC with (a) 100% axial fuel in-
jection (b) premixing, S = 1.98, equivalence ratio 0.89. In Fig.
(a), the term “pressure” refers to the mean pressure, while in Fig.
(b) the term “R.M.S” refers to the R.M.S of the pressure. Figures
from Ref. [112]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.5 Links between different quantities in typical gas turbine combus-
tion instabilities. From Ref. [99]. . . . . . . . . . . . . . . . . . . 18
3.1 Schematic showing the coupling of the CFD and the CMC solvers
according to the type of computation: 0D-CMC or 3D-CMC. . . . 37
4.1 Schematic of the flow studied and the initial condition. . . . . . . 41
4.2 Photograph of the burner assembly. From Ref. [4]. . . . . . . . . 42
4.3 The bluff body and the sudden expansion. All lengths in mm. . . 44
4.4 Snapshots of (a) axial velocity (in m/s) and (b) azimuthal vorticity
(ωθ = ∂v/∂x − ∂u/∂r; in 1/s) on a plane going through the axis
from LES. Unforced flow (Case U). . . . . . . . . . . . . . . . . . 49
xiv
LIST OF FIGURES
4.5 Contour of the time-averaged axial velocity (in m/s) from the LES.
Points A-F are at locations (x, r)=(5,0), (5,15), (5,30), (50,0),
(50,15), (50,30) respectively, in mm; r is distance from the axis
and x the axial distance from the bluff body. Unforced flow (Case
U). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.6 Frequency spectra of the axial velocity from (a) experiment and
(b) LES. Unforced flow (Case U). Locations 1-6 correspond re-
spectively to an (axial, radial) coordinate in mm of: (5,0), (5,15),
(15,0), (15,15), (25,0), and (25,15). Each spectrum has been shifted
upwards by a factor of 103. Points 1 and 2 are, respectively, the
locations A and B marked on Fig. 4.5. . . . . . . . . . . . . . . . 51
4.7 Phase-averaged mean (a,c,e) and RMS (b,d,f) axial velocity from
the LES at the annular exit (x = 0). (a,b): Case A; (c,d): Case B;
(e,f): Case C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.8 Phase-averaged mean (a,b) and RMS (c,d) axial velocities from
experiment and LES. Forced flow, 40 Hz (Case A). The locations
are given in terms of (x, r) in mm and correspond to points A-C
(a,c) and D-F (b,d). . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.9 Phase-averaged mean (a,b) and RMS (c,d) axial velocities from
experiment and LES. Forced flow, 160 Hz (Case B). The locations
are given in terms of (x, r) in mm and correspond to points A-C
(a,c) and D-F (b,d). . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.10 Phase-averaged mean (a,b) and RMS (c,d) axial velocities from
experiment and LES. Forced flow, 320 Hz (Case C). The locations
are given in terms of (x, r) in mm and correspond to points A-C
(a,c) and D-F (b,d). . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.11 Sequence of instantaneous axial velocity snapshots at different con-
secutive instants and over one period for the 40 Hz forced case. . . 60
4.12 Sequence of instantaneous axial velocity snapshots at different con-
secutive instants and over one period for the 160 Hz forced case. . 61
4.13 Frequency spectra of the axial velocity from (a) experiment and
(b) LES. Forced flow, 40 Hz (Case A). Locations as in Fig. 4.6. . 62
xv
LIST OF FIGURES
4.14 Frequency spectra of the axial velocity from (a) experiment and
(b) LES. Forced flow, 160 Hz (Case B). Locations as in Fig. 4.6. . 63
4.15 Frequency spectra of the axial velocity from (a) experiment and
(b) LES. Forced flow, 320 Hz (Case C). Locations as in Fig. 4.6. . 64
4.16 Iso-surfaces of Q = 15 × 106 1/s2 from sequential snapshots from
the LES, showing the evolution of the shed vortices for (a) Cases
A, (b) Case B, and (c) Case C. For the definition of Q, see text. . 65
4.17 Mode 1. (a,b) Isosurfaces of the Q−criterion coloured by the pres-
sure fluctuations. Contours of the fluctuations of (c) the pressure
and (d) the axial velocity. The blue colour shows the negative fluc-
tuations, the red colour shows the positive fluctuations, while the
green colour shows the zero-fluctuation area. Forced case at 160 Hz. 69
4.18 Sequence of the Q−criterion of the reconstructed instantaneous
flow coloured by the reconstructed pressure at different consecutive
instants and over one period using mode 1. Forced case at 160 Hz. 70
4.19 Sequence of the axial velocity of the reconstructed instantaneous
flow at different consecutive instants and over one period using
mode 1. Forced case at 160 Hz. . . . . . . . . . . . . . . . . . . . 71
4.20 Axial velocity fields superimposed over one period. The black lines
represent the instantaneous zero axial velocity isoline. Forced case
at 160 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.21 Mode 2. (a,b) Isosurfaces of the Q−criterion coloured by the pres-
sure fluctuations. Contours of the fluctuations of (c) the pressure
and (d) the axial velocity. Colours as in Fig. 4.17. Forced case at
160 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.22 Sequence of the Q−criterion of the reconstructed instantaneous
flow coloured by the reconstructed pressure at different consecutive
instants and over one period using modes 1 and 2. Forced case at
160 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.23 Sequence of the axial velocity of the reconstructed instantaneous
flow at different consecutive instants and over one period using
modes 1 and 2. Forced case at 160 Hz. . . . . . . . . . . . . . . . 74
xvi
LIST OF FIGURES
4.24 Mode 3. (a,b) Isosurfaces of the Q−criterion coloured by the pres-
sure fluctuations. Contours of the fluctuations of (c) the pressure
and (d) the axial velocity. Colours as in Fig. 4.17. Forced case at
160 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.25 Mode 4. (a,b) Isosurfaces of the Q−criterion coloured by the pres-
sure fluctuations. Contours of the fluctuations of (c) the pressure
and (d) the axial velocity. Colours as in Fig. 4.17. Forced case at
160 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.26 Q−criterion of the reconstructed instantaneous flow over one pe-
riod using modes 3 and 4. Forced case at 160 Hz. . . . . . . . . . 77
4.27 Axial velocity of the reconstructed instantaneous flow over one
period using modes 3 and 4. Forced case at 160 Hz. . . . . . . . . 78
4.28 Mode 6. (a,b) Isosurfaces of the Q−criterion coloured by the pres-
sure fluctuations. Contours of the fluctuations of (c) the pressure
and (d) the axial velocity. Forced case at 160 Hz. . . . . . . . . . 79
4.29 Mode 7. (a,b) Isosurfaces of the Q−criterion coloured by the pres-
sure fluctuations. Contours of the fluctuations of (c) the pressure
and (d) the axial velocity. Forced case at 160 Hz. . . . . . . . . . 80
4.30 Q−criterion of the reconstructed instantaneous flow over one pe-
riod using modes 6 and 7. Forced case at 160 Hz. . . . . . . . . . 81
4.31 Axial velocity of the reconstructed instantaneous flow over one
period using modes 6 and 7. Forced case at 160 Hz. . . . . . . . . 82
4.32 Mode 5. (a,b) Isosurfaces of the Q−criterion coloured by the pres-
sure fluctuations. Contours of the fluctuations of (c) the pressure
and (d) the axial velocity. Forced case at 160 Hz. . . . . . . . . . 83
4.33 Mode 8. (a,b) Isosurfaces of the Q−criterion coloured by the pres-
sure fluctuations. Contours of the fluctuations of (c) the axial
velocity and (d,e) the pressure, with Fig. (e) showing a transverse
plane. Forced case at 160 Hz. . . . . . . . . . . . . . . . . . . . . 83
4.34 Energy distribution of the POD modes. (a) Energy relative per
mode. (b) Cummulative energy. Forced case at 160 Hz. . . . . . . 84
4.35 Fourier analysis of the temporal coefficents of POD modes 1 to 4.
Forced case at 160 Hz. . . . . . . . . . . . . . . . . . . . . . . . . 85
xvii
LIST OF FIGURES
4.36 Fourier analysis of the temporal coefficents of POD modes 5 to 8.
Forced case at 160 Hz. . . . . . . . . . . . . . . . . . . . . . . . . 86
5.1 Delft piloted jet burner. From Ref. [81]. . . . . . . . . . . . . . . 91
5.2 (a) Maximum values of some reactive scalars of the steady flame
against the scalar dissipation rate N0, using the detailed chemistry
GRI-Mech 3.0 (53 species, 325 reactions). The extinction strain
rate is found to be equal to 193 1/s. (b) Conditional profiles of
some reactive scalars from the 0D-CMC computation with N0 =
20 1/s. This solution is used as the prescribed distribution in the
LES/0D-CMC computation and is injected at the pilot location in
the LES/3D-CMC. . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.3 Longitudinal cutting plane (z=0) of the LES grid (1.3M cells). . . 94
5.4 (a) Enlargement of the LES grid (black) and CMC grid (red) in
the transverse direction. A CMC cell contains several LES cells,
the ratio depending on the location inside the domain. Each CMC
cell has its center located at an intersection of the red lines. (b)
Sketch of the CMC boundary conditions: inert everywhere except
for the pilot where a fully burning flamelet is imposed. . . . . . . 95
5.5 Typical instantaneous contours of (a) axial velocity (in m/s) and
(b) z−vorticity (in 1/s) at the same instant. The stoichiometric
iso-surface is shown with the black line. Axes in m. (c): Instanta-
neous iso-surface of Q = 50× 103s−2 colored with the temperature
(in K). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.6 Typical instantaneous contours of the mixture fraction, tempera-
ture and mass fractions of OH at the same instant. The stoichio-
metric iso-surface is shown with the black line. . . . . . . . . . . . 99
5.7 Typical instantaneous contours of the mass fractions of the indi-
cated species at the same instant. The stoichiometric iso-surface
is shown with the black line. . . . . . . . . . . . . . . . . . . . . . 100
5.8 Radial profiles of the mean axial velocity at the indicated axial
position. Experimental data from Ref. [27]. . . . . . . . . . . . . 102
xviii
LIST OF FIGURES
5.9 Radial profiles of the RMS of the axial velocity at the indicated
axial position. Experimental data from Ref. [27]. . . . . . . . . . 103
5.10 Radial profiles of the mean of the mixture fraction at the indicated
axial position. Experimental data from Ref. [27]. . . . . . . . . . 104
5.11 Radial profiles of the RMS of the mixture fraction at the indicated
axial position. Experimental data from Ref. [27]. . . . . . . . . . 105
5.12 Typical instantaneous OH mass fraction contour, with the CMC
grid superimposed. Regions 1 and 2 are discussed in the text. . . 106
5.13 Typical instantaneous OH images, covering the regions x = 15 to
93 mm, 100 to 178 mm and 185 to 263 mm. Each image from the
different regions has been taken at different time.The OH images
(left) are from Ref. [27]. This figure has been kindly provided by
Prof. D. Roekaerts. . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.14 Sequential images of OH with 1 ms spacing in region 2 shown in
Fig. 5.12. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.15 Re-ignition sequence with 0.5 ms spacing in region 1 as shown in
Fig. 5.12. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.16 Integrated FDFs assuming a β function shape for 4 different CMC
cells centred at x = 19.7 mm and x = 23.4 mm (c & a correspond-
ing to Fig. 5.12, domain marked ‘1’) and at x = 229.1 mm and
x = 249.9 mm (d & b corresponding to domain marked ‘2’), at the
same instants as the snapshots in Fig. 5.15 (c & a) and Fig. 5.14
(d & b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.17 Typical instantaneous conditional (“CMC”) and PDF-weighted
conditional average (“CMC AVE”) profiles of the temperature and
OH mass fraction at the indicated axial positions. The PDF aver-
age is done over all the CMC nodes corresponding to a given axial
position and over time. . . . . . . . . . . . . . . . . . . . . . . . . 115
xix
LIST OF FIGURES
5.18 Typical instantaneous iso-surface of ξ = ξst colored according to
the local resolved (a) OH mass fraction, (b) temperature, (c) NO
mass fraction & (d) CO mass fraction at the same instant. Length
of images: 300 mm. All the pictures are seen from the same per-
spective except (a) which has been rotated to highlight the local-
ized extinction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
5.19 Time series of N˜ |0.5, T˜ |ξst, ˜YOH |ξst, ˜YNO|ξst and ˜YCO|ξst at r =
0.58Dj (left, corresponding to the radial position of the pilot) and
at r = 0.82Dj (right) and the indicated x. Time zero refers to the
initialization of the LES. The black dotted lines on the two top
graphs refer to the extinction value of the scalar dissipation rate
(193 1/s). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5.20 N˜ |η at x = 3.29Dj and r = 0.82Dj. The black dotted line refers
to the extinction value of N0 (193 1/s). . . . . . . . . . . . . . . . 118
5.21 Typical instantaneous conditional (“CMC”) and PDF-weighted
conditional average (“CMC AVE”) profiles of (a) the tempera-
ture and (b) CO mass fraction at respectively x = 100 mm and
x = 150 mm and at the indicated radial positions. The PDF aver-
age is done over all the CMC nodes corresponding to a given axial
position and over time. Scatterplots and conditional averages from
experimental data [27] are superimposed for comparison. . . . . . 119
5.22 Radial profiles of the mean temperature at the indicated axial po-
sition. Experimental data from Ref. [27]. . . . . . . . . . . . . . . 120
5.23 Radial profiles of the RMS of the temperature at the indicated
axial position. Experimental data from Ref. [27]. . . . . . . . . . 121
5.24 Radial profiles of the mean YCO at the indicated axial position.
Experimental data from Ref. [27]. . . . . . . . . . . . . . . . . . . 122
5.25 Radial profiles of the RMS of YCO at the indicated axial position.
Experimental data from Ref. [27]. . . . . . . . . . . . . . . . . . . 123
5.26 Radial profiles of the mean YNO at the indicated axial position.
Experimental data from Ref. [27]. . . . . . . . . . . . . . . . . . . 124
5.27 Radial profiles of the RMS of YNO at the indicated axial position.
Experimental data from Ref. [27]. . . . . . . . . . . . . . . . . . . 125
xx
LIST OF FIGURES
6.1 (a) Sketch of the TECFLAM burner. (b) Picture of the swirl flame
and its burner. (c) Dimensions of the TECFLAM burner. From
Ref. [51]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
6.2 Mesh used for the LES computation of the TECFLAM. . . . . . . 149
6.3 Radial profile of the mean tangential velocity 1 mm above the
burner exit. Experimental data from Ref. [51]. . . . . . . . . . . . 150
6.4 (a) Tmax of the steady flame against the scalar dissipation rate
N0. (b) Distributions of some reactive scalars of the steady flame
obtained for N0 = 20 1/s with the ARM2 reduced chemistry mech-
anism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
6.5 Distributions of time-averaged quantities in the reacting flow. White
line: stoichiometric isoline; black line: zero-axial velocity isoline.
Axes in m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
6.6 (a) Mean radial and (b) tangential velocity for the reacting flow.
White line: stoichiometric isoline; black line: zero-axial velocity
isoline. Axes in m. . . . . . . . . . . . . . . . . . . . . . . . . . . 152
6.7 Snapshots at three consecutive instants of (a,c,e) the axial velocity
and (b,d,f) the z−vorticity. White line: stoichiometric isoline;
black line: zero-axial velocity isoline. Axes in m. . . . . . . . . . 153
6.8 Snapshots at three consecutive instants of the mixture fraction.
White line: stoichiometric isoline; black line: zero-axial velocity
isoline. Axes in m. . . . . . . . . . . . . . . . . . . . . . . . . . . 154
6.9 Zoom of the instantaneous axial velocity field inside the burner.
White line: stoichiometric isoline; black line: zero-axial velocity
isoline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
6.10 Radial profiles of the mean axial velocity at the indicated axial
position. Experimental data from Ref. [51]. . . . . . . . . . . . . 156
6.11 Radial profiles of the mean tangential velocity at the indicated
axial position. Experimental data from Ref. [51]. . . . . . . . . . 157
6.12 Radial profiles of the RMS of the axial velocity at the indicated
axial position. Experimental data from Ref. [51]. . . . . . . . . . 158
6.13 Radial profiles of the RMS of the tangential velocity at the indi-
cated axial position. Experimental data from Ref. [51]. . . . . . . 159
xxi
LIST OF FIGURES
6.14 Radial profiles of the mean mixture fraction at the indicated axial
position. Experimental data from Ref. [51]. . . . . . . . . . . . . 160
6.15 Radial profiles of the RMS of the mixture fraction at the indicated
axial position. Experimental data from Ref. [51]. . . . . . . . . . 161
6.16 Inert flow. Snapshots of the (a) axial velocity, (b) pressure, and
(c) mixture fraction. White line: stoichiometric isoline; black line:
zero-axial velocity isoline. Axes in m. . . . . . . . . . . . . . . . . 162
6.17 (a, b) Temporal autocorrelations at the indicated axial and radial
positions. Left/Right: inert/reacting cases. . . . . . . . . . . . . . 163
6.18 (a, b) Temporal autocorrelations at the indicated axial and radial
positions. Left/Right: inert/reacting cases. . . . . . . . . . . . . . 164
6.19 (a, b) Spectra of the axial velocity inside the air pipe at x =
−25 mm & r = 22.5 mm (r = 0.75 D). (c, d) Spectra of the axial
velocity at two positions above the air pipe exit with x = 5 mm &
r = 22.5 mm (r = 0.75 D). Left/Right: inert/reacting cases. . . . 165
6.20 Log-log spectra of the axial velocity at the indicated positions.
The top row corresponds to positions along the centreline and the
bottom row corresponds to positions along the line r = 0.75 Dj.
Left/Right: inert/reacting cases. . . . . . . . . . . . . . . . . . . . 166
6.21 Inert flow. (a) Several instantaneous iso-surfaces of low pressure
(P − P0 = −450 Pa) over one period of rotation. Visualization
of the isothermal structures around the burner. (b) Instantaneous
iso-surfaces of two different low pressure values (blue color: P −
P0 = −250 Pa; green color: P − P0 = −150 Pa) to visualize the
isothermal structures around the burner and inside the combustion
chamber. Axes in m. . . . . . . . . . . . . . . . . . . . . . . . . . 167
6.22 2D POD analysis from the plane x = 5 mm. (a, b) Contribution
to the fluctuation energy for each mode. (c, d). POD time coeffi-
cients (temporal modes) of the first two spatial modes. Left/right:
inert/reacting case. . . . . . . . . . . . . . . . . . . . . . . . . . . 168
6.23 Inert flow. 2D POD modes 1-4 at x = 5 mm. The spectra refer
to the Fourier analysis of the temporal coefficient associated with
each mode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
xxii
LIST OF FIGURES
6.24 Inert flow. 2D POD modes 5-8 at x = 5 mm. The spectra refer
to the Fourier analysis of the temporal coefficient associated with
each mode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
6.25 Inert flow. 2D POD modes 9-12 at x = 5 mm. The spectra refer
to the Fourier analysis of the temporal coefficient associated with
each mode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
6.26 Inert flow. 2D POD modes 13-15 at x = 5 mm. The spectra refer
to the Fourier analysis of the temporal coefficient associated with
each mode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
6.27 Reacting flow. 2D POD modes 1-4 at x = 5 mm. The spectra
refer to the Fourier analysis of the temporal coefficient associated
with each mode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
6.28 Reacting flow. 2D POD modes 5-8 at x = 5 mm. The spectra
refer to the Fourier analysis of the temporal coefficient associated
with each mode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
6.29 Reacting flow. 2D POD modes 9-12 at x = 5 mm. The spectra
refer to the Fourier analysis of the temporal coefficient associated
with each mode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
6.30 Reacting flow. 2D POD modes 13-15 at x = 5 mm. The spectra
refer to the Fourier analysis of the temporal coefficient associated
with each mode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
6.31 3D POD analysis. Contribution to the total fluctuation energy of
each mode: (a) inert case; (b) reacting case. . . . . . . . . . . . . 177
6.32 Inert flow. 3D POD mode 1 (a, b, c) and mode 2 (d, e, f). (a,
d) Isosurfaces of the axial velocity fluctuations with the vectop
map at x = 5 mm superimposed. (b, e, g) Q−criterion coloured
by the axial velocity fluctuations. (c, f) Isosurfaces of the mixture
fraction fluctuations. The negative fluctuations are plotted in blue,
the positive ones in red. . . . . . . . . . . . . . . . . . . . . . . . 178
6.33 Inert flow. 3D PODmode 3 visualized using the Q-criterion coloured
by the axial velocity fluctuations. The negative fluctuations are
plotted in blue, the positive ones in red. . . . . . . . . . . . . . . 179
xxiii
LIST OF FIGURES
6.34 3D POD analysis. Spectral analysis of the POD temporal coeffi-
cients ai(t): (a) inert case; (b) reacting case. . . . . . . . . . . . . 180
6.35 Inert flow. Reconstruction of several snasphots over one period of
rotation based on the 3D POD modes 1 and 2. Visualization of (a)
Q-criterion isosurfaces (blue color) and (b) mixture fraction con-
tours (red color, corresponding to areas where ξ ≥ 0.35 ), applied
to the instantaneous reconstructed flow fields. . . . . . . . . . . . 181
6.36 Reactive flow. 3D POD (a) mode 1 and (b) mode 4. Negative
(blue) and positive (red) isosurfaces of axial velocity fluctuations.
View from above the burner exit. . . . . . . . . . . . . . . . . . . 182
6.37 Reactive POD mode 2 (a, b, c) and mode 3 (d, e, f). (a, d)
Q−criterion applied to the corresponding mode coloured by the
axial velocity fluctuations. (b, e) Q−criterion coloured by the
temperature fluctuations. (c, f) Isosurfaces of the mixture frac-
tion fluctuations. The negative fluctuations are plotted in blue,
the positive ones in red. . . . . . . . . . . . . . . . . . . . . . . . 183
6.38 Reactive POD mode 5 (a, b, c) and mode 6 (d, e, f). (a, d)
Q−criterion coloured by the axial velocity fluctuations. (b, e)
Q−criterion coloured by the temperature fluctuations. (c, f) Iso-
surfaces of the mixture fraction fluctuations. The negative fluctu-
ations are plotted in blue, the positive ones in red. . . . . . . . . . 184
6.39 Visualization of the vortex core using the Q−criterion applied to
a reconstructed snapshot based on modes 1 to 6, coloured by the
reconstructed pressure for the inert case (a) and the temperature
for the reacting case (b). . . . . . . . . . . . . . . . . . . . . . . . 185
7.1 Chemiluminescence emission from the TECFLAM flame. From
Ref. [51] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
xxiv
LIST OF FIGURES
7.2 CMC grid superimposed on the instantanous OH mass fraction.
Each CMC cell has its center located at an intersection of the black
dashed lines. Points 1-4 are at locations (x, r)=(0.13D,0.83D),
(0.13D,0.67D), (0.35D,0.67D), (0.35D,0.83D) respectively (in mm,
with D = 30 mm); r is the distance from the centreline and x the
axial distance from the bluff body. . . . . . . . . . . . . . . . . . . 188
7.3 Typical instantaneous contours of (a, b) the axial velocity, (c) the
mixture fraction and (d) the temperature taken at the same in-
stant. The white line represents the stoichiometric iso-surface. . . 190
7.4 Typical instantaneous contours of the mass fraction of (a) OH, (b)
CO2, (c) NO and (d) CO taken at the same instant. The white
line represents the stoichiometric iso-surface. . . . . . . . . . . . . 192
7.5 Radial profiles of the mean axial velocity at the indicated axial
position. Experimental data from Ref. [51]. . . . . . . . . . . . . 194
7.6 Radial profiles of the mean tangential velocity at the indicated
axial position. Experimental data from Ref. [51]. . . . . . . . . . 195
7.7 Radial profiles of the mean mixture fraction at the indicated axial
position. Experimental data from Ref. [51]. . . . . . . . . . . . . 196
7.8 Radial profiles of the RMS of the axial velocity at the indicated
axial position. Experimental data from Ref. [51]. . . . . . . . . . 198
7.9 Radial profiles of the RMS of the tangential velocity at the indi-
cated axial position. Experimental data from Ref. [51]. . . . . . . 199
7.10 Radial profiles of the RMS of the mixture fraction at the indicated
axial position. Experimental data from Ref. [51]. . . . . . . . . . 200
7.11 Typical instantaneous contours of the stoichiometric mixture frac-
tion coloured by (a) OH mass fraction, (b) the temperature (K),
(c) NO mass fraction and (d) CO mass fraction. . . . . . . . . . . 201
7.12 Instantaneous conditional (“CMC”) profiles at several consecutive
instants of N (scalar dissipation rate), T and OH mass fractions
at the indicated axial positions and at r = 0.83 D (25 mm). . . . 204
7.13 Instantaneous conditional (“CMC”) profiles at several consecutive
instants of CO and NO mass fractions at the indicated axial po-
sitions and at r = 0.83 D (25 mm). . . . . . . . . . . . . . . . . . 205
xxv
LIST OF FIGURES
7.14 Instantaneous conditional (“CMC”) profiles at several consecutive
instants of N (scalar dissipation rate), T and OH mass fractions
at the indicated axial positions and at r = 0.67 D (20 mm). . . . 206
7.15 Instantaneous conditional (“CMC”) profiles at several consecutive
instants of CO and NO mass fractions at the indicated axial po-
sitions and at r = 0.67 D (20 mm). . . . . . . . . . . . . . . . . . 207
7.16 Time series of N˜ |0.5, T˜ |ξst, ˜YOH |ξst, ˜YNO|ξst and ˜YCO|ξst at r =
0.83D (left) and at r = 0.67D (right) at the indicated x. The
black dotted lines on the top two graphs refer to the extinction
value of the scalar dissipation rate (176 1/s). . . . . . . . . . . . . 209
7.17 Sequence of instantaneous contours of the temperature at different
instants separated by 1 ms (from left to right). The white lines
represent the stoichiometric isolines. . . . . . . . . . . . . . . . . . 211
7.18 Sequence of instantaneous contours of YOH at different instants
separated by 1 ms (from left to right). The white lines represent
the stoichiometric isolines. . . . . . . . . . . . . . . . . . . . . . . 212
7.19 Radial profiles of the mean temperature at the indicated axial po-
sition. Experimental data from Ref. [51]. . . . . . . . . . . . . . . 214
7.20 Radial profiles of the RMS of the temperature at the indicated
axial position. Experimental data from Ref. [51]. . . . . . . . . . 215
7.21 Radial profiles of the mean YCH4 at the indicated axial position.
Experimental data from Ref. [51]. . . . . . . . . . . . . . . . . . . 218
7.22 Radial profiles of the RMS of YCH4 at the indicated axial position.
Experimental data from Ref. [51]. . . . . . . . . . . . . . . . . . . 219
7.23 Radial profiles of the mean YO2 at the indicated axial position.
Experimental data from Ref. [51]. . . . . . . . . . . . . . . . . . . 220
7.24 Radial profiles of the RMS of YO2 at the indicated axial position.
Experimental data from Ref. [51]. . . . . . . . . . . . . . . . . . . 221
7.25 Radial profiles of the mean YH2O at the indicated axial position.
Experimental data from Ref. [51]. . . . . . . . . . . . . . . . . . . 222
7.26 Radial profiles of the RMS of YH2O at the indicated axial position.
Experimental data from Ref. [51]. . . . . . . . . . . . . . . . . . . 223
xxvi
LIST OF FIGURES
7.27 Radial profiles of the mean YCO2 at the indicated axial position.
Experimental data from Ref. [51]. . . . . . . . . . . . . . . . . . . 224
7.28 Radial profiles of the RMS of YCO2 at the indicated axial position.
Experimental data from Ref. [51]. . . . . . . . . . . . . . . . . . . 225
7.29 Radial profiles of the mean YCO at the indicated axial position.
Experimental data from Ref. [51]. . . . . . . . . . . . . . . . . . . 226
7.30 Radial profiles of the RMS of YCO at the indicated axial position.
Experimental data from Ref. [51]. . . . . . . . . . . . . . . . . . . 227
xxvii
List of Tables
4.1 Flow conditions studied. U0 = Ub[1 + A sin(2pift)], St = fd/Ub. . 45
4.2 Relative energy of POD modes. . . . . . . . . . . . . . . . . . . . 68
5.1 Numerical setup used by the LES code to model the Delft flame
III. These values are the experimental ones except the ones flagged
with the symbol (*), which have been obtained through the mod-
elling process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.2 Fuel composition used by the CMC code to model the Delft flame
natural gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
6.1 Fuel composition used by the CMC code to model the TECFLAM
natural gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
xxviii
Chapter 1
Introduction
1.1 Swirl flows
Swirl flows are present both in nature and in pratical equipment. In nature, they
can be found in tornadoes, dust devils or waterspouts, while they have a wide
range of applications in engineering. In combustion system, swirling is widely
used, due to a variety of advantages like the reduction of the flame length, a
better stabilization and a cleaner burning [121]. We can quote some pratical uses
of reactive swirl flows such as industrial furnaces, utility boilers, gasoline, diesel
engines and of course gas turbines combustors [37; 42; 67; 124], which is the main
topic of interest of this thesis.
1.2 Motivation of studying swirl flows
Combustors are designed to achieve a complete chemical reaction in the small-
est, lightest and cheapest enclosure possible [42; 52]. Swirl flows allow a better
reaction inside the chamber: the swirl creates regions of reverse flows and hence
recirculation zones that maintain the reactants inside the combustors and allow
a better mixing between oxidizer and fuel. A better reaction is also achieved
by mixing hot gases with fresh combustible mixture, which leads to a reduction
in pollutants emissions. However the aerodynamics of swirl flows is extremely
complex and a strong coupling between the aerodynamics of the swirl flow and
1
1. Introduction
the combustion process arises. Even though swirl flows have been intensively
studied due to their industrial applications, several aspects of their aerodynamics
and combustion process have to be understood further, as it will become evident
from the literature review in Chapter 2. The thesis aims at investigating the
aerodynamics of swirl combustors in detail, in particular the aerodynamics of the
injector, the combustion process occuring in the combustion chambers, and the
coupling between the swirl flow and flame.
1.3 Methods of investigation
The work presented in this thesis is based on Large Eddy Simulations. The choice
of this relatively costly numerical method to compute flow fields compared to the
cheaper Reynolds-averaged Navier-Stokes simulations is justified by the nature of
the computed flows. In LES, the large-scale unsteady motions are explicitly rep-
resented while RANS is based on purely statistical approach regarding turbulent
viscosity or Reynolds stresses. As a result, computations of bluff body flames and
swirling flames, which involve large-scale unsteady motions, are ideal candidates
for LES [11]. Besides, the RANS methods using k− ² methods have already been
found inadequate to predict the kinematic properties of strongly swirling flows,
leading to inaccurate predictions of the stabilization process of turbulent swirl
flames [8].
A first-order Conditional Moment Closure (CMC) has been used to model
combustion throughout the various reactive simulations presented in this thesis.
This model has been developed to study non-premixed combustion [60]. The first
order CMC uses the conditional averages of the reactive scalars in the calculation
of the reaction rate. This assumption is much better than if the averaging was
done in an unconditional manner. The reason is that the fluctuations of species
concentrations and temperature are expected to be mostly related to the mixture
fraction fluctuations [19]. Many non-premixed problems, including flows with re-
circulations behind a bluff-body using RANS [57] or LES [118], and a bluff body
swirl-stabilized methane flame using a RANS method [37], have been successfully
modelled using first-order CMC. The discepancies observed in the predictions
of species in the swirl-stabilized flame were regarded as a consequence of the
2
1. Introduction
shortcomings of the fluid-flow model, especially in the mixture fraction predic-
tion. These results seem encouraging and justify the decision to compute swirling
reactive flows using a coupled LES/CMC formulation, knowing that the recircula-
tion zone in swirling jets exhibits similarities with those produced by bluff bodies
[42].
In order to organize and understand further the large amount of information
contained in the LES datasets of the various simulations, the Proper Orthogonal
Decomposition (POD) method has been widely used throughout this thesis. POD
is used to extract and analyse the structures of the flow and to look for any
interaction with the flow aerodynamics and the combustion process.
1.4 Scope of the thesis
In this thesis, various aspects of swirl flame stabilization are investigated from
both the aerodynamics and combustion points of view. Chapter 2 presents a re-
view of the different aspects of flows and flames that will be investigated through-
out the thesis as well as the challenges that the design of swirl combustors faces.
The chapter ends up with a brief presentation of the motivation for the differ-
ent numerical studies conducted during this PhD work. Chapter 3 presents the
numerical tools used to perform this work. In particular, a comprehensive de-
scription of the LES-CMC formulation used in this thesis is provided, and the
Proper Orthogonal Decomposition method, which has been used throughout this
work, is presented.
Chapters 4 and 5 then present works that investigate key aspects of combus-
tors considered separately. Chapter 4 focuses on the study of isothermal forced
bluff body flows. The configuration is thought of as a model problem for gas
turbine combustors. It allows to understand the aerodynamics of combustors
undergoing self-excited oscillations involving recirculation zones and periodicity,
and without the extra complexities of a swirl and combustion. The Proper Or-
thogonal Decomposition method allows a better understanding of the effects of
the inlet pulsation on the bluff body flows. In Chapter 5, the focus is put on
the combustion process with the study of a piloted non-premixed flame showing
significant finite-rate chemistry effects. The study provides more insights on the
3
1. Introduction
dynamics of localized extinctions and re-ignitions.
Chapters 6 and 7 are the central chapters of this thesis. In these two chap-
ters, an academic non-premixed swirl flow is investigated in-depth for both inert
and reactive configurations. Chapter 6 provides a comprehensive analysis of the
aerodynamics of the burner, by means of spectral analysis, autocorrelations and
Proper Orthogonal Decomposition. Chapter 7 is focused on the study of the com-
bustion process of the swirl flame, in particular the reproduction and analysis of
extinction and flame lift-off.
Finally, the main findings and conclusions from this PhD work, as well as
some guidelines for further research, are summarized in Chapter 8.
4
Chapter 2
Literature review
In this chapter, we briefly present the different aspects of flows and flames that
will be analysed in this thesis. We mainly focus on the study of non-premixed
flames.
2.1 The problem of flame stabilization: local-
ized extinction, lift-off and blow-off
Consider first a premixed configuration, where fuel and air have been completely
mixed before reaching the combustion chamber. The flame in a combustor is
considered to be stable over a range of input parameters, such as the fuel flow
rate or the air/fuel ratio, if the flame does not extinguish or flash back with
variation in the above input parameters [42]. On one hand, when the flow velocity
of a stable flame is decreased until the flame velocity at the burner level exceeds
the flow velocity, the flame flashes back into the burner. On the other hand,
an increase of the flow velocity until exceeding the flame velocity everywhere in
the chamber will lead to either the flame to be extinguished completely or, for
fuel-rich mixtures, it will lift above the burner until a new stable position in the
fuel stream is reached.
Consider now a non-premixed configuration. In this case, the oxidizer and the
fuel are injected through different streams. For a jet flame and for low inlet veloc-
ity, the air and fuel mix up due to molecular diffusion. If now the fuel is ignited, a
5
2. Literature review
laminar flame will develop, and the flame front will be located along the stoichio-
metric mixture fraction. The flame will remain anchored to the burner nozzle. If
the jet velocity is slowly increased, the flow and flame will become increasingly
turbulent. Turns [109] provides a general description of what happens if we keep
on increasing the flow rate. At sufficiently low flow rates, the base of the flame
remains quite close to the burner outlet and the flame is attached. As we keep
on increasing the flow rate, holes will begin to form in the flame sheet at the base
of the flame [109]. With further increase in the flow rate, more and more holes
will appear until there is no continuous flame close to the burner exit: the flame
has lifted-off [109]. At a sufficiently large flow rate, the flame blows off [109].
Thus, Turns identifies two critical flow conditions related to the flame stability:
the lift-off and the blow-off. Masri et al. [73] have investigated several flames
approching blow-off. As the flame approaches blow off, the number of locally
extinguished samples is found to increase significantly. The start of occurrence
of localized extinction depends on the fuel mixture. The flame reignites intermit-
tently further downstream where the mixing rates are more relaxed. Reignition
can only occur as long as there are burnt fluid parcels convected from the intense
mixing neck.
Therefore, in non-premixed configurations, the problem of flame stabilization
consists of maintaining a stable flame at operating conditions, without reaching
the blow-off limit. The solutions to delay the occurrence of blow-off are based
on the transport of hot combustion products at the root of the flame, where
cold reactants are located. This is generally done by using a pilot flame or by
creating one or several recirculation zones that will convect the hot products of
the flame back to its root. In the next section, a recirculation zone without swirl
is considered while the effect of swirl will be investigated in-depth in Section 2.3.
6
2. Literature review
Figure 2.1: Schematic of a bluff-body flow.
2.2 Aerodynamics and stabilization of flames with-
out swirl
2.2.1 Canonical problem for flame stabilization
A bluff body is often introduced in order to create a Central Recirculation Zone
(CRZ) behind the air inlet pipe, while a sudden-expansion creates an Outer Re-
circulation Zone (ORZ), as schematized in Fig. 2.1. There is a re-attachment
length associated with the end of the ORZ (Xr) and a forward stagnation point
at the downstream end of the bluff body wake (Xs). These recirculation zones
are very useful as they behave as flameholders.
In the following, D refers to the diameter of the air flow pipe, d to the ax-
isymmetric bluff body diameter located at the end of the pipe, and Do will be
the diameter of a round enclosure, with d < D < Do (see Fig. 2.1). The bulk
velocity of the flow coming out of the annular passage between the disk and the
inner wall of the pipe is refered as Ub.
7
2. Literature review
2.2.2 Bluff body flows
Consider first a flow with a CRZ created by a bluff body and no sudden expansion.
When the incoming flow is steady and of almost infinite extent compared to the
bluff body (considered here as an infinitely-thin disk), this configuration has been
studied extensively for a wide range of Reynolds number:
Re =
dUb
ν
(2.1)
At very low Reynolds numbers, the separation region behind the disk is stable,
with a toroidal vortex forming the recirculation zone. As the Reynolds number
increases, various instabilities set in and symmetry is lost [36; 46; 103], similar to
what happens to the flow behind a sphere [36; 87], albeit at a different Reynolds
number. The review by Kiya et al. [58] mentions a critical Re of about 140 above
which the wake becomes unsteady; more recent numerical simulations report a
slightly lower value [36; 103]. For Reynolds numbers between this critical value
and for values up to 103 − 105, helical vortices seem to be formed at a natural
frequency fn corresponding to a natural vortex shedding Strouhal number:
Stn =
fnd
Ub
(2.2)
in the range 0.13-0.15 [58; 77]. Huang and Lin [46] reported that no vortex
shedding is found for Re > 1500, although no detailed examination of spectra was
reported in that paper and hence a relatively mild vortex shedding may have been
missed. The helical vortex from the circular disk is a weaker structure compared
to the von Ka´rma´n vortex street from two-dimensional cylinders. Nevertheless,
upon close examination, it can be revealed even at distances as far as 50d from
the disk and Stn = 0.135 has been specifically reported [119].
We should distinguish this helical vortex structure from the Kelvin-Helmholtz
instabilities associated with the shear layers surrounding the recirculation zone.
This instability gives rise to ring vortices that are convected downstream with
the flow. In the wake behind a sphere, the Strouhal number associated with this
instability:
StKH = fKHd/Ub (2.3)
8
2. Literature review
has been measured as a function of Reynolds number. Similar data for the Kelvin-
Helmholtz ring vortices for the shear layers around the CRZ of a disk do not seem
to be available [58], at least expressed as a function of the Reynolds number based
on the disk diameter.
Finally, we mention that the normalized stagnation point location Xs/d in-
creases with Reynolds number for low Reynolds numbers and peaks at about
1.6, but seems to decrease slowly to asymptote to about 1.5 [46; 84; 116] for
high Reynolds numbers. Note that the mean length of the recirculation zone is
a strong function of the disk shape: for conical bluff bodies, the CRZ is longer
than for flat disks [84]. The enclosure also plays a role [116]. Note also that if
the incoming flow is turbulent, the CRZ length may be reduced [84].
2.2.3 Flows behind a sudden expansion
Consider now a flow in an axisymmetric sudden expansion, without a centrally-
placed bluff body, and consider a steady incoming flow. The flow above a two-
dimensional backward-facing step has been studied extensively by experiment and
simulation. The separated shear layer from the corner of the sudden expansion
eventually turns towards the wall and re-attaches, at a distance that depends on
the step height, the Reynolds number, and the boundary layer thickness of the
flow before the step (see Ref. [40], Section 9, for a review and Ref. [29], Ref. [34]
and Ref. [107] for recent simulations and discussions of the main experimental
findings). One important point is that the Kelvin-Helmholtz instabilities of the
shear layer interact with a shedding-type instability to cause large fluctuations of
the reattachment length. In an axisymmetric sudden expansion, the reattachment
length, Xr, depends on the ratio Do/D [30], with Do and D defined in Section
2.2.1, and could be as large as 10 step heights (Do−D)/2. Large-eddy and RANS
simulations are found to reproduce the major features of the flow [41; 122]. Ref.
[24] reported a Strouhal number:
St = fD/Ub (2.4)
of about 0.3 for the re-attachment length fluctuations, attributed to the vortices
from the separated shear layer.
9
2. Literature review
2.2.4 Sudden expansion and bluff body flows
The flows behind a bluff body and over a backward-facing step can be considered
as canonical problems for gas turbine combustors. The sudden expansion and
the recirculation zone behind an axisymmetric bluff body are commonly studied
in the context of flame stabilisation and structure of flames [101]. This flow itself
has been studied in Ref. [102], but only for low Reynolds numbers. Due to the
use of this configuration for flames, velocity [84; 116] and flame emission [28]
measurements have been performed. Both ratios Do/D and D/d affect the sizes
of both CRZ and ORZ.
2.3 Aerodynamics and stabilization of swirl flames
Another solution to create a recirculation zone is by introducing a high swirl
at the flow inlet. The aerodynamics of flows with an imposed swirl are very
rich and the effects of the swirl on the flow field increase with its strengh. This
section presents the main characteristics of the aerodynamics of swirl flows and
emphasizes its role on swirl flame stabilization.
2.3.1 Swirl flow characterization
Swirl flows result from the application of a spiraling motion. A swirl (or az-
imuthal) velocity component is thus imposed to the flow by the use of swirl vanes
[124], axial-plus-tangential entry swirl generators [52] or by direct tangential en-
try into the chamber [42; 96]. Swirl flows, and their effects on the combustion
process in the case of reacting flows, are all strongly dependant on the degree
of swirl imparted to the flow [42]. This degree of swirl is characterized by the
swirl number S. The swirl number is a nondimensional number defined as the
ratio of the axial flux of swirl momentum to the product of the axial flux of axial
momentum and the injector radius R [42; 52; 120; 121; 124]:
S =
∫
ρUθUxrdA
R
∫
ρUx
2dA
(2.5)
10
2. Literature review
where Ux and Uθ are the axial and the tangential components of the mean velocity
respectively, A is the section of the injector and R is a characteristic length,
typically the radius of the cross section plane [120] or the equivalent radius in
case of a non-cylindrical shape [121].
Other important dimensionless parameters characterizing a swirl flow are the
Strouhal number St and the Reynods number Re with:
St =
fD
U
(2.6)
and
Re =
DU
ν
(2.7)
with f being the precession frequency, D a characteristic diameter (typically
D = 2R), U the flow velocity and ν the kinematic viscosity of the fluid [121].
2.3.2 Vortex breakdown and recirculation zone
At low swirl level (Gupta gives S < 0.4 [42], while Doherty gives S < 0.6 [69]),
the centrifugal forces can create significant radial pressure gradients at any axial
position compared to axial pressure gradient. This adverse axial pressure gradient
is not large enough to cause axial recirculation. There is also no coupling between
axial and tangential velocity components [42; 69].
As the swirl number is increased, a strong coupling develops between the
axial and tangential velocity components. Both strong axial and radial pressure
gradients are set up near the nozzle exit [69]. When there is a change in the
cross-sectional area, such as when the flow enters the combustion chamber, the
flow expansion results in a decrease of the radial pressure gradient. This leads
to an increase in the pressure along the centreline as we go downtream [112].
When the axial momentum of the fluid cannot any longer overcome the axial
pressure gradient along the jet axis, a flow reversal occurs and a central toroidal
recirculation zone is set-up [69]. The formation of this recirculation zone, through
a vortex breakdown process [115; 120], acts as an aerodynamic blockage or like a
three dimensional bluff body and helps to stabilize the flame [115] for the same
11
2. Literature review
Figure 2.2: Schematic diagram of processes leading to CRZ formation. From Ref.
[112].
reasons as in bluff body flames. The formation mechanism of a recirculation zone
induced by swirl is summarized in Fig. 2.2. The presence of a confinement affects
the vortex breakdown process as it modifies the tangential velocity and thus the
pressure gradients [112].
The mechanism of vortex swirl generation by devices such as swirlers is due to
strong inertial effects. However, once the vortex flow is generated, the mechanism
that leads to vortex breakdown in high-Reynolds number flows is related largely
to inviscid (dynamical) effects [120]. Vortex breakdown is a highly unstable and
transient flow pattern which occurs due to the instabilities present in swirl flows
such as shear-layer instabilities (like Kelvin-Helmholtz instability) similar to ax-
ial jets and azimuthal shear-layer instabilities created by the radial gradient in
azimuthal velocity. The centrifugal force is another source of instability and leads
to a flow profile corresponding to a vortex [52]. Rusak et al. [97] propose criteria
to predict the stability and the dynamics of vortex breakdown in high Reynolds
number swirl flows. One first defines the inlet swirl ratio as Ω = θ˙Ri/U with
Ri as the inlet section radius, θ˙ as the rotation rate and U as the uniform axial
velocity. Ω represents the swirl number of the swirler at the swirler exit plane.
12
2. Literature review
Two critical swirl ratios, Ω0 < Ω1, are found to exist for a swirl flow in a pipe.
For Ω < Ω0, a columnar flow is found to develop throughout the pipe, which is
the unique solution of the unsteady and axisymmetric Navier-Stokes equations.
For Ω0 < Ω < Ω1 two stable steady-state solutions can develop. One of them de-
scribes a columnar swirl flow while the other one is a swirl flow with a stagnation
breakdown region. Which solution appears will depend on initial disturbances
introduced to the columnar flow inlet. If small perturbations decay in time it is
the columnar state which will prevail while large disturbances enforce a transition
to the breakdown state. This transition is called the breakdown process. At last,
when Ω > Ω1, the columnar swirling flow is unstable and the flow always develops
a vortex breakdown state [120]. Using the work of Rusak et al. [97], these critical
swirl levels can be computed.
2.3.3 Precessing Vortex Core
The vortex breakdown can sometimes display strongly time dependent charac-
teristics, whereby the recirculation zone itself becomes unstable and starts to
precess about its own axis. This situation refers to a Precessing Vortex Core
(PVC) [113]. In any swirl burner flow where a vortex breakdown has occurred,
a large three-dimensional periodic flow structure can appear that is also referred
to as a precessing vortex core [42; 121]. PVC (Fig. 2.3) is usually found at
the boundary of the reverse flow zone [42; 114]. It forms when the forced vor-
tex region of the flow becomes unstable and the axis of the rotation of the flow
inside the swirling recirculation zone starts to precess around the axis of sym-
metry. As a consequence, the vortex breakdown becomes asymmetric and highly
time-dependent [69].
The vortex breakdown can take on several forms, including the appearance
of multiple helical vortices formed in the swirl stream shear layer. It has been
reported that the unsteady dynamics of these particular features can play an
important role in combustion induced oscillations [78; 108].
The combustion process tends to dampen a structure (PVC...) that is present
under isothermal conditions, especially in non-premixed configuration (Fig. 2.4
from Ref. [112]). Even when the vortex core precession is suppressed, the result-
13
2. Literature review
(a) (b)
Figure 2.3: (a) Visualization of a PVC structure as predicted by LES at the exit
of the swirler using an isosurface of low pressure. From Ref. [96]. (b) A sketch
of a PVC. From Ref. [21].
ing swirling flame is unstable and tend to wobble in response to minor perturba-
tions in the flow, most importantly close to the burner exit [112].
Premixed or partially premixed combustion can also produce large PVC simi-
lar in structure to that found isothermally. In that case, it has been reported that
the Strouhal number associated with the PVC in reactive conditions at equiv-
alence ratios around 0.7 may increase by a factor of 2 compared to isothermal
conditions [112].
2.3.4 Stabilization of swirl flames
In order to maintain the flame, a continuous source of ignition must be provided
to the fresh reactants located at the root of the flames. At high velocity, blow-off
occurs if the heat received by the recirculating eddies from the hot combustion
gases is insufficient to maintain a temperature high enough to cause ignition.
As described in the previous section, in jets with high swirl number, when
the angular-to-linear-momentum ratio exceeded a critical value, a toroidal vortex
type recirculation zone appeared in the central region of the flow and close to the
nozzle. This toroidal vortex plays a key role in the stabilization of flames. The
high-intensity turbulence that occurs in the vortex region increases the mixing
14
2. Literature review
(a) Diffusion flame (b) Premixed flame
Figure 2.4: Effect of combustion upon the PVC with (a) 100% axial fuel injection
(b) premixing, S = 1.98, equivalence ratio 0.89. In Fig. (a), the term “pressure”
refers to the mean pressure, while in Fig. (b) the term “R.M.S” refers to the
R.M.S of the pressure. Figures from Ref. [112].
which can be enhanced by up to a factor of 5 [2; 121]. The hot gases and active
chemical species recirculate back to the burner due to the Central Recirculation
Zone (CRZ). Heat and mass are thus transported effectively from combustion
products to fresh combustible mixture [42]. It has also been reported that the
periodic motion of vortex precession enhances the mixing between fuel and ox-
idiser [52]. The improved mixing allows to push back the blow-out limits of
non-premixed flames and to shorthen both the flame length and the distance
from the burner at which the flame is stabilized [121].
The recirculation zone in swirling jets and in bluff body flows exhibits simi-
larities. In the case of bluff body stabilized flames, a region of recirculating flow
appears behind the bluff body. This recirculating system acts as a continuous
source of ignition for the flame that originates behind the bluff-body and spreads
obliquely across the flow: it receives heat from the flame, then carries it back
upstream, and eventually ignites the flow of fuel/air mixture by contact. How-
ever, one of the most important differences is that the blockage in swirling jets
is entirely aerodynamic. There is no need for the presence of a solid surface. In
15
2. Literature review
combustion system, this is a fundamental improvement, as the flame is generally
attached to the bluff body that is therefore exposed to high temperature and to
effects of soot deposition [42]. Other benefits of using a swirl for flame stabiliza-
tion come from the compact flame and the high level of mass recirculation that
are obtained compared to non-swirling flow. Therefore, all industrial combustors
feature a swirl that is intense enough to create a large central recirculation zone.
Several factors influence the size of the recirculation zone, namely the degree
of swirl, the blockage ratio of the flame holder in the stream, divergent walls
if there is no separation of the flow from the walls and the shape of the flame
holder [42]. Changing the amount and nature of fuel injected allows to control the
temperature and the gas composition into the reverse flow zone while variations of
the degree of swirl controlled by the swirl number allows an aerodynamic control
for mixing and reaction [42].
2.4 Combustion instabilities
High amplitude low frequency oscillations in combustors are generally regarded
as undesirable as they can cause large pressure fluctuations leading to damage of
the combustor structures [15; 42; 55]. Among the different types of instabilities
that can affect a combustor, the ones arising from acoustic and fluid dynamic
phenomena will be briefly reviewed.
2.4.1 Acoustic instabilities
In the presence of upstream and boundary ductworks, which impose certain acous-
tic characteristics to the flow, self-excited oscillations may arise in realistic com-
bustors, which cause a strongly-pulsating flow and vortex formation [28, 68].
Acoustic instabilities are characterized by the propagation of acoustic waves in
the combustion chamber. Oscillations arise and their frequency is determined
by the chamber geometry. Thus, if noise is present inside the chamber, certain
frequencies can be selected and amplified by the combustion system. In a com-
bustion chamber, acoustic energy is mainly generated due to variations of the
heat release rate: an unsteady source of heat behaves like a source of sound.
16
2. Literature review
Acoustic waves are thus generated and propagate upstream and downstream of
the flame location. These waves are then reflected at the inlet and outlet sections
of the combustion chamber. The reflected acoustic waves travel back to the flame,
increasing their perturbations and affecting again the instantaneous heat release.
Therefore a coupling between the acoustic field where chemical reactions occur
and the heat release process arises. According to the Rayleigh criterion [92], the
acoustic oscillations will amplify themselves when the fluctuations in heat release
and acoustic pressure at the flame location are in phase with each other. Another
criterion for the system to develop combustion instabilities is that the acoustic en-
ergy received from the fluctuating heat release is larger than the energy lost both
at the boundaries of the chamber and from the viscous dissipation [15; 42; 64; 99].
The physical mechanisms of the flame response to these acoustic perturbations
are strongly dependent on the nature of the flame [15]: partially premixed flames
are very sensitive to equivalence ratio fluctuations [100]. In fully premixed flames
heat release rate fluctuations are linked to variations in the flame surface area.
The pressure fluctuation can be driven by either the oscillation in the flow [31]
or the displacement of the flame anchoring point [9].
2.4.2 Hydrodynamic instabilities
The other types of instabilities that can occur in a combustion chamber are devel-
oped by fluid dynamic phenomena. They lead to combustion fluctuating periodi-
cally inside the combustion chamber. These instabilities are called hydrodynamic
instabilities and appear due to the establishment of certain flow patterns.
The development of a vortex shedding can be a source of instabilities [42;
64]. In this context, acoustic and fluid dynamic instabilities can be strongly
coupled mechanisms in turbulent, premixed combustion systems. The formation
of vortices have thus been identified as a mechanism driving the combustion
instabilities [99]. The formation of these ring-vortex structures can always be
observed together with the occurence of pressure oscillations in highly turbulent
combustors in both non-premixed and premixed systems. They are also thought
to be independent of the type of flame as they are encountered in jet, bluff body
or swirl stabilized flames. The mechanism by which they sustain combustion
17
2. Literature review
Figure 2.5: Links between different quantities in typical gas turbine combustion
instabilities. From Ref. [99].
instabilities is the same as described previously: when toroidal vortices are formed
by rolling-up the fuel-air mixture, they change the mixing and reaction fields of
the steady-state flame. The heat release rate of the flame is modified, leading to
new pressure fluctuations that can create next generations of larger ring-vortex if
the Rayleigh’s criterion is satisfied. A feedback loop can then arise as explained
previously.
The PVC is also responsible for large fluctuations in the velocity and mix-
ing fields. If these fluctuations become coupled with acoustic frequencies of the
combustion chamber, combustion-induced oscillations and high pressure pulsa-
tions could arise. Figure 2.5 summarizes the interactions between the different
mechanisms leading to instability in gas turbine combustion.
2.4.3 Pulsating flows
The previous section has shown that combustion instabilites may lead to self-
excited oscillations developing inside the combustor and create a strong pulsating
flow. The study of a forced pulsating flow may thus be seen as a canonical problem
for combustor experiencing combustion instabilities. In this section, we do not
consider the case of a swirl flow and limit the study to flow composed of a bluff
body and a sudden-expansion. The interaction between the recirculation zones
and the pulsating flow introduces significant complexities compared to the case
described in Section 2.2.1.
18
2. Literature review
2.4.3.1 Bluff body flows
When the incoming flow of a bluff body flow is virtually laminar or with very low
turbulent intensity but is oscillating in a periodic manner, the flow changes in
many respects. Work of this nature for oscillating flow above cylinders has shown
that the vortex shedding frequency may lock-on to the frequency of the flow
oscillation [62]. The possibility of controlling the von Ka´rma´n vortex street for a
cylinder or the wake of the sphere by carefully-placed small-amplitude pulsations
has been reviewed by Choi et al. [23]. Extrapolating the results from pulsating
jets [18], we may expect that ring vortices may be shed from the edge of the
disk when the flow is pulsating at an appropriate Strouhal number, given (for a
circular jet) in the range 0.7-0.9. We are not aware of a detailed examination of
the flow over a disk placed normal to the flow when the flow is oscillating.
2.4.3.2 Flows behind a sudden expansion
A superimposed oscillation above a two-dimensional backward-facing step has
been studied extensively in the context of re-attachment length control [29; 40].
Apparently, even small amplitudes of oscillation can affect greatly the re-attachment
length due to the interaction with the Kelvin-Helmholtz instability. We are not
aware of any simulations or experiments of the flow in an axisymmetric sudden
expansion with an oscillation superimposed to the mean flow.
2.4.3.3 Sudden expansion and bluff body flows
When the incoming flow is oscillating, flow visualization and inferences from flame
studies show that counter-rotating torroidal vortices may be formed at the edge of
the bluff body and at the corner of the sudden expansion [5; 6], depending on the
oscillation frequency and amplitude. In a similar geometry but in the presence of
swirl and premixed combustion, vortices were observed only for forcing above a
critical amplitude, with this critical amplitude increasing sharply as the Strouhal
number, defined as:
St = fd/U (2.8)
19
2. Literature review
decreased [65]. These vortices may then cause significant alterations to the flame
shape and location, which in turn causes a significant change to the overall heat
release in the combustor. Despite the practical relevance of this configuration, and
despite the rapidly growing number of Reynolds-Averaged Navier-Stokes (RANS)
simulations and Large-Eddy Simulations (LES) of this type of flow [3; 43; 99; 123],
with or without swirl, it seems that little effort has been placed in understanding
better the fluid mechanical effects when the flow is oscillating in a compound bluff
body - sudden expansion configuration. This configuration will be investigated
further in Chapter 4.
2.5 Pollutants emissions
2.5.1 Pollutants formation
One of the most undesirable sides of combustion is the formation of pollutants.
The main species of concern found in combustors exhaust are unburned hydro-
carbons, carbon monoxide, soot and oxides of nitrogen [45].
Both hydrocarbon (HC) and carbon monoxide (CO) are pollutants that re-
sult from rich or incomplete combustion. Although hydrocarbons are not toxic,
their production should be avoided as they contribute to the production of smog.
However carbon monoxide is toxic and contribute to heart and respiratory con-
ditions. While they are largely removed by catalytic converters in spark-ignited
engines and in lean premixed combustors, the formation of HC and CO is not
limited in aeroengine gas turbines due to the need to prevent autoignition. In
such turbines there is also often a rich pilot region that keeps the combustion
stable. At low power conditions, there are incomplete reactions for HC and CO
due to the low temperatures [45].
Soot is a collection of Polycyclic Aromatic Hydrocarbons (PAH) or benzene-
like rings emmited from very rich combustion. Combining with other pollutants
and moisture in the atmosphere, they create Particulate Matter (PM). PM are
known to increase mortality rates and are a very challenging problem in the
operation of diesel engines [45].
Nitric Oxides (NOx) are toxic in low concentrations and contribute to the
20
2. Literature review
formation of photochemical smog via a mechanism involving hydrocarbons and
sunlight to form hydrocarbon nitrates and ozone. The amount of smog is generally
limited by the availability of NOx. Its prediction and the limitation of its exhaust
is then of a primary concern for developers as the exhaust thresholds are becoming
more and more strict [45]. To be able to predict their emissions, all physical
phenomena influencing their formation have to be taken into account. They are
generally divided into three categories: The thermal NOx mechanism, which was
discovered by Zel’dovich and operates through the direct oxidation of atmospheric
nitrogen. It is responsible for the largest proportion of NOx emissions in most
combustion systems. It is important at temperatures above 1500 K, which are
easily reached with most fuels used in combustion. It depends exponentially on
temperature which makes it very sensitive to turbulent and acoustic fluctuations
[99]. The fuel NOx, which is created from the nitrogen bound to the hydrocarbon
fuel. Finally, the prompt mechanism is responsible for relatively low emissions
of NOx in most combustion systems but can be important when the fuel-air
mixture is somewhat rich. This mechanism operates through the formation of
hydrocarbon radicals (HCN). Prompt NOx has an exponential dependence on
equivalence ratio [99].
2.5.2 Reduction of emissions
Regarding HC and CO production, they are generally removed by catalytic con-
verters placed in the tailpipe of the spark-ignited engines.
In order to reduce NOx emissions, modern gas turbines for power energy gen-
eration are now often operating under lean-burn conditions [15; 55]: by avoiding
chemical reaction at stoichiometric condition, the flame temperature is reduced.
As a consequence, thermal NOx is reduced. Moreover, excess of air results gener-
ally in complete combustion of fuel, reducing hydrocarbon and carbon monoxide
(CO) emissions. However, some authors have reported an increase in CO forma-
tion [42] in this kind of combustors. The pratical lean premixed combustors are
made complicated to realize due to low reaction rates in lean flames and their
suceptibility to extinction. They also tend to develop combustion instabilities
[15; 42; 55]. On top of producing structural damages, an unstable combustion
21
2. Literature review
is claimed to increase pollutants emissions of the gas turbines [15]. All these
problems have so far made premixing impractical for aero gas turbine, leaving
the problem of NOx emissions in non-premixed flames still alive.
The strategies adopted in the design of Rolls-Royce aero gas turbines to de-
crease NOx emissions are based on the lean burn technology. The new lean burn
technology is based on the principle that with a higher Air-to-Fuel Ratio (AFR),
the flame temperature will decrease and so will the NOx emissions. As a conse-
quence, the aerodynamic combustor design has to change to increase the AFR
ratio near the flame front, but this change also has large implications on the sta-
bility and performance of the combustor. The following description of the rich
and lean burn technologies is based on discussions with Rolls-Royce engineers
during a short placement in Derby, UK.
In a conventional combustor, a rich diffusion flame is generated in a primary
recirculation zone. This rich zone is located at the front of the combustion cham-
ber and provides a high level of resistance to flame out. Therefore it is used
to keep the combustor alight at low power conditions. Throughout large ports
located along the length of the combustor, air is introduced in a transition zone
that dilutes the mixture and enables most of the smoke produced in the rich
zone to be consumed. Overall the combustor is running very lean. However, as
the mixture passes from rich to lean mixture, there are regions of the combustor
where the mixing is at stoichiometric conditions and hence NOx emissions are
high.
To lower NOx emissions significantly, a new combustor has been designed to
operate in lean conditions also in the front part of the combustion chamber. In
this configuration, all the air, apart from the cooling air, is admitted through the
fuel injector to provide a lean burn AFR condition everywhere in the combustor,
which is required for low NOx emissions. As a consequence, there is no longer
large air ports along the combustor walls as in a rich combustor. The lean burn
injector is also found to be much larger, as almost all the air needed for the
combustion process will enter the combustor through the injector.
The drawbacks of lean burn configurations is that there are issues with the
flame stability at low power conditions. In particular, there is a high risk of blow
out. To overcome this problem, a staged combustion is used, where different
22
2. Literature review
zones are created for a specific range of engine operation. At low power, fuel
is supplied only through a small pilot injector while at higher power conditions
more fuel is introduced through large main fuel injectors.
Rocha et al. [93] investigated the influence of an acoustic field on the com-
bustion of a natural gas turbulent jet flames using the Delft burner, which is a
non-premixed piloted jet flame. They found that flames undergoing acoustic os-
cillations show significant changes in their structures. These flames have shorter
length and show premixing characteristics. These premixed characteristics are
due to the acoustic field which increases the reactants mixing convective process
due to the presence of oscillations. There is also a better distribution of tempera-
ture and a decrease of temperature peaks in the flame region. As a consequence,
species formation alteration was found not only in the distribution of NOx but
also in the distribution of O2, CO2 and CO. Schmitt et al. [99] also note that
pressure oscillation can lead to a large change in NO production compared to
stable combustion that they attribute to the equivalence ratio fluctuations ob-
served in the instability mechanism. They conclude that a proper description
of the acoustics in LES of swirl turbulent burner may be necessary in order to
predict not only combustion instabilities but also pollutants emissions. Rocha et
al. [93] conclude that pulsating combustion can be a way to control pollutants
emissions even though it was not possible to say if their acoustic actuation even-
tually increased or decreased the amount of emitted NOx. They see combustion
controlled by an acoustic field as a way to mix reactants in lean mixtures in
order to decrease NOx production without developing the problems associated
with premixing such as ignition in the premixed chamber, flame anchoring and
combustion instabilities.
2.6 Simulations of swirl flames
Numerical simulations of swirl flows have made impressive progress during the
last decade with some recent LES calculations involving practical combustors
[11; 52; 89]. This section briefly reviews some results obtained by numerical
simulations.
23
2. Literature review
2.6.1 Examples of simulations
Simulations of swirl flows have started with computations of axisymmetric, steady
laminar and incompressible flows in the 70’s [63]. Then computations have started
resolving unsteady axisymmetric simulations making it possible to predict ax-
isymmetric breakdown with periodic flow behavior [104]. The first turbulent
swirl flow computations have been based on the k − ² model using RANS for-
mulation [9]. However, since this time, it has been found that RANS approaches
based on the k−² model are too inaccurate for the simulation of strongly swirling
flows due to the presence of evident large-scale unsteady motions in such flows
and fundamental problems with the gradient diffusivity concept [9; 11; 52; 89].
Recently, LES of swirl stabilized combustors have been carried out. In the
case of non-reactive simulations, we can quote the computations of a gas turbine
injector [124] and of the Sydney swirl burner [52]. These computations show good
predictions of the turbulent flow features such as the recirculation structures,
the vortex breakdown, the precessing vortex core [52; 124] or Kelvin-Helmholtz
instabilities [124]. In the reactive simulations of the Sydney swirl burner [52],
LES predictions were found to be less satisfactory. In particular, temperatures
predictions suffer from error propagation due to small deviations in the mixture
fraction. Kim et al. [55] conducted the simulation of both non-reacting and
reacting turbulent flows of a lean-premixed swirl stabilized annular combustor
using LES turbulent model combined with a flamelet library approach to take
into account the turbulent combustion. The vortex breakdown, shear layer and
recirculation zones were reproduced well by the LES. In both the non-reacting
and reacting flows, turbulent structures appear to oscillate periodically in the
confined annular combustor and the strong periodic vortex ring is found to be a
source of combustion oscillation. This comment agrees with other results carried
out in Ref. [15]. In that study, LES of swirl flames acoustically perturbed were
conducted. The main conclusion of the study was that combustion instabilities in
gas turbine engines may also have an aerodynamic nature related to how swirling
flows responded to acoustic perturbations. Other studies have been conducted
where LES and acoustic analysis were used together to analyze swirled premixed
combustor. Roux et al. [96] confirmed that hydrodynamic structures such as
24
2. Literature review
PVC appearing in cold flow can disappear when combustion starts while acoustic
modes are reinforced by combustion.
2.6.2 Prediction of emissions
In Ref. [99], Schmitt et al. take an interest in modelling NOx production. They
claim that the prediction of pollutants is strongly related to the modelling of os-
cillation levels inside the combustors and that the equivalence ratio fluctuations
observed in the instability mechanism are the cause of the higher NO emissions.
Another important mechanism pointed out is the vortex-driven combustion insta-
bilities: the formation of a vortex of unburnt gases causes velocity fluctuations,
and burns after a certain time delay, coupling velocity fluctuations and heat
release fluctuations. The conclusion of the study was that a compressible formu-
lation may be required to get the right fluid mechanics in enclosed flames with
acoustics and undergoing oscillations, and may hence be necessary for this type
of flow in order to predict NO emissions accurately.
Fairweather and Woolley [37] conducted a three dimensional Conditional Mo-
ment Closure (CMC) calculation coupled with a Reynolds-averaged Navier-Stokes
(RANS) method to study a bluff body swirl-stabilized, turbulent non-premixed
methane flame. Some discrepancies in the prediction of species were thought to
arise from the combustion model, which cannot differentiate between diffusion
and partially premixed flames. It was claimed that the model should contain el-
ements of both premixed and non-premixed combustion to deliver better results
[37]. However, Kim and Mastorakos [53] obtained good predictions of the lift-off
height of the lifted flame even if their CMC model did not contain any repre-
sentation of triple flame or edge flames, a typical structure in partially premixed
combustion. Kim and Huh [56] computed a turbulent CH4/H2 flame over a bluff
body using CMC coupled with PDF method and a modified k − ² model for
turbulence, focusing on NO formation using different chemical mechanisms: the
GRI Mech 2.11 and 3.0, and the Miller-Bowman. They found almost identical
results for the major species and temperature. The conditional mean NO mass
fractions by the GRI Mech 2.11 and Miller-Browman mechanism were close to
each other and in agreement with the measurements. However, the GRI Mech
25
2. Literature review
3.0 gave the NO mass fractions about twice as large as those from the other two
mechanisms. Previous results seem to be consistent with these data [7; 95].
2.7 Context of the work and its objectives
As we saw previously, swirling flames can show various aspects of their aero-
dynamics such as precession or vortex formation caused by flow oscillations and
various combustion aspects such as localized extinctions and lift-off. All the above
affect flame stabilization in different ways and are explored through focused sim-
ulations in this thesis.
Chapter 4 investigates the stabilization problem from an aerodynamic point
of view. The canonical configuration previously described in Section 2.2.1 and
composed of a bluff body and a sudden expansion is investigated further, but
this time different monochromatic pulsations are imposed at the flow inlet as
described in Section 2.4.3. This study aims at delivering further insights on the
aerodynamics of combustors experiencing self-exciting oscillations, in the conti-
nuity of the review presented in Section 2.4, but without the extra complexities
of the combustion or the swirl itself. In particular, focus is given to the vortex
shedding occuring when the flow is pulsated at high enough frequency.
Chapter 5 investigates a piloted non-premixed flame. The relatively simple
configuration compared to bluff body or swirl flames allows to analyze further
some key combustion aspects of combustors described in Section 2.1. In par-
ticular, the effects of the pilot flame on flame stabilization are investigated and
further insights on the dynamics of localized extinctions and re-ignition are pro-
vided. The pollutants emissions, which were reviewed in Section 2.5.1, are also
investigated and their analysis allows to evaluate the quality of the LES-CMC
formulation compared to the other simulations and methods presented in Section
2.6.2.
These two previous chapters are thought to be preliminary studies that in-
vestigate independently several aspects of the aerodynamics (Chapter 4) and
combustion process (Chapter 5). Chapter 6 focuses on the aerodynamic stabi-
lization of a swirl flame. In particular, proper orthogonal decomposition of the
LES datasets allows to gain further insight of the PVC-like structures develop-
26
2. Literature review
ing in the burner, which is reviewed in Section 2.3, in both inert and reacting
configurations. Further insights on the dynamics of these structures and their
influence on the flame stabilization in the vicinity of the burner are presented.
This study enriches the understanding of hydrodynamic instabilities presented in
Section 2.4.2.
Finally, Chapter 7 investigates the combustion process occuring in the swirl
flame in detail. In particular, a comprehensive analysis of the lift-off reproduced
by the LES-CMC formulation is provided. The flame dynamics close to the
burner and its stabilization process through the Central Recirculation Zone are
also analyzed, along with pollutants emissions.
27
Chapter 3
Models and codes
3.1 Large Eddy Simulations
The different numerical investigations presented in the thesis have been conducted
using Large-Eddy Simulation (LES). LES is based on the energy-cascade hypoth-
esis: the turbulence is considered to be composed of eddies of different sizes with
different characteristic velocities and timescales. The larger of these eddies are
unstable and break up, transferring their energy to smaller scales and so on, until
the eddies are small enough so that their kinetic energy can be dissipated by the
molecular viscosity [91].
In LES, a low-pass spatial filtering operation is performed. Thus only the
largest structures of the flow field are computed and the small scales have to be
modelled. The filtered continuity and momentum equations are [90; 91]:
∂ρ
∂t
+
∂(ρu˜i)
∂xi
= 0 (3.1)
∂(ρu˜j)
∂t
+
∂(ρu˜iu˜j)
∂xi
= − ∂p
∂xj
+
∂τ˜ij
∂xi
− ∂(ρτ
r
ij)
∂xi
(3.2)
where ρ is the resolved density, u˜i is the resolved velocity in the i direction, τ˜ij is
the resolved stress tensor:
τ˜ij = 2µ
[
S˜ij − 1
3
δij
∂u˜k
∂xk
]
(3.3)
28
3. Models and codes
where S˜ij is the filtered rate-of-strain tensor:
S˜ij =
1
2
(
∂u˜i
∂xj
+
∂u˜j
∂xi
)
(3.4)
and τ rij is the residual stress tensor:
τ rij = u˜iuj − u˜iu˜j (3.5)
The term τ rij appears in unclosed form and needs to be modelled. The dynamic
Smagorinsky model, which can be viewed in two parts, is used here [39]. First,
τ rij is related to the filtered rate-of-strain tensor through a linear eddy viscosity
model:
τ rij − δij/3τ rii = −2νtS˜ij (3.6)
where νt is the sub-grid scale viscosity. Next, νt is modelled as:
νt = (CS∆)
2
S˜ (3.7)
where CS is the Smagorinsky parameter, ∆ is the filter width and S˜ the charac-
teristic magnitude of the filtered rate of strain:
S˜ =
(
2S˜ijS˜ij
)1/2
(3.8)
CS is calculated dynamically using a scale similarity approach [39] and ∆ is equal
to the size of the LES cell which is equal to the cubic root of its volume.
A transport equation for a conserved scalar (the mixture fraction ξ) is also
solved:
∂(ρξ˜)
∂t
+
∂(ρξ˜u˜i)
∂xi
=
∂
∂xi
(ρD
∂ξ˜
∂xi
)− ∂(ρJ
r
i )
∂xi
(3.9)
where ξ˜ is the resolved mixture fraction and Jri represents the scalar transport
due to sub-grid scale fluctuations:
Jri = u˜iξ − u˜iξ˜ (3.10)
Fick’s diffusion law with equal diffusivities for all species has been considered
29
3. Models and codes
and the diffusivity is D = ν/Sc, where a constant Schmidt number Sc = 0.7
has been considered. The unclosed term Jri is modelled similarly to the residual
stress tensor τ rij in the momentum equation and assuming a constant turbulent
Schmidt number Sct = 0.7 [16] i.e. by assuming that the sub-grid scale flux is
proportional to the resolved gradient:
u˜iξ − u˜iξ˜ = −Dt ∂ξ˜
∂xi
(3.11)
In this PhD work, the sub-grid variance of the mixture fraction has been
obtained by the following gradient type model:
ξ˜′′2 = Cv∆2
∂ξ˜
∂xi
∂ξ˜
∂xi
(3.12)
with Cv determined dynamically [25; 88]. For completeness, the filtered transport
equation for ξ˜′′2 is also given below (although it has not been used in this thesis):
∂(ρξ˜′′2)
∂t
+
∂(ρu˜iξ˜′′2)
∂xi
=
∂
∂xi
(ρ(D+Dt)
∂ξ˜′′2
∂xi
)− 2ρN˜ + 2ρ(D+Dt) ∂ξ˜
∂xi
∂ξ˜
∂xi
(3.13)
where N˜ is the scalar dissipation rate, which will be detailed in Section 3.2.2.
The simulations have been performed using the code PRECISE [49], which is
a low Mach number, finite-volume code that uses structured grids. The pressure-
correction equation is solved using the SIMPLE algorithm [85]. Convective trans-
port is discretised using a second-order central scheme, while time derivatives are
discretized with a second-order backward difference scheme and integration in
time is done using the explicit Adams-Bashforth method. PRECISE is fully par-
allelised using domain decomposition. PRECISE has previously been used to
simulate forced ignition of a non-premixed bluff body methane flame [118] with
very good results.
30
3. Models and codes
3.2 Combustion modelling
3.2.1 Mixture fraction
In the thesis, we focus on non-premixed combustion, where fuel and oxidiser
enter separately the combustion chamber. The rate of mixing between fuel and
oxidiser can be described by a conserved scalar, the mixture fraction [10]. It
takes the value of unity in the fuel stream and zero in the oxidiser stream. The
mixture fraction may be physically interpreted as the mass fraction of material
that originated in the fuel stream. The introduction of the mixture fraction
leads to the conserved scalar methods that forms the basis of the models used in
non-premixed turbulent combustion. In the conserved scalar method, the species
mass fractions and temperature (or enthalpy) are considered to be functions of
the mixture fraction only. The aim of the different mixture fraction based models
is to calculate these functions.
3.2.2 3D-CMC
The CMC combustion model developed independenly by Bilger and Klimenko
[60] has been used throughout this PhD work to model combustion. The CMC
solver used for 0D (see Section 3.2.3) and multi-dimensional CMC computations
has been developed in the Hopkinson Laboratory, Department of Engineering,
University of Cambridge. It has been used in two-dimensional studies of a lifted
[53] and an opposed flame [54], but also in auto-ignition problems [72; 125], as
well as in diesel engine simulations [26].
The CMC model has recently been incorporated to the code PRECISE and
details of the implementation can be found in Refs. [117; 118]. The CMC equa-
tions in a LES context are derived by filtering the transport equations for the
reactive scalar Yα [80] and can be written as:
∂Qα
∂t
+ u˜i|η∂Qα
∂xi
= N˜ |η∂
2Qα
∂η2
+ ω˜α|η + ef (3.14)
where Qα = Y˜α|η is the conditionally filtered reactive scalar, u˜i|η is the condition-
31
3. Models and codes
ally filtered velocity, N˜ |η is the conditional filtered scalar dissipation rate, ω˜α|η
is the conditionally filtered reaction rate, while the term:
ef = − 1
ρ¯P˜ (η)
∂
∂xi
[
ρ¯P˜ (η)
(
u˜iYα|η − u˜i|ηQa
)]
(3.15)
is the sub-grid conditional flux. This and the convection term account for the
conditional transport in physical space. All the species are assumed to have equal
diffusivities and the Lewis number is assumed to be unity. The terms ω˜α|η, u˜i|η,
N˜ |η and ef are unclosed and require modelling.
First order closure is used for the chemical reaction rate; the CMC for non-
premixed flames is based on the concept that the fluctuations of the reacting
scalars are correlated with the fluctuations of the mixture fraction [61]. This
leads to the notion of first order closure for the chemical source term in terms of
conditional averages; since the fluctuations of the conditional reacting scalars are
small, they may be neglected and the conditional chemical source term may be
calculated based on the conditional averages of the scalars:
ω˜α|η = ωα(Q1, Q2, ..., Qn) (3.16)
where n is the number of reacting scalars. First order closure will be used through-
out this thesis.
The simple assumption that the conditional velocity is equal to the uncondi-
tional velocity is made here:
u˜i|η = u˜i. (3.17)
The conditionally filtered scalar dissipation rate N˜ |η is modelled by the Am-
plitude Mapping Closure (AMC) model, which is fully described in Refs. [22].
According to this model, the conditional scalar dissipation rate has a given shape
in mixture fraction space, which is scaled according to the local value of the
unconditional scalar dissipation rate:
N˜ |η = N0G(η)
32
3. Models and codes
where
G(η) = exp
(−2[erf−1(2η − 1)]2)
and
N0 =
N˜∫ 1
0
G(η)P˜ (η)dη
(3.18)
where N˜ is the filtered scalar dissipation rate, found by summing the resolved
and the (modelled) sub-grid contributions:
N˜ = N˜res + N˜sgs (3.19)
The resolved scalar dissipation rate is defined as:
N˜res = D
(
∂ξ˜
∂xi
)2
(3.20)
and the sub-grid is estimated by:
N˜sgs =
1
2
CN ξ˜′′2/τt (3.21)
and assuming that the mixing timescale is proportional to a characteristic velocity
timescale for the sub-grid τt = ∆
2/νt. The absence of experimental data for the
scalar dissipation rate in the experiments modelled throughout this PhD work
does not allow to adjust properly the constant CN . As a consequence, the value
CN = 42, which had been previously adjusted to match the experimental results
of conditionally averaged 〈N |η〉 for Sandia flame D [38], has been used. No other
parameter has been tuned. Finally, a gradient model is used for the sub-grid scale
conditional flux:
u˜iYα|η − u˜i|ηQa = −Dt∂Qa
∂xi
(3.22)
3.2.3 0D-CMC
In order to understand the structure of the steady flame and validate the accu-
racy of the chemical mechanisms, distributions against mixture fraction of tem-
perature, T , and species mass fractions, Yα, have been computed using the CMC
33
3. Models and codes
equations in the zero-dimensional formulation. In the 0D-CMC calculations, only
the micromixing and chemical reaction terms are considered:
∂Qα
∂t
= N |η∂
2Qα
∂η2
+ ωα|η (3.23)
where Qα = Yα|η is the conditional reactive scalar, N |η is the conditional scalar
dissipation rate and ωα|η is the conditional reaction rate. The 0D-CMC equations
(Eq. 3.23) do not contain any spatial transport. All the species are assumed to
have equal diffusivities and the Lewis number is assumed to be unity. The terms
ωα|η and N |η are unclosed and require modelling. First order closure is also
provided for the chemical reaction rate. The conditional scalar dissipation rate
N |η is modelled by the Amplitude Mapping Closure (AMC) model, which has
been described in Section 3.2.2. According to this model, the conditional scalar
dissipation rate has a given shape in mixture fraction space, which is scaled by its
peak value, N0, across η-space. N0 is here pre-selected and kept at the prescribed
value while the CMC equations are solved. In order to solve Eq. 3.23, the η-
space is discretised into several nodes clustered around the stoichiometric mixture
fraction ξst. At η = 0 the air stream conditions are imposed and at η = 1 the
fuel stream conditions.
For different values of N0, the unsteady CMC equations (Eq. 3.23) are then
computed until eventually converging to a steady solution. As N0 increases,
the limit where heat is diffused quicker than it is produced is reached and the
flame extinguishes. In this thesis, 0D-CMC has also been used as a sub-grid
combustion model to perform preliminary simulations. The method is similar to
a steady flamelet model with unity Lewis number.
3.2.4 Coupling LES-CMC
Fig. 3.1 summarizes the coupling between the CFD and CMC solvers. This
sequence takes place at each timestep of the simulation. The CFD code computes
the resolved velocity, the resolved mixture fraction, its sub-grid variance and the
filtered scalar dissipation rate. It is assumed that the Filtered probability Density
Function (FDF) P˜ (η) has a β-function shape, which is calculated based on the
34
3. Models and codes
resolved ξ˜ and the modelled sub-grid variance ξ˜′′2 of the mixture fraction (Eq.
3.12). P˜ (η) is therefore computed for each LES cell.
At the end of the LES timestep, the information for u˜i|η and N˜ |η needed in
each CMC node are mass-weighted and PDF-averaged over all LES cells associ-
ated with that CMC node. The integrated conditionally filtered velocity u˜i|η
∗
is
thus obtained through the formula:
u˜i|η
∗
=
∫
CMC cell
P˜ (η) ρ˜|η u˜i|η dV∫
CMC cell
P˜ (η) ρ˜|η dV
(3.24)
assuming that the velocity is constant in η-space (Eq. 3.17).
A filtered probability density function P˜ ∗(η) is computed for each CMC cell by
applying the β-PDF assumption at the CMC resolution. An integrated resolved
mixture fraction is used:
ξ˜∗ =
∫
CMC cell
ρ¯ξ˜dV∫
CMC cell
ρ¯dV
(3.25)
and an integrated sub-grid scale variance. In this thesis, we use the following
formula which has been derived in Ref. [117]:
ξ˜′′2
∗∗
= ξ˜′′2
∗
+ ξ˜2∗ − ξ˜∗2 (3.26)
where
ξ˜′′2
∗
=
∫
CMC cell
ρ¯ξ˜′′2dV∫
CMC cell
ρ¯dV
(3.27)
The first term of Eq. 3.26 is based on the same volume averaged procedure as for
the resolved mixture fraction (Eq. 3.25). The two last terms that appear in the
derivation of Eq. 3.26 account for the variations of the resolved mixture fraction
inside every CMC cell. The different options available for these integrations are
discussed in Ref. [117].
The integrated conditionally filtered scalar dissipation rate N˜ |η∗ is computed
by applying the AMC model (Eqs. 3.18) directly to the CMC cells. This is done
by replacing N0 by:
N0
∗ =
N˜∗∫ 1
0
G(η)P˜ ∗(η)dη
(3.28)
35
3. Models and codes
where N˜∗ is the integrated filtered scalar dissipation rate:
N˜∗ =
∫
CMC cell
ρ¯N˜dV∫
CMC cell
ρ¯dV
(3.29)
The system of CMC equations can then be solved resulting in the conditionally
filtered species mass fractions Qα and the conditionally filtered temperature QT ,
based on which the conditional density is calculated.
In both LES/0D-CMC and LES/3D-CMC, the filtered value of a variable f
can be obtained by integration over η-space:
f˜ =
∫ 1
0
f˜ |ηP˜ (η)dη (3.30)
Note again that P˜ (η) is available at every LES cell, while f˜ |η is available at
each CMC cell, which may encompass many LES cells, the number depending on
each problems studied. Each LES cell uses therefore the conditional temperature
and density from its associated CMC node to find the new unconditional values
of density and temperature after integrating by the presumed sub-grid FDF of
the mixture fraction at the LES resolution (Eq. 3.30). The coupling between the
CMC model and the LES code is thus achieved through density and temperature.
3.3 Proper Orthogonal Decomposition
3.3.1 Principle
LES is a very powerful tool in reproducing temporal variation of 3D flows and
flames. However, most of the analyses of numerical results are still based on
averaged information i.e. radial profiles of the mean quantities and their Root
Mean Squares. In this thesis, we focus on the dynamics of the flow and the
flame. In order to take advantages of the full potential of the LES, the Proper
Orthogonal Decomposition (POD) Method has been applied using the Method
of Snapshots [105]. The idea behind POD is to find an orthonormal vector basis
for which the projection of the turbulent flow/flame fields (i.e. snapshots) on
it maximizes the fluctuation energy for any subset of the basis. Having found
36
3. Models and codes
Figure 3.1: Schematic showing the coupling of the CFD and the CMC solvers
according to the type of computation: 0D-CMC or 3D-CMC.
37
3. Models and codes
such a basis, the first modes contain the most energetic unsteady structures of
the flow and hence some understanding of the flow dynamics can be obtained by
analyzing only a few modes.
3.3.2 Method
POD has been applied to different 3D numerical datasets of both inert and reac-
tive simulations throughout this thesis. The numerical data from the LES mesh
are first interpolated on a coarser grid to decrease the computational load. The
set of interpolated snapshots is then loaded into a self-written MATLAB pro-
gramme. The POD routines are able to compute the spatial POD modes, project
the snapshots on each POD mode to calculate the associated temporal coefficient,
and to reconstructe the snapshots based on any combination of modes. The vari-
ables used to calculate the POD basis always include the three components of the
velocity fluctuations, but other variables have been added depending on the case,
such as the mixture fraction fluctuations, the pressure fluctuations for inert sim-
ulations, while in the reactive case the temperature fluctuations have also been
used. The variables from each snapshot are stored into a single matrix column,
each row corresponding to the values of a variable at a single cell. Hence each
matrix column corresponds to a single snapshot (i.e. the instantaneous fluctua-
tion fields) and these snapshots are organized chronologically inside the matrix.
Unlike previous studies where POD was applied separately to the different vari-
ables of the flame (Ref. [32] or Ref. [33] for extended POD), here POD has been
applied simultaneously to the different variables such as the velocity, the mixture
fraction, the pressure or the temperature. This method is expected to bring to
light the correlations among the flow dynamics, the mixing dynamics and the
flame dynamics. In order to give the same weight to each variable used to per-
form the POD modes computation, the fluctuating component of each quantity
has been divided by its standard deviation. However, in practice it has been
found that the same modes are identified with or without scaling the variables
by their standard deviations. The only differences between the two methods is
a slight discrepancy in the distribution of the modes energy. In the case of a
POD computation with N snapshots on a computational domain of m points, the
38
3. Models and codes
matrix obtained is:
U = [u1...un] =

U11−U¯1
σ(U1)
U21−U¯1
σ(U1)
. . .
UN1 −U¯1
σ(U1)
...
...
...
...
U1m−U¯m
σ(Um)
U2m−U¯m
σ(Um)
. . . U
N
m−U¯m
σ(Um)
...
...
...
...
 (3.31)
The matrix C = UTU of dimension N ×N is then computed. C is a real and
symmetric matrix, and therefore it is diagonalizable in an orthonormal basis. It
has N positive eigenvalues {λi}i⊂[1;N ] and N orthogonal eigenvectors {ai}i⊂[1;N ]
such as Cai = λiai. In order to solve this eigenvalue problem, the MATLAB
routine eig has been used. The solutions are then arranged according to their
eigenvalues as λ1 ≥ λ2 ≥ ... ≥ λN > 0 and the POD modes can be written as
linear combination of the snapshots:
Φi =
∑N
n=1 ainun
‖∑Nn=1 ainun‖ , i = 1...N (3.32)
If Ψ = [Φ1Φ2...ΦN ] is the POD basis, then the fluctuating part of a snapshot
can then be reconstructed as:
Uj =
N∑
i=1
aijΦi = Ψaj, j = 1...N (3.33)
In practice, reconstructing a snapshot using only the first few modes allows
to filter the data by removing the least energetic modes, regarded as noise, and
conserve only the most energetic structures of the flow. The reconstruction can
also be based on some specific modes of the flow, without including the most
energetic ones, if for instance we want to focus on a specific structure such as the
Precessing Vortex Core.
39
Chapter 4
Large-eddy simulations of forced
bluff body flows
4.1 Introduction
4.1.1 Motivation
The isothermal air flow behind an enclosed axisymmetric bluff body, with the
incoming flow being forced at a single frequency and with large amplitude, has
been explored with Large-Eddy Simulations (see Chapter 3, Section 3.1). The
configuration studied is shown schematically in Fig. 4.1. It consists of an air
flow in a pipe of diameter D, the near wake behind an axisymmetric bluff body
(a disk of diameter d) located at the end of the pipe, and a circular enclosure of
diameter Do (d < D < Do). The flow coming out of the annular passage between
the disk and the inner wall of the pipe has time-averaged velocity of Ub, but is
forced to pulsate at given frequencies and amplitudes. We focus on high Reynolds
number flows only. The aim of this chapter is to study this flow numerically by
Large-Eddy Simulation, while velocity measurements of the experimental set-up
have been previously obtained at Cambridge University Engineering Department
(CUED).
The main motivation is that this flow has strong similarities to flows found
in model and realistic combustors. Therefore, the flows behind a bluff body and
over a backward-facing step, when the incoming flow rate is pulsating at large
40
4. Large-eddy simulations of forced bluff body flows
Figure 4.1: Schematic of the flow studied and the initial condition.
amplitudes relative to the mean flow, can be considered as canonical problems
for self-excited combustors (see the literature review in Chapter 2). The den-
sity variations associated with flames of course change the velocity field, but
isothermal studies are useful first steps in understanding the fluid mechanics in
burners. Combustors usually have the additional complexity of swirl, but even
in the absence of swirl the interaction between the inner and outer recirculation
zones and the pulsating flow introduces significant complexities. There are many
aspects that have not been studied in detail yet, as it was demonstrated from the
discussion in the literature review (Chapter 2).
The experimental rig (Fig. 4.2) has been developed previously at Cambridge
[5] and has been used as a burner to study the response of turbulent premixed
flames under acoustic forcing, with the level of forcing commensurate to the one
used in the present inert flow measurements. CFD with a Reynolds-stress model
has also been performed [3] with emphasis on the flame response, while variants
of this burner include its use for non-premixed flames [1] and for sprays [71].
Premixed flames forced at two frequencies (the fundamental and its harmonic)
have also been explored [6].
41
4. Large-eddy simulations of forced bluff body flows
Figure 4.2: Photograph of the burner assembly. From Ref. [4].
42
4. Large-eddy simulations of forced bluff body flows
4.1.2 Objectives
It is evident from the literature review in Chapter 2 that the configuration
schematically shown in Fig. 4.1 is composed of simpler “sub-flows” that have
been widely studied, but the flow has not been examined in its entirety, and
especially when the incoming flow rate is oscillating. Measurements from this ar-
rangement can also serve as validation data for LES of combustors. These show a
great promise in capturing self-excited oscillations, but detailed validation of the
fluid mechanics of pulsating flows is a prerequisite step to increase the reliability
of the simulations.
The main objectives of this chapter are: (i) to examine the vortex formation
process and the mean and fluctuating velocity field in pulsating enclosed bluff
body wakes using large-eddy simulation; and (ii) to understand better the flow
structure in this arrangement and hence be in a position to understand reacting
flow results better.
4.2 Methods
4.2.1 Flow conditions
The flow arrangement is identical to that developed by R. Balachandran (Ref.
[5]) for studying flames, but used for inert (air) flow at ambient temperature and
pressure. The PhD thesis of R. Balachandran also contains useful details [4]. As
shown in Fig. 4.1, one may distinguish various parts of the flow: the annular
jet (AJ), which forms two shear layers (SL) with the central (CRZ) and outer
recirculation zones (ORZ). Figure 4.3 shows the bluff body used and the enclosure
(sudden expansion). The region upstream of the sudden expansion is designed to
facilitate external acoustic forcing and can be operated in the absence or presence
of strong acoustic oscillations.
The rig consists of two concentric circular ducts of length 300 mm. The inner
diameter (ID) of the outer duct was D = 35 mm, which also housed pressure
taps for acoustic pressure measurements. The inner and outer diameter of the
inner pipe were 6 mm and 8 mm respectively; this pipe acts as the holder of the
bluff body. The bluff body was conical (45◦ half-angle) with diameter d = 25 mm,
43
4. Large-eddy simulations of forced bluff body flows
Figure 4.3: The bluff body and the sudden expansion. All lengths in mm.
giving a blockage ratio of 50%. The enclosure was a 80 mm long fused silica quartz
cylinder of inner diameter Do = 70 mm which provided optical access for the
velocity measurements and also avoided air entrainment from the surroundings.
In order to reduce the interference from the acoustics of the downstream geometry
on upstream forcing, the length of the enclosure was chosen to be small so that
its resonant frequency was much higher than the frequency of forcing. The range
of operation of the forcing frequency in the apparatus was between 20 to 400
Hz while the fundamental frequency of the downstream duct is around 1000 Hz,
hence the resonant effects of the downstream geometry are minimized. For details
on the acoustic performance of the plenum, see Section 3 of Ref. [4].
The time-averaged volume flow rate divided by the annular passage area
(pi(D2 − d2)/4) gives the time-averaged bulk velocity Ub and was equal to 10
m/s for all experiments. This gives a Reynolds number Re = dUb/ν equal to
16,000. Experimentally, the flow upstream of the duct (in a plenum about 300
mm long and 200 mm diameter) is pulsed by loudspeakers fed by a signal gener-
ator of varying frequency and voltage, hence producing a pure tone. Due to the
interaction of this tone with the acoustic characteristics of the plenum, a strong
44
4. Large-eddy simulations of forced bluff body flows
Table 4.1: Flow conditions studied. U0 = Ub[1 + A sin(2pift)], St = fd/Ub.
Case Ub(m/s) f (Hz) St A
U 10 0 0 0
A 10 40 0.1 0.89
B 10 160 0.4 0.60
C 10 320 0.8 0.75
velocity oscillation is achieved at the exit of the pipe that is almost monochro-
matic, and the amplitude of this oscillation varies with the forcing frequency.
An approximately sinusoidal fluctuation is therefore superimposed, so that the
velocity at the annular passage follows:
U0 = Ub[1 + A sin(2pift)] (4.1)
with A the ratio of oscillation amplitude to mean flow velocity Ub. In the LES, a
velocity oscillation following the same equation has been imposed at the air pipe
inlet (numerical inlet at x = 25 mm) in order to mimic the loudspeakers action.
The flow conditions studied are summarized in Table 4.1. Three frequencies f
were tested: 40 Hz, 160 Hz and 320 Hz, giving rise to Strouhal number (based on
the bluff body diameter d and Ub) 0.1, 0.4, and 0.8 respectively. The amplitudes
for every one of these frequencies are shown in Table 4.1 and they are in the range
0.6-0.9. It is evident that these amplitudes are much higher than those studied in
the literature of forcing separation regions for control purposes, where amplitudes
in the range of only a few percent are commonly used [29; 40].
As discussed in the Literature Review in Chapter 2, we may expect a weak
helical-type vortex shedding at a Strouhal number of about 0.135, which implies
a frequency of fn = 54 Hz. For the vortices associated with the Kelvin-Helmholtz
instability of the separated shear layer, we must consider the local momentum
thicknesses of the two shear layers (between the annular jet and the central and
outer recirculation zones respectively), but it is difficult to estimate these in the
present problem. A Strouhal number based on the bluff body diameter and the
(steady) incoming velocity for a sphere in unconfined flow, StKH = fKHd/Ub, has
been measured as a function of Reynolds number [58], and for Re = 16000 (which
is the value used in the present experiments), we get StKH = 3 from which we
45
4. Large-eddy simulations of forced bluff body flows
evaluate fKH = 1200 Hz. Although the present flow is confined and the bluff
body is a disk, we may wish to consider this estimate as a guide to the expected
frequency of the shear layer Kelvin-Helmholtz instability, at least of the shear
layer towards the CRZ. Considering now the sudden expansion, we discussed in
the Literature Review the possibility of central jet precession and of a frequency
peak associated with the re-attachment length fluctuations. The slow precession
would be estimated to happen at a frequency of about 0.01Ub/D, extrapolating
the results of Ref. [79] to the present flow, which gives a fp=2.9 Hz. Ref. [24]
reported frD/Ub ≈ 0.3 for the re-attachment length fluctuations, which gives a
frequency of fr = 86 Hz. It is evident that the present forcing frequencies are not
expected to resonate with these natural vortex shedding or instability processes.
A flow without any periodic oscillations at the inlet has also been examined
previously by both experiment [1] and LES [118]. Here it has been recomputed
in order to perform spectral analysis and to provide a reference case to the forced
simulations.
4.2.2 Mesh and modelling
The flows have been simulated numerically with Large-Eddy Simulation (LES)
using the code PRECISE, which is described in Chapter 3, Section 3.1.
The mesh extends 25mm upstream of the bluff body, to allow some flow
development, and 50mm downstream of the cylindrical enclosure. It consists of
1.8M cells. The unforced flow has also been recomputed with the same mesh and
it was found in a earlier work [118] that a finer grid did not improve the results,
which suggests that the present grid is sufficient.
The numerical inlet had an area Ain (slightly smaller than piD
2/4 due to
the diameter of the rod holding the bluff body in place). The mean velocity
there, Uin, has been chosen in order to get a mean velocity of Ub=10 m/s at the
annular opening between the bluff body and the sudden expansion following the
conservation of mass equation:
UinAin = Ubpi(D
2 − d2)/4 (4.2)
The amplitude A (Eq. 4.1) fits exactly the amplitudes obtained in the exper-
46
4. Large-eddy simulations of forced bluff body flows
iments (Table 4.1). The velocity at the inlet is forced at a single frequency,
uniform across the duct and contains white noise in order to trigger instabilities
and turbulence downstream [50]. Therefore, in the simulations, the velocity U0
at the annular passage given by Eq. 4.1 already contains some turbulence due to
the boundary layers at the duct walls from the inlet to the annular opening and
refers to an area-averaged, phase-averaged velocity.
For the 40 and 160 Hz, a timestep of 1.0× 10−5 s has been used, while for the
320 Hz case, the timestep was 5.0×10−6 s. These values ensure the CFL number
is less than 0.3 everywhere in the domain. No-slip velocity conditions have been
enforced on solid walls, while zero gradient boundary condition has been enforced
at the outlet.
The LES for the 40 Hz, 160 Hz and 320 Hz cases have been performed for 14
cycles, 34 cycles and 32 cycles respectively. Phase averaging has been performed
by averaging data from each of these cycles. We expect therefore a relatively large
statistical uncertainty especially for the phase-averaged fluctuations. Spectra
have been calculated with Matlab routines using Welch windowing on the whole
data record.
4.2.3 Data processing and comparison with experiments
Experimental measurements are available at five downstream positions, x=5, 15,
25, 35 and 50 mm, with radial traverses taken in 1 mm increments from the
centerline to as close to the wall as possible.
The coordinate system used is shown in Fig. 4.1. The instantaneous velocity
ui(x, r, t) can be decomposed in three parts:
ui(x, y, z, t) = ui(x, y, z) + uˆi(x, y, z, φ) + u
′
i(x, y, z, t) (4.3)
with ui the time-averaged velocity, uˆi the periodic component of imposed period T
at phase angle φ (0 < φ < 2pi), called velocity modulation, and u′i the fluctuating
or turbulent velocity. This fluctuation is therefore the fluctuation about the
phase-averaged velocity:
〈u〉(φ) = ui(x, y, z) + uˆi(x, y, z, φ) (4.4)
47
4. Large-eddy simulations of forced bluff body flows
In the Results section and dropping the explicit dependence on the spatial
coordinates for simplicity, the phase-averaged mean (〈u〉(φ)) and phase-averaged
velocity variance (〈u′2〉(φ)) are presented. In addition, some phase-averaged quan-
tities are presented at a few selected locations as a function of phase. Finally,
spectra of the instantaneous axial velocity (i.e. including both the cyclic and
turbulent parts) are also shown to determine any peaks and their evolution.
4.3 Results and Discussion
4.3.1 The unforced flow
For the unforced flow (Case U of Table 4.1), direct comparison with the exper-
imental data in terms of axial and radial mean and Root Mean Square (RMS)
velocities has been presented elsewhere [118]. During the present work, the un-
forced simulation was restarted in order to record some time-series of the three
velocity components and perform spectral analysis. The new results from that
simulation are presented here to facilitate the discussion on the forced flow. Very
good agreement with the experimental data of Ref. [1] has been obtained for
both mean and RMS axial and radial velocities. The mean axial velocity has a
peak value of approximately 1.2Ub in the annular jet and a minimum value of
approximately −0.5Ub inside the recirculation zone at x/d = 0.62. After the exit
of the bluff body, mixing makes the velocity profiles more uniform. The zero-
velocity zone is predicted to be approximately 0.8d wide and Xs = 1.2d long,
which is consistent with experimental studies of other flows behind bluff bodies
[116]. The level of fluctuations of the axial velocity is also predicted accurately.
They reach their highest value at the shear layers (at the location of maximum
radial gradient of the mean axial velocity) and they are about 15% of Ub inside
the recirculation zone.
To show more clearly the overall flow structure, typical snapshots of the in-
stantaneous axial velocity and the azimuthal component of the vorticity:
ωθ = ∂v/∂x− ∂u/∂r (4.5)
48
4. Large-eddy simulations of forced bluff body flows
(a) (b)
Figure 4.4: Snapshots of (a) axial velocity (in m/s) and (b) azimuthal vorticity
(ωθ = ∂v/∂x − ∂u/∂r; in 1/s) on a plane going through the axis from LES.
Unforced flow (Case U).
are shown in Fig. 4.4. The high velocity annular jets and the negative velocity
in the CRZ and the ORZ are evident. The vorticity graph shows small Kelvin-
Helmholtz instabilities at the shear layers surrounding the annular jet up to about
x/d = 0.5 and the disintegration of these vortices downstream. These vortices
are smaller than the vortices associated with the forced flow and do not appear in
a regular pattern in space nor with a given frequency in time, in contrast to the
vortices shed in the forced flow, discussed later. The overall rotation of the flow
inside the CRZ is also evident by the prevailing sign of the vorticity. To facilitate
the discussion that follows in Section 4.3.2, Fig. 4.5 shows the time-averaged
axial velocity from LES, with a few points marked. For ease of reference when
comparing the mean and RMS velocities in the forced flow with the unforced
flow, the normalised time-averaged axial velocity (u/Ub) and its RMS (urms/Ub)
value pairs of the unforced flow at these six locations are as follows: A: −0.336,
0.126; B: 1.165, 0.086; C: −0.01, 0.039; D: 0.707, 0.112; E: 0.478, 0.203; and F:
−0.159, 0.090.
Finally, the spectra at a few axial and radial locations from experiment and
49
4. Large-eddy simulations of forced bluff body flows
A B C
D E F
Figure 4.5: Contour of the time-averaged axial velocity (in m/s) from the LES.
Points A-F are at locations (x, r)=(5,0), (5,15), (5,30), (50,0), (50,15), (50,30)
respectively, in mm; r is distance from the axis and x the axial distance from the
bluff body. Unforced flow (Case U).
LES are shown in Fig. 4.6. It is clear that the frequency content increases as
we go downstream and it is higher at the shear layers than in the annular jet or
the CRZ at low x/d, while the frequency content seems to be equally wide for
all r/d at long distances from the bluff body. No clear peaks are discernible in
either the LES or the experiment. The LES shows a broad peak at about 1200
Hz at the outer shear layers and at small axial distances from the bluff body
(not shown here). This peak could be associated with the Kelvin-Helmholtz
instability visualised in Fig. 4.4. A small region with a slope of −5/3 is evident
from both experiment and LES, which suggests that the flow is fully turbulent
except perhaps inside the annular jet and at very short distances from the bluff
body, where the turbulence levels and frequency content are weak.
The comparison between LES and experiment in the unforced flow shows that
the simulations capture the major features of the flow adequately.
4.3.2 Phase-averaged velocities and turbulent intensities
The mean (〈u〉(φ)) and RMS (〈u′2〉1/2(φ)) of phase-averaged axial velocity from
the experiment and LES are discussed here for the forced flows (Cases A-C of
50
4. Large-eddy simulations of forced bluff body flows
101 102 103 104
100
1010
Frequency (Hz)
PS
D/
(U
b.
d)
−5/3
1
6
5
4
3
2
(a)
101 102 103 104
100
1010
Frequency (Hz)
PS
D/
(U
b.
d)
−5/3
1
2
3
4
5
6
(b)
Figure 4.6: Frequency spectra of the axial velocity from (a) experiment and (b)
LES. Unforced flow (Case U). Locations 1-6 correspond respectively to an (axial,
radial) coordinate in mm of: (5,0), (5,15), (15,0), (15,15), (25,0), and (25,15).
Each spectrum has been shifted upwards by a factor of 103. Points 1 and 2 are,
respectively, the locations A and B marked on Fig. 4.5.
Table 4.1). The velocity profiles at the annular exit (i.e. at x = 0) as calculated
from the LES are given in Fig. 4.7. Profiles of the phase-averaged mean and
RMS velocity as a function of phase angle φ are shown in Figs. 4.8, 4.9, and
4.10 for 40, 160, and 320 Hz respectively for the locations marked on Fig. 4.5.
Comparisons will be made between experiment and LES, between the velocities
at the different locations, and between the forced and the unforced flow.
At the inlet, Fig. 4.7, the LES shows that the phase-averaged axial velocity
distribution across the annular opening is similar for all forcing frequencies and
at all phase angles, i.e. it follows the time-varying bulk velocity, although the
boundary layers at the walls fluctuate by a smaller amount than the centre of
the flow at the 160 and 320 Hz forcing. No flow reversal occurs, although at the
trough of the forcing cycle the velocity is very low. The experimental data do not
extend to this location due to the inability of locating the LDV probe so close
to the pipe exit, however the mean and r.m.s. velocities of the unforced flow
are close to experimental values obtained by a separate hot wire system [4]. The
velocity fluctuations peak at the sides of the annular jet and reach high values:
at the particular phase corresponding to the highest velocity through the cycle,
51
4. Large-eddy simulations of forced bluff body flows
when 〈u〉/Ub ≈ 2 in the centre of the annular opening, the maximum phase-
averaged RMS across the opening is about 25-30% of Ub, which is very similar
to the corresponding value from the unforced flow. This is so for all forcing
frequencies tested. This suggests that the turbulence inside the pipe scales with
the time-varying bulk velocity.
For forcing at 40 Hz, 〈u〉 seems to be very well captured by LES for all phase
angles and for all positions shown (Fig. 4.8). The accuracy of the calculation is
similar to that of the unforced flow observed by Ref. [118]. The strong pulsation
is evident at the annular jet (see the curve for Point B, (x, r) = (5, 15)), but the
pulsation seems to be weaker at other positions (this can be visualized by consid-
ering the magnitude of the cyclic fluctuation as a percentage of the time-averaged
velocity, uˆ(φ)/u). If we compare the curves for Point B ((x, r) = (5, 15)) with
the curves for Point E ((x, r) = (50, 15)), locations associated with the annular
jet, it is evident that the peak velocity arrives at the downstream location about
1.1 rad later than at the upstream location, implying a time delay of about 4.8
ms or a “phase speed” of about 10.3 m/s, which is very close to the value of the
bulk velocity Ub. If we now consider the curves for Points A and D, locations
along the centreline, we can observe again good agreement between experiment
and LES and a small relative magnitude of modulation. At (x, r) = (5, 0) (i.e.
inside the CRZ), at two phase angles through the cycle, the velocity may switch
from negative to positive in the experiment (see Fig. 4.8, at about φ = 0.8
and φ = 3.8 rad). The same behaviour is seen in the LES, although the ex-
act phase angle at which the zero-crossings occur are slightly shifted compared
to the experiment. It is evident that inside the CRZ, a frequency doubling has
occurred, with the phase-averaged mean velocity showing two oscillations in a
forcing period. Downstream of the forward stagnation point (Point D), a fre-
quency doubling is not immediately evident (although harmonics are revealed in
the spectra, as discussed later). The outer recirculation zone far from the bluff
body (Point F) shows a pulsation approximately in-phase with the forcing (i.e.
the flow in the annular jet), while at Point C there is a phase shift. At Point F,
which is inside the ORZ, the phase-averaged mean axial velocity switches from
positive to negative, indicating a large fluctuation in the re-attachment length
through the forcing cycle. Although the incoming phase-averaged velocity has a
52
4. Large-eddy simulations of forced bluff body flows
0.4 0.5 0.6 0.7 0.8
0
0.5
1
1.5
2
r/d
U/
U b
 
 
0.97 rad
1.26 rad
2.89 rad
4.40 rad
6.03 rad
no osc.
(a)
0.4 0.5 0.6 0.7 0.80
0.1
0.2
0.3
0.4
0.5
0.6
r/d
u
′/U
b
 
 
0.97 rad
1.26 rad
2.89 rad
4.40 rad
6.03 rad
no osc.
(b)
0.4 0.5 0.6 0.7 0.8
0
0.5
1
1.5
2
r/d
U/
U b
 
 
0.0 rad
1.51 rad
3.01 rad
4.27 rad
4.52 rad
no osc.
(c)
0.4 0.5 0.6 0.7 0.80
0.1
0.2
0.3
0.4
0.5
r/d
u
′/U
b
 
 
0.0 rad
1.51 rad
3.01 rad
4.27 rad
4.52 rad
no osc.
(d)
0.4 0.5 0.6 0.7 0.8
0
0.5
1
1.5
2
r/d
U/
U b
 
 
0.22 rad
0.50 rad
2.26 rad
3.77 rad
5.27 rad
no osc.
(e)
0.4 0.5 0.6 0.7 0.80
0.1
0.2
0.3
0.4
0.5
0.6
r/d
u
′/U
b
 
 
0.22 rad
0.50 rad
2.26 rad
3.77 rad
5.27 rad
no osc.
(f)
Figure 4.7: Phase-averaged mean (a,c,e) and RMS (b,d,f) axial velocity from the
LES at the annular exit (x = 0). (a,b): Case A; (c,d): Case B; (e,f): Case C.
53
4. Large-eddy simulations of forced bluff body flows
virtually pure sine wave periodic behaviour, the wave shape at other locations
is far from this. A comparison with the time-averaged velocities from the forced
flow with the time-averaged velocities of the unforced flow shows that these are
only slightly different close to the bluff body, but they are significantly different
at the downstream locations.
The phase-averaged axial RMS velocities 〈u′2〉1/2(φ) at the same positions are
shown in Figs. 4.8(c) and 4.8(d) as a function of phase angle. The following
observations can be made. (i) Overall good agreement between experiment and
LES is found for most locations. The largest discrepancy is for location F, i.e.
inside the ORZ, and for location A, i.e. inside the CRZ and close to the bluff body.
The relatively large scatter in the LES data is due to the small number of cycles
used. (ii) Close to the bluff body (x=5 mm; Points A-C), the normalised intensity
〈u′2〉1/2/Ub lies between 0.1 and 0.2 and varies little with phase. Far from the bluff
body (x=50 mm; Points D-F), the turbulence intensities reach very large values
(〈u′2〉1/2/Ub ≈ 0.5) and fluctuate significantly with phase angle. These large
values may be associated with large fluctuations of the re-attachment length. (iii)
The intensities reach their peaks at a phase angle that depends on location and
are not everywhere in phase with 〈u〉: the peak values far downstream are reached
when the local mean velocity changes quickest with phase (i.e. when |∂〈u〉/∂φ| is
high), while in the annular jet the turbulence is weakest and becomes a minimum
when the mean velocity reaches its peak. Finally, (iv) a close comparison with
the data of the unforced flow reveals that the phase-averaged fluctuations are
larger than the turbulence intensities in the unforced flow, with the difference
increasing as we go downstream.
For forcing at 160 Hz (Case B), Fig. 4.9, similar conclusions are drawn. In
most locations the 〈u〉(φ) profiles behave as a pure oscillation, although some
distortion is evident. The time-averaged value is close to the average from the
unforced case. The phase-averaged velocity fluctuations are high inside the CRZ
and ORZ and follow, approximately, the phase of the mean velocity. As for the
40 Hz case, the turbulent fluctuations are higher than the unforced flow at the
same position, but they are smaller than for the 40 Hz case. Relatively good
agreement between the LES and experiment is found.
We now consider Case C, i.e. forcing at 320 Hz (Fig. 4.10) and let us first
54
4. Large-eddy simulations of forced bluff body flows
0 2 4 6
−0.5
0
0.5
1
1.5
2
Phase (rad)
<
U>
/U
b
 
 
EXP 5/0
LES
EXP 5/15
LES
EXP 5/30
LES
(a)
0 2 4 6
0
0.5
1
1.5
Phase (rad)
<
U>
/U
b
 
 
EXP 50/0
LES
EXP 50/15
LES
EXP 50/30
LES
(b)
0 2 4 60
0.05
0.1
0.15
0.2
0.25
0.3
Phase (rad)
u
′/U
b
 
 
EXP 5/0
LES
EXP 5/15
LES
EXP 5/30
LES
(c)
0 2 4 60
0.1
0.2
0.3
0.4
0.5
Phase (rad)
u
′/U
b
 
 
EXP 50/0
LES
EXP 50/15
LES
EXP 50/30
LES
(d)
Figure 4.8: Phase-averaged mean (a,b) and RMS (c,d) axial velocities from ex-
periment and LES. Forced flow, 40 Hz (Case A). The locations are given in terms
of (x, r) in mm and correspond to points A-C (a,c) and D-F (b,d).
55
4. Large-eddy simulations of forced bluff body flows
0 2 4 6
−0.5
0
0.5
1
1.5
2
Phase (rad)
<
U>
/U
b
 
 
EXP 5/0
LES
EXP 5/15
LES
EXP 5/30
LES
(a)
0 2 4 6
−0.5
0
0.5
1
1.5
Phase (rad)
<
U>
/U
b
 
 
EXP 50/0
LES
EXP 50/15
LES
EXP 50/30
LES
(b)
0 2 4 60
0.05
0.1
0.15
0.2
0.25
0.3
Phase (rad)
u
′/U
b
 
 
EXP 5/0
LES
EXP 5/15
LES
EXP 5/30
LES
(c)
0 2 4 60
0.1
0.2
0.3
0.4
0.5
Phase (rad)
 
u
′/U
b 
 
 
EXP 50/0
LES
EXP 50/15
LES
EXP 50/30
LES
(d)
Figure 4.9: Phase-averaged mean (a,b) and RMS (c,d) axial velocities from ex-
periment and LES. Forced flow, 160 Hz (Case B). The locations are given in terms
of (x, r) in mm and correspond to points A-C (a,c) and D-F (b,d).
56
4. Large-eddy simulations of forced bluff body flows
focus on the phase-averaged mean velocities. For all locations shown, there is very
good agreement between the experimental data and LES. As in the cases with
forcing at lower frequencies, the annular jet pulsates significantly throughout the
cycle due to the large value of forcing amplitude A used in this flow. However,
in all other locations, the cyclic modulation is much smaller than for forcing at
f = 40 Hz (Fig. 4.8) and also smaller than for forcing at f = 160 Hz (Fig.
4.9). The wave shape now resembles a pure sine wave and frequency doubling
is not evident. A comparison with the time-averaged velocities from this forced
flow with the time-averaged velocities of the unforced flow shows that these are
close everywhere. The turbulence intensities, presented in Figs. 4.10(c) and
4.10(d), also show very good agreement between experiment and LES, except at
(x, r) = (5, 0), where the LES predicts higher fluctuations than the experiment.
The variation of the turbulence during the forcing cycle is much weaker than for
lower forcing frequencies for all positions and is approximately in phase with the
mean velocity variation. As in the other forcing cases, the turbulent fluctuations
are higher than in the unforced flow, but they are smaller than for forcing at 40
and 160 Hz.
A common feature for all forcing frequencies is that the cyclic fluctuation as a
percentage of the time-averaged velocity is lower inside the flow than at the inlet,
and that, at the same location, the random turbulent fluctuations are higher
than in the unforced flow. A comparison of 〈u〉/Ub and 〈u′2〉1/2/Ub between the
various cases shows that, in general, the mean velocity at downstream locations
is altered with forcing, that the velocity modulation uˆ/Ub is largest at low forcing
frequencies, and that 〈u′2〉1/2/Ub decreases with increasing forcing frequency. The
bulk of the flow at high frequencies behaves as a high-pass filter, i.e. it becomes
unresponsive. The results are consistent with the view that the injected energy in
the mean flow eventually becomes turbulent kinetic energy and that this transfer
is most efficient for the 40 Hz case. The LES seems to be able to predict the
phase-averaged mean and RMS velocities reasonably well for all tested forcing
frequencies.
Snapshots sequences of the axial velocity at forcing frequency of 40 Hz (Fig.
4.11) and 160 Hz (Fig. 4.12) confirm the previous observation. In these figures,
the black lines represent the zero-velocity isolines. The CRZ and ORZ are seen
57
4. Large-eddy simulations of forced bluff body flows
0 2 4 6
−0.5
0
0.5
1
1.5
2
Phase (rad)
<
U>
/U
b
 
 
EXP 5/0
LES
EXP 5/15
LES
EXP 5/30
LES
(a)
0 2 4 6
−0.5
0
0.5
1
1.5
Phase (rad)
<
U>
/U
b
 
 
EXP 50/0
LES
EXP 50/15
LES
EXP 50/30
LES
(b)
0 2 4 6
0.1
0.2
0.3
0.4
Phase (rad)
u
′/U
b
 
 
EXP 5/0
LES
EXP 5/15
LES
EXP 5/30
LES
(c)
0 2 4 6
0.15
0.2
0.25
0.3
0.35
0.4
Phase (rad)
u
′/U
b
 
 
EXP 50/0
LES
EXP 50/15
LES
EXP 50/30
LES
(d)
Figure 4.10: Phase-averaged mean (a,b) and RMS (c,d) axial velocities from
experiment and LES. Forced flow, 320 Hz (Case C). The locations are given in
terms of (x, r) in mm and correspond to points A-C (a,c) and D-F (b,d).
58
4. Large-eddy simulations of forced bluff body flows
to pulsate strongly with the incoming flow at 40 Hz (Fig. 4.11), while the whole
flow, in particular the RZs, appears much more frozen at high frequency (160 Hz
case for the animation represented in Fig. 4.12).
4.3.3 Spectra and vortex formation
Spectra of axial velocity from the experiment and the LES are shown in Figs.
4.13, 4.14, and 4.15 for Cases A-C respectively and for a few positions. A com-
parison between the various positions and flow conditions reveals the following
characteristics. (i) A strong peak at the forcing frequency is evident everywhere.
(ii) The broadband turbulence spectrum is similar to the spectrum of the unforced
flow. (iii) Harmonics of the fundamental forcing frequency appear consistently,
but their relative strength varies with position and forcing frequency. (iv) Un-
der some forcing conditions and at some locations, we observe the presence of
a sub-harmonic peak. Finally, (v) the LES and experimental spectra have quite
similar features in terms of presence and relative magnitude of harmonics and the
sub-harmonic. These observations are discussed in more detail below.
At f = 40 Hz, close to the inlet (position 2, (x, r) = (5, 15); this is also
marked Point B on Fig. 4.5), we do not see any harmonics, which provides
evidence of the purity of the forcing. This is so in both the experiment and the
LES. The forcing peak and the harmonics are evident everywhere else. As we go
downstream, the strength of the harmonic increases, while at position 1 (inside
the CRZ; this was also marked Point A on Fig. 4.5), the experiment shows a
first harmonic stronger than the fundamental, something roughly borne out by
the LES as well. The presence of a strong harmonic inside the CRZ was also
observed in the phase-averaged velocities (Fig. 4.8) and is consistent with their
non-sinusoidal behaviour.
At f = 160 Hz (Fig. 4.14), similar observations, in general, can be made,
although now the harmonics are evident even close to the inlet and, inside the
CRZ (spectra 1,3,5), the first harmonic is not stronger than the fundamental as
was the case for 40 Hz forcing. An important qualitative difference observed in
this case in both experiment and LES is the presence of a sub-harmonic broad
peak (at about 80 Hz), in the CRZ which becomes evident in the downstream
59
4. Large-eddy simulations of forced bluff body flows
Figure 4.11: Sequence of instantaneous axial velocity snapshots at different con-
secutive instants and over one period for the 40 Hz forced case.
60
4. Large-eddy simulations of forced bluff body flows
Figure 4.12: Sequence of instantaneous axial velocity snapshots at different con-
secutive instants and over one period for the 160 Hz forced case.
61
4. Large-eddy simulations of forced bluff body flows
101 102 103 104
100
1010
Frequency (Hz)
PS
D/
(U
b.
d)
1
3
2
5
6
4
(a)
101 102 103 104
100
1010
Frequency (Hz)
PS
D/
(U
b.
d)
1
2
3
6
5
4
(b)
Figure 4.13: Frequency spectra of the axial velocity from (a) experiment and (b)
LES. Forced flow, 40 Hz (Case A). Locations as in Fig. 4.6.
locations (positions 3-6; x = 15 and 25 mm).
Finally, with forcing at 320 Hz (Fig. 4.15), the fundamental peak at the
downstream locations has a broader base than at the lower forcing frequencies,
the sub-harmonic is absent, and the fundamental is always stronger than the
harmonics. In general, the LES captures well the experimentally-observed trends
in the spectra, except at the location inside the CRZ and close to the bluff body
(position 1), where the forcing peak is less pronounced in the LES than in the
experiment.
Presence of harmonics is typical of nonlinear phenomena. Monochromatic
acoustic waves propagating in nonlinear medium give birth to harmonics of the
fundamental as the waves propagate further into the medium [35]. However
it has to be emphasized that in our case the presence of harmonics inside the
simulated flow for each forcing frequency is not due to any acoustic phenomena
as PRECISE is an incompressible code. As a consequence, the harmonics found in
the experimental flow may also originate in aerodynamic phenomena and not only
in the acoustic of the flow. Similarly to the theory of acoustic, a Burger’s equation
can be derived in the case of hydrodynamic waves. In the case of a one dimensional
incompressible and inviscid flow, the Navier-Stokes equation simplifies into the
62
4. Large-eddy simulations of forced bluff body flows
101 102 103 104
100
1010
Frequency (Hz)
PS
D/
(U
b.
d)
1
2
3
4
5
6
(a)
101 102 103 104
100
1010
Frequency (Hz)
PS
D/
(U
b.
d)
1
4
5
6
2
3
(b)
Figure 4.14: Frequency spectra of the axial velocity from (a) experiment and (b)
LES. Forced flow, 160 Hz (Case B). Locations as in Fig. 4.6.
Riemann equation as follows:
∂(U)
∂t
+ U
∂(U)
∂x
= 0 (4.6)
The general solution of Eq. 4.6 is U = f(x − Ut) and describes the evolution
of hydrodynamic waves travelling at the fluctuating velocity U . In the case of
streamlines located inside the jet, U ≈ U0, which corroborates the value of the
“phase speed” found in Section 4.3.2.
In order to understand better the flow structure as a function of forcing fre-
quency, LES snapshots were used. Figure 4.16 shows visualisations of the vortices
developed due to the oscillating flow. This is achieved by plotting the quantity
Q, defined as:
Q = (ω2 − 2S˜ijS˜ij)/4 (4.7)
with ω the vorticity magnitude and S˜ij the strain rate calculated from the gradi-
ents of the resolved velocity. PositiveQ has been used extensively to mark vortical
regions in turbulent flows [47; 48]. The figures show iso-surfaces of Q = 15× 106
1/s2 (≈ 94 U2b /d2) as a function of phase angle from snapshots from the LES.
It is evident that the 40 Hz case does not show strong vortex formation at any
point in the cycle. Vortex tubes seem to be randomly oriented. The dominant
presence of the iso-surface of Q in the CRZ denotes the higher vorticity mag-
63
4. Large-eddy simulations of forced bluff body flows
101 102 103 104
100
1010
Frequency (Hz)
PS
D/
(U
b.
d)
1
2
6
5
4
3
(a)
101 102 103 104
100
1010
Frequency (Hz)
PS
D/
(U
b.
d)
1
2
4
5
6
3
(b)
Figure 4.15: Frequency spectra of the axial velocity from (a) experiment and (b)
LES. Forced flow, 320 Hz (Case C). Locations as in Fig. 4.6.
nitude there, as also evident in the unforced case (Fig. 4.4b). At the points
of the cycle where the incoming velocity is low, the magnitude of Q drops and
hence we see low Q for some phase angles in Fig. 4.16a. In contrast to the above
behaviour, the cases with forcing at 160 Hz (Fig. 4.16b) and 320 Hz (Fig. 4.16c)
show vortex rings being shed from either corner of the annular opening (i.e. at
the bluff body corner and at the sudden expansion corner). The shedding seems
to occur when the phase-averaged velocity begins to increase. The outer vortex
ring is convected downstream, becomes highly wrinkled and eventually breaks up
towards the end of the cycle at an axial distance about one bluff body diameter.
The inner vortex ring is again convected downstream, but it breaks up quickly
inside the CRZ, feeding this region with vorticity and hence velocity fluctuations.
The same features are found in Case C (320 Hz; Fig. 4.16c), with the important
additional characteristic that a second set of vortex rings is shed before the first
one is convected out of the domain due to the shorter wavelength of the velocity
modulation.
The presence of vortices shed from the separation points at some forcing
frequencies is consistent with flow visualization studies [6; 65] and with data
concerning flame response [5; 6]. A more detailed comparison with the data of
Ref. [65] with forced premixed flames, shows that while Ref. [65] observed vortex
rings for a Strouhal number of 0.1 (our 40 Hz case; Table 4.1) for an amplitude
64
4. Large-eddy simulations of forced bluff body flows
φ=
0
φ=
0.2
6pi
φ=
0.5
pi
φ=
0.7
4pi
φ=
0.9
8pi
φ=
1.2
2pi
φ=
1.5
4pi
φ=
1.7
8pi
φ=
0
φ=
0.2
6pi
φ=
0.5
pi
φ=
0.7
4pi
φ=
0.9
8pi
φ=
1.2
2pi
φ=
1.5
pi
φ=
1.7
pi
φ=
0.5
pi
φ=
0.9
8pi
φ=
1.2
2pi
φ=
1.9
1pi
φ=
1.4
6pi
φ=
0.7
4pi
φ=
0.2
6pi
φ=
0
(a)
f=
40
 H
z
f=
16
0 
H
z
f=
32
0 
H
z
(b) (c)
Figure 4.16: Iso-surfaces of Q = 15×106 1/s2 from sequential snapshots from the
LES, showing the evolution of the shed vortices for (a) Cases A, (b) Case B, and
(c) Case C. For the definition of Q, see text.
65
4. Large-eddy simulations of forced bluff body flows
A > 0.42, in the present isothermal flow the Strouhal number of 0.1 and A = 0.89
does not show vortex rings. This may suggest that the density difference between
the cold incoming gases in the shear layers and the hot gases inside the CRZ and
ORZ in flames facilitates the formation of vortices. The absence of a well-defined
vortex ring at f = 40 Hz is also consistent with experiments of forced jets [18],
where vortices were formed only above certain frequencies.
The existence of harmonics in the spectra at most conditions except very
early in the flow inlet is consistent with observations in forced jets by Ref. [126],
where a single spectral peak in a low-turbulence jet close to the nozzle gave
rise to multiple harmonics and eventually to a fully-turbulent spectrum with
downstream distance. Case B (160 Hz) has the special feature of the presence of
the sub-harmonic in the spectra (Fig. 4.14). This may be equivalent to vortex
pairing in shear layers or jet columns [126] as the inner vortex ring contracts and
disintegrates while it is being squeezed inside the CRZ (Fig. 4.16).
Finally, the presence of well-defined, regularly-spaced vortices can be used to
explain the difference in turbulence intensities for the various forcing frequencies.
Both experiment and LES show that 〈u′2〉1/2/Ub, in general, decreases with in-
creasing forcing frequency f . As f increases, more vortices are formed, and their
spacing (i.e. the wavelength of the flow oscillation) decreases, which suggests
that there exists a larger number of vortices in the flow with increasing f . The
presence of vorticity associated with these vortices will enhance kinetic energy
dissipation, which will therefore decrease the turbulent velocity fluctuations.
4.4 Proper Orthogonal Decomposition analysis
of the 160Hz forced flow
In order to understand further the structures of the forced bluff body flows, Proper
Orthogonal Decomposition has been applied to the 160 Hz forced case. Here POD
has been based on the three components of the velocity and the pressure. The first
ten modes are reproduced with the spectral analysis of their temporal coefficients.
The analysis provides key insights on the recirculation zones pulsation, vortex
shedding and spectra of such a flow.
66
4. Large-eddy simulations of forced bluff body flows
4.4.1 Mode 1
Mode 1 is represented in Fig. 4.17. Application of the Q−criterion (Figs. 4.17(a)
and 4.17(b)) shows clearly a row of several large outer annular vortex rings dis-
tributed along the chamber of combustion. At least one inner vortex ring shed
from the bluff body edges is also present. As we go further downstream inside
the combustion chamber, the vortices envelopes are more and more wrinkled and
the flow is filled with more and more vorticity. Towards the end of the combus-
tion chamber, the vortices have broken up into small vortical structures. In Fig.
4.17(d), the axial velocity fluctuations of mode 1 have been plotted. The jet is
characterized by a blue color i.e. negative fluctuations of the axial velocity while
the central recirculation zone has positive fluctuations associated with it. This
is expected as the jet entering in the chamber is slowed down by the slower fluid
around it while the fluid in the central recirculation zone tends to be accelerated
by the fast jet fluid. Fig. 4.17(c) shows the pressure fluctuations map of mode
1 and confirms the presence of outer and inner vortex rings in mode 1. The
spectrum of the temporal coefficient associated with mode 1 is represented in
Fig. 4.35. It shows a single and very clear peak at 160 Hz. It is the only mode
to exhibit a single frequency peak. In fact, Proper Orthogonal Decomposition
enforces spatial orthogonality between the POD modes, hence leading to decorre-
lated structures associated with each mode. However, the Fourier analysis of the
temporal coefficients of POD modes shows that, in general, multiple frequencies
are associated with the evolution of each POD mode (Figs. 4.35 and 4.36). Here,
mode 1 is clearly associated with the forced frequency at 160 Hz. Mode 1 can thus
be regarded as a mode associated with the cyclic fluctuations of the flow i.e. the
fluctuations directly associated with the inlet pulsation at 160 Hz. This explains
why this mode alone contains a very large amount of the total fluctuating energy
as reported in Fig. 4.34 and Table 4.2.
The reconstruction of the flow based on the mean flow and mode 1 are visu-
alized in Fig. 4.18 through the Q−criterion. It shows the successive appearance
and disappearance of the different vortex rings inside the combustion chamber.
There is no convection of the rings with a reconstruction based on a single mode.
The reconstruction of the axial velocity is also shown in Fig. 4.19. The black lines
67
4. Large-eddy simulations of forced bluff body flows
Table 4.2: Relative energy of POD modes.
Mode %
Mode 1 86.9443
Mode 2 4.1937
Mode 3 1.5706
Mode 4 1.1035
Mode 5 0.6378
Mode 6 0.3357
Mode 7 0.2930
Mode 8 0.1748
Mode 9 0.1402
Mode 10 0.1321
represent the isoline defined as u = 0. The pulsation of the central recirculation
zone is clearly visible and follows the pulsation of the inlet jet at 160 Hz, although
with a time delay. In Fig. 4.20, the reconstructed axial velocity fields have been
superimposed over one period. The black lines represent the zero-velocity isolines
for each snapshot. It is noticeable that the boundary of the CRZ oscillates like a
standing wave.
4.4.2 Modes 1 and 2
Mode 2 (Fig. 4.21) is similar to mode 1: large annular vortices are also visible
in the upstream flow, although at different positions (Figs. 4.21(a) and 4.21(b)).
They tend to occupy the space between the vortices of mode 1, as a result of the
spacial orthogonality resulting from POD. Two inner vortices are clearly visible
through the Q−criterion in Fig. 4.21(b) and the pressure fluctuations map in
Fig. 4.21(c). The downstream part of the chamber is also filled with vorticity
due to the breakdown of the large vortex rings. As for mode 1, there is a clear
peak at 160 Hz in the spectra of the temporal coefficent associated with mode
2 and represented in Fig. 4.35. However, a small harmonic at 320 Hz is also
visible. Despite their similarities, mode 1 and mode 2 do not form a perfect pair
of modes. In addition to exhibiting discrepancies in their spectra, mode 1 and
mode 2 contain different amount of fluctuations energy: mode 1 accounts for 87 %
of the total energy while mode 2 contains only 4.2 % of the energy (see Fig 4.34
68
4. Large-eddy simulations of forced bluff body flows
(a) (b) (c) (d)
Figure 4.17: Mode 1. (a,b) Isosurfaces of theQ−criterion coloured by the pressure
fluctuations. Contours of the fluctuations of (c) the pressure and (d) the axial
velocity. The blue colour shows the negative fluctuations, the red colour shows
the positive fluctuations, while the green colour shows the zero-fluctuation area.
Forced case at 160 Hz.
and Table 4.2).
If now we perform a reconstruction of the snapshots over one period based on
the two first modes, plot the Q−criterion at different time (Fig. 4.22) and then
animate the figures, a clear vortex shedding at 160 Hz becomes evident and the
vortex rings are seen being convected downstream before breaking up and feeding
the downstream part of the combustion chamber with vorticity.
The reconstruction of the axial velocity based on the two first modes is shown
in Fig. 4.23. The figure gives an insight on the pulsation of the jet and the
recirculation zones. A high velocity bubble can be seen travelling along the jet
while the outer recirculation zone and the central recirculation zone can clearly be
seen pulsating with the incoming flow, again with a time delay. This observation
confirms that mode 1 and mode 2 behave partially like a pair of modes accounting
for the cyclic part of the flow fluctuations i.e. the part of the flow that follows the
sinusoidal pulsations at 160 Hz of the inlet velocity. They describe the shedding
and convection of the double vortex rings inside the combustor at the forced 160
Hz frequency.
69
4. Large-eddy simulations of forced bluff body flows
Figure 4.18: Sequence of the Q−criterion of the reconstructed instantaneous flow
coloured by the reconstructed pressure at different consecutive instants and over
one period using mode 1. Forced case at 160 Hz.
70
4. Large-eddy simulations of forced bluff body flows
Figure 4.19: Sequence of the axial velocity of the reconstructed instantaneous
flow at different consecutive instants and over one period using mode 1. Forced
case at 160 Hz.
71
4. Large-eddy simulations of forced bluff body flows
Figure 4.20: Axial velocity fields superimposed over one period. The black lines
represent the instantaneous zero axial velocity isoline. Forced case at 160 Hz.
(a) (b) (c) (d)
Figure 4.21: Mode 2. (a,b) Isosurfaces of theQ−criterion coloured by the pressure
fluctuations. Contours of the fluctuations of (c) the pressure and (d) the axial
velocity. Colours as in Fig. 4.17. Forced case at 160 Hz.
72
4. Large-eddy simulations of forced bluff body flows
Figure 4.22: Sequence of the Q−criterion of the reconstructed instantaneous flow
coloured by the reconstructed pressure at different consecutive instants and over
one period using modes 1 and 2. Forced case at 160 Hz.
73
4. Large-eddy simulations of forced bluff body flows
Figure 4.23: Sequence of the axial velocity of the reconstructed instantaneous
flow at different consecutive instants and over one period using modes 1 and 2.
Forced case at 160 Hz.
74
4. Large-eddy simulations of forced bluff body flows
(a) (b) (c) (d)
Figure 4.24: Mode 3. (a,b) Isosurfaces of theQ−criterion coloured by the pressure
fluctuations. Contours of the fluctuations of (c) the pressure and (d) the axial
velocity. Colours as in Fig. 4.17. Forced case at 160 Hz.
4.4.3 Modes 3 and 4
Mode 3 (Fig. 4.24) and mode 4 (Fig. 4.25) seem identical. Their Q−criterion
isosurfaces show a row of inner and outer vortices upstream while the chamber is
filled with vorticity further downstream. This is similar to modes 1 and 2. The
main difference in modes 3 and 4 is the number of rings present in the chamber.
It has roughly doubled compared to modes 1 and 2. The vortices in mode 4
occupy the space left empty between two annular vortices of mode 3. If we now
look at the spectra associated with modes 3 and 4 (Fig. 4.35), we see a clear peak
at 320 Hz in both modes, which coresponds to the first harmonic of the forced
frequency. Mode 3 also exhibits a smaller peak at 480 Hz (second harmonic)
while mode 4 contains a small peak at the fundamental (160 Hz) and another
component corresponding to the second harmonic (480 Hz) that has roughly half
the amplitude of the first harmonic. Mode 3 and mode 4 contain similar level
of energy, with mode 3 accounting for 1.6 % of the total energy and mode 4 for
1.1 % (see Fig. 4.34 and Table 4.2).
If now we reconstruct the flow based only on modes 3 and 4, a clear vortex
shedding at 320 Hz is evident from both the bluff body and sudden expansion,
the rings being convected downstream before breaking up (see Q−criterion rep-
resentation in Fig. 4.26). The reconstructed axial velocity field (Fig. 4.27) shows
the convection of pockets of high velocity ejected from the air pipe exit at a fre-
75
4. Large-eddy simulations of forced bluff body flows
(a) (b) (c) (d)
Figure 4.25: Mode 4. (a,b) Isosurfaces of theQ−criterion coloured by the pressure
fluctuations. Contours of the fluctuations of (c) the pressure and (d) the axial
velocity. Colours as in Fig. 4.17. Forced case at 160 Hz.
quency of 320 Hz. This observation and the previous ones show that modes 3 and
4 can be seen, at least partially, as a pair of modes accounting for the shedding
and convection of double vortex rings inside the combustion chamber at the first
harmonic (320 Hz) of the forced frequency (160 Hz). In consequence, this set of
modes (modes 3 and 4) can roughly be understood as a harmonic of the first two
modes (modes 1 and 2).
4.4.4 Modes 6 and 7
Mode 5 is different from the other modes previously described and therefore is
commented later in the text. However, modes 6 and 7 seem again to form a pair
of modes (at least partially) that account for a vortex shedding and their con-
vection, similarly to what has been found for modes (1,2) and modes (2,3). The
Q−criterion applied to modes 6 and 7 (respectively in Figs. 4.28 and 4.29) show
again a row of several annular vortices, and their number has roughly doubled
compared to modes 3 and 4. As for modes 3 and 4, mode 6 and mode 7 contain
similar level of energy, with mode 6 accounting for 0.34 % of the total energy
and mode 7 for 0.29 % (see Fig. 4.34 and Table 4.2). However, in this case,
there is nothing like a single clear peak in these modes spectra but rather four
clear peaks at 320 Hz, 480 Hz, 640 Hz and 800 Hz, corresponding to the four first
harmonics of the flow. In both modes 6 and 7, the higher peak is found at 640
76
4. Large-eddy simulations of forced bluff body flows
Figure 4.26: Q−criterion of the reconstructed instantaneous flow over one period
using modes 3 and 4. Forced case at 160 Hz.
77
4. Large-eddy simulations of forced bluff body flows
Figure 4.27: Axial velocity of the reconstructed instantaneous flow over one period
using modes 3 and 4. Forced case at 160 Hz.
78
4. Large-eddy simulations of forced bluff body flows
(a) (b) (c) (d)
Figure 4.28: Mode 6. (a,b) Isosurfaces of theQ−criterion coloured by the pressure
fluctuations. Contours of the fluctuations of (c) the pressure and (d) the axial
velocity. Forced case at 160 Hz.
Hz. The snapshots reconstruction based on modes 6 and 7 only (Fig. 4.30 for
the Q−criterion and Fig. 4.31 for the axial velocity) shows the vortex rings being
shed then convected away at higher frequency than modes 1 and 2 (160 Hz) and
modes 3 and 4 (480 Hz). Consequently, modes (6,7) could be understood as a
spatial harmonic of modes (1,2) but there is not a single frequency that can be
associated with them. Modes (6,7) are rather associated with an ensemble of four
spectral harmonics of the fundamental (320 Hz, 480 Hz and 640 Hz).
4.4.5 Mode 5
Mode 5 is represented in Fig. 4.32. Unlike the previous modes, it doesn’t have a
frequency peak well above the others, but rather two peaks at the fundamental
frequency (160 Hz) and the second harmonic (480 Hz) (see Fig. 4.36). It con-
tains an intermediate level of energy between modes (3,4) and modes (6,7) with
0.6378 % of the total fluctuating energy. It is interesting to note that there is a
strong correlation between the number of vortex rings present in each mode and
their spectra. Roughly, a doubling of the number of vortex rings (equally spaced
in the combustion chamber) corresponds to a doubling of the frequency. In this
context, mode 5 appears to be an odd mode, as it exhibits characteristics from
both the fundamental frequency and higher frequency modes. On one hand, for
locations close to the combustor center, the Q−criterion applied to mode 5 (Fig.
79
4. Large-eddy simulations of forced bluff body flows
(a) (b) (c)
Figure 4.29: Mode 7. (a,b) Isosurfaces of theQ−criterion coloured by the pressure
fluctuations. Contours of the fluctuations of (c) the pressure and (d) the axial
velocity. Forced case at 160 Hz.
4.32) shows large vortex rings separated by a large vacuum as previously observed
in modes 1 and 2. These modes exhibit their strongest frequency peaks at 160
Hz. Therefore these rings are thought to be associated with the frequency peak
at 160 Hz observed in the spectra of mode 5 (Fig. 4.36). On the other hand, close
to the chamber entrance, a row of close thin vortex rings is observed, as observed
for higher harmonic modes (see modes 3, 4, 6 and 7). The vortex rings close to
the inlet pipe are hence thought to be associated with the frequency peak at 480
Hz observed in mode 5 spectra (Fig. 4.32).
4.4.6 Mode 8
Other modes do not exhibit any vortex rings and they are more complicated to
analyse. There are not reported here, with the exception of mode 8. Mode 8
is interesting through the analysis of its spectra that shows non harmonic fre-
quencies. There are three visible peaks at 44 Hz, 88 Hz and 118 Hz. Therefore
this mode could account for the sub-harmonic previously reported in the axial
velocity spectra of the 160 Hz case (see Fig. 4.14). Different representations of
mode 8 are plotted in Fig. 4.33. It can be noted that mode 8 contains very little
energy, representing only 0.17 % of the total energy (see Fig 4.34 and Table 4.2).
80
4. Large-eddy simulations of forced bluff body flows
Figure 4.30: Q−criterion of the reconstructed instantaneous flow over one period
using modes 6 and 7. Forced case at 160 Hz.
81
4. Large-eddy simulations of forced bluff body flows
Figure 4.31: Axial velocity of the reconstructed instantaneous flow over one period
using modes 6 and 7. Forced case at 160 Hz.
82
4. Large-eddy simulations of forced bluff body flows
(a) (b) (c) (d)
Figure 4.32: Mode 5. (a,b) Isosurfaces of theQ−criterion coloured by the pressure
fluctuations. Contours of the fluctuations of (c) the pressure and (d) the axial
velocity. Forced case at 160 Hz.
(a) (b) (c)
(d) (e)
Figure 4.33: Mode 8. (a,b) Isosurfaces of theQ−criterion coloured by the pressure
fluctuations. Contours of the fluctuations of (c) the axial velocity and (d,e) the
pressure, with Fig. (e) showing a transverse plane. Forced case at 160 Hz.
83
4. Large-eddy simulations of forced bluff body flows
1 2 3 4 5 6 7 8 9 100
20
40
60
80
Modes
%
 E
ne
rg
y 
ca
pt
ur
ed
(a)
1 2 3 4 5 6 7 8 9 100
20
40
60
80
100
Modes
%
 E
ne
rg
y 
ca
pt
ur
ed
(b)
Figure 4.34: Energy distribution of the POD modes. (a) Energy relative per
mode. (b) Cummulative energy. Forced case at 160 Hz.
4.4.7 Conclusions from the POD analysis of the 160 Hz
case
POD analysis of the forced flow at 160 Hz develops further insight on the hy-
drodynamic structures associated with pulsating flows. It seems to indicate that
the harmonics of the forced frequency revealed in the velocity spectra could be
attributed to some weaker vortex sheddings of thinner vortical rings occuring at
harmonic frequencies of the pulsating frequency. These weak vortex sheddings
are superimposed to the large vortex shedding at the forced frequency (160 Hz).
Because of their relative weakness (modes 3 and 4 account together for 2.7 % of
the total fluctuating energy as opposed to the 91.2 % of modes 1 and 2), these
harmonic vortex sheddings have not been detectable by directly applying the
Q−criterion to the LES dataset, even though several threshold values have been
tried. In that sense, POD can be considered as an attractive method to analyse
and reveal the physics underlying our LES datasets. But this analysis reveals
also the limitations of the POD analysis for pulsating flows. In fact, POD, while
enforcing the spatial orthogonality of the modes, describes the temporal evolution
of the modes based on multiple frequencies. Therefore, the method is not able
to separate the different harmonics of the flow into different modes, which would
have led to an easier understanding of these kind of flows.
84
4. Large-eddy simulations of forced bluff body flows
0 500 1000 1500 20000
5
10
15
x 107
f (Hz)
PS
D
(a) Mode 1
0 500 1000 1500 20000
1
2
3
4
5
6x 10
6
f (Hz)
PS
D
(b) Mode 2
0 500 1000 1500 20000
0.5
1
1.5
2
2.5
x 106
f (Hz)
PS
D
(c) Mode 3
0 500 1000 1500 20000
2
4
6
8
10
12
x 105
f (Hz)
PS
D
(d) Mode 4
Figure 4.35: Fourier analysis of the temporal coefficents of POD modes 1 to 4.
Forced case at 160 Hz.
85
4. Large-eddy simulations of forced bluff body flows
0 500 1000 1500 20000
2
4
6
8
10
x 104
f (Hz)
PS
D
(a) Mode 5
0 500 1000 1500 20000
0.5
1
1.5
2
x 105
f (Hz)
PS
D
(b) Mode 6
0 500 1000 1500 20000
0.5
1
1.5
2x 10
5
f (Hz)
PS
D
(c) Mode 7
0 500 1000 1500 20000
2
4
6
8
10
x 104
f (Hz)
PS
D
(d) Mode 8
Figure 4.36: Fourier analysis of the temporal coefficents of POD modes 5 to 8.
Forced case at 160 Hz.
86
4. Large-eddy simulations of forced bluff body flows
4.5 Summary of main findings
The isothermal air flow behind an axisymmetric conical disk, enclosed in a cir-
cular pipe of larger diameter that undergoes a sudden expansion, and with the
incoming flow being forced at a single frequency and with large amplitude, has
been explored with Large-Eddy Simulations. This flow may be thought of as a
model problem for combustors undergoing self-excited oscillations and the results
can help validate LES for complex turbulent flows involving recirculation zones
and periodicity. At low forcing frequencies, the recirculation zone pulsated with
the incoming flow, at a phase lag that depended on spatial location. No clear vor-
tex shedding was observed. At high forcing frequencies, vortices were shed from
the bluff body and the recirculation zone, as a whole, pulsated less. The veloc-
ity spectra showed peaks at various harmonics, whose relative magnitudes varied
with location. These harmonics may be due to extra vortex sheddings occuring
at harmonic frequencies of the forced frequency, as revealed by the POD analy-
sis. A sub-harmonic peak was also observed inside the recirculation zone possibly
due to merging of the shed vortices. The phase-averaged turbulent fluctuations
showed large temporal and spatial variations and were higher than the turbulent
fluctuations of the unforced flow at the same position. The Large-eddy simula-
tions reproduced accurately the experimental findings in terms of phase-averaged
mean and r.m.s. velocities, vortex formation, and spectral peaks.
87
Chapter 5
Conditional Moment
Closure/Large Eddy Simulation
of the Delft-III natural gas
non-premixed jet flame
5.1 Introduction
5.1.1 Motivation
In this chapter, Large Eddy Simulation (LES), coupled with the Conditional Mo-
ment Closure (CMC) sub-grid model and the GRI3 detailed chemical mechanism,
are used to explore the structure of the Delft III piloted turbulent non-premixed
flame. The relatively simple configuration compared to bluff body or swirl flames
allows to analyze key combustion aspects of combustors described in Section 2.1.
In fact, a very detailed dataset [27; 70; 81; 86; 110; 111] is available for the
“Delft III”, which shows significant finite-rate chemistry effects, including local
extinctions and re-ignitions. In addition, the pollutants emitted (CO and NO)
have been measured, and hence this flame offers a very challenging test case for
capturing practically-important combustion phenomena. The Delft Flame III is
also a target in the TNF workshop series (http : //www.sandia.gov/TNF ).
88
5. CMC/LES of the Delft-III natural gas non-premixed jet flame
The use of a quite refined multi-dimensional CMC grid and the detailed chem-
istry, together with the capability of LES to follow local fluctuations of the scalar
dissipation, is expected to capture localised extinctions and re-ignitions, as well
as pollutants emissions. LES also offers advantages due to its ability to capture
turbulent mixing better than Reynolds-Averaged Navier-Stokes (RANS) models,
but often the combustion process occurs at the sub-grid scale and therefore mod-
els are necessary. As a consequence, extensive validation of LES for flames is
necessary to increase the reliability of the available models.
5.1.2 Background works
Several attempts have been conducted to model this flame using RANS formu-
lations and various combustion models, including the transported PDF method
with reduced and detailed chemistry [75; 76; 82; 86]. Nooren et al. [82] and Merci
et al. [76] have shown that transported PDF results are strongly dependent on
the micro-mixing model used, especially in the case of the temperature PDFs,
while Merci et al. [76] reported that it was not possible to predict accurately both
the RMS of the mixture fraction and the amount of local extinction. The CO
mass fraction prediction was considered unsatisfactory whatever mixing model is
used. Nooren et al. [82], Merci et al. [76] and Roekaerts et al. [94], in their
different studies, have also emphasized the importance of an accurate modelling
of the pilot flames.
5.1.3 Objectives
Here, the Conditional Moment Closure (CMC) is used as the combustion sub-
model in LES. The LES is expected to capture better than RANS the mixing in
the flame, and to also track (some of) the scalar dissipation fluctuations that are
thought to be responsible for extinction. CMC is used in its multi-dimensional
form (i.e. no cross-stream averaging is used), which allows the possibility to
capture the local response of the combustion to the imposed scalar dissipation
transients, but also to allow the effects of the pilot to be included. CMC has
previously been used in a LES context to simulate among others the Sandia
flame D [80] with a relatively coarse grid, and with quite refined grids it has been
89
5. CMC/LES of the Delft-III natural gas non-premixed jet flame
used for spark ignition problems [118] and the Sandia flame F [38].
The objectives of the present chapter are: (i) to demonstrate the validity of the
LES-CMC approach, with full detailed chemistry, for a well-characterised non-
premixed flame showing significant finite-rate effects; (ii) to provide some further
insights on the transient events occuring during local extinctions and re-ignitions.
5.2 Method
5.2.1 Model and codes
A first order LES-CMC formulation has been used for this simulation (see Chapter
3). The absence of experimental data for the scalar dissipation rate in the Delft
flame does not allow to adjust properly the constant CN of Eq. 3.21. Here we
use the value CN = 42 previously adjusted to match the experimental results of
〈N |η〉 for Sandia flame D [38]. No other parameter has been tuned.
The detailed chemistry mechanism GRI-Mech 3.0 has been used for these
simulations. This mechanism contains 53 species and 325 reactions [106]. The
refined CMC grid and the use of detailed chemistry makes this a very expensive
calculation.
5.2.2 Flow considered, boundary conditions and numeri-
cal methods
Figure 5.1 shows the flow studied. The Delft III flame is composed of a central
fuel jet, with a velocity at the burner exit of 21.9 m/s (Re = 9700), surrounded by
two concentric coflows of air. The primary air flow velocity is 4.4 m/s (Re = 8800)
and the secondary air flow velocity is 0.3 m/s at the burner exit. The jet has a
diameter of Dj = 6 mm. The inner diameter of the primary air annulus is 15 mm
and its outer diameter is 45 mm. The outer diameter of the secondary air flow
is set to 400 mm for the simulation. In the experiment, the secondary air flow
was produced by positioning the burner in a wind tunnel, its exact configuration
depending on the place where the experiments were conducted (Netherlands or
California). The fuel jet is separated from the primary air stream by a rim of
90
5. CMC/LES of the Delft-III natural gas non-premixed jet flame
Figure 5.1: Delft piloted jet burner. From Ref. [81].
outer diameter 15 mm. The pilot flames are located on this rim. They consist of
12 holes of 0.5 mm diameter located on a circle of 7 mm diameter. These pilot
flames are modelled as an axisymmetric annular ring of 0.5 mm thickness around
the fuel jet. In the experiment, the pilot fuel is different from the jet fuel, but in
order to be in a position to work with a single mixture fraction, the pilot flames
were modelled as a fully-burnt stoichiometric mixture of the jet fuel and air, with
the same mass flow rate as in the experiment. The fuel was natural gas. The
GRI 3.0 chemistry mechanism does not cover all the species in the experiment.
For example, Butane (C4H10), Pentane (C5H12) and Hexane (C6H14) are not
present in this chemistry mechanism. As a result, the missing species have been
re-distributed into other species in order to conserve the total calorific value of
the fuel calculated by means of the individual calorific values. We end up with an
approximation of its composition based on the species available in the GRI-Mech
3.0 mechanism, as reported in Table 5.2. The natural gas used by the CMC code
and the natural gas in the experiment both give a stoichiometric mixture fraction
of ξst = 0.07147. Table 5.1 summarizes the inlet conditions used for the Delft
flame III modelling.
Before starting any multi-dimensional computations, a series of the so-called
91
5. CMC/LES of the Delft-III natural gas non-premixed jet flame
Table 5.1: Numerical setup used by the LES code to model the Delft flame III.
These values are the experimental ones except the ones flagged with the symbol
(*), which have been obtained through the modelling process.
Stream Vel. (m/s) Diam. (mm) Re ξ T (K)
Fuel 21.9 0− 6 9700 1 295
Pilot 13.98(∗) 6(∗)− 7(∗) ξst(∗) 1997.5(∗)
Rim 7(∗)− 15
Primary air flow 4.4 15− 45 8800 0 295
Secondary air flow 0.3 45− 400(∗) 0 295
Table 5.2: Fuel composition used by the CMC code to model the Delft flame
natural gas
Constituents Formula Mass fraction %
CH4 70.013
C2H2 0.0695
C2H4 0.289
C2H6 4.873
C3H8 1.1155
N2 21.54
CO2 2.10
92
5. CMC/LES of the Delft-III natural gas non-premixed jet flame
0 50 100 150 2001700
1800
1900
2000
2100
2200
No (s−1)
T 
(K
)
 
 
T
max
0
0.01
0.02
0.03
0.04
0.05
0.06
Y
102*(YNO)max
(YCO)max
(a)
0 0.25 0.5 0.75 1
500
1000
1500
2000
ξ
T 
(K
)
 
 
T
0
0.01
0.02
0.03
0.04
0.05
0.06
Y
102*YNO
YCO
10*YOH
(b)
Figure 5.2: (a) Maximum values of some reactive scalars of the steady flame
against the scalar dissipation rate N0, using the detailed chemistry GRI-Mech
3.0 (53 species, 325 reactions). The extinction strain rate is found to be equal
to 193 1/s. (b) Conditional profiles of some reactive scalars from the 0D-CMC
computation with N0 = 20 1/s. This solution is used as the prescribed distribu-
tion in the LES/0D-CMC computation and is injected at the pilot location in the
LES/3D-CMC.
“0D-CMC” calculations of the Delft flame III were performed with the above
fuel composition and the detailed GRI-Mech 3.0 chemistry mechanism. 0D-CMC
refers to solving Eq. 3.23 i.e. Eq. 3.14 without spatial transport terms and
for different values of prescribed N˜ |η parametrised by the peak value, N0. As a
result, a set of solutions were obtained that can be understood as steady flamelet
calculations with unity Lewis number. Figure 5.2(a) shows the maximum values
of different reactive scalars (the temperature, YNO & YCO) for different values of
N0. The curve of temperature gives access to two global properties of the flame,
i.e. (i) its operating temperature range, with the flame existing from Tl = 1794 K
up to Tu = 2099 K and (ii) the extinction scalar dissipation rate, which is found
to be:
N0ext = 193 1/s. (5.1)
The latter is a fundamental parameter in the study of localized extinction
that is developed in Section 5.3.3. The figure also reveals the well-known strong
dependency between the temperature and NO production as the two curves have
overall similar trends, while YCO is found to be relatively independent of the
93
5. CMC/LES of the Delft-III natural gas non-premixed jet flame
Figure 5.3: Longitudinal cutting plane (z=0) of the LES grid (1.3M cells).
scalar dissipation rate in the domain of existence of the flame.
The LES grid used for the multi-dimensional computation has a cubic shape
and extends 66Dj in the axial and 33Dj in the radial direction, which is larger
than the range in which experimental data is available (41Dj×6Dj). This is done
in order to allow the flow to develop. The grid created for the simulation is an O-
grid mesh (Fig. 5.3) using a minimum spacing of 0.18 mm across the pilot with a
smooth expansion downstream and radially so that a total of approximately 1.3M
cells (75×60×268) are used. The CMC equations are solved on a structured grid
of 16 × 16 × 32 = 8192 cells, with 32 cells being used in the axial direction and
some refinement being made around the mixing layer of the jet and the primary
coflow. Fig. 5.4(a) shows a part of the LES grid (black line) with its associated
CMC grid superimposed (red line). Each CMC cell has its center located at an
intersection of the red lines.
The LES boundary conditions at the burner exit are the experimentally-
obtained velocities at the jet and the coflows, which are injected with a top-hat
profile and without any added fluctuations. The mixture fraction is set to 1.0 in
the jet, 0.0 in the co-flow and to the value of 0.071, close to the stoichiometric
94
5. CMC/LES of the Delft-III natural gas non-premixed jet flame
(a) (b)
Figure 5.4: (a) Enlargement of the LES grid (black) and CMC grid (red) in the
transverse direction. A CMC cell contains several LES cells, the ratio depending
on the location inside the domain. Each CMC cell has its center located at an
intersection of the red lines. (b) Sketch of the CMC boundary conditions: inert
everywhere except for the pilot where a fully burning flamelet is imposed.
mixture fraction value, in the pilot. The fuel jet and air coflows temperatures are
all set to the experimental value of 295 K. For the pilot, the “0D-CMC” solution
(see above) obtained for N0 = 20 1/s was used. The distribution of some re-
acting scalars in mixture fraction space from this 0D-CMC solution is plotted in
Fig. 5.2(b) and will be commented below. Using this solution, the stoichiometric
temperature and density of the modelled pilot is determined and the modelled
pilot stream velocity is obtained by dividing the experimental pilot mass flow rate
by this stoichiometric 0D-CMC density and the annular area of the pilot. The
inlet conditions at the modelled annular pilot for the simulations are as follows:
velocity 13.98 m/s; mass flow rate 2.3×10−5 kg/s; temperature 1997.5 K; density
0.1611 kg/m3 (Table 5.1).
The boundary conditions for CMC are described in Fig. 5.4(b) and are the
following: inert (i.e. unburnt) distributions of Qα are injected in the jet and the
coflows, while the burning “flamelet” obtained with the prescribed N0 = 20 1/s
is injected in the pilot. Therefore we expect that the physical transport terms
95
5. CMC/LES of the Delft-III natural gas non-premixed jet flame
in Eq. 3.14 will be responsible for “igniting” the rest of the flow (i.e. the Qα’s
becoming those corresponding to burning distributions in mixture fraction space),
which is equivalent to how the flame is ignited in the experiment. Zero gradients
in physical space of all conditional averages are imposed at the sides and the
downstream edge of the domain.
A RANS computation with the 0D-CMC solution was performed first, followed
by a LES simulation using this prescribed “flamelet” everywhere in the flow. We
refer to these different simulations as RANS/0D-CMC and LES/0D-CMC. The
value of N0 = 20 1/s used for these simulations is about 10% of the extinction
value of 193 1/s. Figure 5.2(b) shows the conditional profiles of temperature
and mass fractions of NO, CO and OH for this “flamelet”. The profile shape of
the conditonal YOH profile is noticeable and demonstrates that the reaction zone
occupies only a small range in the mixture fraction space.
The full LES with the CMC equations (Eq. 3.14) is denoted as LES/3D-CMC
and constitutes the main result of the present chapter. Each figure presented in
the next section is for LES/3D-CMC computation unless specified otherwise. The
time-step used was 1.0 × 10−5 s, which ensures that a maximum CFL number
is around 0.65 during a whole stable simulation. This time-step is also expected
to be small enough to capture at least some of the interesting transient events
observed experimentally in the flame such as local extinctions and re-ignitions.
The simulations were carried out on 52 dual-core processors at 3.0 GHz with 2
GB of RAM per core, producing 1.0 ms of simulated time in approximately 147
min. The CMC code took most of the CPU time.
5.3 Results and Discussion
5.3.1 Instantaneous distributions
An instantaneous distribution of the axial velocity is shown in Fig. 5.5(a). The
different streams (jet, pilot, co-flows) are evident. Between the fuel jet and the
primary co-flow, the rim creates a small recirculation zone, which provides another
mechanism to stabilise the flame, in addition to the pilot flame. In Fig. 5.5(b),
the vorticity snapshot reveals that two shear layers develop: an inner one between
96
5. CMC/LES of the Delft-III natural gas non-premixed jet flame
the fuel jet and primary air and an outer one between the primary and secondary
air flows. Close to the burner, Kelvin-Helmholtz instabilities arise along these
shear layers, visualized by the fragmented vorticity contours. Fig. 5.5(c) uses the
Q-criterion method [48] to visualise vortical structures:
Q = (ω2 − 2S˜ijS˜ij)/4 (5.2)
with ω the vorticity magnitude and S˜ij the strain rate, both calculated from
the gradients of the resolved velocity. The Q iso-surfaces have been colored
according to the resolved temperature. In the center, the turbulent fuel jet is
clearly visible. Vortices are formed by the Kelvin-Helmoltz instabilities at the
outer shear layer as described above. These structures are then convected before
eventually breaking-up around 150 mm downstream, increasing the turbulence
intensity there. These instabilities are pronounced along the inner shear layer
due to the large difference of velocities between the fuel jet and the primary co-
flow and are therefore expected to be the main source of turbulence in the fuel
jet.
A snapshot of the mixing field is shown in Fig. 5.6(a). The non-premixed fuel
jet is evident again, flowing out from the burner with a mixture fraction equal to
1 before mixing with the surrounding co-flows. The pilot flame can be located on
this snaphsot by the position of the stoichiometric iso-line (the black line) on the
inlet plane, as the modelled pilot is fed with a stoichiometric mixture of the Delft
flame fuel. The other snaphots in Figs. 5.6 and 5.7 include the instantaneous
contours of the temperature, YNO, YCO and YCO2 at the same instant, and allow
an overall visualization of the flame. In addition, the instantaneous contour of
YOH is represented in Fig. 5.6(c) and will be commented in Section 5.3.3.
5.3.2 Velocity and mixture fraction fields
The calculated mean and RMS of the axial velocity (Fig. 5.8 & 5.9 respectively)
and the mixture fraction (Fig. 5.10 & 5.11 respectively) show a good agreement
with the experimental data. A close observation of the three simulations reveals
that two LES results (LES/0D-CMC and LES/3D-CMC) show some discrepan-
cies, which implies that the local variations of Qα’s, as offered by the 3D-CMC
97
5. CMC/LES of the Delft-III natural gas non-premixed jet flame
(a)
(b) (c)
Figure 5.5: Typical instantaneous contours of (a) axial velocity (in m/s) and (b)
z−vorticity (in 1/s) at the same instant. The stoichiometric iso-surface is shown
with the black line. Axes in m. (c): Instantaneous iso-surface of Q = 50×103s−2
colored with the temperature (in K).
98
5. CMC/LES of the Delft-III natural gas non-premixed jet flame
(a) Mixture fraction
(b) Temperature (K) (c) YOH
Figure 5.6: Typical instantaneous contours of the mixture fraction, temperature
and mass fractions of OH at the same instant. The stoichiometric iso-surface is
shown with the black line.
99
5. CMC/LES of the Delft-III natural gas non-premixed jet flame
(a) YNO
(b) YCO (c) YCO2
Figure 5.7: Typical instantaneous contours of the mass fractions of the indicated
species at the same instant. The stoichiometric iso-surface is shown with the
black line.
100
5. CMC/LES of the Delft-III natural gas non-premixed jet flame
solution, result in a big enough change to the conditional density over the “steady
flamelet” solution to affect the velocity and mixture fraction fields. The mixing
field (Fig. 5.10) predicted by the LES/3D-CMC is closer to the experimental
data than the other simulations, but this is obtained to the detriment of the axial
velocity field. A good example of this behaviour is found at x = 16.7Dj around
the centreline where the 3D-CMC formulation results in the largest changes com-
pared to the 0D formulations in both the velocity and mixing fields (Figs. 5.8 &
5.10). The recirculation zone previously observed in Fig. 5.5(a) is also evident
in Fig. 5.8 at x/Dj = 0.5 (x = 3 mm) and for r/Dj ≈ 1. The absence of inlet
velocity fluctuations in the LES results in an underprediction of the turbulence
intensity in the early part of the jet, as shown in Fig. 5.9 by the RMS of the axial
velocity at x = 0.5Dj. However, further downstream well-developed turbulence is
found everywhere across the jet, showing that the shear layers instabilities have
fed the flow with turbulence: from about 8 jet diameters and up to 33 jet diame-
ters (48 mm<x< 200 mm), the velocity fluctuations are in good agreement with
the data (Fig. 5.9). For x/Dj > 33 the RMS of the mixture fraction and, to a
lesser extent, the velocity fluctuations are overpredicted: at this location in the
domain and further downstream, the LES mesh becomes coarser due to the mesh
expansion, as visualized in Fig. 5.3.
5.3.3 Reaction zone and localised extinctions
In Fig. 5.12, the instantaneous flame front is visualised by the contour of OH
mass fraction. The reaction zone is thinner in this flame compared to other
piloted flames like the Sandia flame F [38]. This is attributed to the absence of
premixing in the fuel jet in Delft III compared to the Sandia F that leads to a
low stoichiometric mixture fraction (ξst ≈ 0.0715) and to a narrower range of
reaction in mixture fraction space, as shown by the conditional profile of OH
mass fraction in Fig. 5.2(b). The reaction zone in Figs. 5.12 & 5.6(c) and the ξst
isoline in Fig. 5.5(a) show that the OH zone is not strongly convoluted close to
the burner. This is attributed to the low ξst that places the reaction zone in the
fuel-lean side of the inner shear layer where the shear stresses are relatively low.
Further downstream (x/Dj = 20), the turbulence has developed in the fuel jet
101
5. CMC/LES of the Delft-III natural gas non-premixed jet flame
0 1 2 3
0
0.5
1
x = 0.5 Dj
r / Dj
<
U>
 / 
U j
 
 
EXP
RANS/OD−CMC
LES/OD
LES/3D−CMC
0 1 2 3
0
0.5
1
x = 8.33 Dj
r / Dj
<
U>
 / 
U j
 
 
EXP
RANS/OD−CMC
LES/OD
LES/3D−CMC
0 1 2 3
0
0.5
1
x = 16.7 Dj
r / Dj
<
U>
 / 
U j
 
 
EXP
RANS/OD−CMC
LES/OD
LES/3D−CMC
0 1 2 3
0
0.5
1
x = 25 Dj
r / Dj
<
U>
 / 
U j
 
 
EXP
RANS/OD−CMC
LES/OD
LES/3D−CMC
0 1 2 3
0
0.5
1
x = 33.3 Dj
r / Dj
<
U>
 / 
U j
 
 
EXP
RANS/OD−CMC
LES/OD
LES/3D−CMC
0 1 2 3
0
0.5
1
x = 41.7 Dj
r / Dj
<
U>
 / 
U j
 
 
EXP
RANS/OD−CMC
LES/OD
LES/3D−CMC
Figure 5.8: Radial profiles of the mean axial velocity at the indicated axial posi-
tion. Experimental data from Ref. [27].
102
5. CMC/LES of the Delft-III natural gas non-premixed jet flame
0 1 2 30
0.125
0.25
x = 0.5 Dj
r / Dj
U R
M
S 
/ U
j
 
 
EXP
LES/OD
LES/3D−CMC
0 1 2 30
0.125
0.25
x = 8.33 Dj
r / Dj
U R
M
S 
/ U
j
 
 
EXP
LES/OD
LES/3D−CMC
0 1 2 30
0.125
0.25
x = 16.7 Dj
r / Dj
U R
M
S 
/ U
j
 
 
EXP
LES/OD
LES/3D−CMC
0 1 2 30
0.125
0.25
x = 25 Dj
r / Dj
U R
M
S 
/ U
j
 
 
EXP
LES/OD
LES/3D−CMC
0 1 2 30
0.125
0.25
x = 33.3 Dj
r / Dj
U R
M
S 
/ U
j
 
 
EXP
LES/OD
LES/3D−CMC
0 1 2 30
0.125
0.25
x = 41.7 Dj
r / Dj
U R
M
S 
/ U
j
 
 
EXP
LES/OD
LES/3D−CMC
Figure 5.9: Radial profiles of the RMS of the axial velocity at the indicated axial
position. Experimental data from Ref. [27].
103
5. CMC/LES of the Delft-III natural gas non-premixed jet flame
0 1 2 3
0
0.5
1
x = 4.17 Dj
r / Dj
<
ξ>
 
 
EXP
RANS/OD−CMC
LES/OD
LES/3D−CMC
0 1 2 3
0
0.5
1
x = 8.33 Dj
r / Dj
<
ξ>
 
 
EXP
RANS/OD−CMC
LES/OD
LES/3D−CMC
0 1 2 3
0
0.5
1
x = 16.7 Dj
r / Dj
<
ξ>
 
 
EXP
RANS/OD−CMC
LES/OD
LES/3D−CMC
0 1 2 3
0
0.5
1
x = 25 Dj
r / Dj
<
ξ>
 
 
EXP
RANS/OD−CMC
LES/OD
LES/3D−CMC
0 1 2 3
0
0.5
1
x = 33.3 Dj
r / Dj
<
ξ>
 
 
EXP
RANS/OD−CMC
LES/OD
LES/3D−CMC
0 1 2 3
0
0.5
1
x = 41.7 Dj
r / Dj
<
ξ>
 
 
EXP
RANS/OD−CMC
LES/OD
LES/3D−CMC
Figure 5.10: Radial profiles of the mean of the mixture fraction at the indicated
axial position. Experimental data from Ref. [27].
104
5. CMC/LES of the Delft-III natural gas non-premixed jet flame
0 1 2 30
0.125
0.25
x = 4.17 Dj
r / Dj
ξ R
M
S
 
 
EXP
LES/OD
LES/3D−CMC
0 1 2 30
0.125
0.25
x = 8.33 Dj
r / Dj
ξ R
M
S
 
 
EXP
LES/OD
LES/3D−CMC
0 1 2 30
0.125
0.25
x = 16.7 Dj
r / Dj
ξ R
M
S
 
 
EXP
LES/OD
LES/3D−CMC
0 1 2 30
0.125
0.25
x = 25 Dj
r / Dj
ξ R
M
S
 
 
EXP
LES/OD
LES/3D−CMC
0 1 2 30
0.125
0.25
x = 33.3 Dj
r / Dj
ξ R
M
S
 
 
EXP
LES/OD
LES/3D−CMC
0 1 2 30
0.125
0.25
x = 41.7 Dj
r / Dj
ξ R
M
S
 
 
EXP
LES/OD
LES/3D−CMC
Figure 5.11: Radial profiles of the RMS of the mixture fraction at the indicated
axial position. Experimental data from Ref. [27].
105
5. CMC/LES of the Delft-III natural gas non-premixed jet flame
Figure 5.12: Typical instantaneous OH mass fraction contour, with the CMC
grid superimposed. Regions 1 and 2 are discussed in the text.
and the OH zone is distorted significantly. The ξst iso-surface has also expanded
to the radial location of the Kelvin-Helmoltz vortices visualized in Fig. 5.5(c) at
around 150 mm downstream, which results in a strong convolution of the OH zone
further than about x/Dj = 25. All these observations are qualitatively consistent
with the experiments as shown by the experimental OH contour visualization in
Fig. 5.13.
In Fig. 5.14, three snapshots separated by 1 ms are shown at around x/Dj =
39 (marked ‘2’ in Fig. 5.12) while in Fig. 5.15 the three snaphots are located at
around x/Dj = 3 (marked ‘1’ in Fig. 5.12) and are separated by 0.5 ms. Both
these sequences show strong variations of the reaction zone, visualized using OH
mass contour. As a result, these two behaviours can appear quite similar at first
glance while the mechanisms behind them and their physical interpretations are
completely different. The drop in the OH mass fraction that appears in the
snapshots marked ‘2’ (Fig. 5.14) is observable from both the LES/0D-CMC and
the LES/3D-CMC computations. In this case, obviously Y˜OH |η does not reach
zero (since a burning distribution is prescribed), even if a sudden fall in OH mass
106
5. CMC/LES of the Delft-III natural gas non-premixed jet flame
Figure 5.13: Typical instantaneous OH images, covering the regions x = 15 to
93 mm, 100 to 178 mm and 185 to 263 mm. Each image from the different regions
has been taken at different time.The OH images (left) are from Ref. [27]. This
figure has been kindly provided by Prof. D. Roekaerts.
107
5. CMC/LES of the Delft-III natural gas non-premixed jet flame
fraction is observed. The mechanism behind this is not linked to an extinction
phenomenon. It is due to the integration over η-space of the conditional OH
mass fraction weighted by the β-PDF, following Eq. 3.30. In this case, the
decrease of OH mass fraction can be understood by analysing the results in Fig.
5.16. As detailed in Section 3.2.4 of Chapter 3, the Filtered probability Density
Function (FDF) is approximated using a β function. Some β-PDF are plotted
at two locations inside each domain of Fig. 5.12, the left part of the figure
corresponding to the domain marked ‘1’ in Fig. 5.12, the right to the domain
marked ‘2’. The different curves for each location correspond respectively to
the same instants as the snapshots in Figs. 5.14 and 5.15. These graphs reveal
that the β-PDF function varies against time and position, according to the value
of the local mixture fraction ξ and its sub-grid variance ξ˜′′2 (see Section 3.2.4).
Keeping in mind that the conditional OH mass fraction profile Y˜OH |η has a shape
close to a δ-function centred on the stoichiometric mixture fraction (Fig. 5.2(b)),
the mechanism behind the OH mass fraction contour variations observed in Fig.
5.14 (domain marked ‘2’) becomes straighforward: when the β-PDF around the
stoichiometric value (shown by a vertical red line) becomes close to zero, the
value of Y˜OH computed through Eq. 3.30 tends to drop drastically, leading to the
observable shrinking of the OH contour at this place of the flame.
On the other hand, the series of snapshots marked ‘1’ (Fig. 5.15) shows the
evolution of a real “flame hole” or localized extinctions close to the burner. In this
case, Y˜OH |η drops to zero inside the hole. This type of behaviour is observable only
with the LES/3D-CMC computation as it takes into account the temporal and
spatial evolution of finite-rate effects. The prediction of these localised extinctions
close to the burner are qualitatively consistent with the experimental observations
from Fig. 5.13.
The analysis of the conditional data from the CMC solver is the only way
to check that there are localized extinction and so to make a clear distinction
between the two kinds of behaviour described above. Figure 5.17 shows the
conditional profiles of the temperature and the OH mass fraction at three axial
positions. At each of these axial position, the conditional profile predicted by the
CMC code has been plotted for all CMC cells at the indicated x and for every
timestep over a period of 78 ms. In order to find a representative conditional
108
5. CMC/LES of the Delft-III natural gas non-premixed jet flame
Figure 5.14: Sequential images of OH with 1 ms spacing in region 2 shown in
Fig. 5.12.
Figure 5.15: Re-ignition sequence with 0.5 ms spacing in region 1 as shown in
Fig. 5.12.
109
5. CMC/LES of the Delft-III natural gas non-premixed jet flame
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
PD
F
ξ
x = 3.9 Dj
 
 
ξ
stoi
t=402 ms after initialization
t=402.5 ms
t=403 ms
(a)
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
PD
F
ξ
x = 41.6 Dj
 
 
ξ
stoi
t=409 ms after initialization
t=410 ms
t=411 ms
(b)
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
PD
F
ξ
x = 3.29 Dj
 
 
ξ
stoi
t=402 ms after initialization
t=402.5 ms
t=403 ms
(c)
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
PD
F
ξ
x = 38.2 Dj
 
 
ξ
stoi
t=409 ms after initialization
t=410 ms
t=411 ms
(d)
Figure 5.16: Integrated FDFs assuming a β function shape for 4 different CMC
cells centred at x = 19.7 mm and x = 23.4 mm (c & a corresponding to Fig.
5.12, domain marked ‘1’) and at x = 229.1 mm and x = 249.9 mm (d & b
corresponding to domain marked ‘2’), at the same instants as the snapshots in
Fig. 5.15 (c & a) and Fig. 5.14 (d & b).
110
5. CMC/LES of the Delft-III natural gas non-premixed jet flame
average for a particular axial location h, the different CMC solutions over time at
that axial position were also PDF-weighted averaged using the following process:
φ˜|η∗(h) =
∫ t2
t1
∫
x=h
φ˜|η P˜ (η) ρ¯ dV dt∫ t2
t1
∫
x=h
P˜ (η) ρ¯ dV dt
(5.3)
where the integration is over all the CMC nodes corresponding to that axial
position and over time, with t1 < t < t2. The graphs allow to visualize that
the LES/3D-CMC formulation predicts a strong fluctuation of the conditional
profiles against the position, both axial and radial, as well as against time. The
former contradicts a previously used hypothesis according to which conditional
moments are independent of the radial position in shear layers [59] and that the
pilot will not affect the radial dependence of conditional moments significantly
[80]. Figure 5.17 reveals that the LES/3D-CMC formulation predicts a succession
of extinction and re-ignition events close to the burner around 3 − 5Dj and the
occasional extinctions and re-ignitions further downstream up to 10Dj.
Figure 5.18(a) gives a 3D visualization of these extinctions by plotting the
stoichiometric mixture fraction iso-surface coloured according to the OH mass
fraction. Areas with YOH reaching zero are surrounded by a black line. It is
evident that: (i) the OH at stoichiometry drops to zero in some locations; (ii)
the OH at stoichiometry is not constant, but fluctuates in space and time. Some
of these variations are due to the integration process over the η-space (Eq. 3.30)
through the fluctuations of the β-PDF as described above (in this case due only
to the mixture fraction variance fluctuations as ξ remains equal to ξst). Most of
the variations of OH mass fraction observed in Fig. 5.18(a) are only captured by
the LES/3D-CMC code through the temporally and spatially-varying Y˜α|ξ that
respond to spatial and temporal variations of N˜ |η.
To clarify this point further, Fig. 5.19 shows time-series of the peak condi-
tional scalar dissipation rate (i.e. at η = 0.5; the value at η = ξst is a constant
proportion of N0 due to the use of the AMC model, see Fig. 5.20), T˜ |ξst ,
Y˜OH |ξst , Y˜NO|ξst and Y˜CO|ξst , at various locations downstream and at radial
locations corresponding to the middle of the annular pilot (r = 0.58Dj, left) and
around the pilot (r = 0.82Dj, right). At x = 3.29Dj and for radial positions be-
111
5. CMC/LES of the Delft-III natural gas non-premixed jet flame
tween r = 0.58Dj and r = 0.82Dj, which are locations where extinctions occur,
the scalar dissipation rate has a very large temporal variation and occasionally
crosses the value corresponding to the extinction of the “0D-CMC” solution. Fig-
ure 5.20 shows the conditionally filtered scalar dissipation rates at x = 3.29Dj
and r = 0.82Dj at different times. The shape of the curves are identical due to
the use of the AMC model. As in the time series, the maximum value of the
conditionally filtered scalar dissipation rate is seen to reach its extinction value
from time to time. Further downstream, the scalar dissipation relaxes and is well
below the extinction value. An examination of the conditional stoichiometric
temperature shows excursions down to about 800K that coincide with zero OH.
This is the footprint of a localized extinction. It is interesting to note that Fig.
5.19 shows that at x = 3.29Dj and for a radial position r = 0.58Dj (left) localised
extinctions occur even if the scalar dissipation rate is slightly below the nominal
value for extinction of the steady flamelet (found to be equal to 193 1/s in Fig.
5.2(a)). This is due to the fact that the transport terms in the CMC equation
are responsible for convecting at the locations of high scalar dissipation the Qα
distributions associated with the incoming, “frozen” shapes from the entry, which
the pilot cannot always ignite successfully. In other words, the localised extinc-
tion at the neighbourhood of the pilot can sometimes be understood as a lack of
“ignition” by the pilot due to the high scalar dissipation rate. It must be em-
phasized that the presence of localised extinctions at these different locations is
qualitatively consistent with the experimental data. In particular, animations of
the resolved OH contour are consistent with experimental visualizations of OH
contour [27; 111] reproduced in Fig. 5.13. The way LES-CMC captures localized
extinctions here is also consistent with similar findings in Ref. [38] for Sandia
flame F using a reduced chemistry scheme.
Further downstream, the LES-CMC produces a smaller degree of extinction
than the experiment. In Fig. 5.21, conditional profiles of temperature and CO
mass fractions are plotted from various instants at a specific axial position and
compare to experimental scatterplots. The different CMC solutions over time
at that axial position are also PDF-weighted averaged for comparison with the
experimental average. These instantaneous conditional profiles predicted by the
LES/3D-CMC formulation, although fluctuating, correspond always to burning
112
5. CMC/LES of the Delft-III natural gas non-premixed jet flame
distributions. The conditional PDF-weighted average temperature and CO mass
fraction show that the model tends to predict more accurately the lean part
than the rich part in η-space. A slight overprediction of the temperature and
mass fraction peaks is visible, which is due to the absence of extinctions in the
simulation at this location, while the experimental scatterplots show that they
still occur occasionally at the location. However, it is obvious that the model has
predicted realistic conditional profiles and that the agreement with experiments
is quite good in general.
5.3.4 Temperature prediction and pollutants emissions
In Fig. 5.18, the instantaneous iso-surfaces of ξ = ξst colored according to the
local resolved (a) OH mass fraction, (b) temperature, (c) NO mass fraction &
(d) CO mass fraction are plotted at the same instant. Figures 5.18 (b), (c) & (d)
show the flame from the same prespective, which allows to compare the pictures
to one another, while the image of OH mass fraction has been rotated to allow the
best visualization of the localized extinction occuring at that instant. Comparison
between Fig. 5.18 (b) and (c) allows to highlight the strong correlation between
YNO and the temperature for any axial position above around 125 mm (21 Dj). In
fact, on the upper part of the flame, temperatures are above 1500 K on average
triggering the formation of NOx through the thermal mechanism. Along the
stoichiometric mixture fraction on the upper part of the flame, YNO is found to
fluctuate strongly with values from less than 1.0× 10−4 to more than 2.0× 10−4.
On the other hand, YNO shows only small fluctuations along the stoichiometric iso-
surface on the lower part of the flame, with the exception of regions were localized
extinctions occur, typically close to the burner. The emission of NO remains low
in the lower part of the flame. One explanation comes from the high sensitivity of
the NO reaction rate on the temperature in the Zel’dovich mechanism while the
temperature remains overall below 1500K in this region. Another explanation
of this low NO production is the presence of localized extinctions in this part of
the flame, which affects strongly the pollutant emissions as developed in the next
paragraph.
The conditional averages for NO and CO are seen to fluctuate as the scalar
113
5. CMC/LES of the Delft-III natural gas non-premixed jet flame
dissipation rate fluctuates (Fig. 5.19). The Y˜NO|ξst at the pilot (Fig. 5.19 left,
blue dotted curve) is high because of the injection of the “burning flamelet” at
this location. As the pilot stream mixes with the surroundings, NO is reduced
and, at the instants of the localised extinction, NO is reduced significantly. It
increases as we go downstream and the flame becomes fully alight. The condi-
tional CO is in reasonable agreement with experiment (Fig. 5.21(b)) and so is
the temperature (Fig. 5.21(a)). The Favre-mean and RMS temperature (Figs.
5.22 & 5.23 respectively) and CO mass fractions (Figs. 5.24 & 5.25 respectively)
compare well with the experiments. A slight underprediction of both reactive
scalars close to the burner (x = 4.17Dj and x = 8.33Dj) could be due to an
over-prediction of extinctions in this part of the flame. Finally, the mass fraction
of NO is, however, increasingly overpredicted as we go downstream (Fig. 5.26
and Fig. 5.27). This may be attributed to the neglect of radiation, which may
be responsible for the slight over-prediction of the temperature, but also to the
chemical scheme used. Significant over-predictions of NO using GRI3 have been
previously observed in both turbulent [20] and laminar flames [7].
5.4 Summary of main findings
A LES - first order CMC formulation has been applied to the Delft III natural
gas non-premixed jet flame. Localised extinctions, which lead to the succession
of burning and extinguished stoichiometric fluid along the flame front, have been
successfully captured. These transient events occur mainly close to the nozzle,
consistent with experimental observations. The simulations reproduce well the
experimental data in terms of time-averaged statistics for velocity, mixture frac-
tion, CO and temperature, with the exception of NO which is overpredicted.
114
5. CMC/LES of the Delft-III natural gas non-premixed jet flame
0 0.2 0.4 0.6 0.8 1
500
1000
1500
2000
T 
(K
)
ξ
x = 3.9 Dj
 
 
CMC x=23.4 mm
CMC AVE
(a)
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
x 10−3
Y O
H
ξ
x = 3.9 Dj
 
 
CMC x=23.4 mm
(b)
0 0.2 0.4 0.6 0.8 1
500
1000
1500
2000
T 
(K
)
ξ
x = 9.88 Dj
 
 
CMC x=59.3 mm
CMC AVE
(c)
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5x 10
−3
Y O
H
ξ
x = 9.88 Dj
 
 
CMC x=59.3 mm
(d)
0 0.2 0.4 0.6 0.8 1
500
1000
1500
2000
T 
(K
)
ξ
x = 32 Dj
 
 
CMC x=192 mm
CMC AVE
(e)
0 0.2 0.4 0.6 0.8 10
1
2
3
4
x 10−3
Y O
H
ξ
x = 32 Dj
 
 
CMC x=192 mm
(f)
Figure 5.17: Typical instantaneous conditional (“CMC”) and PDF-weighted con-
ditional average (“CMC AVE”) profiles of the temperature and OH mass fraction
at the indicated axial positions. The PDF average is done over all the CMC nodes
corresponding to a given axial position and over time.
115
5. CMC/LES of the Delft-III natural gas non-premixed jet flame
(a) (b)
(c) (d)
Figure 5.18: Typical instantaneous iso-surface of ξ = ξst colored according to the
local resolved (a) OH mass fraction, (b) temperature, (c) NO mass fraction &
(d) CO mass fraction at the same instant. Length of images: 300 mm. All the
pictures are seen from the same perspective except (a) which has been rotated to
highlight the localized extinction.
116
5. CMC/LES of the Delft-III natural gas non-premixed jet flame
0.38 0.4 0.42 0.44 0.46 0.480
50
100
150
200
250
300
350
400
Time (s)
Pe
ak
 N
|η 
(1/
s)
 
 
x/Dj=0
x/Dj=3.29
x/Dj=8.33
x/Dj=16.7
x/Dj=25
0.38 0.4 0.42 0.44 0.46 0.480
50
100
150
200
Time (s)
Pe
ak
 N
|η 
(1/
s)
 
 
x/Dj=0
x/Dj=3.29
x/Dj=8.33
x/Dj=16.7
x/Dj=25
0.38 0.4 0.42 0.44 0.46 0.48800
1000
1200
1400
1600
1800
2000
2200
2400
Time (s)
St
oi
ch
. C
on
d.
 T
em
p.
 (K
)
 
 
x/Dj=0
x/Dj=3.29
x/Dj=8.33
x/Dj=16.7
x/Dj=25
0.38 0.4 0.42 0.44 0.46 0.48800
1000
1200
1400
1600
1800
2000
2200
2400
Time (s)
St
oi
ch
. C
on
d.
 T
em
p.
 (K
)
 
 
x/Dj=0
x/Dj=3.29
x/Dj=8.33
x/Dj=16.7
x/Dj=25
0.38 0.4 0.42 0.44 0.46 0.48
0
1
2
3
4
5x 10
−3
Time (s)
St
oi
ch
. C
on
d.
 Y O
H
 
 
x/Dj=0
x/Dj=3.29
x/Dj=8.33
x/Dj=16.7
x/Dj=25
0.38 0.4 0.42 0.44 0.46 0.48
0
1
2
3
4
5x 10
−3
Time (s)
St
oi
ch
. C
on
d.
 Y O
H
 
 
x/Dj=0
x/Dj=3.29
x/Dj=8.33
x/Dj=16.7
x/Dj=25
0.38 0.4 0.42 0.44 0.46 0.48
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
x 10−4
Time (s)
St
oi
ch
. C
on
d.
 Y N
O
 
 
x/Dj=0
x/Dj=3.29
x/Dj=8.33
x/Dj=16.7
x/Dj=25
0.38 0.4 0.42 0.44 0.46 0.48
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
x 10−4
Time (s)
St
oi
ch
. C
on
d.
 Y N
O
 
 
x/Dj=0
x/Dj=3.29
x/Dj=8.33
x/Dj=16.7
x/Dj=25
0.38 0.4 0.42 0.44 0.46 0.480
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
Time (s)
St
oi
ch
. C
on
d.
 Y C
O
 
 
x/Dj=0
x/Dj=3.29
x/Dj=8.33
x/Dj=16.7
x/Dj=25
0.38 0.4 0.42 0.44 0.46 0.480
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
Time (s)
St
oi
ch
. C
on
d.
 Y C
O
 
 
x/Dj=0
x/Dj=3.29
x/Dj=8.33
x/Dj=16.7
x/Dj=25
Figure 5.19: Time series of N˜ |0.5, T˜ |ξst, Y˜OH |ξst, Y˜NO|ξst and Y˜CO|ξst at r =
0.58Dj (left, corresponding to the radial position of the pilot) and at r = 0.82Dj
(right) and the indicated x. Time zero refers to the initialization of the LES. The
black dotted lines on the two top graphs refer to the extinction value of the scalar
dissipation rate (193 1/s).
117
5. CMC/LES of the Delft-III natural gas non-premixed jet flame
0 0.2 0.4 0.6 0.8 1
0
50
100
150
200
250
N
|η 
(1/
s)
ξ
Figure 5.20: N˜ |η at x = 3.29Dj and r = 0.82Dj. The black dotted line refers to
the extinction value of N0 (193 1/s).
118
5. CMC/LES of the Delft-III natural gas non-premixed jet flame
0 0.2 0.4 0.6 0.8 1
250
750
1250
1750
2250
T 
(K
)
ξ
x = 16.7 Dj
 
 
CMC r=0.12Dj
CMC r=0.58Dj
CMC r=2.12Dj
CMC AVE
EXP
EXP AVE
(a)
0 0.2 0.4 0.6 0.8 1
0.01
0.02
0.03
0.04
0.05
0.06
Y C
O
ξ
x = 25 Dj
 
 
CMC r=0.12Dj
CMC r=0.58Dj
CMC r=2.12Dj
CMC AVE
EXP
EXP AVE
(b)
Figure 5.21: Typical instantaneous conditional (“CMC”) and PDF-weighted con-
ditional average (“CMC AVE”) profiles of (a) the temperature and (b) CO mass
fraction at respectively x = 100 mm and x = 150 mm and at the indicated radial
positions. The PDF average is done over all the CMC nodes corresponding to a
given axial position and over time. Scatterplots and conditional averages from
experimental data [27] are superimposed for comparison.
119
5. CMC/LES of the Delft-III natural gas non-premixed jet flame
0 1 2 3
500
1000
1500
2000
x = 4.17 Dj
r / Dj
<
T>
 
 
EXP
RANS/OD−CMC
LES/OD
LES/3D−CMC
0 1 2 3
500
1000
1500
2000
x = 8.33 Dj
r / Dj
<
T>
 
 
EXP
RANS/OD−CMC
LES/OD
LES/3D−CMC
0 1 2 3
500
1000
1500
2000
x = 16.7 Dj
r / Dj
<
T>
 
 
EXP
RANS/OD−CMC
LES/OD
LES/3D−CMC
0 1 2 3
500
1000
1500
2000
x = 25 Dj
r / Dj
<
T>
 
 
EXP
RANS/OD−CMC
LES/OD
LES/3D−CMC
0 1 2 3
500
1000
1500
2000
x = 33.3 Dj
r / Dj
<
T>
 
 
EXP
RANS/OD−CMC
LES/OD
LES/3D−CMC
0 1 2 3
500
1000
1500
2000
x = 41.7 Dj
r / Dj
<
T>
 
 
EXP
RANS/OD−CMC
LES/OD
LES/3D−CMC
Figure 5.22: Radial profiles of the mean temperature at the indicated axial posi-
tion. Experimental data from Ref. [27].
120
5. CMC/LES of the Delft-III natural gas non-premixed jet flame
0 1 2 30
250
500
750
x = 4.17 Dj
r / Dj
T R
M
S
 
 
EXP
LES/OD
LES/3D−CMC
0 1 2 30
250
500
750
x = 8.33 Dj
r / Dj
T R
M
S
 
 
EXP
LES/OD
LES/3D−CMC
0 1 2 30
250
500
750
x = 16.7 Dj
r / Dj
T R
M
S
 
 
EXP
LES/OD
LES/3D−CMC
0 1 2 30
250
500
750
x = 25 Dj
r / Dj
T R
M
S
 
 
EXP
LES/OD
LES/3D−CMC
0 1 2 30
250
500
750
x = 33.3 Dj
r / Dj
T R
M
S
 
 
EXP
LES/OD
LES/3D−CMC
0 1 2 30
250
500
750
x = 41.7 Dj
r / Dj
T R
M
S
 
 
EXP
LES/OD
LES/3D−CMC
Figure 5.23: Radial profiles of the RMS of the temperature at the indicated axial
position. Experimental data from Ref. [27].
121
5. CMC/LES of the Delft-III natural gas non-premixed jet flame
0 1 2 30
0.01
0.02
0.03
0.04
0.05
0.06
x = 4.17 Dj
r / Dj
<
Y C
O
>
 
 
EXP
RANS/OD−CMC
LES/OD
LES/3D−CMC
0 1 2 30
0.01
0.02
0.03
0.04
0.05
0.06
x = 8.33 Dj
r / Dj
<
Y C
O
>
 
 
EXP
RANS/OD−CMC
LES/OD
LES/3D−CMC
0 1 2 30
0.01
0.02
0.03
0.04
0.05
0.06
x = 16.7 Dj
r / Dj
<
Y C
O
>
 
 
EXP
RANS/OD−CMC
LES/OD
LES/3D−CMC
0 1 2 30
0.01
0.02
0.03
0.04
0.05
0.06
x = 25 Dj
r / Dj
<
Y C
O
>
 
 
EXP
RANS/OD−CMC
LES/OD
LES/3D−CMC
0 1 2 30
0.01
0.02
0.03
0.04
0.05
0.06
x = 33.3 Dj
r / Dj
<
Y C
O
>
 
 
EXP
RANS/OD−CMC
LES/OD
LES/3D−CMC
0 1 2 30
0.01
0.02
0.03
0.04
0.05
0.06
x = 41.7 Dj
r / Dj
<
Y C
O
>
 
 
EXP
RANS/OD−CMC
LES/OD
LES/3D−CMC
Figure 5.24: Radial profiles of the mean YCO at the indicated axial position.
Experimental data from Ref. [27].
122
5. CMC/LES of the Delft-III natural gas non-premixed jet flame
0 1 2 30
1.0e−2
2.0e−2
3.0e−2
x = 4.17 Dj
r / Dj
(Y
CO
) RM
S
 
 
EXP
LES/OD
LES/3D−CMC
0 1 2 30
1.0e−2
2.0e−2
3.0e−2
x = 8.33 Dj
r / Dj
(Y
CO
) RM
S
 
 
EXP
LES/OD
LES/3D−CMC
0 1 2 30
1.0e−2
2.0e−2
3.0e−2
x = 16.7 Dj
r / Dj
(Y
CO
) RM
S
 
 
EXP
LES/OD
LES/3D−CMC
0 1 2 30
1.0e−2
2.0e−2
3.0e−2
x = 25 Dj
r / Dj
(Y
CO
) RM
S
 
 
EXP
LES/OD
LES/3D−CMC
0 1 2 30
1.0e−2
2.0e−2
3.0e−2
x = 33.3 Dj
r / Dj
(Y
CO
) RM
S
 
 
EXP
LES/OD
LES/3D−CMC
0 1 2 30
1.0e−2
2.0e−2
3.0e−2
x = 41.7 Dj
r / Dj
(Y
CO
) RM
S
 
 
EXP
LES/OD
LES/3D−CMC
Figure 5.25: Radial profiles of the RMS of YCO at the indicated axial position.
Experimental data from Ref. [27].
123
5. CMC/LES of the Delft-III natural gas non-premixed jet flame
0 1 2 30
1.0e−4
2.0e−4
x = 4.17 Dj
r / Dj
<
Y N
O
>
 
 
EXP
RANS/OD−CMC
LES/OD
LES/3D−CMC
0 1 2 30
1.0e−4
2.0e−4
x = 8.33 Dj
r / Dj
<
Y N
O
>
 
 
EXP
RANS/OD−CMC
LES/OD
LES/3D−CMC
0 1 2 30
1.0e−4
2.0e−4
x = 16.7 Dj
r / Dj
<
Y N
O
>
 
 
EXP
RANS/OD−CMC
LES/OD
LES/3D−CMC
0 1 2 30
1.0e−4
2.0e−4
x = 25 Dj
r / Dj
<
Y N
O
>
 
 
EXP
RANS/OD−CMC
LES/OD
LES/3D−CMC
0 1 2 30
1.0e−4
2.0e−4
x = 33.3 Dj
r / Dj
<
Y N
O
>
 
 
EXP
RANS/OD−CMC
LES/OD
LES/3D−CMC
0 1 2 30
1.0e−4
2.0e−4
x = 41.7 Dj
r / Dj
<
Y N
O
>
 
 
EXP
RANS/OD−CMC
LES/OD
LES/3D−CMC
Figure 5.26: Radial profiles of the mean YNO at the indicated axial position.
Experimental data from Ref. [27].
124
5. CMC/LES of the Delft-III natural gas non-premixed jet flame
0 1 2 30
0.2
0.4
0.6
0.8
1x 10
−4
x = 4.17 Dj
r / Dj
(Y
N
O
) RM
S
 
 
EXP
LES/OD
LES/3D−CMC
0 1 2 30
0.2
0.4
0.6
0.8
1x 10
−4
x = 8.33 Dj
r / Dj
(Y
N
O
) RM
S
 
 
EXP
LES/OD
LES/3D−CMC
0 1 2 30
0.2
0.4
0.6
0.8
1x 10
−4
x = 16.7 Dj
r / Dj
(Y
N
O
) RM
S
 
 
EXP
LES/OD
LES/3D−CMC
0 1 2 30
0.2
0.4
0.6
0.8
1x 10
−4
x = 25 Dj
r / Dj
(Y
N
O
) RM
S
 
 
EXP
LES/OD
LES/3D−CMC
0 1 2 30
0.2
0.4
0.6
0.8
1x 10
−4
x = 33.3 Dj
r / Dj
(Y
N
O
) RM
S
 
 
EXP
LES/OD
LES/3D−CMC
0 1 2 30
0.2
0.4
0.6
0.8
1x 10
−4
x = 41.7 Dj
r / Dj
(Y
N
O
) RM
S
 
 
EXP
LES/OD
LES/3D−CMC
Figure 5.27: Radial profiles of the RMS of YNO at the indicated axial position.
Experimental data from Ref. [27].
125
Chapter 6
Investigation of the aerodynamics
of a non-premixed swirl flame
using LES
6.1 Introduction
6.1.1 Motivation
The confined turbulent swirling non-premixed TECFLAM S09c flame has been
investigated using Large Eddy Simulation and a pre-calculated mixture-fraction-
based flamelet model in a preliminary step to simulate this flame. The analysis of
this swirl flame is of great interest as it mimics the main features that are observed
in industrial burners and offers an opportunity for a better understanding of
their dynamics. The challenge of simulating this swirl flame comes from the
very complex aerodynamics created by the imposed swirl. The swirl leads to the
formation of a Central Recirculation Zone (CRZ) via the Vortex Breakdown (VB)
mechanism [69]. One structure expected in a swirl flow and related to the VB
process is the Precessing Vortex Core [112], described in Section 2.3.3 of Chapter
2. The PVC is expected to interact with the flame and hence induce heat release
fluctuations. Reproducing accurately this large structure or any similar structure
induced by the VB is required to predict accurately the flame dynamics and the
pollutants emission.
126
6. Investigation of the aerodynamics of a non-premixed swirl flame
6.1.2 Background works
The non-premixed TECFLAM configuration has been extensively studied experi-
mentally and is a target of the international workshop on Turbulent Non-premixed
Flames (TNF). Radial profiles of the mixing field, flow field and species concen-
trations are available [12; 13; 14; 51; 66]. Several numerical studies have been
attempted to model this flame. In Ref. [74], a RANS formulation based on a
Reynolds-stress turbulence model, a presumed β−PDF combustion model and
assuming chemical equilibrium was performed. The general behaviour of the flow
field could not be predicted accurately. A LES of the unconfined non-premixed
TECFLAM [17] has also previously been performed using a flamelet model cou-
pled to a β-subgrid PDF. The pattern of the recirculation zones were found to
diverge considerably from the experimental data. This was related to the failure
of the fuel jet to spread radially in the near burner regions, due to the inability of
the simulation to reproduce negative axial velocity in the airstream at the burner
exit. Therefore, the conclusion was that the injector has to be included in the
computational domain, at least partially.
6.1.3 Objectives
In this study, LES is used to solve the flow and mixing fields and has been coupled
with a prescribed first order CMC solution, as a preliminary attempt to model
this complex non-premixed flame. This formulation is relatively fast compared
to the LES coupled with the full CMC equations resolved in a 3D grid at each
LES iteration. Statistical analysis such as spectral analysis, correlations, and
Proper Orthogonal Decomposition can then be performed with a very good sta-
tistical convergence. As a result, a comprehensive analysis of swirl flow structures
(PVC...) has been developed in this chapter, while the next chapter focuses on the
combustion process of such a swirl flame (localized extinctions, lift-off, pollutants
emissions) based on the full 3D-CMC equations. Therefore, the objectives of this
chapter are: (i) to model the main features of the TECFLAM S09c swirl flame;
(ii) to investigate in depth the combustor aerodynamics using various techniques,
in particular the Proper Orthogonal Decomposition (POD), and to compare with
an inert flow simulation; (iii) to provide an initial solution for a second type of
127
6. Investigation of the aerodynamics of a non-premixed swirl flame
LES using three-dimensional CMC, in a future attempt to capture the extinction
observed in this flame experimentally.
6.2 Method
6.2.1 Flow computed
Fig. 6.1 shows the flow studied. The TECFLAM S09c flame is composed of a fuel
jet, with an average injection velocity at the burner exit of 21 m/s, surrounded
by a swirling air jet. The fuel annulus has an inner diameter of 20 mm and an
outer diameter of 26 mm. The air stream bulk velocity at the burner exit is 23
m/s. Its inner diameter is 30 mm and its outer diameter is 60 mm. Movable
blocks inside the burner create the swirl in the air stream. The swirl number is
calculated based on geometrical consideration and the value of S = 0.9 has been
reported for this experiment. The air and fuel streams are separated by a rim
of inner diameter 26 mm and outer diameter 30 mm. The length used for non-
dimensionalisation in this study is the diameter of the bluff body: D=30 mm.
The diameter of the simulated domain is equal to the diameter of the combustion
chamber used in the experiments, which is 500 mm. The computational domain
extends vertically from 50 mm below the burner exit to 350 mm above it, while
the real total length of the combustion chamber is 1 m.
6.2.2 Mesh
The mesh is shown in Fig. 6.2. It reproduces part of the burner. Typically
the numerical inlet has been located at 50 mm upstream of the burner exit. As
stated in Section 6.1.2, it has been reported that the absence of the burner in
the simulated domain leads to a wrong prediction of the recirculation shape.
By including part of the air pipe in the computational domain, the flow can
develop itself before entering the combustion chamber. In particular, flow features
such as the PVC start developing inside the burner [83] and this study aims
at reproducing it. The grid used for these computations is an O-grid mesh,
very refined around the burner air and fuel exits, and with a smooth expansion
128
6. Investigation of the aerodynamics of a non-premixed swirl flame
Table 6.1: Fuel composition used by the CMC code to model the TECFLAM
natural gas
Constituents Formula Mass fraction %
CH4 96.8284
C2H6 0.9184
N2 1.7144
CO2 0.5388
downstream and radially so that a total of approximately 7.9M cells are used
(303× 162× 160).
6.2.3 Large Eddy Simulation and combustion modelling
A LES/0D-CMC formulation (see Section 3.2.3 of Chapter 3 for details of the
numerical formulation) has been used to model the flame. The time-step used
for all the simulations is 5.0× 10−6 s and the simulations were carried out on 23
quad-core CPUs at 2.53 GHz with 24 GB of RAM available per CPU, produc-
ing 1.0 ms of simulated time in approximately 93 min. The reduced chemistry
mechanism ARM2 derived from the detailed GRI-Mech 3.0 mechanism [106] has
been used. This mechanism contains 19 species and 15 reactions. The fuel used
in the experiments was natural gas. The ARM2 chemistry does not cover all the
species in the experiment (such as Propane (C3H8) and Butane (C4H10)). The
missing species have been re-distributed into other species in order to conserve
the total calorific value of the fuel calculated by means of the individual calorific
values. One ends up with an approximation of its composition based on the
species available, as reported in percentage by mass in Table 6.1. The natural
gas approximation used by the CMC code gives a stoichiometric mixture fraction
of ξst CMC = 0.056 while the natural gas in the experiment was reported to give
ξst exp = 0.055 [51]. No-slip velocity conditions have been enforced on solid walls,
while zero gradient boundary condition has been enforced at the outlet.
129
6. Investigation of the aerodynamics of a non-premixed swirl flame
6.2.4 Boundary conditions
The mixture fraction is set to 1 in the fuel stream and 0 in the air stream. Both
stream temperatures are set to the experimental value of 300 K. Imposing the
right velocities at the boundaries is challenging as no experimental data is avail-
able inside the burner. As no swirl is imposed on the fuel stream annulus, the
numerical Boundary Conditions (BCs) for the fuel stream are only located 7 mm
upstream from the fuel exit and a top-hat profile with the same mean velocity
as the experimental one is injected without any added fluctuations. The velocity
BCs in the air annulus are much more complicated to choose as the numerical
inlet is located deep inside the burner and as no experimental data of the velocity
(in particular the tangential component) is available for that location. The only
information provided is the value of the mean axial velocity at the burner exit
and the geometrical swirl number at the swirl generator exit, located upstream
the simulated part of the burner. In order to find the most appropriate BCs, an
extensive parametric study has been conducted. Firstly the tangential velocity
component at the numerical air inlet was chosen in order to reproduce the exper-
imental swirl number S = 0.9. Then several simulations with different tangential
velocities at the numerical air inlet were computed and their results were assessed
against the experimental data 1 mm downstream from the burner exit. The best
match was then selected and is reproduced in Fig. 6.3. The comprehensive flow
analysis presented in the next section is based on this simulation.
6.3 Results and Discussion
6.3.1 Analysis of the steady flame
Prior to run any LES simulation, a series of 0D-CMC calculations (see Section
3.2.3 of Chapter 3) have been performed with the above fuel composition (Table
6.1). The aim of the 0D-CMC computations is to evaluate the quality of the
reduced chemistry mechanism used by the CMC equations and to investigate the
structure of the steady flame. Fig. 6.4(a) shows the maximum temperature of
the flame for different values of N0 for both the GRI3.0 and ARM2 mechanisms.
The results from the 19 species reduced ARM2 mechanism and the 53 species
130
6. Investigation of the aerodynamics of a non-premixed swirl flame
detailed GRI3.0 mechanism agree very well: the maximum temperature of the
flame is Tmax = 2124 K with ARM2 and Tmax = 2130 K with GRI3.0, i.e. a
difference of only 6 K; the extinction scalar dissipation rate is N0ext = 176 1/s
for ARM2 and N0ext = 185 1/s for GRI3.0, i.e. a discrepancy of ∼ 5 %. Figure
6.4(b) shows the burning distribution obtained with the prescribed N0 = 20 1/s.
6.3.2 Mean and instantaneous flow fields
Figures. 6.5 and 6.6 show some time-averaged statistics from the reacting case.
The averaging has been done over 195 ms of simulated time. Figure 6.5(a) shows
the time-averaged axial velocity contour. The black line represents the time-
averaged zero-velocity isoline. The incoming air stream, the Central Recircula-
tion Zones (CRZs), and the Outer Recirculation Zone (ORZ) of the combustion
chamber are evident. We can notice the presence of two CRZs along the centre-
line. Similar behaviours have been reported in Ref. [69]. The fuel jet is visible on
the burner bluff body. The flow exiting from the fuel annulus quickly encounters
the recirculated flow, which pushes back the rich mixture towards the air stream,
leading to a quick and efficient mixing. The white line shows the stoichiometric
mixture fraction isosurface and it is evident that the time-averaged stoichiometric
mixture fraction extends into the air annulus, inside the burner, while only air
has been injected in this pipe at the numerical inlet (ξ = 0). This leads to the
conclusion that a certain amount of fuel is present at the top extremity of the air
pipe. The time-averaged mixture fraction field in Fig. 6.5(b) confirms this ob-
servation. Looking now at the time-averaged temperature (Fig. 6.5(d)), we note
that the flame contour is shaped of the narrow RCZs (visualized by the black
lines). This results in a narrow flame with a very limited expansion along the
combustion chamber. Figure 6.5(c) also reports the time-averaged density, while
Figs. 6.6(a) and 6.6(b) represent respectively the time-averaged radial velocity
and the time-averaged tangential velocity.
Figures 6.7 (a,c,e) and (b,d,f) represent respectively the flow around the
burner from instantaneous snapshots of the axial velocity and out-of-plane vor-
ticity at different instants. Figure 6.9 provides a zoom of Fig. 6.7 (e) around the
burner. From this picture, it is clear that a recirculation occurs inside the burner
131
6. Investigation of the aerodynamics of a non-premixed swirl flame
along the inner wall of the air annulus and that this recirculation is responsible
for sucking some of the fuel injected at the top of the burner inside the air annulus
(the white line represents again the stoichiometric mixture fraction).
The z−vorticity snapshots (Figs. 6.7 (b,d,f)) reveal that two main shear
layers develop in the air swirling jet: one between the air flow and the CRZ and
one between the air flow and the outer flow. Along the shear layers, the large
difference of velocities between the air jet and the rest of the flow leads to the
formation of Kelvin-Helmholtz instabilities, visualized by fragmented vorticity
contours. Further downstream, these instabilities have fed the flow with further
turbulence, leading to the strong convolution of the stoichiometric iso-surface
(white line). The vorticity map shows that significant amount of vorticity is found
in the shear layers, but also in a small region along the inner pipe immediately
before the burner exit.
An animation of the reactive mixing field (Fig. 6.8) shows that a periodic
increase and decrease of the mixture fraction occurs on the upper part of the air
annulus, along the inner wall, from ξ = 0 to values as high as ξ = 0.6 − 0.7.
The fuel stream exiting from the top of the burner bluff body is seen as being
periodically sucked into the air annulus. The stoichiometric mixture fraction
isosurface at this location is therefore pushed down deep inside the air pipe.
The observation of an axial velocity contour animation (Figs. 6.7 (a,c,e)) leads
to the conclusion that both the fuel and air streams close to the burner follow
this oscillating motion. This phenomenon has to be related to the formation of
recirculations along the inner wall of the air annulus, as observed in Fig. 6.9. An
animation of the Z−vorticity (Figs. 6.7 (b,d,f)) shows that the point of separation
of the inner shear layer oscillates along the inner wall, the separation of the air
stream occurring up to 25 mm below the burner exit. The whole phenomenon can
thus be understood as a cycle of separations and recirculations occuring along the
inner wall of the air pipe. These separation-recirculation cycles are responsible
for sucking some amount of the fuel injected at the top of the bluff body into the
air annulus.
132
6. Investigation of the aerodynamics of a non-premixed swirl flame
6.3.3 Mean radial profiles
The following time-averaged quantities of the reactive flow simulated by the
LES/0D-CMC formulation have been computed over 195 ms. Prior to start the
averaging, the flow had already been computed over 160 ms of simulated time in
order to let it develop and obtain a stabilization of its velocity spectra. Figure
6.10 shows the time-averaged radial profiles of the axial velocity at a few axial po-
sitions. The closest available experimental data to the burner exit correspond to
an axial position of x = 0.033D (x = 1 mm). This graph and the time-averaged
radial profiles of the tangential velocity at the same position (Fig. 6.11) shows
that the numerical inlets for the air and fuel streams have been carefully applied
in term of magnitude. The RMS of these quantities (Fig. 6.12 for the RMS of the
axial velocity and Fig. 6.13 for the tangential ones) show that the flow is already
turbulent 1 mm above the burner exit despite the absence of any numerical fluc-
tuations (except white noise) in the velocity profile injected in the air annulus.
However the RMS values remain overall underpredicted at this distance of the
burner. Further downstream, the RMS data show that the flow has become very
turbulent with velocity fluctuations reaching 60% of the injected axial velocity
magnitude in some locations. The computed fluctuations are moving closer and
closer to the experimental data as the downstream distances increase. These very
high values of the RMS quantities found close to the burner exit are remarkable
and will be explained later in this chapter. The axial velocity profile (Fig. 6.10)
is found to be well predicted in the main jet at all axial positions, while there is
an underprediction of the strength of the CRZ above x = 0.667D by a factor of 2.
This underprediction of the CRZ leads to a slight overprediction of the jet veloc-
ity for positions above x = 2.33D. The radial profiles of the tangential velocity
(Fig. 6.11) are very well predicted by the LES for x < 5.33D (x = 160 mm). The
trends of the mixture fraction radial profiles (Fig. 6.14) are also well captured
by the LES despite an overall slight underestimation of the mixing, leading to an
overestimation of ξ in the main jet, while ξ is therefore lightly underestimated
in the area between the jet and the outer walls. The radial profiles of ξ-RMS
(Fig. 6.15) show an overall underestimation of the fluctuations, while once again
the trends are well captured by the formulation. Overall the time-averaged ra-
133
6. Investigation of the aerodynamics of a non-premixed swirl flame
dial profiles compare well with the experiments and the numerical dataset can
therefore be used for further analysis.
6.3.4 Inert simulation
As stated in the Literature Review (Chapter 2), it has been reported that the
combustion process tends to damp the Precessing Vortex Core present in an inert
combustor flow, especially in non-premixed configurations, while some residual
instabilities can still be detected. In order to understand further the separation-
recirculation cycles inside the burner previously described, the inert flow of this
TECFLAM non-premixed configuration has been simulated. There is no experi-
mental data to compare our LES prediction. Nevertheless, the simulation is very
important for the understanding of the complex aerodynamics of the burner and
combustion chamber of swirl combustors, the associated hydrodynamic structures
and how the combustion process modifies the fluid dynamics and the hydrody-
namic structures in swirl flames.
Figure 6.16 shows the inert flow throughout the instantaneous axial velocity
(a), pressure (b) and mixture fraction (c) fields. The fluid dynamics appears to
be rather different from the reactive one. The CRZ has a much more complicated
shape than in the reacting flow. It appears much weaker than in the reacting case,
although it is found to extend much further in both radial and axial directions.
As a result of the CRZ radial expansion increase, the air stream is found to
open up much more than in the reacting case. The area of the CRZ with strong
reverse flow (u > 5 m/s) is limited to the space located directly around the
burner exit and, unlike CRZ of the reactive flow, does not reach the centre of the
combustion chamber. The consequence is that the rich mixture zone of the flow
remains confined around the burner exit at axial positions below x = 70 mm,
while it can reach positions as far as 200 mm in the reactive flow. Along the
centreline, a column of low pressure developing from inside the burner is clearly
visible. This low-pressure column is not visible in the reacting case. If now we
focus on the fluid dynamics inside the burner, we notice that the same kind of
cycle of separations and recirculations occurs along the inner wall of the air pipe
as reported in the reacting case. Once again, this results in a certain amount
134
6. Investigation of the aerodynamics of a non-premixed swirl flame
of fuel being sucked at the top of the air pipe. This can be seen in Fig. 6.16
throughout the stoichiometric fraction isoline, which is also found to enter inside
the air pipe.
6.3.5 Autocorrelation and spectra
To investigate further the temporal evolution of the flow, autocorrelations from
both the inert and reactive flow simulations have been calculated at several po-
sitions in the domain (Figs. 6.17 and 6.18). At x = 0.167D (x = 5 mm), both
the autocorrelations from the inert (left side of the figures) and reactive LES
(right side of the figures) confirm the presence of a periodic component close
to the air annulus exit at two diametrically opposed locations corresponding to
r = 0.75D. At the same axial position no oscillation is observed along the centre-
line (r = 0D) and at the burner edges (r = 1.667D). Further downstream some
oscillations are still observed in the autocorrelations at x = 0.833D (x = 25 mm)
in both the inert and reactive flows. These oscillations are already largely damped
at x = 1.67D (x = 50 mm) and are no longer visible further downstream in the
inert flow. However, the oscillations are found further downstream in the reactive
flow before disappearing around x = 3.33D (x = 100 mm). The oscillations in
the reactive flow can thus be found at higher axial positions than in the inert
flow. This observation will be explained later. By comparing the oscillations
from the inert and reactive flows, we conclude that the period found for the inert
flow is longer than its reactive counterpart, while the oscillations amplitude is
much lower in the reacting case.
In Fig. 6.19(c), the spectra of the axial velocity fluctuations confirm the
presence of oscillations in the inert flow as a clear frequency peak at 392.5 Hz
can be identified at the air annulus exit (x = 5 mm, r = 22.5 mm). A small
harmonic at 785 Hz is also visible. In Fig. 6.19(d), the spectra of the reactive
flow axial velocity at the air annulus exit shows a fundamental at 640 Hz and
several harmonics can also be observed (961 Hz and 1281 Hz) among other small
frequency peaks. A sub-harmonic at 320 Hz is also present in the spectrum. The
difference of fundamental frequencies between the inert flow and the reactive flow
is expected as the recirculation of hot gases in the burner exit vicinity strongly
135
6. Investigation of the aerodynamics of a non-premixed swirl flame
affects the fluid mechanics in this region. The inert and reactive fundamental
frequencies are already observable deep inside the air pipe 25 mm upstream from
the burner exit in Figs. 6.19(a) and 6.19(b) respectively. The sub-harmonic at 320
Hz is also present at this location in the reacting case. This leads to the conclusion
that any structures associated with these frequencies develop themselves deep
inside the burner. Figures 6.19(c) and 6.19(d) also show that the fundamental
frequency amplitude is damped by a factor of 10 when combustion occurs. Some
spectra in log-log format from both the inert and reacting cases have also been
plotted in Fig. 6.20 for reference. From their observation, it is obvious that the
turbulence has developed itself in the downstream part of the flow, despite the
absence of fluctuations injected at the flow inlets (x = −50 mm for the air stream,
x = −7 mm for the fuel stream).
6.3.6 Swirl-induced separation inside the burner
Iso-surfaces of low pressure from the inert simulation are reproduced in Fig.
6.21(a). The isosurface P − P0 = −450 Pa has been plotted in blue and it
shows two low-pressure columns located almost diametrically opposite. Anima-
tions show that these structures rotate around the bluff body at a period cor-
responding to the frequency peak observed in the inert spectra (392.5 Hz). As
a result, they impose their dynamics to the flow inside and close to the burner
and are responsible for the appearance of recirculations in the air annulus as well
as the oscillation of the flow around the burner. The structures are hence ex-
pected to be responsible for the recirculation observed inside the burner as well
as the flow oscillation observed around the burner exit. They are linked to the oc-
curences of flow separation along the air annulus inner wall due to the centrifugal
forces created by the swirl (as observed in the vorticity contour of the reactive
flow plotted in Fig. 6.7). These structures must also generate the high level
of turbulence detected as early as 1 mm above the air pipe exit as commented
previously (Fig. 6.12) for the reacting case. The separation-recirculation cycle
created by these structures is thought to be similar to the flashback phenomenon
observed experimentally in the premixed configuration of the TECFLAM burner
[44]. Along the centreline of the flow, the low-pressure column observed in Fig.
136
6. Investigation of the aerodynamics of a non-premixed swirl flame
6.21(b) (isosurface P −P0 = −250 Pa in blue) represents the vortex core induced
by the swirl in the inert flow.
As the inert and reactive flows experience similar behaviour in and around
the burner, it is expected that similar structures are present in the reactive flow
and that they are also responsible for the occurence of the separation inside the
air pipe. However, in practice, such structures have not been observed with
conventional visualization methods (Q−criterion applied to the instantaneous
velocity components) in the reactive flow. This is consistent with our previous
observation stating that the fundamental frequency amplitude is damped by a
factor of 10 in the reactive flow. Previous studies have also reported that the
combustion tends to remove a large part of the hydrodynamic structures (such
as the PVC), especially in non-premixed configuration, while some remaining
instabilities may still be present in the reactive flow [112]. In order to try to
visualize these structures in the reactive flow and perform further analysis, Proper
Orthogonal Decomposition (POD) of both the inert and reactive flows have been
performed.
6.3.7 Proper Orthogonal Decomposition
POD has been used to visualize, identify and then analyze the structures associ-
ated with the different frequencies observed in the flow spectra. The method has
been applied to both the inert and reactive fields, with the aim of understanding
better how the combustion process affects the flow dynamics. We start with a
POD analysis of 2D LES planar cuts before applying the method to 3D LES
datasets. Details of how the POD has been performed are given in Section 3.3
of Chapter 3. For both the 2D and 3D POD analysis more than 400 snapshots
sampled at 4000 Hz have been used from both the inert and reactive flow fields.
As a result, the data used for each POD span a time interval of more than 100 ms.
6.3.7.1 2D POD
POD has been applied simultaneously to the velocity, pressure and mixture frac-
tion fields of the inert LES datasets for different 2D planar cuts. However, the
modes found at different axial positions close to the burner are similar and only
137
6. Investigation of the aerodynamics of a non-premixed swirl flame
the results from the plane at x = 5 mm are reported here. For the reacting case,
the pressure variable has been replaced by the temperature. The energy distribu-
tions of the modes from both the inert and reacting cases are reproduced in the
first row of Fig. 6.22. The second row represents the time coefficients associated
with the two first modes (left side for the inert case, right side for the reacting
case). The 15 first modes are reproduced in Figs. 6.23, 6.24, 6.25 and 6.26 for
the inert flow, and in Figs. 6.27, 6.28, 6.29 and 6.30 for the reactive flow. In each
figure, the first row represents the axial velocity fluctuations field, the second
row the projected velocity fluctuations vector map, the third row the pressure
fluctuations field (respectively the temperature fluctuations field for the reacting
case) and the forth row the mixture fraction fluctuations field. The red colour
refers to positive fluctuations of the quantity, the blue colour refers to negative
fluctuations, and the green colour refers to a no-fluctuation area. In the last row,
the Fourier analysis of the temporal coefficient associated with the mode has been
plotted. Each column of each figure corresponds to a single mode. The temporal
coefficients are obtained by projection of the fluctuating velocity (a snapshot)
on the POD basis. Using the notation of Section 3.3 with j the discrete time
counter, one obtains:
aj = Ψ
TUj, j = 1...N (6.1)
Inert case We focus here on Figs. 6.23, 6.24, 6.25 and 6.26 that correspond to
the 2D POD analysis of the inert flow. Modes 1 and 2 contain almost the same
amount of energy, respectively 17.9 % and 17.8 % (Fig. 6.22(a)) and represent
clearly the most energetic structures of the flow accounting for 35.7 % of the total
fluctuation energy. Two structures corresponding to negative fluctuations of the
axial velocity (in dark blue in the figure) are visible, surrounded by two structures
of positive velocity fluctuations (in red) due to mass conservation. The same kind
of structures are visible using the pressure field. The vector maps reveal that each
of these structures experiences a rotating motion around themselves, leading to
the conclusion that there are vortices. Each two diametrically opposed vortices
rotate in the same direction around themselves, which is opposite to the direction
of the rotation around themselves of the two other diametrically opposed vortices.
138
6. Investigation of the aerodynamics of a non-premixed swirl flame
The temporal modes a1(t) and a2(t) associated with the spatial modes 1 and 2
are plotted in Fig. 6.22(c). Both feature the same periodic, sinus-like variations
at a frequency of fa1,a2 = 397.1 Hz (see spectra in Fig 6.23 (q)). The phase
angle between the two modes is found to be φa2−a1 =
pi
2
. As a result, when the
contribution of mode 1 is at its maximum, the contribution of mode 2 reaches
zero. These observations show that mode 1 and mode 2 form a pair of mode,
which is associated with the rotation of 4 vortices around the inner wall of the air
pipe. The structures associated with the axial velocity and pressure fluctuations
are induced by the rotation of the low-pressure columns observed in Fig. 6.21(a).
Modes 1 and 2 also exhibit structures throughout the mixture fraction fluctuations
field. Their interpretation, as well as further analysis of these modes, will be given
in Section 6.3.7.2 with the POD analysis of the 3D LES datasets.
Mode 3 contains 5.45 % of the fluctuating energy. No clear structure is visible
but this mode may account for an axial displacement of the CRZ.
Modes 4 and 5 are very interesting. They both contain roughly the same
amout of energy (4.01 % and 4.00 % respectively) and represent also a pair of
modes. Their spectra are identical and show a clear peak at 794.2 Hz, which is
the exact first harmonic of the frequency peak found in modes 1 and 2. This
leads to the interpretation that the pair of modes 4 and 5 actually represents a
harmonic of the pair of modes 1 and 2. The number of vortices in modes 4 and
5 has doubled in the upper part of the figure, compared to modes 1 and 2, while
no clear vortices are visible in the lower part of the figure.
Mode 6 shows two large counter-rotating vortices with a frequency peak at
222.8 Hz and another smaller peak at 377.7 Hz. It contains 3.62 % of the fluctu-
ating energy.
There is no clear interpretation for mode 7. Modes 8 and 9 are very similar
to modes 4 and 5. They contain respectively 2.48 % and 2.45 % of the total
energy. Their spectra also show a frequency peak at 794.2 Hz and they represent
the same structures as in modes 4 and 5, with the exception that this time the
vortices are located on the lower part of the figure. Modes 8 and 9 can then also
be interpreted as accounting for a part of the first harmonic of modes 1 and 2.
Mode 10 is similar to mode 6. It represents two large counter-rotating vortices
with a frequency peak at 213.1 Hz and another smaller peak at 106.5 Hz. Mode
139
6. Investigation of the aerodynamics of a non-premixed swirl flame
11 is also similar to mode 6 and mode 10, with a clear frequency peak at 232.4 Hz.
This leads to the interpretation that modes 6, 10 and 11 are modes that have
not statistically converged and that roughly account for the rotation of two large
vertical vortices in the combustion chamber at a frequency around 215− 230 Hz.
Modes 12 and 13 do not show any clear features. However modes 14 and 15
form a clear pair of modes accounting for the rotation of around 10 vortices around
the burner. They contain respectively 1.19 % and 1.15 % of the total energy.
They clearly show two peaks at 1007 Hz and 1191 Hz. As a result, this pair of
modes must account for some non-linear interaction between a second harmonic
characterizing the rotation of the four vortices around the burner, represented
by modes 1 and 2 (1191 = 3 × 397.1 Hz), and another frequency characterizing
another phenomenon in the flow.
In conclusion, the 2D POD analysis of the inert flow from a plane located
at x = 5 mm above the burner exit shows that 8 modes among the 15 modes
reproduced here account (at least partially) for the dynamics of some rotating
vortices at the burner exit. They corresponds to 50.98 % of the total fluctuating
energy at this distance from the burner. 35.7 % of the energy is contained in the
two fundamental modes (modes 1 and 2), while the 15.28 % of remaining energy
are spread among the two first harmonics of the frequency associated with the
vortices rotation inside the burner.
Reactive case We focus now on Figs. 6.27, 6.28, 6.29 and 6.30, corresponding
to the 2D POD analysis of the reactive flow. The POD analysis from the reacting
LES gives results that are consistent with its inert counterpart, although the
energy distribution is rather different (see Fig. 6.22(b)). The energy distribution
has a stairs-like shape, and several modes appear to behave like pairs of modes
(as several pairs of consecutive modes seem to contains similar amount of energy).
The energy decrease is also much slower than in the inert case, where the first
pair of modes (modes 1 and 2) clearly contained much of the flow fluctuating
energy.
As in the inert case, modes 1 and 2 contain almost the same amount of
energy, although they appear here to be much weaker with (only) 6.68 % and
6.63 % respectively of the total fluctuating energy (Fig. 6.22(b)). They represent
140
6. Investigation of the aerodynamics of a non-premixed swirl flame
the most energetic structures of the flow and account for 13.3 % of the total
fluctuating energy. The structures corresponding to these modes are similar to
their inert counterpart: they consist of four counter-rotating vortices (two by
two) that rotate also as a whole around the burner. The pressure and velocity
fields reveal that the combustion process has rather transformed the shape of the
vortices, which now appear to be much more elongated. The frequency associated
with the temporal coefficients has also been modified by the combustion process.
The vortices are now rotating at 668.3 Hz (see Fig. 6.27 (q)) around the inner
wall of the air annulus. The temporal modes a1(t) and a2(t) associated with the
spatial modes 1 and 2 are plotted in Fig. 6.22(d). As in the inert case, both
feature the same periodic, sinus-like variations.
Modes 3 and 4 are also a pair of modes, featuring six vortices (see for example
the pressure field) rotating around the burner. They account for 5.96 % and
5.90 % respectively of the total energy (11.86 % overall). Their spectra show two
peaks, the strongest at 926 Hz and a smaller one at 964.2 Hz.
Mode 5 seems to be associated with a coupling between the fluctuation of the
pressure and mixture fraction fields in the center of the flow. Its corresponding
spectrum shows a peak at 28.64 Hz and a small one at 343.7 Hz.
Modes 6 and 7 are again a pair of modes that accounts for the rotation of two
thin, elongated vortices around the burner exit. Their spectra show a very clear
peak at 343.7 Hz.
Modes 8 and 9 are a pair of modes representing 8 vortices rotating inside the
burner at a frequency of 1270 Hz, while modes 10 and 11 are a pair of modes
representing 10 vortices rotating inside the burner at a frequency of 1632 Hz.
The other modes do not allow a very clear interpretation and are not commented
here.
In conclusion, the 2D POD analysis of the reactive flow from a plane located
at x = 5 mm above the burner exit shows that at least 10 modes among the 15
modes reproduced here account for the dynamics of the rotating vortices at the
burner exit. They corresponds to 41.19 % of the total fluctuating energy at this
distance from the burner.
141
6. Investigation of the aerodynamics of a non-premixed swirl flame
6.3.7.2 3D POD
3D POD analysis has been performed for both the inert and reactive flows. This
study, coupled with the autocorrelations, spectral analysis and 2D POD analysis
allows to understand further the dynamics of the vortices developing inside the
burner and how the combustion process affects this dynamics.
Inert case Fig. 6.31(a) shows that the first three 3D POD modes of the inert
flow contain much more energy than the rest of the modes and account for 28 %
of the total fluctuation energy. Modes 1 and 2 contain 9.8 % each i.e. 19.6 %
overall of the total fluctuating energy. The first three modes of the velocity and
mixture fraction from the inert simulation are represented in Fig. 6.32 and Fig.
6.33.
Figures 6.32 (a, b, c) and (d, e, f) show respectively mode 1 and mode 2.
Both modes consist of two pairs of vortices as confirmed by the Q−criterion vi-
sualisation in Figs. 6.32 (b, e). The Q−criterion states that a vortical structure
is identified by positive values of Q = (ω2− 2S˜ijS˜ij)/4, with the vorticity magni-
tude and the strain rate calculated from the gradients of the velocity fluctuations
associated with the POD mode. These vortices develop along the inner wall of
the air annulus before expanding inside the combustion chamber at the burner
exit. Figs. 6.32 (a, d) show that each pair of vortices is composed of two diamet-
rically opposed vortices and that each pair is counter-rotating around their own
axis. In addition, one pair is associated with an axial velocity increase and the
other one with a decrease. Modes 1 and 2 are therefore similar. They are only
shifted by a rotation approximately equal to pi/8 around the x-axis. In fact, the
vortices roots in mode 2 are located at positions that correspond to the space
left free of vortices in mode 1, i.e. the space in the plane of the air pipe exit
located between each vortex of mode 1. This is due to the spacial orthogonality
of the modes resulting from the Proper Orthogonal Decomposition. Mode 1 and
mode 2 form therefore a pair of modes that characterizes the rotation of these
four vortex cores as a whole around the inner wall of the burner air pipe. These
structures are thought to be similar to a Precessing Vortex Core (PVC) [112]. In
the presence of the bluff body of the TECFLAM configuration, the precession is
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6. Investigation of the aerodynamics of a non-premixed swirl flame
transformed into a more rotation-like motion of a double helical vortex core.
Fourier analysis (Fig. 6.34(a)) of the temporal coefficients of modes 1 and
2 shows a clear peak at 397.1 Hz (St = fD/Ubulk = 0.518) while their phase
angle is found to be a2a1 = pi/2 (not shown here). By comparing these results
with the ones from the 2D POD analysis, it is clear that modes 1 and modes
2 computed from the 2D and 3D POD analysis of the inert flow are identical.
The frequency reported in Fig. 6.19(c) from the spectral analysis of the axial
velocity at the burner exit is likely to be associated with the rotation of these
vortices. They impose their dynamics to the flow inside the inlet pipe and in the
burner near-field and are responsible for the oscillating behaviour of the flow there.
These Rotating Vortex Cores (RVC) are created by the flow separations occuring
along the inner wall of the air pipe. These separations are themselves due to the
centrifugal forces created by the swirl, as described previously in Section 6.3.6.
These RVC inside the burner are responsible for the presence of recirculations
in the air annulus. On top of that, these structures contribute to the high level
of turbulence observed in the radial profiles 1 mm above the air pipe exit (Fig.
6.12). The separation-recirculation cycle coupled to these Rotating Vortex Cores
is thought to be similar to the flashback phenomenon observed experimentally in
the premixed configuration of the TECFLAM [44].
As described in Section 6.3.6, the presence of the rotating recirculations inside
the burner results in some of the fuel injected at the top of the bluff body being
sucked into the air pipe. This phenomenon has been captured by the POD and
is visible in Figs. 6.32 (c, f) through the plotting of isosurfaces of negative and
positive mixture fraction fluctuations. Here modes 1 and 2 are represented by
two pairs of 2 diametrically opposed structures along the inner walls, each pair
of structures representing respectively a mixture fraction increase or decrease in
the air annulus. Each of these structures is located between two Rotating Vortex
Cores. In addition, modes 1 and 2 are characterized by small pockets of high
mixture fraction fluctuations at radial positions corresponding to the fuel injection
inlet. These pockets are diametrically aligned with the larger structures and
represent mixture fraction fluctuations that are opposite to the fluctuations of the
larger structures in the air pipe. Therefore modes 1 and 2 analyzed through the
fluctuations of the mixture fraction represent the periodic increase and decrease
143
6. Investigation of the aerodynamics of a non-premixed swirl flame
of the mixture fraction inside the air pipe induced by the Rotating Vortex Cores.
The suction of the fuel towards the air pipe results in a decrease of the mixture
fraction at a location just above the fuel annulus exit and next to the vortex-
induced recirculation. The spacial shift between the vortical structures of mode
1 and mode 2 (Figs. 6.32 (a, b) and (d, e) respectively) and the mixing structures
(Figs. 6.32 (c) and (f) respectively) is due to the time-delay occuring between
the passage of a vortex and the displacement of the fuel mass resulting from it.
The interaction between the rotating vortices in the burner and the near-
burner mixing field is also represented in Figs. 6.35. In this set of figures, the
reconstruction at different instants of the inert flow based on modes 1 and 2 is
visualized through the Q−criterion (blue color). The red surfaces represent the
area where the mixture fraction has a value above 0.35. From this montage, it is
evident that the pair of vortices rotates around the burner. An area of fuel-rich
mixture is found to follow each vortex, as the fuel is sucked inside the air annulus
following the passage of a vortex core and its associated recirculation zone.
Mode 3 accounts for 8.46 % of the total energy. Fig. 6.33 represents the
Q−criterion applied to mode 3 velocity fluctuations. Its corresponding 2D vector
map at x = 100 mm has also been plotted. Mode 3 is characterized by two
long column-like counter-rotating vortices located parallel to the centreline of
the combustion chamber. The pressure isosurface of the instantaneous flow field
(Fig. 6.21(b)) shows that one of these vortices (on the left in Fig. 6.33) creates
a low-pressure column inside the flow and is associated with the CRZ created by
the Vortex Breakdown. The second vortex is found to be much weaker. There is
no frequency peak from the spectral analysis of the temporal coefficient a3(t) in
Fig. 6.34(a). In fact, a3(t) = 0 at anytime and the peak observed at 9.685 Hz is
an artefact corresponding to the time interval on which the inert 3D POD was
computed: DtI = 0.10325 ms). Modes 4 to 6 are more difficult to interpret, as
they do not contain a single type of structure or a single frequency peak and are
therefore not reported here.
Reactive case Analysis of Fig. 6.31(b) shows that the distribution of the en-
ergy for the reacting case is rather different from the inert case. Mode 1 accounts
for 8.12 % of the fluctuating energy and is by far the most energetic mode. It
144
6. Investigation of the aerodynamics of a non-premixed swirl flame
is represented in Fig. 6.36(a) by one negative and one positive isosurface of the
axial velocity fluctuations. It does not belong to a pair of modes and, unlike
most of the other modes, does not represent a vortex. It rather accounts for the
axial displacement of the CRZ and hence for a longitudinal motion of the flame.
Fourier analysis of its associated temporal coefficient in Fig. 6.34(b) shows two
small peaks at 28.64 Hz and 57.28 Hz, the sharpest peak at 9.547 Hz correspond-
ing again to the time interval on which the reactive 3D POD has been computed:
DtR = 0.10475 ms.
Reactive modes 2 and 3 respectively account for 4.48 % and 4.32 % of the
energy i.e. 8.8 % overall (Fig. 6.31(b)). They are represented in Fig. 6.37.
They form again a pair of modes and are similar to the 3D POD modes 1 and 2
from the inert flow, except that they contain only two counter-rotating vortices
(against four vortices counter-rotating two by two for modes 1 and 2 of the in-
ert flow). Their interpretation is identical to the ones previously made for the
inert case regarding both the Q−criterion (Figs. 6.32 (b, e)) and the mixture
fraction isosurfaces (Figs. 6.32 (c, f)) representations. Figs. 6.37 (a, d) repre-
sent respectively the Q−criterion applied to modes 2 and 3 and coloured by the
respective axial velocity fluctuations of each mode. Similarly, Figs. 6.37 (b, e)
represent respectively the Q−criterion applied to modes 2 and 3 and coloured by
the respective temperature fluctuations of each mode. These figures show that
the temperature tends to decrease inside the two vortices associated with a de-
crease of the axial velocity and vice versa. The spectra of the temporal modes
associated with the spatial modes 2 and 3 (Fig. 6.34(b)) show a clear peak at
343.7 Hz (St = fD/Ubulk = 0.448), associated with the rotation of the vortices
around the burner. Based on the shape of the vortices associated with the 3D
POD modes 2 and 3 of the reactive flow and their spectral analysis, we conclude
that their 2D counterparts correspond to the pair of modes 6 and 7 of the 2D
POD analysis.
Mode 4 (Fig. 6.36(b)) accounts for an axial displacement as mode 1. Modes
5 and 6 (Figs. 6.38) form again a pair of modes: they are similar to each other
and contribute to 5.84 % (2.94 %+2.90 %) of the energy (Fig. 6.31(b)). They
represent four counter-rotating vortices. Fourier analysis (Fig. 6.34(b)) shows
several peaks present in both modes at 572.8 Hz, 620.5 Hz, 668.3 Hz and 696.9 Hz,
145
6. Investigation of the aerodynamics of a non-premixed swirl flame
i.e. around the double frequency of the modes 2 and 3 (St = 2fD/Ubulk = 0.896).
This leads to the conclusion that the pair of modes 5 and 6 may be understood
as a harmonic of the pair of modes 2 and 3. Therefore the effect of the Rotating
Vortex Core in the reacting case would be represented by (at least) four modes
(modes 2, 3, 5 & 6), which account overall for 14.64 % of the total fluctuation
energy. Following that interpretation, modes 2, 3, 5 & 6 would describe the
dynamics (fundamental and first harmonic) of a single helical vortex core.
Because the spectra of modes 5 and 6 do not show a perfect harmonic of the
frequency associated with modes 2 and 3, another interpretation of these modes
could be that modes 2 and 3 account for a single helical vortex core that rotates
at 343.7 Hz, while modes 5 and 6 could account for a different double helical
vortex core similar to the one captured by modes 1 and 2 of the inert flow (Fig.
6.32). The fact that the number of vortices doubles from modes 2-3 to modes 5-6
could explain why the spectra of modes 5-6 roughly double compared to modes
2-3, leading to the (possibly wrong) interpretation that modes 5-6 are a harmonic
of modes 2-3.
6.3.7.3 Inert versus reactive rotating vortices
Figure 6.39(a) represents the Q−criterion from a snapshot of the inert flow recon-
structed using its 6 first POD modes and coloured by the reconstructed pressure.
Figure 6.39(b) shows a similar reconstruction for the reacting case but the isosur-
face has been coloured by the temperature. A first observation when comparing
the two figures is that the strong vortex observed inside the CRZ of the inert flow
(corresponding to the 3D POD mode 3 of the inert flow) is no longer present in
the reacting case. This is consistent with previous studies that have also reported
that the combustion tends to remove some flow structures, such as the PVC, es-
pecially in non-premixed configuration [112]. A second observation is that the
rolling vortices developed in the burner air annulus extend much further in the
reacting case than in the inert one. Figures 6.37, 6.38 & 6.39(b) show that the
vortex heads reach locations as far as 160 mm above the burner exit when the
flow is burning, compared to an axial expansion limited to a range of 30-40mm for
the inert case (Figs. 6.32 & 6.39(a)). This observation explains why oscillations
146
6. Investigation of the aerodynamics of a non-premixed swirl flame
are found in the autocorrelations further downstream in the reacting case than
in the inert case, as commented in Section 6.3.5.
6.4 Summary of main findings
LES with a pre-calculated flamelet model has been applied to simulate a non-
premixed swirl flame and its inert flow. The formulation is found to reproduce
the experimentally-observed vortex breakdown and the results agree well with
available experimental data for velocity and mixture fraction. Autocorrelation
and spectral analysis reveal the presence of a periodic component inside the air
inlet and around the central bluff body, for both the inert and reactive flows,
while the fundamental frequency of this periodic motion increases by a factor
of 1.6 in the reacting case. In order to investigate further the dynamics of the
flow, Proper Orthogonal Decomposition has been applied. The method shows
that large longitudinal vortices are formed along the air inlet inner wall, whose
axes rotate around the burner. These vortices become highly curved inside the
combustion chamber. They impose their dynamics to the flow in the combustion
chamber and create a cycle of separations and recirculations inside the air annulus,
which is thought to be similar to the flashback phenomenon observed in some
premixed swirl flames. The POD analysis reveals that the dynamics of these
Rotating Vortex Cores (RVC) is mainly represented by one pair of POD modes
in the inert case. The combustion process is found to trigger several other pairs
of modes, resulting in a more complex dynamics for the flow.
147
6. Investigation of the aerodynamics of a non-premixed swirl flame
(a) (b)
(c)
Figure 6.1: (a) Sketch of the TECFLAM burner. (b) Picture of the swirl flame
and its burner. (c) Dimensions of the TECFLAM burner. From Ref. [51].
148
6. Investigation of the aerodynamics of a non-premixed swirl flame
Figure 6.2: Mesh used for the LES computation of the TECFLAM.
149
6. Investigation of the aerodynamics of a non-premixed swirl flame
0 1 2 3 4 5
0
0.5
1
1.5
2
<
W
> 
/ U
ai
r
r / D
 
 
x = 0.0333 D
0D−CMC
EXP
Figure 6.3: Radial profile of the mean tangential velocity 1 mm above the burner
exit. Experimental data from Ref. [51].
0 50 100 150 2001700
1800
1900
2000
2100
2200
Scalar Dissipation rate N0 (1/s)
M
ax
im
um
 te
m
pe
ra
tu
re
 (K
)
 
 
ARM2
GRI3.0
(a)
0 0.25 0.5 0.75 1
500
1000
1500
2000
ξ
T 
(K
)
 
 
T
0
0.01
0.02
0.03
0.04
0.05
0.06
Y
102*YNO
YCO
10*YOH
(b)
Figure 6.4: (a) Tmax of the steady flame against the scalar dissipation rate N0. (b)
Distributions of some reactive scalars of the steady flame obtained for N0 = 20 1/s
with the ARM2 reduced chemistry mechanism.
150
6. Investigation of the aerodynamics of a non-premixed swirl flame
(a) Mean axial velocity (b) Mean mixture fraction
(c) Mean density (d) Mean temperature
Figure 6.5: Distributions of time-averaged quantities in the reacting flow. White
line: stoichiometric isoline; black line: zero-axial velocity isoline. Axes in m.
151
6. Investigation of the aerodynamics of a non-premixed swirl flame
(a) Mean radial velocity
(b) Mean tangential velocity
Figure 6.6: (a) Mean radial and (b) tangential velocity for the reacting flow.
White line: stoichiometric isoline; black line: zero-axial velocity isoline. Axes in
m.
152
6. Investigation of the aerodynamics of a non-premixed swirl flame
(a) (b)
(c) (d)
(e) Axial velocity (m/s) (f) Z−vorticity (m/s2)
Figure 6.7: Snapshots at three consecutive instants of (a,c,e) the axial velocity
and (b,d,f) the z−vorticity. White line: stoichiometric isoline; black line: zero-
axial velocity isoline. Axes in m.
153
6. Investigation of the aerodynamics of a non-premixed swirl flame
(a)
(b)
(c) Mixture fraction
Figure 6.8: Snapshots at three consecutive instants of the mixture fraction. White
line: stoichiometric isoline; black line: zero-axial velocity isoline. Axes in m.
154
6. Investigation of the aerodynamics of a non-premixed swirl flame
Figure 6.9: Zoom of the instantaneous axial velocity field inside the burner. White
line: stoichiometric isoline; black line: zero-axial velocity isoline
155
6. Investigation of the aerodynamics of a non-premixed swirl flame
0 1 2 3 4 5−1
−0.5
0
0.5
1
1.5
2
<
U>
 / 
U a
ir
r / D
 
 
x = 0.0333 D
0D−CMC
EXP
0 1 2 3 4 5−1
−0.5
0
0.5
1
1.5
2
<
U>
 / 
U a
ir
r / D
 
 
x = 0.333 D
0D−CMC
EXP
0 1 2 3 4 5−1
−0.5
0
0.5
1
1.5
2
<
U>
 / 
U a
ir
r / D
 
 
x = 0.667 D
0D−CMC
EXP
0 1 2 3 4 5−1
−0.5
0
0.5
1
1.5
2
<
U>
 / 
U a
ir
r / D
 
 
x = 1 D
0D−CMC
EXP
0 1 2 3 4 5−1
−0.5
0
0.5
1
1.5
2
<
U>
 / 
U a
ir
r / D
 
 
x = 2.33 D
0D−CMC
EXP
0 1 2 3 4 5−1
−0.5
0
0.5
1
1.5
2
<
U>
 / 
U a
ir
r / D
 
 
x = 3 D
0D−CMC
EXP
Figure 6.10: Radial profiles of the mean axial velocity at the indicated axial
position. Experimental data from Ref. [51].
156
6. Investigation of the aerodynamics of a non-premixed swirl flame
0 1 2 3 4 5
0
0.5
1
1.5
2
<
W
> 
/ U
ai
r
r / D
 
 
x = 0.0333 D
0D−CMC
EXP
0 1 2 3 4 5
0
0.5
1
1.5
2
<
W
> 
/ U
ai
r
r / D
 
 
x = 0.333 D
0D−CMC
EXP
0 1 2 3 4 5
0
0.5
1
1.5
2
<
W
> 
/ U
ai
r
r / D
 
 
x = 0.667 D
0D−CMC
EXP
0 1 2 3 4 5
0
0.5
1
1.5
2
<
W
> 
/ U
ai
r
r / D
 
 
x = 1 D
0D−CMC
EXP
0 1 2 3 4 5
0
0.5
1
1.5
2
<
W
> 
/ U
ai
r
r / D
 
 
x = 2.33 D
0D−CMC
EXP
0 1 2 3 4 5
0
0.5
1
1.5
2
<
W
> 
/ U
ai
r
r / D
 
 
x = 3 D
0D−CMC
EXP
Figure 6.11: Radial profiles of the mean tangential velocity at the indicated axial
position. Experimental data from Ref. [51].
157
6. Investigation of the aerodynamics of a non-premixed swirl flame
0 1 2 3 4 50
0.2
0.4
0.6
u
R
M
S 
/ U
ai
r
r / D
 
 
x = 0.0333 D
0D−CMC
EXP
0 1 2 3 4 50
0.2
0.4
0.6
u
R
M
S 
/ U
ai
r
r / D
 
 
x = 0.333 D
0D−CMC
EXP
0 1 2 3 4 50
0.2
0.4
0.6
u
R
M
S 
/ U
ai
r
r / D
 
 
x = 0.667 D
0D−CMC
EXP
0 1 2 3 4 50
0.2
0.4
0.6
u
R
M
S 
/ U
ai
r
r / D
 
 
x = 1 D
0D−CMC
EXP
0 1 2 3 4 50
0.2
0.4
0.6
u
R
M
S 
/ U
ai
r
r / D
 
 
x = 2.33 D
0D−CMC
EXP
0 1 2 3 4 50
0.2
0.4
0.6
u
R
M
S 
/ U
ai
r
r / D
 
 
x = 3 D
0D−CMC
EXP
Figure 6.12: Radial profiles of the RMS of the axial velocity at the indicated axial
position. Experimental data from Ref. [51].
158
6. Investigation of the aerodynamics of a non-premixed swirl flame
0 1 2 3 4 50
0.25
0.5
0.75
W
R
M
S 
/ U
ai
r
r / D
 
 
x = 0.0333 D
0D−CMC
EXP
0 1 2 3 4 50
0.25
0.5
0.75
W
R
M
S 
/ U
ai
r
r / D
 
 
x = 0.333 D
0D−CMC
EXP
0 1 2 3 4 50
0.25
0.5
0.75
W
R
M
S 
/ U
ai
r
r / D
 
 
x = 0.667 D
0D−CMC
EXP
0 1 2 3 4 50
0.25
0.5
0.75
W
R
M
S 
/ U
ai
r
r / D
 
 
x = 1 D
0D−CMC
EXP
0 1 2 3 4 50
0.25
0.5
0.75
W
R
M
S 
/ U
ai
r
r / D
 
 
x = 2.33 D
0D−CMC
EXP
0 1 2 3 4 50
0.25
0.5
0.75
W
R
M
S 
/ U
ai
r
r / D
 
 
x = 3 D
0D−CMC
EXP
Figure 6.13: Radial profiles of the RMS of the tangential velocity at the indicated
axial position. Experimental data from Ref. [51].
159
6. Investigation of the aerodynamics of a non-premixed swirl flame
0 1 2 3 4 50
0.25
0.5
0.75
1
<
ξ>
r / D
 
 
x = 0.333 D
0D−CMC
EXP
0 1 2 3 4 50
0.25
0.5
0.75
1
<
ξ>
r / D
 
 
x = 0.667 D
0D−CMC
EXP
0 1 2 3 4 50
0.25
0.5
0.75
1
<
ξ>
r / D
 
 
x = 1.33 D
0D−CMC
EXP
0 1 2 3 4 50
0.25
0.5
0.75
1
<
ξ>
r / D
 
 
x = 2 D
0D−CMC
EXP
0 1 2 3 4 50
0.25
0.5
0.75
1
<
ξ>
r / D
 
 
x = 3 D
0D−CMC
EXP
0 1 2 3 4 50
0.25
0.5
0.75
1
<
ξ>
r / D
 
 
x = 4 D
0D−CMC
EXP
Figure 6.14: Radial profiles of the mean mixture fraction at the indicated axial
position. Experimental data from Ref. [51].
160
6. Investigation of the aerodynamics of a non-premixed swirl flame
0 1 2 3 4 50
0.2
0.4
0.6
ξ R
M
S
r / D
 
 
x = 0.333 D
0D−CMC
EXP
0 1 2 3 4 50
0.2
0.4
0.6
ξ R
M
S
r / D
 
 
x = 0.667 D
0D−CMC
EXP
0 1 2 3 4 50
0.2
0.4
0.6
ξ R
M
S
r / D
 
 
x = 1.33 D
0D−CMC
EXP
0 1 2 3 4 50
0.2
0.4
0.6
ξ R
M
S
r / D
 
 
x = 2 D
0D−CMC
EXP
0 1 2 3 4 50
0.2
0.4
0.6
ξ R
M
S
r / D
 
 
x = 3 D
0D−CMC
EXP
0 1 2 3 4 50
0.2
0.4
0.6
ξ R
M
S
r / D
 
 
x = 4 D
0D−CMC
EXP
Figure 6.15: Radial profiles of the RMS of the mixture fraction at the indicated
axial position. Experimental data from Ref. [51].
161
6. Investigation of the aerodynamics of a non-premixed swirl flame
(a) Axial velocity (b) Pressure
(c) Mixture fraction
Figure 6.16: Inert flow. Snapshots of the (a) axial velocity, (b) pressure, and (c)
mixture fraction. White line: stoichiometric isoline; black line: zero-axial velocity
isoline. Axes in m.
162
6. Investigation of the aerodynamics of a non-premixed swirl flame
0 0.005 0.01 0.015 0.02 0.025
0
0.5
1
ρ u
u
,t
τ (s)
x/D=0.167
 
 
y/D= −1.667
y/D= −0.75
y/D=0
y/D=0.75
y/D= 1.667
(a)
0 0.005 0.01 0.015 0.02 0.025
−0.2
0
0.2
0.4
0.6
0.8
1
ρ u
u
,t
τ (s)
x/D=0.167
 
 
y/D= −1.667
y/D= −0.75
y/D=0
y/D=0.75
y/D= 1.667
(b)
0 0.005 0.01 0.015 0.02 0.025
0
0.5
1
ρ u
u
,t
τ (s)
x/Dj=0.833
 
 
y/Dj= −0.75
y/Dj=0
y/Dj=0.75
(c)
0 0.005 0.01 0.015 0.02 0.025
−0.2
0
0.2
0.4
0.6
0.8
1
ρ u
u
,t
τ (s)
x/Dj=0.833
 
 
y/Dj= −0.75
y/Dj=0
y/Dj=0.75
(d)
0 0.005 0.01 0.015 0.02 0.025
0
0.5
1
ρ u
u
,t
τ (s)
x/Dj=1.67
 
 
y/Dj= −0.75
y/Dj=0
y/Dj=0.75
(e)
0 0.005 0.01 0.015 0.02 0.025
−0.2
0
0.2
0.4
0.6
0.8
1
ρ u
u
,t
τ (s)
x/Dj=1.67
 
 
y/Dj= −0.75
y/Dj=0
y/Dj=0.75
(f)
Figure 6.17: (a, b) Temporal autocorrelations at the indicated axial and radial
positions. Left/Right: inert/reacting cases.
163
6. Investigation of the aerodynamics of a non-premixed swirl flame
0 0.005 0.01 0.015 0.02 0.025
−0.2
0
0.2
0.4
0.6
0.8
1
ρ u
u
,t
τ (s)
x/Dj=2.5
 
 
y/Dj= −1.667
y/Dj=1.667
(a)
0 0.005 0.01 0.015 0.02 0.025
−0.2
0
0.2
0.4
0.6
0.8
1
ρ u
u
,t
τ (s)
x/Dj=2.5
 
 
y/Dj= −1.667
y/Dj=1.667
(b)
0 0.005 0.01 0.015 0.02 0.025
−0.2
0
0.2
0.4
0.6
0.8
1
ρ u
u
,t
τ (s)
x/Dj=3.33
 
 
y/Dj= −0.75
y/Dj=0
y/Dj=0.75
(c)
0 0.005 0.01 0.015 0.02 0.025
−0.2
0
0.2
0.4
0.6
0.8
1
ρ u
u
,t
τ (s)
x/Dj=3.33
 
 
y/Dj= −0.75
y/Dj=0
y/Dj=0.75
(d)
0 0.005 0.01 0.015 0.02 0.025
−0.2
0
0.2
0.4
0.6
0.8
1
ρ u
u
,t
τ (s)
x/Dj=5
 
 
y/Dj= −1.667
y/Dj= −0.75
y/Dj=0
y/Dj=0.75
y/Dj= 1.667
(e)
0 0.005 0.01 0.015 0.02 0.025
−0.2
0
0.2
0.4
0.6
0.8
1
ρ u
u
,t
τ (s)
x/Dj=5
 
 
y/Dj= −1.667
y/Dj= −0.75
y/Dj=0
y/Dj=0.75
y/Dj= 1.667
(f)
0 0.005 0.01 0.015 0.02 0.025
−0.2
0
0.2
0.4
0.6
0.8
1
ρ u
u
,t
τ (s)
x/Dj=6.67
 
 
y/Dj=0
(g)
0 0.005 0.01 0.015 0.02 0.025
−0.2
0
0.2
0.4
0.6
0.8
1
ρ u
u
,t
τ (s)
x/Dj=6.67
 
 
y/Dj=0
(h)
Figure 6.18: (a, b) Temporal autocorrelations at the indicated axial and radial
positions. Left/Right: inert/reacting cases.
164
6. Investigation of the aerodynamics of a non-premixed swirl flame
(a) (b)
0 500 1000 15000
1
2
3
4
5
6
Frequency (Hz)
PS
D/
(U
b.
D
)
x/D=0.167
 
 
y/D=−0.75
y/D=0.75
(c)
0 500 1000 15000
0.1
0.2
0.3
0.4
Frequency (Hz)
PS
D/
(U
b.
D
)
x/D=0.167
 
 
y/D=−0.75
y/D=0.75
(d)
Figure 6.19: (a, b) Spectra of the axial velocity inside the air pipe at x = −25 mm
& r = 22.5 mm (r = 0.75 D). (c, d) Spectra of the axial velocity at two positions
above the air pipe exit with x = 5 mm & r = 22.5 mm (r = 0.75 D). Left/Right:
inert/reacting cases.
165
6. Investigation of the aerodynamics of a non-premixed swirl flame
101 102 103 104
100
1010
Frequency (Hz)
PS
D/
(U
b.
D
)
y/Dj=0.0
−5/3
x/Dj=0.167
x/Dj=0.833
x/Dj=1.667
x/Dj=3.333
x/Dj=5
x/Dj=6.667
(a)
101 102 103 104
100
1010
Frequency (Hz)
PS
D/
(U
b.
D
)
y/Dj=0.0
−5/3
x/Dj=0.167
x/Dj=0.833
x/Dj=1.667
x/Dj=3.333
x/Dj=5
x/Dj=6.667
(b)
101 102 103 104
100
105
1010
Frequency (Hz)
PS
D/
(U
b.
D
)
y/Dj=−0.75
x/Dj=0.833
x/Dj=1.667
x/Dj=3.333
−5/3
x/Dj=5
x/Dj=0.167
(c)
101 102 103 104
100
105
1010
Frequency (Hz)
PS
D/
(U
b.
D
)
y/Dj=−0.75
x/Dj=0.833
x/Dj=1.667
x/Dj=3.333
−5/3
x/Dj=5
x/Dj=0.167
(d)
Figure 6.20: Log-log spectra of the axial velocity at the indicated positions. The
top row corresponds to positions along the centreline and the bottom row cor-
responds to positions along the line r = 0.75 Dj. Left/Right: inert/reacting
cases.
166
6. Investigation of the aerodynamics of a non-premixed swirl flame
(a)
(b)
Figure 6.21: Inert flow. (a) Several instantaneous iso-surfaces of low pressure
(P −P0 = −450 Pa) over one period of rotation. Visualization of the isothermal
structures around the burner. (b) Instantaneous iso-surfaces of two different low
pressure values (blue color: P−P0 = −250 Pa; green color: P−P0 = −150 Pa) to
visualize the isothermal structures around the burner and inside the combustion
chamber. Axes in m.
167
6. Investigation of the aerodynamics of a non-premixed swirl flame
0 5 10 150
5
10
15
Mode
%
 E
ne
rg
y 
ca
pt
ur
ed
(a)
0 5 10 150
2
4
6
8
Mode
%
 E
ne
rg
y 
ca
pt
ur
ed
(b)
200 220 240 260 280
−1
0
1
2x 10
4
Snapshot
a 1
(t)
, a
2(t
)
 
 
a1
a2
(c)
200 220 240 260 280−1
−0.5
0
0.5
1
x 104
Snapshot
a 1
(t)
, a
2(t
)
 
 
a1
a2
(d)
Figure 6.22: 2D POD analysis from the plane x = 5 mm. (a, b) Contribution to
the fluctuation energy for each mode. (c, d). POD time coefficients (temporal
modes) of the first two spatial modes. Left/right: inert/reacting case.
168
6. Investigation of the aerodynamics of a non-premixed swirl flame
−0.02 0 0.02
−0.02
0
0.02
(a) Mode 1, V
−0.02 0 0.02
−0.02
0
0.02
(b) Mode 2, V
−0.02 0 0.02
−0.02
0
0.02
(c) Mode 3, V
−0.02 0 0.02
−0.02
0
0.02
(d) Mode 4, V
−0.02 0 0.02
−0.02
0
0.02
(e) Mode 1, V
−0.02 0 0.02
−0.02
0
0.02
(f) Mode 2, V
−0.02 0 0.02
−0.02
0
0.02
(g) Mode 3, V
−0.02 0 0.02
−0.02
0
0.02
(h) Mode 4, V
−0.02 0 0.02
−0.02
0
0.02
(i) Mode 1, P
−0.02 0 0.02
−0.02
0
0.02
(j) Mode 2, P
−0.02 0 0.02
−0.02
0
0.02
(k) Mode 3, P
−0.02 0 0.02
−0.02
0
0.02
(l) Mode 4, P
−0.02 0 0.02
−0.02
0
0.02
(m) Mode 1, ξ
−0.02 0 0.02
−0.02
0
0.02
(n) Mode 2, ξ
−0.02 0 0.02
−0.02
0
0.02
(o) Mode 3, ξ
−0.02 0 0.02
−0.02
0
0.02
(p) Mode 4, ξ
0 1000 20000
2
4x 10
6
f (Hz)
PS
D
(q) Mode 1, spec-
trum
0 1000 20000
2
4x 10
6
f (Hz)
PS
D
(r) Mode 2, spectrum
0 1000 20000
5
10x 10
5
f (Hz)
PS
D
(s) Mode 3, spectrum
0 1000 20000
1
2x 10
5
f (Hz)
PS
D
(t) Mode 4, spectrum
Figure 6.23: Inert flow. 2D POD modes 1-4 at x = 5 mm. The spectra refer to
the Fourier analysis of the temporal coefficient associated with each mode.
169
6. Investigation of the aerodynamics of a non-premixed swirl flame
−0.02 0 0.02
−0.02
0
0.02
(a) Mode 5, V
−0.02 0 0.02
−0.02
0
0.02
(b) Mode 6, V
−0.02 0 0.02
−0.02
0
0.02
(c) Mode 7, V
−0.02 0 0.02
−0.02
0
0.02
(d) Mode 8, V
−0.02 0 0.02
−0.02
0
0.02
(e) Mode 5, V
−0.02 0 0.02
−0.02
0
0.02
(f) Mode 6, V
−0.02 0 0.02
−0.02
0
0.02
(g) Mode 7, V
−0.02 0 0.02
−0.02
0
0.02
(h) Mode 8, V
−0.02 0 0.02
−0.02
0
0.02
(i) Mode 5, P
−0.02 0 0.02
−0.02
0
0.02
(j) Mode 6, P
−0.02 0 0.02
−0.02
0
0.02
(k) Mode 7, P
−0.02 0 0.02
−0.02
0
0.02
(l) Mode 8, P
−0.02 0 0.02
−0.02
0
0.02
(m) Mode 5, ξ
−0.02 0 0.02
−0.02
0
0.02
(n) Mode 6, ξ
−0.02 0 0.02
−0.02
0
0.02
(o) Mode 7, ξ
−0.02 0 0.02
−0.02
0
0.02
(p) Mode 8, ξ
0 1000 20000
1
2x 10
5
f (Hz)
PS
D
(q) Mode 5, spec-
trum
0 1000 20000
5
10x 10
4
f (Hz)
PS
D
(r) Mode 6, spectrum
0 1000 20000
5
10x 10
4
f (Hz)
PS
D
(s) Mode 7, spectrum
0 1000 20000
5
10x 10
4
f (Hz)
PS
D
(t) Mode 8, spectrum
Figure 6.24: Inert flow. 2D POD modes 5-8 at x = 5 mm. The spectra refer to
the Fourier analysis of the temporal coefficient associated with each mode.
170
6. Investigation of the aerodynamics of a non-premixed swirl flame
−0.02 0 0.02
−0.02
0
0.02
(a) Mode 9, V
−0.02 0 0.02
−0.02
0
0.02
(b) Mode 10, V
−0.02 0 0.02
−0.02
0
0.02
(c) Mode 11, V
−0.02 0 0.02
−0.02
0
0.02
(d) Mode 12, V
−0.02 0 0.02
−0.02
0
0.02
(e) Mode 9, V
−0.02 0 0.02
−0.02
0
0.02
(f) Mode 10, V
−0.02 0 0.02
−0.02
0
0.02
(g) Mode 11, V
−0.02 0 0.02
−0.02
0
0.02
(h) Mode 12, V
−0.02 0 0.02
−0.02
0
0.02
(i) Mode 9, P
−0.02 0 0.02
−0.02
0
0.02
(j) Mode 10, P
−0.02 0 0.02
−0.02
0
0.02
(k) Mode 11, P
−0.02 0 0.02
−0.02
0
0.02
(l) Mode 12, P
−0.02 0 0.02
−0.02
0
0.02
(m) Mode 9, ξ
−0.02 0 0.02
−0.02
0
0.02
(n) Mode 10, ξ
−0.02 0 0.02
−0.02
0
0.02
(o) Mode 11, ξ
−0.02 0 0.02
−0.02
0
0.02
(p) Mode 12, ξ
0 1000 20000
2
4x 10
4
f (Hz)
PS
D
(q) Mode 9, spec-
trum
0 1000 20000
2
4x 10
4
f (Hz)
PS
D
(r) Mode 10, spec-
trum
0 1000 20000
2
4x 10
4
f (Hz)
PS
D
(s) Mode 11, spec-
trum
0 1000 20000
2
4x 10
4
f (Hz)
PS
D
(t) Mode 12, spec-
trum
Figure 6.25: Inert flow. 2D POD modes 9-12 at x = 5 mm. The spectra refer to
the Fourier analysis of the temporal coefficient associated with each mode.
171
6. Investigation of the aerodynamics of a non-premixed swirl flame
−0.02 0 0.02
−0.02
0
0.02
(a) Mode 13, V
−0.02 0 0.02
−0.02
0
0.02
(b) Mode 14, V
−0.02 0 0.02
−0.02
0
0.02
(c) Mode 15, V
−0.02 0 0.02
−0.02
0
0.02
(d) Mode 13, V
−0.02 0 0.02
−0.02
0
0.02
(e) Mode 14, V
−0.02 0 0.02
−0.02
0
0.02
(f) Mode 15, V
−0.02 0 0.02
−0.02
0
0.02
(g) Mode 13, P
−0.02 0 0.02
−0.02
0
0.02
(h) Mode 14, P
−0.02 0 0.02
−0.02
0
0.02
(i) Mode 15, P
−0.02 0 0.02
−0.02
0
0.02
(j) Mode 13, ξ
−0.02 0 0.02
−0.02
0
0.02
(k) Mode 14, ξ
−0.02 0 0.02
−0.02
0
0.02
(l) Mode 15, ξ
0 1000 20000
1
2x 10
4
f (Hz)
PS
D
(m) Mode 13, spec-
trum
0 1000 20000
2
4x 10
4
f (Hz)
PS
D
(n) Mode 14, spec-
trum
0 1000 20000
1
2x 10
4
f (Hz)
PS
D
(o) Mode 15, spec-
trum
Figure 6.26: Inert flow. 2D POD modes 13-15 at x = 5 mm. The spectra refer
to the Fourier analysis of the temporal coefficient associated with each mode.
172
6. Investigation of the aerodynamics of a non-premixed swirl flame
−0.02 0 0.02
−0.02
0
0.02
(a) Mode 1, V
−0.02 0 0.02
−0.02
0
0.02
(b) Mode 2, V
−0.02 0 0.02
−0.02
0
0.02
(c) Mode 3, V
−0.02 0 0.02
−0.02
0
0.02
(d) Mode 4, V
−0.02 0 0.02
−0.02
0
0.02
(e) Mode 1, V
−0.02 0 0.02
−0.02
0
0.02
(f) Mode 2, V
−0.02 0 0.02
−0.02
0
0.02
(g) Mode 3, V
−0.02 0 0.02
−0.02
0
0.02
(h) Mode 4, V
−0.02 0 0.02
−0.02
0
0.02
(i) Mode 1, T
−0.02 0 0.02
−0.02
0
0.02
(j) Mode 2, T
−0.02 0 0.02
−0.02
0
0.02
(k) Mode 3, T
−0.02 0 0.02
−0.02
0
0.02
(l) Mode 4, T
−0.02 0 0.02
−0.02
0
0.02
(m) Mode 1, ξ
−0.02 0 0.02
−0.02
0
0.02
(n) Mode 2, ξ
−0.02 0 0.02
−0.02
0
0.02
(o) Mode 3, ξ
−0.02 0 0.02
−0.02
0
0.02
(p) Mode 4, ξ
0 1000 20000
2
4x 10
5
f (Hz)
PS
D
(q) Mode 1, spec-
trum
0 1000 20000
1
2x 10
5
f (Hz)
PS
D
(r) Mode 2, spectrum
0 1000 20000
2
4x 10
5
f (Hz)
PS
D
(s) Mode 3, spectrum
0 1000 20000
1
2x 10
5
f (Hz)
PS
D
(t) Mode 4, spectrum
Figure 6.27: Reacting flow. 2D POD modes 1-4 at x = 5 mm. The spectra refer
to the Fourier analysis of the temporal coefficient associated with each mode.
173
6. Investigation of the aerodynamics of a non-premixed swirl flame
−0.02 0 0.02
−0.02
0
0.02
(a) Mode 5, V
−0.02 0 0.02
−0.02
0
0.02
(b) Mode 6, V
−0.02 0 0.02
−0.02
0
0.02
(c) Mode 7, V
−0.02 0 0.02
−0.02
0
0.02
(d) Mode 8, V
−0.02 0 0.02
−0.02
0
0.02
(e) Mode 5, V
−0.02 0 0.02
−0.02
0
0.02
(f) Mode 6, V
−0.02 0 0.02
−0.02
0
0.02
(g) Mode 7, V
−0.02 0 0.02
−0.02
0
0.02
(h) Mode 8, V
−0.02 0 0.02
−0.02
0
0.02
(i) Mode 5, T
−0.02 0 0.02
−0.02
0
0.02
(j) Mode 6, T
−0.02 0 0.02
−0.02
0
0.02
(k) Mode 7, T
−0.02 0 0.02
−0.02
0
0.02
(l) Mode 8, T
−0.02 0 0.02
−0.02
0
0.02
(m) Mode 5, ξ
−0.02 0 0.02
−0.02
0
0.02
(n) Mode 6, ξ
−0.02 0 0.02
−0.02
0
0.02
(o) Mode 7, ξ
−0.02 0 0.02
−0.02
0
0.02
(p) Mode 8, ξ
0 1000 20000
2
4x 10
5
f (Hz)
PS
D
(q) Mode 5, spec-
trum
0 1000 20000
5
10x 10
5
f (Hz)
PS
D
(r) Mode 6, spectrum
0 1000 20000
5
10x 10
5
f (Hz)
PS
D
(s) Mode 7, spectrum
0 1000 20000
5
10x 10
4
f (Hz)
PS
D
(t) Mode 8, spectrum
Figure 6.28: Reacting flow. 2D POD modes 5-8 at x = 5 mm. The spectra refer
to the Fourier analysis of the temporal coefficient associated with each mode.
174
6. Investigation of the aerodynamics of a non-premixed swirl flame
−0.02 0 0.02
−0.02
0
0.02
(a) Mode 9, V
−0.02 0 0.02
−0.02
0
0.02
(b) Mode 10, V
−0.02 0 0.02
−0.02
0
0.02
(c) Mode 11, V
−0.02 0 0.02
−0.02
0
0.02
(d) Mode 12, V
−0.02 0 0.02
−0.02
0
0.02
(e) Mode 9, V
−0.02 0 0.02
−0.02
0
0.02
(f) Mode 10, V
−0.02 0 0.02
−0.02
0
0.02
(g) Mode 11, V
−0.02 0 0.02
−0.02
0
0.02
(h) Mode 12, V
−0.02 0 0.02
−0.02
0
0.02
(i) Mode 9, T
−0.02 0 0.02
−0.02
0
0.02
(j) Mode 10, T
−0.02 0 0.02
−0.02
0
0.02
(k) Mode 11, T
−0.02 0 0.02
−0.02
0
0.02
(l) Mode 12, T
−0.02 0 0.02
−0.02
0
0.02
(m) Mode 9, ξ
−0.02 0 0.02
−0.02
0
0.02
(n) Mode 10, ξ
−0.02 0 0.02
−0.02
0
0.02
(o) Mode 11, ξ
−0.02 0 0.02
−0.02
0
0.02
(p) Mode 12, ξ
0 1000 20000
5
10x 10
4
f (Hz)
PS
D
(q) Mode 9, spec-
trum
0 1000 20000
5
10x 10
4
f (Hz)
PS
D
(r) Mode 10, spec-
trum
0 1000 20000
2
4x 10
4
f (Hz)
PS
D
(s) Mode 11, spec-
trum
0 1000 20000
2
4x 10
4
f (Hz)
PS
D
(t) Mode 12, spec-
trum
Figure 6.29: Reacting flow. 2D POD modes 9-12 at x = 5 mm. The spectra refer
to the Fourier analysis of the temporal coefficient associated with each mode.
175
6. Investigation of the aerodynamics of a non-premixed swirl flame
−0.02 0 0.02
−0.02
0
0.02
(a) Mode 13, V
−0.02 0 0.02
−0.02
0
0.02
(b) Mode 14, V
−0.02 0 0.02
−0.02
0
0.02
(c) Mode 15, V
−0.02 0 0.02
−0.02
0
0.02
(d) Mode 13, V
−0.02 0 0.02
−0.02
0
0.02
(e) Mode 14, V
−0.02 0 0.02
−0.02
0
0.02
(f) Mode 15, V
−0.02 0 0.02
−0.02
0
0.02
(g) Mode 13, T
−0.02 0 0.02
−0.02
0
0.02
(h) Mode 14, T
−0.02 0 0.02
−0.02
0
0.02
(i) Mode 15, T
−0.02 0 0.02
−0.02
0
0.02
(j) Mode 13, ξ
−0.02 0 0.02
−0.02
0
0.02
(k) Mode 14, ξ
−0.02 0 0.02
−0.02
0
0.02
(l) Mode 15, ξ
0 1000 20000
1
2x 10
5
f (Hz)
PS
D
(m) Mode 13, spec-
trum
0 1000 20000
2
4x 10
4
f (Hz)
PS
D
(n) Mode 14, spec-
trum
0 1000 20000
2
4x 10
4
f (Hz)
PS
D
(o) Mode 15, spec-
trum
Figure 6.30: Reacting flow. 2D POD modes 13-15 at x = 5 mm. The spectra refer
to the Fourier analysis of the temporal coefficient associated with each mode.
176
6. Investigation of the aerodynamics of a non-premixed swirl flame
0 5 100
2
4
6
8
10
Mode number
%
 E
ne
rg
y 
ca
pt
ur
ed
(a)
1 2 3 4 5 6 7 8 9 100
2
4
6
8
Mode number
%
 E
ne
rg
y 
ca
pt
ur
ed
(b)
Figure 6.31: 3D POD analysis. Contribution to the total fluctuation energy of
each mode: (a) inert case; (b) reacting case.
177
6. Investigation of the aerodynamics of a non-premixed swirl flame
(a) Mode 1, U (b) Mode 1, Q (c) Mode 1, ξ
(d) Mode 2, U (e) Mode 2, Q (f) Mode 2, ξ
Figure 6.32: Inert flow. 3D POD mode 1 (a, b, c) and mode 2 (d, e, f). (a, d)
Isosurfaces of the axial velocity fluctuations with the vectop map at x = 5 mm
superimposed. (b, e, g) Q−criterion coloured by the axial velocity fluctuations.
(c, f) Isosurfaces of the mixture fraction fluctuations. The negative fluctuations
are plotted in blue, the positive ones in red.
178
6. Investigation of the aerodynamics of a non-premixed swirl flame
Figure 6.33: Inert flow. 3D POD mode 3 visualized using the Q-criterion coloured
by the axial velocity fluctuations. The negative fluctuations are plotted in blue,
the positive ones in red.
179
6. Investigation of the aerodynamics of a non-premixed swirl flame
0 500 10000
1
2
x 107
0 500 10000
1
2
x 107
PS
D/
(U
.D
)
0 500 10000
5
10
x 106
f (Hz)
Inert
mode 1
Inert
mode 2
Inert
mode 3
(a)
0 500 10000
1
2x 10
7
0 500 10000
2
4
x 107
0 500 10000
5x 10
7
PS
D/
(U
.D
)
0 500 10000
5
x 106
0 500 10000
5
x 106
f (Hz) 0 500 1000
0
5
x 106
f (Hz)
Reactive
mode 1
Reactive
mode 2
Reactive
mode 3
Reactive
mode 4
Reactive
mode 5
Reactive
mode 6
(b)
Figure 6.34: 3D POD analysis. Spectral analysis of the POD temporal coefficients
ai(t): (a) inert case; (b) reacting case.
180
6. Investigation of the aerodynamics of a non-premixed swirl flame
Figure 6.35: Inert flow. Reconstruction of several snasphots over one period of
rotation based on the 3D POD modes 1 and 2. Visualization of (a) Q-criterion
isosurfaces (blue color) and (b) mixture fraction contours (red color, correspond-
ing to areas where ξ ≥ 0.35 ), applied to the instantaneous reconstructed flow
fields.
181
6. Investigation of the aerodynamics of a non-premixed swirl flame
(a) Mode 1, U
(b) Mode 4, U
Figure 6.36: Reactive flow. 3D POD (a) mode 1 and (b) mode 4. Negative (blue)
and positive (red) isosurfaces of axial velocity fluctuations. View from above the
burner exit.
182
6. Investigation of the aerodynamics of a non-premixed swirl flame
(a) Mode 2, Q-U (b) Mode 2, Q-T (c) Mode 2, ξ
(d) Mode 3, Q-U (e) Mode 3, Q-T (f) Mode 3, ξ
Figure 6.37: Reactive POD mode 2 (a, b, c) and mode 3 (d, e, f). (a, d)
Q−criterion applied to the corresponding mode coloured by the axial velocity
fluctuations. (b, e) Q−criterion coloured by the temperature fluctuations. (c,
f) Isosurfaces of the mixture fraction fluctuations. The negative fluctuations are
plotted in blue, the positive ones in red.
183
6. Investigation of the aerodynamics of a non-premixed swirl flame
(a) Mode 5, Q-U (b) Mode 5, Q-T (c) Mode 5, ξ
(d) Mode 6, Q-U (e) Mode 6, Q-T (f) Mode 6, ξ
Figure 6.38: Reactive POD mode 5 (a, b, c) and mode 6 (d, e, f). (a, d)
Q−criterion coloured by the axial velocity fluctuations. (b, e) Q−criterion
coloured by the temperature fluctuations. (c, f) Isosurfaces of the mixture frac-
tion fluctuations. The negative fluctuations are plotted in blue, the positive ones
in red.
184
6. Investigation of the aerodynamics of a non-premixed swirl flame
(a)
(b)
Figure 6.39: Visualization of the vortex core using the Q−criterion applied to
a reconstructed snapshot based on modes 1 to 6, coloured by the reconstructed
pressure for the inert case (a) and the temperature for the reacting case (b).
185
Chapter 7
Conditional Moment
Closure/Large Eddy Simulation
of a lifted non-premixed swirl
flame
7.1 Introduction
The confined turbulent swirling non-premixed TECFLAM S09c flame is now in-
vestigated using Large Eddy Simulation coupled to the full equations of the Con-
ditional Moment Closure model. The previous chapter has shown that the fluid
mechanics of the flame can be succesfully predicted by using a LES-flamelet for-
mulation as long as an appropriate mesh is used and that the right boundary
conditions are applied at the numerical inlet (located inside the burner). In Ref.
[51], instantaneous chemiluminescence emissions of the flame has been reported
and an example is reproduced in Fig. 7.1. The image reveals the area where
flame reactions and heat release take place. From the picture, it is evident that
the flame is not attached to the nozzle. A lift-off height of 20-30 mm has been re-
ported in Ref. [51]. While the LES-flamelet formulation has ineluctably predicted
an attached flame, the CMC model has the capacity to extinguish the CMC cells
in which the computational domain has been divided, as it was demonstrated in
186
7. CMC/LES of a lifted non-premixed swirl flame
Figure 7.1: Chemiluminescence emission from the TECFLAM flame. From Ref.
[51]
Chapter 5. The CMC model coupled to LES and its ability to track the vari-
ations of the local scalar dissipation rate had computed strong fluctuations in
the reactive scalars distributions against mixture fraction, leading occasionally to
the prediction of localized extinctions. Provided that the right boundary condi-
tions are used for the CMC equations, the LES-CMC formulation has therefore,
in principle, the ability to reproduce the lift-off observed experimentally in the
non-premixed TECFLAM. This is explored in this chapter.
7.2 Method
7.2.1 Models and codes
A first order LES-CMC formulation has been used for this simulation. The codes
and models used are fully described in Chapter 3. As for the LES/0D-CMC of
the TECFLAM presented in Chapter 6, the CMC equations are computed using
187
7. CMC/LES of a lifted non-premixed swirl flame
Figure 7.2: CMC grid superimposed on the instantanous OH mass fraction. Each
CMC cell has its center located at an intersection of the black dashed lines.
Points 1-4 are at locations (x, r)=(0.13D,0.83D), (0.13D,0.67D), (0.35D,0.67D),
(0.35D,0.83D) respectively (in mm, with D = 30 mm); r is the distance from the
centreline and x the axial distance from the bluff body.
the reduced chemistry mechanism ARM2.
7.2.2 Boundary conditions and numerical methods
This new large eddy simulation has been performed on the same grid as the one
presented in Chapter 6 for the flamelet model (Fig. 6.2). The LES grid contains
7.8M cells. In this simulation, the CMC equations are solved at each LES iteration
on a structured grid of 25× 25× 30 = 18750 cells, with 30 cells being used in the
axial direction. The CMC grid is shown in Fig. 7.2. From the figure, it is obvious
that the CMC cells are clustered around the burner exit in an attempt to follow
the dynamics of the air and fuel streams interaction. The inlet for the CMC grid
188
7. CMC/LES of a lifted non-premixed swirl flame
is located at the exit of the burner (x = 0 mm). Inert (i.e. unburnt) distributions
of Qα are injected at the top of the burner for all CMC cells located at a radius
smaller than the outer radius of the air pipe (r < 30 mm). This corresponds to
an area comprising the air and fuel pipes exit plus the top of bluff body. Putting
“frozen” Qα along the top surface of the bluff body mimics flame quenching there.
Zero gradients in physical space of all conditional averages have been imposed
elsewhere on the edges of the CMC grid. The initial condition for this new LES
simulation is the solution computed with the LES/0D-CMC formulation. For the
CMC equations, the initial solution used is the burning “flamelet” obtained for
N0 = 20 1/s and presented in the previous Chapter (Fig. 6.4(b)).
The time-step used was still 5.0×10−6 s, which ensures a maximum CFL num-
ber varying around 0.35 during the whole simulation and a stable computation.
The simulations were carried out on 24 quad-core processors at 2.53 GHz with 24
GB of RAM per core, producing 1.0 ms of simulated time in approximately 252
min. Hence solving the CMC equations at each LES iteration increases the com-
putation time by a factor of 2.7 as compared to the LES-flamelet computation.
7.3 Results and Discussion
7.3.1 Instantaneous distributions
The flow and mixing fields experience changes when the CMC equations are
solved. The CRZ predicted by the LES/3D-CMC formulation (Figs. 7.3(a) and
7.3(b)) is larger than its 0D-CMC counterpart (Fig. 6.7 of Chapter 6). The CRZ
occupies most of the space on the top of the bluff body, resulting in even larger
and deeper recirculations inside the air pipe than the ones reported in Chapter
6. As a result, even more fuel enters into the air pipe (see the instantaneous
mixture fraction field in Fig. 7.3(c)) and the stoichiometric mixture fraction
isoline is found to enter deeper inside the air pipe (Fig. 7.3(b)). The larger CRZ
results in the main jet expanding more radially. The shape of the stoichiometric
mixture fraction isosurface is also modified. The fuel rich zone of the flame has
shrunk to a narrower space located around the fuel jet exit. The fact that the fuel
jet is more strongly deflected towards the combustion chamber walls leads to a
189
7. CMC/LES of a lifted non-premixed swirl flame
(a) Axial velocity (b) Axial velocity (zoom)
(c) Mixture fraction (d) Temperature (K)
Figure 7.3: Typical instantaneous contours of (a, b) the axial velocity, (c) the
mixture fraction and (d) the temperature taken at the same instant. The white
line represents the stoichiometric iso-surface.
190
7. CMC/LES of a lifted non-premixed swirl flame
quicker mixing between the fuel and air jets in the shear layers. This explains why
the stoichiometric mixture fraction isosurface in the LES/3D-CMC simulation is
shorter than its 0D-CMC counterpart, leading to a shorter flame.
In Figs. 7.3(d) and 7.4 the instantaneous contours of the temperature, YOH ,
YCO2 , YNO and YCO at the same instant have been ploted. They give an insight
on the general shape of the flame. The distribution of these quantities will be
commented later in the light of their mean and RMS radial profiles.
7.3.2 Velocity and mixture fraction fields
Figures 7.5, 7.6 and 7.7 show respectively the time-averaged radial profiles of the
axial velocity, tangential velocity and mixture fraction. The time-averaging has
been conducted over 45 ms and the flow had already been developing for 15 ms
from the LES/0D-CMC solution before starting the averaging. Here we focus
on the red curves, which correspond to the LES/3D-CMC simulation. The blue
curves represent the LES-flamelet (0D-CMC) predictions already presented in
Chapter 6, which have been reproduced here for comparison. From these graphs,
it is evident that solving the full CMC equations has not improved the flow field
prediction compared to the LES/0D-CMC simulation. The 3D-CMC predic-
tions for the mean axial and tangential velocities, which were already good with
the flamelet model, have not changed too much for distances up to at least 1D
(30 mm). Further downstream, for x ≥ 2.33 D (70 mm) the 3D-CMC predictions
of the flow field are less good than their 0D-CMC counterparts, but remaining
satisfactory. The limited deterioration of the time-averaged velocity prediction
for positions far from the burner exit may be due to poor statistical convergence.
In fact, the slow computation of the LES/3D-CMC simulation does not allow to
gather the same amount of data as for the LES-flamelet simulation presented in
Chapter 6. The expansion of the main stream is amplified by the LES/3D-CMC
formulation. This results in the axial velocity peak being shifted to higher radial
positions for axial positions above x = 2.33 D (70 mm). The main stream in the
3D-CMC computation is also found to be wider than predicted by the flamelet
computation, which results in a decrease of the average peak velocity in the main
stream due to mass conservation. The strength of the reverse flow in the Central
191
7. CMC/LES of a lifted non-premixed swirl flame
(a) YOH (b) YCO2
(c) YNO (d) YCO
Figure 7.4: Typical instantaneous contours of the mass fraction of (a) OH, (b)
CO2, (c) NO and (d) CO taken at the same instant. The white line represents
the stoichiometric iso-surface.
192
7. CMC/LES of a lifted non-premixed swirl flame
Recirculation Zone is still underpredicted at each axial position, with no signif-
icant change between the 0D-CMC and 3D-CMC predictions (Fig. 7.5). This
underprediction is limited close to the burner exit and tends to extend further
as we go downstream. Unlike the flow field, the mixing field has been clearly
improved by solving the CMC equations (Fig. 7.7). At x ≤ 0.333 D (20 mm),
the mixture fraction peak is predicted at the right radial position in both the
0D-CMC and 3D-CMC formulations. Moreover, the values of the mean mixture
fraction peak now match closely the experimental ones, with only a slight un-
derprediction of 5 % at x = 10 mm, to be compared to the overprediction of
16.5 % from the 0D-CMC simulation. The mean mixture fraction values along
the centreline have also been improved but remained overpredicted by a factor
of 2. At x = 0.667 D (20 mm), the radial profile of the mean mixture fraction
matches well the experimental data in terms of both trend and magnitude. For
positions above 40 mm (x ≥ 1.33 D), the maximum values of the mean mixture
fraction, while leveling, become overpredicted as compared to experimental re-
sults in both the 0D-CMC and 3D-CMC formulations. Nevertheless solving the
CMC equations results in a noticeable improvement in terms of magnitude of the
mean mixture fraction, while the positions of its peaks are shifted slightly too
far towards the outer part of flow. Overall the LES/3D-CMC results show that
the mixing is accelerated as compared to the LES/0D-CMC. This observation
is to be related to the previous comments made on the instantaneous flow and
mixing fields in Section 7.3.1. The fuel jet is now bent towards the air stream
at almost a perpendicular angle. As a consequence, the mixing of the air and
fuel is accelerated in the shear layers. It can also be noticed that similar gen-
eral behaviours were observed in the simulation of the non-swirl Delft-III piloted
flame in Chapter 5: solving the CMC equations resulted in variations of the local
density strong enough to have modified the flow and mixing fields predicted by
the steady flamelet. While these density fluctuations did not result in an im-
provement of the flow field, the mixing field was however significantly closer to
the experimental one.
Looking now at the RMS quantities (in Fig. 7.8 for the axial velocity, Fig. 7.9
for the tangential one, and Fig. 7.10 for ξ), there is no clear difference between the
0D-CMC and 3D-CMC results for positions close to the burner exit (x ≤ 1 D),
193
7. CMC/LES of a lifted non-premixed swirl flame
0 1 2 3 4 5−1
−0.5
0
0.5
1
1.5
2
<
U>
 / 
U a
ir
r / D
 
 
x = 0.0333 D
0D−CMC
3D−CMC
EXP
0 1 2 3 4 5−1
−0.5
0
0.5
1
1.5
2
<
U>
 / 
U a
ir
r / D
 
 
x = 0.333 D
0D−CMC
3D−CMC
EXP
0 1 2 3 4 5−1
−0.5
0
0.5
1
1.5
2
<
U>
 / 
U a
ir
r / D
 
 
x = 0.667 D
0D−CMC
3D−CMC
EXP
0 1 2 3 4 5−1
−0.5
0
0.5
1
1.5
2
<
U>
 / 
U a
ir
r / D
 
 
x = 1 D
0D−CMC
3D−CMC
EXP
0 1 2 3 4 5−1
−0.5
0
0.5
1
1.5
2
<
U>
 / 
U a
ir
r / D
 
 
x = 2.33 D
0D−CMC
3D−CMC
EXP
0 1 2 3 4 5−1
−0.5
0
0.5
1
1.5
2
<
U>
 / 
U a
ir
r / D
 
 
x = 3 D
0D−CMC
3D−CMC
EXP
Figure 7.5: Radial profiles of the mean axial velocity at the indicated axial posi-
tion. Experimental data from Ref. [51].
194
7. CMC/LES of a lifted non-premixed swirl flame
0 1 2 3 4 5
0
0.5
1
1.5
2
<
W
> 
/ U
ai
r
r / D
 
 
x = 0.0333 D
0D−CMC
3D−CMC
EXP
0 1 2 3 4 5
0
0.5
1
1.5
2
<
W
> 
/ U
ai
r
r / D
 
 
x = 0.333 D
0D−CMC
3D−CMC
EXP
0 1 2 3 4 5
0
0.5
1
1.5
2
<
W
> 
/ U
ai
r
r / D
 
 
x = 0.667 D
0D−CMC
3D−CMC
EXP
0 1 2 3 4 5
0
0.5
1
1.5
2
<
W
> 
/ U
ai
r
r / D
 
 
x = 1 D
0D−CMC
3D−CMC
EXP
0 1 2 3 4 5
0
0.5
1
1.5
2
<
W
> 
/ U
ai
r
r / D
 
 
x = 2.33 D
0D−CMC
3D−CMC
EXP
0 1 2 3 4 5
0
0.5
1
1.5
2
<
W
> 
/ U
ai
r
r / D
 
 
x = 3 D
0D−CMC
3D−CMC
EXP
Figure 7.6: Radial profiles of the mean tangential velocity at the indicated axial
position. Experimental data from Ref. [51].
195
7. CMC/LES of a lifted non-premixed swirl flame
0 1 2 3 4 50
0.25
0.5
0.75
1
<
ξ>
r / D
 
 
x = 0.333 D
0D−CMC
3D−CMC
EXP
0 1 2 3 4 50
0.25
0.5
0.75
1
<
ξ>
r / D
 
 
x = 0.667 D
0D−CMC
3D−CMC
EXP
0 1 2 3 4 50
0.25
0.5
0.75
1
<
ξ>
r / D
 
 
x = 1.33 D
0D−CMC
3D−CMC
EXP
0 1 2 3 4 50
0.25
0.5
0.75
1
<
ξ>
r / D
 
 
x = 2 D
0D−CMC
3D−CMC
EXP
0 1 2 3 4 50
0.25
0.5
0.75
1
<
ξ>
r / D
 
 
x = 3 D
0D−CMC
3D−CMC
EXP
0 1 2 3 4 50
0.25
0.5
0.75
1
<
ξ>
r / D
 
 
x = 4 D
0D−CMC
3D−CMC
EXP
Figure 7.7: Radial profiles of the mean mixture fraction at the indicated axial
position. Experimental data from Ref. [51].
196
7. CMC/LES of a lifted non-premixed swirl flame
and this for both the axial and tangential velocity RMS. Both present a limited
underprediction of the RMS of the axial velocity, while the RMS of the tangential
velocity is better predicted. Further downstream (x ≥ 1 D), the magnitude of the
RMS of the axial velocity has increased and is closer to the experimental ones.
The tangential RMS velocity are now slightly underpredicted. If we look at the
RMS of the mixture fraction from the 3D-CMC simulation, they are found to be
lower than their 0D-CMC values. Overall, the peak RMS values of velocities and
mixture fraction are shifted towards the outer part of the flow in the 3D-CMC
calculations.
7.3.3 Reaction zone and lift-off
The pictures in Fig. 7.11 represent the instantaneous isosurface of the stoichio-
metric mixture fraction plotted at the same instant as the snapshots in Fig. 7.4.
From these figures, it is evident that the ξst−isosurface enters the air pipe and
is attached to its inner wall. The mechanism responsible for the presence of the
fuel inside the air pipe has been extensively described in Chapter 6. If we now
look at Fig. 7.11(a), it is evident that, while the ξst−contour enters the burner,
the flame does not and is lifted at a height of around 20 mm i.e 2/3 D. This is
consistent with the experimental lift-off height of 20 mm reported in Ref. [51].
Figure 7.2 is a zoom of the YOH contour around the burner exit from which the
flame lift-off height is also evident.
Studying again Fig. 7.11(a), we observed that YOH varies strongly in space
at locations where the flow is burning (see also Fig. 7.4(a) with the white line
corresponding to the stoichiometric mixture fraction) as well as in time. The high-
est values of YOH are found in a space located between the flame root (around
x = 2/3 D) and a height of around 2.5 D (75 mm). Further downstream, zones
of high YOH as well as dark zones can be found. These comments are consistent
with the observations reported in Ref. [51] through the record of the experi-
mental chemiluminescence emissions. ξst−contour has also been coloured by the
temperature in Fig. 7.11(b), YNO in Fig. 7.11(c) and YCO in Fig. 7.11(d) and
these figures will be commented later in the text.
197
7. CMC/LES of a lifted non-premixed swirl flame
0 1 2 3 4 50
0.2
0.4
0.6
u
R
M
S 
/ U
ai
r
r / D
 
 
x = 0.0333 D
0D−CMC
3D−CMC
EXP
0 1 2 3 4 50
0.2
0.4
0.6
u
R
M
S 
/ U
ai
r
r / D
 
 
x = 0.333 D
0D−CMC
3D−CMC
EXP
0 1 2 3 4 50
0.2
0.4
0.6
u
R
M
S 
/ U
ai
r
r / D
 
 
x = 0.667 D
0D−CMC
3D−CMC
EXP
0 1 2 3 4 50
0.2
0.4
0.6
u
R
M
S 
/ U
ai
r
r / D
 
 
x = 1 D
0D−CMC
3D−CMC
EXP
0 1 2 3 4 50
0.2
0.4
0.6
u
R
M
S 
/ U
ai
r
r / D
 
 
x = 2.33 D
0D−CMC
3D−CMC
EXP
0 1 2 3 4 50
0.2
0.4
0.6
u
R
M
S 
/ U
ai
r
r / D
 
 
x = 3 D
0D−CMC
3D−CMC
EXP
Figure 7.8: Radial profiles of the RMS of the axial velocity at the indicated axial
position. Experimental data from Ref. [51].
198
7. CMC/LES of a lifted non-premixed swirl flame
0 1 2 3 4 50
0.25
0.5
0.75
W
R
M
S 
/ U
ai
r
r / D
 
 
x = 0.0333 D
0D−CMC
3D−CMC
EXP
0 1 2 3 4 50
0.25
0.5
0.75
W
R
M
S 
/ U
ai
r
r / D
 
 
x = 0.333 D
0D−CMC
3D−CMC
EXP
0 1 2 3 4 50
0.25
0.5
0.75
W
R
M
S 
/ U
ai
r
r / D
 
 
x = 0.667 D
0D−CMC
3D−CMC
EXP
0 1 2 3 4 50
0.25
0.5
0.75
W
R
M
S 
/ U
ai
r
r / D
 
 
x = 1 D
0D−CMC
3D−CMC
EXP
0 1 2 3 4 50
0.25
0.5
0.75
W
R
M
S 
/ U
ai
r
r / D
 
 
x = 2.33 D
0D−CMC
3D−CMC
EXP
0 1 2 3 4 50
0.25
0.5
0.75
W
R
M
S 
/ U
ai
r
r / D
 
 
x = 3 D
0D−CMC
3D−CMC
EXP
Figure 7.9: Radial profiles of the RMS of the tangential velocity at the indicated
axial position. Experimental data from Ref. [51].
199
7. CMC/LES of a lifted non-premixed swirl flame
0 1 2 3 4 50
0.2
0.4
0.6
ξ R
M
S
r / D
 
 
x = 0.333 D
0D−CMC
3D−CMC
EXP
0 1 2 3 4 50
0.2
0.4
0.6
ξ R
M
S
r / D
 
 
x = 0.667 D
0D−CMC
3D−CMC
EXP
0 1 2 3 4 50
0.2
0.4
0.6
ξ R
M
S
r / D
 
 
x = 1.33 D
0D−CMC
3D−CMC
EXP
0 1 2 3 4 50
0.2
0.4
0.6
ξ R
M
S
r / D
 
 
x = 2 D
0D−CMC
3D−CMC
EXP
0 1 2 3 4 50
0.2
0.4
0.6
ξ R
M
S
r / D
 
 
x = 3 D
0D−CMC
3D−CMC
EXP
0 1 2 3 4 50
0.2
0.4
0.6
ξ R
M
S
r / D
 
 
x = 4 D
0D−CMC
3D−CMC
EXP
Figure 7.10: Radial profiles of the RMS of the mixture fraction at the indicated
axial position. Experimental data from Ref. [51].
200
7. CMC/LES of a lifted non-premixed swirl flame
(a) (b)
(c) (d)
Figure 7.11: Typical instantaneous contours of the stoichiometric mixture fraction
coloured by (a) OH mass fraction, (b) the temperature (K), (c) NO mass fraction
and (d) CO mass fraction.
201
7. CMC/LES of a lifted non-premixed swirl flame
7.3.4 Flame dynamics and lift-off
Conditional distributions In order to understand the phenomenon respon-
sible for the flame lift-off, the conditional profiles of T˜ |ξ and Y˜OH |ξ have been
plotted in Figs. 7.12 and 7.14 at different instants and positions in the flow,
while Y˜CO|ξ and Y˜NO|ξ are reported in Figs. 7.13 and 7.15. The correspond-
ing N˜ |η have also been plotted to correlate the fluctuations of the conditional
distributions to the fluctuations from the mixing field and thus understand the
dynamics of the flame. The distributions of several CMC cells located at two
different radial positions above the burner exit have been analyzed. A first set
of CMC cells distributions has been plotted in Figs. 7.12 and 7.13. They are
located at r = 0.83 D (25 mm) from the centreline, which is along the center of
the air annulus exit. Another set of CMC cells distributions is plotted in Figs.
7.14 and 7.15. They correspond to a radial position of r = 0.67 D (20 mm) from
the centreline, which corresponds to a radial position of the inner side of the air
pipe.
The CMC cells investigated in the first row of these figures have their center
located at xc(2) = 4 mm. They are located just above the CMC cells used to
inject the CMC boundary conditions (xcBCs = 2 mm) i.e. an inert distribution in
ξ−space. They are therefore the first cells resolved by the CMC code. We first
look at the distributions in mixture fraction space represented in the first row
of Figs. 7.12 and 7.13. The corresponding CMC cell has its center located at
xc = 0.13 D = 4 mm and rc = 0.83 D, and is represented by Point 1 in Fig. 7.2.
This point is located just above the middle of the air annulus exit. We note that
the conditional temperature remains below 400 K, while the temperature of 300 K
is injected at the CMC boundary conditions (BCs). We now look at the distri-
butions in mixture fraction space represented in the first row of Figs. 7.14 and
7.15. The corresponding CMC cell has its center located at xc = 0.13 D = 4 mm
and rc = 0.67 D (Point 2 in Fig. 7.2). We note that some of the distributions
correspond to burning events, the maximum temperature reaching time to time
values as high as 1200 K. The intermittent ignitions occur in spite of overall high
values of the scalar dissipation rate. In fact, N˜ |η is found to exceed the scalar
dissipation rate extinction limit of the steady flamelet (176 1/s) much often than
202
7. CMC/LES of a lifted non-premixed swirl flame
at the previous CMC cell location (r = 0.83 D).
Further downstream, at x = 0.35 D = 10 mm, the CMC cell distributions are
plotted in the second rows of Figs. 7.12 and 7.13 (rc = 0.83D), and Figs. 7.14 and
7.15 (rc = 0.67 D). The CMC cell located on the side of the inner wall, with rc =
0.67 D, is denoted by Point 3 in Fig. 7.2. Analysis of its conditional distributions
shows that it experiences both fully burning and totally extinguished events.
Between these two extreme cases, the conditional profiles of the temperature,
YOH and pollutants mass fractions (YCO and YNO) fluctuate throughout a wide
range of distributions. The CMC cell located at rc = 0.83 D (Point 4 in Fig. 7.2)
starts only to experience some burning events in its conditional distributions.
For axial positions x ≥ 0.63 D (19 mm), the CMC cells at r = 0.67 D
show fully burning distributions. As we go further downstream, the temporal
variations of N˜ |η become smaller and smaller, leading to limited fluctations of
the Y˜α|ξ distributions, before finally reaching a steady state. The CMC cells at
r = 0.83 D experience a similar behaviour, but for axial positions x ≥ 0.86 D
(26 mm).
Time series To investigate further the dynamics of the flame lift-off, Fig. 7.16
shows time-series of the peak conditional scalar dissipation rate (i.e. at η = 0.5),
T˜ |ξst , Y˜OH |ξst , Y˜NO|ξst and Y˜CO|ξst , at various locations downstream and at
radial locations corresponding again to the middle of the air annulus (r = 0.83D,
left) and its inner side (r = 0.67D, right).
If we first look at the time series corresponding to the radial position of the air
annulus center (r = 0.83D, Fig. 7.16 left), we see that N˜ |ηmax fluctuates strongly
with time at positions close to the burner exit, crossing occasionally the 0D-CMC
extinction limit of 176 1/s for x/D = 0.2 (axial position of 6 mm). A peak value
of 400 1/s is observable. As we go further downstream, the scalar dissipation rate
tends to relax and at x/D = 1 (axial position of 30 mm) it remains below 20 1/s.
Let us now analyse the curves of Y˜α|ξst against time. The curve of Y˜OH |ξst
shows that the flamelets corresponding to the CMC cells are not fully burning
for axial positions below (at least) x = 1D (30 mm). Between the inert distribu-
tion injected at the CMC BCs (x/D = 0.07, x = 2 mm) and the fully burning
state, the flow experiences a series of intermediate states. These different states
203
7. CMC/LES of a lifted non-premixed swirl flame
0 0.2 0.4 0.6 0.8 1
0
100
200
300
400
500
600
(x,R) = (0.13,0.83) D
N
 (1
/s)
ξ
(a)
0 0.2 0.4 0.6 0.8 1
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
(x,R) = (0.13,0.83) D
T 
(K
)
ξ
(b)
0 0.2 0.4 0.6 0.8 1
0
1
2
3
4
5
6
7
x 10−7
(x,R) = (0.13,0.83) D
Y O
H
ξ
(c)
0 0.2 0.4 0.6 0.8 1
0
20
40
60
80
100
120
140
160
180
200
(x,R) = (0.35,0.83) D
N
 (1
/s)
ξ
(d)
0 0.2 0.4 0.6 0.8 1
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
(x,R) = (0.35,0.83) D
T 
(K
)
ξ
(e)
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
x 10−5
(x,R) = (0.35,0.83) D
Y O
H
ξ
(f)
0 0.2 0.4 0.6 0.8 1
0
10
20
30
40
50
60
70
80
90
100
(x,R) = (0.63,0.83) D
N
 (1
/s)
ξ
(g)
0 0.2 0.4 0.6 0.8 1
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
(x,R) = (0.63,0.83) D
T 
(K
)
ξ
(h)
0 0.2 0.4 0.6 0.8 1
0
1
2
3
4
5
x 10−3
(x,R) = (0.63,0.83) D
Y O
H
ξ
(i)
0 0.2 0.4 0.6 0.8 1
0
2
4
6
8
10
12
14
(x,R) = (1.1,0.83) D
N
 (1
/s)
ξ
(j)
0 0.2 0.4 0.6 0.8 1
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
(x,R) = (1.1,0.83) D
T 
(K
)
ξ
(k)
0 0.2 0.4 0.6 0.8 1
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
x 10−3
(x,R) = (1.1,0.83) D
Y O
H
ξ
(l)
Figure 7.12: Instantaneous conditional (“CMC”) profiles at several consecutive
instants of N (scalar dissipation rate), T and OH mass fractions at the indicated
axial positions and at r = 0.83 D (25 mm).
204
7. CMC/LES of a lifted non-premixed swirl flame
0 0.2 0.4 0.6 0.8 1
0
0.5
1
1.5
2
2.5
x 10−3
(x,R) = (0.13,0.83) D
Y C
O
ξ
(a)
0 0.2 0.4 0.6 0.8 1
0
0.5
1
1.5
2
2.5
x 10−6
(x,R) = (0.13,0.83) D
Y N
O
ξ
(b)
0 0.2 0.4 0.6 0.8 1
0
0.005
0.01
0.015
0.02
(x,R) = (0.35,0.83) D
Y C
O
ξ
(c)
0 0.2 0.4 0.6 0.8 1
0
0.5
1
1.5
2
2.5
3
x 10−5
(x,R) = (0.35,0.83) D
Y N
O
ξ
(d)
0 0.2 0.4 0.6 0.8 1
0
0.01
0.02
0.03
0.04
0.05
0.06
(x,R) = (0.63,0.83) D
Y C
O
ξ
(e)
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
1.2
x 10−4
(x,R) = (0.63,0.83) D
Y N
O
ξ
(f)
0 0.2 0.4 0.6 0.8 1
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
(x,R) = (1.1,0.83) D
Y C
O
ξ
(g)
0 0.2 0.4 0.6 0.8 1
0
1
2
3
4
x 10−4
(x,R) = (1.1,0.83) D
Y N
O
ξ
(h)
Figure 7.13: Instantaneous conditional (“CMC”) profiles at several consecutive
instants of CO and NO mass fractions at the indicated axial positions and at
r = 0.83 D (25 mm).
205
7. CMC/LES of a lifted non-premixed swirl flame
0 0.2 0.4 0.6 0.8 1
0
50
100
150
200
250
300
350
400
450
(x,R) = (0.13,0.67) D
N
 (1
/s)
ξ
(a)
0 0.2 0.4 0.6 0.8 1
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
(x,R) = (0.13,0.67) D
T 
(K
)
ξ
(b)
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
x 10−5
(x,R) = (0.13,0.67) D
Y O
H
ξ
(c)
0 0.2 0.4 0.6 0.8 1
0
20
40
60
80
100
120
140
160
180
200
(x,R) = (0.35,0.67) D
N
 (1
/s)
ξ
(d)
0 0.2 0.4 0.6 0.8 1
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
(x,R) = (0.35,0.67) D
T 
(K
)
ξ
(e)
0 0.2 0.4 0.6 0.8 1
0
1
2
3
4
5
x 10−3
(x,R) = (0.35,0.67) D
Y O
H
ξ
(f)
0 0.2 0.4 0.6 0.8 1
0
10
20
30
40
50
60
70
(x,R) = (0.63,0.67) D
N
 (1
/s)
ξ
(g)
0 0.2 0.4 0.6 0.8 1
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
(x,R) = (0.63,0.67) D
T 
(K
)
ξ
(h)
0 0.2 0.4 0.6 0.8 1
0
1
2
3
4
5
x 10−3
(x,R) = (0.63,0.67) D
Y O
H
ξ
(i)
0 0.2 0.4 0.6 0.8 1
0
2
4
6
8
10
12
14
16
(x,R) = (1.1,0.67) D
N
 (1
/s)
ξ
(j)
0 0.2 0.4 0.6 0.8 1
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
(x,R) = (1.1,0.67) D
T 
(K
)
ξ
(k)
0 0.2 0.4 0.6 0.8 1
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
x 10−3
(x,R) = (1.1,0.67) D
Y O
H
ξ
(l)
Figure 7.14: Instantaneous conditional (“CMC”) profiles at several consecutive
instants of N (scalar dissipation rate), T and OH mass fractions at the indicated
axial positions and at r = 0.67 D (20 mm).
206
7. CMC/LES of a lifted non-premixed swirl flame
0 0.2 0.4 0.6 0.8 1
0
0.005
0.01
0.015
0.02
(x,R) = (0.13,0.67) D
Y C
O
ξ
(a)
0 0.2 0.4 0.6 0.8 1
0
0.5
1
1.5
2
2.5 x 10
−5
(x,R) = (0.13,0.67) D
Y N
O
ξ
(b)
0 0.2 0.4 0.6 0.8 1
0
0.01
0.02
0.03
0.04
0.05
0.06
(x,R) = (0.35,0.67) D
Y C
O
ξ
(c)
0 0.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x 10−4
(x,R) = (0.35,0.67) D
Y N
O
ξ
(d)
0 0.2 0.4 0.6 0.8 1
0
0.01
0.02
0.03
0.04
0.05
0.06
(x,R) = (0.63,0.67) D
Y C
O
ξ
(e)
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
x 10−4
(x,R) = (0.63,0.67) D
Y N
O
ξ
(f)
0 0.2 0.4 0.6 0.8 1
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
(x,R) = (1.1,0.67) D
Y C
O
ξ
(g)
0 0.2 0.4 0.6 0.8 1
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
x 10−4
(x,R) = (1.1,0.67) D
Y N
O
ξ
(h)
Figure 7.15: Instantaneous conditional (“CMC”) profiles at several consecutive
instants of CO and NO mass fractions at the indicated axial positions and at
r = 0.67 D (20 mm).
207
7. CMC/LES of a lifted non-premixed swirl flame
correspond to the ignition process of the flamelet and their analysis provides
insights on the flame lift-off dynamics. At x/D = 0.2 (6 mm), the stoichiomet-
ric temperature remains mainly the one of the inert flamelet injected at BCs (i.e.
300 K), with some small overshoots reaching occasionally a temperature of 700 K.
Y˜OH |ξst , Y˜NO|ξst and Y˜CO|ξst remain equal or very close to zero, showing that
the flow is not burning at this position.
At x/D = 0.4 (12 mm), T˜ |ξst shows significant fluctuations, with overall a
clear increase of the stoichiometric temperature, which reaches values as high as
1750 K. However, Y˜OH |ξst remains overall close to zero, with the exception of a
clear overshoot at time t = 0.0425 s. The flamelet at x/D = 0.5 (15 mm) shows
the same general behaviour as the one at x/D = 0.4 (12 mm), but the tempera-
ture has now increased further and reaches occasionally 2000 K. The number of
overshoots of Y˜OH |ξst against time has also considerably increased, but they are
not sufficient to fully ignite the flamelet. For radial positions around r = 0.83D
(corresponding to the radius of the air annulus middle), the area located from
x/D = 0.2 to x/D = 0.5 (i.e. from x = 6 mm to x = 15 mm) corresponds to the
pre-heat zone of the flame. In this area, NO emissions are found to remain low,
while CO emissions can occasionally reach value corresponding to a fully burning
flamelet. From this observation, it can be concluded that the flame lift-off height
has a value between 15 mm to 30 mm at radial positions of r = 0.83D i.e. above
the air annulus middle, which is again consistent with the lift-off height of 20 mm
reported experimentally [51].
If now we investigate the time series from the CMC cells located above the
inner wall of the air pipe (r = 0.67D, Fig. 7.16 right), we can see the same general
behaviour that leads to the full ignition of the flame. However, the process is
found to occur faster at these locations than at the previous ones. For instance,
the flamelets are found to be already fully burning at x/D = 0.5 (15 mm). As a
consequence, the pre-heat zone is located at lower axial positions (0.2 ≤ x/D ≤
0.4, or in mm: 6 ≤ x ≤ 12) and the flame lift-off height at this radial position is
reduced.
The reason for this faster ignition process as we go closer to the radial position
of the air annulus inner wall is to be found in the dynamics of the flow and the
stabilization process of this flame. As no pilot is present in this flame, the ignition
208
7. CMC/LES of a lifted non-premixed swirl flame
0 0.02 0.04 0.06
0
100
200
300
400
Time (s)
Pe
ak
 N
|η 
(1/
s)
 
 
x/D=0.07
x/D=0.2
x/D=0.4
x/D=0.5
x/D=1
0D Ext
0 0.02 0.04 0.06
0
100
200
300
400
500
Time (s)
Pe
ak
 N
|η 
(1/
s)
 
 
x/D=0.07
x/D=0.2
x/D=0.4
x/D=0.5
x/D=1
0D Ext
0 0.02 0.04 0.06
500
1000
1500
2000
Time (s)
St
oi
ch
. C
on
d.
 T
 (K
)
 
 
x/D=0.07
x/D=0.2
x/D=0.4
x/D=0.5
x/D=1
0 0.02 0.04 0.06
500
1000
1500
2000
Time (s)
St
oi
ch
. C
on
d.
 T
 (K
)
 
 
x/D=0.07
x/D=0.2
x/D=0.4
x/D=0.5
x/D=1
0 0.02 0.04 0.06
0
1
2
3
4
5
x 10−3
Time (s)
St
oi
ch
. C
on
d.
 Y O
H
 
 
x/D=0.07
x/D=0.2
x/D=0.4
x/D=0.5
x/D=1
0 0.02 0.04 0.06
0
1
2
3
4
5
x 10−3
Time (s)
St
oi
ch
. C
on
d.
 Y O
H
 
 
x/D=0.07
x/D=0.2
x/D=0.4
x/D=0.5
x/D=1
0 0.02 0.04 0.06
0
1
2
3
x 10−4
Time (s)
St
oi
ch
. C
on
d.
 Y N
O
 
 
x/D=0.07
x/D=0.2
x/D=0.4
x/D=0.5
x/D=1
0 0.02 0.04 0.06
0
1
2
3
4
x 10−4
Time (s)
St
oi
ch
. C
on
d.
 Y N
O
 
 
x/D=0.07
x/D=0.2
x/D=0.4
x/D=0.5
x/D=1
0 0.02 0.04 0.06
0
0.02
0.04
0.06
0.08
Time (s)
St
oi
ch
. C
on
d.
 Y C
O
 
 
x/D=0.07
x/D=0.2
x/D=0.4
x/D=0.5
x/D=1
0 0.02 0.04 0.06
0
0.02
0.04
0.06
0.08
Time (s)
St
oi
ch
. C
on
d.
 Y C
O
 
 
x/D=0.07
x/D=0.2
x/D=0.4
x/D=0.5
x/D=1
Figure 7.16: Time series of N˜ |0.5, T˜ |ξst, Y˜OH |ξst, Y˜NO|ξst and Y˜CO|ξst at r = 0.83D
(left) and at r = 0.67D (right) at the indicated x. The black dotted lines on the
top two graphs refer to the extinction value of the scalar dissipation rate (176 1/s).
209
7. CMC/LES of a lifted non-premixed swirl flame
of the cold flamelets injected at the burner exit has to be done by convection and
diffusion of burning flamelets from neighbouring cells. Animations of the mass
fraction of the reactive scalars (see sequence of snapshots in Fig. 7.17 for the
temperature and in Fig. 7.18 for YOH) show the same process of fluid ignition as
seen from its integrated point of view i.e. through the unconditional values of the
reactive scalars. This process is mainly due to the action of the CRZ coupled to
the dynamics of the burner flow created by the Rotating Vortex Cores described
in Chapter 6. The CRZ carries upstream some burning flamelets towards the top
of the bluff body. At some point, these burning flamelets may encounter the inert
flamelet from and carried away by the air flow. This results in the slow ignition
process of the local CMC cells as observed at r = 0.83D in the left part of Fig.
7.16. On top of that, POD analysis in Chapter 6 has revealed that PVC-like
structures create strong recirculations that occur periodically at a given position
along the air annulus inner wall and just above it. When the flame is burning,
these recirculations tend to periodically suck the burning flamelets above the bluff
body towards the air pipe, decreasing the axial distance necessary for the inert
mixture to fully ignite.
7.3.5 Temperature, species and pollutants prediction
Figure 7.3(d) shows an instantaneous contour of the temperature (in Kelvin)
and Fig. 7.11(b) shows the stoichiometric mixture fraction instantaneous con-
tour coloured by the temperature. From Fig. 7.11(b), the flame lift-off is evident
with the temperature of the flame increasing gradually as one moves downstream.
Figure 7.11(c) shows the same instantaneous contour coloured this time by YNO.
From this figure, it is clear that the area of maximum NO mass fraction cor-
respond to the area of maximum temperature i.e. at the top of the flame. As
for the Delft flame emissions in Chapter 5, a temperature threshold is evident,
the emissions of NO remaining very low for temperature below about 1800 K. In
Fig. 7.11(d), the stoichiometric contour has now been coloured by YCO. While
CO mass fraction close to the burner exit is zero as a consequence of the flame
lift-off, the area of high CO mass fraction is located between the root of the flame
(around x = 20 mm) and a height of around 80 mm. The CO mass fraction is
210
7. CMC/LES of a lifted non-premixed swirl flame
Figure 7.17: Sequence of instantaneous contours of the temperature at different
instants separated by 1 ms (from left to right). The white lines represent the
stoichiometric isolines.
211
7. CMC/LES of a lifted non-premixed swirl flame
Figure 7.18: Sequence of instantaneous contours of YOH at different instants
separated by 1 ms (from left to right). The white lines represent the stoichiometric
isolines.
212
7. CMC/LES of a lifted non-premixed swirl flame
then found to decrease as we go further downstream. Instantaneous contours of
CO2, NO and CO emissions are also presented in Figs. 7.4(b), 7.4(c) and 7.4(d)
respectively. High levels of CO2 are found to develop inside the CRZ. Relatively
high levels of NO emissions are also produced in the CRZ, while CO emissions
are mainly localized along the stoichiometric mixture fraction isoline.
The radial profiles of the mean temperature are plotted in Fig. 7.19. They
show that there has been an improvement in the prediction of the temperature
for positions located between the CRZ and the ORZ. In fact, the LES/0D-CMC
formulation had predicted a peak of temperature inside the shear layer where
the fuel and air jets mix up for axial positions below 1.33 D (40 mm). The
LES/3D-CMC formulation, because of its ability to capture the flame lift-off,
do not predict this peak of temperature. The model captures accurately the
temperature inside the CRZ and main stream close to the burner for positions
up to 20 mm, but overpredict the temperature between the main stream and
the combustion chamber walls. As we go further downstream, the temperature
becomes more and more overpredicted at each radial position of the flow. The
absence of modelling for the cooling system present in the TECFLAM configu-
ration that maintains the walls at 300 K is probably responsible for the general
overprediction of the temperature far from the burner exit. The radial profiles of
the temperature RMS match well the experimental values in terms of trend and
magnitude close to the burner, before becoming increasingly underpredicted as
we go further downstream.
The radial profiles of the mean YCH4, YO2, YH2O, YCO2 and YCO are presented
respectively in Figs. 7.21, 7.23, 7.25, 7.27 and 7.29. A general observation of the
species predictions is that a good match with the experimental data is reached
at positions close to the burner exit. In the flow between the main stream and
the combustion chamber walls (i.e at high radial positions), the discrepancies in
terms of magnitude are generally significant, while both the trend and magni-
tude predictions worsen as we go further downstream. The radial profiles of the
RMS of these quantities (Figs. 7.22, 7.24, 7.26, 7.28 and 7.30 respectively) are
generally predicted satisfactorily in terms of trends, but become increasingly un-
derpredicted as we go further dowsntream. Regarding the pollutants prediction,
no experimental data was reported for NO. The radial profile of the mean YCO
213
7. CMC/LES of a lifted non-premixed swirl flame
0 1 2 3 4
500
1000
1500
2000
<
T 
(K
)>
r / D
 
 
x = 0.333 D
0D−CMC
3D−CMC
EXP
0 1 2 3 4
500
1000
1500
2000
<
T 
(K
)>
r / D
 
 
x = 0.667 D
0D−CMC
3D−CMC
EXP
0 1 2 3 4
500
1000
1500
2000
<
T 
(K
)>
r / D
 
 
x = 1.33 D
0D−CMC
3D−CMC
EXP
0 1 2 3 4
500
1000
1500
2000
<
T 
(K
)>
r / D
 
 
x = 2 D
0D−CMC
3D−CMC
EXP
0 1 2 3 4
500
1000
1500
2000
<
T 
(K
)>
r / D
 
 
x = 3 D
0D−CMC
3D−CMC
EXP
0 1 2 3 4
500
1000
1500
2000
<
T 
(K
)>
r / D
 
 
x = 4 D
0D−CMC
3D−CMC
EXP
Figure 7.19: Radial profiles of the mean temperature at the indicated axial posi-
tion. Experimental data from Ref. [51].
214
7. CMC/LES of a lifted non-premixed swirl flame
0 1 2 3 4 50
100
200
300
400
500
600
700
T R
M
S 
(K
)
r / D
 
 
x = 0.333 D
3D−CMC
EXP
0 1 2 3 4 50
100
200
300
400
500
600
700
T R
M
S 
(K
)
r / D
 
 
x = 0.667 D
3D−CMC
EXP
0 1 2 3 4 50
100
200
300
400
500
600
700
T R
M
S 
(K
)
r / D
 
 
x = 1.33 D
3D−CMC
EXP
0 1 2 3 4 50
100
200
300
400
500
600
700
T R
M
S 
(K
)
r / D
 
 
x = 2 D
3D−CMC
EXP
0 1 2 3 4 50
100
200
300
400
500
600
700
T R
M
S 
(K
)
r / D
 
 
x = 3 D
3D−CMC
EXP
0 1 2 3 4 50
100
200
300
400
500
600
700
T R
M
S 
(K
)
r / D
 
 
x = 4 D
3D−CMC
EXP
Figure 7.20: Radial profiles of the RMS of the temperature at the indicated axial
position. Experimental data from Ref. [51].
215
7. CMC/LES of a lifted non-premixed swirl flame
(Fig. 7.29) matches well the experimental data for positions close to the burner
exit before becoming increasingly overpredicted further dowstream.
7.4 Summary of main findings
The LES - first order CMC formulation has been applied to the confined non-
premixed TECFLAM S09 flame. Solving the full CMC equations in time and
space results in strong variations of the reactive scalars (temperature and species)
distributions against the mixture fraction. As a result these distributions are sig-
nificantly different from the prescribed distributions used for the flamelet model
in Chapter 6. The conditional fluctuations in mixture fraction space result in
strong variations of the local density. In particular, close to the burner exit the
numerical formulation predicts the occurrence of a flame lift-off, with a lift-off
height of around 20 mm, consistent with the experimental data. The flamelet
distributions computed by the CMC model remain inert around the burner exit,
modifying the local density compared to the LES/0D-CMC prediction. Conse-
quently, the fluid mechanics of the flame is modified: the CRZ becomes larger and
the radial expansion of the jet stream accelerates in the downstream part of the
flow. The fuel jet is bent further towards the air stream, increasing the air-fuel
mixing. This phenomenon is responsible for a clear improvement in the mixing
field prediction, showing that the right mixing mechanisms have been captured
by the LES/3D-CMC formulation. However the main jet opening is found to be
too quick far from the burner exit. Regarding the flame lift-off process, the CMC
model coupled to LES is able to capture the stabilization process of the flame:
the CRZ is responsible for carrying back to the root of the flame some burning
flamelets. These flamelets then encounter the inert flamelets injected at the air
pipe exit and ignite them. The dynamics of the ignition process at the flame root
is strongly affected by the aerodynamics of the burner. As described in Chapter
6, the presence of vortex cores rotating inside this type of burner is responsible for
the periodic occurrences of recirculations along the inner wall of the air annulus.
These recirculations attract further the neighbouring burning flamelets towards
the flame root, accelerating the ignition process of the inert flamelets injected
at the air pipe exit and hence improving the stability mechanisms of the lifted
216
7. CMC/LES of a lifted non-premixed swirl flame
flame.
217
7. CMC/LES of a lifted non-premixed swirl flame
0 1 2 3 40
0.1
0.2
0.3
0.4
0.5
0.6
<
Y C
H 4
>
r / D
 
 
x = 0.333 D
3D−CMC
EXP
0 1 2 3 40
0.05
0.1
0.15
0.2
0.25
<
Y C
H 4
>
r / D
 
 
x = 0.667 D
3D−CMC
EXP
0 1 2 3 40
0.02
0.04
0.06
<
Y C
H 4
>
r / D
 
 
x = 1.33 D
3D−CMC
EXP
0 1 2 3 40
0.01
0.02
0.03
0.04
<
Y C
H 4
>
r / D
 
 
x = 2 D
3D−CMC
EXP
0 1 2 3 40
0.005
0.01
0.015
0.02
0.025
<
Y C
H 4
>
r / D
 
 
x = 3 D
3D−CMC
EXP
0 1 2 3 40
0.005
0.01
0.015
<
Y C
H 4
>
r / D
 
 
x = 4 D
3D−CMC
EXP
Figure 7.21: Radial profiles of the mean YCH4 at the indicated axial position.
Experimental data from Ref. [51].
218
7. CMC/LES of a lifted non-premixed swirl flame
0 1 2 3 40
0.1
0.2
0.3
0.4
0.5
<
Y C
H 4
 
R
M
S>
r / D
 
 
x = 0.333 D
3D−CMC
EXP
0 1 2 3 40
0.1
0.2
0.3
0.4
0.5
<
Y C
H 4
 
R
M
S>
r / D
 
 
x = 0.667 D
3D−CMC
EXP
0 1 2 3 40
0.1
0.2
0.3
0.4
0.5
<
Y C
H 4
 
R
M
S>
r / D
 
 
x = 1.33 D
3D−CMC
EXP
0 1 2 3 40
0.1
0.2
0.3
0.4
0.5
<
Y C
H 4
 
R
M
S>
r / D
 
 
x = 2 D
3D−CMC
EXP
0 1 2 3 40
0.1
0.2
0.3
0.4
0.5
<
Y C
H 4
 
R
M
S>
r / D
 
 
x = 3 D
3D−CMC
EXP
0 1 2 3 40
0.1
0.2
0.3
0.4
0.5
<
Y C
H 4
 
R
M
S>
r / D
 
 
x = 4 D
3D−CMC
EXP
Figure 7.22: Radial profiles of the RMS of YCH4 at the indicated axial position.
Experimental data from Ref. [51].
219
7. CMC/LES of a lifted non-premixed swirl flame
0 1 2 3 40
0.05
0.1
0.15
0.2
<
Y O
2>
r / D
 
 
x = 0.333 D
3D−CMC
EXP
0 1 2 3 40
0.05
0.1
0.15
0.2
<
Y O
2>
r / D
 
 
x = 0.667 D
3D−CMC
EXP
0 1 2 3 40
0.05
0.1
0.15
0.2
<
Y O
2>
r / D
 
 
x = 1.33 D
3D−CMC
EXP
0 1 2 3 40
0.05
0.1
0.15
<
Y O
2>
r / D
 
 
x = 2 D
3D−CMC
EXP
0 1 2 3 40
0.02
0.04
0.06
0.08
0.1
0.12
<
Y O
2>
r / D
 
 
x = 3 D
3D−CMC
EXP
0 1 2 3 40
0.02
0.04
0.06
0.08
0.1
<
Y O
2>
r / D
 
 
x = 4 D
3D−CMC
EXP
Figure 7.23: Radial profiles of the mean YO2 at the indicated axial position.
Experimental data from Ref. [51].
220
7. CMC/LES of a lifted non-premixed swirl flame
0 1 2 3 40
0.1
0.2
0.3
0.4
0.5
<
Y O
2 
R
M
S>
r / D
 
 
x = 0.333 D
3D−CMC
EXP
0 1 2 3 40
0.1
0.2
0.3
0.4
0.5
<
Y O
2 
R
M
S>
r / D
 
 
x = 0.667 D
3D−CMC
EXP
0 1 2 3 40
0.1
0.2
0.3
0.4
0.5
<
Y O
2 
R
M
S>
r / D
 
 
x = 1.33 D
3D−CMC
EXP
0 1 2 3 40
0.1
0.2
0.3
0.4
0.5
<
Y O
2 
R
M
S>
r / D
 
 
x = 2 D
3D−CMC
EXP
0 1 2 3 40
0.1
0.2
0.3
0.4
0.5
<
Y O
2 
R
M
S>
r / D
 
 
x = 3 D
3D−CMC
EXP
0 1 2 3 40
0.1
0.2
0.3
0.4
0.5
<
Y O
2 
R
M
S>
r / D
 
 
x = 4 D
3D−CMC
EXP
Figure 7.24: Radial profiles of the RMS of YO2 at the indicated axial position.
Experimental data from Ref. [51].
221
7. CMC/LES of a lifted non-premixed swirl flame
0 1 2 3 40
0.05
0.1
<
Y H
2O
>
r / D
 
 
x = 0.333 D
3D−CMC
EXP
0 1 2 3 40
0.05
0.1
<
Y H
2O
>
r / D
 
 
x = 0.667 D
3D−CMC
EXP
0 1 2 3 40
0.05
0.1
<
Y H
2O
>
r / D
 
 
x = 1.33 D
3D−CMC
EXP
0 1 2 3 40
0.05
0.1
<
Y H
2O
>
r / D
 
 
x = 2 D
3D−CMC
EXP
0 1 2 3 40
0.05
0.1
<
Y H
2O
>
r / D
 
 
x = 3 D
3D−CMC
EXP
0 1 2 3 40
0.05
0.1
<
Y H
2O
>
r / D
 
 
x = 4 D
3D−CMC
EXP
Figure 7.25: Radial profiles of the mean YH2O at the indicated axial position.
Experimental data from Ref. [51].
222
7. CMC/LES of a lifted non-premixed swirl flame
0 1 2 3 40
0.05
0.1
0.15
0.2
0.25
<
Y H
2O
 R
M
S>
r / D
 
 
x = 0.333 D
3D−CMC
EXP
0 1 2 3 40
0.05
0.1
0.15
0.2
0.25
<
Y H
2O
 R
M
S>
r / D
 
 
x = 0.667 D
3D−CMC
EXP
0 1 2 3 40
0.05
0.1
0.15
0.2
0.25
<
Y H
2O
 R
M
S>
r / D
 
 
x = 1.33 D
3D−CMC
EXP
0 1 2 3 40
0.05
0.1
0.15
0.2
0.25
<
Y H
2O
 R
M
S>
r / D
 
 
x = 2 D
3D−CMC
EXP
0 1 2 3 40
0.05
0.1
0.15
0.2
0.25
<
Y H
2O
 R
M
S>
r / D
 
 
x = 3 D
3D−CMC
EXP
0 1 2 3 40
0.05
0.1
0.15
0.2
0.25
<
Y H
2O
 R
M
S>
r / D
 
 
x = 4 D
3D−CMC
EXP
Figure 7.26: Radial profiles of the RMS of YH2O at the indicated axial position.
Experimental data from Ref. [51].
223
7. CMC/LES of a lifted non-premixed swirl flame
0 1 2 3 40
0.05
0.1
<
Y C
O
2>
r / D
 
 
x = 0.333 D
3D−CMC
EXP
0 1 2 3 40
0.05
0.1
<
Y C
O
2>
r / D
 
 
x = 0.667 D
3D−CMC
EXP
0 1 2 3 40
0.05
0.1
<
Y C
O
2>
r / D
 
 
x = 1.33 D
3D−CMC
EXP
0 1 2 3 40
0.05
0.1
<
Y C
O
2>
r / D
 
 
x = 2 D
3D−CMC
EXP
0 1 2 3 40
0.05
0.1
<
Y C
O
2>
r / D
 
 
x = 3 D
3D−CMC
EXP
0 1 2 3 40
0.05
0.1
<
Y C
O
2>
r / D
 
 
x = 4 D
3D−CMC
EXP
Figure 7.27: Radial profiles of the mean YCO2 at the indicated axial position.
Experimental data from Ref. [51].
224
7. CMC/LES of a lifted non-premixed swirl flame
0 1 2 3 40
0.05
0.1
0.15
0.2
0.25
<
Y C
O
2 
R
M
S>
r / D
 
 
x = 0.333 D
3D−CMC
EXP
0 1 2 3 40
0.05
0.1
0.15
0.2
0.25
<
Y C
O
2 
R
M
S>
r / D
 
 
x = 0.667 D
3D−CMC
EXP
0 1 2 3 40
0.05
0.1
0.15
0.2
0.25
<
Y C
O
2 
R
M
S>
r / D
 
 
x = 1.33 D
3D−CMC
EXP
0 1 2 3 40
0.05
0.1
0.15
0.2
0.25
<
Y C
O
2 
R
M
S>
r / D
 
 
x = 2 D
3D−CMC
EXP
0 1 2 3 40
0.05
0.1
0.15
0.2
0.25
<
Y C
O
2 
R
M
S>
r / D
 
 
x = 3 D
3D−CMC
EXP
0 1 2 3 40
0.05
0.1
0.15
0.2
0.25
<
Y C
O
2 
R
M
S>
r / D
 
 
x = 4 D
3D−CMC
EXP
Figure 7.28: Radial profiles of the RMS of YCO2 at the indicated axial position.
Experimental data from Ref. [51].
225
7. CMC/LES of a lifted non-premixed swirl flame
0 1 2 3 40
0.01
0.02
0.03
0.04
0.05
0.06
<
Y C
O
>
r / D
 
 
x = 0.333 D
3D−CMC
EXP
0 1 2 3 40
0.01
0.02
0.03
0.04
0.05
0.06
<
Y C
O
>
r / D
 
 
x = 0.667 D
3D−CMC
EXP
0 1 2 3 40
0.01
0.02
0.03
0.04
0.05
0.06
<
Y C
O
>
r / D
 
 
x = 1.33 D
3D−CMC
EXP
0 1 2 3 40
0.01
0.02
0.03
0.04
0.05
0.06
<
Y C
O
>
r / D
 
 
x = 2 D
3D−CMC
EXP
0 1 2 3 40
0.01
0.02
0.03
0.04
0.05
0.06
<
Y C
O
>
r / D
 
 
x = 3 D
3D−CMC
EXP
0 1 2 3 40
0.01
0.02
0.03
0.04
0.05
0.06
<
Y C
O
>
r / D
 
 
x = 4 D
3D−CMC
EXP
Figure 7.29: Radial profiles of the mean YCO at the indicated axial position.
Experimental data from Ref. [51].
226
7. CMC/LES of a lifted non-premixed swirl flame
0 1 2 3 40
0.05
0.1
0.15
0.2
0.25
<
Y C
O
 R
M
S>
r / D
 
 
x = 0.333 D
3D−CMC
EXP
0 1 2 3 40
0.05
0.1
0.15
0.2
0.25
<
Y C
O
 R
M
S>
r / D
 
 
x = 0.667 D
3D−CMC
EXP
0 1 2 3 40
0.05
0.1
0.15
0.2
0.25
<
Y C
O
 R
M
S>
r / D
 
 
x = 1.33 D
3D−CMC
EXP
0 1 2 3 40
0.05
0.1
0.15
0.2
0.25
<
Y C
O
 R
M
S>
r / D
 
 
x = 2 D
3D−CMC
EXP
0 1 2 3 40
0.05
0.1
0.15
0.2
0.25
<
Y C
O
 R
M
S>
r / D
 
 
x = 3 D
3D−CMC
EXP
0 1 2 3 40
0.05
0.1
0.15
0.2
0.25
<
Y C
O
 R
M
S>
r / D
 
 
x = 4 D
3D−CMC
EXP
Figure 7.30: Radial profiles of the RMS of YCO at the indicated axial position.
Experimental data from Ref. [51].
227
Chapter 8
Conclusions
8.1 Overview of the PhD work
In the present PhD work, several numerical simulations were conducted in order
to further our understanding of the flame stabilization in swirl combustors. In
the literature review presented in Chapter 2, a few key aspects of swirl flames
requiring further investigations were identified. These aspects of swirl flames can
be divided into two categories: the aerodynamics and combustion. The first two
studies presented in this thesis are regarded as preliminary investigations. They
focused on two academic configurations without swirl, but containing some im-
portant features present in swirl combustors. The first work (Chapter 4) analysed
inert forced bluff body flows and the associated vortex shedding, while the second
work (Chapter 5) analysed a piloted non-premixed flame and its succession of lo-
calized extinctions and re-ignitions reproduced by the LES-CMC code. The next
two chapters represented an in-depth investigation of an academic non-premixed
swirl flame. In Chapter 6 the aerodynamics of this swirl flame and its inert flow
were investigated, with further insights developed on the Precessing Vortex Core-
like structures developing inside the burner and their influence on the flow and
flame dynamics. Finally, in Chapter 7, the use of a LES-CMC formulation allowed
the analysis of the flame lift-off observed in experiments. The interaction between
the aerodynamics and the combustion were investigated, in particular the effect
of the Central Recirculation Zone and the PVCs in the burner. Throughout the
thesis, we have made used of the Proper Orthogonal Decomposition method to
228
8. Conclusions
organize and analyze the datasets from the LES simulations. In this chapter,
we give a summary of the main findings presented in this thesis and provide
guidelines for further research.
8.2 LES of forced bluff body flows
In Chapter 4, isothermal air flows behind an axisymmetric conical bluff body,
enclosed in a circular pipe of larger diameter that undergoes a sudden expansion,
and with the incoming flow being forced at different single frequency (40 Hz,
160 Hz, 320 Hz) and with large amplitude, have been explored with Large-Eddy
Simulations. This flow may be thought of as a model problem for combustors
undergoing selft-excited oscillations.
• The Large-Eddy Simulations reproduced accurately the experimental find-
ings in terms of phase-averaged mean and R.M.S. velocities, vortex forma-
tion, and spectral peaks.
• At low forcing frequencies, the recirculation zone was found to pulsate with
the incoming flow, at a phase lag that depended on spatial location. No
clear vortex shedding was observed.
• At high forcing frequencies, double vortex rings were shed from both the
bluff body and inlet pipe edges at the pulsating frequency. The recirculation
zone, as a whole, pulsated less.
• The phase-averaged turbulent fluctuations showed large temporal and spa-
tial variations and were higher than the turbulent fluctuations of the un-
forced flow at the same position.
• The velocity spectra showed peaks at various harmonics of the pulsating
frequency, whose relative magnitudes varied with location.
• Proper Orthogonal Decomposition analysis of the pulsating flow at 160 Hz,
in particular snapshot reconstruction based on pairs of POD modes, led to
the interpretation that the harmonics observed in the flow were associated
229
8. Conclusions
with some weak extra vortex sheddings occuring at harmonics of the forced
frequency.
• Most of the fluctuating energy of the flow came from the deterministic part
of the flow i.e. the part of the flow pulsating at the forced frequency.
• In this POD analysis, the pairs of POD modes roughly represented the
convection inside the combustion chamber of the double vortex rings shed
at the pulsating frequency or one of its harmonics.
8.3 CMC/LES of the Delft-III natural gas non-
premixed jet flame
In Chapter 5, Large-Eddy Simulation (LES), coupled with a first order 3D Con-
ditional Moment Closure (CMC) sub-grid model and the GRI3 detailed chemical
mechanism, have been used to explore the structure of the Delft III piloted tur-
bulent non-premixed flame. A LES coupled with a prescribed first order CMC
solution has also been computed for comparison with the LES-CMC solution.
• The LES-CMC formulation reproduced the experimental observations well
in terms of time-averaged statistics for velocity, mixture fraction, CO and
temperature, with an exception of NO, which is overpredicted.
• Solving the CMC equations and updating the local density at each LES
iteration resulted in a clear improvement of the mixture fraction radial pro-
files predictions, while no clear improvement was observed for the velocity
predictions, which remain good.
• Localised extinctions, which led to the succession of burning and extin-
guished stoichiometric fluid along the flame front, were successfully cap-
tured.
• The sequence of localized extinctions and re-ignitions mainly occured close
to the nozzle, consistent with experimental observations.
230
8. Conclusions
• The localized extinctions observed close to the nozzle regularly occured
for values of the scalar dissipation rate below the quasi-steady extinction
value. In fact, a significant proportion of the localized exctinctions observed
close to the burner have to be understood as a lack of ignition of the inert
flamelets injected at the flow inlet.
8.4 Investigation of the aerodynamics of a non-
premixed swirl flame using LES
In Chapter 6, large-eddy simulation was used to solve the flow and mixing fields
of the confined turbulent non-premixed TECFLAM S09c flame and its inert flow.
For the reactive computation, LES was coupled with a prescribed first order CMC
solution, as a preliminary attempt to model this swirl flame. This formulation
was relatively fast compared to the LES coupled with the full CMC equations
resolved at each LES iteration. Statistical analysis such as spectral analysis,
correlations, and Proper Orthogonal Decomposition could then be performed
with a very good statistical convergence. As a result, a comprehensive analysis
of swirl flow aerodynamics was developed in this chapter.
• The LES-flamelet formulation, despite the fact that it could not capture
localized extinctions, was found to reproduce the experimentally-observed
formation of a Central Recirculation Zone via the Vortex Breakdown mech-
anism. The results agreed well with available experimental data for velocity
and mixture fraction.
• Autocorrelation and spectral analysis revealed the presence of a periodic
component inside the air inlet pipe and around the central bluff body, for
both the inert and reactive flows.
• The fundamental frequency of this periodic motion increased by a factor of
1.6 in the reacting case.
• The coupled use of POD with LES allowed to identify the vortical structures
of the flow and their associated frequency.
231
8. Conclusions
• The POD computation was based on a combination of several flow quan-
tities such as the pressure or the mixture fraction in addition to the three
velocity components. This resulted in a better identification of the impor-
tant structures of the flow and brought to light the correlation between the
vortex precession and the flow mixing.
• POD of the LES datasets revealed that large single and double helical lon-
gitudinal vortices, similar to a PVC, were formed along the air inlet inner
wall, whose axes rotated around the burner. These vortices became highly
curved inside the combustion chamber.
• The rotation of the vortical structures around the central bluff body were
characterized by at least one pair of POD modes in both the inert and
reacting cases.
• Spectral analysis of the corresponding temporal modes revealed that these
vortices are responsible for the periodic component observed around the
burner.
• Further pairs of modes, sometimes interpreted as harmonics of the fun-
damental pair of modes, were also present in the flow. The combustion
process was found to trigger several other pairs of modes, resulting in a
more complex dynamics of the flow.
• In the reactive flow, the vortices were more elongated and they extended
much further inside the combustor compared to the inert case. This con-
firmed the observations from the spectra and autocorrelations of the axial
velocity where the periodic component was observed much further inside
the combustion chamber for the reactive flow.
• A long low-pressure column was also observed in the inert swirl flow along
the centreline of the combustion chamber, while this structure was damped
by the combustion.
232
8. Conclusions
8.5 CMC/LES of a lifted non-premixed swirl
flame
In Chapter 7, the confined turbulent swirling non-premixed TECFLAM S09c
flame was investigated using Large Eddy Simulation coupled to the full equations
of the first order Conditional Moment Closure model.
• Consistently with the results observed in Chapter 5, solving the CMC equa-
tions at each LES iteration resulted in a clear improvement of mixture frac-
tion radial profiles predictions, in particular close to the burner. However,
the full CMC formulation also resulted in a slight overprediction of the jet
expansion prediction far from the burner exit.
• Overall the results compared well with the experimental data in terms of
mixture fraction and velocity.
• The temperature was well predicted close to the burner, but discrepancies
increased further downstrean or closer to the chamber wall. In term of CO
mass fraction, the prediction was satisfactory for axial positions lower than
1 diameter of the bluff body. YCO was then overall overpredicted.
• The LES-CMC code was able to capture the flame lift-off evident ex-
periementally. The stabilization process of the flame was also captured by
the numerical formulation: the CRZ carries back to the root of the flame
some burning fluid, which then ignites the reactants injected at the air pipe
exit.
• The recirculations created by the PVC-like structures described in Chapter
6 seemed to influence greatly the stability mechanisms of the lifted flame,
the dynamics of which could be captured by the CMC code.
8.6 Guidelines for further studies
In this section, we suggest few topics for further investigations.
233
8. Conclusions
• In this thesis, LES coupled to the CMC model has been used to provide
more insights on the transient events occuring in reactive flows. In particu-
lar, the CMC model has been found to be capable of reproducing localized
extinctions and flame lift-off, which is a great improvement compared to the
capability of a flamelet model. From a statistical point of view, it was found
in the simulations of both a piloted non-premixed flame and a non-premixed
swirl flame that solving the CMC equations resulted in strong enough varia-
tions of the local density to modify the velocity and mixture fraction fields.
In both cases, the application of the advanced combustion model showed
a clear improvement of the mixture fraction prediction, while the axial
velocity prediction generally showed a slight worsening. An analysis and
understanding of this behaviour is well worth of further investigation.
• In the simulations presented in this thesis, only some white noise was added
to the top-hat profiles used for the numerical inlet velocities. It would be
worth injecting some turbulent fluctuations at the numerical inlets to re-
produce the turbulence of the flow in the burner and investigate its effects
on the flame structure. For instance, the Kelvin-Helmholtz instabilities
observed in Chapter 5 might not have remained visible at such axial dis-
tances from the burner exit if turbulent fluctuations had been added to the
numerical inlet velocities.
• Another aspect of the thesis work is the comprehensive analysis of the flow
based on Proper Orthogonal Decomposition. Several variables were used
to perform POD analysis in an attempt to bring to light correlations be-
tween the flow, mixing and combustion dynamics. However, the results
obtained were always interpreted from an aerodynamic point of view. As
a result, it could be worth performing POD of LES datasets based on the
scalar dissipation rate and YOH simultaneously in order to analyze further
the dynamics of localized extinctions and flame lift-off. POD analysis based
simultaneously on the velocity components and YOH could also reveal more
information on the interaction between the flow aerodynamics and the com-
bustion.
234
8. Conclusions
• In the study of the TECFLAM burner in Chapter 6, the dynamics of the
hydrodynamic structures (i.e. their rotation or precession) was always char-
acterized by (at least) a pair of modes. The spectral analysis of these
modes generally showed a single frequency peak and the interpretation of
the modes was therefore straightforward. However, for the vortex shedding
observed in the bluff body pulsating flows (Chapter 4), the POD analysis
has shown some of its limitations. In fact, the Proper Orthogonal Decom-
position method, while enforcing the spatial orthogonality of the modes,
computed an evolution of the modes based on multiple frequencies. The
method did not separate each harmonic of the flow into a specific mode. As
a consequence, we suggest that other analytical methods should be tried,
such as the Dynamic Mode Decomposition [98]. With this method, the
orthogonality is enforced in the frequency space rather than in the physical
space, which could lead to an easier interpretation of the different modes in
certain cases.
235
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