EXPERIMENTAL AND NUMERICAL INVESTIGATION OF CONFINED
PREMIXED FLAME
By
Younis Mahal Najim

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Mechanical Engineering - Doctor of Philosophy
2017

ABSTRACT
EXPERIMENTAL AND NUMERICAL INVESTIGATION OF CONFINED PREMIXED
FLAME
By
Younis Mahal Najim
Understanding the dynamics of premixed flames propagating during constant volume combustion is key to enhancing the performance of existing combustion devices, which provide 80% of
the world’s energy supply, and reducing the impact of pollution on the environment. This work
experimentally and numerically investigates confined premixed flame propagation in an initially
quiescent mixture. Three combustion chambers are used; a curved wave disc engine channel and
rectilinear channels of aspect ratio 7 and 10. The mixture is methane/air and syngas (H2 /CO)/air
initially at atmospheric pressure and room temperature. The channel walls are assumed to be
isothermal to incorporate the effect of heat transfer. For two-dimensional analysis, the reaction rate
is modeled using both detailed and reduced kinetic mechanisms. The mass diffusion is investigated
using three different diffusion models with different levels of approximation; the multicomponent
diffusion model of Chapman-Enskog including the Soret effect; the mixture-averaged model; and
constant Lewis number. For three-dimensional analysis, a large eddy simulation coupled with the
transport equation of the reaction progress variable is used. In this work, the reaction rate predicted
using the Boger model of algebraic flame surface density is modified by incorporating a transient
flame speed that accounts for the variation in the temperature and pressure of the unburned gases.
The experimental measurements include schlieren photography to track the flame structure and
propagation speed, and the pressure-time history during the combustion process is measured by
a pressure sensor mounted in the channel wall. The experimental measurements validate the numerical simulation results and provide further understanding of the flame and pressure dynamics.

Unlike behavior previously reported in straight or 90◦ bend channels, premixed flame propagation
in the wave disc engine channel exhibits different features: the convex tulip flame converts back
into a concave flame and thus reveals the influence of channel geometry on flame evolution. The
experiments show that the rate of pressure change eventually becomes negative mainly due to heat
losses that engender a correspondingly slower flame propagation during the final stage of burning.
The analysis of the numerical results reveals the effect of the interaction between the flame front,
pressure field, and flame-induced flow on flame evolution during all stages of flame structure development. The results also demonstrate that both multicomponent diffusion with the Soret effect
and the mixture-averaged model produce slightly different results in flame speed, structure, peak
temperature, and average pressure for the methane/air mixture, while the deviation is more pronounced for syngas flames. The methane/air flame produced by the unity Lewis number model,
however, lags behind its counterparts during early stages and dramatically accelerates, at which
time the values of peak temperature and average pressure show unrealistic behavior. Furthermore,
unity Lewis number flames develop an artificial second tulip flame after the first tulip flame is annihilated. This second tulip flame is neither observed in the Chapman-Enskog and mixture-average
simulations, nor in the experiments. This reveals the role of the Lewis number in the intrinsic
thermodiffusive flame instabilities and tulip flame formation. The three-dimensional simulation
uncovers an interesting behavior for the flame structure that is introduced here as a “transverse
tulip” flame, which has not been previously reported. The “transverse tulip” flame evolves in the
direction perpendicular to that of the initial tulip flame after the latter undergoes the transition from
cusped convex back to the concave finger shape. The commonly used Zimont model produces an
unrealistically diffused flame front. The large eddy simulation coupled with the here-modified algebraic flame surface density overcomes this issue and reproduces the experimental observations
of the flame structure, pressure-time history, and burning time with good agreement.

Copyright by
YOUNIS MAHAL NAJIM
2017

ACKNOWLEDGMENTS

This work would not have been possible without an unforgettable and enriching association with
the Turbomachinery Laboratory and Combustion Laboratory at Michigan State University.
I would like to express my deep sense of gratitude and indebtedness to my advisor, Prof. Norbert Mueller, for providing me the opportunity and guidance throughout my PhD study. His keen
interest and personal involvement during this study is beyond words of gratitude.
I am deeply indebted to Prof. Indrek Wichman for his close association with every part of this
project and for providing space in his laboratory to set up and run my experiments. I am incredibly
grateful to Prof. Charles Petty for his invaluable advices and discussion about the turbulence
modeling which led me to understand various aspects of turbulence modeling and realizability.
Many thanks go to Prof. Abraham Engeda for his helpful criticisms and suggestions as members
of the supervisory committee for this dissertation.
I wish to thank my colleagues within the Turbomachinery Laboratory, for their continuous
help and every bit of their valuable input. I gratefully acknowledge the Higher Committee For
Education Development and Ministry of Higher Education and Scientific Research in Iraq for the
unique opportunities given to me, allowing me to pursue my PhD degree.
At last but not the least, I would like to thank my family for their endless support in achieving
this great success in my life. I am forever grateful for all the assistance and encouragement they
have provided throughout my academic life.

v

TABLE OF CONTENTS

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ix

KEY TO SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv
KEY TO ABBREVIATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix
Chapter 1
INTRODUCTION
1.1 Background . . . . . . . .
1.2 Motivation and Objectives
1.3 Thesis Outline . . . . . . .

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Chapter 2
LITERATURE REVIEW - CONFINED PREMIXED FLAME
2.1 Dynamics of confined premixed flame . . . . . . . . . . . . . . . . . . .
2.2 Molecular Diffusion Impact on Confined Premixed Flame . . . . . . . . .
2.3 Syngas Premixed Flame . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Turbulent Premixed Flame . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 3
GOVERNING EQUATIONS AND MODELING
3.1 Laminar Premixed Flames . . . . . . . . . . . . . . . . .
3.1.1 Reaction rate - Kinetic Mechanism . . . . . . . . .
3.1.2 Molecular diffusion . . . . . . . . . . . . . . . . .
3.1.2.1 Lewis Number . . . . . . . . . . . . . .
3.1.3 Gas properties . . . . . . . . . . . . . . . . . . . .
3.2 Turbulent Premixed Flame . . . . . . . . . . . . . . . . .
3.2.1 Large Eddy Simulation . . . . . . . . . . . . . . .
3.2.1.1 LES filtering . . . . . . . . . . . . . . .
3.2.1.2 Filtered Conservation Equations . . . . .
3.2.1.3 Subgrid Scale Model . . . . . . . . . . .
3.2.2 Combustion Model- Flamelet Concept . . . . . . .
3.2.2.1 Flame Speed Closure . . . . . . . . . . .
3.3 Boundary and Initial Conditions . . . . . . . . . . . . . .
3.3.1 Numerics . . . . . . . . . . . . . . . . . . . . . .

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Chapter 4
EXPERIMENT SETUP
4.1 Combustion Chambers . . . . .
4.2 Experiment Setup . . . . . . . .
4.3 Methods of Measurement . . . .

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Chapter 5
EXPERIMENTAL AND NUMERICAL SIMULATION
5.1 Flame Front Evolution . . . . . . . . . . . . . . . . . . . . . . .
5.1.1 Non-symmetrical Tulip Flame . . . . . . . . . . . . . . .
5.1.2 Diffusion impact . . . . . . . . . . . . . . . . . . . . . .
5.1.2.1 Methane/air flame . . . . . . . . . . . . . . . .
5.1.2.2 Syngas flame . . . . . . . . . . . . . . . . . . .
5.2 Pressure Dynamics and Flame Speed . . . . . . . . . . . . . . . .
5.3 Flame-Induced Flow . . . . . . . . . . . . . . . . . . . . . . . .
5.3.1 Flame-induced flow and vorticity . . . . . . . . . . . . . .
5.3.2 Flame flow interaction . . . . . . . . . . . . . . . . . . .
5.4 Impact of Soret effect . . . . . . . . . . . . . . . . . . . . . . . .
5.5 Influence of Effective Lewis Number . . . . . . . . . . . . . . . .
5.6 Characteristic Burning Regime . . . . . . . . . . . . . . . . . . .
5.7 Influence of Mixture stoichiometry on Syngas Flames . . . . . . .
5.7.1 Flame structure . . . . . . . . . . . . . . . . . . . . . . .
5.7.2 Pressure dynamics . . . . . . . . . . . . . . . . . . . . .
5.7.3 Flame-flow interaction . . . . . . . . . . . . . . . . . . .

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Chapter 6
FLAME SURFACE DENSITY FOR LES
6.1 Three-Dimensional Structure of the Flame Front . .
6.1.1 Transverse tulip flame . . . . . . . . . . . .
6.1.2 3D flame dynamics in a rectangular channel
6.1.3 Flame surface density . . . . . . . . . . . .
6.1.4 Turbulent flame speed . . . . . . . . . . . .
6.1.5 Assessment of AFSD . . . . . . . . . . . .

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Chapter 7
CONCLUSIONS AND RECOMMENDATIONS . . . . . . . . . . . . . 121
7.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
7.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
Appendix A Grid Resolution Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
Appendix B Turbulent Flame Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

vii

LIST OF TABLES

Table 3.1:

Chemical-Kinetic Mechanisms used in this work. . . . . . . . . . . . . . . . . 21

Table 3.2:

Mass diffusion Coefficient for Multicomponent, mixture-average, and constant
Lewis number. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

Table 3.3:

Summary of CFD simulation cases. . . . . . . . . . . . . . . . . . . . . . . . . 42

Table 5.1:

Cases for syngas flame simulations. . . . . . . . . . . . . . . . . . . . . . . . . 92

Table A.1: CFD cases used to examine grid resolution. . . . . . . . . . . . . . . . . . . . . 127

viii

LIST OF FIGURES

Figure 1.1:

Schematic diagram illustrating premixed flames structure. . . . . . . . . . . .

2

Figure 1.2:

Schematic design of the wave disc engine. . . . . . . . . . . . . . . . . . . . .

5

Figure 2.1:

Sequence of flame phases developed in a rectangular channel. . . . . . . . . .

9

Figure 2.2:

Modified turbulent flames regimes Poinsot & Veynante (2005) and Peters (1999) 17

Figure 3.1:

Flame speed predicted by San Diego kinetic mechanisms and tested against
available experimental data from literature Beeckmann et al. (2014), Halter
et al. (2005), Vagelopoulos & Egolfopoulos (1998), Qin & Ju (2005). The
analysis consists one-dimensional free propagating, premixed flame. . . . . . . 24

Figure 3.2:

Laminar flame speed for syngas kinetic mechanism of Kèromnès et al. (2013)
validated with available experimental data Hassan et al. (1997), Burbano et al.
(2011). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Figure 3.3:

Laminar flame speed for DRM19, San Diego Mech. under different operating
pressures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Figure 3.4:

Laminar flame speed for DRM19 and San Diego Mech. under different reactants temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Figure 3.5:

Turbulence energy spectrum regimes . . . . . . . . . . . . . . . . . . . . . . 34

Figure 4.1:

Schematic diagram of computational domain. . . . . . . . . . . . . . . . . . . 44

Figure 4.2:

Schematic diagram of single wave disc engine channel used for experimental
measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Figure 4.3:

Closed rectangular channel serves as combustion chamber . . . . . . . . . . . 45

Figure 4.4:

Schematic diagram of the experimental setup. The premixed flame images are
measured at rate 3600 f ps, and the pressure readings are sampled at 5 kHz. . . 47

Figure 4.5:

Pressure measurements tested against available data from literature DunnRankin et al. (1988) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

Figure 4.6:

Normalized values of average pressure measurements for stoichiometric CH4 /
air flame. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

ix

Figure 4.7:

Raw data recorded by pressure transducer for eight(8) experiment to ensure
the reproducibility of the tests. . . . . . . . . . . . . . . . . . . . . . . . . . 50

Figure 5.1:

Evolution of the WDE confined premixed flame using schlieren photography
(images on the lift) and mass fraction contours of HCO, which serve to track
the flame locus, from the numerical simulations (images on the right): (a-d)
hemispherical expansion and evolution to a concave “finger” flame; (e) inner
part of lateral flame touches the inner sidewall; (f) outer part of lateral flame
touches the outer sidewall and flame front flattens; (g) initial formation of tulip
flame cusp which generates the characteristic convex tulip flame shape; (h-k)
inner flame tongue grows by radially displacing the flame cusp toward the
outer sidewall ; (l) upper flame tongue disappears; (n-o) tulip flame converted
to curved flame. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

Figure 5.2:

Comparison between the experimental and numerical simulations of the normalized flame locations XF /XF max . Also shown is the ratio of these normalized flame locations, showing that the numerical flame evolution is always
faster than the experimental flame evolution. . . . . . . . . . . . . . . . . . . 56

Figure 5.3:

Methane/air premixed flame front development; (on the right) flame shadowgraphy and (on the left) flame fronts for M(I), M(II), and M(III) models: (a-f)
flame of M(III) lags behind M(I) and M(II) and small discrepancy can be observed between M(II) and M(II) in b, (g-h) M(III) flame is ahead of M(I) and
M(II);(i-k) M(III) develops a second tulip flame; (l) M(I), M(II), and M(III)
and converted into concave flames. . . . . . . . . . . . . . . . . . . . . . . . 59

Figure 5.4:

Flame tip distance from igniter location recorded at the channel centerline for
models M(I), M(II), M(III) and the experiment. The initial condition from
which time is reached is the instant at which all flames have penetrated 5 mm
into the channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

Figure 5.5:

Premixed syngas flame front development for M(I), M(II), and M(III) diffusion
models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

Figure 5.6:

Experimental measurements of normalized flame speed, normalized pressure
P[bar]/3.15, normalized rate of pressure change (dP/dt)[bar/s]/866, and
normalized pressure second derivative. The numbers in these denominators
are maximum values that are used to scale all of the curves for improved visualization. The data shown are averages of eight separate experiments. Also
shown on the right-hand scale is the experimentally measured variance of the
pressure data, indicating it to be under 1%. The experiments measure flame
position: flame speed is obtained by differentiation. . . . . . . . . . . . . . . . 66

x

Figure 5.7:

Interaction between flame front and flame-induced flow: (a) burned gas produced by lateral flame moves from sidewalls toward the centerline of the channel, and then is deflected along the channel centerline; (b) inner lateral flame
is quenched while upper lateral flame continues to thrust the burned gases toward the inner wall and is then deflected toward the flame front; (c) inversion
of burned gas flow; (a-c) vorticity is generated in the near wall region of the
channel by the forward forced flow; (d-f) vorticity is generated in burned gas
behind the flame front by the rearward forced flow. The change in flame morphology from concave to convex occurs between (c) and (d) as the tulip is
formed while the change from convex to concave occurs between (e) and (f)
as the concave flame front is reconstituted. . . . . . . . . . . . . . . . . . . . 70

Figure 5.8:

Velocity field induced by the flame at different combustion time. . . . . . . . . 71

Figure 5.9:

Flame-induced flow and the characteristic saddle points of unity Lewis number
flame: (a) spherical flame surrounds saddle point; (b) finger flame front away
from saddle point ; (c) saddle point moves close to skirt flame; (d-f) saddle
point moves close to lower tongue of the first and second tulip flame; (g-h) no
saddle point was observed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

Figure 5.10: Soret effect impact on the CH4 species concentration plotted along the normalized channel width in the unburned region. . . . . . . . . . . . . . . . . . . . 76
Figure 5.11: Soret effect impact on the AR species concentration plotted along the normalized channel width in the unburned region. . . . . . . . . . . . . . . . . . . . 76
Figure 5.12: Soret effect impact on the O2 species concentration plotted along the normalized channel width in the unburned region. . . . . . . . . . . . . . . . . . . . 77
Figure 5.13: Soret effect impact on the N2 species concentration plotted along the normalized channel width in the unburned region. . . . . . . . . . . . . . . . . . . . 77
Figure 5.14: Soret effect impact on the H2 O species concentration plotted along the normalized channel width in the burned region. . . . . . . . . . . . . . . . . . . . 78
Figure 5.15: Soret effect impact on the CO2 species concentration plotted along the normalized channel width in the burned region. . . . . . . . . . . . . . . . . . . . 79
Figure 5.16: Soret effect impact on the H2 species concentration plotted along the normalized channel width in the burned region. . . . . . . . . . . . . . . . . . . . . . 79
Figure 5.17: Soret effect impact on the O species concentration plotted along the normalized channel width in the burned region. . . . . . . . . . . . . . . . . . . . . . 80

xi

Figure 5.18: Mass fraction of H2 and CO distributed across the WDE channel for the case
M(I). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Figure 5.19: Mass fraction of O2 and N2 distributed across the WDE channel forthe case
M(I). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Figure 5.20: Mass diffusion flux due to Soret effect at, 14.96 ms for: (a) CH4 ; (b) O2 ; (c)
CO2 ; (d) N2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
Figure 5.21: Average pressure developed in the WDE channel under three different diffusion model M(I), M(II), and M(III) for stoichiometric methane/air. . . . . . . 85
Figure 5.22: Peak temperature developed in the WDE channel under three different diffusion model M(I), M(II), and M(III) for stoichiometric methane/air. . . . . . . 85
Figure 5.23: Average pressure developed in the WDE channel under three different diffusion model M(I), M(II), and M(III) for syngas/air of φ = 0.7 and 50% H2 . . . 86
Figure 5.24: Peak temperature developed in the WDE channel under three different diffusion model M(I), M(II), and M(III) for syngas/air of φ = 0.7 and 50% H2 . . . 87
Figure 5.25: Evolution of effective Lewis number derived from case M(II) for methane/air
mixture at different combustion time. . . . . . . . . . . . . . . . . . . . . . . 88
Figure 5.26: Normalized inverse Peclet number ratio N /N(2) versus normalized total time
t/tmax . The hydrodynamic Regime (1), and the thermodiffusive Regime (2)
occupy 10 and 20% of the total time. The heat-loss Regime (3) occupies the
remaining 70% of the burn time. . . . . . . . . . . . . . . . . . . . . . . . . . 90
Figure 5.27: Syngas flame structure for different stoichiometric ratios and hydrogen content
(C1-9). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
Figure 5.28: Syngas combustion time for different mixture stoichiometry. . . . . . . . . . . 95
Figure 5.29: Instantaneous syngas flame distance for different mixture stoichiometry. . . . . 96
Figure 5.30: Time-history of the channel average pressure under different mixture stoichiometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Figure 5.31: Time-history of the normalized pressure under different mixture stoichiometry.

98

Figure 5.32: Normalized syngas flame distance for different mixture stoichiometry. . . . . . 99

xii

Figure 5.33: Flame front interaction with flame-induced flow for stoichiometric ratio of 0.7
for different combustion time, hydrogen content, and flame front position at
the channel centerline. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Figure 5.34: Flame front interaction with flame-induced flow for stoichiometric ratio of 1.0
for different combustion time, hydrogen content, and flame front position at
the channel centerline. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
Figure 5.35: Flame front interaction with flame-induced flow for stoichiometric ratio of 1.5
for different combustion time, hydrogen content, and flame front position at
the channel centerline. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Figure 6.1:

Flame structure evolution;(a) hemispherical flame, (b) finger flame, (c) skirt
flame (d) straight flame front on transverse plane and concave flame on lateral
plane, (e) non-symmetric tulip flame on lateral plane, (f) initial tulip flame
back to concave finger shape (g-h) transverse tulip flame. . . . . . . . . . . . . 106

Figure 6.2:

Experiment flame front shadowgraphy (on the left side) and numerical simulation flame front on plane z = 0 mm and z = 7.25 mm projected on one plane
(on the right side). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

Figure 6.3:

Three-dimensional, flame front structure developed in a rectangular chamber.
(a) spherical expansion of ignition kernel, (b) finger-flame expansion, (c) skirtflame, (d) tulip-flame. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

Figure 6.4:

Evolution of flame structure, flame-induced flow, and dynamics of saddle
point. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

Figure 6.5:

Flame surface density and product formation rate for WDE channel. . . . . . . 112

Figure 6.6:

Flame surface density and product formation rate for the rectangular chamber. . 112

Figure 6.7:

Variation of flame speed during the flame propagation in the WDE channel. . . 114

Figure 6.8:

Temperature of unburned gases and average pressure developed in the WDE
channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

Figure 6.9:

Transient flame speed developed in a rectangular channel. . . . . . . . . . . . 116

Figure 6.10: Unburned gases average temperature and pressure for premixed flame propagating in the rectangular channel. . . . . . . . . . . . . . . . . . . . . . . . . 116
Figure 6.11: Time-history of the average pressure developed in a rectangular chamber. . . . 118

xiii

Figure 6.12: Comparison between flame predicted by algebraic flame surface density and
experimental observation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
Figure 6.13: Comparison between modified algebraic flame surface density and Zimont model120
Figure A.1: Flame front structure and flame-generated flow predicted by (a) current mesh
size(150 × 1500) and (b) finer mesh(300 × 3000). . . . . . . . . . . . . . . . 128
Figure A.2: Average pressure of the syngas/air premixed flames. . . . . . . . . . . . . . . 129
Figure A.3: Methane/air flame front structure predicted by 0.05 mm and 0.025 mm maximum cell sizes. The Flames front are represented by C2 H6 contours. . . . . . . 130
Figure A.4: Mass fraction of HCO species plotted along a line of 0.8 mm passing through
the methane/air flames front. . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
Figure B.1: Maximum cell Reynolds number evaluated during flame propagating in the 3D
rectangular channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
Figure B.2: Maximum cell Reynolds number evaluated during flame propagating in WDE
channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
Figure B.3: Average DamkĂśhler number for WDE channel. . . . . . . . . . . . . . . . . . 133
Figure B.4: Unburned gases density developed during flame propagation in a rectangular
channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
Figure B.5: Unburned gases density developed during flame propagation in the WDE channel. Also showing the mixture average density. . . . . . . . . . . . . . . . . . 134

xiv

KEY TO SYMBOLS

English Symbols
Af j

pre-exponential factor of reaction j

c

reaction progress variable

cp

specific heat capacity

Da

DamkĂśler number

Dkl

multicomponent mass diffusion coefficient

DT k

thermal diffusion coefficient of species k

d

distance to the closest wall

Ej

activation energy of reaction j

e

total energy

Fk

diffusion driving force

G(xi )

LES filter function

h

enthalpy

Hko

enthalpy of species k evaluated at standard condition

I

matrix identity

Jk

molecular mass flux of species k

Ka

Karlovitz number

kB

Boltzmann constant

Kf j

forward rate of reaction j constants

Kr j

reverse rate of reaction j constants

Le

Lewis number

Ls

characteristic length in WALE SGS model
xv

lt

integral length scale

Mk

molecular weight of species k

Ns

total number of mixture species

N

non-dimensional characteristic time ratio

p

pressure

patm

atmospheric pressure

Pr

Prandtl number

Qi

Progress of reaction

q

net energy crossing the control volume surface by the mechanisms of
molecular conduction and diffusion of species k

R

gas constant, 8314 (J/kgK)

Ret

turbulent Reynolds number

Sko

entropy of species k evaluated at standard condition

Sl

laminar flame speed

Slre f

laminar flame speed evaluated at standard conditions

t

time

T

temperature

Tu

unburned gases temperature

T

stress tensor based on the Newtonian fluid assumption

T∗

dimensionless temperature (T ∗ = T /(ε/kB )k )

u

the mass average velocity vector of the gas mixture, u = (u, v, w)

Vk

diffusion velocity of the species k

Xk

mole fraction of species k

xvi

x, y, z

Cartesian coordinates axis

Yk

mass fraction of species k

(˜)

filtered quantity for LES

Greek Symbols
Îą

thermal diffusivity of the mixture

βj

temperature exponent of reaction j

∆

the LES filter width

δi j

Kronecker delta function

Îľk

the Lennard-Jones potential well depth

Îş

von KĂĄrmĂĄn constant

Îť

thermal conductivity

Âľ

mixture-average dynamic viscosity

ÂľSGS

subgrid-scale viscosity

00

νk j
0

stoichiometric coefficients of products of species k

νk j

stoichiometric coefficients of reactants of species k

∇

the gradient operator

ρ

density

ρu

unburned gases density

ÎŁ

flame surface density

σi j

subfilter stresses

σk

the Lennard-Jones collision diameter

φ

equivalence ratio

xvii

ψs

stoichiometric ratio air to fuel ratio

ΩE

collision integral function

ωk

molar rate of production of species k,

ωT

heat release term

τl

the integral turbulent timescale

τc

the chemical or reaction rate timescale

xviii

KEY TO ABBREVIATIONS

AFSD

algebraic flame surface density

BML

Bray Moss Libby model

CNC

Computer Numerical Control

CV

constant volume

DNS

direct numerical simulation

fps

frame per second

FSD

flame surface density

LES

large eddy simulation

M(I)

multicomponent diffusion model with Soret effect included

M(II)

mixture-averaged diffusion model

M(III)

constant Lewis number

PDE

pulse detonation engine

RANS

Reynolds Averaged Navier Stokes equations

SGS

subgrid-scale

WALE

wall-adapting local eddy-viscosity subgrid-scale model

WDE

wave disc engine

xix

Chapter 1
INTRODUCTION

1.1

Background

Combustion is a chemical reaction in which the oxidizer rapidly reacts with the fuel and liberates
heat. The fuel can be a solid (such as wood and coal), liquid (such as gasoline and hydrocarbon
fuel), and gas (such as natural gas). The combustion field is extremely broad and can be classified
based on the way the fuel and oxidizer are introduced in the flame zone. In premixed flames, as
their name implies, the fuel and oxidizer are thoroughly mixed at the molecular level prior to their
burning. This combustion mode is used in many practical combustion devices such as gasolinefueled internal combustion engines, lean premixed in a power-generating gas turbine, gas appliance
stoves. The structure of premixed flames is illustrated in Fig. 1.1.
On the other hand, the non-premixed flames in which the fuel and oxidizer are separately
introduced into the combustion chamber where they must mix before significant reaction can commence. Such flames are used in many combustion processes where the reaction rate is controlled
by mixing processes which are due to molecular diffusion, convection, and turbulent mixing.
Other combustion modes are the laminar and turbulent flames depending on the flow, whether it
is laminar or turbulent. Moreover, in gasdynamics, the terms deflagration and detonation are used
to describe another combustion modes in which the flames propagate at subsonic and supersonic
speed, respectively.

1

Mass diffusion, radicals

Lewis Nu. =

Reaction zone
𝝎𝑻

Perfectly mixed
Reactants

𝒖𝒖
𝒑𝒖
𝝆𝒖
𝑻𝒖
𝒌 = 𝟏. . 𝑵𝒖

Preheat zone

Heat diffusion

Heat diffusion
Mass diffusion

𝒖𝒃
𝒑𝒃
Perfectly mixed
𝝆𝒃
products
𝑻𝒃
𝒌 = 𝟏. . 𝑵𝒃
𝑻𝒃

Flame zone

Product mass fraction

Oxidizer mass fraction

Fuel mass fraction
Reaction rate

Temperature

Figure 1.1: Schematic diagram illustrating premixed flames structure.
The premixed flames involves two distinct zones; preheat and reaction zones. In the preheat
zone, the energy diffuses from the burnt high temperature region and heats the mixture to the
temperature where combustion reactions commence. The main fuels oxidize into products in the
reaction zone where the heat of combustion is released. Also, the concentration and temperature
gradient in the reaction zone represent a potential driving force for radicals and species diffusion.
The heat and mass diffusion play crucial role in the combustion process and flame structure. The
ratio between heat and mass diffusion is known as Lewis number.
Unlike non-premixed flames, the premixed flames are characterized by laminar flame speed
which can be defined as the propagation speed normal to the unwrinkled flame surface. The laminar
flame speed is one of the most important property of a combustible mixture that depends on the
thermochemical and transport properties of the mixture, and therefore it provides information about
the reactivity and diffusivity of the reacting mixture Shang et al. (2016). It is also used as a basis
2

for turbulent flame speed and to validate the chemical kinetic mechanism.
The increase in turbulence intensity in the vicinity of flame front changes the flame structure
from laminar smooth front to wrinkled, corrugated, stretched, thickened flame and end up with
flame quenching when the Kolmogorov length scale becomes larger than the flame stretch limit
Poinsot & Veynante (2005), Peters (2000). The turbulence mixing speed up the transport of heat
and radicals at the flame front and hence increase the reactivity and flame speed.

1.2

Motivation and Objectives

Combustion are essential process for power generation which indisputably represents a primary
driving potential of human development. Currently, 85% of the energy consumed in the United
States comes from combustion of hydrocarbon fuel such as natural gas, petroleum, and coal McIlroy et al. (2006). However, the increase in global energy demand and the limitation of hydrocarbon
energy sources in addition to environmental concerns exert continuous need for highly efficient
combustion devices and alternative energy resources. Natural gas and syngas offer an alternative
and attractive source of energy by diversifying the energy use and emitting less CO2 per unit of
energy compared to oil and coal which helps to slow down the impact of fossil fuel combustion on
climate change. The availability of natural gas is deemed to be potentially larger than both conventional crude oil and unconventional resources combined. In the United State, the production of
natural gas increased by 35% from 2005 to 2013 and its share of the total U.S. energy consumption
rose from 23% to 28% U.S Department of Energy (2015).
This particular work is motivated by research and development of the wave disc engine (WDE),
which was designed and built at Michigan State University (MSU). A schematic design of WDE
is shown in Fig. 1.2. The thermodynamic foundation of this engine is the Humphrey cycle that

3

utilizes an internal combustion engine cycle consisting of compression which is mainly performed
through pressure waves, constant volume combustion, work extraction from hot gases expansion,
and heat rejection to the ambient. All these processes take place in radial arranged and curved
channels mounted around the WDE shaft.
The WDE must work at high frequencies in order to produce power with a reasonable efficiency. Details concerning the wave disc engine concept can be found in Sun et al. (2012), Sun
(2011), Kiran (2013). It has been demonstrated that the time for combustion inside the WDE channel consumes about 95% of the total cycle time Hariharan & Wichman (2014). This indicates that
the time required for the burning process limits the WDE from operating at high frequencies, which
is a key issue for improving its performance. This also shows that the time remaining for the work
extraction stroke is brief compared with the cycle time. Any attempt to extract more work should
be accompanied by increasing the time for work harvesting. Accelerating the flame propagation
rate inside the WDE channel can reduce the burning time and allow the WDE to operate at higher
rotational speeds in order to produce more work Johansen (2009).
The main objectives of this work is as follow:
• To better understand the pressure and flame dynamics inside the wave disc engine channel
channel. This is an essential step toward establishing a reference point from which future
advancements in flame and burning acceleration in WDEs can be assessed.
• To provide further understanding on the impact of diffusion models and thermal diffusion
on the dynamics of premixed methane/air and syngas/air flames propagating in a curved
non-symmetrical closed channel. The influence of mixture stoichiometry on syngas flame
structure and pressure dynamics is also examined.
• Since the available computational resources can’t handle the the three dimensional model
4

Fresh Air-Fuel Mixture
Burnt Exhaust Gas

Shock wave
Combustion

Figure 1.2: Schematic design of the wave disc engine.
with detailed chemistry and diffusion model, the three-dimensional model of WDE and rectangular channel (38 mm × 38 mm × 279.4 mm) is solved using large eddy simulation and
single transport equation for reaction progress variable in which the source term is predicted
using the algebraic flame surface density modified by including a temperature-and pressuredependent laminar flame speed.
• Since the premixed flame propagates into quiescent mixture and the flow induced by the
flame is evolving with time, an adaptive switch is used between Metghalchi-Keck flamespeed correlation for laminar flow and Zimont flame speed closure model for turbulent flow.
• To validate the numerical simulation results, experimental measurements for wave disc engine and rectangular channel are conducted using schlieren photography to track the absolute
speed and structure of the flame and pressure sensor is mounted on the channel wall to record
the pressure time-history during combustion process.

5

1.3

Thesis Outline

This dissertation is a compilation of experimental and numerical simulations aimed at understanding the pressure dynamics and the temporal development of flame structure in confined chambers.
Chapter 2 gives an overview of the confined premixed flame, proposed mechanism for tulip flame
formation and mass diffusion impact on the flame and pressure. Chapter 3 of the thesis provides
a summary of the governing equations describing a incompressible reactive mixture of gases and
reaction modeling for laminar and turbulent flame. Chapter 4 presents the experimental setup and
method of measurements. A discussion of experimental and numerical simulation results for twodimensional premixed flame as well as the mass and thermal diffusion impact on the flame structure
and pressure time-history are presented in Chapter 5. Chapter 6 discusses the main elements of
three-dimensional evolution of flame and flame generated flow in both WDE and rectangular channel. Finally, a conclusions from the present work and recommendation for the future studies are
described in Chapter 7.

6

Chapter 2
LITERATURE REVIEW - CONFINED
PREMIXED FLAME
The confined premixed flames represent 99% of practical combustion devices which recover heat
released in furnaces or mechanical power in engines such as internal combustion engines, pulse
detonation engines, the wave rotor and the wave disc engine (WDE). In addition, the study of both
premixed flame spread and the explosion of reacting gases in confined spaces is relevant for safety
in silos, mines, oil refinery, and petro-chemical processes Ogle, 2017. However, the analysis of
confined flames is much complicated than freely propagating flames, mainly due to heat exchange
with walls, flame-acoustic interaction, and complex geometry of combustion chambers. In the
next sections, the main features of flame structure developed in a confined, curved and straight
channels are reviewed from literature sources. The impact of diffusion transport and turbulence on
the confined flame structure is also reviewed and discussed.

2.1

Dynamics of confined premixed flame

Constant volume (CV) premixed flame propagation usually associated with the formation of tulip
flame which has a long and interesting history. This history began over eighty years ago when
Ellis published an experimental study of premixed flame propagation inside a closed cylinder,

7

marking the start of a new era in premixed flame research Ellis (1928). Subsequent studies have
shown that a premixed flame propagating in a channel of aspect ratio larger than approximately two
(2) experiences essentially four phases that have been observed and reproduced in numerical and
experimental studies Ponizy et al. (2014), Xiao et al. (2014b), Hariharan & Wichman (2014). These
phases are shown in Fig. 2.1: (a) after ignition, the flame surface propagates spherically at constant
flame speed; (b) a finger- shaped flame propagates axially away from the ignition source (spark)
with rapidly increasing flame surface area; (c) a flame skirt is formed when the flame touches
the sidewalls. The lateral parts of the flame skirt are annihilated by the cold sidewalls leading
to a dramatic reduction in the flame surface area, and the flame propagation speed is decreased;
(d) the flame subsequently flattens and begins to fold and finally develops into a tulip flame, which
propagates to the end of the channel Xiao et al. (2012a), Xiao et al. (2013). A fifth stage, introduced
and discussed in this work, is found in the numerical analysis and verified experimentally, is the
slow extinction of the flame at the far wall by heat losses.
The evolution of the flame shape leads to an important question. What is the physical interpretation for the flame shape changes, especially the tulip flame, and which flow parameter is most
responsible?
Many mechanisms have been proposed to answer this question by studying the key parameters involved in the flame morphology development and evolution. Some of the proposed mechanisms are: Darrieus- Landau and other combustion/heat transfer instabilities Gonzalez et al. (1992),
Dunn-Rankin et al. (1988), Chomiak & Hou (1996), Matalon & McGreevy (1994), the interaction
between flame and vortex motion generated on the burned gas side due to vorticity produced by
the flame Matalon & Metzener (1997), Kiran et al. (2014), Xiao et al. (2013), the saddle point motion across the flame front Hariharan & Wichman (2014), quenching of the flame by the sidewalls
and the viscous effect Ellis (1928), Starke & Roth (1986), Lewis & v. Elbe (1987). Most of these
8

(a) Hemispherical flame
(b) Finger flame
(c) Skirt flame
(d) Tulip flame

Figure 2.1: Sequence of flame phases developed in a rectangular channel.
studies were conducted using straight channels and tubes, which in some cases were open and
partially open ended Clanet & Searby (1996). It is important to note that the notion of four stages
of combustion ((a)-(d) above) was formalized by Clanet and Searby Clanet & Searby (1996), in
whose work on open-ended tubes there was no flame quenching: our work has extended the num-

9

ber of flame stages to five. Concerning the fundamental science of the physics of flame evolution,
there is currently no universally acknowledged dominant mechanism for tulip flame formation and
evolution in a closed CV chamber. Furthermore, no flow or combustion parameter has been found
directly responsible for the evolving flame shape. Thus it is not possible, to date, to neutralize this
hypothetical effect in order to generate a confined premixed flame without showing the dramatic
shape change from concave initial flame to convex tulip flame Ponizy et al. (2014). Nevertheless,
the work of Hariharan & Wichman (2014), Zhou et al. (2006) and Ponizy et al. Ponizy et al.
(2014) has made substantial progress toward this goal. It is instructive to quote from the latter: “It
should be stressed... that the intrinsic instabilities of the flame front (Rayleigh-Taylor, RichtmeyerMeshkov or Darrius-Landau) are not involved in this process (of flame front inversion). Indeed,
the reverse flow which is responsible for the flame front inversion (concave to convex tulip) always
starts in the zone close to the ignition point and not at the flame front.” Ponizy et al. (2014). These
statements are supported by the work in Hariharan & Wichman (2014) which discusses in detail
the manifestation of the various flame events in terms of the flow field topology, and specifically
in terms of the characteristic saddle point, which propagates through the flow field as a geometric
and temporal harbinger of flame front morphological change.
The mechanism of tulip flame formation and the other flame phases are important for combustion acceleration because the flame shape and surface area have a direct influence on the burning
rate. Knowing how to increase the flame surface area under specific conditions is a key aspect of
flame acceleration for an increased burning rate. The majority of previous studies were carried
out using straight channels or tubes. However, the WDE chamber currently under investigation
is shaped by two arcs of different radii (Fig. 4.2) and thus it is of interest to examine the channel curvature impact on flame dynamics. The study of premixed laminar flame propagation in a
closed rectangular channel with a 90◦ bend has been carried out experimentally and numerically
10

by B. Zhou et al. Zhou et al. (2006). They observed a phenomenon they characterized as “flame
shedding” when the flame propagated through the first 45◦ of the bend. The flame could generate a
thrust force pushing the unburned gases forward, producing a flame-induced flow which appeared
to be responsible for the tulip flame formation after the flame left the bend vicinity. The influence
of mixture composition in hydrogen-methane-air on flames in a 90◦ pipeline with a high aspect
ratio was experimentally investigated by Emami et al. Emami et al. (2013). The bend influences
the fluctuation of flame speed and pressure, producing a potential hazard risk for the pipeline.
Xiao at al. Xiao et al. (2014a) carried out an experimental and numerical study on a closed combustion tube with a 90◦ bend. The tulip flame that had developed in the straight channel section
disappeared when it entered the channel bend where the lower tongue of tulip flame grew while
the upper finger was annihilated. The convex tulip flame evolved, as in the current work, into a
concave flame, although the evolution was not smooth.
Some general conclusions may be drawn from these studies: (1) The dynamics of premixed
flames propagating in a closed CV chamber is a complex phenomenon that involves the mutuallyinteracting processes of fluid dynamics, heat transfer and chemical kinetics. No unique and certain
mechanism has yet been proposed to explain tulip flame formation. (2) The bending of the combustion chamber has a critical influence on the flame dynamics; it may annihilate the tulip flame and
convert it to a concave flame, while producing fluctuations in flame speed and pressure. (3) The
previous literature indicates that there is a lack of work on the non-symmetrical confining chamber
curvature effect on premixed flame dynamics. These effects can be found in many particular CV
chambers like internal combustion engines or the WDE.

11

2.2

Molecular Diffusion Impact on Confined Premixed Flame

Recently, the numerical simulation has provided critical information about the dynamics of confined premixed flame. It was shown that a considerable discrepancy was observed in flame speed
Smooke (2013), Liu et al. (2015), Bongers & De Goey (2003), flame extinction Williams (2001)
Xin et al. (2015),Grcar et al. (2009), soot formation Dworkin et al. (2009), ignition condition Andac & Egolfopoulos (2007), Han & Chen (2015) and other flame characteristics when they are
predicted by different diffusion models. This emphasizes the importance of diffusion model to
accurately resolve the confined premixed flame characteristics. Ern and Giovangigli Ern & Giovangigli (1999) have numerically investigated the impact of multicomponent diffusion on counter
flow and freely propagating laminar premixed methane/air and hydrogen/air steady flames using
detailed reaction mechanism and three different diffusion models. It was shown that thermal diffusion has an obvious effect on hydrogen flame speed and no significant impact on methane flame.
Higher peak temperature was obtained when the thermal diffusion is included while no significant
impact of diffusion models on peak temperature. In another study, the effect of multicomponent
and thermal diffusion on methane/air diffusion flame was numerically investigated using relatively
detailed combustion mechanism (25 chemical reactions between16 species). It was found that the
multicomponent diffusion model predicts 8% larger flame length, 4% larger flame sheet thickness,
and 5 K lower maximum flame temperature compared with simple Fick’s law model Kleijn &
Akker (1999). The contribution of thermal diffusion or Soret effect was also found to increase and
reduce the stretched flame speed during early stages of flame propagation for light and heavy fuel,
respectively Han & Chen (2015). It was shown that the multicomponent transport affects the flame
extinction limit for both methane and hydrogen fuels. Another study by Grcar et al.Grcar et al.
(2009) has shown that the multicomponent transport model in lean hydrogen-air flames predicted

12

“hotter, significantly faster flames with much faster extinction and division of cellular structures”.
A comprehensive review by Hilbert et al. Hilbert et al. (2004) included more than 200 publications
on turbulent flames with detailed chemistry and multidimensional diffusion model. This review
study concluded that the impact of multicomponent diffusion model plays essential role on local
flame structure especially for curved lean or rich freely propagating flames. The literature review
indicates growing interest of using more elaborate diffusion model to provide further understanding of premixed flame; however, the computational cost of solving the multicomponent diffusion
model seemed to be the main reason for making simple diffusion models e.g. constant Lewis and
Schmidt number commonly used in combustion simulations Giacomazzi et al. (2007). It is instructive to quote from the latter that “these assumptions (of constant Lewis and Schmidt number)
have never been theoretically justified nor verified in practical flame”, and hence it is important to
investigate how much the main characteristics of unsteady premixed flame propagating in closed
channel would deviate by using simple diffusion model of unity Lewis number and more elaborate
multicomponent diffusion models including thermal diffusion? Since the overwhelming literature
concerning the impact of diffusion model on premixed flame was focusing on turbulent and laminar diffusion flame configurations and little attention has obviously been given to multicomponent
diffusion effects in confined premixed laminar flames. Part of this work is dedicated to provide
further understanding on the impact of diffusion models and thermal diffusion on the dynamics of
premixed stoichiometric flames propagating in two-dimensional, curved non-symmetrical closed
channel.

13

2.3

Syngas Premixed Flame

synthesized gas (usually named syngas) is primarily a mixture of hydrogen and carbon monoxide
mixed in different volumetric percentage with other diluents such as nitrogen (N2 ), steam (H2 O), or
carbon dioxide (CO2 ). Syngas is one of the promising alternative fuel and environmentally clean
source of renewable energy because it can be produced from variety of primary fuel sources such
as biomass, coal, and hydrocarbon fuels and hence diversifying energy supply. The recent development in the integrated gasification combined cycle (IGCC) power plants have attracted considerable attention in syngas flame dynamics due to its industrial importance in reducing the CO2
emission, and diversifying the power plant driving fuel such as biomass, hydrocarbons, and coal.
Therefore, the syngas fuel plays a crucial role in facilitating carbon-free power generation using
(IGCC) technology Zhang et al. (2016), Tuncer & Mendez-Vilas (2013). The adjustment of syngas compositions is highly depended on the primary fuel components and gasification processes.
Therefore, the volumetric content of H2 and CO in syngas fuels varies significantly according to
the type of production processes, which in turn pose challenges in controlling the syngas flame behavior such as flashback, thermos-acoustic instabilities, NOx emission due to drastic variation in
chemical and transport properties as well as the laminar flame speed between hydrogen and hydrocarbon fuel. The other challenge is to design a fuel flexible, combustion chamber that can tackle
the variability in syngas fuel compositions. This requires a solid knowledge about confined flame
dynamics under wide range of mixture stoichiometry. Brambilla et al. (2015) reported a numerical
and experimental investigation of syngas premixed flame in a 7 mm height mesoscale, open end
channel at atmospheric pressure. Dinesh et al. (2016, 2015b,a) presented a DNS study about syngas flame propagation with high hydrogen content and different turbulent Reynolds number (50,
100, 150) at elevated pressure (1-4 bar). It is observed that the cellular flame structure of syngas is

14

highly depended on the elevated pressure under different initial turbulent conditions.
The present study undertakes a numerical investigation of premixed syngas flames propagating
in a 2D, rectangular, closed channel of aspect ratio of 10 (10 mm in height ×100 mm in length)
for different stoichiometric ratio (0.7, 1.0, 1.5) and H2 /CO ratio (1:4, 1:1, 4:1). The dynamics of
premixed syngas flame propagating in a closed channel has not been investigated in the literature.
Among fundamental combustion parameters required to better understand the propagation of syngas burning, flame topology, pressure time-history, and burning rate are the most important since
it directly related to industrial combustors.

2.4

Turbulent Premixed Flame

Generally speaking, turbulent flame definition comes from the change in flame structure as it propagates through turbulent flow field. Many experimental and numerical studies have proven that
increasing turbulence level changes the flame structure from laminar smooth front to wrinkled,
corrugated, stretched, thickened flame and end up with flame quenching when the Kolmogorov
length scale becomes larger than the flame stretch limit Poinsot & Veynante (2005). These observations were characterized by DamkĂśhler (1947) and two distinct regimes have been identified
based on the turbulence effect on the flame structure (Fig. 2.2):
1. Regime of large scale turbulence (Da > 1 ) where the flame is thinner than the Kolmogorov
scale and the chemical time scale is shorter than the turbulent time scale (Ka < 1). The flame
structure is wrinkled by turbulence motion but remains comparable to the laminar flame.
2. Regime of a small scale turbulence (Da << 1) in which the reactant and products are mixed
by small turbulence eddies. The flame structure at this regime is usually referred as “well
stirred reactor” or broken reaction zone Peters (2000).
15

A third regime, which is named “thickened flame regime” or “distributed reaction zones.”,
was identified later in the regime of Ka > 1 and Da > 1 where the chemical time scale is shorter
than the turbulent integral time scale but the flame thickness is larger than the Kolmogorov length
scale. In this regime, the turbulence eddies interacts with the reactants and products transport and
hence modifies the flame inner structure, more details can be found in Poinsot & Veynante (2005),
Glassman et al. (2015).
In the large scale turbulence regime, the flame is represented as a collection of small but finite
laminar flame elements and propagate locally with the laminar flame speed. These thin layers
are embedded within turbulent flow, one dimensional, time depended and strongly interact with
flame-generated flow Peters (1988). Based on the flamelet concept, the reaction rate is obtained as
the product of laminar flame speed, which depends on local pressure and temperature, and flame
surface area density Bray & Cant (1991), GĂźlder & Smallwood (2007).
The definition of flame surface density here comes to simplify the difficulties associated with
the temporal evolution of scalar surfaces embedded in turbulent flows, which are difficult to quantify directly Swaminathan & Bray (2011). Marble & Broadwell (1977) introduced the density of
isosurface per unit volume which is defined at each Eulerian cube in the computational domain.
In this work, the temporal variation of mixture temperature and pressure on the premixed flame
speed is incorporated with the algebraic flame surface density to estimate the reaction rate. The
evolution of three-dimensional confined flame structure is studied for low turbulence intensities
which is developed by flame-generated flow.

16

Ka=100
o

u’/SL

Da=1

Thickened Flames
Well-Stirred Reactor
Da<1

Thickened-Wrinkled Flame

Ka=1

Ret=1
Wrinkled Flame
(Flamelets regime)

1

Ka<1
Laminar Flames

1

lt/δ

Figure 2.2: Modified turbulent flames regimes Poinsot & Veynante (2005) and Peters (1999)

17

Chapter 3
GOVERNING EQUATIONS AND
MODELING
The remarkable development of combustion science is gained by theory, experiment, numerical
simulation and the combination between them. Over the past 60 years, the computer hardware and
high-performance computational technologies have advanced significantly making the numerical
simulation a truly competitive research tool with experiment and theory that provides invaluable
information about the combustion phenomena. The computation of premixed flames in practical
combustion chambers such as industrial furnaces, internal combustion engines and gas turbines
chamber is, however, an expensive task and exceeds the current computational capabilities Smooke
(2013); Kleijn & Akker (1999). This is due to; (1) a large number of species and chemical reactions
required for combustion mechanism of the hydrocarbon fuels; (2) the difficulties arising from
turbulence-flame interaction; (3) a wide range of time scales and strong coupling between chemical
reactions, diffusion and transport, and flow dynamics result in very stiff differential equations, (4)
the mixture properties are strong function of temperature which varies with time in constant volume
combustion.

18

3.1

Laminar Premixed Flames

The modeling of laminar premixed flame is of critical importance because it represents the foundation and elementary blocks of the turbulent flames, which exits in the majority of industrial
chambers. Under the concept of flamelet assumption, for example, the turbulent flame can be presented as a collections of stretched, thin, one-dimensional, laminar flamelet embedded within turbulent flow field Williams (1975), Peters (1988). Furthermore, both laminar and turbulent flames
produce the same adiabatic flame temperature and pressure which is critical for industrial combustion chambers. However, the confined premixed flame propagation relies on a complex physical
phenomena that involves; (1) complex combustion chemistry represented by hundreds of chemical
reactions between typically 30-50 of chemical species for simple hydrocarbon fuel; (2) the reaction
zone reside within very narrow space of order (0.1 mm) which required fine computational grids
to capture the rapid change in mixture compositions and properties; (3) complex multi-physics
phenomena and inherently multidimensional which involves stiff numerical equations due to wide
range of time scale for chemical reactions, diffusion, and fluid dynamics; (4) a huge temperature
gradient requires the thermo-chemical and transport properties to be represented as a strong function of local temperature Smooke (2013); Kleijn & Akker (1999). For these reasons, the threedimensional systems with detailed chemistry and complex diffusion model are well beyond our
current computational ability. In this section, the governing equations are presented for laminar
confined premixed flame propagating in two-dimensional channel.

∂ρ
+ ∇ · ρu = 0
∂t

(3.1)

∂ ρu
+ ∇ · ρuu = ∇ · S + f
∂t

(3.2)

19

∂ ρe
+ ∇ · (u(ρe + p)) = ωT + ∇ · (u · S) − ∇q + u · f
∂t
∂ ρYk
+ ∇ · ρuYk = ∇ · Jk + ωk ,
k ∈ S[1...Ns ]
∂t

 Ns
ρRT
Yk −1
,
Mm = ∑
p=
Mm
k=1 Mk

(3.3)
(3.4)

(3.5)

S = −pI + T

(3.6)

2
T = µ(∇u + (∇u)T ) − ∇ · uI
3

(3.7)

Ns

Ns

q = −λ ∇T + ∑ ρukYk hk = −λ ∇T + ∑ ρukYk
k=1

k=1
Ns

e=

p

Z T
To

c pk dT

1

∑ Yk hk − ρ + 2 uu

(3.8)

(3.9)

k=1

The unknowns variables (primitive variable) in the governing equations are: u = (u, v, w), the
mass average velocity vector of the gas mixture; T, temperature; P, pressure; Yk , mass fraction of
species k, k ∈ S[1...Ns ]; and ρ, mixture density. The equations also contains other quantities of: t,
time; e, specific energy defined in Eq. 3.9; T, stress tensor based on the Newtonian fluid assumption defined in Eq. 3.7; q, net energy crossing the control volume surface by the mechanisms of
molecular conduction and diffusion of species k defined in Eq. 3.8; Jk , diffusion flux defined in
Eq. 3.19; uk , diffusion velocity of species k, which will be discussed further in section 3.1.2; Âľ,
mixture-average dynamic viscosity; and Îť , mixture-averaged thermal conductivity.
The aforementioned two-dimensional, compressible Navier-Stokes equations for laminar premixed flame are solved using a pressure-based solver in which the pressure and velocity are coupled using the SIMPLE scheme. Space is discretized using a second-order upwind scheme and the
transient solution was advanced using a first order implicit scheme with dual time stepping.

20

3.1.1

Reaction rate - Kinetic Mechanism

The prediction of the net rate of heat released from premixed flame, ωT , and other flame characteristics is a fundamental problem and one of the remaining challenging issues in combustion
modeling Smooke (2013). This requires a reliable design of detailed chemical-kinetics mechanism which is, for hydrocarbon combustion, usually required large number of chemical reactions between dozens of intermediate species that appears in fraction of mm and within fraction
of millisecond and therefore required an expensive computational task Kiran et al. (2013), Matalon (2009), Xiao et al. (2015), Kleijn & Akker (1999). The combustion mechanisms used in this
work are the San Diego combustion mechanism which consists 244 reactions between 50 species
Chemical-Kinetic Mechanisms for Combustion Applications, San Diego Mechanism web page,
Mechanical and Aerospace Engineering (Combustion Research), University of California at San
Diego (2014), the DRM19 reduced mechanism based on GRI-Mech 1.2 which consists 84 elementary reactions between 19 species Frenklach & M. (1994), and H2 /CO syngas mechanism
Kèromnès et al. (2013), see table 3.1.
Mechanism

Type

No. Species

No. reactions

San Diego Mechanism

Detailed reaction mechanism

50

244

DRM19

Reduced from GRI-Mech 1.2

21

84

Syngas H2 /CO

Detailed Mechanism

15

48

Table 3.1: Chemical-Kinetic Mechanisms used in this work.

The heat release due to chemical reaction, ωT , is the highest term in the energy equation within
the reaction zone and it is responsible for temperature rising hence no indices is needed for this
term so as the temperature for all mixture components. The heat released is determined based
on the sum of mass creation or destruction of each species multiplied by the associated energy
21

released or absorbed as follow:
Ns

ω̇T = − ∑ ∆hof Mk ω̇k

(3.10)

k=1
Nr

00

0

ω̇k = − ∑ (νk j − νk j )Q j

(3.11)

i=1

Ns

Ns

0

00

Qi = K f j ∏ [Xk ]νk j − Kr j ∏ [Xk ]νk j
k=1

(3.12)

k=1


K f j = A f j T β j exp

E

− RTj



 o

00
0
∆Sk ∆Hko
Ns
(νk j −νk j )
−
K f j  Patm ∑k=1
=
exp R RT
Kr j
RT
∆Soj

Ns

∆H oj

Ns

Sko
= ∑ (νk j − νk j )
R
R
k=1
00

0

Hko
= ∑ (νk j − νk j )
RT
RT
k=1
00

0

(3.13)
(3.14)

(3.15)

(3.16)

The quantities in the chemical model equations are: ωk , molar production rate of species k; Mk ,
molecular weight of species k; Qi , reaction rate of progress defined for each reaction j, j ∈ R[1...Nr ]
00

0

that involve species k; νk j , νk j , stoichiometric coefficients of products and reactants of species k
in reaction j, respectively; K f j , forward rate of reaction j constants, which is not really constant
but rather strong function of temperature T as shown in the Arrhenius expression of Eq. 3.13,
moreover, it depends on both temperature and pressure in the fall off reactions; Kr j , reverse rate
of reaction j constants and it is estimated based on the thermodynamic equilibrium as shown
in Eq. 3.14; A f j , pre-exponential factor of reaction j; β j , temperature exponent of reaction j;
E j , activation energy of reaction j; Sko , and Hko , entropy and enthalpy of species k evaluated at
temperature T and pressure Patm and tabulated as polynomial coefficients in the thermochemical
properties data file.

22

s
There are two common ways to satisfy the constrain of species mass conservation ∑N
k=1 Yk = 1;

the first one is to distribute the residuals all over the species mass fraction which is weighted by
the species mass fraction; the second approach is to assume that the most abundant species (N2 in
this work) behaves as a dilute and its mass fraction is set to one minus the sum of all other species
mass fractions as:
Ns −1

YNs = 1 −

∑ Yk

(3.17)

k=1

The performance of the reaction mechanisms used in this work is tested by solving one dimensional, premixed, freely propagating flame speed for each mechanism and compared with available
experimental data from literature, see Figs. 3.1, 3.2.
The effect of initial pressure, unburned temperature, and equivalence ratio on the laminar flame
speed are also plotted to assess the sensitivity of combustion mechanisms, see Figs. 3.3, 3.4. The
multicomponent diffusion and Soret effect were also included in this analysis. The chemical model
is solved at the end of each time step using CHINEMKIN-CFD solver which performs the integration over all the chemical reactions at the associated species concentrations calculated by the flow
solver.

23

60
San Diego Mech. (2014)
DRM19
Beeckmann et al. (2014)
Halter at al. (2010)
Qin and Ju (2005)
Vagelopouos and Egolfopoulos (1998)

55

Laminar flame speed (cm/s)

50
E

45
40

E
E E

35

E
E

E

30

E

25

E
E

20

E
E

E

15

E

10
5

0.4

0.6

0.8

1

1.2

1.4

1.6

Equivalence ratio φ

Figure 3.1: Flame speed predicted by San Diego kinetic mechanisms and tested against available
experimental data from literature Beeckmann et al. (2014), Halter et al. (2005), Vagelopoulos &
Egolfopoulos (1998), Qin & Ju (2005). The analysis consists one-dimensional free propagating,
premixed flame.

225
200

Laminar flame speed (cm/s)

175
150
125
100
75

Burbano et al. (2011)
Hassan et al. (1997)
Curran et al. (2013

50
25
0

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Equivalence ratio φ

Figure 3.2: Laminar flame speed for syngas kinetic mechanism of Kèromnès et al. (2013) validated
with available experimental data Hassan et al. (1997), Burbano et al. (2011).
24

45
40

Laminar flame speed (cm/s)

35
30
25
20
15
10
DRM19 (1 atm)
DRM19 (2.5 atm)
DRM19 (5 atm)
San Diego Mech (1 atm)
San Diego Mech (2.5 atm)
San Diego Mech (5 atm)

5
0

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

Equivalence ratio, φ

Figure 3.3: Laminar flame speed for DRM19, San Diego Mech. under different operating pressures.
100
90

Laminar flame speed (cm/s)

80
70
60
50
40
30
DRM19 (298 K)
DRM19 (350 K)
DRM19 (400 K)
DRM19 (450 K)
DRM19 (500 K)
San Diego (298 K)
San Diego (350 K)
San Diego (400 K)
San Diego (450 K)
San Diego (500 K)

20
10
0
0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

Equivalence ratio, φ

Figure 3.4: Laminar flame speed for DRM19 and San Diego Mech. under different reactants
temperature.
25

3.1.2

Molecular diffusion

In multicomponent mixture, a species moves with diffusion velocity if there exist a gradient in
species concentration, temperature, pressure or external force. The general expression for diffusion
velocity can be written as:
Ns

Vk = − ∑ Dkl Fk − DT,k
k=1

∇T
T

(3.18)

Here the Fk is the driving force which takes into account the gradient of species concentration,
pressure, and external force of being non-uniformly distributed over mixture species. Dkl is the
multicomponent diffusion coefficient of species k into species l, DkT is the thermal diffusion coefficient of species k. In this work, the external forces acting equally on each species in the mixture.
The driving force resulting from pressure gradient in the flow field is a differential effect that result
from spatial fluctuation of pressure and becomes effective only when the molecular weight of the
chemical species deviates considerably from the mean molecular weight of the mixture Smooke
(2013), Grcar et al. (2009). The diffusion of species due to pressure gradient is usually small and
negligible and hence is omitted in this study Vedachalam et al. (2015), Kleijn & Akker (1999). The
second term in Eq. 3.19 refers to the thermal diffusion (Soret effect, thermophoresis, or thermodiffusion) in which the heavy and light molecules exhibit different response to the forces exerted
by temperature gradient which increases the concentration of the heavy molecules on the cold side
and light molecules on the hot side Eslamian (2012), Dworkin et al. (2009). Thus the resulting
molecular mass flux Jk may be expressed by multicomponent extension of the Chapman-Enskog
theory Bird et al. (2007):
Ns



∇T
Jk = ρkVk = − ∑ ρDkl ∇Yk − DT,k
T
k=1

26

(3.19)

The net of these driving potentials result in moving the species with a diffusion velocity Vk , which
represent the core of diffusion problem that is traditionally known as extremely complicated since
no explicit information is provided by kinetic theory for the diffusion transport coefficient but instead linear systems of diffusion equations whose dimension Ns × Ns , which need to be solved on
each computational grid point De Charentenay & Ern (2002). Therefore the modelling and computation of multicomponent diffusion is computationally expensive Smooke (2013), Giacomazzi et al.
(2007), Giovangigli (2014). In recent years, a considerable progress has been made in simplifying
the multicomponent diffusion models based on level of approximation, reduction mechanism, and
improving the numerical algorithm for solving the resulting linear system Xin et al. (2015), Hilbert
et al. (2004), Ern & Giovangigli (2008). Three different diffusion models depending on the level of
approximation are used in this work; multicomponent diffusion of Chapman-Enskog model M(I);
mixture-averaged diffusion model M(II); constant Lewis number diffusion model M(III), to emphasis the effect of multicomponent diffusion model on flame structure evolution and pressure time
history, see table 3.2.

27

Model

Formula

M(I)

Dkl = 0.010635

Description
T 3/2
1/2
ps Mkl (σk +σl )2 ΩE

a modified version of Chapman-Enskog model
McGee (1991),Chapman & Cowling (1970). Thermal diffusion is included.

M(II)

Dkm =

1−Xk
N
∑ j,sj6=k X j /Dk j

Mixture-average diffusion model based on Fickian
model. No thermal diffusion was included.

M(III) Dkm =

Îťk
ρc pk Le

Constant Lewis number. No thermal diffusion was
included. Le = 1.0 for CH4 /air mixture and Le =
0.57 for syngas/air mixture.

Table 3.2: Mass diffusion Coefficient for Multicomponent, mixture-average, and constant Lewis
number.

The first model M(I) is based on kinetic theory using the effective Lennard-Jones diameter
(σk + σl )/2 which indicates the interaction characteristic length between k and l, and collision
integral function ΩE = ΩE (T ∗ ), where, T ∗ = T /(ε/kB )kl , is the dimensionless temperature and εkl ,
kB are the effective Lennard-Jones potential well depth for the collision and Boltzmann constant,
respectively. The integral function ΩE can be expressed as Reid & Sherwood (1966):

ΩE (T ∗ ) =

1
(T ∗ )0.145

Îľ

=
kB kl

r

+

1
(T ∗ + 0.5)2

Îľ
 Îľ

kB k kB l

(3.20)

(3.21)

The values of parameters, (σ , (ξ/kB )), are provided for each species k by the transport data file.
The thermal diffusion coefficient was found using composition-depended and empirical-based ex-

28

pression as Kuo (2005):
"
DT k = −2.59 × 10−7 T 0.659

Mk0.511 Xk
N

s
Mk0.511 Xk
∑k=1

#"
−Yk

N

s
Mk0.511 Xk
∑k=1
Ns
Mk0.511 Xk
∑k=1

#
(3.22)

In the second model M(II) we consider a binary diffusion between species k and mixture following Fick’s law approximation where nitrogen contribute more than 70% of the mixture weight and
hence we assume that the mixture diffusion coefficient are dominated by nitrogen diffusion coefficient. The third model M(III) represent the simplest diffusion model which assumes that the
thermal diffusivity is sufficient to know and equivalent to the diffusion coefficient. In other words,
the case of unity Lewis number assumes that the speeds of heat and species diffusion are the same.
The constant Lewis number case M(III) is implemented by allowing the mass diffusivity to vary
with the associated thermal diffusivity so that the Lewis number of each individual species remains
equal and constant.

3.1.2.1

Lewis Number

Lewis number is defined as the ratio of thermal diffusivity of the unburned mixture to mass the
mass diffusivity of the deficient reactant which represents the energy balance at the flame and
hence it has a direct effect on the intrinsic thermodiffusive instabilities, extinction, and stretch
effects on flames Poinsot & Veynante (2005). For a mixture with single fuel component such as
methane/air mixture, the Lewis number can be expressed as:

Lem =

Îť
ρc p Dkm

(3.23)

Here the thermal diffusivity of the unburned mixture and Dkm is the mass diffusivity of the deficient
reactant which represent the fuel component for lean mixture and oxidizer for rich mixtures. An29

other definition proposed by Matalon (2014) based on the weighted average of the individual Lewis
numbers. Based on the former definition, the effective Lewis number for methane/air mixture can
be written as:
Ns

Lee f f =

∑ Xk Lek

(3.24)

k=1

When the mixture consists more than one fuel component such as syngas which consists of two
primary fuel, hydrogen and carbon monoxide, the estimation of the effective Lewis number is not
trivial and still area of active research Bouvet et al. (2013), some of these approaches are:
1. Effective Lewis number based on the heat releases from fuel components Wu et al. (2011):

LeQ = 1 +

Qk1 (Lek1 − 1) + Qk2 Lek2
(Qk1 + Qk2 )

(3.25)

2. Linear effective Lewis number based on the volume fraction and Lewis number of the mixture fuel components Muppala et al. (2009), Bouvet et al. (2013):

LeV = Xk1 Lek1 + Xk2 Lek2

(3.26)

3. Effective diffusivity approach Dinkelacker et al. (2011):

LeD =

Îą
Xk1 Lek1 + Xk2 Lek2

(3.27)

where subscripts k1 and k2 represent the first and second component of the fuel, Q is the amount
of heat released from the associated fuel component, Xk is the molar fraction of component k.

30

3.1.3

Gas properties

The propagation of premixed flame in closed chamber of isothermal walls is characterized by sequential change in flame speed and structure, mixture composition, pressure, and temperature for
both burned and unburned gases which results in considerable variation in species thermochemical
(c p , Sko , Hko ) and transport (Âľ, Îť ) properties of the individual species and consequently the mixture.
The thermochemical properties of species are determined following CHEMKIN’s polynomial format CHEMKIN-PRO 15131 (2013) whose coefficients are provided in the thermochemical data
file. The mixture specific heat capacity at constant pressure is obtained based on mixing law of
mass fraction which is commonly used in combustion modeling Kleijn & Akker (1999):
Ns

cp =

∑ Yk c pk

(3.28)

k=1

The kinetic theory assuming the Lennard-Jones intermolecular potential energy is used to estimate
the transport properties as (Âľ, Îť ) of pure species Kleijn & Akker (1999):

µk = 2.67 × 10−6

Mk T
σk2 ΩE



14 c p Mk 1
15 R
Îťk =
Âľk
+
4 Mk
15 R
3

(3.29)

(3.30)

An appropriate scheme using semiempirical formula, which was proved to be the most rigorous
and satisfactory approach, is used to obtain mixture-average viscosity and thermal conductivity as
Bird et al. (2007), Kleijn (1995):
Ns

Âľ=

XÂľ

∑ ∑Ns k Xkφ

k=1

l=1 l kl

31

(3.31)

Ns

Îť=

XÎť

∑ ∑Ns k Xkφ

(3.32)

l=1 l kl

k=1

Where φkl is dimensionless quantity and it can be expressed as:
  1   1 2

 1
Mk − 2
Âľk 2 Mk 4
1
1+
φkl = √ 1 +
Ml
Âľl
Ml
8

(3.33)

The parameters for kinetic theory (Lennard-Jones parameters) which account for intermolecular interaction, are taken from CHEMKIN transport data file.

3.2

Turbulent Premixed Flame

Since large computational resources are required for solving the reaction rate using detailed chemical kinetics, a considerable attention has been paid by the combustion community towards finding
an alternative combustion model that is tractable and computationally affordable. One common approach that is used for premixed flames is to solve one transport equation for the reaction progress
variable. However, replacing the expensive combustion mechanism comes with the price of losing
information about essential quantities:
• The reaction rate which needs to be modeled in order to close the progress variable equation. This term remains a challenge and active area of research in the combustion modeling
field. The majority of combustion community accept the definition for turbulent flames as
a collection of small but finite laminar flame elements called flamelet GĂźlder & Smallwood
(2007). Based on this assumption, the reaction rate can be approximated by the product of
flame speed and flame surface area density Bray & Cant (1991).
• The diffusion coefficient of the reaction progress variable. Since no molecular informa-

32

tion about reaction progress variable can be provided and utilized to obtain the molecular
diffusion, the kinematic information is used to estimate the diffusion coefficient under the
assumption of high turbulent mixing intensity.
The challenge arising from modeling the reaction rate reside in the definition of the reaction rate
itself which is the rate at which reactants are consumed at the flame surface. This obviously
requires information about flame speed and the flame surface area which both currently represent
a central problem in premixed flame modeling and it has been a subject of a large number of
experimental and theoretical studies.

3.2.1

Large Eddy Simulation

The turbulent flows are characterized over wide a range of scales that extend from the largest
scales, which are typically associated and comparable in size to the characteristic length of the
mean flow, to the smallest scales, which are responsible for the dissipation of turbulence kinetic
energy. Theoretically, it is possible to directly resolve the whole range of spatial and temporal
scales of the turbulence flows using direct numerical simulation, in which no turbulence model
9/4

is needed. However, the computational cost of DNS, which is proportional to Ret , exceeds the
current computational capabilities for practical engineering problem that involves high Reynolds
number.
In LES technique, the large eddies, which depend on computational domain and boundary
conditions of the flow, are resolved directly on the grid points, while the small scales, which are
less dependent on the geometry and are consequently more universal and isotropic, are implicitly
modeled using a subgrid-scale model. LES thus falls between DNS and RANS in terms of cost
and accuracy because it resolves some range of turbulence scales and models the rest, see Fig. 3.5.

33

DNS (all scales resolved on the grid)

𝐸(𝜅)

Computational cost

LES (small eddies
are modeled)

LES (Large eddies resolved on the grid)
RANS (all scales are modeled)

Energy
containing
eddies
•carry most of
the energy
•interact with
the mean flow

Small isotropic
scales
(Dissipation range)

Inertial subrange
Characterized by the flow of
energy

𝐸 𝜅 = 𝐶𝑜𝑛𝑠. 𝜀 2/3 𝜅 −5/3
(Kolmogorov spectrum law)

𝜅𝑐

𝜅

Figure 3.5: Turbulence energy spectrum regimes
3.2.1.1

LES filtering

In the large eddy simulation technique, the large and small scales fields are separated by filtering
the governing conservation equations. One of the commonly used filters is the box filter, which
is weighted averaging for a given volume of the physical space, and the spectral cut-off filter in
which the quantities greater than a given cut-off frequency are truncated Pope (2000). The spatial
filtered quantity φ̃ can be expressed as:

Z

φ̃ (xi ) =

φ (xi0 )G(xi , xi0 )dxi0 ,

Ω

34

(3.34)

Where G is the LES filter function. For box in the physical space, the filter function G can be
defined as:
G(xi ) =





 ∆13 , i f



0,

|xi | ≤ ∆/2,
(3.35)

otherwise,

For Gaussian filter:
G(xi ) =

6
exp(−6|xi |/∆2 ).
π∆2

(3.36)

For spectral cut-off filter:
G(xi ) =





1, i f

κ ≤ κc ,
(3.37)




0, otherwise,
Where i = 1, 2, 3. and ∆ is the filter width. The density-averaged (or Favre) filtering operator is
incorporated here so that φ̃ (xi ) =

3.2.1.2

f
ρφ
ρ .

Filtered Conservation Equations

The low-Mach number, Navier-Stokes equations equations are spatially filtered:

∂ ρ ∂ (ρ ũi )
+
= 0.
∂t
∂ xi

(3.38)


∂ σi j ∂ p̃
∂
∂
∂ 
(ρ ũi ) +
(ρ ũi ũ j ) =
−
−
ρ ug
i u j − ρ ũi ũ j .
∂t
∂xj
∂ x j ∂ xi ∂ x j

(3.39)

Mass

Momentum

Energy


∂
∂
∂  ∂ T̃ 
∂  g
(ρ h̃s ) +
(ρ ũi h̃s ) = ω̃T +
Îť
−
ρ(ui hs − ũi h̃s ) .
∂t
∂ xi
∂ xi
∂ xi
∂ xi

Progress variable

(3.40)


∂
∂
∂ 
∂ c̃ 
∂ 
ρDc
ρ(f
ui c − ũi c̃) . (3.41)
(ρ c̃) +
(ρ ũi c̃) = ω̃k +
−
∂t
∂ xi
∂ xi
∂ xi
∂ xi
p̃ = ρ̃RT̃

35

(3.42)

where
σi j = ¾

 ∂ ũ

i

∂xj

+

∂ ũ j  2 ∂ ũl
− µ
δi j
∂ xi
3 ∂ xl

(3.43)

Here ũi is the filtered velocity component, p̃ is the flow filtered pressure, T̃ is the filtered temperature, ρ is the filtered density, h̃s is the sensible enthalpy, c̃ is the filtered reaction progress variable.
The subgrid terms are modeled based on the gradient diffusion approximation:
Subgrid-scale stresses:

ρ ug
i u j − ρ ũi ũ j = −µSGS

∂ ũi ∂ u˜j
+
∂ x j ∂ xi


(3.44)

Subgrid enthalpy flux term:

ρ(ug
i hs − ũi h̃s ) =

µSGS ∂ h̃s µSGS c̃ p ∂ T̃
=
PrSGS ∂ xi
PrSGS ∂ xi

(3.45)

Subgrid scalar flux term:
ρ(f
ui c − ũi c̃) =

µSGS ∂ c̃
ScSGS ∂ xi

(3.46)

Here PrSGS is the subgrid Prandtl number equal to 0.85.
The compressible Navier-Stokes equations were solved using a pressure-based solver in which
the pressure and velocity are coupled using the SIMPLE scheme. Space is discretized using
second-order scheme for pressure and a central differencing scheme for density, momentum, energy, and reaction progress variables. The transient formulation was advanced using a bounded
second-order implicit scheme with dual time stepping ANSYSr Academic Research (2015).

36

3.2.1.3

Subgrid Scale Model

Since the flame structure dynamics showed no signs of high turbulence intensities Najim et al.
(2015), Hariharan & Wichman (2014) the flow generated by the flame is of low turbulent intensities. This requires a turbulent model capable of handling low turbulent or even laminar flow region.
The wall-adapting local eddy-viscosity (WALE) is used here to model the subgrid-scale viscosity
ÂľSGS because:(1) the model return zero subgrid-scale viscosity in the laminar zone which allows
accurate treatment of laminar zones that are expected in this particular case where the premixed
flame starts at quiescent mixture and laminar flame propagation is expected. (2) this model use
implicit damping effect and hence predicts accurately the behavior near-wall flow which becomes
important in confined flame propagation ÂľSGS Nicoud & Ducros (1999). The wall-adapting local
eddy-viscosity is expressed as:

3/2
Sidj Sidj
¾sgs = ρLs2 
5/4
5/2 
+ Sidj Sidj
S̃i j S̃i j

1
Sidj =
2



∂ ũi
∂xj

2



∂ ũ j
+
∂ xi

2 !



1
∂ ũi 2
− δi j
3
∂ xi

1 ∂ ũi ∂ ũ j
S̃i j =
+
2 ∂ x j ∂ xi

!

1 ∂ ũi ∂ ũ j
S̃i j =
+
2 ∂ x j ∂ xi

!

Ls = min





CwV 1/3



κd

37

(3.47)

(3.48)

(3.49)

(3.50)

(3.51)

The model constant Cw is 0.325, the von KĂĄrmĂĄn constant Îş, and the distance to the closest channel
wall d.

3.2.2

Combustion Model- Flamelet Concept

In this work, for three-dimensional problem, the combustion is modeled by solving single transport
equation for reaction progress variable in which the reaction rate is predicted using algebraic flame
surface density and flame speed closure. The heat release, ωT , in the energy equation can be
expressed as:
ω̃T = QLHV Y f ω̃c

(3.52)

Where QLHV is the heat of combustion of the associated fuel and Y f is the fuel mass fraction. The
source term, ωc , in the transport equation for the progress variable, is dominant within the flame
region (or brush) which can be recognized when the reaction progress variable changes from the
state of the unburned zone (c = 0) to the state of burned zone (c = 1). Therefore, the gradient of the
reaction progress variable represents the surface moving, relative to fresh gases, with flame speed
(Sl ) and at which the artificial reactants is burned. Since no flame exist when c = 0 and c = 1, it
is convenient to search for the flame by using the Bray-Moss-Libby (BML) expression for RANS
which involves the c(1 − c) which gives zero everywhere except when c has a non-zero gradient.
Later, this expression was modified by Boger at al. Boger et al. (1998) to be used for LES by
introducing model constant and filter size β c(1 − c)/∆,

 c̃(1 − c̃) 
˜
ω̃c = ρu Sl Σ f = ρu Sl 4β
∆

38

(3.53)

Here the flame surface density Σ f , the LES filter width ∆, the model constant β is 0.2, the unburned
gases density ρu , the flame speed closure Sl .
The term 4β c̃(1 − c̃)/∆ is known as algebraic flame surface area density because it has algebraic form to describe the flame surface area and it could be more complicated and requires a
transport equation to account for turbulent flame stretching, flame dilatation, expansion of burned
gas, normal propagation, and dissipation of flame area. Details about the transport equation for
flame surface area density can be found in Veynante & Vervisch (2002); Swaminathan & Bray
(2011).

3.2.2.1

Flame Speed Closure

The key to the modeling of premixed combustion is the flame speed closure which plays a crucial
role in the prediction of the reaction rate. The flame speed depends mainly on the flow parameter
and the laminar flame speed which is a function of the fuel concentration, equivalence ratio, unburned gases temperature, pressure, and thermochemical properties. Turbulence can also wrinkle
the flame surface by large eddies or thicken the flame by small eddies. In constant volume combustion, the temperature and pressure unburned gases change during combustion time. To account
for the variation in temperature and pressure of the unburned gases, an experimental correlation
suggested by Metghalchi and Keck Metghalchi & Keck (1980) is incorporated in the flame speed
equation.

Sl = Slre f

Tu
Tre f

!ΨT

p

!ΨP

pre f

(1 − 2.1Ydil )

Slre f = Θ1 + Θ2 (φ − φM )2
Slre f = Θ1 + Θ2 (φ − φM )2 ,

ΨT = 2.18 − 0.8(φ − 1),
39

(3.54)
(3.55)

ΨP = −0.16 + 0.22(φ − 1) (3.56)

Here the reference laminar flame speed, Sl re f , is evaluated at standards temperature (Tre f ) and
pressure (Pre f ) for methane/air mixture. The dilution mass fraction Ydil , the equivalence ratio φ ,
the flame speed Sl , the unburned gases temperature and pressure Tu and P, respectively.
To account for turbulence generated by the flame, the Zimont turbulent flame speed closure is
used Zimont et al. (1998):
St = Fz u0 D0.25
a

(3.57)

Where the Fz is the model constant, u0 is the root-mean-square (rms) velocity, and Da is
the DamkĂśhler number which is the ratio between turbulent integral timescale to reaction rate
timescales, Da =

τc
τl .

Since the flame starts in quiescent mixture, the methodology here is to moni-

tor the turbulence development and check after each time step by comparing St and Sl and choose
the dominant one.

3.3
3.3.1

Boundary and Initial Conditions
Numerics

The mesh is one of the most important components of the numerical simulation. In our study,
the mesh or grid was generated using ICEM-CFD and the cell size depends on the combustion
modeling scheme and type of the reacting mixture. The mesh size and time step were first estimated
by solving one-dimensional, freely propagating flame using the same chemical mechanism and
multicomponent diffusion model with Soret effect included.
For stoichiometric methane/air mixture of the San Diego mechanism, the computational domain area for the WDE channel is 568.5 mm2 and is discretized in space with a maximum cell size
of 0.1 mm. The cell height next to the channel wall boundaries is 0.02 mm with a growth rate fac-

40

tor of 1.2, which generates 110,000 cells in the entire computational domain. This appeared to be
sufficient to capture the premixed methane/air flame. For syngas premixed flame, the WDE channel is discretized in space into 277800 quadrilateral cells with maximum and minimum cell size of
0.05 mm and 0.011 mm, respectively, see Fig. 4.1. The two dimensional, rectangular channel (10
mm × 100 mm) is discretized in space into 200000 quadrilateral cells with cell size of 0.07 mm.
The time step size varies between 10−8 − 10−6 s. A mesh independence studies were conducted to
ensure that the grid resolution is sufficient to capture the premixed flame propagating in initially
quiescent and confined mixture, see Appendix. A.
For the tree-dimensional model, the maximum and minimum grid size is 0.4 mm and 0.08 mm
with inflation ratio of 1.2 near channel walls. The time step is also selected to maintain the CourantFriedrichs-Lewy number (CFL) below 0.25. The cell size, reaction mechanisms, and other details
are summarized in table. 3.3

41

Combustion Chamber
WDE, 2D

Combustion Model

Flow model

CH4 /air (Detailed kinetic mechanism, Chemical- DNS

Mesh size

Time step size

0.1-0.02 mm 10−8 -10−6 s

Kinetic Mechanisms for Combustion Applications,
San Diego Mechanism web page, Mechanical and
Aerospace Engineering (Combustion Research), University of California at San Diego (2014))
WDE, 2D

CH4 /air (Reduced DRM19, Kazakov & Frenklach DNS

0.05 mm

10−7 − 5 × 10−6 s

0.07 mm

10−8 − 10−7 s

(1994)) and H2 /CO/air (Detailed mechanism, Kèromnès et al. (2013))
Rectangular Ch, 2D

H2 /CO/air (Detailed mechanism, Kèromnès et al. DNS
(2013))

WDE and rectangular

Algebraic flame surface density and transient flame LES

Ch, 3D

speed
Table 3.3: Summary of CFD simulation cases.

42

0.4-0.08 mm CFL < 0.25

Chapter 4
EXPERIMENT SETUP

4.1

Combustion Chambers

Two closed channels that serve as combustion chambers in this work; the WDE channel as depicted
in Fig. 4.1 and rectangular channel which is commonly used in the literature (Fig. 4.3). The WDE
channel sidewalls are formed by two circular arcs of different center position; the inner and outer
arc are 76.3 mm and 87.6 mm, respectively. The inlet and outlet ports of the channel are generated
by another two arcs of 100 mm and 200 mm, respectively. The channel depth is 20 mm and parallel
to the line perpendicular to the plane of Fig. 4.1. More details about the WDE channel design and
other WDE configuration can be found in Sun (2011), Kiran (2013). The channel was machined
using computer numerical control (CNC) machining. The top and bottom sides of the chamber
are closed along its depth by two optically accessible, temperature and pressure-resistant glass
ceramic sheets which are necessary for our schlieren system as shown in Fig. 4.2. The size of the
rectangular chamber is 38 mm × 38 mm × 279.6 mm which is manufactured in similar way as the
WDE channel.

43

Figure 4.1: Schematic diagram of computational domain.

The combustion chambers are instrumented with two quick connectors isolating valves for inlet
and outlet, spark plug, pressure sensor. The quick connectors valves are mounted on the channel
sidewall and are used for evacuating, cleaning, charging and discharging the combustion chamber.
The spark plug is located at the channel left wall (inlet port) as shown in Fig. 4.2.

44

Figure 4.2: Schematic diagram of single wave disc engine channel used for experimental measurements

38 𝑚𝑚

𝑦

Ignition

𝑧

𝑥

279.4 𝑚𝑚

Figure 4.3: Closed rectangular channel serves as combustion chamber
45

4.2

Experiment Setup

Figure 4.4 shows a schematic diagram of the experimental setup. This is composed, firstly and
most importantly, of the combustion chamber which are either the WDE channel or the rectangular
channel that serve as the CV combustion chamber. In addition, a piezoelectric crystal Kistler
pressure sensor (type 6052C) is connected to a Dual Mode Charge Amplifier (type 5010) to record
the pressure-time history. The pressure sensor was calibrated as instructed in the manual and tested
using available data from the literature Dunn-Rankin & Sawyer (1998),Kuzuu et al. (1996), see
Figs 4.5, 4.6. The pressure sensor reading was sampled at a rate of 5 kHz. The flame propagation
was captured using a z-type schlieren photographic system consisting of a high speed video camera
(Photron FASTCAM SA4 500K-C1) operating at 3600 fps, a point light source, a knife edge, and
two concave mirrors of 6” diameter and 60” focal length. A spark plug is flush mounted on the
channel end wall. MSD Blaster is used to power the spark plug with 10 mJ of energy for every
spark discharge.

46

Point light source
Mixture Preparing Vessel
Isolating Valve
Condenser

Isolating Valve

Concave Mirror 2

Concave Mirror 1

Wave Disc Engine
Channel

Ashcroft pressure gauge

Pressure Sensor

MSD Spark-Plug
MSD Blaster
Dual Mode Charge
Amplifier

Knife edge

Data acquisition modules

High speed Camera

Computer

Figure 4.4: Schematic diagram of the experimental setup. The premixed flame images are measured at rate 3600 f ps, and the pressure readings are sampled at 5 kHz.
47

4.3

Methods of Measurement

The experimental results discussed in this work were carried out for a stoichiometric methane-air
mixture at initial temperature and pressure of 296 K and 102.65 kPa, respectively. The mixture
was prepared in a separate vessel to ensure proper mixing using Dalton’s law of partial pressures.
The mixture was ignited using an MSD 10 mm spark plug mounted on a threaded hole through the
center of the chamber inlet port. Ten (10) mJ of electrical energy was supplied to the spark-plug
using an MSD Blaster coil. The experimental procedure was as follows:
(1) Flush the channel with compressed air for 30 s to remove any combustion residuals remaining in the channel.
(2) Evacuate the channel up to -720 mmHg (96 kPa) and then fill with combustible mixture. The
remaining air inside the channel (5.325 kPa) was taken into consideration according to the
following equation when the mixture was prepared:

v
c
Pf uel = Pair
+ Pair


 1 R f uel
φ ψs Rair

(4.1)

Here, ψs is the stoichiometric air to fuel ratio for methane, ψs = 17.194 kg air/kg f uel, Rair ,
v ,Pc , P
and R f uel are the gas constants for air and methane, respectively, Pair
f uel are the absoair

lute partial pressures for air in the vessel, chamber, and methane in the vessel, respectively,
v + Pc ) and φ , the
and φ is the equivalence ratio measured as kg fuel/kg air. For specific (Pair
air

partial pressure Pf uel was calculated using Eq. (3.1) and the methane was added to the vessel
v + Pc + P
until the total mixture pressure of Pair
f uel was attained.
air

(3) A time delay of 30 s is employed before the spark-plug is activated in order to insure proper
mixing and in order to eliminate any mixture motion inside the channel, thereby satisfying
48

360
330
300
270
240
210
180
150
120
90
60
30
0

0

10

20

30

40

50

60

70

80

90

100

110

120

Figure 4.5: Pressure measurements tested against available data from literature Dunn-Rankin et al.
(1988)
the initial quiescent mixture condition.
(4) The high speed camera and pressure sensor is triggered shortly before spark-plug activation
to initiate combustion. The data are recorded using a data acquisition system with a LabView
interface.
To ensure the reproducibility of the flame structure and pressure dynamics, the quantity of mixture
prepared in the vessel was sufficient for running eight (8) experiments. The experiments were
reproducible and representative data are shown in Fig. 4.7.

49

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

Figure 4.6: Normalized values of average pressure measurements for stoichiometric CH4 / air
flame.

Raw data from pressure transducer

90
xxxxxxxx
xx
x
x
xx
x
x
80
x
x
x
x
x
x
x
x
x
x
x
x
x
x
70
x
x
x
x
x
x
x
x
x
x
x
x
x
x
60
x
x
x
x
x
x
xx
x
x
x
x
x
x
x
50
x
x
x
x
x
x
x
xxx
xx
40
xx
x
x
xx
xx
x
x
30
xx
xx
xx
x
x
xxx
xxx
xxx
20
xxx
x
x
x
x
x
x
10
x
x
x
x
xx
0 xxxxx

Exp. 1
Exp. 2
Exp. 3
Exp. 4
Exp. 5
Exp. 6
Exp. 7
Exp. 8

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Time (s)

Figure 4.7: Raw data recorded by pressure transducer for eight(8) experiment to ensure the reproducibility of the tests.
50

Chapter 5
EXPERIMENTAL AND NUMERICAL
SIMULATION

5.1

Flame Front Evolution

In this section, we present and discuss the dynamics of laminar premixed flames. The evolution of flame structure under different fuels, kinetics mechanism, diffusion models, and mixture
stoichiometry is also discussed. The flame-induced flow, flame speed, average pressure and temperature developed in the WDE and rectangular channels are also inspected.

5.1.1

Non-symmetrical Tulip Flame

A numerical simulation of San Diego mechanism is conducted for two-dimensional WDE channel
to understand the flame structure evolution in a non-symmetrical, curved channel. The transition
of an ignition source to a concave finger flame to a convex “tulip” flame, and then the “tulip”
once again into a concave flame under the WDE converging curvature effect of Fig. 4.2, represents
an important transition process occurring for premixed flames in confined CV combustion. These
characteristic flame features, along with the transition events generated by the combustor geometry
of Fig. 4.2, are examined experimentally and numerically in this subsection.
Figure 5.1 shows the temporal sequence of the WDE flame propagation images. High-speed
51

schlieren experimental photographic images are shown on the left whereas mass fraction contours
of HCO obtained from the numerical simulation to track the flame front are shown on the right.
The color scale illustrates the flame structure evolution. Comparison of the images at the indicated
times shows that the numerical scheme reproduced features of the flame that were recorded by
high speed schlieren photography. The premixed flame exhibits different features than presented
in the literature for straight channels Hariharan & Wichman (2014), Ellis (1928), Dunn-Rankin &
Sawyer (1998) and channels with a 90◦ bend Ponizy et al. (2014), Emami et al. (2013), Xiao et al.
(2014a).
Five main dynamic flame features or phases were recorded using schlieren photography that
were also reproduced in numerical simulations. The first phase I starts after ignition in which
the flame expands hemispherically with approximately constant flame propagation speed. This
phase, which is brief and shows distinct signs of flame front acceleration soon after it begins,
lasts in our study for only approximately 3 ms. We note that this time interval generally depends
on how far the flame kernel is placed from the chamber walls, see Fig. 5.1a-Fig. 5.1d, and see
Kiran et al. (2014), where the ignition kernel is located several mm from the wall and produces
a distinctly non-spherical initial flame. Phase II takes place over the approximate time interval
3-5 ms, see Fig. 5.1d-Fig. 5.1c. The phase II flame propagates forward faster than toward the
sidewalls while gaining surface area, which accelerates the flame. It is this phase that Clanet
and Searby Clanet & Searby (1996) have characterized, using a very simple ad-hoc model, as
having exponentially increasing flame speed. In phase II the chamber geometry (curvature) starts
to impose itself by shaping the flame front, turning the flame front tip down toward the lower
sidewall instead of forming a uniform finger-shaped flame that has been extensively reported for
straight channels. When the flame skirt Clanet & Searby (1996) approaches the sidewalls, the
trapped fresh mixture is consumed by the flame at a low rate due to the influence of viscosity
52

in the region near the wall and the even stronger influence of heat losses to the cold sidewalls.
The viscous flow phenomenon has been referred to as “squish flow” Dunn-Rankin et al. (1988).
Phase III appears during the approximate time interval 5-10 ms, where the lateral flame sides
touch the lower sidewall before touching the upper wall and are gradually quenched. This results
in a diminishment of the lateral part of the flame surface area leading to a deceleration of the
flame front in laboratory coordinates. The flame is quenched on the inner sidewall faster than
the outer sidewall because of the channel curvature effect, see Fig. 5.1e- Fig. 5.1f, in qualitative
agreement with previous research on pipes and channels with 90◦ bends. Just after the lateral part
of the flame is completely quenched at approximately 10 ms, phase IV begins. Here, the flame
front continues to move along the inner wall faster than the flame close to the outer wall, while
the flame in the middle region lags behind. This leads to the development of a non-symmetric
tulip flame with its cusp pointing toward the burned gases, as shown in Fig. 5.1g- Fig. 5.1n. The
flame tongue near the inner sidewall is longer with a rounded tip, while the upper flame tongue
is much smaller. Over time, the inner flame tongue continues to grow by radially displacing the
tulip flame cusp toward the outer sidewall, which action eventually consumes the upper flame
tongue. As a consequence, the tulip flame diminishes during this time interval and completely
disappears once the flame cusp touches the outer sidewall at approximately 17 ms. A concave
propagating flame is thereafter reconstituted. The reconstitution of the concave flame, which is
exhibited in the converged-curved channel, has not been reported in straight channels. In 90◦
channels, a similar process occurs, although the evolution is less clearly and smoothly exhibited
than it is here for the gradual bend of our channel. Finally, phase V occurs when the flame is
converted into a convex flame that subsequently experiences no major morphology changes until
it approaches the channel end and extinguishes at the termination of combustion, at approximately
65 ms (Fig. 5.1o). This phase consumes approximately 75% of the combustion time, indicating
53

that the quenching phase occupies the bulk of the combustion time. In the beginning of this stage
the mass consumption rate continues to increase. Near the end of combustion, at impending flame
quenching, it finally plummets to its final value of zero. A theoretical and numerical analysis of
premixed flame quenching for the plane flame/wall was carried out by Wichman and Bruneaux
Wichman & Bruneaux (1995).

54

(a)

t=0.11 ms

(f)

t=6.51 ms

(k)

t=12.99 ms

(b)

t=1.39 ms

(g)

t=7.79 ms

(l)

t=14.29 ms

(c)

t=2.67 ms

(h)

t=9.07 ms

(m)

t=15.49 ms

(d)

t=3.95 ms

(i)

t=10.35 ms

(n)

t=16.75 ms

(e)

t=5.23 ms

(j)

t=11.63 ms

(o)

38.35 ms

Figure 5.1: Evolution of the WDE confined premixed flame using schlieren photography (images
on the lift) and mass fraction contours of HCO, which serve to track the flame locus, from the
numerical simulations (images on the right): (a-d) hemispherical expansion and evolution to a
concave “finger” flame; (e) inner part of lateral flame touches the inner sidewall; (f) outer part of
lateral flame touches the outer sidewall and flame front flattens; (g) initial formation of tulip flame
cusp which generates the characteristic convex tulip flame shape; (h-k) inner flame tongue grows
by radially displacing the flame cusp toward the outer sidewall ; (l) upper flame tongue disappears;
(n-o) tulip flame converted to curved flame.
55

1.8
Normalized flame distance (experiment)
Normalized flame distance (numerical simulations)

1.6

Numerical to experimental ratio

Normalized flame distance xF/xFmax

1.4

1.2

1

0.8

0.6

0.4

0.2

0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Normalized time (t/tmax)

Figure 5.2: Comparison between the experimental and numerical simulations of the normalized
flame locations XF /XF max . Also shown is the ratio of these normalized flame locations, showing
that the numerical flame evolution is always faster than the experimental flame evolution.

The flame locations were determined from Fig. 5.1 and normalized by the length of mid-line
between the inner and outer arcs of the channel XF /XFmax and plotted versus normalized time
t/tmax to provide a quantitative comparison between the experiment and the numerical simulation,
see Fig. 5.2. The direct comparison between overall burn times and time differences between the
various burning regimes (or phases) (I)-(V) indicates that the numerical evolution is always faster
than the experimental evolution. A possible explanation is that despite the basic two dimensional
appearance of the laboratory flame, it is a three dimensional entity with “side losses” of heat and
radical species to the glass walls along the channel depth axis (see Fig. 4.2), in addition to having
a possibly 3-D secondary flow structure.
56

5.1.2

Diffusion impact

5.1.2.1

Methane/air flame

In Fig. 5.3, the evolution of a premixed stoichiometric methane/air flame front in a curved closed
channel is shown for the diffusion models M(I), M(II), M(III) (on the left) and compared to a
shadowgraph experiment (on the right). The models M(I) and M(II) produce miniscule discrepancies in flame position and structure. The largest discrepancy between M(I) and M(II) was during
the accelerated finger flame stage, in which the flame rapidly adds surface area when the hydrodynamic effect of burned gas expansion is dominant. This occurs 3-5 ms after ignition (Figs. 5.3a-b,
5.4). When the lateral flames touch the cold sidewalls, M(I) and M(II) collapse and almost no
discrepancy is seen between them through to the end of combustion. Thus, the mixture-average
diffusion model is sufficient to describe combustion when air is the oxidizer and the multicomponent mixture is approximated as a binary mixture in which nitrogen is dominant.
Flame M(III) deviates from M(I) and M(II) and lags behind them as early as 0.9 ms after
ignition. This deviation grows with time and reaches a maximum shortly before the lateral M(I)
and M(II) flames touch the sidewalls and decelerate (Fig. 5.3b-d). Since M(I), and M(II) initially
propagate faster than M(III), they touch the sidewalls and slow down before M(III), which catches
them to reduce the flame position discrepancy between them (see Figs. 5.3d-e, 5.4).
The evolution of the tulip flame inside a similar curved channel was investigated previously
Najim et al. (2015). The lower tulip flame tongue for M(I) and M(II) start growing at around
9 ms, whereas the tulip flame lower tongue for M(III) was observed at approximately 11 ms
(see Figs. 5.3e-f). Similar to the previous work Najim et al. (2015), the lower tongue grows by
displacing the tulip flame cusp toward the upper sidewall. This shrinks the upper tongue to convert
the flame front again into a concave shape. One of the most pronounced differences in M(III)

57

is observed 11.8 ms when the growing lower tongue of M(III) suddenly accelerates much faster
than its counterparts M(I) and M(II) (Fig. 5.3f-g). At this time, the diminished upper tongue of
M(III) shows less rounding than its counterparts(Fig. 5.3g).The nature of the influence of the three
diffusion models on the flame structure can be observed at about 15 ms. Here the dominant lower
tongue of M(III) decelerates and produces a second, smaller tulip flame while M(I), M(II) and
the experiment flame remain concave and propagate slowly to the end of the channel (Fig. 5.3hl). Like its predecessor, the second MIII tulip is annihilated when the flame cusp moves toward
the upper sidewall. Thisshrinks the upper flame tongue and leaves behind a growing lower flame
tongue. This evolves into a concave flame, which propagates (lags) behind M(I) and M(II) to
the end of the channel (Fig. 5.3i-l). The M(III) flame differs quantitatively and qualitatively from
M(I) and M(II) as well as the experiments.
The flame distance is summarized in Fig. 5.4. Model M(III) describes the premixed flame in
the early stage to 11 ms, when the hydrodynamic phenomena associated with thermal expansion
dominates. After 11 ms, M(III) becomes unrealistic and fails to follow the experiment and models
M(I) and M(II). In the experiment, the ignition produces an initial flame of diameter 5 mm whereas
the numerical simulation ignition is modeled by patching an area of 2 mm diameter at the hot spot.
To unify the results, the reference point for beginning the comparison of the experimental and
numerical flame tip distance is chosen to be 5 mm.
The mixture-average model M(II) predicts the flame speed and structure in good agreement
with the elaborate multicomponent diffusion model M(I). This agrees with the results of Ern
and Giovangigli Ern & Giovangigli (1999) for a freely propagating flame. However, this result is
confined to a stoichiometric methane/air mixture in which N2 is 72.3% of the mixture weight.

58

Experiment

Numerical simulation
(a) 3 ms

(b) 5 ms

(c) 6 ms

(d) 8 ms

(e) 10 ms

(f) 11 ms

(g) 13 ms

(h) 15 ms

(i) 16 ms

(j) 19 ms

(k) 22 ms

(l) 55 ms

MI

M II

M III

Figure 5.3: Methane/air premixed flame front development; (on the right) flame shadowgraphy
and (on the left) flame fronts for M(I), M(II), and M(III) models: (a-f) flame of M(III) lags
behind M(I) and M(II) and small discrepancy can be observed between M(II) and M(II) in b, (gh) M(III) flame is ahead of M(I) and M(II);(i-k) M(III) develops a second tulip flame; (l) M(I),
M(II), and M(III) and converted into concave flames.

59

The second tulip flame, which is produced only by model M(III), is of great importance for
understanding the dynamics of confined premixed flames since neither the experiment nor models
M(I) and M(II) produce reconstituted tulip flames. The global balance between heat and mass
diffusion occasioned by putting Le = 1 is responsible for the second tulip flame. Thus, it appears
that in certain flame stages a crucial role is played in tulip flame formation by Le, as discussed by
Dunn-Rankin et al. (1988) and more recently by Ponizy et al. (2014).

70

60

Flame position (mm)

50

40

30

20

M(I)
M(II)
M(III)
Experiment

10

0

0

10

20

30

40
Time (ms)

50

60

70

Figure 5.4: Flame tip distance from igniter location recorded at the channel centerline for models
M(I), M(II), M(III) and the experiment. The initial condition from which time is reached is the
instant at which all flames have penetrated 5 mm into the channel.

60

5.1.2.2

Syngas flame

The flame fronts for lean premixed syngas flames of φ = 0.7 and 50% H2 are shown in Fig. 5.5
for three different diffusion models; Chapman-Enskog M(I), mixture-averaged M(II), and Le =
0.575 =

Îť
ρc p Dkl .

Unlike previously discussed of methane/air flame, the syngas flames exhibit more pronounced
change in flame front structure under different diffusion models. The constant Lewis number
case M(III) under predicts the flame propagation speed throughout the combustion process. The
mixture-averaged model M(II) exhibits more pronounced deviation from the multicomponent
model of Chapman-Enskog M(I) than previously discussed for methane/air flames. The multicomponent model predicts flame front wrinkles at earlier time than mixture-avergaed model, see
Fig. 5.5-c. However, both M(I) and M(II) models predict similar average flame propagation speed.
Fig. 5.5-c,f indicates that constant Lewis number is unable to produces the cellular structure of the
flame front. However, Fig. 5.5-f shows very smooth wrinkles on the flame front.

61

(a) t=1.05 (ms)

(b) t=2.05 (ms)

(c) t=2.55 (ms)

(d) t=3.55 (ms)

(e) t=4.55 (ms)

(f) t=5.55 (ms)

(g) t=18.55 (ms)
M(I)

M(II)

M(III)

Figure 5.5: Premixed syngas flame front development for M(I), M(II), and M(III) diffusion models.
62

5.2

Pressure Dynamics and Flame Speed

Figure 5.6 shows the experimental flame speed and pressure evolution during methane/air flame
propagating in the WDE channel. By excluding minor effects like dissociation and phase change
of H2 O and considering the flame as a surface propagating at the observed flame speed, the rate at
which the fuel is oxidized (or the rate of heat release) is proportional to the absolute flame speed
and the flame surface area. In CV combustion, the pressure can be predicted by the net rate of heat
addition, which can be simplified to specifying the average temperature change inside the vessel.
The ideal gas equation, p = mRT /V , states that the chamber pressure is a function of temperature,
T, when the quantity mR/V is constant. Thus in order to describe various important aspects of
CV combustion, we examine the normalized rate of pressure change along with the behavior of
instantaneous normalized flame speed, as shown in Fig. 5.6.
It is evident from Fig. 5.6 and from previous research ( Hariharan & Wichman (2014), Ellis
(1928), Ponizy et al. (2014), Xiao et al. (2013), Dunn-Rankin et al. (1988), etc.) that the flame
speed and the pressure change history are related to one another. It is our contention that the
phases of flame dynamic evolution are recognizable in the temporal structure of the absolute flame
speed and the pressure field during burning.
Consider first the flame speed. Here we define an average flame speed by calculating the mean
value of five (5) points on the flame front. We do this because tracking many points on the flame
front yields a consistent average flame speed. Two points are taken at the intersection of the flame
with the upper and lower sidewalls, while the other three points are equally spaced throughout the
particular section of the channel height.
Consider now the pressure field. Here we shall use the experimentally measured pressure
p(t), which, as indicated in Fig. 5.6 is the average over eight (8) tests, as well as its first deriva-

63

tive (d p(t)/dt) and its second derivative (d 2 p(t)/dt 2 ) as “signatures” for the various combustion
phases, in conjunction with the flame speed measurements discussed above. The derivative yields
local extrema of p(t) whereas the second derivative yields inflection points of p(t) as well as locations where the change of p(t) is most rapidly increasing or decreasing. For the sake of clarity or
presentation, the pressure, pressure derivative and second derivative are normalized such that their
maximum values are unity (Fig. 5.6).
Physically, positive values of d p(t)/dt indicate that as the pressure increases, the flame, which
does not necessarily accelerate, is burning vigorously enough to provide sufficient thermal energy
for pressure rise. Equation (4), for example, can be rewritten as D(ρE)/Dt = d p/dt when the
following three qualifiers are acknowledged: (1) we consider regions outside the flame (where
the chemical reaction term is exactly zero); (2) we neglect viscous dissipation; and (3) we disregard gradient transport of thermal energy. In the limit of a flame sheet model (infinitesimal flame
thickness) the volume occupied by the flame front in the CV channel is negligible. The preceding
equation directly relates thermal energy accumulation (loss) to the rate of pressure rise (fall). Thus,
negative values of d p(t)/dt suggest a weakening, decaying flame. The normalized first and second
derivatives, d p(t)/dt and d 2 p(t)/dt 2 , provide specific quantitative information on the structure of
the pressure time-history and therefore, by extension, a rational, quantifiable sectioning of the five
combustion phases.
Phase I, the ignition phase, is characterized by positive values of d p(t)/dt and d 2 p(t)/dt 2 : here
the flame is growing radially unobstructed and unaware of the surrounding CV confinement. Phase
I may be taken to end when d p(t)/dt is highest. This occurs when d(d p(t)/dt)/dt is a maximum.
Consider now phase II, where the spherically expanding flame undergoes transition into the
concave “finger” flame extensively discussed by Clanet and Searby Clanet & Searby (1996) in their
open-ended circular tube experiments. The pressure in the CV chamber continues to monotonically
64

raise after phase I with large and increasing d p(t)/dt. However, at approximately a normalized
time of 0.07 the value of d p(t)/dt attains a maximum value after which it decreases. The maximum
value of d p(t)/dt is where one finds d 2 p(t)/dt 2 = 0. This behavior of the pressure trace can also
be seen in the p(t) curve although not as distinctly as for the d p(t)/dt curve. We believe that at
this instant the flame skirts first touch the walls and then begin their rapid approach toward the
flame front from behind the flame (see Fig. 5.1d- Fig. 5.1g): for this reason, the averaged flame
front speed increases although the middle section of the flame front is slowing down. In general,
locating the maximum of d p(t)/dt seems to be a more reliable indicator of flame skirt touchdown
than is visual ascertainment of the same. In phase II, the cross-section averaged flame speed
still increases monotonically while also lagging with respect to the pressure trace. The averaging
process using five points along the flame sheet produces a flame speed that is generally larger than
would be found by sampling the flame speed at the center of the channel, because of the rapid
acceleration of the sides of the flame as they quench along the cold walls. This phase is the only
one in which the averaging process described above could possibly yield deceptive average flame
speeds. Phase III, which is taken to begin at the maximum of d p(t)/dt at normalized time 0.07,
can be approximately characterized by the strong decrease throughout of d p(t)/dt. The value of
p continues to increase though at a consistently diminished rate, hence the second derivative is
always negative with a minimum value approximately in the middle of this phase. The latter part
of phase III is characterized by the deceleration of the flame front caused by the quenching of the
flame edges by the cold channel walls culminating, at the end of this phase, in a local minimum of
the flame speed. However, the flame is sufficiently strong to maintain a pressure rise as reflected
in the positive value throughout of d p(t)/dt. At the end of phase III, the flame is essentially flat.
From Fig. 5.1h this occurs approximately when t = 9.1ms/65ms = 0.14. A more careful evaluation
of the flame images indicates that the flatness occurs almost exactly when the normalized time is
65

0.1
Norm. flame speed
Norm. pressure

0.09

Norm. press. 1st derv.
Norm. press. 2nd derv.

0.8

St. dev. of exp. press.

0.08
0.6
0.07

Normalized values

0.4
0.06
0.2
0.05
0

Standard deviation of pressure measurements

1

0.04
-0.2
0.03
-0.4
0.02

0.01

Phase V

Phase IV

Phase III

Phase I

-0.8

Phase II

-0.6

-1

0
0

0.1

0.2

0.3

0.4
0.5
0.6
Normalized time (t/tmax)

0.7

0.8

0.9

1

Figure 5.6: Experimental measurements of normalized flame speed, normalized pressure
P[bar]/3.15, normalized rate of pressure change (dP/dt)[bar/s]/866, and normalized pressure
second derivative. The numbers in these denominators are maximum values that are used to scale
all of the curves for improved visualization. The data shown are averages of eight separate experiments. Also shown on the right-hand scale is the experimentally measured variance of the
pressure data, indicating it to be under 1%. The experiments measure flame position: flame speed
is obtained by differentiation.

66

0.15, as indicated in Fig. 5.6. This particular instant of burning was not included in Figs. 3a-o.
Phase IV begins with the formation of the flat flame front (Fig. 5.1h) which occurs in Fig. 5.6
at t = 0.14. At this time the flame speed acquires a local minimum value as very nearly does the
local value of d p(t)/dt. Phase IV ends when the tulip flame vanishes at t = 16.7ms/65ms = 0.26
in normalized units (Fig. 5.1n). This endpoint coincides with a local maximum rate of increase of
d p(t)/dt, where d 2 p(t)/dt 2 is maximum. The newly reconstituted concave flame front has a large
(relative) surface area, much as in phase II, and thus energy addition via D(ρE)/Dt = d p/dt once
again increases rapidly before the flame begins its decay toward extinction in the quenching phase
V, described below.
In phase V, the heat losses to the cold walls become more pronounced as the flame struggles
to pass through the narrow space between the channel walls as it moves toward the channel end in
search of as-yet-unburned reactant. These heat losses, which can be calculated from the numerical simulation and which begin at the start of stage V, are not shown in the present work. The
flame front displays a continuous reduction in flame surface area. In phase V the rate of pressure
change d p(t)/dt becomes negative, which indicates that the thermal energy ρE in the channel is
decreasing due to the weakness of the flame induced by heat losses. A discussion and an explicit
calculation of this behavior is found in Kiran et al. Kiran et al. (2014). In phase V, The pressure
curve reaches its maximum at about 0.37 of the combustion time (which occurs between Fig. 5.1n
and Fig. 5.1o), after which d p(t)/dt drops below zero. The pressure then starts to decrease and the
flame in this phase decelerates. A marked reduction in flame speed and rate of pressure change is
observed around 90% of combustion time, t = 0.9 which indicates the time of flame quenching at
the channel end wall.

67

5.3

Flame-Induced Flow

Once the combustion reaction starts and become self sufficient, the heat release term increased
significantly in the reaction zone, which in turn hike the temperature and consequently the pressure.
This environment induces flow called flame-induced flow which interacts afterward with flame
front and contributes to flame dynamics evolution Jeung & Cho (1989).

5.3.1

Flame-induced flow and vorticity

The flow induced by the flame can create an environment near the flame front that subsequently
alters flame evolution Kiran et al. (2014), Zhou et al. (2006), Xiao et al. (2012a). Here, we confine
our discussion to the results of the simulation. In Fig. 5.7, the flame tracked by mass fraction contours of HCO and velocity vectors are plotted over a vorticity scale colored surface to characterize
the interaction between flame front and flame-induced flow. As indicated previously in Sec. 3.1,
the flame zone HCO distribution appeared to be adequately resolved in the simulations.
During the hemispherical expansion of the flame kernel, the burned gas flow produced from the
lateral flame moves from the sidewalls toward the centerline of the channel and is then deflected
axially downstream along the channel centerline toward the flame front, in the same direction of
unburned gas moving ahead of the flame (Fig. 5.7a, Fig. 5.8). It is certain that this flow pattern
contributes to the acceleration of the flame front during phases I-II. It is also evident that the flow
pushed by lateral sections of the flame front is affected by chamber geometry, which narrows along
its length (Fig. 4.2). This forward “push” of the unburned gases until about 7 ms (see Fig. 5.7a,
Fig. 5.7b, and Fig. 5.7c) produces a large velocity gradient near the upstream channel walls, which
generates a local vorticity maximum at the walls along with a narrow high-vorticity layer near
the walls. This wall-generated vorticity is about a factor of five (5) larger than the local flame-

68

generated vorticity as is denoted by the color scaling in these figures. At approximately 5 ms, the
lateral flame starts to touch the inner sidewall, which stops the forward propulsion of the flow from
the bottom toward the centerline of the channel. The upper lateral flame, which has not yet touched
the wall, continues to thrust the burned gases toward the inner wall, which are then deflected toward
the flame front. These gases move downstream near the inner sidewall instead of the middle of the
channel. The net effect is to accelerate the flame front near the inner sidewall as shown in Fig. 5.7b,
and Fig. 5.8 making the flame “bulge” somewhat in this vicinity. During this time the upper lateral
flame starts touching the top sidewall, producing fewer burned gases. No more burned gases
can be observed moving from the lower segment of the lateral flame from approximately 5.5 ms
onward (Fig. 5.7b). By this time, the majority of burned gases are produced by the flame front
and hence deflected toward the ignition point while the unburned gases ahead of the flame front
continue their movement downstream, see Fig. 5.7c. This inversion in burned gas flow can be
clearly observed after t ∟
= 6 ms/65ms = 0.092 at the time when flame propagation experiences a
significant deceleration during phase IV, see Fig. 5.6. The inversion in burned gas flow occurred
2-4 ms before the tulip flame cusp was first observed at around 10.5 ms. This indicates a distinct
role played by inversion on premixed flame evolution Ponizy et al. (2014). The results also show
that after the inversion of the burned gas flow, an increase in vorticity is observed behind the flame
front. By contrast, a reduction is observed in the vorticity near the sidewalls in the unburned
upstream region. Thus, the bulk velocity of unburned gas ahead of flame front slows down after
flow inversion, see Fig. 5.7c, Fig. 5.7d, Fig. 5.7e, and Fig. 5.7f. This slowdown is caused in part
by compression and by reverse flow of the vertical motion induced in this region by the forward
thrust toward the sides of the channel. After that the tulip flame propagates downstream where
the flame cusp moving toward the upper sidewall and the tulip flame is reverting to its pre-tulip
concave shape (Fig. 5.7e). The burnt gases at this time move upstream while the fresh mixture
69

t=4.01 ms

t=6.11 ms

t=5.25 ms

(a)

t=11.11 ms

t=14.55 ms

(d)

(c)

(b)

t=31.67 ms

(e)

(f)

Figure 5.7: Interaction between flame front and flame-induced flow: (a) burned gas produced by
lateral flame moves from sidewalls toward the centerline of the channel, and then is deflected along
the channel centerline; (b) inner lateral flame is quenched while upper lateral flame continues to
thrust the burned gases toward the inner wall and is then deflected toward the flame front; (c)
inversion of burned gas flow; (a-c) vorticity is generated in the near wall region of the channel by
the forward forced flow; (d-f) vorticity is generated in burned gas behind the flame front by the
rearward forced flow. The change in flame morphology from concave to convex occurs between
(c) and (d) as the tulip is formed while the change from convex to concave occurs between (e) and
(f) as the concave flame front is reconstituted.

70

continues to move downstream until the flame quenches at the channel end wall, see Fig. 5.7f.

Velocity

Velocity

Velocity

Velocity

Velocity

Velocity

Velocity

Velocity

Velocity

Velocity

Velocity

Velocity

Velocity

Velocity

Figure 5.8: Velocity field induced by the flame at different combustion time.

5.3.2

Flame flow interaction

The small scale (high frequency) intrinsic instabilities of confined premixed flame propagating into
quiescent mixture are basically caused by two main phenomena; the hydrodynamical phenomena

71

associated with thermal expansion of burned gases or flame-induced flows, and thermodiffusive
phenomena controlled by Lewis number Kadowaki et al. (2005), Clavin (1985). Fig. 5.9 shows the
flow interaction with flame front of M(III). In the spherical and finger flame stage of Fig. 5.9a, the
hydrodynamical phenomena associated with thermal expansion of burned gases is dominant. The
flow near the flame front can be characterized by alignment angle between burned and unburned
gases and the saddle point fitted near the ignition zone in the place where the burned gases produced by lateral flame are deflected toward flame front (Fig. 5.9a,b). Both burned and unburned
flows are aligned to each other near the channel centerline and moving away from ignition which
accelerates the flame front at this area while the flame slows down away from channel center toward the sidewalls as the alignment angle increase and approach maximum near the sidewalls. It
is certain that the local absolute flame propagation speed is highly affected by the alignment angle
between burned and unburned flows with inverse proportions, see Fig. 5.9a,b. Once the lateral
flames annihilated by the cold sidewalls, the burned gases turned back into ignition zone and saddle point moves close to and behind the flame front on the downstream side at the place where the
cusp of the tulip flame will be established later (Fig. 5.9c). Once the cusp and lower tongue of
the tulip flame start evolving, the saddle point again moves next to and behind the lower tongue
flame front and stay there till the upper tongue is fully diminished by growing lower tongue and
the second tulip flame starts evolving (Fig. 5.9d-f). It can be observed that the lower tongue of the
second tulip flame is free of the saddle point unlike its predecessor, which gives evidence that the
present of saddle point close to the flame front indicate that the flame front has the tendency to
fold. It can be concluded from these results and work of Hariharan et al. Hariharan & Wichman
(2014) that the movement of the saddle point presents a certain evidence that the flame-generated
flow significantly contributes to the dynamics of the flame front and tulip flame formation.

72

(a) t=1.96 ms

(e) t=12.96 ms

(b) t=5.96 ms

(f) t=15.96 ms

(c) t=7.36 ms

(g) t=19.96 ms

(d) t=10.96 ms

(a) t=64.96 ms

Figure 5.9: Flame-induced flow and the characteristic saddle points of unity Lewis number flame:
(a) spherical flame surrounds saddle point; (b) finger flame front away from saddle point ; (c)
saddle point moves close to skirt flame; (d-f) saddle point moves close to lower tongue of the first
and second tulip flame; (g-h) no saddle point was observed.
73

In Fig. 5.7 and Fig. 5.8 the saddle point and various nodes and half saddles are not directly
visible in the WDE channel as they were in the straight channel, see Fig. 6.4. The saddle point
is identified in velocity vector plots as regions of very slow flow surrounded by fluid flowing
in opposite directions along perpendicular axes. Such a flow pattern is evident in Fig. 5.7 and
Fig. 5.8. Thus, Fig. 5.7a shows that nascent saddle formed right after ignition, and Fig. 5.7b
shows that the saddle has moved close to and behind the flame front on the downstream side. In
Fig. 5.7c the saddle is located along the flame front on its straighter edge toward the inside sidewall.
Fig. 5.7d shows that the saddle point is located in front of the flame on its upstream side, whence
the tulip shape of the flame front as discussed out in Section 6.1.2. It is not clear from Fig. 5.7e
and Fig. 5.7f, where the saddle point is located after the concave flame front reconstitutes itself,
although a careful examination of Fig. 5.7e suggests that it resides at or very near the flame front.
The characteristic flow feature of saddle point motion appears to remain intact even when the CV
chamber is a complex, curved shape.
The relevance of the motion of the saddle point consists of its direct relation to the fundamental
structure of the flow field behind, at and in front of the flame during its evolution. Much effort has
been expended in theoretical and physical discussions focusing on the basic nature of the transition from concave to convex tulip flame, for example whether it is governed by Rayleigh-Taylor,
Richtmeyer-Meshkov or Darrius-Landau instability mechanisms. In fact, it is governed by none
of these (Hariharan & Wichman (2014), Ponizy et al. (2014)), instead manifesting as the consequence of intense flame-flow interaction of a minimally two-dimensional kind: the formation of
the tulip in straight channels and in the moderately curved channel studied here is the outgrowth of
a complex flame-flow interaction whose most distinct and recognizable feature is the propagating
saddle point.

74

5.4

Impact of Soret effect

In transport phenomena, Soret diffusion is the mechanism by which light (heavy) molecules are
transported in multicomponent mixture toward (away from) the hot region driven by temperature
gradient. To explore the Soret effect on mixture stoichiometry, the distribution of trapped reactants
species between the flame front and the channel end wall was plotted versus normalized channel’s
width at arbitrary time of 55 ms where the temperature of fresh gases at the channel’s center
approaches 400 K due to the confinement effect, see Figs. 5.10, 5.11, 5.12, 5.13. The results
reveals that the concentration of relatively light species such as CH4 near the cold sidewalls of
the channel is lower than the hot zone in the middle of the channel by 4.1% (Fig. 5.10), whereas
the relatively heavy species like AR and O2 has opposite concentration distribution by 2.28% and
0.88%, respectively, see Figs. 5.11, 5.12. Since the temperature gradient between the burned
gases and cold sidewalls is much higher than unburned gases region, the Soret effect on species
concentration become even more pronounced. The nitrogen N2 , for example, has 1.312% higher
concentration near the cold sidewalls in the burned gases side compared to 0.0075% in unburned
gases side, (Fig. 5.13). The unburned mixture species show uniform and constant distribution when
the Soret effect is not considered such M(II) and M(III) (Fig. 5.11)

75

0.0565

0.056

0.0555

0.055

0.0545

0.054

0.0535

0.053

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 5.10: Soret effect impact on the CH4 species concentration plotted along the normalized
channel width in the unburned region.
0.01235

0.0123

0.01225

0.0122

0.01215

0.0121

0.01205

0.012

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 5.11: Soret effect impact on the AR species concentration plotted along the normalized
channel width in the unburned region.
76

0.2208

0.2204

0.22

0.2196

0.2192

0.2188

0.2184

0.218

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 5.12: Soret effect impact on the O2 species concentration plotted along the normalized
channel width in the unburned region.
0.714

0.7125

0.711

0.7095

0.708

0.7065

0.705

0.7035
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 5.13: Soret effect impact on the N2 species concentration plotted along the normalized
channel width in the unburned region.
77

In the burned region where characterized by higher temperature, more species get involved,
dissociation phenomena, and phase change, the transport of products species e.g. CO2 , H2 O, N2 ,
etc., reveals complicated transport behavior for species like H2 O, see Fig. 5.14. The distribution of
products species in the burned region correlates with the temperature gradient distribution which is
driven by the burned gases velocity field. The CO2 species concentration (Fig. 5.15) exhibit similar
behavior as O2 (FIg.5.12)with higher gradient near the wall due to higher temperature gradient and
larger molecular weight while once again the H2 species diffuses in the opposite direct.
0.126

0.123

0.12

0.117

0.114

0.111

0.108

0.105

0.102

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 5.14: Soret effect impact on the H2 O species concentration plotted along the normalized
channel width in the burned region.

78

0.171
0.168
0.165
0.162
0.159
0.156
0.153
0.15
0.147
0.144
0.141
0.138
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 5.15: Soret effect impact on the CO2 species concentration plotted along the normalized
channel width in the burned region.
0.0003
0.00027
0.00024
0.00021
0.00018
0.00015
0.00012
9E-05
6E-05
3E-05
0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 5.16: Soret effect impact on the H2 species concentration plotted along the normalized
channel width in the burned region.
79

9E-05

7.5E-05

6E-05

4.5E-05

3E-05

1.5E-05

0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 5.17: Soret effect impact on the O species concentration plotted along the normalized channel width in the burned region.

In syngas/air mixture, the light species of H2 shows strong and opposite transport compared
with CO due to the Soret effect which modifies mixture stoichiometry. The H2 concentration can
be ∟10% more near the channel cold walls while the maximum difference in CO concentration is
approximately 1.35% (Fig. 5.18). The O2 and N2 species migrate in the opposite direction to H2
species as shown in Fig. 5.19.

80

0.0182

0.01819

0.01818

0.01817

0.01816

0.01815

0.01814

0.01813

0.01812

Figure 5.18: Mass fraction of H2 and CO distributed across the WDE channel for the case M(I).

0.72715

0.7271

0.72705

0.727

0.72695

0.7269

0.72685

Figure 5.19: Mass fraction of O2 and N2 distributed across the WDE channel forthe case M(I).

81

The mass flux (kg/(m2 s)) of CH4 , O2 , N2 , and CO2 due to the Soret effect at 14.96 ms shows
that the relatively light species such as CH4 and N2 have a negative mass flux near the cold sidewalls, which means that they migrate against the temperature gradient from low to high temperature
region, see Fig. 5.25a,d. An opposite behavior can be observed for relatively heavy species like
CO2 and O2 , see Fig. 5.20b,c.
The results show the quantitative contribution of Soret effect in changing the mixture stoichiometry ahead of the flame and near the chamber cold sidewalls. The mixture near the cold
sidewalls is obviously lean mixture of equivalence ratio 1.03 since the CH4 migrates away from
the cold wall whereas the O2 migrates toward the cold walls due to Soret effect. These changes
in species concentration, however left no significant effect on flame absolute speed and structure
(Fig. 5.3), peak temperature (Fig. 5.22), and average pressure (Fig. 5.22), nevertheless the transport behavior of multicomponent mixture is of critical importance in safety and pollution areas.
The same conclusion was drawn from previous work of Yang et al. Yang et al. (2011) where Soret
effect on freely propagating n-butane/air mixture was considered.

82

(a)

(b)

(c)

(d)

Figure 5.20: Mass diffusion flux due to Soret effect at, 14.96 ms for: (a) CH4 ; (b) O2 ; (c) CO2 ; (d)
N2 .

83

5.5

Influence of Effective Lewis Number

As it is used to compare the molecular diffusion speeds of species versus heat, the Lewis number
for laminar premixed flame is of critical importance since it has a direct effect on the intrinsic
thermodiffusive instabilities, stretching, extinction, and other flame features Poinsot & Veynante
(2005).
The comparison between time history of peak temperature and average pressure using unity
Lewis number model M(III) and more detailed diffusion models M(I), and M(II) is presented in
Figs. 5.22, 5.21. The peak temperature and average pressure of unity Lewis number are following
but lagging behind its counterparts of M(I) and M(II) up to the combustion time of 11.8 ms, after
which time the peak temperature (Figs. 5.22) as well as the average pressure (Figs. 5.21) of unity
Lewis number increase drastically and jump above the values of M(I) and M(II) during the time
11.8 to 17.6, during which time the expansion of lower flame tongue speed of M(III) is accelerated
dramatically faster than other flames of M(I) and M(II) as we have discussed in Section 5.1.2.
Furthermore, the unity Lewis number model develops a new secondary tulip flame at about 16 ms
after the first primary tulip flame was completely annihilated which has never been reported in
any previous study. These deviations in peak temperature, average pressure, and flame dynamics
for unity Lewis number model are however unrealistic since neither the models M(I) and M(II)
nor the experiments in the previous work Najim et al. (2015) produce such behavior. This reveals
that the Lewis number cannot be assumed as unity or even constant in a situation where we have
stretched tulip flame since we are dealing with multicomponent mixture in which the temperature,
the pressure, and the mixture composition are changing with space and time.

84

Figure 5.21: Average pressure developed in the WDE channel under three different diffusion model
M(I), M(II), and M(III) for stoichiometric methane/air.

2900
2800
2700
2600
2500
2400
2300
2200
2100
2000

0

10

20

30

40

50

60

70

Figure 5.22: Peak temperature developed in the WDE channel under three different diffusion
model M(I), M(II), and M(III) for stoichiometric methane/air.

For syngas/air of φ = 0.7 and hydrogen content 50% by mass, the Lewis number was estimated
85

for reactants at atmospheric pressure and room temperature. Since the mixture is lean, the Lewis
number must evaluated based on the fuel components (H2 and CO) as D´ ippolito (2015):

Le =

Îą
XH2 DH2 m + XCO DCO m

(5.1)

Where ι is the mixture thermal diffusivity (ι = Ν /ρc p ), DH2 m , DCO m is the diffusion coefficients
of H2 and CO into the mixture, respectively. Based on this analysis, the effective Lewis number is
estimated to be 0.57.
The peak temperature and average pressure of case M(III) exhibit moderate differences from
M(I) and M(II) (Figs. 5.23, 5.24) possibly because the Lewis number for the syngas/air mixture
is evaluated at the initial state (Le = 0.57) D´ ippolito (2015).

Figure 5.23: Average pressure developed in the WDE channel under three different diffusion model
M(I), M(II), and M(III) for syngas/air of φ = 0.7 and 50% H2 .

86

2600

2500

2400

2300

2200

2100

2000

1900

1800

0

2

4

6

8

10

12

14

16

18

20

Figure 5.24: Peak temperature developed in the WDE channel under three different diffusion
model M(I), M(II), and M(III) for syngas/air of φ = 0.7 and 50% H2 .

The effective Lewis number can be formulated based on heat release, volume fraction, and
diffusional properties of the main fuel components as reviewed by Bouvet et al. (2013). It is our
understanding that all mixture species contribute to the overall transport of heat and mass, therefore
the effective Lewis number is estimated based on the volume fraction of all individual species not
s
only the fuel components. Thus we define Lee f f = ∑N
k=1 Xk Lek . Figure 5.25 for the evolution

of the effective Lewis number shows that the unburned methane/air mixture is nearly constant,
approximately 1.139 during combustion. However, Lee f f decreases to between 1.10-1.02 close to
the flame front in the unburned mixture (Fig. 5.25g): the species molecular diffusivity is lower than
its thermal diffusivity. Since the front shape of the lower, dominant tulip flame tongue is convex
toward the unburned gases, the reactants diffuse from a large to a small area thereby following
a convergent path. This decreases the laminar flame speed below the planar flame value, see
Figs. 5.25b-d. Consequently, this environment stabilizes the flame front and reduces the tendency

87

for it to fold Kadowaki et al. (2005), Poinsot & Veynante (2005). It can be seen from Fig. 5.25g
that the effective Lewis number is time dependent, showing different behaviors near the flame front
before and after flow inversion.

(a) 5 ms

(d) 16 ms

(b) 9 ms

(e) 22.4 ms

(c) 12 ms

(f) 55 ms
Lines at which plot (g) is
constructed
Effective Lewis number

(g)

Figure 5.25: Evolution of effective Lewis number derived from case M(II) for methane/air mixture
at different combustion time.

After inversion (i.e. when thermodiffusive phenomena become dominant), Lee f f drops below

88

unity (∟ 0.9) within the flame front. The progressively narrowing space at the end of the channel
likely prevents the flame from folding and reproducing the tulip flame observed in constant cross
section channels Xiao et al. (2012b). It can be deduced from these behaviors that the flame tendency to fold is increased by assigning Le = 1 to the fresh gases ahead of the flame front since its
“natural” response is to develop a Le < 1 region in front of the flame (indicating more pronounced
mass transport). This suggests that decreased mass transport favors the formation of the artificial
folded flame of Fig. 5.3.

5.6

Characteristic Burning Regime

The discussion in Section 5.5 reveals three different burning regimes (Fig. 5.26). Regime (1) of
dominant hydrodynamical phenomena, where the flame structure only slightly influenced by the
diffusion, hence the M(III) flame structure agrees with experimental observation; regime (2) of
dominant thermodiffusion phenomena, where the diffusion model influences the flame structure
and other thermochemical properties. In this regime, model M(III) is insufficient and yield an unrealistic flame structure,peak temperature, and pressure; regime (3), in which the flame propagates
slowly into the narrowing space ahead of it. The flame in Regime (3) is unable to produce a tulip
flame but rather generates a concave (finger) flame. To characterize these regimes, we introduce
the non-dimensional characteristic time ratio:

Hydrodynamic time scale
=
N =
Di f f usive time scale

L
Uave
L2
Dimave

=

1
Uave L/Dimave

(5.2)

Here, the characteristic length, L, is the local channel width, the volumetric average velocity magnitude, Uave , the volumetric average mass diffusion coefficient between unburned and burned gases,

89

Dimave . Shown in Fig. 5.26 is a plot of the ratio N /N(2) where N(2) is the value of N in the
Regime (2), versus the normalized time t/tmax . Consequently, N /N(2) has average value unity
in Regime (2) but is large by a factor of ten in Regime (1), the hydrodynamic regime, and smaller
by a factor of ten in the heat-loss Regime (3). The rescaled time variable ranges between zero and
unity indicates that the bulk of the transition processes have ended at approximately 30% of the
total burn time.
10
𝑡𝑛 =0.25

𝐷𝑖𝑚𝑎𝑣𝑔
𝑈𝑎𝑣𝑔 𝐿
𝒩
=
𝐷𝑖𝑚𝑎𝑣𝑔
𝒩(2)
𝑈𝑎𝑣𝑔 𝐿

(2)

Region (2)
Tulip flame development
Dominant thermodiffusive phenomena

Region (3)
Concave flame propagates to the channel end wall
Narrow channel and heat-loss effect
𝑡𝑛 =0.92

1
Region (1)
Hemispherical and finger flame
Dominant hydrodynamic phenomena
𝑡𝑛 =0.83

0.1
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

t/tmax

Figure 5.26: Normalized inverse Peclet number ratio N /N(2) versus normalized total time t/tmax .
The hydrodynamic Regime (1), and the thermodiffusive Regime (2) occupy 10 and 20% of the
total time. The heat-loss Regime (3) occupies the remaining 70% of the burn time.

90

5.7
5.7.1

Influence of Mixture stoichiometry on Syngas Flames
Flame structure

The evolution of syngas premixed flame structure propagating in a rectangular channel is described
for nine (9) cases of different stoichiometry, see table 5.1. It be seen from Fig. 5.27 that the
confined, premixed syngas flames exhibit several distinct modes. For all nine (9) cases, the process
of syngas flame propagation in rectangular channel starts with hemispherical expansion of the
flame kernel followed by elongated finger-shaped flame which expands axially and gains more
surface area. A dramatic reduction of the flame surface area takes place after the flame skirt
annihilated by the channel side wall leading to the formation of tulip flame with cusp pointing
towards burned gases. This evolution of flame structure has been reproduced experimentally and
numerically as we discussed before Ponizy et al. (2014), Dunn-Rankin & Sawyer (1998), Clanet
& Searby (1996), Hariharan & Wichman (2014), Xiao et al. (2015), Xiao et al. (2012b), Jeung &
Cho (1989), Dunn-Rankin et al. (1988), Matalon & McGreevy (1994). However, the syngas flames
show unique structure evolution after the tulip flame is fully established, see Fig. 5.27 from 5.0 ms
to 18 ms. The flames of C2, and C3 at 11 ms exhibit a unconventional structure where the tulip
flame evolves into highly wrinkled, corrugated curved shape-flame and then to less wrinkled flame
front and end up with laminar-like type of flame front with backward cusp when it get closer to
the channel end wall. The results also indicates that the temporal change in syngas flame structure
is highly dependent on the stoichiometric ratio and hydrogen content in the mixture (Fig. 5.27).
The mixture stoichiometry affects the combustion time significantly. For example, the flame of
C9 approach the channel end wall at 8.5 ms while for C1, it takes 28 ms, which means 3.3 times
the time required for C9 (Fig. 5.28). As can be seen in Fig. 5.28, the rate of flame acceleration
by increasing the hydrogen content in the mixture depends on the mixture stoichiometric ratio and
91

it is higher when φ = 0.7 than φ = 1.5. Also, when increasing the hydrogen content from 20%
to 50%, the syngas flame accelerate much faster when hydrogen content in the mixture goes from
50% to 80%, see Figs. 5.29, 5.29
Mixture

Stoichiometric ratio

Hydrogen Content (% by mass)

C1

0.7

20

C2

0.7

50

C3

0.7

80

C4

1.0

20

C5

1.0

50

C6

1.0

80

C7

1.5

20

C8

1.5

50

C9

1.5

80

Table 5.1: Cases for syngas flame simulations.

92

0.4 ms
0.8 ms
1.0 ms
1.5 ms
2.0 ms
3.0 ms

C4
C5
C6

C7
C8
C9

18.0 ms 14.0 ms 11.0 ms

9.0 ms

7.0 ms

5.0 ms

4.0 ms

C1
C2
C3

MM/CM

0

1

2

3

4

5

6

7

8

9

10

Figure 5.27: Syngas flame structure for different stoichiometric ratios and hydrogen content (C19).
93

Figures 5.27, 5.28, 5.29 reveal that the C9 mixture (φ = 1.5 with 80% hydrogen content)
produces faster flame propagation speed while the slowest propagation speed is produced by C1
(φ = 0.7 and 20% hydrogen content). Since the laminar flame speed approaches maximum near the
stoichiometric conditions for conventional hydrocarbon fuels, see Fig. 3.1, it becomes even more
interesting when we see that the propagation speeds of rich mixture case C9 (φ = 1.5, 80% H2 ) is
faster than stoichiometric mixture of C6 (φ = 1.0, 80% H2 ). This unique feature of syngas flame
has a great impact on the industrial combustion chambers that working on syngas/air mixture.
The analysis of one-dimensional, freely propagating syngas laminar flame reported by Sun et al.
(2007), Singh et al. (2012) and Kèromnès et al. (2013) has verified this behavior (Fig. 3.2) in
which the laminar flame speed for syngas approaches maximum at about φ = 2. Figure. 5.27 also
shows that the temporal evolution of flame structure for C9 is faster than other cases. It can be
concluded from Fig. 5.28 that the propagation speed of syngas flames nonlinearly increases when
the hydrogen content in the mixture is increased. It can be seen from Fig. 5.28, however, that
propagation speed slightly increases when the hydrogen content goes from 50% to 80%.

94

28

φ=0.7
φ=1.0
φ=1.5

Combustion end time (ms)

26
24
22
20
18
16
14
12
10
8

20

30

40

50

60

70

80

% H2 Content (by mass)

Figure 5.28: Syngas combustion time for different mixture stoichiometry.

95

100

Average flame position (mm)

90
80
70
60
50

φ=0.7, 20% Η 2
φ=0.7, 50% Η 2
φ=0.7, 80% Η 2
φ=1.0, 20% Η 2
φ=1.0, 50% Η 2
φ=1.0, 80% Η 2
φ=1.5, 20% Η 2
φ=1.5, 50% Η 2
φ=1.5, 80% Η 2

40
30
20
10
0

0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

Time (ms)

Figure 5.29: Instantaneous syngas flame distance for different mixture stoichiometry.

5.7.2

Pressure dynamics

The average pressure of the channel starts build up after the ignition kernel expansion and increases
exponentially during the axial expansion of the finger-flame at around 0.07% of the combustion
time, see Figs. 5.30, 5.31. The pressure time-history correlate with the evolution of associated
flame structure as discussed in Sec. 5.7.1. Faster propagation speed, as in C9, result in higher
rate of pressure increase and vice versa. The normalized average pressure is presented in Fig.5.31
which reveals that the pressure data collapsed regardless the stoichiometry and hydrogen content.
By neglecting the short exponential increase of the pressure during the finger-flame expansion, a

96

conclude can be drawn from Fig. 5.31 such that:

p

t

=

Pmax
|{z}

Normalized pressure

(5.3)

tmax
|{z}

Normalized time

Where p is the channel average pressure, Pmax is the maximum average pressure attained, t is the
time, and tmax is the time at which the flame approaches the channel end wall.
5.5
5

Average pressure (bar)

4.5
4
3.5
3
2.5

φ=0.7, 20% Η 2
φ=0.7, 50% Η 2
φ=0.7, 80% Η 2
φ=1.0, 20% Η 2
φ=1.0, 50% Η 2
φ=1.0, 80% Η 2
φ=1.5, 20% Η 2
φ=1.5, 50% Η 2
φ=1.5, 80% Η 2

2
1.5
1
0.5
0

0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

Time (ms)

Figure 5.30: Time-history of the channel average pressure under different mixture stoichiometry.

This equation tells us that regardless the syngas mixture stoichiometry condition, the channel
average pressure p at any time t can be estimated by knowing the maximum pressure and the
combustion time. The maximum average pressure is mainly controlled by the heat released from
combustion and the heat lost to the channel cold walls or the heat accumulated in the channel which
result in increasing the average temperature and consequently increasing the average pressure since
97

the mixture average density remains unchanged due to CV combustion.
Same behavior is obtained with the normalized instantaneous flame front distance presented
in Fig. 5.32. It can be concluded that the temporal instantaneous flame front distance collapse
when normalized by the channel length (100 mm) and plotted versus the normalized time. Furthermore, this behavior is verified experimentally for stoichiometric methane/air flame propagating in
a rectangular channel, see Fig. 4.6.
1
0.9
+x

+x

+x

+x

+x

+x+x+x
+

x+
+ +
+

+x
+x

Normalized pressure, p/Pmax

0.8

+x
+
x

0.7
0.6
+
x
+x
+
x
+
x
+
x
+
x
x+

0.5
0.4
0.3

+
x

x+

+
x

x+

x+

x+

+
x

x+
+x
+x
+x

0.2
0.1
0 x +x
0

+
x

+
x
+
x

+
+x
x

0.1

+
x

+
x

+x

+x
+
x

0.2

0.3

0.4

0.5

0.6

0.7

0.8

φ=0.7, 20% Η 2
φ=0.7, 50% Η 2
φ=0.7, 80% Η 2
φ=1.0, 20% Η 2
φ=1.0, 50% Η 2
φ=1.0, 80% Η 2
φ=1.5, 20% Η 2
φ=1.5, 50% Η 2
φ=1.5, 80% Η 2
0.9

1

1.1

1.2

Normalized time , t/tmax

Figure 5.31: Time-history of the normalized pressure under different mixture stoichiometry.

98

1
0.9
+

0.8

x

+ x

+

+
+ x
+ x
x
x +
x +
+
x

x

Normalized flame position

+

+

0.7

x

x

+
+

0.6

x

+x
+x

0.5

+

x

φ=0.7, 20% Η 2
φ=0.7, 50% Η 2
φ=0.7, 80% Η 2
φ=1.0, 20% Η 2
φ=1.0, 50% Η 2
φ=1.0, 80% Η 2
φ=1.5, 20% Η 2
φ=1.5, 50% Η 2
φ=1.5, 80% Η 2

+

x

0.4

+

x

+

x

0.3

x+

+
x

0.2

+

x

+

+

x

0.1

x

+

x

+

0x
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Normalized time , t/tmax

Figure 5.32: Normalized syngas flame distance for different mixture stoichiometry.

5.7.3

Flame-flow interaction

The interaction between flame front and flame-induced flow for different combustion time and
hydrogen content are presented for φ = 0.7, φ = 1.0, and φ = 1.5 in Figs. 5.33, 5.34, and 5.34,
respectively. It is evident from these figures that the different mixtures stoichiometry develop
different flame front structure and subsequent flame-induced flow pattern. All mixtures produces
the conventional tulip flames with two tongue pointing towards the unburned gases and one cusp
pointing towards the burned gases. With the increase of hydrogen fraction for same equivalence
ratio, the flame wrinkles tend to increase on the flame front while it decreases with the increase
of the stoichiometric ratio. This agrees with the experimental observations of the spherical syngas

99

flame propagation in closed chamber conducted by Li et al. (2014). It is also evident that the flame
wrinkles and flame instabilities decreases when the pressure build up before the combustion ends
which has never been reported in the literature. The flames of φ = 0.7 and φ = 1.0 develop a
convex front at the end of the combustion time after the flame approaches 80-90% of the channel
length while the flame of φ = 1.5 develops a concave-like shape and for all hydrogen content
fraction.
Figures. 5.33, 5.34, 5.35 show that the flow intensity increases with the increase in the mixture
stoichiometric ratio and hydrogen mass fraction due to the increase in laminar flame speed which,
in turn, increases the reaction rate.
The vortical flow is formed in the burned gases region behind the tulip flame cusp is more
pronounced for mixtures of φ = 1.0 and φ = 1.5 (Figs. 5.34, 5.35). The results show that stagnations point develop behind the tulip flame tongues in the burned region which remarks the flame
tendency to fold at that region.
The flame propagation speed decelerates near the channel end wall due to the high pressure
developed in the closed channel. The impact of high pressure on the flame front structure depends
on stoichiometric ratio. When the syngas/air mixture is rich (φ = 1.5), the high pressure smooths
the flame front and the flame tend to be a laminar-like flame at the end of the combustion and for
different hydrogen content (Fig. 5.35). On the other hand, the flame still generates a wrinkled front
in the high pressure environment when the mixture stoichiometric ratio is 0.7 and less wrinkled
front is seen for mixture of φ = 1.0.

100

20%H2

50%H2

80%H2

Velocity (m/s)

Figure 5.33: Flame front interaction with flame-induced flow for stoichiometric ratio of 0.7 for
different combustion time, hydrogen content, and flame front position at the channel centerline.

101

20%H2

50%H2

80%H2

Velocity (m/s)

Figure 5.34: Flame front interaction with flame-induced flow for stoichiometric ratio of 1.0 for
different combustion time, hydrogen content, and flame front position at the channel centerline.

102

20% H2

50% H2

80% H2

Velocity (m/s)

Figure 5.35: Flame front interaction with flame-induced flow for stoichiometric ratio of 1.5 for
different combustion time, hydrogen content, and flame front position at the channel centerline.

103

Chapter 6
FLAME SURFACE DENSITY FOR LES

6.1
6.1.1

Three-Dimensional Structure of the Flame Front
Transverse tulip flame

Figure 6.1 shows the structural evolution of three-dimensional premixed flame propagating in a
closed-curved channel. After ignition, the flame expands hemispherically with approximately constant flame speed. Finger flame then takes place at 4.5 ms with the flame front deflected toward
lower sidewall. During this time, the burned and unburned gases are moving away from ignition
location due to burned gases expansion. The flame touches the inner sidewall at approximately 5
ms and the outer sidewall at 6 ms, and the bottom and top sidewalls at about 8 ms. Once the flame
touches all sidewalls, the burned gases flow is inverted toward ignition location causing a dramatical deceleration in flame propagation speed. As a consequence, the saddle points moves closely to
the flame front, see Fig. 6.1-d. At this time, the non-symmetric tulip flame on the lateral xy plane
starts developing to cusped convex shape with large lower tongue near inner sidewall and small
rounded tongue near outer sidewalls (Fig. 6.1-e). During the time 20 ms, the three-dimensional
simulation conducted here uncovers an interesting behavior for the flame structure on the xz plane.
We observed what may be referred as a “transverse tulip” flame which is developed in the direction perpendicular to that of the initial tulip flame after the latter underwent the transition from
cusped convex back to concave finger shape. This “transverse tulip” flame is symmetric across
104

transverse xz planes and it has two tongues which accelerate near the sidewalls while the concave
finger flame in the xy plane, at z=0, decelerates and lags behind. During the combustion time 22-40
ms the “transverse tulip” flame tongues start growing by moving forward and toward the channel
centerline. At the time when the two tongues are about to touch each other at the channel middle
xy plane, the finger flame in the middle plane experiences minimum propagation speed (approaching zero). This leads to more pronounced cusp pointing toward burned gases for the “transverse
tulip” flame which continues into a tulip shape that persisted to the end of the channel. The flameinduced flow on the transverse xz plane shows dramatic pattern changes through the evolution of
“transverse tulip” flame. The burned gases flow patterns are driven by the difference in burned
gases velocity produced by the flame tongues, which produces higher velocity, and near cusp region, which is of low burned gases velocity, see Fig. 6.1. The flow patterns behind “transverse
tulip” flame can be characterized by vortical motion that continuously changes depending on the
structure of the “transverse tulip” flame.
The comparison between experiments and numerical simulation results indicates that the algebraic flame surface density with Metghalchi-Keck correlation for flame speed are capable of
reproducing the main features of flame structure and propagation speed, see Fig. 6.2 a-d. The
initial tulip flame cusp predicted by numerical simulation, however, appears more rounded and
smoother than experiment (Fig. 6.2 d) and San Diego kinetic mechanism reported in Najim et al.
(2015) because of the coarse mesh used here to afford the three-dimensional model which in turn
diffuses and smooths the relatively sharp changes that taking place in flame front. The “transverse
tulip” flame can be observed in Fig. 6.2 f, in which the two tongues of “transverse tulip”, at
z = 7.25 mm, are leading the finger concave flame in the middle plane (z = 0 mm) and hence they
seem clearly in the experiment shadowgraph in contrast with the finger flame which hiding behind
and appears faint and fade.
105

y

z
x

(a) 2.0 ms

(b) 5.0 ms

(c) 9.0 ms

(d) 11.0 ms

(e) 15.0 ms

(f) 23.0 ms

(g) 30.0 ms

(h) 44.0 ms

Velocity (m/s)

Figure 6.1: Flame structure evolution;(a) hemispherical flame, (b) finger flame, (c) skirt flame (d)
straight flame front on transverse plane and concave flame on lateral plane, (e) non-symmetric
tulip flame on lateral plane, (f) initial tulip flame back to concave finger shape (g-h) transverse
tulip flame.

106

(a) 2.0 ms

(b) 5.0 ms

(c) 11.0 ms

(d) 15.0 ms

(e) 23.0 ms

(f) 45.0 ms
Flame on plane z=0 mm

Flame on plane z=7.25 mm

Figure 6.2: Experiment flame front shadowgraphy (on the left side) and numerical simulation flame
front on plane z = 0 mm and z = 7.25 mm projected on one plane (on the right side).
107

6.1.2

3D flame dynamics in a rectangular channel

Figures 6.4, 6.3 indicate that the algebraic flame surface density modified by incorporating the
temporal change in the unburned gases temperature and pressure is capable of reproducing the main
features of the premixed flame propagating in a closed rectangular channel which was reported in
Hariharan & Wichman (2014); Ponizy et al. (2014); Xiao et al. (2015). As described previously,
flame expands hemispherically after ignition with approximately constant flame propagation speed
(Fig. 6.3-a). The flame then takes elongated finger-shape and accelerates dramatically in the axial
direction gaining more surface area. During finger flame phase, the burned gases produced from
the lateral flame near the channel sidewalls moves toward the centerline of the channel and is
then deflected axially along the channel centerline toward the flame front, in the same direction of
unburned gas moving ahead of the flame as shown in Fig. 6.3-b. This flow pattern produces a saddle
point near ignition point, see Fig.6.4 at approximately 20 ms. When the flame skirt is annihilated
by the channel sidewalls, which rapidly reduces the flame surface area and reaction rate as well, the
flame front flattens and experiences minimum propagation speed, see Fig. 6.4. The burned gases
flow is inverted toward ignition location after most the lateral flames are annihilated by the channel
sidewalls while the unburned gases continues to move towards the channel end wall, see Fig. 6.3-c.
At this time, the saddle point moves close to the flame front which indicates the tendency of flame
to fold. When saddle point approaches the flame front, the flame structure starts a transition from
convex to concave and end up with a cusp pointing to the burnt region followed by the formation
of tulip flame as shown in Fig. 6.3-d. At this time, the saddle point moves next to the flame front
in the unburned region. The tulip flame propagates with nearly constant speed to the channel’s end
wall and saddle point moves slowly away from the flame from front towards unburned region, see
Fig.6.4.

108

(a)

(b)

(c)

(d)

Figure 6.3: Three-dimensional, flame front structure developed in a rectangular chamber. (a)
spherical expansion of ignition kernel, (b) finger-flame expansion, (c) skirt-flame, (d) tulip-flame.
109

S

S

S

S

S

S

S

S

Velocity (m/s)

Figure 6.4: Evolution of flame structure, flame-induced flow, and dynamics of saddle point.

110

6.1.3

Flame surface density

The flame surface density area shown in Figs. 6.5, 6.6 provides important information about how
the evolution of flame structure affects the flame surface area and consequently the reaction rate.
The flame surface density has a unit of

1
m

which represents the flame area per unit volume eval-

uated at each computational element. The result in Figs. 6.5, 6.6 indicates that the flame surface
significantly increases during the finger-shape flame expansion (Figs. 6.5, 6.6) in which the flame
expands in all direction gaining more flame surface area which appears clearly before 6 and 20 ms
in Fig. 6.5 and Fig. 6.6, respectively. A rapid reduction in flame surface density is seen when the
flame approaches the channel cold walls and loses the lateral parts of its surfaces which dramatically reduces the flame surface density and so affects the reaction rate as well, see Figs. 6.5, 6.6.
The flame surface area slightly increases when the lower tongue of the initial tulip grows toward
the outer sidewalls at approximately 15 ms for the WDE channel, which is about the time when the
two tongues of “transverse tulip” flame grow forward and toward channel middle plane (Fig. 6.5).
When the initial tulip flame back into finger concave shape and “transverse tulip” flame is developed, the flame surface area decreases at a constant rate which accounts for the convergence
of channel walls. Similar behavior can be seen in the rectangular channel when the flame surface
density increases again at a low rate after the two tongues of the tulip flame accelerate axially faster
than the flame cusp which results in net increase in flame surface area at approximately 48 ms, see
Fig. 6.6. It is evident from Figs. 6.5, 6.6 that the reaction rate is highly dependent on the flame
surface density and both have almost the same structure which emphasizes the importance of flame
surface density in combustion modeling.

111

50

140

Flame surface density
Product formation rate

45

120

100

35
30

80

25
60

20
15

40

Product formation rate (1/s)

Flame surface density (1/m)

40

10
20
5
0

0

5

10

15

20

25

30

35

40

45

50

55

60

0

Time (ms)

Figure 6.5: Flame surface density and product formation rate for WDE channel.

45

35

Flame surface density
Product formation rate

40

30

25

30
25

20

20
15

15
10

10

Product formation rate (1/s)

Flame surface density (1/m)

35

5
5
0
-5

0

20

40

60

80

100

120

140

160

0
180

Time (ms)

Figure 6.6: Flame surface density and product formation rate for the rectangular chamber.

112

6.1.4

Turbulent flame speed

When a premixed flame starts accidentally in quiescent mixture and propagates through confined
chambers, the temperature, pressure, and density of the unburned gases vary considerably during
the combustion time(Figs. 6.8, 6.10). To reproduce an appropriate flame propagation speed, the
temporal change of temperature and pressure of the mixture need to be incorporated. The laminar
flame speed is proportional to transient temperature and inversely proportional to the transient
average pressure of the unburned gases Metghalchi & Keck (1980), Turns (2012). However, the
net effect of this combination works in favor of the flame speed because of the coupling between
pressure and temperature in a constant volume combustion. Therefore, the flame speed shows high
dependence on the unburned gases temperature and both reach maximum before the initial tulip
flame backs into finger concave flame at approximately 22.5 ms, see Figs.6.7, 6.8. This is because
the exponent of unburned gases temperature term in Eq. 3.54 is higher than the exponent of pressure
term by order of magnitude. The details on determining the temporal unburned gases density is
presented in Appendix. B. Other turbulent flow parameters are not incorporated in the flame speed
model since the flame starts in quiescent mixture and generates flow with low turbulence intensity,
see Appendix B.

113

75
70

Flame speed (cm/s)

65
60
55
50
45
40
35
30

0

5

10

15

20

25

30

35

40

45

50

55

60

Time (ms)

Figure 6.7: Variation of flame speed during the flame propagation in the WDE channel.

When the flame approaching the channel end wall, the net effect of transient unburned gases
temperature and pressure works against flame speed which becomes even less than the reference
value of the laminar flame speed for stoichiometric methane/air mixture (Sl re f ) at 55 ms (Fig. 6.7).
This behavior agrees with the experiment and numerical simulation presented in Section 5.2.

114

420

4

410
3.5
400

Teamperature (K)

380

2.5

370
2

360
350

1.5

340
1

330
320

0.5

310

Unburned gases temperature
Average pressure

300
290

Average pressure (bar)

3

390

0

5

10

15

20

25

30

35

40

45

50

55

0

60

-0.5

Time (ms)

Figure 6.8: Temperature of unburned gases and average pressure developed in the WDE channel.

The variation of flame speed during the combustion in a rectangular channel shows different
behavior as shown in Fig. 6.9, which implies that the combustion chamber geometry influence the
flame speed. The flame speed in a rectangular channel also shows a strong dependence on the
unburned mixture temperature with four (5) distinct regions. (1) in this region, the flame speed
remains almost constant with the standard laminar flame speed (Sl re f ) up to around 8 ms, (2)
exponential acceleration in flame speed following the increase in the unburned region temperature
by compression effect and last up to 32 ms, see Figs.6.9, 6.10 (3) the flame speed then increases at
about constant rate between 40-140 ms, (4) the flame speed decreases when the temperature of the
unburned gases decreases due to heat loses to the channel walls, (5) when the flame approaches the
channel end wall, the temperature of the remaining unburned mixture trapped between the flame
and the wall increases again by the heat transport due to conduction and mixing which increases
the flame speed again short before the flame annihilation at the channel end wall.
115

95

Turbulent Flame Speed

90

Turbulent Flame Speed (cm/s)

85
80
75
70
65
60
55
50
45
40

0

20

40

60

80

100

120

140

160

180

Time (ms)

Figure 6.9: Transient flame speed developed in a rectangular channel.

500

7

480

5

440
420

4
400
3

380
360

Pressure (bar)

Unburned gases temperature (K)

6
460

2

340
1

320

Unburned gases temperature
Average pressure

300
280

0
0

20

40

60

80

100

120

140

160

180

Time (ms)

Figure 6.10: Unburned gases average temperature and pressure for premixed flame propagating in
the rectangular channel.

116

6.1.5

Assessment of AFSD

As we mentioned in Section 3.2.2 that the concept of flame surface density is originally derived
for reacting flow that is characterized by high mixing intensity. The comparison of numerical
simulation results with the experimental data for the rectangular chamber verified that this model
successfully reproduces the main features of the confined premixed flame. The model is in good
agreement with the experimental observation during hemispherical and finger flame expansion as
shown in Fig. 6.12 a-c. The model, however, overpredicts the time at which the flame flattens
(Fig. 6.12 d). This might be due to a deficit in the prediction of flame extinction on the channel
sidewall which requires detailed information about chemical reactions and species transport that
we dismissed in the methodology conducted here.
The pressure time-history curve shown in Fig. 6.11 demonstrates that the model is sufficient
for describing the reaction rate and the associated combustion time which is coupled with average
pressure developed and other mixture properties.

117

1.1

Experiment
Numerical Simulation

1

Normalized average pressure

0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

Normalized time

Figure 6.11: Time-history of the average pressure developed in a rectangular chamber.

118

(a) 6.0 ms

Experiment
(b) 17.0 ms

Numerical

(c) 20.0 ms

(d) 28.0 ms

(e) 34.0 ms

(f) 40.0 ms

Figure 6.12: Comparison between flame predicted by algebraic flame surface density and experimental observation.

To further assess the transient algebraic flame surface density, the LES and Zimont model with
it’s default parameters values are used to model the confined premixed flame in the rectangular
channel. The flame predicted by Zimont model shows deficiency in two aspects; (1) the flame
propagation speed is over predicted and (2) unrealistic and diffused flame front. During the tulip
flame formation, the spatial gradient of the progress variable extended over the tulip flame tongues
which doesn’t agree with experimental observations in Fig. 6.12.
The combination of large eddy simulation with eddy viscosity modeled by Wall-Adapting Lo119

cal eddy-viscosity and modified algebraic flame surface density addresses thees issues with the
Zimont model as shown in Fig. 6.13.

(a) 7.2 ms

Modified AFSD

(f) 60.2 ms

(e) 40.2 ms

(d) 30.2 ms

(c) 20.2 ms

(b) 10.2 ms

Zimont model

Figure 6.13: Comparison between modified algebraic flame surface density and Zimont model

120

Chapter 7
CONCLUSIONS AND
RECOMMENDATIONS

7.1

Conclusion

This dissertation investigates the propagation of confined premixed flame through closed chamber
of isothermal walls and initially quiescent mixture. For two-dimensional analysis, the reaction rate
is modeled using detailed and reduced kinetic mechanisms. The mass diffusion is investigated
using three different diffusion models with different level of approximation; the multicomponent
diffusion model of Chapman-Enskog including Soret effect; the mixture-averaged; and constant
Lewis number. For three-dimensional simulation, the large eddy simulation coupled with the reaction progress variable equation is used to model the confined premixed flame in the WDE and
rectangular channel. The reaction rate is predicted using Boger model of algebraic flame surface
density modified with transient flame speed. The syngas flame dynamics in a rectangular channel
of aspect ratio 10 was investigated numerically under different hydrogen content and mixture stoichiometry. Experiment tests were conducted for both WDE and rectangular channel to validate the
numerical simulation results and to gain further understanding about the dynamics of the confined
premixed flame and resulting pressure growth.
Several conclusions may be drawn from this work.

121

(1) The numerical simulation using the San-Diego mechanism reproduced the main features of
experimentally observed flame evolution. The numerical results explored the flame front and
flame-induced flow interaction in all flame phases.
(2) The premixed flame propagating in the WDE channel exhibits a conversion from convex
(phases I, II) to tulip (phase III) and then from a tulip back to a concave (phase IV) and
finally into a more or less steadily propagating flame that eventually is extinguished at the
far wall (phase V). In these stages, a weak outer flame is observed and a reduction in heat
release is indicated by the diminishment of p(t).
(3) The pressure, its derivative and its second derivative provide information about the flame
stages. The high pressure sampling rate suggests its usefulness as a diagnostic of the events
occurring in the CV chamber.
(4) The rate of pressure rise during CV combustion becomes negative because of heat loss and
weak flame propagation (phase (V)).
(5) The major important deviation between experiment and simulation was the three dimensionality of the former contrasted with the two dimensionality of the latter. The consequences of
this difference was discussed in the context of Fig. 5.2.The flame speed using a 2-D simulation is slightly faster than the experiment due excluded "side losses".
(6) In spite of (5), the comparison in Fig. 5.2 shows that the overall sequence of events is temporally identical. Similar processes occur at identically proportionate times.
(7) The flame speed experiences dramatic deceleration during the last phase (V), which consumes approximately 75

122

(8) The flame generated vorticity is largest along the walls, approximately 5X larger than flamegenerated vorticity. Prior to tulip formation, vorticity is generated at the upstream walls.
After tulip destruction (second convex flame) vorticity is primarily generated at the downstream walls.
(9) The Chapman-Enskog multicomponent model M(I) and the mixture-average model M(I)
produce almost the same flame structure, peak temperature, average pressure. The maximum
deviation in flame distance between these two models was observed at about 3-5 ms when
the hydrodynamical phenomena associated with thermal expansion is dominated.
(10) The Soret effect slightly changes the mixture stoichiometry and the equivalence ratio decreased near the cold sidewalls by 3%. The results revealed that the effect of thermal diffusion increases as the difference between the fuel species and oxygen weight increases. The
distribution of species concentration in the burned region shows complicated behavior since
higher temperature gradient exists, more species get involved, and dissociation phenomena.
(11) The flame dynamics under unity Lewis number can be characterized into three regions:
(11-1) Before the lateral flames touch the sidewalls, the hydrodynamic phenomena driven by
flame-induced flow is dominant and the unity Lewis number of M(III) is sufficient but
producing slower propagation speed compared with M(I) and M(II).
(11-2) When the lower tongue of the tulip flame start to expand toward the upper tongue at
about 11.8 ms, a sudden acceleration in the flame M(III) is observed, the peak temperature approaches unrealistic values (from 2460 K to 2830 K), and the average pressure
showed more pronounced deviation from the values of M(I) and M(II). This accelerated flame ends by producing an artificial, second tulip flame of smaller size which
neither observed in M(I), M(II), our in the experiment work Najim et al. (2015).
123

(11-3) Once the second tulip flame of M(III) annihilated following similar scenario of its predecessor, it starts lagging behind its counterparts of M(I) and M(II) to end of channel.
(11-4) The syngas/air flame unable to produce wrinkled front when constant Lewis number
(Le = 0.57) is used. The multicomponent and mixture-averaged diffusion models generate similar wrinkling density on the flame front.
(12) The values of effective Lewis number for methane/air mixture is above unity (1.13) and it
decreases to about 1.07-1.05 when it get closer to the flame vicinity. This slow down the reactivity and stabilize the flame front because the flame develops a convex shape Dinkelacker
et al. (2011). Close to the upper tongue and the cusp of the tulip flame, the value of Lee f f
drop even below unity as indication of increasing the flame tendency to fold and wrinkle its
front. Later on the grown front of lower tulip flame tongue, the Lee f f also drop below unity
flatten the following concave flame immersed from flame lower tongue.
(13) The influence of mixture stoichiometry on syngas/air flame can be seen in the combustion
time, flame structure, and pressure developed. Unlike hydrocarbon fuels, higher propagation
speed take place when the mixture is rich at approximately φ = 2.0. The flame propagation
speed decelerates near the channel end wall when the average channel pressure is high.
(14) The syngas flame develops more wrinkles when the mixture lean at elevated pressure. When
the syngas/air mixture is rich (φ = 1.5), the high pressure smooths the flame front and the
flame tend to be a laminar-like flame at the end of the combustion and for different hydrogen
content (Fig. 5.35).
(15) The large eddy simulation and modified Boger model of algebraic flame surface density
used for three-dimensional confined premixed, stoichiometric methane/air flame reproduced,

124

with good agreement, the experimental observations of the main features of flame structure,
pressure time-history, and burning time.
(16) The increase in unburned gases temperature and pressure during burning works in favor of
flame speed which increases rapidly during finger flame expansion and nearly at a constant
rate during after tulip flame is developed.
(17) The Boger model overpredicts the time at which flame front flattens which emphasizes the
common deficit of the flame extinction in the turbulent premixed confined flame modeling.

7.2

Recommendations

The dissertation established a reference point from which future advancements in flame and burning acceleration in WDEs and PDE can be assessed. Since these engines must work at high frequencies in order to produce power with a reasonable efficiency, it is recommended that a more
realistic turbulence intensity be used for initial condition in order to account for the effect of flow
developed during the previous charging process under rotating frame of reference. This should
be used in parallel with more advanced optical diagnostics such as Particle Image Velocimetry
(PIV) which further provide quantitative information about the velocity field and flame dynamics.
The flame can be significantly accelerated through WDE and PDE channel by generating a certain level of turbulence, therefor, a more advanced algebraic flame surface density that accounts
for flame stretching, curvature, and flame-turbulence interaction is certainly recommended for the
three-dimensional large eddy simulation. One way to increase the turbulence intensity is through
flow circulation between two successive channels.

125

APPENDICES

126

Appendix A
Grid Resolution Test
As we mentioned in Section 3.3.1, the mesh size is estimated using freely propagating premixed
flame. The grid resolution in this work is examined by conducting mesh sensitivity study. Two
cases are used for mesh study and summarized in table. A.1. For WDE channel, the premixed
methane/air (DRM19) is used with refined cell size of 0.025 mm. In the rectangular channel, the
premixed syngas/air (φ = 1.5, 80% H2 ) flame which exhibits faster propagation speed and hence
it would be more sensitive to the mesh resolution than any other cases in this work. The current
mesh size of the syngas/air flame is (150 × 1500) and examined with finer mesh(300 × 3000).
Fuel

Channel

Current cell size

Refined Cell Size

Methane/air (DRM19)

WDE

0.05

0.025 mm

Syngas/air (φ = 1.5, 80% H2 )

Rectangular

(150 × 1500)

(300 × 3000)

Table A.1: CFD cases used to examine grid resolution.

The comparison between these cases reveals that current grid resolution used in the syngas
or methane flames are sufficient and generates similar flame structure and propagation speed, see
Fig. A.1. The flame-generated flow is quantitatively the same in both syngas and methane flames.
In rectangular channel, the saddle point developed in front of the syngas/air flame cusp at the
channel centerline and vortical motion developed behind the flame cusp in the burned gases region.
However, the results shows slightly different flame position at the channel centerline where the

127

flame with finer mesh advances by 1.1 mm at the same combustion time. The channel average
pressure for both cases is shown in Fig. A.2. It can be seen that the fine mesh case predict slightly
higher pressure than the current mesh case.
(a) Mesh (150x1500), t=2.7 (ms), flame position at channel Centerline=55.2 (mm)

(b) Mesh (300x3000), t=2.7 (ms), flame position at channel Centerline=56.3 (mm)

Figure A.1: Flame front structure and flame-generated flow predicted by (a) current mesh
size(150 × 1500) and (b) finer mesh(300 × 3000).

The methane/air flames front structure for the current and refined cell sizes are shown in
Fig. A.3. Figure. A.3 indicates that the current and refined grid resolutions and generate simi128

lar flame structure. The refined mesh generates, however, more HCO species within the flame
front. The flame front thickness is slightly reduced by the refined mesh.
1.6

Current Mesh (150x1500)
Fine Mesh (300x3000)

1.4

1.2

Average Pressure (bar)

1

0.8

0.6

0.4

0.2

0
0

0.5

1

1.5

2

2.5

3

3.5

Time (ms)

Figure A.2: Average pressure of the syngas/air premixed flames.

129

4

Combustion time=0.007576 s

Current cell size
0.05 mm

Refined cell size (4x)
0.025 mm

Figure A.3: Methane/air flame front structure predicted by 0.05 mm and 0.025 mm maximum cell
sizes. The Flames front are represented by C2 H6 contours.

4E-05
Current mesh
Refined mesh 4X

3.5E-05

3E-05

2.5E-05

2E-05

1.5E-05

1E-05

5E-06

0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Figure A.4: Mass fraction of HCO species plotted along a line of 0.8 mm passing through the
methane/air flames front.

130

Appendix B
Turbulent Flame Model

Turbulence Intensity
In this Section, the turbulence parameters are presented to assess the turbulence intensity developed during the three-dimensional, premixed flame propagation. In Fig. B.1, the maximum cell
Reynolds number is plotted versus burning time in the rectangular channel and showing proportional behavior with the local velocity.
450
400

Max Cell Re

Max. cell Reynolds number

350
300
250
200
150
100
50
0
-50

0

20

40

60

80

100

120

140

160

180

Time (ms)

Figure B.1: Maximum cell Reynolds number evaluated during flame propagating in the 3D rectangular channel.

131

The cell Re increases during the spherical flame expansion during which the burned gases
dramatically expands toward the cold, unburned region. Figure. B.1 reveals that the maximum
cell Re showing high fluctuation at the time when the flame front annihilated by the channel end
wall causing significant disturbance for the flame-generated flow. Since the flame at the end of the
WDE channel shows weak propagation, the cell Re progressively decrease during this time.
100

Max. cell Reynolds number

90

Max. cell Reynolds number

80
70
60
50
40
30
20
10
0

0

5

10

15

20

25

30

35

40

45

50

55

60

Time (ms)

Figure B.2: Maximum cell Reynolds number evaluated during flame propagating in WDE channel.

The flow effect on the flame front structure is generally quantified using DamkĂśhler number
(Da =

τc
τl ).

Figure B.3 shows large DamkĂśhler numbers evolution during burning which indicates

that the chemical time scale τc is much smaller than the flow time scale τl and represent the case
of infinitely fast chemistry. It can be seen that the DamkĂśhler number curve in Fig. B.3 exhibits a
reverse behavior to the maximum cell Reynolds number presented in Fig. B.2.

132

3.5E+06

Average Da number

DamkĂśhler number (Da)

3E+06

2.5E+06

2E+06

1.5E+06

1E+06

500000

0

0

5

10

15

20

25

30

35

40

45

50

55

60

Time (ms)

Figure B.3: Average DamkĂśhler number for WDE channel.

Calculation of unburned gases density
In confined chambers, the flame front represent a surface that separates the burned and unburned
regions. The thermochemical and transport properties of the burned gases are significantly different
from unburned gases. The unburned gases density is calculated as the weighted average of the
unburnt density in a computational element at which the reaction progress variable is less than
0.001. When the reaction progress variable is larger than 0.001 everywhere in the domain, then
the unburnt density is the minimum density in all computational elements. In constant volume
combustion, the average density is constant for the entire mixture because the total mass remains
unchanged during burning. The density of the unburned gases, however, increases, as the pressure
build up in the channel, see Figs. B.4, B.5.

133

5.5

Unburned gases density

5

Unburned gases density (kg/m3)

4.5
4
3.5
3
2.5
2
1.5
1
0.5
0

0

20

40

60

80

100

120

140

160

180

Time (ms)

Figure B.4: Unburned gases density developed during flame propagation in a rectangular channel.

5

Mixture average density
Unburned gases density

4.5
4

Density (kg/m3)

3.5
3
2.5
2
1.5
1
0.5

0

5

10

15

20

25

30

35

40

45

50

55

60

Time (ms)

Figure B.5: Unburned gases density developed during flame propagation in the WDE channel.
Also showing the mixture average density.

134

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