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Experimental investigation of the propagation and extinction of edge-flames

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Experimental investigation of the propagation and extinction of edge-flames

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EXPERIMENTAL INVESTIGATION OF THE PROPAGATION AND

EXTINCTION OF EDGE-FLAMES

by

David Baldwin Clayton

A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements of the Degree
DOCTOR OF PHILOSOPHY
(MECHANICAL ENGINEERING)

August 2007

Copyright 2007 David Baldwin Clayton

ii

Dedication

My family’s faith in me has been an everlasting source of encouragement and
support for as long as I can remember. They are always ready to lift my spirits
during difficult times, never letting me give up on my dreams and for that I am truly
grateful. Everything that I have learned and everything I have become would not
have been possible without them, and for that I dedicate this dissertation to my
family.

iii

Acknowledgements

First, I must offer my thanks and appreciation to Dr. Paul D. Ronney for
sticking with me as my advisor during my many years of study at USC. Through
thick and thin he never gave up on me and continually inspired me to become a
better student and scientist.
The members of my dissertation and guidance committee, Dr. Fokion
Egolofopoulos, Dr. Hai Wang, Dr. C. Ted Lee, and Dr. Denis Phares, have freely
given their time and expertise. I thank them for their contribution and support.
I must also thank the many friends, colleagues, and teachers I’ve met during
my educational path who have supported my development. In particular, I need to
sincerely thank Dr. Min Suk Cha for inviting me to conduct this research in South
Korea. The year and a half working in Daejeon was truly a once-in-a-lifetime
experience that I will cherish for a lifetime.

iv

Table of Contents

Dedication ii

Acknowledgements iii

List of Tables vi

List of Figures vii

Abbreviations xiii

Abstract xiv

Chapter 1: Introduction 1
1.1 Motivation 1
1.2 Edge-Flame Theory and Background 3
1.2.1 Nonpremixed Edge-Flames 3
1.2.2 Premixed Edge-Flames 5
1.2.3 Low Lewis Number Edge-Flames and Instabilities 6
1.3 Research Objectives 13

Chapter 2: Methodology 14
2.1 Apparatus and Procedures 14
2.2 Measurements and Diagnostics 20
2.3 Selection of Test Conditions 23

Chapter 3: Twin Hydrocarbon Edge-Flames 28
3.1 Effect of Mixture Strength 28
3.2 Effect of Lewis Number 36

Chapter 4: Single Hydrocarbon Edge-Flames 42
4.1 Effect of Mixture Strength 42
4.2 Effect of Lewis Number 47

Chapter 5: Low Lewis Number Edge-Flames 53
5.1 Diffusive-Thermal Instability at Low Lewis Number 53
5.2 Twin Premixed H
2
-Air Edge-Flames 57
5.2.1 Stability and Extinction Limits 57
5.2.2 Effect of Mixture Strength 61

v

5.3 Single Premixed H
2
-Air Edge-Flames 63
5.3.1 Stability and Extinction Limits 63
5.3.2 Effect of Mixture Strength 67

5.4 Nonpremixed H
2
-Air Edge-Flames 68
5.4.1 Stability and Extinction Limits 68
5.4.2 Effect of Mixture Strength 72

Chapter 6: Conclusions 75
6.1 Premixed Hydrocarbon Edge-Flames 75
6.2 Low Lewis Number Edge-Flames 76
6.3 Future Research Possibilities 77

Bibliography 79

vi

List of Tables

Table 1: Experimental conditions and corresponding flame properties 28
for twin premixed flame properties.

Table 2: Experimental conditions and corresponding flame properties 42
for single premixed edge-flame.

vii

List of Figures

Figure 1: Flame propagating over a fuel bed. 2

Figure 2: Candle flame under microgravity conditions. 2

Figure 3: Lean methane-air flame propagating upwards in a vertical tube. 2

Figure 4: Schematic diagrams of conventional “thin” flamelet (moderate 9
and high Le) [left], proposed broken flamelet (low Le) [center],
and distributed combustion (any Le, at very high turbulence
levels) [right].

Figure 5: Shadowgraph image of moderately wrinkled flames, 8.26% H
2
11
in air, strain rate 60/s, field of view 1.3 cm high (Kaiser et al.,
2000).

Figure 6: Moving tubes, 6.96% H
2
in air, strain rate 56 s
-1
, field of view 11
1.3 cm high (Kaiser et al., 2000).

Figure 7: Stationary single tube, 6.64% H
2
in air, strain rate 60 s
-1
, field 11
of view 1.3 cm high (Kaiser et al., 2000).

Figure 8: Side view of moving tubes, 6.96% H
2
in air, strain rate 60 s
-1
11
(Kaiser et al., 2000).

Figure 9: Schematic diagram of counterflow slot-jet apparatus (not 15
shown: gas piping and water cooling lines).

Figure 10: Close-up view of counterflow slot-jet burner showing central 17
jet, sheath flow jets, and ceramic burner spacers with electrically
heated wires.

Figure 11: Effect of sheath flow velocity on edge-flame propagation velocity 18
(U
edge
) for nonpremixed conditions (Cha and Ronney, 2006).

Figure 12: Basic experimental flow system diagram 19
Figure 13: U
edge
as a function of burner horizontal lengthwise position for 22
single premixed 3.2% C
3
H
8
in air, strain rate = 28.6 s
-1
, d = 7 mm.

viii
Figure 14: Estimated operating conditions for slot-jet burner at 8.3% 26
CH
4
– 91.7% air baseline mixture. Shaded region denotes
desired range of operating parameters.

Figure 15: Twin CH
4
-air flames at moderate strain ( σ = 107 s
-1
). 29
Figure 16: Twin CH
4
-air flames at high strain ( σ = 213 s
-1
). 29
Figure 17: Figure 17: U
edge
vs. σ for twin, methane-air edge flame indicating 30
representative experimental error.

Figure 18: Effect of dimensional strain rate ( σ) on dimensional edge speed 32
(U
edge
) for various twin CH
4
-air edge-flame mixtures. Number
associated with each curve refers to the mixture fuel percent.
Dashed lines and unfilled markers correspond to short-length
edge-flames, positive speed refers to leading head and negative
speed refers to trailing tail for a given strain rate. (a) Raw data.
(b) Scaled U
edge
vs. nondimensional strain rate ε.

Figure 19: Effect of nondimensional strain rate ( ε) on the nondimensional 33
edge-flame propagation speed (U) for different values of the
nondimensional heat loss (κ) as computed by Daou et al. (2003).

Figure 20: Map of propagation modes and extinction limits for twin 35
edge-flames with heat loss factor κ and nondimensional
strain rate ε. (a) Experimental results for CH
4
-air mixtures.
(b) Numerical predictions from Daou et al. (2003).

Figure 21: Effect of nondimensional strain rate on scaled U
edge
for various 36
twin CH
4
-O
2
-CO
2
mixtures (Le ≈ 0.8) with d = 5 mm. Also
shown for comparison is a CH
4
/air (Le ≈ 1) case.

Figure 22: Schematic of curved flame for Lewis number < 1 showing the 37
relative imbalance of reduced heat diffusion away from the flame
front and increased fuel diffusion towards the flame front leading
to increased reaction rate and local burning velocity.

Figure 23: Grayscale images of direct emission from twin premixed 38
edge-flames, exposure time = 2 ms, global strain rate ( σ)
shown in each image, premixed fuel/O
2
/diluent enters from
both top and bottom, all flames propagate from left to right,
height of each image roughly corresponds to jet spacing d.

ix

Figure 24: Computed contours of reaction rate and temperature from 39
Daou et al. (2003) with β = 8, α = 0.85, and Le = 1 for twin
premixed edge-flames at three different dimensionless strain
rates. Contours are symmetric with respect to y = 0. Advancing
edge-flames (i.e. positive scaled edge speed U) move from right
to left.

Figure 25: Effect of nondimensional strain rate on scaled U
edge
for various 40
twin C
3
H
8
-air mixtures (Le ≈ 1.8) with d = 7 mm. Also shown
for comparison is a CH
4
/air (Le ≈ 1) case.

Figure 26: Average nondimensional strain rate ε at high-ε extinction for 41
twin premixed edge-flames. Results shown for CH
4
-air (Le ≈ 1),
C
3
H
8
-air (Le ≈ 1.8), and CH
4
-O
2
-CO
2
(Le ≈ 0.8) with error bars
corresponding to one standard deviation.

Figure 27: Single CH
4
-air flame at low strain ( σ = 67 s
-1
). 43

Figure 28: Single CH
4
-air flame at high strain breaking limit ( σ = 88 s
-1
). 43

Figure 29: Effect of dimensional strain rate ( σ) on dimensional edge speed 45
(U
edge
) for various single CH
4
-air edge-flame mixtures at d = 7.5
mm. Number associated with each curve refers to the mixture
fuel percent, but the curves for 10% and 11% are mixtures with
stoichiometric CH
4
-O
2
but reduced N
2
from that of air. Dashed
lines and unfilled markers correspond to short-length edge-flames,
positive speed refers to leading head and negative speed refers to
trailing tail for a given strain rate. (a) Raw data. (b) Scaled U
edge

vs. nondimensional strain rate ε.

Figure 30: Map of propagation modes and extinction limits for single 46
CH
4
-air edge-flames with heat loss factor κ and
nondimensional strain rate ε.

Figure 31: Effect of nondimensional strain rate on scaled U
edge
for various 47
single CH
4
-O
2
-CO
2
mixtures (Le ≈ 0.8) with d = 5 mm. Also
shown for comparison is a CH
4
-air (Le ≈ 1) case. Dashed lines
and open markers indicate short-length edge-flames.

Figure 32: Effect of nondimensional strain rate on scaled U
edge
for various 48
single C
3
H
8
-air mixtures (Le ≈ 1.8) with d = 7 mm. Also shown
for comparison is a CH
4
-air (Le ≈ 1) case. Dashed lines and open
markers indicate short-length edge-flames.
x

Figure 33: Temperature contours (top two plots) and reaction rate contours 49
(bottom two plots) for advancing single premixed edge-flame
with 1/Da = 0.329 as calculated by Daou et al. (2003).

Figure 34: Grayscale images of direct emission from single premixed 50
edge-flames, exposure time = 2 mm, global strain rate ( σ) shown
in each image, premixed fuel/air enters from bottom and counterflow
air enters from top, all flames propagate from left to right, height of
each image roughly corresponds to jet spacing.

Figure 35: Average nondimensional strain rate ε at high-ε limit (breaking 52
flame limit) for single premixed edge-flames. Results shown for
CH
4
-air (Le ≈ 1), C
3
H
8
-air (Le ≈ 1.8), and CH
4
-O
2
-CO
2
(Le ≈ 0.8)
with error bars corresponding to one standard deviation.

Figure 36: Stability and extinction limits for twin H
2
-air flames in a slot-jet 58
counterflow configuration, jet spacing = 12.5 mm, Z
st
= 0.8.

Figure 37: Shadowgraph images of twin premixed H
2
-air flames. Reactive 60
mixture enters from both upper and lower jets, jet spacing = 12.5
mm. (a) Nearly planar twin flames, 7.5% H
2
, strain rate = 128 s
-1
.

Figure 37(b): Moderately wrinkled flames, 7.5% H
2
, strain rate 24 s
-1
. 60

Figure 37(c): Uniformly wrinkled twin flames, 6.5% H
2
, strain rate = 24 s
-1
. 60

Figure 37(d): Single stationary tube, 5.5% H
2
, strain rate = 104 s
-1
. 60

Figure 37(e): Twin stationary tubes, 5.5% H
2
, strain rate = 72 s
-1
. 60

Figure 37(f): Multiple tubes moving outward from center, 5.5% H
2
, 60
strain rate = 56 s
-1
.

Figure 37(g): Fully connected string of tubes, 5.5% H
2
, strain rate 24 s
-1
. 60

Figure 38: Effect of dimensional strain rate ( σ) on dimensional U
edge
for 62
d = 12.5 mm, Z
st
= 0.8, and various fuel concentrations for twin
premixed H
2
-air flames.

Figure 39: Stability and extinction limits for single H
2
-air flames in a slot-jet 64
counterflow configuration, jet spacing = 12.5 mm, Z
st
= 0.8.

xi
Figure 40: Shadowgraph images of single premixed H
2
-air flames. Reactive 65
mixture enters from lower jet, inert enters from upper jets,
jet spacing = 12.5 mm. (a) Non-uniformly wrinkled flame,
10.5% H
2
, strain rate = 120 s
-1
.

Figure 40(b): Uniformly wrinkled flame where wrinkles randomly move 65
left and right making clear visualization difficult, 10.5% H
2
,
strain rate = 72 s
-1
.

Figure 40(c): Uniformly wrinkled and stationary, 9.5% H
2
, strain rate = 24 s
-1
. 66

Figure 40(d): Uniformly wrinkled and stationary, 9.5% H
2
, strain rate = 16 s
-1
. 66

Figure 40(e): Single tube, 8.5% H
2
, strain rate = 56 s
-1
. 66

Figure 40(f): Fully connected string of tubes, 9% H
2
, strain rate = 56 s
-1
. 66

Figure 41: Effect of dimensional strain rate ( σ) on dimensional U
edge
for 68
d = 12.5 mm, Z
st
= 0.8, and various fuel concentrations for single
premixed H
2
-air flames.

Figure 42: Stability and extinction limits for nonpremixed H
2
-air flames in 70
a slot-jet counterflow configuration, jet spacing = 12.5 mm, Z
st
= 0.8.

Figure 43: Shadowgraph images of nonpremixed H
2
-O
2
-N
2
flames. H
2
/N
2
71
enters from lower jet, O
2
/N
2
enters from upper jets, jet spacing =
12.5 mm. (a) Fully connected string of tubes, 6.06% H
2
,
strain rate = 96 s
-1
.

Figure 43(b): Connected tubes transitioning to planar flame, 6.06% H
2
, 71
strain rate = 64 s
-1
.

Figure 43(c): Planar flame, 6.06% H
2
, strain rate = 48 s
-1
. 71

Figure 43(d): Resulting flame structure from broken planar flame, 6.67% H
2
, 71
strain rate = 24 s
-1
.

Figure 43(e): Single stationary tube at center of burner, 5.88% H
2,
71
strain rate = 112 s
-1
.

Figure 43(f): Twin stationary tubes on verge of splitting into multiple tubes, 71
5.88% H
2
, strain rate = 104 s
-1
.

xii
Figure 43(g): Multiple tubes generated from center of burner and 71
propagating outwards, 5.88% H
2
, strain rate = 80 s
-1
.

Figure 44: Effect of dimensional strain rate ( σ) on dimensional U
edge
for 73
d = 12.5 mm, Z
st
= 0.8, and various fuel concentrations for
nonpremixed H
2
-air flames.

xiii

Abbreviations

D Mass diffusivity

Da Damköhler number

Ka Karlovitz number

Le Lewis number

Pe Peclet number

Re
jet
Slot-jet Reynolds number

S
L
Laminar burning velocity

T
ad
Adiabatic flame temperature

U
edge
Flame edge velocity

U
jet
Slot-jet flow velocity

U
sheath
Sheath flow velocity

Z
st
Stoichiometric mixture fraction

α Thermal diffusivity

β Zeldovich number

ε Non-dimensional strain rate
κ Non-dimensional heat loss parameter
φ Fuel-air equivalence ratio
ρ Density
σ Global strain rate
σ
ext
Critical global extinction strain
xiv

Abstract

Propagation rates (U
edge
) of various hydrocarbon premixed edge-flames are
directly measured as a function of global strain rate ( σ), mixture strength, and Lewis
number (Le). Using a counterflow slot-jet burner with electrical heaters at each end,
both advancing (positive U
edge
) and retreating (negative U
edge
) edge-flames can be
studied as they propagate across the long dimension of the burner. Results are
presented for twin and single premixed edge-flames in terms of the effects of a
nondimensional strain rate (ε) and nondimensional heat loss (κ) on a scaled
propagation rate. Twin edge-flames exhibited two extinction limits, corresponding
to a high- σ strain induced limit and a low- σ heat loss induced limit. A similar low- σ
limit is identified for single edge-flames but at high- σ the flames break apart due to
an apparent strain induced instability rather than extinction. Propagation rates
clearly show a strong dependence on Le and close-up images of the premixed edge-
flames show that high (low) Le lead to weaker (stronger) edge-flame propagation.
Overall, experimental findings agree closely with theoretical predictions.
Additionally, the effects of diffusive-thermal instability on mixtures with very low
Le in the counterflow strained configuration are examined. Stability maps and
propagation rates for twin premixed, single premixed, and nonpremixed H
2
-air
flames indicate the importance of heat losses to the burner at low strain and the
dependence of flame propagation on global strain rate in relation to the burner
configuration. As predicted, low Le flames in the counterflow configuration form
xv
individual and connected tubes as a means of existing beyond typical extinction
strain rates. The tubes transition into wrinkled flames and then into planar flame
structures as strain decreases. Propagation rates for the lean H
2
flames generally
increase with increasing strain and are not affected by the instability mode and
resulting the flame shape.

1
Chapter 1

Introduction

1.1 Motivation

A great deal of emphasis is currently placed on designing accurate models of
turbulent flow fields and their impact on reacting flows and flame front behavior. In
a turbulent system, the flame may develop holes in regions where the strain caused
by velocity fluctuations leads to flame curvature great enough to cause localized
extinction. These holes can act in a variety of ways. If the local strain is large
enough or the mixture conditions are unsuitable, the edge creating the hole will move
away from the unburned reactants within the hole thereby causing the hole to grow.
Such a flame edge is known as an extinction front. If the gas mixture within the hole
contains the proper balance of unburned reactants and the local strain decreases
sufficiently, the hole may close, or heal itself via an ignition front or advancing edge.
For the past decade, the transition from a burning to a non-burning state, such
as a hole or tear created in a turbulent field, has been studied via the use of a
simplified model known as an edge-flame. Like one-dimensional flames such as the
plane deflagration and the one-dimensional diffusion flame, edge-flames are
idealized two-dimensional representations of more complex combustion phenomena
that provide insight necessary to better understand flames with edges (Buckmaster
2002). In addition to holes in turbulent flames, many situations arise in combustion
where edge-flames are important. A flame spreading over a fuel bed (Fig. 1), a
candle flame in microgravity (Fig. 2), and a lean methane/air flame in a tube (Fig. 3)

are all cases which may exhibit a flame with an edge for which the propagation rates
and/or extinction limits are important and directly related to the edge characteristics
(Buckmaster, 2002).

Figure 1: Flame propagating over a fuel bed.

Figure 2: Candle flame under microgravity conditions.

Figure 3: Lean methane-air flame propagating upwards in a vertical tube.
2

1.2 Edge-Flame Theory and Background

1.2.1 Nonpremixed Edge-Flames

In recent work by Cha and Ronney (2006), extensive experiments mapped
out nonpremixed edge-flame propagation rates including both ignition (advancing)
and extinction (retreating) fronts while illustrating the effect of strain rate (by
varying jet exit velocity and burner separation distance), mixture strength (by
varying the level of dilution with an inert gas), impact of heat loss (by varying jet
spacing), and Lewis number (by varying fuel and diluent type). Through using a
counterflow slot-jet burner with resistance heated anchors at each end they were able
to successfully measure retreating (extinction) fronts which showed close agreement
to numerical calculations by Daou et al. (2002). The way each of these properties
affects the propagation rates of edge-flames provide a comprehensive understanding
of their dynamics and extinction properties (Cha and Ronney, 2006).
According to current theory (Vedarajan and Buckmaster, 1997; Vedarajan et
al., 1998; Daou and Liñán, 1998) the edge velocity is negative (retreating) in high-
strain regions and positive (advancing) in low-strain regions. The global strain rate
for a counterflow slot-jet is given by

⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
ρ
ρ
+ = σ
upper
lower
upper
lower
upper
U
U
d
U
1 (1)
where σ is the global strain rate, U
upper
and U
lower
are the upper and lower jet exit
velocities, ρ
upper
and ρ
lower
are the corresponding densities of the streams, and d is the
3

nozzle separation. For the experiments to discussed in following chapters, the two
streams will have nearly equal densities, and thus the simplified relation

d
U U
lower upper
+
= σ (2)
is appropriate. The local strain will vary in the stream-wise direction, i.e. the
direction of flow coming from the jets, due to thermal expansion effects. For
comparison of uniformly strained flames and edge-flames, the global strain is
typically considered to be the more appropriate parameter, since correlations of
strain effects for turbulent flames (Bradley, 1992) employ global strain rate estimates
based on the cold-gas conditions. Ahead of the flame front in the cold-gas, constant-
density region, Eq. (2) is valid. Most early experiments on uniformly strained
flames, e.g., Ishizuka and Tsuji (1980), reported only global strain rates, and most
theoretical works on edge-flames (Buckmaster, 1997; Vedarajan and Buckmaster,
1998; Vedarajan et al., 1998; Daou and Liñán, 1999) have used the constant-density
assumption, thereby ignoring the issue of thermal expansion. At present, it is not
known whether a unique "local" strain rate can be defined for a two-dimensional
structure such as an edge-flame, considering how difficult it has been to determine a
proper definition of strain rate at the flame front for a conventional one-dimensional
counterflow flame (Liu and Ronney, 1999). When creating nonpremixed flames in a
counterflow experiment, the process of which will be discussed further in the next
chapter, the most flexible reactant configuration for the two jets is fuel-diluent vs.
oxygen-diluent, which results in a flame at the location where the two reactants meet
in stoichiometric proportion, or where all oxygen is consumed via the oxidation
4

5
process, and can be varied based on the initial fuel and oxygen fractions within their
respective streams.

1.2.2 Premixed Edge-Flames

While premixed edge-flame experiments have been conducted in the past
(Liu and Ronney, 1999), further study is necessary to characterize their propagation
rates and extinction limits. A similar approach to the work by Cha and Ronney
(2006) was conducted to fully characterize premixed edge-flame propagation by
studying the effect of strain rate (σ), mixture strength, and Lewis number (Le) using
the same counterflow slot-jet burner.
For premixed flames, two counterflow configurations are possible: premixed
combustible gas vs. inert gas where a single flame is produced, and premixed gas vs.
premixed gas where twin flames are produced on either side of the stagnation plane.
The former may be more relevant to turbulent flames since one side of the flame
front has fresh reactants whereas the other side has burned products, however, the
twin-flame configuration is considered here also because it is frequently employed in
studies of strained laminar flames and may be relevant to highly wrinkled flames at
high turbulence levels where back-to-back flames may exist (Liu and Ronney, 1999).
Theory suggests that single premixed edge-flame studies are relevant to laminar
flame quenching, e.g., of rising flames in tubes subject to buoyancy-induced flow
(Vedarajan and Buckmaster, 1997).
For nonpremixed and premixed flames, Daou et al. (2002, 2003, 2004)
expressed the effects of strain and heat losses in terms of a dimensionless flame

thickness, ε, and a dimensionless heat loss parameter, κ. These nondimensional
parameters are expressed for the two flow configurations (i.e., nonpremixed and
premixed) as
[]
[]
[],
,
2
,
2
2
2
1
2
2
1
2
premixed and d nonpremixe
S
and
premixed
S
d nonpremixe
S
o
L
L
L
κ
α
β κ
σα
ε
σα
β ε
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
≡
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
≡
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
≡
(3)

where ε can be thought of as the square root of as a scaled Karlovitz number, Ka, i.e.
the ratio of strain rate to chemical reaction rate, and κ as the inverse square of a
Peclet number, i.e., ratio of bulk heat transfer to conductive heat transfer, based on S
L
.
In Eq. (3), β is the non-dimensional activation energy (Zeldovich number), α is the
gas thermal diffusivity, S
L
is the laminar burning velocity of a stoichiometric mixture
of the fuel and oxidizer, and κ
o
is a linear volumetric heat loss coefficient with units
of inverse seconds (Cha and Ronney, 2006). These non-dimensional parameters for
strain rate and heat loss provide a means of comparing the experimental results with
the computational results of Daou et al. (2002, 2003, 2004).

1.2.3 Low Lewis Number Edge-Flames and Instabilities

Lean H
2
-air combustion is unique and entirely different than hydrocarbon-air
combustion because of its lower minimum flame temperatures supporting
combustion (thus lower thermal expansion ratios), lower Le and lower radiative
6

7
emission. Hydrogen is an environmentally attractive fuel, but use of lean H
2
-air
combustion is limited by the lack of knowledge of the complex interactions between
flame instabilities, heat losses, hydrodynamic strain and flame front curvature. By
employing properly designed experiments, it is possible to develop a more
comprehensive understanding of the propagation rates of lean H
2
-air edge-flames,
and thus low-Le turbulent flows.
To assess the effects of hydrodynamic strain with minimized thermal
expansion effects, the propagation rates, extinction conditions and stability properties
of lean H
2
-air edge-flames were studied in the counterflow slot-jet burner. These
experiments included limited characterization of non-planar flame structures
previously identified and characterized (Kaiser et al., 2000), that occur only in low-
Le mixtures due to diffusive-thermal instabilities. For low-Le premixed and
nonpremixed flames, the instability created by the low thermal diffusivity can affect
the wrinkling characteristics and lead to cellular flame structures unseen in other
configurations. Kaiser et al. (2000) reported the effects of strain on the diffusive-
thermal instabilities by examining the stability and extinction limits for lean H
2

flames but the propagation rates were not investigated.
Although Le effects play an important role in the behavior of H
2
-air flames,
the manner in which virtually all prior H
2
-air flame studies have been conducted do
not allow for a proper examination of such effects. By varying the fuel-to-air ratio in
premixed flame studies, the equivalence ratio (φ) changes along with the adiabatic

flame temperature (T
ad
), thus changing the laminar burning velocity (S
L
) and reaction
rates of the mixture:
ratio O Fuel tric Stoichiome
ratio mole O Fuel
2
2
≡ φ (4)
Since the Lewis numbers of H
2
and O
2
in air are about 0.3 and 1.0,
respectively, when the stoichiometrically limiting reactant changes from H
2
to O
2
, Le
increases from 0.3 to 1.0. Under such conditions diffusive-thermal instabilities
(DTI), which will be shown to exist only when Le is significantly less than unity,
will cease to occur. This is a critical issue in the transition from H
2
-limited reaction
to O
2
-limited reaction, and thus the transition from unstable to stable flames, occurs
not at φ = 1, as expected but at a much lower φ (Joulin and Mitani, 1981; Joulin,
1987; Ronney et al., 1994). Consequently, results of experiments using only H
2
-air
mixtures can be very misleading because effects due to changing T
ad
cannot be
separated from effects due to changing Lewis number.
The laminar flamelet model does not apply for mixtures with low Le because
even with a uniform mixture in a uniform strain field the inherent diffusive-thermal
instability that occurs in low Lewis number mixtures will result in a non-uniform
flame front, perhaps like that shown in Fig. 4 (center). Moreover, the instability is
8

Figure 4: Schematic diagrams of conventional “thin” flamelet (moderate and
high Le) [left], proposed broken flamelet (low Le) [center], and distributed
combustion (any Le, at very high turbulence levels) [right].

strongly affected by strain (Sivashinsky et al., 1982, Buckmaster and Short, 1999;
Daou and Liñán, 1999). This issue is relevant to turbulent combustion of hydrogen
since Lewis number is known to affect the wrinkling characteristics and burning
rates of turbulent flames (Abdel-Gayed et al., 1984; Wu et al., 1990; Bradley, 1992),
and moreover the strain and front curvature induced by turbulence will affect these
wrinkling characteristics.
Computations by a number of authors, starting with Buckmaster and Short
(1999) and Daou and Liñán (1999) predict a remarkable set of behaviors for strained
flames in low-Le mixtures. For low strain, moderately wrinkled flames are predicted.
For sufficiently high strain, the flame structure becomes discontinuous, resulting in
“flame tubes” elongated in the direction of extensional strain, which enables the
flame to survive in the presence of strain that would cause it to extinguish were it
forced to remain planar or moderately wrinkled. In essence, the weakening of the
flame by strain is taken to an extreme condition for which it cannot survive without
9

10
the intensification caused by curvature. This can only occur for low-Le mixtures
because only at low Le is the curved flame more robust than a flat flame. An infinite
chain of traveling tubes is predicted for moderately high strain whereas two then one
isolated stationary tube(s) are predicted at progressively higher strain. Yet higher
strain causes complete flame extinguishment. This behavior is somewhat analogous
to spherically-symmetric “flame balls” observed in microgravity experiments
(Ronney et al., 1994; Ronney et al., 1998) where in that case radiative transfer rather
than extensional strain is the prevailing loss mechanism. In both cases the
enhancement of flame temperature due to low Le causes the curved flame to survive
where a plane flame could not (Kaiser et al., 2000).
Experimental evidence of such structures was noticed by Kaiser et al. (2000)
using a counterflow slot-jet apparatus. Figures 8 through 11 show the sequence of
behavior from moderately wrinkled flames (Fig. 5), to moving tubes (Fig. 6), to
isolated flame tubes (Fig. 7), to extinction as predicted by Buckmaster and Short
(1999) and Daou and Liñán (1999). The side view shown in Fig. 8 confirms that the
structures are indeed tube-like. In interpreting these images, note that a
shadowgraph system is sensitive to the second spatial derivative of temperature.
Since the effect of heat release in a steady one-dimensional flame is a change in the
second spatial derivative of temperature (Williams, 1985), the shadowgraph
technique indirectly visualizes regions of high heat release rate.

Figure 5: Shadowgraph image of
moderately wrinkled flames, 8.26% H
2

in air, strain rate 60 s
-1
, field of view
1.3 cm high (Kaiser et al., 2000).
Figure 6: Moving tubes, 6.96% H
2
in
air, strain rate 56 s
-1
, field of view 1.3
cm high (Kaiser et al., 2000).
Figure 7: Stationary single tube, 6.64%
H
2
in air, strain rate 60 s
-1
, field of view
1.3 cm high (Kaiser et al., 2000).
Figure 8: Side view of moving tubes,
6.96% H
2
in air, strain rate 60 s
-1

(Kaiser et al., 2000).

The unusual flame structures seen in Figs. 5 through 8 are unlike a laminar-
like flame that is wrinkled by turbulence (the laminar flamelet, Fig. 4, left). The
predicted and observed structures can never occur in hydrocarbon-air mixtures,
regardless of the turbulence level, because Le is too high.
For low-Le mixtures, the diffusive-thermal instabilities can actually lead to
flame front temperatures higher than the adiabatic value for a homogeneous mixture
(Ronney et al. 1994). Of course, this also means that in other regions flame
temperature must be below adiabatic (Fig. 4, center). Turbulent lean H
2
-air flames
are likely to behave similarly (e.g., Fig. 4, center). This means that emission
performance of such flames cannot be assessed based on one-dimensional
calculations, as some authors have attempted for lean H
2
-air (Marinov et al., 1998).
In this context it is critical to examine the effect of equivalence ratio (φ), independent
of the fuel concentration. This is because theory (Joulin, 1987) shows that, at least
11

12
for spherical flame balls, the transition from lean-burning to rich burning at the
chemical reaction occurs at φ = Le
H2
/Le
O2
≈ 0.3, not at φ = 1.
Clearly the existence of these unusual flame structures in strained lean H
2
-air
mixtures has an impact on turbulent combustion in H
2
systems. Again, it should be
emphasized that laminar flamelet models (which assume structures like that shown in
Fig. 4, left) cannot apply to such flames. The goal here is to identify and
understanding these types of flame structures (e.g. flat flames, cellular flames,
stationary tubes, moving tubes, etc.) and measure their propagation rates for both
premixed and nonpremixed low-Le conditions. It is expected that many types of
edge flames, continuous and broken, advancing, retreating, nonpremixed, single
premixed, and twin premixed will exist for these flames and the edge-flame
experiments will be used to predict which type are most prevalent for a given set of
mixture and turbulence properties while compiling their propagation rates. As is the
case with nonpremixed edge-flames and premixed edge-flames, the propagation rates
of low-Le H
2
flames has never been experimentally studied and is therefore
necessary to aid in creating accurate turbulent combustion models. To assess the
effects of hydrodynamic strain (always present in turbulent engine-like flows) with
minimized thermal expansion effects, the propagation rates, extinction conditions
and stability properties of edge-flames will be studied in a counterflow slot-jet
burner.

13
1.3 Research Objectives

The goal of this dissertation is to study the effects of strain rate (by varying
U
jet
), mixture strength, heat loss (by varying jet spacing or stoichiometric mixture
fraction), Lewis number (by varying fuel and diluent type), and flame location
relative to the stagnation surface (by varying stoichiometric mixture fraction) on the
propagation rates of premixed hydrocarbon edge-flames and nonpremixed H
2
-air
edge flames in a counterflow slot-jet configuration and thereby provide a detailed
map of their dynamics and extinction properties. At present, there are no libraries
containing propagation rates of premixed edge-flames, especially detailed
information regarding propagation rates for low-Le flames where diffusive-thermal
instabilities are likely to occur under counterflow strain conditions.

14
Chapter 2

Methodology

2.1 Apparatus and Procedures

Numerous flow configurations have been used in the past in the study of
edge-flames. For example, a co-annular counterflow burner was used by Carnell and
Renfro (2005) to create a strain rate gradient to stabilize an edge-flame and Kioni et.
al. (1993) utilized a diverging tube wall burner to study stabilized triple flames. One
of the most common is the counterflow round-jet, i.e. axisymmetric-jet, apparatus.
However, round-jets are unsuitable for the proposed experiments due to the fact that
extensional strain occurs in both coordinate directions parallel to the plane of the
flame. A counterflow slot-jet, or rectangular-jet, overcomes this problem by only
creating extensional strain in the direction orthogonal to the slots themselves with
only a very small extensional strain along the length of the slots (the long dimension)
which means there is a very small strain in the direction of edge propagation (Kaiser
et al., 2000). This small extensional strain along the direction of edge-flame
propagation will be accounted for during data analysis. See Fig. 9 below for a
simplified front-view schematic of the counterflow slot-jet apparatus used for all
three experiments.

Figure 9: Schematic diagram of counterflow slot-jet apparatus (not shown: gas
piping and water cooling lines).

Another preferential reason for the slot-jet configuration is that computations
(Ashurst et al., 1987) have shown that highly strained regions of turbulent flows
exhibit a most probable ratio of strain along the three principal axes in the ratio
0.75:0.25:-1, where positive values denote extensional strain. Thus, highly strained
regions, where flame stretch effects are most important, do not typically exhibit
nearly equal rates of extensional strain along two of the principal axes. The
counterflow slot-jet configuration provides strain rates in the ratio 1:0:-1 whereas
round jets provide 0.5:0.5:-1. Thus, the slot-jet configuration provides straining
characteristics that are more representative of the conditions of flames in strongly
turbulent flows than round, or axisymmetric, jets can provide. Also, because the
convection velocity in the long dimension of the slot is small, the propagation rate
viewed in the laboratory reference frame is nearly identical to the propagation speed
relative to the unburned gas ahead of the edge-flame simplifying data interpretation
(Cha and Ronney, 2006).
15

16
Based on the discussion in the previous paragraphs, the counterflow slot-jet
apparatus is deemed to be the most appropriate for this study, in which the objective
is to map the propagation rates of nonpremixed and premixed edge-flames in a
controlled, systematic way. Moreover, the counterflow slot-jet apparatus essentially
duplicates the configuration employed in many of the aforementioned computational
studies (Vedarajan et al., 1998; Daou et al., 1999; Daou et al., 2002; Daou et al.,
2004). Three different flow variations of the counterflow slot-jet are employed in
this work. For premixed flames as previously mentioned, two configurations are
possible: premixed combustible gas vs. inert gas, where a single flame is produced,
and premixed gas vs. premixed gas, where twin flames are produced on either side of
the stagnation plane. For nonpremixed edge-flames, only one counterflow
configuration is possible, namely a fuel + inert mixture vs. an oxygen + inert mixture,
which exhibits a single flame at the location where the reactant fluxes are in
stoichiometric proportion.
The counterflow slot-jet burner employed (Fig. 10) for the experiments
consists of two 0.5 cm × 13 cm central rectangular jets for a slot aspect ratio of 26:1
which results in nearly plane strain in the plane orthogonal to the edge propagation
(Cha and Ronney, 2006). A small flow may occur in the direction orthogonal to the
jets, or in the direction of edge-flame propagation, so small ceramic spacers, see Fig.
10, were placed at both ends between the upper and lower jets to help minimize any
unwanted extensional strain in this direction.

central jet
d
ceramic spacer
Ceramic spacer
nitrogen
sheath
hot wire
Hot wire
lower burner
Lower slot- jet

Nitrogen sheath jets
Central jet
upper burner Upper slot-jet
Figure 10: Close-up view of counterflow slot-jet burner showing central jet,
sheath flow jets, and ceramic burner spacers with electrically heated wires.

While boundary layers likely develop on the spacers due to the upper and lower jet
flows, they should be contained near the outer edges of the burner. It will be shown
that at the center of the burner, where the edge-flame propagation speed is measured,
any strain in the direction of propagation or effect of boundary layers at the ends is
negligible.
Equal values of U
jet
were employed for the upper and lower streams. On both
sides of these jets, additional 0.5 cm × 13 cm slot jets provided N
2
sheath flow to
suppress the shear layer between the flame jets and the ambient atmosphere, as well
17

as prevent any possible mixing of the fuel jet with ambient air in the case of
nonpremixed flames. All six jets were filled with steel wool and the jet exits were
fitted with stainless steel honeycomb (0.7 mm channel width) to ensure uniformity of
the exit flow. Figure 10, above, shows a clearer view of the main central jet and
sheath flow jets for the counterflow burner’s lower slot-jet. The jets (and thus the
gases at the jet exits) were maintained at room temperature by water cooling.
Commercial mass flow controllers with accuracy ±1% of full scale (calibrated with
wet-test meters) controlled the gas flows. The sheath flow velocities (U
sheath
) were
set to match the central jets, i.e. U
sheath
= U
jet
, in order to measure true edge
propagation speeds. Figure 11 below shows the edge-flame propagation speed, U
edge
,
as a function of the ratio of U
sheath
to U
jet
for a nonpremixed CH
4
-O
2
-N
2
edge-flame
(Cha and Ronney, 2006). The edge-flame propagation speed is fairly insensitive for
a range of velocities near U
sheath
= U
jet
. The fluid dynamics issues of premixed edge-
flames will be similar if the same slot-jet burner is used so the same sheath flow
condition, U
sheath
≈ U
jet
, is adequate.

Figure 11: Effect of sheath flow velocity on edge-flame propagation velocity
(U
edge
) for nonpremixed conditions from Cha and Ronney (2006).
18

Figure 12 shows a schematic representation of the basic flow system utilized
for the experiments. For conditions which require very low U
jet
, it may be necessary
to partially enclose the apparatus in a ventilated box to shield the test section from
room drafts.

Figure 12: Basic experimental flow system diagram.
19
Advancing edge-flames (U
edge
> 0) are produced by establishing a uniform
flame between the counterflow slot-jets, extinguishing or “erasing” part of the flame
starting at one end and moving to the other end by sweeping a small (3 mm
diameter) round jet of N
2
across the length of the slot, leaving only a small burning
region at one end, then suddenly removing the N
2
jet. This procedure resulted in an
edge-flame that propagated across the length of the slot, thereby reestablishing the
uniform flame. Producing retreating edge-flames (U
edge
< 0) is more difficult. It is
not possible to simply establish a flame between the slot-jets and trigger extinction at
one end since there is virtually no convective velocity in the direction of propagation
which is needed to maintain an extinction front in the counterflow. In other words,

20
both ends of the uniform flame created between the slots would spontaneously
retreat and thus extinguish the flame since and never allow adequate insight into the
stretch and heat loss limits, both of which occur below σ
ext
.

Consequently, the conditions for which U
edge
< 0 are not directly accessible in
a slot-jet apparatus with “bare” slot ends. To overcome this limitation, electrical
wire resistance heaters were added to the ceramic spacers (Fig. 10) at both ends of
the slots. These heated wires (temperature approximately 1300K) acted as anchors
by increasing the mixture enthalpy near the spacers and holding the flame ends in
place. Retreating edge-flames could then be triggered with a jet of N
2
that both
extinguished the flame in an unheated region adjacent to the end heaters and
prevented the heaters from re-igniting the flame end.
For the experiments dealing with low-Le flames where the influence of strain
on diffusive-thermal instabilities is important, it should be noted that the current
apparatus is a modified version of the original used by Kaiser et al. (2000). Since
their original work on the subject, the slots now have an increased aspect ratio [26:1
compared to original 7.6:1] and previous work did not have the added feature of
sheath flows on each side of the upper and lower jets to suppress shear instabilities.

2.2 Measurements and Diagnostics

The majority of information necessary in this study was collected by various
optical imaging techniques used to record edge-flame propagation, which are listed
below:

21
• Color digital video camera: A standard color digital video camera with 30 Hz
frame rate, 10ms shutter speed is used for most cases in which a low U
edge
is
expected. When used in conjunction with a wide-angle lens, the color digital
video camera captures the entire burner apparatus length but close enough to
accurately record the edge location.
• Princeton Instruments intensified CCD camera: In order to provide a visual
representation of edge-flame intensity, the intensified CCD camera, with 2
ms shutter speed, captures close-up grey-scale images based on perceived
flame intensity of the propagating edge-flame which can later be false-
colored.
• Photron FASTCAM ultima 1024 high-speed camera: For cases where U
edge

will be too fast for the color digital video camera, it is necessary to use a
camera with a higher frame rate in order to capture the edge propagation and
determine U
edge
. The Photron FASTCAM has a maximum frame rate in
excess of 250 frames/sec for the given flame intensities, which is adequate to
capture edge-flames with propagation speeds as high as 500 cm/s.
• Shadowgraph visualization: H
2
-air flames in the mixtures of interest are
practically transparent in the visible spectrum so a He-Ne laser shadowgraph
system is used in conjunction with the Photron high-speed camera to provide
visible recordings of the edge-flame propagation. One benefit of a
shadowgraph system for the current study is that it is sensitive to the second
spatial derivative of the index of refraction. Since for a gas the index of

fraction is proportional to density, which in turn is inversely proportional to
temperature for the nearly constant pressure flames examined here, the
shadowgraph provides a qualitative image of the regions of large second
spatial derivative of temperature. Since the effect of heat release in a steady
one-dimensional flame is a change in the second spatial derivative of
temperature (Williams, 1985) the shadowgraph technique provides a means
to visualize regions of high heat release rate (Kaiser et al., 2000).

As in the nonpremixed edge-flame experiments by Cha and Ronney (2006),
proper determination of U
edge
was determined from the recorded videos by plotting
the propagation speeds in the laboratory reference frame as a function of position (x)
along the slot-jet apparatus. This can be accomplished by a frame-by-frame analysis
of the videos. For some mixtures, such as the C
3
H
8
-air mixture shown in Fig. 13, the
linear least squares fit between -2 cm and +2 cm shows a nearly constant propagation
15
20
25
30
-4 -3 -2 -1 0 1 2 3 4
U
edge
[cm/s]
Burner lengthwise coordinate [cm]
Linear least squares fit
U
edge
(x = 0) = 25 cm/s

Figure 13: U
edge
as a function of horizontal lengthwise position for single
premixed 3.2% C
3
H
8
in air, strain rate = 28.6 cm/s, d = 7 mm.

22

23
speed. In a case such as this, the propagation speed is assumed to be unaffected by
any velocity gradients in the direction of propagation. If a linear, or near linear,
nonzero relationship is suggested then it may be determined that U
edge
is constant and
in the presence of a small, nearly constant velocity gradient along the slot. This
gradient should be in the form dU
edge
(x)/dx and U
edge
will be taken near the center of
the slot-jets where symmetry predicts no velocity gradient exists (Cha and Ronney,
2006).

2.3 Selection of Test Conditions

Main fuels considered in this study are gaseous methane (CH
4
), propane
(C
3
H
8
) and hydrogen (H
2
). For the premixed edge-flame experiments, CH
4
and C
3
H
8

were used in conjunction with oxygen (O
2
), nitrogen (N
2
), carbon dioxide (CO
2
), and
air to form combustible mixtures of interest. By using the two fuels and various
oxidizer/diluent combinations, it was possible to test mixtures with different values
of Le as well as different mixture strengths. The gap between the upper and lower
slot-jets is varied depending on mixture used in order to maintain an equivalent Pe
jet
,
where Pe
jet
= U
jet
d/α is the Peclet number or ratio of bulk heat transfer to conductive
heat transfer. Maintaining an equal Pe
jet
between mixtures tested maintains the heat
transfer rate at a constant value and prevents disparate rates from affecting edge-
flame propagation rates. CH
4
and C
3
H
8
are widely used both experimentally and
computationally since they are relatively easier to model than large molecule
hydrocarbons they are logical choices here in order to facilitate comparisons.
Whenever possible, mixtures will be chosen based on keeping the laminar burning

24
velocities equal or as close to equal as possible. In all likelihood, certain mixtures
will be too weak for the slot-jet burner and will therefore need increased fuel
concentration which will in turn change the burning velocity. Lean H
2
-air and H
2
-
O
2
-N
2
combinations, with Le
fuel
≈ 0.3, were used for experiments focusing on
diffusive-thermal instabilities of low Le flames and their subsequent propagation
rates. Twin premixed, single premixed, and nonpremixed configurations were used.
In order to control the nonpremixed flame location, the lower jet contained H
2
-N
2

and the upper jet contained O
2
-N
2
. By varying the concentrations of each, while
maintaining equal jet flow rates, it was possible to change the stoichiometric mixture
fraction, Z
st
, thus the flame location.
In similar fashion to the experimental design in Cha and Ronney (2006), it is
advantageous to briefly consider four experimental limits when targeting cases to
study experimentally with the slot-jet counterflow burner. The high strain limit and
the heat loss extinction limit must be conceptually analyzed in order to select
mixtures and conditions that will not be adversely affected by turbulence and
buoyancy, the third and fourth limits. For these calculations α is evaluated at
ambient temperature. A temperature-averaged value could potentially provide more
accurate results, but the increase in α with temperature will be offset to a large extent
by an increase in convection velocity due to thermal expansion (Cha and Ronney,
2006).
• Strain-induced extinction: Daou et al. (2002) predict that for Le ≈ 1, ε ≈ 2.5 at
this limit for nonpremixed counterflow flames, and that this limit is nearly

25
independent of the heat loss parameter κ. For premixed flames, the limit is ε
≈ 0.8 (Daou et al., 2003). Because equal jet velocities are employed and the
densities of the two streams are nearly equal, Eq. (2) is valid and in
conjunction with Eq. (3) gives the extinction criteria; U
jet
≈ (2.5/β)
2
(S
L
2
d/α)
[nonpremixed], U
jet
≈ (0.8)
2
(S
L
2
d/α) [premixed] (Cha and Ronney, 2006).
• Heat loss induced extinction: Daou et al. (2002, 2003) predict that the heat
loss limit occurs at ε ≈ 15κ for nonpremixed flames and ε ≈ κ for premixed
flames. Estimating κ
0
≈ hA∆T/(ρC
p
V∆T), a volumetric heat loss coefficient
where h ≈ 3.77k/d is the heat transfer coefficient for laminar flow between
two infinite parallel plates, k is the gas thermal conductivity, A is the area for
heat transfer (= twice the area of 1 jet exit cross-section, A
jet
) and V is the gas
volume (= A
jet
d). This results in κ
0
≈ 3.77(k/d)(A)/(ρC
p
A
jet
d) ≈ 7.54α/d
2

which can be substituted into Eq. (3) leading to κ ≈ β(α/S
L
2
)(7.54α/d
2
) ≈
7.54β(α/(S
L
d))
2
. The heat loss criteria for extinction for nonpremixed and
premixed flames become U
jet
≈ (15)
2
(7.54)
2
(α/d)
3
/S
L
2
and (7.54)
2
β
2
(α/d)
3
/S
L
2
,
respectively (Cha and Ronney, 2006).
• Turbulent flow: A transition to unsteady and possibly turbulent flow was
observed in experiments by Cha and Ronney (2006) at Re
jet
≡ U
jet
w/ν > 500,
where w is the jet width (= 0.5 cm for our experiments) and ν is the gas
viscosity at ambient conditions.
• Buoyancy-dominated flow: At sufficiently low U
jet
, unstable flame behavior
was observed, apparently due to buoyancy-induced convection. An estimate

of the condition for which buoyancy effects become significant is when U
jet

equals the buoyant convection velocity ≈ 0.3{g(d/2)}
1/2
, where d/2 rather than
d is chosen as the characteristic dimension only the upper half of the jet gap
contains gas with an unstable density gradient (Cha and Ronney, 2006).

The four criteria explained above are plotted in Fig. 14. The target parameter
space for the experiments is shown by the shaded region between the limits. Also
shown in Fig. 14 via the dashed lines are combinations of U
jet
vs. d for two values of

1
10
100
00.5 1 1.5
Turbulent
Strain extinction
Heat loss
extinction
Buoyancy effects
σ = 100 s
-1
σ = 20 s
-1
U
jet
[cm/s]
Jet spacing (d) [cm]
2
Figure 14: Estimated operating conditions for slot-jet burner for 8.3% CH
4
–
91.7% air baseline mixture. Shaded region denotes desired range of operating
parameters.

the strain rate σ. It is apparent from the figure that small values of d are best for
investigating the heat loss limits. Cha and Ronney (2006) showed that for the slot-jet
26

27
burner to be used in these experiments changing d had minimal impact on the
propagation speed except near the low strain limit. Experiments will be conducted in
order to determine propagation rates from low- σ to high- σ extinction for the selected
fuels. Specifically, mixtures will be chosen in order to observe the two extinction
limits whenever possible while varying important parameters, such as Le, Z
st
, and κ,
one at a time for the largest possible range of each. This should provide a
comprehensive examination of edge-flame propagation rates and any stability or
extinction limits of interest.

28
Chapter 3

Twin Hydrocarbon Edge-Flames

3.1 Effect of Mixture Strength

Table 1 shows the mixtures and associated properties of the twin premixed
edge-flames evaluated in this study. The values of the laminar burning velocity, S
L
,
in the table were computed using the Sandia flame code with the GRI 3.0 chemical
kinetics mechanism (Smith et al.) for methane and Wang mechanism (Qin et al.,
2000) for propane. The Zeldovich number β is the nondimensional activation energy
given by E(T
ad
-T
∞
)/(RT
ad
2
), where T
ad
is the adiabatic flame temperature, T
∞
is the
ambient temperature, and E/R is the activation temperature calculated from a linear
fit of ln(S
L
) vs. 1/T
ad
, which has a slope of –E/2R. The method of estimating κ was
described in section 2.3 of the previous chapter.
Mixture
composition
Fuel Percent
or Inert Ratio
(Q)
S
L
(cm/s)
d
(cm)
(ρ
u
/ρ
b
)
α
(cm
2
/s)
β
κ
5.2 5.70 0.75 5.07 0.200 11.7 0.1927
5.3 6.29 0.75 5.13 0.200 11.5 0.1550
5.6 8.26 0.75 5.34 0.200 10.9 0.0853
5.8 9.72 0.75 5.47 0.200 10.5 0.0595
6.0 11.3 0.75 5.60 0.200 9.95 0.0420
CH
4
-Air
(Le
fuel
= 0.96;
Le
O2
= 1.10)
6.5 15.5 0.75 5.93 0.200 8.52 0.0191
7.153 4.0 0.50 6.12 0.121 14.2 0.3912
6.813 5.0 0.50 6.25 0.122 14.1 0.2523
CH
4
/O
2
/CO
2
(1/2/Q)
(Le
fuel
= 0.74;
Le
O2
= 0.86)
6.536 6.0 0.50 6.37 0.123 13.9 0.1766
2.6 17.5 0.70 6.05 0.189 7.02 0.0126
2.7 19.4 0.70 6.21 0.189 6.63 0.0097
C
3
H
8
-Air
(Le
fuel
= 1.86;
Le
O2
= 1.05)
2.8 21.3 0.70 6.37 0.188 6.18 0.0074
Table 1: Experimental conditions and corresponding flame properties for twin
premixed edge-flames.

Figures 15 and 16 show digital photographs of two representative CH
4
-air
twin flames produced by the slot-jet counterflow burner. At low and moderate strain,
as in Fig. 15, two planar flames are visible equidistant from the stagnation plane
located at the midpoint between the upper and lower jets. With increasing strain, i.e.
U
jet
from the upper and lower jets, the distance between the two flames decreases
until only a single flame appears visible as in Fig. 16. Close-up images and
descriptions of the propagating edge-flames measured are included in the next
section.

Figure 15: Twin CH
4
-air flames at moderate strain ( σ = 107 s
-1
).

29

Figure 16: Twin CH
4
-air flames at high strain ( σ = 213 s
-1
).

To examine the experimental error associated with measuring the edge-flame
speed, the propagation rate as a function of global strain rate is plotted with
corresponding error bars in Fig. 17. Three to five measurements are taken at each
strain rate and averaged to determine the edge-flame propagation speed at that
particular strain rate. The difference of a single measurement from the average is
nearly always less than 5%. Figure 17 shows that for 5.6% CH
4
the average error for
each measured edge speed is negligible which holds true for all twin premixed
results.

-60
-40
-20
0
20
40
0 20 40 60 80 100 120 140 160
U
edge
[cm/s]
σ [1/s]
5.6% CH
4
/ 94.4% air
d = 7.5 mm

Figure 17: U
edge
vs. σ for twin, methane-air edge flame indicating representative
experimental error.

Edge-flame propagation speeds, U
edge
, for CH
4
-air mixtures are plotted in Fig.
18(a) as a function of global strain rate, σ (= 2U
jet
/d), indicating both low- σ and high-
σ extinction limits. U
edge
is lower for leaner mixtures for all values of σ. Strong
mixtures, thus smaller κ and smaller impact of heat loss, exhibit “short-length”
flames near the low- σ limit whereas leaner mixtures exhibit retreating edge-flames.
“Short-length” flames are single or multiple flames on the order of 1 cm in length,
with both a leading edge and trailing tail, advancing from one side of the burner to
the other. “Short-length” flames occur at a low- σ limit near σ ≈ 12 ± 1 s
-1
for the
three strongest mixtures shown in Fig. 18. “Short-length” flames are only observed
near the low- σ extinction limit when the heated wire at the slot end is on as was also
observed for very strong CH
4
-O
2
-N
2
nonpremixed edge-flames (Cha and Ronney,
2006). The “short-length” flames exist because the leading edge leaves behind a
combination of products and reactants which is unable to sustain the trailing flame
30

31
due to heat losses and possibly buoyancy. For all conditions where the high- σ limit
was reached, retreating edge-flames were observed. The high-σ extinction limit
varies considerably for each mixture, but was not reached for the two richest
mixtures, 6.5% and 6% CH
4
, due to burner flow limitations.
Figure 18(b) shows the same information in nondimensional form. U
edge
is
scaled by S
L
(ρ
u
/ρ
b
) and is plotted against the dimensionless strain rate, ε, defined by
Daou et al. (2003) as ε ≡ ( σα /(2S
L
2
))
1/2
. The scaling factor S
L
(ρ
u
/ρ
b
) used in Fig.
18(b) is based on the scaling of triple flames with large mixing thicknesses
developed by Reutsch et al. (1995) and represents the gas expansion experienced by
the burned product gases. The hot combustion products have a lower density, ρ
b
,
than the unburned reactants, ρ
u
, and are essentially trapped between the twin flames.
Conservation of mass dictates that the propagating edge speed must increase to
account for the expansion of burned products. It should be noted that U
edge
is
measured in the laboratory reference frame while the flame burning velocity, S
L
, is
computed relative to the unburned gas ahead of the propagating edge-flame. Figure
18(b) shows scaled U
edge
on the order of 1 so the scaling provides an appropriate
means of comparing data at varying mixture strengths.

-100
-50
0
50
100
10 100
U
edge
[cm/s]
σ [1/s]
CH
4
/air
d = 7.5 mm
% CH
4
= 6.5
5.2
5.3
6.0
5.8
5.6
Number associated with each
curve corresponds to fuel percent
Short-length
edge-flames

(a)

-2
-1.5
-1
-0.5
0
0.5
1
1.5
0 0.1 0.2 0.3 0.4 0.5
U
edge
/(S
L
(ρ
u
/ρ
b
))
ε
% CH
4
= 6.5
6.0
5.8
5.6
5.2
5.3
Number associated with each
curve corresponds to fuel percent
Short-length
edge-flames
CH
4
/air
d = 7.5 mm

(b)

Figure 18: Effect of dimensional strain rate ( σ) on dimensional edge speed
(U
edge
) for various twin CH
4
-air edge-flame mixtures. Number associated with
each curve refers to the mixture fuel percent. Dashed lines and unfilled
markers correspond to short-length edge-flames, positive speed refers to leading
head and negative speed refers to trailing tail for a given strain rate. (a) Raw
data. (b) Scaled U
edge
vs. nondimensional strain rate ε.

32

Figure 19 shows the dimensionless edge speed plotted as a function of the
dimensionless strain rate ε for multiple values of κ as computed by Daou et al.
(2003). Figure 19 shows a few qualitative similarities compared to the experimental
results in Fig. 18(b). For κ ≈ 0.12, Daou et al. predict isolated edge-flames at the
low strain limit which is their term for “short-length” flames. As ε increases from
the lower limit, the propagation speed decreases monotonically. For a similar
experimental heat loss factor of 0.1, corresponding to a mixture of approximately
5.4% CH
4
– 94.6% air, Fig. 18(b) suggests that retreating edge-flames would exist at
the low strain limit and the overall shape of the curve would resemble the Fig. 19
curve for κ = 0.15 meaning the values of k are different by approximately 50% on a
purely qualitative level. In general, experiments predict “short-length” flames for κ
≤ 0.08.
.
Figure 19: Effect of nondimensional strain rate ( ε) on the nondimensional edge-
flame propagation speed (U) for different values of the nondimensional heat loss
(κ) as computed by Daou et al. (2003).

33

34
As κ increases above 0.1, the experiments and computations begin to agree
more closely. When κ = 0.15, Daou et al. (2003) show in Fig. 19 that at low strain
the edge-flame has negative propagation speeds which increase to positive values for
moderate ε before decreasing back to negative values as the high strain limit is
approached. 5.3% CH
4
in Fig. 18(b) follows a very similar trend at a nearly identical
dimensionless heat loss parameter, κ = 0.155. The total range of ε over which the
twin edge-flames exist for both the experiments and numerical calculations is also
remarkably close, approximately 0.1 at low-ε to between 0.4 and 0.5 for high-ε.
To summarize the effect of mixture strength, a map of flame behavior in κ- ε
space is shown in Fig. 20(a) along with the corresponding predictions by Daou et al.
(2003) in Fig. 20(b). Similarities between the two plots include (1) the strain-
induced extinction limit occurs near ε = 0.35, (2) the heat-loss-induced limit occurs
along a limit line with roughly ε ≈ 1.5κ, and (3) the ultimate extinction limit, where
strain and heat loss limits converge, is near κ = 0.25 which is approximately ten
times larger than single premixed flames indicating that twin flames are much
stronger due to the back-to-back configuration. However, one major difference is
between the experiments and numerical calculations lies with “short-length” flames.
Daou et al. determined that isolated edge-flames, i.e. “short-length” edge-flames,
only exist at a very small region near κ ≈ 0.12 while experiments showed they exist
for κ ≤ 0.08. Also, the experiment was unable to reach values of strain to fully
examine the high-ε and low-κ region of the propagation map.

0
0.1
0.2
0.3
0.4
0.5
0.6
0 0.05 0.1 0.15 0.2 0.25
Heat loss factor κ
Nondimensional stretch rate ε
extinction
extinction
advancing
retreating
Short-length
edge-flames

(a)

0
0.1
0.2
0.3
0.4
0.5
0.6
0 0.05 0.1 0.15 0.2 0.25 0.3
Heat loss factor κ
Nondimensional stretch rate ε
extinction
retreating
advancing
extinction
Short-length
edge-flames

(b)

Figure 20: Map of propagation modes and extinction limits for twin edge-flames
in terms of heat loss factor κ and nondimensional strain rate ε. (a)
Experimental results for CH
4
-air mixtures. (b) Numerical predictions from
Daou et al. (2003).

35

3.2 Effect of Lewis Number

Edge-flame propagation speeds for Le < 1 mixtures are shown in Fig. 21. By
using CH
4
-O
2
-CO
2
mixtures, the fuel and oxygen Lewis numbers are nearly equal
and both are slightly less than unity (see Table 1). Figure 21 shows that Le < 1
mixtures have much higher scaled values of U
edge
than Le ≈ 1 mixtures having
similar S
L
(thus κ). The high- σ extinction limit occurs at ε = 0.66 ± 0.02 for the
mixtures shown in Fig. 21, which is higher than that for Le ≈ 1 mixtures (Fig. 18(b)),
but for each mixture family having nearly the same Le, the extinction limits are
nearly independent of S
L
(thus κ).
-2
-1.5
-1
-0.5
0
0.5
1
1.5
0.1 0.2 0.3 0.4 0.5 0.6 0.7
CH
4
/air, 6.3
CH
4
/O
2
/CO
2
, 6
CH
4
/O
2
/CO
2
, 5
CH
4
/O
2
/CO
2
, 4
ε
U
edge
/(S
L
(ρ
u
/ρ
b
))
Mixture S
L
(cm/s)

Figure 21: Effect of nondimensional strain rate on scaled U
edge
for various twin
CH
4
-O
2
-CO
2
mixtures (Le ≈ 0.8) with d = 5 mm. Also shown for comparison is
a CH
4
-air (Le ≈ 1) case.

To better understand why the change in Le results in such a large change in
U
edge
, it is necessary to remember that Le equals the thermal diffusivity of the
36

37
stoichiometrically limiting reactant divided by the mass diffusivity of the bulk
mixture. In this case, the mixtures are lean so the fuel is the limiting reactant and
since its Lewis number is less than one the mass diffusion into the reaction zone is
greater than the thermal diffusion away from the reaction zone. Figure 22 further
illustrates this point for a curved flame. With Le < 1, the thermal enthalpy loss in the
curved or stretched region is less than the chemical enthalpy gain. This results in an
increase in local flame temperature at the curved region thus greatly increasing the
reaction rate and leading to an increase in the local burning velocity. This can be
seen experimentally in Fig. 22 which shows grayscale images of direct emission for
twin edge-flames at Le = 1, Le < 1, and Le > 1. The curved leading edge of the CH
4
-
O
2
-CO
2
flames for Le < 1 are much brighter than the CH
4
-air flames where Le ≈ 1
implying that the reaction rate and intensity of the flame is much greater for Le < 1.

Figure 22: Schematic of curved flame for Lewis number < 1 showing the
relative imbalance of reduced heat diffusion away from the flame front and
increased fuel diffusion towards the flame front leading to increased reaction
rate and local burning velocity.

Flame
front
Burned gas
Unburned gas Direction of
propagation
Heat
diffusion
Heat
diffusion
Fuel
diffusion
Fuel
diffusion

38

Figure 23: Grayscale images of direct emission from twin premixed edge-fla

mes, exposure time = 2 ms,
global strain rate ( σ) shown in each image, premixed fuel/O
2
/diluent enters from both top and bottom, all
flames propagate from left to right, height of each image roughly corresponds to jet spacing.
σ = 10.7 s
-1

σ = 160 s
-1
σ = 220 s
-1
σ = 12 s
-1
σ = 16 s
-1
σ = 240 s
-1
σ = 340 s
-1
σ = 58 s
-1
σ = 87 s
-1
σ = 26.1 s
-1
σ = 14.5 s
-1
C
3
H
8
-Air, Le > 1, d = 7 mm CH
4
-O
2
-CO
2
, Le < 1, d = 5 mm CH
4
-Air, Le ≈ 1, d = 7.5 mm
σ = 10.7 s
-
1
σ = 26.7 s
-1
R
h
Short-length
edge-flames at
low strain
Advancing
edge-flames
at low strain
Advancing
edge-flames at
medium strain
etreating
igh strain
edge-flames at

Figure 24 below displays computed temperature (top) and reaction rate
(bottom) contours from Daou et al. (2003) for κ = 0.12, β = 8, α = 0.85, and Le = 1.
As ε decreases, the flames move further apart as seen by the reaction rate contours
increasing in the y-direction until eventually becoming a “short-length” flame at ε =
0.1 when the trailing planar flames are extinguished. Plots of temperature and
reaction rate qualitatively agree with pictures in Fig. 23.

Figure 24: Computed contours of reaction rate and temperature from Daou et
al. (2003) with β = 8, α = 0.85, and Le = 1 for twin premixed edge-flames at
three different dimensionless strain rates. Contours are symmetric with respect
to y = 0. Advancing edge-flames (i.e. positive scaled edge speed U) move from
right to left.

The effects of the nondimensional flame thickness ε on the scaled edge-flame
propagation speed for C
3
H
8
-air with fuel Le > 1 are shown in Fig. 25. Data for a
39

CH
4
/air mixture (Le ≈ 1) with a lower S
L
than the weakest C
3
H
8
-air mixture tested
are also shown for comparison purposes. Figure 25 shows that the values of U
edge

are much lower for the Le > 1 cases even at higher S
L
(thus lower heat loss parameter
κ) and same ε. It should be noted that none of the C
3
H
8
/air mixtures tested exhibit
“short-length” flames or retreating edge-flames.
-1
-0.5
0
0.5
1
0 0.1 0.2 0.3 0.4 0.5
CH
4
/air 9.7
C
3
H
8
/air 21.3
C
3
H
8
/air 19.4
C
3
H
8
/air 17.5
U
edge
/(S
L
(ρ
u
/ρ
b
))
ε
Mixture S
L
(cm/s)

Figure 25: Effect of nondimensional strain rate on scaled U
edge
for various twin
C
3
H
8
-air mixtures (Le ≈ 1.8) with d = 7 mm. Also shown for comparison is a
CH
4
-air (Le ≈ 1) case.

The images in Fig. 23 show the curved leading edge of the C
3
H
8
-air is less bright
than the rest of the flame implying that the point of highest curvature is the weakest
point of the flame. When compared to CH
4
-O
2
-CO
2
and CH
4
-air flames it is
apparent that when the fuel Le > 1 the curvature effect has a negative impact on the
reaction rate and local burning velocity.
One final important characteristic to note is that extinction at high-ε occurs at
nearly the same value of ε for all mixtures of a given family. In other words, the
40

high strain extinction limit is not affected by the amount of fuel, thus the laminar
burning velocity and adiabatic flame temperature. This is shown in Fig. 26 as a plot
of ε at the high strain extinction limit as a function of Lewis number. Although only
3 to 5 mixtures were used at each value of Le, the standard deviation shown via the
vertical error bars in Fig. 26 is small. Also, as Le increases the value of ε at high
strain extinction also decreases which further supports the previously mentioned
effect Lewis number has on the relative strength of the propagating edge-flames. For
a small increase, say from 0.8 to 1, the nondimensional strain rate at extinction
decreases by over 30%. An even greater decrease in the high strain extinction limit
occurs as Le increases to 1.8. A similar trend will be shown for single premixed
edge-flames at high strain, but for single flames the high strain limit is not at
extinction but rather a limit that results in the flame breaking apart near the center of
the burner leaving two unsteady flames.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.60.8 1 1.2 1.41.6 1.8
Lewis number
Dimensionless strain rate
at high strain extinction
2

Figure 26: Average nondimensional strain rate ε at high-ε extinction for twin
premixed edge-flames. Results shown for CH
4
-air (Le ≈ 1), C
3
H
8
-air (Le ≈ 1.8),
and CH
4
-O
2
-CO
2
(Le ≈ 0.8) with error bars corresponding to one standard
deviation.
41

42
Chapter 4

Single Hydrocarbon Edge-Flames

4.1 Effect of Mixture Strength

Table 2 shows the mixtures and associated flame properties for the single
premixed edge-flames studied. The values of S
L
, β, and κ were determined in an
identical fashion as described in Chapters 2 and 3. Two of the mixtures listed under
the CH
4
-air mixtures were more specifically CH
4
-O
2
-N
2
mixtures with CH
4
/O
2
/N
2

volume ratios of 1/2/7 and 1/2/6. These two mixtures maintained a stoichiometric
CH
4
-O
2
ratio but with less N
2
than a fuel-air mixture so that artificially fast laminar
burning velocities could be obtained by increasing the adiabatic flame temperature
without altering the mixture stoichiometry.
Mixture
composition
Fuel % or
inert ratio
(Q)
S
L
(cm/s)
d
(cm)
(ρ
u
/ρ
b
)
1/2
α
(cm
2
/s)
β
κ
6.9 15.75 0.75 2.48 0.200 7.81
0.0116
7.2 17.9 0.75 2.51 0.200 7.27
0.0083
7.75 23.1 0.75 2.58 0.200 6.54
0.0050
8.3 28.6 0.75 2.64 0.200 5.60
0.0031
9.0 34.7 0.75 2.70 0.200 5.03
0.0021
1/2/7
(CH
4
/O
2
/N
2
)
47.0 0.75 2.77 0.200 10.3
0.0025
CH
4
-Air
(Le
fuel
= 0.96;
Le
O2
= 1.10)
1/2/6
(CH
4
/O
2
/N
2
)
61.3 0.75 2.84 0.200 10.1
0.0014
5.964 8.0 0.50 2.58 0.125 14.0 0.1033
5.566 10.0 0.50 2.61 0.126 14.3 0.0685
CH
4
/O
2
/CO
2
(1/2/Q)
(Le
fuel
= 0.74;
Le
O2
= 0.86)
5.240 12.0 0.50 2.65 0.127
14.5 0.0488
3.2 28.6 0.70 2.64 0.187 5.26 0.0036
3.35 31.4 0.70 2.68 0.186 4.88 0.0027
C
3
H
8
-Air
(Le
fuel
= 1.86;
Le
O2
= 1.05)
3.55 34.6 0.70 2.73 0.185 4.60 0.0021
Table 2: Experimental conditions and corresponding flame properties for single
premixed edge-flames.

Figures 27 and 28 show digital photographs of two representative CH
4
-air
twin flames produced by the slot-jet counterflow burner. At low and moderate strain,
as in Fig. 27, a single planar flame is visible on the fuel side of the stagnation plane
close to the lower jet. For single flames, the premixed reactants enter from the lower
jet while inert air enters from the top jet. With increasing strain, i.e. U
jet
from the
upper and lower jets, the flame moves away from the lower jet but still resides below
the stagnation plane. Figure 28 shows a representative single flame at the high strain
limit at which point it breaks into two separate flames. These two flames do not
completely extinguish but they also do not reconnect into a single planar flame.
Possible reasons for the breaking phenomenon will be discussed below. Close-up
images and descriptions of the propagating edge-flames measured are included in the
next section.

Figure 27: Single CH
4
-air flame at low strain ( σ = 67 s
-1
).

Figure 28: Single CH
4
-air flame at high strain breaking limit ( σ = 88 s
-1
).

Edge-flame propagation speeds, U
edge
, for single CH
4
-air mixtures are plotted
in Fig. 29(a) as a function of global strain rate, σ (= 2U
jet
/d), indicating both low- σ
and high- σ extinction limits. As with twin premixed edge-flames, U
edge
is lower for
weaker mixtures for all values of σ. Additionally, all mixtures tested exhibit “short-

43

44
length” flames near the low- σ limit and nowhere else. For sufficiently high strain,
the flame spontaneously breaks resulting in a non-periodic oscillation of the
remaining flame sections, thus neither retreating edge-flames nor a high strain
extinction limit were found. This high- σ phenomenon appears to be a stability limit
associated with the counterflow burner used in these tests and is discussed further
below.
Figure 29 shows lean CH
4
-air flames with fuel concentrations between 6.9%
and 9% and two mixtures, denoted by the volume ratios 1/2/6 and 1/2/7, containing
CH
4
/O
2
/N
2
where the fuel-oxygen ratio is held at stoichiometric but the amount of N
2

is less than that of air. By reducing the amount of N
2
diluting the mixture, it was
possible to produce edge-flames with much higher propagation speeds without
changing the equivalence ratio. These two mixtures follow the same overall trend as
the baseline CH
4
-air mixtures. At the low strain heat loss induced limit they exhibit
“short-length” flames before showing increasing U
edge
with σ and ultimately a
decrease in U
edge
approaching a scaled value on the order of one closely matching the
fuel-air mixtures.
Figure 29(b) shows the same information as Fig. 29(a) in non-dimensional
form. U
edge
is scaled by S
L
(ρ
u
/ρ
b
)
1/2
and is plotted against the dimensionless flame
thickness, ε, proposed by Daou et al. (2003). Here the scaling incorporates the
density ratio to the one-half power as shown in Reutsch et al. (1995) for triple flames
and Cha and Ronney for nonpremixed counterflow edge-flames. Because the edge-

flame is now only a single flame, as opposed to the twin configuration, the square
root of (ρ
u
/ρ
b
) is used and provides scaled valued of U
edge
on the order of 1.
-200
-100
0
100
200
300
400
500
10 100
U
edge
[cm/s]
σ [1/s]
9.0
8.3
7.75 7.2
6.9 = % CH
4
CH
4
/O
2
/N
2
=
1/2/6
1/2/7
d = 7.5 mm
Number associated with
each curve represents
CH
4
/O
2
/N
2
volume
fraction or % CH
4
in air

(a)
-2
-1
0
1
2
3
0 0.05 0.1 0.15
U
edge
/(S
L
(ρ
u
/ρ
b
)
1/2
)
ε
9.0
8.3
7.75
7.2
6.9 = % CH
2
CH
4
/O
2
/N
2
= 1/2/6
1/2/7
Number associated with each
curve represents CH
4
/ O
2
/ N
2

volume fraction or %CH
4
in air
d = 7.5 mm

(b)

Figure 29: Effect of dimensional strain rate ( σ) on dimensional edge speed
(U
edge
) for various single CH
4
-air edge-flame mixtures at d = 7.5 mm. Number
associated with each curve refers to the mixture fuel percent, but the curves for
10% and 11% are mixtures with stoichiometric CH
4
-O
2
but reduced N
2
from
that of air. Dashed lines and unfilled markers correspond to short-length edge-
flames, positive speed refers to leading head and negative speed refers to
trailing tail for a given strain rate. (a) Raw data. (b) Scaled U
edge
vs.
nondimensional strain rate ε.
45

To summarize the effect of mixture strength, a map of flame behavior in κ- ε
space is shown in Fig. 30. Of note, strain-induced extinction occurs near ε = 0.15
and is not strongly dependent on κ (line A). Heat-loss-induced extinction occurs
along a limit line with roughly ε ≈ 6κ and ultimate extinction near κ = 0.02 (line B),
which is approximately ten times smaller than twin premixed flames (Fig. 20a)
indicating single premixed edge-flames are much weaker. Unfortunately, no
comprehensive numerical works exist for single premixed edge-flames in which to
compare these experimental propagation speeds. Propagation speeds have been
calculated (Vedarajan and Buckmaster, 1998), but not enough data currently exists
for which a proper comparison can be made. One interesting comparison to twin
premixed flames is that “short-length” flames exist for every single mixture (thus
every value of κ) tested whereas they only exist at relatively low values of κ for twin
edge-flames. Also, retreating edge-flames are never observed for single mixtures but
are seen for twin mixtures when heat loss becomes large.
0
0.05
0.1
0.15
0 0.005 0.01 0.015 0.02 0.025
Heat loss factor κ
Nondimensional stretch rate ε
advancing
extinction
extinction
short-length edge-flame region

Figure 30: Map of propagation modes and extinction limits for single CH
4
-air
edge-flames with heat loss factor κ and nondimensional strain rate ε.
46

4.2 Effect of Lewis Number

Edge-flame propagation speeds for Le < 1 mixtures are shown in Fig. 31. By
using lean CH
4
-O
2
-CO
2
mixtures (Le ≈ 0.8), the fuel and oxygen Lewis numbers are
nearly equal and both are less than unity. Figure 31 shows that Le < 1 mixtures have
much higher scaled values of U
edge
than Le ≈ 1 mixtures having similar S
L
(thus κ).
The high- σ extinction limit occurs at much higher ε than that for Le ≈ 1 mixtures
(Fig. 29(b)) or Le > 1 (Fig. 32), but for each mixture family having nearly the same
Le, the extinction limits are nearly independent of S
L
(thus κ). The Le effect is not as
pronounced as in twin flames where the maximum scaled U
edge
for Le < 1 mixtures is
nearly six times that of Le ≈ 1 mixtures at similar S
L
.

-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
0.05 0.1 0.15 0.2 0.25 0.3
CH
4
/air, 18
CH
4
/O
2
/CO
2
, 12
CH
4
/O
2
/CO
2
, 10
CH
4
/O
2
/CO
2
, 8
U
edge
/(S
L
(ρ
υ
/ρ
b
)
1/2
)
ε
Mixture S
L
(cm/s)

47
Figure 31: Effect of nondimensional strain rate on scaled U
edge
for various single
CH
4
-O
2
-CO
2
mixtures (Le ≈ 0.8) with d = 5 mm. Also shown for comparison is
a CH
4
-air (Le ≈ 1) case. Dashed lines and open markers indicate short-length
edge-flames.

The effects of the nondimensional flame thickness ε on scaled, single edge-
flame propagation speed for lean mixtures with fuel Le larger than unity are shown
in Fig. 32. Data for a CH
4
-air mixture (Le ≈ 1) with S
L
approximately equal to the
strongest C
3
H
8
-air (Le ≈ 1.8) mixture tested are also shown for comparison purposes.
Figure 32 shows that the values of U
edge
are much lower for the Le > 1 cases even at
similar S
L
(thus similar heat loss parameter κ) and same ε. The stronger CH
4
-O
2
-CO
2

flames exhibit “short-length” flames at the low- ε limit for all mixtures tested
possibly implying that the existence of “short-length” flames depends on the relative
strength of the edge-flame since the C
3
H
8
-air flames did not exhibit “short-length”
flames.

-1
-0.5
0
0.5
1
1.5
2
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
CH
4
/air, 34.7
C
3
H
8
/air, 34.6
C
3
H
8
/air, 31.4
C
3
H
8
/air, 28.6
U
edge
/(S
L
(ρ
u
/ρ
b
)
1/2
)
ε
Mixture S
L
(cm/s)

Figure 32: Effect of nondimensional strain rate on scaled U
edge
for various single
C
3
H
8
-air mixtures (Le ≈ 1.8) with d = 7 mm. Also shown for comparison is a
CH
4
-air (Le ≈ 1) case. Dashed lines and open markers indicate short-length
edge-flames.
48

49

Contours of temperature (top) and reaction rate (bottom) from Vedarajan and
Buckmaster (1998) are shown in Fig. 33. The temperature and reaction rate pair on
the left is at ignition while the pair on the right is after propagating for a time period
of 6/ σ. The lower right hand section showing reaction rate contours for the
propagating edge-flame is qualitatively similar to the experimental single premixed
edge-flames. Visual analysis of the edge-flames produced by the slot-jet
counterflow burner indicates a thin planar flame sheet with a leading edge curved
away from the reactant jet. The model by Vedarajan and Buckmaster also
successfully predict the location of the flame on the side of the stagnation plane
closer to the premixed reactant jet flow.

Figure 33: Temperature contours (top two plots) and reaction rate contours
(bottom two plots) for advancing single premixed edge-flame with 1/Da = 0.329
as calculated by Vedarajan and Buckmaster (1998).
50

le images of direct emission from single premixed edge-flames, exposure time = 2 mm,

Figure 34: Greysca
global strain rate ( σ) shown in each image, premixed fuel/air enters from bottom and counterflow air enters
from top, all flames propagate from left to right, height of each image roughly corresponds to jet spacing.
σ = 50 s
-1
σ = 28.6 s
-1
σ = 18.7 s
-1

σ = 80 s
-1
σ = 16 s
-1
σ = 60 s
-1
CH
4
-Air, Le ≈ 1, d = 7.5 mm CH
4
-O
2
-CO
2
, Le < 1, d = 5 mm
Advancing
edge-flames at
low strain
Short-length
advancing edge-
flames at low strain
σ =78.6 s
-1
σ = 160 s
-1
σ = 160 s
-1
C
3
H
8
-Air, Le > 1, d = 7 mm
Advancing
edge-flames at
high strain

51
The images in Fig. 34 show direct emission from advancing single
premixed edge-flames. For reference, the premixed reactants enter form the bottom
and the inert air enters from the top. Qualitatively these images look very similar
to the reaction rate contours on the lower right hand side of Fig. 33. Additionally,
as Le becomes smaller, the curved leading edge becomes brighter and thicker
leading to the conclusion that the temperature and reaction rate are higher. This
corresponds to the trends shown above in Fig. 31 and Fig. 32 which show
propagation speed is higher for mixtures with lower Le even with the laminar
burning velocity is much lower than a comparable Le =1 mixture.
Further examination of the high strain limit at which point all single
premixed edge-flames broke apart reveals that the dimensionless strain rate ε is
approximately equal for each mixture family with common Le. Figure 35 below
shows the average value of ε for the three Lewis numbers tested along with error
bars of one standard deviation. If single flame breaking in the slot-jet counterflow
configuration was a by-product of the burner geometry or flow system, then all the
mixtures tested should break at nearly the same value of U
jet
. However, as the
mixture for a given Le become richer, thus higher S
L
, the flame remained intact
until a higher ε.
As was the case with twin premixed edge-flames, the high-ε limit occurs at
nearly the same value of ε for all mixtures of a given family with common Le. In
other words, the high strain flame breaking limit is not affected by the amount of

fuel, thus the laminar burning velocity and adiabatic flame temperature. This is
shown in Fig. 35 as a plot of ε at the high strain extinction limit as a function of
Lewis number. Although only 3 to 5 mixtures were used at each value of Le, the
standard deviation shown via the vertical error bars in Fig. 35 is small with the
exception of Le ≈ 0.8 where a single mixture broke at a much lower dimensionless
strain rate. Furthermore, the relative strength based on Le demonstrated above in
Figs. 31, 32, and 34 is shown by the difference in values of ε at which each mixture
broke. ε is nearly 2.5 times greater for Le ≈ 0.8 than for Le ≈ 1.8. In the future,
this is an important aspect of single premixed flames that must be investigated
further in order to determine if the breaking trend at high strain is due to the burner
used in this study or if it truly results from some physical condition of the flame.
0
0.05
0.1
0.15
0.2
0.25
0.3
0.6 0.8 1 1.2 1.4 1.6 1.8 2
Lewis number
Dimensionless strain rate
at high strain extinction

Figure 35: Average nondimensional strain rate ε at high-ε limit (breaking
flame limit) for single premixed edge-flames. Results shown for CH
4
-air (Le ≈
1), C
3
H
8
-air (Le ≈ 1.8), and CH
4
-O
2
-CO
2
(Le ≈ 0.8) with error bars
corresponding to one standard deviation.

52

53
Chapter 5

Low Lewis Number Edge-Flames

5.1 Diffusive-Thermal Instability at Low Lewis Number

At sufficiently low Lewis number, both premixed and nonpremixed flames
exhibit diffusive-thermal instability (DTI) which can lead to cellular flame
structures and theory predicts that flame stretch due to hydrodynamic strain or
flame curvature affects such instabilities (Sivashinsky, 1977; Ronney, 1990; Kim et
al., 1996). Stretch effects on low-Le DTI is an important aspect of turbulent
combustion of fuels such as hydrogen since the instability changes the wrinkling
characteristics and burning rates.
The strength of the stretch effect on low-Le DTI can be characterized by a
Damköhler number (Da), which is the ratio of the chemical reaction rate to the
residence time or stretch rate. For flames approximated by one-step Arrhenius
kinetics, Da ≡ Ae
-β
σ
-1
, where A is a pre-exponential factor, β is the same
nondimensional activation energy discussed in previous chapters, and σ is the
global strain rate (Kaiser et al., 2000).
DTI is predicted for all unstretched premixed flames when the Le of the
limiting reactant is sufficiently low (Sivashinsky, 1977). Additionally, heat losses
should increase the range of Le for which the instability occurs (Joulin and Clavin,
1979). For mixtures in which Le is only slightly less than 1, Sivashinsky et al.
(1982) and Buckmaster and Ludford (1983) showed that flame stretch due to

54
extensional hydrodynamic strain can suppress the instability. Likewise, Matalon
and Erneux (1984) showed the curvature of expanding spherical flames, which are
stretched in a similar manner, also suppresses the instability (Kaiser et al., 2000).
Computational studies focusing on cases where Le is far from unity have
expanded on the theory. Buckmaster and Short (1999) and Daou and Liñán (1999)
showed that instabilities will occur at all Da for stretched flames in a counterflow
configuration when Le is low enough, even below the value of Da at extinction. In
cases below the Da at extinction, the flame structure becomes discontinuous and
forms flame tubes which are elongated in the direction of extensional strain. The
flame is able to survive at a strain rate that would typically extinguish planar or
moderately wrinkled flames. Buckmaster and Short (1999) predicted a transition
from an infinite chain of tubes at moderately low Da to one or two isolated
stationary tubes at progressively lower Da before complete extinguishment at even
lower Da. This behavior can be compared to spherically symmetric flame balls in
microgravity conditions (Ronney et al., 1998) where radiative heat transfer is the
prevailing loss mechanism instead of extensional strain. In the case of both
strained tubes and radiating spheres at microgravity, the low Le enhancement
allows the curved flame to survive where a plane flame could not all while the main
loss mechanism prevents the flame from growing in size (Kaiser et al., 2000).
Ishizuka et al. (1982) and Ishizuka and Law (1982) experimentally
examined lean, premixed CH
4
-air and rich, premixed C
3
H
8
-air mixtures in a
counterflow, with Lewis numbers of about 0.95 and 0.80 respectively, but did not

55
find the wide range of theoretically described flame structures. For near-unity Le,
flame stretch suppressed the cellular instability in accordance with Near-
Equidiffusional Flame (NEF) model predictions. However, lean CH
4
-O
2
-CO
2

mixtures (Le = 0.86) exhibited cellular flame structures at high Da and not at lower
Da, in agreement with NEF predictions. This corroborates Buckmaster and Short
(1999) who predicted flame tubes at Le = 0.3 but not Le = 0.5, and Daou and Liñán
(1999) who predicted flame tubes for Le = 1/2 but not Le = 5/8. Both experiments
and theory thereby show that flame tubes should form at sufficiently low Le and
stretch suppresses the instabilities that lead to tube formation for mixtures with Le
close to unity (Kaiser et al., 2000).
Nonpremixed flame behavior is predicted to be quite different from that of
premixed flames. DTI is believed to occur only at low values of Da near extinction
since when Da is high the structure of the flame sheet is determined only by mixing
parameters without consideration to chemical reaction. At these conditions the
flame is unconditionally stable (Kim et al., 1996). When Da is low, reactants may
leak through the flame front resulting in partial premixing of reactants and thus the
local heat release rate increasing the dependence on chemical reaction rates in
addition to mixing rates (Liñán, 1974). Now the diffusive-thermal instability
occurs for both the diffusion flame regime of nonpremixed flames in which an
amount on the order of 1/β of both reactants leak through the front as well as the
premixed flame regime of nonpremixed flames in which an amount of one reactant
on the order of 1 leaks though the flame front (Kim et al., 1996; Kim, 1997).

56
Similar results are predicted for both the convective-diffusion flame and the
strained-counterflow configuration (Kim and Lee, 1999; Kim, 1996; Kim, 1997).
The models and experiments both show that for the low-Le DTI to occur Da must
be sufficiently low and the Lewis number must be sufficient small. The
experiments also show similar results are obtained if the driving mechanism for
extinction is heat loss, which occurs at very low strain rates or high Da (Kaiser et
al., 2000).
Computations by Thatcher et al. (1999) indicate that for β = 10 and equal
Lewis numbers of fuel and oxidant, Lewis number must be less than about 0.50 to
observe the onset of tube-like behavior for nonpremixed flames. Similar flame
structures as premixed flames were predicted as Da decreases: plane flames, an
array of flame tubes, isolated flame tubes and finally extinction (Kaiser et al.,
2000). However, Daou and Liñán (1998) did not predict any tube-like behavior,
even with Le
fuel
= 3/8 and Le
ox
= 1. Experimentally, Liu and Ronney (1999) found
behavior suggesting a single isolated flame tube in H
2
-N
2
vs. O
2
-N
2
flames near
extinction where Le
fuel
= 0.30 and Le
ox
= 1.0, but Shay and Ronney (1998) found
no such behavior for CH
4
-CO
2
vs. O
2
-CO
2
with Le
fu
= 0.72 and Le
ox
= 0.87. Chen
et al. (1992) concluded that CH
4
-CO
2
vs. O
2
-CO
2
mixtures were only marginally
capable of producing cellular structures in nonpremixed flames near extinction,
even though similar premixed flames readily produced cells at high Da (Liu and
Ronney, 1999). Consequently, a sufficiently low Le is necessary in order to
observe the predicted sequence of flame-tube behavior (Kaiser et al., 2000).

57
The goal of the current work was to determine the effect of flame stretch
and thus Da on the diffusive-thermal instability of flames in low Lewis number
mixtures for the slot-jet counterflow burner and to determine if the progression of
behavior from continuous flames to chains of tubes to isolated tubes as predicted
theoretically as Da is decreased (by reducing the mixture strength, thus decreasing
T
ad
and increasing β and/or by increasing the strain rate) can be observed
experimentally. Additionally, in order to add to the edge-flame propagation rate
information obtained in Chapters 3 and 4, it is of use to measure the propagation
rates for all possible flame structures observed as a function of strain (Kaiser et al.,
2000) for lean H
2
-air mixtures with Le ≈ 0.3.

5.2 Twin Premixed H
2
-Air Edge-Flames

5.2.1 Stability and Extinction Limits

Figure 36 shows the various twin premixed H
2
-air flame structures and
instabilities observed including the approximate transition between each. Region I
indicates the presence of single stationary tubes and occurs at the leanest mixture
that would ignite and form a stable structure, which was 5.25% H
2
– 94.75% air.
Likewise, individual stationary tubes exist in region II but at the same fuel
concentration will form multiple connected tubes (region III) as the strain rate
decreases. As indicated by the vertical dashed lines in Fig. 36, there are separate
distinct regions of flame stability that share common characteristics as far as shapes
and stability modes but differ in the relative transition between modes. For

instance, at 5.5% H
2
and σ = 25 s
-1
multiple moving tubes develop. At the same
strain rate but slightly higher fuel concentration, i.e. 6% H
2
, the flames are now
uniformly wrinkled. In order to get multiple moving tubes at 6% H
2
one must
increase the strain rate to values greater than 40 s
-1
. A similar trend occurs when
moving above 6.75% H
2
.
For a fixed fuel concentration, a single extinction limit is observed at low σ,
which occurs very close to σ = 7 s
-1
for moderate to rich mixtures and increases
slightly for leaner mixtures. As indicated by the vertical dashed lines in Fig. 36,
there are four distinct regions of flame stability that share common characteristics
as far as shapes and stability modes but differ in the relative transition between
modes.
0
20
40
60
80
100
120
4.55 5.56 6.57 7.58 8
Strain rate [1/s]
% H
2
.5
Extinction
Nearly planar
and stable
Multiple
moving
tubes
Uniformly wrinkled
Wrinkled with
unstable ends
Uniformly
wrinkled
I
II
III

Figure 36: Stability and extinction limits for twin H
2
-air flames in a slot-jet
counterflow configuration, jet spacing = 12.5 mm, Z
st
= 0.8.

58

59
Premixed counterflow flames produce a dual-limit both theoretically and
experimentally when subjected to radiative heat loss (Buckmaster, 1997; Ju et al.,
1999; Guo et al., 1997). Since the current experiments are not conducted at
microgravity, radiation effects would have little effect due to the dominance of
buoyancy. The data shown in Fig. 36 indicates the heat loss is likely conductive
loss to the jets rather than radiative loss, since it was found that edge-flame
propagation speed near the lower limit was sensitive to d for the slot-jet burner
used in the current investigation (Cha and Ronney, 2006). The current water-
cooled honeycomb filled nozzles would cause conductive losses in a way similar to
premixed flames stabilized on a porous-plug burner, since for both types of
apparatus at low exit velocities (less than S
L
) the flame will be attached to the plug
or nozzle but unable to propagate upstream because the pore or honeycomb
dimension is far smaller than the mixture quenching distance. However, due to
limitations in the maximum strain rate attainable for the current slot-jet counterflow
burner, the predicted high strain limit was not observed.
Figure 37 (a - g) shows a series of grayscale shadowgraph images of various
twin premixed H
2
-air flames. As predicted computationally, several different types
of instabilities are observed as Da decreases, either by reducing fuel concentration
or increasing σ (Buckmaster and Short, 1999). For example, note the progression
of instability behavior seen in Figure 36 for 7.5% H
2
as the strain rate decreases.
For sufficiently high strain, two nearly planar or moderately wrinkled flames are
observed (Figure 37(a)).

Figure 37: Shadowgraph images of twin premixed H
2
-air flames. Reactive
mixture enters from both upper and lower jets, jet spacing = 12.5 mm. (a)
Nearly planar twin flames, 7.5% H
2
, strain rate = 128 s
-1
.

Figure 37(b): Moderately wrinkled flames, 7.5% H
2
, strain rate 24 s
-1
.

Figure 37(c): Uniformly wrinkled twin flames, 6.5% H
2
, strain rate = 24 s
-1
.

Figure 37(d): Single stationary tube, 5.5% H
2
, strain rate = 104 s
-1
.

Figure 37(e): Twin stationary tubes, 5.5% H
2
, strain rate = 72 s
-1
.

Figure 37(f): Multiple tubes moving outward from center, 5.5% H
2
, strain rate
= 56 s
-1
.

Figure 37(g): Fully connected string of tubes, 5.5% H
2
, strain rate 24 s
-1
.

60

61

As the strain rate decreases, the wrinkling increases until the top flame becomes
uniform across the length of the burner (Fig. 37(b)) and eventually both upper and
lower flames form a uniformly wrinkled shape (Fig. 37(c)). For mixtures with H
2

concentrations greater than 6.75%, as shown in Fig. 36, the transition from planar
flames to wrinkled flames occurs at increasing strain as the concentration of H
2

increases while the low strain extinction limit is nearly constant.
At lean mixtures near the extinction limit, high strain now leads to the
formation of the predicted single and double stationary tubes at the center of the
burner (Fig. 37(d) and Fig. 37(e)) which are illustrated in regions I and II in Fig. 36.
The stationary tubes transition to multiple moving tubes (Fig. 37(f)) as strain
decreases and eventually form a fully connected string of tubes (Fig. 37(g)). The
fully connected tubes occur in region III in Fig. 36 as well as at high strain for
mixtures between 5.75% and 6.75% H
2
.
Single, twin, and multiple unconnected tubes generally do not exhibit a
round cross-section but instead appear slightly elongated in the horizontal direction,
which is unstrained. This is likely due to the compressive strain in the horizontal
direction and is consistent with theoretical predictions (Buckmaster and Short,
1999; Daou and Liñán, 1999).

5.2.2 Effect of Mixture Strength

Figure 38 shows the dimensional edge-flame propagation rate U
edge
as a
function of strain rate σ for four twin H
2
-air mixtures. As the amount of H
2

decreases, U
edge
decreases across the entire range of σ. Also, the range of σ for
which the flames propagate decreases as the amount of H
2
decreases. Only positive
propagation speeds, i.e. advancing flames, exist. For all mixtures except 5.5% H
2
,
U
edge
increases linearly as strain increases. There exists a transition between 5.5%
and 6% H
2
at which point the slope of U
edge
vs. σ changes from positive to negative.
0
10
20
30
40
50
0 20406080 100 120 140
U
edge
[cm/s]
σ [1/s]
% H
2
: 7
6.5
6
5.5
stationary tube(s)
stability limit
for 6% H
2
-air

Figure 38: Effect of dimensional strain rate ( σ) on dimensional U
edge
for d =
12.5 mm, Z
st
= 0.8, and various fuel concentrations for twin premixed H
2
-air
flames.

62
For 7% H
2
, the values of U
edge
include propagation of near planar flames at
high strain, non-uniformly wrinkled flames at moderate strain, and uniformly
wrinkled flames at low strain. This implies that the wrinkled flame shape may
have little impact on the speed of the edge-flame. Likewise, the curve for 6.5% H
2

includes data for multiple tubes at high strain and uniformly wrinkled flames at
moderate to

63
low strain. Multiple connected tubes can be erased with the N
2
jet resulting in an
advancing string of connected tubes. Even with multiple flame shapes and
instabilities present the propagation rate overall trend is linear. Both curves, those
for 6.5% and 7% in Fig. 30, extend beyond the range of the apparatus as indicated
by arrows.
6% H
2
follow a similar linear trend but reaches a stability limit at an
approximate strain rate of 136 s
-1
. At this point the mixture produces multiple
unconnected tubes possibly in an early transition state towards single stationary
tubes. Obtaining a propagation speed is not possible but it should not be
considered a high strain extinction limit. Theoretically, 6.5% and 7% may
eventually reach a similar state if the current burner could reach higher global strain
rates. The short, downward sloping curve for 5.5% H
2
ends at the point ( σ = 40 s
-1
)
where multiple connected tubes transition to single or twin stationary tubes. Single
and twin tubes simply extinguish when erased with the N
2
jet and ignition with a
torch at one side of the burner fails to ignite an advancing single tube at high strain.

5.3 Single Premixed H
2
-Air Edge-Flames

5.3.1 Stability and Extinction Limits

For single premixed flames, the weakest mixtures that could be burned were
around 8.5% H
2
as opposed to 5.25% H
2
for twin premixed flames. This difference
is expected because heat loss is greater for a single premixed flame impinging on a
cold inert stream than for twin back-to-back premixed flames. As with twin flames,

only a low strain extinction limit was found since apparatus limitations prevented
the examination of the proposed stretch limit at high strain as can be seen in Fig. 39.
The single premixed H
2
-air flames exhibit “short-length” flames at the low strain
limit as was the case with twin premixed H
2
-air flames. Figure 39 indicates a
variety of flame instability modes depending on the strain rate and amount of H
2
in
the reactive mixture.
Regions I and II in Fig. 39 indicate the existence of stationary individual
tubes, region II indicates moving unconnected tubes, and regions IV and V
indicated fully connected tubes all of which are discussed below.
0
20
40
60
80
100
120
140
8 9 10 11 12 13
% H
2
Extinction
Strain rate [1/s]
Non-uniformly wrinkled
Uniformly wrinkled
Uniformly wrinkled, unstable
Uniformly wrinkled, stable on lower jet
I
II
III
IV
V

Figure 39: Stability and extinction limits for single H
2
-air flames in a slot-jet
counterflow configuration, jet spacing = 12.5 mm, Z
st
= 0.8.

Figure 40 (a - f) shows shadowgraph images of the single premixed flame
structures and instabilities. For example, note the progression of instability
64

behavior seen in Figure 31 for 10.5% H
2
as the strain rate decreases. For
sufficiently high strain, the single premixed flame is non-uniformly wrinkled (Fig.
40(a)) but transitions to a uniformly wrinkled flame as the strain decreases (Fig.
40(b)). As shown in Fig. 40(c) and Fig. 40(d) for 9.5% H
2
, the flame eventually
forms a very uniform shape and sits on the lower jet at very low strain.
At lean mixtures near the extinction limit, high strain now leads to the
formation of the predicted single stationary tubes at the center of the burner (Fig.
40(e)) which are illustrated in regions I and II in Fig. 39. The stationary tubes
transition to multiple, unconnected moving tubes (region III in Fig. 39) for lean
mixtures around 9% H
2
and eventually form fully connected strings of tubes
(regions IV and V in Fig. 39). Fig. 40(e) shows a single tube located at the center
of the burner and Fig. 40(f) shows a fully connected string of tubes.

Figure 40: Shadowgraph images of single premixed H
2
-air flames. Reactive
mixture enters from lower jet, inert enters from upper jets, jet spacing = 12.5
mm. (a) Non-uniformly wrinkled flame, 10.5% H
2
, strain rate = 120 s
-1
.

Figure 40(b): Uniformly wrinkled flame, wrinkles randomly move left and
right making visualization difficult, 10.5% H
2
, strain rate = 72 s
-1
.

65

Figure 40(c): Uniformly wrinkled and stationary, 9.5% H
2
, strain rate = 24 s
-1
.

Figure 40(d): Uniformly wrinkled and stationary, 9.5% H
2
, strain rate = 16 s
-1
.

Figure 40(e): Single tube, 8.5% H
2
, strain rate = 56 s
-1
.

Figure 40(f): Fully connected string of tubes, 9% H
2
, strain rate = 56 s
-1
.

At lean mixtures near the extinction limit, high strain now leads to the
formation of the predicted single stationary tubes at the center of the burner (Fig.
40(e)) which are illustrated in regions I and II in Fig. 39. The stationary tubes
transition to multiple, unconnected moving tubes (region III in Fig. 39) for lean
mixtures around 9% H
2
and eventually form fully connected strings of tubes
(regions IV and V in Fig. 39). Fig. 40(e) shows a single tube located at the center
of the burner and Fig. 40(f) shows a fully connected string of tubes.

66

67
5.3.2 Effect of Mixture Strength

Figure 41 shows the dimensional edge-flame propagation rate U
edge
as a
function of strain rate σ for four single H
2
-air mixtures. As the amount of H
2

decreases, U
edge
decreases across the entire range of σ. Also, the range of σ for
which the flames propagate decreases as the amount of H
2
decreases. Only positive
propagation speeds, i.e. advancing flames, exist. Unlike twin H
2
-air edge-flames,
these single mixtures do not show a linear increase in Uedge as σ increases. Instead,
U
edge
beings to level off between σ = 80 – 100 s
-1
before slightly decreasing beyond
100 s
-1
. This nonlinear relationship between U
edge
and σ is likely a result of the
increased role of heat loss for single flames. As the strain decreases the flame
moves closer to the lower jet and loses heat to both the cold inert gas in the upper
counterflow stream but also to the jet itself via conduction. As seen in Fig. 40(c)
and Fig. 40(d), the flame is essentially sitting on the lower jet which increases the
amount of heat loss and decreases the reaction rate and overall strength of the flame.

0
10
20
30
40
50
0 204060 80 100 120 140
U
edge
[cm/s]
σ [1/s]
% H
2
: 10.5
10
9.5
9
stationary
tubes

Figure 41: Effect of dimensional strain rate ( σ) on dimensional U
edge
for d =
12.5 mm, Z
st
= 0.8, and various fuel concentrations for single premixed H
2
-air
flames.

The data shown for each mixture in Fig. 41 includes propagation speeds for
more than one type of flame structure. As explained in section 5.2.2 regarding twin
edge-flames, the propagation trend does not appear to depend strongly on the flame
shape for planar and wrinkled flames.

5.4 Nonpremixed H
2
-Air Edge-Flames

5.4.1 Stability and Extinction Limits

Many nonpremixed counterflow experiments utilize fuel-air mixtures which
inherently have very small values of the stoichiometric mixture fraction, Z
st
. Z
st

affects the flame position relative to the stagnation plane is defined as Z
st
= 1/(1 +
νX
f
/X
o
), where ν is the stoichiometric oxygen to fuel mass ratio, X
f
and X
o
represent
68

69
the initial mass fraction of fuel and oxygen for each stream, respectively. When Z
st

is small as is the case with fuel-air mixtures, the flame resides far on the air side.
Since the position of the flame relative to the upper and lower jets is an important
consideration, it was necessary to check the full range of Z
st
when determining
possible nonpremixed flame behaviors and instabilities. To accomplish this, the
upper jet contained a mixture of O
2
and N
2
while the lower jet contained a mixture
of H
2
and N
2
. The upper and lower jets were held at equal velocities as in all the
previous experiments.
For Z
st
< 0.8, only planar flames were found for all experimentally feasible
values of strain rate and global fuel percent. No mixture was ignitable for Z
st
> 0.8.
However, for a very narrow range at, or near, Z
st
= 0.8 it was possible to ignite
single and multiple tubes in addition to planar flames. All following data and
information corresponds to Z
st
= 0.8.
Figure 42 shows the regions of behavior exhibited by nonpremixed H
2
-O
2
-
N
2
flames for Z
st
= 0.8. Results are shown in terms of the strain rate vs. global
percent of H
2
on a volume basis. For a jet spacing of 12.5 mm, the leanest mixture
possible was 5.8% H
2
which is much closer to the leanest twin premixed case
(5.25% H
2
) than single premixed (8.5% H
2
). This is reasonable since both the fuel
and oxidizer streams are preheated by heat transfer from the flame.

0
50
100
150
5.6 5.8 6 6.2 6.4 6.6 6.8
Strain rate [1/s]
% H
2
Multiple moving tubes
Planar
Single,
stationary tubes
Extinction
Planar flame breaks apart, pieces form
hook-like structure but remain in contact
Flame pieces no longer stay in contact

Figure 42: Stability and extinction limits for nonpremixed H
2
-air flames in a
slot-jet counterflow configuration, jet spacing = 12.5 mm, Z
st
= 0.8.

Figure 43(a-g) shows shadowgraph images of the observed flame structures.
At high strain (or low Da) the nonpremixed flames form multiple tubes (Fig. 43(a)).
For H
2
= 6.06%, a transition from fully connected tubes to a flame that is nearly
planar but with a few remain tubes at the center (Fig. 43(b)) occurs as strain
decreases. At even lower strain, the nonpremixed flame becomes fully planar (Fig.
43(c)). Instead of reaching a low strain extinction limit, the planar flame breaks
into multiple pieces (Fig. 43(d)) that stay connected at first but eventually oscillate
in an unsteady fashion at slightly lower strain.

70

Figure 43: Shadowgraph images of nonpremixed H
2
-O
2
-N
2
flames. H
2
/N
2

enters from lower jet, O
2
/N
2
enters from upper jets, jet spacing = 12.5 mm. (a)
Fully connected string of tubes, 6.06% H
2
, strain rate = 96 s
-1
.

Figure 43(b): Connected tubes transitioning to planar flame, 6.06% H
2
, strain
rate = 64 s
-1
.

Figure 35(c): Planar flame, 6.06% H
2
, strain rate = 48 s
-1
.

Figure 43(d): Resulting flame structure from broken planar flame, 6.67% H
2
,
strain rate = 24 s
-1
.

Figure 43(e): Single stationary tube at center of burner, 5.88% H
2,
strain rate
= 112 s
-1
.

Figure 43(f): Twin stationary tubes on verge of splitting into multiple tubes,
5.88% H
2
, strain rate = 104 s
-1
.

Figure 43(g): Multiple tubes generated from center of burner and propagating
outwards, 5.88% H
2
, strain rate = 80 s
-1
.

71

72
Near the lean flammability limit, it was possible to ignite single tubes at high strain
(Fig. 43(e)). As with premixed flames, the cross-section of the tubes is not round
but is generally somewhat longer dimension in the unstrained direction (the
horizontal direction in these figures) than in the compressive strain direction (the
vertical direction in these figures). It is noteworthy that the premixed tubes (Fig.
37(e)) and nonpremixed tubes (Fig. 40(e)) are similar. This is probably because in
the nonpremixed case the strain rate is well above the extinction value for the
planar flame and thus the reactant streams mix without burning initially, causing
the flame to assume a somewhat premixed-like character. As strain decreases, the
single stationary tube begins to split (Fig. 43(f)) before forming multiple moving
tubes which propagate from the center outwards towards each end (Fig. 43(g)).

5.4.2 Effect of Mixture Strength

Figure 44 shows the dimensional edge-flame propagation rate U
edge
as a
function of strain rate σ for three nonpremixed H
2
-air mixtures. U
edge
is lower for
all values of σ as H
2
decreases. As was seen with premixed H
2
-air flames, the
range of σ for which the flames propagate decreases as the amount of H
2
decreases.
Only positive propagation speeds exist and U
edge
clearly shows a linear dependence
on σ. This linear trend matches the propagation vs. strain relationship from twin
premixed flames since both reactant streams are preheated prior to meeting.

0
10
20
30
40
50
60
0 20 40 60 80 100 120 140
U
edge
[cm/s]
σ [1/s]
H
2
/ O
2
/ N
2
volume ratio :1 / 2 / 11
1 / 2 / 12.5
1 / 2 / 14
stationary tubes

Figure 44: Effect of dimensional strain rate ( σ) on dimensional U
edge
for d =
12.5 mm, Z
st
= 0.8, and various fuel concentrations for nonpremixed H
2
-air
flames.

As seen above in Fig. 44, the low strain stability limit for nonpremixed H
2
-
air flames occurs when the planar flame breaks into multiple pieces, eventually
making it impossible for the flame to propagate. The low strain limits for the three
mixtures shown in Fig. 44 correspond to point at which the flame is broken and
will no longer propagate. The mixtures 1/2/11 and 1/2/12.5, which are global
volume ratios of H
2
/O
2
/N
2
, have nearly the same low strain propagation limit while
1/2/14 breaks at a much higher low strain limit. Additionally, 1/2/14 begins
forming individual stationary tubes at a strain rate around 90 s
-1
so a high strain
extinction limit is not observed. 1/2/11 and 1/2/12.5 do not reach a high strain
73

74
extinction or propagation limit due to flow limitations in the burner preventing
higher strain rates.

75

Chapter 6

Conclusions

6.1 Premixed Hydrocarbon Edge-Flames

A counterflow slot-jet burner was used to characterize twin and single
premixed edge-flames for CH
4
and C
3
H
8
in terms of the global strain rate ( σ),
mixture strength, and Lewis number (Le). Results were presented as a function of
dimensionless stretch rate ε, related to σ, and dimensionless heat loss parameter κ.
Twin edge-flames exhibited two extinction limits, corresponding to a high- σ strain
induced limit and a low- σ heat loss induced limit. A similar low- σ limit is
identified for single edge-flames but at high- σ the single flames break apart due to
an apparent strain induced instability rather than extinction. This breaking limit
occurred at nearly the same value of ε for a given mixture family implying that the
laminar burning velocity and adiabatic flame temperature have little affect. At the
low strain limit, rich CH
4
-air mixtures in the twin configuration exhibit “short-
length” edge-flames while lean mixtures lead to retreating flames. Near the high
strain limit, CH
4
-air edge-flames retreat for all twin premixed conditions tested.
Single premixed edge-flames also exhibit “short-length” edge-flames near the low
strain limit and under no conditions exhibit retreating edges. Propagation rates
clearly show a strong dependence on Le and close-up images of the premixed edge-
flames show that high (low) Le lead to weaker (stronger) edge-flame propagation.
Using edge-flame propagation scaling derived by Reutsch et al. (1995) is

76
appropriate when careful consideration is taken into the flame configuration since
twin edge-flames are inherently stronger than single edge-flames due to their back-
to-back nature. Scaled propagation rates for twin edge-flames closely match
theoretical predictions by Daou et al. (2003) but currently there are few
comprehensive numerical works for single premixed edge-flames.

6.2 Low-Le Edge-Flames

The effects of diffusive-thermal instability on mixtures with very low Le in
the counterflow strained configuration were examined for twin premixed, single
premixed, and nonpremixed flames. Stability maps indicate the importance of heat
losses to the burner at low strain and the dependence of flame propagation on
global strain rate in relation to the burner configuration. As predicted, low Le
flames in the counterflow configuration form individual and connected tubes as a
means of existing beyond typical extinction strain rates for lean mixtures. For
decreasing strain, the tubes transition to wrinkled flames and ultimately into planar
flame structures. For nonpremixed flames, tube structures only occurred for a very
small range of stoichiometric mixture fraction and fuel concentration.
For each flame type, the propagation rate across the length of the burner
was measured as a function of the strain rate. Twin premixed flames and
nonpremixed flames showed a linearly increasing propagation speed with
increasing strain while single premixed flames exhibited a nonlinear increasing

77
trend. Interestingly, the flame shape had no noticeable impact on the impact of
strain rate propagation speed regardless of the flow configuration.

6.3 Future Research Possibilities

First and foremost, a more comprehensive numerical analysis is needed for
single premixed edge-flame propagation rates. While single flames have been
shown to propagate, the breaking limit at high strain has not been seen numerically.
Also, “short-length” flames have not been seen for a wide range of mixtures as has
been demonstrated experimentally.
While the experiments described above qualitatively match many of the
numerical models for edge-flame propagation, a few areas still require attention.
For instance, most models use a volumetric term to handle heat loss experienced by
the edge-flame. It is possible to compare experimental results to this method of
modelling heat loss but a more accurate approach would be to use a gradient driven
heat loss term instead. The most significant heat loss in the counterflow
experiments detailed above is that to the burners themselves. Since heat loss to the
burners is most significant at low strain rates as the flame(s) move closer to the jet
exists, a better heat loss model could lead to better correlation between model and
experiment at low strain regions. Twin premixed edge-flames predicted by Daou et
al (2003) produce “short-length” edge-flames at low strain but at a higher and very
small range of heat loss parameter than the experiments. This discrepancy should

78
be evaluated closely if edge-flame propagation rate data is to be used in turbulent
models.
Experimentally, mixtures with common Le for both twin and single
premixed edge-flames had nearly identical values of nondimensional strain rate at
their high strain limit. Twin flames extinguished after propagation rates became
negative (thus retreating) while single flames experienced the breaking flame
phenomena. These limits decreased as Le increased but at each Le the limit was
very close regardless of the stoichiometry. Few mixtures were tested in the study
presented here so more information is necessary if a clear relationship between
mixture, Le, and high strain limits can be determined. To accomplish this,
experiments will need to obtain higher strain rates in order to reach the high strain
limit of stronger, faster edge-flames.
Propagation rates for H
2
-air flames in the slot-jet counterflow burner could
only be obtained for a very small range of strain due to the speed and strength of
the mixtures. Even for very lean mixtures, the edge-flame propagation only
showed increasing values with increasing strain for twin premixed and
nonpremixed conditions. It is necessary to obtain data for the entire range of strain
for which the flames propagate so a burner with higher maximum strain is essential.
With information regarding both low strain and high strain limits for H2-air, the
experimental study of edge-flame propagation rates will be wide-ranging.

79

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Abstract (if available)

Abstract Propagation rates (Uedge) of various hydrocarbon premixed edge-flames are directly measured as a function of global strain rate, mixture strength, and Lewis number (Le). Using a counterflow slot-jet burner with electrical heaters at each end, both advancing (positive Uedge) and retreating (negative Uedge) edge-flames can be studied as they propagate across the long dimension of the burner. Results are presented for twin and single premixed edge-flames in terms of the effects of a nondimensional strain rate and nondimensional heat loss on a scaled propagation rate. Twin edge-flames exhibited two extinction limits, corresponding to a high-strain limit induced by strain and a low-strain heat loss induced limit. A similar low-strain limit is identified for single edge-flames but at high-strain the flames break apart due to an apparent strain induced instability rather than extinction. Propagation rates clearly show a strong dependence on Le and close-up images of the premixed edge-flames show that high (low) Le lead to weaker (stronger) edge-flame propagation. Overall, experimental findings agree closely with theoretical predictions. Additionally, the effects of diffusive-thermal instability on mixtures with very low Le in the counterflow strained configuration are examined. Stability maps and propagation rates for twin premixed, single premixed, and nonpremixed H2-air flames indicate the importance of heat losses to the burner at low strain and the dependence of flame propagation on global strain rate in relation to the burner configuration. As predicted, low Le flames in the counterflow configuration form individual and connected tubes as a means of existing beyond typical extinction strain rates. The tubes transition into wrinkled flames and then into planar flame structures as strain decreases. Propagation rates for the lean H2 flames generally increase with increasing strain and are not affected by the instability mode and resulting the flame shape.

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Asset Metadata

Creator Clayton, David Baldwin (author)

Core Title Experimental investigation of the propagation and extinction of edge-flames

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Mechanical Engineering

Publication Date 07/17/2007

Defense Date 06/28/2007

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag edge-flame,hydrocarbon,hydrogen,OAI-PMH Harvest,short-length,slot-jet

Language English

Advisor Ronney, Paul D. (committee chair), Egolfopoulos, Fokion N. (committee member), Lee, C. Ted Jr. (committee member)

Creator Email davidcla@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m624

Unique identifier UC1352943

Identifier etd-Clayton-20070717 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-527923 (legacy record id),usctheses-m624 (legacy record id)

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Dmrecord 527923

Document Type Dissertation

Rights Clayton, David Baldwin

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

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Repository Location Los Angeles, California

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