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Studies of methane counterflow flames at low pressures
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Studies of methane counterflow flames at low pressures
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Content
STUDIES OF METHANE COUNTERFLOW FLAMES AT LOW PRESSURES
by
Robert Roe Burrell
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(MECHANICAL ENGINEERING)
May 2017
Copyright 2017 Robert Roe Burrell
i
Table of Contents
Acknowledgements iv
Abstract 1
Chapter 1: Introduction
1.1 Background and Significance 2
1.2 Laminar Flames 4
1.2.1 Laminar Flame Speed and Scaling Analysis 9
1.2.2 Flame Stretch and Scaling Analysis 11
1.2.3 Flame Extinction and Scaling Analysis 13
1.3 Pressure Dependent Combustion Kinetics 15
1.4 Objectives 16
1.5 References 17
Chapter 2: Experimental Methods
2.1 Experimental Approach 19
2.2 Screened-Duct Straight-Tube Counterflow Burners 21
2.3 Gaseous Flow 24
2.4 Particle Image Velocimetry and Seeding Subsystem 26
2.5 Experimental Determination of Laminar Flame Speeds 32
2.6 Experimental Determination of Extinction Limits 35
2.7 Data Processing 36
2.8 References 40
ii
Chapter 3: Numerical Methods
3.1 Laminar Flame Speeds 42
3.2 Strained Counterflow Flames 43
3.3 Sensitivity Analysis 46
3.4 Integrated Reaction Flux Analysis 46
3.5 References 48
Chapter 4: Two-Dimensional Effects in Counterflow Methane Flames
4.1 Introduction 50
4.2 Experimental Approach 52
4.3 Modeling Approach 54
4.4 Results and Discussion 54
4.4.1 Flow Fields 54
4.4.2 Laminar Flame Speeds 56
4.4.3 Premixed Flame Extinction 58
4.4.4 Non-Premixed Flame Extinction 61
4.5 Concluding Remarks 62
4.6 Acknowledgements 63
4.7 References 64
iii
Chapter 5: Two Phase Modeling of Counterflow Flame Propagation and Extinction
5.1 Introduction 67
5.2 Modeling Approach 69
5.3 Results and Discussion 72
5.4 Concluding Remarks 77
5.5 References 79
Chapter 6: Methane Flame Propagation and Extinction at Low Pressures
6.1 Introduction 80
6.1.1 Pressure Dependent Combustion Kinetics 82
6.2 Experimental Approach 83
6.3 Modeling Approach 85
6.4 Results and Discussion 86
6.4.1 Boundary Phase Velocity Slip 86
6.4.2 Laminar Flame Speeds 87
6.4.3 Non-Premixed Flame Extinction 95
6.5 Concluding Remarks 100
6.6 References 102
Closing and Recommendations 104
iv
Acknowledgements
It takes a village to raise a PhD and I’d like to thank many of the people who have made
this thesis possible. Sam Graves, Silvana Martinez-Vargas, Irice Castro, Melissa Medeiros, and
the rest of the academic advisement staff in the Aerospace and Mechanical Engineering
Department for help with classes and ordering materials that I somehow turned into a working
experiment. Denise Galindo, Rodney Yates, Matt Gilpin, Wilson Chan, and Ben Bycroft with the
undergraduate laboratory instructional staff with whom I learned much despite many distressing
years as a teaching assistant. Professor Egolfopoulos for serving as my advisor, sharing resources,
vetting my work, and passing along job opportunities. Professor Ronney for his willingness to
share ideas and serve on my defense committee. Professor Spedding for providing me with
opportunities to contribute to the department and help with job applications. Professor Shing for
serving on my defense committee. Don Wiggins, the other skilled machinists in the USC machine
shop, and Paul Harris for interpreting my suspect technical drawings and turning them into what I
really needed. Brian and Cassie for supporting my sanity twice a week during TRX fitness classes.
Carolin and Jim Burrell for support and an extra bed whenever I needed it. My colleagues in
suffering including DJ Lee, Stelios Koumlis, Vyaas Gururajan, Jagan Jayachandran, Hugo
Burbano, Okjoo Park, Peter Veloo, Chris Xiouris, Jennifer Smolke, Laurel Paxton, Prabu
Sellappan, Trystan Madison, Ed Wagner, Orlando Delpino-Gonzalez, and Giacomo Castiglioni
for sharing ideas, happy hours, laughter, and fun.
Above all, a heartfelt appreciation to my parents, Cecilia Seykora Burrell and Dr. Robert
Lee Burrell, who dragged me kicking-and-screaming through childhood and into doctorhood.
I’m glad that I made it, but I sure as hell would not want to do it all over again.
1
Abstract
Methane is the smallest hydrocarbon molecule, the fuel most widely studied in fundamental
flame structure studies, and a major component of natural gas. Despite many decades of research
into the fundamental chemical kinetics involved in methane oxidation, ongoing advancements in
research suggest that more progress can be made. Though practical combustors of industrial and
commercial significance operate at high pressures and turbulent flow conditions, fundamental
understanding of combustion chemistry in flames is more readily obtained for low pressure and
laminar flow conditions.
Measurements were performed from 1 to 0.1 atmospheres for premixed methane/air and
non-premixed methane-nitrogen/oxygen flames in a counterflow. Comparative modeling with
quasi-one-dimensional strained flame codes revealed bias-induced errors in measured velocities
up to 8% at 0.1 atmospheres due to tracer particle phase velocity slip in the low density gas reacting
flow. To address this, a numerically-assisted correction scheme consisting of direct simulation of
the particle phase dynamics in counterflow was implemented. Addition of reactions describing
the prompt dissociation of formyl radicals to an otherwise unmodified USC Mech II kinetic model
was found to enhance computed flame reactivity and substantially improve the predictive
capability of computed results for measurements at the lowest pressures studied. Yet, the same
modifications lead to overprediction of flame data at 1 atmosphere where results from the
unmodified USC Mech II kinetic mechanism agreed well with ambient pressure flame data. The
apparent failure of a single kinetic model to capture pressure dependence in methane flames
motivates continued skepticism regarding the current understanding of pressure dependence in
kinetic models, even for the simplest fuels.
2
Chapter 1
Introduction
1.1. Background and Significance
In pursuit of a better world, combustion energy technologies are among the foremost
factors driving human development. So-called “fossil fuels” have historically dominated human
energy consumption because they were, and continue to be, relatively cheap and safe to obtain and
use. Concurrent with a widening appreciation for the consequences of mindless resource
consumption is the reality that the world will continue to rely on combustion energy for the
foreseeable future [1.1]. Much study and commentary has gone into the science and policy
defining responsible use of combustion sources, for which the reader is directed to better qualified
specialists (e.g. [1.2]). The focus of the present dissertation is to support a more complete
understanding of fundamental combustion physics which may be exploited by humankind to
optimize the use of combustion technologies.
Practical combustors typically operate at high pressures and in turbulent flows, conditions
which challenge existing methods for studying fundamental combustion processes. Instead,
laboratory scale experiments exploit systems with reduced complexity. For the study of chemical
kinetics, spatially homogenous systems including shock tubes [1.3], perfectly stirred reactors [1.4],
rapid compression machines [1.5], and turbulent plug flow reactors [1.6] can eliminate
complications arising from diffusive transport. Assessing kinetics in the presence of steep
temperature and species concentration gradients can be achieved in laminar flames, such as
stagnation flow flames, spherically expanding flames, and burner-stabilized flames [1.7].
Importantly, each of these experimental methods can be modeled with efficient computational
3
codes that are either spatially zero-dimensional, in the case of homogenous reactors, or one-
dimensional in the case of laminar flames. These codes permit the inclusion of detailed
descriptions of chemical kinetics and molecular transport which otherwise contribute toward the
intractable nature of fully three-dimensional and turbulent direct numerical simulations.
Experiments performed for this thesis took place in an opposed-jet stagnation flow, also
known as a counterflow, shown schematically in Figure 1.1. In a counterflow, two axisymmetric,
impinging burners of exit diameter 𝐷 𝑛𝑜𝑧𝑧 are separated by a distance 𝐿 𝑛𝑜𝑧𝑧 . The coordinate system
is defined for axial, 𝑥 , and radial, 𝑟 , components originating at the center of the exit plane for one
burner. Ideal burners are designed to produce plug flow velocity conditions, that is, a uniform
axial velocity, 𝑣 𝑥 , and zero radial velocity, 𝑣 𝑟 , across the burner exit. Impinging jets generate an
ellipsoidal stagnation pressure field whose isocontours are represented by dashed ellipses in Figure
1.1.
Figure 1.1: Schematic of a counterflow.
This apparatus generally permits study of laminar, planar, and axisymmetric premixed and
non-premixed flames spanning approximately two orders of magnitude in pressure from 0.1 to 10
4
atmospheres. For the present work, measurements were performed at atmospheric pressures and
below to determine the laminar flame speed, 𝑆 𝑢 0
, and extinction strain rate, 𝜅 𝑒𝑥𝑡 , in premixed flames
and 𝜅 𝑒𝑥𝑡 in non-premixed flames. Data were compared with computed results from quasi-one-
dimensional flame codes to understand fundamental controlling mechanisms including the role of
counterflow velocity field structure on measured data and the kinetics governing low pressure
flame propagation and extinction.
1.2. Laminar Flames
A laminar flame is an emergent combustion phenomenon resulting from high activation
energy kinetics and the conversion of chemical energy stored in the bonds of fuel molecules, and
in the presence of an oxidizer, to thermal energy and combustion products. A prototypical laminar
flame consists of a thin, reactive-diffusive zone where reactants are consumed and products formed
with heat release. Two limiting modes of combustion are possible depending on the degree of fuel
and oxidizer mixing prior to combustion.
In premixed flames the fuel and oxidizer are homogenously mixed prior to reaching the
flame and the resulting flame structure exhibits two zones, as shown in Figure 1.2. The upstream
side of the flame is a convective-diffusive transport zone, 𝛿 𝐷 , where fuel and oxidizer begin to
react due to diffusion of heat and intermediate species from the main reaction zone, 𝛿 𝑅 . Far
downstream from the main reaction zone, a convective-equilibrium zone contains high
temperatures and concentrations of combustion products. One significant consequence of this
flame structure is that premixed flames can propagate into fresh mixture. A convenient way to
approximate the flame thickness, 𝛿 𝑓 = 𝛿 𝐷 + 𝛿 𝑅 , can be obtained from the temperature profile. The
5
tangent line at the point of maximum temperature gradient is extrapolated to intersect the free
stream temperature on the upstream side and maximum temperature on the downstream side.
Finally, the upstream edge of 𝛿 𝑅 can be defined as the point of minimum temperature curvature,
min (
𝑑 2
𝑇 𝑑 𝑥 2
).
Figure 1.2: Structure of a freely propagating premixed flame.
The relative availability of fuel and oxygen in the mixture can be described by the
equivalence ratio, defined:
𝜙 =
(
𝑌 𝑓𝑢𝑒𝑙 𝑌 𝑂 2
)
𝑎𝑐𝑡𝑢𝑎𝑙 (
𝑌 𝑓𝑢𝑒𝑙 𝑌 𝑂 2
)
𝑠𝑡
(Eqn. 1.1)
6
where, 𝑌 𝑓𝑢𝑒𝑙 is the fuel mass fraction and 𝑌 𝑂 2
is the oxygen mass fraction. The numerator is the
actual mass ratio and the denominator is mass ratio at stoichiometric conditions. For a methane
and diatomic oxygen system the molar stoichiometric balance can be written:
CH
4
+ 2O
2
→ CO
2
+ 2H
2
O (Eqn. 1.2)
In Eqn. 1.2, 𝜙 = 1 and the mixture is called stoichiometric. There is a tendency for
complete consumption of reactants to form CO2 and H2O and nearly the highest possible flame
temperatures. For 𝜙 < 1, the mixture is called fuel-lean because there is excess O2 which passes
unreacted through the flame, absorbing thermal energy, and resulting in reduced flame
temperatures. For 𝜙 > 1, the mixture is called fuel-rich because there is insufficient O2 to convert
all carbon and hydrogen in the fuel to complete combustion products. Incomplete combustion
products, e.g. fuel fragments, H2, and CO, retain chemical energy instead of releasing it as heat.
Therefore, rich flames also tend to produce reduced flame temperatures. Engineers exploit control
over 𝜙 to design combustion systems which have different temperatures, flame strengths, and
product emission profiles.
In non-premixed flames, shown in Figure 1.3, the fuel and oxidizer are initially separated
so the reactants must mix before they can burn. There is no equilibrium zone and instead there are
two convective-diffusive transport zones on either side of the main reaction zone, 𝛿 𝐷 ,𝑂 for the
oxidizer side and 𝛿 𝐷 ,𝐹 for the fuel side. The flame front stabilizes near 𝑥 𝑠𝑡
, the position where the
diffusive flux of reactants exists in stoichiometric proportions, and thus non-premixed flames are
also called diffusion flames. Perturbation of the flame front toward either the fuel or oxidizer side
violates the requirement of stoichiometric reactant flux so that non-premixed flames cannot
propagate into fresh mixture. This quality gives non-premixed flames a safety advantage over
7
premixed flames in technological applications, but they do tend to burn at nearly maximum flame
temperatures which leads to less control over flame strength and product emissions.
Figure 1.3: Structure of a strained, counterflow, non-premixed flame in physical space formed by
N2 diluted CH4 supplied from the left boundary and pure O2 supplied from the right boundary.
Non-premixed flames can be characterized in mixture fraction space, 𝑍 , where:
𝑍 =
𝜈 𝑌 𝑓𝑢𝑒𝑙 − 𝑌 𝑂 2
+ 𝑌 𝑂 2,𝑜 𝜈 𝑌 𝑓𝑢𝑒𝑙 ,𝑓 + 𝑌 𝑂 2,𝑜
(Eqn. 1.3)
Here, 𝜈 ≡ (𝑌 𝑂 2
/𝑌 𝑓𝑢𝑒𝑙 )
𝑠𝑡
is the stoichiometric mass ratio, which for CH4/O2 reactants is
approximately 4, 𝑌 𝑓𝑢𝑒𝑙 is the local fuel mass fraction, 𝑌 𝑂 2
is the local oxidizer mass fraction, 𝑌 𝑂 2,𝑜
is the supplied diatomic oxygen mass fraction in the oxidizer stream, and 𝑌 𝑓𝑢𝑒𝑙 ,𝑓 is the supplied
fuel mass fraction in the fuel stream. For the unreacted fuel stream, 𝑍 = 1 by substitution of 𝑌 𝑂 2
=
0 into Eqn. 1.3. For the oxidizer stream, 𝑍 = 0, by substitution of 𝑌 𝑓𝑢𝑒𝑙 = 0 and noting that 𝑌 𝑂 2
=
𝑌 𝑂 2,𝑜 . The location of the flame front may be approximated by imposing stoichiometric reactant
8
composition, (𝜈 𝑌 𝑓𝑢𝑒𝑙 − 𝑌 𝑂 2
) = 0, upon which Eqn. 1.3 simplifies to the stoichiometric mixture
fraction:
𝑍 𝑠𝑡
=
𝑌 𝑂 2,𝑜 𝜈 𝑌 𝑓𝑢𝑒𝑙 ,𝑓 + 𝑌 𝑂 2,𝑜
(Eqn. 1.4)
which depends only on the unreacted boundary compositions of the fuel and oxidizer streams.
Transforming Figure 1.3 from physical space to mixture fraction space results in Figure 1.4:
Figure 1.4: Structure of a strained, counterflow, non-premixed flame in mixture fraction space
formed by N2 diluted CH4 supplied from the right boundary and pure O2 supplied from the left
boundary.
Thus, 𝑍 and 𝑍 𝑠𝑡
may be used to characterize non-premixed flames analogously to 𝜙 in premixed
flames. In fact, 𝑍 and 𝜙 are related by:
𝜙 =
𝑍 (1− 𝑍 )
(1− 𝑍 𝑠𝑡
)
𝑍 𝑠𝑡
(Eqn. 1.5)
It follows that a stream containing fuel but no oxidizer, i.e., 𝑍 = 1, corresponds to 𝜙 = ∞ and an
oxidizer-only reactant stream, i.e., 𝑍 = 0, corresponds to 𝜙 = 0. Near the flame front, 𝑍 = 𝑍 𝑠𝑡
9
and 𝜙 = 1. It should be noted that many ostensibly non-premixed combustors may locally be
partially premixed due to reactant mixing. Such systems can exhibit characteristics of both
premixed and non-premixed flames.
1.2.1. Laminar Flame Speed and Scaling Analysis
Since premixed flames can propagate into fresh mixture, one very important global
property is the flame burning velocity which is an indicator of the exothermicity, reactivity, and
diffusivity of the combustible mixture. The laminar flame speed, 𝑆 𝑢 0
, is defined on the unburned
side of a steady, one-dimensional, planar, adiabatic, and stretch-free premixed flame propagating
into an infinite domain, shown schematically in Figure 1.5. It has been shown that:
𝑆 𝑢 0
~√𝜔 √𝐷
(Eqn. 1.6)
where 𝜔 is the overall reactivity and 𝐷 is the overall diffusivity (e.g., [1.8]). Fundamentally, 𝑆 𝑢 0
reflects the mass burning rate per unit flame front area, 𝑚 0
, but it is often easier to measure velocity
and thus 𝑆 𝑢 0
is more commonly reported than 𝑚 0
. As shown in Figure 1.5 the two are related
through the unburned mixture mass density, 𝜌 𝑢 . On a burned side of the flame, 𝑚 0
relates the
burned gas flame speed, 𝑆 𝑏 0
, and the burned gas mass density, 𝜌 𝑏 0
.
Flames strictly conforming to the definition required for 𝑆 𝑢 0
are not achieved in
experiments. In general, stable flames are produced with the assistance of a mechanism external
to the flame such as aerodynamic stretch or heat loss. These external influences modify the mass
burning rate and flame speed away from their ideal values. State-of-the-art techniques for
experimentally determining 𝑆 𝑢 0
s center on the systematic quantification of the effect of an external
stabilization mechanism to characterize their influence. In stagnation flow flames (e.g., [1.10])
10
and spherically expanding flames (e.g., [1.11]), flame response to aerodynamic stretch may be
measured and extrapolated to zero stretch. In heat-flux method flames (e.g., [1.12]), flame
response to heat loss/gain may be measured and then interpolated to adiabatic conditions. In each
case 𝑆 𝑢 0
is measured indirectly and therefore subject to the nature of the extrapolation/interpolation
method employed.
Figure 1.5: Schematic of a premixed, steady, one-dimensional, planar, adiabatic, and stretch-free
flame from Ref. 1.9.
Since measured 𝑆 𝑢 0
s include information about a reacting mixture’s exothermicity,
reactivity, and diffusivity, they are robust targets for kinetic model validation (e.g., [1.10]) and
uncertainty minimization (e.g., [1.13]). It is necessary, but insufficient, for computations
performed with a properly constructed kinetic model to predict measured 𝑆 𝑢 0
s over the range of
conditions intended for its use. The description of reaction rates in kinetic models contain many
parameters, on the order of hundreds or thousands for CH4 oxidation, and only a few of these have
been measured or calculated with high confidence. The vast majority of reaction rates are
estimated. However, it is known that the chemistry controlling flame propagation depends mostly
on a relatively narrow subset of all possible reactions. Uncertainty in many reactions has negligible
impact on computed 𝑆 𝑢 0
s.
11
1.2.2. Flame Stretch and Scaling Analysis
The concept of flame stretch, 𝜅 , was introduced by Bela Karlovitz [1.14] and generalized
by Forman Williams [1.15] as the rate of fractional flame surface growth/compression:
𝜅 =
1
𝐴 𝑑𝐴 𝑑𝑡
(Eqn. 1.7)
It can be decomposed into two fluid dynamic sources [1.16]:
𝜅 = ∇
𝑡 ∙ 𝑣 𝑡 ⃗⃗⃗ + (𝑉 ⃗
∙ 𝑛⃗ )(∇
t
∙ 𝑛⃗ )
(Eqn. 1.8)
where ∇
𝑡 is the tangential (to the flame surface) gradient operator, 𝑣 𝑡 ⃗⃗⃗ is the tangential velocity
vector, 𝑉 ⃗
is the flame surface velocity vector, and 𝑛⃗ is the surface normal vector oriented toward
the unburned gas. The first term in Eqn. 1.8 represents flow nonuniformity, called strain rate, and
the second represents a flame surface that is both unsteady (𝑉 ⃗
∙ 𝑛⃗ ≠ 0) and curved (∇
t
∙ 𝑛⃗ ≠ 0).
Stagnation flow flames in an axisymmetric counterflow, which are steady (𝑉 ⃗
∙ 𝑛⃗ = 0) and planar
(∇
t
∙ 𝑛⃗ = 0), experience positive stretch from strain rate (∇
𝑡 ∙ 𝑣 𝑡 ⃗⃗⃗ ≠ 0). Along the stagnation
streamline, ∇
𝑡 ∙ 𝑣 𝑡 ⃗⃗⃗ = 2
𝑑 𝑢 𝑟 𝑑𝑟
and with continuity in cylindrical coordinates:
𝜅 = −
𝑑 𝑣 𝑥 𝑑𝑥
(Eqn. 1.9)
To determine 𝑆 𝑢 0
s in a counterflow, strained flame propagation velocities are measured as
a function of 𝜅 at some reference location in the flow field and extrapolated to 𝜅 = 0 𝑠 −1
. Thus,
counterflow experiments should be performed for the smallest possible magnitude of 𝜅 to limit
uncertainty and bias resulting from extrapolation. Practically, small magnitude in 𝜅 is achieved
by either low burner exit velocities or large burner separation distances. In the former case, the
strained flame speed can eventually overcome the burner exit velocity whereupon flashback occurs
and the flame propagates into the burner tube. In the latter case, flames eventually transition to a
negatively stretched Bunsen flame. Exploiting the transition from a positively stretched
12
counterflow flame to a negatively stretched Bunsen flame has been explored as a method to
directly measure 𝑆 𝑢 0
without extrapolation [1.17].
Stretch modifies flame structure in a manner dependent on the mixture’s Lewis number:
𝐿𝑒 ≡
𝛼 𝐷
(Eqn. 1.10)
where 𝛼 and 𝐷 are the characteristic mixture thermal and mass diffusivities, respectively. For
sufficiently lean or rich flames in a mixture dominated by inert N2, as for flames burning in air, 𝛼
is determined by N2 and 𝐷 by the deficient reactant. Both 𝛼 and 𝐷 scale approximately with the
inverse square root of species molecular weight so:
𝐿𝑒 ≅ √
𝑀 𝑊 𝑑𝑒𝑓 𝑀 𝑊 𝑁 2
(Eqn. 1.11)
where 𝑀𝑊
𝑑𝑒𝑓 is the molecular weight of the deficient reactant and 𝑀 𝑊 𝑁 2
the molecular weight
of N2.
For positively stretched counterflow flames, shown schematically in Figure 1.6, diffusive
transport occurs normal to the flame surface while convective transport occurs along streamlines.
Heat from the flame diffuses upstream and some is lost to external streamlines while reactant mass
is gained from external streamlines. Thus, 𝐿𝑒 > 1 means that the heat loss effect dominates and
flames are weakened compared to the stretch-free case. Conversely, for 𝐿𝑒 < 1 the reactant gain
effect is more important and the flame is strengthened. Additionally, preferential diffusion of
reactants occurs such that the lighter reactant transports more efficiently from external streamlines
into the flame and the local equivalence ratio is modified compared to the free stream value.
13
Figure 1.6: Schematic of aerodynamically stretched planar flame from Ref. 1.9 showing
convective transport along streamlines and diffusive transport normal to flame surface.
1.2.3. Flame Extinction and Scaling Analysis
Both premixed and non-premixed flames are susceptible to spontaneous quenching of
chemical reactions leading to flame extinction when the Damköhler number, defined as the ratio
of characteristic flow transport time, 𝜏 𝐿 , to chemical reaction time, 𝜏 𝐶 , approaches unity:
𝐷𝑎 ≡
𝜏 𝐿 𝜏 𝐶 → 1
(Eqn. 1.12)
Premixed flames can propagate to adjust their position to match local flow conditions.
Increased flow rate in a counterflow leads to increased flame stretch and pushes the flame closer
to the stagnation plane. Extinction results either from reduced flame temperatures due to excessive
heat loss when 𝐿𝑒 > 1 or insufficient chemical residence time as the flame becomes restrained
against the stagnation plane when 𝐿𝑒 ≤ 1 [1.8]. The Karlovitz number, 𝐾𝑎 , is the inverse of 𝐷𝑎
and can be described for premixed counterflow flames in terms of the local flame thickness, 𝛿 𝐹 , a
reference flame propagation speed, 𝑆 𝑢 ,𝑟𝑒𝑓 , and reference strain rate, 𝜅 𝑟𝑒𝑓
:
14
𝐾𝑎 =
𝛿 𝐹 𝑆 𝑢 ,𝑟𝑒𝑓
𝜅 𝑟𝑒𝑓
(Eqn. 1.13)
Appropriate local definitions of 𝑆 𝑢 ,𝑟𝑒𝑓
and 𝜅 𝑟𝑒𝑓
, defined in Figure 2.13, have been shown to
produce 𝐾 𝑎 𝑒𝑥𝑡 ≅ 1 at the extinction state for a wide range of fuel types, equivalence ratios,
pressures, and unburned reactant temperatures [1.18]. Using global properties instead as a first
approximation,
𝛿 𝐹 𝑆 𝑢 ,𝑟𝑒𝑓 ⁄ ≅
𝐷 (𝑆 𝑢 0
)
2
⁄
, where 𝐷 is the mixture characteristic diffusivity, and given
𝑆 𝑢 0
~√𝜔 , then 𝜅 𝑟𝑒𝑓
at extinction scales with the overall reactivity:
𝜅 𝑒𝑥𝑡 ~𝜔 (Eqn. 1.14)
Thus, premixed flame extinction measurements give insight into the premixed flame chemistry
and are useful for validating kinetic models.
Non-premixed flames, which cannot propagate, are not able to adjust their position based
on flow rate and the flame location is instead determined by where reactant flux satisfies the
stoichiometric condition. Extinction occurs due to thinning of the reaction zone leading to
incomplete reaction. In counterflow flames, the non-premixed flame thickness, and thus available
residence time, is proportional to the inverse square root of the reference strain rate, 𝛿 𝐹 ~𝜅 𝑟𝑒𝑓
−
1
2
[1.8]. The characteristic flow time scale, 𝜏 𝐿 , in non-premixed flames may be described by the
inverse of the scalar dissipation rate evaluated at the stoichiometric mixture fraction, i.e. 𝜏 𝐿 ≡ 𝜒 𝑠𝑡
−1
,
where 𝜒 𝑠𝑡
≅ 2𝜈 |
𝑑𝑍
𝑑𝑥
|
𝑠𝑡
2
, 𝜈 is the mixture kinematic viscosity, 𝑍 is the mixture fraction, and 𝑥 the
spatial coordinate through the flame along the stagnation streamline. Like premixed flame
extinction, non-premixed flame extinction is strongly sensitive to chemical kinetics (e.g., [1.19]),
thus non-premixed flame extinction measurements give insight into non-premixed flame chemistry
and may also be used for validating kinetic models.
15
1.3. Pressure Dependent Combustion Kinetics
The reaction rate of an elementary chemical reaction, 𝜔 𝑒𝑙𝑒𝑚 , is traditionally described to
depend on pressure in two ways. The first, based on the idea that reactants must collide and
physically interact before reaction can occur, is codified in the Law of Mass Action which states
that 𝜔 𝑒𝑙𝑒𝑚 is proportional to the product of the concentrations of the reactants. Consequently,
𝜔 𝑒𝑙𝑒𝑚 ~𝑝 𝑚 , where 𝑝 is pressure and 𝑚 is the reaction molecularity. For ter-, bi-, and unimolecular
reactions, 𝑚 = 3, 2, and 1, respectively. Given this pressure dependence, rates of three body
reactions can become negligible compared to bi- and uni-molecular reactions for sufficiently low
pressures or even dominant for sufficiently high pressures. The second component of pressure
dependence is through the rate coefficient, 𝑘 , which describes the nature of energy transfer
between and within colliding species. For some reactions 𝑘 is independent of pressure while for
others the pressure dependence is an active area of research [1.20]. Uncertainty in 𝑘 can be a
factor of five or greater [1.21].
Study of low pressure flames occurs mainly in the context of chemical speciation and flame
structure measurements in premixed burner-stabilized flames (e.g. [1.7] and [1.22]). These
measurements offer a detailed picture into the relative concentrations of various reactant,
intermediate, and product species through the flame. A recent example aided the development of
a kinetic model for the butanol isomers [1.23]. However, there is strong evidence that intrusive
flame sampling introduces experimental uncertainties [1.24]. Thus, kinetic models developed with
the assistance of low pressure flame data may be contaminated by these experimental uncertainties
leading to challenges when extending the kinetic model to higher pressures relevant for practical
combustors.
16
1.4. Objectives
There are two main objectives for the present thesis. The first is to reevaluate the use of
the counterflow configuration for flame propagation and extinction measurements and establish
best practices for obtaining high quality data. Specifically, the role of flow field structure on the
applicability of quasi-one-dimensional computational modeling. Comparisons between
measurements and quasi-one-dimensional modeling results are extensively used for interpreting
counterflow flame data and assisting with kinetic model validation and uncertainty minimization.
It is essential that uncertainties and biases in reported data are well characterized.
The second objective is to develop a method for flame propagation and extinction
measurements in low pressure counterflow flames. Extending counterflow flame measurements
to these challenging conditions is motivated in part by the uncertainties encountered in low
pressure flame speciation measurements. Toward this goal, the quality of flow velocity
measurement by particle velocimetry methods was found to suffer unacceptable biases leading to
the development of a process for data correction. Measurements of propagation velocities for
CH4/air flames and extinction states in non-premixed CH4-N2/O2 flames are reported at pressures
down to 0.1 atm. These measurements are expected to be useful for kinetic model validation and
reaction rate uncertainty minimization.
17
1.5. References
[1.1] Annual Energy Outlook 2016, U.S. Dept. of Energy, Energy Information
Administration, 2016. Available online: www.eia.gov/outlooks/aeo
[1.2] G. E. Likens, Front Ecol. Environ. 2010 8(6), e1-e9.
[1.3] R. K. Hanson, D. F. Davidson, Prog. Energy Combust. Sci. 44 (2014) 103-114.
[1.4] P. S. Veloo, P. Dagaut, C. Togbe, G. Dayma, S. M. Sarathy, C. K. Westbrook, F. N.
Egolfopoulos, Proceed. Combust. Inst. 34 (2013) 599-606.
[1.5] C. J. Sung, H. J. Curran, Prog. Energy Combust. Sci. 44 (2014) 1-18.
[1.6] F. L. Dryer, F. M. Haas, J. Santner, T. I Farouk, M. Chaos, Prog. Energy Combust. Sci.
44 (2014) 19-39.
[1.7] F. N. Egolfopoulos, N. Hansen, Y. Ju, K. Kohse-Höinghaus, C. K. Law, F. Qi, Prog.
Energy Combust. Sci. 43 (2014) 36-67.
[1.8] C. K. Law, Combustion Physics, Cambridge University Press, Cambridge, 2006.
[1.9] C. K. Law, Proceed. Combust. Inst. 22 (1988) 1381-1402.
[1.10] P. S. Veloo, Y. L. Wang, F. N. Egolfopoulos, C. K. Westbrook, Combust. Flame 157
(2010) 1989-2004.
[1.11] J. Jayachandran, A. Lefebvre, R. Zhao, F. Halter, E. Varea, B. Renou, F. N.
Egolfopoulos, Proceed. Combust. Inst. 35 (2015) 695-702.
[1.12] Bosschaart, K. J., Analysis of the heat flux method for measuring burning velocities,
PhD Dissertation, Technische Universiteit Eindhoven (2002) DOI: 10.6100/IR560010,
accessed Nov. 2016.
[1.13] O. Park, P. S. Veloo, D. A. Sheen, Y. Tao, F. N. Egolfopoulos, H. Wang, Combust.
Flame 172 (2016) 136-152.
[1.14] B. Karlovitz, D. W. Denniston, Jr., D. H. Knapschaefer, F. E. Wells, Symp. (Int’l) on
Combust. 4 (1953) 613-620.
[1.15] F. A. Williams, AGARD Conference Proceedings 164 (1975).
[1.16] S. H. Chung and C. K. Law, Combust. Flame 55 (1984) 123-125.
[1.17] C. M. Vagelopoulos, F. N. Egolfopoulos, Proceed. Combust. Inst. 27 (1998) 513-519.
[1.18] E. S. Cho, S. H. Chung, T. K. OH, Combust. Sci. and Tech. 178 (2006) 1559-1584.
18
[1.19] C. Ji, Y. L. Wang, F. N. Egolfopoulos, J. Propul. Power, 27-4 (2011) 856-863.
[1.20] M. J. Pilling, Science 34, 6214 (2014) 1183-1184.
[1.21] D. L. Baulch, C. J. Cobos, R. A. Cox, C. Esser, P. Frank, Th. Just, J. A. Kerr, M. J.
Pilling, J. Troe, R. W. Walker, J. Warnatz, J. Phys. Chem. Ref. Data 21, 411 (1992)
411-734.
[1.22] N. Hansen, T. A. Cool, P. R. Westmoreland, K. Kohse-Höinghaus, Prog. Energy
Combust. Sci. 35 (2009) 168-191.
[1.23] A. Frassoldati, R. Grana, T. Faravelli, E. Ranzi, P. Oßwald, K. Kohse-Höinghaus,
Combust. Flame 159 (2012) 2295-2311.
[1.24] V. Gururajan, F. N. Egolfopoulos, K. Kohse-Höinghaus, Proceed. Combust. Inst. 35
(2015) 821-829.
19
Chapter 2
Experimental Methods
2.1. Experimental Approach
All experiments were performed in an axisymmetric counterflow system, depicted
schematically in Figure 2.1, at either ambient pressure and unburned reactant temperature or for
subatmospheric pressures and elevated reactant temperatures. Between the two opposed-flow
burner nozzles, a stagnation flow was established where flames were stabilized.
Figure 2.1: Schematic of the experimental system arranged for a twin, premixed flame
configuration.
The opposed-jet burners were housed in a chamber with pressure monitored by a digital
absolute pressure gauge (Omega DPG100AD-100G) and maintained by supplying controlled
nitrogen in-flow (Gilmore Liquid Air UN 1977) to provide an inert environment to suppress
20
secondary reaction away from the flames and controlled out-flow of exhaust gases through a
vacuum pump (Sogevac® SV40 B). Air oxidizer was supplied by an in-house compressor, pure
oxygen oxidizer by bottled O2 (Gilmore Liquid Air Extra Dry Grade 99.5%), and fuel by bottled
methane (Gilmore Liquid Air CP Grade 99%). Flowing water through a copper coil wrapped
around the upper burner prevented overheating from the flames due to buoyancy. The
measurement diagnostic was planar, two-dimensional particle velocimetry in the symmetry plane
extending from the bottom burner exit to the top burner exit. A pneumatic nebulizer generated an
oil aerosol within a spray chamber which was then passed through an inline particle filter. The
particle delivery and particle velocimetry subsystems are discussed more in-depth in section 2.4.
Figure 2.2: Color enhanced schematic of experimental pressure chamber with counterflow burners
installed including (left) side view, (center) front view, and (right) oblique view.
Two important length scales for a counterflow are shown in Figure 2.3, the nozzle diameter,
𝐷 𝑛𝑜𝑧𝑧 , and the separation distance between the two burners, 𝐿 𝑛𝑜𝑧𝑧 . The aspect ratio
𝐿 𝑛𝑜𝑧𝑧 𝐷 𝑛𝑜𝑧𝑧 ⁄
has an important influence on the flow structure between the burners. For example, the quasi-one-
dimensional stagnation flow codes used for computing flame structure as described in Chapter 3
21
strictly apply in the limit 𝐷 𝑛𝑜𝑧𝑧 → ∞. In experiments this can be reasonably well approximated
for
𝐿 𝑛𝑜𝑧 𝑧 𝐷 𝑛𝑜𝑧𝑧 ⁄ ≈ 1. To suppress flow instability at moderate-to-high Reynolds number, 𝐷 𝑛𝑜𝑧𝑧 is
limited to sizes on the order of a few centimeters or smaller. To allow sufficient room for flow
velocity measurement upstream from the flame front, 𝐿 𝑛𝑜𝑧 𝑧 must be on the order of centimeters
or larger. When
𝐿 𝑛𝑜𝑧𝑧 𝐷 𝑛𝑜𝑧𝑧 ⁄ ≫ 1 the flow structure resembles two free jets and stabilized flames
are of the Bunsen rather than stagnation type, but
𝐿 𝑛𝑜𝑧𝑧 𝐷 𝑛𝑜𝑧𝑧 ⁄ < 1 can produce strong pressure
field feedback into the burners and distort the flow structure, as discussed in Chapter 4. Typical
values reported in the literature range 0.5 <
𝐿 𝑛𝑜𝑧𝑧 𝐷 𝑛𝑜𝑧𝑧 ⁄ < 1.5.
Figure 2.3: Schematic of (left) symmetric, twin, premixed, CH4/air flames, and (right) a non-
premixed CH4-N2/air flame in counterflow. The axisymmetric coordinate system origin is defined
along the system centerline at the exit of one burner.
2.2. Screened-Duct Straight-Tube Counterflow Burners
Figure 2.4 and Figure 2.5 show the burners used in the present work. Starting from the
upstream side, an end cap with a NPT fitting accepted reactants and sealed the burner tube holder
to the upstream housing. The inner diameter of the burner tube holder sealed around the outer
22
diameter of the burner tube via O-rings and was held in place with set screws. The upstream
housing was sealed to the mounting flange and had several tapped holes for introduction of coflow
inert gas as well as power leads for heating cable (McMaster-Carr 4550T162) wrapped around the
burner tube. Temperature was monitored by a surface-mounted K-type thermocouple (McMaster-
Carr 3648K34) between the outer surface of the burner tube and inner surface of the heating cable
and was controlled (Omega CN9110A) to maintain a desired exit temperature. The downstream
housing sealed to the opposite side of the mounting flange and to the coflow cap. Between the
coflow cap and downstream housing was a perforated plate which fit around the outer diameter of
the burner tube, locating the burner tube within the assembly. A nitrogen coflow issued from an
approximately ~1 mm thick annular opening between the downstream end of the burner tube and
coflow cap to isolate the main jet from the quiescent environment.
All burner materials were made from 304 stainless steel, except for the burner tube which
was 316 alloy and upstream housing which was 303 alloy. Pressure tightness and isolation of
reactants was achieved with appropriately sized Buna-N O-rings at every surface interface.
Figure 2.4: Color enhanced side view schematics of counterflow burner including (top) view
detailing individual components and (bottom) configuration as fully assembled.
23
Figure 2.5: Color enhanced oblique view schematics of counterflow burner components.
The downstream end of the burner tube was designed to include a threaded cap, as shown
in Figure 2.6. Compressed between the burner cap and main tube were several flow conditioning
screens and square-profile Viton O-rings. Starting from the upstream side, the flow conditioning
section was configured: O-ring, 100-mesh screen, 200-mesh screen, O-ring, and finally 100-mesh
screen against the burner exit. Both screen types were made of precision mesh 304 stainless steel.
The 100-mesh (McMaster-Carr 9656T18) was made with 0.0055 inch openings and 0.0021 inch
wire diameters and the 200-mesh (McMaster-Carr 9656T19) with 0.0029 inch openings and
0.0021 inch wire diameters. A distance of 5𝐷 𝑛𝑜𝑧𝑧 upstream from the burner exit and separated by
2𝐷 𝑛𝑜𝑧𝑧 was an additional pair of 60-mesh 304 stainless steel screens held in place by friction. The
60-mesh screen (McMaster-Carr 85385T95) was made with 0.009 inch openings and 0.0075 inch
wire diameters. Two burner sizes were used, 𝐷 𝑛𝑜𝑧𝑧 = 21 and 28 mm.
24
Figure 2.6: Schematic of downstream end of the burner tube with flow conditioning screen
configuration.
2.3. Gaseous Flow
Each reactant gas flow was metered by an independent gas delivery system composed of a
choked-flow nozzle (O’Keefe Controls Co.®) paired with a digital pressure gauge (Omega®
DPG1000B-100G) and calibrated using either a wet gas meter (Sinagawa Corporation® W-NK),
dry gas meter (Bios® Definer 220), or a bubble flow meter. The flow rate through a choked orifice
depends only on the upstream absolute pressure and is independent of downstream pressure so that
downstream disturbances do not affect the delivery of reactants.
Given a gage reading on a pressure gauge, 𝑝 𝑔 , the measured flow rate through the flow
meter, 𝑉 ̇ , can be scaled to reference conditions, 𝑉 ̇ 𝑟𝑒𝑓 , via:
25
𝑉 ̇ 𝑟𝑒𝑓 = 𝑉 ̇ 𝑇 𝑟𝑒𝑓
𝑝 𝑟𝑒𝑓
𝑝 𝑚𝑒𝑡𝑒𝑟 ,𝑎 𝑇 𝑚𝑒𝑡𝑒𝑟
(Eqn. 2.1)
where reference conditions were 𝑇 𝑟𝑒𝑓
= 298.15 K and 𝑝 𝑟𝑒𝑓
= 1 atm, 𝑇 𝑚𝑒𝑡𝑒𝑟 is the gas absolute
temperature in the flow meter, and 𝑝 𝑚𝑒𝑡𝑒𝑟 ,𝑎 is the gas absolute pressure in the flow meter calculated
by:
𝑝 𝑚𝑒𝑡𝑒𝑟 ,𝑎 = 𝑝 𝑎𝑚𝑏 ,𝑎 + 𝑝 𝑚𝑒𝑡𝑒𝑟 ,𝑔 − 𝑐 𝑣𝑎𝑝 𝑝 𝑣𝑎𝑝 (Eqn. 2.2)
Here, 𝑝 𝑎𝑚𝑏 ,𝑎 is the absolute ambient pressure, 𝑝 𝑚𝑒𝑡𝑒𝑟 ,𝑔 is the gage pressure inside the flow meter,
𝑝 𝑣𝑎𝑝 is the vapor pressure of water at 𝑇 𝑚𝑒𝑡𝑒𝑟 , and 𝑐 𝑣𝑎𝑝 is a constant that accounts for the efficiency
of water vapor uptake into the gas. For the dry gas meter 𝑐 𝑣𝑎𝑝 = 0 due to the lack of water in the
flow meter, while for the wet gas meter 𝑐 𝑣𝑎𝑝 = 0.9 and for the bubble meter 𝑐 𝑣𝑎𝑝 = 0.8.
For each gas flow, a set of 𝑉 ̇ 𝑟𝑒𝑓
spanning a range of 𝑝 𝑎 was measured to produce a linear
calibration curve for use in experiments:
𝑉 ̇ 𝑟𝑒𝑓 = 𝑚 𝑝 𝑎 + 𝑏
(Eqn. 2.3)
where 𝑚 is the slope and 𝑏 the offset of the curve fit and 𝑝 𝑎 = 𝑝 𝑎𝑚𝑏 ,𝑎 + 𝑝 𝑔 is the absolute pressure
at the pressure gauge upstream of the choked orifice. A graphical example of Eqn. 2.3 is shown
in Figure 2.7. Using 𝑚 and 𝑏 determined for Eqn. 2.3, any desired 𝑉 ̇ 𝑟𝑒𝑓
within the range of
calibrated 𝑝 𝑎 may be chosen for experiments. Finally, 𝑉 ̇ 𝑟𝑒𝑓 was adjusted to experimentally realized
temperature and pressure at the burner exit, 𝑇 𝑏𝑢𝑟𝑛 and 𝑝 𝑏𝑢𝑟𝑛 , respectively, via:
𝑉 ̇ 𝑏𝑢𝑟𝑛 = 𝑉 ̇ 𝑟𝑒𝑓 𝑇 𝑏𝑢𝑟𝑛 𝑝 𝑏𝑢𝑟𝑛 𝑝 𝑟𝑒𝑓 𝑇 𝑟𝑒𝑓
(Eqn. 2.4)
26
Figure 2.7: Example of flow rate calibration curve.
2.4. Particle Image Velocimetry and Seeding Subsystem
Particle velocimetry methods for flow field characterization are well established in
counterflow flames and include laser Doppler velocimetry (LDV) (e.g., [2.1]-[2.3]), particle
image velocimetry (PIV) (e.g., [2.4] and [2.5]), and particle streak velocimetry (PSV) (e.g., [2.6]).
The present work continues in this tradition with flow velocity measurement by PIV.
Minimum requirements for a PIV system include a light source, camera for image
acquisition, and flow seeder. The general concept of PIV, shown in Figure 2.8, is to capture images
separated by a well-defined time interval, 𝑑𝑡 , and determine the spatial displacement of seeding
particles over this interval. From the known spatial displacement and time interval velocity can
be calculated. One crucial assumption is that the particle displacements over 𝑑𝑡 should be small
27
enough to be nearly a simple linear translation. That is, PIV typically obtains no information about
the path seeding particles take over the time interval, only the starting and ending locations.
First image Second image Displacement field
𝑑𝑡
+
→
Figure 2.8: Conceptualization of PIV-based determination of spatial displacement field for an
artificially-imposed image shift of -3 pixels in the horizontal and +5 pixels vertical directions.
Instead of tracking individual particles, a method known as particle tracking velocimetry
(PTV), PIV is subset of correlation imaging velocimetry (CIV) which uses correlation and pattern
matching algorithms to determine the displacement of small patches of image texture. Thus, one
displacement vector is determined for each small patch of image texture and the result over an
entire image is typically a uniform Eulerian grid of displacement vectors. Good image texture can
be achieved by imaging bright particles against a dark background and using as much of the
dynamic range of the camera sensor as possible without over-exposing the image. Fincham and
Spedding [2.7] provided an excellent overview of PIV in experimental fluid dynamics.
Digital cameras acquire images on a two-dimensional array of discrete pixels where the
image information is stored as a matrix of integer values representing the light intensity at each
pixel location, shown in Figure 2.9. It is the task of the correlation algorithm to find the most
likely displacement of small patches of texture, for example that defined within the red square of
Figure 2.9. The source of image texture is not limited to spherical seeding particles and even
28
streaks of light/darkness, reflections, distortions from the optics, spurious particles, or other
interference may contribute, usually with negative consequences. In principle, any source of
image texture in acquired images will affect the results.
Figure 2.9: Demonstration of image texture for an 8-bit image with (left) full frame image and
(right) integer intensity values for area bounded by red square. Each pixel in an 8-bit image may
assume 2
8
= 256 possible intensity values.
A Q-switched dual-head Big Sky® Ultra Nd:YAG laser frequency doubled to emit 532 nm
light was used in all experiments. The collimated light was diverged with a spherical biconvex
lens and then converged with a cylindrical plano-concave lens to generate a laser line coincident
with the plane of symmetry between the counterflow burners. Images were acquired on a PCO®
PixelFly 12-bit CCD camera with 1392 x 1040 pixels of resolution fitted with a 200 mm Nikon
Micro-NIKKOR f/4D lens. A Thorlabs® FL-532-3 bandpass filter was installed between the
camera lens and CCD array to filter out extraneous light. Resulting resolution in real space was
between 0.01284 and 0.03623 mm per pixel. Timing synchronization between the laser and
camera, including Q-switching and flash lamp triggering, was facilitated by a LaVision®
29
Programmable Timing Unit (PTU) Version 9. Acquired images were processed with LaVision®
DaVis 7.2 and displacement fields determined by two-dimensional cross-correlation.
Silicone oil (Alfa Aesar CAS# 63148-62-9) flow seeding particles were introduced via a
Meinhard® HEN-170-A0.3 pneumatic nebulizer into a conical spray chamber, shown in Figure
2.10. The high velocity gas and particle mixture exiting the nebulizer impinged upon the bottom
surface of the spray chamber to remove the largest aerosol particles by impact. Subsequently, the
two-phase mixture passed through a 5 μm inline particle filter (McMaster-Carr® 4414K71) before
combining with the main reactant flow.
Figure 2.10: Schematic of seeding delivery subsystem.
It has been claimed that HEN-type nebulizers produce sub-micrometer sized seeding
particles [2.8]. This statement was analyzed in view of two arguments. First, light scattering
efficiency of a spherical particle drops off sharply when the particle diameter is equal to or smaller
30
than the wavelength of the incident light. The scattered light power by a spherical particle is
defined:
𝑃 𝑠 = 𝐶 𝑠 𝐼 0
(Eqn. 2.5)
where 𝐶 𝑠 is scattering cross section and 𝐼 0
is the incident light intensity. For incident light at 532
nm, the right axis of Figure 2.11 shows the scattered power for spherical particles with an index
of refraction 𝑛 = 1.6 [2.9]. Second, the HEN-type nebulizer used in the present thesis is known
to produce particles diameters less than 15 μm [2.10]. Further, if all particles larger than 5 μm
were eliminated by impact on the spray chamber and within the inline filter, then the particle size
distribution can be estimated as on the left axis of Figure 2.11.
Figure 2.11: (Right axis) Scattered light power for spherical particles with 𝑛 =1.6 [2.9] and (left
axis) particle size distribution for HEN-type nebulizers with 5 𝜇 m filtering [2.10].
Combining the effects of light scattering and particle size distribution by multiplying the
particle size distribution curve by the scattered power curve results in Figure 2.12 which shows
that a peak in the total scattered light power occurs for particles slightly larger than 1 μm. Based
31
on this model, 82% of scattered light power occurs for particle diameters between 0.8 and 3.5 μm.
Particles larger than 3.5 μm, though very effective at scattering light, exist in small proportion.
Particles below 0.8 μm, though numerous, scatter very little light. While HEN-type nebulizers do
produce sub-μm sized particles, a more relevant metric for the present application is to determine
which particles produce the greatest contribution to image texture. In this context, a more
thoughtful description of the particle sizes acquired on the camera sensor is a polydisperse
distribution of particles between 0.8 – 3.5 μm in diameter. In Chapter 5 it was shown that the
present measurements are insensitive to variations in particle diameter between 0.5 and 5 μm.
Thus, for simplicity, a nominal particle size was chosen for the present thesis to be 1 μm.
Figure 2.12: Contribution of different particle sizes to image texture in PIV applications. Particle
diameters between 0.8 and 3.5 micrometers accounted for 82% of scattered power.
32
2.5. Experimental Determination of Laminar Flame Speeds
In the 1980s, Wu and Law [2.1] were the first to derive 𝑆 𝑢 0
from strained counterflow
flames. More recent applications take advantage of updated measurement and extrapolation
techniques and include 𝑆 𝑢 0
s of gaseous fuels (e.g. [2.11]), liquid oxygenate fuels (e.g. [2.12]-
[2.15]), and neat or blended jet fuel surrogates (e.g. [2.16]-[2.18]).
When local measurements are sought, the axial velocity profile along the system stagnation
streamline is the primary target. A schematic example is plotted with the corresponding
temperature profile in Figure 2.13. The velocity profile is a hybrid of that produced by an
unreacting stagnation flow with thermal expansion from the flame [2.1]. Four relevant velocity
quantities appear in this profile, the reference velocity defined as the minimum velocity ahead of
the flame, 𝑆 𝑢 ,𝑟𝑒𝑓 , the reference strain rate defined as maximum magnitude of the axial velocity
gradient ahead of the flame, 𝜅 𝑟𝑒𝑓
, and the boundary values of axial velocity and axial velocity
gradient, 𝑣 𝑥 ,𝑒𝑥𝑖𝑡 and 𝜅 𝑒𝑥𝑖𝑡 , respectively.
Along with boundary conditions 𝑣 𝑥 ,𝑒𝑥𝑖𝑡 and 𝜅 𝑒𝑥𝑖𝑡 , the variation of 𝑆 𝑢 ,𝑟𝑒𝑓 with 𝜅 𝑟𝑒𝑓
,
hereafter referred to as the “flame response”, was measured and then extrapolated to 𝜅 𝑟𝑒𝑓
= 0 to
derive 𝑆 𝑢 0
. A desired mixture composition was produced via calibrated sonic orifices and the total
flow rate of this mixture controlled by a bypass valve. Since the silicone oil seeding vaporized at
temperatures above 473 Kelvin, velocity measurements were available only just past the point
marked 𝑆 𝑢 ,𝑟𝑒𝑓 . The temperature profile was not measured.
33
Figure 2.13: Schematic axial velocity and temperature profiles along the stagnation streamline of
a stagnation flow with key velocity observable definitions.
Theory for weakly stretched flames predicts a linear dependence of 𝑆 𝑢 ,𝑟𝑒𝑓
with 𝜅 𝑟𝑒𝑓
[2.19],
which was exploited in early studies (e.g. [2.1]-[2.3]). However, it is now known that the variation
of 𝑆 𝑢 ,𝑟𝑒𝑓 with 𝜅 𝑟𝑒𝑓
is actually nonlinear because of heat conduction from the flame front to the
location of 𝑆 𝑢 ,𝑟𝑒𝑓
[2.20] and linear extrapolations bias toward greater extrapolated values of 𝑆 𝑢 0
[2.16].
Fundamentally, it is the strained flame response measurements, not he extrapolated 𝑆 𝑢 0
,
which have scientific value. Reporting 𝑆 𝑢 0
is a matter of convenience to give a single parameter
description of flame behavior to, for example, facilitate comparison of flame data from different
systems or use as scaling factors in turbulent combustion. With this in mind, computationally-
assisted nonlinear extrapolations were performed in the manner introduced by Wang et al. [2.21]
34
and revised by Mittal and coworkers [2.22], including experimentally measured boundary velocity
gradients [2.16].
Figure 2.14: Demonstration of numerically-assisted extrapolation of 𝑆 𝑢 0
from strained flame data.
Shown in Figure 2.14, the flame response was computed with a quasi-one-dimensional
opposed-jet flame code and fit with a 2
nd
order polynomial. A vertical offset, δ𝑆 𝑢 0
, was then applied
to the computed flame response curve to best fit the 𝑁 measured values as determined by a
weighted least squares fit. The function minimized was:
∑ 𝑤 𝑖 (𝑆 𝑢 ,𝑟𝑒𝑓 ,𝐸𝑋𝑃 ,𝑖 − 𝑆 𝑢 ,𝑟𝑒𝑓 ,𝐶𝑂𝑀𝑃 ,𝑖 )
2
𝑖 =1,𝑁
(Eqn. 2.6)
where 𝑆 𝑢 ,𝑟𝑒𝑓 ,𝐸𝑋𝑃 ,𝑖 and 𝑆 𝑢 ,𝑟𝑒𝑓 ,𝐶𝑂𝑀𝑃 ,𝑖 are, respectively, the experimental and computed reference
velocities at the same 𝜅 𝑟𝑒𝑓 ,𝑖 , 𝑤 𝑖 = 𝜎 𝑖 −2
is the weighting, and 𝜎 𝑖 is the 1-sigma experimental
35
uncertainty of 𝑆 𝑢 ,𝑟𝑒𝑓 ,𝐸𝑋𝑃 ,𝑖 . Overall uncertainty in extrapolated 𝑆 𝑢 0
was determined with the 95%
confidence interval of the curve fit defined:
Δ𝑆 𝑢 0
= 1.96∗ ∑
[𝑆 𝑢 ,𝑟𝑒𝑓 ,𝐸𝑋𝑃 ,𝑖 − (𝑆 𝑢 ,𝑟𝑒𝑓 ,𝐶𝑂𝑀𝑃 ,𝑖 + δ𝑆 𝑢 0
)]
2
𝑁 𝑖 =1,𝑁
(Eqn. 2.7)
The effect of uncertainty in 𝜅 𝑟𝑒𝑓
was neglected because of the very low sensitivity of extrapolated
𝑆 𝑢 0
to variations in 𝜅 𝑟𝑒𝑓
. The experimentally determined laminar flame speed is:
𝑆 𝑢 0
= 𝑆 𝑢 ,𝑐 0
+ δ𝑆 𝑢 0
(Eqn. 2.8)
where 𝑆 𝑢 ,𝑐 0
is the value of 𝑆 𝑢 0
computed with PREMIX. Measured values are reported as 𝑆 𝑢 0
± Δ𝑆 𝑢 0
. It
has been shown that small uncertainties in reaction rates and transport coefficients have negligible
effect on the shape of the computed flame response curve (e.g. [2.16] and [2.21]).
2.6. Experimental Determination of Extinction Limits
Measurement of extinction limits in the counterflow configuration is well established in
premixed and non-premixed flames (e.g. [2.3], [2.12], [2.15], [2.16], [2.21], and [2.23]-[2.26]).
For this thesis, extinction limits were determined in symmetric, twin premixed flames and single
non-premixed flames. In all cases, the jet momenta were matched so that the stagnation plane
rested near the midway plane between the burners. A near limit flame was established, the
prevailing 𝜅 𝑟𝑒𝑓
was measured, and then the fuel flow rate was gently perturbed to achieve
extinction whereupon 𝜅 𝑟𝑒𝑓
was defined as the extinction strain rate, 𝜅 𝑒𝑥𝑡 . For nonpremixed and
lean premixed flames, the fuel flow rate was reduced ~0.5% to achieve extinction while for rich
premixed flames the fuel flow rate was increased ~0.5%. For sufficiently small fuel flow
perturbations, there is a negligible effect on the aerodynamic state of the system and the determined
36
extinction limits can be considered a direct measurement. As with flame propagation
measurements, boundary velocity conditions were measured for inclusion in one-dimensional
modeling.
2.7. Data Processing
The introduction of silicone oil seeding particles in low concentrations has been shown to
have negligible impact on flame measurements at ambient pressures [2.27]. This result was
confirmed for the present conditions by noting that the total flow rate at extinction for select non-
premixed flames at 𝑝 = 0.1 atm both with and without seeding particles were indistinguishable.
For measurements obtained when 𝑝 ≤ 0.25 atm, it was common to observe sparse seeding
number densities in acquired PIV images, e.g., Figure 2.15. Instead of increasing the rate of
seeding particle delivery, which can ultimately alter the flame chemistry and structure through fuel
augmentation by excess silicone oil, special data processing procedures were undertaken.
Figure 2.15: Comparison of typical seeding particle number density for (left) 𝑝 = 1 atm and
(right) 𝑝 = 0.1 atm.
37
First, the PIV correlation algorithm was instructed to reject calculated displacements
associated with weak correlation strength. Each instantaneous vector field could then be
incomplete, having “holes” where correlation strength fell below the threshold. Because the
counterflow flames were steady, between twenty and fifty instantaneous flow field measurements,
depending on seeding density, were obtained for each flow field. It was ensured that the average
velocity at each point was calculated from a minimum of twenty independent samples. The set
was ensemble averaged to yield a mean vector field used as the nominal velocity data and a 1σ
standard deviation velocity vector field used to define velocity measurement uncertainty. This
process is shown in Figure 2.16.
Figure 2.16: Representation of data processing procedure. (Left) A sparse, instantaneous
velocity field, (center) mean vector field from 50 instantaneous samples, and (right) 1𝜎 standard
deviation scalar field.
38
Direct measurement of velocity at the burner exit was impossible because the burner
blocked particle tracers from the camera’s view. To address this, post-processing of the measured
centerline profile was performed based on the supposition that centerline measurements adhered
to assumptions of the quasi-one-dimensional strained flame codes detailed in Chapter 3. That is,
the axial velocity profile was quadratic in space, and thus the strain profile was linear, from the
burner exit until near the flame preheat zone.
Shown in Figure 2.17, curve fits were produced beginning with a linear least squares fit of
the measured strain rate profile starting from the 2
nd
or 3
rd
point from the burner exit until the point
of maximum strain magnitude. The fit was extrapolated to the boundary to produce the boundary
strain rate, 𝜅 𝑒𝑥𝑖𝑡 , and the maximum magnitude of strain rate over the fit interval, 𝜅 𝑟𝑒𝑓
. Integrating
the fitted strain rate line produced a quadratic expression with an integration constant determined
by a least squares fit of the quadratic expression to the velocity profile data. The boundary axial
velocity value from this quadratic curve fit was defined as 𝑣 𝑥 ,𝑒𝑥𝑖𝑡 .
Figure 2.17: Example of measured centerline (top) velocity profile and (bottom) strain rate
profile with curve fits and definition of measured observables.
39
Next, a linear relationship between 𝜅 𝑒𝑥𝑖𝑡 and 𝑣 𝑥 ,𝑒𝑥𝑖𝑡 was assumed for a given set of flame
measurements to capture the effect of non-constant boundary velocity gradients on flame response
in one-dimensional modeling. In this context, a “set” constituted all centerline velocity profiles
acquired to produce one reported 𝑆 𝑢 0
, in the case of propagation measurements, or all centerline
velocity profiles acquired across all mixture compositions at a single pressure for extinction state
measurements. An example from propagation measurements is shown in Figure 2.18 where it can
be seen that boundary velocity gradients were nonzero and proportional to the exit velocity.
Figure 2.18: Example of line fit for determination of variable velocity gradient boundary
conditions.
40
2.8. References
[2.1] C. K. Wu, C. K. Law, Proceed. Combust. Inst. 20 (1984) 1941-1949.
[2.2] F. N. Egolfopoulos, P. Cho, C. K. Law, Combust. Flame 76 (1989) 375-391.
[2.3] H. K. Chelliah, C. K. Law, T. Ueda, M. D. Smooke, F. A. Williams, Proceed. Combust.
Inst. 23 (1991) 503-511.
[2.4] Y. Dong, C. M. Vagelopoulos, G. R. Spedding, F. N. Egolfopoulos, Proceed. Combust.
Inst. 29 (2002) 1419-1426.
[2.5] T. Hirasawa, C. J. Sung, A. Joshi, Z. Yang, H. Wang, C. K. Law, Proceed. Combust.
Inst. 29 (2002) 1427-1434.
[2.6] J. M. Bergthorson, D. G. Goodwin, P. E. Dimotakis, Proceed. Combust. Inst. 30 (2005)
1637-1644.
[2.7] A. M. Fincham, G. R. Spedding, Exp. Fluids 23 (1997) 449-462.
[2.8] P. S. Veloo, Studies of combustion characteristics of alcohols, aldehydes, and ketones,
PhD Dissertation, Univ. of Southern California (2011)
http://digitallibrary.usc.edu/cdm/search/field/identi/searchterm/uscthesesreloadpub_V
olume71%252Fetd-VelooPeter-52.pdf, accessed Nov. 2016.
[2.9] A. Melling, Meas. Sci. Technol. 8 (1997) 1406-1416.
[2.10] J.-L. Todoli, J.-M. Mermet, Liquid Sample Introduction in ICP Spectrometry: A
Practical Guide, Elsevier Science (2011) e-Textbook.
[2.11] O. Park, P. S. Veloo, D. A. Sheen, Y. Tao, F. N. Egolfopoulos, H. Wang, Combust.
Flame 172 (2016) 136-152.
[2.12] P. S. Veloo, Y. L. Wang, F. N. Egolfopoulos, C. K. Westbrook, Combust. Flame 157
(2010) 1989-2004.
[2.13] P. S. Veloo, F. N. Egolfopoulos, Proceed. Combust. Inst. 33 (2011) 987-993.
[2.14] Y. L. Wang, D. J. Lee, C. K. Westbrook, F. N. Egolfopoulos, T. T. Tsotsis, Combust.
Flame 161 (2014) 810-817.
[2.15] Y. L Wang, Q. Feng, F. N. Egolfopoulos, C. K. Westbrook, Combust. Flame 158
(2011) 1507-1519.
[2.16] C. Ji, E. Dames, Y. L. Wang, H. Wang, F. N. Egolfopoulos, Combust. Flames 157
(2010) 277-287.
[2.17] C. Ji, F. N. Egolfopoulos, Proceed. Combust. Inst. 33 (2011) 955-961.
41
[2.18] B. Li, N. Liu, R. Zhao, H. Zhang, F. N. Egolfopoulos, Proceed. Combust. Inst. 34
(2013) 727-733.
[2.19] M. Matalon, B. J. Matkowsky, J. Fluid Mech., 124 (1982) 239.
[2.20] J. H. Tien, M. Matalon, Combust. Flame 84 (1991) 238-248.
[2.21] Y. L. Wang, A. T. Holley, C. Ji, F. N. Egolfopoulos, T. T. Tsotsis, H. J. Curran,
Proceed. Combust. Inst. 32 (2009) 1035-1042.
[2.22] V. Mittal, H. Pitsch, F. N. Egolfopoulos, Combust. Theory. Model., 16-3 (2012) 419-
433.
[2.23] O. Park, P. S. Veloo, H. Burbano, F. N. Egolfopoulos, Combust. Flame 162 (2015)
1078-1094.
[2.24] C. B. Oh, A. Hamins, M. Bundy, J. Park, Combust. Theory Model. 12-2 (2008) 283-
302.
[2.25] B. G. Sarnacki, G. Esposito, R. H. Krauss, H. K. Chelliah, Combust. Flame 159 (2012)
1026-1043.
[2.26] U. Niemann, K. Seshadri, F. A. Williams, Combust. Flame 161 (2014) 138-146.
[2.27] T. Ueda, Y. Yahagi, M. Mizomoto. Trnas. JSME B 57 (1991) 3255-3259.
42
Chapter 3
Numerical Methods
3.1. Laminar Flame Speeds
Modeling 𝑆 𝑢 0
was achieved with the PREMIX code which solves the governing equations
for a freely propagating, steady, isobaric, one-dimensional flame [3.1]. These are equations for
continuity, conservation of energy, and conservation of species with the ideal gas equation of state.
Being isobaric, the need for a momentum equation is replaced by the condition of constant
thermodynamic pressure. Solution variables are the temperature and chemical composition at each
grid point and the mass flux eigenvalue, 𝑚 ̇ , which is constant throughout the domain. This
boundary value problem is discretized by finite difference approximations to form a system of
nonlinear algebraic equations. The present computational method was developed by Dixon-Lewis
[3.2], Warnatz [3.3], Miller and coworkers [3.4, 3.5], Smooke and coworkers [3.6], Kee and
coworkers [3.7] , and Grcar and coworkers [3.8].
Because there is a system of nonlinear algebraic equations to be solved, direct solution is
impossible and instead an iterative method is used. The damped-modified Newton method is an
efficient root finding algorithm that features a quadratic rate of convergence when the solution
estimate lies within Newton’s domain of convergence. Producing an appropriate solution estimate
is not trivial as the governing equations are stiff. Largely, computational stiffness is due to the
severe nonlinearities in the energy equation’s chemical source term. First, a solution is attempted
on a coarse grid, as few as 5 or 6 grid points, because Newton’s domain of convergence is largest
for coarse grids. A philosophy of coarse-to-fine grid refinement takes advantage of the fact that
converged solutions on coarse grids tend to be within the domain of convergence for an
43
incrementally more refined grid. Second, providing a user specified temperature profile eliminates
the energy equation and the related computational difficulties. From this, an internally consistent
estimate of the species composition and mass flux is produced. Third, upon failure of the Newton
algorithm to converge, the solution estimate is conditioned by a slow but robust time marching
procedure which can bring the estimate into Newton’s domain of convergence. Finally, once a
converged solution has been found, adaptive grid refinement efficiently places new grid points in
regions of large solution variable gradient or curvature.
PREMIX is integrated with the Sandia CHEMKIN [3.9] and Transport [3.10] subroutine
libraries for evaluation of thermochemistry and transport properties, respectively. Transport
options include either the mixture averaged or multicomponent formulation for diffusion velocities
[3.11] and thermal diffusion due to Soret effect. Binary diffusion coefficients of H and H 2 with
select key species are based on an updated set [3.12]. Thermal radiation is included at the optically
thin limit for radiating species CO, CH4, CO2, and H2O [3.13].
All results of this thesis were computed with the multicomponent transport formulation,
Soret effect, thermal radiation, and grid refinement sufficient for grid-independent solutions.
3.2. Strained Counterflow Flames
Modeling of strained counterflow flames, including flame propagation response curves,
𝑆 𝑢 ,𝑟𝑒𝑓 vs. 𝜅 𝑟𝑒𝑓
, and non-premixed flame extinction states, was achieved with a quasi-one-
dimensional opposed-jet code [3.7, 3.13]. The code is similar to PREMIX in structure, being an
eigenvalue problem, except that the eigenvalue is the radial pressure curvature,
1
𝑟 𝑑𝑝
𝑑𝑟
, and there is an
additional governing equation for conservation of radial momentum.
44
Radial and axial velocity components are linked by the streamfunction:
𝜓 (𝑥 ,𝑟 ) = 𝑟 2
𝑈 (𝑥 ) (Eqn. 3.1)
where 𝑟 is the radial coordinate and the function 𝑈 depends only on the axial coordinate. The axial
velocity, 𝑣 𝑋 , is obtained:
𝑣 𝑥 =
1
𝑟𝜌
𝜕𝜓
𝜕𝑟
=
2𝑈 𝜌
(Eqn. 3.2)
and radial velocity, 𝑣 𝑟 :
𝑣 𝑟 =
−
1
𝑟𝜌
𝜕𝜓
𝜕𝑥
= −
𝑟 𝜌 𝑑𝑈 𝑑𝑥
(Eqn. 3.3)
Since 𝑣 𝑥 and 𝑣 𝑟 are functions only of 𝑥 , so are all solution variables and the problem is
computationally one-dimensional. Properties at any 𝑟 are trivially calculated once a solution in 𝑥
is found, therefore the solution is quasi-one-dimensional. One consequence of the streamfunction
approach is that the code explicitly models a configuration with zero radial gradient in solution
variables 𝑈 ,
𝑑𝑈
𝑑𝑥
, temperature, and species composition. Applying this requirement to Eqn. 3.2, it
can be seen that no radial dependence in 𝑣 𝑥 is permitted while applying it to Eqn. 3.3 results in the
possibility of either zero or linear radial dependence of 𝑣 𝑟 . Therefore, quasi-one-dimensional
modeling should only be applied to experiments that substantially conform to these restrictions.
The original application of the strained flame code was to model symmetric, twin,
premixed flames but it has been modified [3.13] to allow independent boundary conditions at either
boundary necessary for non-premixed flames and it does allow for boundary velocity gradients
[3.7].
Flame propagation response curves, 𝑆 𝑢 ,𝑟𝑒𝑓
vs. 𝜅 𝑟𝑒𝑓
, and extinction states were modeled by
including experimentally realized boundary conditions for unburned reactant temperature, reactant
composition, velocity, velocity gradient, thermodynamic pressure, and finite domain size on the
45
system centerline (e.g., [3.14]). All simulations included multicomponent transport [3.15], Soret
effect, thermal radiation, and grid refinement sufficient for grid-independent solutions.
To compute extinction states, first a vigorously burning flame was established and the
velocity at both boundaries increased while satisfying the condition of equal momentum flux until
a near limit flame was reached. At the extinction state, the flame burning intensity, as suggested
by, for example, the maximum temperature or H radial concentration, is characterized by a turning
point behavior as shown in Figure 3.1. Solution around this turning point was achieved with a
two-point continuation approach by imposing the concentration of H radicals at the two locations
of its maximum spatial gradient on either side of its peak value [3.16]. This internal boundary
condition allows boundary velocity, and thus 𝜅 𝑟𝑒𝑓
, to become a solution variable. The computed
value of 𝜅 𝑟𝑒𝑓
at the turning point was defined as the computed extinction strain rate, 𝜅 𝑒𝑥𝑡 .
Figure 3.1: Illustrations of (left) turning point behavior at the computed flame extinction state and
(right) two-point continuation based on hydrogen radical concentration.
46
3.3. Sensitivity Analysis
Sensitivity analysis is a technique used to understand how a solution depends on model
parameters [3.1]. The PREMIX code allows the calculation of logarithmic sensitivity coefficients
of 𝑆 𝑢 0
to kinetics:
𝐴 𝑖 𝑆 𝑢 0
𝜕 𝑆 𝑢 0
𝜕 𝐴 𝑖
(Eqn. 3.4)
or to diffusion [3.17]:
𝐷 𝑗𝑘
𝑆 𝑢 0
𝜕 𝑆 𝑢 0
𝜕 𝐷 𝑗𝑘
(Eqn. 3.5)
where 𝐴 𝑖 is the Arrhenius pre-exponential factor of the 𝑖 th reaction and 𝐷 𝑗𝑘
is the binary diffusion
coefficient between species 𝑗 and species 𝑘 . In the opposed-jet code, calculated logarithmic
sensitivity coefficients for 𝜅 𝑒𝑥𝑡 follow an analogous formula with 𝜅 𝑒𝑥𝑡 replacing 𝑆 𝑢 0
in Eqn. 3.4
and Eqn. 3.5.
3.4. Integrated Reaction Flux Analysis
Reaction flux analysis reveals the computed pathways for species production and
consumption (e.g., [3.18]). The rate of progress variable for the 𝑖 th reaction, 𝑞 𝑖 , is:
𝑞 𝑖 = 𝑘 𝑓 ,𝑖 ∏[𝑋 𝑗 ]
𝜈 𝑗𝑖
′
− 𝑘 𝑟 ,𝑖 𝑗 =1,𝐽 ∏[𝑋 𝑗 ]
𝜈 𝑗𝑖
′′
𝑗 =1,𝐽
(Eqn. 3.6)
where 𝑘 𝑓 ,𝑖 and 𝑘 𝑟 ,𝑖 are the forward and reverse reaction rate coefficients, [𝑋 𝑗 ] is the molar
concentration of the 𝑗 th species, and 𝜈 𝑗𝑖
′
and 𝜈 𝑗𝑖
′′
the forward and reverse stoichiometric coefficients,
respectively. Eqn. 3.6 may be integrated over the entire computational domain or a specific subset
to probe certain regions of the flame. Either way, the spatially integrated 𝑞 𝑖 is then multiplied by
47
the stoichiometric coefficient of the species of interest in the 𝑖 th reaction to yield the
production/consumption contribution from that species and reaction 𝑖 .
48
3.5. References
[3.1] R. J. Kee, J. F. Grcar, M. D. Smooke, J. A. Miller, A FORTRAN Program for
Modeling Steady Laminar One-Dimensional Premixed Flames, Sandia
Report.SAND85-8240, Sandia National Laboratories, 1985.
[3.2] G. Dixon-Lewis, P. Roy. Soc. A, 298-1455 (1967) 495-315.
[3.3] J. Warnatz, Proc. Combust. Inst. 18 (1981) 369-384.
[3.4] J. A. Miller, R. E. Mitchell, M. D. Smooke, R. J. Kee, Proc. Combust. Inst. 19
(1982) 181–196.
[3.5] J. A. Miller, M. D. Smooke, R. M. Green, R. J. Kee, Comb. Sci. Tech. 34 (1983)
149-176.
[3.6] M. D. Smooke, J. A. Miller, R. J. Kee, Comb. Sci. Tech. 34 (1983) 79-90.
[3.7] R.J. Kee, J.A. Miller, G.H. Evans, G. Dixon-Lewis, Proc. Comb. Inst. 22 (1988)
1479–1494.
[3.8] J. F. Grcar, R. J. Kee, M. D. Smooke, J.A. Miller, Proc. Comb. Inst. 21 (1986)
1773-1782.
[3.9] R. J. Kee, F. M. Rupley, J. A. Miller, Chemkin-II: A Fortran Chemical Kinetics
Package for the Analysis of Gas-Phase Chemical Kinetics, Sandia Report
SAND89-8009, Sandia National Laboratories, 1989.
[3.10] R. J. Kee, J. Warnatz, J. A. Miller, A Fortran Computer Code Package for the
Evaluation of Gas-Phase Viscosities, Conductivities, and Diffusion Coefficients,
Sandia Report SAND83-8209, Sandia National Laboratories, 1983.
[3.11] A.E. Lutz, R.J. Kee, J.F. Grcar, F.M. Rupley, Oppdif: A Fortran Program For
Computing Opposed-Flow Diffusion Flames, Sandia Report SAND96-8243,
Sandia National Laboratories, 1997.
[3.12] Y. Dong, A.T. Holley, M.G. Andac, F.N. Egolfopoulos, S.G. Davis, P. Middha,
H. Wang, Combust. Flame 142 (2005) 374–387.
[3.13] F.N. Egolfopoulos, Proc. Comb. Inst. 25 (1994) 1375–1381
[3.14] C. Ji, E. Dames, Y.L. Wang, H. Wang, F.N. Egolfopoulos, Combust. Flame 157
(2010) 277–287.
[3.15] Y.L. Wang, P.S. Veloo, F.N. Egolfopoulos, T.T. Tsotsis, Proc. Combust. Inst. 33
(2011) 1003-1010.
[3.16] F.N. Egolfopoulos, P.E. Dimotakis, Proc. Comb. Inst. 27 (1998) 641–648.
49
[3.17] A.T. Holley, E. Dames, X. You, H. Wang, F.N. Egolfopoulos, Proc. Combust.
Inst. 32 (2009) 1157-1163.
[3.18] J. F. Grcar, M. S. Day, J. B. Bell, Combust. Theor. Model. 10-4 (2006) 559-579.
50
Chapter 4
Two-Dimensional Effects in Counterflow Methane Flames
4.1. Introduction
The counterflow configuration was developed in the 1950s and it has been an invaluable
tool for experimental study of laminar flames (e.g., [4.1]) along with one-dimensional (1D) models
(e.g., [4.2]-[4.5]) that were subsequently developed. At the same time, computational efficiency
afforded by 1D models comes at the expense of generality; only carefully designed counterflow
experiments are suitable for comparison. When properly implemented, counterflow flames may
provide high quality flame data over a wide range of thermodynamic conditions [4.1], and such
data contain important physical and chemical information.
Data from two classes of experimental burner design are widely compared to 1D modeling
results; straight-tube burners with flow conditioning screens (e.g., [4.6] and [4.7]) and high-
contraction-ratio contoured-nozzle burners (e.g., [4.8]-[4.11]). Both designs are idealized to
produce plug-flow conditions and the data are modeled using 1D codes by imposing zero velocity
gradient boundary conditions. Flows that generate sufficiently strong stagnation pressure fields
deviate from plug-flow conditions and are characterized by velocity gradients at the burner exit,
which should be included as boundary conditions in modeling. A strong stagnation pressure field
is often suggested from observation of a “dimple” on the flame surface that is convex on the
upstream side and indicates velocity non-uniformity at the burner exit.
Early studies seeking experimental verification of 1D modeling assumptions include that
of Chelliah et al. [4.12], who identified plug flow boundary conditions in counterflow experiments,
and Rolon and coworkers [4.13] who concluded that realistic flow fields could fail to reproduce
51
plug flow conditions. Frouzakis et al. [4.14] and Park and Hamins [4.15] determined that 1D
simulation results agree with axisymmetric two-dimensional (2D) simulations with uniform axial
velocity exit profiles at the burner exit. Bergthorson and coworkers [4.16] investigated the
accuracy of 1D modeling in contoured-nozzle generated premixed flames and found agreement
provided, in part, that the velocity boundary conditions were measured and implemented in the
simulations. Oh et al. [4.6] used straight-tube burners with flow conditioning screens and found
1D modeling compatible centerline extinction for high strain rates but 2D effects for lower strain
rates. Ji et al. [4.8] quantified the effect of boundary velocity gradients in contoured-nozzle
extinction measurements. Sarnacki et al. [4.10] identified a stagnation pressure field of ellipsoidal
geometry to be the physical mechanism causing departure from plug flow assumptions. Mittal et
al. [4.17] attributed the departure from 1D behavior in non-uniform exit velocity profiles to the
presence of temperature curvature at the system centerline because of flow non-uniformity.
Bouvet et al. [4.11] studied contoured-nozzle generated premixed flames and traced
inconsistencies with 1D modeling to the assumption of constant pressure curvature eigenvalue.
Niemann et al. [4.7] determined that straight-tube burners with flow conditioning screens can
capture 1D plug flow assumptions to within an accuracy of 5% in unreacting flows, allowing the
use of a one parameter analytical description of the effective (global) strain rate [4.18] in lieu of
local flow measurements. Johnson et al. [4.19] corroborated the assertion of Ref. 4.7 and further
confirmed that contoured-nozzle burners are accurately modeled with 1D codes when appropriate
boundary conditions are included.
In the present study, experiments and computations were performed to quantify the
sensitivity of measured laminar flame speeds, 𝑆 𝑢 0
s, and extinction strain rates, 𝜅 𝑒𝑥𝑡 𝑠 , in lean
premixed CH4/air and 𝜅 𝑒𝑥𝑡 𝑠 in non-premixed CH4-N2/air flames to the velocity boundary
52
conditions in straight-tube counterflow burners. The data were compared with 1D modeling
results to assess their compatibility with 1D assumptions and highlight pitfalls for kinetic model
validation.
4.2. Experimental Approach
The measurements were carried out in a counterflow configuration using straight-tube
burners at ambient atmospheric pressure and temperature. Burner diameter, 𝐷 = 21 mm, and
burner separation distance, 𝐿 = 15.3 mm, were chosen to mimic the geometry of Ref. 4.7 and allow
for well-resolved local velocity measurements. A set of two 60 mesh flow conditioning screens
separated by ~2𝐷 were placed within the burner tubes ~5𝐷 upstream from the exit and formed the
basis for two configurations; Type A with no additional modifications and Type B with an
additional set of stacked 200 mesh screens at the exit. Flow velocities were measured using
particle image velocimetry (PIV) with ~1 μm silicone oil flow tracers generated by a pneumatic
nebulizer (Meinhard HEN-170-A0.2). Direct flame imaging was obtained with a CMOS
monochrome high-speed camera (Phantom v710). A system schematic is shown in Figure 4.1.
53
Figure 4.1: Schematic of the experimental system as configured for symmetric, premixed flames.
The premixed flames studies were carried out in the symmetric twin-flame configuration
(e.g. [4.20]) for lean CH4/air mixtures. Non-premixed flames were established by counterflowing
fuel/inert mixtures against air. 𝑆 𝑢 0
and 𝜅 𝑒𝑥𝑡 were determined using flow velocity measurements
along the stagnation streamline. A reference velocity, 𝑆 𝑢 ,𝑟𝑒𝑓 , and a reference strain rate, 𝜅 𝑟𝑒𝑓
,
were defined as the minimum axial velocity and maximum norm of the axial velocity gradient in
the axial direction, respectively, ahead of the flame front (e.g., [4.1], [4.8], and [4.20]). Velocity
and velocity gradient boundary conditions were measured and included in 1D simulations. 𝑆 𝑢 0
was
derived using a numerically-assisted, non-linear extrapolation approach (e.g., [4.8] and [4.21]-
[4.24]). Measured 𝜅 𝑒𝑥𝑡 in both premixed and non-premixed flames was achieved by first
establishing a near-limit flame and then gently reducing the fuel flow rate by up to 0.5% to achieve
extinction (e.g., [4.8] and [4.21]-[4.24]). The uncertainty of the reported data was quantified based
on repeated trials and is reported as ±1𝜎 standard deviation from the mean value. Uncertainty in
flow composition has been shown to be less than 0.5% [4.23].
54
4.3. Modeling Approach
Detailed 1D modeling was based on the Sandia CHEMKIN [4.25] and Transport [4.26]
subroutine libraries. Freely propagating flames were computed with the PREMIX code [4.3],
while the counterflow flames were simulated using an opposed-jet code [4.4, 4.24]. Both codes
include radiation at the optically thin limit, Soret diffusion, and an updated description of H and
H2 diffusion coefficients [4.27]. The stretched flame simulations accounted for the measured
boundary velocity gradients and for a finite a spatial domain of 15.3 mm. The extinction states
were computed by first establishing a vigorously burning flame and subsequently increasing the
boundary velocity until flame extinction was approached. Near extinction, a two-point approach
was employed whereby the problem was solved with exit velocity, and thus strain rate, as a
dependent variable (e.g., [4.8]). All simulations employed the multicomponent transport
formulation. The USC Mech II kinetic mechanism [4.28] was reduced to include only H2/CO/C1-
C2 species resulting in 38 species and 249 reactions.
4.4. Results and Discussion
4.4.1. Flow Fields
Representative radial, 𝑣 𝑟 , and axial, 𝑣 𝑥 , velocity profiles for Type A and Type B burners
were measured about 1 mm from the burner exit for an equivalence ratio 𝜙 = 0.542, normalized
by |𝑣 𝑥 |
𝑚𝑎𝑥
, and are compared in Figure 4.2. Compared to Type B, Type A burners produced
strong radial nonuniformity of 𝑣 𝑥 as well as greater radial gradients of 𝑣 𝑟 , which due to continuity
implies greater axial gradients of 𝑣 𝑥 . Neither configuration produced strictly plug-flow conditions
55
but existing literature suggests that this may be accounted for in 1D modeling by including the
measured axial velocity gradients at the boundary.
Figure 4.2: Measured reacting flow velocity profiles measured 1 mm form the burner exit near
extinction for 𝜙 = 0.542: (left) Type A and (right) Type B burners.
Many details of the experimental flow field cannot be captured by centerline and boundary
measurements, for example the distribution of 𝑣 𝑟 and its radial gradient, as well as 𝑣 𝑥 and its axial
gradient as shown in Figure 4.3. For Type A flow fields shown in the top of Figure 4.3, all flow
quantities exhibited radial dependence. Among these, 𝑣 𝑥 and both velocity gradients were greatest
in magnitude towards the outer edges of the flow field, although the radial variation of 𝑣 𝑥 appeared
to diminish at 𝑥 /𝐷 locations downstream. Type B flow fields shown in the bottom of Figure 4.3
exhibited notably less radial dependence; 𝑣 𝑥 and both velocity gradients at the flame front were
maximum in magnitude and nearly uniform over the central 50% of the radial domain. The strong
radial non-uniformity of 𝑣 𝑥 in Type A flow fields was an explicit violation of 1D modeling
assumptions in which only 𝑣 𝑟 is permitted to vary linearly with radius.
56
Figure 4.3: Normalized comparison of measured flow field structure near extinction at 𝜙 = 0.542
for (top) Type A burner and (bottom) Type B burner. Lightest (darkest) color corresponds to
maximum (minimum) magnitude.
4.4.2. Laminar Flame Speeds
Measured and computed 𝑆 𝑢 0
s for lean CH4/air flames are shown in Figure 4.4 along with
select data from Ref. 4.29. The computations over-predict the measurements over the range of
conditions studied and the measured 𝑆 𝑢 0
s using either burner type agree with those reported in Ref.
4.29. Given combustion theory that suggests 𝑆 𝑢 0
~ √𝜔 , where 𝜔 is the overall reactivity, the results
in Figure 4.4 suggest that for the present conditions the measured reactivity was overpredicted by
57
the computations. The kinetic model is known to overpredict the reactivity of lean CH4/air flames
(e.g., [4.29]), explaining the difference between computed and measured values.
Figure 4.4: Measured and computed laminar flame speeds for CH4/air mixtures at 𝑝 = 1 atm and
𝑇 𝑢 = 298 K.
As both Type A and Type B data were the same, the measured 𝑆 𝑢 0
was found to be
insensitive to the exit velocity profile shape, in apparent contradiction with the observations of
Ref. 4.17. However, in Ref. 4.17 the differences between uniform and non-uniform exit velocity
profiles result in 3-5% variation of 𝑆 𝑢 ,𝑟𝑒𝑓
, which was within the present measurement uncertainties,
and a maximum of 8% variation in 𝜅 𝑟𝑒𝑓
. For CH4/air flames the Lewis number, 𝐿𝑒 , is slightly less
than one and strain rate only weakly affects flame intensity. Thus, the sensitivity of extrapolated
𝑆 𝑢 0
to variations in uncertainty 𝜅 𝑟𝑒𝑓
was small [4.30, 4.31] and the overall uncertainty was
dominated by 𝑆 𝑢 ,𝑟𝑒𝑓 . These observations may not apply to flames with sufficiently large 𝐿𝑒 due
to greater sensitivity of flame intensity to strain rate.
58
4.4.3. Premixed Flame Extinction
Measured and computed 𝜅 𝑒𝑥𝑡 s for lean, premixed CH4/air flames are shown on the left in
Figure 4.5. The simulation results again overpredicted the data, which was consistent with the
propagation results. Direct comparison of measured values between different burner types was
inappropriate because 𝜅 𝑒𝑥𝑡 also depends on the magnitude of the boundary velocity gradient [4.8].
This effect is demonstrated in the modeling results of Figure 4.5 where the increased boundary
velocity gradients of Type A burners implemented in computations resulted in greater 𝜅 𝑒𝑥𝑡 values
relative to Type B that exhibited milder exit velocity gradients.
Figure 4.5: Extinction strain rates of premixed CH4/air flames at 𝑝 = 1 atm and 𝑇 𝑢 = 298 K
including (left) measured and computed results and (right) the ratio of computed to measured.
As 𝜅 𝑒𝑥𝑡 ~𝜔 (e.g. [4.23]), the notable sensitivity of 𝜅 𝑒𝑥𝑡 to kinetics means that any
uncertainties in its measurement could impact the validation of various rate constants in detailed
kinetic models. Thus 𝜅 𝑒𝑥𝑡 data obtained with different burner types were compared indirectly
through 1D simulations. The quantity
𝜅 𝑒𝑥𝑡 ,𝑠𝑖𝑚
𝜅 𝑒𝑥𝑡 ,𝑒𝑥𝑝 can be interpreted as a comparison of the overall
reactivity suggested by simulations to the measured reactivity. It approaches unity when
59
simulations and experiments agree. The right side of Figure 4.5 depicts the variation of
𝜅 𝑒𝑥𝑡 ,𝑠𝑖𝑚
𝜅 𝑒𝑥𝑡 ,𝑒𝑥𝑝
with 𝜙 and it can be seen that the computed values exceeded the measured ones, in Type A burners
non-monotonically up to a factor of 2.4 and in Type B burners monotonically up to a factor of 1.7.
The interpretation of the global reactivity based on the data derived in Type A and Type B burners
differ, which suggests that at least one data set is incompatible with the 1D modeling results.
Given the sub-unity 𝐿𝑒 for CH4/air mixtures, the flames were strengthened by increasing
strain rate, merged at the stagnation plane, and became restrained from further movement
whereupon insufficient chemical residence time caused extinction [4.32]. It is also known that the
flame surface follows the shape of the incoming flow field (e.g. [4.33]). Therefore, for nonuniform
𝑣 𝑥 profiles generated by Type A burners, show on the left of Figure 4.2 and top of Figure 4.3, the
flames first approached the stagnation plane and initiated extinction at locations away from the
centerline. These flames did appear visually planar near extinction because symmetry and
conservation of momentum dictated that axial flow velocity must approach zero close to the
stagnation plane and 𝑣 𝑥 non-uniformity was compressed as discussed in section 4.4.1.
The dynamic behavior of the extinction process was captured with a high-speed camera
and images are shown in Figure 4.6. Time 𝑡 = 0 ms corresponds to the moment that extinction
initiated. Extinction in Type A burners was observed to initiate at a location away from the
centerline, followed by transition to a propagating edge flame which momentarily surrounded the
still-burning flame core, and eventually resulted in global extinction around 𝑡 = 70 ms.
Unavoidable minor asymmetry in the system geometry caused extinction to initiate on the right
side of the images. For Type B burners, extinction initiated near the centerline before transitioning
to an outwardly propagating edge flame followed by global extinction near 𝑡 = 30 ms. It should be
60
noted that both burners produced apparently flat flame shapes near the centerline, suggesting that
a visual inspection of flame topography is insufficient to ensure flow field quality.
Figure 4.6: Evolution of the extinction process for lean CH4/air flames produced by (top) Type
A and (bottom) Type B burners.
When extinction initiated on the centerline, the direction of edge flame propagation
coincided with that of 𝑣 𝑟 while for off-center extinction the edge flame propagated opposite to 𝑣 𝑟 .
This resulted measurably different time scales from initiation to completion of the extinction
process, i.e., 30 vs. 70 ms. Discussion on edge flame dynamics may be found in, e.g., Ref. 4.34.
Several physical mechanisms resulted in the trends observed in premixed flame extinction.
First, locally off-center extinction transitioning to global extinction in Type A burners produced
𝜅 𝑒𝑥𝑡 values that were systematically lower because the measured centerline velocity profiles were
not representative of the extinction state. Next, the magnitude of flow non-uniformity has been
shown [4.7] to scale with flow momentum and burner separation distance as 𝜌 𝑣 𝑥 2
(
𝐷 𝐿 )
2
. For the
fixed 𝐿 /𝐷 employed presently, extinction of stronger flames at greater 𝜙 necessitated greater 𝑣 𝑥 .
The ellipsoidal stagnation pressure isocontours [4.10] preferentially decelerated the centerline
axial velocity compared to the edges and enhanced the exit velocity non-uniformity with increased
flow rate. Third, there was also a buoyancy effect, which is typically negligible along the system
61
centerline, but can play an important role in the flame periphery where Type A burner extinction
was observed (e.g., [4.35]).
Based on this analysis, the difference between measured 𝜅 𝑒𝑥𝑡 s along the centerline of Type
A and Type B burners was attributed to the non-uniformity of the incoming flow that caused off-
center extinction initiation for the Type A burners. The difference between measured and
computed values using Type B burners was attributed to kinetic effects, as demonstrated in
previous studies for lean CH4/air flames (e.g., [4.29]). The non-monotonic behavior for Type A
flames shown on the right side of Figure 4.5 may be explained by buoyancy for the lower 𝜙 s,
which more directly affects the fluid mechanics of the jet outer edges. For higher 𝜙 s, the boundary
flow non-uniformity increased with flow rate and the off-center extinction propensity was
magnified but the buoyancy effect was suppressed. The conclusions derived for the near-unity 𝐿𝑒
CH4/air flames studied presently are expected to hold, at least qualitatively, for mixtures in which
differential diffusion plays a more profound role.
4.4.4. Non-Premixed Flame Extinction
Measured and computed 𝜅 𝑒𝑥𝑡 s for non-premixed CH4-N2/air flames are shown in Figure
4.7. As with premixed flame extinction, a direct comparison of the measured values was
inappropriate due to different boundary velocity gradients. Also similar to premixed extinction,
the notable sensitivity of non-premixed 𝜅 𝑒𝑥𝑡 to kinetics [4.8] dictates that any uncertainties in its
measurement could impact the validation of reaction rate parameters.
Data derived with Type B burners were within 30% of the modeling predictions for all
cases and the agreement improved with increasing fuel mole fraction, 𝑋 𝐶𝐻 4
. In contrast, the
62
agreement between data derived in the Type A burners and predictions became notably more poor
with increasing 𝑋 𝐶𝐻 4
, up to a factor of 2.6. Like premixed flame extinction, the extinction of non-
premixed flames initiated at off-center locations for Type A burners and at the center for Type B
burners. The velocity gradients and strain rate distributions were determined to be like those
shown in Figure 4.3. The relatively close agreement between the computed and measured 𝜅 𝑒𝑥𝑡
values in Type B burners does not contradict the results of Figure 4.5 as the kinetic regimes were
different.
Figure 4.7: Extinction strain rates of non-premixed CH4-N2/air flames: (left) measured and
computed results and (right) ratio of computed to measured values.
4.5. Concluding Remarks
Laminar flame speeds and extinction rate rates of premixed CH4/air flames and extinction
strain rates of non-premixed CH4-N2/air flames were measured in the counterflow configuration
with burners producing at their exits either uniform or non-uniform axial velocity profiles.
Measured data were simulated with a one-dimensional code and a detailed C2 kinetic model.
Inconsistencies were observed between one-dimensional modeling results and centerline
63
extinction measurements in burners with non-uniform exit axial velocity profiles, leading to large
disagreements between computed values and data. In burners with uniform exit axial velocity
profiles, one-dimensional modeling was found to be appropriate for centerline extinction
measurements and these measurements were in substantially better agreement with the computed
values. The flame speed measurements were found to be insensitive to the burner exit axial
velocity shape. Thus, the impact of flow field shape on the presently studied flame properties was
demonstrated and the implication for validation of kinetic rate parameters was evaluated. Though
analysis was limited to straight-tube burners, it is likely that the effects of flow non-uniformity
could appear in any counterflow configuration where both the stagnation pressure gradients are
sufficiently high and the location of flow-conditioning screens sufficiently far upstream from the
burner exit.
4.6. Acknowledgements
This material was based upon work supported as part of the CEFRC, an Energy Frontier
Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic
Energy Sciences under Award Number DE-SC0001198. Additional thanks to Mr. Christodoulos
Xiouris for assistance with the high-speed videography and Prof. Paul D. Ronney for discussions
on edge flame dynamics.
64
4.7. References
[4.1] F.N. Egolfopoulos, N. Hansen, Y. Ju, K. Kohse-Höinghaus, C.K. Law, F. Qi,
Prog. Energy Combust. Sci.43 (2014) 36-67.
[4.2] G. Dixon-Lewis, Proc. R. Soc. Lond. A 298 (1455) (1967) 495-513.
[4.3] R.J. Kee, J.F. Grcar, M.D. Smooke, J.A. Miller, A FORTRAN Program for
Modeling Steady Laminar One-Dimensional Premixed Flames, Report No.
SAND85-8240 Sandia National Laboratories, 1985.
[4.4] R.J. Kee, J.A. Miller, G.H. Evans, G. Dixon-Lewis, Symp. (Int.) Combust. 22
(1989) 1479-1494
[4.5] M.D. Smooke, Proc. Combust. Inst. 34 (2013) 65-98.
[4.6] C.B. Oh, A. Hamins, M. Bundy, J. Park, Combust. Theory Model. 12 (2) (2008)
283-302.
[4.7] U. Niemann, K. Seshadri, F.A. Williams, Combust. Flame 161 (2014) 138-146.
[4.8] C. Ji, E. Dames, Y.L. Wang, H. Wang, F.N. Egolfopoulos, Combust Flame 157
(2010) 277-287.
[4.9] J.M Bergthorson, S.D. Salisbury, P.E. Dimotakis, J. Fluid Mech. 681 (2011)
340-369.
[4.10] B.G. Sarnacki, G. Esposito, R.H. Krauss, H.K. Chelliah, Combust. Flame 159
(2012) 1026-1043.
[4.11] N. Bouvet, D. Davidenko, C. Chauveau, L. Pillier, Y. Yoon, Combust. Flame
161 (2104) 438-452.
[4.12] H.K. Chelliah, C.K. Law, T. Ueda, M.D. Smooke, F.A. Williams, Symp. (Int.)
Combust. 23 (1990) 503-511.
[4.13] J.C. Rolon, D. Veynante, J.P. Martin, Expts. Fluids 11 (1991) 313-324.
[4.14] C.E. Frouzakis, J. Lee, A.G. Tomboulides, K. Boulouchos, Symp. (Int.)
Combust. 27 (1998) 571-577.
[4.15] W.C. Park, A. Hamins, KSME Int. Jour. 16 (2) (2002) 262-269.
[4.16] J.M Bergthorson, D.G. Goodwin, P.E. Dimotakis, Proc. Combust. Inst. 30
(2005) 1637-1644.
[4.17] V. Mittal, H. Pitsch, F. Egolfopoulos, Combust. Theory Model. 16 (3) (2012)
419-433.
65
[4.18] K. Seshadri, F.A. Williams, Int. J. Heat Mass Transfer 21 (1978) 251-253.
[4.19] R.F. Johnson, A.C. VanDine, G.L. Esposito, H.K. Chelliah, Combust. Sci.
Tech. 187 (2015) 37-59.
[4.20] O. Park, P.S. Veloo, F.N. Egolfopoulos, Proc. Combust. Inst. 34 (2013) 711-
718
[4.21] P.S. Veloo, Y.L. Wang, F.N. Egolfopoulos, C.K. Westbrook, Combust. Flame
157 (2010) 1989-2004.
[4.22] Y.L. Wang, A.T. Holley, C. Ji, F.N. Egolfopoulos, T.T. Tsotsis, H.J. Curran,
Proc. Combust. Inst. 32 (2009) 1035-1042.
[4.23] C. Ji, Y.L. Wang, F.N. Egolfopoulos, J. Prop. Power 27 (4) (2011) 856-863.
[4.24] F.N. Egolfopoulos, Symp. (Int.) Combust. 25 (1994) 1375-1381.
[4.25] R.J. Kee, F.M. Rupley, J.A. Miller, Chemkin-II: A Fortran Chemical Kinetics
Package for the Analysis of Gas-Phase Chemical Kinetics, Report
No.SAND89- 8009, Sandia National Laboratories,1989.
[4.26] R.J. Kee, J. Warnatz, J.A. Miller, A FORTRAN Computer Code Package for
the Evaluation of Gas Phase Viscosities, Conductivities and Diffusion
Coefficients, Report No. SAND83-8209, Sandia National Laboratories, 1983.
[4.27] Y. Dong, A.T. Holley, M.G. Andac, F. N. Egolfopoulos, S. G. Davis, P.
Middha, H. Wang, Combust. Flame 142 (2005) 374–387.
[4.28] H. Wang, X. You, A.V. Joshi, et al., USC Mech Version II. High Temperature
Combustion Reaction Model of H2/CO/C1–C4 Compound, 2007, available at
http://www.ignis.usc.edu/USC_Mech_II.htm.
[4.29] O. Park, P.S. Veloo, N. Liu, F.N. Egolfopoulos, Proc. Combust. Inst. 33 (2011)
877-894.
[4.30] J. Jayachandran, R. Zhao, F.N. Egolfopoulos, Combust. Flame 161 (2014)
2305-2316.
[4.31] J. Jayachandran, A. Lefebvre, R. Zhao, F. Halter, E. Varea, B. Renou, F.N.
Egolfopoulos, Proc. Combust Inst. 35 (2015) 695-702.
[4.32] C.K. Law, Combustion Physics, Cambridge University Press, New York, NY,
U.S.A, 2006, p. 410.
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66
[4.34] M.S. Cha, P.D. Ronney, Combust. Flame 146 (2006) 312-328.
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67
Chapter 5
Two Phase Modeling of Counterflow Flame Propagation and Extinction
5.1. Introduction
Particle velocimetry techniques are based on measurement of small tracer particles
dispersed within a flow. If the particles respond with high fidelity to flow accelerations, then the
measured particle velocity can be used as a surrogate for the gas velocity. Significant applications
of particle velocimetry in stagnation flames include Laser Doppler Anemometry (LDA) (e.g.,
[5.1]-[5.3]), Particle Image Velocimetry (PIV) (e.g., [5.4] and [5.5]), and Particle Streak
Velocimetry (PSV)(e.g., [5.6]). A common rule-of-thumb for high fidelity particle motion is to
seek a Stokes number much less than one:
𝑆𝑡𝑘 ≡
𝜏 𝑝 𝜏 𝑔
(Eqn. 5.1)
where 𝜏 𝑝 is the characteristic particle response time and 𝜏 𝑔 is the charactertistic flow acceleration
time.
Along the stagnation streamline and upstream of the flame front in a gaseous counterflow,
the characteristic flow time can be defined as the reciprocal of the reference strain rate in the gas
phase, 𝜏 𝑔 ≡ 𝜅 𝑟𝑒𝑓 ,𝑔 −1
. If the drag force dominates particle motion and the particle phase mass density
is much greater than the gas phase mass density, then the particle response time may be
approximated by 𝜏 𝑝 =
𝜌 𝑝 𝑑 𝑝 2
18𝜇 𝑔 1
Φ
, where 𝜌 𝑝 is the particle mass density, 𝑑 𝑝 is the particle diameter,
𝜇 𝑔 is the gas dynamic viscosity, and Φ is a factor between 0 and 1 that accounts for the effects of
particle phase velocity slip and finite particle Reynolds number, 𝑅 𝑒 𝑝 ≡
|𝑢 𝑔 −𝑢 𝑝 |𝑑 𝑝 𝜈 𝑔 [5.7].
68
Substituting into Eqn. 5.1:
𝑆𝑡𝑘 =
𝜌 𝑝 𝑑 𝑝 2
18𝜇 𝑔 Φ
𝜅 𝑟𝑒𝑓 ,𝑔
(Eqn. 5.2)
Thus, small 𝑆𝑡𝑘 implies some combination of small values for 𝜌 𝑝 , 𝑑 𝑝 2
, and 𝜅 𝑟𝑒𝑓 ,𝑔 , a large value
for 𝜇 𝑔 , and Φ ≈ 1. Based on Ref 5.8, Φ can be defined:
Φ =
1+0.15𝑅 𝑒 𝑝 0.687
𝐶
(Eqn. 5.3)
where 𝐶 is the Cunningham slip correction factor. This analysis neglects the influence of other
forces on the particles, for example gravitational forces or thermophoretic forces, which can also
be important along the centerline of a stagnation flow.
Phase velocity slip is defined as the condition that 𝑅 𝑒 𝑝 ≠ 0, i.e., 𝑢 𝑝 ≠ 𝑢 𝑔 . For tracer
particles used in counterflow flames, phase slip is undesirable and its consequences have been
addressed in the literature. Sung and Law [5.2] suggested thermophoretic corrections to measured
particle velocities in regions of high temperature gradient. Egolfopoulos and Campbell [5.8] used
a quasi-one-dimensional opposed-jet code with dynamic and thermal coupling of a dispersed
particle phase to the gas phase to identify phase velocity slip when particles became sufficiently
large. Bergthorson et al. [5.9] considered thermophoretic and drag forces to model particle
dynamics along the centerline of a stagnation flow to correct for phase velocity slip and finite
sampling bias in measurements. The present study seeks to extend these studies to develop a
numerical approach to systematically quantify and correct for the effects of tracer particle phase
velocity slip in stagnation flow flame propagation and extinction measurements.
69
5.2. Modeling Approach
Counterflow flames were simulated using a quasi-one-dimensional opposed-jet code
[5.10, 5.11] including integration with the Sandia CHEMKIN [5.12] and Transport [5.13]
subroutine libraries, the multicomponent diffusion velocity formulation, radiation at the optically
thin limit, Soret diffusion, and an updated description of H and H2 diffusion coefficients [5.14].
The kinetic model used was that of Labbe and coworkers [5.15] which consisted of 111 species
and 924 reactions.
Two methods for computing the particle phase dynamics were explored. The first
approach, two-way coupling, simultaneously solved equations for the thermally and dynamically
coupled gas and particle phases (e.g., [5.8]). It was assumed that the particle number densities
were sufficiently sparse as to eliminate particle-particle interactions, the particle internal
temperature was homogenous, and radiation from the particle to gas phase was negligible. The
second method, one-way coupling, assumed that the gas phase imposed upon the particles but that
there was no feedback from the particle phase to the gas. In this case, the particle dynamics were
obtained by post-processing of the gas phase solution (e.g., [5.2] and [5.9]).
Since it was determined in section 5.3 that one-way coupling was sufficient, only the one-
way coupled equation of motion for the particle phase along the stagnation streamline is presented
here:
𝑚 𝑝 𝑑 𝑣 𝑥 ,𝑝 𝑑𝑡 = 𝐹 𝑆𝐷
+ 𝐹 𝑇𝑃
+ 𝐹 𝐺𝑅
(Eqn. 5.4)
where 𝑚 𝑝 =
𝜋 6
𝑑 𝑝 3
𝜌 𝑝 is the particle mass, 𝑣 𝑥 ,𝑝 the particle axial velocity, 𝑡 is time, 𝐹 𝑆𝐷
is the drag
force, 𝐹 𝑇𝑃
is the thermophoretic force, and 𝐹 𝐺𝑅
is the gravitational force.
The modified Stokes drag force:
70
𝐹 𝑆𝐷
=
−3𝜋 𝜇 𝑔 𝑑 𝑝 (𝑢 𝑝 − 𝑢 𝑔 )
𝐶 (1+ 0.15𝑅 𝑒 𝑝 0.687
)
(Eqn. 5.5)
corrected for finite particle Reynolds number, 𝑅 𝑒 𝑝 . The Cunningham slip factor, 𝐶 , accounted for
reduced drag in low density gases with respect to the particle Knudsen number, 𝐾𝑛 =
2𝑙 𝑓𝑝
𝑑 𝑝 , where
𝑙 𝑓𝑝
is the gas mean free path. In the Knudsen-Weber form:
𝐶 = 1+ 𝐾𝑛 [𝛼 + 𝛽 exp (−𝛾 /𝐾𝑛 )] (Eqn. 5.6)
and the constants 𝛼 =1.155, 𝛽 = 0.471, and 𝛾 =0.596 were used for oil droplets in air [5.16].
The thermophoretic force due to gas phase temperature gradient was:
𝐹 𝑇𝑃
=
−6𝜋 𝜇 𝑔 𝜈 𝑔 𝑑 𝑝 𝐶 𝑠 (
𝜆 𝑔 𝜆 𝑝 + 𝐶 𝑡 𝐾𝑛 )
∇𝑇 𝑔 𝑇 𝑔 (1 + 3𝐶 𝑚 𝐾𝑛 )(1 + 2
𝜆 𝑔 𝜆 𝑝 + 2 𝐶 𝑡 𝐾𝑛 )
(Eqn. 5.7)
where 𝜈 𝑔 =
𝜇 𝑔 𝜌 𝑔 is the kinematic viscosity, 𝜆 𝑔 and 𝜆 𝑝 are the gas and particle phase thermal
conductivities, 𝑇 𝑔 is the gas temperature, and fitting constants 𝐶 𝑠 =1.14, 𝐶 𝑡 =1.17, and 𝐶 𝑚 =2.18.
The gravitational force was:
𝐹 𝐺𝑅
= −𝑚 𝑝 𝑔 (Eqn. 5.8)
where 𝑔 is the acceleration due to gravity. Detailed discussion of these forces in the context of the
more generally applicable two-way coupling is available in the study of Egolfopoulos and
Campbell [5.8].
The parameter space for this numerical study was determined based on conditions realized
experimentally in Chapter 6, i.e., particle diameters between 0.5 and 5 μm, particle mass density
of 0.963 g/cm
3
relevant to silicone oil (Alfa Aesar CAS# 63148-62-9), premixed methane/air
flames, a thermodynamic pressure 𝑝 = 0.1 atmosphere, unburned reactant temperature 𝑇 𝑢 = 343
71
K, and a finite spatial domain of 30 mm. Additionally, plug flow bound conditions, or zero
boundary velocity gradients, were assumed.
To distinguish between the particle and gas phases, definitions were adopted as shown in
Figure 5.1. The axial velocity and velocity gradient for both phases was assumed to be equal at
the upstream boundary. Further downstream and ahead of the flame front, the gas phase reference
strain rate, 𝜅 𝑟𝑒𝑓 ,𝑔 , and the particle phase reference strain rate, 𝜅 𝑟𝑒𝑓 ,𝑝 , were defined as the maximum
magnitude of the axial velocity gradient in the axial direction for each respective phase. The gas
phase reference velocity, 𝑆 𝑢 ,𝑟𝑒𝑓 ,𝑔 , and particle phase reference velocity, 𝑆 𝑢 ,𝑟𝑒𝑓 ,𝑝 , were defined as
the minimum velocity ahead of the flame for each respective phase. Definitions of 𝑆 𝑢 ,𝑟𝑒𝑓 ,𝑝 and
𝜅 𝑟𝑒𝑓 ,𝑝 correspond to 𝑆 𝑢 ,𝑟𝑒𝑓
and 𝜅 𝑟𝑒𝑓
from previous chapters where it was implicitly assumed that
𝑆 𝑢 ,𝑟𝑒𝑓 ,𝑔 = 𝑆 𝑢 ,𝑟𝑒𝑓 ,𝑝 and 𝜅 𝑟𝑒𝑓 ,𝑔 = 𝜅 𝑟𝑒𝑓 ,𝑝 .
Figure 5.1: Schematic of centerline velocity and temperature profiles for gas and particle phases.
72
5.3. Results and Discussion
Computed strained flame response curves, 𝑆 𝑢 ,𝑟𝑒𝑓
𝑣𝑠 . 𝜅 𝑟𝑒𝑓
, at an equivalence ratio 𝜙 = 1
are shown in Figure 5.2. At high strain rates, they revealed less than 1% difference in 𝑆 𝑢 ,𝑟𝑒𝑓 and
𝜅 𝑟𝑒𝑓
between one-way and two-way coupling approaches. The difference between gas and particle
phases was 5% and 2% in 𝑆 𝑢 ,𝑟𝑒𝑓 and 𝜅 𝑟𝑒𝑓
, respectively. At low strain rates, there was only 2%
difference in 𝑆 𝑢 ,𝑟𝑒𝑓 between the gas and particle phases and negligible difference in 𝜅 𝑟𝑒𝑓
. Thus,
particle phase results with one-way coupling closely approximated results of the more rigorous
two-way coupling approach and particle dynamics differed from the gas phase. As one-way
coupling was much less computationally expensive, it was adopted throughout the remaining
results. One note of caution, notable differences between two-way and one-way coupling results
were observed inside the preheat and reaction layers of the flame and one-way coupling is not
recommended for use in these zones.
Figure 5.2: Comparison of strained flame response curves computed for the gas phase and particle
phase with either one-way or two-way coupling for CH4/air with 𝜙 = 1, 𝑝 = 0.1 atm, 𝑇 𝑢 = 343 K,
and 𝑑 𝑝 = 1 𝜇 m.
73
The role of particle diameter, 𝑑 𝑝 , on particle dynamics was investigated in a computed
CH4/air premixed twin flame at 𝜙 = 1, 𝑝 = 0.1 atm, and 𝑇 𝑢 = 343 K. as. As discussed in section
2.4, the range of particle sizes available in experiments was 0.5 μm < 𝑑 𝑝 < 5 μm. Here, 0.5 μm
will be called “small” particles and 5 μm will be called “large” particles. Computed velocity and
strain profiles, shown in Figure 5.3 for a representative case, show that small particles better
followed the gas phase, especially far upstream of the flame front. However, neither particle size
closely followed the gas phase near and within the flame preheat zone. 𝑆 𝑢 ,𝑟𝑒𝑓 ,𝑝 was generally lower
in magnitude than 𝑆 𝑢 ,𝑟𝑒𝑓 ,𝑔 and 𝜅 𝑟𝑒𝑓 ,𝑝 greater in magnitude than 𝜅 𝑟𝑒𝑓 ,𝑔 .
Figure 5.3 Comparison (top) velocity and (bottom) strain profiles for a CH4/air flame with 𝜙 = 1,
𝑝 = 0.1 atm, and 𝑇 𝑢 = 343 K and different particle sizes.
Computed strained flame response curves using both large and small particles, shown in
Figure 5.4, were within 1.3% of each other and therefore indistinguishable from each other in
measurements given typical uncertainty around 3%. The difference between particle and gas
phase computations was more pronounced, up to 6% for small particles and 4% for large particles
74
in 𝑆 𝑢 ,𝑟𝑒𝑓 . Differences in 𝜅 𝑟𝑒𝑓
between the gas and particles phases were small for small particles,
a maximum of 2%, but notable for large particles at 8%. Since strained flame measurements on
the particle phase are routinely used to extrapolate 𝑆 𝑢 0
, as illustrated in Figure 2.14, any bias in the
acquired data will also result in bias on the extrapolated 𝑆 𝑢 0
. Additionally, measurement of
extinction states necessarily occurs for the highest possible values of 𝜅 𝑟𝑒𝑓
where the present
observations suggest that substantial measurement bias may be incurred, especially for larger
particles. Thus, the present results demonstrate the importance of accounting for and correcting
phase velocity slip biases in low pressure counterflow flame measurements.
Figure 5.4 Comparison of the effect of particle size on computed strained flame response curves
for CH4/air with 𝜙 = 1, 𝑝 = 0.1 atm, and 𝑇 𝑢 = 343 K.
The forces acting on the particles were investigated as shown in Figure 5.5 for 𝑑 𝑝 = 1 μm.
Of the three particle forces, gravity was found to be negligible, in agreement with Refs. 5.8 and
5.9, drag was important throughout the domain, and thermophoresis played a role only inside and
75
beyond the preheat zone. Using the chain rule so that
𝑑 𝑣 𝑥 ,𝑝 𝑑𝑡
=
𝑑 𝑣 𝑥 ,𝑝 𝑑𝑥
𝑑𝑥
𝑑𝑡
=
𝑑 𝑣 𝑥 ,𝑝 𝑑𝑥
𝑣 𝑥 ,𝑝 and limiting
interest to the drag-dominated domain far upstream of the flame preheat zone, Eqn. 5.4 becomes:
𝑑 𝑣 𝑥 ,𝑝 𝑑𝑥 =
𝐹 𝑆𝐷
𝑚 𝑝 𝑣 𝑥 ,𝑝
(Eqn. 5.9)
The nature of the particle strain rate in this domain, and in particular 𝑘 𝑟𝑒𝑓 ,𝑝 , depended only on the
drag force and particle momentum. At low pressures, the drag force was weakened due to its
inverse dependence on 𝐶 , which increases with reduced pressure, and on its nearly direct
dependence on 𝜌 𝑔 through 𝑅 𝑒 𝑝 , which reduces with reduced pressure. Thus, low pressure
measurements of 𝜅 𝑟𝑒𝑓 ,𝑝 , including extinction state measurements, with practical values of particle
mass density and size will be subject to some degree of phase velocity slip leading to measurement
bias.
At 𝑆 𝑢 ,𝑟𝑒𝑓 ,𝑝 , where
𝑑 𝑣 𝑥 ,𝑝 𝑑𝑡
= 0 and drag and thermophoresis were important, one can express
from Eqn. 5.4:
𝐹 𝑆𝐷
= −𝐹 𝑇𝑃
(Eqn. 5.10)
and the nature of 𝑆 𝑢 ,𝑟𝑒𝑓 ,𝑝 depended on a balance between drag and thermophoresis. Near 𝑆 𝑢 ,𝑟𝑒𝑓 ,𝑝 ,
thermophoresis tended to slow down the particle velocity rather than allow it to accelerate with
drag and achieve a velocity minimum. The thermophoretic effect was reduced somewhat in the
present low pressure flames because it is directly proportional to the relative gas phase temperature
gradient which was more mild than in higher pressure flames. Still, the inability of the drag force
to efficiently direct the particle motion allows the particle to penetrate farther into the preheat zone
before reaching its velocity minimum. For these reasons, measurements of 𝑆 𝑢 ,𝑟𝑒𝑓 ,𝑝 also incur bias.
76
Figure 5.5 Comparison of computed particle forces along the centerline of a counterflow CH4/air
flame with 𝜙 = 1, 𝑝 = 0.1 atm, 𝑇 𝑢 = 343 K, and 𝑑 𝑝 = 1 𝜇 m.
The sensitivity of the present observations to the description of particle force sub-models
was tested by computing 𝑆 𝑢 ,𝑟𝑒𝑓 ,𝑝 and 𝜅 𝑟𝑒𝑓 ,𝑝 with nominal values for 𝐹 𝐷𝑅
and 𝐹 𝑇𝑃
and then again
by modifying either 𝐹 𝐷𝑅
or 𝐹 𝑇𝑃
by a constant ±10% throughout the domain. Resulting centerline
velocity profiles are shown in Figure 5.6. The imposed ±10% modification to either force changed
the computed 𝑆 𝑢 ,𝑟𝑒𝑓 ,𝑝 and 𝜅 𝑟𝑒𝑓 ,𝑝 values by a maximum of 0.4%. Therefore, the computed particle
dynamics were deemed insensitive to the exact descriptions of 𝐹 𝐷𝑅
and 𝐹 𝑇𝑃
.
77
Figure 5.6 Computed centerline gas axial velocity profiles for a CH4/air flame with 𝜙 = 1, 𝑝 =
0.1 atm, 𝑇 𝑢 = 343 K, and 𝑑 𝑝 = 1 𝜇 m compared to particle velocity profiles with nominal particle
forces and ±10% modification to (top) thermophoretic force and (bottom) drag force.
5.4. Concluding Remarks
Dynamics of silicone oil tracer particles were computed along the stagnation streamline in
a twin, premixed, counterflow CH4/air flame for 𝜙 = 1, 𝑝 = 0.1 atmosphere, and 𝑇 𝑢 = 343 K. The
numerical approach was based on a one-way coupling assumption considering drag,
thermophoretic, and gravitational forces acting on a spherical particle. Computed particle velocity
profiles differed from the gas phase by up to 6% in velocity and up to 8% in strain rate, but
computed particle velocity profiles of any particle size were within 2% of each other for all velocity
78
quantities. These conclusions were found to be insensitive to a 10% modification of either particle
drag or thermophoresis, while gravitational forces were found to be negligible in all cases. Based
on this, the present computational method for evaluating phase velocity slip in low pressure
counterflow flames was considered quantitative in nature. Since particles do not closely follow
the gas phase throughout the computed domain, the effect of phase velocity slip can lead to
measurement bias in experimental determination of flame propagation velocities and extinction
states. To address this bias, centerline velocity measurements performed on tracer particles should
be compared to the computed particle phase and not to computed gas phase velocity profiles.
79
5.5. References
[5.1] C. K. Wu, C. K. Law, Proceed. Combust. Inst. 20 (1984) 1941-1949.
[5.2] C. J. Sung, C. K. Law, Combust. Sci. and Tech. 99 (1994) 119-132.
[5.3] O. Park, P. S. Veloo, H. Burbano, F. N. Egolfopoulos, Combust. Flame 162
(2015) 1078-1094.
[5.4] Y. Dong, C. M. Vagelopoulos, G. R. Spedding, F. N. Egolfopoulos, Proceed.
Combust. Inst. 29 (2002) 1419-1426.
[5.5] T. Hirasawa, C. J. Sung, A. Joshi, Z. Yang, H. Wang, C. K. Law, Proceed.
Combust Inst. 29 (2002) 1427-1434.
[5.6] J .M Bergthorson, D. G. Goodwin, P. E. Dimotakis, Proceed. Combust. Inst.
30 (2005) 1637-1644.
[5.7] R. J. Adrian, J. Westerweel, Particle Image Velocimetry, Cambridge:
Cambridge University Press, 2011.
[5.8] F. N. Egolfopoulos, C. S. Campbell, Combust. Flame 117 (1999) 206-226.
[5.9] J. M. Bergthorson, P. E. Dimotakis, Exp. Fluids 41 (2006) 255-263.
[5.10] R.J. Kee, J.A. Miller, G.H. Evans, G. Dixon-Lewis, Symp. (Int.) Combust. 22
(1989) 1479-1494
[5.11] F.N. Egolfopoulos, Symp. (Int.) Combust. 25 (1994) 1375-1381.
[5.12] R.J. Kee, F.M. Rupley, J.A. Miller, Chemkin-II: A Fortran Chemical Kinetics
Package for the Analysis of Gas-Phase Chemical Kinetics, Report
No.SAND89- 8009, Sandia National Laboratories,1989.
[5.13] R.J. Kee, J. Warnatz, J.A. Miller, A FORTRAN Computer Code Package for
the Evaluation of Gas Phase Viscosities, Conductivities and Diffusion
Coefficients, Report No. SAND83-8209, Sandia National Laboratories, 1983.
[5.14] Y. Dong, A.T. Holley, M.G. Andac, F. N. Egolfopoulos, S. G. Davis, P.
Middha, H. Wang, Combust. Flame 142 (2005) 374–387.
[5.15] N. J. Labbe, R. Sivaramakrishnan, C. F. Goldsmith, Y. Georgievskii, J. A.
Miller, S. J. Klippenstein, Proceed. Combust. Inst. 36 (2016) IN PRESS.
[5.16] M. D. Allen, O. G. Raabe, J. Aerosol Sci., 13-6 (1982) 537-547.
80
Chapter 6
Methane Flame Propagation and Extinction at Low Pressures
6.1. Introduction
Practical combustors typically operate under high pressure and turbulent conditions which
are unsuitable for study of fundamental combustion processes. For this purpose, low pressure
laminar flames with quasi-one-dimensional structure which conform to the assumptions of
computationally efficient models can be produced in the laboratory. Comparison between these
measurements and simulations are used for studying fundamental combustion processes because
they may include detailed descriptions of chemical kinetics and molecular transport (e.g., [6.1] and
[6.2]). Measurements of global flame properties, such as laminar flame speeds, 𝑆 𝑢 0
s, and extinction
strain rates, 𝜅 𝑒𝑥𝑡 s, are widely reported at atmospheric and greater pressures to provide targets for
kinetic model validation and reaction rate uncertainty minimization (e.g., [6.3] and [6.4]).
Global flame properties capture the overall effect of numerous elementary chemical
reactions. Detailed information about flame structure can be derived from low pressure (~30 torr
or ~0.04 atmospheres) premixed burner-stabilized flames (PBSFs). These flames are broad
enough to permit high-resolution sampling of temperature and chemical species by an intrusive
sampling probe or optical diagnostics. However, the intrusive introduction of a sampling probe
modifies the flame structure (e.g., [6.5]) and can be a major source of experimental uncertainty.
Developing kinetic models can benefit from the insight provided by both flame structure and
global flame property measurements.
Recent reviews document the use of PBSFs to develop kinetic models [6.1, 6.2] and the
use of 𝑆 𝑢 0
s for kinetic model validation [6.1, 6.6] and reaction rate uncertainty minimization [6.7].
81
There are very few studies reporting 𝑆 𝑢 0
s and, to the author’s knowledge, no studies reporting 𝜅 𝑒𝑥𝑡 s,
at subatmospheric pressures. A representative sample of 𝑆 𝑢 0
data useful for kinetic model
validation was collected in a recent review by Ranzi and coworkers [6.6] who included thirty-six
sources for data at atmospheric pressure, sixteen for higher pressures, and only two sources for
subatmospheric flames. The two subatmospheric studies, both at 𝑝 = 0.5 atm, were those of
Egolfopoulos, Zhu, and Law [6.8] who measured 𝑆 𝑢 0
𝑠 for flames of CH4, C2H2, C2H4, C2H6, and
C3H8/air mixtures in a counterflow and Hassan et al. [6.9] who measured 𝑆 𝑢 0
s for flames of CH4/air
mixtures in spherically expanding flames. An additional study by Konnov, Riemeijer, and de
Goey [6.10] reported 𝑆 𝑢 0
s of CH4/air and CH4/H2/air mixtures at 298 K and 0.2 ≤ 𝑝 ≤ 1
atmospheres in heat-flux stabilized flames. Additionally, Law and coworkers measured 𝑆 𝑢 0
𝑠 in
spherically expanding flames of H2/N2/O2 mixtures down to 0.25 atmospheres [6.11].
The relative scarcity of subatmospheric flame data might be understood considering
comments in a recent study [6.12] which claimed that studying counterflow flames at “pressures
below 0.03 atm… would be both difficult and rather uninteresting for most combustion purposes.”
One key experimental difficulty associated with low pressure counterflow flames, the reliable
measurement of flow velocities, was addressed in Chapter 5. A primary goal of this work is to
demonstrate that low pressure flame data does have scientific value. Thus, presented here are
measured and computed CH4/air 𝑆 𝑢 0
s and CH4-N2/O2 non-premixed flame 𝜅 𝑒𝑥𝑡 s at subatmospheric
conditions down to 0.1 atmospheres in a counterflow
82
6.1.1. Pressure Dependent Combustion Kinetics
The reaction rate of an elementary chemical reaction, 𝜔 𝑒𝑙𝑒𝑚 , is traditionally described to
depend on pressure in two ways. The first, based on the idea that reactants must collide and
physically interact before reaction can occur, is codified in the Law of Mass Action which states
that 𝜔 𝑒𝑙𝑒𝑚 is proportional to the concentrations of the reactants. Consequently, 𝜔 𝑒𝑙𝑒𝑚 ~𝑝 𝑚 , where
𝑚 is the reaction molecularity and 𝑚 = 3, 2, and 1 for ter-, bi-, and unimolecular reactions,
respectively. Relative to bi- and unimolecular reactions, reaction rates of three body reactions can
potentially be reduced with appropriately low pressures until their role becomes negligible. The
second description of pressure dependence is in the rate coefficient, 𝑘 , which describes the nature
of energy transfer between and within colliding species [6.13]. The pressure dependence of 𝑘 is
an active area of research and therefore subject to notable uncertainties in many cases [6.14].
In contrast to the attenuating effect of low pressures on three-body reactions, recent work
by Labbe and coworkers [6.15, 6.16] suggested that low pressures enhance the prompt dissociation
of HCO radicals to H and CO. Describing HCO as a “weakly bound radical”, the authors of Ref.
6.15 proposed that some portion of the highly energized HCO radicals produced in the flame do
not stabilize at local thermal equilibrium, but instead may dissociate to H and CO. Including HCO
prompt dissociation in calculations enhances reactivity as a source of H radicals and CO. It was
shown that including HCO prompt dissociation in flame computations has a notable effect on fuels
which tend to produce HCO from CH2O. For example, computed CH4/air 𝑆 𝑢 0
s at 1 atmosphere
were shown to increase by up to 8% upon addition of reactions for HCO prompt dissociation.
83
6.2. Experimental Approach
Measurements were performed in the counterflow configuration using straight-tube
burners at reduced pressures and elevated unburned reactant temperatures. 𝑆 𝑢 0
s were measured in
the symmetric, twin flame configuration with 𝑇 𝑢 = 343 K and 𝜙 = 0.8, 1.0, and 1.2 at 𝑝 = 0.50,
0.25, and 0.15 atmospheres and for 0.7 ≤ 𝜙 ≤ 1.2 at 𝑝 = 0.1 atmosphere. Non-premixed flame
𝜅 𝑒𝑥𝑡 𝑠 were measured for CH4-N2 mixtures against pure O2 at 𝑝 = 0.10 atm with 𝑇 𝐶𝐻 4−𝑁 2
= 343
K and 𝑇 𝑂 2
= 296 K. When 𝑝 ≥ 0.25 atm, the burner diameter was 𝐷 𝑛𝑜𝑧𝑧 = 21 mm and separation
distance was 𝐿 𝑛𝑜𝑧𝑧 = 16 mm. When 𝑝 ≤ 0.15 atm, 𝐷 𝑛𝑜𝑧𝑧 = 28 mm and 𝐿 𝑛𝑜𝑧𝑧 = 20 mm, except
for flame propagation measurements at 𝑝 = 0.10 atmosphere where 𝐿 𝑛𝑜𝑧𝑧 = 30 mm.
To ensure flow boundary conditions that conform to the assumptions of one-dimensional
computational models (e.g. [6.17]), flow conditioning screens were placed within the burner tubes
at the burner exit and about 5𝐷 𝑛𝑜𝑧𝑧 upstream as shown schematically in Figure 2.6. Flow velocities
were measured using particle image velocimetry with silicone oil (Alfa Aesar CAS# 63148-62-9)
droplet flow tracers produced by a pneumatic nebulizer (Meinhard HEN-170-A0.3). The high
velocity gas and particle mixture exiting the nebulizer was impinged onto the wall of a spray
chamber and then passed through an inline 5 μm particle filter to prevent large particles from
reaching the measurement zone. A schematic of the overall system is shown in Figure 6.1 and
extensive discussion of the experimental methods is available in Chapter 2.
84
Figure 6.1: Schematic of the experimental system in a premixed, twin flame configuration.
𝑆 𝑢 0
s and 𝜅 𝑒𝑥𝑡 s were determined using local flow velocity measurements along the
stagnation streamline. In acknowledgement of the presence of phase velocity slip in velocity
measurements, explicit distinction was made between the particle phase, denoted with subscript
“𝑝 ”, and the gas phase, denoted with subscript “𝑔 ”. Shown in Figure 6.2, a reference particle
phase velocity, 𝑆 𝑢 ,𝑟𝑒𝑓 ,𝑝 , and reference particle phase strain rate, 𝜅 𝑟𝑒𝑓 ,𝑝 , were defined as the
minimum axial velocity and the maximum norm of the axial velocity gradient in the axial direction,
respectively, ahead of the flame from. These correspond exactly to definitions of 𝑆 𝑢 ,𝑟𝑒𝑓
and 𝜅 𝑟𝑒𝑓
from previous chapters. 𝑆 𝑢 ,𝑟𝑒𝑓 ,𝑔 and 𝜅 𝑟𝑒𝑓 ,𝑔 were defined on the gas phase analogously to their
particle phase counterparts. Axial velocity and velocity gradient at the burner exit were measured
for use as boundary conditions in one-dimensional simulations (e.g., [6.17] and [6.18]).
85
Figure 6.2: Representative gas and particle phase centerline axial velocity profiles with definitions
of observables.
Processing of acquired centerline axial velocity profiles was necessary due to added
uncertainty resulting from low tracer particle seeding densities at low pressures. These procedures
are discussed in section 2.7.
6.3. Modeling Approach
Freely propagating flames were computed with the PREMIX code [6.19], while strained,
counterflow flames were computed using an opposed-jet code [6.20, 6.21]. Both codes include
radiation at the optically thin limit, Soret diffusion, an updated description of H and H2 diffusion
86
coefficients [6.22], and were linked with the Sandia CHEMKIN [6.23] and Transport [6.24]
subroutine libraries. The strained flame simulations accounted for the experimental boundary
velocity gradients and for a finite spatial domain. Particle phase dynamics were computed based
on a one-way coupling assumption and 1 μm particle diameter, details of which are available in
Chapter 5.
Extinction states were computed by first establishing a vigorously burning flame and
subsequently increasing the boundary velocity until the extinction state was approached. Near
extinction, a two-point continuation was employed whereby the problem was solved with exit
velocity, and therefore strain rate, as a dependent variable (e.g. [6.25]). All simulations employed
the multicomponent transport formulation and grid resolutions sufficient to produce grid-
independent results. Two kinetic models were used, USC Mech II [6.26], hereafter called
“USCM2”, with 111 species and 784 reactions and the mechanism of Labbe et al. [6.16], hereafter
called “USCM2 + HCO”, which consisted of USC Mech II with additional reactions describing
HCO prompt dissociation resulting in 111 species and 924 reactions,.
6.4. Results and Discussion
6.4.1. Boundary Phase Velocity Slip
To address the possibility of phase velocity slip as the burner exit, the total volumetric
flowrate, 𝑄 ̇ , was calculated from the measured axial velocity profile across the burner exit plane,
at 𝑇 𝑢 = 343 K, 𝑝 = 0.1 atmosphere, and a Reynolds number 𝑅𝑒 ≈ 200, as shown Figure 6.3, and
compared to 𝑄 ̇ = 850 cm
3
/s from sonic orifice calibrations. The measured and calibrated 𝑄 ̇ s were
87
equal and therefore phase velocity slip at the boundary was neglected. Thus, the particle phase
boundary velocity and velocity gradients were assumed equal to the gas phase.
Figure 6.3: Measured counterflow axial velocity profile at the burner exit for 𝑇 𝑢 = 343 K, 𝑝 =
0.1 atm, and 𝑅𝑒 ≈ 200 in air.
6.4.2. Laminar Flame Speeds
Measured and computed 𝑆 𝑢 0
𝑠 for CH4/air flames with 𝑇 𝑢 = 343 K and 0.1 ≤ 𝑝 ≤ 1 atm are
shown in Figure 6.4. Reported values at 𝑝 = 1 atm were adapted from Park et al. [6.27] at 𝑇 𝑢 =
298 K and scaled to 343 K using Eqn. 6.1:
𝑆 𝑢 ,343
0
=𝑆 𝑢 ,298
0
𝑆 𝑢 ,343,𝑐𝑜𝑚𝑝 0
𝑆 𝑢 ,298,𝑐𝑜𝑚𝑝 0
(Eqn. 6.1)
88
where 𝑆 𝑢 ,343
0
is the value shown in Figure 6.4 at 343 K, 𝑆 𝑢 ,298
0
is the measured value reported in
Ref. 6.27 at 298 K, 𝑆 𝑢 ,343,𝑐𝑜𝑚𝑝 0
is the value computed with the USCM2+HCO kinetic model at 343
K, and 𝑆 𝑢 ,298,𝑐𝑜𝑚𝑝 0
is the value computed at 298 K. This computationally-assisted scaling captures
both the effect of density differences and, to the first order, kinetic differences.
Figure 6.4: Measured and computed 𝑆 𝑢 0
s of CH4/air flames for 𝑇 𝑢 = 343 K and 0.1 atm ≤ 𝑝 ≤ 1
atm.
At 𝑝 = 1 atm, computations using USCM2 closely predict the data while computations
using USCM2+HCO overpredict the measurements. At 𝑝 = 0.1 atmosphere, computations using
USCM2 underpredicted the data while those using USCM2+HCO show good agreement. At
intermediate pressures, the measurements fell between the predictions of either model.
Disagreement between experiments and modeling with USCM2 at low pressures were notable
89
because it has been shown that computations of CH4/air 𝑆 𝑢 0
s with USCM2 closely match
measurements over the range 1 ≤ 𝑝 ≤ 4 atm [6.27]. Measured and computed 𝑆 𝑢 0
𝑠 for CH4/air
flames with 𝑇 𝑢 = 343 K and 𝑝 = 0.1 atmosphere are shown in Figure 6.5. Predictions of 𝑆 𝑢 0
using
USCM2 notably underpredict the data across the whole range of 𝜙 while predictions using
USCM2+HCO agreed with the measurements.
Figure 6.5: Measured and computed 𝑆 𝑢 0
s of CH4/air flames for 𝑇 𝑢 = 343 K and 𝑝 = 0.1 atm.
Reasons for the differences in computed 𝑆 𝑢 0
between the models were explored based on
sensitivity and reaction flux analyses in a freely propagating CH4/air flame with 𝜙 = 1, 𝑇 𝑢 = 343
K, and 𝑝 = 0.1 atm. The sensitivity of computed 𝑆 𝑢 0
to kinetics is shown in Figure 6.6. As is
often found in hydrocarbon flame propagation studies at higher pressures, the most sensitive
90
reactions include the main branching reaction R1 and main CO oxidation reaction R3. Results
from both models suggest similar sensitivity to elementary reactions consuming HCO (R2, R4,
and R9) and CH3 (R5 and R8). However, 𝑆 𝑢 0
s computed with USCM2+HCO indicated additional
sensitivity to CH2O consumption reactions, R6 and R7, that were insensitive in results computed
with USCM2. Reaction R6 is the prompt dissociation analogue of reaction R7 and is not an
elementary reaction, but rather an ad hoc modification to represent a series of processes including
consumption of CH2O and formation/dissociation of HCO. Therefore, it does not exist in USCM2
so that its calculated sensitivity coefficient with USCM2 was zero.
Figure 6.6: Comparison of computed logarithmic sensitivity coefficients of 𝑆 𝑢 0
to kinetics for
CH4/air flames with 𝜙 = 1, 𝑇 𝑢 = 343 K, and 𝑝 = 0.1 atm.
91
Computed reaction flux analysis for freely propagating CH4/air flames with 𝜙 = 1, 𝑇 𝑢 =
343 K, and 𝑝 = 0.1 atm is shown in Figure 6.7. Both kinetic models indicated H-abstraction from
CH4 to CH3 radicals followed by three major pathways. The path proceeding through CH2
*
showed
strong similarities in both models and it was concluded that the role of HCO prompt dissociation
did not strongly affect this pathway for the present conditions. Similarly, the path proceeding
through C2H6 showed mainly minor differences, although consumption routes of C2H3 forming
C2H2 did show notable differences which could imply differences propensity for soot formation.
However, C2 species exist in low concentrations in the presently studied CH4/air flame so that C2
kinetics do not exert a strong influence on computed 𝑆 𝑢 0
.
Figure 6.7: Computed consumption pathways for CH4/air flames with 𝜙 = 1, 𝑇 𝑢 = 343 K, and
𝑝 = 0.1 atm.
92
Significant differences between the kinetic models were observed along the dominant
CH2O path, in agreement with Ref. 19. Results of USCM2 showed complete consumption of
CH2O to HCO while results of USCM2+HCO permitted an additional pathway accounting for
20% of CH2O consumption directed to CO. This additional pathway was one possible route for
HCO prompt dissociation and was mediated mainly by reaction R6. The additional sensitivity of
reactions R6 and R7 in USCM2+HCO was explained based on a competition between them to
consume CH2O. Reaction R6 enhanced reactivity because it consumed CH2O, skipped over HCO,
and directly formed CO along with chain propagation of an H radical which may then participate
in the critical main branching reaction R1. Reaction R7 did not enhance flame reactivity in the
same way because it consumed CH2O to HCO along with chain termination of an H radical.
Results using USCM2 showed about 93% conversion of HCO to CO and zero recombination of
HCO to CH2O. This contrasts with results using USCM2+HCO where 87% of HCO converted to
CO and 19% of HCO recombined to CH2O.
Mole fraction profiles computed for key carbon-containing species were normalized by the
peak value computed using USCM2 and are shown in Figure 6.8. Intermediate species CH2O and
CO were found to assume similar peak values using either USCM2 or USCM2+HCO while peak
values of HCO were about 10% lower using USCM2+HCO, as may be suggested by reduced
formation rates due to dissociation. The location of the peak concentrations was found to occur
earlier in the flame when using USCM2+HCO, an indication of enhanced fuel consumption and
reactivity.
93
Figure 6.8: Computed concentration profiles of select carbon-containing species for CH4/air
flames with 𝜙 = 1, 𝑇 𝑢 = 343 K, and 𝑝 = 0.1 atm. Values were normalized by the peak value
computed with USCM2.
Mole fraction profiles computed for active radical species were normalized by the peak
value computed using USCM2 and are shown in Figure 6.9. It was observed that radical species
H, O, and OH existed in greater concentrations throughout the computational domain when using
USCM2+HCO, especially near the respective peak values, and that peak values occurred earlier
in the flame. Peak concentrations of H and O radicals were about 20% greater when using
USCM2+HCO, although peak values of OH radicals were similar between models.
94
Figure 6.9: Computed concentration profiles of select active radical species for CH4/air flames
with 𝜙 = 1, 𝑇 𝑢 = 343 K, and 𝑝 = 0.1 atm. Values were normalized by the peak value obtained
with USCM2.
The greater availability of active radicals when using USCM2+HCO resulted in enhanced
rates of highly sensitive elementary reactions as shown for reactions R1, R3, and R9 in Figure
6.10. The peak forward rate of the main branching reaction R1 was nearly 25% greater when using
USCM2+HCO. A kinetic rather than thermal cause for the 𝑆 𝑢 0
and flame structure differences was
further supported based on the nearly identical maximum flame temperatures of 1950 K using
either kinetic model.
95
Figure 6.10: Computed forward reaction rate profiles of select sensitive reactions for CH4/air
flames with 𝜙 = 1, 𝑇 𝑢 = 343 K, and 𝑝 = 0.1 atm. Values were normalized by the peak value
obtained with USCM2.
6.4.3. Non-Premixed Flame Extinction
Measured and computed 𝜅 𝑒𝑥𝑡 s for CH4-N2/O2 non-premixed flames with 𝑇 𝐶𝐻 4−𝑁 2
= 343
K, 𝑇 𝑂 2
= 296 K and 𝑝 = 0.1 atmosphere are shown in Figure 6.11. Computed 𝜅 𝑒𝑥𝑡 s using either
model underpredicted the data, although those computed using USCM2+HCO were notably closer
to the measured data compared to those computed using USCM2.
96
Figure 6.11: Measured and computed 𝜅 𝑒𝑥𝑡 s for CH4-N2/O2 non-premixed flames with 𝑇 𝐶𝐻 4−𝑁 2
=
343 K, 𝑇 𝑂 2
= 296 K and 𝑝 = 0.1 atm.
Reasons for the differences in computed 𝜅 𝑒𝑥𝑡 between the models were explored based on
sensitivity and reaction flux analysis in a non-premixed CH4-N2/O2 flame with 𝑋 𝐶𝐻 4
= 0.112,
𝑇 𝐶𝐻 4−𝑁 2
= 343 K, 𝑇 𝑂 2
= 296 K and 𝑝 = 0.1 atm. Sensitivity of computed 𝜅 𝑒𝑥𝑡 to kinetics is
shown in Figure 6.12 where a slightly different set of reactions was observed compared to those
appearing in the sensitivity analysis of 𝑆 𝑢 0
. Among the differences, reactions R6, R7, and R8 no
longer appeared among the most sensitive and were replaced by reactions R10, R11, and R12.
Reaction R10 was the only fuel consumption reaction to appear among the most sensitive reactions
for either flame propagation or extinction computations, although the magnitude of its sensitivity
97
coefficient was modest compared to other reactions. Reaction R11 is the main three-body
termination reaction which often appears in sensitivity analyses at higher pressures. Its importance
in these low pressure flames was explained based on the relatively low flame temperatures, and
therefore relatively high mass densities, in calculations of 𝜅 𝑒𝑥𝑡 where 𝑇 𝑚𝑎𝑥
≈ 1550 K. This
maximum temperature was about 80% of that observed in flame propagation. Overall, the
calculated sensitivities of 𝜅 𝑒𝑥𝑡 to reaction rates did not reveal strong differences between the
kinetic models despite the large differences in calculated 𝜅 𝑒𝑥𝑡 s.
Figure 6.12: Comparison of computed logarithmic sensitivity coefficients of 𝜅 𝑒𝑥𝑡 to kinetics for
CH4-N2/O2 flames with 𝑋 𝐶𝐻 4
= 0.112, 𝑇 𝐶𝐻 4−𝑁 2
= 343 K, 𝑇 𝑂 2
= 296 K and 𝑝 = 0.1 atm.
A reaction flux analysis for the same flame at the extinction state is shown in Figure 6.13.
The main observations made for flame propagation reaction flux analysis also applied for non-
98
premixed flame extinction, however, activity by H radicals was somewhat suppressed and activity
by O and OH radicals enhanced.
Figure 6.13: Fuel consumption pathways computed at 𝜅 𝑒𝑥𝑡 for 𝑋 𝐶𝐻 4
= 0.112, 𝑇 𝐶𝐻 4−𝑁 2
= 343 K,
𝑇 𝑂 2
= 296 K and 𝑝 = 0.1 atm.
Mole fraction profiles computed for key carbon-containing species normalized by the
maximum value computed using USCM2 are shown in Figure 6.14 and normalized mole fraction
profiles computed for active radical species are shown in Figure 6.15. Peak concentrations of
CH2O and CO were similar between model results while HCO peak concentrations were somewhat
lower when using USCM2+HCO. Additionally, it was observed that H radicals existed in greater
concentrations throughout the flame when using USCM2+HCO, while O and OH radicals existed
in similar or lower concentrations. 𝜅 𝑒𝑥𝑡 calculated by USCM2+HCO at 𝑋 𝐶𝐻 4
= 0.112 was 21%
99
higher than that calculated using USCM2 while peak flame temperatures at extinction calculated
using USCM2+HCO (~1540 K) were about 50 K lower compared to USCM2 (~1590 K). This
again highlights that the enhanced reactivity observed in the present study when including prompt
HCO dissociation was due primarily to kinetic rather than thermal effects.
Figure 6.14: Carbon-containing intermediate species profiles computed at 𝜅 𝑒𝑥𝑡 for 𝑋 𝐶𝐻 4
= 0.112,
𝑇 𝐶𝐻 4−𝑁 2
= 343 K, 𝑇 𝑂 2
= 296 K and 𝑝 = 0.1 atm. Values are normalized by the maximum values
computed using USCM2. In each plot, the upper branch coincides with the fuel side of the flame
and the lower branch with the oxidizer side.
100
Figure 6.15: Active radical species profiles computed at 𝜅 𝑒𝑥𝑡 for 𝑋 𝐶𝐻 4
= 0.112, 𝑇 𝐶𝐻 4−𝑁 2
= 343
K, 𝑇 𝑂 2
= 296 K and 𝑝 = 0.1 atm. Values are normalized by the maximum values computed using
USCM2. In each plot, the upper branch coincides with the oxidizer side of the flame and the lower
branch with the fuel side.
6.5. Concluding Remarks
Laminar flame speeds of methane/air flames and extinction strain rates of non-premixed
methane-nitrogen/oxygen flames were measured in a counterflow at subatmospheric pressures.
Two kinetic models were used to compute values for comparison with measured data, the USC
Mech II kinetic model and another which consisted of USC Mech II with additional reactions to
describe formyl prompt dissociation. In agreement with previous research, it was found that
reactions for formyl prompt dissociation enhanced reactivity as indicated by greater computed
values of laminar flame speeds and extinction strain rates. At 0.1 atmosphere, and when using the
101
kinetic model with formyl prompt dissociation, the kinetics of formaldehyde consumption were
sensitized in freely propagating flame calculations, but not in strained flame computations at the
extinction state. Data at the lowest pressures studied were better predicted with the kinetic model
including reactions for formyl radical prompt dissociation while data at atmospheric pressure were
better predicted by the kinetic model without formyl radical prompt dissociation. The inability of
a single kinetic model to capture the pressure dependence of flame propagation speeds and
extinction states suggests persisting uncertainty in the kinetics of hydrocarbon oxidation,
especially for reactions related to formyl radical production and consumption.
102
6.6. References
[6.1] F. N. Egolfopoulos, N. Hanse, Y. Ju, K. Kohse-Höinghaus, C. K. Law, F. Qi, Prog.
Energ. Combust. 43 (2014) 36-67.
[6.2] N. Hansen, T. A. Cool, P. R. Westmoreland, K. Kohse-Höinghaus, Prog. Energ.
Combust. 35 (2009) 168-191.
[6.3] O. Park, P. S. Veloo, D. A. Sheen, Y. Tao, F. N. Egolfopoulos, H. Wang, Combust.
Flame 172 (2016) 136-152.
[6.4] P. S. Veloo, Y. L. Wang, F. N. Egolfopoulos, C. K. Westbrook, Combust. Flame 157
(2010) 1989-2004.
[6.5] V. Gururajan, F. N. Egolfopoulos, K. Kohse-Höinghaus, Proceed. Combust. Inst. 35
(2015) 821-829.
[6.6] E. Ranzi, A. Frassoldati, R. Grana, A. Cuoci, T. Faravelli, A. P. Kelley, C. K. Law,
Prog. Energ. Combust. 38 (2012) 468-501.
[6.7] H. Wang, D. A. Sheen, Prog. Energ. Combust. 47 (2015) 1-31.
[6.8] F. N. Egolfopoulos, D. L. Zhu, C. K. Law, Proceed. Combust. Inst. 23 (1990) 471-
478.
[6.9] M. I. Hassan, K. T. Aung, G. M. Faeth, Combust. Flame 115 (1998) 539-550.
[6.10] A. A. Konnov, R. Riemeijer, L. P. H. de Goey, Fuel 89 (2010) 1392-1396.
[6.11] S. Yang, X. Yang, F. Wu, Y. Ju, C. K. Law, Proceed. Combust. Inst. 36 (2017) 491-
498.
[6.12] U. Niemann, K. Seshadri, F. A. Williams, Combust. Flame 162 (2015) 1540-1549.
[6.13] M. J. Pilling, Science 346-6214 (2014) 1183-1184.
[6.14] D. L. Baluch, C. J. Cobos, R. A. Cox, C. Esser, P. Frank, Th. Just, J. A. Kerr M. J.
Pilling, J. Troe, R. W. Walker, J. Warnatz, J. Phys. Chem. Ref. Data 21, 411 (1992)
411-734.
[6.15] N. J. Labbe, R. Sivaramakrishnan, C. F. Goldsmith, Y. Georgievskii, J. A. Miller, S. J.
Klippenstein, J. Phys. Chem. Lett. 7 (2016) 85-89.
[6.16] N. J. Labbe, R. Sivaramakrishnan, C. F. Goldsmith, Y. Georgievskii, J. A. Miller, S. J.
Klippenstein, Proceed. Combust. Inst. 36 (2016) IN PRESS.
[6.17] R. R. Burrell, R. Zhao, D. J. Lee, H. Burbano, F. N. Egolfopoulos, Proceed. Combust.
Inst. 36 (2016) IN PRESS.
103
[6.18] C. Ji, E. Dames, Y. L. Wang, H. Wang, F. N. Egolfopoulos, Combust. Flame 157
(2010) 277-287.
[6.19] R. J. Kee, J. F. Grcar, M. D. Smooke, J. A. Miller, A FORTRAN Program for
Modeling Steady Laminar One-Dimensional Premixed Flames, Sandia
Report.SAND85-8240, Sandia National Laboratories, 1985.
[6.20] R.J. Kee, J.A. Miller, G.H. Evans, G. Dixon-Lewis, Proc. Comb. Inst. 22 (1988)
1479–1494.
[6.21] F.N. Egolfopoulos, Proc. Comb. Inst. 25 (1994) 1375–1381
[6.22] Y. Dong, A.T. Holley, M.G. Andac, F.N. Egolfopoulos, S.G. Davis, P. Middha, H.
Wang, Combust. Flame 142 (2005) 374–387.
[6.23] R. J. Kee, F. M. Rupley, J. A. Miller, Chemkin-II: A Fortran Chemical Kinetics
Package for the Analysis of Gas-Phase Chemical Kinetics, Sandia Report SAND89-
8009, Sandia National Laboratories, 1989.
[6.24] R. J. Kee, J. Warnatz, J. A. Miller, A Fortran Computer Code Package for the
Evaluation of Gas-Phase Viscosities, Conductivities, and Diffusion Coefficients,
Sandia Report SAND83-8209, Sandia National Laboratories, 1983.
[6.25] F.N. Egolfopoulos, P.E. Dimotakis, Proc. Comb. Inst. 27 (1998) 641–648.
[6.26] H. Wang, X. You, A.V. Joshi, et al., USC Mech Version II. High Temperature
Combustion Reaction Model of H2/CO/C1–C4 Compound, 2007, available at
http://www.ignis.usc.edu/USC_Mech_II.htm.
[6.27] O. Park, P. S. Veloo, N. Liu, F. N. Egolfopoulos, Proceed. Combust. Inst. 33 (2011)
877-894.
104
Closing and Recommendations
Methane combustion is sure to be an important source of energy for the foreseeable future
as a cheap, safe, and low carbon alternative to other fossil fuel sources. Despite decades of research
into the fundamental processes that govern high temperature methane oxidation, comprehensive
understanding will require more effort. Low pressure flames present an excellent platform to study
low pressure flame kinetics which can inform understanding at higher pressures. Without a
comprehensive foundation, extrapolating existing knowledge to higher pressures relevant for
practical combustors can introduce problems.
Therefore, the following recommendations are made. The role of formyl radical chemistry
should be explored through comparative measurements and simulations in flames where
formaldehyde and formyl radical kinetics play an important role, for example, methanol, ethanol,
formaldehyde, and methyl formate. Obtaining the lowest possible pressures ensures the strongest
possible sensitization of the relevant kinetics. Additionally, low pressure flame propagation and
extinction state measurements should be performed for a series of small hydrocarbon molecules
that constitute the foundational chemistry in larger fuels used in propulsion and power generation
applications. Good targets are ethane, propane, the butane isomers, ethylene, acetylene, propene,
and the isobutene isomers.
In the hurry to reach experimental conditions which are directly relevant to practical
combustors, the subatmospheric pressure regime has been largely ignored. Hopefully this thesis
has demonstrated that such a narrowly-focused approach can neglect potential useful studies. It is
only through diligent and comprehensive investigation that a complete picture can be formed.
Abstract (if available)
Abstract
Methane is the smallest hydrocarbon molecule, the fuel most widely studied in fundamental flame structure studies, and a major component of natural gas. Despite many decades of research into the fundamental chemical kinetics involved in methane oxidation, ongoing advancements in research suggest that more progress can be made. Though practical combustors of industrial and commercial significance operate at high pressures and turbulent flow conditions, fundamental understanding of combustion chemistry in flames is more readily obtained for low pressure and laminar flow conditions. ❧ Measurements were performed from 1 to 0.1 atmospheres for premixed methane/air and non-premixed methane-nitrogen/oxygen flames in a counterflow. Comparative modeling with quasi-one-dimensional strained flame codes revealed bias-induced errors in measured velocities up to 8% at 0.1 atmospheres due to tracer particle phase velocity slip in the low density gas reacting flow. To address this, a numerically-assisted correction scheme consisting of direct simulation of the particle phase dynamics in counterflow was implemented. Addition of reactions describing the prompt dissociation of formyl radicals to an otherwise unmodified USC Mech II kinetic model was found to enhance computed flame reactivity and substantially improve the predictive capability of computed results for measurements at the lowest pressures studied. Yet, the same modifications lead to overprediction of flame data at 1 atmosphere where results from the unmodified USC Mech II kinetic mechanism agreed well with ambient pressure flame data. The apparent failure of a single kinetic model to capture pressure dependence in methane flames motivates continued skepticism regarding the current understanding of pressure dependence in kinetic models, even for the simplest fuels.
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Asset Metadata
Creator
Burrell, Robert Roe
(author)
Core Title
Studies of methane counterflow flames at low pressures
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Mechanical Engineering
Degree Conferral Date
2017-05
Publication Date
04/18/2017
Defense Date
12/06/2016
Publisher
Los Angeles, California
(original),
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
chemical kinetics,combustion,combustion simulation,counterflow,diffusion flame,flame extinction,formyl radical,laminar flame speed,low pressure flame,methane,non-premixed,non-premixed flame,OAI-PMH Harvest,particle dynamics,particle image velocimetry,premixed,premixed flame
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Contributor
Electronically uploaded by the author
(provenance)
Advisor
Egolfopoulos, Fokion (
committee chair
), Ronney, Paul (
committee member
), Shing, Katherine (
committee member
)
Creator Email
rburrell@usc.edu,roeburrell@gmail.com
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-oUC11255801
Unique identifier
UC11255801
Identifier
etd-BurrellRob-5222.pdf (filename)
Legacy Identifier
etd-BurrellRob-5222
Dmrecord
359351
Document Type
Dissertation
Format
theses (aat)
Rights
Burrell, Robert Roe
Internet Media Type
application/pdf
Type
texts
Source
University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
(collection)
Access Conditions
The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright.
Repository Name
University of Southern California Digital Library
Repository Location
USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA
Repository Email
cisadmin@lib.usc.edu
Tags
chemical kinetics
combustion
combustion simulation
counterflow
diffusion flame
flame extinction
formyl radical
laminar flame speed
low pressure flame
methane
non-premixed
non-premixed flame
particle dynamics
particle image velocimetry
premixed
premixed flame