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Pressure effects on C₁-C₂ hydrocarbon laminar flames
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Pressure effects on C₁-C₂ hydrocarbon laminar flames
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Content
1
Pressure Effects on C
1
-C
2
Hydrocarbon
Laminar Flames
By
Hugo Burbano
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
in Partial Fulfillment of the
Requirements of the Degree
DOCTOR OF PHILOSOPHY
(MECHANICAL ENGINEERING)
December 2017
2
Contents
Acknowledgements ................................................................................................................................. 4
Abstract ................................................................................................................................................... 7
1. Introduction, Combustion Theory and Literature Review .............................................................. 8
1.1 Introduction .............................................................................................................................. 8
1.2 Laminar Flames and Considerations at High Pressures ......................................................... 10
1.2.1 Types of flames ............................................................................................................... 10
1.2.2 Laminar flame speed ....................................................................................................... 12
1.2.3 Flame stretch ................................................................................................................... 13
1.2.4 Counterflow configuration .............................................................................................. 14
1.2.5 Flame extinction.............................................................................................................. 18
1.3 Literature Review ................................................................................................................... 21
1.3.1 Two dimensional effects in the counterflow configuration ............................................ 21
1.3.2 Difficulties in high pressure counterflow experiments ................................................... 23
1.3.3 Experimental studies on C2 hydrocarbon flames ............................................................ 24
1.4 Objectives ............................................................................................................................... 25
1.5 References .............................................................................................................................. 26
2. Experimental Methodology .............................................................................................................. 34
2.1 Important considerations in the counterflow technique at high pressures ............................. 34
2.1.1 Burner design .................................................................................................................. 34
2.1.2 Flow Panel ...................................................................................................................... 35
2.1.3 Seeding system................................................................................................................ 37
2.2 Experimental setup ................................................................................................................. 39
2.3 Measurements of the axial velocity profile ............................................................................ 40
2.4 Flame extinction measurements ............................................................................................. 41
2.5 Laminar flame speed measurements with the counterflow technique ................................... 43
2.6 Uncertainty quantification of flame extinction measurements .............................................. 44
2.6.1 Uncertainty from LDV data post-processing ....................................................................... 45
2.6.2 Uncertainty from mixture preparation and boundary conditions ......................................... 48
3
2.7 References .............................................................................................................................. 51
3. Numerical methodology................................................................................................................ 54
3.1 PREMIX ................................................................................................................................. 54
3.2 Opposed Jet Code ................................................................................................................... 55
3.3 Numerically assisted extrapolation method for laminar flame speed determination ............. 56
3.4 Extinction strain rate calculation ............................................................................................ 57
3.5 Sensitivity Analysis ................................................................................................................ 58
3.6 Reaction path analysis ............................................................................................................ 59
3.7 References .............................................................................................................................. 60
4. Pressure Effect on the Extinction of Premixed and Non-Premixed C 1-C2 Hydrocarbon Flames ..... 62
4.1 Experimental Approach .............................................................................................................. 62
4.2 Numerical Approach ................................................................................................................... 63
4.3 Results ......................................................................................................................................... 64
4.3.1 Global strain rate or local strain rate? .................................................................................. 64
4.3.2 Importance of extinction strain rate experiments................................................................. 68
4.3.3 C2H6 results .......................................................................................................................... 70
4.3.4 C2H2 results .......................................................................................................................... 80
4.3.5 C2H4 results .......................................................................................................................... 89
4.3.6 C2H4 non-premixed flames results ....................................................................................... 91
4.3.7 CH4 results ........................................................................................................................... 94
4.5 References ................................................................................................................................... 97
Abstract ................................................................................................. Error! Bookmark not defined.
Future Work Recommendations ........................................................................................................... 99
4
Acknowledgements
This has been a long journey that I could not have successfully completed without the help of many
people. First, I want to thank my advisor, Professor Fokion Egolfopoulos, for giving me the opportunity
to be part of his lab, and for always sharing his experience and knowledge during these years. I
especially appreciate his patience and trust in my abilities during the most difficult times of these
journey, when it seemed the experiment was never going to work and the results were not the ones that
we expected. These were the toughest situations I have encountered as a researcher and have given me
the most valuable lessons in my career.
I am also very grateful for having the opportunity to meet extraordinary people that inspired me to
be a better researcher. Roe Burrell and DJ Lee first come to mind, since we shared very similar struggles
to make our experiments work to perfection. I am very proud of the rigorous scientific work we did to
achieve this. The collaboration with Chris Xiouris was also very important to complement and support
the findings reported in this thesis, but most importantly, his friendship during these years will be
always appreciated. My gratitude also goes to Okjoo Park, Aydin Jalali and Francesco Carbone for
sharing their experience as senior lab members during my first Ph.D. years, and to Vyaas Gururajan,
Jagan Jayachandran, Tailai Ye, Abtin Asari, Runhua Zhao, Ashkan Movaghar and Robert Lawson for
their help and the moments to share our frustrations and happiness from the lab work.
I want to thank the staff of the AME Department, especially Silvana Martinez, Sam Graves and Irice
Castro, for their continuous and disinterested help during all these years. I am very thankful to the
magnificent staff of the Engineering Machine Shop, Donald Wiggins and Gary Kuepper, for their
contributions to build my experiment, especially their help in making my complicated burner design a
reality, which was the pivotal moment that made my experiments finally work.
I have also had the fortune to have people that supported me in a more personal level. I thank
Professor Andrea Hodge for her support and sharing her experience during these years, and Leonardo
Velasco for his friendship and the countless moments spent out of school. I am especially grateful to
Rodriguez Reyes family for embracing me as one of their members, for their admirable kindness and
disinterested help; they were truly my family far from home and I will never forget it.
Above all, I want to thank my family for always being present when I needed them the most, for
their great support throughout these years, and for their unconditional love. My achievements would
have not been possible without them.
5
Finally, I want to remember my grandad Ovidio, friend Gaby, uncle Cesar and Professor Francisco
Cadavid, who unfortunately passed away during these Ph.D. years and who would have been very
happy to see me become a Doctor.
6
Dedicado a Luz Dary, Javier, Ricardo y Ana por su amor y compañía.
7
Abstract
Due to the hierarchical nature of hydrocarbon combustion kinetics and the fast decomposition rates
of large molecular weight fuels, it has been established that H 2/CO/C1–C4 kinetics are controlling to a
large extent various flame phenomena including propagation and extinction. For practical reasons, the
reduction of a kinetic model size can be made more efficiently by reducing the heavy fuels cracking
into few reaction steps and coupling it with a detailed model of H 2/CO/C1–C4 kinetics. C2 chemistry
also plays an important role in the formation of polycyclic aromatic hydrocarbons formation, which is
the bottleneck for soot formation. Additionally, despite the evident importance of flame experiments
at high pressures, due to its complex non-linear effect on flame phenomena, very few studies have been
reported for C2 flames under these conditions, especially for extinction of premixed and non-premixed
flames. The main objective of this thesis is to provide archival data at high pressures for the test,
development and optimization of the C 1-C2 chemistry of kinetic models.
An experimental methodology to conduct high pressure counterflow flame experiments was
developed. A new burner design for accurate measurement of extinction conditions was developed, as
well as a new seeding system for Laser Doppler Velocimetry measurements of the velocity field of
premixed flames at pressures above 1 atm. For the first time, a detailed uncertainty quantification
methodology was implemented for local extinction strain rate measurements. This methodology
considers the error propagation from velocity field data postprocessing, fuel and oxidizer mixture
preparation, and boundary conditions.
Measurements of local extinction strain rates of C 1-C2 hydrocarbon non-premixed flames were
conducted from 0.6 to 7 atm. These data are reported for the first time for C 2H2 non-premixed flames.
Additionally, measurements of the local strain rate of C 1-C2 hydrocarbon premixed flames at lean and
rich conditions were conducted from 1 to 4 atm for the first time. These data were compared with
numerical results that used state of the art kinetic models, and reactions or reaction pathways that need
revision were identified. It is worth mentioning, that considerable discrepancies were found for the
C2H2 rich flames; suggesting that a major revision to the corresponding kinetics is needed.
8
1. Introduction, Combustion Theory and Literature Review
1.1 Introduction
The study of combustion at high pressures is essential from the practical and fundamental points of
view. Practical systems, like internal combustion engines and gas turbines, operate at elevated pressures
to achieve higher power output and efficiency. Currently, these systems are developed or optimized
with the aid of computational tools, which use detailed or simplified transport and chemical kinetic
models to predict the combustion behavior. A fundamental understanding of the effect of pressure on
a variety of combustion phenomena is then needed to test and develop these models. For this purpose,
the development of zero or one dimensional experimental techniques, with well-defined boundary
conditions and fluid mechanics, to obtain archival data at high pressures is greatly needed.
Pressure, temperature, and composition are the thermodynamic parameters that control the final
equilibrium state of a combustible mixture, as well as the progress of the reactions leading to that state.
Due to the complex nature of chemical kinetic models that are controlled by two and three body
reactions a strong non-linear dependence on pressure is observed. Convective and diffusive transport
are also affected by pressure through its thermodynamic relation with density.
Despite the evident importance of high pressure experiments, a small fraction of experimental
combustion studies are carried out at these conditions. In a survey of 120 papers on the experimental
determination of laminar flame speeds only 27% report data at high pressures [1]. This is in fact greatly
associated to the experimental difficulties that are encountered as the pressure is increased; cost, safety
issues, flow and flame instabilities, excessive soot load, diagnostic challenges due to a reduction in
flame thickness [2].
Due to the hierarchical nature of hydrocarbons combustion kinetics and the fast decomposition rates
of large molecular weight fuels, it has been established that H 2/CO/C1–C4 kinetics are controlling to a
large extent various flame phenomena including propagation and extinction [3-5]. Recently, with the
aim of reducing model size efficiently, efforts have been made to develop kinetic models where the
heavy fuel cracking is lumped into few short steps, and this is coupled with a detailed model of
H2/CO/C1–C4 kinetics [4]. Therefore, it is evident that a major focus in the study of the combustion
characteristic of these lighter species is required.
9
The oxidation of H2 has been extensively investigated because it is the foundation of any kinetic
model and due to the particular characteristics of H 2 flames that make it an important target to analyze
different combustion phenomena. Laminar flame speeds (e.g. [6-8]), ignition ([9,10]), and extinction
(e.g. [11-13]) studies of H2 flames have been carried out at a wide range of pressures and
concentrations. Due to the increasing interest on syngas as an alternative fuel, H 2/CO laminar flames
have also been extensively studied: laminar flame speeds (e.g. [14-17]), ignition ([18]), and extinction
(e.g. [19,20]). CH4 has arguably been the most studied fuel in all of the combustion fields with laminar
flames speed (e.g. [21-23]), ignition (e.g. [9]), and extinction (e.g. [9,24]) studies not being the
exception. Surprisingly, this trend is over when a survey on C 2 laminar flame studies is carried out.
Only seven studies have been reported for laminar flame speeds [25-31], two for ignition [27,32] and
one for extinction at high pressures [24]. Data on C 2H2 flames is particularly deficient as well as
extinction data for all the C2 hydrocarbons. For the case of C3 and C4 laminar flames, most of the
studies are focused on the determination of laminar flames speeds (e.g. [26,33-37]) and few of them
on ignition and extinction (e.g. [27,32,38]). High pressure experiments for C 3-C4 hydrocarbons are
limited due to experimental difficulties in their vaporization at such conditions. This is not an issue for
the case of C2 hydrocarbons, but very few studies at high pressures have been reported. Therefore,
more experimental studies on C 2 flames are required to provide archival data for optimization or
validation of kinetic models.
It is worth mentioning that C2 chemistry plays an important role in soot formation. This process
starts with the formation of polycyclic aromatic hydrocarbons, PAHs, from unburned hydrocarbon
intermediates, with C2 species being among the main contributors. PAHs then coalesce and form
clusters; process known as particle nucleation. Then, the clusters undergo further coagulation and
coalesce to form spherical particles that are known as soot. PAHs formation is the bottleneck in soot
formation, and it has been shown to be very sensitive to gas phase chemistry, local flame conditions,
and fuel structure and composition [39-41]. Accurate prediction of PAHs formation requires high
precision in gas phase chemistry [39]. Thus, this reinforces the need for more experimental studies on
C2 laminar flames.
Flame propagation and extinction are both high-temperature kinetic phenomena that have been
studied to optimize or test chemical kinetic models. When using a kinetic model that closely predicts
laminar flame speed data, it is expected that extinction limit data should be closely predicted as well.
However, previous studies have shown that this is not necessarily the case [11,42]. Sensitivity analysis
10
on transport coefficients revealed that the extinction strain rate exhibits higher sensitivity to fuel
diffusivity compared to kinetics. It is also known that compared to kinetics, reactant diffusion can have
a comparable or even greater effect on the flame behavior especially under near-extinction conditions
(e.g.,[11,42,43]). Therefore, additional work on flame extinction can result in improvements on the
determination of diffusion coefficients. Additionally, it has been shown [44], that uncertainties in
kinetic model predictions can be reduced notably by using more experimental data as constraints and
by accounting also for the associated data uncertainty.
For the reasons expressed above, the main objective of the present work is the experimental study
of C2 hydrocarbon flame phenomena at high pressures, with the aim of providing archival data for
optimization or validation of transport and chemical kinetic models. This study will focus in extinction
measurements of premixed and non-premixed flames using the counterflow configuration.
1.2 Laminar Flames and Considerations at High Pressures
A flame is a thin non-equilibrium region where a rapid conversion of reactants to products takes
place resulting in heat release. In this thin region, large gradients of species concentrations and
temperature are present. Adequate experimental configurations, where fluid mechanics can be
accurately replicated by a numerical model, can provide valuable data to assess kinetic and transport
models of different fuels under a wide range of conditions.
1.2.1 Types of flames
Two fundamental modes of combustion are possible, premixed and non-premixed. In premixed
flames reactants are mixed at the molecular level before the reaction zone. These flames exhibit wave-
like propagation into the unburned mixture. This propagation speed is sensitive to fundamental
processes of kinetics and molecular transport. Two distinct regions can be identified in premixed
flames, Fig. 1.1. A broad preheat zone, 𝑙 , where reactants are preheated due to a balance between
convection and diffusion; and a thin reactive-diffusive zone, 𝑙 , where reaction occurs.
11
Figure 1.1. Premixed Flame Structure
In the case of non-premixed flames reactants mix only at the time of combustion. Reactants are
transported inside the reaction zone through diffusion mostly and convection in some cases. The flame
is located where fuel and oxidizer fluxes are in stoichiometric proportions. Therefore, this type of
flames are not characterized by a propagation speed, and they can be defined as a motionless sink of
reactants. Transport time scales are usually one order of magnitude higher than kinetic time scales, and
therefore are the rate limiting parameter in the overall flame burning. These flames are characterized
by a broad convection-diffusion zone and a very thin reaction zone, Fig. 1.2.
Figure 1.2. Non-Premixed Flame Structure
12
1.2.2 Laminar flame speed
Figure 1.3. Structure of the Ideal Flame in the laminar flame speed definition
The laminar flame speed, 𝑆 , is defined as the propagation speed of a steady, laminar, one-
dimensional, planar, stretch-free , and adiabatic flame (Fig. 1.3). The term 𝑆 is widely used due to the
fact that velocities can be measured experimentally, as opposed to the laminar mass burning rate, 𝑓 ,
which is the best parameter to characterize a reacting mixture, especially when the effect of pressure is
studied. 𝑓 represents the actual mass that is burned and it is related to 𝑆 as:
𝑆 =
Eq. (1.1)
where 𝜌 is the unburned mixture density. 𝑓 is an important fundamental property of a reacting
mixture, being a measure of its reactivity, diffusivity, and exothermicity, as shown by combustion
theory:
𝑓 ~𝑝 𝜆 /𝐶 𝑒 Eq. (1.2)
where 𝑝 is the mixture pressure, 𝑛 is the overall reaction order, 𝜆 the mixture thermal conductivity, 𝐶
the mixture specific heat, 𝐸 the overall activation energy, 𝑅 the universal gas constant, and 𝑇 the
adiabatic flame temperature. The quantity under the square root represents the mixture diffusivity and
the other terms represent the mixture reactivity.
The accurate experimental measurement of 𝑓 is essential for validating kinetic models as well as
for turbulent combustion, where it is used as a very important scaling parameter. However, obtaining
this type of ideal flame experimentally is quite challenging because real flames are subject to external
13
phenomena, like curvature, unsteadiness, flow non-uniformity, or heat loss. Some of these phenomena
are usually necessary to stabilize a flame. Therefore, direct measurements of 𝑓 are impossible and
different experimental configurations have to account for methodologies to correct the effects of these
external phenomena.
Finally, under the Ideal Flame Model assumptions, it can be shown that diffusion balances
convection within the preheat zone, 𝑙 . Thus, the flame thickness of this zone can be derived as the
ratio of two scales, which are the thermal diffusivity, 𝜆 /𝜌𝐶 , and the flow velocity of the unburned
mixture, 𝑢 = 𝑆 . Then, by using Eq. 2.1, 𝑙 can be expressed as:
𝑙 =
/ Eq. (1.3)
This is a very important result for the case of high pressure studies. According to Eq. 1.2, when the
reaction order is positive an increase in the mass burning rate is expected as pressure is increased.
Therefore, at high pressures the flame thickness decreases considerably, which has major implications
in experimental studies at those conditions. Thinner flames are more susceptible to flow instabilities
induced by any imperfections in the experimental setup. Additionally, higher resolution experimental
techniques are required if measurements of species, temperature, and velocity within the flame zone
are needed. These reasons make experimental studies at high pressures very challenging.
1.2.3 Flame stretch
Most practical flames are stabilized via aerodynamic stretch, which is induced through flow non-
uniformity, flame curvature, or flame motion (e.g., [45]). Flame stretch, 𝐾 , can be understood as a
timescale associated with the generation or compression of flame surface, 𝐴 , in a Lagrangian frame of
reference.
𝐾 =
Eq. (1.4)
𝐾 can also be expressed in terms of flow velocity as [46]:
𝐾 = ∇
∙ 𝒗 , + 𝑽 ∙ 𝒏 ∙ (∇
∙ 𝒏 ) Eq. (1.5)
where ∇
is the tangential gradient operator along the flame surface, 𝒗 , is the tangential component
of the flow velocity at the flame, 𝑽 is the flame velocity, and 𝒏 is the unit normal vector of the flame
14
surface pointed in the direction of the unburned gas. It is important to note that by definition the
tangential velocity component of the flame surface, 𝑽 , , is equal to the tangential component of the
flow velocity, 𝒗 , . This equation shows that there are three stretch induced effects. The first term
represents the influence of flow non non-uniformity along the flame surface, referred as aerodynamic
straining. In the second term, the first parenthesis represents the stretch experienced by a non-stationary
flame, and the second one represents the contribution of flame curvature.
When comparing the effect of stretch on flames of different burning intensities, it is convenient to
use a non-dimensional stretch rate. According to Eq. 1.4, 𝐾 has units of 𝑠 and it can be non-
dimensionalized based on an appropriately defined flame time, 𝑡 , that indicates the time it takes to
complete the oxidation process. This non-dimensional stretch rate is called the Karlovitz number and
it is defined as:
𝐾𝑎 = 𝐾 ∙ 𝑡 Eq. (1.6)
For premixed flames, the flame time can be defined as the ratio of the flame thickness, 𝑙 , and the
laminar flame speed, 𝑆 :
𝐾𝑎 = 𝐾 ∙ Eq. (1.7)
𝑙 can be expressed as 𝑙 = 𝐷 /𝑆 , where 𝐷 is a characteristic diffusion coefficient of the reacting
mixure, and 𝐾𝑎 reduces to:
𝐾𝑎 = 𝐾 ∙ ( )
Eq. (1.8)
Typically, low 𝐾𝑎 represent vigorously burning flames (𝐾𝑎 ≪ 1), and 𝐾𝑎 ~1 represent weakly
burning flames, which can be close to extinction states (e.g., [47,48]).
1.2.4 Counterflow configuration
In this configuration, a planar flame is stabilized in a decelerating, stagnation flow field. This flow
can be achieved by flowing a jet against a liquid or solid surface, or by two counterflowing jets of equal
momenta. These jets are usually generated with aerodynamically shaped contoured nozzles or straight
nozzles with flow conditioning screens; both methods aiming to achieve uniform velocity at the exit of
15
the nozzle. Depending on the composition of the reactants in the two streams the resulting configuration
can be twin premixed flames, single premixed flames or non-premixed flames, as shown in Fig 1.4.
Figure 1.4. Types of flames obtained in the counterflow configuration: a) Twin premixed flames, b)
Single premixed flame, c) Non-premixed flame
These flames are steady, planar, laminar and nearly adiabatic as there is no downstream conductive
heat loss, with the only loss being thermal radiation, which is small. However, their stabilization is
achieved via velocity gradients, which implies that in this configuration flames are always stretched.
According to Eq. 1.5 for this case the stretch is equal to the flow strain rate and it can be quantified in
cylindrical coordinates as:
𝐾 =
(𝑟 ∙ 𝑣 ) Eq. (1.9)
where 𝑣 is the radial component of the velocity, which is tangential to the flame surface. On the other
hand, the role of the axial velocity gradient is to allow the flame to adjust at a location where its speed
will be equal to the local normal component of the flow velocity.
The nozzles have to be designed carefully to obtain flows that are suitable for comparison with 1D
models. The model developed by Kee et al. [49] has been widely used as the main reference for
different models to compute counterflow flames. In this model, the two-dimensional axisymmetric
flow field is reduced to a quasi-one-dimensional flow when a streamfunction in the form 𝜓 (𝑥 , 𝑟 ) ≡
𝑟 𝑈 (𝑥 ) is introduced. This streamfunction satisfies the mass continuity equation when defined as
follows:
= 𝑟𝜌𝑢 = 2𝑟𝑈 Eq. (1.10)
−
= 𝑟𝜌𝑣 = −𝑟 Eq. (1.11)
16
where 𝑢 and 𝑣 are the flow velocities in the 𝑥 and 𝑟 directions, respectively. The boundary conditions
that are compatible with the above functions have to represent the flows that are characteristic of
counterflow experiments. Uniform flow with zero axial velocity gradient, plug flow, and uniform flow
with axial velocity gradient, potential flow, at the exit of the nozzles are the type of flows that have to
be obtained experimentally in order to be accurately represented by the boundary conditions of the
models.
Under the assumptions stated above, it can be shown that the flames are quasi-one-dimensional near
the centerline and all properties depend only on the axial coordinate with the exception of the radial
velocity, 𝑣 , which varies linearly with the radius, 𝑟 . Additionally, using the continuity equation in the
hydrodynamic zone where density can be assumed constant, it can be shown that the stretch can be
expressed as:
𝐾 = −
Eq. (1.12)
This result has major implications, given the fact that this is a variable that can be directly determined
by measuring the axial velocity profile, and that is a direct indicator of the effect of the flow on the
flame. Furthermore, experimental data can be extrapolated to Ideal Flame conditions when 𝑑𝑢 /𝑑𝑥
tends to zero.
Fig. 1.5 shows the variation of the axial velocity along the centerline for the counterflow
configuration for a premixed flame, where four regions can be identified. A hydrodynamic zone where
the flow decelerates, a preheat zone and reaction zone where the flow accelerates due to thermal
diffusion and thermal expansion, and an equilibrium zone where the flow decelerates completely when
it reaches the stagnation plane. It is clearly seen that 𝐾 and 𝑢 vary along the centerline, which makes
necessary to define parameters that characterize a counterflow flame. Two variables that can be
measured experimentally are designated as the characterizing parameters: the maximum magnitude of
𝑑𝑢 /𝑑𝑥 in the hydrodynamic zone, 𝐾 , and the minimum velocity before the flow is accelerated due to
thermal expansion that is defined as the reference flame speed, 𝑆 , . A very similar structure is
observed for the case of non-premixed flames, with the only difference being where 𝑆 , is defined
because this will depend on whether the flame is located on the fuel or oxidizer side. A more detailed
discussion on why the characteristic stretch is chosen in the hydrodynamic zone is given in the
following section.
17
Figure 1.5. Axial velocity profile along the stagnation streamline and definition of the strain rate and
reference flame speed.
From Eq. 1.10 and 1.11, it is clearly seen that 𝐾 scales with the strain rate distribution within the
flame zone. It is also important to consider that 𝑆 , is only used for experimental convenience and
has to be distinguished from the actual stretched flame speed, 𝑆 , that is the propagation speed of a
stretched flame at the location where the temperature starts rising. 𝑆 scales with 𝑆 , , and both are
dependent on 𝐾 . This dependence can be determined experimentally by varying the flow rates in both
nozzles while keeping momentum balance (Fig. 1.6). If these experimental data are obtained at low
strain values, an extrapolation procedure to zero strain can be implemented to determine the laminar
flame speed, 𝑆 . However, care has to be taken because 𝑆 , vs. 𝐾 is not linear at low strain values,
as it has been demonstrated theoretically by Matalon and Tien [50] and numerically by Egolfopoulos
and coworkers [43,51,52].
18
Figure 1.6. Variation of the experimentally measured reference flame speed with strain rate
1.2.5 Flame extinction
Flame extinction can only occur due to stretch or heat loss, or a coupling of the two. The effect of
stretch can be assessed by considering different length scales of the flow field. Based on large scales
of fluid mechanics, where the flame can be seen as a thin sheet, hydrodynamic stretch can be defined.
In the case of the counterflow configuration, the effects of this type of stretch manifest through changes
in flame area due to tangential velocity gradients, as shown in Eq. 1.9, but do not affect the burning
rate and flame temperature. On the other hand, when considering the scales within the transport zone,
the flame response is very sensitive to the rates of molecular transport of mass and heat. This type of
stretch is defined as flame stretch and it can affect the residence time within the reaction zone, the
completeness of the reactions, and the flame temperature. Hydrodynamic and flame stretch are strongly
coupled, as the magnitude of the latter directly depends on the fluid mechanics events outside the
transport zone. Flame phenomena like ignition, extinction, and burning rate modification can only be
captured by considering the effect of flame stretch.
In the counterflow configuration, flame stretch continuously varies within the reaction zone as a
consequence of the change of velocity due to thermal expansion (Fig. 1.5). To aid the analysis of the
effects of flame stretch on the flame response, a characteristic stretch that can also be determined
experimentally needs to be defined. Flame stretch throughout the flame zone is what actually affects
the flame response, and the stretch at the burned edge of the flame appears to be the most characteristic
variable. However, defining stretch at this boundary is complicated as the burned edge of the flame is
19
not a well defined boundary because completion to equilibrium products is not guaranteed for all cases.
Additionally, experimental measurements of the velocity flow field, using non-intrusive techniques
like Particle Tracking Velocimetry or Laser Doppler Velocimetry, in the flame region is not reliable
because seeding particles are affected by thermophoresis and then do not follow the flow [53-55].
Therefore, defining flame stretch in the hydrodynamic zone, 𝐾 , is more convenient numerically and
experimentally, as it has been discussed in the previous section. 𝐾 is a well defined quantity and at its
location processes of molecular transport and chemical kinetics are not present. Thus, 𝐾 is a
characteristic variable that is more suitable for comparison between experimental data and numerical
results.
For premixed flames, an important parameter to analyze the effect of diffusive transport on flame
response under stretch and heat loss is the Lewis number, 𝐿𝑒 :
𝐿𝑒 =
, Eq. (1.13)
where 𝛼 is the thermal diffusivity of the mixture and 𝐷 , is the mass diffusivity of the deficient specie.
𝛼 is mostly determined by the abundant species, which typically is N 2, and 𝐷 , is determined by the
fuel or O2 at lean and rich conditions, respectively. 𝐿𝑒 compares the rate of diffusion of heat from the
flame to the fresh mixture to the rate of diffusion of mass of the deficient species from the fresh mixture
to the flame. Given that 𝛼 and 𝐷 , are inversely proportional to the square root of the molecular weight,
a quick estimate of 𝐿𝑒 can be computed as follows:
𝜙 < 1: 𝐿𝑒 =
~
Eq. (1.14)
𝜙 > 1: 𝐿𝑒 =
~ Eq. (1.15)
In the counterflow configuration there is a particular transport asymmetry. Diffusive transport of
mass and heat is normal to the flame surface, as gradients of temperature and species only occur in the
axial direction, while convective transport is in the direction of the streamlines. As shown in Fig. 1.7,
heat from the flame is conducted upstream to external streamlines that later skip the flame downstream,
and conversely, mass is diffused from external streamlines to the flame. It is important to note that
diffusion processes dominate convection processes at low stretch rates.
20
Figure 1.7. Schematic of a stretched counterflow flame
For diffusionally neutral mixtures, where 𝐿𝑒 = 1, the rate of heat loss to the external streamlines is
balanced with the enthalpy coming from the mass gained from external streamlines. In this case only
two mechanisms can cause flame extinction; restraining and heat loss to an external surface. For
adiabatic and restrained flames, like the twin flame configuration, when the stretch rate is high enough
to displace the flame on the stagnation plane and it cannot adjust its location, a significant reduction in
flame thickness and residence time is induced. Thus, the completion of chemical reactions is reduced
and reactant leakage through the flame zone occurs. Extinction is achieved when reactant leakage is
high enough to reduce the heat generation needed to sustain the combustion process. For non-adiabatic
configurations, like stagnation flames stabilized against a solid surface, high stretch rates will displace
the flame to the stagnation surface. Thus, heat loss and reactant leakage induced by stretch will be
coupled.
To analyze diffusionally imbalanced mixtures, three transport coefficients need to be considered.
Thermal diffusivity of the mixture, 𝛼 , mass diffusivity of the deficient reactant, 𝐷 , and mass diffusivity
of the excess reactant, 𝐷 . Two types of phenomena can be observed at off-stoichiometric conditions,
where the 𝐿𝑒 needs to be considered, and at near-stoichiometric conditions, where preferential diffusion
is considered through the 𝐷 /𝐷 ratio. When 𝐿𝑒 < 1, the enthalpy coming from the mass gained through
diffusion is greater than the heat loss from the flame, and more intense burning is observed. On the
contrary, less intense burning is observed when 𝐿𝑒 > 1. For preferential diffusion, when 𝐷 /𝐷 > 1
the mixture will become more stoichiometric and more intense burning is observed. The opposite is
observed when 𝐷 /𝐷 < 1. For both cases in which the burning intensity is increased, extinction is
achieved when the stretch is high enough to move the flame on the stagnation plane and the residence
21
time is reduced to allow reactant leakage. A different extinction process is observed for the cases where
the burning intensity decreases. Flame temperature and burning intensity decrease as the stretch is
increased and extinction occurs as a consequence of a decline in reactivity. This extinction occurs while
the flame is away from the stagnation plane.
As explained in a previous section, when premixed flames are close to extinction 𝐾𝑎 ~1. By using
the definitions given in Eq. 1.2 and 1.8, it can be shown that:
𝐾 ~𝜔 Eq. (1.15)
where 𝜔 is the overall reaction rate. This is a very important indicator that at extinction conditions,
premixed flames are more sensitive to chemical kinetics compared to 𝑓 .
As it has been analyzed in section 1.2.2, the burning rate increases as the pressure is increased. This
has major implications for extinction experiments at high pressures because a higher burning rate
requires a higher stretch rate to achieve flame extinction. Then higher mass flow rates are required as
pressure increases but, as it will be pointed out in the following section, there is a limitation in the
counterflow configuration in terms of the flow regime that has to be kept laminar. Therefore, extinction
experiments at high pressure experiments are only suitable for mixtures with high levels of dilution for
non-premixed flames, and for very lean or rich conditions for premixed flames that have low burning
rates.
Finally, non-premixed flames are very susceptible to reactant leakage. This type of flames cannot
adjust their location since they do not have a propagation speed. Due to the fact that fuel and oxygen
are transported towards each other from opposite sides of the flame, and that at high stretch rates they
can miss each other, susceptibility to extinction is increased. Reactant leakage is increased as stretch is
increased, which subsequently reduces flame temperature until the combustion process cannot be
sustained.
1.3 Literature Review
1.3.1 Two dimensional effects in the counterflow configuration
The counterflow configuration was developed in the 1950s and it has been an invaluable tool for the
experimental study of laminar flame phenomena [56]. One-dimensional (1D) models (e.g., [49,57-59])
were subsequently developed and have been widely used for optimization or validation of transport
22
and chemical kinetic models. However, only carefully designed counterflow experiments are suitable
for comparison with these models, as the boundary conditions and fluid mechanics have to match.
When properly implemented, counterflow flames provide high quality flame data that contain
important physical and chemical information [56].
Two classes of burner design have been identified as compatible with 1D models assumptions;
straight tube burners with flow conditioning screens (e.g., [60,61]) and high-contraction-ratio
contoured burners (e.g., [43,62-64]). In the first case, plug flow conditions are achieved and the
velocity gradient in the hydrodynamic zone can be used as a characteristic strain rate experienced by
the flame. In the second case, near potential flow conditions are achieved and boundary velocity
gradients also have to be considered.
Verification that the 1D models assumptions accurately describe experimental counterflow
measurements has been studied since the early 1990’s. Chelliah et al. [65] identified that assuming plug
flow boundary conditions resulted in good agreement with experimental data and that the maximum
axial velocity gradient is a good parameter to characterize flame stretch. Rolon et al. [66] concluded
that potential flow assumptions fail to predict cold flow velocity field measurements. Frouzakis et al.
[67] and Park and Hamins [68] determined that results derived from 1D and axisymmetric two-
dimensional (2D) simulations closely agree when plug flow boundary conditions are implemented, and
the burner separation distance and diameter are kept equal. Bergthorson et al. [69] investigated the
accuracy of 1D models in contoured-nozzle-generated premixed flames and found reasonable
agreement provided that the velocity boundary conditions were measured and implemented in the
simulations. Oh et al. [60] used straight-tube burners with flow conditioning screens and found 1D
compatible centerline extinction for high strain rates but two-dimensional effects for lower strain rates.
Ji et al. [43] reported that the boundary axial velocity gradients must be measured and accounted for in
1D models for suitable comparisons with flame extinction data. Sarnacki et al. [63] confirmed the
findings in Ref. [69], where the implementation of complete velocity boundary conditions in 1D models
is needed, and identified an ellipsoidal pressure field at the stagnation plane to be the physical
mechanism causing departure from plug flow assumptions. Mittal et al. [70] also confirmed the validity
of 1D models assumptions if plug flow is considered, and attributed the departure from 1D assumptions
in non-uniform exit velocity profiles to the presence of temperature curvature along the system
centerline as a result of flow non-uniformity. Bouvet et al. [64] studied contour-nozzle generated
premixed flames and traced inconsistencies with 1D modeling to the assumption of constant pressure
23
derivative eigenvalue. Niemann et al. [61] determined that straight tube burners with flow conditioning
screens can reproduce 1D plug flow assumptions to within an accuracy of 5% in unreacting flows, and
that for the case of contoured nozzles accounting for the axial velocity gradient at the boundary is
necessary. Johnson et al. [71] corroborated the assertions of Ref. [61] and further confirmed that
contour-type burners are sufficiently modeled with 1D codes when appropriate boundary conditions
are included.
Finally, the study by Burrell et al. [72] made a careful evaluation of the effect of flowfield geometry
on flame propagation and extinction of atmospheric CH 4/N2/air flames in the counterflow
configuration. Laminar flame speeds and extinction strain rates for lean premixed and non-premixed
flames were measured in axisymmetric burners producing either uniform or non-uniform axial velocity
exit profiles. Particle image velocimetry was used to characterize the two-dimensional flowfield
between the burners. Laminar flame speeds were found to be insensitive to the burner exit velocity
profile shape but extinction measurements were strongly affected. In non-uniform flows, two-
dimensional flow field measurements revealed significant radial dependence of flow quantities and
high-speed video captured off-center initiation of extinction. Thus, centerline measurements did not
represent the extinction state properly, given the direct contradiction to one-dimensional modeling
assumptions, and the data was deemed unreliable for kinetic model validation. Flames in uniform
flows were found to exhibit minimal radial dependence with extinction initiating at near-centerline
locations.
1.3.2 Difficulties in high pressure counterflow experiments
From a fundamental point of view, difficulties are related with flame stability because the flow
laminarity and the flame thickness decrease as pressure is increased. The first and most important
limitation in this experiment is the Reynolds number, 𝑅𝑒 , restriction on the laminarity of the flow
coming from the nozzles [2,61]. The critical value of 𝑅𝑒 above which the flow begins to become
turbulent is not very well stablished. Figura and Gomez [2] have shown that the criterion of the 𝑅𝑒 <
2000 for fully developed flow is not sufficiently conservative for a counterflow flame of good quality,
and it is highly dependent on the irregularities present in the experimental apparatus and the specific
burner design. Such irregularities have a more considerable effect in flame stability when flame
thickness decreases as both length scales become comparable.
24
Buoyancy can also affect flame stability as pressure is increased. Different approaches to analyze
this effect have been reported. Niemann et al. [61] considered the Grashof number as the relevant
parameter regarding buoyancy, and concluded that flame stability is not affected at atmospheric
pressures but a considerable effect can be observed at high pressures. Recommendations to conduct
experiments at high pressures in reduced-gravity environments, replace N 2 by Helium, and reduction
in the nozzle diameter were given. Figura and Gomez [2] concluded that counterflow flames are
relatively immune from buoyancy instabilities, although it can change flame position, when
considering the Richardson number in their analysis. They also concluded that buoyancy does not affect
the vicinity of the flow centerline as long as the strain rates are not considerably low, and that this
possible effect is reduced even more when both counter-flowing jets are surrounded by inert coflows.
They finally recommended using contoured nozzles when pressure is above 10 atm, reduce burner
diameters, and replace N2 by Helium to increase flame thickness.
Most of the studies at high pressure with the counterflow configuration have been conducted up to
pressures of 7 atm (e.g. [21,22,25,27,32]). Only a few studies for pressures above 10 atm have been
carried out. Gomez and coworkers [2,73,74] have developed a counterflow experimental facility for
non-premixed flames that can be stable up to 30 atm but at low strain rates of the order of 40 1/s for
temperature and species measurements under very limited conditions. Such low strain rate values are
not suitable for flame propagation, extinction or ignition studies. Ravikrishna [75] measured NO
concentration in non-premixed flames from 6 to 15 atm at a strain rate of 30 1/s. Finally, Williams and
coworkers [12,24,61] developed an experimental facility for non-premixed extinction experiments up
to 20 atm, with strain rates ranging from 150 to 200 1/s at the highest pressures.
1.3.3 Experimental studies on C2 hydrocarbon flames
Most of the experimental studies have focused on the measurement of the laminar flame speed, 𝑆 .
Egolfopoulos et al. [25] measured 𝑆 ′𝑠 of C2H2, C2H4 and C2H6 flames from 0.25 to 3 atm for lean and
rich concentrations using the counterflow configuration, and linear extrapolations were used to get zero
stretch corrected data. Numerical results show good agreement with experimental data, except for C 2H2
rich flames, and over-predictions are observed as pressure increases. Hassan et al. [26] used spherical
expanding flames to measure 𝑆 ′𝑠 of C2H4 and C2H6 flames from 0.5 to 4.0 atm for a wide range of
equivalence ratios; zero stretch data were obtained using linear extrapolations. Good agreement with
25
numerical predictions were reported for C2H6 data, while C2H4 was over-predicted at all experimental
conditions. Jomaas et al. [27] measured 𝑆 ′𝑠 of C2H2 flames at 1 and 2 atm, and C2H4 and C2H6 flames
from 1 to 5 atm, at different equivalence ratios with the spherical expanding flame method. Numerical
results over-predicted C2H2 and C2H4 data at atmospheric conditions but better agreements were
observed as pressure increased, while an opposite trend was observed for the case of C 2H6 data. Kumar
et al. [28] measured 𝑆 ′𝑠 of C2H4 flames at different equivalence ratios and mixture preheat
temperatures varying from 298 to 470 K in the counterflow configuration; linear extrapolations were
used to get zero stretch corrected data. As temperature is increased, numerical results over-predict the
data. Park et al. [29] used the counterflow configuration to measure 𝑆 ′𝑠 of C2H2, C2H4 and C2H6 at 1
atm, and used a computational assisted approach to extrapolate the data to zero stretch. Good agreement
with numerical results was reported, although some discrepancies are observed at rich conditions.
Santner et al. [30] measured 𝑆 ′𝑠 of lean C2H4 flames from 1 to 10 atm by using spherical expanding
flames, and data was corrected to zero stretch using linear extrapolations. It is clearly shown that as the
pressure increases, the numerical results over-prediction increases. Shen et al. [31] used spherically
expanding flames to measure 𝑆 ′𝑠 of C2H2 at lean and rich conditions from 1 to 20 atm and assessed
the effect of CO2 and HO2 addition; zero stretch data was obtained with a non-linear extrapolation
method. Over-predictions of the data by the numerical results increased with pressure.
Available data on high pressure ignition and extinction of C 2 hydrocarbons flames is very limited.
Jomaas et al. [27] measured ignition temperatures of C 2H4 and C2H6 non-premixed flames from 1 to 7
atm using the counterflow configuration and reported numerical results over-predictions at all
conditions. Fotache et al. [32] used the counterflow configuration to measure the ignition temperature
of C2H6 non-premixed flames from 0.2 to 8 atm. Numerical data over-predicts the experimental data at
all conditions. Niemann et al. [24] measured global strain rates of C 2H6 and C2H4 non-premixed flames
from 1 to 20 atm and considerable disagreements between data and model predictions were identified
as pressure increases.
1.4 Objectives
The first objective of the present thesis is to develop an experimental methodology to measure
accurately extinction conditions of premixed and non-premixed flames at pressures above 1 atm. This
implies, the establishment of the best experimental practices to produce flow fields and flames that are
26
in accordance with the assumptions of quasi-one-dimensional models of the counterflow configuration.
Additionally, the development of an uncertainty quantification methodology for the measurement of
local extinction strain rates, taking into account the uncertainties coming from velocity field
measurements and mixture preparation.
The data available on laminar C2 hydrocarbon flames at high pressures is very limited, especially
for extinction conditions. No extinction data of C 2H2 non-premixed flames have been reported, and the
data reported for CH4, C2H4 and C2H4 non-premixed flames shows very significant discrepancies with
numerical results. Therefore, the second objective is to measure extinction strain rates of C 1-C2
hydrocarbon non-premixed flames from 0.5 to 7 atm. Additionally, no extinction data for CH 4
premixed flames above 1 atm and C2 hydrocarbon premixed flames at any pressure range have been
reported, then measuring these extinction strain rates from 1 to 4 atm is the third objective of this
proposal. Finally, these data will be used to assess the performance of recently developed chemical
kinetic and transport models. Sensitivity analysis and reaction path analysis will be also conducted with
the aim of identifying possible kinetic pathways and binary diffusion coefficients that need
improvement.
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nitrogen diffusion flames, Symp. Int. Combust. 23 (1991) 503-511.
[66] J. Rolon, D. Veynante, J. Martin, F. Durst, Counter jet stagnation flows, Exp. Fluids. 11 (1991)
313-324.
[67] C. Frouzakis, J. Lee, A. Tomboulides, K. Boulouchos, Symp. Int. Combust. 27 (1998) 571-577.
[68] W. Park, A. Hamins, Investigation of velocity boundary conditions in counterflow flames, KSME
international journal. 16 (2002) 262-269.
[69] J.M. Bergthorson, D.G. Goodwin, P.E. Dimotakis, Particle streak velocimetry and CH laser-
induced fluorescence diagnostics in strained, premixed, methane–air flames, Proceedings of the
Combustion Institute. 30 (2005) 1637-1644.
33
[70] V. Mittal, H. Pitsch, F. Egolfopoulos, Assessment of counterflow to measure laminar burning
velocities using direct numerical simulations, Combustion Theory and Modelling. 16 (2012) 419-433.
[71] R. Johnson, A. VanDine, G. Esposito, H. Chelliah, On the Axisymmetric Counterflow Flame
Simulations: Is There an Optimal Nozzle Diameter and Separation Distance to Apply Quasi One-
Dimensional Theory? Combustion Sci. Technol. 187 (2015) 37-59.
[72] R.R. Burrell, R. Zhao, D.J. Lee, H. Burbano, F.N. Egolfopoulos, Two-dimensional effects in
counterflow methane flames, Proceedings of the Combustion Institute. 36 (2017) 1387-1394.
[73] L. Figura, A. Gomez, Structure of incipiently sooting ethylene–nitrogen counterflow diffusion
flames at high pressures, Combust. Flame. 161 (2014) 1587-1603.
[74] L. Figura, F. Carbone, A. Gomez, Challenges and artifacts of probing high-pressure counterflow
laminar diffusion flames, Proceedings of the Combustion Institute. 35 (2015) 1871-1878.
[75] R. Ravikrishna, S.V. Naik, C. Cooper, N.M. Laurendeau, Quantitative laser-induced fluorescence
measurements and modeling of nitric oxide in high-pressure (6–15 atm) counterflow diffusion flames,
Combustion Sci. Technol. 176 (2004) 1-21.
34
2. Experimental Methodology
2.1 Important considerations in the counterflow technique at high pressures
2.1.1 Burner design
As explained in section 1.2.4, special care is needed in the design of the burners to obtain flames
that are planar and axisymmetric and whose boundary conditions are compatible with quasi-one-
dimensional models. Following the recommendations by Burrell et al. [1], a straight tube burner design
with flow conditioning screens at the exit was implemented. At the burner exit, a removable cap that
is screwed to the burner main body allows the placement of a set of two stainless steel meshes and two
1 mm diameter O-rings, as shown in Fig. 2.1. The number of wires per inch squared of the stainless
steel meshes is critical because it has to be fine enough to generate very uniform flow at the burner exit
at pressures above 1 atm, because any considerable discontinuity in the exit velocity profiles can
become comparable to the length scale of the flame thickness and cause flame instabilities.
Additionally, the number of meshes per inch squared cannot be very high because the spacing between
wires can become comparable to the diameter of the seeding particles used for velocity field
measurements, and this increases the chances of clogging the meshes and consequently developing
flame instabilities. After several trials, the most optimal number of wires per inch squared was found
to be 150 x 150 (McMaster-Carr Ref: 85385T104) with 0.0026” wires diameter and 0.0041” opening
between wires. Two burner diameter sizes are considered, 𝐷 = 6.3 𝑚𝑚 for experiments starting at 2
atm and up to 7 atm, and 𝐷 = 11 𝑚𝑚 for experiments below 2atm.
Figure 2.1. Schematic of the burner design
35
This new burner design allows obtaining a top-hat velocity profile at any pressure studied in the present
thesis, as is shown in Fig 2.2. Burrell et al. [1] demonstrated that this velocity profile guarantees the
measurements of the actual local extinction strain rate at the centerline of the flow field. This design
prevents the effect of the uneven pressure distribution at the stagnation plane to affect the flow field
upstream of the burner exit due to the presence of the conditioning screens. For other burner designs in
which there are not conditioning screens at the exit, flames are stable when the flow Reynolds number
is below 1000. In the case of this new burner design, flame stability is improved considerably and the
flow Reynolds number can go up to 1800.
Figure 2.2. Radial velocity profile at burner exit with no flame at 4atm
2.1.2 Flow Panel
To measure gaseous flow rates of N2, O2, and C1-C2 hydrocarbons an independent set of sonic
nozzles (O’Keefe Controls Co.) and digital pressures gauges (Omega DPG8000-500) are used. These
sonic nozzles are calibrated using a wet-test meter (Sinagawa Corporation W-NK-1). Fig. 2.3 shows
an picture of the flow panel used. To keep sonic conditions at the maximum pressure, around 7 atm for
the present study, the flow has to be supplied by the pressure gauges at a minimum of 14 atm (191
psig). Above these pressures stainless steel piping is needed. A flow panel that can work up to 35 atm
(500psig) upstream pressures was designed for this experiment. Finally, as explained in section 1.2.5,
very lean premixed flames or diluted non-premixed flames have to be studied at high pressures, which
requires low flow rates of fuel supplied at very high upstream pressures. Therefore, very small sonic
nozzles with orifice sizes of 25 to 50𝜇𝑚 are used (Ref.#1 and #2 from O’Keefe Controls Co.). The
0
10
20
30
40
50
60
70
-4 -3 -2 -1 0 1 2 3 4
Velocity (cm/s)
r (mm)
36
main advantage of using sonic nozzles is that when operated under sonic conditions the flow rate is
independent of the downstream pressure or any downstream instability.
Figure 2.3. Flow panel
Each sonic nozzle was calibrated at pressures ranging from 50 psig to 500 psig. The corresponding
flow rates are measured at actual atmospheric conditions, 𝑃 and 𝑇 , and are corrected to
standard conditions, 𝑃 = 101.3 𝐾𝑃𝑎 and 𝑇 = 298.15 𝐾 , as follows:
𝑄 = 𝑄 ×
×
Eq. (2.1)
where the corrected pressure is 𝑃 = 𝑃 + 𝑃 and 𝑃 is the vapor pressure at 𝑇
conditions. A calibration curve (𝑃 vs 𝑄 ) is generated from these measurement and it is used to
find the 𝑃 for any 𝑄 required in the experiment. The uncertainties of the wet test meter are ±0.15
and ±0.1% of the flow rate measured when the flow rate is more than half or less than half the maximum
flow rate than can be measured, respectively. The uncertainties in the pressures gauges is ±0.25% of
the total scale (± 1.25 psig for a 500psig gauge). These uncertainties are taken into account to calculate
the uncertainty propagation of the calibration curve into the final mixture compositio. This procedure
is explained in more detail in section 2.6.
37
2.1.3 Seeding system
Flow seeding is a very important issue when using Laser Doppler Velocimetry, LDV, or Digital
Particle Velocimetry, DPIV, techniques, especially the selection of the size of the seeding particles.
The diameter of these particles should be small enough to guarantee accurate tracking of the flow, but
not too small so that the light scattered can be detected. When the Reynolds number of the particle in
the flow is much less than unity, Stokes’ drag law is applicable and it can be assumed that the particle
velocity measured is equal to the gas phase velocity. It has been shown that in the case of the
counterflow configuration, where significant velocity gradients are present, velocity slip can occur if
the particle diameter is not below 5 𝜇𝑚 [2-4]. A final consideration is that the material of the seeding
particles must not affect the flame chemistry.
For the present study, silicon oil (Alfa Aesar CAS# 63148-62-9) is to generate the droplets that are
used to seed the flow. The boiling point of silicone oil is above 570 𝐾 , which is high enough for the
droplets to survive further downstream of the minimum point of the axial velocity profile, 𝑆 , .
Although silicon oil is not inert, previous studies have shown that the amounts used for seeding do not
affect the flame chemistry [5]. Typically, the Meinhard
®
high efficiency nebulizer (HEN) is chosen to
generate droplets of the order of 5 − 10 𝜇𝑚 at very low flow rates, 10 to 300 𝜇𝐿 /𝑚𝑖𝑛 . In this type of
nebulizer the particles are generated by a carrier gas, N2 or air, that is choked at the tip and that aspirates
and atomizes the silicon oil from a central capillary, as shown in Fig. 2.4. Additionally, this type of
nebulizer can be operated up to 8 atm, which is crucial for flow measurements at high pressures. The
silicon oil flow rate is regulated by a high-accuracy syringe pump (Chemyx® Nexus 6000) suitable for
high-pressure environments.
Figure 2.4. Meinhard
®
nebulizer
38
For the non-premixed flames extinction experiments the use of the HEN nebulizer was very
effective to keep a good amount of seeding without affecting the flame structure due to clogging of the
meshes. However, for high pressure experiments flames are more susceptible to flow instabilities, as
discussed at the end of section 1.2.2, especially for premixed flames. Experimentally this was very
evident when measuring the local strain rates of premixed flames above 2 atm; clogging of the meshes
was affecting the flame structure considerably due to clogging of the meshes after minutes of seeding
the flow. Therefore, a new seeding device that generates smaller seeding particles was designed. This
seeding device is based on a modified design of a Laskin nozzle [6]. Laskin nozzles are usually used
in applications where high seeding flow rates are needed and accuracy in the flow rate of the seeded
flow is not a necessity. This new seeding device consist of a mixing chamber that is filled with silicon
oil up to 50% of its capacity. In the center a calibrated sonic nozzle is submerged in the silicon oil and
with an upstream pressure ranging from 100 to 300 psig, depending on the amount of seeding particles
needed, generates small bubbles. Submicron silicon oil particles are embedded inside this bubbles due
to the interaction of the high speed jet and the bath of silicon oil surrounding it. This submicron particles
scape when the small bubbles reach the surface and are mixed with the main flow coming from the
inlet of the chamber. With the inclusion of the sonic nozzle to generate the bubbles, it is also possible
to accurately account for the flow rate of gas used in the seeding process, which is crucial to set the
correct flow rates needed to generate the flames under the desired mixture compositions. Fig. 2.5 show
a schematic of the modified Laskin nozzle design.
Figure 2.5. Left: Modified Laskin nozzle. Right: Schematic of the operation principle
39
Both seeding systems must not generate considerable flow perturbations as well as excessive flow
seeding that can affect the flame chemistry or clog the burner meshes. Both systems allow for the
modulation of the appropriate flow rate of silicon oil needed according to the experiment pressure and
mixture flow rates. Finally, the seeded flow is filtered with a 5 μm inline particle filter (McMaster-Carr
Ref.#: 4414K71) to avoid big silicon oil droplets clogging the meshes.
2.2 Experimental setup
The schematic of the experimental configuration for non-premixed flames is shown in Fig. 2.6. A
newly developed chamber that operates for pressures between 0.1 and 20 atm was used to enclose the
counterflow burner assembly. Specially designed flanges allow assembling burners with diameters D
= 6.3, 11, 14 and 22 mm, which are used for various ranges of Reynolds numbers, so that the burner
separation distance, L, can be varied independently of D. Four fused silica windows allow optical
access. Direct flame imaging was obtained with a CMOS monochrome high-speed camera (Phantom
v710). For the case of non-premixed flames the mixture of N2 and fuel was injected in the top burner
to decrease possible effect of buoyancy in the flame structure. As it was mentioned in the previous
section, the HEN Nebulizer was used to seed the flow of the mixture of N 2 and O2 and consequently
the axial velocity profile was measured in the oxidizer side for all experiments.
Figure 2.6. Schematic of the experimental apparatus for non-premixed flames.
40
Fig. 2.7. shows a schematic of the experimental setup used for premixed flames. In this case the reactive
mixture of Fuel, N2 and O2 is seeded using the modified Laskin nozzle described in the previous section
and is injected in the top burner, and therefore the axial velocity profile is measured in that region of
the flame.
Figure 2.7. Schematic of the experimental apparatus for premixed flames.
2.3 Measurements of the axial velocity profile
The axial flow velocities are measured along the stagnation streamline using a mini Laser Doppler
Velocimetry system (MSE INC.). The miniLDV probe contains a laser, beam shaping optics, and
receiving and detection optics, which do not require alignment or calibration. The laser power is
140 𝑚𝑊 at a wavelength of 658 𝑛𝑚 . The prove volume, where the two laser beams intersect, has
dimensions of 30×60×200 𝜇𝑚 ; 60 𝜇𝑚 is the dimension along the axial axis, which allows for
sufficient resolution of any velocity changes along the central axial axis of the flame. For a single
location at least 100 velocity measurements are averaged. The miniLDV probe is displaced along the
axial axis every 50 to 100 𝜇𝑚 to accurately resolve the velocity profiles.
Excellent flame stability is essential in LDV measurements, since these are obtained within a time
of the order of a second at each location. During the time period needed to measure a complete velocity
41
profile, small flow perturbations can result in flame displacement and thus average velocities are
recorded at each point. These perturbation do not affect the value of 𝐾 considerably, but can have a
notable effect on 𝑆 , . Therefore, the design and setup of the burners and the seeding system has to
be of considerable precision because these perturbations complicate experiments especially at high
pressures.
Finally, it is important to note the effect of flame edge interference with the signal that the miniLDV
probe detects. The flame edge is a zone of high vorticity where the local index of refraction changes
considerably as a result of the mixing of the hot flame products and the cold N 2 surrounding the flame,
and thus the signal detected in this region does not represent the actual flow conditions. This effect is
more noticeable as pressures increases due to the fact that buoyancy increases and displaces the edge
of the bottom flame to the region where velocity measurements take place. This effect is not observed
in the top flame as the edge is always displaced by buoyancy forces to a location above the exit of the
top burner, as shown for the case of cold flow in Fig. 2.8. Therefore, velocity measurements are taken
in the top burner.
Figure 2.8. Detail of the location of the edges of the top jet.
2.4 Flame extinction measurements
Premixed flames are generated using the single flame configuration (Fig 1.4b), where a jet with a
mixture of fuel, N2 and O2 impinges a jet with N2. Non-premixed flames are generated by counter-
flowing an ambient temperature air jet against a fuel/N2 jet (Fig 1.4c). In both configurations, the jet
momenta were matched at all conditions.
Local extinction strain rates, 𝐾 ′𝑠 , are measured directly using the methodology previously
developed by Dong et al. [7] and Holley et al. [8]. Near-extinction flames are established and the
prevailing strain rate, 𝐾 , is determined as the maximum value of the absolute value of the axial velocity
42
gradient in the hydrodynamic zone; on the air side for non-premixed flames and on the fuel-oxidizer
side for premixed flames. In the case of non-premixed and lean premixed flames extinction is achieved
by a slight reduction of the fuel flow rate, while for rich premixed flames a slight increase in the fuel
flow rate is needed. It has been shown both experimentally and numerically that 𝐾 is minimally affected
through such slight variations of the fuel flow rate (less than 0.5%) and it can be defined as the actual
local 𝐾 ′𝑠 [9,10], Fig. 2.9. In addition to the thermodynamic states of the unburned reactants, the
two additional parameters that are needed as input to the simulations of flame extinction limits are the
separation distance, 𝐿 [11], and the axial velocity gradient along the centerline at the burner exit, 𝛼 ,
[9,12] that is determined from the LDV measurements, Fig. 2.9.
Figure 2.9. Axial velocity profile along the center line and definition of the parameters measured in
extinction experiments.
𝐿 is a very important parameter to be considered in extinction studies. One of the main assumptions
to model the counterflow configuration is that the diameter of the burner nozzles, 𝐷 , is infinitely large
compared to 𝐿 [12]. This is not possible to achieve experimentally, especially at high pressure
conditions where 𝐷 has to be particularly small to keep a laminar flow regime (6.3 mm for this study).
The ratio 𝐿/𝐷 needs to be kept as small as possible but not to the point that the spatial resolution
available for measurements is compromised. Studies have shown that values of 𝐿/𝐷 ≈ 1 result in flow
43
fields that are in very close agreement with the models assumptions [13-15]. For 𝐿 /𝐷 > 1.5 the flow
behaves as a free jet initially and downstream as a stagnation flow, thus comparisons with model
predictions are not suitable [14,16].
Finally, to keep a laminar flow regime, Reynolds numbers have to be kept below 1800 for the burner
type used in the this thesis. As it has been discussed at the end of section 1.2.5, the burning rate increases
as pressure is increased and higher stretch rates are required to achieve extinction for the same mixture
conditions. Therefore, at the highest pressure that is achieved in this study, which is 7 atm for non-
premixed flame and 4atm for premixed flames, the compositions of flames that extinguish at the
limiting Reynolds number are defined. Then, these compositions are kept constant to determine
extinction conditions while pressure is decreased.
2.5 Laminar flame speed measurements with the counterflow technique
𝑆 ′𝑠 are determined in the single flame configuration, as shown schematically in Fig. 1.4b.
Measurements are initiated at a finite 𝐾 that is reduced by small quantities using a bypass installed
upstream of the burners. 𝑆 , is measured at every single 𝐾 until conditions where low strain are
affected by heat loss to the burner rim, Fig. 2.9. For a given mixture and a given 𝜙 , the measured
𝑆 , ′𝑠 are plotted against the corresponding 𝐾 values and by extrapolating to zero stretch, 𝐾 = 0, 𝑆
is determined. Previous studies have shown that linear extrapolations can over estimate 𝑆 by 5-20%
because the effect of thermal expansion at low 𝐾 is not accounted for [9,13]. Additionally, non-linear
extrapolations methods where the effect of thermal expansion is studied through asymptotic analysis
(e.g. [17]) have been shown to not be valid in all cases [13]. Therefore, a computationally assisted non-
linear extrapolation method developed by Egolfopoulos and coworkers [9,18-20] is used for a more
accurate determination of 𝑆 ′𝑠 , as shown in Fig. 2.10.
The computationally assisted method consists of the computation of the response of 𝑆 , vs. 𝐾
with an opposed jet code until low 𝐾 values are reached and heat loss to the burner boundary is not
considerable. Then, a vertical displacement, ∆𝑆 , is applied to this computed curve to fit the
experimental 𝑆 , vs 𝐾 data points measured until the minimum least square difference is reached.
Finally, the experimental laminar flame speed, 𝑆 , , is computed by adding ∆𝑆 to the laminar flames
speed computed with a one-dimensional flame code, 𝑆 , . It is important to mention that
44
experimental 𝛼 values are considered in the computation of the 𝑆 , vs. 𝐾 curve. More details on this
method and both codes used will be given in the numerical methods section (Chapter 3).
Figure 2.10. Numerically-assisted extrapolation to get 𝑆 from strained flame data.
In order to minimize uncertainties coming from the extrapolation methods, measurements al low
strain rates are preferred but this requires a flame that is stabilized at low flow rates. However, this is
not always possible because at such flow rates two phenomena can occur. First, the boundary layer
thickness increases and the radial pressure gradients can overwhelm the inertia of the flow, which can
develop a dip in the centerline and two local peaks between the centerline and the burner rim.
Measurements in flames with such curvature effect are not suitable for comparison with numerical
models. And second, locally the flow velocity can be comparable to the burning velocity of the mixture
and flashback can occur.
2.6 Uncertainty quantification of flame extinction measurements
The methodology proposed by Xiouris et a. [21] for the case of spherically expanding flames was
implemented. It is worth mentioning that no thorough studies of uncertainty quantification and
propagation have been reported for local extinction strain rates. Due to the nature of experiment, in
which LDV measurements of the axial velocity profile take a considerable amount of time (5-10
0
5
10
15
20
25
30
35
40
45
50
0 100 200 300 400 500 600
Su,ref (cm/s)
Kref (1/s)
Experiments
1D Modeling
Best Fit
Suo Modeling
Suo, exp
∆𝑆 ∆𝑆 C
2
H
2
ϕ=0.8, P = 1.5 atm
𝑆 Modeling
𝑆 Experiment
45
minutes) and the cost of the supplies to conduct the experiment at high pressures, many repetitions are
not possible to carry out an accurate statistical analysis. Therefore, the following uncertainty
quantification methodology is implemented.
The general equation for uncertainty propagation from all parameters, 𝑄 , to the function or variable
𝐹 = 𝐹 (𝑄 , 𝑄 , … , 𝑄 ) is [22-24]:
𝑎 = ∑ 𝑎 + ∑ ∑ , 𝑎 Eq. (2.2)
where 𝑀 is the number of parameters involved, 𝑎 is the uncertainty of each parameter 𝑄 , 𝑎 the
correlation coefficient between parameters 𝑄 and 𝑄 , and 𝑎 the final propagated uncertainty of 𝐹 .
Hereafter, the notation 𝑎 will be used to represent uncertainties. One of the main assumptions is that
errors are by default normally distributed and ±𝑎 is the representation of the 68% confidence interval.
Eq. 2.2 can be written in matrix form as:
𝑎 = 𝐷 𝐶𝐷 Eq. (2.3)
where 𝐷 is the vector column having as elements the partial derivatives of 𝐹 with respect to the
parameters 𝑄 , and 𝐶 the covariance matrix calculated as (𝐴 𝐴 )
. 𝐴 is the weighted design matrix
that is a function of the uncertainties of the parameters 𝑄 [22]. This matrix formulation will be used in
the data processing of the LDV measurements and the calibration curves of the sonic nozzles. The
previous equations are only valid when small perturbations around the mean value are considered.
This procedure can be divided in two parts to compute the total uncertainty of 𝐾 :
𝑎 = 𝑎 , + 𝑎 , Eq. (2.4)
where 𝑎 , is the uncertainty from the LDV data post-processing, and 𝑎 , is the uncertainty
propagated from the mixture preparation and the boundary conditions.
2.6.1 Uncertainty from LDV data post-processing
The uncertainties of 𝑆 , , 𝐾 and 𝛼 are computed based on the polynomial fit of the LDV data.
This procedure will be described by taking as an example the axial velocity profile measured for a C 2H4
single premixed flame at 𝜙 = 0.8 and 𝑃 = 4 𝑎𝑡𝑚 close to extinction. Fig. 2.11 shows the axial velocity
profile measured with the LDV technique. At the location of each data point, the LDV system measures
46
between 100 and 500 times the axial velocity and reports the standard deviation of the average value
reported. The standard deviation of each point is considered in the polynomial fit to calculate the
coefficients 𝐶 and the corresponding Jacobian matrix, 𝐽 , which is equal to the weighted design matrix,
𝐴 . The polynomial fit is carried out using the subroutines available in MATLAB.
Figure 2.11. Axial velocity profile for C2H4 premixed flame close to extinction.𝜙 = 0.8, oxidizer
17%O2-83%N2 and 𝑃 = 4 𝑎𝑡𝑚 .
The variables of interest are the axial velocity 𝐹 = 𝑈 (𝑥 ) and the strain rate 𝐹 = 𝑑𝑈 (𝑥 ) 𝑑𝑥 ⁄ . From
the polynomial fit the covariance matrix 𝐶 that is constant at any location is determined. Also, the
partial derivatives of the variable of interest with respect to the polynomial coefficients, 𝜕𝐹 /𝜕𝐶 , that
are a function of the location, are determined to form vector 𝐷 . Finally, the uncertainty of any variable
of interest, 𝐹 , is calculated using Eq. 2.3 at any location of interest.
To determine 𝐾 and its uncertainty, the region of interest to carry out the polynomial fit has to be
selected first. A fourth order polynomial has been determined to be the most accurate one to calculate
𝐾 . Fig. 2.12 shows the polynomial fit to the axial velocity data in the region where the maximum
strain rate is located, along with the uncertainties and residuals of the fit. Fig. 2.12c shows the estimated
values of the strain rate and their uncertainties at various locations. The maximum strain rate, the
corresponding uncertainty and its location are also shown. In general, the uncertainty in the 𝐾 values
measured is in the range of 4-6% for all cases. For this analysis this uncertainty is defined as 𝑎 , .
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
20
30
40
50
60
70
80
90
X (cm)
U (cm/s)
Data
Poly Fit
47
Figure 2.12. Local extinction strain rate and its uncertainty of a C 2H4 premixed flame close to
extinction. 𝜙 = 0.8, oxidizer 17%O2-83%N2 and 𝑃 = 4 𝑎𝑡𝑚 .
The region surrounding the minimum velocity location is fitted with a third order polynomial to
determine 𝑆 , and its uncertainty. The polynomial fit to the axial velocity data along with the
uncertainties and residuals are shown in Fig 2.13. The minimum axial velocity, the corresponding
uncertainty and its location are also shown. In general, the uncertainty in the 𝑆 , values measured is
between 1 to 3% for all cases.
Finally, as it is not possible to conduct LDV measurements exactly at the exit of the burner, an
extrapolation of the data located upstream of the location of the maximum strain rate is carried out to
estimate the axial velocity and the strain rate at the exit of the burner, 𝛼 and 𝑈 , respectively. Based
on polynomial fits to axial velocity profiles obtained numerically, it was determined that a second order
polynomial was the most optimal to fit the data. Fig. 2.14 shows the polynomial fit to the axial velocity
data in the region close to the burner exit and its residuals and uncertainty, along with the extrapolated
value at the burner exit and its uncertainty. Fig. 2.14c shows the estimated values of the strain rate and
their uncertainties, and the extrapolated value that corresponds to 𝛼 and its uncertainty. The
uncertainties in 𝑈 are between 1-3% and for 𝛼 between 5-7%.
0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2
20
25
30
35
40
45
50
X (cm)
U (cm/s)
Fit
Error bars
Data
0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
X (cm)
Residuals (%)
Poly Fit
X (cm)
X (cm)
U (cm/s) Residuals (%)
a)
b)
0.145 0.15 0.155 0.16 0.165 0.17 0.175 0.18 0.185 0.19 0.195
-600
-400
-200
0
200
400
X (cm)
K (1/s)
Fit
Error bars
Kextinction
𝐾 𝑒𝑥𝑡 = 505 ± 30 1/s
X (cm)
K (1/s)
c)
48
Figure 2.13. Reference flame speed and its uncertainty of a C 2H4 premixed flame close to
extinction. 𝜙 = 0.8, oxidizer 17%O2-83%N2 and 𝑃 = 4 𝑎𝑡𝑚 .
Figure 2.14. Extrapolated exit velocity and exit strain rate and their uncertainties for a C 2H4
premixed flame close to extinction. 𝜙 = 0.8, oxidizer 17%O2-83%N2 and 𝑃 = 4 𝑎𝑡𝑚 .
2.6.2 Uncertainty from mixture preparation and boundary conditions
The error propagation to local extinction strain rate coming from the mixture preparation takes into
account the uncertainties in the flow rates of N2, O2 and fuel. For the case of the boundary conditions
0.17 0.175 0.18 0.185 0.19 0.195 0.2
22
24
26
28
30
32
X (cm)
U (cm/s)
Fit
Error bars
Data
Suref
0.17 0.175 0.18 0.185 0.19 0.195 0.2
-0.4
-0.2
0
0.2
0.4
X (cm)
Residuals (%)
Poly Fit
U (cm/s) Residuals (%)
X (cm)
X (cm)
a)
b)
𝑆 𝑢 ,
𝑟𝑒𝑓 = 23.2 ± 0.4 cm/s
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
X (cm)
Residuals (%)
Poly Fit
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
30
40
50
60
70
80
90
X (cm )
U (cm/s)
Poly Fit
Error bars
Data
Uexit
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
-450
-400
-350
-300
-250
-200
-150
X (cm)
K (1/s)
Poly Fit
Error bars
Kexit
X (cm)
X (cm)
X (cm)
U (cm/s) Residuals (%)
K (1/s)
α = 193.8 ± 8.8 1/s
a)
c)
b)
𝑈 𝑒𝑥𝑖𝑡 = 86.3 ± 1.6 cm/s
49
consider the uncertainties in the temperature of the gases, the pressure inside the chamber, the
separation distance (𝐿 ) and the uncertainty in 𝛼 calculated in the previous section. The uncertainties
of all these parameters, 𝑄 , is not correlated because each of them are measured independently and this
simplifies Eq. 2.2 to:
𝑎 , = ∑ 𝑎 Eq. (2.5)
The uncertainty, 𝑎 , of each parameter 𝑄 is determined based on the accuracy of the instruments
reported by the manufacturer. Regarding the boundary conditions, for the pressure measured inside the
chamber a pressure gauge with an accuracy of ±0.5 psi was used. The K thermocouple used to measure
the temperature of the jets has an accuracy of ±1.1 K. For the separation distance and uncertainty of
±0.1 mm was estimated. The uncertainty of 𝛼 is estimated in the procedure described in the previous
section.
The uncertainties in the flow rates that affect the mixture preparation were estimated by calculating
the uncertainty coming from the calibration curves of the sonic nozzles used. In section 2.1.2 the
process to generate the calibration curves is explained. The uncertainty in the pressure gauges used to
set the flow is ± 1.25 psi. The uncertainties of the wet test meter are ±0.15 and ±0.1% of the flow rate
measured when the flow rate is more than half or less than half the maximum flow rate, respectively.
Similar to the methodology explained in the previous section, uncertainty of each point from the
calibration curve is considered in the polynomial fit to calculate the coefficients 𝐶 and the
corresponding Jacobian matrix, 𝐽 , which is equal to the weighted design matrix, 𝐴 . The polynomial fit
is carried out using the subroutines available in MATLAB. From the polynomial fit the covariance
matrix 𝐶 is determined, as well as the partial derivatives of the flow rate with respect to the polynomial
coefficients, 𝜕𝑄 /𝜕𝐶 , to form vector 𝐷 . Finally, the uncertainty, 𝑎 , of any flow rate, 𝑄 , is calculated
using Eq. 2.3 at any pressure of the gauge.
To estimate all the partial derivatives, 𝜕𝐹 /𝜕𝑄 , it is necessary to compute 𝐾 using a brute force
approach. For each experimental condition, one of parameters previously mentioned, 𝑄 , is modified
approximately by a quantity equal to the corresponding 𝑎 , while the other 𝑄 parameters were kept
constant. From this approach is possible to compute the Logarithmic Sensitivity Coefficients, 𝐿𝑆𝐶 =
𝑑 (𝑙𝑛𝐾 )/𝑑 (𝑄 ) at any given experimental condition and identify the parameter that considerably
50
affect 𝐾 and consequently have to be measured with higher accuracy. Fig. 2.15 and 2.16 show the
𝐿𝑆𝐶 for premixed flames of C2H4 at 3 atm at lean and rich conditions, respectively.
Figure 2.15. Logarithmic Sensitivity Coefficients for a C 2H4 premixed flame close to extinction.
𝜙 = 0.8, oxidizer 17%O2-83%N2 and 𝑃 = 3 𝑎𝑡𝑚 .
Figure 2.16. Logarithmic Sensitivity Coefficients for a C 2H4 premixed flame close to extinction.
𝜙 = 1.4, oxidizer 17%O2-83%N2 and 𝑃 = 3 𝑎𝑡𝑚 .
As expected, for the case of lean flames the sensitivity of 𝐾 to the flow rates of N2 and fuels is
considerable. The sensitivity to the flow rate of O 2 is the highest for the case of rich flames, although
the sensitivity to the flow rate of N2 is still considerable. This type of analysis is very useful to design
very accurate experiments because indicate the parameters that have to be measured with the highest
accuracy.
-8 -6 -4 -2 0 2 4 6
C
2
H
4
ϕ=0.8, P = 3atm
(𝐾𝑒𝑥𝑡, 𝑄 )
(𝐾𝑒𝑥𝑡, 𝐿)
(𝐾𝑒𝑥𝑡, 𝛼)
(𝐾𝑒𝑥𝑡, 𝑃)
(𝐾𝑒𝑥𝑡, 𝑄 )
(𝐾𝑒𝑥𝑡, 𝑇)
(𝐾𝑒𝑥𝑡, 𝑄 )
Logarithmic Sensitivity Coefficients
-15 -10 -5 0 5 10 15 20
C
2
H
4
ϕ=1.4, P = 3atm
(𝐾𝑒𝑥𝑡, 𝑄 )
(𝐾𝑒𝑥𝑡, 𝐿)
(𝐾𝑒𝑥𝑡, 𝛼)
(𝐾𝑒𝑥𝑡, 𝑃)
(𝐾𝑒𝑥𝑡, 𝑄 )
(𝐾𝑒𝑥𝑡, 𝑇)
(𝐾𝑒𝑥𝑡, 𝑄 )
Logarithmic Sensitivity Coefficients
51
2.7 References
[1] R.R. Burrell, R. Zhao, D.J. Lee, H. Burbano, F.N. Egolfopoulos, Two-dimensional effects in
counterflow methane flames, Proceedings of the Combustion Institute. 36 (2017) 1387-1394.
[2] C. Sung, C. Law, R. L AXELBAUM, Thermophoretic effects on seeding particles in LDV
measurements of flames, Combustion Sci. Technol. 99 (1994) 119-132.
[3] C. Sung, J. Kistler, M. Nishioka, C. Law, Further studies on effects of thermophoresis on seeding
particles in LDV measurements of strained flames, Combust. Flame. 105 (1996) 189-201.
[4] F.N. Egolfopoulos, C.S. Campbell, Dynamics and structure of dusty reacting flows: inert particles
in strained, laminar, premixed flames, Combust. Flame. 117 (1999) 206-226.
[5] Y. Dong, C.M. Vagelopoulos, G.R. Spedding, F.N. Egolfopoulos, Measurement of laminar flame
speeds through digital particle image velocimetry: mixtures of methane and ethane with hydrogen,
oxygen, nitrogen, and helium, Proceedings of the combustion institute. 29 (2002) 1419-1426.
[6] C. Kähler, B. Sammler, J. Kompenhans, Generation and control of tracer particles for optical flow
investigations in air, Exp. Fluids. 33 (2002) 736-742.
[7] Y. Dong, A.T. Holley, M.G. Andac, F.N. Egolfopoulos, S.G. Davis, P. Middha, H. Wang,
Extinction of premixed H2/air flames: Chemical kinetics and molecular diffusion effects, Combust.
Flame. 142 (2005) 374-387.
[8] A. Holley, Y. Dong, M. Andac, F. Egolfopoulos, Extinction of premixed flames of practical liquid
fuels: Experiments and simulations, Combust. Flame. 144 (2006) 448-460.
[9] C. Ji, E. Dames, Y.L. Wang, H. Wang, F.N. Egolfopoulos, Propagation and extinction of premixed
C5–C12 n-alkane flames, Combust. Flame. 157 (2010) 277-287.
52
[10] Y.L. Wang, P.S. Veloo, F.N. Egolfopoulos, T.T. Tsotsis, A comparative study on the extinction
characteristics of non-premixed dimethyl ether and ethanol flames, Proceedings of the Combustion
Institute. 33 (2011) 1003-1010.
[11] F.N. Egolfopoulos, Geometric and radiation effects on steady and unsteady strained laminar
flames, Symp. Int. Combust. 25 (1994) 1375-1381.
[12] R.J. Kee, J.A. Miller, G.H. Evans, G. Dixon-Lewis, A computational model of the structure and
extinction of strained, opposed flow, premixed methane-air flames, Symp. Int. Combust. 22 (1989)
1479-1494.
[13] F.N. Egolfopoulos, N. Hansen, Y. Ju, K. Kohse-Höinghaus, C.K. Law, F. Qi, Advances and
challenges in laminar flame experiments and implications for combustion chemistry, Progress in
Energy and Combustion Science. 43 (2014) 36-67.
[14] B.G. Sarnacki, G. Esposito, R.H. Krauss, H.K. Chelliah, Extinction limits and associated
uncertainties of nonpremixed counterflow flames of methane, ethylene, propylene and n-butane in air,
Combust. Flame. 159 (2012) 1026-1043.
[15] J.M. Bergthorson, S.D. Salusbury, P.E. Dimotakis, Experiments and modelling of premixed
laminar stagnation flame hydrodynamics, J. Fluid Mech. 681 (2011) 340-369.
[16] C.M. Vagelopoulos, F.N. Egolfopoulos, Symp. Int. Combust. 27 (1998) 513-519.
[17] J. Tien, M. Matalon, On the burning velocity of stretched flames, Combust. Flame. 84 (1991) 238-
248.
[18] Y. Wang, A. Holley, C. Ji, F. Egolfopoulos, T. Tsotsis, H. Curran, Propagation and extinction of
premixed dimethyl-ether/air flames, Proceedings of the Combustion Institute. 32 (2009) 1035-1042.
[19] C. Ji, Y.L. Wang, F.N. Egolfopoulos, Flame studies of conventional and alternative jet fuels, J.
Propul. Power. 27 (2011) 856-863.
53
[20] P.S. Veloo, Y.L. Wang, F.N. Egolfopoulos, C.K. Westbrook, A comparative experimental and
computational study of methanol, ethanol, and n-butanol flames, Combust. Flame. 157 (2010) 1989-
2004.
[21] C. Xiouris, T. Ye, J. Jayachandran, F.N. Egolfopoulos, Laminar flame speeds under engine-
relevant conditions: Uncertainty quantification and minimization in spherically expanding flame
experiments, Combust. Flame. 163 (2016) 270-283.
[22] I. Hughes, T. Hase, Measurements and their Uncertainties: A Practical Guide to Modern Error
Analysis, Oxford University Press, 2010.
[23] D. Sivia, Data Analysis: A Bayesian Tutorial (Oxford Science Publications), (1996).
[24] J.R. Taylor, An Introduction to Error Analysis 2nd edn (Sausalito, CA, (1997).
54
3. Numerical methodology
Experiments are numerically simulated by solving the conservation equations of mass, species
concentration, energy, and momentum in the case of the counter flow configuration. 𝑆 ′𝑠 are computed
using the PREMIX code [1,2] and the counterflow configuration is simulated using an opposed-jet flow
code [3,4]. Both codes have been modified to account for the thermal radiation of CH 4, CO, CO2 and
H2O at the optically thin limit [5], as well as for the Soret effect. Additionally, both codes are integrated
with the CHEMKIN [6] and the Sandia transport subroutine libraries [7]. The H and H2 diffusion
coefficients of several key pairs are based on a recently updated set of Lennard-Jones parameters [8],
and all simulations are performed using the multicomponent transport formulation.
3.1 PREMIX
This code predicts the temperature and species distribution of a freely propagating, isobaric,
adiabatic, and one-dimensional flame [1]. The code solves the conservation of mass, species, and
energy equations, which are discretized by finite difference approximations to reduce the boundary
value problem to a system of algebraic equations. The mass flow rate is treated as an eigenvalue of the
problem. Then, an additional boundary condition is introduced, which fixes the location of the flame
by specifying the temperature at one point. The other boundary conditions consist of the initial reactants
composition and temperature at the cold boundary, and vanishing gradients at the hot boundary. The
code needs a starting estimate of the products at the hot boundary, flame location and thickness, and
temperature profile to begin the iteration process. The temperature profile estimate eliminates the
energy equation for the first solution step and, therefore, convergence difficulties related to non-
linearities coming from the reaction rates. A damped-modified Newton algorithm is used to solve the
system of algebraic equations. If this algorithm fails to converge, the solution estimate is conditioned
by a time integration, which provides a new starting point that is closer to the solution to the algorithm.
Computations start in a coarse mesh, usually of seven grid points, and adaptive placement of new mesh
points is done in regions where the solution shows large gradient or curvature. The computations stop,
when addition of new grid point does not affect the solution.
The laminar flame speed values, 𝑆 ′𝑠 , computed and reported in this thesis correspond to conditions
in which transport properties were calculated with the Multi-component formulation, radiation and
55
Soret effect were considered, and the values of GRAD and CURV parameters were set below 0.02 to
guarantee grid independent solutions.
3.2 Opposed Jet Code
This code computes the steady-state solution for axisymmetric premixed or non-premixed flames
between two opposing jets [3]. The two-dimensional axisymmetric flow field is reduced to a quasi-
one-dimensional flow when a streamfunction in the form 𝜓 (𝑥 , 𝑟 ) ≡ 𝑟 𝑈 (𝑥 ) is introduced. This
streamfunction satisfies the mass continuity equation when defined as follows:
= 𝑟𝜌𝑢 = 2𝑟𝑈 Eq. (3.1)
−
= 𝑟𝜌𝑣 = −𝑟 Eq. (3.2)
where 𝑢 and 𝑣 are the flow velocities in the axial, 𝑥 , and radial, 𝑟 , directions, respectively. Assuming
that 𝑢 is only a function of 𝑥 , implies that temperature, species mass fraction, and density are also
functions of 𝑥 only. Introducing the above definitions into the momentum equations, reduces these
partial differential equations to third order ordinary differential equations. Also, it can be shown that
both pressure gradients,
and
, are functions of 𝑥 only, and that the radial pressure gradient is
constant and can be defined as an eigenvalue of the problem:
= 𝐻 Eq. (3.3)
Additionally, the axial momentum equation decouples from the system of equations. Therefore, the
code solves the conservation of mass, radial momentum, species, and energy equations along the
stagnation streamline. These equations are discretized by second order finite difference approximations
to reduce the boundary value problem to a system of algebraic equations. The boundary conditions
consist of the reactants composition and velocity at both cold boundaries for the case of single premixed
and non-premixed flames. For twin flames, symmetry at the stagnation plane is assumed and vanishing
gradients are defined at this location. An important feature of this formulation is that axial velocity
gradients can be defined at the boundaries, which is a very important variable to take into account to
make suitable comparisons with counterflow experimental data, as it will be discussed later. The
procedure to solve the equations is the same as the one explained for the PREMIX code.
56
The local extinction strain rates, 𝐾 ′𝑠 , computed and reported in this thesis correspond to
conditions in which transport properties were calculated with the Multi-component formulation,
radiation and Soret effect were considered, the number of grid points is set to 600 and is distributed
according to the gradients of temperature to keep the values of GRAD and CURV parameters below
0.05.
3.3 Numerically assisted extrapolation method for laminar flame speed determination
In this method developed by Egolfopoulos and coworkers [9-12], at a given 𝜙 and nozzle separation
distance, 𝐿 , the response of 𝑆 , vs. 𝐾 is computed with the opposed jet code until low 𝐾 values are
reached and heat loss to the burner boundary is not considerable. Then, a vertical displacement, ∆𝑆 ,
is applied to this computed curve to fit the experimental 𝑆 , vs 𝐾 data points measured until the
minimum least square difference is reached. Finally, the experimental laminar flame speed, 𝑆 , , is
computed by adding ∆𝑆 to the laminar flames speed computed with the PREMIX code, 𝑆 , . It is
important to mention that experimental 𝛼 values are considered in the computation of the 𝑆 , vs. 𝐾
curve.
Figure 3.1. Example of the non-linear extrapolation method
0
5
10
15
20
25
30
35
40
45
50
0 100 200 300 400 500 600
Su,ref (cm/s)
Kref (1/s)
Experiments
1D Modeling
Best Fit
Suo Modeling
Suo, exp
∆𝑆 ∆𝑆 C
2
H
2
ϕ=0.8, P = 1.5 atm
𝑆 Modeling
𝑆 Experiment
57
The shape of the curve computed provides a close representation of the nonlinear behavior at low
𝐾 ′𝑠 because it includes realistic description of fluid mechanics, chemical kinetics, and molecular
transport. Additionally, this shape does not depend to the first order on uncertainties related to kinetics
and transport. Therefore this method provides a more accurate description of the non-linear dependence
of 𝑆 , on 𝐾 , compared to other methods based on assumptions, like linear behavior (e.g. [13-15]),
one-step chemistry and simplified transport (e.g. [16]).
3.4 Extinction strain rate calculation
In the extinction strain rate calculations, a vigorously burning flame is first established at a given 𝜙
or Fuel/N2 ratio for premixed and non-premixed flames, respectively. Subsequently, 𝐾 is increased via
increase of the flow rates of both opposing jets, while keeping the momenta balanced, until extinction
occurs. At the extinction state, the response of any flame property to the strain rate is characterized by
a turning-point behavior. This results in a singular point, where the corresponding 𝐾 can be considered
as the actual 𝐾 , Fig. 3.2. The code has been modified to solve around this singular point by
introducing internal boundary conditions, so that 𝐾 becomes a dependent variable instead of an
independent one [17]. A two-point continuation approach is implemented by imposing a predetermined
temperature or species mass fraction, at two points in the flow field, so that the strain rate is solved for,
rather than imposed as a boundary condition. Following the recommendations of Nishioka et al. [18],
locations where the temperature or species concentrations have maximum slopes are chosen as the two
points.
As mentioned in section 2.4, in order to compute 𝐾 ′𝑠 accurately, additional to the thermodynamic
states of the unburned reactants the experimental values of the burners separation distance, 𝐿 , and the
axial velocity gradient along the centerline at the burner exit, 𝛼 , need to be considered [3,10]. The
magnitude of 𝐿 and 𝛼 affect the stretch rate distribution within the transport and reaction zones, which
also affects the burning intensity.
58
Figure 3.2. Computation of the extinction strain rate
Finally, previous studies have reported that the choice of the transport formulation for the transport
coefficients has a notable effect on the determination of 𝐾 [10,11,19]. Using the mixture average
formulation to compute 𝐾 results in considerable discrepancies compared to when the
multicomponent formulation is used. Therefore, the latter formulation is adopted for all the
computations in the present study. For the case of C 1-C2 chemistry the use of this formulation does not
represent a major computational time expense given that the size of the kinetic models is small
compared to that of heavier hydrocarbons.
3.5 Sensitivity Analysis
Sensitivity analysis is a very useful tool to assess the effects of chemical kinetics and molecular
diffusion on 𝑆 and 𝐾 . Standard CHEMKIN-based codes, like PREMIX, allow automated sensitivity
analysis of 𝑆 , temperature, and species concentrations to all reaction rate constants, but this was not
the case for 𝐾 in the Opposed Jet code. Egolfopoulos and coworkers [8,19,20] have developed a
numerical approach to account for the sensitivities of 𝐾 to all reaction rates as well as to the binary
diffusion coefficients. This was achieved by realizing, as described in section 4.4, that 𝐾 becomes a
dependent variable when a two-point continuation approach is implemented. As a result it is possible
to perform rigorous sensitivity analysis of 𝐾 with respect to reaction rates at the exact location that
59
it is determined experimentally in the hydrodynamic zone. The logarithmic sensitivity coefficients are
expressed as:
Eq. (3.4)
and
Eq. (3.5)
where 𝐴 is the Arrhenius pre-exponential factor of reaction 𝑖 .
Additionally, the capability of performing sensitivity calculations of the various dependent flame
properties on binary diffusion coefficient was also implemented by a “brute force” approach for the
PREMIX and Opposed Jet codes by Egolfopoulos and coworkers [8,19,20]. The mass diffusivity of
each specie 𝑖 to specie j, 𝐷 , , is perturbed by ±25% and then the corresponding 𝐾 values are
determined. Finally, the logarithmic sensitivities are estimated by computing:
, , Eq. (3.4)
and
, , Eq. (3.5)
3.6 Reaction path analysis
This analysis is used to identify the pathways that contribute to the production or consumption of a
species, 𝑘 , of interest. For this purpose the rate of progress, 𝑞 , of all the reactions is computed as
follows:
𝑞 = 𝑘 ∏ [𝑋 ]
− 𝑘 ∏ [𝑋 ]
Eq. (3.6)
where [𝑋 ] is the molar concentration of the 𝑘 species in reaction 𝑖 , 𝜐 the stoichiometric coefficients
of the reactants, 𝜐 the stoichiometric coefficients of the products, and 𝑘 and 𝑘 are the forward and
reverse rate constants of reaction 𝑖 , respectively. Subsequently, the rates of progress are integrated
along the whole computational domain and the reactions that contribute to the production or
consumption of the species, 𝑘 , of interest are identified. The total production or consumption of the
species is computed and the contribution percentage of each contributing reaction is computed. This
60
procedure is repeated for the species that contributed to the production or consumption of the initial
species of interest, and in this way the reaction pathways are constructed.
3.7 References
[1] R.J. Kee, J.F. Grcar, M. Smooke, J. Miller, E. Meeks, PREMIX: a Fortran program for modeling
steady laminar one-dimensional premixed flames, Sandia National Laboratories Report. (1985).
[2] J.F. Grcar, R.J. Kee, M.D. Smooke, J.A. Miller, Symp. Int. Combust. 21 (1988) 1773-1782.
[3] R.J. Kee, J.A. Miller, G.H. Evans, G. Dixon-Lewis, A computational model of the structure and
extinction of strained, opposed flow, premixed methane-air flames, Symp. Int. Combust. 22 (1989)
1479-1494.
[4] F.N. Egolfopoulos, C.S. Campbell, Unsteady counterflowing strained diffusion flames: diffusion-
limited frequency response. Journal of Fluid Mechanics, J. Fluid Mech. 318 (1996) 1-29.
[5] F.N. Egolfopoulos, Geometric and radiation effects on steady and unsteady strained laminar flames,
Symp. Int. Combust. 25 (1994) 1375-1381.
[6] R. Kee, F. Rupley, J. Miller, There is no corresponding record for this reference. (1989).
[7] R. Kee, J. Warnatz, J. Miller, SAND83-8209, Sandia National Laboratories. (1983).
[8] Y. Dong, A.T. Holley, M.G. Andac, F.N. Egolfopoulos, S.G. Davis, P. Middha, H. Wang,
Extinction of premixed H2/air flames: Chemical kinetics and molecular diffusion effects, Combust.
Flame. 142 (2005) 374-387.
[9] Y. Wang, A. Holley, C. Ji, F. Egolfopoulos, T. Tsotsis, H. Curran, Propagation and extinction of
premixed dimethyl-ether/air flames, Proceedings of the Combustion Institute. 32 (2009) 1035-1042.
[10] C. Ji, E. Dames, Y.L. Wang, H. Wang, F.N. Egolfopoulos, Propagation and extinction of premixed
C5–C12 n-alkane flames, Combust. Flame. 157 (2010) 277-287.
61
[11] C. Ji, Y.L. Wang, F.N. Egolfopoulos, Flame studies of conventional and alternative jet fuels, J.
Propul. Power. 27 (2011) 856-863.
[12] P.S. Veloo, Y.L. Wang, F.N. Egolfopoulos, C.K. Westbrook, A comparative experimental and
computational study of methanol, ethanol, and n-butanol flames, Combust. Flame. 157 (2010) 1989-
2004.
[13] C. Law, D. Zhu, G. Yu, Symp. Int. Combust. 21 (1988) 1419-1426.
[14] C. Wu, C. Law, Symp. Int. Combust. 20 (1985) 1941-1949.
[15] D. Zhu, F. Egolfopoulos, C. Law, Symp. Int. Combust. 22 (1989) 1537-1545.
[16] J. Tien, M. Matalon, On the burning velocity of stretched flames, Combust. Flame. 84 (1991) 238-
248.
[17] F.N. Egolfopoulos, P.E. Dimotakis, Symp. Int. Combust. 27 (1998) 641-648.
[18] M. Nishioka, C. Law, T. Takeno, A flame-controlling continuation method for generating S-curve
responses with detailed chemistry, Combust. Flame. 104 (1996) 328-342.
[19] A.T. Holley, X.Q. You, E. Dames, H. Wang, F.N. Egolfopoulos, Sensitivity of propagation and
extinction of large hydrocarbon flames to fuel diffusion, Proceedings of the Combustion Institute. 32
(2009) 1157-1163.
[20] A. Holley, Y. Dong, M. Andac, F. Egolfopoulos, Extinction of premixed flames of practical liquid
fuels: Experiments and simulations, Combust. Flame. 144 (2006) 448-460.
62
4. Pressure Effect on the Extinction of Premixed and Non-Premixed C1-C2
Hydrocarbon Flames
4.1 Experimental Approach
For non-premixed flames the experiments were carried out at pressures in the range, 𝑝 , 0.6 ≤𝑝 ≤ 7
atm, and ambient unburned reactant temperature of 293 K for CH 4, C2H6, C2H4, and C2H2 flames. By
counterflowing a fuel/N2 jet against an ambient air jet, while keeping the momenta balanced, the flames
were generated. The molar ratios in the fuel-carrying jet were fixed for each fuel at 𝑋 /𝑋 = 0.40,
𝑋 /𝑋 = 0.14, 𝑋 /𝑋 = 0.11, and 𝑋 /𝑋 = 0.08, where 𝑋 is the mole fraction of species
𝑖 . These values were chosen by experimental trial and error to achieve stable flames at the highest
pressure, where the Reynolds number is a limitation, and at the lowest pressure, where low strain rates
flames are difficult to generate. Table 4.1 summarizes the experimental conditions.
Fuel X Fuel/X N2
Oxidizer composition
Pressure (atm)
%O 2 %N 2
CH4 0.4 21 79 0.8-7
C2H6 0.14 21 79 1-7
C2H4 0.11 21 79 0.8-7
C2H2 0.08 21 79 06-5
Table 4.1 Experimental conditions for extinction strain rates of non-premixed flames
In the case of premixed flames, the experiments were carried out at pressures in the range 1.0 ≤𝑝 ≤
4 atm, and ambient unburned reactant temperature of 293 K. The single flame configuration was used,
in which a fuel/N2/O2 jet impinges a N2 jet while keeping the momenta balanced. The main difficulty
was to define a single fuel/N2/O2 composition that allowed generating stable flames for the entire
pressure range. In the present study, the composition of the reacting mixture was defined
experimentally until stable flames were generated at the highest Reynolds number possible, around
1500-1600. However, the local extinction strain rate, 𝐾 , decreases abruptly at pressures below 2atm
and flames reach extinction at very low strain rates for the reacting mixture defined at high pressures,
which complicates achieving stable flames at low pressures. Therefore, for the cases of 1 and 1.5 atm
63
the equivalence ratio was kept constant but the ratio of O 2/N2 was increased so that extinction
conditions were achieved at higher strain rates and consequently stable flames were generated. Table
4.2 summarizes the experimental conditions used for premixed flames.
Fuel ϕ
Oxidizer composition
T ad (K) Pressure (atm)
%O 2 %N 2
CH 4
0.85
21 79 2070 1-1.5
23 77 2175 2-4
1.18
21 79 2150 1-1.5
23 77 2260 2-4
C 2H 6
0.8
20 80 1980 1-1.5
22 78 2090 2-4
1.37
20 80 2000 1-1.5
22 78 2210 2-4
C 2H 4
0.8
17 83 1905 1-1.5
18 82 1975 2-4
1.4
17 83 1985 1-1.5
18 82 2055 2-4
C 2H 2
0.8
12.5 77.5 1725 1-1.5
13.5 76.5 1820 2-4
1.37
12.5 77.5 1920 1-1.5
13.5 76.5 2020 2-4
Table 4.2 Experimental conditions for extinction strain rates of premixed flames
A burner with a diameter 𝐷 = 6.3 𝑚𝑚 was used for the pressure range 2 ≤𝑝 ≤ 7 atm, while a burner
with diameter 𝐷 = 11 𝑚𝑚 was used for 0.5 ≤𝑝 ≤ 2 atm. For all 𝑝 ′𝑠 and 𝐷 ′𝑠 , 𝐿 = 6.3 𝑚𝑚 was used to
allow for sufficient spatial resolution for the velocity measurements.
4.2 Numerical Approach
USC Mech II [1] was selected as the reference kinetic model for the analysis of the effects of
chemistry on 𝐾 ′𝑠 . This model describes describe the high-temperature combustion kinetics of H 2/CO
and C1-C4 hydrocarbons, and consists of 111 species and 784 elementary reactions. Two recently
developed kinetic models based on optimizations of USC Mech II were selected. The model developed
64
by Dames et al. [2] that modified and optimized C 2H2 and C2H4 sensitive reactions, and therefore will
be used to analyze the effects of these modifications in the predictions of of C 2H2 and C2H4 and identify
reactions and reaction pathways that need improvement. For this study the pentanone chemistry of
Dames et al. was not considered and a total of 88 species and 556 elementary reactions are considered.
The second one is the Foundational Fuel Chemistry Model version 1.0 [3], FFCM-1, that made a major
revision to H2, H2O2, CO, CH2O, CH4, and a limited set of C2H6 chemistry with the Method of
Uncertainty Minimization using Polynomial Chaos Expansions (MUM-PCE) [4]. This model consists
of 38 species and 291 elementary reactions and will be used to analyze the cases of CH 4 and C2H6
flames to identify reactions and reaction pathways that need improvement. Additionally, San Diego
Mech [5] that describes the high-temperature combustion kinetics of H 2/CO and C1-C3 hydrocarbons
and consists of 50 species and 246 reactions will be used for the non-premixed flame analysis. It is
important to take into considerations that all these previous models optimized part of the reactions rates
against experimental data such laminar flame speeds, ignition delay times, and species profiles from
flow reactors.
Finally, a recently updated HP-Mech [6] is also considered; it describes the high-temperature
combustion kinetics of H2/CO and C1-C3 hydrocarbons and consists of 92 species and 615 reactions.
This kinetic model has been developed with a different philosophy to the one of the previous models
mentioned, in which the reaction rates are not optimized against experimental values and upon addition
of new reaction pathways the model predictability is expected to improve. This kinetic model will be
used to compute 𝐾 ′𝑠 for all the experimental cases.
4.3 Results
4.3.1 Global strain rate or local strain rate?
Two experimental and numerical approaches are widely used to measure the characteristic
extinction strain rate in the counterflow configuration. The first one is the global strain rate, originally
proposed by Seshadri and Williams [7], in which there is no need to measure the axial velocity profile
along the centerline because only the exit velocity of the burner is needed. If the momenta of both jets
is balanced, the global extinction strain rate can be defined as:
𝐾 , =
Eq. (4.1)
65
where 𝑉 is the axial exit velocity of one of the jets corresponding to the side where 𝐾 , needs
to be computed. This approximation is obtained from asymptotic analysis and is only applicable under
special conditions; the Reynolds number of the laminar jet is presumed to be large and there is no strain
rate in the axial velocity at the burner exit, 𝛼 = 0. Due to its simplicity and the fact that LDV or PIV
measurements of the velocity fields are not needed, this approach is widely used.. However, typically
the studies that use this approach do not asses the flow field conditions and confirm that there velocity
profile generated at the exit of the burners have a top-hat shape (as shown in section 2.1.1) and have a
very low strain rate. It is important to mention that the value of 𝑉 is estimated from the flow rate at
extinction and the measurement of the burner diameter, thus this can be a considerable source of error
if a top hat velocity profile is not achieved. The way the global strain rate is determined experimentally
is also carried out in numerical computations to have a suitable test or validation of kinetic models.
The second approach, which is the one used in this thesis, measures the local extinction strain rate
𝐾 , as it is explained in section 2.4. This requires the implementation of LDV and PIV techniques
that complicate the experiment considerably, especially as pressure increases (Refer to Chapter 2 for
more details). In this approach no assumption are made regarding the Reynolds number of the flow and
the value of 𝛼 , which in turn has to be measured and used as a boundary condition in numerical
computations for a suitable test or validation of kinetic models.
For the case of non-premixed flames of CH4 the global and local strain rates were computed and
compared with numerical computations to evaluate which approach is more appropriate. Fig 4.1 shows
the experimental and numerical results obtained with USC Mech II for the local extinction strain rate,
𝐾 . The corresponding 𝛼 values of each experiment ere included as boundary condition in numerical
computations. The disagreement with USC Mech II is between ±5%.
66
Figure 4.1. Experimental and computed local extinction strain rate of non-premixed CH 4 flames as a
function of pressure.
Fig. 4.2 shows the experimental and numerical results obtained with USC Mech II for the global
extinction strain rate, 𝐾 , for two cases: the first one with 𝑉 estimated with the flow rate at
extinction and the burner diameter, and the second with the value of 𝑉 obtained with the LDV data
post-processing (Exp. Corrected). For the first case, the disagreement with USC Mech II is between
±20%, while for the second case the disagreement is ±7%. This proves the importance for accurately
determining 𝑉 . Even though the burner design used in the study generates a top-hat velocity profile at
the burner exit the assumption that 𝑉 can be calculated from the flow rate and the burner diameter can
generate a bit source of error in 𝐾 , and affect comparisons with numerical computations. With
the second case, it is also proved that the actual experimental measurement of 𝑉 improves the
estimation of 𝐾 , considerably and this approach is more suitable for comparison with numerical
computations. Finally, comparing with the results of Fig. 4.1, the determination of 𝑉 from LDV
measurements seems to provide an accurate 𝐾 , value that can be fairly compared with
numerical computations. This is due to the fact that the 𝛼 values for the present experiments have a
maximum of 80 1/s that do not affect at a great extent the definition of 𝐾 , . However, this is not
the case for premixed flames where 𝛼 can reach considerably high values, as it will shown next.
67
Figure 4.2. Experimental and computed global extinction strain rate of non-premixed CH 4 flames as
a function of pressure. Blue symbols correspond to the case in which the global strain rate was
calculated using the LDV data.
Niemann et al. [8] performed PIV measurements of the velocity field for the case of cold flow and
reported very small values of 𝛼 and that this affects the determination of 𝐾 , in less than 5%.
However, these measurements were not performed for the case when a flame was present and in which
the effect of thermal expansion generated by the flame modifies the velocity field considerably. The
following example shows that the value of 𝛼 changes considerably when a flame is present. Fig. 4.3
shows the axial velocity profile along with the estimated exit velocity and 𝛼 for cold flow conditions
corresponding to a single premixed flame of C 2H4 at 𝜙 = 0.8 and 4 atm with oxidizer 17% O2 and 87%
N2 close to extinction. It can be seen that the value of 𝛼 is about 10% the value of 𝐾 , . Fig. 4.4
shows the same data but when the flame is present. It is clearly seen that although the value of the
velocity at the exit of the burner, 𝑉 , has not changed significantly, the value of 𝛼 has increased
considerably and now represents about a 30% of the value of 𝐾 , . Therefore, under these
experimental conditions the definition of 𝐾 , is not valid anymore. For these reasons, in this
thesis the reported experimental and numerical values correspond to the local extinction strain rate,
𝐾 , and the values of 𝛼 are always considered in the numerical computations.
68
Figure 4.3. Axial velocity profile and strain rate under cold flow conditions corresponding to a
single premixed flame of C2H4 at 𝝓 = 𝟎 . 𝟖 and 4 atm with oxidizer 17% O2 and 87% N2 close to
extinction.
Figure 4.4. Axial velocity profile and strain rate corresponding to a single premixed flame of
C2H4 at 𝝓 = 𝟎 . 𝟖 and 4 atm with oxidizer 17% O2 and 87% N2 close to extinction.
4.3.2 Importance of extinction strain rate experiments
As it was mentioned in the introduction, the measurement of parameters that are sensitive to the
rates of reactions and diffusion coefficient pairs that make up a kinetic model is a key objective in
combustion research. Laminar flame speeds exhibit in some cases considerable sensitivities to the rates
of some important reactions in combustion, like the main branching reaction H + O 2 → OH + O (R1)
and the main termination reaction H + O2 (+M) → HO2 (+M) (R2). To evaluate the importance of
experiments to measure the local extinction strain rate, the logarithmic sensitivities to the rate constants
of USC Mech II of the laminar flames speed, 𝑆 , and the local strain rate, 𝐾 , of premix and non-
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
10
20
30
40
50
60
70
80
90
X (cm)
U (cm/s)
Poly Fit
Error bars
Data
Uexit
Uexit = 80.1 ± 1.1 cm/s
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
-500
-450
-400
-350
-300
-250
-200
-150
-100
-50
0
X (cm)
K (1/s)
Poly Fit
Error bars
Kexit
α =49.7 ± 2.9 1/s
X (cm) X (cm)
U (cm/s)
K (1/s)
a)
b)
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
35
40
45
50
55
60
65
70
75
80
85
X (cm)
U (cm/s)
Poly Fit
Error bars
Data
Uexit
Uexit = 79.3 ± 2.6 cm/s
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
-400
-350
-300
-250
-200
-150
-100
X (cm)
K (1/s)
Poly Fit
Error bars
Kexit
α = 140 ± 13 1/s
X (cm) X (cm)
U (cm/s)
K (1/s)
a)
b)
69
premixed flames of C2H2 at 1 and 4 atm has been computed. Details of the mixture compositions for
each flame is given in Fig. 4.5. As it can be seen the scale (from -1.0 to 2.0) for the logarithmic
sensitivities was kept constant for the three cases for an adequate comparison. It is evident that the 𝐾
of premixed flames exhibits the highest sensitivity to the rates constants at 1 and 4 atm, and that its
sensitivity is the one that increases the most with pressure. This result suggests that 𝐾 of premixed
flames is a parameter that can provide significant information in the test, optimization and validation
of any kinetic model.
Figure 4.5. Logarithmic sensitivities to kinetics with USC Mech II for C 2H2 flames at 1 and 4 atm
for a) Laminar flame speed with 𝝓 = 𝟏. 𝟑 , b) Extinction strain rate of a non-premixed flame with
Xfuel/XN2=0.08, c) Extinction strain rate of a premixed flame with 𝝓 = 𝟏. 𝟑𝟕 .
For the case of the sensitivity to diffusion coefficient pairs, using USC Mech II, the corresponding
logarithmic sensitivities of the laminar flames speed, 𝑆 , and the local strain rate, 𝐾 , of premix and
non-premixed flames of C2H2 at 1 and 4 atm has been computed. Boundary conditions are identical to
the ones described in Fig. 4.5. Results are shown in Fig 4.6, in which the scale (from -0.6 to 0.8) for
the logarithmic sensitivities was kept constant in all cases for an adequate comparison. The 𝐾 of
non- premixed flames exhibits the highest sensitivity to the diffusion coefficient pairs at 1 and 4 atm.
This result highlights that 𝐾 of non-premixed flames is a parameter that can provide significant
information in the test, optimization and validation of the transport data base of any kinetic model.
70
Figure 4.6. Logarithmic sensitivities to diffusion coefficient pairs with USC Mech II for C 2H2
flames at 1 and 4 atm for a) Laminar flame speed with 𝝓 = 𝟏 . 𝟑 , b) Extinction strain rate of a non-
premixed flame with XFuel/XN2=0.08, c) Extinction strain rate of a premixed flame with 𝝓 = 𝟏 . 𝟑𝟕 .
4.3.3 C2H6 results
Fig. 4.7 shows the 𝐾 measured for premixed C2H6 flames at lean conditions and comparisons
with computations using USC Mech II and FFCM-1. The numerical results with the USC Mech II
model over-predict the data by more than 15% for all cases, but in the case of FFCM-1 model there is
a very good agreement. It is important to take into account how these two mechanisms predict 𝑆 data
for similar compositions for the following analysis. Fig. 4.8 shows the 𝑆 measured by Xiouris [9] for
lean C2H6 flames and comparisons with computations using USC Mech II and FFCM-1. Here it can be
confirmed that USC Mech II is over-predicting the data for all cases, although at a lesser amount
compared to the case of 𝐾 . This can be explained by the fact shown in the previous section, 𝐾 is
a parameter more sensitive to kinetics than 𝑆 , as can be seen in Fig. 4.9. for the case of P = 4atm.
Therefore, if a kinetic model over-predicts 𝑆 data, it is expected to over-predict 𝐾 by a larger
amount, as it is observed in the present case.
-0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80
N2-C2H2
N2-O2
N2-H
N2-H2O
N2-CO
CO-C2H2
O2-CO
N2-CH4
H2O-O2
4 atm
1 atm
-0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80
N2-C2H2
N2-O2
N2-CO
O2-CO2
N2-H
CO2-C2H2
N2-H2O
N2-CO2
H2O-O2
4 atm
1 atm
-0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80
N2-HE
N2-O2
H-HE
O2-HE
N2-H
O2-CO
N2-C2H2
H2O-HE
O2-CO2
4 atm
1 atm
𝐴 𝑆 𝜕𝑆 𝜕𝐴 𝐴 𝐾 𝑒𝑥𝑡 𝜕𝐾 𝑒𝑥𝑡 𝜕𝐴 𝐴 𝐾 𝑒𝑥𝑡 𝜕𝐾 𝑒𝑥𝑡 𝜕𝐴 Logarithmic Sensitivity Logarithmic Sensitivity Logarithmic Sensitivity
Laminar Flame Speed ϕ=1.3
𝑇 = 298 K
𝑇 𝑎𝑑 = 2100 K
Oxidizer
%O
2
=10.8
%N
2
=26.8
%He=62.4
𝑇 = 293 K
𝑇 𝑎𝑑 = 1920 K
Oxidizer
%O
2
=12.5
%N
2
=87.5
Extinction Strain Rate ϕ=1.37 Extinction Strain Rate X
fuel
/X
N2
=0.08
𝑇 = 293 K
Oxidizer
%O
2
=21.0
%N
2
=79.0
a) b) c)
71
Figure 4.7. a) Local extinction strain rate for C2H6 flames with 𝜙 = 0.8 at different pressures.
For P < 2atm oxidizer is 22 %O2 and 78 %N2 (Tad = 2090 K), for P ≥ 2atm oxidizer is 20 %O2 and
80 %N2 (Tad = 1980 K). b) Percentage difference of the kinetic models with respect to the
experimental data.
Figure 4.8. a) Laminar flame speeds for C2H6 flames with 𝜙 = 0.8 at different pressures, oxidizer
is 17.2% O2, 24.8% N2 and 57.9% He (T ad=2100 K), data taken by Xiouris [9]. b) Percentage
difference of the kinetic models with respect to the experimental data.
72
Figure 4.9. Logarithmic sensitivities to kinetics with USC Mech II for C 2H6 flames at 4 atm for a)
Laminar flame speed with 𝝓 = 𝟎 . 𝟖 , b) Extinction strain rate of a premixed flame with 𝝓 = 𝟎 . 𝟖 .
It is also very important to note that the improvements made in FFCM-1 to USC Mech II resulted
in a much better prediction of 𝑆 and 𝐾 data, as it can be seen in Fig. 4.7 and Fig. 4.8. To identify
the most important improvements a sensitivity analysis to kinetics was conducted for 𝐾 of the lean
premixed C2H6 flames at 4 atm using both kinetic models. These results can be seen in Fig. 4.10 along
with the computations of the relative changes of the most important reaction rates of FFCM-1 with
respect to USC Mech II. The rates of the main branching reaction H + O 2 → OH + O can change by
10% in some cases and most importantly the rate of the main CO oxidation reaction, CO + OH → CO2
+ H has decreased by 12%. However, the most relevant case occurs in the rate of the CH 3 recombination
reaction CH3 + H +(M) → CH4 (+M) that has decreased by almost 30% at some conditions. The rates
of the two most important reactions that exhibit a positive sensitivity has decreased, which can explain
the improvement in the FFCM-1 predictions of 𝑆 and 𝐾 . However, it is important to point out that
this significant improvement is the result of a more comprehensive optimization of the rates of USC
Mech II and it was not only focused in the reactions shown by in the sensitivity analysis.
Logarithmic Sensitivity
Laminar Flame Speed ϕ=0.8 Extinction Strain Rate ϕ=0.8
-0.40 -0.20 0.00 0.20 0.40 0.60 0.80
H+O2<=>O+OH
CO+OH<=>CO2+H
C2H4+H(+M)<=>C2H5(+M)
2CH3<=>H+C2H5
CH3+H(+M)<=>CH4(+M)
H+O2(+M)<=>HO2(+M)
CH3+OH<=>CH2*+H2O
H+OH+M<=>H2O+M
HO2+H<=>2OH
HCO+H2O<=>CO+H+H2O
HCO+H<=>CO+H2
4 atm
𝑇 = 298 K
𝑇 𝑎𝑑 = 2100 K
Oxidizer
%O
2
=17.2
%N
2
=24.8
%He=57.9
𝐴 𝑆 𝜕𝑆 𝜕𝐴 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80
H+O2<=>O+OH
CO+OH<=>CO2+H
H+O2(+M)<=>HO2(+M)
C2H4+H(+M)<=>C2H5(+M)
2CH3<=>H+C2H5
CH3+H(+M)<=>CH4(+M)
HO2+H<=>2OH
CH3+OH<=>CH2*+H2O
H+OH+M<=>H2O+M
CH3+HO2<=>CH3O+OH
C2H4+OH<=>C2H3+H2O
4 atm
𝑇 = 293 K
𝑇 𝑎𝑑 = 2090 K
Oxidizer
%O
2
=20
%N
2
=80
𝐴 𝐾 𝑒𝑥𝑡 𝜕𝐾 𝑒𝑥𝑡 𝜕𝐴 Logarithmic Sensitivity
a)
b)
73
Figure 4.10. Logarithmic sensitivities to kinetics with USC Mech II and FFCM-1 of the local
extinction strain rate of C2H6 flames at 4 atm with 𝝓 = 𝟎 . 𝟖 .
To further analyze the improvements made in FFCM-1, a reaction path analysis was conducted at
extinction conditions of the lean premixed C 2H6 flames at 4 atm using both kinetic models. Fig. 4.11
shows the most important pathways for the consumption of C 2H6. The most significant changes can be
observed in the CH2+O2 reactions that now have pathways that go directly to CO and CO2 instead of
going through the HCO pathway. Additionally, the branching ratio of C 2H3 + O2 → HCO +CH2O and
C2H3 + O2 → CH2CHO +O and most of the C2H3 chemistry goes through the HCO pathway. Finally,
the CH3 chemistry now has some pathways that go directly to CO and CH 2O.
-0.40 0.00 0.40 0.80
H+O2<=>O+OH
CO+OH<=>CO2+H
H+O2(+M)<=>HO2(+M)
C2H4+H(+M)<=>C2H5(+M)
2CH3<=>H+C2H5
CH3+H(+M)<=>CH4(+M)
HO2+H<=>2OH
HCO+M<=>H+CO+M
C2H4+OH<=>C2H3+H2O
CH3+HO2<=>OH+CH3O
HO2+H<=>H2+O2
HCO+OH<=>H2O+CO
OH+H2<=>H+H2O
USC mech II
FFCM-1
𝐴 𝐾 𝑒𝑥𝑡 𝜕𝐾 𝑒𝑥𝑡 𝜕𝐴 Logarithmic Sensitivity
𝑇 = 293 K
𝑇 𝑎𝑑 = 2090 K
Oxidizer
%O
2
=20
%N
2
=80
K
FFCM
≈ (0.9-0.98)*K
USCII
K
FFCM
≈ (0.88)*K
USCII
K
FFCM
≈ (0.92-0.96)*K
USCII
K
FFCM
≈ (0.98-1.11)*K
USCII
K
FFCM
≈ (1.53)*K
USCII
K
FFCM
≈ (0.68-0.88)*K
USCII
K
FFCM
≈ (0.43-0.47)*K
USCII
K
FFCM
≈ (0.79)*K
USCII
K
FFCM
≈ (1.0-1.68)*K
USCII
K
FFCM
≈ (0.75-0.98)*K
USCII
K
FFCM
≈ (4)*K
USCII
K
FFCM
≈ (1.3)*K
USCII
K
FFCM
≈ (1.01-1.13)*K
USCII
74
Figure 4.11. Reaction path analysis at extinction conditions of C2H6 flames at 4 atm with 𝝓 =
𝟎 . 𝟖 . Black: USC Mech II, Red: FFCM-1.
Fig. 4.12 shows the 𝐾 measured for premixed C2H6 flames at rich conditions and comparisons
with computations using USC Mech II and FFCM-1. The numerical results with the USC Mech II
model are in good agreement for all cases above 2 atm and around 10% overprediction for lower
pressures. In the case of FFCM-1 model an over-prediction close to 15% is observed for all cases. As
in the case of lean flames, it is important to take into account how these two mechanisms predict 𝑆
data for similar compositions for the following analysis. Fig. 4.13 shows the 𝑆 measured by Xiouris
[9] for rich C2H6 flames and comparisons with computations using USC Mech II and FFCM-1. Here it
can be confirmed that FFCM-1 results are above the ones reported by USC Mech II, which agrees with
the trend observed in Fig. 4.12. This can be explained by the fact shown in the previous section, 𝐾
is a parameter more sensitive to kinetics than 𝑆 , as can be seen in Fig. 4.13. for the case of P = 4atm.
Once again is confirmed that if a kinetic model over-predicts 𝑆 data, it is expected to over-predict
𝐾 by a larger amount.
USCM2
FFCM-1
C
2
H
6
K
ext
ϕ=0.8, 4atm
C
2
H
6
C
2
H
5
+OH (59%-53%)
+H (27%-28%)
+O (14%-16%)
CH
3
+O (37%-22%)
+H (21%-30%)
+H(+M) (60%-60%)
HCO
C
2
H
4
C
2
H
3
+OH (41%-49%)
+O (15%-0%)
+H (0-10%)
+O 2 (16%-38%)
C
2
H
2
(+M) (27%-30%)
CH
2
CHO
+O 2 (31%-18%)
CH
2
CO
HCCO
CO
CH
4
CH
2
*
CH
2
O
CH
2
CH
CO
2
+OH (98%-98%)
+O (74%-71%)
+M (19%-39%)
+O2 (14%-0%)
+OH (20%-18%)
+H (9%-0%)
+H (25%-40%)
+O (20 %-20%)
+O
2
(33%-36%)
+O (30%-24%)
+H(+M) (13%-12%)
+OH (66%-62%)
+H (17%-15%)
+O (17%-23%)
+N 2 (49%-54%)
+H 2 O (16%-12%)
+O 2 (0%- 15%)
+H (11%-20%)
+H 2 O (23%-18%)
+OH (63%-43%)
+H (26%-47%)
+O (10%-9%)
X
X
+O 2 (16%-0%)
X
CH
3
O
+M (97%)
+O (10%)
+O 2 (13%)
+O 2 (13%)
+O 2 (18%)
+M (29%-52%)
+H 2 O (34%-10%)
+O 2 (29%-31%)
+OH (11%)
+O 2 (9%)
75
Figure 4.12. a) Local extinction strain rate for C2H6 flames with 𝜙 = 1.37 at different pressures.
For P < 2atm oxidizer is 22 %O2 and 78 %N2 (Tad = 2110 K), for P ≥ 2atm oxidizer is 20 %O2 and
80 %N2 (Tad = 2000K). b) Percentage difference of the kinetic models with respect to the
experimental data.
Figure 4.13. a) Laminar flame speeds for C2H6 flames with 𝜙 = 1.3 at different pressures,
oxidizer is 16.2% O2, 25.1% N2 and 58.7% He (T ad=2100K), data taken by Xiouris [9]. b)
Percentage difference of the kinetic models with respect to the experimental data.
76
Figure 4.14. Logarithmic sensitivities to kinetics with USC Mech II for C 2H6 flames at 4 atm for
a) Laminar flame speed with 𝝓 = 𝟏 . 𝟑 , b) Extinction strain rate of a premixed flame with 𝝓 = 𝟏 . 𝟑𝟕 .
The modifications made in FFCM-1 to USC Mech II resulted in much higher predicted values for
𝑆 and 𝐾 data, as it can be seen in Fig. 4.12 and Fig. 4.13. To identify the most important
modifications a sensitivity analysis to kinetics was conducted for 𝐾 of the rich premixed C2H6 flames
at 4 atm using both kinetic models. These results can be seen in Fig. 4.15 along with the computations
of the relative changes of the most important reaction rates of FFCM-1 with respect to USC Mech II.
-1.00 -0.50 0.00 0.50 1.00 1.50 2.00 2.50
H+O2<=>O+OH
CH3+H(+M)<=>CH4(+M)
2CH3<=>H+C2H5
C2H4+H(+M)<=>C2H5(+M)
H+OH+M<=>H2O+M
HCO+H<=>CO+H2
C2H3+H<=>C2H2+H2
C2H3(+M)<=>C2H2+H(+M)
CH3+O<=>CH2O+H
HCO+H2O<=>CO+H+H2O
CH2+O2<=>HCO+OH
4 atm
Logarithmic Sensitivity
𝐴 𝑆 𝜕𝑆 𝜕𝐴 𝑇 = 298 K
𝑇 𝑎𝑑 = 2100 K
Oxidizer
%O
2
=16.2
%N
2
=25.1
%He=58.7
Laminar Flame Speed ϕ=1.3
-1.00 -0.50 0.00 0.50 1.00 1.50 2.00 2.50
H+O2<=>O+OH
CH3+H(+M)<=>CH4(+M)
2CH3<=>H+C2H5
C2H4+H(+M)<=>C2H5(+M)
CH3+O<=>CH2O+H
C2H3+H<=>C2H2+H2
CH2+O2<=>HCO+OH
CH3+HO2<=>CH3O+OH
H+OH+M<=>H2O+M
C2H4+OH<=>C2H3+H2O
C2H3+O2<=>CH2CHO+O
4 atm
Extinction Strain Rate ϕ=1.37
𝑇 = 293 K
𝑇 𝑎𝑑 = 2000 K
Oxidizer
%O
2
=20
%N
2
=80
𝐴 𝐾 𝑒𝑥𝑡 𝜕𝐾 𝑒𝑥𝑡 𝜕𝐴 Logarithmic Sensitivity
a)
b)
77
Figure 4.15. Logarithmic sensitivities to kinetics with USC Mech II and FFCM-1 of the local
extinction strain rate of C2H6 flames at 4 atm with 𝝓 = 𝟏 . 𝟑𝟕 .
To further analyze the modifications made in FFCM-1, a reaction path analysis was conducted at
extinction conditions of the rich premixed C 2H6 flames at 4 atm using both kinetic models. Fig. 4.16
shows the most important pathways for the consumption of C 2H6. The most significant changes can be
observed in the CH2+O2 reactions that now have pathways that go directly to CO and CO2 instead of
going through the HCO pathway. Additionally, the branching ratio of C 2H3 + O2 → HCO +CH2O and
C2H3 + O2 → CH2CHO +O and most of the C2H3 chemistry goes through the HCO pathway. Finally,
the CH3 chemistry now has some pathways that go directly to CO and CH 2O.
Logarithmic Sensitivity
-1.50 -0.50 0.50 1.50 2.50
H+O2<=>O+OH
CH3+H(+M)<=>CH4(+M)
2CH3<=>H+C2H5
C2H4+H(+M)<=>C2H5(+M)
CH3+O<=>CH2O+H
C2H3+H<=>C2H2+H2
CH2+O2<=>HCO+OH
HCO+M<=>H+CO+M
CH3+HO2<=>OH+CH3O
CH2OH+H<=>OH+CH3
C2H4+H<=>C2H3+H2
HCO+H<=>H2+CO
C2H3+O2<=>HCO+CH2O
USC mech II
FFCM-1
𝐴 𝐾 𝑒𝑥𝑡 𝜕𝐾 𝑒𝑥𝑡 𝜕𝐴 𝑇 = 293 K
𝑇 𝑎𝑑 = 2000 K
Oxidizer
%O
2
=20
%N
2
=80
K
FFCM
≈ (0.9-0.98)*K
USCII
K
FFCM
≈ (0.68-0.88)*K
USCII
K
FFCM
≈ (1.53)*K
USCII
K
FFCM
≈ (0.98-1.11)*K
USCII
K
FFCM
≈ (0.68)*K
USCII
K
FFCM
≈ (0.013)*K
USCII
K
FFCM
≈ (0.43-0.47)*K
USCII
Different CH
2
+O
2
Chemistry
K
FFCM
≈ (0.75-0.98)*K
USCII
K
FFCM
≈ (7.3-7.9)*K
USCII
K
FFCM
≈ (0.71)*K
USCII
K
FFCM
≈ (2.0-2.4)*K
USCII
K
FFCM
≈ (1.23-2.66)*K
USCII
Logarithmic Sensitivity
78
Figure 4.16. Reaction path analysis at extinction conditions of C2H6 flames at 4 atm with 𝜙 = 1.37.
Black: USC Mech II, Red: FFCM-1.
To complete the analysis on C2H6 flames, Fig 4.17 shows the 𝐾 measured for non-premixed C 2H6
flames and comparisons with computations using USC Mech II, FFCM-1 and HP-Mech. The numerical
results with the USC Mech II model are in very good agreement with the experimental data for most
conditions (10% below). HP-Mech and FFCM-1 have a similar behavior and under predict the data up
to 20%.
USCM2
FFCM-1
C
2
H
6
K
ext
ϕ=1.37, 4atm C
2
H
6
C
2
H
5
+OH (59%-56%)
+H (32%-27%)
+O (8%-9%)
CH
3
+O (21%-12%)
+H (17%-27%)
+H(+M) (72%-67%)
HCO
C
2
H
4
C
2
H
3
+OH (38%-34%)
+H (27%-42%)
+O (9%-2%)
+O 2 (7%-20%)
C
2
H
2
(+M) (52%-56%)
+H (12%-0%)
CH
2
CHO
+O 2 (15%-10%)
CH
2
CO
HCCO
CO
CH
4
CH
2
*
CH
2
O
CH
2
CH
CO
2
+OH (99%-98%)
+O (69%-64%)
+M (26%-49%)
+H (25%-40%)
+O (20 %-20%)
+O 2 (33%-36%)
+O (15%-13%)
+OH (0%-5%)
+H(+M) (36%-31%)
+H (55%-52%)
+OH (37%-37%)
+O (7%-11%)
+N 2 (44%)
+H
2
O (20%)
+H (40%)
+H 2 O (55%)
+H (64%-82%)
+OH (31%-14%)
X
X
+CO 2 (11%)
X
CH
3
O
+M (98%)
+O (5%)
+M (33%-72%)
+H 2 O (48%-2%)
+O 2 (12%-14%)
+O (17%-17%)
X
79
Figure 4.17. a) Local extinction strain rate for C2H6 non-premixed flames at different pressures.
Oxidizer is 21 %O2 and 79 %N2. b) Percentage difference of the kinetic models with respect to the
experimental data.
Figure 4.18. Reaction path analysis at extinction conditions of C2H6 non-premixed flames at 4 atm.
Black: USC Mech II, Red: FFCM-1.
USCM2
FFCM-1
C
2
H
6
K
ext
X
fuel
/X
N2
=0.14, 4atm C
2
H
6
C
2
H
5
+H (61%-61%)
+OH (31%-25%)
+O (6%-6%)
CH
3
+O (30%-16%)
+H (13%-18%)
+H(+M) (79%-80%)
HCO
C
2
H
4
C
2
H
3
+OH (44%-46%)
+H (12%-24%)
+O (11%-2%)
+O 2 (13%-30%)
C
2
H
2
(+M) (37%-44%)
+H (9%-0%)
CH
2
CHO
+O 2 (24%-14%)
CH
2
CO
HCCO
CO
CH
4
CH
2
*
CH
2
O
CH
2
CH
CO
2
+OH (99%-99%)
+O (74%-69%)
+M (27%-46%)
+O 2 (32%-32%)
+O (13 %-12%)
+CH 3 (8%-2%)
+O (22%-18%)
+H(+M) (24%-21%)
+OH (61%-56%)
+H (27%-26%)
+O (12%-17%)
+N 2 (53%-58%)
+H 2 O (20%-11%)
+H (15%-27%)
+H 2 O (38%-32%)
+OH (54%-32%)
+H (38%-65%)
X
X
+CO 2 (10%-7%)
+O (8%)
+M (40%-72%)
+H 2 O (41%-2%)
+O 2 (13%-13%)
+O (18%-18%)
+OH (14%)
+O 2 (11%)
+O 2 (11%)
+O 2 (16%)
+OH (11%)
+O 2 (9%)
+O 2 (10%)
80
4.3.4 C2H2 results
Fig. 4.19 shows the 𝐾 measured for premixed C2H2 flames at rich conditions and comparisons
with computations using USC Mech II and Dames et al. The numerical results with the USC Mech II
model significantly over-predicts the data by more than 100% for cases below 2 atm and more than
200% for cases above this pressure. In the case of Dames et al. over-predictions are still considerable,
50% below 2 atm and 100% above this pressure. These discrepancies can be alarming and could
indicate a potential error in the experimental data, thus it is important to take into account how these
two mechanisms predict 𝑆 data for similar compositions for the following analysis. Fig. 4.20 shows
the 𝑆 measured by Xiouris [9] for rich C2H2 flames and comparisons with computations using USC
Mech II and Dames et al. It can be confirmed that both mechanisms are overpredicting the 𝑆 data as
well. However, these discrepancies are not of the order of the ones for the 𝐾 case. 𝐾 is a parameter
more sensitive to kinetics than 𝑆 , and as can be seen in Fig. 4.21. for the case of P = 4atm this
sensitivity is almost four times higher if the sensitivity of the main branching reaction is considered.
As it was shown in the C2H6 case, if a kinetic model over-predicts 𝑆 data, it is expected to over-predict
𝐾 by a larger amount, and this could be the reasons of such high over-prediciton.
Figure 4.19. a) Local extinction strain rate for C2H2 flames with 𝜙 = 1.37 at different pressures.
For P < 2atm oxidizer is 13.5 %O2 and 86.5 %N2 (Tad = 2021 K), for P ≥ 2atm oxidizer is 12.5 %O 2
and 87.5 %N2 (Tad = 1920 K). b) Percentage difference of the kinetic models with respect to the
experimental data.
81
Figure 4.20. a) Laminar flame speeds for C2H2 flames with 𝜙 = 1.3 at different pressures,
oxidizer is 10.8% O2, 26.8% N2 and 62.4% He (T ad=2100 K), data taken by Xiouris [9]. b)
Percentage difference of the kinetic models with respect to the experimental data.
Figure 4.21. Logarithmic sensitivities to kinetics with USC Mech II for C 2H2 flames at 4 atm for
a) Laminar flame speed with 𝝓 = 𝟏. 𝟑 , b) Extinction strain rate of a premixed flame with 𝝓 = 𝟏. 𝟑𝟕 .
-1.00 -0.50 0.00 0.50 1.00 1.50 2.00
H+O2<=>O+OH
CO+OH<=>CO2+H
HCO+M<=>H+CO+M
CH3+H(+M)<=>CH4(+M)
HCCO+O2<=>OH+2CO
HCCO+H<=>CH2*+CO
HCO+H<=>CO+H2
H+OH+M<=>H2O+M
H+O2(+M)<=>HO2(+M)
C2H3+O2<=>CH2CHO+O
CH2*+O2<=>H+OH+CO
4 atm
1 atm
𝐴 𝑆 𝜕𝑆 𝜕𝐴 -1.00 -0.50 0.00 0.50 1.00 1.50 2.00
H+O2<=>O+OH
CH3+H(+M)<=>CH4(+M)
HCCO+O2<=>OH+2CO
H+O2(+M)<=>HO2(+M)
C2H3+O2<=>CH2CHO+O
HCO+M<=>H+CO+M
HCCO+H<=>CH2*+CO
HCO+H<=>CO+H2
H+OH+M<=>H2O+M
CH3+HO2<=>CH3O+OH
C2H3+H<=>C2H2+H2
4 atm
1 atm
𝐴 𝐾 𝑒𝑥𝑡 𝜕𝐾 𝑒𝑥𝑡 𝜕𝐴 Logarithmic Sensitivity Logarithmic Sensitivity
Laminar Flame Speed ϕ=1.3
𝑇 = 298 K
𝑇 𝑎𝑑 = 2100 K
Oxidizer
%O
2
=10.8
%N
2
=26.8
%He=62.4
𝑇 = 293 K
𝑇 𝑎𝑑 = 1920 K
Oxidizer
%O
2
=12.5
%N
2
=87.5
Extinction Strain Rate ϕ=1.37
a)
b)
82
Xiouris [9] explored the causes of these discrepancies at rich conditions further in two cases. For
the first one, Fig 4.22 shows the 𝑆 measured for rich C2H2 flames at constant ϕ = 1.3 and P = 3 atm
at three different adiabatic flames temperatures. It is clearly seen that the over-prediction of USC Mech
II increases considerably, up to 35%, if the adiabatic temperature is decreased. For the second case,
Fig. 4.23 shows the 𝑆 measured for rich C2H2 flames at constant Tad = 1000 K and P = 3 atm at
different equivalence ratios. The results show that USC Mech II predicts 𝑆 at lean condition but the
discrepancies increase considerably as the experimental conditions move to richer flames; over-
predictions can be up to 50%. If the experimental conditions of the present measurements are recalled,
the adiabatic flame temperature of the mixture is 1920 K, which is considerably lower to the
temperatures reported in Fig. 4.23 and also the equivalence ratio is considerably high. Along with the
sensitivity results shown in Fig 4.21, this confirms that over-predictions of 𝐾 by 100% to 200% can
be expected, and that is very unlikely that an experimental error is the cause of such over-predictions.
Figure 4.22. a) Laminar flame speeds for C2H2 flames with 𝜙 = 1.3 and P = 3 atm at different
temperatures, data taken by Xiouris [9]. b) Percentage difference of USC Mech II computations with
respect to the experimental data.
83
Figure 4.23. a) Laminar flame speeds for C2H2 flames with Tad = 2100 K and P = 3 atm at
different equivalence ratios, data taken by Xiouris [9]. b) Percentage difference of USC Mech II
computations with respect to the experimental data.
To further prove the validity of the present 𝐾 measurements for C2H2 flames at rich conditions,
at the current conditions using the same counterflow setup the laminar flame speed at 1.5 atm was
measured using the computationally assisted non-linear extrapolation methodology described in
section 2.5. Results are shown in Fig. 4.24, comparing with numerical computation using USC Mech
II for 𝑆 , the overprediction is 16%, which exactly matches with the over-predictions of the spherically
expanding flames case reported in Fig. 4.20. For the case of 𝐾 the over-prediction is 125 %. This
result proves that the present experimental methodology is correct and that the cause of the considerable
over-predictions of 𝐾 at rich conditions are problems in the kinetic models.
Before the analysis is continued for C2H2 rich flames, it is worth checking what is happening with
𝐾 measurements at lean conditions. Fig. 4.25 shows the 𝐾 measured for premixed C2H2 flames at
lean conditions and comparisons with computations using USC Mech II and Dames et al. Contrary to
what was observed for the case of rich flames, there is very good agreement with the experimental data
for both mechanisms. An over-prediction around 5% is observed for USC Mech II, while Dames et al.
under-predicts the data around 5%. It is also important to take into account how these two mechanisms
predict 𝑆 data for lean conditions. Fig. 4.26 shows the 𝑆 measured by Xiouris [9] for lean C2H2
flames and similar trends are observed compared to the 𝐾 case. USC Mech II and Dames et al are
in very close agreement with the data.
84
Figure 4.24. Laminar flame speed and local extinction strain rate for a C 2H2 flame with 𝜙 = 1.37
at P = 1.5 atm using the current counterflow setup. Oxidizer: 13.5% O 2 and 86.5% N2 (Tad = 2020
K).
Figure 4.25. a) Local extinction strain rate for C2H2 flames with 𝜙 = 0.8 at different pressures.
For P < 2atm oxidizer is 13.5% O2 and 86.5% N2 (Tad = 1820 K), for P ≥ 2atm oxidizer is 12.5 %O 2
and 87.5 %N2 (Tad = 1730 K). b) Percentage difference of the kinetic models with respect to the
experimental data.
20
25
30
35
40
45
50
55
60
0 500 1000 1500 2000
Su,ref (cm/s)
Kref (1/s)
Experiments
1D-Modeling
Best Fit
Suo Modeling
Suo, exp
Kext, Modeling
Kext, Exp
K
ref
(1/s)
S
u,ref
(cm/s)
𝑆 Modeling
𝑆 Experiment
𝐾 Modeling
𝐾 Experiment
∆𝑆 ∆𝑆 C
2
H
2
Laminar Flame Speed 𝜙 =1.37 P=1.5atm
85
Figure 4.26. a) Laminar flame speeds for C2H2 flames with 𝜙 = 0.8 at different pressures,
oxidizer is 12.9% O2, 26.1% N2 and 61.0% He (T ad=2100 K), data taken by Xiouris [9]. b)
Percentage difference of the kinetic models with respect to the experimental data.
It is also very important to note that the improvements made in Dames et al. to USC Mech II resulted
in a much better prediction of 𝑆 and 𝐾 data, especially at rich conditions, Fig. 4.19 and Fig. 4.20.
Additionally, the surprising different trends found at lean and rich conditions regarding the
predictability of numerical computations needs further analysis. To identify the most important
improvements a sensitivity analysis to kinetics was conducted for 𝐾 of lean and rich premixed C2H2
flames at 4 atm using both kinetic models. These results can be seen in Fig. 4.27 along with the
computations of the relative changes of the most important reaction rates of Dames et al. with respect
to USC Mech II. As it can be seen, very few changes in the rates of the most important reactions were
made, with the exception of the main branching reaction H + O 2 → OH + O can change by 5% in some
cases. The rates of the HCO chemistry decreased for Dames et al., especially HCO + M → CO + H +
M, which is important for lean and rich conditions. However, the biggest difference is observed for the
CH2 + O2 reactions and pathways, which were completely updated by Dames et al. Although the CH 2
+ O2 shows a small sensitivity, it seems that is the main reason for the improvements made in this
model.
86
Figure 4.27. Logarithmic sensitivities to kinetics with USC Mech II and Dame et a1. of the local
extinction strain rate of C2H2 flames at 4 atm with 𝝓 = 𝟎 . 𝟖 and 𝝓 = 𝟏 . 𝟑𝟕 .
To further analyze the improvements made in Dames et al. and the effect of CH 2 + O2 chemistry at
rich conditions a reaction path analysis was conducted at extinction conditions of the rich premixed
C2H2 flames at 4 atm using both kinetic models. Fig. 4.28 shows the most important pathways for the
consumption of C2H2. The most significant changes can be observed in the CH 2+O2 reactions that now
have pathways that go directly to CO and CO2 instead of going through the HCO pathway. Therefore,
the updates in this chemistry seems to be the main reason for the improvements by Dames et al.
To analyze why the CH2 + O2 chemistry is not as important at lean conditions than at rich conditions,
a reaction path analysis was conducted at extinction conditions of the lean premixed C 2H2 flames at 4
atm using both kinetic models. Fig. 4.29 shows the most important pathways for the consumption of
C2H2. It is clearly observed that for lean conditions the direct path of HCCO to CO considerably
enhanced and the CH2 is not as important.
-1.00 -0.50 0.00 0.50 1.00 1.50 2.00
H+O2<=>O+OH
CH3+H(+M)<=>CH4(+M)
H+O2(+M)<=>HO2(+M)
HCO+M<=>CO+H+M
HCCO+O2<=>OH+2CO
HCO+H<=>CO+H2
HCCO+H<=>CH2*+CO
CH3+HO2<=>CH3O+OH
CH2+O2<=>HCO+OH
CH2+O2<=>OH+H+CO
CH2+O2<=>2H+CO2
C2H3+O2<=>CH2CHO+O
H+OH+M<=>H2O+M
HCO+O2<=>CO+HO2
C2H3+H<=>C2H2+H2
USC mech II
Dames et al.
-1.00 -0.50 0.00 0.50 1.00
H+O2<=>O+OH
CO+OH<=>CO2+H
H+O2(+M)<=>HO2(+M)
HO2+H<=>2OH
C2H2+O<=>HCCO+H
CO+OH<=>CO2+H
HCO+M<=>CO+H+M
H+OH+M<=>H2O+M
HCCO+O2<=>OH+2CO
OH+HO2<=>H2O+O2
HCO+O2<=>CO+HO2
HCCO+H<=>CH2*+CO
C2H3(+M)<=>C2H2+H(+M)
C2H3+O2<=>CH2CHO+O
USC mech II
Dames et al.
Logarithmic Sensitivity Logarithmic Sensitivity
Reaction rate of Dames
et al. is between ±5%
of USC Mech II value
Reaction rate of Dames
et al. is 2.2 times slower
than the USC Mech II
value
𝐴 𝐾 𝑒𝑥𝑡 𝜕𝐾 𝑒𝑥𝑡 𝜕𝐴 𝑇 = 293 K
𝑇 𝑎𝑑 = 1920 K
Oxidizer
%O
2
=12.5
%N
2
=87.5
Extinction Strain Rate ϕ=1.37, 4atm
𝐴 𝐾 𝑒𝑥𝑡 𝜕𝐾 𝑒𝑥𝑡 𝜕𝐴 𝑇 = 293 K
𝑇 𝑎𝑑 = 1726 K
Oxidizer
%O
2
=12.5
%N
2
=87.5
Extinction Strain Rate ϕ=0.8, 4atm
Reaction rate of Dames
et al. is 1.2-1.6 times
slower than the USC
Mech II value
Different CH
2
+O
2
chemistry
87
Figure 4.28. Reaction path analysis at extinction conditions of C2H2 flames at 4 atm with 𝜙 = 1.37.
Black: USC Mech II, Red: Dames et al.
Figure 4.29. Reaction path analysis at extinction conditions of C2H2 flames at 4 atm with 𝜙 = 0.8.
Black: USC Mech II, Red: Dames et al.
C
2
H
2
HCCO
CH
2
C
2
H
3
+O (50%-51%)
CH
2
*
+H(+M) (17%-16%)
+O (13%-13%)
+H (53%-46%)
+O 2 (25%-27%)
CH
2
CHO
+O 2 (25%-25%)
HCO
+O 2 (38%-40%)
CH
2
CO
+O 2 (25%-24%)
CH
3
+H (90%-96%)
+H (41%-27%)
+O (22%-22%)
CH
2
O
+H (53%-54%)
+OH (44%-42%)
+O 2 (36%-0%)
CH
+H (38%-41%)
CH
2
O
+O 2 (38%-36%)
+CO2 (11%-12%)
+H 2 O (30%-32%)
+H (53%-54%)
+OH (44%-42%)
CO CO
2
+M (42%-35%)
+O 2 (22%-21%)
+H 2 O (19%-25%)
+H (10%-10%)
+OH (98%-98%)
+O 2 (12%)
+O 2 (7%)
+O 2 (17%)
USCM2
Dames et al.
C
2
H
2
K
ext
ϕ=1.37, 4atm
C
2
H
2
K
ext
ϕ=0.8, 4atm
C
2
H
2
HCCO
CH
2
C
2
H
3
+O (56%-58%)
CH
2
*
+H(+M) (17%-18%)
+O (15%-14%)
+H (25%-23%)
+O 2 (46%-50%)
+O (13%-13%)
CH
2
CHO
+O 2 (33%-34%)
HCO
+O 2 (46%-47%)
CH
2
CO
+O 2 (35%-32%)
CH
3
+H (59%-64%)
+H (38%-32%)
+O (29%-34%)
CH
2
O
+H (20%-21%)
+OH (73%-71%)
+O 2 (63%-0%)
CH
+H (10%-13%)
CH
2
O
+O 2 (76%-76%)
+H 2 O (12%-12%)
CO CO
2
+M (31%-22%)
+O
2
(48%-47%)
+H 2 O (10%-12%)
+H (5%-5%)
+OH (3%- 10%)
+OH (98%-98%)
+O 2 (15%-17%)
+OH (33%-32%)
+H (20%-21%)
+OH (73%-71%)
+O 2 (24%)
+O 2 (13%)
+O
2
(32%)
USCM2
Dames et al.
88
To complete the analysis on C2H2 flames, Fig 4.30 shows the 𝐾 measured for non-premixed C 2H2
flames and comparisons with computations using USC Mech II, Dames et al. and HP-Mech. The
numerical results with USC Mech II and HP-Mech models are in very good agreement with the
experimental data for most conditions (10% below). Dames et al. under-predicts the data up to 30%.
Figure 4.30. a) Local extinction strain rate for C2H6 non-premixed flames at different pressures.
Oxidizer is 21 %O2 and 79 %N2. b) Percentage difference of the kinetic models with respect to the
experimental data.
Figure 4.31. Reaction path analysis at extinction conditions of C2H2 non-premixed flames at 4 atm.
Black: USC Mech II, Red: FFCM-1.
C
2
H
2
K
ext
X
fuel
/X
N2
=0.08, 4atm
USCM2
Dames et al.
C
2
H
2
HCCO
CH
2
C
2
H
3
+O (47%-46%)
CH
2
*
+H(+M) (26%-27%)
+O (12%-12%)
+H (26%-21%)
+O 2 (48%-54%)
+O (7%-8%)
CH
2
CHO
+O 2 (30%-32%)
HCO
+O 2 (43%-46%)
CH
2
CO
+O 2 (21%-20%)
(+M ) (21%-30%)
CH
3
+H (77%-84%)
+H (30%-19%)
+O (17%-20%)
CH
2
O
+H (33%-32%)
+OH (61%-61%)
+O 2 (62%-0%)
CH
+H (9%-10%)
CH
2
O
+O 2 (64%-66%)
+CO 2 (10%-9%)
+H 2 O (20%-18%)
CO CO
2
+M (49%-37%)
+O 2 (26%-29%)
+H 2 O (15%-20%)
+OH (98%-98%)
+O 2 (10%-13%)
+OH (17%-15%)
+H (33%-32%)
+OH (61%-61%)
(30%-25%)
+O 2 (24%)
+O 2 (13%)
+O 2 (32%)
89
4.3.5 C2H4 results
Fig. 4.32 and Fig. 4.33 show the 𝐾 measured for premixed C2H4 flames at lean and rich
conditions, respectively, and comparisons with computations using USC Mech II, Dames et al. and
HP-Mech. Fig. 4.34 and 4.35 shows the 𝑆 measured by Xiouris [9] for lean and rich C2H4 flames and
comparisons with computations using USC Mech II and Dames et al.
Figure 4.32. a) Local extinction strain rate for C2H4 flames with 𝜙 = 0.8 at different pressures.
For P < 2atm oxidizer is 18% O2 and 82% N2 (Tad = 1975 K), for P ≥ 2atm oxidizer is 17% O2 and
83% N2 (Tad = 1905 K). b) Percentage difference of the kinetic models with respect to the
experimental data.
Figure 4.33. a) Local extinction strain rate for C2H4 flames with 𝜙 = 1.4 at different pressures.
For P < 2atm oxidizer is 18% O2 and 82% N2 (Tad = 2055 K), for P ≥ 2atm oxidizer is 17% O2 and
83% N2 (Tad = 1985 K). b) Percentage difference of the kinetic models with respect to the
experimental data.
90
Figure 4.34. a) Laminar flame speeds for C2H2 flames with 𝜙 = 0.8 at different pressures, oxidizer is
15.4% O2, 25.4% N2 and 59.3% He (T ad=2100 K), data taken by Xiouris [9]. b) Percentage
difference of the kinetic models with respect to the experimental data.
Figure 4.35. a) Laminar flame speeds for C2H2 flames with 𝜙 = 1.3 at different pressures, oxidizer is
13.8% O2, 25.9% N2 and 60.4% He (T ad=2100 K), data taken by Xiouris [9]. b) Percentage
difference of the kinetic models with respect to the experimental data.
Regarding the non-premixed C2H4 results are more detailed analysis is required, so the following
section will discuss these results.
91
4.3.6 C2H4 non-premixed flames results
To complete the analysis on C2H4 flames, Fig 4.36 shows the 𝐾 measured for non-premixed C 2H4
flames and comparisons with computations using San Diego mech and HP-Mech.
Figure 4.36. a) Local extinction strain rate for C2H4 non-premixed flames at different pressures.
Oxidizer is 21 %O2 and 79 %N2. b) Percentage difference of the kinetic models with respect to the
experimental data.
As it has been reported in previous studies [10, 11] the sensitivity of 𝐾 to binary diffusion
coefficients, BDC’s, has to be considered also during the validation of kinetic models. Fig. 4.37 depicts
the sensitivity results of 𝐾 to BDC’s for C2H4 flames at four different pressures. The highest
sensitivity is observed for the C2H4-N2 BDC with a value that is of the same order as the sensitivity on
the main branching reaction for all pressures. Similar results were observed for all fuels studied,
emphasizing thus the importance of estimating accurately the fuel-N 2 BDC’s in non-premixed flames.
92
Figure 4.37. Logarithmic sensitivity coefficients of extinction strain rates to binary diffusion
coefficients for a C2H4 flame with XC
2
H
4
/XN
2
= 0.11 at various pressures.
The Lennard-Jones parameters for C1-C2 fuels used in the USC Mech II, FFCM-1 and Dames et al.
models are the same, but in the case of San Diego Mech and HP-Mech use different parameters for C 2
fuels. Table 4.3 lists the Lennard-Jones parameters used for all kinetic models. Some significant
differences can be observed in these parameters.
Kinetic Model Fuel Potential Well Depth
𝜖 /𝐾 (K)
Collision Diameter
σ (Å)
USC Mech II
FFCM
Dames et al.
CH 4 141.4 3.746
C 2H 6 252.3 4.302
C 2H 4 280.8 3.971
C 2H 2 209.0 4.100
HP-Mech
San Diego Mech
CH 4 141.4 3.746
C 2H 6 247.5 4.350
C 2H 4 238.4 3.496
C 2H 2 265.3 3.721
Table 4.3. Lennard-Jones parameters for the C1-C2 fuels used in all kinetic models.
93
The computed fuel-N2 BDC’s for all C2 fuels using the USC Mech II and then San Diego Mech are
shown in Fig. 4.38 as a function of temperature at 6 atm. Considerable differences are observed for
the case of the C2H4-N2 BDC, with values of the USC Mech II being lower by 14%.
Figure 4.38. Binary diffusion coefficients of C 2-fuels to N2 as function of temperatures computed at a
p = 6 atm.
Figure 4.39. a) Local extinction strain rate for C 2H4 non-premixed flames at different pressures.
Oxidizer is 21 %O2 and 79 %N2. b) Percentage difference of the kinetic models with respect to the
experimental data.
94
Since 𝐾 sensitivity to the C2H4-N2 BDC is positive and, as shown in Fig. 4.36, San Diego Mech
considerably over-predicts the 𝐾 data of C2H4 flames, the C2H4 Lennard-Jones parameters of San
Diego Mech and HP-Mech were replaced by those of USC Mech II and the 𝐾 were computed with
these modifications. Fig. 4.39 depicts the computed 𝐾 ′𝑠 of C2H4 flames using the modified models
along with the data and the agreements are notably closer for the case of San Diego Mech.
Finally , Fig 4.40 shows the 𝐾 measured for non-premixed C2H4 flames and comparisons with
computations using USC Mech II, Dames et al. and HP-Mech.
Figure 4.40. a) Local extinction strain rate for CH4 non-premixed flames at different pressures.
Oxidizer is 21 %O2 and 79 %N2. b) Percentage difference of the kinetic models with respect to the
experimental data.
4.3.7 CH4 results
Fig. 4.41 and Fig. 4.42 show the 𝐾 measured for premixed CH4 flames at lean and rich conditions,
respectively, and comparisons with computations using USC Mech II, FFCM-1 and HP-Mech. Fig.
4.43 and 4.44 shows the 𝑆 measured by Xiouris [9] for lean and rich C 2H4 flames and comparisons
with computations using USC Mech II, FFCM-1 and HP-Mech.
95
Figure 4.41. a) Local extinction strain rate for CH4 flames with 𝜙 = 0.85 at different pressures.
For P < 2atm oxidizer is 23% O2 and 77% N2 (Tad = 2170 K), for P ≥ 2atm oxidizer is 21% O2 and
79% N2 (Tad = 2070 K). b) Percentage difference of the kinetic models with respect to the
experimental data.
Figure 4.42. a) Local extinction strain rate for CH4 flames with 𝜙 = 1.18 at different pressures.
For P < 2atm oxidizer is 23% O2 and 77% N2 (Tad = 2260 K), for P ≥ 2atm oxidizer is 21% O2 and
79% N2 (Tad = 2150 K). b) Percentage difference of the kinetic models with respect to the
experimental data.
96
Figure 4.43. a) Laminar flame speeds for CH4 flames with 𝜙 = 0.8 at different pressures, oxidizer is
19.5% O2, 24.2% N2 and 56.4% He (T ad=2200 K), data taken by Xiouris [9]. b) Percentage
difference of the kinetic models with respect to the experimental data.
Figure 4.44. a) Laminar flame speeds for CH4 flames with 𝜙 = 1.3 at different pressures, oxidizer
is 18.7% O2, 24.4% N2 and 56.9% He (T ad=2100 K), data taken by Xiouris [9]. b) Percentage
difference of the kinetic models with respect to the experimental data.
To complete the analysis on CH4 flames, Fig 4.45 shows the 𝐾 measured for non-premixed CH4
flames and comparisons with computations using USC Mech II, FFCM-1 and HP-Mech.
97
Figure 4.45. a) Local extinction strain rate for CH4 non-premixed flames at different pressures.
Oxidizer is 21 %O2 and 79 %N2. b) Percentage difference of the kinetic models with respect to the
experimental data.
4.5 References
[1] H. Wang, X. You, A.V. Joshi, S.G. Davis, A. Laskin, F.N. Egolfopoulos, C.K. Law, (2007)USC
Mech Version II. High-Temperature Combustion Reaction Model of H2/CO/C1-C4 Compounds.
http://ignis.usc.edu/USC_Mech_II.htm.
[2] E.E. Dames, K. Lam, D.F. Davidson, R.K. Hanson, Combust. Flame. 161 (2014) 1135-1145.
[3] G.P. Smith, Y. Tao, H. Wang, (2016)Foundational Fuel Chemistry Model Version 1.0 (FFCM-
1). http://nanoenergy.stanford.edu/ffcm1.
[4] D.A. Sheen, X. You, H. Wang, T. Løvås, Proceedings of the Combustion Institute. 32 (2009) 535-
542.
[5] "Chemical-Kinetic Mechanisms for Combustion Applications", San Diego Mechanism web page,
Mechanical and Aerospace Engineering (Combustion Research), University of California at San Diego
(http://combustion.ucsd.edu). (2016).
98
[6] X. Shen, X. Yang, J. Santner, J. Sun, Y. Ju, Proceedings of the Combustion Institute. 35 (2015)
721-728.
[7] K. Seshadri, F.A. Williams, Int. J. Heat Mass Transfer. 21 (1978) 251-253.
[8] U. Niemann, K. Seshadri, F.A. Williams, Combust. Flame. 162 (2015) 1540-1549.
[9] C. Xiouris, (2017)Thesis: Studies of High-Pressure Flame Phenomena Using Spherically
Expanding Flames.
[10] Y. Dong, A.T. Holley, M.G. Andac, F.N. Egolfopoulos, S.G. Davis, P. Middha, H. Wang,
Combust. Flame. 142 (2005) 374-387.
[11] A. Holley, Y. Dong, M. Andac, F. Egolfopoulos, Combust. Flame. 144 (2006) 448-460.
99
Future Work Recommendations
In the present thesis the importance of extinction strain rate measurements of premixed and non-
premixed flames to test, optimize and validate kinetic models of any fuel of interest was proven, given
the high sensitivity of this parameter to kinetic rates and binary diffusion coefficients. Archival data
was provided for the case of C1-C2 hydrocarbons that helped identify reactions and pathways that need
revision. As it was discussed in the introduction section, the importance of having H 2/CO/C1–C4 kinetic
models with high predicting capabilities is crucial for the subsequent development of high temperature
kinetic models of heavier hydrocarbons and the accurate prediction of soot formation. Therefore, it is
recommended to implement the experimental methodology described in this thesis for the case of
H2/CO mixtures and C3–C4 hydrocarbons. These set of data should be complemented with laminar
flame speed measurements at high pressure conditions using the spherically expanding flame
technique, since it was proven to be critical in the interpretation of the extinction strain rate results.
Due to the current state of the art developments in the spherically expanding flame technique at constant
volume, laminar flame speed measurements of H 2/CO and C1–C4 hydrocarbon flames at engine
relevant conditions are of great relevance. These data will provide strong constrains for the
development of kinetic models at such conditions.
From the assessment of the current kinetic models provided in this thesis, it was shown the
importance of the formyl radical (HCO) pathway in the final oxidation steps of C 1–C2 hydrocarbons
and the discrepancies among kinetic models in the reactions describing it. Therefore, measurement of
the laminar flame speed of formaldehyde (CH2O) flames at a wide range of pressures will be of great
value. Additionally, the set of CH2+O2 reactions was shown to be critical in the case of C 2 hydrocarbon
chemistry and uncertainties in their rates to be one of the main sources of error in the prediction of the
experimental data provided. Finding experimental conditions that are highly sensitive to these set of
reactions will be key to make a considerable improvement in H 2/CO/C1–C4 kinetic models. Finally,
given the high uncertainty in the collision efficiency of water in third body reactions, water addition
effects in the extinction strain rate and laminar flames speed of H2/CO and C1–C4 hydrocarbons flames
at high pressures should be evaluated.
Abstract (if available)
Abstract
Due to the hierarchical nature of hydrocarbon combustion kinetics and the fast decomposition rates of large molecular weight fuels, it has been established that H₂/CO/C₁–C₄ kinetics are controlling to a large extent various flame phenomena including propagation and extinction. For practical reasons, the reduction of a kinetic model size can be made more efficiently by reducing the heavy fuels cracking into few reaction steps and coupling it with a detailed model of H₂/CO/C₁–C₄ kinetics. C₂ chemistry also plays an important role in the formation of polycyclic aromatic hydrocarbons formation, which is the bottleneck for soot formation. Additionally, despite the evident importance of flame experiments at high pressures, due to its complex non-linear effect on flame phenomena, very few studies have been reported for C₂ flames under these conditions, especially for extinction of premixed and non-premixed flames. The main objective of this thesis is to provide archival data at high pressures for the test, development and optimization of the C₁-C₂ chemistry of kinetic models. ❧ An experimental methodology to conduct high pressure counterflow flame experiments was developed. A new burner design for accurate measurement of extinction conditions was developed, as well as a new seeding system for Laser Doppler Velocimetry measurements of the velocity field of premixed flames at pressures above 1 atm. For the first time, a detailed uncertainty quantification methodology was implemented for local extinction strain rate measurements. This methodology considers the error propagation from velocity field data postprocessing, fuel and oxidizer mixture preparation, and boundary conditions. ❧ Measurements of local extinction strain rates of C₁-C₂ hydrocarbon non-premixed flames were conducted from 0.6 to 7 atm. These data are reported for the first time for C₂H₂ non-premixed flames. Additionally, measurements of the local strain rate of C₁-C₂ hydrocarbon premixed flames at lean and rich conditions were conducted from 1 to 4 atm for the first time. These data were compared with numerical results that used state of the art kinetic models, and reactions or reaction pathways that need revision were identified. It is worth mentioning, that considerable discrepancies were found for the C₂H₂ rich flames
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Asset Metadata
Creator
Burbano, Hugo Javier
(author)
Core Title
Pressure effects on C₁-C₂ hydrocarbon laminar flames
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Mechanical Engineering
Publication Date
12/11/2018
Defense Date
10/20/2017
Publisher
University of Southern California
(original),
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Tag
acetylene,counterflow flame,ethane,ethylene,extinction,laminar flame,laminar flame speed,methane,OAI-PMH Harvest,pressure,strain rate
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Egolfopoulos, Fokion (
committee chair
), Jessen, Kristian (
committee member
), Ronney, Paul (
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Tags
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