Close
About
FAQ
Home
Collections
Login
USC Login
Register
0
Selected
Invert selection
Deselect all
Deselect all
Click here to refresh results
Click here to refresh results
USC
/
Digital Library
/
University of Southern California Dissertations and Theses
/
Modeling investigations of fundamental combustion phenomena in low-dimensional configurations
(USC Thesis Other)
Modeling investigations of fundamental combustion phenomena in low-dimensional configurations
PDF
Download
Share
Open document
Flip pages
Contact Us
Contact Us
Copy asset link
Request this asset
Transcript (if available)
Content
1
Modeling Investigations of Fundamental Combustion
Phenomena in Low-Dimensional Configurations
by
Jagannath Jayachandran
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTERHN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(MECHANICAL ENGINEERING)
May 2016
2
Table of Contents
Abstract ......................................................................................................................................................... 4
Acknowledgement ........................................................................................................................................ 6
Chapter 1 – Introduction and Literature Review .......................................................................................... 8
1.1 Introduction ....................................................................................................................................... 8
1.2 Objectives ......................................................................................................................................... 24
1.3 Relevant publications ....................................................................................................................... 25
Chapter 2 – Methodology: Detailed numerical simulations ....................................................................... 26
2.1 Freely propagating and counterflow flames .................................................................................... 26
2.2 Spherically expanding flames ........................................................................................................... 26
2.2.1 Validation of TORC .................................................................................................................... 29
Chapter 3 – Molecular transport and radiation effects in spherically expanding flames under constant
pressure conditions ..................................................................................................................................... 33
3.1 Numerical Approach ........................................................................................................................ 33
3.2 Results and discussion...................................................................................................................... 35
3.2.1 Differential diffusion effects and extrapolation uncertainties ................................................. 35
3.2.2 Radiation effects for SEF’s ......................................................................................................... 44
3.3 Concluding remarks ......................................................................................................................... 51
Chapter 4 – A Study of Propagation of Spherically Expanding and Counterflow Laminar Flames Using
Direct Measurements and Numerical Simulations ..................................................................................... 52
4.1 Experimental Approach ................................................................................................................... 52
4.1.1 Spherically expanding flames .................................................................................................... 52
4.1.2 Counterflow flames ................................................................................................................... 53
4.2 Numerical Approach ........................................................................................................................ 53
4.3 Results and discussion...................................................................................................................... 54
4.3.1 Direct measurements and simulations ..................................................................................... 54
4.3.2 Extrapolation uncertainties ....................................................................................................... 59
4.4 Concluding remarks ......................................................................................................................... 63
Chapter 5 – Determination of laminar flame speeds during the compression stage of constant volume
spherically expanding flame propagation ................................................................................................... 65
5.1 Modeling approach .......................................................................................................................... 66
5.2 Results and discussion...................................................................................................................... 67
3
5.3 Concluding remarks ......................................................................................................................... 73
Chapter 6 – Thermal and Ludwig-Soret diffusion effects on near-boundary ignition behavior of reacting
mixtures ...................................................................................................................................................... 74
6.1 Modeling approach .......................................................................................................................... 74
6.2 Parameter space .............................................................................................................................. 75
6.3 Results and discussion...................................................................................................................... 76
6.4 Concluding remarks ......................................................................................................................... 85
Chapter 7 – Summary and future directions of research ........................................................................... 87
Appendix: One dimensional conservation equations in spherical coordinates ......................................... 90
References .................................................................................................................................................. 92
4
Abstract
Numerical simulations were utilized to investigate phenomena in legacy flame propagation
and ignition experiments that could result in non-ideal effects and thus incorrect interpretation of
experimental measurements. Specifically, spherically expanding flames were studied in the
context of heat loss and molecular transport effects. Ignition adjacent to a cold wall was also
examined for mixtures that exhibited the negative temperature coefficient behavior, and species
stratification due to Ludwig-Soret diffusion. For this purpose, a transient one-dimensional
reacting flow code was developed to accurately simulate flame propagation and ignition in the
low Mach number regime.
Computations of flames of heavy molecular weight fuel/air mixtures revealed that the
response of such flames to stretch is governed by different mechanisms for fuel-lean and fuel-
rich mixtures. The dynamics of lean mixtures are controlled by the Lewis number which
quantifies the non-equidiffusion of heat from and chemical energy into the flame, while for rich
mixtures, the response to stretch is governed by the difference in diffusivities between the fuel
and oxidizer. It was further demonstrated that, extrapolation equations derived based on
numerous simplifying assumptions, when utilized to derive laminar flame speeds from constant
pressure spherically expanding flame experimental data, result in substantial uncertainties in the
stretch-corrected values. Simulation results also showed that the radiation heat loss from the
burned gas ball can lead to non-ideal fluid dynamic effects that imparts uncertainties in the flame
speeds derived using flame expansion rate measurements and that additional measurement of the
unburned gas velocity is required to circumvent the flow induced uncertainty.
Consistency between data obtained from counterflow and spherically expanding flame
configurations was established by comparing the difference between direct measurements and
detailed simulation results for each configuration. The consistency obtained when avoiding the
erroneous extrapolation procedure transformed into discrepancy when results post-extrapolation
are compared.
Measurements made during the compression stage of spherically expanding flame
propagation in a constant volume vessel is identified as the ideal method to probe flame
propagation at conditions of high pressure and temperature. Computations revealed that the
5
flame speeds derived from pressure measurements are highly sensitive to the accuracy of burned
gas mass fraction as a function of pressure, which is traditionally determined using
thermodynamics-based models. Thus, neglecting radiation energy loss from the burned gas can
result in errors in flame speed as large as 15%. Besides, simulation results illustrated that
measurements made during the compression stage do not require stretch correction as the
compression induced fluid flow results in near stretch-free flames.
Simulations performed to study the influence of the thermal boundary layer adjacent to a cold
wall on the ignition behavior of a combustible gas revealed that exothermic centers could
preferentially develop locally in the boundary layer for mixtures that exhibit the negative
temperature coefficient behavior and also for mixtures that can stratify as a result of Ludwig-
Soret diffusion. This inhomogeneous ignition could result in incorrect interpretation of
experimental data from legacy kinetic experiments and could play a role central to the initiation
of knock in engines.
.
6
Acknowledgement
The past six years have been an incredible journey of scientific learning and adventure. For
this I am forever indebted to my advisor, Prof. Egolfopoulos, for giving me this opportunity, and
for patiently training me in the ways of scientific enquiry, as well as teaching me how to
communicate the same to others. His ways of breaking down complicated problems and coming
up with simple solutions, and creative ways to turn one knob at a time have become central to
my thought process. Last but not least, the infectious nature of his never-ending optimism and
enthusiasm got me through tough times.
I would also like to thank Prof. Hai Wang and my advisor for the way they taught the
introductory combustion courses, which formed the main motivation for me to probe deeper and
pursue a PhD.
I would like to thank the following people for the great collaborative work: Runhua -
differential diffusion and errors introduced due to extrapolation practices; Chris and Tailai -
physics of spherically expanding flames; and A. Lefebvre, F. Halter, E. Varea and B. Renou for
the study that demonstrated that extrapolation procedures are erroneous and that the data
obtained from spherically expanding and counter-flow flame experiments are consistent.
Long and occasionally heated discussions with lab as well as department colleagues,
especially Vyaas and Prabu, have helped significantly improve and polish my understanding of
concepts and ideas, and also served as a window to new techniques, both experimental and
numerical. Equally important were the happy hour philosophical discourses which included also
Stelios, Giacomo and others - these formed, in a way, the force that kept the train on the tracks.
I would also like to thank Archna for helping me find a balance between ideal and practical,
and thus stay sane. Also, all my friends out here and back in India who have supported and been
part of my life and this journey.
I am grateful to my parents and brother for their unconditional love and support, and also for
standing by the decisions I made.
7
Dedicated to Madhu and Molly, for their love and sacrifices.
8
Chapter 1 – Introduction and Literature Review
1.1 Introduction
Energy is essential to the sustenance of human life and, the progress of civilization and
quality of life. Purifying water, cooking food, and space heating to achieve endurable
temperatures form the most vital needs. Figure 1 depicts the world energy consumption by fuel
type during the past 45 years [1]. It is evident that more than 80% of the energy consumed was
generated from fossil combustion in the year 2014, and future projections [2] do not indicate any
major changes in this trend. Figure 2 illustrates that the energy consumption per capita varies
drastically, sometimes by more than a factor of 5, between the developed and developing
countries. Thus, a forecast based solely on improved quality of life in developing countries,
points to substantially increased total energy consumption. Depleting fossil fuel resources, ever-
growing evidence pointing to global warming due to combustion-generated greenhouse gases,
and the deteriorating quality of the air we breathe as a result of pollutants formed during
combustion, motivates research to explore efficient and environment-friendly combustion
strategies and suitable alternatives to fossil fuels.
Figure 1. World energy consumption in Terawatt-hours by fuel type, 1965 –2014 [1].
9
Figure 2. Energy consumption per capita in Tonne oil equivalent during the year 2014 [1].
Combustion is a multi-scale and multi-physics discipline with length and time scales
extending from very small scales, as in the case of atomic level interactions governed by
quantum mechanics, to large scale turbulent flames found in engines. One way of interpreting
combustion research would be to compare it to a chain made of multiple links. Each link forms
an indispensable part of the chain and in this case represents investigation carried out in a limited
span of length and time scales. Figure 3 delineates the scales involved and the corresponding
areas of study. Low-dimensional reacting systems which include shock tubes, flow reactors,
laminar flames, etc., form one these many links and constitutes the connection between the
chemical model development and turbulent flames.
10
Figure 3. Illustration of multi-physics and multi-scale nature of combustion [Courtesy: Prof.
C.K. Law].
Turbulent flames account for majority of heat release in practical combustion devices.
Designing efficient combustors, which follow prescribed emission regulations and burn
conventional and alternate fuels, require numerical simulations. Performing such computations
accurately requires sufficiently resolving all time and length scales of transport (molecular and
turbulent convective) and chemistry in the presence of radiative heat transfer. The chemical
model, which is a compilation of the rate parameters of elementary reactions, and the transport
and thermodynamic properties of species’, is an input to the turbulent flame simulation. The
accurate determination of rate parameters continues to be an experimental and theoretical
challenge, and often extrapolation is required to obtain values at thermodynamic conditions
11
encountered in practical systems [3]. Thus, the chemical models need to be validated against
experimental data obtained over a wide range of conditions/phenomena to constrain the attendant
uncertainty. Ideally this should be performed in homogeneous reactors where the effects of
transport are negligible. However, since all possible thermodynamic conditions are not
achievable in such systems (e.g., shock tubes, perfectly stirred reactors, and flow reactors), and
the fact that these chemical models will eventually have to describe flame phenomena accurately,
structure and properties of laminar flames in well-controlled environments are used as validation
targets. In flames, the presence of heat and mass transport results in a wide range of
species/temperature conditions which in turn would sensitize reaction pathways that could
otherwise be suppressed in homogeneous experimental conditions. Additionally, laminar flames
in canonical configurations can be utilized to understand the coupling between fluid mechanics,
mass diffusion, and chemistry, which becomes increasingly difficult to do in turbulent
combustion regimes.
Flames fall into two categories based on the burning rate controlling physics: non-premixed
flames that are diffusion/mixing controlled and, premixed flames that are limited by flame
propagation and hence to a certain extent by chemical kinetics. In a non-premixed flame, the
reactants which are initially not mixed diffuse towards the reaction layer where combustion
occurs at stoichiometric proportions resulting in high temperatures. This reactant stratified and
high temperature environment is conducive to pollutant formation, and cannot be manipulated
easily to result in faster and cleaner burning [4][5]. On the other hand, burning rates and
pollutant formation in premixed flames can be easily controlled by varying the equivalence ratio,
pressure, and temperature of the unburned mixture. However, most practical combustors like
coal burners, Diesel engines, jet and rocket engines, etc burn fuel in non-premixed flames. Spark
ignition (SI) engines are the only major premixed flame combustors and their efficiency is
primarily governed by the maximum achievable compression ratio [6]. Premature ignition of the
unburned gas or knocking combustion, limits the compression ratio and hence the efficiency of
SI engines [6]. The aforementioned factors have led to significant efforts in the recent past to
develop new technologies that are reactivity controlled as opposed to diffusion/mixing controlled
so as to have better control over the combustion process: this direction of change was urged by
Weinberg [4]. Newly developed engine technologies like the Homogenous Charge Compression
Ignition (HCCI) and Reactivity Controlled Compression Ignition (RCCI) burn premixed charge
12
and operates at low equivalence ratio and high pressure conditions relative to SI engines, to
simultaneously reduce pollutants and improve efficiency.
Hydrocarbon oxidation is of hierarchical nature. In the High Temperature Chemistry (HTC)
regime [5], large hydrocarbon molecules undergo breakdown reactions to form C
1
-C
3
fragments,
which is then converted to H
2
and CO before being completely oxidized to H
2
O and CO
2
[5][7][8]. For this regime, the rate of oxidation is most sensitive to H
2
and C
1
-C
3
oxidation
chemistry [7][8]. However, this is not the case for the Low Temperature Chemistry (LTC)
regime which is characterized by the formation of significant amounts of alkylperoxy radicals.
LTC oxidation is strongly sensitive to the initial steps which involve large alkylperoxy radicals
and ketohydroperoxides [7][9]. Since oxidation in the LTC regime is relatively slow compared
to the HTC regime, these pathways become important only at high pressures in practical
combustors when the time scales of these reactions are comparable to the time scales of the
combustor. The same reason also motivates experimental measurements at high pressure, as
long duration combustion experiments can lead to significantly increased uncertainties stemming
from heat loss, etc. Also, it has been shown through various studies that LTC does play an
important role in the auto-ignition of the unburned gas that results in knock in SI engines [9][10].
As efforts are made to improve engine efficiency by increasing the compression ratio and
consequently burn at higher pressures and temperatures, super-critical thermodynamic conditions
can be encountered. This regime in which the fluid behavior departs from that of an ideal gas
appears to be least understood and explored. Experimental investigation of fundamental physics
at these conditions could lead to discoveries that might subsequently lead to disruptive changes
in engine technology.
From the above discussion, it can be concluded that there is need for accurate experimental
data at thermodynamic conditions of high pressure and temperature to understand combustion
physics and consequently develop and validate kinetic models. This thesis primarily deals with
identifying and subsequently minimizing uncertainties that could be introduced in experimentally
derived flame data. An independent investigation is also performed to investigate the
modification in ignition behavior of mixture due a cold thermal boundary layer; the development
of local exothermic centers in an otherwise homogeneous reacting mixture. This could
potentially have implications on results obtained from “homogeneous” kinetic reactors like
shock tubes and Rapid Compression Machines (RCM) and could also be an important
13
mechanism in the initiation of knock. The remainder of this chapter presents an overview of
previous studies and analyses that would motivate the specific problems investigated in this
thesis.
Figure 4 summarizes the configurations and measurements that are appropriate for
deriving fundamental flame data that can be used to develop/validate kinetic models at various
pressures. Speciation study of burner stabilized flames are possible only at pressures, p < 1 atm
so that flames are thick enough to ensure sufficient spatial resolution. For 0.2 < p < 10 atm,
laminar flame speeds,
o
S
u
, and ignition and extinction limits of stagnation diffusion and premixed
flames can be measured. For p > 10 atm,
o
S
u
is the fundamental flame property that has been
measured with confidence [11].
Figure 4. Experimental approaches and measurements applicable for laminar flame studies at
various pressures in bar [11].
14
The laminar flame speed,
o
S
u
, defined as the propagation speed of a steady, laminar, one-
dimensional, planar, adiabatic flame, is a fundamental property of any combustible mixture and
is a measure of the mixture’s reactivity, diffusivity, and exothermicity [5]. The accurate
knowledge of
o
S
u
is essential towards validating kinetic models (e.g. [12]) and constraining
uncertainties of rate constants [13]. Furthermore,
o
S
u
along with the Markstein length, L, which
characterizes the response of laminar flame propagation to stretch, are inputs in turbulent flame
models under conditions that the flamelet concept is applicable [14][15][16].
First reported measurements of
o
S
u
was in 1867 by Bunsen [17] who varied the exit velocity
of a laminar combustible mixture jet emanating from a tube, until flashback occurred. Since then,
a large number of data have been reported in the literature derived from Bunsen flames
(e.g.,[18][19][20]), Spherically Expanding Flames (SEF) under constant pressure (e.g.,[21]-[25])
and volume (e.g.,[26]-[32]) conditions, Counter-Flow Flames (CFF) (e.g.,[8][33][34]), and
recently the heat flux method (e.g.,[35][36][37]). The significant progress made in the
experimental and numerical fronts can be found in the following review articles [11][38]-[44].
Notable scatter, by as much as 25 cm/s (70%), was persistent in published
o
S
u
’s of
stoichiometric methane/air flames [11] until the 1980’s when the effect of flame stretch [45] on
flame propagation was accounted for and subtracted from the measurements reducing thus the
experimental uncertainty notably [33][46][47][48]. Despite this progress, due to the relatively
low sensitivity of
o
S
u
to chemical kinetics [49], there is need for experimental data with even
lower uncertainty compared to what is reported currently so that they can be used for validating
as well as constraining the uncertainty of kinetic models [13].
Among the various methods for measuring
o
S
u
, the CFF and the SEF configurations are well
established and widely used, as they are considered to result in reliable data. Despite the fact
that considerable effort has been devoted to understanding the intricacies and physics behind
each approach, significant discrepancies persist in reported data, even when using the same
method. Figure 5 depicts the relative deviation of experimental
o
S
u
with a normalized
equivalence ratio ϕ/(1+ϕ) [50], where ϕ is the equivalence ratio, of n-heptane/air mixtures
reported in different studies from the data of Ji et al. [8] that are used as the reference value.
15
Figure 5. Deviation of experimental
o
S
u
’s of n-heptane/air mixtures at p = 1 atm from that of Ji
et al. [8] (T
u
= 353 K) represented by the solid line. Data represented by symbols include: ( ●)
Kelley et al. [51] (T
u
= 353 K), ( ♦ ) Smallbone et al. [52] (T
u
= 350 K) and (x) Kumar et al.
[53] (T
u
= 360 K).
One can observe the increasing discrepancy between data obtained using the SEF [51] and
CFF [8][52][53] configurations for off-stoichiometric ϕ > 1 mixtures; corrections of the data
reported in Refs. 15 and 16 to account for the different unburned mixture temperatures, T
u
, were
made using the recommendation of Wu et al. [54]. It is evident that the disparity between the
o
S
u
data sets increases with ϕ and this trend persists for flames of several high molecular weight,
MW, fuels [8]. For ϕ > 1 hydrocarbon/air mixtures, air is abundant on both mass and molar basis
compared to the fuel. Thus, the thermal diffusivity of the mixture is nearly that of nitrogen, and
hence a Lewis number, Le, calculated based on oxygen, being the deficient reactant for ϕ > 1
mixtures, will be close to unity as shown in Fig. 6a regardless of the fuel MW. Yet, a high
sensitivity of L to ϕ has been reported, for example, for rich n-butane/air mixtures [55].
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
0.35 0.4 0.45 0.5 0.55 0.6 0.65
Flame Speed, Deviation from a reference
Normalized Equivalence Ratio, Φ = ϕ/(1+ ϕ)
Kumar
Kelly
Smallbone
Ji et al. Baseline
16
(a) (b)
Figure 6. (a) Variation of Le with carbon number for n-alkane/air mixtures at p = 1 atm and
T
u
= 298 K, for ϕ = 0.7 (dashed line) and ϕ = 1.4 (solid line). (b) Variation of the ratio of oxygen
diffusivity to fuel diffusivity with carbon number for ϕ = 1.4 n-alkane/air mixtures at p = 1 atm
and T
u
= 298 K.
These inconsistencies point to possible uncertainties in the experimental determination of
o
S
u
,
and could be associated with mixture composition, i.e. ϕ, diagnostic equipment and techniques,
data analysis, and finally data interpretation. In order to tackle uncertainties associated with each
experimental approach, detailed understanding of the physics controlling the flame behavior and
response to fluid mechanics and loss mechanisms is required.
At pressures less than 10 atm,
o
S
u
can be measured using the CFF approach in which steady,
laminar, and planar flames (e.g. [16][33]) are established. Under such conditions, the only
parameter that can be varied for a given set of thermodynamic conditions is the flame stretch,
and this effect can be characterized readily using available quasi-one dimensional codes (e.g.
[56]). The method involves the determination of the axial velocity profile along the system
centerline and subsequently the identification of two distinct observables. A reference flame
speed, S
u,ref
, which is the minimum velocity just upstream of the flame, and a characteristic
stretch, K, which is the maximum absolute value of the axial velocity gradient in the
hydrodynamic zone. Thus, by varying S
u,ref
with K in the experiments, it was proposed [16][33]
that
o
S
u
can be determined by performing an extrapolation of the experimental data to zero stretch
17
given that as K 0, S
u,ref
should degenerate to
o
S
u
. Majority of the studies have used
asymptotically derived linear [33] and non-linear [57] equations to perform extrapolations.
Recently, Egolfopoulos and co-workers [8][58][59] introduced a computationally assisted
approach in quantifying the non-linear variation of S
u,ref
with K. Specifically, direct numerical
simulations (DNS) of the experiments were carried out with detailed description of molecular
transport and chemical kinetics to avoid simplifying assumptions used in asymptotic analysis.
Thus, the variation of S
u,ref
with K is computed and can be used to perform the non-linear
extrapolations of the experimental data.
Ji et al. [8] showed that for the same sets of experimental data of C
5
-C
12
n-alkanes, linear
extrapolation yield higher s for fuel rich mixtures, as compared to nonlinear extrapolation
using the computationally assisted approach. Considering also the results shown in Fig. 3, it is
reasonable to assume that the discrepancies between reported
o
S
u
s for ϕ > 1 mixtures could be
attributed partially to the extrapolations.
The SEF approach has been used extensively for measuring
o
S
u
due to the wide pressure
range of applicability (0.5 < p < 50 atm), the relative simplicity of diagnostics, and the well
defined stretch rate that makes the determination of the burned gas Markstein length, L
b
,
straightforward (e.g.,[21]-[32]). The commonly used method involves tracking using Schlieren
or shadowgraph the flame radius, R
f
, of the expanding flame as a function of time, t, during the
initial phase of propagation during which the pressure rise is negligible [22]. The flame speed
with respect to the burned gas is defined as S
b
dR
f
/dt, based on the assumption that the burned
gas is stationary, and the flame stretch is defined as K (2/R
f
)(dR
f
/dt) (e.g. [22]). During one
experiment, the variation of S
b
with K is monitored and through extrapolation to K = 0 the stretch
free S
b
o
value is determined. Subsequently,
o
S
u
is determined through the density correction as
o
S
u
S
b
o
(
b
/
u
).
The majority of the
o
S
u
s reported in the literature utilizing this approach (e.g. [22]-[25]) were
extracted using linear extrapolations to determine S
b
o
.
S
b
= S
b
o
– L
b
K (1)
o
S
u
18
where L
b
is the burned gas Markstein length.
Kelley and Law [55] identified that for mixtures with Le ≠ 1.0 and Karlovitz numbers, Ka,
[5] relevant to experiments, S
b
varies non-linearly with K and proposed a quasi-steady non-linear
extrapolation equation, which was derived originally by Ronney and Sivashinsky [60] for flames
of mixtures sufficiently far from stoichiometry, constant transport properties, and one-step
reaction:
(S
b
/S
b
o
)
2
ln(S
b
/S
b
o
)
2
= -2 L
b
K/S
b
o
(2)
Subsequently, Kelley et al. [61] relaxed the quasi-steady assumption and proposed an
improved non-linear extrapolation formula; a review of all extrapolation methodologies can be
found in Refs. [61] and [62].
Uncertainties associated with prolonged effects of ignition during the initial stages of flame
propagation [63][64], fluid dynamic effects induced by using a cylindrical rather than a spherical
chamber [65] and compression induced flow [66] resulting from pressure rise have been studied
and accounted for.
Mclean et al. [67] carried out a numerical study and determined that the radiation losses in
SEF’s can cause a systematic underestimation of
o
S
u
. It has been established also from previous
studies that radiation affects flame propagation notably only for mixtures at near limit conditions
[68]. Chen [69] performed DNS of near-limit CH
4
/air mixtures to investigate the effects of
radiation heat loss and reabsorption. It was shown that radiation heat loss from the burned gas
could cause an inward flow and that accounting for reabsorption moderates the overall heat loss
from the burned gas. Santner et al. [70] showed that S
b
o
of slow flames could be affected
significantly by the burned gas cooling. In the same study a correction methodology to obtain
accurate S
b
o
values was proposed based on an analytical model for fluid flow coupled with an
optically thin limit (OTL) model for radiation. However, this correction method has to be used
with caution, especially for high-pressure flames for which reabsorption can be important
(e.g.[71][72]).
Lecordier and coworkers [73][74] performed for the first time direct measurements of the
flow velocities during the constant pressure phase in SEF experiments by seeding the flow with
silicon oil droplets and using kHz-level particle image velocimetry (PIV). Thus, the
19
displacement velocity with respect to the unburned gas, U
n
, was determined as U
n
U
g
- S
b
[75],
where U
g
is the maximum velocity upstream of the flame. In these experiments S
b
and K are
determined readily once the temporal variation of R
f
is known; R
f
is defined as the location at
which the droplets have been vaporized completely.
o
S
u
is then obtained by extrapolating U
n
to
K = 0. This approach provides direct measurements of the unburned gas velocity and does not
require the use of the density correction to obtain
o
S
u
, which introduces the questionable
assumption of equilibrium in the burned gas that in reality is affected by radiation and its density
varies both in time and space. Renou and coworkers (e.g. [76]) extended this technique to
flames of liquid fuels and demonstrated that discrepancies exist between
o
S
u
values measured
using PIV and those determined using the Schlieren or shadowgraph approach.
A survey of nearly 120 papers published in major combustion journals on the experimental
determination of
o
u
S , reveals that 65% of the measurements have been carried out at p = 1 atm,
while only 8% for p < 1 atm and 27% for p > 1 atm. It is noted also, that the majority of the
published
o
u
S data, regardless of pressure, correspond to unburned mixture temperatures, T
u
,
that are either ambient or slightly elevated. Furthermore, the number of flame propagation
studies for gaseous fuels is notably higher than those corresponding to liquid fuels.
With few exceptions,
o
u
S data are scarce for conditions encountered in piston and jet
engines, that is for liquid fuel flames at p = 20-50 atm and T
u
= 700-800 K, given that
measurements can be rather challenging and highly uncertain. In order for liquid fuels to exist in
the vapor phase at engine-like pressures, the required T
u
must be high enough and could result in
fuel decomposition both in burner type steady state and static experiments. The vast majority of
the flame data reported in the literature during the last 10 years or so for liquid fuels have been
measured at T
u
< 500 K to avoid decomposition in CFFs (e.g.,[8][53]) and SEFs at constant
pressure (e.g.,[51]).
Burner-type experiments such as Bunsen, counterflow, and burner-stabilized flames (e.g.,
[8][19][36]) are operating under steady state conditions. On the other hand, in order for the
reactants to reach a quiescent state in static SEF experiments, several minutes are required upon
the completion of the reactant filling process. T
u
higher than 500 K in constant pressure SEF
experiments could result in fuel decomposition within the several minutes period between filling
20
the chamber and ignition. Additionally, high T
u
could reduce the effectiveness of the sealing
materials and compromise the overall integrity of the apparatus. Thus, in constant pressure SEF
experiments (e.g., [25][76]) in which measurements are obtained before the compression stage,
only moderate T
u
values can be tolerated.
The pressure rise (compression) stage of SEF propagation in a perfectly spherical chamber
was utilized for the first time to determine
o
S
u
by Lewis and von Elbe [26]. As the SEF
propagates outwards, the unburned gas is isentropically compressed [43], resulting thus in an
increase in its pressure, P, and temperature, T
u
. Hence the flame speed, S
u
, derived at each instant
corresponds to a different thermodynamic condition of the unburned gas. Assuming an infinitely
thin and smooth spherical flame, and isentropic compression of the unburned gas, Fiock and
Marvin [77] derived
33
2
3
wf
f
u
fu
RR
dR
dP
S
dt R P dt
(3)
In Eqn. 3, γ
u
is the heat capacity ratio of the unburned gas, R
w
the chamber radius, and P the
thermodynamic pressure. As the presence of optical access compromises the sphericity of the
experimental vessel, and thus the validity of Eqn. 3, P constitutes the sole experimental
observable in the constant volume SEF experiment. Hence the variation of flame radius, R
f
, with
pressure, henceforth abbreviated [R
f
, P], needs to be modeled to obtain S
u
from Eqn. 3.
Thermodynamics based models to determine [R
f
, P] were developed with different levels of
complexity and simplifying assumptions [28][30][43]. A review of the historical development of
the experiment and the attending equations that describe thermodynamic state of the burned and
unburned gas
1
could be found in Ref. [43].
The capability of the constant volume SEF experiment to measure
o
S
u
at engine relevant
conditions was recognized by Babkin and co-workers [78], Ryan and Lestz [79], and Metghalchi
and Keck [29][30]. Metghalchi and Keck [30] performed measurements for both gaseous as well
as liquid fuel and oxidizer mixtures at P ≤ 40 atm and T
u
≤ 700 K. These conditions were
achieved by an experiment with initial mixture pressure, P
o
= 7.6 atm and temperature,
1
To obtain [R
f
, P] one needs to determine accurately the thermodynamic state of the burned and unburned gas along
with the fraction of gas that is burned, at each P.
21
T
u,o
= 500 K. Unlike the case in steady state burner-type experiments and constant pressure
SEFs, high T
u
s are attained in a duration of O(10) milliseconds during the compression stage of
the constant volume SEF, which is a short enough time to result in fuel decomposition.
Additionally, for the same reason, the experimental design is significantly less complex and safer
in comparison, as the experimental system need not be heated and maintained at high
temperatures at which measurements need to be made.
While the approach of Lewis and von Elbe [26] was a meritorious one, concerns have been
raised about the potential formation of cells that could be unaccounted for in cases that optical
access was not possible as well as about potential stretch effects. Metghalchi and co-workers
[80][81] resolved the issue of cell formation, by performing measurements first in a cylindrical
chamber with optical access and identify thus reactant compositions for which thermal-diffusive
and/or hydrodynamic instabilities do not develop during the compression stage when the flame
radius is large and the stretch is small. Then, identical initial conditions were established in a
perfectly spherical chamber for which the assumptions of the thermodynamic model are
applicable. Regarding stretch effects, Metghalchi and co-workers [80][81] argued that they
should be small at large flame radii and supported this argument by a series of carefully executed
experiments. However, Chen at al. [66] performed numerical simulations of constant volume
SEFs and recommended a correction methodology to subtract the effect of stretch citing that
these effects could be important during the initial stages of pressure rise.
Failure to account for heat loss when interpreting experimental data could potentially result
in erroneous
o
S
u
values as the thermodynamic state of the unburned and burned gas will be
different at the same pressure with and without heat loss. Heat loss could be in the form of
conduction to the electrodes and chamber wall, and due to radiation from the burned gas.
Metghalchi and co-workers [30][82] examined the extent of these effects and concluded that they
could be neglected for conditions for which measurements were made.
As pointed out in the previous paragraphs, inconsistencies exist between experimental
measurements from different and same configurations, as well as between conclusions made
regarding what assumptions could be employed to extract
o
S
u
from directly measured
experimental data. Since
o
S
u
is not a directly measured but derived quantity, those differences
could be attributed to: (i) Experimental uncertainties related to the unburned mixture
22
thermodynamic state and measuring approach among others; (ii) Radiative effects, non-
negligible burned gas velocity, and/or density ratio assumption in SEFs; (iii) Extrapolation
models and range of validity; and (iv) Potential geometrical effects. These factors form the
motivation for all but one objective chosen for the current study. Before listing the objectives,
we review the literature to identify factors that can lead to development of localized exothermic
centers in homogenous reacting mixtures, also the motivation for the last objective.
Ignition is referred to as homogeneous when it occurs simultaneously throughout the mixture
that is spatially under uniform thermodynamic conditions. This is seldom the case in any
combustion system whether it is a practical device or a low dimensional laboratory experiment
designed for kinetic studies. In most cases, heat release is localized in space followed by the
development of different modes of propagating reacting fronts (e.g.,[83]-[89]). Voevodosky and
Soloukhin [83] and Meyer and Oppenheim [84] identified first the presence of localized
exothermicity in shock tube experiments. It has been shown by experimental and numerical
studies that these “exothermic centers” could lead to detonations (e.g., [84][88][90][91]) and
could potentially be the cause for knocking combustion of the unburned gas ahead of the
propagating flame in spark ignition (SI) engines.
Exothermic centers could develop in a reacting mixture as a result of inhomogeneities in
temperature and species caused by thermal and/or catalytic surface effects, the presence of
dispersed hot/catalytic particles, etc. [9]. Thermal inhomogeneities can be caused also through
the interaction of turbulent flow fields and boundary layers, BL, as is the case for example in SI
engines and rapid compression machines (RCM) (e.g.,[92][93]), and due to shock-BL
interactions in shock tubes [e.g.,[94][95]]. Griffiths and co-workers [96] identified that ignition
could first occur at a location that is at a lower temperature relative to its surrounding, for fuel/air
mixtures that exhibit the negative temperature coefficient (NTC) behavior. Griffiths et al. [96]
performed a numerical simulation utilizing a turbulence model and a reduced chemical scheme
to model ignition in an RCM. They observed that reactivity originated close to the wall where
the temperature was lower compared to the adiabatic core. This peculiar result could be
understood by considering Fig. 7, which depicts the variation of ignition delay time,
ign
, with the
inverse of temperature; the computational methods will be presented in Chap. 2 and 6. For the
sake of argument, assume that the bulk of gas in the RCM is at T ~ 950 K that corresponds to the
ignition delay peak depicted in Fig. 7. Regions near the wall that are at a lower temperature say
23
T ~ 800 K due to the presence of heat loss, will have an ignition delay that is shorter than the
bulk of hot gas, and can potentially ignite first. Subsequent studies were aimed at characterizing
temperature fields in RCMs and demonstrated that temperature inhomogeneities that originated
from BL-vortex interaction were leveled out during the first stage heat release for fuel/air
mixtures that displayed NTC behavior [92][97].
Figure 7. Computed ignition delay times under adiabatic conditions as a function of (1000/T) for
ϕ = 0.73, n-C
7
H
16
/air mixture at an initial pressure of 13.5 atm. The boxed region represents the
range of initial temperature conditions for which ignition first occurred in the boundary layer
with wall temperature, T
w
= 500 K. Ignition delay time is defined as the instant in time when the
temperature becomes 400 K greater than the initial temperature.
Exothermic centers have been observed to develop close to the wall in RCMs (e.g.,[89]) and
shock tubes (e.g.,[84]), which are key experimental facilities to obtain data for kinetic model
development and validation, as well as in experiments designed to provide insight into the
physics of the knock (e.g.,[87][88]). In spite of compelling experimental evidence, studies aimed
at identifying conditions for which localized ignition could happen in the thermal BL near a cold
wall, taking into consideration effects resulting from thermal and species gradients could not be
found in the literature.
Detailed numerical simulation is adopted as the tool in this thesis to study flame and ignition
physics and investigate the uncertainties associated with interpretation of experimental data. The
many advantages of using DNS over experiments are: (1) the spatial and temporal evolution of
all pertinent properties/variables can be obtained; (2) contributions of each phenomena or
individual terms in the governing equations can be calculated and thus used to understand the
interplay between various transport processes and chemistry and vice versa; and (3) the ability to
24
vary only one parameter at a time and investigate the corresponding effects (in other words, “turn
one knob at a time”). Combustion, a being highly non-linear and coupled multi-physics
phenomena makes experimentally altering only one parameter extremely difficult.
1.2 Objectives
Based on all the aforementioned considerations, the main objectives of this study are:
(1) To develop a code to perform DNS of flame propagation during the constant pressure as
well as the compression regime. DNS is a useful tool in that temporal and spatial
evolution of all the pertinent properties (variables) can be obtained within the
uncertainty of the chemical model and assumptions of the mathematical model. This is
advantageous to elucidate flame physics, especially in the case of SEFs for which the
experimental diagnostics have only been able to characterize S
b
using
Schlieren/shadowgraph and fresh gas velocity profile using PIV during constant pressure
propagation, and chamber pressure during the compression phase..
(2) Utilize DNS results to assess uncertainties in determining
o
S
u
from constant pressure
SEFs under realistic experimental conditions. The emphasis was on transport along with
quantification of extrapolation uncertainty, and radiation effects. While Le effects have
been studied extensively in past pertinent studies, this is not the case for reactant
differential diffusion that can be rather important for large MW fuels as evident from
Fig. 6b in which the ratio of oxygen to fuel diffusivities is shown to increase with the
fuel carbon number for ϕ = 1.4 n-alkane/air mixtures. The effect of radiation was
assessed also for SEF’s in the context of the various approaches available for deriving
the raw experimental data.
(3) To evaluate consistency between measurements obtained from CFF and constant
pressure SEF experiments indirectly, by comparing direct measurements obtained from
each configuration against the respective high fidelity DNS results computed utilizing
identical descriptions of transport and kinetics, and to quantify the bias introduced by
extrapolation practices.
(4) To analyze and quantify the uncertainties that arise from failing to account for radiation
heat loss and stretch effects while interpreting experimental data obtained during the
compression stage of SEF propagation in a perfectly spherical vessel.
25
(5) To investigate parametrically the ignition behavior of quiescent combustible mixtures,
which exhibit NTC behavior, adjacent to a cold wall using 1-D detailed numerical
simulations. An additional goal was to investigate whether the Ludwig-Soret (L-S)
diffusion, driven by the steep temperature gradients near the wall, has a significant effect
on the near-wall reactant concentrations for reacting mixtures that have contrasting
molecular weights, and whether the ignition behavior could thus be modified.
1.3 Relevant publications
Since some studies in this dissertation have been part of investigations that were
collaborative in nature and often included a combined experimental and numerical study, the list
of relevant publications that corresponds to, or amounted from each chapter are provided below
for the reader who is interested in the details of the experimental work or the cooperative aspects
which makes the study complete.
Chapter 3. J. Jayachandran, R. Zhao, F.N. Egolfopoulos, “Determination of laminar flame
speeds using stagnation and spherically expanding flames: Molecular transport and radiation
effects”, Combust. Flame 161 (2014) 2305-2316.
Chapter 4. J. Jayachandran, A. Lefebvre, R. Zhao, F. Halter, E. Varea, B. Renou, F.N.
Egolfopoulos, “A study of propagation of spherically expanding and counterflow flames using
direct measurements and numerical simulations”, Proc. Combust. Inst. 35 (2015) 695-702.
Chapter 5. 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.
Chapter 6. J. Jayachandran, F.N. Egolfopoulos, “Thermal and Ludwid-Soret diffusion effects on
near-boundary ignition behavior of reacting mixtures”, submitted for presentation at the 36th
International Symposium on Combustion.
26
Chapter 2 – Methodology: Detailed numerical simulations
Simulating a flame involves solving the mass, species’, momentum, and energy conservation
equations. The set of governing equations are highly non-linear owing to the exponential
dependence of the source terms on temperature. The highly non-linear nature of the chemical
source term along with the stiffness property of the equations demands special solution strategies
as compared to the non-reacting case, especially for transient problems [99]. This chapter
describes the various codes that have been used in the current study to assess the validity of
current practices in determining
o
S
u
using the CFF and SEF approaches.
2.1 Freely propagating and counterflow flames
o
S
u
’s and variation of S
u,ref
with K for CFF’s were computed respectively, using the PREMIX
code [100][101] and an opposed-jet flow code [102] that was originally developed by Kee and
co-workers [56]. Both codes were integrated with the CHEMKIN [103] and the Sandia transport
[104][105] subroutine libraries. The H and H
2
diffusion coefficients of several key pairs are
based on the recently updated set [106]. Both codes have been modified to account for thermal
radiation (OTL) of CH
4
, CO, CO
2
, and H
2
O [102][107]. The PREMIX code [100][101] and the
opposed-jet flow code [102] are steady state codes and haven been validated and used in multiple
studies.
2.2 Spherically expanding flames
The outward propagation of a spherical flame from an ignition kernel is a transient process
and hence has to be numerically treated as an initial value problem. The time scales associated
with chemistry, specifically the production and destruction rates of highly reactive radicals, are
short compared to that of transport. This renders the set of governing equations stiff as the time
step imposed to maintain stability when using explicit time stepping strategies is orders of
magnitude smaller compared to the time step required to sustain the required accuracy when
27
using an implicit method
2
[99]. Circumventing this problem by utilizing operator splitting
strategies [64][108] can be tricky for stiff problems which have a range of time-scales [109].
Thus, a choice of implicit time stepping is made to temporally integrate the equations as
described below.
The Transient One-dimensional Reacting flow Code (TORC) was developed using the
PREMIX code [46,47] as the framework to simulate 1-D SEFs. The conservation equations for
mass, species, and energy (Appendix A1) are solved numerically as a function of time in
spherical coordinates
3
[63]. Assuming that all flames studied are deflagrations and result in low
Mach number, Ma, flows, the velocity field can be obtained using the mass conservation
equation without having to solve the momentum conservation equation [63].
Constant pressure SEFs were simulated in a domain 0 ≤ R ≤ R
w
for which mass was allowed
to leave the boundary at R
w
; R = 0 represents the center of the spherical domain. This resulted in
solving for temperature, T, velocity, u, and species mass fractions, Y as a function of space and
time with the following boundary conditions, BC,
= 0,
= 0 ,
= 0 (BC1)
= 0 ,
= 0 (BC2)
where V
K
is the diffusion velocity of species K. Note that only one boundary condition for u is
allowed and is specified at the center of the domain.
For modeling SEF propagation in a constant volume spherical domain thus accounting for
compression, pressure, P, needs to be solved for in addition to the aforementioned quantities. P
is assumed to vary in time but not in space, given the small Mach numbers associated with SEFs.
The following BCs were implemented for the confined volume SEF simulations
= 0,
= 0,
= 0 (BC3)
2
Implicit methods for non-linear initial value problems are significantly more expensive compared to explicit
methods as the temporal gradient used to advance the solution to the next time step utilizes the solution at the next
time step, rendering the solution procedure iterative in nature.
3
One dimensional problems in other geometries can be simulated as well by modifying the governing equations as
was done for the ignition adjacent to a wall problem studied in Chap. 6.
28
= 0 or
,
= 0,
= 0 (BC4)
Note that the chamber wall at R
w
can be treated as either adiabatic or isothermal by specifying its
temperature T
wall
. A difficulty in implementing two BCs for velocity is encountered, as the
continuity equation involves only its first derivative, and it was overcome by solving the
additional equation dP/dr = 0 at each grid point [110].
The method of lines approach was adopted to solve the stiff non-linear system of equations,
which involves the replacement of spatial derivatives with discrete difference approximations,
relying on an ordinary differential equation (ODE) solver to perform the time integration. This
simplifies the method of solution as the ODE solver takes the burden of time step selection to
maintain stability and control local error of the evolving solution. Finite difference
approximations were used for spatial discretization. Second order upwind and central finite
difference schemes, both derived for second order accuracy on a non-uniform grid [111], were
used to discretize the convective and diffusive terms respectively.
The set of discretized equations form a differential algebraic equation (DAE) system of index
1 [112], with u being the only algebraic variable. Time integration of this DAE system was
performed using the DASPK [113]-[116] solver, which implements a backward-difference
formula with adaptive time step and order control. The inclusion of the additional “pressure”
equation at each grid point, for constant volume SEFs, imparts a banded structure to the Jacobian
matrix of partial derivatives, which is central to Newton’s method implemented by DASPK, thus
reducing the required memory.
An adaptive grid methodology was developed as computational efficiency is severely
compromised if a static mesh is used for a moving flame problem. The spatial domain was
divided into N regions of different grid point densities (L1,L2,…,LN), each having uniform grid
spacing. The algorithm ensures that the flame is always located within the region of highest
mesh point density (L1) and that the other regions are distributed around the L1 such that the
furthest region (LN) will have the least mesh density. Grid restructuring was performed every
time the flame separation from the L1 boundary was within a user defined tolerance. In order to
overcome the computational overhead of restarting DASPK every time a re-gridding process was
completed, a “flying/warm restart” was facilitated by interpolating the solutions at previous time
29
steps on to the new grid [117][118][119]. Thus, the solver can continue integrating using the
higher order multistep method and/or using a larger time step. The restructuring of the mesh was
done in such a way that the grid points located in the flame remain intact to avoid interpolation
errors. A monotone cubic Hermite interpolation [120] technique as suggested by Hyman et al.
[119] was found to work the best.
DASPK requires the initial condition to satisfy the governing DAE system of equations [116]
or in other words needs to be consistent with respect to the governing equations. To obtain
consistent initial conditions, the transient terms were discretized using the backward Euler
method and the system of equations were integrated in time over a couple of small time steps
(depending on the time scales of the problem) using a modified Newton method implemented in
the TWOPNT [121] solver. The error resulting from the inconsistent initial condition was
noticed to disappear in a few time steps resulting in a consistent initial condition.
The kinetic, thermodynamic, transport and radiation calculations were performed similarly
to PREMIX [100][103][104][105].
2.2.1 Validation of TORC
In order to validate TORC, transient simulations of planar flames were performed and the
results were compared against those obtained using PREMIX [100][101], a steady state code
used to compute
o
S
u
. Figures 8-10 illustrates how closely the profiles of temperature, H mass
fraction, and HO
2
mass fraction obtained from TORC compares to PREMIX [100][101]
calculations for a ϕ = 1.0 CH
4
/air flame. A 17-species chemical model with 78 reactions,
obtained by Directed Relation Graph [122], DRG, reduction of USC-Mech II [123], was used for
the computation. The discrepancy between
o
S
u
s obtained using the two codes was less than 2 %.
30
Figure 8. Comparison of spatial temperature profiles obtained from computations of a ϕ = 1.0
CH
4
/air flame using TORC and Premix code.
Figure 9. Comparison of spatial H mass fraction profiles obtained from computations of a
ϕ = 1.0 CH
4
/air flame using TORC and Premix code.
31
Figure 10. Comparison of spatial HO
2
mass fraction profiles obtained from computations of a
ϕ = 1.0 CH
4
/air flame using TORC and Premix code.
Figures 11 and 12 depict the working of the adaptive grid algorithm with 8 grid-levels. The
grid follows the flame and ensures that the flame region is always located in the grid level with
highest mesh point density.
32
Figure 11. Spatial temperature profiles obtained using TORC indicating the location of a
propagating ϕ = 1.0 CH
4
/air flame at different times of the simulation.
Figure 12. Grid point density as a function of space for a ϕ = 1.0 CH
4
/air at different times
computed using TORC. The times correspond to that of Fig. 9.
33
Chapter 3 – Molecular transport and radiation effects in spherically
expanding flames under constant pressure conditions
This chapter investigates potential uncertainties introduced in
o
S
u
that could result from
incorrect interpretation of the directly measured constant pressure SEF data. The validity of
using extrapolation equations derived using asymptotic methods, to subtract the effect of stretch,
is investigated for mixtures that exhibit non-equidiffusion effects. Specifically, differential
diffusion effects, as described in the Chap. 1, are analyzed as they have been overlooked in past
studies in which Lewis number, Le, is solely used to describe flame dynamics [5][60].
Furthermore, the consequence of neglecting radiation heat loss from the burned gas ball is
assessed in the context of different approaches for obtaining
o
S
u
from SEFs i.e., measurement of
burned flame speed, S
b
, using shadowgraph/schlieren photography, and measuring the
displacement velocity with respect to the unburned gas, U
n
, using Particle Image Velocimetry,
PIV.
3.1 Numerical Approach
DNS of constant pressure SEFs were performed using TORC and
o
S
u
s were calculated using
the Premix code [100][101]. In order to reduce the computational cost, CH
4
/air flames were
studied and employed two models obtained from USC-Mech II [123] using the Directed
Relations Graph, DRG, reduction strategy [122]. The reduction was done using an array of
PREMIX solutions for lean and rich mixtures separately. For ϕ = 0.7 and 1.0 a model consisting
of 17 species and 78 reactions was used, while for ϕ = 1.4 the reduced model included 24 species
and 137 reactions. The maximum heat release rate was used as a marker to track R
f
as a function
of t. S
b
is obtained by differentiating a 3
rd
order polynomial used to fit locally the variation of R
f
with t, and as mentioned earlier, stretch rate, K (2/R
f
)(dR
f
/dt).
A domain of radius
= 25 cm was used in the simulations. At t = 0, a stagnant pocket of
hot burned gases of radius 2.5 mm surrounded by the unburned combustible gas mixture was
used to achieve ignition. It should be noted that while
= 25 cm is of no relevance to the
actual experimental conditions it is large enough radius at which near-zero stretch rates, K, are
34
reached and at which the extrapolations are carried out. The SEF DNS results were treated as
“data” for the range of K’s that are typically used in experiments, and subsequently Eqns. 1 and 2
were used to perform extrapolations. Equations 1 and 2 are listed again for the sake of
completeness.
S
b
= S
b
o
– L
b
K (1)
(S
b
/S
b
o
)
2
ln(S
b
/S
b
o
)
2
= -2 L
b
K/S
b
o
(2)
In these equations, S
b
and S
b
o
are the stretched and stretch-free flame speeds respectively relative
to the burned gas, and L
b
is the burned Markstein length.
The advantage of this approach is that both the response of flame propagation to K from
high to near-zero values and
o
S
u
are known so that the merits and shortcomings of extrapolation
Eqns. 1 and 2 can be assessed.
Furthermore, the DNS approach allows for the rigorous assessment of reactant differential
diffusion effects. A parametric study was performed on the effect of the fuel diffusivity on the
response of CH
4
/air flames to K given the relatively small size of the kinetic model, essential for
unsteady DNS of SEF’s, and the fact that diffusivities of CH
4
and O
2
do not differ substantially.
The variation of the CH
4
diffusivity was implemented through modification of its Lennard-Jones
(L-J) parameters. The unperturbed case is referred to as OD (original diffusivity). ID (increased
diffusivity) and DD (decreased diffusivity) refer to the cases in which the L-J parameters of CH
4
were replaced with those of H
2
and n-C
12
H
26
respectively. This approach ensures that the
chemistry is consistent in all computations, and also circumvents the complexities associated
with fuel cracking which high MW fuels are susceptible to. The values of Le and ratio of fuel to
oxygen diffusivities in the mixture are shown in Table 1 for ϕ = 0.7, 1.0, and 1.4.
35
ϕ Le D
fuel
/D
O2
Original L-J Parameters (OD)
0.7 1.0 1.14
1.0 N/A 1.16
1.4 1.1 1.17
n-C
12
H
26
L-J Parameters (DD)
0.7 2.3 0.45
1.0 N/A 0.48
1.4 1.0 0.51
H
2
L-J Parameters (ID)
0.7 0.7 1.67
1.0 N/A 1.67
1.4 1.2 1.68
Table 1. Lewis number, Le and ratio of fuel to O
2
diffusivities for the mixtures used in the
present study.
3.2 Results and discussion
3.2.1 Differential diffusion effects and extrapolation uncertainties
Figure 13 depicts the variation of
o
S
u
with ϕ for CH
4
/air mixtures for various CH
4
diffusivities, D
CH4
, while in Fig. 14 the logarithmic sensitivity coefficients of
o
S
u
to the CH
4
-N
2
and O
2
-N
2
binary diffusion coefficients are shown. Results indicate that the modification of
D
CH4
has an opposite effect on
o
S
u
for ϕ < 1.0 and ϕ ≥ 1.0.
36
Figure 13. Computed
o
S
u
’s of CH
4
/air flames at p = 1 atm and T
u
= 298 K using USC-Mech II.
( ─) OD; (---) DD; (-
.
-) ID.
Figure 14. Logarithmic sensitivity coefficients of
o
S
u
to the CH
4
-N
2
(black) and O
2
-N
2
(grey)
binary diffusion coefficients for CH
4
/air flames at p = 1 atm, T
u
= 298 K, and various ϕ’s.
5
10
15
20
25
30
35
40
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Laminar Flame Speed, (cm/s)
Equivalence Ratio,
-0.6 -0.4 -0.2 0 0.2 0.4
ϕ=1.4
ϕ=1.0
ϕ=0.7
37
Details of the flame structure are shown in Fig. 15, and it can be seen that a change in D
CH4
results in a corresponding change in its diffusion length relative to O
2
. The diffusion length of
CH
4
for a ϕ = 1.4 CH
4
/air flame computed with DD (Fig. 15b) is reduced compared to the OD
case (Fig. 15a). Thus, Y
CH
4
and the local equivalence ratio, ϕ
local
, increase at the location at
which the CH
4
consumption initiates as shown in Fig. 16, which results in the reduction of
reactivity, shown also in Fig. 16. Similar analysis can be used to explain the dependence of
o
S
u
on D
CH4
for all mixtures shown in Table 1. Furthermore, it is of interest to note that the
dependence of
o
S
u
on D
CH4
is not captured by the following equation that is based on Le
considerations [5]:
o
S
u
(Le ≠ 1) =
o
S
u
(Le = 1) Le (3)
(a) (b)
Figure 15. (a) Normalized mass fraction profiles of CH
4
( ┄ ) and O
2
( ─), and CH
4
consumption rate profile ( ─) for a = 1.4 freely propagating CH
4
/air flame at T
u
= 298 K and
p = 1 atm, computed using USC-Mech II and OD. (b) Normalized mass fraction profiles of CH
4
( ┄ ) and O
2
( ─), and CH
4
consumption rate profile ( ─) for a freely propagating flame at
T
u
= 298 K, p = 1 atm, and = 1.4, computed using USC-Mech II and DD.
0.0E+00
5.0E-04
1.0E-03
1.5E-03
2.0E-03
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.05 0.1 0.15 0.2
CH
4
Consumption Rate (mole/cm
3
·s)
Normalized Mass Fraction
Spatial Location (cm)
0.0E+00
5.0E-04
1.0E-03
1.5E-03
2.0E-03
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.05 0.1 0.15 0.2
Spatial Location (cm)
CH
4
Consumption Rate (mole/cm
3
·s)
Normalized Mass Fraction
38
Figure 16. Variation of ϕ
local
with temperature in a ϕ = 1.4 freely propagating CH
4
/air flame at
p = 1 atm, and T
u
= 298 K computed using USC-Mech II with OD ( ●) and DD ( ■), and variation
of CH
4
consumption rate with temperature with OD ( ─) and DD (-
.
-).
CH
4
/air SEF’s were computed for a wide range of R
f
’s and the computed S
b
values for
1 cm < R
f
< 3 cm were used for performing extrapolation using Eqn. 1 and 2. This R
f
range is
used typically in experiments (e.g. [24][25]) so that the data are not affected by the ignition
energy and pressure rise [63][66]. The simulations were performed for adiabatic flames (ADB),
i.e. without considering radiation, with ID, OD, and DD and the variation of S
b
/S
b
o
with Ka is
shown in Figs. 17, 18, and 19 for ϕ = 0.7, ϕ = 1.0, and ϕ = 1.4 respectively.
0.0E+00
5.0E-04
1.0E-03
1.5E-03
2.0E-03
0.6
0.8
1
1.2
1.4
1.6
1.8
2
300 500 700 900 1100 1300 1500 1700 1900
CH
4
Consumption Rate (mole/cm
3
·s)
Local Equivalence Ratio,
local
Temperature (K)
39
Figure 17. Variation of S
b
/S
b
o
with Ka of a ϕ = 0.7 CH
4
/air SEF (ADB) at p = 1 atm and
T
u
= 298 K computed using a reduced USC Mech II with ID ( ■), OD ( ●), and DD ( ▲). ID (-
.
-),
OD ( ─), and DD (---) correspond to fitting using Eq. 2. The full range DNS results are shown in
hollow symbols, while the DNS results used for fitting Eq. 2 are shown in solid symbols.
0.6
0.7
0.8
0.9
1
1.1
0 0.02 0.04 0.06 0.08 0.1
S
b
/S
b
o
Karlovitz number , Ka
0.6
0.7
0.8
0.9
1
1.1
0 0.02 0.04 0.06 0.08 0.1
S
b
/S
b
o
Karlovitz number , Ka
40
Figure 18. Variation of S
b
/S
b
o
with Ka of a ϕ = 1.0 CH
4
/air SEF (ADB) at p = 1 atm and
T
u
= 298 K computed using a reduced USC Mech II with ID ( ■), OD ( ●), and DD ( ▲). ID (-
.
-),
OD ( ─), and DD (---) correspond to fitting using Eq. 2. The full range DNS results are shown in
hollow symbols, while the DNS results used for fitting Eq. 2 are shown in solid symbols.
Figure 19. Variation of S
b
/S
b
o
with Ka of a ϕ = 1.4 CH
4
/air SEF (ADB) at p = 1 atm and
T
u
= 298 K computed using a reduced USC Mech II with ID ( ■), OD ( ●), and DD ( ▲). ID (-
.
-),
OD ( ─), and DD (---) correspond to fitting using Eq. 2. The full range DNS results are shown in
hollow symbols, while the DNS results used for fitting Eq. 2 are shown in solid symbols.
The extrapolation errors resulting from using the non-linear Eqn. 2 are discussed. With DD,
the extrapolation error in S
b
o
is approximately 6% for the lean and rich flames. Extrapolations of
the ϕ = 1.4 results obtained with OD and ID result in errors of 4.5% and 10% respectively. It is
also of interest to note that for flames with positive L
b
, the variation of S
b
with Ka is nearly
linear despite the high sensitivity of S
b
to Ka, and that Eqn. 2 always generates a highly non-
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
0 0.05 0.1 0.15 0.2 0.25
S
b
/S
b
o
Karlovitz number , Ka
41
linear curve for such flames especially when the S
b .
vs. K slope is steep. In general, mixtures
with Le ≠ 1.0 and/or notable differences between the fuel and O
2
diffusivities, the magnitude of
the extrapolation error increases. Other than the aforementioned conditions, the extrapolation
error was determined to be in general below 3%. Extrapolation errors when using Eqn. 1 and 2
for all individual cases is listed in Table 2.
Spherically Expanding Flames Error %
ϕ Fuel Diffusivity Non-linear Linear
0.7
Original (OD) -2.0 -1.1
Decreased (DD) -5.0 1.2
Increased (ID) 0.3 0.5
1
Original (OD) -3.1 -2.1
Decreased (DD) -3.3 -1.9
Increased (ID) -2.6 -1.8
1.4
Original (OD) -4.2 1.6
Decreased (DD) 6.6 7.6
Increased (ID) -10.5 -0.5
Table 2. Errors resulting from using linear (Eqn. 1) and non-linear (Eqn. 2) extrapolation
equations to obtain
o
S
u
from SEF data. The errors were derived from numerical simulations of
CH
4
/air mixtures with original and modified diffusivities at T
u
= 298 K and p = 1 atm.
For SEF’s, S
b
represents the flame propagation speed with respect to the stationary burned
gas at adiabatic conditions. The variation of HRR
tot
with Ka is shown in Fig. 20 for ϕ = 1.4 and
it can be seen that the behavior computed using ID, OD, and DD is similar to that of S
b
/S
b
o
with
Ka shown in Fig. 19 indicating that S
b
is a good indicator of the overall burning intensity. From
Figs. 17-19 it is apparent also that there is a significant change in slope of the S
b
/S
b
o
vs. Ka curve
when D
CH4
is modified for the ϕ = 0.7 and 1.4 mixtures. The results for the ϕ = 0.7 mixture
shown in Fig. 17 can be explained based on Le ≠ 1.0 (Table 1) effects caused by the imbalance
of energy loss from and energy gain by the reaction zone [5]. For the ϕ = 1.4 mixture however,
42
even though Le 1.0 (Table 1) for all hydrocarbons, a substantial increase in S
b
/S
b
o
and HRR
tot
with Ka is seen for the DD case for which there is a notable difference between D
CH4
and D
O2
.
Thus, the diffusion rate of O
2
towards the reaction zone increases compared to CH
4
with
increasing K, making thus the mixture more stoichiometric and increasing the overall reactivity
[5]. For the ϕ = 1.0 mixture the slope of S
b
/S
b
o
with Ka does not change for the different D
CH4
values. This is due to the fact that for near-stoichiometric mixtures there is a minor sensitivity of
the overall reactivity to modifications in ϕ as it reaches a maximum value. Further analysis and
confirmation of the differential diffusion effect using the CFF configuration can be found in Ref.
[124].
Figure 20. Variation of HRR
tot
with Ka of a ϕ = 1.4 CH
4
/air SEF at p = 1 atm and T
u
= 298 K
computed using a reduced USC-Mech II with ID (-
.
-), OD ( ─), and DD (---).
20
25
30
35
40
45
50
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
Total Heat Release Rate (J/cm
2
·s)
Karlovitz number , Ka
43
Figure 21. Variation of S
b
/S
b
o
with Ka of CH
4
/air SEF’s (ADB) at p = 1 atm and T
u
= 298 K
computed using a reduced USC Mech II with DD for ϕ = 0.7 ( ■), ϕ = 1.0 ( ●), and ϕ = 1.4 ( ▲).
Figure 21 depicts the variation of S
b
/S
b
o
with Ka for ϕ = 0.7, ϕ = 1.0, and ϕ = 1.4 computed
with DD that is representative of high MW hydrocarbons, and the results are consistent with
experimental results of n-butane/air mixtures [55]. More specifically, the sign of L
b
for heavy
hydrocarbons changes from positive for ϕ < 1.0 to negative for ϕ > 1.0. For ϕ < 1.0 mixtures of
high MW hydrocarbons the flame response is controlled by Le effects, whereas for ϕ > 1.0
differential diffusion is the controlling factor.
Kelley et al. [61] used asymptotic analysis to account for differential diffusion effects, and
they showed that there is a non-monotonic variation of the flame speed with stretch for near
stoichiometric mixtures with contrasting fuel and oxygen diffusivities. Using the formulation
obtained in Ref. [61] for extrapolations to obtain accurate flame speeds was not feasible due to
the large number of parameters that have to be determined by fitting the extrapolation equation
to the experimental data. Hence all extrapolation equations were obtained by invoking the
assumption that the reactant differential diffusion effect is negligible (for off-stoichiometric
mixtures) and that Le solely governs the flame dynamics. In the present study it was shown that
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
0 0.02 0.04 0.06 0.08 0.1
S
b
/S
b
o
Karlovitz number , Ka
44
this assumption is not valid for rich mixtures of large MW hydrocarbons and thus using such an
equation to extrapolate experimental data can lead to notable errors.
3.2.2 Radiation effects for SEF’s
Figure 22 depicts the spatial temperature profiles for a ϕ = 1.0 CH
4
/air SEF at p = 5 atm that
has propagated to R
f
= 8 cm. Recall, that the adiabatic and optically thin limit cases are
represented by ADB and OTL respectively. In order to account for potential re-absorption,
additional simulations were carried out by using half of the Planck’s mean absorption coefficient
represented by HOTL, which is in a way is equivalent to reabsorption of half the energy emitted
by the burned gas within the burned gas itself. This is applicable only to scenarios where the
unburned gas is spectrally transparent to the radiation from the burned gas. It is apparent that the
presence of radiation results in a notable reduction of the temperature of the burned gases and the
assumption of equilibrium does not hold.
Figure 22. Temperature profiles for a ϕ = 1.0 CH
4
/air SEF at p = 5 atm, T
u
= 298 K, and
R
f
= 8 cm computed using a reduced USC Mech II with ADB ( ─), OTL (---), and HOTL (-
.
-).
0
500
1000
1500
2000
2500
0 5 10 15 20 25 30
Temperature, T (K)
Radius, R (cm)
45
The spatial variation of the gas velocity for the conditions of Fig. 22 is shown in Fig. 23. The
radial inward flow, observed as negative velocities, is a result of density change in the burned
gas due to radiative heat loss. It is seen that the extent of this inward flow is reduced with
reabsorption, e.g. HOTL, as the total heat loss is reduced, which is consistent with the findings of
Chen [69].
Figure 23. Velocity profiles for a ϕ = 1.0 CH
4
/air SEF at p = 5 atm, T
u
= 298 K, and R
f
= 8 cm
computed using a reduced USC Mech II with ADB ( ─), OTL (---), and HOTL (-
.
-).
Figure 24 illustrates the variation of S
b
with K, and the discrepancies that can be induced due
to extrapolations to K = 0 are apparent. As expected, in the presence of radiation S
b
is reduced
and as a result the effect of inward flow is augmented at large radii, which is evident also by the
equation derived by Santner et al. [70]. However, the reported results for OTL and HOTL may
not be entirely physical, given that at very large radii some of the lost energy may be reabsorbed
due to large optical thickness. Nevertheless, caution is recommended when SEF raw data are
-20
0
20
40
60
80
100
120
0 5 10 15 20 25 30
Velocity, V (cm/s)
Radius, R (cm)
46
interpreted as Santner et al. [70] has suggested also.
Figure 24. Variation of S
b
with K of a ϕ = 1.0 CH
4
/air SEF at p = 1 atm and T
u
= 298 K
computed using a reduced USC Mech II with with ADB ( ●), OTL ( ▲), and HOTL ( ■). ADB
( ─), OTL (---), and HOTL (-
.
-) correspond to fitting using Eq. 2. The full range DNS results
are shown in hollow symbols, while the DNS results used for fitting Eq. 2 are shown in solid
symbols.
90
100
110
120
130
140
0 50 100 150 200 250
S
b
(cm/s)
Stretch Rate, K (s
-1
)
47
ϕ
Pressure
(atm)
% Difference between
OTL & ADB
o
S
u
’s
from
freely propagating
flame simulations
% Difference between
OTL & ADB
extrapolated S
b
o
’s from
SEF data
0.7 1 -0.4 -4.0
1.0 1 -0.2 -2.0
1.4 1 -2.4 -6.2
0.8 5 -0.1 -6.0
1.0 5 -0.1 -4.6
Table 3. Differences in
o
S
u
’s between the ADB and OTL cases as obtained from freely
propagating flame simulations, and in S
b
o
’s obtained by extrapolating the SEF results for the
ADB and OTL cases.
Table 3 illustrates the errors induced when the S
b
data derived using OTL are used to extract
S
b
o
for CH
4
/air mixtures at various conditions. The percentage difference in
o
S
u
calculated using
the PREMIX code between the OTL and ADB conditions represents the difference that should
be obtained after extrapolating S
b
at the corresponding conditions to obtain S
b
o
, as they are
linearly related through the continuity equation. Results show that the error due to cooling of the
burned gas increases for off-stoichiometric mixtures and at high pressures, in agreement with the
findings of Santner et al. [70] in that the slower flames are affected most by the radiative heat
loss given that more time is available for the burned gases to cool during the duration of the
experiment.
The alternative approach of Lecordier and coworkers [73][74] was evaluated also using the
computed SEF structures from which in addition to S
b
the values of U
g
were extracted as well so
that the displacement velocity U
n
U
g
- S
b
[75] can be evaluated. Figure 25 compares the
variations of S
b
and U
n
with K, for the ADB, OTL, and HOTL cases. It is of interest to note that
while radiation has a major effect on S
b
, its effect on U
n
is minor as its values computed in all
three cases collapse in a single curve. Mathematically, radiation affects similarly S
b
and U
g
through the inward flow, so that its effect is subtracted out. From a physical point of view this
48
result is reasonable, as U
n
is a measure of the stretched flame speed with respect to the unburned
gas, which is not affected from radiation for mixtures that are not close to the flammability limits
[68].
Figure 25. Variation of S
b
(solid) and U
n
(hollow) with K of a ϕ = 1.0 CH
4
/air SEF at p = 5 atm
and T
u
= 298 K computed using a reduced USC Mech II with ADB ( ●), OTL ( ▲), and HOTL ( ■).
Radiation calculations involving spectrally resolved emission and absorption are
computationally expensive and prone to uncertainty due to simplifying assumptions required to
make the numerical simulation feasible [125]. Therefore, by measuring U
n
the complications
associated with accurate reabsorption calculations needed to model the experimental data are
circumvented, and enables using the OTL model to simulate SEF’s to reasonable accuracy for
mixtures which have limited overlap of spectral bands with the burned products and are far from
the flammability limit. Any approach in SEF’s is not applicable for near-limits for which
o
S
u
can
be of the order of 10 cm/s or less [68][69], given that buoyancy will dominate the flame behavior
16
16.5
17
17.5
18
18.5
19
90
95
100
105
110
115
120
125
130
0 50 100 150 200 250
U
n
(cm/s)
S
b
(cm/s)
Stretch Rate, K (s
-1
)
49
and will cause severe distortion of the flame surface in experiments.
In order to extrapolate the experimental U
n
data to obtain
o
S
u
, Renou and coworkers [76] used
the formula of Kelley and Law [55] derived for the unburned flame propagation speed, defined
as the flow velocity relative to the flame upstream of the preheat zone where the temperature rise
is negligible. Figure 26 depicts U
n
as a function of Ka for ϕ = 1.4 CH
4
/air mixtures computed
with ID, OD and DD, the cases examined in Fig. 19 along with the extrapolation curves obtained
using the formula of Kelley and Law [55]. It is evident from Fig. 19 and Fig. 26 that the trends
of variation of
and U
n
with Ka are different and that U
n
unlike
and HRR
tot
(Fig. 20) is not a
proper indicator of the burning intensity.
Figure 26. Variation of U
n
/
o
S
u
with Ka for a ϕ = 1.4 CH
4
/air SEF at p = 1 atm and T
u
= 298 K
computed using a reduced USC Mech II with ID ( ■), OD (●), and DD ( ▲). ID (-
.
-), OD ( ─),
and DD (---) correspond to fitting using the equation derived by Kelley and Law [21]. The full
range DNS results are shown in hollow symbols, while the DNS results used for fitting the
extrapolation equation are shown in solid symbols.
Extracting the unburned flame propagation speed from an unsteady flame in a non-planar
flow geometry is not trivial. Dixon-Lewis and Islam [126] simulated a planar steady flame in a
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
0 0.05 0.1 0.15 0.2 0.25
U
n
/S
u
o
Karlovitz number , Ka
50
quasi-1D diverging flow geometry and showed that the flame speed can be obtained by density
correction of the flow velocity at the location of peak reaction rate. It became evident also from
the simulations in the current study that this point of maximum velocity (U
g
), used to compute
U
n
, is influenced by thermal dilatation as shown in Fig. 27 which is a plot depicting the variation
of temperature at the location of maximum velocity with stretch. These observations are
indicative of the fact that U
n
, obtained from U
g
, is not the actual unburned stretched flame speed,
but a reference flame speed similarly to S
u,ref
in CFF’s. Using the equation of Kelley and Law
[55], which does not account for thermal dilatation and geometric effects, to extrapolate U
n
could
result in substantial error in the extrapolated value of
o
S
u
. This increased uncertainty is evident
from the difference in extrapolation errors of U
n
and
depicted by Figs. 26 and 19 respectively
and the consistent over prediction of the known
o
S
u
values in all cases.
Figure 27. Variation of temperature at location of maximum velocity (U
g
)
with stretch for a
ϕ = 1.4 CH
4
/air SEF at p = 1 atm and T
u
= 298 K.
300
305
310
315
320
325
0 100 200 300 400 500 600
Stretch rate, K (s
-1
)
Temperature at U
g
location (K)
51
3.3 Concluding remarks
Direct numerical simulations of spherically expanding flames were carried out in order to
assess uncertainties stemming from current practices that are used to interpret experimental data
and derive the laminar flame speed. The analysis focused on the effects of molecular transport
and thermal radiation. The results of the simulations were treated as data in the range of stretch
rates that are encountered in experiments, and were used to perform extrapolations to zero stretch
using formulas that have been derived from asymptotic analyses. The validity of these practices
was tested upon comparing the results against the known answers of the direct numerical
simulations.
The effect of molecular transport was studied by varying the fuel diffusivity. It was
concluded that for fuel lean hydrocarbon/air mixtures, the preferential diffusion of heat or mass
as manifested by the Lewis number dominates the flame response to stretch. For fuel rich
mixtures, the controlling factor was determined to be the differential diffusion of the reactants
into the reaction zone for heavy hydrocarbons. It was found also that using extrapolation
equations derived based on asymptotics analysis and simplifying assumptions to obtain the
laminar flame speeds, could result in significant errors for rich flames of heavy hydrocarbons.
Numerical simulations of spherically expanding flames with radiative heat loss revealed that
the standard approach of measuring the flame propagation speed relative to the burned gas using
the shadowgraph/Schlieren techniques, could result in a systematic under-prediction of the true
laminar flame speed due to an inward flow induced by the density change in the burned gas.
Furthermore, it was shown that by simultaneously measuring the maximum velocity upstream of
the flame and the burned flame speed and evaluating thus the displacement speed relative to the
fresh gases, this error could be avoided. It was determined that there is a negligible effect of the
density change in the burned gas due to radiation on the displacement speed relative to the fresh
gas.
52
Chapter 4 – A Study of Propagation of Spherically Expanding and
Counterflow Laminar Flames Using Direct Measurements and
Numerical Simulations
o
S
u
is not a directly measured but derived quantity and inconsistencies exist between data
reported from Counterflow flame (CFF) and spherically expanding flame (SEF) experiments, as
detailed in Chap 1 and 3. The investigation presented in this chapter is directed towards
resolving some of these issues, and involved for the first time a combined experimental and
computational approach in both SEF’s and CFF’s under the same conditions. The main
innovation was that direct velocity measurements and direct numerical simulations (DNS) were
carried out in both configurations. The specific goals of this study were: (1) To measure and
compute propagation speeds in stretched flames. The thermodynamic conditions were chosen so
that radiation had no measurable effect on the propagation of SEF’s. Fuels with well-known
combustion kinetics were used. Thus the consistency between measured and not extrapolated
data obtained in both configurations could be evaluated indirectly through comparisons against
reliable high-fidelity DNS results; (2) To quantify the bias introduced by extrapolation practices
using both the experimental and computed results and comparing against the predicted 1D planar
laminar flame speed that is the reference value. In doing so, it will be emphasized that a kinetic
model could be validated with better accuracy using the stretched flame results both from
experiments and DNS; and (3) To compare the
o
S
u
results obtained in SEF’s using the variations
of both S
b
and U
n
with the stretch rate.
4.1 Experimental Approach
4.1.1 Spherically expanding flames
SEF experiments were performed by Renou and coworkers at CORIA [76][127]. The
experiment and apparatus are described in detail in Refs. [76][124]. S
b
and U
g
are obtained from
high-speed laser tomography recordings, by using the new PIV algorithm presented in [76]. The
chamber is seeded with silicone oil droplets (Rhodorsil), which vaporize at an isotherm of about
580 K. This boiling point temperature is high enough for the seeding droplets to exist well into
the preheat zone, allowing for the determination of U
g
. The effects of seeding on the flame
53
dynamics, e.g. chemical and sensible enthalpy and re-absorption of radiative energy, have been
checked by performing shadowgraph measurements with and without seeding in the facility of
Orléans [129] and no measurable effect was identified in a spherical chamber. From the
tomographic measurements, both the time evolution of the flame radius R
f
and spatial fresh gas
velocity profiles can be obtained. S
b
is determined through S
b
=
where is obtained by
a localized quadratic fitting of radius as a function of time. As mentioned earlier, the
displacement speed is computed as U
n
S
b
-U
g
.
All measurements were performed for 0.7 ≤ ϕ ≤ 1.4 and p = 0.1 MPa, and T
u
= 298 K for
C
2
H
4
/(0.167 O
2
+ 0.833 N
2
) mixtures, and T
u
= 373 K for n-C
7
H
16
/air mixtures. The oxidizer
was diluted for C
2
H
4
flames, in order to reduce the propagation rates to values similar to those of
n-alkane/air flames and thus reduce experimental uncertainties. For each condition, 5 trials were
performed to highlight the high level of repeatability of the measurements.
4.1.2 Counterflow flames
The experiments were carried out using the counterflow configuration at USC by Runhua
Zhao [8][124]. The burner diameter and separation distance are 14 mm. All gaseous flow rates
were metered using sonic nozzles. A high-precision pump, with a reported flow rate accuracy of
±0.5%, is used to inject liquid fuel and a glass nebulizer is used to generate micron-size liquid
fuel droplets which are mixed with hot air to achieve complete vaporization [8]. Uncertainty in ϕ
is no larger than 0.5%. A K-type thermocouple is used to monitor T
u
at the center of the burner
exit. The axial flow velocities were determined along the centerline using PIV [8], with
submicron silicon oil droplets as flow tracers, to determine S
u,ref
and K.
All measurements were performed at p = 1 atm (0.101325 MPa), while all other conditions
were identical to those used in SEF’s.
4.2 Numerical Approach
Premix code [100][101] and the modified opposed-jet code [102] are used to compute
o
S
u
’s
and S
u,ref
as a function of stretch respectively. Details of all the codes have been presented in
Chapter 2. The USC Mech II kinetic model [123] was used for the C
2
H
4
flame simulations. For
54
modeling n-C
7
H
16
flames, the JetSurF 1.0 [131] model was reduced to 100 species and 803
reactions using DRG [122].
Adiabatic (ADB) and non-adiabatic (OTM) SEF simulations were performed using TORC in
a domain of size 25 cm, in order to assess potential radiation effects. A hot pocket of burned gas
of radius 1.8 mm surrounded by the unburned mixture was used as an initial condition that led to
ignition. R
f
was identified as the 580 K isotherm, which is the boiling point of the silicon oil
droplets used as tracer particles in the experiments. S
b
and U
g
were derived readily from the
solutions.
4.3 Results and discussion
4.3.1 Direct measurements and simulations
Figure 28 and 29 depict the directly measured S
b
and U
g
from SEF’s and S
u,ref
from CFF’s
along with the corresponding DNS results at various ϕ’s for C
2
H
4
and n-C
7
H
16
flames
respectively.
0
50
100
150
200
250
300
0 100 200 300 400 500 600 700
S
b
, cm/s
Stretch Rate, K, s
-1
55
Figure 28. Experimental and computed S
b
(top), U
g
(center), and S
u,ref
(bottom) as functions of
stretch rate for C
2
H
4
flames. Symbols: experimental data; Thick lines: ADB simulations for
SEF’s and OTM simulations for CFF’s; Dotted lines: OTM simulations for SEF’s only.
0
50
100
150
200
250
0 100 200 300 400 500 600 700
U
g
, cm/s
Stretch Rate, K, s
-1
0
10
20
30
40
50
0 100 200 300 400
S
u,ref
, cm/s
Stretch Rate, K, s
-1
φ = 0.7 φ = 1.0
φ = 1.2 φ = 1.4
φ = 0.7 φ = 1.0
φ = 1.2 φ = 1.4
56
0
50
100
150
200
250
300
350
0 100 200 300 400 500 600 700
S
b
, cm/s
Stretch Rate, K, s
-1
0
50
100
150
200
250
300
0 100 200 300 400 500 600 700
U
g
, cm/s
Stretch Rate, K, s
-1
57
Figure 29. Experimental and computed S
b
(top), U
g
(center), and S
u,ref
(bottom) as functions of
stretch rate for n-C
7
H
16
flames. Symbols: experimental data; Thick lines: ADB simulations for
SEF’s and OTM simulations for CFF’s; Dotted lines: OTM simulations for SEF’s only.
SEF’s were modeled using both ADB and OTM approaches and results show that under the
present conditions radiation does not have a significant effect on either S
b
or U
g
for these
relatively fast flames. CFF’s were modeled using the OTM approach but the results obtained
with ADB are known to be indistinguishable from those obtained with OTM for non near-limit
flames [130]. As mentioned in the Introduction, the choice of conditions was made to avoid
complications stemming from radiation effects. However, if radiation effects were notable for
SEF’s, the DNS results could be compared only with the experimental U
n
whose values are
insensitive to the presence of radiation as shown in Chap. 3. Additionally, it would not be
possible to derive any information regarding S
b
whose value depends directly on the burned gas
velocity, and it is used as the main measurable quantity in the vast majority of SEF experiments.
0
10
20
30
40
50
60
70
0 100 200 300 400
S
u,ref
, cm/s
Stretch Rate, K, s
-1
φ = 0.7 φ = 1.0
φ = 1.2 φ = 1.4
φ = 0.7 φ = 1.0
φ = 1.2 φ = 1.4
58
Figure 30. Mean difference and standard deviation of experimentally measured S
b
, U
g
, U
n
, and
S
u,ref
from the computed values, as a function of equivalence ratio
The experimental and computed S
b
, U
g
, and S
u,ref
appear to be in good agreement. As
expected, U
g
and S
u,ref
that are measured using PIV, exhibit a larger scatter compared to S
b
. The
difference on a percentage basis of the experimental S
b
, U
g
, U
n
, and S
u,ref
from the corresponding
DNS results were computed. For each property and ϕ, a mean difference and the corresponding
standard deviation
over the entire range of stretch rates was calculated, and Fig. 30 depicts the
results as function of ϕ for both C
2
H
4
and n-C
7
H
16
flames. First, it is interesting to note the
consistency with which the model under-predicts or over-predicts the two different SEF
-15%
-10%
-5%
0%
5%
10%
15%
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Difference from simulations
ϕ
C
2
H
4
flames
Sb
Ug
Su,n
Suref
S
b
U
g
S
u,ref
U
n
-15%
-10%
-5%
0%
5%
10%
15%
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Difference from simulations
ϕ
n-C
7
H
16
flames
59
measured values (S
b
and U
g
), which were obtained by completely different approaches. Second,
the results show that direct measurements obtained in two completely different experimental
systems are in close agreement with those obtained from the respective DNS, with most cases
being within 4%. This is an important point as it demonstrates that within the experimental
uncertainty, the two approaches for measuring
o
S
u
are consistent with each other and that they
provide very similar information. This conclusion was made possible simply because the
directly measured properties were compared indirectly with each other through accurately
performed DNS, without complications introduced by uncertainties associated with
extrapolations. It is of interest to note also, that while U
n
appears to have a larger standard
deviation among all properties, being the difference of two much larger values, it exhibits on the
average very similar differences from the DNS results as all other properties.
4.3.2 Extrapolation uncertainties
The SEF DNS results in the range 1 cm ≤ R
f
≤ 2 cm were treated as “data,” an R
f
range for
which experimental data are typically obtained to avoid ignition and compression effects. Linear
[22] and non-linear [55] extrapolations together with density corrections were utilized to obtain
o
S
u
from the flame radius as a function of time “data”.
o
S
u
’s were also extracted from the U
n
values applying the method adopted by Varea et al. [76] in which the non-linear equation of
Kelley et al. [55] was used. The DNS-based extrapolation error, which is calculated as the
difference between the
o
S
u
value extracted from stretched DNS results employing extrapolations
and the
o
S
u
value that is known as it can be computed using the Premix code , is shown in Fig. 31
as function of ϕ for both C
2
H
4
and n-C
7
H
16
flames.
60
Figure 31. Deviation of DNS-based extrapolated
o
S
u
values from computed ones as function of
equivalence ratio for SEF’s using two different ranges of flame radii for extrapolation:
1 cm ≤ R
f
≤ 2 cm (left) and 1 cm ≤ R
f
≤ 6 cm (right). Error values represented by symbols: (×)
linear method for S
b
; (□) non-linear method for S
b
; and (Δ) non-linear method for U
n
.
It is seen that for C
2
H
4
flames, the extrapolation deviations when S
b
information is used are
considerably small except for near stoichiometric conditions where predictions from both
methods are at most 4% lower than the correct value. It is also of interest to note that for most
ϕ’s linear extrapolations reproduce closely the correct value of
, while the non-linear ones
result in lower values. This is expected as C
2
H
4
, N
2
, and O
2
have similar diffusivities so that Le
and differential diffusion effects are absent and the linear S
b
vs. K behavior is warranted (see
Chap. 3).
In the case of n-C
7
H
16
flames, non-linear extrapolations using S
b
data under predict the correct
value for ϕ = 0.7 by 5%, whereas for ϕ = 1.4 both linear and non-linear extrapolations over-
predict
by about 5%. Similar to C
2
H
4
flames, linear extrapolation reproduces very closely the
correct value for ϕ = 0.7 that is reasonable as for this Le > 1 mixture a near-linear S
b
vs. K
behavior is expected (see Chap. 3). It was found also that for ϕ = 0.7, S
b
decreases with K while
-6%
-4%
-2%
0%
2%
4%
6%
8%
10%
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Extrapolation error
ϕ
C
2
H
4
flames
1 cm ≤ R
f
≤ 2 cm
-4%
-3%
-2%
-1%
0%
1%
2%
3%
4%
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Extrapolation error
ϕ
C
2
H
4
flames
1 cm ≤ R
f
≤ 6 cm
-6%
-4%
-2%
0%
2%
4%
6%
8%
10%
12%
14%
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Extrapolation error
ϕ
n-C
7
H
16
flames
1 cm ≤ R
f
≤ 2 cm
-10%
-8%
-6%
-4%
-2%
0%
2%
4%
6%
8%
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Extrapolation error
ϕ
n-C
7
H
16
flames
1 cm ≤ R
f
≤ 6 cm
61
for ϕ = 1.4 it increases. For ϕ = 0.7, Le > 1 and as K increases the loss of heat from the reaction
zone cannot be balanced by gain of fuel resulting in the reduction of the overall reaction rate [5].
The behavior for ϕ = 1.4 cannot be explained based on a Le argument as Le 1 based on O
2
that
is the deficient reactant. On the other hand, considering the reactant differential diffusion given
that the diffusivity of O
2
is greater than n-C
7
H
16
, increasing K results in progressively more
stoichiometric ϕ within the flame zone that tends to increase the overall reaction rate (see Chap.
3).
For C
2
H
4
and n-C
7
H
16
flames, non-linear extrapolation of U
n
using the equation for unburned
(upstream) flame speed from Ref. [55] results in a consistent over prediction of
o
S
u
by more than
5%. U
n
is affected by thermal dilation and geometry as described in Chap. 3, and the
extrapolation formula does not account for these effects.
The effect of the date range was considered as well by increasing it by a factor of five. Using
DNS “data” in the range 1 cm ≤ R
f
≤ 6 cm to extrapolate, results in considerably improved
prediction of both
o
S
u
and
in majority of cases as shown in Fig. 31. However, for the ϕ = 0.7,
1.1 and 1.3 cases an increase in extrapolation error is noticed when the non-linear equation to
obtain
is used which is indicative of the fact that asymptotic equations are unable to capture
the flame dynamics. Thus, precaution has to be taken when using a large experimental chamber
to extend the range of experimental data. Furthermore, utilizing data at smaller radii to increase
data range may result in errors from ignition related effects and, the existing extrapolation
formulas may not be reliable at very high stretch rates.
62
Figure 32. Deviation of experiment-based extrapolated
o
S
u
values from computed ones as
function of equivalence ratio. Differences represented by symbols: (◊) non-linear method for
S
u,ref
from CFF’s; (×) linear method for S
b
; (□) non-linear method for S
b
; and (Δ) non-linear
method for U
n
from SEF’s.
The deviations of the
o
S
u
values obtained through extrapolations using experimental data from
the
o
S
u
values obtained through 1D planar computations were determined. The CFF extrapolated
values were corrected to 0.1 MPa for consistency. The results are shown in Fig. 32 as function
of ϕ for both C
2
H
4
and n-C
7
H
16
flames. The deviations for the U
n
extrapolated values are 5% or
-15%
-10%
-5%
0%
5%
10%
15%
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Extrapolation error
ϕ
C
2
H
4
flames
-15%
-10%
-5%
0%
5%
10%
15%
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Extrapolation error
ϕ
n-C
7
H
16
flames
63
greater for most cases. In the case of C
2
H
4
flames, the deviations are at most 5% when CFF data
are used for ϕ = 0.7 and 1.4, for which flames are weaker and slower. For n-C
7
H
16
flames, the
deviation for ϕ = 0.7 is nearly 15% for
.
A straightforward explanation of the results of Fig. 32 cannot be derived readily.
Experimental measurements have inherent uncertainties, on which however one needs to
superimpose uncertainties associated with extrapolation formulas to determine
o
S
u
that may or
may not be able to capture the stretch effects under all conditions. It is noted however that the
deviations from computed values of
o
S
u
are substantially different compared to those reported in
Fig. 30, in which direct measurements and simulations were compared for SEF’s for which
existing extrapolation equations were used. Nevertheless, the deviation of the values obtained by
DNS-assisted extrapolation of CFF data is consistent with the corresponding values in Fig. 30.
For SEF’s, the previously mentioned inconsistencies will be augmented further if radiation
induced flow (see Chap. 3) is neglected for flame conditions in which the effect is significant.
Additionally, a major issue could be raised regarding the validity of the density correction
approach that is based on the assumption of a single density value for the burned gases. It has
been shown in Chap. 3 that due to radiation there is a continuous variation of density throughout
the burned gas region.
4.4 Concluding remarks
This is the first study aiming to consolidate and compare quantitatively data obtained in
spherically expanding and counterflow flames using direct measurements as well as direct
numerical simulations of ethylene and n-heptane flames. In both configurations, particle image
velocimetry was used to determine the velocity fields and derive thus directly the physical
quantities of relevance to the determination of laminar flame speeds. The simulations included
the use of detailed description of chemical kinetics and molecular transport, and accurate time
stepping in modeling spherically expanding flames
Considering only directly measured or directly computed quantities, uncertainties associated
with extrapolations and/or density corrections for the case of spherically expanding flames are
64
eliminated. The consistency between the two configurations was confirmed as in both cases the
data were predicted closely by the numerical simulations within their inherent uncertainty.
However, upon introducing linear and non-linear extrapolations as well as density corrections,
the uncertainty increases. It was found also that under certain conditions non-linear
extrapolations for spherically expanding flames are not reproducing known values at zero
stretch, failing to capture the response of the flame to stretch. Typically, such formulas are
derived based on simplified assumptions and while elegant and insightful they may not be
appropriate for deriving experimental data of high fidelity against which kinetic rate parameters
will be validated.
65
Chapter 5 – Determination of laminar flame speeds during the
compression stage of constant volume spherically expanding flame
propagation
As discussed in Chap. 1, measurements made during the compression stage of SEF
propagation in a constant volume perfectly spherical chamber, appears to be the only feasible
approach to measure
o
S
u
s at engine relevant conditions that constitute unburned gas
thermodynamic states of simultaneous high pressure, P, and temperature, T
u
. P, assumed to be
constant throughout the chamber, constitutes the sole experimental measurable for these
experiments. Flame speed, S
u
, can then be derived using Eqn. 3 if radius of the flame, R
f
, as a
function of P, [R
f
, P], is known, as detailed in the Chap. 1. Equation 3 is presented once again for
the sake of completeness:
33
2
3
wf
f
u
fu
RR
dR
dP
S
dt R P dt
(3)
In Eqn. 3, γ
u
is the heat capacity ratio of the unburned gas, R
w
the chamber radius.
TORC, being a transient code, requires thousands of flame computations, thus making the
simulation an expensive procedure. Thus utilizing simplified thermodynamics-based models, as
was done in previous studies [26][28][30] appears to be the prudent choice to make to obtain [R
f
,
P]. These thermodynamics-based models utilize many assumptions such as adiabaticity of the
burned gas, infinitely thin flame, equilibrated burned gas, etc. In this chapter, detailed numerical
simulations, DNS, of constant volume SEFs are performed to evaluate inaccuracies/uncertainties
that could result from the aforementioned assumptions as well as potential stretch effects, when
extracting
o
S
u
from experimental pressure measurements. Furthermore, to reduce uncertainties
stemming from the aforementioned factors, improved experimental design strategies along with
new diagnostic approaches are proposed.
66
5.1 Modeling approach
o
u
S was computed using the PREMIX code [100][101] and SEF propagation in a constant
volume domain was simulated using TORC. Details of TORC relating to assumptions employed
and boundary conditions imposed can be found in Chapter 2.
In TORC, an adaptive grid algorithm is utilized as computational efficiency is severely
compromised if a static uniform mesh is used for a moving flame problem, as detailed in
Chap. 2. The constant volume problem is especially challenging as the flame thickness
decreases during the compression stage, requiring high spatial resolution at the location of the
flame at each instant. This prescribed the finest sub-grid to have a resolution that is sufficient for
the thinnest flame (final stages of compression) and, width sufficient to accommodate the
thickest flame (constant pressure region). The flame thickness is resolved using at least 50
points at all time and this condition ensured grid independent solutions.
Both codes are integrated with the CHEMKIN [103] and Sandia transport subroutine libraries
[105] and is also capable of performing calculations involving radiation heat loss in the optically
thin limit, OTL.
The PREMIX computed
o
u
S value constitutes the “known” answer of the speed of a freely
propagating flame based on the kinetic and transport models used in DNS. These “baseline”
values can be used then to quantify non-ideal effects like stretch, heat loss, etc., present in flames
by analyzing deviations from the known
o
u
S value.
A Helium diluted (H
2
:CO = 20:80) syngas mixture, which will be referred to as Mixture 1, of
equivalence ratio, = 0.8, initial temperature at the start of the experiment, T
u
,
o
= 298 K, and
adiabatic flame temperature, T
ad =
1800 K was used in this study. Note that T
u
, the unburned gas
temperature changes continuously during the compression stage. The composition of Mixture 1
is as follows: X
H2
= 0.0257, X
CO
= 0.1028, X
O2
= 0.0803 and X
HE
= 0.7912 where X represents the
mole fraction. All simulations were performed using the kinetic model of Davis and co-workers
[132].
67
5.2 Results and discussion
DNS results obtained using TORC were utilized to validate [R
f
, P] results obtained from a
thermodynamics-based model that was developed by Tailai Ye at USC. Details of the
thermodynamics-based model along with thermodynamic conditions of the combustible mixture
used and comparison plots can be found in Ref. [133]. It was shown that for adiabatic
conditions, [R
f
, P] results obtained from both codes were similar.
Figure. 33. (a) and (b). Variation of R
f
and dP/dt with P for constant volume SEF computations
performed using TORC for Case A employing the ADB assumption (─); with conductive heat
loss (---); and with OTL-based radiation heat loss (-
.
-). (c) and (d) Percentage difference of R
f
and dP/dt computed for the case with conductive heat loss (---); and OTL-based radiation heat
loss (-
.
-) from that of the ADB case, obtained using results shown in (a) and (b).
In order to evaluate the validity of the adiabatic, ADB, assumption that was invoked in most
previous constant volume SEF studies, computations were performed for Case A using TORC
including OTL-based radiation heat loss and conduction to the wall; Case A corresponds to
68
Mixture 1 at P
o
= 6 atm and T
u,o
= 298 K in a domain of size R
w
= 10.16 cm
4
. The heat
conduction was modeled using an isothermal wall boundary condition, T
wall
= T
u,o
, which is an
accurate and conservative estimate given the large heat capacity of the stainless steel vessel.
Figures 33a and 33b depict respectively the variation of R
f
and dP/dt with P for Case A. P,
the sole experimental observable, is chosen as the independent variable as it uniquely identifies
the thermodynamic condition of the unburned gas, excluding the thermal boundary layer at the
wall. The results obtained with conductive heat loss overlaps with those of the ADB case. Also,
the effect of radiation heat loss has a more profound effect on dP/dt compared to R
f
. Figures 33c
and 33d illustrate the extent of each heat loss effect by showing the percentage difference
reflected in R
f
and dP/dt when compared to the ADB case. The difference in R
f
is less than 1.5%
in the case of the OTL-based radiative loss, which is consistent with the estimates of Metghalchi
and co-workers [30][82]. However, the radiation heat loss can result in up to 13% difference in
dP/dt, which has been overlooked in previous studies. Also note that the effect of conduction
heat loss on R
f
and dP/dt is less than 0.5% even in the presence of the highly conductive helium
in the mixture, and thus can be considered as minor.
Figure. 34. Variation of S
u
with P computed using SEF computations performed using TORC
with the ADB (---) and OTL (-
.
-) assumptions and Eqn. 3 for Case A. The solid line (─)
corresponds to S
u
calculated using Eqn. 3 with dP/dt from the OTL-based TORC simulation and
[R
f
, P] from the ADB TORC simulation.
4
The choice of R
w
= 10.16 cm was made as it is the radius of the spherical combustion chamber at USC. Also, a
chamber at least this big was chosen as it was believed that the flames have to be large to be stretch-free.
69
In order to evaluate the effect of radiation heat loss on the flame speed, S
u
was calculated
using TORC with the ADB and OTL assumptions and Eqn.3 using the DNS results as input. It is
evident from Fig. 34, that the S
u
as computed by Eqn. 3 and using the dP/dt and [R
f
, P] variation
either from the ADB or OTL computations, is nearly indistinguishable which is consistent with
the well-established result that radiation affects flame propagation only for near-limit mixtures
[68]. However, in all previous studies, the [R
f
, P] variation obtained using a thermodynamic
model employing the ADB assumption was utilized to extract S
u
from the experimental pressure
measurements, which are inherently affected by radiation heat loss. To assess the consequence
of employing the ADB assumption, dP/dt from the OTL TORC simulation result is treated as
“experimental data” and S
u
is then calculated using [R
f
, P] from the ADB TORC simulation
result for the same conditions and the result is shown in Fig. 34 as well. It is of interest to
observe that a difference of 1.5% in [R
f
, P], as evident from Fig. 33c, can result in a difference of
up to 15% in S
u
values, calculated using the same dP/dt values. Evaluating the individual terms
of Eqn. 3 reveal that the factor that multiplies dP/dt is the most sensitive to a perturbation of [R
f
,
P] and causes the notable difference in S
u
.
It is important to note the high sensitivity of the S
u
, which is derived using Eqn. 3 and
utilizing as input experimental dP/dt measurements and a theoretically modeled [R
f
, P], to the
[R
f
, P]. Inaccuracies in the theoretical model that amounts to a variation of 1% in [R
f
, P] can
amount to greater than 10% error in S
u
. Thus, one needs to be cautious while employing
simplifying assumptions in the thermodynamic-based models and make sure that the error thus
introduced in [R
f
, P] is negligible.
To assess the influence of size of the combustion chamber on the magnitude of radiation heat
loss effect, constant volume SEF simulations were performed for Mixture 1 at P
o
= 6 atm and
T
u,o
= 298 K for three domain sizes, R
w
= 3, 5 and 10.16 cm. The percentage difference of dP/dt
results from simulations including radiation loss from that of adiabatic ones are shown as a
function of P in Fig. 35. Results indicate that the effect of radiation heat loss on dP/dt is
attenuated for smaller chamber sizes. This result is consistent with the following simple
analysis. Ratio of OTL-based radiation heat loss to heat release rate of flame ~ (volume of
burned gas ball/area of flame) ~ R
f
. For similar thermodynamic conditions of the unburned
70
mixture, the flame in the larger chamber will have a larger radius and hence suffer an increased
effect in pressure rise due to increased heat loss from the burned gas.
Figure 35. Percentage difference reflected in dP/dt for simulations with OTL radiation.
Another interesting conclusion from Fig. 34 is that there is need for performing simultaneous
measurements of P and R
f
, which will allow for the accurate determination of S
u
, circumventing
thus the exacerbating effect of radiation heat loss. This is analogous to what has been proposed
in Chap. 3 for the case of constant pressure SEF experiments.
The effect of stretch on S
u
was assessed similarly to Chen et al. [66]. The presence of stretch
can suppress instabilities, which is desirable, but will affect S
u
, which is undesirable as
corrections will be needed to derive
o
u
S . Simulations were performed for Mixture 1 at
P
o
= 3 atm and T
u,o
= 298 K for three chamber sizes of R
w
= 3, 5, and 10.16 cm. The initial
thermodynamic condition was chosen such that the mixture demonstrated substantial non-
equidiffusion effects in the case of the constant pressure SEF simulation.
71
Figure. 36. Variation of (a) Ka and (b) S
u
as a function of P/P
o
for constant volume SEF
computations performed using TORC for Mixture 1 at T
u,o =
298 K and
P
o
= 3 atm for three
chamber sizes, R
w
= 3 cm (-
.
-), R
w
= 5 cm (
...
), and R
w
= 10.16 cm (---). The solid line (─) in
(b) represents the stretch free
o
u
S values computed for unburned gas conditions extracted from
the constant volume SEF results.
Figures 36a and 36b depict the change of Karlovitz number Ka ≡ K/(α/S
u
2
) and S
u
respectively during the course of flame propagation for the three chamber sizes, where α is the
thermal diffusivity of the mixture at unburned conditions.
o
u
S s computed at the same unburned
gas conditions are also shown in Fig. 36b to discern the extent to which S
u
is affected by stretch.
Results indicate that for values of (P/P
o
) greater than 2.5, Ka reduces to very small values and, S
u
differs from
o
u
S
by less than 1.5% even for the smaller chamber with R
w
= 3 cm.
72
To elucidate the reason why stretch decreases rapidly with increasing pressure, the variations
of dR
f
/dt
with R
f
obtained from constant volume (R
w
= 3 cm) simulations and constant pressure
simulations are shown in Fig. 37; note that dR
f
/dt ≠ S
b
because the burned gas is not stationary
during the compression stage. dR
f
/dt, which determines the magnitude of the stretch rate for a
fixed R
f
, decreases rapidly in the constant volume case with the pressure rise when compared to
the constant pressure case. Note that the decrease of dR
f
/dt happens despite the increase in
o
u
S
(or S
b
), which is shown in Fig 36b. The compression-induced inward flow [66] is the cause for
this significant reduction in dR
f
/dt. This results in near stretch-free flames for high values of
(P/P
o
), which fortuitously corresponds to the range where experimental pressure measurements
are of high fidelity due to the large values of dP/dt. It is also of interest to note that an additional
contribution of (1/ )(d /dt) to stretch rate exists as a result of temporal variation of pressure
[134][135]. However, this contribution is negligible, as the deviation of S
u
from
o
u
S
seems to be
insignificant as evident from Fig. 36b.
Figure. 37. Variation of the computed dR
f
/dt with R
f
using TORC for Mixture 1 at T
u,o =
298 K
and
P
o
= 3 atm; dashed line (---): constant pressure; solid line (─) constant volume.
73
5.3 Concluding remarks
Numerical simulations were utilized to assess uncertainties that could be imparted in flame
speeds derived from pressure measurements made during the compression stage of constant
volume spherically expanding flames. Simulations were first carried out to assess the validity of
the adiabatic assumption used in all previous thermodynamic models to extract the flame speed
from the experimental pressure trace. It was found that neglecting radiation heat loss when
interpreting experimental data could lead to uncertainty as large as 15%. It was also shown that
measurements made when pressure has risen substantially (~ 2.5 times the initial value),
correspond to flames that are stretch free, hence requiring no stretch corrections.
Simulation results indicate that reducing the chamber radius by half would decrease the
effect of radiation heat loss on the derived flame speed by a similar factor. Since, it was also
shown that the stretch rate become negligible during the later stages of compression, a small
combustion chamber should be the preferred choice of future experiment designs.
It was also demonstrated using simulation results that by simultaneously measuring temporal
variation of pressure and radius of the flame, the error arising from radiation heat loss can be
circumvented. Hence, implementing a diagnostic to measure the radius of the flame without
compromising the sphericity of the chamber could also be a possible future direction of research.
74
Chapter 6 – Thermal and Ludwig-Soret diffusion effects on near-
boundary ignition behavior of reacting mixtures
As mentioned in Chap. 1, there has been evidence in literature that under certain conditions
legacy reactor experiments may exhibit inhomogeneities that could potentially reduce the
scientific value of the reported data. Additionally, the initiation of knock in spark ignition
engines has been observed to occur close to the cylinder wall. In this study, detailed one-
dimensional simulations were carried out in order to provide additional insight into the
aforementioned observations. The main focus of the present investigation is on the effects of a
colder wall relatively to the core of the reacting mixture, and the attendant development of
thermal boundary layers. Ignition behavior of fuels that exhibit distinct negative temperature
coefficient (NTC) behavior, and mixtures that can result in species stratification of light and
heavy species due to Ludwig-Soret (L-S) diffusion was investigated.
6.1 Modeling approach
A 1-D Cartesian domain, 8.70 cm long, bounded by two walls is chosen for the current study.
Assuming symmetry about the center, only half the domain (4.35 cm) is simulated. The transient
one-dimensional reacting flow code (TORC) is used to perform high fidelity, fully implicit time
integration of the spatially discretized conservation equations for mass, species’ mass fractions
and energy (see Chap. 2) . A non-uniform grid is employed such that the BL was resolved with
the finest mesh of grid spacing 0.7 – 1.4 μm, to ensure grid independent solutions. TORC is a
low Mach number code that can capture pressure change in time but not in space; compressible
gas dynamic effects are not accounted for. The aim of the current study is to investigate the
development of local exothermic centers and not to examine what type of a reacting front it
would evolve into, which would be a topic of a future study.
The initial condition imposed is of uniform temperature, T
o
, species concentrations, and
pressure, P
o
. Velocity of the gas is set to zero everywhere. The boundary conditions imposed
are:
= 0,
= 0,
= 0 (BC1)
,
= 0,
= 0 (BC2)
75
where T represents the temperature, x the spatial coordinate, and u the gas velocity, and V
k
the
diffusion velocity of species k. The center of the domain is at x = 0 and the wall boundary is at
x = x
w
= 4.35 cm.
6.2 Parameter space
n-C
7
H
16
/air mixtures, which is known to exhibit strong NTC behavior, is chosen to study the
effect of NTC on ignition of the mixture near a “cold” wall that results in a thermal BL. Table 4
depicts the conditions examined for n-C
7
H
16
/air mixtures that span a range of T
o
’s, equivalence
ratios (ϕ), P
o
’s, and T
w
’s. Thermodynamic conditions chosen are inspired from the work of
Ciezki and Adomeit [136]. The kinetic model utilized for the simulation of n-C
7
H
16
/air mixtures
is the recently published San Diego Mech [137], which includes low temperature chemistry,
LTC, and has been validated against the data from Ref. [136].
Case ϕ
Initial
pressure, P
o
(atm)
Initial temperature, T
o
(K)
Wall temperature, T
w
(K)
Location
of hot
ignition
A 0.73 13.5 950 950 Core
B 0.73 13.5 950 500 BL
C: a,b 0.73 13.5 900, 1000 500 BL
D: a-c 0.73 13.5 850, 1050, 1100 500 Core
E: a-d 0.73 13.5 950 350, 400, 600, 700 BL
F 1.0 13.5 910 500 BL
G 2.0 13.5 950 500 BL
H 0.73 42.0 1000 500 BL
Table 4. Thermodynamic conditions along with the wall boundary temperature, T
w
, for the
simulations conducted for n-C
7
H
16
/air mixtures. ‘Location of hot ignition’ column denotes
whether ignition happened first in the boundary layer (BL) or homogeneously in the core of the
gas excluding the boundary layer (Core).
76
To investigate the importance of L-S effect in a reacting BL, a highly inert-diluted by Argon,
stoichiometric H
2
/O
2
/Ar mixture with H
2
:O
2
:Ar = 4:2:94 molar ratios, at T
o
= 925 K and
P
o
= 3.5 atm is chosen [138]. Additional simulations are performed for case B in Table 4 to
demonstrate that L-S effect is indeed important for heavy hydrocarbons as pointed out by Rosner
et al. [139].
6.3 Results and discussion
Since it is the first time TORC is being used to study ignition phenomena, 1-D simulations
that did not include boundary layer heat loss were first performed, and the results thus obtained
were compared to the results from the 0-D SENKIN code [140] for similar thermodynamic
conditions, in Fig. 38. The excellent agreement between the results from two codes
demonstrates the ability of TORC to capture ignition accurately.
Figure 38. Comparison of results obtained from the 1-D code, TORC, (symbols) against
simulations performed using 0-D code, SENKIN (lines) for an equivalence ratio = 0.73, n-
C
7
H
16
/air mixture at an initial pressure of 13.5 atm and initial temperature of 950 K. For TORC
simulations the wall boundary temperature was set equal to 950 K. The kinetic model used for
both simulations was the San Diego mech. Green and red, symbols and curves, represent Y
HO2
and P respectively.
77
Figure 39 depicts of the rate of change of pressure, dP/dt, as a function of time, t, for a
ϕ = 0.73, n-C
7
H
16
/air mixture with T
o
= 950 K and P
o
= 13.5 atm for two different wall boundary
conditions, T
w
= 950 K (Case A) and T
w
= 500 K (Case B). For Case A there is no wall heat loss
as the mixture and the boundary are initially at the same temperature, and hence no BL develops
until the temperature of the gas rises significantly due to heat release. This is in contrast to Case
B for which the boundary is at a significantly lower temperature resulting in formation of a BL.
The presence of heat loss is illustrated by the dP/dt values in Fig. 39, which are positive for Case
A and negative for case B when t < 0.7 ms.
Figure 39. dP/dt as a function of t for the ϕ = 0.73, n-C
7
H
16
/air mixture with T
o
= 950 K,
P
o
= 13.5 atm. Solid line ( ─) represents Case A with T
w
= 950 K, and dashed line (-
.
-) Case B
with T
w
= 500 K.
Figure 40. Y
OH
as a function of x and T at different instants of time in the temporal vicinity of
t = 1 ms.
78
The first interesting observation in Fig. 39 is the “bump” in dP/dt that occurs around
t = 1 ms. To explain this behavior, the OH mass fraction, Y
OH
, is plotted as a function of x as
well as T, at different instants of time in Fig. 40. It can be seen that OH radicals are produced
close to the wall (x
w
= 4.35 cm) corresponding to the location where T ~ 850 K. The peak Y
OH
first increases and then decreases with t. The temperature at which this happens and the
evolution of peak Y
OH
, are representative of the first stage (cold) ignition that happens at these
thermodynamic conditions [9][137]. The spatially localized heat release associated with this first
stage ignition causes the non-monotonic variation of dP/dt. Also, note that at t = 5.6 ms, the
peak Y
OH
has migrated to a location further from the wall boundary which corresponds to a
region of higher T.
Figure 41. Variations of T and Y
OH
as functions of t. Solid line represents the value at center
(x = 0) and the dashed line the maximum value in the domain respectively.
To better demonstrate the increased chemical activity in the BL, values of T and Y
OH
at the
center (x = 0) are compared against their respective maximum values in the entire spatial domain,
as a function of t, for Case B in Fig. 41. The “cold” first stage heat release does not result in a
noticeable increase in local temperature beyond the core temperature. This is reasonable if we
take into account the fact that the magnitude of heat release during this stage is not substantial
and that the presence of significant conductive loss resulting from the steep gradient in T near the
wall distributes the heat in the boundary layer. However, at t > 5 ms, the maximum values of T
79
and Y
OH
start deviating significantly from the corresponding values at the center or the more or
less uniform core.
Figure 42. Time evolution of the spatial profiles of T, Y
H
, and Y
CH2O
capturing ignition in the
boundary layer for Case B.
In order to elucidate the physics leading to this deviation, Fig. 42 depicts the temporal
evolution of T, Y
H
, and Y
CH2O
as a function of space from t = t
i
= 6.78 ms. It is evident from the
thermal and H radical runaway that is observed in Fig. 5 that “hot” ignition has taken place in the
BL. The rapid consumption of formaldehyde (CH
2
O), a key LTC intermediate formed from the
decomposition of the carbonyl hydroperoxide [137], demonstrates the shift in regime from low to
80
high temperature chemistry. The Y
H
profile at end of ignition (t
i
+ 5.5 μs) resembles that of two
flames (deflagrations) propagating away from the region where ignition occurred; note that the
time duration for the ignition process depicted in Fig. 42 and the attending heat release is 5.5 μs.
A simple calculation of the distance a sound wave would travel through air at 1050 K, which is
the average temperature of the surrounding gas, in 5.5 μs, yields 3.5 mm. These details indicate
that this particular ignition event could result in development of compressible gas dynamic
features and warrants the use of a fully compressible code to capture whether the ignition kernel
will develop into a deflagration or detonation.
The effect of T
o
on whether ignition takes place first at the boundary layer or the core, was
addressed by performing simulations using similar conditions of case B but with different T
o
’s
(Cases Ca, Cb, Da-c). For T
o
= 900 K (Ca) and T
o
= 1000 K (Cb), similar to case B, ignition
initiates in the BL. However, for T
o
= 850 K and T
o
≥ 1050 K, ignition initiates homogeneously
in the core region. Thus, BL ignition only happens for a window of initial temperatures as
illustrated by the boxed peninsula in the ignition delay-temperature diagram in Fig. 7 (Chap.1).
To evaluate the effect heat loss has on the evolution of BL ignition kernel, computations
were performed again with conditions similar to Case B but with different T
w
’s (Case E: a-d).
For 350 K ≤ T
w
≤ 700 K ignition initiates in the BL. The effect of heat loss on the runaway
process was also evaluated and the results presented in Fig. 43. For low T
w
s, the magnitude of
peak Y
OH
radical concentrations were reduced by a small amount and the ignition retarded by a
short duration. Overall, low T
w
s were observed to affect the ignition behavior minimally.
81
Figure 43. Maximum OH mass fraction Y
OH
in the domain as a function of t for different T
w
’s
(Cases E: a-d in the main manuscript) for an equivalence ratio = 0.73, n-C
7
H
16
/air mixture at an
initial pressure of 13.5 atm and initial temperature of 950 K.
Simulations performed for ϕ = 1.0 and 2.0 (Cases F and G) and at P
o
= 42 atm (Case H), also
showed that ignition initiated in the BL. It is worthwhile to mention that even though
ign
for
P
o
= 42 atm is an order of magnitude less compared to Case B, ignition still initiates in the BL.
To analyze the influence of L-S diffusion in the BL, Fig. 44 depicts the H
2
and Ar mass
fractions at t = 2.3 ms from the simulation of the H
2
/O
2
/Ar mixture described in Section 3.
Ludwig-Soret diffusion is turned on for this simulation and T
w
is fixed at 500 K throughout the
simulation. The results reveal that species concentration stratification is established within the
thermal BL due to the L-S diffusion driven by the temperature gradient. H
2
diffuses away from
the cold wall towards the hotter core while Ar migrates in the opposite direction, resulting a less
diluted, higher H
2
content mixture, where the temperature starts deviating (x ~ 4.20 cm) from
that of the core.
82
Figure 44. Y
H2
and Y
Ar
as a function of x at t = 2.3 ms for results obtained for a simulation with
Ludwig-Soret effect turned on; H
2
:O
2
:Ar = 4:2:94 mixture (molar ratios) at T
o
= 925 K,
P
o
= 3.5 atm, and T
w
= 500 K. Green and red lines represent Y
H2
and Y
Ar
respectively.
To analyze the effect that the transient species’ stratification has on the ignition behavior,
Fig. 45 depicts the temporal evolution of T, Y
H2
, Y
H
and Y
O2
. It is important to clarify at this point
that
ign
is greatly extended due to the decrease in pressure and temperature of the gas throughout
the domain due to heat loss from the system. It is seen that the heat release, indicated by the
temperature rise, proceeds at a faster rate locally where the boundary layer meets the core
(x ~ 2.8 cm). Also, note the localized increase in H radical concentration due to chain branching,
and the attendant decrease in H
2
and O
2
mass fractions due to increased consumption rates. At
this location of increased chemical activity, temperature is initially only a few Kelvin lower than
that at the core, and is where the synergistic effect of high temperature and favorable species’
concentrations is maximized. As the sensitivity of
ign
to temperature is much greater than that to
species concentration for the thermodynamic conditions considered herein, this location tends to
be closer to the high temperature region in comparison to the most favorable species
concentration. In contrast to the n-C
7
H
16
/air ignition that initiated in the BL case as depicted in
Fig. 42, the time scale of the localized thermal and radical runaway caused by the L-S diffusion
appear to be of the same order compared to that of the core. This is evident in Fig. 45, where the
T and species concentrations in the core also change substantially with time. Again, it has to be
taken into consideration that by using a low Mach number code, pressure is forced to equilibrate
instantaneously thus preventing local energy build up. The evolution of this exothermic region
could potentially be more explosive if compressible effects are taken into consideration.
83
Figure 45. Temporal evolution of T, Y
H2
, Y
H
and Y
O2
for results obtained for a simulation with
Ludwig-Soret effect turned on; H
2
:O
2
:Ar = 4:2:94 mixture (molar ratios) at T
o
= 925 K,
P
o
= 3.5 atm, and T
w
= 500 K. Symbols represent T and Y
H
and lines represent Y
H2
and Y
O2
for
(a) and (b) respectively.
To clarify that this local increase in reactivity is not a result of numerical errors, a simulation
with similar conditions as above but with the L-S diffusion disabled, was performed and results
are presented in Fig. 46. It was observed that ignition initiates homogenously in the core and
thus shows that indeed L-S diffusion can cause increased heat release rates in the cold thermal
boundary layer close to the wall.
84
Figure 46. Temporal evolution of temperature and hydrogen mass fraction, Y
H2
, for results
obtained from a TORC simulation with Ludwig-Soret effect disabled; H
2
:O
2
:Ar = 4:2:94 mixture
(molar ratios) at initial temperature, T
o
= 925 K, initial pressure, P
o
= 3.5 atm, and wall
temperature, T
w
= 500 K. Symbols represent T and lines represent Y
H
respectively.
Similar ignition behavior was obtained for T
w
= 300 K and 700 K for same mixture
conditions as above showing that thermal losses do not play a major role in the development of
the local exothermic center. However, when T
o
was raised to 1025 K, ignition took place
homogeneously in the core. At T
o
= 925 K,
ign
is two orders of magnitude greater than that at
T
o
= 1025 K. Thus, when the time scale of ignition becomes relatively short the effect of L-S
diffusion becomes negligible.
Rosner et al. [139] have pointed out that L-S effect becomes increasingly important for heavy
species. To assess the importance of the L-S effect for ignition of heavy hydrocarbon and air
mixtures close to the wall, Case B (n-C
7
H
16
/air) is simulated again with chemical source terms
set to zero. Figure 47 depicts the time evolution of n-C
7
H
16
and N
2
in the thermal boundary
layer. n-C
7
H
16
is the relatively heavy species and is seen to migrate towards the cold boundary,
and N
2
vice versa. Simulations that include reactivity showed that the L-S effect has a minor
85
effect on the ignition behavior, and that ignition initiates similarly to the manner shown in Figs.
41 and 42.
Figure 47. Temporal evolution of Y
n-C7H16
and Y
N2
for results obtained for a simulation with
Ludwig-Soret effect enabled and conditions of Case B. Symbols represent Y
n-C7H16
and lines
represent Y
N2
respectively.
6.4 Concluding remarks
The ignition of initially uniform quiescent fuel/air mixtures in the presence of a thermal
boundary layer induced by a relatively cold wall was numerically investigated. The focus of the
study was on the spatial development of reactivity for mixtures that exhibited negative
temperature coefficient behavior and the stratification of the reactant concentrations due to
Ludwig-Soret diffusion that is driven by the steep temperature gradients in the boundary layer.
Simulations were performed for n-C
7
H
16
/air and H
2
/O
2
/Ar mixtures. It was demonstrated that
both the negative temperature coefficient behavior and Ludwig-Soret diffusion can potentially
lead to the formation of local exothermic centers in the vicinity of the cold wall. In the presence
of negative temperature coefficient behavior, the local exothermic centers were found to develop
within the boundary layer for a wide range of ignition time scales. On the other hand the
analogous Ludwig-Soret diffusion effect seems to diminish for mixtures for short ignition delay
times. The results were explained based on analyses of the computed reacting layer structures
and following the effects of thermal and reactant concentration stratifications.
86
The results of the present study are expected to be of direct relevance to homogeneous
reactor experiments and spark ignition engine operation, in view of the wall effects on the
ignition propensity of the reacting mixtures. In the case of reactor experiments, the wall effects
could reduce the value of the reported data under a range of thermodynamic conditions. In the
case of the spark ignition engine, the wall effects could play a role in its knocking propensity. In
both cases evidence derived by assuming only the behavior of the core gas may be inconclusive
or even incorrect if boundary layer effects are not accounted properly.
87
Chapter 7 – Summary and future directions of research
The central theme of this dissertation was to utilize detailed numerical simulations to
investigate and elucidate complex physical processes that occur in low-dimensional legacy
experiments which are used to obtain archival data that will subsequently be used for chemical
kinetic model development and validation. A deeper understanding of the physics revealed that
neglecting certain phenomena like for example heat loss and fluid dynamic effects, while
interpreting experimental data can potentially lead to substantial errors in the derived combustion
properties.
In order to perform specific studies, the Transient One-dimensional Reacting-flow Code,
TORC, was developed to integrate in time the conservation equations of mass, species and
energy. This low Mach number code utilizes fully implicit time stepping along with an adaptive
grid algorithm to accurately simulate one-dimensional transient flame propagation.
TORC was used to study the molecular diffusion and radiation effects in constant pressure
spherically expanding flames, which experimentally corresponds to measurements made during
initial stages of flame propagation in a constant volume vessel. A parametric study performed by
varying the diffusivity of fuel revealed that stratification of fuel and oxygen can occur in the
flame, resulting in the modification of the local equivalence ratio and consequently the burning
rate for a freely propagating stretch-free flame. Moreover, when the flame is subjected to
stretch, the lighter reactant diffuses into the flame in preference to the heavier species. This
“differential diffusion” effect was shown to be pronounced for fuel-rich heavy hydrocarbon/air
mixtures. Thus it was demonstrated that while the Lewis number governs the flame dynamics
for fuel-lean heavy hydrocarbon/air flames, differential diffusion controls flame dynamics of
fuel-rich flames of the same. Additionally, it was shown that using asymptotically derived
extrapolation equations that are derived based on many assumptions (for example - Lewis
number being the sole parameter that controls flame dynamics) can result in substantial errors in
the derived stretch-free laminar flame speeds. Simulations that included radiation heat loss
indicated that inward fluid motion is setup in the burned gas as a result of its density change. A
consequence of this fluid flow is that utilizing the traditional approach of measuring the rate of
expansion of the flame to obtain the burned flame speed can result in notable errors especially
for slow flames. Furthermore, it was demonstrated that the flame displacement speed relative to
the unburned gas, which can be determined by measuring simultaneously the rate of flame
88
expansion and unburned gas velocity, is unaffected by radiation heat loss and hence can be
considered as a preferred observable.
For the first time, a combined experimental and numerical study of spherically expanding
and counter-flow flames under constant pressure conditions was performed to demonstrate the
consistency of experimental data from both configurations. Specifically, consistency was
established by comparing directly measured data and detailed simulations of the particular
experiment, thus avoiding extrapolation procedures. Furthermore, it was shown that using
extrapolation equations derived based on simplifying assumptions can result in incorrect laminar
speeds thus causing differences between the flame speeds derived from the two configurations.
Spherically expanding flame propagation during the compression stage in a perfectly
spherical constant volume vessel was investigated with emphasis on heat loss and stretch effects.
Results indicated that the assumption of adiabaticity of the burned gas which was invoked in
most previous studies to derive flame speeds from pressure measurements can lead to substantial
errors in the flame speed. Additionally, it was illustrated that by measuring simultaneously the
pressure and radius of the flame, the uncertainties imparted due to heat loss can be circumvented.
Results of computations also revealed that the Karlovitz number decreased substantially to
negligible values during the compression stage owing to the compression induced inward flow,
thus resulting in near stretch-free flames.
TORC was also used to investigate thermal boundary layer effects on ignition of a
combustible mixture adjacent to a cold wall; focus was on mixtures that exhibited the negative
temperature coefficient behavior and, mixtures with fuel and oxidizer having contrasting
molecular weights thus exhibiting Ludwig-Soret diffusion. Simulations revealed that exothermic
centers could preferentially develop in the thermal boundary layer as a result of increased
reactivity at lower temperatures for mixtures with negative temperature coefficient behavior as
well as reactant stratification due to Ludwig-Soret diffusion. This result could have implications
in experimental data obtained from legacy reactor experiments like shock tubes, rapid
compression machines, etc and can potentially be central to initiation of ignition in unburned gas
that leads to knock in spark ignition engines.
Having spent the last six years thinking about above mentioned topics, the following are my
comments/opinions regarding future directions of research. The spherical expanding flame
technique is the ideal configuration for flame speed measurements at high pressures. Performing
89
extrapolations to obtain stretch-free values is always an uncertainty imparting procedure and is
required for constant pressure spherically expanding flames. However, near stretch-free flames
are obtained during the compression stage of flame propagation in a spherical vessel, but are
subjected to radiation heat loss induced uncertainty if pressure constitutes the only measurement.
Since accurately accounting for radiation heat loss is a challenging and uncertainty prone task,
the best alternative appears to be measuring the radius of the flame along with pressure to
circumvent this difficulty. Although an experimentally formidable task, this in my opinion is a
path worth treading when considering the following gains. The experiment can also be used as a
slow compression machine to study kinetics of the unburned gas evolution at conditions of high
pressure and low temperature. This device unlike the shock tube and rapid compression machine
is devoid of complex fluid phenomena like vortex shedding and shock-boundary layer interaction
that result in inhomogeneities which can potentially compromise the low-dimensionality and
accuracy of the experiments. Additionally, absorption measurements can potentially be used to
measure the radius of the burned gas ball, and independently to track the evolution of species in
the unburned gas as a function of time during the course of the experiment.
I feel it is of utmost importance to study boundary layer effects on ignition for non-ideal
environments that are present in engines and legacy experiments with regards to the negative
temperature coefficient behavior and Ludwig-Soret diffusion. Numerical simulations that
include turbulence and complex fluid flow similar to what is present in engines, etc can reveal
the physics related to localized exothermic center development in such systems and may prove to
be central to engine design as well as development of new technology such as Homogeneous
Charge Compression Engines.
90
Appendix: One dimensional conservation equations in spherical
coordinates
E1. Conservation of mass
E2. Conservation of species
E3. Conservation of momentum
E4. Conservation of energy
E5. Equation of state
- density of the mixture
- fluid velocity in radial direction
- mass fraction of i
th
species
- mole fraction of i
th
species
- diffusion velocity of i
th
species
- volumetric production rate of i
th
species
- dynamic viscocity
– heat capacity of the mixture
91
- heat capacity of i
th
species
- temperature
- thermal conductivity
– pressure
- enthalpy of formation of i
th
species
- universal gas constant
- molecular mass of i
th
species
92
References
[1] BP: Statistical Review of World Energy, 2015.
[2] U.S. Energy Information Administration. International Energy Outlook 2013. DOE/EIA-
0484 (2013).
[3] M.J. Pilling, Proc. Combust. Inst. 32 (2009) 27-44.
[4] F.J. Weinberg, Symp. (Int.) Combust. 15 (1975) 1-17.
[5] C.K. Law, Combustion Physics, Cambridge University Press, 2008.
[6] J.B. Heywood, Internal Combustion Engine Fundamentals, McGraw-Hill, New York
(1988).
[7] H.J. Curran, P. Gaffuri, W.J. Pitz, C.K. Westbrook, Combust. Flame 114 (1998) 149-177.
[8] C. Ji, E. Dames, Y.L. Wang, H. Wang, F.N. Egolfopoulos, Combust. Flame 157 (2010)
277-287.
[9] M.J. Pilling, Low-Temperature Combustion and Autoignition, Elsevier Science,
Amsterdam, 1997.
[10] J.F. Griffiths, B.J. Whitaker, Combust. Flame 131 (2002) 286-399.
[11] 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,
Prog. Energy Combust. Sci. 43 (2014) 36-67.
[12] C.K. Law, C.J. Sung, H. Wang, T.F. Lu, AIAA J. 41 (2003) 1629-1646.
[13] D.A. Sheen, H. Wang, Combust. Flame 158 (2011) 2358-2374.
[14] P.A. Libby, F.A. Williams, Combust. Flame 44 (1982) 287-303.
[15] N. Peters, Twenty-First Symposium (International) on Combustion (1986) 1231-1250.
[16] C.K. Law, D.L. Zhu, G. Yu, Proc. Combust. Inst. 21 (1986) 1419–1426.
[17] R. Bunsen, On the temperature of flames of carbon monoxide and hydrogen, Pogg. Ann.
Phys. u. Chem. 131 (1867) 161-179.
[18] F.A. Smith, S.F. Pickering, Measurements of flame velocity by a modified burner
method, Jour. Research Nat. Bur. Std. 17 (1936).
[19] N. Bouvet, C. Chauveau, I. Gökalp, S.-Y. Lee, R.J. Santoro, Characterization of syngas
laminar flames using the Bunsen burner configuration, Int. J. of Hydrogen Energy 36
(2011) 992-1005.
93
[20] J. Natarajan, T. Lieuwen, J. Seitzman, Laminar flame speeds of H
2
/CO mixtures: effect
of CO
2
dilution, preheat temperature, and pressure, Combust. Flame 151 (2007) 104-119.
[21] F.W. Stevens, The rate of flame propagation in gaseous explosive reactions, J. Am.
Chem. Soc. 48 (1926) 1896-1906.
[22] D.R. Dowdy, D.B. Smith, S.C. Taylor, The use of expanding spherical flames to
determine burning velocities and stretch effects in hydrogen/air mixtures, Symp. (Int.)
Combust. 23 (1991) 325-332.
[23] S. Kwon, L.K. Tseng, G.M. Faeth, Laminar burning velocities and transition to unstable
flames in H
2
/O
2
/N
2
and C
3
H
8
/O
2
/N
2
mixtures, Combust. Flame 90 (1992) 230-246.
[24] S.D. Tse, D.L. Zhu, C.K. Law, Morphology and burning rates of expanding spherical
flames in H
2
/O
2
/inert mixtures up to 60 atmospheres, Proc. Combust. Inst. 28 (2000)
1793-1800.
[25] X. Qin, Y. Ju, Measurements of burning velocities of dimethyl ether and air premixed
flames at elevated pressures, Proc. Combust. Inst. 30 (2005) 233-240.
[26] B. Lewis, G. von Elbe, Determination of the speed of flames and the temperature
distribution in a spherical bomb from time ‐pressure explosion records, J. Chem. Phys. 2
(1934) 283-290.
[27] E.F. Fiock, C.F. Marvin (Jr), The measurement of flame speeds, Chem. Rev. 21 (1937)
367-387.
[28] D. Bradley, A. Mitcheson, A., Mathematical solutions for explosions in spherical vessels,
Combust. Flame 26 (1976) 201-217.
[29] M. Metghalchi, J.C. Keck, Laminar burning velocity of propane-air mixtures at high
temperature and pressure, Combust. Flame 38 (1980) 143-154.
[30] M. Metghalchi, J.C. Keck, Burning velocities of mixtures of air with methanol, isooctane,
and indolene at high pressure and temperature, Combust. Flame 48 (1982) 191-210.
[31] K. Eisazadeh-Far, A. Moghaddas, J. Al-Mulki, H. Metghalchi, Laminar burning speeds
of ethanol/air/diluent mixtures, Proc. Combust. Inst. 33 (2011) 1021-1027.
[32] A. Moghaddas, K. Eisazadeh-Far, H. Metghalchi, Laminar burning speed measurement
of premixed n-decane/air mixtures using spherically expanding flames at high
temperatures and pressures, Combust. Flame 159 (2012) 1437-1443.
94
[33] C.K. Wu, C.K. Law, On the determination of laminar flame speeds from stretched
flames, Symp. (Int.) Combust. 20 (1984) 1941–1949.
[34] D.L. Zhu, F.N. Egolfopoulos, C.K. Law, Experimental and numerical determination of
laminar flame speeds of methane/(Ar, N
2
, CO
2
)-air mixtures as function of stoichiometry,
pressure, and flame temperature, Symp. (Int.) Combust. 22 (1988) 1537–1545.
[35] L.P.H. de Goey, A. van Maaren, R.M. Quax, Stabilization of adiabatic premixed laminar
flames on a flat flame burner, Combust Sci Technol. 92 (1993) 201-207.
[36] K.J. Bosschaart, L.P.H. de Goey, Detailed analysis of the heat flux method for measuring
burning velocities, Combust. Flame 132 (2003) 170-180.
[37] M. Goswami, S.C.R. Derks, K. Coumans, W.J. Slikker, M.H. de Andrade Oliveira,
R.J.M. Bastiaans, C.C.M. Luijten, L.P.H. de Goey, A.A. Konnov, The effect of elevated
pressures on the laminar burning velocity of methane+air mixtures, Combust. Flame 160
(2013) 1627-1635.
[38] G.E. Andrews, D. Bradley, Determination of burning velocities: a critical review,
Combust. Flame 18 (1972) 133-153.
[39] J.W. Linnett, Methods of measuring burning velocities, Symp. (Int.) Combust. 4 (1953)
20-35.
[40] E.F. Fiock, Physical measurements in gas dynamics and combustion, in high speed
aerodynamics and jet propulsion (Part 1, R.W. Ladenburg, Ed.; Part 2, B. Lewis, R.N.
Pease, H.S. Taylor, Eds.), Oxford University Press, London and New York (1955), Vol.
9, p. 409.
[41] A.G. Gaydon, A.G., H.G. Wolfhard, Flames-their structure, radiation and temperature,
2nd Ed., Chapman & Hall, London (1960), pp. 56-88.
[42] R.M. Fristrom, A.A. Westenberg, Flame structure, 1st Ed., McGraw-Hill, New York
(1965), pp. 133-140.
[43] C.J. Rallis, A.M. Garforth, The determination of laminar burning velocity, Prog. Energy
Combust. Sci. 6 (1980) 303-329.
[44] E. Ranzi, A. Frassoldati, R. Grana, A. Cuoci, T. Faravelli, A.P. Kelley, C.K. Law,
Hierarchical and comparative kinetic modeling of laminar flame speeds of hydrocarbon
and oxygenated fuels, Prog. Energy Combust. Sci. 38 (2012) 468-501.
[45] F.A. Williams, Combustion Theory, Benjamin Cummins, Palo Alto, CA, 1985.
95
[46] J.D. Buckmaster, Acta Astronaut. 6 (1979) 741-769.
[47] M. Matalon, Combust. Sci. Technol. 31 (1983) 169-181.
[48] S.H. Chung, C.K. Law, Combust. Flame 55 (1984) 123-125.
[49] A.T. Holley, X.Q. You, E. Dames, H. Wang, F.N. Egolfopoulos, Proc. Combust. Inst. 32
(2009) 1157-1163.
[50] C.K. Law, F. Wu, F.N. Egolfopoulos, V. Gururajan, H. Wang, Combust. Sci. Technol.
187 (2015) 27-36.
[51] A.P. Kelley, A.J. Smallbone, D.L. Zhu, C.K. Law, Proc. Combust. Inst. 33 (2011) 963-
970.
[52] A.J. Smallbone, W. Liu, C. Law, X. You, H. Wang, Proc. Combust. Inst. 32 (2009) 1245-
1252.
[53] K. Kumar, J.E. Freeh, C.J. Sung, Y. Huang, J. Propuls. Power 23 (2007) 428-436.
[54] F. Wu, A.P. Kelley, C.K. Law, Combust. Flame 159 (2012) 1417-1425.
[55] A.P. Kelley, C.K. Law, Combust. Flame 156 (2009) 1844-1851.
[56] R.J. Kee, J.A. Miller, G.H. Evans, G. Dixon-Lewis, Proc. Combust. Inst. 22 (1988)
1479–1494.
[57] J.H. Tien, M. Matalon, Combust. Flame 84 (1991) 238-248.
[58] Y.L. Wang, A.T. Holley, C. Ji, F.N. Egolfopoulos, T.T. Tsotsis, H. Curran, Proc.
Combust. Inst. 32 (2009) 1035–1042.
[59] P.S. Veloo, Y.L. Wang, F.N. Egolfopoulos, C.K. Westbrook, Combust. Flame 157 (2010)
1989-2004.
[60] P.D. Ronney, G.I. Sivashinksy, SIAM J. Appl. Math. 49 (1989) 1029-1046.
[61] A.P. Kelley, J.K. Bechtold, C.K. Law, J. Fluid Mech. 691 (2012) 26-51.
[62] Z. Chen, Combust. Flame 158 (2011) 291-300.
[63] D. Bradley, P.H. Gaskell, X.J. Gu, Combust. Flame 104 (1996) 176-198.
[64] Z. Chen, M.P. Burke, Y. Ju, Proc. Combust. Inst. 32 (2009) 1253-1260.
[65] M.P. Burke, Z. Chen, Y. Ju, F.L. Dryer, Combust. Flame 156 (2009) 771-779.
[66] Z. Chen, M.P. Burke, Y. Ju, Combust. Theor. Model. 13 (2009) 343-364.
[67] I.C. Mclean, D.B. Smith, S.C. Taylor, Proc. Combust. Inst. 25 (1994) 749-757.
[68] C.K. Law, F.N. Egolfopoulos, Proc. Combust. Inst. 24 (1992) 137-144.
[69] Z. Chen, Combust. Flame 157 (2010) 2267-2276.
96
[70] J. Santner, F.M. Haas, Y. Ju, F.L. Dryer, Combust. Flame 161 (2014) 147-153.
[71] Z. Chen, X. Qin, B. Xu, Y. Ju, F. Liu, Proc. Combust. Inst. 31 (2007) 2693-2700.
[72] J. Ruan, H. Kobayashi, T. Niioka, Y. Ju, Combust. Flame (2001) 225-230.
[73] B. Lecordier. Etude de l ’interaction de la propagation d ’une flamme de prémélange avec
le champ aréodynamique par association de la tomographie laser et de la PIV. PhD
Thesis Report, Université de Rouen, France, 1997.
[74] S. Balusamy, A. Cessou, B. Lecordier, Exp. Fluids 50 (2011) 1109-1121.
[75] G.E. Andrews, D. Bradley, Combust. Flame 19 (1972) 275-288.
[76] E. Varea, V. Modica, A. Vandel, B. Renou, Combust. Flame 159 (2012) 577-590.
[77] E.F. Fiock, C.F. Marvin (Jr), The measurement of flame speeds, Chem. Rev. 21 (1937)
367-387.
[78] V.S. Babkin, A.V. Vyun, L.S. Kozachinko, Combustion, Explosion and Shock Waves
3:221 (1967).
[79] T.W. Ryan, S.S. Lestz, Automotive Engineering Congress, Paper 800103, Detroit (1980).
[80] K. Eisazadeh-Far, A. Moghaddas, J. Al-Mulki, H. Metghalchi, Laminar burning speeds
of ethanol/air/diluent mixtures, Proc. Combust. Inst. 33 (2011) 1021-1027.
[81] A. Moghaddas, K. Eisazadeh-Far, H. Metghalchi, Laminar burning speed measurement
of premixed n-decane/air mixtures using spherically expanding flames at high
temperatures and pressures, Combust. Flame 159 (2012) 1437-1443.
[82] F. Parsinejad, C. Arcari, H. Metghalchi, Flame structure and burning speed of JP-10 air
mixtures, Combust. Sci. Tech. 178 (2006) 975-1000.
[83] V.V. Voevodsky, R. I. Soloukhin, Symp. (Int.) Combust. 10 (1965) 279-283.
[84] J.W. Meyer, A.K. Oppenheim, Symp. (Int.) Combust. 13 (1971) 1153-1164.
[85] R. Blumenthal, K. Fieweger, K.H. Komp, G. Adomeit, Combust. Sci. Tech. 113 (1996)
137-166.
[86] G. König, C.G.W. Sheppard, SAE Trans. 99 (1990), 820-843.
[87] R. Schieβl, U. Maas, Combust. Flame 133 (2003) 19-27.
[88] N. Kawahara, E. Tomita, Y. Sakata, Proc. Combust. Inst. 31 (2007) 2999-3006.
[89] S.M. Walton, X. He, B. T. Zigler, M.S. Wooldridge, A. Atreya, Combust. Flame 150
(2007) 246-262.
[90] X. Gu, D.R. Emerson, D. Bradley, Combust. Flame 133 (2003) 63-74.
97
[91] P. Dai, Z. Chen, Combust. Flame 162 (2015) 4183-4193.
[92] J. Clarkson, J.F. Griffiths, J.P. MacNamara, B.J. Whitaker, Combust. Flame 125 (2001)
1162-1175.
[93] G. Mittal, M.P. Raju, C.J. Sung, Combust. Flame 157 (2010) 1316-1324.
[94] R. A. Strehlow, A. Cohen, J. Chem. Phys. 30 (1959) 257-265.
[95] K.P. Grogan, M. Ihme, Proc. Combust. Inst. 35 (2015) 2181-2189.
[96] J.F. Griffiths, D.J. Rose, M. Screiber, J. Meyer, K.F. Knoche, Combust. Flame 91 (1992)
209-212.
[97] P. Desgroux, R. Minetti, L.R. Sochet, Combust. Sci. Tech. 113 (1996) 193-203.
[98] D.E. Rosner, Transport Processes in Chemically Reacting Flow Systems, Dover
Publications (2000).
[99] J.A. Miller, R.J. Kee, C.K. Westbrook, Chemical Kinetics and Combustion Modeling,
Ann. Rev. Phys. Chem. 41 (1990) 345-387.
[100] R.J. Kee, J.F. Grcar, M.D. Smooke, J.A. Miller, Premix: A FORTRAN Program for
Modeling Steady Laminar One-dimensional Premixed Flames, Sandia Report, SAND85-
8240, Sandia National Laboratories, 1985.
[101] J.F. Grcar, R.J. Kee, M.D. Smooke, J.A. Miller, Proc. Combust. Inst. 21 (1986) 1773–
1782.
[102] F.N. Egolfopoulos, Proc. Combust. Inst. 25 (1994) 1375–1381.
[103] R.J. Kee, F.M. Rupley, J.A. Miller, Chemkin-II: A Fortran Chemical Kinetics Package
for the Analysis of Gas-Phase Chemical Kinetics, Sandia Report, SAND89-8009, Sandia
National Laboratories, 1989.
[104] R. J. Kee, F. M. Rupley, J. A. Miller, M. E. Coltrin, J. F. Grcar, E. Meeks, H. K. Moffat,
A. E. Lutz, G. DixonLewis, M. D. Smooke, J. Warnatz, G. H. Evans, R. S. Larson, R. E.
Mitchell, L. R. Petzold, W. C. Reynolds, M. Caracotsios, W. E. Stewart, P. Glarborg, C.
Wang, O. Adigun, CHEMKIN Collection, Release 3.6, Reaction Design, Inc., San Diego,
CA (2000).
[105] R.J. Kee, J. Warnatz, J.A. Miller, A FORTRAN Computer Code Package for the
Evaluation of Gas-phase Viscosities, Conductivities, and Diffusion Coefficients, Sandia
Report, SAND83-8209, Sandia National Laboratories, 1983.
98
[106] Y. Dong, A.T. Holley, M.G. Andac, F.N. Egolfopoulos, S.G. Davis, P. Middha, H.
Wang, Combust. Flame 142 (2005) 374–387.
[107] G.L. Hubbard, C.L. Tien, ASME J. Heat Transfer 100 (1978) 235-239.
[108] G. Strang, On the construction and comparison of difference schemes, SIAM J. Numer.
Anal. 5 (1968) 506–517.
[109] B. Sportisse, An analysis of operator splitting techniques in the stiff case, J. Comput.
Phys. 161 (2000) 140–168
[110] U. Maas, J. Warnatz, Ignition processes in hydrogen oxygen mixtures, Combust. Flame
74 (1988) 53-59.
[111] C. Hirsch, Numerical computation of internal and external flows: the fundamentals of
computational fluid dynamics (Vol 1), Butterworth-Heinemann, 2007.
[112] K.E. Brenan, S.L. Campbell, L.R. Petzold, Numerical Solution of Initial–Value Problems
in Differential Algebraic Equations, Second Edition, SIAM, 1995.
[113] L.R. Petzold, A Desription of DASSL: A Differential/Algebraic System Solver, in
Scientific Computing, R.S. Stepleman et al. (Eds.), North-Holland, Amsterdam, 1983, pp.
65-68.
[114] P.N. Brown, A.C. Hindmarsh, J. Applied Mathematics and Computation 31 (1989) 40-
91.
[115] P.N. Brown, A.C. Hindmarsh, L.R. Petzold, SIAM J. Sci. Comp. 15 (1994) 1467-1488.
[116] P.N. Brown, A.C. Hindmarsh, L.R. Petzold, SIAM J. Sci. Comp. 19 (1998) 1495-1512.
[117] M. Berzins, P.J. Capon, P.K. Jimak, Appl. Numer. Math. 26 (1998) 117-133.
[118] S. Li, Adaptive mesh methods and software for time dependent partial differential
equations, Ph.D. Thesis, Department of Computer Science, University of Minnesota
(1998).
[119] J.M. Hyman, S Li, L.R. Petzold, Computers and Mathematics with Applications 46
(2003) 1511-1524.
[120] J.M. Hyman, SIAM J. Sci. Stat. Comp. 4 (1983) 645-654.
[121] J.F. Grcar, The Twopnt Program for Boundary Value Problems, Sandia National
Laboratories Report SAND91-8230, April (1992).
[122] T. Lu, C.K. Law, Proc. Combust. Inst. 30 (2005) 1333–1341.
99
[123] H. Wang, X. You, A. V. Joshi, Scott G. Davis, A. Laskin, F.N. Egolfopoulos C. K. Law,
USC-Mech Version II. High-Temperature Combustion Reaction Model of H2/CO/C1-C4
Compounds. http://ignis.usc.edu/USC_Mech_II.htm.
[124] J. Jayachandran, R. Zhao, F.N. Egolfopoulos, Combust. Flame 161 (2014) 2305-2316.
[125] P.D. Nguyen, V. Moureau, L. Verviisch, N. Perret, J. Phys: Conf. Ser. 369 (2012)
012017.
[126] G. Dixon-Lewis, S.M. Islam, Proc. Combust. Inst. 25 (1994) 1341-1347.
[127] E. Varea, V. Modica, B. Renou, A.M. Boukhalfa, Proc. Combust. Inst. 34 (2013) 735-
744.
[128] J. Jayachandran, A. Lefebvre, R. Zhao, F. Halter, E. Varea, B. Renou, F.N. Egolfopoulos,
Proc. Combust. Inst. 35 (2015) 695-702.
[129] F. Halter, T. Tahtouh, C. Mounaim-Roussele, Combust. Flame 157 (2010) 1825-1832.
[130] F.N. Egolfopoulos, Proc. Combust. Inst. 25 (1994) 1375–1381.
[131] B. Sirjean, E. Dames, D. A. Sheen, X. You, C. Sung, A. T. Holley, F. N. Egolfopoulos,
H. Wang, S. S. Vasu, D. F. Davidson, R. K. Hanson, H. Pitsch, C. T. Bowman, A.
Kelley, C. K. Law, W. Tsang, N. P. Cernansky, D. L. Miller, A. Violi, R. P. Lindstedt,
“A High-Temperature Chemical Kinetic Model of n-Alkane Oxidation, JetSurF Version
1.0,” http://melchior.usc.edu/JetSurF/JetSurF1.0/ Index.html.
[132] S.G. Davis, A. V. Joshi, H. Wang, F.N. Egolfopoulos, An optimized kinetic model of
H
2
/CO combustion, Proc. Combust. Inst. 30 (2005) 1283-1292.
[133] 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.
[134] P. Clavin, G. Joulin, Flamelet library for turbulent wrinkled flames, Turbulent Reactive
Flows, Springer, 1989, pp. 213-240.
[135] L.P.H. de Goey, J.H.M. Ten Thije Boonkkamp, A mass-based definition of flame stretch
for flames with finite thickness, Combust. Sci. Tech. 122 (1997) 399-405.
[136] H.K. Ciezki, G. Adomeit, Combust. Flame 93 (1993) 421-433.
[137] J.C. Prince, F.A. Williams, G.E. Ovando, Fuel 149 (2015) 138-142.
[138] G. A. Pang, D.F. Davidson, R.K. Hanson, Proc. Combust. Inst. 32 (2009) 181-188.
[139] D.E. Rosner, R.S. Israel, B. La Mantia, Combust. Flame 123 (2000) 547-560.
100
[140] A.E. Lutz, R.J. Kee, J.A. Miller, SENKIN: A FORTRAN program for predicting
homogeneous gas phase chemical kinetics with sensitivity analysis, SANDIA National
Laboratories Report, SAND87-8248, Livermore , CA, 1990.
Abstract (if available)
Abstract
Numerical simulations were utilized to investigate phenomena in legacy flame propagation and ignition experiments that could result in non-ideal effects and thus incorrect interpretation of experimental measurements. Specifically, spherically expanding flames were studied in the context of heat loss and molecular transport effects. Ignition adjacent to a cold wall was also examined for mixtures that exhibited the negative temperature coefficient behavior, and species stratification due to Ludwig-Soret diffusion. For this purpose, a transient one-dimensional reacting flow code was developed to accurately simulate flame propagation and ignition in the low Mach number regime. ❧ Computations of flames of heavy molecular weight fuel/air mixtures revealed that the response of such flames to stretch is governed by different mechanisms for fuel-lean and fuel-rich mixtures. The dynamics of lean mixtures are controlled by the Lewis number which quantifies the non-equidiffusion of heat from and chemical energy into the flame, while for rich mixtures, the response to stretch is governed by the difference in diffusivities between the fuel and oxidizer. It was further demonstrated that, extrapolation equations derived based on numerous simplifying assumptions, when utilized to derive laminar flame speeds from constant pressure spherically expanding flame experimental data, result in substantial uncertainties in the stretch-corrected values. Simulation results also showed that the radiation heat loss from the burned gas ball can lead to non-ideal fluid dynamic effects that imparts uncertainties in the flame speeds derived using flame expansion rate measurements and that additional measurement of the unburned gas velocity is required to circumvent the flow induced uncertainty. ❧ Consistency between data obtained from counterflow and spherically expanding flame configurations was established by comparing the difference between direct measurements and detailed simulation results for each configuration. The consistency obtained when avoiding the erroneous extrapolation procedure transformed into discrepancy when results post-extrapolation are compared. ❧ Measurements made during the compression stage of spherically expanding flame propagation in a constant volume vessel is identified as the ideal method to probe flame propagation at conditions of high pressure and temperature. Computations revealed that the flame speeds derived from pressure measurements are highly sensitive to the accuracy of burned gas mass fraction as a function of pressure, which is traditionally determined using thermodynamics-based models. Thus, neglecting radiation energy loss from the burned gas can result in errors in flame speed as large as 15%. Besides, simulation results illustrated that measurements made during the compression stage do not require stretch correction as the compression induced fluid flow results in near stretch-free flames. ❧ Simulations performed to study the influence of the thermal boundary layer adjacent to a cold wall on the ignition behavior of a combustible gas revealed that exothermic centers could preferentially develop locally in the boundary layer for mixtures that exhibit the negative temperature coefficient behavior and also for mixtures that can stratify as a result of Ludwig-Soret diffusion. This inhomogeneous ignition could result in incorrect interpretation of experimental data from legacy kinetic experiments and could play a role central to the initiation of knock in engines.
Linked assets
University of Southern California Dissertations and Theses
Conceptually similar
PDF
Experimental studies of high pressure combustion using spherically expanding flames
PDF
Studies of combustion characteristics of heavy hydrocarbons in simple and complex flows
PDF
End-gas autoignition investigations using confined spherically expanding flames
PDF
Flame ignition studies of conventional and alternative jet fuels and surrogate components
PDF
Determination of laminar flame speeds under engine relevant conditions
PDF
Investigations of fuel effects on turbulent premixed jet flames
PDF
Experimental and kinetic modeling studies of flames of H₂, CO, and C₁-C₄ hydrocarbons
PDF
Accuracy and feasibility of combustion studies under engine relevant conditions
PDF
Pressure effects on C₁-C₂ hydrocarbon laminar flames
PDF
Studies of methane counterflow flames at low pressures
PDF
Flame characteristics in quasi-2D channels: stability, rates and scaling
PDF
Studies of siloxane decomposition in biomethane combustion
PDF
Studies on the flame dynamics and kinetics of alcohols and liquid hydrocarbon fuels
PDF
Experimental investigation of the propagation and extinction of edge-flames
PDF
CFD design of jet-stirred chambers for turbulent flame and chemical kinetics experiments
PDF
Direct numerical simulation of mixing and combustion under canonical shock turbulence interaction
PDF
The use of carbon molecule sieve and Pd membranes for conventional and reactive applications
Asset Metadata
Creator
Jayachandran, Jagannath
(author)
Core Title
Modeling investigations of fundamental combustion phenomena in low-dimensional configurations
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Mechanical Engineering
Publication Date
04/19/2016
Defense Date
04/18/2016
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
boundary layer effect,chemical kinetics,ignition phenomena,laminar flame speed,Ludwig-Soret effect,negative temperature coefficient,OAI-PMH Harvest,premixed flames,Soret effect,spherically expanding flame
Format
application/pdf
(imt)
Language
English
Contributor
Electronically uploaded by the author
(provenance)
Advisor
Egolfopoulos, Fokion N. (
committee chair
), Ronney, Paul D. (
committee member
), Tsotsis, Theodore T. (
committee member
)
Creator Email
jagannath.j9@gmail.com,jjayacha@usc.edu
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-c40-232322
Unique identifier
UC11278149
Identifier
etd-Jayachandr-4285.pdf (filename),usctheses-c40-232322 (legacy record id)
Legacy Identifier
etd-Jayachandr-4285.pdf
Dmrecord
232322
Document Type
Dissertation
Format
application/pdf (imt)
Rights
Jayachandran, Jagannath
Type
texts
Source
University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
(collection)
Access Conditions
The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...
Repository Name
University of Southern California Digital Library
Repository Location
USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA
Tags
boundary layer effect
chemical kinetics
ignition phenomena
laminar flame speed
Ludwig-Soret effect
negative temperature coefficient
premixed flames
Soret effect
spherically expanding flame