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ABSTRACT
Quantitative Characterization of Species, Temperature, and Particles in
Steady and Time-Varying Laminar Flames by Optical Methods
Andrew M. Schaffer
2001
Optical techniques are used to characterize steady and time-varying laminar flames in
order to verify computational models and non-optical measurements. The first set of
measurements determines major species concentration, temperature, and flame front
profiles in a steady and flow-modulated laminar methane diffusion flame through
Rayleigh and Spontaneous Raman scattering techniques. These experimental results are
compared to the computational profiles of the group of Professor Mitchell Smooke. The
next set of measurements determines temperature and soot particle size and volume
fraction in a sooting ethylene, laminar diffusion flame through laser-induced
incandescence techniques. A model is developed to extract particle size information from
the incandescence signal. Soot particle size is compared with particle sizes obtained from
soot sampling measurements. The final set of measurements determines particle and
aggregate information of nanoparticles synthesized in a premixed laminar flame through
laser-induced incandescence and laser light scattering techniques.
Quantitative Characterization ofSpecies, Temperature, and Particles in
Steady and Time-Varying Laminar Flames by Optical Methods
A DissertationPresented to the Faculty of the Graduate School
ofYale University
in Candidacy for the Degree ofDoctor of Philosophy
by
Andrew M. Schaffer
Dissertation Director: Professor Marshall B. Long
December 2001
2001 by Andrew M. Schaffer
All rights reserved.
ACKNOWLEDGEMENTS
I would like to thank my advisor, Professor Marshall Long, for his guidance, insight, and
friendship throughout my dissertation research. I would also like to thank Professor
Daniel Rosner for inspiration and good ideas throughout our collaborative efforts with his
group. Thanks to Barbara LaMantia and Charles McEnally for their friendship during our
collaborative efforts.
I would like to thank Professor Mitchell Smooke and his group, who performed much of
the computational work compared to the experimental work in this thesis. Thanks to
Mikhail Noskov and Beth Bennett for the computational counterpart to a major part my
work, and for the constant insightful discussion about numerical computations.
I would like to express my appreciation to the other members of my thesis committee,
Professor Richard Chang and Professor Kurt Gibble, who have both had a positive impact
on my career as a graduate student, and Professor Kevin Lyons, who has graciously
agreed to be the outside reader of my thesis.
This work is dedicated to my wife, Julie, and our son, Evan, who have given me
overwhelming support and joy, and have shown an infinite amount of patience.
ii
TABLE OF CONTENTS
LIST OF FIGURES................................................................................... vi
LIST OF TABLES ..................................................................................... x
TABLE OF NOMENCLATURE.............................................................. xi
CHAPTER 1 INTRODUCTION ............................................................. 1
CHAPTER 2 LIGHT SCATTERING TECHNIQUES ......................... 62.1 Introduction.......................................................................................62.2 Rayleigh and Raman scattering..........................................................72.3 Laser-induced incandescence...........................................................162.4 Chemiluminescence.........................................................................202.5 Laser light scattering .......................................................................212.6 Laser absorption ..............................................................................23
CHAPTER 3 CHARACTERIZATION OF A STEADY AND TIME-VARYING, AXISYMMETRIC, LAMINARDIFFUSION FLAME...................................................... 26
3.1 Introduction.....................................................................................263.2 Flame and Burner Characterization..................................................283.3. Boundary Conditions......................................................................30
3.3.1 Steady Flame.........................................................................303.3.2 Particle Image Velocimetry ...................................................313.3.3 Time-varying Flame ..............................................................36
3.4 Computational Modeling.................................................................413.4.1 Unforced ...............................................................................413.4.2 Forced ...................................................................................42
3.5 Measurement of CH* via Chemiluminescence.................................423.5.1 Introduction...........................................................................423.5.2 Experimental Setup and Acquisition ......................................433.5.3 Image processing...................................................................453.5.4 CH* profiles for the steady and time-varying flame...............47
iii
3.6 Fuel Concentration, Temperature, andMixture Fraction Measurement........................................................483.6.1 Theory and introduction.........................................................483.6.2 Experimental Setup ...............................................................553.6.3 Acquisition ............................................................................57
3.6.4 Data Processing .....................................................................583.6.5 Calculation of fuel concentration, temperature, and mixture
fraction..................................................................................613.7 Multi-species Measurement using Difference Raman
and Rayleigh Scattering...................................................................623.7.1 Difference Scattering.............................................................633.7.2 Multi-species technique in calculation of temperature and
species number density..........................................................673.7.3 Setup .....................................................................................683.7.4 Unforced Case Acquisition ....................................................723.7.5 Forced Case Acquisition........................................................74
3.7.6 Processing .............................................................................743.7.7 Determination of the temperature dependence of the
bandwidth factor τm(T) ..........................................................82
3.7.8 Temperature and Species Concentration Calculation.............863.8 Discussion on experimental techniques............................................88
3.8.1 Effectiveness of two scalar technique ....................................88
3.8.2 Effectiveness of difference Raman technique.........................923.9 Comparison of experimental and computational profiles .................94
3.9.1 Steady Flame.........................................................................943.9.2 Forced Flame.......................................................................104
3.10 Summary.....................................................................................124
CHAPTER 4 SOOT AND TEMPERATURE CHARACTERIZATIONA SOOTING, LAMINAR, ETHYLENEDIFFUSION FLAME................................................... 126
4.1 Introduction...................................................................................1264.2 Flame and Burner Characterization................................................1274.3 Computational Model....................................................................1284.4 Probe measurement of temperature and soot volume fraction ........128
iv
4.5 Experimental determination of temperature using thetwo scalar technique ......................................................................1294.5.1 Optical imaging setup for temperature measurement............1294.5.2 Processing ...........................................................................1314.5.3 Calculation of Temperature .................................................132
4.5.4 Two scalar temperature comparison with probemeasurements and computations .........................................132
4.6 Determination of the soot volume fraction profile usinglaser-induced incandescence..........................................................1344.6.1 Introduction and theory........................................................1344.6.2 LII imaging setup ................................................................1364.6.3 Data acquisition...................................................................1384.6.4 Processing ..........................................................................1424.6.5 Error estimates of the LII technique in determining
soot volume fraction............................................................1434.7 LII soot volume fraction comparison to probe measurements
and computations ..........................................................................1484.8 Primary soot particle size using time-resolved LII .........................148
4.8.1 Introduction.........................................................................1484.8.2 Time-resolved LII setup.......................................................1534.8.3 Time-resolved LII data acquisition ......................................1564.8.4 Qualitative analysis of the time-resolved LII signals ............1564.8.5 Calculation of particle size distribution from LII data ..........1614.8.6 Grid sampling of soot particles ............................................1654.8.7 Comparison of LII-derived and grid sampling particle
size distributions .................................................................1674.8.8 Sensitivity analysis of LII-derived particle sizing technique.167
4.9 Time-resolved laser light scattering and laser absorption ...............1714.9.1 Introduction.........................................................................1714.9.2 Setup for LLS and laser absorption experiment....................1724.9.3 Acquisition of LLS and laser absorption ..............................1734.9.4 LLS/Absorption results........................................................175
4.10 Error estimates of the absorption/scattering technique .................1794.11 Summary.....................................................................................179
v
CHAPTER 5 CHARACTERIZATION OF NANOPARTICLESTRUCTURES SYNTHESIZED IN A PREMIXED,METHANE/AIR FLAT FLAME.................................. 183
5.1 Introduction...................................................................................1835.2 Burner and Flame..........................................................................1845.3. Measurement of the LII spectrum .................................................187
5.3.1 LII spectrum setup and acquisition ......................................1875.3.2 LII Spectrum processing......................................................1905.3.4 LII spectrum results .............................................................192
5.4 Sampling of iron oxide particles ....................................................198
5.5 X-ray diffraction of the particle material........................................2005.6 Time-resolved LII and laser light scattering experiment ................202
5.6.1 Experimental setup and acquisition......................................2025.6.2 Qualitative analysis of time-resolved LII data ......................2065.6.3 Particle sizing model, parameters, and procedure.................2095.6.4 Particle distribution results from LII data analysis ...............2135.6.5 Results of LLS.....................................................................220
5.7 Conclusion ....................................................................................223
CHAPTER 6 SUMMARY AND CONCLUSIONS............................. 226
REFERENCES....................................................................................... 231
vi
LIST OF FIGURES
Figure 3.1 Forced flame burner. ................................................................................. 29Figure 3.2 Computational and PIV velocity profiles 1 mm above the burner. ............. 35Figure 3.3 Computational and PIV fuel tube centerline velocity for 30% modulation
of flow in the fuel tube as a function of forcing phase.. ............................. 39Figure 3.4 Fuel tube centerline velocity and speaker forcing signal for 30% modulation
in the fuel flow as a function of forcing phase. .......................................... 40Figure 3.5 Experimental setup for CH* chemiluminescence....................................... 44Figure 3.6 CH* profiles for 30% and 50% flow modulation....................................... 46
Figure 3.7 Burke-Schumann flame configuration ....................................................... 51Figure 3.8 Experimental setup for two scalar imaging................................................ 56Figure 3.9 Methane Raman intensity profile (arbitrary scale) from the two scalar
experiment ................................................................................................ 59Figure 3.10 Multi-species experimental setup .............................................................. 69Figure 3.11 Sample images from multi-species/ difference Raman experiment ............ 76Figure 3.12 Intensity spectrum (arbitrary units) taken from the region of maximal C2
fluorescence interference of the images in Figure 3.11 (marked with avertical white rectangle in Fig. 3.11) ......................................................... 78
Figure 3.13 Intensity profiles (arbitrary units) of Ids for oxygen Ramanand Iyz for C2 fluorescence. ........................................................................ 80
Figure 3.14 Experimental and simulated Raman spectra for nitrogen atT = 300 K and T = 2000 K ........................................................................ 84
Figure 3.15 Difference Raman signal temperature dependence .................................... 85Figure 3.16 Methane Raman intensity profiles (arbitrary units) from experiments........ 90Figure 3.17 Two-scalar calculation of mixture fraction and temperature based on
computational data, compared to ξCHO and computational temperature based
on computations........................................................................................ 91
Figure 3.18 Measured (multi-species technique) and computedtemperature (degrees Kelvin) for the steady flame..................................... 95
Figure 3.19 Measured (multi-species technique) and computedcarbon dioxide mole fractions for the steady flame.................................... 96
Figure 3.20 Measured (multi-species technique) and computed water mole fractionsfor the steady flame................................................................................... 97
Figure 3.21 Measured (multi-species technique) and computed carbon monoxidemole fractions for the steady flame............................................................ 98
vii
Figure 3.22 Measured (multi-species technique) and computed hydrogenmole fractions for the steady flame............................................................ 99
Figure 3.23 Measured (multi-species technique) and computedmethane mole fractions for the steady flame............................................ 100
Figure 3.24 Measured (multi-species technique) and computed
nitrogen mole fractions for the steady flame............................................ 101Figure 3.25 Measured (multi-species technique) and computed
oxygen mole fractions for the steady flame. ............................................ 102Figure 3.26 Radial and centerline plots of temperature, water, and carbon dioxide for
steady flame experiments (multi-species technique) and computations.... 103Figure 3.27 Temperature profiles of the multi-species and two scalar techniques
for 30% flow modulation ........................................................................ 105Figure 3.28 Temperature lineplots of the two-scalar and multispecies
technique for 30% flow modulation. ....................................................... 106Figure 3.29 Mixture fraction profiles of the multi-species and two scalar techniques
for 30% flow modulation ........................................................................ 109
Figure 3.30 Two scalar and multi-species mixture fraction plots for30% flow modulation.............................................................................. 110
Figure 3.31 Temperature profiles (degrees K) of experiments (multi-species) andcomputations for 30% flow modulation................................................... 112
Figure 3.32 Temperature lineplots (degrees K) of experiments (multi-species) andcomputation for 30% flow modulation. ................................................... 113
Figure 3.33 Carbon dioxide mole fraction profiles of experiments (multi-species) andcomputations for 30% flow modulation................................................... 114
Figure 3.34 Carbon dioxide mole fraction lineplots of experiments (multi-species) andcomputations for 30% flow modulation................................................... 115
Figure 3.35 Water mole fraction profiles of experiments (multi-species) and
computations for 30% flow modulation................................................... 116Figure 3.36 Water mole fraction lineplots of experiments (multi-species) and
computations for 30% flow modulation................................................... 117Figure 3.37 Temperature profiles (degrees K) of experiments (multi-species)
and computations for 50% flow modulation.. .......................................... 118Figure 3.38 Temperature lineplots (degrees K) of experiments (multi-species)
and computations for 50% flow modulation.. .......................................... 119Figure 3.39 Carbon dioxide mole fraction profiles of experiments (multi-species) and
computations for 50% flow modulation................................................... 120Figure 3.40 Carbon dioxide mole fraction lineplots of experiments (multi-species) and
computations for 50% flow modulation................................................... 121
viii
Figure 3.41 Water mole fraction profiles of experiments (multi-species) andcomputations for 50% flow modulation................................................... 122
Figure 3.42 Water mole fraction lineplots of experiments (multi-species) andcomputations for 50% flow modulation................................................... 123
Figure 4.1 Temperature profiles from experiments and computations-32% ethylene flame................................................................................133
Figure 4.2 LII Imaging Setup..................................................................................137Figure 4.3 Variation of time-integrated LII signal with laser fluence
from LII imaging. ..................................................................................140Figure 4.4 Calculated LII response to variations in laser fluence across
the height of the laser sheet.. ..................................................................141Figure 4.5 Shot-to-Shot LII Fluctuation.. ................................................................144Figure 4.6 Interference on ethylene Raman data......................................................146Figure 4.7 Experimental and Computational Soot Volume Fraction-
32% Ethylene Flame. .............................................................................147Figure 4.8 Select properties of carbon and nitrogen.................................................150Figure 4.9 Time-resolved LII setup. ........................................................................155Figure 4.10 Time-resolved LII curves at various laser fluences. ................................157Figure 4.11 Time-integrated LII signals vs. laser fluence.. ........................................158Figure 4.12 Time-resolved LII signals for various laser fluences...............................160Figure 4.13 Curve fit to the soot LII data ..................................................................166Figure 4.14 Primary soot particle size distributions from grid sampling
measurements and from the LII-derived particle size distribution. ..........168Figure 4.15 Effect of change in parameter value on the predicted particle size ..........170Figure 4.16 Time-resolved Scattering/Absorption Setup ...........................................174
Figure 4.17 Time-resolved change in elastic scattering and absorption of thesooty region (measured with the Ar+ laser) due to the YAG laser pulse atvarious YAG laser fluences....................................................................176
Figure 4.18 Time-resolved change in elastic scattering of the sooty region (measuredwith Ar+ laser) due to YAG laser pulse with laser fluence = 0.15 J/cm2. 177
Figure 5.1 Burner for iron oxide particle production ................................................ 185Figure 5.2 Experimental LII spectrum setup............................................................. 188Figure 5.3 Flame emission spectrum. ....................................................................... 191
ix
Figure 5.4 Raw LII spectrum and the LII spectrum corrected for optical throughputand detector efficiencies.......................................................................... 193
Figure 5.5 LII spectrum for several laser fluences. ................................................... 194Figure 5.6 Delayed and prompt detection of LII spectrum........................................ 196Figure 5.7 LII spectrum for several heights above the burner ................................... 197
Figure 5.8 TEM images of thermophoretically sampled particles forflame #1 and flame #2............................................................................. 199
Figure 5.9 Xray diffraction peaks of sample (top graph) and ofpure hematite (bottom graph) .................................................................. 201
Figure 5.10 Time-resolved LII and laser light scattering setup. .................................. 203Figure 5.11 Time-resolved LII at several laser fluences. ............................................ 205Figure 5.12 Time-resolved LII at several laser fluences. ............................................ 207Figure 5.13 Time-resolved LII at two different laser fluences for
flame #1 and flame #2............................................................................. 208Figure 5.14 Time-integrated LII signals for flame #1 and flame #1
as a function of laser fluence. .................................................................. 210
Figure 5.15 Select hematite and nitrogen properties ................................................... 212Figure 5.16 Least-squares fits to the experimental LII curves using a
lognormal (1 and 2 mode) and normal (1 and 2 mode) particle sizedistribution for flame #1 and flame #2..................................................... 214
Figure 5.17 Comparison of LII-derived particle size distributions with grid samplingparticle size distributions ........................................................................ 216
Figure 5.18 LII curves generated from grid sampling data.......................................... 219Figure 5.19 LLS vs. fluence for flame #1 and flame #2.............................................. 221
x
LIST OF TABLES
Table 4.1 Parameters used in the soot LII analysis ................................................... 151Table 5.1 Flow and flame conditions for the seeded premixed methane flame.......... 186Table 5.2 Parameters used in nanoparticle LII analysis............................................. 213Table 5.3 χ values for the fit to the LII data using various size distributions............. 215
xi
Table of Nomenclature
A21 Einstein A coefficient (s-1)a particle radius
mean of the classical polarizability tensor
a' mean of the quantum mechanical polarizability tensora0 initial particle radiusa0 particle radius where the particle size distribution is a maximuma0,1 a0 for mode #1 of a multi-modal size distributiona0,2 a0 for mode #2 of a multi-modal size distributionaes particle radius for a volume-equivalent spherebj,j Placzek-Teller coefficientsbj j±2,
c speed of lightC constantCa absorption cross section for isolated spherules
Cs total scattering cross section for isolated spherulesCp
νν scattering cross section for light perpendicular to the incident light
polarization for an isolated spheruleCa
νν scattering cross section for light perpendicular to the incident light
polarization for an aggregate of spherulescv
* mean specific heat (at constant volume) between Tg and Tp
cp specific heat (at constant pressure) of the particle materialD coefficient of diffusionDf fractal dimension
rE electric field
eb Planck functionE(m) refractive index function Im[(m2 - 1)/(m2 + 1)]F(m) refractive index function |(m2 – 1)/(m2 + 2)|2
fv volume fractiong(λ) spectral detection efficiency
h Planck constant
h h/2πH sensible enthalpy cpT/QI intensity of incident lightI0 laser intensityIem particle emission intensity
xii
Iiz scattering intensity polarized in the i for an input light source polarizealong the z direction
Iiz,Ray Rayleigh scattering intensity polarized in the i for an input light sourcepolarized along the z direction
Iiz,Ram,m Raman scattering intensity of species m polarized in the i for an input light
source polarized along the z directioni (-1)0.5
J rotational quantum numberk wave number of light 2π/λkB Boltzmann constantkƒ fractal prefactor
Kabs absorption cross section of an isolated spheruleKe extinction coefficientKn Knudsen numberlg mean free pathm complex refractive indexmg mass of a gas particlemp rate of mass change of a particle
M magnification of the optical systemnp number of particles per aggregateNa number density of aggregatesNp particle number densityNm number density of species mN* number density of an excited-state speciesNtot total number density of all speciesn number of particlesp(a0) particle size distribution function
P pressurepg gas pressurepv
* vapor pressure at a reference temperaturepO2
partial pressure of oxygen
rp dipole moment
Q lower calorific value of the fuelq 2ksin(θ/2)
R gas constantRg radius of gyrationri location of particle i within an aggregate with origin at the center of mass
Sem emission intensity relative to background emission
xiii
rs displacement vectorT temperatureTp particle temperatureTp,0 initial particle temperatureTg gas temperature
Tp* particle temperature at a reference point
V volumeVp individual particle volumeVem emission volume (cm3)
rv velocityvg mean thermal speed of the gas molecules (Maxwellian)
vv mean thermal speed of the vapor
Wf molecular weight of the fuelWmix molecular weight of the mixtureWi molecular weight of species iWv molecular weight of the particle vapor speciesx' coordinate of the in-plane emission distributionxpixels number of pixel columns in the image
rX1 position of the particle image for the first exposure
rX2 position of the particle image for the second exposure, at a time ∆t after
the first exposureX mole fractionXm mole fraction of species mY mass fractionYF fuel mass fraction
Greek terms
α thermal accommodation coefficient
αv evaporation coefficient
α electronic polarizability tensorα iz polarizability components
αzz on-axis polarizability components
αyz off-axis polarizability components
αxz
β volumetric thermal expansion coefficientconserved scalar
γ* mean value of (cv + R)/cv between Tg and Tp
xiv
γ anisotropy of the classical polarizability tensor
γ' anisotropy of the quantum mechanical polarizability tensor
∆Hv heat of vaporization
ξ mixture fractionξFT two scalar mixture fraction based on YF and cpT/Q
ξCHO mixture fraction based on mass fraction of C, H, and O
ε spectral emissivity
ε0 dielectric constant
ƒ form factorκ imaginary part of the refractive index
λ wavelength
λem emission wavelength
λex excitation wavelength
η detector efficiency in counts per photon
dimensionless parameter hc/λkBT
ηem η(λ = λem)
ν vibrational quantum number
νi stoichiometric coefficients of ν ν νF O PF O P+ →νO
νF
ρm depolarization ratio of species m
ρ density
ρp particle density
σ size distribution spread parameter
σ1 σ for mode #1 of a multi-modal size distribution
σ2 σ for mode #2 of a multi-modal size distribution
σSB Stefan-Boltzmann constant
σRay Air, Rayleigh scattering cross section for air
σRay He, Rayleigh scattering cross section for helium
∂σ∂Ω
m iz,
differential scattering cross section for species m, collection of light
polarized along the i axis, and incident light polarized along the z axis∂σ∂Ω
Ram m iz, ,
differential Raman scattering cross section for species m, collection of
light polarized along the i axis, and incident light polarized along the zaxis
xv
∂σ∂Ω
eff iz Ray, ,
differential Rayleigh scattering cross section for collection of light
polarized along the i axis and incident light polarized along the z axis,where the contribution of each species is weighted by its mole fraction
θ angle (degrees)
τ integration time (s)
bandwidth factor correctionω frequency of light (s-1)
chemical production rateΩ detection solid angle
χ least-squares error parameter
1
Chapter 1
Introduction
Optical diagnostic techniques are used effectively in combustion systems as a method of
quantifying the system without disturbing the system itself. Light emitted from and
scattered off of these systems gives information of species concentrations, temperature,
velocity, and particle size and concentration. These signals are often spectral and
temporal signatures that are specific to a particular species or possibly the dimensions of
particles or particle aggregates. Use of a monochromatic, coherent light source along with
fast optical detection equipment allows easy detection and interpretation of these signals
due to the high spatial, temporal, and spectral resolution achieved. The lack of divergence
of lasers allows for remote measurements in systems where this would not otherwise be
possible with physical probes.
There is a recognized need in the world today for tighter controls on pollutant emissions
for industrial factories, automobiles and power plants. Laser diagnostic techniques offer
long term monitoring of these emissions, whereas a physical device will eventually
corrupt due to deposits and corrosion. Monitoring can be done on not only current
combustion facilities, but can provide feedback for the construction of more efficient,
cleaner burning combustion facilities.
2
As the level of detail and sophistication of numerical modeling increases, laser
measurements are often the only means available with the spatial resolution and
sensitivity needed to check the computational results. Experimental confirmation of
these simulations provides the necessary confidence to extend the computational models
to systems of increasing complexity. With better models, it is easier to develop and
evaluate new, more complex practical devices that are both more efficient and have a
lesser impact on the environment.
Certain combustion-generated materials have properties that make them of considerable
economic importance. For an example, thin films created by deposition of combustion-
synthesized particles have special magnetic and optical properties are used in data storage
and communications technologies. The monitoring of the production of these materials is
critical to the special properties of the films. Laser diagnostics provide real-time
monitoring of the synthesized materials and thus a feedback loop in the production of
these materials.
This dissertation introduces the optical techniques of Raman and Rayleigh scattering,
laser-induced incandescence (LII), laser light scattering (Mie scattering), absorption,
flame emission (chemiluminescence), and particle image velocimetry, and applies these
3
techniques to simple, ideal combustion systems (i.e. systems which have an axis of
symmetry and are repeatable over any length of time or at least over a specified period).
These techniques are used in conjunction with modeled quantities to quantify the systems
in terms of velocity, temperature, gaseous species and particle concentrations, and
particle and aggregate dimensions. Results obtained are compared to computational
results and with the results of non-optical experiments.
Chapter 2 describes the fundamental theory behind the diagnostic techniques used. The
fundamental principles behind the optical techniques used to relate the optical signals to
the underlying physical quantities such as temperature, concentration, size, etc.
Chapter 3 presents the quantitative characterization of a non-sooting laminar methane,
coflowing diffusion flame using several techniques. The techniques are performed on a
flame with steady fuel flow and on a time varying flame where the fuel flow is
modulated. Chemiluminescence is used to determine the variation in flame structure due
to the flow modulation. Next, Rayleigh and fuel Raman scattering are used as a two
scalar measurement to determine temperature and mixture fraction for the forced flame.
Finally, a technique using Rayleigh and multi-species Raman scattering is used to
determine major species concentration, temperature and mixture fraction in the steady
and time-varying flames. A sub-technique of this approach involves using the orthogonal
4
polarized Raman scattering signals to eliminate fluorescence interference on the Raman
signals. The results of the two-scalar technique are compared to the mixture fraction and
temperature obtained from the multi-species technique. The results of the multi-species
technique are compared to computations of temperature and major species
concentrations. The effectiveness and error estimates of the two techniques are discussed.
Chapter 4 presents the quantitative characterization of a sooting, laminar, ethylene,
coflowing diffusion flame. Rayleigh and fuel Raman scattering are used in the two scalar
technique to obtain a temperature image. The two scalar temperature is compared to
computations and thermocouple probe measurements. Time-integrated LII is used to
quantify soot volume fraction in the flame. LII results are compared to probe sampling
measurements of soot volume fraction along with computations. Time-resolved LII is
used along with modeling to obtain soot particle size distributions and to estimated mass
vaporization limits of the soot particles. LII-derived particle size distributions are
compared to particle-sampling derived particle size distributions. Time-resolved
absorption and laser light scattering are used to study the effect of the laser pulse on the
particles/aggregates.
Chapter 5 presents the characterization of inorganic nanoparticles created downstream of
a premixed laminar methane/air flame. Time-resolved LII is used along with modeling to
5
obtain primary particle size distributions and to estimate mass vaporization limits of the
particles. Time-resolved Mie scattering of the particles is used to obtain aggregate size
information and to study the effect of the laser on aggregates. LII-derived particle size
distributions and aggregate information inferred from laser light scattering measurements
are compared to grid sampling particle/aggregate distributions.
6
Chapter 2Light Scattering Techniques
2.1 Introduction
Optical techniques used today in combustion are based on optical principles known for
some time. Emission spectroscopy dates back to 1857 when Swan observed C2 emissions
from flames [Gaydon 1974]. In 1871, Lord Raleigh formalized earlier observations that
light preferentially scatters in the blue. In 1928, Raman and Krishnan observed a
modified scattering of light in a medium that occurs at an altered wavelength from the
incident light [Long 1977].
Optical measurements are remote and non-intrusive, allowing for measurements at the
specific location and time of interest, as opposed to waiting for products which exit the
volume of interest in a sampling approach. Optical techniques often detect spectral
signatures of atoms or molecules which can be detected by no other available method.
In practical combustion systems, the hostile environment may prohibit the use of physical
probes.
7
The use of lasers offers high spatial and temporal resolution, allowing for instantaneous
multi-dimensional measurements. A pulsed laser is often used to permit the region of
interest to be frozen in time and space. The high repetition rate of some lasers allows for
good frequency tracking of time dependent events such as turbulence. Lasers offer the
opportunity to study the fundamentals of atoms/molecules by probing specific
atomic/molecular states. With a very fast laser pulse along with a fast repetition rate,
molecular phenomena such as energy transfer/chemical reactions can be studied.
2.2 Rayleigh and Raman scattering
When an electric field is incident on a medium, it induces electric dipoles in the medium
which mainly line up in the polarization direction of the electric field. The degree of
induced polarization is related to the strength of the electric field. For a molecule, the
dipole moment p→
induced by an electric field E→
is
r rp E= ε α0
˜ (2.1)
where the electronic polarizability α of a molecule is a tensor in general. This
8
polarizability characterizes how easily the light will induce a dipole moment for a given
molecule.
A medium can have different polarizabilites along different axes. This means that for a
given input wave with E→
along a defined axis, some of the induced dipoles will line up in
orthogonal directions to E→
, as well as along the direction of E→
. For many of the gases
important in combustion, the moment along the incident E→
field direction is
approximately two orders of magnitude greater than off axis moments. This principle is
the motivation behind the difference Raman and Rayleigh scattering techniques discussed
in Chapter 3. Defining the incident E→
along the z axis, α zz is the polarizability for
dipoles pointing in the same direction as the input E→
field (i.e. on axis terms), where
( α αyz xz, ) are the polarizabilities terms for dipoles with components pointing in
orthogonal directions to E→
(i.e. off axis terms).
Polarizability can be expanded in powers of E→
, which results in a term linear with E→
field and terms proportional to a higher power of the E→
field. Higher order processes,
even at high input E→
fields ( such as a laser with power density ~ 109 W/cm2) have a
dipole moment that is approximately 10-3 times the preceding lower order dipole moment.
9
If the polarization is time varying, electromagnetic radiation is emitted from the medium
with the same time variation as the incident polarization of the electromagnetic field. This
new EM wave combines with the incident wave- however, there is a phase lag between
the old and new waves as there is some response time of the medium to produce
oscillating dipoles in response to the incident light.
One resulting combination is a wave scattered with the same frequency as the oscillation
of the incident EM wave (thus an elastically scattered wave). This is called Rayleigh
scattering. It is a linear process and therefore the induced dipole moment of the medium
is linear with the strength of the incident E→
field.
Another combination of the waves is the result of the interaction of the induced EM wave
from the oscillating dipoles with the oscillation or rotation of a molecule about its
equilibrium position. This interaction produces a scattered wave that is shifted from the
oscillation frequency by the frequency of a particular vibrational and/or rotational mode
of the molecule. The resulting frequency of the scattered wave can be higher than the
initial EM wave frequency (Stokes shifted) or lower in frequency (anti-Stokes). This is
therefore an inelastic process, and is termed Raman scattering.
10
The total power of a scattered wave from an induced dipole is
P p E~
~
ω ω ε α42
402
2 2→
=
( )r
(2.2)
For a linear process as Raman and Rayleigh scattering the dipole moment is linear in E→
and therefore P ~ E I→
2
~ , where I is the intensity of the input radiation source.
In a gas, molecules are randomly oriented with respect to one another. Therefore, one
must average α~
2
over all orientations of the molecules. Defining E→
along the z-axis,
the average of the square of the polarizability terms
α γzz a( ) = +( )2 2 21
4545 4
(2.3)
α α γyz xz( ) = ( ) = ( )2 2 21
15
where a is called the mean and γ is the anisotropy. The mean consists only of on axis
polarizability terms, and the anisotropy consists of only off axis terms. For most
scattering processes in typical combustion gases, a is almost two orders of magnitude
larger than γ.
In a typical experiment, scattered signals are collected at an angle from the laser axis to
avoid scattering interferences. An ideal location is perpendicular to the axis. This permits
11
easy two-dimensional imaging, since detection at another angle would require a
transformation of the projected image.
In this experiment, a linearly polarized laser interacts with multiple gaseous species to
produce Raman and Rayleigh scattering. If the polarization axis of the laser is defined as
the z-axis, the laser propagation direction is defined as the y-axis, and the scattering is
collected along the x-axis, the contribution from species m to the radiant intensity of the
scattered light polarized along each of these axes is
I N Iyz mo
m yz m, ,~90 0
2 4( ) ( )
α ω (2.4)
I N Izz mo
m zz m, ,~90 0
2 4( ) ( ) α ω
I xz mo
, 0 0( ) =
The above scattered intensity equations can be arranged in the general form
I CN VIiz m mm iz
,,
=
0
∂σ∂Ω
(2.5)
The depolarization ρm of species m is defined as the ratio of the scattered light intensity
perpendicular to the incident light polarization divided by the scattered light intensity
parallel to the incident light polarization. Combining (2.3) and (2.4),
ραα
γγm
yz m
zz m
yz m
zz m
m
m m
I
I a= = =
+,
,
,
,
( )
( )
2
2
2
2 2
345 4
(2.6)
12
Therefore a completely depolarized molecular transition ( am = 0) gives ρm = 3/4. This
ratio is molecule specific. Tabulated values of ρm are obtained from other work [Penney
1972, Woodward 1967, Murphy 1977, Rowell 1971, Schrötter 1979, Holzer 1973].
In Rayleigh scattering, the scattering intensities of all species m in the probe volume
spectrally overlap, since Rayleigh scattering is an elastic phenomenon. The resultant
Rayleigh signal is therefore the sum of the scattering intensities of all species. Using the
general scattering intensity of (2.5):
I I CVIdd
N
CVI Ndd
X
iz Ray iz Ray mm m iz Ray
mm
totm iz Ray
mm
, , ,, ,
, ,
= ∑ =
∑
=
∑
0
0
σ
σ
Ω
Ω
(2.7)
=
CVI N
ddtot
eff iz Ray0
σΩ , ,
Through the ideal gas law, NP
k TtotB
= , one can relate the Rayleigh signal to temperature,
I CVIPkT
ddiz Ray
eff iz Ray,
, ,
=
0
σΩ
(2.8)
If one calibrates the Rayleigh scattering signal of the experiment with a Rayleigh signal
of known composition and temperature (labeled "ref"), and assuming constant pressure as
in the simple systems we will be studying, one can relate the Rayleigh signal to the
temperature T from (2.8):
13
TI ref
II
I ref
dd
dd
refT ref
aI
iz Ray
iz Ray
eff iz Ray
eff iz Ray
T
iz Ray
=
=,
,
, ,
, ,
,
( )
( ) ( )( )0
0
σ
σΩ
Ω
(2.9)
where aT depends upon the local composition and is independent of temperature.
In Raman scattering, one detects scattering at a frequency shifted from the laser
frequency by an amount specific to a particular vibrational-rotational mode of a
molecular species. Thus the Raman scattering signal for a specific molecular species can
in general be isolated from elastic scattering and from the Raman scattering signals of
other species. The Raman scattering intensity for species m is related to the number
density of species m through (2.5) I CN VIiz m mm iz
,,
=
0
∂σ∂Ω
I CN VIRam iz m mRam m iz
, ,, ,
=
0
∂σ∂Ω
(2.10)
If one calibrates the experimental Raman signal of species m with a Raman signal of a
known quantity of a species n at a known temperature ("ref"), one can relate the Raman
signal to the number density Nm using (2.10):
NI
I refI ref
IN ref
dd
T
dd
Tm
iz Ram m
iz Ram nn
iz Ram nref
iz Ram m
=
, ,
, ,
, ,
, ,
( )( )
( )( )
( )
0
0
σ
σΩ
Ω
(2.11)
The Raman cross section does have a temperature dependence. This temperature
dependence is the result of the quantized levels of the rotational/vibrational states of a
14
molecule. Higher rotational/vibrational energy levels are populated when the temperature
increases, thus decreasing the signal in each level. From a full quantum mechanical
model, the temperature dependence of the Raman cross section of a molecule which
behaves as an ideal harmonic oscillator is:
11− −( )−
exp( / )hω k TB (2.12)
Rotational states (if any) of a molecule may interact with the vibrational states of a
molecule, to produce Raman transitions dependent upon ν and J, the respective
vibrational and rotational levels. It is also possible to have purely rotational transitions.
Rotational levels are much closer together than vibrational levels (≈ 10 cm-1 separation
compared to ≈ 1000 cm-1 separation typically for vibrational levels). To be able to resolve
rotational levels spectrally, one needs spectral resolution on the order of 10 cm-1 to
separate out the different rotational transitions. It is quite a bit easier to resolve
vibrational-rotation Raman shifts. Quantum mechanics yields certain selection rules of
the Raman transitions. For vibrational/rotational Raman (referred to as just vibrational
Raman), these rules are ∆ν=+/-1 and ∆J=0,+/-2. From Placzek polarizability theory, the
average of the square of the derived polarizability tensor components over all orientations
for individual transitions in diatomic molecules are
Q branch (∆J = 0, ∆ν = +1) ( ) ( ' ) ( ),'ν γ+ +
1445
2 2a bJ J (2.13)
15
O, S branch (∆J = +/-2, ∆ν = +1)445
1 22( ) ( ),
'ν γ+ ±bJ J
where bJ,J and bJ±2,J are Placzek-Teller coefficients and γ' and a' are the mean and
anisotropy of the derived polarizability tensor. Q branch transitions depend upon the
mean and anisotropy while O and S transitions depend only on the anisotropy of the
derived polarizability tensor. This implies that the Q branch transition typically have a
much larger Raman cross section than O and S branch transitions. This also implies that
O and S transitions are completely depolarized, and Q transitions are highly polarized.
Not all vibrational/rotational modes of a molecule are Raman active- this is highly
dependent on the symmetry of the molecule.
In theory, all Q-branch (∆ν = ± 1, ∆J=0) transitions originating from different vibrational
levels overlap perfectly since vibrational energy levels are equally spaced. In practice,
the Q-branch spreads out slightly due to the anharmonicity of the vibration, as well as
some coupling between rotation and vibration [Eckbreth 1996]. The O and S branches
(∆ν = ± 1, ∆J=± 2) are far more diffuse than the Q-branch since the energy difference
between rotational levels increases with increasing J. Since the number of rotational
levels populated increases with increasing temperature, the spectral width of the O and S
branches broaden significantly as the temperature rises.
16
2.3 Laser-induced incandescence
Laser-induced incandescence is the emission of blackbody-like radiation from particles
that are heated to temperatures well above ambient by a high intensity laser source. The
qualitiative theory and early experiments on laser-induced incandescence (LII) were done
by Eckbreth [Eckbreth, 1977]. The conservation equation for a particle heated by a laser
was first given by Melton [Melton 1984]. The model presented in this work adapts the
original model to the free molecular regime, and includes terms that are significant yet
unaccounted for in the Melton model [Rosner 2001, Filippov and Rosner 2000a, Rosner
2000]. From energy conservation, the equation for a particle that is subject to laser
heating is:
K a I ap v
T T mH
WT T
K deabs
g gp g p
v
vSB p g
abs
em
π απ γγ
π σ η η ηη
η
20
2 4 4 43
211
1 151
− +−
− + − −−∫
*
* ( / ) ˙ ( / ) ( )( )∆
− =43
03π ρa cdTdtp p (2.14)
In the first term of (2.14), Kabs(a, λ) is determined in the Rayleigh limit, where the radius
of the particle, a, is small compared to the excitation wavelength, λex, of the light
absorbed (2
1πλ
a << ), yielding
laser energyabsorbed/ time
rate of heattransfer tomedium
rate of energyused for particlevaporization
rate of blackbodyradiation loss
rate of internalenergy rise ofthe particle
0
17
K aa m
mabsex
( , ) Imλ πλ
= −+
8 12
2
2 (2.15)
In general, the real and imaginary parts of m will depend upon temperature and excitation
wavelength. The first term of (2.14) is time dependent since I0 is time dependent.
The second term in (2.14) is the rate of heat transfer in the free molecular limit, where the
mean free path in the surrounding gas, lg, is taken to be large compared to the particle
radius- i.e. the Knudsen number is large (Knl
ag= >>1). The mean thermal speed of
molecules in the gas, vg , is derived from a Maxwellian distribution of particles
vk T
mg
B g
g
=
8
1 2
π
/
(2.16)
The average adiabatic constant, γ*, equals (cv*+R)/cv
*, where cv* is the mean value of the
specific heat (at constant volume) between the gas and particle temperatures. The thermal
accommodation coefficient, α, equals 1 if reflection of the gas molecules off the particle
surface is completely diffuse.
The third term of (2.14) is the rate of energy lost due to mass vaporization. This term
competes with particle heating to limit the maximum temperature a particle can reach.
18
The fourth term in (2.14) is generally neglected since it is small compared to the other
terms below 10000 K. Maximum particle temperatures are typically 4000 K for
carbonaceous particles, as vaporization begins to severely limit the temperature rise
above this point.
The particle density, ρp, in the last term of (2.14) is approximately constant, although the
thermal expansion of the particle is taken into account. From mass balance, the mass flux
is
m
adadt
a dTdt
WRT
p vpp v
v
pv p4 32π
ρ β α= − = − (2.17)
The mean thermal velocity of the particle vapor, vv , is calculated from a Maxwellian
distribution of particles. The vapor pressure of the particle material, pv, is assumed to take
the form of the Clapeyron equation
p pH
RT
T
Tv vv
p
p
p
= −
**
*
exp∆
1 (2.18)
The particle density changes with temperature according to
ρ ρ βp p g p gT T T T( ) ( )exp ( )= − −( ) (2.19)
where Tg is the reference gas temperature and ρp(Tg) is known.
19
The imaginary part of the index of refraction, κ, will scale with the particle density and
will therefore change with particle temperature
κ κ β( ) ( )exp( ( ))T T T Tg p g= − − (2.20)
For a known initial particle temperature Tp,0 and radius a0, and a known time dependent
laser power density I0, (2.14) and (2.17) may be numerically integrated to determine
Tp(t,a0,I0) and a(t,a0,I0), the time dependence of the particle temperature and particle
radius.
The emission intensity of a particle at a detection wavelength λ em is
I a e Tem b em p= 4 2π ε λ( , ) (2.21)
where e T
e
b em p em hc
kTem p
( , ) ~λ λλ
−
−
5 1
1
(2.22)
Since ε λ= K aabs em( , ), (2.21) becomes
I a K a e Tem em b em p= 4 2π λ λ( , ) ( , ) (2.23)
Iem is time dependent as both a and Tp vary with time. The relative incandescence signal
at time t for a particle is then
S I T t a t I T aem em p em p= −( ( ), ( )) ( , ),00
(2.24)
where Tp,0 and a0 are the particle temperature and radius before the laser pulse arrives.
20
The relative incandescence from a distribution of particles, with initial particle size
distribution p(a0) centered at a0 and ranging from a1 to a2, over a spectral region ranging
from λ1 to λ2, within a volume V, at time t is
J t N S a t T t p a g da d dVp ema
a
Vp( ) ( ( ), ( )) ( ) ( )= ∫∫∫
1
2
1
20 0 0
λ
λ
λ λ (2.25)
The only quantity with inherent spatial dependence is the laser intensity. When
numerically integrating (2.14) and (2.17) to get a(t) and Tp(t) for different values of a0,
the spatial variation in I0 must be taken into account.
2.4 Chemiluminescence
Chemiluminescence is the emission of photons by an atom or molecule that has been
excited by chemical interaction to an electronically-excited state. The signal is directly
proportional to the rate at which the atom/molecule spontaneously emits photons, called
the Einstein A coefficient. The measured emission signal is given by [Hertz 1988]
S A V Nem em= 1
4 21πτ εη*Ω (2.26)
The spectral dependence of the emission is a signature of the excited state molecule,
making molecules/atoms with known emission curves easy to detect.
21
Since there is no laser sheet to define a measurement plane, the emission signal collected
is an integration of the emission over the line of sight between the flame and a
corresponding pixel location of the two-dimensional imaging system. Since intermediates
in laminar, diffusion flames such as CH and OH occur in a very thin region of the flame,
largely away from the centerline (except near the flame tip), the emission intensity has
cylindrical symmetry. A tomographic inversion technique, called Abel inversion,
converts the line- of-sight integrated emission signal into a two-dimensional in-plane
emission intensity image. The Abel technique assumes a perfectly axisymmetric signal
distribution, and the collection of only infinitely thin and parallel rays. Therefore,
collection must be done as far away from the flame as possible, along with largest lens f/
possible, to allow approximately parallel rays to be collected [Hughey 1982, Dasch 1994,
Walsh 2000].
2.5 Laser light scattering
Laser light scattering (LLS) of particles refers to the elastic scattering of laser light off of
particles. LLS gives information on particle size, number density, and morphology. For
aggregate particle structure, LLS determines the radius of gyration, Rg, of an aggregate
22
[ Rn
rgp
ii
np2 2
1
1==∑ ]. Early soot experiments attempted to infer soot paticle sizes and number
densities using Mie theory [Kent and Wagner 1982, Santoro et al. 1983]. This theory
assumes particles are spherical. Thus to determine the scattering from an aggregate using
this theory, a volume-equivalent radius (aes) of an aggregate must be determined, and
used in place of the particle radius of a single particle (a):
aes/a = np1/3 (2.27)
This implies that an aggregate, no matter how complex in structure, will scatter the same
amount of light as a spherical particle that has a volume equal to that of the aggregate.
More recent work has shown the equivalent sphere-Mie theory to inaccurately predict aes
for large (np>10) aggregates. [Köylu, 1996].The predictions become more inaccurate for
larger np. From Rayleigh theory (2πa/λ<<1), the scattering cross section for scattering off
an individual particle with polarization parallel to the light source polarization is [Köylu
1993]
Ca F m
kpνν θ θ( ) ~
( )cos ( )
6
22 (2.28)
where F(m) is a function of the index of refraction, and θ is the angle at which the
scattering is collected relative to the forward scattering direction. For aggregates, a more
realistic theory than the equivalent sphere Mie theory is the Rayleigh-Debye-Gans theory,
which accounts for the closely spaced particles within the aggregate. Taking into account
23
the effects of phase differences in the scattering from individual particles, the parallel
scattering cross section for an aggregate is
C n C qRap
pgνν νν= ƒ2 ( ) (2.29)
where ƒ( )qRg is the form factor of aggregates of any shape and q k= 2 2sin( / )θ . If one
models the aggregates as fractals with fractal dimension Df , the form factor is [Dobbins
and Megaridis 1991]
ƒ =−
( ) expqRq R
gg
2 2
3q2Rg
2<3Df/2 Guinier regime (2.30)
= ( )− ƒq Rg
D2 2 2/q2Rg
2>3Df/2 Power law regime
The relationship between np and Rg for a fractal is
n kR
apg
D
=
ƒ
ƒ
(2.31)
Using (2.29-2.31) one arrives at an expression for the parallel scattering cross section of a
fractal-like aggregate:
C n C aqn
ka
pp p
DF
νν νν= −
ƒ
2 2
2
13
exp ( )
/
q2Rg2<3Df/2 Guinier regime (2.32)
C n Ck
aqa
pp
DFνν νν= ƒ
( )q2Rg
2>3Df/2 Power law regime
2.6 Laser absorption
24
The measurement of laser absorption in a medium involves recording the intensity of
laser light entering a medium and recording the intensity of light after it has passed
through the medium. The ratio of the two intensities gives information about the bulk
absorption properties of the material, which depends upon the refractive index, m,
primary particle diameter, a, and particle volume fraction of the material. In the Rayleigh
limit, (2πa /λ<<1), the absorption cross section for isolated primary spherical particles is
Given by (2.15) Ca m
maex
= −+
8 12
2
2
πλ
Im (Note Kabs is renamed Ca here to be consistent
with the spectral extinction literature). The extinction coefficient, Ke, is related to Ca and
the total scattering cross section, Cs, through [Köylu 1996]
K N C Ce p a s= +( ) (2.33)
For an input light intensity, I0 , the output intensity, I, through a medium of length L is
given by Beer's law :
I I K Lo e= −exp( ) (2.34)
The condition for applicability of this equation is an optically thin medium, i.e.
KeL<<1. This condition can be relaxed as long as absorption is the dominant mechanism,
i.e., NpCsL<<1 [Bohren 1983]. In this limit,
K N Ce p a= (2.35)
25
The basic principles of the optical techniques used in the experiments have been
described in this chapter. The final equations used to determine physical quantities from
the measurements are developed in the experimental sections as a given technique is
used.
26
Chapter 3Characterization of a Steady and Time-Varying,
Axisymmetric, Laminar Diffusion Flame
3.1 Introduction
Laminar, two-dimensional flames (with one axis of symmetry) are well suited to laser-
diagnostic studies and computational modeling due to their stability ( i.e. remaining
frozen in space) and their symmetry. This allows for signal averaging in the experiment,
which will greatly improve the signal-to-noise ratio for a weak optical process used as the
diagnostic tool. The simple, symmetric and predictable flows of these flames allow for
computational modeling that includes both detailed chemistry and full fluid mechanics.
In turbulent combustion modeling, it is impossible computationally to incorporate both
the turbulent fluid mechanical models and detailed chemistry, so reduced reaction
mechanisms need to be developed. Another class of flames has been studied to bridge
the gap between laminar and turbulent flames: time-varying laminar flames. This flame
may be formed by imposing a periodic fluctuation in the flow of a laminar flame. This
flame offers the advantage a repeatable interaction of chemistry and fluid mechanics.
Therefore a detailed chemistry model along with the well-defined fluid mechanical model
can be applied to computationally model this flame. Information on chemistry and flow
interaction in these flames can be used to help modelers develop better models for
turbulent combustion. The repeatable environment and detailed chemistry calculations
27
make it possible to evaluate different possible reduced mechanisms, which in turn may be
applied to the turbulent combustion models. The turbulent combustion simulations may
then be used to help design practical combustion devices, where combustion is almost
always turbulent. Since many different reactions comprise the detailed chemistry model,
each of which is described by an uncertain reaction rate, the results obtained in the
numerical simulations must be verified experimentally.
3.2 Flame and Burner Characterization
The flame studied here is a lifted, axisymmetric laminar diffusion flame. The fuel is
methane, diluted with nitrogen (35% dilution by volume) to reduce soot production in the
flame. Methane is used for its simple structure that allows for detailed computational
modeling. The flame is lifted to prevent heat loss to the burner, which will simplify the
computations. The suppression of soot production allows us experimentally to measure
species concentrations and temperature in every part of the flame, while also allowing
less complex modeling. The flame is surrounded by a coflowing annular region of air
which prevents dust particles from entering the system, as well as helping to lift the flame
from the burner. This flame has been computationally modeled with full C2 and nitrogen
chemistry [Smooke 1996], and has been the basis for a number of computational and
experimental comparisons [Smooke 1996, 1992, 1990, Xu 1993], as well as previous
28
theses [Marran 1997, Lin 1995, Xu 1991]. Major species and temperature measurements
have been taken on this system using spontaneous Raman scattering [Lin 1995, Xu 1993,
Smooke 1990]. These experiments produced significant interferences from fluorescence
of fuel fragments just rich of the flame zone. Difference Raman scattering [Marran 1997]
is effectively applied to eliminate these interferences.
The burner is shown in Figure 3.1. The burner consists of a cylindrical fuel tube
surrounded by an annular region containing a 1/64" cell honeycomb, which is flush with
the top of the fuel tube. The honeycomb straightens the flow of air to produce a radially
constant coflowing region. The 6.8 cm long fuel tube is almost 3 times longer than the
length needed for fully developed pipe flow under the conditions studied. The fuel tube
inlet is open, producing a parabolic radial velocity profile across the tube (Poseille flow),
with a maximum velocity along the tube centerline. The fuel tube has an inner diameter
of 4 mm and a wall thickness of 0.5 mm, and is attached at the bottom to a plenum. The
coflow region has a diameter of 5 cm. A loudspeaker is attached to the bottom of the
plenum. This speaker is used to generate the time-varying laminar flame by modulating
the fuel flowrate. Similar time-varying diffusion flames have been studied
29
Figure 3.1 Forced flame burner.
Fuel Jet
Air
Fuel
Loudspeaker
4 mm Glass Beads
Fine Steel Wool
80 Mesh Screen
1/64" Honeycomb
30
experimentally [Skaggs and Miller 1996, Smyth et al. 1993, Mohammed et al. 1998].
This study represents the most complete characterization of a flow-modulated flame in
the current literature.
3.3. Boundary Conditions
3.3.1 Steady Flame
The flow of the fuel has a constant, average fuel exit velocity (at the burner surface)
across the fuel tube of 35 cm/s with a peak velocity along the tube centerline of 70 cm/s.
In the steady flame, the flow remains constant in time. The coflow region maintains a
radially constant flow of 35 cm/s. The two coflowing regions have a matched average
inlet velocity to minimize sheer effects in the boundary between them. The flow
conditions are chosen to lift the flame off the burner while remaining in the laminar
regime (i.e. flame is constant in space and time), and have fully developed Poseille flow
in the fuel tube. Flow boundary conditions near the burner surface are verified and
matched with computational flow boundary conditions using Particle Image Velocimetry
(PIV).
31
3.3.2 Particle Image Velocimetry
Particle image velocimetry determines velocity in a gas or liquid by acquiring multiple
consecutive, planar exposures of Mie-scattered light from particles seeded into the flow.
Techniques used fall into 1 of 2 categories:(1) acquiring multiple consecutive exposures
with a single image, such that the image has multiple images of the same particle, or
(2) acquiring separate consecutive images, such that each image contains one particle
image for each particle. The distance and direction of the flow in the measurement plane
are determined. Since the time between exposures is known, one can determine the flow
velocity by the following expression:
rr r r
vs
M tX X
M t= = −
∆ ∆1 2 (3.1)
where M is the magnification of the image, ∆t is the time between exposures, and r rX X1 2,
are the image positions of Mie scattering off a particle in exposure 1 and exposure 2
respectively. PIV requires the consecutive particle images to be similar in intensity and
size in order to correlate the image pair. This requires either the same light source for
consecutive exposures or two equal intensity, spatially overlapping light sources for
consecutive images. Rather than identify individual image pairs, the average particle
displacement is computed over an interrogation window of the PIV images using
correlation algorithms. For technique (1), under the assumption that the imaging device
32
only detects intensity and not color, for a single particle it is not known which particle
image refers to rX1 and which to
rX2 . This leads to a directional ambiguity in the
measurement. Also, zero velocity cannot be measured as the particle images will be right
on top of each other. Therefore technique (2) is considered an improved technique, and is
used in the velocity measurements here. The drawback of technique (2) is the
requirement for equipment capable of acquiring consecutive images separated by ∆t,
appropriate for the flow studied.
In this experiment, Mie scattering images of sugar particles seeded into cold flowing
gases are used for the PIV analysis to verify velocities near the burner inlet for the fuel
tube and coflow regions. A flow of room temperature air with flow rates matching that of
the flows for the experiment is seeded with sugar particles (TSI particle generator Model
9306, with a concentration of 1 g/L sugar in a 50/50 water/methanol mixture). Under
these conditions the atomizer produces sugar particles approximately 1-2 µm in diameter.
It is important that the particles effectively track the gas flows for PIV to give desirable
results. Using the relationship of Melling [Melling 1997] that takes into account the
maximum frequency of the gas motion, seed particle density, gas density, and gas
viscosity, one can determine the maximum allowable particle diameter that will track the
flow exactly. For the forced flame, 20 Hz is the maximum frequency of motion, which
33
yields a maximum allowable particle diameter of 20 µm. Therefore the 1-2 µm sugar
particles should track the flow exactly. The fuel tube and coflow regions both are seeded.
Seeding densities are chosen to produce at least 8 particle images within the interrogation
region of the correlation [Keane 1992]. A frequency doubled Nd:YAG laser (532nm
wavelength, 10 Hz rep rate) is Q-switched twice for each repetition to produce two
consecutive green light pulses of 8 ns duration. These consecutive laser pulses are needed
for the consecutive Mie-scattering images. Laser pulse separation is 250 µs, and each
pulse has approximately the same energy and energy distribution. This time separation is
found to give the most reliable results using a cross correlation algorithm for interpreting
flow velocities. The laser is focused over the burner with a cylindrical lens, producing a
vertical laser sheet 10 mm tall. The laser sheet is located 1 mm off the burner surface, as
moving the beam closer to the surface caused significant elastic scattering interference in
the images. The consecutive laser pulses produce Mie scattering from sugar particles at
two consecutive instances. The Mie scattering is collected at 90 degrees to the laser by a
fast CCD camera (Cooke Sensicam), which can record two images less than 1 µs apart.
Consecutive Mie scattering-images from the seeded particles are obtained. The
magnification of the images corresponds to 140 pixels/mm. Each imaged region is 9 mm
wide and 7 mm tall, including regions above the jet and above the coflow on both sides of
the jet. A cross correlation algorithm is applied to the image pairs to determine flow
velocities. The size of the FFT interrogation region for the cross correlation is 64 pixels x
34
64 pixels (or 450 µm x 450 µm). The PIV algorithm produces velocity vectors with a
vector separation of 32 pixels (or 225 µm) in both the horizontal and vertical directions.
The interrogation region in image 2 is displaced from image 1 by the average particle
displacement vector from particles on image 1 to particles on image 2. This eliminates
the undesired affect of particles leaving the interrogation region from image 1 to image 2.
Also, the beam thickness is chosen to be thick enough to eliminate particles leaving the
image plane from image 1 to image 2. Conversely, the beam thickness needs to be thin
enough such that the image volume does not produce out of focus particle images, which
would limit the accuracy of the velocity determination. The laser beam waist is measured
by replacing the cylindrical lens with a spherical lens of same focal length, focusing the
laser beam to a line across the burner, and imaging the Mie scattering from sugar
particles onto the CCD camera. The measured beam waist is 400 µm.
PIV results indicate a parabolic axial flow above the fuel tube at the burner surface as
well as downstream from the surface, along with a uniform axial flow in the coflow
region. There is no detected radial velocity components from the PIV measurements.
These results are compared to the computational boundary conditions at the burner
surface. Figure 3.2 shows the computational velocity profile at 1 mm above the burner
surface compared to the experimental profile obtained by PIV 1 mm above the burner
35
Figure 3.2 Computational and PIV velocity profiles 1 mm above the burner.The velocity vectors are parallel to the burner axis.
Burner Inlet Velocity
0
100
200
300
400
500
600
700
radial position(mm)
Tube wall
Coflow Fuel Tube
Centerline
02.0 1.03.04.0
PIV
Computational
velo
city
(m
m/s
)
36
surface. The two profiles show good agreement, with a slightly larger dead zone (region
above the wall of the fuel tube where the velocity is minimal and flat) in the experiment
than in the computation boundary condition. Also the experimental velocity along
centerline is slightly lower (5%). The dead zone length difference may be attributed to
the physical geometry of the honeycomb mating with the fuel tube, while the slight
centerline difference may be due to non-ideal Poseille flow above the fuel tube, or slight
inaccuracy in flow metering.
Slight variation in the dead zone length and slight variation in centerline inlet velocity
produces at most a 1 mm difference in flame lift-off height in the computations.
However, the flame structure remains unaltered. Therefore, slight differences in
experimental and computational boundary conditions should not produce flame profile
differences.
3.3.3 Time-varying Flame
The same volumetric flow rates used in the unforced case are applied to the time-varying
flame. The loudspeaker is driven with a 20 Hz sine wave from a function generator
(HP 33120A). The modulation frequency is chosen as a convenient multiple of the laser
repetition rate rate (10 Hz). The peak-to-peak amplitude of the sine wave is set to 0.7V
37
to produce 30% flow modulation and to 1.225V to produce 50% flow modulation along
the fuel tube centerline at burner inlet. The reason for studying these specific modulations
is to have a system with enough modulation to make a significant difference from the
steady case but not to create an overly modulated system where the local strain rates may
be too high and computations would be very difficult. This flame oscillates at the
modulation frequency, but does not naturally flicker when there is no modulation
frequency applied to the speaker. Natural flickering in diffusion flames has been studied
by several researchers [Cetegen 1993, Chen 1988, Hamins 1992], and are observed to
flicker at single frequencies. This oscillation frequency is inversely proportional to the
square root of the burner diameter. The oscillation occurring in these jet flames is thought
by several researchers to be caused by the instability of the buoyant plume generated by
the flame and by the interaction of the flame with the plume-generated vortices [Chen
1993, Hamins 1992]. Recent work suggests the oscillations to be caused by flow
instabilities near the wall of the fuel jet [Maxworthy 1999].
The PIV experiment to verify boundary conditions is described in the previous section. In
this experiment, the function generator is synchronized with the laser, camera, and a
delay generator to allow acquisition of any particular phase of the forcing modulation.
PIV images are taken over 1 period of modulation at 10 equally spaced phases of the
forcing. To obtain the most reliable velocity measurements at each phase, the delay
38
between consecutive laser pulses is varied from 0.1 to 0.4 ms, depending on the specific
phase (or fuel tube exit velocity). The effect is to have similar particle displacements
between the consecutive Mie scattering images for each phase. The maximum variation
in flow velocity over the time between consecutive images produces a maximum particle
image displacement fluctuation, ∂x, of 3 µm or 0.4 pixels. Since particle images are 1-2
pixels in diameter (di), and interrogation regions are 64 pixels in length (d1), the criteria
of Keane for reliable velocity determination using the cross correlation algorithm are
satisfied :
∂x/d1 < .03 (3.2)
∂x/di < 1
Peak centerline velocities near the burner inlet, as well as velocity profiles across the
burner near the surface and downstream, are compared with the computational boundary
conditions over each point in phase space where data is acquired.
The results of the PIV indicate a sinusoidal variation in centerline
velocity closely resembling the computational modulation condition for 30% and 50%
modulation (see Figure 3.3 for the 30% modulation case). The only difference is the
average centerline exit velocity, which is 67 cm/s, as measured by PIV in the unforced
flame. In Figure 3.4, notice the phase lag between the forcing function to the speaker and
39
Figure 3.3 Computational and PIV fuel tube centerline velocity for 30% modulation of flow in the fuel tube as a function of forcing phase. Points are taken 1 mm above the burner surface.
Centerline Inlet Velocity30% modulation
40.0
50.0
60.0
70.0
80.0
90.0
100.0
0 20 40 60
time(ms)
PIVComputational
velo
city
(cm
/s)
40
Figure 3.4 Fuel tube centerline velocity and speaker forcing signal for 30% modulation
in the fuel flow as a function of forcing phase. Notice the phase difference between thevelocity (upper curve) and the forcing signal (lower curve)
Centerline Inlet velocity and Speaker Forcing Signal30%flow modulation
Forcing Signal(V)
0
20
40
60
80
100
0 10 20 30 40 50 60
time(ms)
forcing signalvelocity
+0.70
-0.70
Vel
ocit
y(m
m/s
)
41
the velocities for the 30% modulation case. No radial velocity components are detected
with PIV. The velocity profile across the fuel tube remains parabolic over the observed
phases of the forcing, while the coflow velocity remains constant in time and spatially
uniform over the modulation.
3.4 Computational Modeling
Computations on the flame are obtained by the group of Professor Mitchell Smooke at
Yale University. Two-dimensional species concentration and temperature profiles are
obtained and compared with experiments.
3.4.1 Unforced
The conservation equations are formulated with velocity-vorticity variables (containing
vorticity terms). The equations have first order accuracy in space for diffusive and
convective terms and second order accuracy in space for viscous terms. The steady-state
equations are discretized on a non-uniform, non-adaptive grid. The chemical mechanism
contains C1 chemistry and involves 20 chemical species.
42
3.4.2 Forced
The conservation equations are formulated with velocity-vorticity variables (containing
vorticity terms). The equations have first order accuracy in space for diffusive and
convective terms and second order accuracy in space for viscous terms. The equations
have second order accuracy in time. The time-dependent equations are discretized on a
non-uniform, non-adaptive grid. The chemical mechanism used involves 15 chemical
species.
3.5 Measurement of CH* via Chemiluminescence
3.5.1 Introduction
Chemically-excited CH (or CH*, the A2∆ molecular state of CH) is the source of blue
light in hydrocarbon diffusion flames. CH* occurs in a very spatially thin, small high
temperature region in diffusion flames, and is a good marker of the flame front. CH*
concentration in flames is spatially coincident with CH concentration [Walsh 2000].
Therefore, measurements of CH* indicate the spatial distribution of CH in the flame. The
radical CH* is also known to play a role in the C2 reaction chain [Najm 1998].
43
CH* chemiluminesces via the the A2∆ -> X2Π transition. From (2.26)
S A V Nem em= 1
4 21πτ εη*Ω the CH* emission signal Sem is proportional to the number
density N* of CH*. In this experiment there is only determination of relative CH* number
density. The purpose of this experiment is to observe the effect of the flow modulation on
the flame front at different phases of the forcing before more quantitative measurements
are performed.
3.5.2 Experimental Setup and Acquisition
The setup is shown in Figure 3.5. CH* flame emission is collected with a f/8 50mm lens
at a distance of 50 cm from the burner. The collected light passes through an interference
filter centered at 430 nm (10 nm bandpass) and is focused onto a gated, image intensified
(1 ms gate time) CCD camera (Photometrics CC200). This spectral region contains the
maximum CH* emission (from the (0,0) bandhead of the A2∆ -> X2Π transition). This
spectral region also has minimal interferences from flame emission signals of other
species. Images are obtained for the steady and time-varying flames. For the latter,
images are obtained for 10 equally spaced phases (5 ms intervals) over one period (50
ms) of the forcing. Five of the phases correspond to phases of acquisition for the two
44
Inte
nsif
ied
CC
DC
amer
a
Inte
rfer
ence
Filt
er
Len
ses
Fun
ctio
nG
ener
ator
Mec
hani
cal S
hutt
er
Com
pute
r
Bur
ner
Lou
dspe
aker
Exp
erim
enta
l Set
up
Fig
ure
3.5
Exp
erim
enta
l set
up f
or C
H*
emis
sion
mea
sure
men
t
45
scalar and multispecies measurements. Acquisitions are phase locked and integrated over
200 intensifier gates. The 1 ms gate time is small enough compared to the 50 ms period
of forcing that there there is little change in the flame over the gate time, and large
enough to acquire sufficient signal.
For several of the phases there is significant interference from soot emission. For these
phases, data is acquired at a separate time in the same manner as described above, but
with a sharp cut colored glass filter (03FCG-115, Melles Griot - cuts off light with a
wavelength below 680 nm) replacing the interference filter. There is no detectable CH*
emission through this filter- the light which passes through is blackbody emission from
soot. This data is used to correct the raw CH* images.
Images of dark current and fixed pattern detector noise are acquired for the same
integration time as the data. These images serve as the background on the CH* images
and soot images.
3.5.3 Image processing
46
The detector dark current image ID is subtracted from both the soot emission and CH*
emission images ICH*(x,y) and Isoot(x,y). The background subtracted soot image is scaled
by an empirical factor c, and subtracted from the background subtracted CH* emission
image:
I x y I x y I c I x y ICH corr CH D soot D*, *( , ) ( , ) ( , )= −( ) − −( ) (3.3)
The image is cropped such that one half of the axisymmetric image remains (x=0 now
corresponds to the centerline of the flame). For each vertical pixel height y of the
corrected emission image, an Abel inversion is performed to convert the integrated line-
of-sight collection of CH* emission into an in-plane two-dimensional CH* emission
profile. The large object distance and large f/ helps eliminate foreshortening and parallax-
this is critical since the Abel inversion assumes that parallel light rays are collected. The
inverted two-dimensional emission profile is calculated by the following equation:
I x yI x y
xx x x
x x xCH Abelx x
xpixelsCH corr
*,'
*,/
/( ' , )( , )
log( ' )
( ) (( ) ' )= ∑
+ −+ + + −
=
11 1
2 2 1 2
2 2 1 2π∂
∂(3.4)
The derivative ∂
∂I x y
xCH corr*, ( , )
is calculated using a least-squares approximation to three
consecutive pixel values [Dasch 1994, Walsh 2000]. The two-dimensional emission
47
profile is mirrored to obtain a full symmetric profile, and the image size is scaled and
cropped.
3.5.4 CH* profiles for the steady and time-varying flame
Shown in Figure 3.6 are the CH* profiles for the steady flame, 30% and 50% flow-
modulated flames. Five equally spaced phases ("a"-"e") of the forced flame that span one
period are shown in the figure. Also indicated is the centerline fuel exit velocity for each
phase of the forcing. The flame length is the shortest at phase "a". Then the flame length
increases at successive phases "b"-"e". The degree of flame curvature is minimal at phase
"e" and maximal at phase "b". From the profiles it appears that the flame starts to "pinch
off" at phase "a" and continues to "pinch off" at phase "b", while the downstream flame
portion convects upward and out of the measurement area. As expected, the 50% flow
modulation shows greater curvature in flame profiles and more drastic modulation than
the 30% case. There is no apparent phase lag between the 30% and 50% modulations.
3.6 Fuel Concentration, Temperature, and Mixture Fraction Measurement
using the Two Scalar Technique
3.6.1 Theory and introduction
48
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
r(m
m)
r(m
m)
r(m
m)
r(m
m)
r(m
m)
min
max
0.04
40
0
6080100
120 0
0.01
0.02
0.03
20
0.05
0.06
stea
dy f
lam
e
Cen
terl
ine
fuel
exi
t vel
ocity
vs.
tim
e
v(cm/s)
time(
s)d
cb
ae
(ii)
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4r(
mm
)r(
mm
)r(
mm
)r(
mm
)r(
mm
)
(a)
(b)
(c)
(d)
(e)
(a)
(b)
(c)
(d)
(e)
(i)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
stea
dy
r(m
m)
30% 50
%
Fig
ure
3.6
(i)
Exp
erim
enta
l CH
* pr
ofile
s fo
r 30
% a
nd 5
0% m
odul
atio
n.
(i
i) C
ente
rlin
e fu
el e
xit v
eloc
ity v
s. ti
me
(for
50%
mod
ulat
ion)
. Pha
ses
whe
re d
ata
is ta
ken
are
mar
ked
by a
,b,c
,d,e
on
the
grap
h an
d co
rres
pond
to th
e im
ages
labe
lled
likew
ise.
Ste
ady
flam
e im
age
is s
how
n on
the
far
left
. The
ste
ady
flam
e fu
el e
xit v
eloc
ity is
indi
cate
d in
the
grap
h.
49
Mixture fraction is a useful non-dimensional parameter that can be useful in comparing
the behavior of flames of different geometries and stoichiometries. It is defined as the
mass fraction of all atoms originating in the fuel stream. For practical purposes, reduced
formulations of mixture fraction are desired to limit the number of measurements needed
to calculate mixture fraction.
The two scalar method determines the mixture fraction and temperature from the
measurement of fuel concentration and Rayleigh scattering. The two scalar measurement
approach has been applied to the study of laminar as well as turbulent nonpremixed
flames [Stårner 1994, 1996, Kelman et al. 1994, Frank 1994]. A recent improvement in
the two-scalar method [Fielding 2001] improves the measurement of mixture fraction
near the flame front.
One method for obtaining reduced definitions of mixture fraction is outlined below:
The energy and chemical species conservation equations may be combined into a single
equation through the use of coupling functions, α, that obey the equation
L( )α ω= (3.5)
where L is an operator defined by
L v D( ) [ ]α ρ α ρ α= ∇ ⋅ − ∇r(3.6)
50
A conserved scalar ß is a linear combination of coupling functions which satisfies
L ß( ) = 0 (3.7)
independently of the knowledge of chemical reaction rates. If one assumes
equal mass and thermal diffussivities (i.e. Lewis number = mass diffusivity/ thermal
diffusivity = 1), equal species diffusivities, and a 1-step reaction between fuel F and
Oxidant O
ν ν νF O PF O P+ → (3.8)
the fuel mass fraction YF and the sensible enthalpy H=cpT/Q may be combined into a
conserved scalar
βFT F pY c T Q= + / (3.9)
Alternatively, Bilger formulated a conserved scalar based on the mass fractions Zi of C,
H, and O [Bilger 1990]:
βν ν νCHO
C
C C
H
H H
O
O O
ZW
ZW
ZW
= + −2 (3.10)
where νi are the stoichiometric coefficients of the atom balance equation
ν ν νC H OC H O P+ + → (3.11)
This definition of β allows for intermediate reactions to take place between reactants and
products, different diffusion coefficients for the involved chemical species, and preserves
the stoichiometric mixture from the stoichiometric equation (F+O -> H2O+ CO2).
Therefore βCHO gives a more rigorous representation of the physical process than βFT .
51
Figure 3.7 Burke-Schumann flame configuration. Thefuel and oxidizer streams are denoted 1 and 2 respectively.
Oxidizer OxidizerFuel
2 21
52
The advantage of βFT is the requirement of two measurements as opposed to
measurement of every major species containing C, H, and O for βCHO.
For a simple flame geometry described by Burke and Schumann, shown in Fig. 3.7, the
fuel exits a cylindrical tube, which is surrounded by a concentric tube through which
oxidizer exits. The fuel and oxidizer streams are denoted 1 and 2 respectively.
Then the mixture fraction may be defined in terms of ß:
ξ β ββ β
= −−
2
1 2
(3.12)
Therefore, ξ = 1 in the fuel stream and ξ = 0 in the oxidizer stream. Using the ideal gas
law, and assuming constant pressure, fuel mass fraction is related to fuel number density
by:
YNN
WW
NN ref
N refN
WW
NN ref
X ref TT ref
WWf
f
tot
f
mix
f
tot
f
mix
f f
mix
= = =( )
( )( )
( )( )
(3.13)
where "ref" refers to a reference species of known concentration and temperature. Fuel
mass fraction and enthalpy can be expressed in terms of Rayleigh and fuel Raman
scattering intensities. Assuming the reference species is fuel and the Raman cross section
for the fuel does not vary much with temperature,
(2.11) NI
I refI ref
IN ref
dd
T
dd
Tm
iz Ram m
iz Ram nn
iz Ram nref
iz Ram m
=
, ,
, ,
, ,
, ,
( )( )
( )( )
( )
0
0
σ
σΩ
Ω
becomes
53
NI
I refI ref
IN reff
iz Ram f
iz Ram f
≈ , ,
, , ( )( )
( )0
0
(3.14)
Combining with (3.13) YNN
WW
NN ref
N refN
WW
NN ref
X ref TT ref
WWf
f
tot
f
mix
f
tot
f
mix
f f
mix
= = =( )
( )( )
( )( )
and (2.9) TI ref
II
I ref
dd
dd
refT ref
aI
iz Ray
iz Ray
eff iz Ray
eff iz Ray
T
iz Ray
=
=,
,
, ,
, ,
,
( )
( ) ( )( )0
0
σ
σΩ
Ω
gives
Y CI
WaIf
Ram f
mix
T
Ray
= 1, (3.15)
H Cc
QaI
p T
Ray
= 2 (3.16)
where CX ref W I ref
I reff Ray
Ram f1 =
( ) ( )
( ),
and C I refRay2 = ( ) are constants. (Note the subscript "iz"
is dropped as the signals measured are integrated over all polarization directions.)
Combining (3.9) βFT F pY c T Q= + / , (3.12) ξ β ββ β
= −−
2
1 2
, (3.15), and (3.16), the
mixture fraction formulation based on the conserved scalar βFT can be expressed in terms
of fuel concentration and Rayleigh scattering intensity:
ξ FTT Ram f
mix Ray
p T Ray pCa I
W IC
c a I c T
Q= +
−3 4
2 2, ,( / )(3.17)
where CC
Y c T c T QF p p3
1
1 1 1 2 2
=+ −, , ,( ) /
and CQ
Y c T c T QF p p4
1 1 1 2 2
1=+ −
/( ) /, , ,
are constants.
54
Therefore one can determine ξ and T from two scalar measurements in a flame: Rayleigh
scattering and fuel Raman scattering (one can use an alternative scalar measurement for
fuel concentration, as long as the signal intensity is proportional to fuel concentration.)
The terms aT,Wmix, and cp are all functions of ξ and reactedness, r, which is defined by
rT T
T Tad
= −−
2
2
(3.18)
It has been shown by recent work that defining aT,Wmix, and cp as a function of ξ FT gives
a two scalar mixture fraction which is closer to ξCHO than if aT,Wmix, and cp are defined as
funtions of ξCHO. In the unreacted (frozen) regions, aT, Wmix, and Cp (with subscript "fr")
are all linear with ξ , and usually nonlinear with ξ in the reacting regions (with subscript
"r"). The terms in the reacted region are modeled from computations. The resulting terms
aT, Wmix, and Cp are linear functions of reactedness and take the form (showing aT as an
example)
a r a raT T fr T r= − +( ) , ,1 (3.19)
With reference data at known concentrations and temperatures for the Rayleigh and fuel
Raman signal, C1 and C2 can be determined. Initially, ξ and r are set equal to zero. Then
all the functional terms (aT,Wmix, and Cp) are calculated. Using these terms, ξ FT is
calculated from (3.17), and temperature is calculated from (2.9) T aI ref
ITRay
Ray
=( )
. From
55
(3.18) r is calculated. This new ξ and r are used to calculate aT,W, and Cp again, and the
process is repeated until there is convergence.
3.6.2 Experimental Setup
The setup is shown in Figure 3.8. A frequency doubled, Q-switched Nd:YAG laser ( 532
nm wavelength, 10 Hz rep rate), producing green light pulses of 8 ns in duration and
energy/pulse of 200 mJ is focused by a cylindrical lens into a vertical sheet 18 mm tall
over the burner surface. Rayleigh scattering and Raman scattering are collected
perpendicular to the laser with a 50 mm focal length camera lens (with f/ 1.8 for Raman
and f/ 5.6 for Rayleigh imaging). The acquisition of the Rayleigh and Raman signal is
done independently of one another, justified by the repeatability of the flame. An
interference filter is used to spectrally isolate the Rayleigh and Raman scattering. For
Rayleigh imaging, an interference filter centered at 532 nm (10 nm bandpass) is placed
just behind the lens. A bandpass of 10 nm implies the throughput of the filter decreases to
50% of its maximum at +/- 5 nm from the wavelength of maximum throughput, and
typically less than 5% of maximum throughput at +/- 10 nm . For fuel Raman imaging,
an interference filter centered at 630 nm (10 nm bandpass) is used, which corresponds to
the spectral region of the Stokes-shifted methane Raman scattering using the specific
56
Figure 3.8 Experimental setup for two scalar imaging
laser
burner
50 mm camera lens
interference filter
CCD camera
delaygenerator
image intensifier
Computer
Two scalar setup
57
laser wavelength of 532 nm. The collected signals are imaged onto an intensified CCD
camera (Photometrics-CC200), where the data is digitized and transferred to a computer.
Pixel magnification is 12.5 pix/mm, and the corresponding imaged region contains the
fuel jet centerline out to a region of ambient air above the coflow. The laser beam
waist is estimated by replacing the cylindrical lens with a spherical lens of same focal
length, focusing the laser down to a line over the burner, and imaging the Rayleigh
scattering of air onto the CCD. A beam waist of 240 µm is estimated.
3.6.3 Acquisition
The laser is synchronized with the intensifier gate and camera with digital delay
generators to allow acquisition only when a laser pulse is present. This minimizes broad
spectral interferences from the flame such as luminosity. Since the flame is repeatable in
time, the scattering from many laser pulses can be averaged together on the CCD chip.
This greatly improves the signal-to-noise ratio of the images, especially for the much
weaker Raman process. Raman images are integrated over 600 laser pulses and Rayleigh
images are integrated over 100 laser pulses. Data are acquired at two different heights
above the burner at separate times. The first height has the bottom edge of the laser sheet
5 mm off of the burner surface, as moving closer to the surface caused significant elastic
scattering interferences from the burner. The next height had the bottom edge of the sheet
58
18 mm above the burner surface. These images, after processing, are tiled together to
form single Rayleigh and Raman images.
In the raw methane Raman images at an approximate downstream location of 20 mm, one
begins observing significant interferences in the hot regions of the flame where the fuel
starts to disappear (see Figure 3.9), possibly from laser-induced incandescence of soot.
Therefore, data are only acquired with the laser beam at the height closest to the burner
for the Raman images. The laser, intensifier, and camera are synchronized to a delay
generator, such that data can be acquired at a specific phase of the forcing. Data are taken
for the 30% modulation case over one period of the forcing at five equally spaced
intervals (10 ms apart) such that one phase corresponds to the minimum fuel tube exit
velocity for the forcing cycle.
3.6.4 Data Processing
The raw images are downloaded onto a computer, where one can perform mathematical
operations on them at each pixel location (x,y). An image is acquired to measure detector
dark current and fixed pattern noise by closing the camera shutter. This signal ID is
subtracted from the raw Raman signal IRam,Flame. Background elastic scattering
59
Figure 3.9 Methane Raman intensity profile (arbitrary scale) from the two scalarexperiment. The color scale is chosen to saturate most of the methane Raman signal toeasily see the interference signal (inside the white box).
min
max
0 4 8-8 -4
5
10
15
20
25
30
35
40
r(mm)
z(m
m)
60
interferences in the Rayleigh signal are corrected for using the Rayleigh signal from a
uniform field, room temperature calibration of pure helium I x yRay He, ( , ) and the Rayleigh
signal from a uniform field, pure air room temperature calibration I x yRay Air, ( , ) . The
background signal I x yRay b, ( , ) on the raw Rayleigh flame data I x yRay Flame, ( , ) is [Long
1993]
I x y I x y I x y I x yRay b Ray HeRay He
Ray Air Ray HeRay Air Ray He, ,
,
, ,, ,( , ) ( , ) ( , ) ( , )= −
−−( )σ
σ σ(3.20)
Optical throughput and variation in laser beam intensity profile are corrected for by
dividing the background subtracted images by Raman and Rayleigh images of uniform
field, room temperature flows of pure air and pure methane, I x yRay Air, ( , ) and
I x yRam Meth, ( , ) respectively. These signals are also corrected for background noise and
interference. The pure fuels also serve as reference data for the Rayleigh signal in
ambient air and the methane Raman signal at ambient temperature. The corrected
Rayleigh and Raman signals are
I x yI x y I x y
I x y I x yRay corrRay Flame Ray b
Ray Air Ray b,
, ,
, ,
( , )( , ) ( , )
( , ) ( , )=
−−
(3.21)
I x yI x y I x y
I x y I x yRam corrRam Flame D
Ram Meth D,
,
,
( , )( , ) ( , )
( , ) ( , )=
−−
Since the reference data and flame data are taken at different times, there is a chance that
the laser intensity profile changes. This will produce horizontal stripes of signal variation
61
most noticeable in the Rayleigh image. The stripes are corrected for using a rectangle in
the ambient air region of the corrected Raleigh image that extends from the top to the
bottom of the image. This rectangle is converted into a stripe image that is the same size
as the corrected Rayleigh image. The stripes are removed when the corrected Rayleigh
image is divided by the stripe image.
3.6.5 Calculation of fuel concentration, temperature, and mixture fraction
For Wmix, aT, and Cp, computations of the steady flame for 65/35 CH4/N2 are used to
determine these quantities in the reacted part of the flame as a function of local mixture
fraction. The mixture fraction is calculated from the computations at each location using
the mixture fraction formulation based on the conserved scalar made up of fuel mass
fraction and enthalpy ( ξ FT ). When calculating ξ FT from two scalar experimental
measurements, the ξ dependence of Wmix, aT, and Cp based on ξ FT gives better agreement
with ξCHO near the flame front than if the ξ dependence of Wmix, aT, and Cp is based on
ξCHO [Fielding 2001].
The experimentally measured quantities IRay, IRam, the calculated functional dependencies
W FT( )ξ , aT FT( )ξ , cp FT( )ξ , and the known quantities C3, C4, Q are substituted into (3.17)
62
ξ FTT Ram
Ray
p T Ray pCa IWI
Cc a I c T
Q= +
−3 4
2 2( / ), . Initially, ξ FT is set equal to zero and T is set
equal to 300K (i.e. r=0) in the initial calculation of Wmix, aT, and cp. Next , ξ FT is
calculated in the above equation (3.17). Temperature is calculated from (2.9) TaI
T
Ray
= ,
and used to calculate r from (3.18) rT T
T Tad
= −−
2
2
. The calculated values of ξ FT and r are
substituted into Wmix, aT, and cp and the process is repeated until there is convergence in
ξ FT . The final values of ξ FT and r are substituted into aT and T is calculated from (2.9).
This entire iterative procedure is done for each pixel location (x,y) in the images. Final
images are cropped and mirrored to obtain a full symmetric profile about the fuel tube
centerline.
3.7 Multi-species Measurement using Difference Raman and Rayleigh Scattering
For hydrocarbon diffusion flames, hydrocarbon fragments and soot precursors are
generated in the hot fuel rich areas of the flame. C2 species produce broadband
fluorescence in the visible when excited by a visible laser wavelength. [Beretta et al.
1985, Masri et al. 1987, Osborne et al. 1996]. This makes vibrational Stokes-shifted
Raman signals from species that exist slightly to the rich side of the flame front hard to
discriminate against this interference. The difference Raman scattering technique has
63
been applied in the past to reduce the C2 fluorescence interferences from this flame in the
unforced case [Marran 1997].
In the present experiment, simultaneous two-dimensional profiles of temperature and
mole fractions of N2, CO2, CH4, H2, O2, CO, and H2O in the steady and time-varying
flame are measured. Temperature and species concentrations are calculated with
measurements of vibrational Stokes-shifted Raman scattering and Rayleigh scattering.
Similar techniques have been demonstrated [Reckers et al. 1993]. Using difference
Raman scattering, the C2 fluorescence interference in this flame are eliminated down to
shot noise levels of the fluorescence signal. The steady flame profiles are compared to
computations as a verification of the multi-species/difference Raman technique. Next,
this technique is applied to the forced flame, and the results are compared to
computations.
3.7.1 Difference Scattering
Difference scattering is the collection of vibrational Q-branch Raman scattered light
intensities under two orthogonal linear polarizations: Izz parallel and Iyz perpendicular to
the laser polarization, using a linear polarized laser source. The difference scattering
signal is
64
Ids= Izz- Iyz (3.22)
In practice, the laser is not completely linearly polarized and the ability of the collection
system to reject one of the linear polarizations is not perfect. This will lead to a scale
factor on Ids that is eliminated when the difference scattering intensity from the data is
normalized to reference data. From the quantum mechanical treatment of Raman
transitions, each Raman Q-branch transition has a rotational dependence [Holzer 1973],
and thus a temperature dependence as well. In general, the depolarization of the Q-branch
is so small that this J dependence will be insignificant on the scale of experimental error.
For Q-branch Raman transitions ρm is typically 0.02-0.05 [Penney et al. 1972,
Woodward 1967, Murphy 1977], and therefore vibrational Q-branch Raman scattering
(and Rayleigh scattering) are highly polarized along the polarization axis of the laser
(assuming a linearly polarized laser).
For laser-induced fluorescence, there is an initial preferred polarization of the dipole
radiation. In the case of a molecule, if there are “fast” rotations of the molecule which
occur in a time smaller than the decay time of fluorescence, the fluorescence is randomly
polarized if the signal is averaged over its decay time. If the fluorescence interference
from C2 is determined to be randomly polarized when compared to the gate time of signal
acquisition, one should be able to eliminate this interference through difference Raman
scattering.
65
From (2.7) I CVI Ndd
Xiz Ray totm iz Ray
mm
,, ,
=
∑0
σΩ
, (3.22), and the ideal gas law
NP
kTtot = , the difference Rayleigh scattering signal is inversely proportional to
temperature
I CVI Ndd
X CVIP
kTddds Ray tot
m zz Raym Ray m
m eff ds Ray,
, ,,
, ,
( )=
−
∑ =
0 01
σ ρ σΩ Ω
(3.23)
Normalizing the difference Rayleigh signal by reference data,
TI ref
II
I ref
dd
dd
refT ref
aI
ds Ray
ds Ray
eff ds Ray
eff ds Ray
T
ds Ray
=
=,
,
, ,
, ,
'
,
( )
( ) ( )( )0
0
σ
σΩ
Ω
(3.24)
where aT' depends on the difference Rayleigh cross section (as opposed to aT).
From (2.8) I CN VIRam iz m mRam m iz
, ,, ,
=
0
∂σ∂Ω
and (3.22), the difference Raman scattering
intensity of species m is proportional to the number density of that species
I CVI N CVI NRam ds m mRam m zz
m Ram mRam ds m
, ,, ,
,, ,
( )=
−
=
0 01
∂σ∂
ρ ∂σ∂Ω Ω
(3.25)
Normalizing the difference Raman signal with reference data
NI
I refI ref
IN ref
dd
T
dd
Tm
ds Ram m
ds Ram nn
ds Ram nref
ds Ram m
=
, ,
, ,
, ,
, ,
( )( )
( )( )
( )
0
0
σ
σΩ
Ω
(3.26)
66
The scattered signal intensities are integrated over a particular spectral detection
bandwidth. The bandwidth factor, or fraction of scattered signal detected, depends upon
the spectral detection bandwidth and spectral lineshape of a signal, as well as collection
efficiency. For Raman scattering, changes in temperature can significantly change the
spectral lineshape of the signal. In this experiment, the spectral detection bandwidths only
contain part of the spectrum of the scattered signals. Therefore, as a Raman lineshape
changes, the amount of scattered signal within the detection bandwidth changes.
Prediction of the change in Raman lineshapes with temperature is needed for accurate
determination of the temperature dependent part of the bandwidth factor, τm(T), for each
Raman species. (See section 3.7.7 for calculation of τm(T).) The number density in (3.26)
becomes
NI
I refI ref
IN ref
dd
T
dd
Tm
ds Ram m
ds Ram nn
ds Ram nref
ds Ram m
=
, ,
, ,
, ,
, ,
( )( )
( )( )
( )
0
00
σ
σΩ
Ω
τm(T) (3.27)
dd ds Ram m
σΩ
, ,
is calculated at a reference temperature To and the temperature dependence
of dd ds Ram m
σΩ
, ,
is incorporated into τm(T). The ratio
dd
T
dd
T
ds Ram nref
ds Ram m
σ
σΩ
Ω
, ,
, ,
( )
( )0
can be determined
with calibration data of species m at known concentrations and fixed temperature T0.
67
Once τm(T) and
dd
T
dd
T
ds Ram nref
ds Ram m
σ
σΩ
Ω
, ,
, ,
( )
( )0
are determined then one can calculate number density
of species m from (3.27).
3.7.2 Multi-species technique in calculation of temperature and species number density
In this technique one measures Rayleigh scattering and Stokes Raman scattering
intensities for all the major species on a horizontal line through the center of the desired
region. The laser is focused down with a large focal length lens that produces an
approximately uniform diameter beam through the region of interest. Since the Raman
and Rayleigh signals have different spectral locations, Raman and Rayleigh signals can
be spatially isolated from each other by spectrally dispersing the scattered light, allowing
simultaneous measurement of Rayleigh scattering and Raman scattering of the major
species. Raman scattering is known to be proportional to Nm, and Rayleigh scattering is
known to be proportional to Ntot (and inversely proportional to T from the ideal gas law).
Since Nm is measured for the major species, then Ntot can be approximately calculated
since N Ntot mm
≈ ∑ . With Nm measured for the major species , one can calculate the
effective Rayleigh scattering cross section. The combination of the Rayleigh signal with
the Raleigh cross section gives temperature. This value of T is used to give a better value
68
of Nm for the major species since this term does depend on temperature. The calculation
is then iterated until convergence is achieved.
Calculations are performed separately at each spatial location (usually defined by a pixel
of a digital detector) along the horizontal line at a given height. In this experiment, line
measurements are performed at many different heights above the burner, producing a
two-dimensional composite slice through the flame. The difference scattering technique
is performed for the measurement of Rayleigh and each Raman scattering signal.
3.7.3 Setup
Shown in Figure 3.10 is the experimental setup. The second harmonic of a flashlamp
pumped, Q-switched Nd:YAG laser (10 Hz rep rate, 532 nm) is focused into a line over
the center of the burner. The output polarization direction of the laser is vertical. The
laser is Q-switched twice per flashlamp pulse producing two consecutive green laser
pulses 8 ns in duration and separated by 95 µs with an average energy of 300 mJ per
double pulse- this prevents breakdown of air. An energy meter (Laser Probe RjP-734)
records the single-shot laser energy using a reflection off the lens. The computer
downloads the laser energy for each shot, and sums them as the data are acquired for a
single image. This total laser energy is used to correct for the effects of laser energy drift
69
Inte
nsif
ied
CC
DC
amer
a
Q-s
wit
ched
Nd:
YA
GL
aser
(53
2 nm
)
Spec
trog
raph
f/4
Col
ored
Gla
ss F
ilter
Len
ses
Fun
ctio
nG
ener
ator
Pol
ariz
atio
n se
lect
or
Exp
erim
enta
l Set
up
Mec
hani
cal S
hutt
er
Pow
er M
eter
Com
pute
r
Bur
ner
Lou
dspe
aker
Fig
ure
3.10
Exp
erim
enta
l set
up f
or th
e m
ulti-
exp
erim
ent.
The
pol
ariz
atio
n se
lect
ortr
ansm
its li
ght t
hat i
s ei
ther
pol
ariz
ed p
erpe
ndic
ular
or
para
llel t
o th
e la
ser
pola
riza
tion.
70
over the course of an experiment. Light from the Raman and Rayleigh scattering is
collected at 90 degrees to the incident beam with a single 85 mm f/1.8 camera lens that
provides a magnification of 0.8 and focuses the light on the horizontal entrance slit of an
imaging spectrograph (Spex 270M, 0.27 m focal length, f/4, 300 groves/mm ruled
grating, 500 nm blaze angle, 300 µm entrance slit). This magnification matches the
effective f/# of the lens to the spectrograph, and also allows imaging from the flame
centerline out to ambient air. A modified liquid crystal shutter (Displaytech PV100AC)
passes the desired polarization, enabling us to measure Izz and Iyz independently. This
modified shutter consists of a crystal that is oriented such that when +/- 15 Volts is
placed across it, the polarization of incident light is rotated by 90 degrees. The light then
passes through a linear polarizer oriented to pass only vertically polarized light. Since the
light always enters the spectrograph with vertical polarization, this eliminates the need to
correct for differences in spectrograph grating efficiency for different polarizations. As a
check to the effectiveness of the technique at eliminating randomly polarized light, a
randomly polarized mercury light source is collected under the two orthogonal
polarizations. The difference between the two orthogonal polarizations eliminates the
signal down to its shot noise limit.
Upon entering the imaging spectrograph the light is dispersed into its component
wavelengths, while preserving the spatial information along the entrance slit. This spatial
71
/ spectral information is collected with an 18 mm gated Gen-II image intensifier (DEP
XX1450DH) which is optically coupled with f/1.4 camera optics to a cooled slow scan
15-bit dynamic range 512 x 512 pixel CCD (Princeton Instruments TE/CCD-512 TKM).
The intensifier gain is adjusted to optimize the signal-to-noise of the data, and is gated on
for 1 µs around the laser pulse to eliminate background luminosity from the flame. The
intensifier, CCD, and laser are synchronized with digital delay generators to only allow
acquisition only when a laser pulse is present. The beam waist is measured by imaging
Rayleigh scattered light of pure methane. The slit width is shortened until there is a
noticeable change in width of the Rayleigh line image, which is observed at a slit width
of 240 µm. With a magnification of 0.8, the correspondind beam waist is determined to
be 300 µm. Spatial resolution is approximately 200 µm (horizontal) x 300 µm (depth),
and spectral resolution is approximately 3 nm. Spatial resolution is estimated by imaging
a 50 µm diam. wire oriented vertically above the burner. Spectral resolution is estimated
by closing the slit down to 50 µm and measuring the width of the methane Rayleigh line.
The resultant 512 x 256 pixel images cover approximately 170 nm in the spectral
dimension by 14 mm in the spatial dimension. The spectral coverage of each flame
image (vertical direction) was large enough to permit observation of the Rayleigh line
(@ 532 nm) simultaneously with the hydrogen Raman line (@ 683 nm), while the spatial
axis (horizontal direction) imaged a radial profile from the centerline of the jet out to the
72
ambient air at all downstream locations. Each image is transferred and stored in a
computer.
3.7.4 Unforced Case Acquisition
The signal-to-noise of the Raman data is increased by integrating the scattered light
resulting from 1200 consecutive laser pulses (two per 100 ms period) on the CCD over a
60 second period. Integration of the scattered light over the 1200 consecutive laser shots
produced a Rayleigh signal just above the fuel jet center that was close to the maximum
dynamic range of the CCD (14bit, or 32767 levels), so the full dynamic range of the CCD
was exploited. Scattered light with polarizations parallel and perpendicular to the laser
polarization (Izz and Iyz) is imaged onto the CCD in separate and consecutive 60 second
periods for a given height above the burner.
In order to obtain the radial information at the different downstream locations, the burner
described in Section 3.2 is placed on a computer controlled z-translation stage. Data are
acquired at heights above the burner ranging from 2 mm to 52 mm, in steps of 0.5 mm
closer to the burner and 1 mm farther downstream, since the length scales in the flame
increased significantly at downstream locations.
73
The reference signal used for carbon dioxide, carbon monoxide, water, hydrogen, and the
C2 fluorescence is nitrogen Raman from room temperature, pure air. The spectrograph
grating is rotated such that the nitrogen Raman line in clean air overlaps with a particular
Raman line for the flame data. This will equalize the optical throughput of the Raman
lines and reference data. The reference signal for oxygen and nitrogen are the O2 and N2
Raman signals in room temperature, pure air. The reference signal for methane is the
Raman signal of room temperature, pure methane. Signal integration time of the
reference data is the same (or scaled to be an equivalent integration) as the flame data.
Calibrations are recorded for each of the major species: methane, oxygen, nitrogen,
carbon dioxide, water, carbon monoxide, and hydrogen for a known quantity of each
species at a known temperature. The difference Raman signals are measured directly at
room temperature for CO2, O2, N2, CH4, and H2. The difference Raman signal for H2O is
measured in the post flame region of several premixed methane / air flat flames (φ = 0.8,
1.0, 1.2) using equilibrium calculations to calibrate the water Raman signal. The room
temperature difference Raman signal for CO is calculated from RAMSES code [Hassel
1996] by determining the ratio of difference Raman signals of CO and N2 at room
temperature (for an equal concentration), and then scaling by the difference Raman signal
of N2 from the calibration data.
74
Images are obtained for an equivalent acquisition time as the flame data with the camera
shutter closed to measure detector dark current and fixed pattern detector noise.
3.7.5 Forced Case Acquisition
Since the time-varying flame is cyclical in time, one can phase lock the measurements
over many forcing cycles to measure quantities at various phases of the forcing. This is
achieved by synchronizing the function generator with the laser and intensifier with
digital delay generators. Data are acquired as described above for 5 equally spaced
phases of the forcing spanning one period of the forcing (10 ms intervals). Each phase
acquisition is done at separate times from other phase acquisitions. The measurement
gate times are determined by the intensifier gate time of 1 µs. There is no variation in
flows or flame structure over this short as time; thus the measurements are instantaneous
with respect to the forcing.
3.7.6 Processing
The images of dark current are subtracted from each spectral/spatial image of flame data
at each pixel location (x,y). A resulting sample image is shown in Figure 3.11 for
scattering intensities with polarization of the scattering parallel Izz and perpendicular Iyz to
75
the laser polarization and the difference scattering intensity of these signals Ids . This data
is acquired 18 mm above the burner.
The Stokes-shifted Raman lines for the species measured in the figure are labeled, along
with the Rayleigh line. The jet centerline and coflow region are labelled in each image.
Note the significant C2 fluorescence interference in the two vertical and horizontal
scattering images. Note that the color scale is purposely chosen to saturate the stronger
transitions in order to view the weaker transitions. Each species (and Rayleigh) are
integrated over a spectral window (marked with horizontal rectangles). Spectral window
size is chosen to be large enough to account for spectral broadening of the lines due to
temperature increase, but small enough to minimize line overlap with other species (a.k.a.
crosstalk). Also note the CO2 Raman vibrational modes. The Raman transition of the
2ν2 vibrational mode is used for the CO2 concentration measurements because of less
crosstalk with the O2 line as compared with the transition of the ν1 symmetric stretch
vibrational mode. Shown in Figure 3.12 is a lineplot taken along the vertical line of the
images of Figure 3.11 marked by the white vertical rectangles. This represents the region
of maximal C2 interference in the images of Fig. 3.11. Notice the large C2 fluorescence
interference from the C2(0,1) fluorescence bandhead (near 1560 nm) in Izz and Iyz
that is eliminated in the difference scattering signal Ids. Also notice the broadband
76
-400
-800
-120
0
-160
0
-200
0
-240
0
-280
0
-320
0
-360
0
-400
0
-440
0H
ydro
gen
Wat
er
Nitr
ogen
Oxy
gen
Ray
leig
h
CO
Cof
low
48
12
Jet
Cen
ter
r(m
m)
I zz
I yz
Ids
Max
Min
Cof
low
48
12
Jet
Cen
ter
r(m
m)
Cof
low
48
12
Jet
Cen
ter
r(m
m)
0
C2
fluo
resc
ence
CO
2(2ν
2)C
O2(
ν 1)
Met
hane
(ν1)
Fig
. 3.1
1 Sa
mpl
e im
ages
of
I zz,
Iyz
, Ids
(ar
bitr
ary
units
) ta
ken
18 m
m d
owns
trea
m. T
he h
oriz
onta
l whi
te r
ecta
ngle
sre
pres
ent t
he s
pect
ral w
indo
w o
ver
whi
ch th
e R
aman
spe
cies
(an
d R
ayle
igh)
sig
nals
are
inte
grat
ed. T
he c
olor
sca
lein
this
fig
ure
is c
hose
n to
sat
urat
e st
rong
tran
sitio
ns in
ord
er to
vie
w w
eake
r tr
ansi
tions
.
Shift(cm-1)
77
fluorescence interference that is present in Izz and Iyz and absent in Ids. This point in the
flame is on the rich side of the flame front, and no oxygen should be present, yet a signal
persists for Ids within the spectral region of the O2 Raman transition. This unexplained
signal can also be seen in Ids between the Raman lines of O2 and CO in
Figure 3.12. There also appears to be an interfering signal in Ids on the CO2 and CO
Raman lines. These signals that persist in Ids may possibly be resonance Raman scattering
of PAH species formed just rich of the flame front. Resonance Raman occurs when the
laser frequency is near an electronic transition of a particular species, and can produce
Raman scattering intensities several orders of magnitude greater than non-resonant
Raman scattering. PAH concentrations in methane diffusion flames are on the order of
parts-per-million [Petarca 1989] which is two to three orders of magnitude under the
detection limits for non-resonant Raman transitions in this experiment.
The C2 fluorescence signal is monitored near the C2(0,1) fluorescence bandhead and
images are obtained for Izz and Iyz in the same manner as the images for the flame species.
The Cc fluorescence signal should have approximately the same spatial distribution as the
PAH resonance Raman signal. Therefore the C2 fluorescence image Izz or Iyz may be used
78
Figure 3.12 Intensity spectrum (arbitrary units) taken from the region ofmaximal C2 fluorescence interference of the images in Figure 3.11 (marked
with a verticalwhite rectangle in Fig. 3.11). The light gray rectangles representthe spectral region over which the signals are integrated. Notice the largeinterference fromthe C2(0,1) fluorescence bandhead region which is present inIzz and Iyz but eliminated in Ids. Also note the residual signals in Ids near the O2
and CO Raman transitions, which is believed to be resonance Raman fromPAH species.
Lineplot of Spectral Intensities Izz, Iyz, and Ids
50
150
250
350
450
550
525 550 575 600 625 650 675
wavelength(nm)
Rayleigh CO2(ν1)CO2(2ν2)
O2 N2CO CH4 H2O H2
IzzIyzIds
C2(0,1)
PAH
inte
nsit
y(ar
bitr
ary
unit
s)
79
as an empirical correction for the resonant PAH resonance Raman signals which interfere
on Ids for O2, CO2, and CO. The 'yz' fluorescence image is used as there will be less
interference from highly polarized Raman signals than in the 'zz' fluorescence image.
Shown in Figure 3.13 is Ids for O2 along with the 'yz' fluorescence image. Notice the
interference on the O2 signal just rich of the flame front. This interference region has
approximately the same spatial distribution as the 'yz' fluorescence image.
The integrated signals for each species (and Rayleigh) at each height are tiled together to
form raw spatial images for the vertically and horizontally polarized scattered light. The
difference between the two polarizations is taken for each species (and Rayleigh) spatial
image. The difference scattering images are then normalized by appropriate reference
data to correct for optical throughput, laser intensity variation, and spectral detection
efficiencies.
80
Figure 3.13 Intensity profiles (arbitrary units) of Ids for oxygen Raman and Iyz
for C2 fluorescence. Notice the similar spatial profile of the interference region onthe O2 Raman signal and the C2 fluorescence profile.
0 4 8-8 -4
5
10
15
20
25
30
35
40
45
50
55
60 Ids (Oxygen)
z(m
m)
z(m
m)
r(mm)
interference
0 4 8-8 -4
5
10
15
20
25
30
35
40
45
50
55
60
r(mm)
Iyz (C2 fluorescence)
max
min
81
The correction for the PAH Raman interference is made for the O2, CO2, and CO images.
The C2 fluorescence 'yz' image is scaled by an empirical factor and subtracted from each
image.
The images now are corrected for the spectral overlap of Raman signals, or crosstalk. The
spectral dispersion of the Raman lines is in the vertical direction, represented by the
variable y. The spectral window used to integrate the Raman signal of species i is
centered at yi and the integrated signal over the spectral window of species i is
I y I y I yi i i j i( ) ( ) ( )= + (3.28)
where Ii(yi) is the Raman signal from species i in the spectral window of species i, and
Ij(yi) is the Raman signal from species j in the spectral window of species i. The crosstalk
ratio
cI y T
I y Tj ij i
j j→ =
( , )
( , )0
0 (3.29)
is calculated with reference gases at room temperature T0. In general, c j i→ depends on
temperature, but a room temperature value gives a reasonable correction for most species.
Using (3.28) and (3.29), I yi i( ) can be extracted from I yi( )
I y I y c I yi i i j i j j( ) ( ) ( )= − → (3.30)
The room temperature crosstalk ratio of N2->CO undercorrects for the N2->CO crosstalk
in the hot flame regions (T=Th) just lean of the flame where CO signal should disappear
82
in the absence of crosstalk. With this knowledge and the knowledge that CO signal
should disappear in the ambient region (T=Tc) in the absence of crosstalk, the N2-> CO
crosstalk can be approximated as a linear funtion of I yN( )2
I y I y I y TI y T I y TI y T I y T
I y I y TCO CO CO CO hCO CO h
N N hN N h( ) ( ) ( , )
( , ) ( , )( , ) ( , )
( ) ( , )= − − −−
−( )0
02 2
2 2 (3.31)
The most significant crosstalk is between CO2 and O2 due to the proximity of their
respective Raman lines (see Fig. 3.11). The cross talk correction for CO2-> O2 is done in
succession to the crosstalk correction for O2-> CO2 [Dibble,1987]. With the knowledge
that the O2 signal should be zero at T=Th
I y I y c I yI y T
I y T c I y TCO CO CO O CO OCO h
CO h O CO O h2 2 2 2 2 2
2
2 2 2 2
( ) ( ) ( )( , )
( , ) ( , )= −( ) −
→→
(3.32)
I y I yI y T
I y TI yO O O
O h
CO hCO CO2 2 2
2
2
2 2( ) ( )
( , )
( , )( )= −
(3.33)
3.7.7 Determination of the temperature dependence of the bandwidth factor τm(T)
In this experiment, only part of the Raman line for a specific species falls within the
spectral window for that species. As temperature increases, the Raman lines spread out
spectrally due to the population of higher rotational J states (for non-Q-branch
83
transitions), so even less of the Raman signal is captured in the window. In addition, the
Raman cross sections have a temperature dependence that must be accounted for.
To obtain the temperature dependence of the bandwidth factor τm(T) for O2, CO, N2, and
H2, a numerical simulation of the spectra that incorporates the depolarization ratio for
each Raman branch (O, Q, and S), accurate spectrograph dispersion, and a realistic slit
function is used [Hassel 1996]. The slit function is obtained by imaging the Rayleigh
scattered line of methane, since the methane Rayleigh line should be the thinnest spectral
line measured, as methane does not posses a rotational Raman spectrum. The Raman
spectra at various temperatures are integrated over their respective spectral windows used
in the flame measurements, and τm(T) is determined. For CO2, spectral line data [Miles
1996] is convolved with the slit function to get the CO2 Raman spectra at various
temperatures. This spectrum is integrated over the CO2 spectral window, and τm(T) is
determined. τm(T) for H2O and CH4 is approximated by the simple Boltzmann term of
(2.12) 11− −( )−
exp( / )hω k TB .
84
Figure 3.14 Experimental and simulated Raman spectra for nitrogen atT = 300 K and T = 2000 K. The simulated nitrogen spectra are obtainedusing RAMSES code.
00.10.20.30.40.50.60.70.80.9
1
606.00 607.00 608.00 609.00 610.00 611.00 612.00 613.00 614.00
wavelength (nm)
Inte
nsit
y (A
rb. u
nits
)
Simulated and measured nitrogen Raman spectrum at 300 K and 2000 K
experiment, 2000 Ksimulated, 2000 K
experiment, 300 Ksimulated, 300 K
85
Figure 3.15 Difference Raman signal temperature dependence. Signals arenormalized to unity at 300 K. Signals are obtained from simulationsof Raman spectra, except for CH4 and H2O which are given a Boltzmanntemperature dependence.
Difference Raman Signal Temperature Dependence
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
300 800 1300 1800
Temperature(K)
O2N2CH4H2OCO
H2CO2 (2ν2 )
CO2 (ν1 )
I ds(
arbi
trar
y un
its)
86
The experimental and simulated Raman spectra for nitrogen are compared at
temperatures of 300K and 2000K.(Fig. 3.14) Excellent agreement is found between the
observed and calculated spectra. Figure 3.15 shows the computed temperature
dependencies of the difference Raman signals of each species. This data has been
normalized to unity at 300 K, and the spectral windows used to evaluate the simulated
temperature dependence are identical to the windows used in the experiment. Carbon
dioxide has the largest temperature correction, corresponding to an increase in the signal
by over 160% at 2000 K. Hydrogen and oxygen show negative trends with temperature,
indicating that the Raman signal is spreading out of the spectral window for these
species.
3.7.8 Temperature and Species Concentration Calculation
Calculations are performed separately at each pixel location (x,y) of the images. As a
starting point, one sets τm T( ) = 1 for all species m. With Ids,Ram,m determined from the
experiment for all major species and appropriate reference data Ids,Ram,n(ref), one gets a
first order calculation of each species number density from (3.27)
NI
I refI ref
IN ref
dd
T
dd
Tm
ds Ram m
ds Ram nn
ds Ram nref
ds Ram m
=
, ,
, ,
, ,
, ,
( )( )
( )( )
( )
0
00
σ
σΩ
Ω
τm(T)
87
(The ratio
dd
T
dd
T
ds Ram nref
ds Ram m
σ
σΩ
Ω
, ,
, ,
( )
( )0
is calculated from calibration data.) With these values for
Nm, one now calculates N Ntot mm
≈ ∑ . One then calculates the effective difference
Rayleigh cross section dd N
dd
Neff ds Ray tot m zz Ray
m Ray mm
σ σ ρΩ Ω
≈
−
∑
, , , ,,( )
11 , where one
knows the 'zz' Rayleigh cross sections, a first order number density of each species (and
Ntot), and the Rayleigh depolarizations. (This same calculation is performed for
dd
refeff ds Ray
σΩ
, ,
( ) .) With Ids,Ray determined from the experiment along with appropriate
reference data Ids,Ray(ref), one calculates a temperature from (3.24)
TI ref
II
I ref
dd
dd
refT ref
aI
ds Ray
ds Ray
eff ds Ray
eff ds Ray
T
ds Ray
=
=,
,
, ,
, ,
'
,
( )
( ) ( )( )0
0
σ
σΩ
Ω
. With this temperature, one
calculates τm T( ) for each species. This gives a more refined estimate of species number
density in (3.27). Then the process is iterated until convergence of the number densities
and temperature is achieved. Final values of species number densities are converted into
mole fractions.
3.8 Discussion on experimental techniques
88
3.8.1 Effectiveness of two scalar technique
As previously mentioned there is an interference signal on the fuel Raman images that
occurs just to the rich side of the flame. It is identified as an interference signal since it
develops downstream of the burner, where the fuel has just disappeared; therefore it is
not methane Raman signal. The likely source of this interference is fluorescence from C2
species. As seen in Figure 3.12 from the flame spectrum, there is a significant
fluorescence signal from the C2(0,1) bandhead at 560 nm. This signal can be picked up
through the 630 nm interference filter, although at a modest spectral throughput. Also
contributing to this signal is the broadband C2 and PAH fluorescence signal also seen in
Fig. 3.12.
Although data was only taken for Raman images at a maximum height downstream of 20
mm, the interference signal starts to be seen in the data at around 15 mm (see Figure 3.9).
The fuel Raman data in these locations is therefore unreliable. In addition, there is the
fuel Raman signal downstream of 20 mm that is not recorded. Although this signal is
small (relative to the fuel Raman signal at burner inlet), it will still significantly
contribute to the calculation of mixture fraction and temperature.
89
Figure 3.16 shows a comparison of corrected methane Raman images obtained with the
two experimental techniques for a particular phase of the 30% modulation case. With the
exception of the interference region, there is good agreement of the two profiles less than
20 mm downstream. The methane Raman signal in the multi-species measurement is
shown to extend well beyond 20 mm downstream. Therefore the mixture fraction and
temperature for the two scalar data have unreliable values in regions above the 20 mm
height where methane is present but the methane Raman signal is not recorded.
To understand the effectiveness of the two scalar algorithm in calculating mixture
fraction and temperature, the two scalar calculation is performed on the computational
data. The temperature and mixture fraction derived from the two scalar method are
compared to the mixture fraction ξCHO in ( 3.1) (based on the mass fractions of carbon,
hydrogen, and oxygen) and computational temperature in the lineplots of Figure 3.17. In
the axial centerline plot of mixture fraction the curves show good agreement upstream,
but the curves separate downstream of 20 mm. The two scalar mixture fraction in this
region appears to be artificially low (by 0.05 at peak deviation). The range of mixture
fractions where the curves deviate is 0.07 to 0.2 (0.1 is the stoichiometric mixture
fraction). This range is also where the mixture fraction curves deviate in the radial
lineplot of mixture fraction taken 9 mm downstream of the burner. The centerline
90
Figure 3.16 Methane Raman intensity profiles (arbitrary units)from experiments. Notice the interference (white box) in thetwo scalar measurement.
0 4 8-8 -4
5
10
15
20
25
30
35
40
45
50
55
60
0 4 8-8 -4
5
10
15
20
25
30
35
40
45
50
55
60Difference Raman Two Scalar
Methane Raman Signal
z(m
m)
r(mm)r(mm)
z(m
m)
min
max
91
Figure 3.17 Two-scalar calculation of mixture fraction and temperature based oncomputational data, compared to ξCHO and computational temperature based on
computations.
Mixture fraction- radial
00.10.20.30.40.50.60.70.80.9
0 2.5 5 7.5 10
radial distance(mm)
two-scalar
Mixture fraction- centerline
0
0.2
0.4
0.6
0.8
1
1.2
0 20 40 60
height(mm)
two-scalar
ξ CHO ξ CHO
Tem
pera
ture
(K
)
Tem
pera
ture
(K
)
Mix
ture
fra
ctio
n
Mix
ture
fra
ctio
n
Temperature-radial
0200400600800
100012001400160018002000
0 2.5 5 7.5 10
radial distance(mm)
comptwo-scalar
Temperature-centerline
300
550
800
1050
1300
1550
1800
0 20 40 60
height(mm)
comptwo-scalar
92
temperature lineplot shows good agreement upstream, but the curves separate
downstream of 20 mm (as does the mixture fraction centerline plots). The two scalar
temperature appears to be artificially low (by 100 K at peak temperature). The radial
temperature lineplot taken 9 mm downstream, however, shows good agreement at each
radial flame position.
The inaccuracies of the two scalar formulation of temperature and mixture fraction can be
attributed to the assumption of single step chemistry. Intermediate species will affect the
temperature and mixture fraction near stoichiometric. The advantage of this technique is
the determination of temperature, fuel concentration, and mixture fraction from only two
scalar measurements.
3.8.2 Effectiveness of difference Raman technique
One needs to determine how effective the difference Raman/ multi-species technique is in
discriminating the relatively weak Raman signals from the large fluorescence
interferences. If the C2 fluorescence is determined to be randomly polarized over the gate
time of the image intensifier, one should be able to eliminate the fluorescence signal
down to shot noise levels of the fluorescence.
93
The spatial and spectral region of highest interference from the C2 fluorescence in the
flame is determined, and the time dependence of the polarization of this signal is
investigated. The camera-intensifier system is replaced with a photomultiplier tube
(PMT) (Hamamatsu R928). With an exit slit placed on the spectrograph, light only in the
spectral region of interest is passed to the PMT. The fluorescence signal is digitized on a
digital oscilloscope (Techtronix, 500MS/s sampling rate), terminated with 50 ohms. The
time resolved C2 fluorescence signal intensities Izz and Iyz are recorded independently.
PMT and oscilloscope response time is approximately 2 ns. The time decay of the laser
pulse (1/e intensity point) τ laser = 4ns, and the time decay of the fluorescence τC210= ns.
The peak signal and time decay of each signal are almost identical. When these signals
are integrated over their lifetimes and are subtracted from one another, the result is within
noise levels of the fluorescence signals. In conclusion, the C2 fluorescence is randomly
polarized over the lifetime of the fluorescence. Therefore the difference Raman technique
reduces the C2 fluorescence interference on Raman data to shot noise of the fluorescence.
To determine the effectiveness of the difference Raman technique one must compare the
noise of the C2 fluorescence interference on the difference Raman signals. The noise is
defined as the rms of a signal over a region where the signal is approximately constant.
The weakest Raman signal, which also has significant interference from C2 fluorescence,
94
is CO. Let I x yyz C CO, ( , )2 → represent the C2 fluorescence interference on the raw 'yz' image
of CO (Iyz,CO(x,y)). Let σyz C CO dx dy, ( , )2 → represent the noise of the C2 fluorescence
interference calculated in the small region (dx,dy) in the 'yz' CO image. Since the peak
intensity of Ids,CO(x,y) is 90 counts (arbitrary units) and the Raman depolarization of CO
ρCO = 0.038, then Iyz,CO(x,y) should have negligible CO signal. Thus,
I x y I x yyz C CO yz CO, ,( , ) ( , )2 → ≈ . Note that σ σds C CO yz C CO, ,2 2
2→ →≈ (due to the subtraction of
one noisy signal from another). One finds that I x y x yds CO yz C CO, ,( , ) ( , )> −>22
σ for all points
(x,y) containing CO, and therefore the CO difference Raman signal is effectively
discriminated from the C2 fluorescence noise.
3.9 Comparison of experimental and computational profiles
3.9.1 Steady Flame
Steady flame profiles of temperature, CO2 , H2O, CO, N2, O2, H2, and CH4 mole fractions
are shown in Figures 3.18-3.25 for the multi-species experiment and computations.
Profiles of temperature, CH4, CO2, N2, and O2, and H2O show very good agreement in
terms of spatial variation in flame structure and peak concentrations. The only apparent
difference is the difference in flame lift-off height. Because of the extremely small signal,
95
Figure 3.18 Measured (multi-species technique) and computed
temperature (degrees Kelvin) for the steady flame.
0 4 8-8 -4
5
10
15
20
25
30
35
40
45
50
55
60
0 4 8-8 -4
5
10
15
20
25
30
35
40
45
50
55
60Experimental Numerical
Temperature
z(m
m)
r(mm)r(mm)300 300
1950 1950
z(m
m)
96
Figure 3.19 Measured (multi-species technique) and computedcarbon dioxide mole fractions for the steady flame.
0 4 8-8 -4
5
10
15
20
25
30
35
40
45
50
55
60
0 4 8-8 -4
5
10
15
20
25
30
35
40
45
50
55
60Experimental Numerical
Carbon Dioxide
z(m
m)
r(mm)r(mm)
0.097
0
0.097
0
z(m
m)
97
Figure 3.20 Measured (multi-species technique) and computed watermole fractions for the steady flame.
0 4 8-8 -4
5
10
15
20
25
30
35
40
45
50
55
60
0 4 8-8 -4
5
10
15
20
25
30
35
40
45
50
55
60Experimental Numerical
Water
z(m
m)
r(mm)r(mm)
0.162
0
0.162
0
z(m
m)
98
Figure 3.21 Measured (multi-species technique) and computed carbonmonoxide mole fractions for the steady flame.
0 4 8-8 -4
5
10
15
20
25
30
35
40
45
50
55
60
0 4 8-8 -4
5
10
15
20
25
30
35
40
45
50
55
60Experimental Numerical
Carbon Monoxide
z(m
m)
r(mm)r(mm)
0.042 0.042
0 0
z(m
m)
99
Figure 3.22 Measured (multi-species technique) and computedhydrogen mole fractions for the steady flame.
0 4 8-8 -4
5
10
15
20
25
30
35
40
45
50
55
60
0 4 8-8 -4
5
10
15
20
25
30
35
40
45
50
55
60Experimental Numerical
Hydrogen
z(m
m)
r(mm)r(mm)
0.023
0
0.023
0
z(m
m)
100
Figure 3.23 Measured (multi-species technique) and computedmethane mole fractions for the steady flame.
0 4 8-8 -4
5
10
15
20
25
30
35
40
45
50
55
60
0 4 8-8 -4
5
10
15
20
25
30
35
40
45
50
55
60Experimental Numerical
Methane
z(m
m)
r(mm)r(mm)
0 0
0.65 0.65
z(m
m)
101
Figure 3.24 Measured (multi-species technique) and computednitrogen mole fractions for the steady flame.
0 4 8-8 -4
5
10
15
20
25
30
35
40
45
50
55
60
0 4 8-8 -4
5
10
15
20
25
30
35
40
45
50
55
60Experimental Numerical
Nitrogen
z(m
m)
r(mm)r(mm)
0.79
0.35 0.35
0.79
z(m
m)
102
Figure 3.25 Measured (multi-species technique) and computedoxygen mole fractions for the steady flame.
0 4 8-8 -4
5
10
15
20
25
30
35
40
45
50
55
60
0 4 8-8 -4
5
10
15
20
25
30
35
40
45
50
55
60Experimental Numerical
Oxygen
z(m
m)
r(mm)r(mm)
0.210 0.210
0 0
z(m
m)
103
Figure 3.26 Radial and centerline plots of temperature, water, and carbondioxide for steady flame experiments (multi-species technique) andcomputations.The radial plots are taken 10.5 mm above burner for thecomputations and 9 mm above burner for the experiment to account for lift-off
differences.
Temperature (K)-center
0
500
1000
1500
2000
2500
0 10 20 30 40 50 60
height (mm)
Temperature (K)-radial
0
500
1000
1500
2000
2500
0 2 4 6 8 10
radial (mm)
Carbon Dioxide (mole fraction)-radial
0
0.02
0.04
0.06
0.08
0.1
0 2 4 6 8 10
radial (mm)
Water (mole fraction)-center
0
0.05
0.1
0.15
0.2
0.25
0 10 20 30 40 50 60
height (mm)
Water (mole fraction)-radial
0
0.05
0.1
0.15
0.2
0 2 4 6 8 10
radial (mm)
Carbon Dioxide (mole fraction)-center
0
0.02
0.04
0.06
0.08
0.1
0 10 20 30 40 50 60
height (mm)
experiment computations
104
the CO and H2 profiles are quite noisy. They are smoothed by using a gaussian smoothing
technique (σx= σy=1.71 pixels, smoothed over a 7x7 pixel area) to improve the signal-to
noise-ratio. The profile comparison for CO is remarkably good considering the relatively
low signal-to-noise of the CO image compared to the other species. The experimental
hydrogen profile is not as good a comparison to computations, but the peak signal and
general shape is the same in both the experiment and computations. Shown in Figure 3.26
are lineplots of radial and centerline lineplots of CO2, H2O, and temperature for the multi-
species experiment and computations. The radial profiles are taken at a height of 9 mm
above the burner. The radial plots show good agreement in terms of spatial variation and
peak values. The centerline plots show good agreement in spatial variation and peak
values as well. The most apparent difference is the flame lift-off height between the
computations and experiment.
3.9.2 Forced Flame
Figure 3.27 shows profiles of temperature for the multi-species experiment and the two
scalar experiment for the case of 30% flow modulation. Images are taken at five equally
spaced phases spanning one period of forcing, where the figure labeled "d" is the phase
where the centerline fuel tube exit velocity is at its minimum over the forcing period. The
spatial region where interference is observed on the two scalar methane Raman signals as
105
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-4r(
mm
)r(
mm
)r(
mm
)r(
mm
)r(
mm
)
0.04
40 0
6080100
120 0
0.01
0.02
0.03
20
0.05
0.06
stea
dy f
lam
e
Cen
terl
ine
fuel
exi
t vel
ocity
vs.
tim
e
v(cm/s)
time(
s)d
cb
ae
(iii)
5101520253035404550
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5101520253035404550
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8-8
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5101520253035404550
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5101520253035404550
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8-8
-4
5101520253035404550
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8-8
-4r(
mm
)r(
mm
)r(
mm
)r(
mm
)r(
mm
)
(a)
(b)
(c)
(d)
(e)
(a)
(b)
(c)
(d)
(e)
(ii)
stea
dy
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
300
K
(i)
1960
K
Fig
ure
3.27
Tem
pera
ture
pro
file
s fo
r 30
% m
odul
atio
n (i
n de
gree
s K
).
(i
) M
ulti-
spec
ies
mea
sure
men
t. (i
i) T
wo
scal
ar. (
iii)
Cen
terl
ine
fuel
exit
velo
city
vs.
tim
e. P
hase
s w
here
dat
a is
take
n ar
e m
arke
d by
a,b,
c,d,
e on
the
grap
h an
d co
rres
pond
to th
e im
ages
labe
lled
likew
ise.
Stea
dy f
lam
e im
age
is s
how
n on
the
far
left
. The
ste
ady
flam
e
fu
el e
xit v
eloc
ity is
indi
cate
d in
the
grap
h. U
nrel
iabl
e da
ta r
egio
n fr
om
tw
o sc
alar
ram
an d
ata
is c
onta
ined
in th
e da
rk b
lue
boxe
s.
106
Figure 3.28 Temperature lineplots of the two-scalar and multispecies technique for 30%flow modulation. Radial data is taken 9 mm above burner.
phase
a
b
c
d
e
Temperature(K)-Phase dcenterline
0
500
1000
1500
2000
2500
0 20 40 60
height(mm)
two-scalarmulti-species
Temperature(K)-Phase ccenterline
0
500
1000
1500
2000
0 20 40 60
height(mm)
two-scalarmulti-species
Temperature(K)-Phase bcenterline
0
500
10001500
2000
2500
0 20 40 60
height(mm)
two-scalarmulti-species
Temperature(K)-Phase bradial
0
500
1000
1500
2000
0 5 10
radial(mm)
two-scalarmulti-species
Temperature(K)-Phase cradial
0
500
1000
1500
2000
0 5 10
radial(mm)
two-scalarmulti-species
Temperature(K)-Phase dradial
0
500
1000
1500
2000
0 5 10
radial(mm)
two-scalarmulti-species
Temperature-Phase acenterline
0
500
1000
1500
2000
0 20 40 60
height(mm)
two-scalarmulti-species
Temperature(K)-Phase aradial
0
500
1000
1500
2000
0 5 10
radial(mm)
two-scalar
multi-species
Temperature(K)-Phase ecenterline
0
500
1000
1500
2000
0 20 40 60
height(mm)
two-scalarmulti-species
Temperature(K)-Phase eradial
0
500
1000
1500
2000
0 5 10
radial(mm)
two-scalarmulti-species
107
well as the region where the methane Raman signal is present in the multi-species
measurement (downstream of 20 mm) but not recorded for the two scalar experiment is
blocked out in the images with a dark blue box. The oval region blocked out in phase "a"
for the multi-species temperature is a region where there is large elastic scattering
interference on the Rayleigh image. The most likely cause of this interference is
scattering from soot particles. The experimental images indicate similar modulations in
flame structure over the forcing period, with slightly less of a modulation in the two
scalar experiment, as is most apparent in phases (d) and (e). This is a good check on the
reproducibility of the forcing by the loudspeaker used. The profiles show good agreement
in lift off height, flame height, general flame shape, and absolute peak temperatures.
Plotted in Fig. 3.28 is the axial centerline temperature as well as the radial temperature 9
mm downstream. The broken part of the centerline curves for the two-scalar experiment
correspond to the blocked out regions in Figure 3.27. Radial temperatures 9 mm
downstream agree well, especially near stoichiometric and on the lean side. The major
difference in the radial plots is along the centerline, where the temperature is consistently
lower in the multi-species experiment. The centerline plots show good agreement in peak
temperature and temperature variation near stoichiometric, but the sharp rise in
temperature on the rich side of the flame front (along the centerline) occurs significantly
farther downstream in the multi-species experiment, which is most apparent in phase "c"
and "d". There is possibly some elastic scattering interference on the Rayleigh data in the
108
multi-species experiment in the region where the fuel disappears, which is not corrected
for in the Rayleigh images. This will produce an artificially high Rayleigh intensity and
thus an artificially low temperature in this region.
Figures 3.29 and 3.30 show mixture fraction plots and profiles for the multi-species and
two-scalar experiments. Shown in red outline is the stoichiometric contour. Profiles and
lineplots show good agreement. The major difference in the two techniques is seen along
the centerline near stoichiometric. The mixture fraction for the two-scalar experiment is
consistently lower than the multi-species mixture fraction in this region. The discrepancy
here is due to the assumptions of one-step chemistry in the two-scalar formulation of
mixture fraction. (This is seen in the comparison of mixture fraction formulations on the
computations in Figure 3.15.)
109
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-4
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8-8
-4
5101520253035404550
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8-8
-4r(
mm
)r(
mm
)r(
mm
)r(
mm
)r(
mm
)
0.04
40 0
6080100
120 0
0.01
0.02
0.03
20
0.05
0.06
stea
dy f
lam
e
Cen
terl
ine
fuel
exi
t vel
ocity
vs.
tim
e
v(cm/s)
time(
s)d
cb
ae
(iii)
5101520253035404550
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8-8
-4
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8-8
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5101520253035404550
04
8-8
-4r(
mm
)r(
mm
)r(
mm
)r(
mm
)r(
mm
)
(a)
(b)
(c)
(d)
(e)
(a)
(b)
(c)
(d)
(e)
(ii)
(i)
stea
dy
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
01
Fig
ure
3.29
Mix
ture
fra
ctio
n pr
ofile
s fo
r 30
% m
odul
atio
n.
(i
) M
ulti-
spec
ies
mea
sure
men
t. (i
i) T
wo
scal
ar. (
iii)
Cen
terl
ine
fuel
exit
velo
city
vs.
tim
e. P
hase
s w
here
dat
a is
take
n ar
e m
arke
d by
a,b,
c,d,
e on
the
grap
h an
d co
rres
pond
to th
e im
ages
labe
lled
likew
ise.
Stea
dy f
lam
e im
age
is s
how
n on
the
far
left
. The
ste
ady
flam
e
fu
el e
xit v
eloc
ity is
indi
cate
d in
the
grap
h. U
nrel
iabl
e da
ta r
egio
n fr
om
tw
o sc
alar
ram
an d
ata
is c
onta
ined
in th
e da
rk b
lue
boxe
s.
110
Figure 3.30 Two scalar and multi-species mixture fraction plots for30% flow modulation. Radial data is taken 9 mm above burner.
Mixture fraction-Phase acenterline
0
0.20.4
0.60.8
1
0 20 40
height(mm)
two-scalar
Mixture fraction-Phase aradial
00.20.40.60.8
1
0 5 10
radial distance(mm)
two-scalar
Mixture fraction-Phase e centerline
0
0.2
0.4
0.6
0.8
1
0 10 20 30 40
height(mm)
two-scalar
Mixture fraction-Phase eradial
0
0.2
0.4
0.6
0.8
1
0 5 10
radial distance(mm)
two-scalar
Mixture fraction-Phase cradial
00.20.40.60.8
11.2
0 5 10
radial distance(mm)
two-scalar
phase
a
b
c
d
e
Mixture fraction-Phase b centerline
00.20.40.60.8
11.2
0 20 40 60
height(mm)
two-scalar
Mixture fraction-Phase c centerline
0
0.2
0.4
0.6
0.8
1
0 20 40 60
height(mm)
two-scalar
Mixture fraction-Phase dcenterline
0
0.2
0.4
0.6
0.8
1
0 20 40 60
height(mm)
two-scalar
Mixture fraction-Phase bradial
00.20.40.60.8
11.2
0 2.5 5 7.5 10
radial distance(mm)
two-scalar
Mixture fraction-Phase dradial
0
0.2
0.4
0.6
0.8
0 2.5 5 7.5 10
radial distance(mm)
two-scalar
ξ CHO
ξ CHO
ξ CHO
ξ CHO
ξ CHO
ξ CHO
ξ CHO
ξ CHO
ξ CHO
ξ CHO
111
Figures 3.31-3.36 show profiles and lineplots of temperature, CO2, and H2O for the
computations and the multi-species experiment for the case of 30% modulation.
Temperature profiles indicate a greater modulation for the experiment than observed in
the computations. Phase "b" in the experiment indicates a region where the flame begins
to "pinch off" at a height of 35 mm, a phenomenon which is not observed in phase "b" of
the computations. Temperature lineplots indicate good agreement in peak centerline
temperatures and in flame lift-off height. The difference in the variation of centerline
temperatures also indicates the more modest computational modulation. Radial
temperature profiles indicate good agreement of temperature variation, but peak radial
temperatures are lower in the experiment. Profiles and plots of both CO2 and H2O
indicate good agreement in peak values, and centerline and radial variation.
Figures 3.37-3.42 show profiles and lineplots of temperature, CO2, and H2O for the
computations and the multi-species experiment for the case of 50% modulation. As in the
30% modulation case, the computations show a significantly smaller modulation than the
experiment. One observes a significant degree of "pinching off" of the flame in phases
112
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4r(
mm
)r(
mm
)r(
mm
)r(
mm
)r(
mm
)30
0 K
1950
K
0.04
40
0
6080100
120 0
0.01
0.02
0.03
20
0.05
0.06
stea
dy f
lam
e
Cen
terl
ine
fuel
exi
t vel
ocity
vs.
tim
e
v(cm/s)
time(
s)d
cb
ae
(iii)
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4r(
mm
)r(
mm
)r(
mm
)r(
mm
)r(
mm
)
(a)
(b)
(c)
(d)
(e)
(a)
(b)
(c)
(d)
(e)
(ii)
(i)
stea
dy
z(mm)
Fig
ure
3.31
Tem
pera
ture
pro
file
s fo
r 30
% m
odul
atio
n (i
n de
gree
s K
).
(i
) M
ulti-
spec
ies
mea
sure
men
t. (i
i) C
ompu
tatio
ns. (
iii)
Cen
terl
ine
fuel
exit
velo
city
vs.
tim
e. P
hase
s w
here
dat
a is
take
n ar
e m
arke
d by
a,b,
c,d,
e on
the
grap
h an
d co
rres
pond
to th
e im
ages
labe
lled
likew
ise.
Stea
dy f
lam
e im
age
is s
how
n on
the
far
left
. The
ste
ady
flam
e
fu
el e
xit v
eloc
ity is
indi
cate
d in
the
grap
h. U
nrel
iabl
e da
ta r
egio
n fr
om
tw
o sc
alar
ram
an d
ata
is c
onta
ined
in th
e da
rk b
lue
boxe
s.
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
stea
dy
r(m
m)
r(m
m)
113
Figure 3.32 Temperature lineplots (degrees K) of experiments (multi-species) andcomputation for 30% flow modulation. Radial data is taken 9 mm above burner.
Temperature(K)-radial
0
500
1000
1500
2000
2500
0 5 10
radial distance(mm)
compexp
Temperature(K)-radial
0
500
1000
1500
2000
2500
0 5 10
radial distance(mm)
compexp
a
b
c
d
e
phase
Temperature (K)-centerline
0
500
1000
1500
2000
2500
0 20 40 60 80
height(mm)
compexp
Temperature(K)-radial
0
500
1000
1500
2000
2500
0 5 10
height(mm)
compexp
Temperature(K)-centerline
0
500
1000
1500
2000
2500
0 20 40 60 80
height(mm)
compexp
Temperature(K)-centerline
0
500
1000
1500
2000
2500
0 20 40 60 80
height(mm)
compexp
Temperature(K)-radial
0
500
1000
1500
2000
2500
0 5 10
radial distance(mm)
compexp
Temperature(K)-centerline
0
500
1000
1500
2000
2500
0 20 40 60 80
height(mm)
compexp
Temperature(K)-radial
0
500
1000
1500
2000
2500
0 5 10
radial distance(mm)
compexp
Temperature(K)-centerline
0
500
1000
1500
2000
2500
0 20 40 60 80
height(mm)
comp
114
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4r(
mm
)r(
mm
)r(
mm
)r(
mm
)r(
mm
)0
0.09
6 (iii)
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4r(
mm
)r(
mm
)r(
mm
)r(
mm
)r(
mm
)
(a)
(b)
(c)
(d)
(e)
(a)
(b)
(c)
(d)
(e)
(ii)
(i)
stea
dy
z(mm)
z(mm)
z(mm)
z(mm)
Fig
ure
3.33
Car
bon
diox
ide
prof
iles
for
30%
mod
ulat
ion
(mol
e fr
actio
n).
(i)
Mul
ti-sp
ecie
s m
easu
rem
ent.
(ii)
Com
puta
tions
. (iii
) C
ente
rlin
e fu
el
ex
it ve
loci
ty v
s. ti
me.
Pha
ses
whe
re d
ata
is ta
ken
are
mar
ked
by
a,
b,c,
d,e
on th
e gr
aph
and
corr
espo
nd to
the
imag
es la
belle
d lik
ewis
e.
St
eady
fla
me
imag
e is
sho
wn
on th
e fa
r le
ft. T
he s
tead
y fl
ame
fuel
exi
t vel
ocity
is in
dica
ted
in th
e gr
aph.
Unr
elia
ble
data
reg
ion
from
two
scal
ar r
aman
dat
a is
con
tain
ed in
the
dark
blu
e bo
xes.
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
stea
dy
0.04
40
0
6080100
120 0
0.01
0.02
0.03
20
0.05
0.06
stea
dy f
lam
e
Cen
terl
ine
fuel
exi
t vel
ocity
vs.
tim
e
v(cm/s)
time(
s)d
cb
ae
r(m
m)
r(m
m)
115
Figure 3.34 Carbon dioxide mole fraction lineplots of experiments (multi-species) andcomputations for 30% flow modulation. Radial data is taken 9 mm above burner.
a
b
c
d
e
phase
Carbon dioxide mole fraction-radial
0
0.02
0.04
0.06
0.08
0.1
0 5 10
radial distance(mm)
compexp
Carbon dioxide mole fraction-centerline
0
0.02
0.04
0.06
0.08
0.1
0.12
0 20 40 60 80
height(mm)
compexp
Carbon dioxide mole fraction-radial
0
0.02
0.04
0.06
0.08
0.1
0 5 10
radial distance(mm)
compexp
Carbon dioxide mole fraction-centerline
00.020.040.060.08
0.10.12
0 20 40 60 80
height(mm)
compexp
Carbon dioxide mole fraction-radial
0
0.02
0.04
0.06
0.08
0.1
0 5 10
radial distance(mm)
compexp
Carbon dioxide mole fraction-radial
00.020.040.060.08
0.1
0 5 10
radial distance(mm)
compexp
Carbon dioxide mole fraction-centerline
00.020.040.060.08
0.10.12
0 20 40 60 80
height(mm)
compexp
Carbon dioxide mole fraction-centerline
00.020.040.060.08
0.10.12
0 20 40 60 80
height(mm)
compexp
Carbon dioxide mole fraction-radial
00.02
0.040.06
0.080.1
0 5 10
radial distance(mm)
compexp
Carbon dioxide mole fraction-centerline
00.020.040.060.08
0.10.12
0 50 100
height(mm)
compexp
116
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4r(
mm
)r(
mm
)r(
mm
)r(
mm
)r(
mm
)0
0.16
0
(iii)
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4r(
mm
)r(
mm
)r(
mm
)r(
mm
)r(
mm
)
(a)
(b)
(c)
(d)
(e)
(a)
(b)
(c)
(d)
(e)
(ii)
(i)
stea
dy
z(mm)
z(mm)
z(mm)
z(mm)
Fig
ure
3.35
Wat
er p
rofi
les
for
30%
mod
ulat
ion
(mol
e fr
actio
n).
(i)
Mul
ti-sp
ecie
s m
easu
rem
ent.
(ii)
Com
puta
tions
. (iii
) C
ente
rlin
e fu
el
ex
it ve
loci
ty v
s. ti
me.
Pha
ses
whe
re d
ata
is ta
ken
are
mar
ked
by
a,
b,c,
d,e
on th
e gr
aph
and
corr
espo
nd to
the
imag
es la
belle
d lik
ewis
e.
St
eady
fla
me
imag
e is
sho
wn
on th
e fa
r le
ft. T
he s
tead
y fl
ame
fuel
exi
t vel
ocity
is in
dica
ted
in th
e gr
aph.
Unr
elia
ble
data
reg
ion
from
two
scal
ar r
aman
dat
a is
con
tain
ed in
the
dark
blu
e bo
xes.
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
stea
dy
0.04
40
0
6080100
120 0
0.01
0.02
0.03
20
0.05
0.06
stea
dy f
lam
e
Cen
terl
ine
fuel
exi
t vel
ocity
vs.
tim
e
v(cm/s)
time(
s)d
cb
ae
r(m
m)
r(m
m)
117
Figure 3.36 Water mole fraction lineplots of experiments (multi-species) and computations for 30% flow modulation. Radial data is taken 9 mm above burner.
a
b
c
d
e
phase
Water mole fraction-radial
0
0.05
0.1
0.15
0.2
0 5 10
radial distance(mm)
compexp
Water mole fraction-centerline
0
0.05
0.1
0.15
0.2
0.25
0 20 40 60 80
height(mm)
compexp
Water mole fraction-radial
0
0.05
0.1
0.15
0.2
0 5 10
radial distance(mm)
compexp
Water mole fraction-centerline
0
0.05
0.1
0.15
0.2
0.25
0 20 40 60 80
height(mm)
compexp
Water mole fraction-centerline
0
0.050.1
0.150.2
0.25
0 20 40 60 80
height(mm)
compexp
Water mole fraction-radial
0
0.05
0.1
0.15
0.2
0 5 10
radial distance(mm)
compexp
Water mole fraction-centerline
0
0.05
0.1
0.15
0.2
0 20 40 60 80
height(mm)
compexp
Water mole fraction-radial
0
0.05
0.1
0.15
0.2
0 5 10
radial distance(mm)
compexp
Water mole fraction-centerline
0
0.05
0.1
0.15
0.2
0 20 40 60 80
height(mm)
compexp
Water mole fraction-radial
0
0.05
0.1
0.15
0.2
0 5 10
radial distance(mm)
compexp
118
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4r(
mm
)r(
mm
)r(
mm
)r(
mm
)r(
mm
)30
0 K
1950
K
0.04
40
0
6080100
120 0
0.01
0.02
0.03
20
0.05
0.06
stea
dy f
lam
e
Cen
terl
ine
fuel
exi
t vel
ocity
vs.
tim
e
v(cm/s)
time(
s)d
cb
ae
(iii)
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4r(
mm
)r(
mm
)r(
mm
)r(
mm
)r(
mm
)
(a)
(b)
(c)
(d)
(e)
(a)
(b)
(c)
(d)
(e)
(ii)
(i)
stea
dy
z(mm)
z(mm)
z(mm)
Fig
ure
3.37
Tem
pera
ture
pro
file
s fo
r 50
% m
odul
atio
n (i
n de
gree
s K
).
(i
) M
ulti-
spec
ies
mea
sure
men
t. (i
i) C
ompu
tatio
ns. (
iii)
Cen
terl
ine
fuel
exit
velo
city
vs.
tim
e. P
hase
s w
here
dat
a is
take
n ar
e m
arke
d by
a,b,
c,d,
e on
the
grap
h an
d co
rres
pond
to th
e im
ages
labe
lled
likew
ise.
Stea
dy f
lam
e im
age
is s
how
n on
the
far
left
. The
ste
ady
flam
e
fu
el e
xit v
eloc
ity is
indi
cate
d in
the
grap
h. U
nrel
iabl
e da
ta r
egio
n fr
om
tw
o sc
alar
ram
an d
ata
is c
onta
ined
in th
e da
rk b
lue
boxe
s.
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
stea
dy
r(m
m)
r(m
m)
119
Figure 3.38 Temperature lineplots (degrees K) of experiments (multi-species) and computations for 50% flow modulation. Radial data is taken 9 mm above burner.
a
b
c
d
e
Temperature(K)-radial
0
500
1000
1500
2000
0 5 10
radial distance(mm)
compexp
Temperature(K)-radial
0
500
1000
1500
2000
0 5 10
radial distance(mm)
compexp
Temperature(K)-radial
0
500
1000
1500
2000
0 2 4 6 8 10
radial distance(mm)
compexp
Temperature(K)-centerline
0
500
1000
1500
2000
2500
0 20 40 60 80
height(mm)
compexpc
phase
Temperature(K)-radial
0
500
1000
1500
2000
0 5 10
radial distance(mm)
compexp
Temperature(K)-centerline
0
500
1000
1500
2000
2500
0 20 40 60 80
height(mm)
compexp
Temperature(K)-radial
0
500
1000
1500
2000
2500
0 5 10
radial distance(mm)
compexp
Temperature(K)-centerline
0
500
1000
1500
2000
2500
0 20 40 60 80
height(mm)
compexp
Temperature(K)-centerline
0
500
1000
1500
2000
2500
0 20 40 60 80
height(mm)
compexp
Temperature(K)-centerline
0
500
1000
1500
2000
2500
0 20 40 60 80
height(mm)
compexp
120
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4r(
mm
)r(
mm
)r(
mm
)r(
mm
)r(
mm
)0
0.04
40
0
6080100
120 0
0.01
0.02
0.03
20
0.05
0.06
stea
dy f
lam
e
Cen
terl
ine
fuel
exi
t vel
ocity
vs.
tim
e
v(cm/s)
time(
s)d
cb
ae
(iii)
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4r(
mm
)r(
mm
)r(
mm
)r(
mm
)r(
mm
)
(a)
(b)
(c)
(d)
(e)
(a)
(b)
(c)
(d)
(e)
(ii)
(i)
stea
dy
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
stea
dy
r(m
m)
r(m
m)
Fig
ure
3.39
Car
bon
diox
ide
prof
iles
for
50%
mod
ulat
ion
(mol
e fr
actio
n).
(i)
Mul
ti-sp
ecie
s m
easu
rem
ent.
(ii)
Com
puta
tions
. (iii
) C
ente
rlin
e fu
el
ex
it ve
loci
ty v
s. ti
me.
Pha
ses
whe
re d
ata
is ta
ken
are
mar
ked
by
a,
b,c,
d,e
on th
e gr
aph
and
corr
espo
nd to
the
imag
es la
belle
d lik
ewis
e.
St
eady
fla
me
imag
e is
sho
wn
on th
e fa
r le
ft. T
he s
tead
y fl
ame
fuel
exi
t vel
ocity
is in
dica
ted
in th
e gr
aph.
Unr
elia
ble
data
reg
ion
from
two
scal
ar r
aman
dat
a is
con
tain
ed in
the
dark
blu
e bo
xes.
121
Figure 3.40 Carbon dioxide mole fraction lineplots of experiments (multi-species) andcomputations for 50% flow modulation. Radial data is taken 9 mm above burner.
a
b
c
d
e
Carbon dioxide mole fraction-radial
0
0.02
0.04
0.06
0.08
0.1
0.12
0 5 10
radial distance(mm)
compexp
Carbon dioxide mole fraction-radial
0
0.02
0.04
0.06
0.08
0.1
0 5 10
radial distance(mm)
compexp
Carbon dioxide mole fraction-radial
0
0.02
0.04
0.06
0.08
0.1
0 5 10
radial distance(mm)
compexp
Carbon dioxide mole fraction-centerline
0
0.02
0.04
0.06
0.08
0.1
0.12
0 20 40 60 80
height(mm)
compexp
c
Carbon dioxide mole fraction-centerline
0
0.02
0.04
0.06
0.08
0.1
0.12
0 20 40 60 80
height(mm)
compexp`
Carbon dioxide mole fraction-centerline
0
0.02
0.04
0.06
0.08
0.1
0.12
0 20 40 60 80
height(mm)
compexp
Carbon dioxide mole fraction-radial
0
0.02
0.04
0.06
0.08
0.1
0 5 10
radial distance(mm)
compexp
Carbon dioxide mole fraction-centerline
0
0.020.04
0.060.08
0.10.12
0.14
0 20 40 60 80
height(mm)
compexp
Carbon dioxide mole fraction-radial
0
0.02
0.04
0.06
0.08
0.1
0 5 10
radial distance(mm)
compexp
Carbon dioxide mole fraction-centerline
0
0.02
0.04
0.06
0.08
0.1
0.12
0 20 40 60 80
height(mm)
compexp
phase
122
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4r(
mm
)r(
mm
)r(
mm
)r(
mm
)r(
mm
)0
0.16
0
0.04
40
0
6080100
120 0
0.01
0.02
0.03
20
0.05
0.06
stea
dy f
lam
e
Cen
terl
ine
fuel
exi
t vel
ocity
vs.
tim
e
v(cm/s)
time(
s)d
cb
ae
(iii)
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4
5101520253035404550
04
8-8
-4r(
mm
)r(
mm
)r(
mm
)r(
mm
)r(
mm
)
(a)
(b)
(c)
(d)
(e)
(a)
(b)
(c)
(d)
(e)
(ii)
(i)
stea
dy
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
z(mm)
stea
dy
r(m
m)
r(m
m)
Fig
ure
3.41
Wat
er p
rofi
les
for
50%
mod
ulat
ion
(mol
e fr
actio
n).
(i)
Mul
ti-sp
ecie
s m
easu
rem
ent.
(ii)
Com
puta
tions
. (iii
) C
ente
rlin
e fu
el
ex
it ve
loci
ty v
s. ti
me.
Pha
ses
whe
re d
ata
is ta
ken
are
mar
ked
by
a,
b,c,
d,e
on th
e gr
aph
and
corr
espo
nd to
the
imag
es la
belle
d lik
ewis
e.
St
eady
fla
me
imag
e is
sho
wn
on th
e fa
r le
ft. T
he s
tead
y fl
ame
fuel
exi
t vel
ocity
is in
dica
ted
in th
e gr
aph.
Unr
elia
ble
data
reg
ion
from
two
scal
ar r
aman
dat
a is
con
tain
ed in
the
dark
blu
e bo
xes.
123
Figure 3.42 Water mole fraction lineplots of experiments (multi-species) and
computations for 50% flow modulation. Radial data is taken 9 mm above burner.
a
b
c
d
e
phase
Water mole fraction-radial
0
0.05
0.1
0.15
0.2
0 5 10
radial distance(mm)
compexp
Water mole fraction-centerline
0
0.05
0.1
0.15
0.2
0 20 40 60 80
height(mm)
compexp
Water mole fraction-radial
0
0.05
0.1
0.15
0.2
0 5 10
radial distance(mm)
compexp
Water mole fraction-centerline
0
0.05
0.1
0.15
0.2
0 20 40 60 80
height(mm)
compexp
Water mole fraction-radial
0
0.05
0.1
0.15
0.2
0 5 10
radial distance(mm)
compexp
Water mole fraction-centerline
0
0.050.1
0.150.2
0.25
0 20 40 60 80
height(mm)
compexp
Water mole fraction-radial
0
0.05
0.1
0.15
0.2
0 5 10
radial distance(mm)
compexp
Water mole fraction-centerline
00.05
0.10.15
0.20.25
0 50 100
height(mm)
compexp
Water mole fraction-radial
0
0.05
0.1
0.15
0.2
0 5 10
radial distance(mm)
compexp
Water mole fraction-centerline
0
0.05
0.1
0.15
0.2
0 20 40 60 80
height(mm)
compexp
124
"a", "b" and "c" in the experiment. The computations do show this "pinching off"
phenomenon in phases "b" and "c", but to a lesser extent than seen in the experiment. The
experiment and computations show good agreement in lift off height and in peak values
(except a lower peak radial temperature for the experiments). Radial plots indicate a
slightly wider flame in the experiment, although the variation in species and temperature
on the lean side of the flame agree well.
3.10 Summary
A steady and time-varying laminar methane diffusion flame is quantified in terms of
flame structure, species concentrations, mixture fraction, and temperature.
Chemiluminescence gives a quick and inexpensive way of accurately determining the
flame structure and lift off height of a flame. CH* chemiluminescence produces CH*
number density images that give a preliminary picture of the effect of the flow
modulation on the flame shape over the period of the forcing. The flame front stretches
and then "pinches off," shrinking the upstream portion of the flame back down while the
downstream portion convects farther downstream.
The two scalar technique produces images of the mixture fraction and temperature of the
steady and time-varying flame through the measurement of only two scalar quantities in
125
the flame. This technique produces good agreement away from stoichiometric when
compared with a major species measurement of temperature and mixture fraction. The
two-scalar technique gives a lower than expected mixture fraction near stoichiometric
than a major species measurement, due to the approximations in the two-scalar derivation
of mixture fraction. Interference on the fuel Raman image prevents quantitative
measurements in the interference regions. The two-scalar technique does offer a much
quicker and easier way to get temperature and mixture fraction than a measurement of all
of the major flame species. In addition, the two scalar technique can be applied much
more readily to a flame where there is less or no repeatability.
The multi-species technique produces images of temperature and major species
concentrations for the steady and time-varying flames. The difference Raman sub-
technique eliminates C2 and PAH interference on the weak Raman signals. In the steady
flame, the multi-species experiment produces results that agree well with the
computations in terms of spatial distribution and absolute values. For the forced flame,
the computations indicate a more modest forcing than experiments- further refinement in
the computations is needed. However, there is good agreement in peak values, lift-off
height, and in radial distributions 9 mm above the burner.
126
Chapter 4Soot and temperature characterization of
a sooting, laminar, ethylene diffusion flame
4.1 Introduction
There has been an increase in concern over the past decade for the environmental impact
of combustion generated soot. Soot is a major pollutant from diesel engines. Studies have
shown inhalation of soot particles as a health risk, leading to respiratory problems and
possibly some types of cancer. Tighter emission standards will require these engines to
produce less soot. Soot is important in the transfer of heat in flames, and can
significantly contribute to thermal loads on combustor walls. Measuring soot emission
will lead to better models that predict soot creation and destruction in combustion
environments. These models can then be used to help build combustors that reduce or
control soot production.
Although most practical combustors involve complex interactions of fluid mechanics and
chemistry, an axisymmetric, laminar flame allows for the ability to model the interaction
of soot with detailed flame chemistry. Since soot plays a key role in radiative heat
transfer in flames, determination of local temperatures along with soot characterization is
127
vitally important. In order to test these models, experiments are needed that produce high
spatial and temporal resolution in the detection of soot and measurement of temperature.
4.2 Flame and Burner Characterization
The same burner and configuration used in Chapter 3 is used in this experiment. The
flame is an axisymmetric, coflowing laminar diffusion flame. The flame is lifted to
prevent uncertain inlet boundary conditions due to heat loss to the burner. The fuel is
32% ethylene diluted with nitrogen. Ethylene is chosen for its high sooting tendencies
and its relatively simple structure for modeling purposes as compared to larger
hydrocarbons. This flame and similar ethylene diffusions flames have been well
characterized by experiments and computations [McEnally et al. 1998, Ni et al. 1995,
Wainnier and Seitzman 1999, Smyth et al. 1985]. This work represents the most complete
characterization of a sooting ethylene flame in the literature. The average fuel flow
velocity at inlet is 35 cm/s and is matched to the coflow velocity to minimize sheer
effects. This velocity is enough to produce a lifted flame but small enough to allow a
stable flame. From PIV measurements of velocity, there is no detected radial velocity
component.
128
4.3 Computational Model
Computations for this flame are done by Professor Mitchell Smooke [McEnally et al.
1998] at Yale University. The model utilizes velocity -vorticity formulation (i.e.
containing vorticity terms) of the gas-phase conservation equations along with transport
conservation equations for soot. The chemical mechanism for ethylene has 45 species and
233 reactions, and is based on GRI Mech 1.2. The conservation equations are initially
solved on a two dimensional mesh for a particle-free flame using a time-dependent
approach. Then the soot equations are incorporated and an adaptive gridding method is
used.
4.4 Probe measurement of temperature and soot volume fraction
Thermocouple measurements are performed by McEnally [McEnally et al.1998] at Yale
University. Temperature is measured with a 75 µm wire thermocouple. Rapid insertion of
the thermocouple into the flame minimizes soot deposition onto the thermocouple. A
correction is made for the radiative heat transfer to the thermocouple.
Soot volume fraction is measured with the same thermocouple using a technique where
the volume fraction is determined by the soot mass transfer rate to the thermocouple
129
junction [Eisner and Rosner 1985]. The full flame profile is obtained by translating the
thermocouple to known positions in the flame.
4.5 Experimental determination of temperature using the two scalar technique
The temperature field is determined optically using the two scalar approach of Stårner
[Stårner et al 1996] as a comparison to the probe measurement of temperature, and to
achieve a temperature measurement with better spatial resolution. This approach involves
the measurement of fuel concentration and Rayleigh scattering. In this experiment, fuel
Raman scattering is used as a measure of fuel concentration. The two scalar technique is
described in detail in Chapter 3.
4.5.1 Optical imaging setup for temperature measurement
The setup is shown in Figure 3.7 in Chapter 3. The second harmonic of a Q-switched
Nd:YAG laser emits 532 nm pulses of 8 ns in duration, at a 10 Hz rep rate. The laser is
magnified by a 3 X telescope and focused by a cylindrical lens of focal length 50 cm into
a 15.2 mm tall vertical sheet over the center of the burner. The scattered light is collected
perpendicular to the laser axis with a 50 mm camera lens( f/1.4 for Raman imaging, f/5.6
for Rayleigh imaging). Resulting pixel magnification is 12.5 pix/mm. The light passes
130
through an appropriate interference filter and then is focused onto an image intensified
CCD camera (Photometrics CC200). The laser, intensifier, and camera are synchronized
with digital delay generators such that data is only acquired when a laser pulse is present.
The intensifier gate time is 1 µs, which is small enough to prevent the acquisition of large
interfering flame luminosity. Since the flame is laminar, the scattering signal from many
laser pulses can be integrated on the CCD chip. Data is acquired for Rayleigh and Stokes-
shifted Q-branch Raman scattering at separate times, as justified by the repeatability of
the flame. The images are then downloaded to a computer for processing.
For Rayleigh scattering, images at two downstream locations are acquired. Rayleigh
images are integrated over 100 laser pulses. For the first set of images the laser sheet is 3
mm off the surface of the burner, as going any closer to the burner caused significant
elastic scattering interference. The next height had the bottom edge of the laser sheet at
the visible flame tip (28 mm off the burner surface). Data could not be acquired in the
intermediate flame heights because of the significant elastic scattering interference in this
region from soot particles. A 532 nm interference filter (10 nm bandpass) is used to
collect the Rayleigh scattering and reject signals outside this spectral range. Laser energy
is set to 195 mJ/pulse. Data are acquired similarly for calibrations and background signals
of uniform, pure gas flows of helium, air, and ethylene at room temperature. The laser
beam waist is estimated by replacing the cylindrical lens with a spherical lens of equal
131
focal length, and focusing the laser down to a line over the burner. Rayleigh scattered
light from the beam is imaged onto the camera, and the FWHM beam waist is measured
to be 300 µm.
For the ethylene Raman imaging, the laser is focused into a line across the burner with
approximate beam waist of 300 µm. Laser energy is reduced to 36 mJ/pulse to prevent
laser breakdown since the laser is now focused down to a point. Raman signals are
integrated over 200 laser pulses. Twenty Stokes-shifted ethylene Raman signals are
acquired at different heights above the burner, in steps of 0.5 mm. The line data are then
tiled together to form images. A 630 nm (10 nm FWHM) interference filter collects the
Stokes-shifted ethylene Raman scattering from the C-H stretch vibrational mode. Images
are also acquired from a uniform ethylene flow at room temperature and from
background flame luminosity present in the Raman data.
4.5.2 Processing
The Raman and Rayleigh images are corrected for throughput, detector dark counts, and
background as described in Section 3.4.2. Uniform fields of pure air and pure ethylene at
room temperature serve as calibration to the Rayleigh and Raman images.
132
4.5.3 Calculation of Temperature
Two scalar temperature calculation is described in Section 3.3.4. The functional
dependence of aT ,Cp, and Wmix on mixture fraction are obtained from computations of
this flame. The iterative process converges in four or less iterations. Final temperature
images are cropped, then mirrored and scaled to obtain a full symmetric temperature
profile. These profiles are then compared to temperature profiles from computations and
thermocouple measurements.
4.5.4 Two scalar temperature comparison with probe measurements and computations
Figure 4.1 shows the two-dimensional profile of temperature as determined by
thermocouple, computational, and the two scalar techniques. Good agreement is seen in
the profiles downstream, and upstream of the soot region. No meaningful Rayleigh data
can be obtained in the sooty region due to the significant elastic scattering from the soot,
and C2 fluorescence. The two scalar temperature shows similar temperature distribution,
lift off height, and peak temperatures as the probe measurements and computations. The
two scalar technique produces a slightly lower peak flame temperature than in the
thermocouple measurement and computations. Thermocouple measurements near the
133
05
-5r
(mm
)
2044
Cal
cula
ted
The
rmoc
oupl
e
298
Tw
o sc
alar
05
-5r
(mm
)0
5-5
r (m
m)
10203040 0
z (mm)
Fig
ure
4.1
Tem
pera
ture
Pro
file
Com
pari
sons
(K
)
134
fuel tube seem to overpredict the temperature here, as compared to the two scalar and
computational temperature profiles.
4.6 Determination of the soot volume fraction profile using laser-induced incandescence
4.6.1 Introduction and theory
Laser-induced incandescence (LII) has been used effectively to determine soot volume
fraction and particle size in sooting environments such as laminar flames [Mewes and
Seitzmann 1997, Ni 1995, Vander Wal 1994, 1996], ideal soot generators [Seitzmann
1999], and in diesel engines [Pinson et al. 1993]. The advantages of the LII technique are
high spatial resolution, good detection limits, and the non-intrusive interaction with the
combustion environment. At sufficient laser intensities, LII signal is shown to be
proportional to soot volume fraction. In this case, the measurement of soot volume
fraction involves simply the luminosity-subtracted, time-integrated LII signal along with
an appropriate calibration constant.
If one assumes a monodisperse distribution of particles with diameter a0, particle volume
fraction can be defined as
135
f N av po= ( )π
6
3(4.1)
In the limit of high laser power, and when the maximum particle temperature is reached
(dT/dt=0), (2.17) m
adadt
a dTdt
WRT
p vpp v
v
pv p4 32π
ρ β α= − = − can be substituted into
(2.14)
K a I ap v
T T mH
WT T
K deabs
g gp g p
v
vSB p g
abs
em
π απ γγ
π σ η η ηη
η
20
2 4 4 43
211
1 151
− +−
− + − −−∫
*
* ( / ) ˙ ( / ) ( )( )∆
− =43
03π ρa cdTdtp p to yield:
K a IH
RTp vabs v
v
pv pπ α2
0 0,max − =∆(4.2)
With (2.15) K aa m
mabsex
( , ) Imλ πλ
= −+
8 12
2
2 one can solve (4.2) for Tp in terms of a, I0,max.
Substituting this expression for Tp into the expression for LII intensity (2.25)
J t N S a t T t p a g da d dVp ema
a
Vp( ) ( ( ), ( )) ( ) ( )= ∫∫∫
1
2
1
20 0 0
λ
λ
λ λ , J reduces to
J C N p a a dapa
ax= ∫1
0 0 0
1
2
( )( ) (4.3)
where x c em= + −3 1λ , c is a constant dependent upon particle material properties (0.154
for carbonaceous particles), and λ em is in microns. If one assumes a very narrow particle
size distribution, (4.3) becomes
J C N ap
c em= ( ) + −
10 3 1λ
(4.4)
136
Comparing (4.4) and (4.1), the incandescence in the high temperature part of the LII
curve is approximately linear with fv. Inaccuracies in the assumption of linearity of LII
signal with fv are discussed in Seitzman [Mewes and Seitzman 1997] for various λ em ,
various time integration gates around the LII signal, and variations in particle size.
4.6.2 LII imaging setup
The setup for the LII imaging measurement of soot volume fraction is shown in
Figure 4.2. The second harmonic of a Q-switched Nd:YAG (10Hz rep rate) laser is
magnified by a 3 x telescope, and then focused with a cylindrical 50 mm focal length lens
into a vertical sheet across the center of the burner, with the bottom edge of the sheet 8
mm off the burner surface. The magnification and vertical placement of the laser sheet is
intended to capture most of the LII signal within a region of the laser sheet where the
laser fluence variations are small, as variations in laser fluence will complicate the LII
analysis. The LII signal is collected perpendicular to the laser axis by a f/1.4 50 mm focal
length camera lens. The collected light then passes through a 450 nm (10 nm bandpass)
interference filter. This spectral region is known to have minimal interference from flame
emission and C2 fluorescence with a 532 nm excitation wavelength in hydrocarbon
flames [Vander Wal and Weiland 1994, Wainner and
137
Figure 4.2 LII Imaging Setup
Nd:YAG Laser532 nm
30 cm f.l.
f/1.8 50 mm f.l. lens
CCD450 nm
ComputerEnergy Meter
interference filter
delaygenerator
imageintensifier
138
Seitzman 1999], and less error in soot volume fraction measurements from variation in
particle size and temperature as compared with longer detection wavelengths [Mewes and
Seitzman 1997]. Although a green excitation laser is known to produce significant
fluorescent interference from C2 species in the visible, this occurs only at fluences > 5
J/cm2, well above the fluences at which data is acquired in this experiment [Seitzmann
1999]. The incandescence is then focused onto an image intensified, cooled CCD camera.
Pixel magnification of the images is 10 pix/mm.
4.6.3 Data acquisition
The intensifier gate is widened to 2 µs to detect the entire incandescence signal over its
decay. The intensifier, laser, and camera are synchronized with digital delay generators to
capture the prompt rise of the LII signal along with the full decay of the signal. Although
it has been shown that a prompt 50 ns gate would result in less error in volume fraction
measurement for a change in particle diameter [Mewes and Seitzman 1997], the time
response of the intensifier gating may cause greater problems. The intensifier time
response is approximately 50 ns to turn on and 50 ns to turn off, for a step function input
signal to the cathode. Therefore if the intensifier turned off during the LII signal decay,
there would be a substantial chance for inconsistency as to when the intensifier is off and
139
no longer intensifying the incandescence signal. Therefore the signal is acquired over the
entire LII signal when the intensifier is fully "on".
In the region of greatest incandescence signal a survey is conducted of incandescence
signal versus laser fluence. At lower laser fluences, the incandescence signal increases
with laser fluence. This dependence starts to flatten out at sufficient fluences where
vaporization competes with particle heating. The laser fluence range used in the final
image acquisition of the incandescence signal is the fluence range where the
incandescence signal variation with laser fluence is small compared with the LII signal
variation with laser fluence at lower fluences. The resulting LII signal vs. laser fluence
curve is shown in Figure 4.3. The threshold laser fluence (the fluence at which the LII
signal becomes independent of laser fluence) of 1 J /cm2 is observed here, which is
approximately the same threshold fluence determined by Santoro [Quay et al. 1994] for a
similar ethylene diffusion flame and excitation scheme.
Shot-to-shot variation in LII images is recorded for 10 laser shots. Each single shot is
processed separately, then compared to each other. Then the average of these 10 is
compared to a single shot.
140
Figure 4.3 Variation of time-integrated LII signal with laser fluencefrom LII imaging. 532nm laser excitation. A 2 µs integration
window is used, including the rise of the LII signal.
0
500
1000
1500
2000
2500
3000
3500
4000
4500
0 1 2 3
Laser Fluence(J/cm^2)
LII
Sig
nal (
Arb
. uni
ts)
141
Figure 4.4 Calculated LII response to variations in laser fluence acrossthe height of the laser sheet. Shown in light gray is the region where LIIsignal is detected in the experiment.
Calculated LII response to variation in laser fluence vs. position within laser sheet
00.20.40.60.8
11.21.41.6
0 5 10 15 20 25 30 35 40
vertical position(mm)
laser fluenceLII response
00.460.921.381.842.32.763.223.68
Cal
cula
ted
LII
res
pons
e (A
rb.)
laser fluence (J/cm2)
region ofdetectable LII
142
Images of flame luminosity, detector dark current, and uniform field are acquired to
correct the raw LII images for luminosity background and optical throughput. Raman
scattering of a uniform field of pure ethylene at room temperature is acquired to
determine the variation in laser fluence vs. height above burner (HAB). This curve is
used along with the LII vs. laser fluence curve (Figure 4.3) to obtain the expected
variation in LII signal vs. position within the laser sheet. Figure 4.4 shows the variation in
laser fluence across the sheet as well as the expected variation in LII response due to the
variation in laser fluence. The region of detectable LII signal is marked in the figure. The
maximum expected variation in LII signal due to laser fluence variation within the sheet
is 7% within the region containing LII signal. Therefore no correction to the LII signal is
made.
4.6.4 Processing
Images of flame luminosity Ilum(x,y) are subtracted from the raw LII images ILII,flame (x,y)
to correct for background luminosity interference. A uniform field, diffuse white light
image Idiff(x,y) is used to correct the background corrected LII images for optical
throughput. Detector dark current ID is used for the background of the uniform field
image. The throughput and background corrected LII image is given by
143
I x yI x y I x y
I x y I x yLII corLII flame lum
diff D,
,( , )( , ) ( , )
( , ) ( , )0 =−
−(4.5)
Final images are then scaled and compared with probe measurements and computations.
The LII image intensity is calibrated with the probe measurement such that the peak soot
volume fraction of the probe measurement matches the peak LII signal.
4.6.5 Error estimates of the LII technique in determining soot volume fraction
Figure 4.5 shows the single shot LII images. Shot-to-shot, the LII profile does not vary
appreciably. The profiles are structurally similar compared to each other, and to the
average over ten shots. Also shown is the peak LII signals shot to shot. There is not more
than a 7% variation in peak signal. Therefore, it is reasonable to integrate the LII signal
over many shots, and therefore increase the detection sensitivity. One may observe a
slight asymmetry in the soot profiles in the main soot-containing region. This is most
likely due to asymmetry in the flows.
The LII signal is assumed to be proportional to soot volume fraction where there is
measurable signal. However, particle size has a significant effect on LII signal, since
larger particles reach higher peak temperatures, and thus emit more per soot volume
fraction. It is assumed for this flame that the primary particle size distribution is small.
144
Figure 4.5 Shot-to-Shot LII Fluctuation. The far rightimage is an integration of 15 shots. The graph shows the LIIintensity taken from the region of maximum LII signal.
single shots
15 shots
0
200
400
600
800
1000
1200
1400
1600
0 5 10
Shot-to-Shot LII Signal
min max
10
20
30
0 4-4 0 4-4 0 4-4 0 4-4 0 4-4
z(mm)
r(mm)
LII
Int
ensi
ty (
Arb
.)
Shot number
145
This is verified by TEM images from a carbon grid deposition technique. Grid samples
are taken along the flame centerline at heights where there is significant soot volume
fraction as measured by LII.
The temperature of the particles before laser heating will affect the peak temperature
reached, the cooling decay, and thus the LII signal. As seen with the computational
temperature data, the variation in gas temperature over the soot-containing regions is at
most 100 K. Compared to the temperature to which the particles are heated
(~ 2500 K)[Filippov 1999] there will be an insignificant difference in the LII signal decay
for a gas temperature difference of 100 K.
Other than for a small flame luminosity, which is subtracted off of the LII signal, there is
no apparent interfering signal within the spectral window of the 450 nm filter. At very
high fluences, it is known that a 532nm excitation will excite C2 species, which fluoresce
across the visible, and would interfere with this signal [Seitzman 1999]. The wing tips of
an interference signal can be seen on the ethylene Raman data (Fig. 4.6). This
interference is either laser-induced incandescence of the soot or C2 fluorescence. It has
been stated that using the fundamental of the YAG laser (1064 nm) is more desirable as it
produces less C2 Swan band interference [Vander Wal 1994]. A good check would be to
compare the LII images at excitation wavelength of 532 nm to that at 1064 nm.
146
Figure 4.6 Interference on ethylene Raman data.The region of interference is indicated in the image.
Ethylene Raman
jet center Interference
min max
r(mm)
4 8
z(mm)
4
8
12
147
Figure 4.7 Experimental and Computational Soot Volume Fraction.32% Ethylene Flame.
LII
10
20
30
0
0 4-4
r (mm)
0 4-4 0 4-4
ProbeComputed
10
20
30
0
z (m
m)
7.7 E-7
0
9.9 E-7
0
r (mm) r (mm)
z (m
m)
148
4.7 LII soot volume fraction comparison to probe measurements and computations
Figure 4.7 shows a comparison of soot volume fraction profiles for LII, probe, and
computational techniques. The probe and LII measurement have peak soot volume
fractions along the centerline, at the same height above burner, approximately 21 mm.
The computations peak along the wings and extend closer to the burner than is the case
for the probe measurements. The LII soot volume fraction does not extend down as far as
the probe measurements in the wings of the volume fraction profiles. One explanation for
this is that the probe can detect translucent particles such as soot precursors (which
appear closer to the burner surface than mature soot) which do not absorb the visible laser
energy, and thus the LII technique would not detect.
4.8 Primary soot particle size using time-resolved LII
4.8.1 Introduction
Time-resolved LII (tires-LII) is used to determine the size distribution of soot in the
flame. Others have used tires-LII to determine particle size in flames with other
techniques, but all based on the model initially proposed by Melton [Will et al. 1995,
Mewes and Seitzman 1997]. An improved model is developed to analyze the time decay
149
of the time resolved LII curves to obtain the primary particle size distribution. This model
is applicable in the free molecular regime and incorporates effects unaccounted for in
previous models such as thermal particle swelling and gas impingement cooling [Rosner
2001, Filippov and Rosner 2000a, Rosner 2000]. The model is used by a novel search
procedure to determine particle size distributions.
One can simultaneously numerically integrate the energy flux equation (2.14)
K a I ap v
T T mH
WT T
K deabs
g gp g p
v
vSB p g
abs
em
π απ γγ
π σ η η ηη
η
20
2 4 4 43
211
1 151
− +−
− + − −−∫
*
* ( / ) ˙ ( / ) ( )( )∆
− =43
03π ρa cdTdtp p
and the mass flux balance equation (2.17) m
adadt
a dTdt
WRT
p vpp v
v
pv p4 32π
ρ β α= − = − to
obtain the time dependence of the particle radius a(t,a0,I0) and temperature Tp(t,a0,I0) for
an initial particle radius a0 and a laser power density I r t0 ( , )r
where rr represents a
position within the probed volume.
The relevant properties of soot and the surrounding gas are summarized in Table 4.1 and
Figure 4.8 on the following page. For calculation of Kabs the index of refraction of soot
(or carbon) must be known. The index of refraction of carbon is taken from the work of
Lee and Tien [Lee and Tien 1981]. The refractive index is dependent on both
150
Figure 4.8 Select properties of carbon and nitrogen
20
22
24
26
28
30
0 2000 4000 6000
00.20.40.60.8
11.21.41.61.8
2
300 500 700 900 1100
wavelength (nm)
Index of Refraction - Carbon [Lee and Tien 1981] Temperature = 1400 K
real
imaginary
index ofrefraction (m)
Temperature (K)
Cp( J/mol-K)
Specific Heat of Carbon [JANAF 1985]
7.37.47.57.67.77.87.9
8
1000 2000 3000 4000 5000
Temperature(K)
Adiabatic Ratio -Nitrogen [JANAF 1985]
γγ
**
+−
11
γ * +1
γ * −1
151
Table 4.1 Parameters used in the soot LII analysis
αv [Thorn and Winslow 1957] ∆Hv(kJ/g-mole) [JANAF 1985]
( soot -> C1 ) 0.4 711.932( soot -> C2 ) 0.3 818.136( soot -> C3 ) 0.1 765.315
Tp*(K) 1300
pv*(atm) (C1) 5.0582x10-5 [Rosner 2001a]
pv*(atm) (C2) 2.4547x10-5
pv*(atm) (C3) 2.5351x10-4
Tg(K) 1580βgraphite (K
-1) 2.1x10-5 [Avallone and Baumeister 1996]
α 1
temperature and wavelength of the incident light. The carbon index of refraction vs.
wavelength for a temperature of 1600 K is used in the model.
Vaporized soot will contain C1, C2, C3, etc., each with a different evaporation coefficient.
For the mass vaporization term of (2.17), the mass vaporizations of all possible vapor
species Ci (weighted by its respective evaporation coefficient) are summed together:
˙,
,, ,
m
adadt
a dTdt
W
RTp vp
p p v iv i
pv i p i
Ci4 32πρ ρ β α= − = −∑
The literature only has evaporation data for C1, C2, C3 [Thorn and Winslow 1957], and
therefore these three species are used in the sum. Vapor pressure curves for each of the
152
species are estimated using the form of (2.18) p pH
RT
T
Tv vv
p
p
p
= −
**exp
∆1 and JANAF
tables [JANAF 1985, Rosner 2001a] for the relevant parameters.
The gas temperature in the region of peak soot concentration is unknown from the two
scalar measurement as this region produced elastic scattering interference on the
Rayleigh data. The gas temperature measured just outside this region is used as an
approximate gas temperature within the sooty region. The temperature dependence of the
specific heat of carbon is obtained from JANAF [JANAF 1985]. The temperature
dependence of γ* for the gas surrounding the soot is estimated from JANAF [JANAF
1985], based on the properties of nitrogen since the majority of the surrounding gas is
nitrogen. The thermal accommodation coefficient is assumed to be unity. A value for α
of 0.3 is quoted in the literature for nitrogen initially at 300 K near a flat graphite surface
at 1200 K [LeRoy et al. 1997]. The affect on the predicted particle size due to uncertainty
in α is investigated in section 4.8.8.
From numerical integration of (2.25) J t N S a t T t p a g da d dVp ema
a
Vp( ) ( ( ), ( )) ( ) ( )= ∫∫∫
1
2
1
20 0 0
λ
λ
λ λ
one is able to calculate the relative time resolved LII intensity J(t), for a particle
distribution p(a0) ranging from a1 to a2 and integrated over spectral region from λ1 to λ2
153
with a spectral detection efficiency g(λ). Only a relative intensity curve is calculated,
since an absolute intensity curve would involve knowledge of Np and optical efficiencies
of the collection system.
J(t) is known from the experimental data. The only unknown is p(a0). To obtain p(a0)
from the above equation, the integral must be inverted. If one defines the kernel function
K(a0,t) by
K a t N S a t a I T t a I g dVdp em pV
( , ) ( ( , , ), ( , , )) ( )0 00
00
1
2
= ∫∫ λ λλ
λ
(4.6)
(2.25) becomes a Fredholm integral equation of the first kind
J t K a t p a daa
a
( ) ( , ) ( )= ∫ 0 0 0
1
2
(4.7)
The solution to this equation for p(a0) is a non-linear iterative procedure developed by
Twomey [Twomey 1977] and improved by Markowski and others [Markowski 1987,
Filippov 1990]. This technique assumes the particle distribution is smooth and
continuous. A novel technique presented in this work utilizes the least squares method by
generating the best fit to J(t) by successive guesses at p(a0) until the error of the fit to J(t)
is minimized.
4.8.2 Time-resolved LII setup
154
Setup for the experiment is shown in Fig 4.9. The fundamental wavelength of the
Nd:YAG laser (1064nm) produces near infrared laser pulses of 8 ns in duration. The laser
beam is unfocused, and is sent through a 0.5 mm diameter pinhole. A uniform intensity
cross section region of the YAG beam is steered through the pinhole. The intent is to get
a uniform beam intensity cross section (i.e., a top hat profile) to minimize spatial
variation in laser fluence which will complicate the analysis of the LII curves. The
pinhole is positioned as close as possible to the burner center (10 cm away), as diffraction
effects are minimized at shorter distances after the aperture. The resulting beam cross
section above the burner is calculated from diffraction theory. The resulting
beam profile can be approximated by a gaussian function with σ = 100 µm. The laser
passes through the burner centerline at a height of 21 mm above the burner, the region of
maximal soot concentration as determined by LII imaging. The spatial profile of soot
volume fraction is known from LII imaging. The LII signal is collected perpendicular to
the laser with a f/1.8 50 mm focal length lens. The collected incandescence is focused
onto a 0.5 mm vertical slit. The signal that passes through the slit is collected by a
photomultiplier tube (PMT) (HammamatsuR928). The signal is not spectrally filtered
before entering the PMT because the cathode of the PMT is not sensitive to the elastically
scattered light at 1064 nm. The object magnification is 1, and the resulting optical sample
volume is 500x200x200 µm3. The PMT signal is sent to a digital oscilloscope
(Techtronix, 500 Msamples/s) where the signal is digitized. The PMT
155
Figure 4.9 Time-resolved LII setup.
Nd:YAG Laser106 4 nm
0.5 mm Pinhole
0.5 mm Slit
PMT
Oscilloscope
Photodiode
f / 1 .0
Energy Meter
Time Resolved
Comput er
156
response time is 2 ns, which should be adequate for the LII curves with expected decay
times of approximately 1000 ns for 20-30 nm soot particles [Will et al. 1995]. The shot-
to-shot pulse energy is recorded by a power meter after the beam has passed though the
flame. The temporal laser pulse is recorded with a 2 ns rise time photodiode and digitized
on the scope.
4.8.3 Time-resolved LII data acquisition
Laser fluence is varied from approximately 0.05 J/cm2 to 5 J/cm2, and time-resolved LII
curves are acquired. Single-shot time-resolved LII signals are acquired along with the
temporal laser pulse and laser energy. Weaker signals are averaged over 8 and 64 pulses
and are compared to the single shot LII signals at the same fluence to make sure there is
no loss of information or signal distortion caused by integrating signals.
4.8.4 Qualitative analysis of the time-resolved LII signals
Figure 4.10 shows a sample of time-resolved LII decay curves at various laser fluences.
The peak LII signal is greater as fluence is increased. This makes sense because the
particles are heated by the laser to higher peak temperatures as the laser fluence is
increased, producing an increased amount of incandescence. These signals are then time
157
Figure 4.10 Time-resolved LII curves at various laser fluences.
Laser fluence (J/cm2)
0.120.61.1
2.1
time (ns)
LII
sig
nal (
Arb
.)
0
200
400
600
800
1000
0 100 200 300 400 500
158
laser fluence (J/cm2)
Figure 4.11 Time-integrated LII signals vs. laser fluence. Integration gate is 1 µs and includes the rise of the LII signal.
0
10000
20000
30000
40000
50000
60000
70000
80000
0 0.5 1 1.5 2 2.5
tim
e-in
tegr
ated
L
II (
Arb
.)
159
integrated with a gate of 1 µs to include the peak signal as well as the decay. Figure 4.11
shows the time-integrated LII signals versus laser fluence. (Note that the LII imaging and
time-resolved measurements are performed with different excitation wavelengths so
their respective LII vs. fluence curves will not in general be the same.) The time-
integrated LII signals increases with fluence below a fluence of 1 J/cm2. Between a
fluence of 1 and 2 J/cm2, the curve begins to flatten out. This is due to the competition of
mass vaporization with laser heating. The particle vaporization will limit the maximum
temperature a laser-heated particle can reach. The integration time window is changed to
50 ns and is gated around the peak LII signals. This curve shows the same dependence on
laser fluence as the curve with a 1 µs gate.
The time-resolved LII signals are normalized by their peaks as shown in Figure 4.12. As
the laser fluence is increased, the initial decay rate of the LII signal increases. This makes
sense because particles with a higher peak temperature will cool at a faster rate, and
therefore the respective LII signal will decay at a faster rate. The difference in decay rates
of the LII curves becomes smaller as laser fluence is increased. This indicates a limited
maximum temperature value as laser fluence is increased. Also shown in Fig. 4.12 is the
temporal laser profile. The temporal laser pulse width will limit the particle sizes that can
be detected, as smaller particles will cool at a faster rate. Particles with
160
Figure 4.12 Time-resolved LII signals for various laserfluences. Signals are normalized to their peaks.Also shown is the time-resolved laser pulse intensity.
0
2 5
5 0
7 5
100
125
0 100 200 300 400 500
Laser fluence (J/cm2)
0.120.61.1
2.1
laser
Nor
mal
ized
LII
(A
rb. u
nits
)
time (ns)
161
cooling rates equal to or greater than the laser pulse decay rate cannot be extracted from
the model.
The model used to extract primary particle size information from LII data does not
account for aggregate break-up or aggregate restructuring. Some recent experiments have
shown that a laser with a particular laser fluence can sometimes alter the structure of the
soot aggregates without inducing substantial vaporization, i.e. at fluences below
vaporization threshold [Vander Wal 1998]. If restructuring and break-up occurs, particle
heating may compete with the restructuring or break-up, leading to a lower than
predicted maximum temperature (and thus a longer relative decay time for peak
normalized LII curves).
4.8.5 Calculation of particle size distribution from LII data
As an initial approach to finding the particle distribution, a least-squares procedure is
developed. This approach allows for single mode and bi-modal particle distributions. The
form of the distribution of a single mode is assumed to be either lognormal or normal
with parameters a0 and σ where p(a0) is the peak of the mode and σ is the characteristic
spread of the mode. A least squares approach is used to find the optimal curve fit to the
data, where the minimization parameter χ is defined by
162
χ = −∑=
1 2
1NJ t J td i c i
i
N
( ( ) ( )) (4.8)
where N is the number of points, Jd(t) represents the time resolved LII intensity curve
obtained from experiments, and Jc(t) represent the time-resolved LII intensity curve
generated from (2.25) J t N S a t T t p a g da d dVp ema
a
Vp( ) ( ( ), ( )) ( ) ( )= ∫∫∫
1
2
1
20 0 0
λ
λ
λ λ for a given
particle distribution. The curves are normalized to their peak values. Data from the rise
portion of the LII signals are not used in the curve analysis. Criteria for the value of χ
that must be achieved for a “good” fit is determined from the sensitivity of χ to the fit
parameters.
The parameters that must be determined are a0 and σ for a single mode distribution and
a0,1, a0,2, σ1, σ2, and g12 for a bi-modal distribution, where g12 is the ratio of the peaks of
mode 1 and mode 2. A single mode distribution is used first, as it will involve less
computational time, and most particle synthesis processes produce a single mode
distribution.
A large part of the procedure is based on inspection of the computed curves versus the
data, and the knowledge of the effect on the time decay of the curves when a0 and σ are
varied. The curve can be broken into two parts- the initial fast decay of the curve (part 1),
163
and then the slower decay region (part 2). The parameter σ is fixed at a small value to
approximate a monodisperse distribution. The parameter a0 is adjusted until the fit to
part 1 of the curve produces a minimum χ ( call it χ(1)). Then the value of a0 is held
constant while σ is increased gradually until the fit to part 2 of the curve produces a
minimum χ (call it χ(2)). The χ value of the entire curve is also calculated here. An
increase of σ will decrease the curve decay rate (increase the slope of the curve) in part 1
of the curve. Now σ is fixed, and a0 is gradually decreased, which has the effect of
increasing the curve decay rate (as smaller particles cool faster than large ones). The
value of a0 is decreased until the fit to part 1 of the curve produces a minimum in χ(1). The
procedure is repeated until there is convergence in the minimum value for χ.
If the procedure for a single mode distribution does not produce a reasonable fit to the
data, a bi-modal distribution algorithm is applied. The LII data curve is broken into two
parts. The first part of the curve has an initial steep drop in intensity. This part of the
curve will be affected by both distribution modes. The second part of the LII curve has a
relatively slow decay in signal. Since small particles have a faster LII decay than larger
particles, the contribution to the LII signal in the second part of the curve from larger
particles dominates. Thus the curve fit in the second part of the curve will be largely
unaffected by the parameters in the first part of the curve (as long as particle distributions
164
do not begin to overlap). Two separate fits are done using the single mode procedure for
the first and second parts of the curve. After a reasonable fit is achieved for each of the
two parts of the curve, the two distributions are combined linearly with the parameter g12,
and a new fit is generated for the entire curve (and χ of the entire curve is calculated).
The value of g12 is adjusted to produce a minimal value of χ for the second part of the
curve, call it χ2. (Note the difference between χ2 and χ(2). The minimization terms χ(1) and
χ(2) are determined in the single mode procedure used to obtain χ1 and χ2 separately.) The
value of a0 and σ for the second part of the curve is fixed, and the value of a0 for the first
part of the curve is varied to achieve a minimal value of χ for the first part of the curve,
call it χ1. The value g12 is adjusted again to produce a minimal χ2. This process is
repeated until there is convergence in the value of χ for the entire curve.
LII experimental data is analyzed to extract a soot particle size distribution from the
model. An LII experimental curve taken 22 mm above the burner is analyzed. The
measured laser fluence is 0.12 J/cm2. Laser spatial intensity profile is gaussian with σ =
100 µm. Laser temporal intensity profile is gaussian with σ = 3.7 ns. The particle size
distribution is assumed to be normal for one case and lognormal for another case. The
detection sensitivity g(λ) is known from the PMT spectral sensitivity. Convergence of the
165
iterative procedure that minimizes χ is achieved with less than twenty calculations of
Jc(t).
4.8.6 Grid sampling of soot particles
Results of the LII-derived soot particle distributions are compared to thermophoretic
probe samples of soot obtained from the flame. This experiment is performed by the
group of Professor Daniel Rosner at Yale University. It has been shown that the
orientation-averaged thermophoretic properties of aggregates are insensitive to aggregate
size and structure [Rosner et al. 1991]. In the free-molecule regime, the orientation-
averaged thermophoretic diffusivity of an aggregate varies by only 8% from that of a
single particle. Even though soot forms aggregates under the present conditions,
thermophoretic sampling should give a true representation of the particles/aggregates in
the flame. A rapid grid insertion technique [Köylu et al. 1997, Xing et al. 1999] is used to
extract soot particles at the same location in the flame as the LII measurement. The grids
are imaged by a transmission electron microscope (TEM) giving image magnifications on
the order of 100,000 X. Statistical analysis is performed on the particle images.
166
Figure 4.13 Curve fit to the soot LII data. Z = 22 above burner.Laser fluence = 0.12 J/cm2. For the normal particle size distribution,a0 = 10 nm, σ = 6 nm, χ = 1.0. For the lognormal distribution,
a0 = 10 nm, σ = .13, χ = 1.2.
LII
sig
nal (
Arb
.)
LII data
Soot LII data fit to curves of modelLaser Fluence = 0.12 J/cm2
0
10
20
30
40
50
60
0 100 200 300 400
time(ns)
fit-normal
fit-lognormal
167
4.8.7 Comparison of LII-derived and grid sampling particle size distributions
Figure 4.13 shows the fit of the model to the LII data for the conditions above. A value of
χ = 1.0 is achieved for a generated curve using a normal particle size distribution, with a0
= 10 nm and σ = 6 nm. A value of χ = 1.2 is achieved for a generated curve using a
lognormal particle size distribution with a0 = 10 nm and σ = 0.13.
The noise of the LII signal is approximately equal to the error of the two fits, and
therefore there is good agreement between the experimental and computed LII curves.
Figure 4.14 compares particle diameter (i.e., 2a) distributions obtained from time-
resolved LII and TEM images of the grids containing soot samples. The mean of the
lognormal and normal particle diameter distributions is identically 2a0= 20 nm, as
compared to 2a0 = 22 nm for TEM-derived particle sizes. All three distributions are
narrow and have similar distribution widths.
4.8.8 Sensitivity analysis of LII-derived particle sizing technique
A sensitivity analysis is done to see the effect of the change in parameters on the change
in predicted particle size from the model and search procedure. A reference LII curve is
168
Figure 4.14 Primary soot particle size distributions from grid samplingmeasurements and from the LII-derived particle size distribution.Height = 22 mm above the burner.
PDF sampled soot
Soot size distribution comparison
0
0.2
0.4
0.6
0.8
1
1.2
0 10 20 30 40
diam(nm)
normal
lognormal
169
generated using the same parameter values for the soot LII curve analysis in Section
4.8.6. The mean particle diameter is selected to be 20 nm as is determined in the soot LII
data analysis. For simplicity, a monodisperse distribution is used. The LII curve
generated with these parameters is used as the reference LII signal. One parameter is
changed at a time. The least-squares procedure is used to find the mean particle diameter
that gives the LII curve with the best fit to the reference LII curve.
Graphs illustrating the effect on predicted particle size due to variation in a parameter
value are shown in Figure 4.15. Shown in light gray are the reference values used to
calculate the reference LII signal. Since the gas temperature uncertainty is less than ± 50
K, the corresponding predicted particle diameter is in the range from 19 nm to 21.5 nm.
The volume expansion coefficient, β, for graphite is in the range from 2.1x10-5/K to
6.6x10-5/K [Rosner 2001a]. This range in β leads to a negligible change in predicted
particle diameter. The thermal accommodation coefficient, α, is not well known for
nitrogen impingement on carbon for Tg = 1600 K and Tp = 2500 K [Rosner 2001b]. The
value for α can be anywhere from 0.3 ( for Tg = 300 K and Tgraphite= 1200 K [LeRoy et al.
1997 and Rosner 2001a]) to 1. This gives a range of predicted particle diameter from 6
nm to 20 nm. The value of α must be known with better certainty to give more
confidence in the prediction of particle size from the model. The refractive index vs.
170
Figure 4.15 Effect of change in parameter values on predicted particlesize. Shown in light gray are the reference values used to generate theLII reference signal.
Predicted particle diam. vs.Gas temperature
10
15
20
25
30
35
40
1000 1200 1400 1600 1800 2000
Gas Temperature(K)
Pre
dict
ed p
arti
cle
diam
. (nm
)
Pre
dict
ed p
arti
cle
diam
. (nm
)
Pre
dict
ed p
arti
cle
diam
. (nm
)P
redi
cted
par
ticl
e di
am. (
nm)
Pre
dict
ed p
arti
cle
diam
. (nm
)
α (thermal accommodation coeff.)
reference valuesfor soot LII analysis
Predited particle diam. vs. Im[m] at 1064 nm (soot)
15
17
19
21
23
25
0 0.2 0.4 0.6 0.8 1
Im[m] at 1064 nm
Predicted particle diam. vs.Thermal accommodation coefficient
0
5
10
15
20
25
0 0.5 1 1.5
Predicted particle diameter vs.Volume expansion coefficient (soot)
15
17
19
21
23
25
0.0E+00 2.0E-04 4.0E-04 6.0E-04
ß (volume expansion coefficient)
Predicted particle diam. vs.Re[m] at 1064 nm (soot)
5
10
15
20
25
30
1.3 1.5 1.7 1.9 2.1 2.3
Re[m] at 1064 nm
171
wavelength curves in Figure 4.8 are shifted by the same amount at each wavelength for
the sensitivity analysis. Values for the imaginary part of the refractive index of soot
range in the literature [Lee and Tien 1981] from 0.5 to 0.8 at 1064 nm. This gives a range
in predicted particle diameter from 18 nm to 20 nm. Values for the real part of the
refractive index of soot range in the literature from 1.6 to 1.9 at 1064 nm. This gives a
range of predicted particle diameter from 16 nm to 20 nm.
4.9 Time-resolved laser light scattering and laser absorption
4.9.1 Introduction
Recently, researchers have shown that for aggregated particles such as soot, the laser
used to heat the soot for LII experiments may cause structural changes in the aggregates
and aggregate breakup [Vander Wal 1998]. This phenomenon can occur independently of
particle vaporization if the proper laser fluence is chosen.
In order to see if there are structural changes in the soot due to the laser pulse, time-
resolved laser light scattering (LLS) and laser absorption (or extinction) measurements
are performed. Time-resolved absorption in similar flames has been performed by others
172
but on longer time scales. From (2.32) C
aE m
kabs =
4 3
2
πλ
( ) (in the Rayleigh limit) the
extinction coefficient is proportional to Npa3. As seen from (2.34) I I K Le= −0 exp( ),
any change in either Np or a will change the absorption ratio I/Io. If particles are
vaporized, this ratio will decrease. This ratio is independent of aggregate parameters such
as fractal dimension Df and radius of gyration Rg. Therefore I/Io should be insensitive to
the restructuring/break-up of aggregates. From Chapter 2, scattering cross sections are
dependent upon Rg and Df, as well as np, and therefore the LLS signal will change if any
of these parameters change. Ideally, one would like to isolate aggregate
restructuring/break-up from vaporization by finding a laser fluence large enough to cause
aggregate restructure/break-up and small enough to not cause significant particle
vaporization.
4.9.2 Setup for LLS and laser absorption experiment
Time-resolved LLS and laser extinction are measured with a pump-probe setup shown in
Figure 4.16. The fundamental of a Q-switched ND:YAG laser (1064 nm) is used to heat
the soot particles in the sooty flame region. A CW Ar+ laser is used for measurement of
extinction and laser light scattering. The Ar+ laser is tuned to the 488 nm transition
producing a CW blue laser beam. The two beams are made collinear and pass over the
173
center of the burner in opposite directions, at a beam center height of 22 mm above the
burner. The YAG beam is apertured with an iris with a diameter of 2.5 mm. The Ar+
laser is focused down over the center of the burner. The scattering signal is collected at
90 degrees to the laser axis by a 50 cm f.l. f/1.4 lens. The collected light passes through
an interference filter centered at 488 nm and is focused onto the same aperture/PMT
configuration as for the tires-LII measurement. The PMT is terminated with 93 ohms and
the output signal is digitized on the scope, and sent to the computer for analysis. A
beamsplitter is placed in the path of the beams, on the side of the burner away from the
Ar+ laser. This reflects a fraction of the energy of the YAG beam and Ar+ laser in
opposite directions. The reflected YAG beam is collected by a energy meter to monitor
the shot-to-shot YAG energy. The reflected Ar+ laser passes through a 488nm (10 nm
bandpass) interference filter and onto a PIN silicon photodiode. This photodiode records
the change in Ar+ laser intensity as the flame absorption changes. The photodiode is
connected to the digital scope with a 93 ohm termination, where the signal is digitized
and downloaded onto the computer.
4.9.3 Acquisition of LLS and laser absorption
The laser fluence of the YAG laser is varied, and the time-resolved scattering and
absorption signal are recorded just before, during, and after the YAG pulse. Signals are
174
Figure 4.16 Time-resolved Scattering/Absorption Setup
Aperture
Mirror
Photomultiplier Tube
Ar+ Laser
Nd:YAG LaserEnergy Meter
Burner
f/1.8 50 mm lens
Interference Filter
Photodiode
50 cm f.l. lens
0.5 mm slit
Beamsplitter
ND FilterInterference Filter
Scattering Absorption
175
integrated over 256 YAG pulses to improve the signal-to-noise ratio of the
measurements. A correction to the scattering signal is made to account for LII
interference. This correction is acquired by turning off the Ar+ laser while leaving on the
YAG laser. The shot-to-shot laser energy is also monitored as mentioned in section 4.9.2.
4.9.4 LLS/Absorption results
Time-resolved scattering and absorption for several fluences are shown in Fig. 4.17.
Marked in the charts is the time of maximum YAG laser intensity (the YAG laser pulse
width is approximately 8 ns). As one can see from the scattering graph, there is
significant change in scattering signal after the YAG pulse (-50% for a fluence of 0.15
J/cm2) at fluences well below vaporization threshold (i.e. << 1 J/cm2). The change in
scattering signal increases for increased laser fluence. The absorption graph indicates no
significant change in absorption after the YAG pulse at fluences below threshold. At a
fluence of 0.9 J/cm2 (near vaporization threshold), the absorption signal just begins to
show absorption changes (-5%). At a laser fluence well above vaporization threshold (4
J/cm2), there is a significant change in absorption (-20%). Figure 4.18 shows the time-
resolved scattering signal on longer time scales than Figure 4.17, for the YAG laser
176
Figure 4.17 Time-resolved change in elastic scattering and absorption of the sootyregion (measured with the Ar+ laser) due to the YAG laser pulse at various YAG laserfluences. The time of peak YAG pulse intensity is marked with a dashed line.
0.15
0.9
4.0
0.15
0.56
time of YAG laser pulse peak intensity(pulse width= 8 ns)
laser fluence (J/cm2)
Cha
nge
in a
bsor
btio
n (%
)
laser fluence (J/cm2)
Cha
nge
in e
last
ic s
catt
erin
g(%
)
% Change in Scattering vs time
- 1 0 0
- 8 0
- 6 0
- 4 0
- 2 0
0
2 0
0 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5
time(µs)
%Change in absorption vs. time
- 1 0 0
- 8 0
- 6 0
- 4 0
- 2 0
0
2 0
0 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5
time(µs)
177
Figure 4.18 Time-resolved change in elastic scattering of the sooty region (measuredwith the Ar+ laser) due to a YAG laser pulse with laser fluence = 0.15 J/cm2.
- 1 0 0
- 8 0
- 6 0
- 4 0
- 2 0
0
2 0
- 5 0 0 5 0 100 150 200 250 300
t0peak YAGlaser intensity(8 ns pulse width)
%Change in elastic scattering vs time Laser fluence = 0.15 J/cm2
Cha
nge
in e
last
ic s
catte
ring
(%)
time (µs)
t0
t1
Ar+
YAG
2.5 mm
flow
Ar+
soot region heated by YAG
soot region heated by YAG
flow
t1
178
fluence of 0.15 J/cm2. Marked in the figure (in addition to the time of maximum YAG
pulse intensity) is the time, t1, when the volume of soot heated by the YAG pulse has
convected 0.3 mm downstream. This distance is estimated by knowing the approximate
flow velocities and apertured YAG beam dimensions. (The flow velocity along the
centerline and 20 mm above the burner is estimated from computations to be ~ 130
cm/s.) After the YAG pulse, the scattering suddenly drops, and then increases gradually.
At t1, the scattering signal has recovered to its initial level before the YAG pulse ( at t <
t0). Note that the probe volume of the Ar+ laser is still well within the heated soot region
at t1. For the next 90 µs after t1, there is a positive change in scattering signal as compared
to the scattering before the YAG pulse (with a peak of ~+8% change). The scattering then
returns to its initial level before the YAG pulse.
Results indicate significant aggregate breakup/restructuring at laser fluences well below
vaporization threshold. The positive change in scattering at time t1 in Figure 4.18 may be
indicative of restructuring after aggregate breakup, resulting in a larger aggregate radius
(Rg) than that of the unheated soot. Vander Wal indicated from grid sampling and
probe/pump LII experiments that the LII pulse can cause a re-structuring of the soot after
aggregate breakup [Vander Wal 1998].
179
4.10 Error estimates of the absorption/scattering technique
The scattering detector signal magnitude of unheated soot in the flame corresponds to a
13.5 mV deflection on the oscilloscope. The noise on that signal is 0.4 mV giving a lower
detection limit of 3% change in scattering. The absorption detector signal in the presence
of the flame subtracted from the detector signal without the flame corresponds to a 4mV
deflection on the oscilloscope. The noise on that signal is 0.3 mV giving a lower
detection limit of 7.5% change in absorption. This relatively high value is due to the
small path length through the sooting flame (5 mm) and the peak soot volume fraction of
10-6. Absorption measurements could be improved with flames of higher soot levels (e.g.
an ethylene flame with less N2 dilution), or multiple passes of the laser through the flame.
4.11 Summary
A temperature profile is determined using the two scalar technique. The two scalar
temperature profile agrees with the thermocouple measurement and computational
temperature profile in general flame structure, flame length, and lift off height. Peak
temperature in the two scalar measurement is 10% lower than in the computations and
thermocouple measurement. No meaningful measurement can be made in the soot-
containing region due to the elastic scattering of the soot particles.
180
Soot volume fraction profiles from LII imaging are measured in the ethylene flame.
Comparison with soot volume fraction profiles obtained by probe measurements and
computations indicates a peak in soot volume fraction at 22 mm above the burner for the
probe and LII measurements. Computational and probe measurements of soot volume
fraction show longer wings in the soot volume fraction profiles. The LII technique is not
sensitive to translucent soot that is formed closer to the burner than mature soot.
A primary particle size distribution of soot particles is obtained from analysis of the time-
resolved LII curves. The distribution obtained agrees with the distribution from TEM
pictures of grid sampling measurements. The good agreement of particle size
distributions obtained from LII curve analysis with TEM measurements verifies the
model and iterative procedure used in the LII signal analysis for laser fluences
substantially below particle vaporization threshold. The model may not produce as
accurate a result for laser fluences that cause significant vaporization. A sensitivity
analysis indicates that parameters such as refractive index and thermal accommodation
coefficient must be known to a high degree of certainty for the predicted particle sizes to
be known with high certainty. Parameters such as thermal expansion coefficient and gas
temperature only need to be known approximately for high certainty of the predicted
particle sizes.
181
Time-resolved scattering and absorption measurements have shown a significant initial
decrease in elastic scattering signal due to the morphological effects of the LII laser on
the soot, at laser fluences well below the soot vaporization threshold. No decrease in
absorption is observed until the LII laser fluence approaches the soot vaporization
threshold. Results indicate aggregate break-up and restructuring due to the LII laser,
which is not accounted for in the model used in the LII analysis. Also not included in the
model are several other effects related to the aggregation of particles that may be
significant in the LII analysis. One is a net shielding effect that reduces the rate of gas
impingement on the particles. This effect is estimated to reduce the accommodation
coefficient by a factor of (Na)1/8 [Rosner 2001a]. For Na = 100, the reduction factor is
estimated to be 1.7. Another effect is a net energy focusing by aggregates that increases
the laser energy absorbed by the average particle. There is not uniform agreement on the
significance of this effect in the literature. Mackowski states that for Na = 100, the energy
absorbed by the average particle increases by 24%, while Farias estimates only a 8%
increase in energy absorbed [Mackowski 1995 and Farias et al. 1995]. These effects
should be incorporated into the model in the future.
In future experiments, LII/LLS/absorption measurements could be used to estimate soot
aggregate bond strength and radius of gyration Rg. These in-situ measurement techniques
182
may be applicable to industry where they could eventually be used to help monitor and
control particulate formation in combustion environments.
183
Chapter 5Characterization of nanoparticle structures
synthesized in a premixed, methane/air flat flame
5.1 Introduction
Ultrafine powders like carbon black and silica are produced by condensation of vapor
which is formed by combustion synthesis. These and other ultrafine powders have special
magnetic, optical, or electrical properties that make them of economic importance. The
nanometer grain size and special nanostructures of the powders is what gives these
substances their special properties. Therefore, control of production of the particulates
which make up the powders is vitally important. This requires in-situ monitoring of the
particulates. The use of laser diagnostics offers an instantaneous, remote, non-intrusive
method of monitoring the formation and characterizing these particulates. In particular,
laser light scattering (LLS) and laser-induced incandescence (LII) can be used to study
particle/aggregate size, number density, and volume fraction. LLS and LII may be able to
give an estimate of bond strength between particles, and particle vaporization thresholds
in some cases. LLS and LII can also be used to monitor production of undesirable
combustion-synthesized particulates such as fly ash and soot when burning oil or coal.
184
In the present experiment, we produce iron oxide particles in a flame (γ-Fe2O3, or
hematite). Iron oxide is chosen for its absorption properties in the green part of the
spectrum, since the laser of choice is the Nd:YAG, which can produce plenty of energy at
its second harmonic wavelength of 532 nm. In order to get the most repeatable conditions
possible, and allowing for lean enough conditions for the iron atoms to oxidize, a laminar
premixed flat flame (essentially a one dimensional flame) is used to produce the
particulates.
5.2 Burner and Flame
The burner is shown in Figure 5.1. The premixed flame is stabilized on an inner cylinder
of diameter 6.35 cm. This cylinder contains glass beads and wire mesh screens to diffuse
the flow. A honeycomb of cell size 1/32" sits on top of the inner cylinder and is used to
straighten the flow. This cylinder is surrounded by another cylinder through which flows
an air coflow, to help minimize the radial flow component. The flame is a lean premixed
flat flame with a premixture of methane, air, and water vapor containing dissolved FeCl2.
The flame sits 1-2 mm off the burner surface, and is lean to allow enough oxygen and
time for the Fe particles to oxidize post flame to produce Fe2O3. The flame emission is
dominated by a yellowish orange color that is distinct from the color of soot emission.
185
Figure 5.1 Burner for iron oxide particle production
Fuel/Air/Seeding
4 mm Glass Beads
80 Mesh Screen
1/32" Honeycomb
Air Air
6.35 cm
2 mm 2 cm
6 cm
186
Two flow conditions are used to produce two flames (#1 and #2) of differing
stoichiometry, temperature, and flow velocity:
Table 5.1 Flow and flame conditions for the seeded premixed methane flame
flows:___________________#1 ____________________#2__________
methane: 2.61 lpm 0.90 lpm
air+particles: 36.9 lpm 15.7 lpm
(air+particles)/fuel: ________14.1 17.4___________
equilib. flame temp. 1804 K 1572 K
inlet flow velocity 20.8 cm/s 8.7 cm/s
equivalence ratio 0.71 0.57
FeCl2 particles are introduced into the flame by seeding particles into the gas flows. A
solution of FeCl2 (actually iron(II) chloride tetrahydrate) in water is placed into an
atomizer (TSI model 9606). The atomizer is pressurized to 30 psi of air. A high pressure
jet of air passes over the top of several vertical tubes that are in contact with the solution
at the bottom of the tubes, drawing the solution into the flow. The solution and air impact
187
onto a sphere at high speeds, allowing the smallest droplets to pass and rejecting the
larger droplets. The droplets are dried by the air flow and only particles remain. The
FeCl2 (tetrahydrate) solution concentration is 625 g FeCl2-4H2O/ 1L H2O. The solution is
drawn into the flow at a rate of 0.68 ml/min for (#1) and 0.29 ml/min for (#2).
5.3. Measurement of the LII spectrum
Time-integrated LII spectra for flame #1 are acquired at various laser fluences, heights
above burner, and acquisition gate delays. A flame emission spectrum (no laser) is first
acquired to determine the spectral region with minimal interference on the LII signal.
Based on this information, a suitable spectral region is chosen for the LII measurement.
5.3.1 LII spectrum setup and acquisition
The experimental setup is shown in Figure 5.2. The second harmonic of a Q-switched
Nd:YAG laser (532 nm, 8 ns pulse width) produces a laser beam of which a portion
passes through the rectangular aperture of height 3.81 mm and width 1.52 mm. A
uniform intensity of the beam is steered through the aperture, producing an output beam
with an approximately "top hat" profile, as observed by the elastic scattering from the
beam. The resulting beam passes over the center of the burner at heights ranging from 2-
188
Figure 5.2 Experimental LII spectrum setup
Aperture
Mirror
Spectrograph f/4
Nd:YAG Laser
Energy Meter
Burner
f/1.8 50 mm lens
0.2 mm slit
Colored GlassCCD Camera
Time-integrated LII spectrum experimental setup
189
12 cm. The incandescence, flame, emission, and elastically scattered light are collected
perpendicular to the beam by a 50 mm f.l. lens. For the LII measurement, an appropriate
colored glass filter is placed behind the collection lens. The spectral region over which
the filter transmits light is chosen for its minimal flame emission and other interference,
good spectral detection efficiency and complete attenuation of the elastically scattered
light. The filter transmits in the 380 - 475 nm range, and is used in the time-resolved LII
experiment as well. The incandescence is focused onto the vertical entrance slit (width =
200 µm) of a spectrometer (Spex 270, f/4, 0.27 m f.l.). The light is then dispersed by the
grating and focused onto an image intensified CCD camera. The digitized image is then
downloaded to a computer.
The intensifier, camera, and laser are synchronized to only record data near the time of a
laser pulse. First, the LII spectrum is recorded at various laser fluences. The integration
time gate on the intensifier is set to 1 µs to acquire signal over the rise, peak, and full
decay of the incandescence signal. The data is acquired 5 cm downstream of the burner,
where the flame and LII signal are stable. The acquisition is integrated over 100 laser
pulses to improve signal-to-noise ratio.
190
Second, the laser fluence is fixed and the height above the burner is varied from 5 cm to
11 cm. Third, the integration gate on the intensifier is set to its minimum (100 ns), the
height and laser fluence are fixed, and the delay of the intensifier gate is varied with
respect to the rise of the laser pulse.
5.3.2 LII Spectrum processing
Flame emission images (no laser) are acquired with the same integration times as the LII
data. This data is subtracted from the raw LII images to account for the interference of
flame emission on the LII signal. The background-subtracted LII images are then
corrected for spatial throughput, spectral detection efficiency of the intensifier, and
spectral throughput of the colored glass filter. Images are integrated over their spatial
dimension (as the signal should not vary spatially at a given height above burner) and
reduced to lineplots of signal intensity over a spectral range.
5.3.3 Flame emission results
Shown in Figure 5.3 is the corrected lineplot of flame emission intensity vs. wavelength.
The flame emission signal appears to peak around 594 nm and decays at the same rate
toward the blue or red. Based on the flame emission curve, the ideal spectral filter for the
191
Figure 5.3 Flame emission spectrum. Shown in gray is the spectral regionchosen for the time-resolved LII experiments
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
370 470 570 670
wavelength(nm)
spectral region chosenfor LII experiments
Flame emission scan
flam
e em
issi
on in
tens
ity
(arb
. uni
ts)
192
LII experiment could either transmit far toward the red or blue part of the spectrum,
where the flame emission is minimal. A filter that transmits in the blue is chosen because
the detection sensitivity of the intensifier as well as the PMT peak in the blue part of the
spectrum. The spectral transmission of the filter chosen for the LII experiments (380-470
nm, Corning 5-57 colored glass filter) also rejects any measurable elastically scattered
light (@ 532 nm).
5.3.4 LII spectrum results
Figure 5.4 shows a raw LII spectrum for a given fluence, and the signal corrected for
throughput, filter response, and detection sensitivities. Figure 5.5 shows the LII scans for
several laser fluences. The LII spectra indicate broad, blackbody emission-like curves.
The incandescence increases toward the red part of the spectrum, which makes sense
because the peak emission wavelength for a blackbody radiating at 4000 K, an estimate
for Tmax of a particle heated by a laser [Filippov 1999], is in the infrared. One does notice
a slight decrease in LII signal to the red of 450 nm. A similar drop in LII signal to the red
of 450 nm is observed by Vander Wal for a 532 nm excitation of soot from a premixed
ethylene flame [Vander Wal and Weiland 1994]. The overall LII signal increases with
laser fluences from 0.33 to 0.47 J/cm2, then decreases at higher laser fluences. This
decrease in signal at higher laser fluences is the result of mass loss due to particle
193
Figure 5.4 Raw LII spectrum and the LII spectrum corrected for optical throughputand detector efficiencies. Also shown is the spectral response of the collection.
spectral responseuncorrected LIIcorrected LII
Corrected and uncorrected LII spectrum
0
1000
2000
3000
4000
5000
6000
380 400 420 440 460
wavelength(nm)
LII
sig
nal (
Arb
. uni
ts)
194
Figure 5.5 LII spectrum for several laser fluences.
LII
Sig
nal (
Arb
. uni
ts)
LII spectrum at various laser fluences
0
500
1000
1500
2000
2500
380 400 420 440 460
wavelength(nm)
0.47 J/cm2
0.33 J/cm2
0.69 J/cm2
1.09 J/cm2
1.57 J/cm2
195
vaporization. Beginning at a laser fluence of 0.69 J/cm2 one observes an intensity peak
near 405 nm that increases in intensity at higher fluences. Also apparent at
0.69 J/cm2 is an intensity peak near 380 nm that intensifies at higher fluences. At a laser
fluence of 1.09 J/cm2 and higher one observes two distinct peaks near
380 nm. In his study of iron nanostructures with LII, Vander Wal [Vander Wal 1999]
noticed a sharp peak in LII signal at high laser fluences (compared to the blackbody-like
variation of incandescence with wavelength) at 370 nm for excitation with a laser at 1064
nm. At a delayed signal detection of 50 ns from the rise of the 8 ns width of the laser
pulse, this peak disappeared, indicating that it is likely to be emission from an excited-
state of a species formed by particle vaporization (since these events are typically 10 -9-
10-8 s long). Figure 5.6 shows the LII spectrum for a laser fluence of 1.57 J/cm2, with the
detection gate set to capture the peak LII signal, and with the detection gate delayed by
65 ns from the rise of the laser pulse. One sees the drastic reduction of the unknown
peaks near 308 nm and 405 nm, indicating these peaks to be excited-state emission from
a species formed during vaporization.
Figure 5.7 shows LII spectra at three different heights above the burner. One sees an
increase in overall incandescence as one goes from 5.25 cm to 8.25 cm downstream, but
no increase from 8.25 cm to 11.25 cm downstream. The initial increase indicates either
an increase in number density or increase in primary particle size. From a comparison of
196
Figure 5.6 Delayed and prompt detection of LII spectrum.Laser fluence = 1.57 J/cm2.
prompt gate
65 ns delayed gate
LII spectrum(corrected)Delayed gate vs non-delayed gate
0
500
1000
1500
2000
380 400 420 440 460
wavelength(nm)
LII
Sig
nal (
Arb
. Uni
ts)
197
Figure 5.7 LII spectrum for several heights above the burner
5.25 cm8.25 cm11.25 cm
LII spectrum at various heights
0
1000
2000
3000
380 400 420 440 460
wavelength(nm)
LII
Sig
nal (
Arb
. Uni
ts)
198
(4.1) f N av po= ( )π
6
3 and (4.4) J C N ap
c em= ( ) + −
10 3 1λ
, the spectrally and temporally
integrated LII signal at sufficient laser fluences is linear with ƒv and therefore goes as
~Npa3. One can intuitively see that longer residence times in the flame may allow the
creation of bigger or more numerous Fe2O3 particles. At far distances downstream, the
post flame gases spread out, and the number density will decrease.
5.4 Sampling of iron oxide particles
The sampling experiment and data reduction are performed by the group of Professor
Daniel Rosner at Yale University. Iron oxide particles are sampled from the post-flame
region and statistically analyzed. Deposition of the particulates onto a thin carbon grid is
performed at the same height above the burner as the LII data acquisition. The grids are
circular and approximately 3 mm in diameter. The deposition technique is identical to the
technique used by Köylu and others [Köylu 1997, Xing 1999] and involves fast insertion
(80 ms in the flame) of the carbon grid into the flame region, minimizing oxidation and
damage to the grid. The grids are then imaged with a TEM, producing particle images at
magnifications on the order of 100,000 X. From the images, particle size distributions are
obtained, along with information on particle aggregation.
199
Figure 5.8 TEM images of thermophoretically sampled particles forflame #1 and flame #2.
flame #1
flame#2
100 nm
100 nm
200
TEM images of the particles from flame #1 are shown in Figure 5.8. The magnification is
indicated in the image. Aggregation is present only for flame #2.
There appears to be a large number of particles within a narrow size distribution, and
there also appears to be a few relatively large-size particles. For flame #2, particle
aggregation is seen in the TEM images (Figures 5.8), where the estimated average value
of np ~ 3-5 particles/aggregate. The majority of primary particles in the images from
both flame #1 and #2 are 5-15 nm in diameter. Dividing the particles into bins of
various particle size ranges yields particle size distributions that are compared to the
results of the time-resolved LII experiment. (Results are shown along with the LII-
derived particle size distributions in Section 5.6.)
5.5 X-ray diffraction of the particle material
The X-ray diffraction experiment and data analysis is performed by the group of
Professor Wei Tong at Yale University. X-ray diffraction is used to determine the
stoichiometry of the particulate matter produced in the flame. A metal plate is placed
above the flame, and the particulate material is deposited onto the plate for twelve hours.
The deposited material is scraped off of the plate, forming a powder to be used by the X-
ray diffraction apparatus. The diffraction scan produces diffraction peaks at various
201
Figure 5.9 Xray diffraction peaks of sample (top graph) and of pure hematite
(bottom graph). Three unknown peaks in the sample are marked.
unknown peakssample
pure hematite
angle (degrees)
Inte
nsit
y (A
rb.)
202
angles of the sample with respect to the incident X-rays. These peaks are then compared
to a database of diffraction peaks of pure compounds.
Results of X-ray diffraction indicate hematite to be the most likely molecule in the
sample. Shown in Figure 5.9 are the diffraction peaks of the sample compared with the
diffraction peaks of pure hematite. Three unknown peaks are marked on the graph, which
may be other iron compounds, or possibly some chlorinated compounds (as the seed
material used is FeCl2).
5.6 Time-resolved LII and laser light scattering experiment
5.6.1 Experimental setup and acquisition
Time-resolved laser light scattering (LLS) and laser-induced incandescence (LII) are used
to obtain primary particle size, detect particle aggregation and estimate aggregate size,
and to study the effects of laser fluence on the particles/aggregates [Rosner et al. 2001b].
The experimental setup is shown in Figure 5.10. The second harmonic of a Q-switched,
Nd:YAG laser (10 Hz rep rate, 532 nm, 8ns pulse width) produces a laser beam of which
a portion passes through a rectangular aperture of height 3.81 mm and width 1.52 mm.
The output beam has approximately a top hat intensity profile in height and width, which
203
Figure 5.10 Time-resolved LII and laser light scattering setup.
Aperture
Mirror
Photomultiplier Tube
Nd:YAG Laser
Energy Meter
Burner
f/1.8 50 mm lens
Interference Filter
Photodiode
0.5 mm slit
Colored Glass
LIIScattering
204
is observed from the sharp, well-defined edges of the elastic scattering. The beam passes
over the center of the burner at heights varying from 2-12 cm above the burner.
The burner is placed on a z translation stage to easily change the height above burner. For
LII, the incandescence is collected at 90 degrees to the laser with a 20 cm f.l. lens, then
through a sharp cut colored glass filter that passes light in the spectral region 380-475
nm, and highly rejects the elastically scattered light (@ 532 nm). The incandescence is
focused onto a 3 mm square aperture, and the output light is collected by a
photomultiplier tube (Hamamatsu R928), which has a response time of 2 ns. For LLS, the
elastic scattering signal is collected at 45 degrees to the laser axis by a 30 mm f.l. lens,
and then through an interference filter centered at 532 nm (10 nm bandpass). The
transmitted signal then is collected by a photodiode, which has a 2 ns response time. Both
the time-resolved LII and LLS signals are digitized on a fast digital oscilloscope (500
Msamples/sec). Single-shot data are acquired along with signals integrated over 8 and 64
laser shots. The laser fluence is varied over a wide range of fluences and recorded by an
energy meter. The LLS and LII signals are recorded at each fluence for conditions (#1)
and (#2).
No processing is needed, as the background flame emission signal is negligible. Spectral
and optical sensitivities are incorporated into the model for the time-resolved LII curves.
205
Figure 5.11 Time-resolved LII at several laser fluences.
.09 J/cm2
.11 J/cm2
.14 J/cm2
.17 J/cm2
.23 J/cm2
.29 J/cm2
.40 J/cm2
tires-LII vs laser fluence-flame#1
0
500
1000
1500
2000
2500
3000
0 100 200 300 400
time (ns)
LII
inte
nsit
y (A
rb.)
206
5.6.2 Qualitative analysis of time-resolved LII data
Figure 5.11 shows time-resolved LII curves for flame #1 for varying laser fluences. The
characteristic sharp rise in LII signal is followed by a relatively slow decay in signal. The
rise in signal is the region where the laser is heating the particles, and the signal decay
region is where the laser pulse is gone, and the particles cool by convection. Shown in
Figure 5.12 are the same curves normalized by their peaks. Included is a time response of
the PMT to the elastic scattering of the particles, which is representative of the PMT time
response to the laser pulse. The time response of the PMT is important as it affects the
time decay of the LII curves, while also limiting the size of the particles that one can
analyze. As noted in Chapter 2, smaller particles will cool faster, and therefore this limits
this technique to analysis of particles large enough to have a characteristic decay time
greater than the PMT response time. In this figure, the LII signals exactly follow the laser
pulse on the signal rise portion of the curves, while the decay time of the signal decreases
with increasing laser fluence. This makes sense since particles that see larger fluences
will heat to higher temperatures, and thus their cooling rate will be initially faster. There
does seem to be a limiting curve as one gets higher and higher in fluence, however. This
is due to the particles having a maximum temperature limited by particle vaporization
effects which increases at higher fluences. Thus the vaporization of the particles
competes with the laser heating effect at high fluences.
207
Figure 5.12 Time-resolved LII at several laser fluences. Signals are normalized to thepeak intensity. Also indicated is the time-varying laser pulse intensity, measured fromelastic scattering with the PMT.
.09 J/cm2
.11 J/cm2
.14 J/cm2
.17 J/cm2
.23 J/cm2
.29 J/cm2
.40 J/cm2
laser
tires-LII (normalized) vs. laser fluence-flame#1
0
500
1000
1500
2000
2500
0 100 200 300 400
time(ns)
LII
inte
nsit
y (A
rb.)
208
Figure 5.13 Time-resolved LII at two different laser fluences for flame #1 and flame #2.Curves are normalized to the peak intensity. Also shown is the normalized LII signal forsoot with a laser fluence of 0.12 J/cm2, and the time-varying laser pulse intensity.
nanoparticle tires-LII (normalized)for flame #1 and flame #2
compared to soot LII
0
10
20
30
40
50
60
70
80
90
100
0 100 200 300 400
time(ns)
flame #2, 0.14 J/cm2flame #1, 0.14 J/cm2
flame #1, 0.09 J/cm2
flame #2, 0.09 J/cm2
laser
soot, 0.12 J/cm2
LII
(ar
b. u
nits
)
209
Figure 5.13 compares the peak-normalized curves for two different laser fluences of
flame #1 and #2, and a soot LII curve for a fluence of 0.12 J/cm2. The signal decay time
for a given laser fluence is similar for flame #1 and #2. The curves indicate that the
primary particle size from flame #1 and #2 should be roughly the same, and smaller than
soot particles. Shown in Figure 5.14 is the time integration of the LII curves (not
normalized by the peaks) over a 50 ns gate around the laser pulse, plotted vs. laser
fluence for flame#1 and #2. The time-integrated LII curves for the two flame conditions
show similar laser fluence dependence below 0.2 J/cm2. Both curves begin to flatten near
0.2-0.25 J/cm2, where vaporization begins to affect the LII curves and competes with
particle heating.
5.6.3 Particle sizing model, parameters, and procedure
The model and procedure used to obtain primary soot particle size distributions in
Chapter 4 from time-resolved LII curves is used here as well. Parameters specific to the
particle material and flame conditions are discussed here.
Since data is taken in the post-flame region of a premixed flame, the gas temperature, Tg,
is determined via thermodynamic equilibrium calculations for the mixture. All gas
properties are based on the properties of N2, as this species dominates the equilibrium
210
Figure 5.14 Time-integrated LII signals for flame #1 and flame #1 as afunction of laser fluence. The integration gate is 50 ns, and includes the riseof the time-resolved LII signal.
Integrated LII (50 ns gate) vs laser fluenceflame #1 vs. flame #2
0
2000
4000
6000
8000
10000
12000
14000
0 0.1 0.2 0.3 0.4 0.5
laser fluence(J/cm 2)
flame #1
flame #2
211
state (75% by volume). No data is available for vapor pressure (or heat of vaporization)
of Fe2O3. Instead, the heat of vaporization is calculated from the chemical equilibrium
equation
Fe2O3(s) = 2 FeO(g) + (1/2) O2(g) (5.1)
using the enthalpies of FeO and O2 (see Table 5.2) , obtained from JANAF tables
[JANAF 1985]. Therefore there will be a ( ) /pO2
1 4− dependence in the effective FeO
vapor pressure. The O2 pressure in the post flame region, is estimated from
thermodynamic equilibrium calculations. In the above equation, it is assumed that FeO is
the dominant Fe carrier. The effective FeO vapor pressure is [Rosner 2001a]
p E pTv FeO O,
/( . )( )exp( . ( ))= − −−2 774 9 44 29 11700
2
1 4 (atm) (5.2)
The mass flux of FeO is calculated from (2.17)
m
adadt
a dTdt
WRT
p vpp v
v
pv p4 32π
ρ β α= − = − (5.3)
The mass flux of Fe2O3 can be related to the mass flux of FeO from mass conservation of
(5.1),
˙ ˙m
am
a
W
WFe O FeO Fe O
FeO
2 3 2 3
4 4122 2π π
= (5.4)
This expression is used for the mass flux term in the mass flux and energy flux equations.
The following graphs in Figure 5.15 and the thermodynamic quantities in Table 5.2 are
used in the model:
212
Figure 5.15 Select hematite and nitrogen properties
γ*+1
γ*−1
Adiabatic Ratioγ*+1
γ*−1-Nitrogen
realimaginary
7.37.47.57.67.77.87.9
8
1000 2000 3000 4000 5000
Temperature(K)
Heat capacity(at constant pressure)-hematite
142
144
146
148
150
1000 2000 3000 4000 5000
Temperature(K)
Cp
(J/m
ol-K
)in
dex
of r
efra
ctio
n
Index of refraction (m)hematite(T=300K)
00.5
11.5
22.5
33.5
300 350 400 450 500 550
wavelength(nm)
[JANAF 1985]
[Hsu and Matijevic 1985]
[JANAF 1985]
213
Table 5.2 Parameters used in nanoparticle LII analysis
Flame#1 Flame#2
H (T) - H (kJ/mol)O0
O0
2 2 ,298K 51.7 44.3 [JANAF 1985]
H (T) - H (kJ/mol)FeO0
F0
eO K,298 54.4 46.8 [JANAF 1985]
∆Hf FeO,0 (kJ/mol) 221.3 226.4 [JANAF 1985]
Tg(K) 1804 1572p(O2) (atm) 0.0547 0.0807∆Hv Fe O, 2 3
( J/g) 7,845 7,845
βFe O K2 3
1( )− 3.0x10-5
pv,FeO(1700 K) (atm) 2.774x10-9 [Rosner 2001]Tp
* (K) 1700
5.6.4 Particle distribution results from LII data analysis
LII data curves for a laser fluence of 0.09 J/cm2 are analyzed with the model for flames
#1 and #2. Figure 5.16 shows LII data for flames #1 and #2 along with the best fit LII
curve from the model for a bi-modal normal and lognormal particle size distribution and
a single mode normal and lognormal distribution. Also indicated for each curve is its
respective χ value. The χ value for each fit is indicated in the table below:
214
Figure 5.16 Least-squares fits to the experimental LII curves using a lognormal(1 and 2 mode) and normal (1 and 2 mode) particle size distribution for flame #1 andflame #2. Laser fluence = 0.09 J/cm2 for the LII curves of flame #1 and flame #2.
Least squares fit to LII data-flame#1laser fluence = 0.09 J/cm2
0
5
10
15
20
25
30
35
40
45
50
0 100 200 300 400 500 600time(ns)
LII
sig
nal (
arb.
uni
ts)
LII
sig
nal (
arb.
uni
ts)
fit- normal (2-modes)fit- normal (1-mode)
LII datafit- lognormal (1-mode)
fit- normal (2-modes)fit- normal (1-mode)
LII datafit- lognormal (1-mode)
Least-squares fit to LII data-flame#2laser fluence = 0.09 J/cm2
0
5
10
15
20
25
30
35
40
45
50
0 100 200 300 400 500 600
time(ns)
fit-lognormal (2-modes)
fit-lognormal (2-modes)
215
Table 5.3 χ values for the fit to the LII data using various size distributions
fit normal-1 mode lognormal-1 mode normal-2 modes lognormal-2 modes
χ, flame #1 3.0 1.9 1.0 0.7
χ, flame #2 3.7 2.9 0.6 0.5
Clearly the bi-modal particle size (normal and lognormal) distribution gives a better fit
than the single mode normal and lognormal distribution for the overall curves.
Particle size distributions obtained from the best-fit curves for a bi-modal normal, bi-
modal lognormal, single mode normal, and single mode lognormal particle size
distribution are compared with particle- sampled size distributions in Figure 5.17 for
flames #1 and #2. For particle-sampled size distributions, the dependent axis of the
graphs in the figure represents the total particle volume ( n x Vp) while the independent
axis represents the volume for a single particle (Vp). There is good agreement of the bi-
modal lognormal and bi-modal normal particle distributions with the grid sampling
particle size distributions for flame #1 with the primary particle distribution mode at Vp =
33 -1436 nm3 (corresponding to a particle diameter range 2a = 4 -14 nm ). There is also
216
Figure 5.17 Comparison of LII-derived particle size distributions with grid samplingparticle size distributions. The dependent axis values for the grid sampling represent thetotal particle volume (n x Vp). Also indicated is the total number of particles sampled forflame #1 and flame #2.
Size distributions for hematiteflame #1
0.E+00
1.E+05
2.E+05
3.E+05
4.E+05
5.E+05
6.E+05
7.E+05
8.E+05
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06
individual primary particle volume(nm3)
Particles sampled1900
Particles sampled
960
tota
l vol
ume
(nm
3 )
grid samplingnormal (2 modes)normal (1 mode)lognormal (1 mode)
grid samplingnormal (2 modes)normal (1 mode)lognormal (1 mode)
Size distributions for hematiteflame#2
0.E+00
1.E+04
2.E+04
3.E+04
4.E+04
5.E+04
6.E+04
7.E+04
8.E+04
9.E+04
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06
individual primary particle volume(nm3)
tota
l vol
ume
(nm
3 )
lognormal (2 modes)
lognormal (2 modes)
217
agreement of the bi-modal lognormal and bi-modal normal particle size distributions
with the grid sampling particle size distributions for flame #1 for larger particle size
modes at Vp = 7238 - 590,000 nm3 (corresponding to a particle diameter range 2a = 24 -
104 nm). The best agreement with the grid-sampling distribution for the larger particle
size modes for flame #1 is with the bi-lognormal distribution. The bi-modal lognormal
and normal distributions for flame #2 and the grid sampling distribution show good
agreement for the primary particle distribution mode at Vp = 4 – 2460 nm3 (corresponding
to a particle diameter range 2a = 2 – 18 nm). The grid sampling particle size distribution
for flame #2 lacks the large particle size distribution as seen in the bi-modal particle size
distributions for flame #2. In the particle sampling distribution for flame #1, the particle
bins of intermediate and large particle sizes contain only a few particles, which yields a
large relative statistical uncertainty compared to the primary particle bin (which contains
1893 particles). For an ideal comparison of particle sampling and LII-derived particle
size distributions, the number of particles sampled should be equal to the number of
particles within the probe volume of the LII experiment. Using the known seeding and
flow conditions along with the known LII probe volume, the estimated number of
hematite particles within the LII probe volume is ~ 1014 (compared to 1900 particles
sampled for flame #1). Therefore a particle size distribution mode with a peak four orders
of magnitude smaller than the primary mode will have statistical significance in the LII-
derived particle distributions.
218
The particle-sampling size distributions for flame #1 are used to compute an LII curve
from the model. This curve is then compared to the LII curve for flame #1 by calculation
of the fit parameter χ. LII curves are computed using one, several, or all particle bins
from the particle sampling measurements of flame #1. Figure 5.18 shows the particle
sampling-computed LII curves compared with measured LII curve of flame #1 for a laser
fluence of 0.09 J/cm2. Bin 1 (1893 particles, 10 nm mean particle diam.) generates a
curve with χ = 5.0. Bin 2 (3 particles, 27.5 nm mean particle diam.) generates a curve
with χ = 7.2. Bins 1-2 generates a curve almost identical to the curve of Bin 1, with χ =
4.6. Adding the 2 particles of Bin 3 (42.5 mean particle diam.) to 1896 particles of Bins
1-2 yields a curve with χ = 3.2. Adding the single particle of Bin 4 (65 nm mean particle
diam.) to the 1898 particles of Bins 1-3 yields a curve with χ = 1.1. Adding the single
particle of Bin 5 to the 1899 particles of Bins 1-4 yields a curve with a relatively poor fit
(χ = 7.0).
The above analysis shows the extreme sensitivity of LII decay curves to large particles,
even if there are only a small amount relative to the relatively smaller particles. It is more
appropriate to consider the particle volume contribution within a given particle size range
rather than just the number of particles within a given size range. This makes sense
219
Figure 5.18 LII curves generated from grid sampling data. The particle bins used togenerate each curve are indicated to the right of the graph. All curves are normalized tothe peak LII intensity.
particle bins included#1#2#1+#2#1+#2+#3
#1+#2+#3+#4all bins
lii data-flame #1
18933211
particle diam.bin range(nm)
1 4 - 1 42 24 -343 34 -444 64 -745 94-104
LII curves generated from sampling data vs. LII data-flame#1
0
10
20
30
40
50
60
0 100 200 300 400 500
time(ns)
Laser fluence = 0.09 J/cm2
220
because at sufficient laser fluences it is known that ILII ~ ƒv, and since ƒv ~ Nda3,
then ILII ~ Nda3. It is therefore beneficial to produce particles that result in a single mode
size distribution that can be modeled with a normal or lognormal distribution.
5.6.5 Results of LLS
Figure 5.19 shows the comparison of the Mie-scattered signal from flame #1 and flame
#2 as the laser fluence is varied. The systematic error is indicated for each data point. At
low laser fluences (below 0.025 J/cm2) the scattering from the particles created in flame
#2 is 5 times as large as the scattering from the particles created in flame #1. The
scattering plot vs. laser fluence for flame #1 is linear over the region (0 - 0.23 J/cm2).
This is expected from Mie scattering theory since the scattering cross section is linear
with laser intensity. Above a laser fluence of 0.23 J/cm2, the curve for flame #1 deviates
from a linear curve, where the dependence on fluence is now less than linear. As
indicated from the integrated LII intensity vs. laser fluence curve (Fig. 5.14), this is the
region where mass loss due to vaporization begins to occur. The curve for flame #2 is
linear over the range of fluences (0 - 0.025 J/cm2). The curve begins to have a laser
fluence dependence less than linear at a fluence of 0.025 J/cm2, which is well below the
221
Figure 5.19 LLS vs. fluence for flame #1 and flame #2. Indicated in the figure are linearregression fits to portions of the data and systematic error on the measurements. Theshaded rectangles represent linear fits to the data within the standard deviation of the fit.
Scattering vs. Fluence
fluence(J/cm2)
scat
teri
ng s
igna
l (ar
b. u
nits
)
Scattering vs. Fluence
fluence(J/cm2)
flame#2
flame#1
standard deviationof fits, flame#2
linear fit to pts. 6-20, flame #2
linear fit to pts. 1-20,flame#1
linear fit to pts. 1-5,flame #2
scat
teri
ng s
igna
l (ar
b. u
nits
)
0
50100
150200
250300
350400
450
0 0.1 0.2 0.3 0.4
flame#2
flame#1
standard deviationof fits, flame#2
linear fit to pts. 6-20, flame #2
linear fit pts 1-20,flame#1
linear fit to pts. 1-5,flame #2
0
20
40
60
80
100
120
140
0 0.02 0.04 0.06 0.08 0.1
222
fluence where vaporization is occurring (see Fig. 5.14). At higher fluences, the curve
again becomes linear, until a fluence of 0.23 J/cm2 is reached and vaporization effects
decrease the scattering dependence on laser fluence.
The factor of five difference in scattering intensities at low fluence between flames #1
and #2 can be explained from Rayleigh-Debye-Gans theory. For isolated spherical
particles the scattering signal is
I N Cpp
pνν νν θ= ( ) (5.5)
where Cpνν θ( ) is defined in (2.28) C
a F mk
pνν θ θ( ) ~
( )cos ( )
6
22 . The scattering signal for
an aggregate with aggregate number density Na is
I N Caa
aνν νν θ= ( ) (5.6)
where Caνν θ( ) is defined in (2.29) C n C qRa
pp
gνν νν= ƒ2 ( ). Since the particle volume
fraction should be conserved for equivalent seed levels in the flame,
Nanp = Np (5.7)
Combining (5.5), (5.6), and (5.7), the ratio of scattering signals for isolated particles and
aggregates is
II
N n qR
Nn qR
a
pa p g
pp g
νν
νν
=ƒ
= ƒ2 ( )
( ) (5.8)
223
The form factor ƒ calculated from the results of the TEM particle images of flame#2
(where roughly, np~ 4 and Rg~31/2a0) is approximately equal to one. Therefore the ratio of
scattering signals should be approximately equal to np~ 4, which is the approximate ratio
of scattering signals from LLS at low laser fluences between flame #2 and flame #1.
The deviation in the curve of flame #2 from linearity (in Fig. 5.19) at a fluence of 0.025
J/cm2 cannot be explained by vaporization, since the integrated LII curve (Fig. 5.14)
shows vaporization effects only at higher fluences. ( i.e. above 0.23 J/cm2). A possible
explanation of this phenomenon is laser-induced aggregate breakup. Further experimental
work is needed to investigate aggregate breakup. A better experimental setup to study
aggregate breakup would involve the use of a pump and probe laser. Therefore, the pump
laser can be varied in fluence, while the probe laser (CW preferably) independently
monitors the scattering at a fixed laser fluence. This isolates the change in scattering
signal due to morphological changes in the system from the change in scattering due to
the change in laser fluence. This technique is used in the study of soot in Chapter 4.
5.7 Conclusion
Particles of hematite are effectively produced in a seeded premixed flame, as verified by
X-ray diffraction of particle material and TEM images of particles deposited on a grid.
224
Variation in flame conditions produces similar primary particle size distributions.
However, certain conditions will allow for particle aggregation while other conditions do
not. The particle size distributions for grid sampling show good agreement with the
LII-derived bimodal (normal and lognormal) particle size distributions for both flame
conditions. LII-derived particle size distributions indicate a bi (or multi)-modal
distribution for both flame conditions, with a peak total volume distribution for the
smaller particle size mode one order of magnitude larger than the larger particle size
modes. Grid sampling measurements indicate a few relatively large particles in flame #1
that are not present in the TEM images of flame #2. A lack of statistics may be the cause
of this discrepancy. The origin of these sparse, larger particles is not well understood. For
the current experimental conditions (seed levels, flowrates, etc.), the maximum diameter
a hematite particle can grow to be is approximately 35 nm for a data acquisition height of
4 cm. A possible explanation for these large particles is particle growth on the burner
honeycomb, followed by periodic break away [Rosner 2001a].
A model based on the Melton model is developed and used with a novel search procedure
to back out particle distributions from time resolved LII data, for a known laser fluence,
within a known spectral region, and a known excitation wavelength. The primary particle
size distribution mode shows good agreement with TEM measurements. The fit of the LII
curve modeled from a bimodal distribution to the data gives a better fit than the fit of the
225
LII curve modeled from single mode distributions. This technique is limited to particle
size distributions of at most two modes, laser fluences that produce negligible mass
vaporization, and particle sizes that have LII signal decay times sufficiently longer than
the decay time of the laser pulse. Also the time response of the detection system must be
fast enough to have sufficient number of sample points of the data.
Laser light scattering shows a fivefold increase in signal for the two flame conditions
used. The degree of aggregation in the second flame conditions that is determined from
LLS agrees well with the observed aggregation from TEM images. For the aggregated
particles, there is a region where the scattering signal is non-linear with laser fluences
below the fluence needed for vaporization, which may be indicative of aggregate
breakup. Further experiments are needed along with an improved setup with a pump-
probe system to separate the effects of increase in scattering due to laser fluence, and
decrease in scattering due to aggregate break-up.
226
Chapter 6Summary and Conclusions
Several axisymmetric laminar flame systems are successfully characterized in terms of
particle and species concentrations, temperature, and particle size distribution through the
use of Rayleigh and spontaneous Raman scattering, laser light scattering, flame emission,
laser-induced incandescence and laser absorption techniques. The quantities derived from
the optical measurements show good agreement with the quantities obtained by non-
optical measurements and computations.
An axisymmetric steady and time-varying laminar methane diffusion flame is
characterized in terms of two-dimensional profiles of species concentrations,
temperature, and mixture fraction using Rayleigh and spontaneous Raman scattering.
Images of temperature and mixture fraction derived from the two scalar technique show
good agreement with the temperature and mixture fraction obtained with the multi-
species Raman scattering technique away from stoichiometric. The discrepancy in the
images around stoichiometric is due to the inherent assumptions of the two scalar
technique, which does not account for flame intermediates and differential diffusion.
Difference Raman scattering effectively eliminates the C2 and PAH fluorescence
inteference on the species Raman signals of oxygen, carbon monoxide and carbon
227
dioxide. An empirical correction effectively eliminates the remaining interference seen
just rich of the flame front, which may possibly be enhanced PAH Raman scattering.
Further work is needed to investigate the source of this weak remnant Raman signal.
For the steady flame, two-dimensional profiles of major species concentrations and
temperature derived from Rayleigh and multi-species difference Raman measurements
show good agreement with the computations in terms of flame structure, flame length,
and absolute concentrations and temperature. For the forced flame, measurements
indicate a larger modulation than indicated by the computations. For the experiments,
certain phases of the forcing indicate a distinct region where the flame "pinches off". The
computations indicate a significantly less defined "pinch off" region. The "pinch off"
phenomenon is more pronounced as the flow modulation increases from 30% to 50%.
The region downstream of the "pinch" has significant elastic scattering interference
where Rayleigh data cannot be interpreted. This indicates significant soot production in
the forced flame, as opposed to the insignificant amounts of soot produced in the steady
flame. Further work is needed to investigate the soot produced at these specific phases of
the forcing, possibly with the use of LII, LLS, and laser absorption.
An axisymmetric, laminar, sooting, ethylene diffusion flame is characterized in terms of
two-dimensional profiles of soot volume fraction and temperature, and point
228
measurements of soot particle size distributions and aggregate information using
Rayleigh and fuel Raman scattering, LII, LLS, and laser absorption. A temperature image
derived from the two scalar technique shows good agreement with thermocouple probe
measurements and computations of temperature in terms of flame length, lift-off height
and flame structure. The peak flame temperature from the two scalar technique is 7%
lower than the computations and thermocouple measurement. A region of elastic
scattering interference from soot prevents optical measurements of temperature in this
region.
A two-dimensional profile of soot volume fraction obtained from time-integrated LII
shows similar structure near the peak signal region compared to probe measurements and
computations. The probe and LII measurements peak along the centerline while the
computations peak along the wings. The lack of detectable soot from LII in the wings of
the flame may indicate the soot in this region of the flame is transparent to the laser.
Soot particle size distributions obtained from time-resolved LII signals show good
agreement with particle sampling-derived particle size distributions in terms of peak
location and size distribution. Both measurements produce a peak soot particle size
distribution near 20-22 nm in diameter. Sensitivity analysis reveals that the particle size
prediction by the model is quite sensitive to parameters such as thermal accommodation
229
coefficient and refractive index. In future work, The model used to interpret the LII
signals can be improved by including aggregate effects on the LII signal such as heat
shielding and enhanced energy absorption.
Time-resolved LLS and laser absorption experiments indicate a laser fluence region that
alters the soot aggregate structure while not causing significant mass vaporization.
Further work is needed to investigate the effect of the laser on soot aggregate structure.
One should be able to estimate the bond strength of the aggregates from this technique.
Hematite nanoparticles produced in an axysymmetric premixed laminar flame are
characterized in terms of point measurements of particle size distributions and aggregate
information using time-resolved LII and LLS. Two flame conditions produce similar size
particles, with one flame producing isolated spherules and the other producing
aggregates, as observed in the TEM pictures of particle sampling measurements. Both the
LII-derived distribution and grid sampling distributions determine the major primary
particle size distribution mode to be 5-15 nm in diameter for both flames. The best fit to
the LII curve for both flames assumes a bi-modal lognormal distribution, where the
second mode has a particle size distribution of 20-50 nm in diameter for both flame
conditions, and is approximately an order of magnitude smaller in total particle volume
than the major size distribution mode. Grid sampling measurements indicate a relatively
230
few large and intermediate particles in the samples for the conditions producing isolated
spherules, but these particle are not observed in the samples for conditions producing
aggregates.
The grid sampling particle size distribution for the flame conditions producing isolated
spherules is used to generate an LII curve to compare to the experimental LII curve.
Results indicate extreme sensitivity of the LII signal to the addition of a relatively few,
relatively large diameter particles. It is therefore recommended to find the right
conditions or compound to produce a single mode distribution since this will simplify the
analysis of the LII data.
Laser and optical diagnostic techniques will have economic, environmental, and scientific
importance in the current combustion technologies, and the new technologies that
develop every day. Large combustion driven generators and propulsion systems will
employ in-situ monitoring and feedback systems containing optical diagnostics to
increase efficiency. In contrast, the miniaturization of technology produces a increasing
need for laser and optical diagnostics on the microscale and nanoscale.
231
References
Avallone, E.H., Baumeister III, T., Marks’ Standard Handbook for Mechanical
Engineers, McGraw-Hill, New York (1996).
Beretta, F., Cincotti, V., D’Alessio, A., Menna, P., Combust. Flame, 61:211-218 (1985).
Bilger, R.W., Stårner, S.H., and Kee, R.J., “On Reduced Mechanisms for Methane-AirCombustion in Nonpremixed Flames,” Combust. Flame, 80:135-149 (1990).
Bohren, C.F. and Huffman, D.R. Absorption and Scattering of Light by Small Particles,Wiley, New York, pp. 69-81 (1983).
Cetegen, B.M. and Ahmed, T.A., “Experiments on the periodic instability of buoyantplumes and pool fires,” Combust. Flame, 66: 81-86 (1993).
Chen, L.D. and Roquemore, W.M., “Visualization of jet flames,” Combust. Flame 66:81-86 (1986).
Dasch, C. J., “One-dimensional tomography: a comparison of Abel, onion-peeling, andfiltered backprojection methods,” Appled Optics 31: 1146-1152 (1992).
Dibble, R.W., Masri, A.R., and Bilger, R.W., “The Spontaneous Raman ScatteringTechnique Applied to Nonpremixed Flames of Methane,” Combust. Flame
67:189 (1987).
Dobbins, R.A. and Megaridis, C.M., “Absorption and Scattering of Light by Polydisperseaggregates,” Appl. Optics, 30:4747-4754 (1991).
Eckbreth, A. C., Laser Diagnostics for Combustion Temperature and Species. AbacusPress, Cambridge, Massachusetts (1996).
232
Eckbreth, A.C., “Effects of Laser-Modulated Particulate Incandescence on RamanScattering Diagnostics,” J. Appl. Phys. 48: 4473 (1977).
Eisner, A.D. and Rosner, D.E, “ Experimental Studies of Soot ParticleThermophoresis in Non-Isothermal Combustion Gases Using Thermocouple
Response Techniques,” Comb. and Flame 61:153-166 (1985).
Farias et al., ASME Trans., J Heat Transfer 117:158 (1995).
Fielding, J., “ Two-dimensional scalar measurements for turbulent flamecharacterization,” Thesis, Yale University (2001).
Filippov, A. V., Markus, M. W., and Roth, P., “In-situ characterization of ultrafineparticles by laser-induced incandescence: sizing and particle structuredetermination,” Journal of Aerosol Science, 30:71-87 (1999).
Filippov, A.V., and Rosner, D.E., “Energy transfer between an aerosol particle and gas athigh temperature ratios in the Knudsen transition regime,” Internat, J. Heat and
Mass Transf. 43:127-138 (2000a).
Filippov, A V. Zurita, M. Rosner, D E., “Morphology and physical properties of fractal-like aggregates,” Journal of Aerosol Science. 31 SUPPL. 1:S92-S93 (2000b).
Frank, J.H., Lyons, K.M., Marran, D.F., Long, M.B., Stårner, S.H., and Bilger, R.W.(1994), “Mixture Fraction Imaging in Turbulent Nonpremixed HydrocarbonFlames,” Twenty-Fifth Symposium (International) on Combustion, TheCombustion Institute, pp. 1159-1166.
Gaydon, A.G., The Spectroscopy of Flames, 2ed., John Wiley & Sons, New York(1974).
Hamins, A., Yang, J.C., Kashiwagi, T., “An experimental investigation of the pulsationfrequency of flames,” Twenty-fourth Symposium (International) on Combustion,The Combustion Institute, 1998, pp. 1695-1702 (1992).
233
Hassel, E. P., 1996, RAMSES Spectral Synthesis code, University of Darmstadt,[email protected]
Hertz, H. M., and Faris, G. W., “Emission Tomography of Flame Radicals,” Optics
Letters 13:351-353 (1988).
Holzer, W., Le Duff, Y., and Altmann, K., “J Dependence of the Depolarization Ratio ofthe Rotational Components of the Q branch of H2 and D2 Raman Band,” J. Chem.
Phys., 58:642 (1973).
Hsu, W.P., and Matijevic, “Optical properties of monodisperse hematite hydrosols,”Appl. Optics 24:1623-1630 (1985).
Hughey, B. J., and Santavicca, D. A., “Comparison of techniques for reconstructingaxisymmetric reacting flow fields from absorption measurements,” Combustion
Science and Technology 29:167-180 (1982).
JANAF Thermochemical tables, J. Phys Chem. Ref. Data, 14, Suppl 1 (1985).
Keane, R.D. and Adrian, R.J., “Theory of cross-correlation analysis of PIV images,”Appl. Scient. Research, 49: 191-215 (1992).
Kelman, J.B., Masri, A.R., Stårner, S.H., Bilger, R.W. (1994), “Wide-Field ConservedScalar Imaging in Turbulent Diffusion Flames by a Raman and RayleighMethod,” Twenty-Fifth Symposium (International) on Combustion, TheCombustion Institute, pp. 1141-1147.
Kent, J.H., and Wagner, H. Gg., “Soot particle measurements in diffusion
flames,”Combustion and Flame, 47:53-65 (1982).
234
Köylu, Ü.Ö., “Quantitative analysis of in situ optical diagnostics for inferring particle/aggregate parameters in flames: implications for soot surface growth and totalemissivity,” Combust. Flame, 109:488-500 (1996).
Köylu, Ü.Ö., “Radiative properties of flame-generated soot,” J. Heat Transfer, 115:409
(1993).
Köylu et al, “Simultaneous measurements of soot volume fraction and particlesize/microstructure in flames using a thermophoretic sampling technique,”Combust. Flame, 110:494-507 (1997).
Lee, S. C. and Tien, C. L., Symposium (International) on Combustion. 1981, pp. 1159-1166 (1981).
Leroy, O., Perrin, J., Pealat, M., Jolly, J., “ Thermal accommodation of a gas on a surfaceand heat transfer in CVD and PECVD experiments,” J. Phys D: Appl. Phys., 30:
499-509 (1997).
Lin, P., “Quantitative Charactarization of a Laminar Axisymmetric Nitrogen DilutedMethane/Air Diffusion Flame,” Thesis, Yale University (1995).
Long, D.A., Raman Spectroscopy, McGraw-Hill, New York (1993).
Long, M.B., in Instrumentation for Flows with Combustion (A.M.K.P. Taylor, Ed.),467, Academic Press (1993).
Lynch, J.F, Ruderer, C.G., Duckworth, W.H. (eds.), Engineering Properties of Selected
Ceramic Materials, American Ceramic Society (1966).
Mackowski, D.W., Appl. Optics 34:3535-3545 (1995).
235
Marran, D.F., “Quantitative Two-Dimensional Laser Diagnostics in Idealized and
Practical Combustion Systems,” Thesis, Yale University (1997).
Markowski, G.R. , “Improving Twomey’s algorithm for inversion of aerosol particle
measurement data,” Aerosol Sci. Technol., 7:127-141 (1987).
Masri, A. R., Bilger, R. W., and Dibble, R. W., “‘Fluorescence’ Interference with RamanMeasurements in Nonpremixed Flames of Methane,” Combust. Flame 68:109(1987).
Maxworthy, T., “The flickering candle: transition to a global oscillation in a thermalplume,” J. Fluid Mech., 390:297-323 (1999).
McEnally, C S. Schaffer, A M. Long, M B. Pfefferle, L D. Smooke, M D. Colket, M B.Hall, R J., “Computational and experimental study of soot formation in a coflow,
laminar ethylene diffusion flame,” Symposium (International) on Combustion. v 11998. pp. 1497-1505.
Melling, A.,”Tracer particles and seeding for particle image velocimetry,” Meas. Sci.
Technol., 8:1406-1416 (1997).
Melton, L.A., “Soot diagnostics based on laser heating,” Appl. Optics. 23:2201 (1984).
Mewes, B., and Seitzman, J. M., “Soot volume fraction and particle size measurementswith laser-induced incandescence,” Applied Optics, 36:709-717 (1997).
Miles, P., Carbon Dioxide Spectral Synthesis code, Sandia National Labs (1996).
236
Murphy, W. F., “The Rayleigh Depolarization Ratio and Rotational Raman Spectrum ofWater Vapor and the Polarizability Components for the Water Molecule,” J.
Chem. Phys. 67:5877 (1977).
Najm, H.N., Paul, P.H., Mueller, C.J., and Wyckoff, P.S., “On the adequacy of certainexperimental observables as measurements of flame burning rate,”Combustion
and Flame, 113:312-332 (1998).
Ni, T., Pinson, J.A., Gupta, S., Santoro, R.J., “Two-dimensional imaging of soot volumefraction by the use of laser-induced incandescence,” Appl. Optics, 34: 7083(1995).
Osborne, R. J., Brown, T. M., Pitz, R. W., Tanoff, M. A., Smooke, M. D., “Study ofStructure and Emissions of Partially-Premixed Methane Flames ins LaminarCounterflow,” AIAA 96-0212 (1996).
Penney, C. M., Goldman, L. M., and Lapp, M., “Raman Scattering Cross Sections,”
Nature Phys. Sci. 235:110 (1972).
Petarca, L, and Marconi, F, “Fluorescence Spectra and Polycyclic Aromatic Species in aN-Heptane Diffusion Flame,” Combust. Flame 78:308 (1989).
Pinson, R.A., “Quantitative, planar soot measurements in a D.I. diesel engine using laser-induced incandescence and light scattering,” SAE paper 932650 (Society ofAutomotive Engineers, Warrensdale, PA, 1993).
Quay, B., Lee, T.W., Ni, T., Santoro, R.J., “Spatially-resolved measurements of sootvolume fraction using laser-induced incandescence,” Combust Flame 97:384-392
(1994).
Reckers, W., Huwel, L., Grunefeld, G., Andresen, P. Spatially-resolved multi-species andtemperature analysis in hydrogen flames. Applied Optics 32: pp. 907-18 (1993).
237
Rosner, D.E. Private communication (2001a).
Rosner, D.E., Transport Processes in Chemically Reacting Flow Systems, DoverPublications (2000).
Rosner, D. E. , Schaffer, A.M., Long,, M.B. and La Mantia, B., “In-Situ, Real-TimeSizing Of Inorganic Nano-Particle Populations In Flames Using Laser-InducedIncandescence,” To be presented at 20th Annual AAAR Conference, October 15-19, 2001, Portland, Oregon USA (2001b)
Rosner, D.E., Mackowski D.W. and Garcia-Ybarra, P., “Size- and Structure-Insensitivityof the Thermophoretic Transport of Aggregated Soot Particles in Gases,”Combustion Science and Technology 80: 1-3, 87-101 (1991).
Rowell, R. L., Aval, G. M., Barrett, J. J., “Rayleigh-Raman Depolarization of Laser LightScattered by Gases,” J. Chem. Phys. 54:1960 (1971).
Santoro, R.J., Semerjian, H.G., and Dobbins, R.A. Combust. Flame 51:203-218 (1983).
Schrötter, H. W., and and Klöckner, H. W., “Raman Scattering Cross Sections in Gasesand Liquids” in Raman Spectroscopy of Gases and Liquids (A. Weber, ed),Springer-Verlag, Berlin (1979).
Skaggs, R.R. and Miller, J.H., “Tunable Diode Laser Absorption Measurements ofCarbon Monoxide and Temperature in a Time-Varying, Methane/Air, Non-premixed Flame,” Twenty-sixth Symposium (International) on Combustion, TheCombustion Institute, 1996, p. 1181.
Smooke, M. D., Ern, A., Tanoff, M. A., Valdati, B. A., Mohammed, R. K., Marran, D. F.,Long, M. B., “Computational and Experimental Study of Nitric Oxide in anAxisymmetric Laminar Diffusion Flame,” Twenty-sixth Symposium
(International) on Combustion, The Combustion Institute, 1996, pp 2161-2170.
238
Smooke, M. D., Xu, Y, Zurn, R. M., Lin, P., Frank, J. H., Long, M. B., “Computationaland Experimental Study of OH and CH Radicals in Axisymmetric LaminarDiffusion Flames” Twenty-fourth Symposium (International) on Combustion, TheCombustion Institute, 1992, p. 813.
Smooke, M. D., Lin, P., Lam, J. K., Long, M. B., “Computational and ExperimentalStudy of a Laminar Axisymmetric Methane-Air Diffusion Flame” Twenty-third
Symposium (International) on Combustion, The Combustion Institute, 1990, p.575.
Smyth, K.C., Harrington,J.E., Johnson,E.L., and Pitts,W.M., “Greatly enhanced sootscattering in flickering CH4/Air Diffusion Flames,” Combust. Flame, 95:229-239(1993).
Smyth, K. C., Miller, J. H., Doorfman, R. C., Mallard, W. G., and R. J. Santoro, “SootInception in a Methane / Air Diffusion Flame as Characterized by Detailed
Species Profiles,” Combustion and Flame, 62:157 (1985).
Stårner, S.H., Bilger, R.W., Lyons, K.M., Frank, J.H., Long, M.B., “Conserved ScalarMeasurements in Turbulent Diffusion Flames by a Raman and Rayleigh RibbonImaging Method,” Combust. Flame, 99:347-354 (1994).
Stårner, S.H., Bilger, R.W., Frank, J.H., Marran, D.F., and Long, M.B., “MixtureFraction Imaging in a Lifted Methane Jet Flame,” Combust. Flame, 107:307-313(1996)
Thorn, R.J. and Winslow, G.H., “Vaporization Coefficient of Graphite and Computation
of Equilibrium Vaporization,” J. Chem. Phys., 26:186, (1957).
Twomey, S. Introduction to the Mathematics of Inversion in Remote Sensing and Indirect
Measurement. Elsevier, Amsterdam (1977).
239
Vander Wal, R. L., and Weiland, K. J., “Laser-induced incandescence: Development andcharacterization towards a measurement of soot-volume fraction,” Applied
Physics B, 59:445-452 (1994).
Vander Wal, R. L., “Laser-induced incandescence: detection issues,” Applied Optics,
35:6548-6559 (1996).
Vander Wal, R.L et al., “Laser-induced incandescence applied to metal nanostructures,”Applied Optics, 38:5867 (1999).
Vander Wal, R. L., Ticich, T. M., and Stephens, A. B., “Optical and microscopyinvestigations of soot structure alterations by laser-induced incandescence,”Applied Physics B, 67:15-123 (1998).
Wainner, R.T. and Seitzman, J.M., “Soot diagnostics using laser-induced incancdescencein flames and exhaust flows,” 37th Aerospace Sciences Meeting, Reno, NV, Jan
11-14, 1999, paper AIAA 99-0640.
Walsh, K.T., “ Effect of light-collection geometry on reconstruction errors in Abelinversions,” Optics Letters 25:457-9 (2000).
Will, S., Schraml, S., Leipertz, A., “Two-dimensional soot particle-sizing by time-resolved laser-induced incandescence,” Optics Letters, 20:2342 (1995)
Woodward, L. A., “General Introduction” in Raman Spectroscopy, Theory and Practice
(H. A. Szymanski, ed), Plenum Press, New York (1967).
Xing, Y., Koylu, U.O. and Rosner, D.E., “In Situ Light ScatteringMeasurements of Morphologically Evolving Flame Synthesized OxideNano-aggregates,” Appl. Optics 38:2686-2697(1999).
Xu, Y., Smooke, M. D., Lin, P., and Long, M. B., “Primitive Variable Modeling ofMultidimensional Laminar Flames,” Comb. Sci. Tech., 90:289 (1993).
240
Xu, Y., Numerical Calculations of an Axisymmetric Laminar Diffusion Flame wih
Detailed and Reduced Reaction Mechanisms, Thesis, Yale University (1991).
