PhD Thesis of Vishal Toro - University of Groningen · Quantification of the Raman Scattering and...
Transcript of PhD Thesis of Vishal Toro - University of Groningen · Quantification of the Raman Scattering and...
University of Groningen
Experimental study of the structure of laminar axisymmetric H2/air diffusion flamesToro, Vishal Vijay
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Quantification of the Raman Scattering and LIF Data
37
3Quantification of the Raman Scattering and LIF
Data
Chapter 3
38
3.1 General introduction
In the present work the non-intrusive laser diagnostic methods described in Ch. 2
have been used to derive species concentrations and temperatures in laminar diffusion
flames. Extracting quantitative information using these techniques, however, requires
special considerations [1]. For example, knowledge of the temperature-dependent
scattering cross-sections of the species of interest is needed for obtaining mole
fractions and temperature using spontaneous Raman scattering technique. Similarly,
quantitative use of laser induced fluorescence (LIF) for flame diagnostics requires
knowledge of temperature and composition dependent parameters such as quenching
rates, line widths, etc. In most cases, for extracting quantitative information, separate
calibration procedures must be conducted in media where composition and
temperatures are known. This chapter describes the procedures followed to quantify
the spontaneous Raman scattering and LIF data used in this work.
3.2 Quantitative information from Raman measurements
As shown in Eq. 2.1, the measured Raman intensity is dependent upon the
incident laser power, effective Raman scattering cross-section and the concentration
of the species of interest [2,3]. The effective scattering cross-section in turn depends
on the local temperature, excitation wavelength and experimental parameters such as
the quantum efficiency of the detector, spectrometer bandwidth, etc. In one approach,
the effective cross-sections of all species at the laser wavelength are determined
through calibration in flames with known composition and temperature [4-7]. But, this
procedure is tedious, because the calibration needs a large number of flames and the
temperatures of these flames should be measured independently, preferably
maintaining the same composition at different temperatures.
Major species concentrations and temperatures can also be obtained by fitting the
experimental Raman spectrum, provided the functional dependence of the Raman
cross-sections of all flame components on wavelength and temperature is known [8].
In this approach, the calibration procedure is simplified to the determination of the
apparatus function and the overall response of the detector system, which can be
achieved by a single daily measurement of the Raman signal in a medium having
known composition and temperature, such as room-temperature air. More importantly,
this procedure uses all spectral information, which can potentially increase precision,
and interfering signals in the measured spectrum can be detected and removed.
Quantification of the Raman Scattering and LIF Data
39
The Raman cross-sections of diatomic molecules are known with good accuracy,
and their use in the fitting code is straightforward [8-11]. The knowledge of the cross-
sections of polyatomic molecules, however, is limited and may require calibration.
The Raman spectrum of CO2 has been adequately described over the range from room
to flame temperatures [8,12] and the spectral data can be used reliably in the fit. The
Raman spectrum of CH4 is currently available only at lower temperatures (<1000 K),
and requires more information at higher temperatures. Fortunately, in most of the
cases, CH4 is hardly present in substantial quantities in hydrocarbon combustion at
temperatures above 1500 K, and therefore one can approximate its concentration to
zero at these temperatures. Thus, for quantitative work, uncertainty remains about the
CH4 Raman spectrum in the temperature region 1000 - 1500 K. However, in this work
the CH4 Raman spectrum was not measured in this temperature range, and this
problem was avoided. Water is formed in substantial quantities during combustion of
hydrogen-containing species. The calculation of the Raman spectrum for this
asymmetric-top molecule is far more complicated than for the diatomic and linear
triatomic molecules [13]. Lapp [14] obtained the vibrational-rotational Raman
signature of water molecules, which is dependent upon temperature, but he called
attention to the need for more information on the broad spectrum of water at high
temperatures. A better characterization of the spectra at high temperatures is
especially important for flame studies.
In this chapter, an approach is presented to conduct quantitative Raman
measurements in the hot gases of laminar premixed CH4/air and H2/air flames and to
assess the capability of the Raman system for obtaining concentrations and
temperatures accurately by spectral fitting. For this purpose, a computer program was
written to fit the calculated spectra to the experimental spectra. To include fitting of
the water spectrum, the Raman spectra of water in a wide range of temperature were
measured. To assess the accuracy of the measurements, the Raman temperatures were
compared to those obtained by CARS. The species mole fractions in post-flame gases
were compared with those expected at equilibrium. As will be seen below, use of this
fitting procedure simplified the quantification to a single daily calibration
measurement.
3.3 Calculation of Raman spectra
As given in Ch. 2, the intensity of the measured Raman signal of species j can be
written in general as
Chapter 3
40
Ij ( ) = Pl Nj
( )
jd
d
Ω lε, (2.1)
where( )
jd
d
Ω
νσis the differential cross-section of species j at frequency ν . For the
Raman signal of species j measured by one pixel of the photodetector, Eq. 2.1 can be
rewritten as
( )ipjI ν =
( ) ( )
T
x
d
dC j
j
i
i
i
ν
ν
νε
/
, (3.1)
where Ipj is the intensity in photons/s, xj is the mole fraction of species j and iν is the
frequency corresponding to the ith
pixel of the photodetector, respectively. In this
equation, ( )iνε is the spectral sensitivity of the detection system, which can be
determined by measuring radiation of a light source with known emission
characteristics, such as tungsten lamp. In Eq. 3.1, C’
is a constant which includes the
laser power, collecting solid angle and length of measurement volume, and can be
written as
k
Pl
hc
PC l'
∆Ω= (3.2)
The measured Raman intensity for a multicomponent system can be written as
( ) ( )bg
'meas
1 i
j
j
i
i
i
j
iI
Tx
d
dCI +
Ω
νσ
ν
νε= , (3.3)
where Imeas is the measured intensity of the raw spectrum, Ibg is the measured
background signal. The measured background signal Ibg is added to Eq. 3.3 to account
for intensities arising from other (non-Raman) radiating processes. In Eq. 3.3, the
values of mole fractions (xj) and temperature (T) are unknown parameters, while the
values of the rest of the parameters are known either theoretically or determined
through calibration. As the cross-sections of diatomic molecules are known, the values
of the calibration constants C’
can be retrieved when the Raman spectra are measured
in media (such as ambient air) with known concentrations of these species. When the
number of measured spectral points (number of pixels of the photodetector) is larger
than the number of unknowns; the unknown parameters can be found using a least-
square fitting method.
Quantification of the Raman Scattering and LIF Data
41
3.4 Experimental procedure for calibrating the Raman system
Flat flame burners, such as McKenna Products burner, have been proven as an
excellent system for calibrating Raman signals [5,6,15,16]. Using these burners, good
spatial uniformity of the post-flame region can be obtained and a wide range of
temperatures and gas compositions can be achieved by varying stoichiometry or flow
Figure 3.1 McKenna burner along with a heat exchanger device used to calibrate the Raman
signals over the range of temperature and composition of flue gases. Measuring location is
indicated at the exit of the heat exchanger device where the laser beam is focused.
rates. In the present calibration procedure, a McKenna burner, along with specially
built heat exchangers, were used to obtain a wide range of temperatures and
compositions of the hot gas for the Raman measurements. The burner and heat
exchanger are shown schematically in Fig. 3.1. The heat exchanger consisted of a
bundle of stainless tubes. The stainless tubes were welded together to obtain a uniform
radial temperature distribution (maximum difference ∼ 30 K) across the exit plane. A
cooling coil was wrapped around the tubes just above the burner. Similar heat
McKenna burner
Heat exchanger
Cooling water
Laser beam
10 –
100
cm
Chapter 3
42
exchangers of different lengths were constructed to obtain different gas temperatures
at the measuring location. Each heat exchanger was placed as close to the burner as
possible to prevent mixing of the flue gases with the surrounding air. This ensured that
the composition of the flue gases downstream at the measuring point remained
unchanged. Temperatures ranging from ∼ 2200 K (above the CH4/air premixed flame
without any heat exchanger) to ∼ 450 K were obtained with a step of about 150 K.
The optical scheme used for the Raman scattering measurements is described in
detail in Ch. 2. The Raman and CARS measurements were performed on premixed
CH4/air and H2/air flames. The flow rates of methane, hydrogen and air were
measured by mass flow meters (Bronkhorst) and the equivalence ratios were
determined by measuring the methane and oxygen concentrations in the fuel-air
mixtures by an infrared and paramagnetic analyzer, respectively, in the Maihak Unor
710 module.
3.5 Results and discussion for the Raman data
The coefficient C/, as we can see in Eq. 3.2, is dependent only upon parameters
of the experimental setup. Before proceeding further, the constancy of C/
was
examined. For this purpose, the Raman spectra of pure gases and air were measured at
room temperature, and the coefficient C/
was determined by fitting each Raman
spectrum. The coefficients C/, obtained in this manner were normalized to that of pure
N2, and plotted as a function of wavelength of the Raman transition, shown in Fig. 3.2.
Figure 3.2 Calibration coefficients calculated for different species.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
560 580 600 620 640 660 680 700
wavelength, nm
no
rmal
ized
cali
bra
tio
nco
effi
cien
t
H2N2
CH4
CO2
O2
Quantification of the Raman Scattering and LIF Data
43
As can be seen in the figure, the normalized coefficients determined in CO2, CH4
and H2 remain within 10% of that for N2. However for oxygen, the normalized
coefficient is significantly higher than those derived for the other species. One
possible reason for this discrepancy is the resonant enhancement of the O2 Raman
signal because of the proximity of the B3Σu electronic state, as indicated in [17]. We
remark here that the Raman cross-section has been measured using low-power CW
laser, in contrast with the pulsed high-power laser used here. This could have an
impact on the resonance-enhanced Raman cross-section. To correct for this
discrepancy, in the Raman fitting program the scattering cross-section of O2 is
decreased by 30% the literature value.
The Raman signatures of water in the temperature range 450 – 2200 K were
obtained using the burner arrangement shown in Fig. 3.1 and stored as a library of
spectra in the fitting program. As an example, Fig. 3.3 shows the water Raman spectra
at four different temperatures in CH4/air flames at φ = 1. In this figure, we see the
Figure 3.3 Raman spectra of water at different temperatures, as obtained through the
calibration study on premixed CH4/air flames at φ =1
0
50
100
150
200
250
300
350
400
640 650 660 670 680
wavelength, nm
Ram
ansi
gn
al,co
un
ts
790 K
0
50
100
150
200
250
640 650 660 670 680
wavelength, nm
Ram
ansi
gn
al,co
un
ts
1300 K
0
20
40
60
80
100
120
640 650 660 670 680
wavelength, nm
Ram
ansi
gn
al,co
un
ts 1815 K
0
10
20
30
40
50
60
70
80
640 650 660 670 680
wavelength, nm
Ram
ansi
gn
al,co
un
ts
2200 K
a b
c d
Chapter 3
44
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
0 0.0005 0.001 0.0015 0.002 0.0025 0.003
1/T
inte
gra
ted
signal
inte
nsi
t
N2
H2O
progressive change in the Raman signal intensity and shape over the range of
temperatures from 790 (Fig. 3.3a) to 2200 K (Fig. 3.3d). Particularly interesting is the
considerable spread in the Raman spectrum at high temperatures.
Whereas the Raman spectra are fitted in the present work for deriving the
temperature and species concentrations, it is interesting to assess the double harmonic
approximation for calculation of the vibrational Raman spectrum. In this
approximation, the differential Raman scattering cross-section for species j is given by
[11] as
( ) ( ) ( )
[ ]/kTh
jshift,
/
i
jiec
ah
d
d−
−νµ
γ+ν−ν
=
Ω
σ
18
45
4
4
2/24
0
, (3.4)
where /a and /γ are the mean and anisotropy invariants of the polarizability tensor, h
is the Planck’s constant and µ is the reduced mass of the species. Using this equation,
we can estimate the behavior of the scattering cross-section of any species as a
function of temperature. For N2 in the temperature range from 400 to 2000 K, the
value of the differential cross-section remains relatively constant due to only 20%
variation in the factor [ ]/kThie−
−1 in Eq. 3.4, and the Raman signal intensity is
estimated to vary roughly linearly with 1/T, as can be seen in Fig. 3.4. Similarly, Eq.
Figure 3.4 Integrated Raman signal intensity for N2 and H2O molecules as a function of
temperature.
Quantification of the Raman Scattering and LIF Data
45
3.4 predicts the H2O Raman scattering cross-section to vary only by ∼ 7% over the
temperature range 400 to 2000 K and the Raman signal intensity for this molecule is
also expected to vary linearly with 1/T in this temperature range. The integrated
Raman intensities are plotted against 1/T for N2 and H2O in Fig. 3.4, which supports
the use of double harmonic approximation for the H2O molecule.
Figure 3.5 shows the results of fitting flame spectra of a stoichiometric premixed
CH4/air flame with and without the heat exchanger; the corresponding CARS
measurements indicate that the temperatures in the flames in Fig. 3.5a and 3.5b are
785 K and 2170 K, respectively. The Raman measurements at the lower temperatures
were conducted at the laser energies ∼ 135 mJ/pulse to avoid the optical breakdown,
and at higher temperature, the laser energy was increased up to 185 mJ/pulse. The
signal intensities (counts) in these plots are absolute.
Chapter 3
46
0
100
200
300
400
500
600
550 570 590 610 630 650 670 690
wavelength, nm
inte
nsi
ty,
cou
nts
expt
fitting
0
20
40
60
80
100
120
140
160
180
200
550 570 590 610 630 650 670 690
wavelength, nm
inte
nsi
ty,
cou
nts
expt
fitting
CO2
CO2
N2
N2
H2O
H2O
a
b
Figure 3.5 Plots showing experimental and fitted Raman spectra in the stoichiometric CH4/air
flames at different temperatures. The table shows the results obtained from fitting the Raman
spectra and their comparison against the equilibrium species compositions of the burnt gas
mixture for the conditions used.
T(K)
(CARS)T(K)(Raman)
[CH4] [N2] [O2] [H2O] [CO2] [CO] [H2]
Equilibrium
@ 770 K- - - 0.706 0.0 0.189 0.0950 0.0 0.0
Equilibrium
@ 2180 K- - - 0.702 0.0038 0.184 0.0872 0.0073 0.00295
Figure 3.5a 785 762 0.0 0.68 0.008 0.188 0.105 0.01 0.004
Figure 3.5b 2170 2196 0.00 0.66 0.028 0.194 0.088 0.015 0.012
Quantification of the Raman Scattering and LIF Data
47
In Fig. 3.5, as expected for the post-flame gases of a stoichiometric CH4/air
flame, the measured Raman spectra show mainly N2, CO2 and H2O. The temperature
dependence of the Raman spectrum can be observed through the shapes and peak
intensities of the Raman bands. Particularly, the spread in the Raman bands and the
reduction of the peak intensities at higher temperature is seen for all the species. The
results obtained from the fit show excellent agreement between the CARS and the
Raman temperatures. The difference in the measured and equilibrium mole fractions
of N2, CO2 and H2O is no more than 10% (relative). The results of the fit even reflect
small quantities of CO (Fig. 3.6), which is barely seen in the magnified scale of Fig.
3.5b.
Figure 3.6 The magnified image of the spectrum shown in Fig. 3.5b. Here, the spectral fit
detects the presence of trace CO at the measuring location.
The results obtained in a stoichiometric premixed H2/air flame, shown in Fig.
3.7a and 3.7b, are also in excellent agreement with the equilibrium approximation. As
expected, the composition at the measuring location mainly consists of N2 and H2O.
Here too, the spectral intensities and lineshapes at different temperatures are well
reproduced by the fit.
0
5
10
15
20
25
30
550 570 590 610 630
wavelength, nm
inte
nsi
ty,co
un
ts
expt
fitting
CO
N2
CO2
Chapter 3
48
.
Figure 3.7 Plots showing experimental and fitted Raman spectra in stoichiometric H2/air
flames at different temperatures. The table shows the results obtained from fitting the Raman
spectra and their comparison against the equilibrium species compositions present in the
burnt gas mixture for the conditions used.
Temp(K)
(CARS)
Temp(K)
(Raman)[N2] [O2] [H2O] [H2]
Equilibrium
@ 570 K- - 0.645 0.0 0.346 0.0
Equilibrium
@ 1720 K- - 0.645 0.0002 0.345 0.0006
Figure 3.7a 566 570 0.62 0.0 0.36 0.01
Figure 3.7b 1719 1738 0.64 0.01 0.33 0.0
0
100
200
300
400
500
600
700
550 570 590 610 630 650 670 690
wavelength, nm
inte
nsi
ty,
cou
nts
expt.
fitting
0
50
100
150
200
250
300
550 570 590 610 630 650 670 690
wavelength, nm
inte
nsi
ty,co
un
ts
expt
fitting
N2 H2O
O2
N2
H2O
a
b
Quantification of the Raman Scattering and LIF Data
49
In the current work on coflow diffusion flames, where sharp radial gradients in
species distributions were present, only 4 CCD pixels in the spatial direction were
binned to increase the spatial resolution, which decreased the signal-to-noise ratio
(SNR) of the Raman spectrum compared to that obtained above by binning 256 pixels.
This was especially of concern when collecting data in the hot regions of the hydrogen
diffusion flames, where the Raman signal intensities were low and the data possessed
significant noise. Thus it was essential to test the ability of the spectral fitting program
to obtain mole fractions and temperatures accurately using the noisier data at high
temperatures. This test was performed by measuring the Raman spectra with different
exposure times. Figure 3.8a shows a flame spectrum with 10s exposure time and 10
accumulations, while Fig. 3.8b shows the flame spectrum with 1s exposure time and
10 accumulations. The values obtained by fitting are reported in the corresponding
table.
Chapter 3
50
Figure 3.8 Plots showing experimental and fitted Raman spectra in stoichiometric CH4/air
flames. The experimental Raman data were collected in the same flame with different signal
collection time to obtain different signal to noise ratios (SNR) in the plots.
Temp(K)
(CARS)
Temp(K)
(Raman)[N2] [O2] [H2O] [CO2] [CO] [H2]
Equilibrium
@ 2180 K - - 0.701 0.0038 0.184 0.0871 0.0073 0.0029
Figure 3.8a 2193 2180 0.66 0.02 0.19 0.08 0.02 0.0
Figure 3.8b 2193 2188 0.65 0.01 0.20 0.08 0.03 0.0
0
200
400
600
800
1000
1200
1400
1600
1800
550 570 590 610 630 650 670 690
wavelength, nm
inte
nsity,
counts
expt
fitting
0
20
40
60
80
100
120
140
160
180
550 570 590 610 630 650 670 690
wavelength, nm
inte
nsi
ty,co
unts
expt
fitting
CO2
CO2
H2O
H2O
N2
N2
a
b
Quantification of the Raman Scattering and LIF Data
51
The mole fractions and temperatures obtained after fitting the experimental
spectra in Fig. 3.8a and 3.8b are in excellent agreement, in spite of the substantially
poorer SNR in Fig. 3.8b.
3.6 Conclusions for the quantitative Raman diagnostics
Spectral fitting of the measured Raman spectra greatly simplifies the experimental
procedure; only a single daily calibration measurement of the Raman signal is
required. Comparing the measured composition in post-flame gases with equilibrium
concentrations, we can conclude that the accuracy of the present Raman setup is better
than 10% (relative) for major species with mole fraction ≥ 0.1 and 0.01 mole fraction
for lower concentrations. The temperatures obtained by the Raman measurements in
methane and hydrogen flames are in excellent agreement with those obtained by
CARS, with a maximum of 50 K difference between them. The excellent agreement
achieved in the species mole fractions and temperatures by fitting the experimental
spectra with different SNR indicates that the fitting code can even be used to fit
moderate quality spectra.
3.7 Quantification of the LIF data: introduction
In last few decades, much effort has been devoted towards measuring the
hydroxyl (OH) radical, which is an important participant in many key chemical
reactions involved in the ignition of the fuel mixture, flame propagation and processes
in the burnt flue gases. Laser induced fluorescence (LIF) has proved to be the best
method for OH diagnostics in flame due to its sensitivity, selectivity and spatial
resolution [18].
For a simple two level system in the linear regime, the following expression for the
LIF signal is obtained by modifying Eq. 2.4 in Ch. 2:
F = lAAc
h
π
Ω
421 ( )21
121
)( ATQ
IBN0
+G(T), (3.5)
where G(T) = +∞
∞−
dTgL ),()( , is the overlap of the laser line L( ν ), and the absorption
profile g( ,T ). The rest of the symbols were defined in Ch.2. Based on this
expression, the measured LIF signal can be simply written as
Chapter 3
52
0
0.5
1
1.5
2
2.5
3
3.5
4
300 800 1300 1800 2300 2800
temperature, K
Y(T
)
N2/5
O2
H2
CO2
H2O
F = C fb(T) XabsT
1
)(21
21
TQA
A
+G(T), (3.6)
where C is a calibration coefficient that contains the geometrical factors and detection
efficiencies, fb(T) is the Boltzmann fraction and Xabs is the mole fraction of the species
[19, 20].
It is clear from Eq. 3.6 that to quantify the LIF signals, the geometrical and the
temperature dependent parameters should be determined. The geometrical factor can
be determined experimentally, for example, by measuring the intensity of Rayleigh
scattering. In the present work, the total partition sum for OH molecule was calculated
using the method described in [21], while the values of the initial state energies were
taken from [22]. Collisional quenching rates and the convolution integral can also be
calculated, provided collider concentrations and their collisional cross-sections are
known. The temperature dependent OH quenching cross-sections for O2, H2, H2O,
CH4, CO and CO2 molecules were taken from [23]. Absorption lines of OH in flame
spectra can be described by a Voigt profile, which is the convolution of the Lorentzian
line shape due to intermolecular collisions with the Gaussian line shape arising from
molecular motions (Doppler broadening). The collisional line broadening parameters
have been taken from [24, 25]. The spontaneous emission coefficients were taken
from reference [26].
Figure 3.9 Plot showing temperature dependent function Y(T) as a function of temperature for
different species
Quantification of the Raman Scattering and LIF Data
53
To illustrate temperature dependence of fluorescence signal, the temperature-
dependent term Y(T)= (F/C)XOH is shown in Fig. 3.9 for different collisional partners.
In this figure, we see that the value of Y(T) calculated for N2 is significantly higher
than other major species over the range of temperature because of the low quenching
cross-section of N2. Thus, in the flames regions having significant nitrogen
concentrations, we can expect the higher values of Y(T).
3.8 Quantifying the OH LIF data in diffusion flames
To determine the absolute value of the OH mole fraction, we make use of a
calibration flame; here, a lean-premixed flat flame was used [27]. In this case, the
local OH mole fraction in diffusion flames was calculated using Eq. 3.6 as
XOH, diff. =( )( )
( )OH,cal
diff
cal
cal
diff. XTY
TY
F
F
, (3.7)
where XOH,cal denotes the OH mole fraction obtained in the calibration flame, and
subscripts (diff) and (cal) denote diffusion and calibration flame, respectively. For
measurements in the diffusion flames, the following procedure was followed. First the
LIF signal in the center of the calibration flame was collected. Then the diffusion
flame burner was placed at the measuring location, and the profiles of the LIF signals
in the diffusion flames were measured. The consistency in the LIF data was then
verified by repeating the measurement of the LIF signal in the premixed flame. In all
experiments, the settings of the detection system were unchanged.
For calibration purposes, the direct OH measurements are preferred over
calculations, because OH mole fraction is very sensitive to the operational conditions
[28]. In this work, the results of direct laser absorption measurements in a lean-
premixed flame [27] were used to calibrate the OH LIF data. The calibration
measurements were performed using a flat near-adiabatic premixed CH4/air flame at φ
= 0.8 (mass flux ρ ϑ = 0.028 g/cm2s), stabilized on the McKenna burner. In this flame,
at height of 15 mm above the burner surface, the OH mole fraction derived from the
absorption measurements was 1550 ppm and temperature 1970 K (CARS
measurements); these data were used for calibration purposes.
Chapter 3
54
Figure 3.10 Plots showing the distribution of the major species, temperature (a) and
temperature dependent factor Y(T) (b) as a function of radial distance at z = 3 mm in H2/air
diffusion flame ( ϑ = 18 cm/s).
To calculate Y(T), the local temperatures and concentrations of the major species
are required. In the calibration flame, the mole fractions of the major species were
obtained from the calculations using the PREMIX code in CHEMKIN II [29] with the
GRI-MECH 3.0 [30] chemical mechanism. For diffusion flames, the major species
and temperature data obtained from the Raman scattering and CARS measurements
were used to calculate Y(T)diff. Figure 3.10 shows an example of the distribution of
Y(T) along the radial distance in a diffusion flame at z = 3 mm (Ch. 4, 18 cm/s exit
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-15 -10 -5 0 5 10 15
radial distance, mm
mo
lefr
acti
on
300
500
700
900
1100
1300
1500
1700
1900
2100
2300
temp
erature,
K
H2
N2
O2
H2O
T
a
0
0.5
1
1.5
2
2.5
3
3.5
4
-15 -10 -5 0 5 10 15radial distance, mm
Y(T
)
b
Quantification of the Raman Scattering and LIF Data
55
velocity). As expected from the results of the calculations shown in Fig. 3.9, the factor
Y(T) in Fig. 3.10 is seen decreasing from the regions of high N2 concentrations to a
minimum in the high temperature zones (caused by the high quenching rate of water).
The strong dependence of the fluorescence signal upon composition is also illustrated
Figure 3.11 Plot showing temperature dependent factor Y(T) as a function of temperature in
H2 diffusion flame (18 cm/s average exit velocity and z = 3 mm).
by Fig. 3.11. In this figure, Y(T) shown in Fig. 3.10 is plotted as a function of the
measured local temperature. The figure shows two “branches”, one following the
temperature increase from the center line (r = 0, center of the fuel jet), and one branch
following the temperature increase beginning in pure air at r ∼ 12 mm. As can be seen,
a difference of a factor of three can be observed between the fluorescence signals at
the same temperature on the fuel lean side of the flame as compared to the rich side of
the diffusion flame.
This strong dependence of LIF signals upon flame composition results in a
propagation of noise from the Raman measurements into the derived OH
concentrations. This effect is especially distinguishable at high temperatures, where
the Raman data possess significant noise. As an illustration, Fig. 3.12 shows data
0
0.5
1
1.5
2
2.5
3
3.5
4
0 500 1000 1500 2000 2500
temperature, K
Y(T
)
Fuel side
Oxidizer side
Chapter 3
56
0
200
400
600
800
1000
1200
1400
1600
-15 -10 -5 0 5 10 15
LIF
sig
nal
,co
un
ts
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
-15 -10 -5 0 5 10 15
mo
lefr
acti
on
300
700
1100
1500
1900
2300
temp
erature,
K
N2
O2
H2O
T
a
b
0
1000
2000
3000
4000
5000
6000
-15 -10 -5 0 5 10 15
OH
,p
pm
radial distance, mm
c
Figure 3.12 Plots showing (a) the measured LIF signal distribution (b) the major species and
temperature profiles and (c) the measured (points) and smoothed (line) OH concentration data
in H2/air diffusion flame (18 cm/s average exit velocity) at z = Tmax.
Quantification of the Raman Scattering and LIF Data
57
obtained from radial profiles measured at the position of the maximum centerline
temperature in a pure H2/air diffusion flame (Ch. 4, 18 cm/s average exit velocity).
We see that the measured LIF signal (Fig. 3.12a) and temperature (Fig. 3.12b)
profiles at this axial distance show a smooth distribution, while the derived OH mole
fractions (Fig. 3.12c, points) possess significant scatter. The noise in the OH
concentration profiles originates from the major species profiles (see Ch. 4). To derive
a smooth distribution of the OH mole fraction, the major species data have been
smoothed first and then used for quenching corrections (Fig. 3.12c, solid line).
3.9 Conclusions for quantifying LIF measurements
The LIF data in the diffusion flames are quantified by correcting for the
temperature and collisional dependent factors based on the CARS and Raman
measurements, using measurements in a “calibration” flame to derive the absolute
values. We see that the noise in the Raman data can make a substantial contribution to
the noise in the LIF results.
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