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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