NASA Contractor Report 185218

f

/1 -.3,..5

Saturated Fluorescence Measurements

of the Hydroxyl Radical in Laminar

High-Pressure Flames

Campbell D. Carter, Galen B. King, and

Normand M. Laurendeau

Purdue University

West Lafayette, Indiana

February 1990

Prepared for

Lewis Research Center

Under Grant NAG3-351

NationalAeronauticsand

SpaceAdministration

(NA_A-CR-18521_)

MEA_UPEMENTS OF THE HY_ _QXYL RADICAL

LAMINAR HTGH-PRESSURE

(_urdue univ.) 222 p

SATUKATFD FLUORESCENCE

IN

FLAMES Final Report

CSCL 14_

N90-22022

TABLE OF CONTENTS

LIST OF SYMBOLS ......................................................................................................................

ABSTRACT ..................................................................................................................................

CHAPTER 1 INTRODUCTION .................................................................................................

1.1 Background .................................................................................................................

1.2 Thesis Contents ..........................................................................................................

CHAPTER 2 - LITERATURE REVIEW .......................................................................................

2.1 Laser-Saturated Fluorescence ..................................................................................

2,2 Other Methods ............................................................................................................

CHAPTER 3 - FEASIBILITY OF HYDROXYl. CONCENTRATION MEASUREMENTS BY

LASER-SATURATED FLUORESCENCE IN HIGH-PRESSURE FLAMES .......

Page

iii

viii

1

1

4

7

7

19

23

4.1 Combustion Facility for High-Pressure Flame Studies ............................................ 54

4,1.1 Introduction ................................................................................................... 54

4.1.2 High-Pressure Facility .................................................................................. 55

4.1.3 Areas for Improvement ................................................................................. 63

4,2 Spectroscopic Equipment ......................................................................................... 64

4.2.1 Fluorescence Experiments .......................................................................... 64

4,2.2 Absorption Experiments .............................................................................. 75

CHAPTER 4 EXPERIMENTAL APPARATUS .......................................................................... 54

3,1 Introduction ................................................................................................................. 23

3,2 Adequacy of the Rate-Equation Approach ............................................................... 24

3.3 The LSF Method .......................................................................................................... 25

3.4 Laser-Excitation Dynamics ......................................................................................... 30

3.4.1 Rotational Relaxation Model ........................................................................ 31

3.4.2 Electronic Quenching Model ....................................................................... 33

3.4.3 Vibrational Relaxation Model ....................................................................... 33

3.4.4 Excitation Model ........................................................................................... 34

3, 5 Test of Rotational Relaxation/Electronic Quenching Models .............................. 35

3.6 Results and Discussion .......................................................................................... 38

3,7 Conclusions ............................................................................................................ 52
Page

CHAPTER5 - LASER-INDUCEDFLUORESCENCEMEASUREMENTSOFOHINLAMINAR

C2Hs/O2/N 2 FLAMES AT HIGH PRESSURE .................................................... 81

5.1 Introduction ................................................................................................................. 81

5.2 Experimental Apparatus ............................................................................................. 81

5.3 Results and Discussion .............................................................................................. 85

5.4 Summary ..................................................................................................................... 96

CHAPTER 6 - SATURATED FLUORESCENCE MEASUREMENTS OF THE HYDROXYL

RADICAL IN LAMINAR HIGH-PRESSURE 02H6/O2/N 2 FLAMES ................... 98

6.1 Introduction .............................................................................. 98

6.2 Theory .......................................................................................................................... 99

6.3 Experimental Apparatus ............................................................................................. 102

6.4 Results and Discussion .............................................................................................. 108

6.4.1 Saturation Measurements ............................................................................ 108

6.4.2 Fluorescence/Absorption Measurements .................................................. 1t4

6.5 Conclusions ................................................................................................................ 125

CHAPTER 7 QUENCHING-INDEPENDENT SATURATED FLUORESCENCE MEASUREMENTS OF THE HYDROXYL RADICAL IN LAMINAR HIGH-PRESSURE

C2Hs/O2/N2 FLAMES .........................................................................................

127

7.1 Introduction ................................................................................................................. 127

7.2 Theory .......................................................................................................................... 128

7.3 Experimental Apparatus ............................................................................................. 133

7.4 Results and Discussion .............................................................................................. 138

7.5 Conclusions ............... 152

CHAPTER 8 CONCLUSIONS AND RECOMMENDATIONS ................................................. 154

8.1 Conclusions ................................................................................................................ 154

8.2 Recommendations ...................................................................................................... 156

LIST OF REFERENCES .............................................................................................................. 159

APPENDICES

Appendix A -

Appendix B -

Appendix C -

Appendix D -

Appendix E

Flow Control Routine .................................................................................... 165

Absorption Theory and Sensitivity Analysis for Collisional Linewidths ..... 184

Error Analysis of Absorption Measurements .............................................. 200

Saturation of an Inhomogeneously-Broadened A2_+,--X2][ (0,0) Transition of OH ...................................................................................................... 202

Gaussian Quadrature Formula for the Weighting Function

W(x) = 1/(1 + x2) .......................................................................................... 212

11
LIST OF SYMBOLS

English Symbols

sm_y_m__._J_l

A

A

a

A_

A(i,j)

A v

B

Bm

Bu#

C

d

E(D

FIand F2

f

fB

fb

(Fc)

fc

FIB

Description

Parameter in Chan-Daily-Crosley model

Integrated absorption

Line broadening parameter

Einstein coefficient for the observed fluorescence transition

Einstein coefficient for spontaneous emission from energy level

i to energy level j

Spectral absorption

Function In Chan-Daily-Crosley model

Einstein coefficient for absorption from level / to level u

Einstein coefficient for stimulated emission from level u to level /

Speed of light

Laser probe diameter

Energy of rotational level i

Notation for spin split rotational energy levels

Parameter in Chan-Daily-Crosley model

Change in the Boltzmann fraction relative to the calibration

condition

Fraction of population in the excited electronic state quenched

to the vibrational bath levels (v" > 0)

Spatially-averaged depletion of the laser-coupled levels

Fluorescence calibration factor

Fluorescence correction factor for linewidth variation relative to

the calibration condition

Boltzmann fraction of lower laser-coupled level

Units

cm

cm-1

S-1

S-1

cm 2

cm3-cm-1/J-s

cm3-cm-1/J-s

cm/s

cm

cm-1

cm-3/V

tti
Symbol

fv

fo

FWHM

g/

gu

g(O

H

h

If

l,o

IL

[r

K

k

k(u)

I

L _fr

m

N

N C

nG

NI

nl(v)

Description

Ratio of rate coefficients for (1) transfer from v" > 0 to v" = 0 and

(2) electronic quenching (Qe)

Fluorescence quenching correction factor

Full width at haft maximum

Degeneracy of rotational level I

Degeneracy of rotational level u

Degeneracy of rotational level i

Normalized slitfunction

Height of monochromator slit image at the laser beam

Plank constant

Fluorescence intensity

Fluorescence intensity at coordinates (y=O,z=O)

Laser irradiance

Laser irradiance at the beam center line and temporal peak

Rotational quantum number. J" and J" are the respective

rotational quantum numbers inthe ground and excited electronic

states.

Absorption parameter

Boitzmann constant

Absorption coefficient

Lower laser-coupled rotational level

Effective path length for absorption

Mass of species of interest

Rotational quantum number. N" and N' are the respective

rotational quantum numbers inthe ground and excited electronic

states.

Population in the collisionally-excited rotational energy levels

Number of ground-state rotational levels modelled

Population of the lower laser-coupled rotational energy level

Population of the lower laser-coupled rotational energy level at

equilibrium

Spectral population of the lower laser-coupled rovibronic level

Units

1/cm-t

cm

J-s

W/cm2-sr

W/cm2-sr

W/cm 2

W/cm 2

J/K

cm-1

..

cm

g

1/cm3

1/cm 3

1/cm3

1/cm3-cm -1

|V
n o(u)

Nu

Nu

nu(v)

NT

P

Qc

QD

Oe(i,j)

Oe(i)orOe

Qeff

ar(i,j)

Or(i) or Qr

Ov(i,j)

Or(i) or Qv

r

Sf

_,m

T

t

tp

u

v

v(y;a)

v

q

W

DescriDtio.n_

Spectral population of the lower laser-coupled rovibronic level

at equilibrium

Population of the upper laser-coupled rovibronic level

Normalized population of the upper laser-coupled rovibronic

level

Spectral population of the upper laser-coupled rovibronic level

Total species population

Pressure

Frequency of dephasing collisions

Frequency of Doppler-changing non-quenching collisions

Rate coefficient for electronic quenching from level ito level j

Rate coefficient for electronic quenching from level i

Effective rate coefficient for collision-induced transfer from

excited rotational level u

Rate coefficient for rotational energy transfer from level ito level

i

Rate coefficient for rotational energy transfer from level i

Rate coefficient for vibrational energy transfer from level ito level

J

Rate coefficient for vibrational energy transfer from level i

Radial distance from laser beam center line

Fluorescence signal

Fluorescence signal at maximum laser power

Temperature

Time

Time at which the laser pulse peaks

Upper laser-coupled rotational level

Vibrational quantum state, v"and v"are the respective vibrational

states in the ground and excited electronic states.

Voigt function

Average relative velocity between species of interest and species

q

Width of monochromator slit image at the laser beam

Units

1/cm3-cm-1

1/cm 3

1/cm3-cm-1

l/cm 3

atm

S-1

S-1

S-1

S-1

S-1

S-1

S-1

S-1

S-1

cm

V

V

K

S

S

cm/s

cm
W

W'

Wp"

Wul

X

Xi

Y(y;a)

Y

YLm

AYLm

YLc

Description

Halfwidth of the laser irradiance profile

Saturation parameter

Saturation parameter at the laser beam center line and temporal

peak

Relative saturation parameter

Spectral saturation parameter as a function of frequency v or

nondimensional frequency y, respectively

Rate coefficient for laser absorption from level I to level u

Rate coefficient for absorption (from levels / to u) at the laser

beam center line and temporal peak

Rate coefficient for stimulated emission from level u to level I

Lateral distance across iaser beam

Mole fraction of i-th species

Normalized line profile

Nondimensional frequency

Nondimensional central frequency of the m-th laser mode

Nondimensional spectral separation of the laser modes

Nondimensional central frequency of the laser spectral profile

Units

cm

s-1

s-1

cm

1/cm-1

oGreek Symbols

Symbol

O_sat

Pat

F

6

E

Description

Degree of saturation

Degree of saturation at the laser beam center line and temporal

peak

Function in Chan-Daily-Crosley model

Local depletion of the laser-coupled levels

Broadening coefficient for the i-th collision partner

Absolute uncertainty

Relative uncertainty

Ratio of the B-parameter in the ground electronic state to that in

the excited state

Units

.=

cm-l/atm

--

vl

0
e

/F

vO

uf

VLm

A,ULm

VLo

ArC

AUD

A_ L

AUN

P0

Pm

Pv

ae(i,j)

ae(O or oe

Or(i,i)

at(i) or O"r

a _ (i,j)

t3

Description

Efficiency of the fluorescence detection system, which

incorporates (I)the efficiencythefluorescence optics(including

the lenses,mirrors,and grating),(2)the spectralefficiency(i.e.,

the fractionofthe spectralprofilepassed by the exitslit),and (3)

the sensitivityof the PMT (V/W).

Parameter in Chan-Daily-Crosley model

Wavelength

Frequency

Central frequency of the transitionof interest

Central frequency of the observed fluorescence transition

Central frequency of the m-th lasermode

Spectral separation ofthe lasermodes

Central frequency of the laserspectralprofile

Collisionallinewidth(FWHM)

Doppler linewidth(FWHM)

Laser linewidth(FWHM)

Natural linewidth(FWHM)

Monochromator resolution

Energy density of the centralmode of the laserspectralprofile

Energy density of the m-th lasermode

Spectral energy density

Collisionalcross sectionforelectronicquenching from levelito

levelj

Collisionalcross section forthe totalelectronicquenching from

leveli(fora specificspecies)

Collisionalcross section forrotationalenergy transferfrom level

ito levelj

Collisionalcross section for the totalrotationalenergy transfer

from leveli(fora specificspecies)

Cross section (fortransfer from level ito levelj) describing

collisionswith species q and energy transfermode m (withm =

e, v, or r)

Parameter in Chan-Daily-Crosley model

Equivalence ratio

Solid angle

xvi

Units

v/w

nm

cm-t

cm-1

cm-1

cm-1

cm-1

cm-1

cm-1

cm-1

cm-1

cm-1

cm-1

J/cm 3

J/cm 3

J/cm3-cm-1

crr¢

cm 2

cm 2

cm 2

cm2

sr

vll
ABSTRACT

We have investigated theoretically and experimentally the efficacy of laser-saturated

fluorescence (LSF) for OH concentration measurements in high-pressure flames. Using a numerical

model describing the interaction of hydroxyl with nonuniform laser excitation, we have studied the

effect of pressure on the validity of the balanced cross-rate model and the sensitivity of the

depopulation of the laser-coupled levels to the ratio of rate coefficients describing (1) electronic

quenching to 2]C+(v">0) and (2) vibrational relaxation from v">0 to v"=0. At sufficiently high

pressures and near-saturated conditions, the total population of the laser-coupled levels reaches

an asymptotic value, which is insensitive to the degree of saturation. When the ratio of electronic

quenching to vibrational relaxation is small and the rate coefficients for rotational transfer in the

ground and excited electronic states are nearly the same, the balanced cross-rate model remains

a good approximation for all pressures. When the above ratio is large, depopulation of the

laser-coupled levels becomes significantat highpressures, and thus the balanced cross-rate model

no Iongerholds. Under these conditions, however, knowledge of the depletion of the laser-coupled

levels can be used to correct the model.

A combustion facility for operation up to 20 atm was developed to allow LSF measurements

of OH in high-pressure flames. Using this facility, we achieved partial saturation in laminar

high-pressure (_<12.3 atm) C2H6]O2/N 2 flames. To evaluate the limits of the balanced cross-rate

model, we compared absorption and calibrated LSF measurements at 3.1 and 6.1 atm. The

fluorescence voltages were calibrated with absorption measurements inan atmospheric flame and

corrected for their finite sensitivityto quenching with (1) estimated quenching rate coefficients and

(2) an in situ measurement from a technique employing two fluorescence detection geometries.

While the absorption and calibrated fluorescence measurements compare well at 3.1 atm, the OH

fluorescence values are -25% below the absorption measurements at 6.1 atm, indicating an

effective error of -25% in the balanced cross-rate model. We anticipate that with

atmospheric-pressure fluorescence calibration and a measurement or a reasonable estimate of

the quenching correction factor, one can measure OH concentrations within +50% at pressures

up to 10 atm.
CHAPTER1

INTRODUCTION

1.1Background

Measurementsof flame species by optical methods, such as laser-induced fluorescence

(LIF), have proved valuable inelucidating chemical and physical processes occurring in combustion

environments (Eckbreth, 1988). Fluorescence measurements are relevant to the study of a broad

range of practical combustion topics including turbulent flames, engine knock, pollutant formation,

and flame stability. Linear fluorescence methods are particularly usefulfor turbulent flames, where

2-D images ofrelative species concentrations can yield insight into the complex interaction between

chemistry and the flow field. In comparison, laser-saturated fluorescence (LSF), which is currently

limited to point-wise or perhaps 1-D measurements, is attractive because it can provide reliable

absolute species concentrations. Moreover, unlike linear fluorescence, LSF measurements are

insensitive to the rate coefficients for both laser excitation and collisional de-excitation. As a

consequence, in situ calibration of the fluorescence signal is not necessary: a calibration factor

determined in one flame (through techniques such as Rayleigh scattering or absorption) can more

easily be applied to other flames where calibration is more difficult or perhaps impossible [e.g.,

turbulent or sooting flames (Lucht et al., 1984, 1985; Drake et al., 1984, 1985)].

Since LSF was first proposed as a combustion diagnostic (Piepmeier, 1972a; Daily, 1977), it

has been used to detect the diatomic molecules (32(Baronavski and McDonald, 1977; Mailander,

1978), MgO (Pasternack et al., 1978), CN (Bonczyk and Shirley, 1979; Verdieck and Bonczyk, 1981),

CH (Mailander, 1977; Bonczyk and Shirley, 1979; Verdieck and Bonczyk, 1981; Kohse-Hoinghaus

et ai., 1983, 1984; Takubo et al., 1983), OH (Lucht et al., 1978, 1983, 1984, 1985; Kohse-Hoinghaus,

1983, 1984, 1986; Drake et al., 1984, 1985; Salmon and Laurendeau, 1985a, 1985b) and NH (Salmon

et al., 1984) in subatmospheric and atmospheric flames. Initial experiments (Pasternack et al.,

1978; Bonczyk and Shirley, 1978; Verdieck and Bonczyk, 1981) showed significant disagreement

between fluorescence and independent absorption measurements. Later, however, Lucht et al.
(1983) and Salmon and Laurendeau (1985a) compared LSF measurements of OH concentration

(calibrated using Rayleigh scattering) with independent absorption measurements in low-pressure

(72 torr) laminar H2/O2/Ar flames and demonstrated that saturation can be used to obtain accurate

number densities (+_15-25%) under these conditions.

2

r-

_tt/lU Wul

" ]7

Figure 1.1 Energy level structure and population transfer mechanisms. W/. and Wul are the rate

Coefficients for absorption and Stimulated ernission, respectively. Qr, Qv, arid Qe are

the rate coefficients for rotational relaxation, vibrational relaxation, and electronic

quenching, respectively.

In a typical experiment employing LSF, molecules initially in a rotational level within the lowest

vibrational level of the ground electronic state are excited through absorption to a rotational level

in the v" = 0 level of an excited electronic state (Fig. 1.1). Spontaneous emission, stimulated

emission, and the collisional energy exchange processes--rotational relaxation, vibrational

relaxation, and electronic quenching--transfer population from the upper laser-coupled level to other
rovibronic levels of the excited and ground electronic states. Likewise, in the ground state, the

lower laser-coupled level is re-populated bythese same process. The rate equation describing the

population of the upper laser-coupled level is

d N=

_= N,h,',o- N_(h'_,* Q,_) (I.1)

dl

where Nu and NI are the instantaneous populations of the upper and lower laser-coupled levels,

respectively, and Wlu and Wul are the respective rate coefficients for absorption and stimulated

emission. Qeff, the effective rate coefficient for collisional depopulation of the directly-excited level,

includes contributions from rotational and vibrational energy transfer, electronic quenching and

spontaneous emission. When the population of the directly-excited rotational level peaks during

laser excitation, steady-state conditions apply, and we can write

N ]

u

- (I.?)

IV t g_lfl,,+Qoftlh".,

where gl and gv are the respective degeneracies of levels I and u and guWut = g/Wl u. In general,

the population Nu can be related to N o,the desired unperturbed population of level/, by

N.+N,=(i-y)N ° (I.3)

The population N o is related to the species number density through the Boltzmann fraction, and

the parameter 1 - ,/is the fraction of the original population remaining in the laser-coupled levels

and is determined by the collision environment (i.e., the temperature and concentrations of the

collision partners for the molecule of interest). Combining Eqs. (1.2) and (1.3) gives

g. o (1 t) N. =_N,(I -y)a,.,

g_÷g,,

where ecsat, the degree of saturation, is given by

a,,o, = 1 + _-; (I.';)

and W" = Wtu/Qeff is the saturation parameter. We note that when gu = gl and W' _>10, then C_sat>_

95%.

The fluorescence signal is given by the integral of the local excited-state population over the

imaged volume; i.e.,

3
hcv /At (qll fv -- !

S/= 4r_ ) No(x, y, z)dV (1.6)

where _f (cm-1) is the frequency of the observed transition, Af (s-l) is the Einstein coefficient for

spontaneous emission, r/is the net efficiency of the detection system, and f_ is the solid angle

defined by the collection optics. When the unperturbed number density N °does not vary throughout

the imaged volume, we can solve for this quantity and obtain

NO gL+g, 4_St t = (1.7)

g" hcv/A_(q.(_) fv(l -V)a,°,dV

By rearranging this equation we obtain

(1-y)ct,o, dV g_+g., 4r(S//N o

<Fc>_ = , (1.8)

fva,.,dv g" hcv,A/(qf_) f,a,o,dV

which represents the spatially-averaged fraction of population remaining inthe laser-coupled levels.

Note that insofar as Wlu is independent of x (e.g., along the beam center line), (Fc) reduces to 1 -

./. The influence of the spatial profile of the laser beam and the degree to which 7 deviates from

zero complicates LSF measurements. These complications become more important at high

pressure.

1.2 Contents of Report

in this report, we focus on the efficacy of the LSF method for measurement of OH concentration

in high-pressure flames. In particular, we have investigated theoretically and experimentally the

validity of the balanced cross-rate model (Lucht et ai., 1980), which Lucht et al. (1983) and Salmon

and Laurendeau (1985a) used successfully at low pressure to relate the measured quantity Nu to

the unperturbed number density N o. In essence, the model states that the laser-coupled levels

experience approximately no net depletion; i.e.,

N=+ Nt,, N °, (I.9)

The utility of this model, as opposed to Eq. (1.3), is that it requires no knowledge of the collisional

environment; consequently, fluorescence measurements can be related more easily to the desired
speciesnumberdensity. When Eq. (1.9) cannot be used due to depletion of the laser-coupled

levels and this depletion cannot be accurately measured, LSF can lose much of its attractiveness

over linear fluorescence methods.

In the following chapter, we review the literature, with a focus on recent studies involving

laser-saturated fluorescence. This review also describes some alternate methods for making

quenching-insensitive concentration measurements in flames. Chapters 3 through 7 contain

papers which have been published, recently submitted, or are in preparation for publication in

refereed journals. In Chapter 3, which was published in Applied Optics (Carter et al., 1987), we

perform a feasibility study on the application of LSF to the measurement of OH concentration in

high-pressure flames. Using a numerical model for the collisional dynamics of the OH molecule

under nonuniform laser excitation, we investigate the effect of pressure on the validity of the balanced

cross-rate model and the sensitivity of the depopulation of the laser-coupled levels to the ratio of

rate coefficients describing (1) electronic quenching to the ground-state vibrational levels for which

v" > 0 and (2) vibrational relaxation from v" > 0 to v" = 0.

In Chapter 4, we describe the experimental apparatus. This includes a description of the

high-pressure combustion facility, which we have developed in the course of this work and which

will be used in future high-pressure combustion studies employing spectroscopic methods; this

section of Chapter 4 was published in the Review of Scientific Instruments (Carter, et al., 1989). In

Chapter 5, we present relative concentration measurements of OH in lean premixed C2Hs/O2/N2

flames at high-pressure (P _<12.6 arm). For this experiment we made no explicit use of saturation

of the transition; rather, we were interested in the feasibility of probing the reaction zone in

high-pressure laminar flat flames, thereby potentially allowing the study of high-pressure flame

chemistry. We also discuss problems encountered using LIF under these conditions. This chapter

has been accepted for publication as a short communication in Combustion Science and

Technology.

In Chapter 6, we describe experiments to evaluate the efficacy of LSF for OH concentration

measurements in high-pressure combustion environments. In addition to demonstrating that

saturation is possible in high-pressure C2H_O2/N2 flames, we evaluate the limits of the balanced

cross-rate model, Eq. (1.9), by comparing absorption and calibrated LSF measurements up to a

pressure of _6 atm. The fluorescence measurements are calibrated with absorption measurements

at 1 atm, and in this way, we compare (F¢)p, the spatially-averaged population fraction of the
laser-coupledlevelsat pressure P, to (Fc_1,the population fraction at atmospheric pressure. We

also present absolute OH concentration profiles for lean flames at about 1, 3, 6, 9 and 12 arm; to

our knowledge, these are the first high-pressure absolute concentration measurements of OH

performed with LIF. Chapter 7 describes the use of a method suggested by Cottereau (1986) for

making quenching-independent measurements with LSF. This technique employs two detection

geometries, including two monochromators. The ratio of the resulting fluorescence signals can be

used to correct the fluorescence signals for their finite sensitivity to quenching. Finally, Chapter 8

presents conclusions and recommendations for future work with LSF.

\
CHAPTER 2

LITERATURE REVIEW

2.1 Laser-Saturated Fluorescence

Utilization of laser-saturated fluorescence (LSF) as a diagnostic tool for concentration

measurements was initiallyproposed by Piepmeier (1972a), who noted that saturation of an atomic

transition would have the benefit of greatly increasing the fluorescence emission, while reducing

the dependence of the emission on changes in laser irradiance and collisional quenching. Daily

(1977) also realized the potential of the LSF technique to circumvent the so-called quenching

problem, thus allowing concentration measurements of atomic and molecular species in complex

reacting flows. Because of their simpler energy level structure and larger absorption cross section,

saturated fluorescence was initiallyapplied to atoms, with the majority of experiments using sodium

(Lucht et al., 1983; Alkemade, 1985).

The LSF method has been applied to the diatomic molecules C2, CN, CH, MgO, OH, and NH.

The aim of the initialexperiments (seeTable 2.1) was to make absolute concentration measurements

in flames; some of the deficiencies of these experiments included the following:

1. an inability to adequately determine experimental parameters such

as effective probe volume, photomultiplier gain, and detection

efficiency;

2. the use of a relatively high pressure, i.e., 1 atm, and excitation with

laser pulses of long temporal width, e.g. >_l#s, which can enhance

noncyclic processes such as laser-induced photochemistry and the

population of bath energy levels;

3. the lack of spectral, temporal, and spatial resolution, thus making

absolute concentration measurements difficult if not impossible.
Furthermore, as observed by Lucht (t981), since none of these experiments used more than one

flame condition, the dependence of the saturated fluorescence measurements on collisional

de-excitation could not be assessed.

Table 2.1 Initial experiments with laser-saturated

fluorescence.

Molecule Investigators

C2

CH

CN

MgO

OH

Baronavski and McDonald (1977)

Mailander (1978)

Mailander (1978)

Bonczyk and Shirley (1979)

Verdieck and Bonczyk (1981)

Bonczyk and Shirley (1979)

Verdieck and Bonczyk (1981)

Pasternack et al. (1978)

Lucht et al. (1978)

In 1980, Lucht et al. (1980b) used a set of rate equations, each describing the population of

a rotationaiievel in either the XZl](v"=0) or A2_+(v'=0) states of the OH molecule, to determine

the validity of the so-called balanced cross-rate model, which states that the population in the

laser-coupled levels remains approximately constant (and equal to the initial population of the lower

level), since the rates of transfer into and out of the coupled levels are balanced. That is,

N=+ N," IV ° (2.1)

where Nu and NI are the respective populations in the upper and lower laser-coupled levels and

N ois the initial population of level I. For the simulated conditions of the burnt-gas region in an

atmospheric-pressure H2/air flame, they found that with a nanosecond pulse-length laser, the

depopulation of the laser-coupled levels is small.

By employing the balanced cross-rate model, Lucht et al. (1981,1983) subsequently verified

experimentally that saturation of a molecular transition could yield accurate, absolute number

densities in low-pressure flames. Saturation of OH molecules was effected in flat laminar

subatmospheric H2/O 2 flames (diluted with either Ar or Nz) by using a Nd:YAG-pumped dye laser

with a pulse energy of -4 mJ at -310 nm and a nominal pulse length of 10 ns. To resolve the

temporal peak of the fluorescence pulse and thereby ensure steady-state conditions as well as
obtainafluorescencesignalatpeaksaturation,the350pswindowofa1-GHzsamplingoscilloscope

waspositionedat the temporal maximum of the fluorescence signal. The small spectral (-2 cm-1)

and spatial (45 #mx 3 ram) windows, provided by the monochromator exit and entrance slits,

respectively, enhanced the observed saturation. By pumping the P1(5) and Q1(10) lines (and

observing fluorescence from the R1(3) and P1(11) transitions, respectively) Lucht et at. (1983) were

able to achieve a degree of saturation estimated at 90-95%. This value, however, was uncertain

because the degree of saturation is difficult to estimate owing to nonuniform illumination of the

sampling volume (Salmon and Laurendeau, 1985a).

The detection parameters for the LSF measurements were obtained using Rayleigh scattering

(Lucht, 1981). The depth of the scattering volume, assumed to be equivalent to the height of the

volume, was estimated by opening the entrance slit until the signal became constant; the depth of

the fluorescence probe volume was also obtained in this way. To evaluate the efficacy of the LSF

method and the calibration procedure employing Rayleigh scattering, the fluorescence

measurements, each an average of 1200 laser shots, were compared with absorption

measurements at 72torr in lean, stoichiometric, and rich H2/O2/Ar flames. Figure 2.1 shows profiles

of OH number density for the lean flame determined from LSF and absorption measurements, and

the results from a calculation using a one-dimensional code for reacting flows (Peterson, 1981).

The OH concentrations derived from the Ql(10)/Pl(11) excitation/detection scheme were 30%

higher than values from the P1(5)/1:11(3) scheme; the profile shown in Fig. 2.1 is the average of the

two curves. The saturated fluorescence measurements were also corrected using a factor obtained

by matching the uncorrected measurement at the peak of the absorption profile with the

corresponding absorption concentration. At this peak, the LSF (uncorrected) and absorption

measurements were within 15%; however, the estimated path length was an important source of

uncertainty in the absorption measurements. In addition to the absolute concentration

measurements, Lucht et al. (1983) showed that over the range of 30 to 242 torr (in an H2/O2/N2

flame), the ratio of number densities from saturated fluorescence and absorption was approximately

constant, which shows that sensitivity to quenching has been reduced significantly.

Lucht et al. (1982) also made temperature measurements in the 72-torr, H2/O2/Ar flames

described above using the LSF method. As with concentration measurements with LSF, each

excitation/fluorescence line pair should have good spectral isolation in absorption and emission;

an additional constraint is that the two lower laser-coupled rotational levels must have a large energy

difference to reduce the sensitivity to systematic errors. Lucht et al. (1982) determined two
I

E

t,.)

Ow

v

.m

ta.)

C3

E

Z

"r"

O

3

2

I

I I

/

!

/

I

/

#

/

I

/

/

o Absorption

• Saturated Fluorescence

Corrected Saturated Fluorescence

o Theory ( Peterson, 1981)

•-'------ Temperature

l I

O0 I0 20

Distance Above Burner (mm)

-1500

-I000

- 500

v

=3

.e.-,

_J

Q..

E

Figure 2.1 Hydroxyl number density profiles in a lean H2/O2/Ar flame at a pressure of 72 torr and

an equivalence ratio of 0.6 (Lucht et al., 1981). The error bar on the absorption curve

corresponds to the standard deviation of the OH number densities calculated from ten

absorption lines,

10
temperature profiles from LSF in each of the lean, stoichiometric, and rich flames using the following

excitation/detection transitions: (a) Pl(5)/Rl(3) and Ql(13)/Pl(14); (b) Ql(10)/Pl(16) and

Ql(13)/Pl(14). The temperature profiles from LSF were compared with those calculated from

absorption and thermocouple measurements and from the one-dimensional chemical kinetics code

(Peterson, 1981). In the burnt-gas region of the lean and stoichiometric flames, temperatures

determined from scheme (a) consistently gave values 100.200 K higher than those from the other

methods, while measurements from scheme (b) yielded temperatures in good agreement with those

from absorption, thermocouples and numerical computation. However, in the burnt-gas region of

the rich flame, both LSF schemes gave temperatures higher than those obtained with

thermocouples and the calculations.

Based on the above experiments, Lucht et al. (1983) postulated that a significant source of

error in the LSF measurements could arise from polarization effects. In an anisotropic magnetic or

electric field, the total angular momentum J of a molecule is spatially quantized, and as a

consequence, under excitation by a linearly polarized source, fluorescence from the pumped level

can be significantly polarized. However, Altkorn and Zare (1984) showthat for an isotropic molecular

distribution of the J vectors, saturation decreases the degree of polarization. Furthermore, collisions

also reduce the fluorescence polarization, though both Doherty and Crosley (1984) and Zizak et

al. (1986) observed polarized fluorescence from the directly-excited level in atmospheric-pressure

flames.

Kohse-Hoinghaus et al. (1983,1984) used the LSF method to measure CH and OH

concentrations in a laminar premixed C2H2/O2 flame at 10 torr. To obtain concentrations from the

measured fluorescence signal, they (1) used the balanced cross-rate model and (2) solved

analytically the rate equation describing Nu [Eq. (1.1)] for a rectangular laser irradiance pulse,

I t = If 0 < t < "_t (2.2)

] t =0 t -> T t

where I _ is the peak irradiance produced by the laser system and rE was chosen so that the

rectangular pulse had the same energy flux (J/crn2) as the actual pulse. Comparing the results

from this model with one which used a more realistic laser pulse showed that this model

approximates well the saturation characteristics of a two-level system. The effective saturation

volume,

V. H= f(N./N_)dxdydz , (2.3)

]]
was then obtained using the irradiance distribution of the laser and the analytical expression for

Nu. This method does not make explicit use of the saturation condition, W' _ 1; rather,

Kohse-Hoinghaus et el. (1983,1984) extracted the effective quenching rate Qe_ by monitoring the

fluorescence decay. The success of this model is, of course, due in part to the reduced sensitivity

of Veff to the modelling parameters [e.g., the energy density (J/cm3) under saturated conditions].

Kohse-Hoinghaus et el. (1983,1984) verified their procedure by demonstrating good agreement

between the number density of OH determined from LSF and that measured from a fluorescence

method suggested by Stepowski and Cottereau (1979).

To build a data base of OH concentration measurements (for later comparison with calculated

values), Kohse-Hoinghaus et el. (1986) applied their saturated fluorescence technique to lean and

rich laminar premixed H2/O2(/Ar ), CH4/O 2, and C2H2/O2 flames at low pressure (30 and 72 torr).

To calibrate the fluorescence signals, they employed two independent methods: (1) measuring a

signal of known intensity produced by scattering the laser beam from a ground quartz disk; (2)

measuring Raman scattering from the Q branch of N2. The two methods gave the same calibration

constant within 5%. As explained above, this saturated fluorescence approach relies on a

measurement of Q_, the effective quenching rate; in the 30 torr flames, the variation of Qe_ with

position and equivalence ratio was less than 30%. In addition to the concentration measurements,

Kohse-Hoinghaus et el. (1986) measured temperature profiles in each of the flames using

laser-induced fluorescence (LIF). This was accomplished by delaying the fluorescence

measurements--relative to the laser pulse--until thermalization of the excited-state rotational

population had occurred; in the 72 torr flame, for example, Kohse-Hoinghaus et el. waited 60 ns to

collect fluorescence. Comparison of the OH concentration profile in the H2/O2/Ar flame (at 72 torr)

to calculated values (using the measured temperature profile) show good agreement.

Lucht et el. (1985) applied the LSF method to measurement of OH in near-sooting and sooting,

flat, laminar, atmospheric-pressure CHjO2/N2 flames. The LSF signals were calibrated using a

combined absorption/fluorescence method applied in a lean flame (_ = 0.78), where the OH

concentration was much greater; the LSF method could then be used to determine number densities

in three rich flames (_ = 1.68, i.85, and 2.02). With the absorption/fluorescence technique (Figl

2.2), the total number density, NT, at position x is determined from the path-integrated number

density by

N T(x)--- m] 2_N T(_;)a_, (2.4)

L _/f "

]2
where, L_tr, the effective path length for fluorescence measurements at position x, is derived from

the radial dependence of the normalized OH fluorescence signal, i.e.,

L;,,. f_i (.,)

Lucht et al. (1985) used the QI (8) and P1 (9) lines for excitation and detection, respectively, since

the population in the ground-state rotational level varies only 10% between 1000 and 2600 K. For

the rich flames, the principal source of interference--which determined the detection limit--for the

fluorescence measurements was rotational Raman scattering from N2, which was observable as a

consequence of the small OH concentration.

Absorption Beam

{_ _urner ;(/.(41

_ Laser Beam

Figure 2.2 Absorption/fluorescence sampling geometry.

A single-shot, LSF method has also been developed for application in turbulent flames (Lucht

et al., 1984; Drake et al., 1984). Hydroxyl concentration measurements were made at atmospheric

pressure in an H2/air, turbulent, diffusion flame with a spatial and temporal resolution of -0.1 ram3

and -2 ns, respectively, and an estimated accuracy of +_30%. As with the experiments in the rich

CH4/O2/N2 flames, the Q1(8)/Pl(9) excitation/detection line pair was used to minimize the

]3
dependence of N oon temperature. The calibration factor for the measurements in the turbulent

flames was obtained by replacing the nonpremixed burner with a laminar flat-flame burner and

comparing a concentration determined from the combined absorption/fluorescence method with

the relative concentration determined from the signal-averaged, LSF method. Probability density

functions of OH concentration from the laminar flame gave a relative standard deviation of about

7%; attenuating the fluorescence signal by a factor of 10 increased this figure to 25%, implying that

the precision of the single-shot data was limited by the number of photons collected. Examination

of the radial profiles of OH concentration in the laminar diffusion flames led Lucht et al. (1984) to

also conclude that at least in these flames, variation in the index of refraction was not great enough

to cause significant beam steering or defocusing. The LSF technique was then used to make

absolute concentration measurements in laminar (Reynolds number, Re = 660), transitional (Re

= 1600), and turbulent (Re = 8500) diffusion flames. These measurements confirmed, for the first

time, the existence of a superequilibrium concentration of OH in turbulent nonpremixed flames.

Drake et al. (1985) used these OH concentration measurements to compare the LSF method

with planar laser-induced fluorescence (PLIF) measurements. With PLIF, one expands the laser

radiation into a sheet and then detects fluorescence from the molecules in the plane of the beam.

In this experiment, fluorescence was detected with a 100 by 100 photodiode array camera system,

which imaged a 30 x 30 mm area of the flame and gave a spatial resolution of 0.3 x 0.3 x 0.4 mm.

The PLIF measurements were calibrated at the peak of the average fluorescence intensity by the

corresponding average OH concentration obtained with LSF. Once normalized in this way, the

agreement between average concentrations of OH from PLIF and LSF was surprisingly good in the

laminar, transitional, and turbulent flames, with the only significant disagreement occurring in the

fuel rich portion of the flame zone, where the electronic quenching rate (and therefore the

fluorescence yield) may change significantly. This conclusion was strengthened by calculations

of the variation in quenching as a function of the mixture ratio for an H2/air diffusion flame. These

calculations--using published collision cross sections and assumed temperature

dependencies--showed that indeed under these conditions the net electronic quenching rate is

sensitive to the local mixture ratio in the rich region of the flame. In the turbulent flame, agreement

between measurements of the rms fluctuations in OH concentration from the two methods was

also very good; in the laminar and transitional flames, however, the rms fluctuations measured by

PLIF gave values about twice those from LSF. Drake et al. (1985) suggested that the higher

14
fluctuationsinthelaminar and transitional flames resulted from noise in the PLIF detection system;

the fluctuations of OH concentraion in the turbulent flame, however, were sufficient to overcome

the noise in the detection system.

Salmon et al. (1984) appliedthe LSF method to measurement of NH concentration in a laminar,

premixed, CH4/N20/Ar flat flame at a pressure of 50 torr. As with the previous experiments of Lucht

et al. (1983,1984,1985), they used the balanced cross-rate model to relate the population in the

upper laser-coupled level to the population originally in the lower laser-coupled level. Excitation of

rotational transitions in the A3]-[-X3_-(0,0) band of NH was accomplished by Raman shifting the

frequency-doubled output of the Nd:YAG-pumped dye laser system; this gave a pulse energy of

about 2.5 mJ at 337 nm. Salmon et al. used the Pl(5)/Rl(3), Pl(7)/Rl(5), and Pl(11)/Rl(9)

excitation/detection line pairs, and optical detection parameters were determined with Rayleigh

scattering measurements. In addition, for accurate calibration using Rayleigh scattering, they made

corrections to the fluorescence measurements to account for poor saturation in the wings of the

laser profile (Salmon et al., 1985a). The resulting number densities were compared with those

calculated from the absorptionfluorescence method. At the peak NH concentration, measurements

from absorption and LSF agreed to within about 20%.

Salmon and Laurendeau (1985a), in the first paper of atwo-part study, presented a calibration

technique for LSF using Rayleigh scattering. The technique, which eliminates the dependence of

LSF on absorption measurements, makes use of an Abel transformation to extract _f(0,0), the

fluorescence emission at the beam center line, from It(y) [- J'_f(x,y)dx], the fluorescence intensity

profile, i.e.,

¢1(0'0) = ---_rmr _/(Y 2-r2) r°o '

where r is the distance from the beam center line and R is the extent of the measured fluorescence

intensity profile. The new calibration methodwas applied to LSF measurements of OH concentration

in a 72 tort H2/O2/Ar flame; these measurements were compared with those determined from the

combined absorption/fluorescence method described above, though the effective path length was

determined only at 5 mm above the burner. The absorption and LSF measurements showed good

agreement (within + 10%) to a height of -8 mm; thereafter, the two concentration measurements

showed increasing disagreement. Salmon and Laurendeau (1985a) attributed this deviation to

entrainment of the N 2 guard flow. Presumably, then, this disagreement between the LSF and

15
absorption measurements would be reduced by determining the effective path length Leff at heights

greater than 8 mm. Salmon and Laurendeau (1985a) also noted that the good agreement between

number densities derived from absorption and LSF suggests that the fluorescence was not

significantly polarized; however, they did not measure the degree of polarization.

In their second paper, Salmon and Laurendeau (1985b) presented an investigation of the

effects of nonuniform irradiance of the laser probe volume on LSF measurements. Using a measured

Rayleigh scattering profile and the assumption of an axisymmetric laser irradiance profile, they

deduced that the spatial dependence of the irradiance could be described with a Gaussian or a

quasi-Lorentzian function. To model the saturation effects within the probe volume, they employed

both a steady-state two-level and a time-dependent four-level model--two levels describing the

laser-coupled levels and two levels describing neighboring rotational levels in the respective ground

and excited electronic states. Salmon and Laurendeau were able to compare the relative saturation

along the center line of the laser beam with that averaged throughout the probe volume for spatial

excitation profiles described with Gaussian and quasi-Lorentzian functions. The saturation behavior

and the sensitivity to the center-line laser irradiance determined from the experimental data of Lucht

et al. (1981, t 983) were bracketed by the curves calculated using the Gaussian and quasi-Lorentzian

excitation functions. Salmon and Laurendeau noted that failure to account for the effect of the

wings can lead to erroneous results when the transition is assumed to be well-saturated and the

measurements are calibrated by a method that does not give an absolute number density (e.g.,

Rayleigh scattering).

To test the validity of the balanced cross-rate model, Salmon and Laurendeau (1985b)

proposed constructing curves of If(0)/Ef(0,0), the effective depth of the probe volume at the beam

center line, versus W/u/Qen, prepared by (1) varying the laser irradiance (and thus W/u) at constant

pressure and (2) varying the pressure (and thus Qeff) at constant laser irradiance. This effective

depth, D._, is proportional to the spatially-averaged population fraction remaining in the

laser-coupled levels,

/-

D_ = j( ] - y)a,o,(x, o)dx (2.7)

Here, 1 - ,,/is the fraction of the original population remaining in the laser-coupled levels and asat

is the degree of saturation,

a,a =[] +g"/(g'+g")?-' h"" ' (2.8)

16
where W" = Wlu/Qeff is the saturation parameter. Consequently, for the same saturation parameter

the ratio of b _ at two _lifferent pressures gives the ratio of the spatially-averaged population fraction

(see Eq. 1.8), i.e.,

[D:], [<,: >],

I= !

The ratio of (Fc) as a function of pressure to {Fc) at the calibration condition, and not the magnitude

of (Fc), is perhaps the more important parameter, since the variation of this ratio with collisional

environment increases the uncertainty of any number density measurement (when the calibration

and the desired measurements are performed under different conditions). One difficulty with this

approach, however, is assuring that W/u/Qeff is constant at different pressures, since the nature of

the broadening changes from predominantly Doppler (heterogeneous) broadening at 1 arm to a

combination of collisional (homogeneous) and Doppler broadening at higher pressures. Hence,

with increasing pressure, one cannot assure that WjQe. will remain constant when IL/Qe. is kept

constant. A similar qualitative approach is to simply compare the shape of the saturation curves

at different pressures. At pressures where depletion of the laser-coupled levels is significant, a

decrease in the slope of the curve at a high degree of saturation may be observable.

Using a rate-equation model, Campbell (1984a,1984b) simulated the dynamics of the OH

molecule for excitation of an isolated transition in the (0,0) and (0,1) bands of the A2_+-X2][

electronic transition. The model included about 40 rotational energy levels in each of the three

lowest vibrational levels (v=O, 1,2) of the ground and excited electronic states. The resulting 232

rate equations were solved and Nu, the population determined from the multilevel model, was

compared to N.,2, the population predicted from the simple two-level model (i.e., the balanced

cross-rate model). The conditions for the calculations simulated the burnt-gas region of a

stoichiometric CH4/air flame at 2000 K. Though collisional energy exchange processes in the

hydroxyl molecule have been studied extensively, in general, they are not yet described well by

theory or experiment. Therefore, Campbell studied the sensitivity of the ratio of populations N./Nu,2

to the rate coefficients describing the various collisional energy exchange processes (i.e., electronic

quenching and rotational and vibrational relaxation). The results show that prediction of species

number densities with the balanced cross-rate model can result in significant errors, particularly at

pressures of I atm and above. However, because Campbell used low excitation energies for many

17
of his cases, predicted errors using the two-level model arise from both depopulation of the

laser-coupled levels and a low degree of saturation. Nevertheless, Campbell's (1984a) results show

that the depopulation of the laser-coupled levels can be significant for high pressure or for long

temporal pulse lengths.

Cottereau (1986) suggested an alternative procedure which accounts for

spatially-nonuniform saturation. This technique, which could be used for single-shot LSF

measurements, requires two monochromators for the detection of the fluorescence--one with the

slit axis parallel (scheme A) and the other with the slit axis perpendicular (scheme B) to the laser

beam axis--to measure the fluorescence. The two detection schemes yield different saturation

functions, with the geometry having the slit axis parallel to the beam axis giving the higher degree

of saturation for equivalent slit dimensions (Daily, 1978). For scheme A, the fluorescence signal

can be obtained by combining Eqs. (1.4)-(1.6). Thus,

S/A=CN°(GAh;A-QA) " (! - y)1¢'(r)/t,'p'ctr ]0 2i[rl,.(r)/iV ,+g./[l.p.(g,+g,) ]

(2. )

while for scheme B the signal is similarly given by

Sja=CN°(rlsHsIV,_8) fo- (] -¥)w'(r)/w/dr 2W.(r)/idp.+g./[l+/p.(g,+g,) ] . (2.1 1)

where C accounts for constants such as the Einstein A-coefficient, r/Aand 7/8are the net efficiencies

of the respective fluorescence detection systems, 13Aand t3B are the solid angles of fluorescence

collection for the two geometries, and WA, HB and We are the relevant probe dimensions for the

two geometries. Consequently, the ratio of the two relationships is a function only of the center-line

saturation parameter, Wp', the spatial dependence of the saturation parameter, W'(r)/Wp', and the

ratio of the detection parameters for the two geometries, K; i.e.,

where the relationship

StA= { IL(r) }

(2.12)

IL(r) I_'(r) (2.13)

I,(0) l,¢p"

has been used. Insofar as the detection parameters and IL(r)/IL(0), the spatial dependence of the

laser irradiance, remain constant, SfA/SfB depends only on the center-line saturation parameter.

Applying this method requires the following procedure.

18
1. Selecta flame and calibrate the fluorescence signals from both

geometries (with measurements from absorption spectroSCopy or

Rayleigh scattering, for example).

2. tn the calibration flame, generate saturation curves for the two

geometries by varying the laser irradiance, being careful not to

change the spatial dependence of IL. Since the relative laser

irradiance is approximately equivalent to the relative saturation

parameter, Wr', when Q_ is constant, the curve SfA/SfB versus IL

defines the calibration function Wr'(SfA/SfB ). This function should be

defined over the range of expected values of Wr'.

3. At the condition of interest, measure SfAand SfB; from the calibration

Curve Wr'(SfA/SfB) determine the value of Wr'. With this value and

either saturation curve SfA(VVr') or SfB(VVr" ), determine the fractional

change in fluorescence intensity due to the change in the relative

saturation parameter. This value (for geometry A or B) is then used

to correct the fluorescence signal (from geometry A or B) for any

change in the saturation parameter between the calibration flame

and the flame of interest.

Thus, at the condition of interest, the number density NT is given by

N

NT=Sj.fcfo ' ]-_ f, , (2.14)

!

where fc (cm-a/V) is the calibration factor (determined in step 1), fo is the quenching correction

factor, which accounts for the fractional change in Wr', and the fi are additional correction factors

(for variations in Boltzmann fraction, etc.). Use of this technique is discussed in detail in Chapter

7.

2.2 Other Methods

We now discuss alternate optical methods for quantitative detection of molecular species

such as OH in practical combustors; like LSF, these methods potentially circumvent the so-called

quenching problem. First, Barlow et al. (1989a,1989b) reported single-shot measurements of OH

using simultaneous linear LIF and vibrational Raman-scattering of H2, 02, N2, and H2O (using the

Stokes bands) in nonpremixed turbulent jet flames. The N2 anti-Stokes and Rayleigh scattering

19
signals were monitored; flame temperatures could then be calculated from the N2 Raman

measurements or more accurately from the ideal gas law, by using the total number density derived

from the Raman measurements. Two lasers, with colinear beams, were used: (1) DIANA, a

flash-lamp-pumped dye laser (,_ = 532 nm, with 1 J for each 2-#s pulse) for the scattering

measurements, and (2) a Nd:YAG-pumped, frequency-doubled dye laser for the OH fluorescence

measurements. To ensure operation in the linear fluorescence regime, Barlow et al. employed a

large beam diameter at the probe volume and excited the $21(8) transition [of the (v'= 0,v'= 0) band]

using -0.1 mJ per pulse. Rather than monitoring the P- or Q-branches, they detected the weaker

R-branch to reduce fluorescence trapping; the peak fluorescence signals in the turbulent flame

corresponded to -600 photoelectrons. In addition, part of the UV laser beam was split off and sent

to a laminar flame where the fluorescence was monitored to ensure that the laser wavelength was

centered on the $21(8) line. The 10 signals (6 scattering, 2 fluorescence, and 2 photodiode signals)

were each recorded with a gated integrator, and the signals were then processed with a computer.

To accurately calculate OH number densities, correction factors were applied to the recorded

fluorescence signals (on a shot-by-shot basis) to account for variations in quenching and the ground

state Boltzmann fraction. In addition Barlow et al. (1989a, 1989b) applied a correction factor for

the average amount of fluorescence trapping; this was estimated from horizontal fluorescence

scans across the turbulent flame. This problem could be avoided by exciting transitions in the (1,0)

band and detecting (1,1) band fluorescence; however, sufficient quenching data is not available

for the A2_.+ (v= 1) state. To correct the fluorescence yield for changes in electronic quenching,

Barlow et al. fit collisional cross sections calculated by Garland and Crosley (1986) to a relationship

of the form

o(T)= A_ ÷ A2o -T/l°°° + A3e -T/2°°° (2.15)

where T (K) is the flame temperature. The resulting quenching correction factor was small when

the flame was locally lean and increasingly large when the flame was locally fuel-rich.

Andresen et al. (1988) discussed the potential of reducing the sensitivity of LIF measurements

to quenching by exciting the molecule of interest to a fast predissociating state. Predissociation is

a process whereby a molecule undergoes a radiationless transition from a discrete state to a

continuous state--one corresponding to dissociation--at the same energy (Herzberg, 1950).

Sensitivity to quenching is reduced when the time for predissociation is short compared to the time

for collisional quenching. Though Andresen et al. (1988) focus on the efficacy of this approach for

2O
temperaturemeasurements, the same technique could be applied to concentration measurements

as well. In particular, Andresen et al. (1988) suggest that a KrF exctmer laser, with a tunable range

from 248.0 to 248.9 nm, could be used to detect the OH, 02, and H20 molecules. With the high

energies per pulse of excimer lasers (e.g., 400 mJ/pulse in a bandwidth of 0.5 cm-1 with their KrF

laser), 2-D concentrations or temperatures could be obtained even while exciting very weak

transitions. For OH, the KrF laser was employed to excite a number of transitions in the

A2:C+.-XZ][(3,0) band; flame temperatures were obtained from excitation spectra, while monitoring

fluorescence only from the (3,2) P-, Q-, or R-branch transitions originating from the directly-excited

rotational level. To minimize polarization effects, fluorescence was measured from (1) P-or R-branch

transitions when a Q-branch transition was excited or (2) a Q-branch transition when P- or R-branch

transitions were excited. Andresen et al. (1988) note that accurate single-shot temperature

measurements may be possible with 02 and OH by excitation of two closely-lying lines. For instance,

they observe that the P2(8) (_ = 248.457 nm) and the R1(15) (,_ = 248.476 nm) lines of OH could

be excited simultaneously with a broad-band excimer laser; because the ground states of these

transitions are separated by -3000 cm -1, the method offers good sensitivity to temperature.

However, measurements of OH fluorescence spectra show some rotational and vibrational energy

transfer within the 2_+ state in H2/O 2 and C4Hlo/O 2 flames, demonstrating that the fluorescence

measurements are somewhat sensitive to quenching. In addition, with an assumed temperature

and rotational energy transfer cross section (in the v'=3 state), Andresen et al. estimated the

predissociation time to be 100 ps. Predissociation times for the 2E +,v" = 5 and 6 states have been

determined to be less than 10 ps (Carlone and Dalby, 1969).

Schwarzwald et al. (1987,1988) reported measurements of quenching lifetimes for OH

(1987,1988) and CN (1988) in atmospheric-pressure flames with a streak camera and a home-built

picosecond laser. The laser system included an excimer laser (delivering 8 ns pulses at 308 nm),

which pumped a quenched transient dye laser (QTDL). The 200-ps pulses from the QTDL laser

then pumped a distributed feedback dye laser (DFDL); the resulting laser pulses had a temporal

width of 20-40 ps and a bandwidth of 0.003 nm. Wavelength tuning the laser system over a range

of several nm was achieved via rotation of a mirror system in the DFDL (Schwarzwald et al., 1988).

The output of the DFDL was then frequency doubled using a #-BaB204 crystal, yielding an energy

of 15 #J for OH excitation and 5 to 20 #J for CN excitation. For OH, fluorescence lifetimes, which

were averaged over 50 to 100 laser shots, of the N = 5 rotational level in the 2_+ state were -2 ns

over a range of equivalence ratios and throughout the burnt-gas region in premixed CH4Jair flat

21
flames.Thoughthismethodcanbeappliedto laminarhigh-pressure(>1 atm)flamesto correct

fluorescenceyieldsfor quenchingvariations,it cannotcurrentlybeapplied to turbulent flames,

since single-shot fluorescence lifetime measurements are required.

Elzinga et al. (1987) and Fiechtner et al. (1988,1989) described the asynchronous optical

sampling (ASOPS) method, which unlike fluorescence techniques uses a coherent beam to carry

the signal. The ASOPS method is similar to the conventional pump/probe technique, but it employs

two dye lasers (a pump and a probe laser), each of which is synchronously-pumped by the second

harmonic of a mode-locked Nd:YAG laser. By mode-locking the two Nd:YAG lasers at slightly

different frequencies, the picosecond pulses of the pump and probe lasers walk in and out of phase

at the beat frequency. This provides a method whereby sub-nanosecond events are mapped into

the millisecond regime, thus obviating the need for fast detection electronics. The method not only

allows measurement of collisional quenching rates, but also a means to make quenching-corrected

concentration measurements on a time scale shorter than that for turbulent fluctuations. One goal

of this work is to detect important flame radicals such as OH, though to date detection only of

rhodamine B (Elzinga et al., 1987) and sodium (Fiechtner et al., 1988; 1989) has been reported.

Recent experiments (Fiechtner et al. 1989) used mode-locking frequencies of -82 MHz and a beat

frequency of -10 kHz to measure the quenching rate coefficient of the 3P state of sodium in a

laminar C2H4/O2/N2 flame. The pump and probe beams were crossed at -5 °, resulting in an

estimated interaction length of 0.5 mm. In one arrangement, the pump laser was tuned to the

3S1/2--,3P3r_ transition (589.0 nm), while the probe laser was tuned to the 3P1/'z-,5Slr2 transition

(615.4 rim). To increase the signal-to-noise ratio a dual-photodiode voltage-subtraction detector

(i.e., a differential detector) was used. A portion of the probe beam (A) was picked off before

interaction with the pump beam in the flame. Its intensity (measured by one of the photodiodes)

was then adjusted to equal the intensity of the signal-carrying probe beam (beam B, measured by

the other photodiode) with no sodium present in the flame; to derive the absorption signal, the

intensity of beam A was then subtracted from that of beam B. Using this differential detector and

a digitizing oscilloscope, Fiechtner et al. (1989) were able to measure quenching rate coefficients

by averaging only 256 decay curves. A typical value for this flame was 1.8 x 109s-l, withthe average

decay curve exhibiting 0.4% relative error.

22
CHAPTER3

FEASIBILITYOFHYDROXYLCONCENTRATIONMEASUREMENTS

BYLASER-SATURATEDFLUORESCENCEINHIGH-PRESSUREFLAMES

3.1Introduction

Since laser-saturated fluorescence (LSF) was first proposed as a combustion diagnostic

(Piepmeier, 1972; Daily, 1977), the method has been used to detect the diatomic molecules C2

(Baronavski and McDonald, 1977), MgO (Pasternack et al., 1977), CN (Verdieck and Bonczyk, 1981 ),

CH (Verdieck and Bonczyk, 1981; Kohse-Hoinghaus et al., 1983), OH (Kohse-Hoinghaus et al.,

1983; Lucht et al., 1983; Salmon and Laurendeau, 1985a), and NH (Salmon et al., 1984) in

atmospheric and subatmospheric flames. Although initial experiments disagreed with absorption

measurements by factors of two or more, recent experiments provide results which show agreement

within 15-25% (Lucht et al., 1983; Salmon and Laurendeau, 1985a; Salmon et al., 1984).

The saturated fluorescence method is attractive because, in principle, one can eliminate a

primary difficulty of linear fluorescence--the dependence of the fluorescence signal on both the

collisional environment and the laser power fluctuations. In typical laboratory experiments using

nonsooting laminar flat flames, one can usually calibrate fluorescence measurements using

absorption, and thus the LSF method offers no substantial advantage. For nonpremixed flames,

planar fluorescence (which is a linear technique because of the low irradiance of the expanded

beam) can provide 2-D images of the reaction zone in a single laser shot (Lee et alo, 1986). However,

in turbulent flames, particularly in rich conditions (Drake and Pitz, 1985), characterization of the

collisional environment can be difficult if not impossible. Consequently, the LSF method is valuable

for quantitative concentration measurements in such practical systems.

Although saturated OH fluorescence has been applied at atmospheric pressure to sooting

laminar flames (Lucht et al., 1985) and to turbulent nonpremixed flames (Drake et al., 1984; Lucht

et al., 1984), the method requires further study for application in complex high-pressure combustion

environments. In this chapter, we present the results of a numerical investigation into the effect of

23
pressureonthe efficacy of the balanced cross-rate model and thus on the potential for saturated

fluorescence measurements at pressures > 1 arm So that the sole collision partner for the OH

radical is H20, we performed the calculations for the burnt-gas region of a stoichiometric H2/O2

flame at 2000 K.

3.2 Adequacy of the Rate-Equation Approach

The rate-equation approach, which we have used to model the excitation dynamics of the

OH molecule, is conceptually as well as mathematically simpler than the quantum-mechanical

density-matrix approach. Unfortunately, modelling the excitation process with rate equations fails

to account for optical nutations which can arise during excitation by coherent radiation. Such

coherent transients, i.e., oscillations of the excited-level population, will not be observed when (1)

the effective coherence time of the excitation source is short compared to the reciprocal of the

absorption or stimulated emission rate coefficient (Altkorn and Zare, 1984), or (2) the characteristic

time for damping is short compared to the smallest time interval which can be resolved with the

detection system (Macomber, 1968). A second complication is that our rate-equation approach

fails to deal with the distribution of modes characteristic of Nd:YAG-pumped dye lasers. When the

distribution of energy among the modes varies either from pulse to pulse or during an individual

pulse, fluctuations in the excited-level population can occur. This is particularly true at

subatmospheric pressure since the linewidth of the excited transition is narrow and primarily Doppler

broadened.

At sufficiently low pressure, the characteristic time for damping is long, and thus the

rate-equation approach might not be expected to adequately model the population in the

laser-coupled energy levels. However, as observed by Aitkom and Zare (1984), the utility of the

rate equations is not as limited as the above criteria suggest. First, because the spatial profile of

pulsed dye lasers is inhomogeneous, the integration of fluorescence across the probe volume will

usually mask coherent effects. Second, averaging of the fluorescence signal over many laser shots

will also mask fluctuations-in the excited-state population, thus-erlsuring the adequacy of the

rate-equation approximation even in cases where it is inappropriate for individual laser shots.

At higher pressures the collision frequency rises; hence, the characteristic time for damping

decreases and the transition linewidths are broadened. One important consequence is that the

population of the excited level becomes less sensitive to the distribution of mode intensities since

more modes are now connected to the excited transition. A second consequence is that the larger

24
number of exciting modes decreases the effective coherence time of the laser. A third consequence

is that with the greater collision frequency, oscillations in the excited-state population are more

quickly damped out. Thus, with increasing pressure, the rate-equation approach more closely

approximates the density-matrix approach. We also note that Lucht et al. (1984) have made

single-shot LSF measurements of OH concentration in a laminar, atmospheric, H2/air flame,

Examination of the measured probability density function demonstrates that significant fluctuations,

owing to either coherent effects or variations in the modal intensity distribution, were not present

at the peak of the fluorescence pulse.

3.3 The LSF Method

During laser excitation, molecules initially in a rotational energy level within the lowest

vibrational level of the ground electronic state are excited through absorption to a rotational level

in the ground vibrational level of an excited electronic state. Spontaneous emission, stimulated

emission, and collisional energy-exchange processes--rotational relaxation, vibrational relaxation,

and electronic quenching--transfer population from the directly-excited rotational level to other

rotational levels in the upper and the ground electronic states (Fig. 3.1).

The rate equation for the population of the upper laser-coupled level is

dN.

--=dr N,Iv'_=-N.(V.t +Q.It) ' (3.1)

where NI and Nu are the populations of the lower and upper laser-coupled rotational levels,

respectively, Wlu and Wut and are the respective rate coefficients for absorption and stimulated

emission, and Qe. is the effective rate coefficient for depopulation of the directly-excited level by

both collisional-processes and spontaneous emission. Upon laser excitation, the population peaks

and steady-state conditions apply, so that Eq. (3,1) becomes

N. l

-- = , (3.2)

Ni g_/g=+Q,tt/_zi.

where gu and gl are the respective degeneracies of the upper and lower laser-coupled levels and

guWut= glWlu.

The population of the laser-coupled levels can be related to the unperturbed population N o

of the lower laser-coupled level by

25
Wlu Wul

/

II

il

Figure 3.1 Energy level structure and population transfer mechanisms. Wju and Wul are the rate

coefficients for absorption and stimulated emission, respectively. Qr, Qv, and Qe are

the rate coefficients for rotational relaxation, vibrational relaxation, and electronic

quenching, respectively.

N.+N,=(I -y)N °, (3.3)

Here, 1 - -/is the fraction of the original population remaining in the laser-coupled levels, and N o

is related to the desired spectes number density through the Boltzmann fraction. At low pressures,

-7_ 0 and Eq. (3.3) reduces to the familiar balanced cross-rate model, Nu + Nt _ N o(Salmon and

Laurendeau, 1985; Lucht et al., 1980). Combining Eqs. (3.2) and (3.3) yields

N.= --g" N Ot(l-y)a,o t , (3.4)

g_+g.

where asat, the degree of saturation, is

26
h,/, ,

and the saturation parameter W' is given by

( 3.'J )

hr'= 1,__=/Q,ff (3.6)

Equation (3.4) demonstrates that the species number density can now be calculated from N oby

determining Nu from the measured fluorescence signal and accounting for asat and 3'.

Because the spatial irradiance profile of the laser is nonuniform, the population in the upper

laser-coupled level will vary with position. Consequently, the fluorescence intensity across the

entrance slit to the monochromator must be expressed through an appropriate integral of Nu. Figure

3.2 shows the fluorescence collection volume as determined by the image of the monochromator

entrance slit along the laser beam. For this geometry, the fluorescence intensity (W/cm2-sr) across

the image of the slit is given by

hcvlA! f N,(x, y,2)dx (3.7) /t(Y'z)= 4n .,

where _f (cm -1) is the frequency of the observed transition, Af (s-1) is the rate coefficient for

spontaneous emission, and Nu(x,y,z) is the local number density of the upper laser-coupled level.

If the dimensions of the slit imaged on the laser beam are small compared to the characteristic

dimensions for the radial and longitudinal variation in laser irradiance, then the fluorescence intensity

can be taken as approximately uniform across the monochromator slit [i.e., If(y,z) _=] o= lf(O,O)].

Under these conditions, Eqs. (3.4) and (3.7) can be combined to obtain

No=g,+g._ 4_1_ ('3.8)

g" ttcv/Al f (l - V)e,.,ctx

where f(1 - '7)asatdx is the effective depth of the collection volume (i.e., the depth for which the

fluorescence signal is equivalent to that resulting from complete saturation and no depopulation

from the laser-coupled levels) (Salmon and Laurendeau, 1985). Hence, Eq. (3.8) finally expresses

the unperturbed number density N °as a function of the measured fluorescence intensity ! o.

Further understanding can be gained by rearranging Eq. (3.8) to give

27
/ \

\

\

\

z

\

\

\

\

\

Collection

Volume

Axis

Figure 3.2 Geometry of the fluorescence collection volume.

f( 1 -

y)a,_,dx

. A/O=__gt ÷gU 4nl_ (,3.9)

f a,atd_x g" hcvlA/ f a,atd.\

The right-hand side of Eq. (3.9) does not depend explicitly on the depopulation of the laser-coupled

levels. Rather, depletion is reflected in a decrease in I o, and because N o is unaffected, /Fcl =

[f(1-_)c_satclx/f(_satdx ] represents the spatially-averaged population fraction remaining in the

laser-coupled levels. Along the center line of the laser irradiance profile, {Fc/ reduces to 1 - %

which is equivalent t0 the ideal case of a spatially:uniform irradiance profile.

The parameter 1 - -),is approximately unity, and thus the balanced cross-rate model is valid

at time r, if the integrated population transfer rates into (Rin) and out of (Rout) the laser-coupled

levels are balanced, i.e.,

'(R,,- " 0 (3.10) R o_, ) dt

28
For an ideal two-level system, Rin = Rout, and Eq. (3.10) holds exactly; however, for real multilevel

systems, the rates are not likely to equal one another. Hence, those processes which transfer

population to levels other than the laser-coupled levels complicate the use of LSF for measurement

of species concentrations.

Whereas rotational energy transfer in the ground electronic state replenishes the

laser-coupled levels, rotational transfer in the excited electronic state depletes the laser-coupled

levels. Rotational transfer to the nearby rotational levels of the excited state provides additiona_

pathways for electronic quenching to the ground state. Those molecules quenched into the v'" =

0 level are again part of the rotational reservoir for the laser-coupled levels; however, the molecules

quenched to the v" > 0 levels may cascade slowly to the ground vibrational level, thus further

depleting the laser-coupled levels. Consequently, the fractional depopulation _/is sensitive to the

rate coefficient for rotational energy transfer in the excited electronic state for two reasons. First,

an increase in Qr, the rate coefficient for transfer from the upper laser-coupled level, further populates

the surrounding rotational manifold resulting in a depletion of the v" = 0 level and therefore the

laser-coupled levels. Second, an increase in Qr(u) provides more molecules that can be quenched

to the v" > 0 levels, again resulting in a depletion of the laser-coupled levels.

The condition for saturation at any location is given by W' l_ 1. Thus, from Eqs. (3.4) and

(3.5), (xsat-' 1 and

N " g----L---"( I - y)N ° (3. I 1 )

u I

gl+g_

When W" >__10 and g, = gl, the degree of saturation is greater than 95%. Also, when the spectral

irradiance profile of the laser is broad compared to the absorption profile, the saturation parameter

is nearly proportional to the ratio of laser irradiance _N/crn2) to pressure, and therefore the laser

irradiance must increase approximately linearly with pressure to maintain the same degree of

saturation. For example, with an H2/O2/Ar flame at atmospheric pressure and a laser pulse

containing -4 mJ of energy, the maximum saturation parameter achievable along the center line

of the beam with our Molectron Nd:YAG/dye laser system and a focused spot size of about 0.4 mm

is estimated to be 40 (Salmon and Laurendeau, 1985b). To ensure that at peak excitation W" >_

10 in this flame at pressures above about 4 arm, we would need to increase the laser irradiance by

decreasing the focused spot size of the beam.

29
3.4 Laser.Excitation Dynamics

We have modeledthe population transfer between and within the A2]C + and the x2r[ vibrational

manifolds of OH using a linear system of rate equations. The upper electronic manifold is described

by a single vibrational level, v" = 0, containing 29 rotational levels (N' = 0 to N' = 14; J' = N" _+1/2).

The lower electronic manifold has two vibrational levels, one being the v" = 0 level, containing 26

rotational levels N" = 1 to N" = 13; J" = N" _+ 1/2), and the other being a vibrational bath level v"

> 0 with no rotational levels. Modelling the v" > 0 levels as a single level is a consequence of the

dearth of experimental and theoretical data describing quenching into and vibrational transfer within

and out of the v" > 0 levels of the hydroxyl molecule at flame temperatures.

A general FORTRAN 77 program, compatible with the Cyber 205 at Purdue University, was

written to set up the Jacobian matrix describing the system of 56 rate equations for this model. To

account for the effect of the temporal and spatial dependence of the irradiance for a laser pulse,

the rate equations are integrated temporally for each specified spatial location. The

spatially-averaged population fraction in the laser-coupled levels, (Fc), can then be obtained from

_,+g.f (tv./NT)dx

<F_>= (3.12)

g= / _,atdx

which is derived by combining Eqs. (3.7) and (3.9).

For the rotational levels not coupled by the laser (i_,u,/) the generalized rate equation at any

location is

dN(i--._)=Z[N(j)Q(j,i)]-N(i)EQ(i.]) , (3.]3)

di j I

where i and j refer to all energy levels in both the upper and lower electronic states. Q(i,j), the rate

coefficient for transfer from level i to level j, is the sum of rate coefficients for spontaneous emission,

electronic quenching, rotational relaxation, and vibrational relaxation,

Q(i, ]) = A(i. j) + O..(i, j) + Or(i, j) + O,,(i, j) (3. ] 4)

The above rate coefficients are nonzero only when levels i and j are physically connected. For

example, the rate coefficient for spontaneous emission A(i,l') _ 0 only when level i is radiatively

coupled to level j.

Similarly, for the upper laser-coupled level (i=u) the local rate equation is

3O
tit

!

Comparing Eqs. (3.1) and (3.15), the effective rate coefficient for depopulation

laser-coupled level is given by

(3. I'.;)

of the upper

Q,/,,=_Q(u,j)-¥(u---_) 'z N(j)Q(j.n) (3.16)

/

For the lower laser-coupled level (i=/),

¢IN(I)=_].¥(j)Q(j,/)]+N(t_)I,.,.,__N(/)[_Q(I,j)+ [,',,1 rtt

I

(:3.17)

3.4.1 Rotational Relaxation Model

Lengel and Crosley (1977) initiallysuggested empirical equations for rotational energy transfer

in OH at room temperature, and later, Chan and Daily (1980) modified these equations for use at

flame temperatures. Recently, Lucht et al. (1986) further modified the relations and provided

parameters for collisions with water vapor (Table 3.1), which were derived from a comparison of

experimental spectra and synthetic spectra generated with a dynamic model similar to the one

described in this paper. The comparison employed experimental spectra from excitation of the

P1(2), Pt (5), R2(4), and QI (10) lines of OH in an H2/O2/N 2 flame (Dieke and Crosswhite, 1962).

The empirical equations describing the collisional cross section for upward rotational transfer

from level i to level j [E(j) > E(i)] are

(_r(i,j)=B[N'(i)]g(j)oxp[F(AN',AJ')-/t(3OO/T)gAE] (3.18)

for transfer with AN" #=0, and

a,(i, j) = [ B[ N'( i)]g(j)(T /300 )* (3.19)

for transfer with _N' = 0. Briefly, BIN'(i)] (cm2) accounts for the variation in cross section with initial

rotational quantum number N'(i), ['(AN',&J')accounts for changes in the quantum numbers N' and

J' during collisions, and A (cm) and 0 determine the dependence of the cross section on the energy

d'fference AE (cm-_) between levels i and j. For the AN" = 0 case, the constant f corrects the

BIN'(i)] values and _ accounts for the influence of flame temperature. Though these parameters

were determined for rotational energy transfer in the excited electronic state, we use them to describe

rotational transfer in the ground electronic state, since the rotational constants for these two states

are nearly the same for the hydroxyl radical.

31
Table 3.1 Optimized rate parameters for rotational transfer in A2_ + (v=0) OH

for collisions with H20 (Lucht et al., 1986). _

A = 0.0060 cm f = 0.10 8 = 0.7 _ = 0.8

N' or B [N'] F(AN'=&J') r(AN#=&J') er(i)

AN" 10"16 cm 2 10-16 cm2

0 1.60 .... 85

1 1.60 1.40 -0.50 117

2 1.45 1.20 -1.00 145

3 1.30 0.30 -1.30 167

4 1.20 -0.25 - 1.50 184

5 1.20 -1.20 -2.00 204

6 1.00 -1.90 -2.50 203

7 0.85 -3.00 -3.00 194

8 0.70 -3.80 -3.80 176

9 0.50 -4.70 -4.70 148

10 0.40 -6.00 -6.00 122

11 0.40 -6.00 -6.00 108

12 0.40 -6.00 -6.00 102

13 0.40 -6.00 -6.00 92

14 0.40 -6.00 -6.00 66

a or(i), the total cross section for rotational transfer from level i [at(i) = _-

]*l

or(i,j)], is calculated from the listed parameters and a temperature of 2000 K.

The collisional rate coefficient for any population transfer process is related to the respective

cross section by

Q,,(i, j) = __ Nqciq ( i. j)[J q (3.20)

q

where Nq (cm -3) is the number density of the collision partner q, (;_ (i,j) (cm2) is the cross section

for collisions with species q, v q (cm/s) is the average relative velocity between OH and species q.

and the subscript m denotes the mode of energy transfer (e, r, v). Note that Eq. (3.20) accounts

for the influence of pressure on the LSF signal through the number density Nq. For upward rotational

relaxation, Qr(i,j) is obtained by substitution of Eqs. (3.18) or (3.19) into Eq. (3.20), and for downward

rotational transfer, the rate coefficients are calculated using the principle of detailed balancing with

a translational temperature of 2000 K_

32
3.4.2 Electronic Quenching Model

To our knowledge, the distribution of electronic quenching to the vibrational energy levels of

the ground electronic state of the hydroxyl radical is not adequately described by theory or

experiment. Thus, to study this distributive effect, we formulate electronic quenching as a function

of the parameter fb, the fraction of molecules quenched to the vibrational bath level. For transfer

to v" > 0,

Q,(_,b) = fbQ,(i) (3.21)

and for transfer to v" = O,

Q,(i.j)=(l-/,)Qo(i)/n_ , j,,b (._.22)

where Qe(i) is the total rate coefficient for electronic quenching from rotational level i in the excited

electronic state, and nGis the number of rotational levels in v" = 0. Thus, we assume that quenching

is equally likely to each rotational level of v" = 0. Copeland et al. (1985) have measured the

dependence of quenching on rotational level for A2_+(v'=0) OH with several collision partners at

room temperature. However, the effect of flame temperature on the observed rotational-level

dependence is uncertain. Hence, we use quenching rate coefficients that are independent of N'.

Fairchild et al. (1983) measured electronic quenching cross sections for collisions of OH with

several species at elevated temperatures (- 1000-1500 K). We have extrapolated the average cross

section for collisions with H2O, c%= 26.3 x 10-16 cm2 at about 1200 K, to a temperature of 2000 K

by using the approach of Drake and Pitz (1985),

or,(2000) = <_°{]200)(]20012000) ``2 (3.2:_)

The resulting cross section for electronic quenching is 20 x 10-16 cm2; the rate coefficient Qe is

obtained from ae via Eq. (3.20).

3.4.3 Vibrational Relaxation Model

The existing experimental data for vibrational energy transfer within the OH molecule are from

studies of the A2]C+ state (Schofield, 1979; German, 1976; Lengel and Crosley, 1978; Smith and

Crosley, 1983). Consequently, as with rotational relaxation, one can only infer rate coefficients for

vibrational transfer inthe ground 2T[state. In an experiment performed at room temperature, Lengel

and Crosley (1978) determined cross sections forvibrational transfer in the excited state of OH due

to collisions with atomic and diatomic species. They suggest that energy transfer between OH and

33
the diatomic collision partners takes place during long-lived collisions, resulting in efficient transfer

of vibrational energy (e.g., with N2 as the collision partner, av = 24.7 x 10-16cm2 for v" = 1 --, 0

transfer). Recently, Crosley and Smith (1983) investigated vibrational transfer in the burnt-gas

region of a CH4/air flame (T = 1900 K) and deduced the Qv/Qe ratio for A2P.+ (v"= 1-,0) as a function

of rotational quantum number N' in v" = 1. The values of Qv/Qe were found to decrease with

increasing N', ranging from about 0.65 at N' = 1 to about 0.4 at N' = 15.

Because of the uncertainty in the cross sections for electronic quenching to the v" = 0 level

and for vibrational transfer in the ground state of OH, we found it convenient to express the rate

coefficient for vibrational relaxation from the bath level to the v" -- 0 level in terms of the parameter

fvand the quenching rate coefficient Qe. As with quenching to v" = 0, we assume that the population

transfer is independent of the rotational level in v" = 0; therefore,

Q_(b, j) = [,Q,/_c (3.2J.)

Consequently, the effect of quenching to the v" > 0 vibrational levels is qualitatively described by

the parameters fb and fv. Because the path by which molecules excited to the upper electronic

state return to the v" = 0 level of the ground electronic state can be complicated, we do not attempt

to attach a strong physical meaning to that portion of the dynamic model describing the bath level.

If, for instance, the distribution of OH molecules quenched to the ground electronic state changed

to favor the higher vibrational levels, the net rate of population transfer back to v" = 0 might decrease,

resulting in a larger population in the vibrational bath level and thus a greater depopulation of the

directly-excited levels.

3.4.4 Excitation Model

The frequencies of the OH transitions for spontaneous emission are tabulated in Dieke and

Crosswhite (1962), and the associated rate coefficients for spontaneous emission, A(i,j), are taken

from Dimpfl and Kinsey (1979). For each of the computational runs, the transition is excited with a

pulse described by a Gaussian dependence in both space and time,

lg ,.( x, t) = Id f, exp(- x2 /r_)exp[-( t- t +,)2 / t_ ] (3.2,'5)

Here, x is the lateral distance from the center line of the irradiance profile (see Fig. 3.2), tp iSthe

time at which the pulse peaks, and _J _. is the peak rate coefficient for excitation. The spatial and

temporal halfwidths, rw and tw, respectively, were chosen to be consistent with our laser system

(rw = 0.2 mm, tw = 1.8 ns). Temporal integration of the rate equations was performed with the

34
routineDGEAR(IMSL,Houston,TX). Since the spatial dependence of the excitation function is

Gaussian, a Gauss-Hermite quadrature formula with a 20th degree Hermite polynomial (Korn and

Korn, 1968; Abramowitz and Stegun, 1968) was used for spatial integration of Nu(x) and esat(x).

In principle, the peak excitation rate coefficient can be related to the spontaneous emission

rate coefficient, A(u,/), and the peak irradiance of the focused laser beam by assuming, for example,

a Lorentzian spectral profile that is much greater than the absorption linewidth [Salmon and

Laurendeau, 1985b; see also Eq. (6.14)]; however, we have made no attempt here to determine

the excitation rate coefficient from the irradiance of our laser system. Instead, we specify a peak

center-line saturation parameter Wp' = W _',/Q_ >_ 10, which assures that at x = 0 and t = tp the

transition is well saturated.

3.5 Test of Rotational Relaxation/Electronic Quenching Models

Recently, Zizak et al. (1986) measured the relative excited-state, rotational-level population

of OH in the burnt-gas region of three atmospheric, laminar, premixed flames using linear,

laser-induced fluorescence (see Table 3.2). The distribution of population among the rotational

levels depended strongly on the directly-excited level but was relatively independent of temperature

and flame type. Given the relative, steady-state populations in the rotational levels of A2Z;+ (v'=0),

Zizak et al. (1986) determined the ratio between Nu, the population in the directly-excited level, and

Nc, the total population of the neighboring rotational levels. The ratio Nu/Nc characterizes the

collisional processes in the excited state, and therefore comparison of these experimental values

to calculated Nu/Nc values for the simulated H2/O2 flame provides a test of the reasonableness of

our models for electronic quenching and rotational relaxation.

The rotational distributions for the simulated 1"12/O2flame were obtained at atmospheric

pressure and at the temporal and spatial peak of the excitation pulse. As with the experimentally

determined distributions, the calculated populations had reached their steady-state values. Note

that since the relative steady-state populations, N(i)/N(u), are determined solely by the collisional

rate coefficients for v', there is no difference between relative rotational distributions produced under

linear and saturated conditions.

Figure 3.3 shows the variation in the calculated and experimental values of Nu/Nc with the

excited F1(N') levels. The uncertainty in the calculated Nu/Nc ratio due to the limited number of

rotational levels (0< N' $14) increases with the pumped quantum number; therefore, we performed

the calculations only for N' _<12. Also shown in Fig. 3.3 are similar measurements made by Smith

35
0.4

0.3

I I I I I I 't I ! f- I i I I I

o • D

"_ 0.2

2

0.1

t

D • C H 4- 0 2- Ar n

• CH4- air

4, C2Hz- air

0 CH4- air

I l i,, I [ ....! I [ l l l J I

5 10

Excited rotational level (N')

,e,

1 1

15

Figure 3.3 Comparison of calculated and experimental ratios (see Table 3.2) of the population

in the directly-excited level, Nu, to the total population of the collisionally-excited,

neighboring rotational levels, No, as a function of the pumped rotational level. The

closed symbols are the data of Zizak et al. (1986), while the open symbols are the

data of Smith and Crosley (1981).

36
v

Z

I.__.,.I

tRotational level (N')

O 5 iO

IIIII I I I I i I I I

H2-O z flame

& FI levels

• F'e levels

CH4-oir flame

a F= levels

o Fz levels

1 1 1

33

15

i

i I I

%

A

I I I I 1 I

32 34 35 36 37

Energy (cm -_) ,, 103

Figure 3.4 Comparison of the relative rotational-level populations in the simulated H2/O 2 flame

and in the experimental CH4Jairflame (Zizak et al., 1986) for excitation of the Q1(1O)

line. The Boltzmann distribution at 2000 Kis shown by the dashed line. For comparative

purposes, the experimental distribution has been normalized so that for the excited

F1 (10) level, Ikr ,"p = N _,Jc ''u u "

37
Table 3.2 Flames used for comparison of the

calculated and experimental ratios Nu/Nc.B

Flame _ T (K)

CH4/airb 1.1 1950

CH4JO2/Arb 1.0 1950

C2H2/airb 1.25 2380

CH4Jairc 0.86 1900

H2/O 2 1.0 2000

The equivalence ratio is denoted by 4).

b Zizak et al. (1986)

c Smith and Crosley (1981)

and Crosley (1981) in a CH4/air flame (see Table 3.2). For N' > 5, the calculated and experimental

values compare well, both showing a rise in Nu/Nc with increasing N'. However, for low N',

considerable differences exist in the experimental data among the different flames. The higher

Nu/Nc values for the simulated H2/O2 and experimental CH4/O2/Ar flames might be related to the

lack of N2 compared to the CH4Jair and C2H2/air flames. Since Nu/Nc is sensitive to the Qe/Z Qr(u,j)

ratio, Nu/Nc could increase at lower N" owing to enhanced quenching or reduced rotational

relaxation.

In Fig. 3.4, we compare the relative rotational-level populations from the experimental CH4Jair

flame (Zizak et al., 1986) with the populations from the simulated H2/O2 flame for excitation of the

Q1(10) line. The calculated populations agree well with those measured by Zizak et al. (1986). For

excitation of low N"levels, the populations do not agree as well, which is expected from comparison

of the calculated and experimental Nu/Nc values in Fig. 3.3. In general, however, the good agreement

between our calculated results and the experimental data of Zizak et al. (1986), as demonstrated

in Figs. 3.3 and 3.4, provides confidence in the utility of the dynamic model for analysis of the

laser-saturated fluorescence method at high pressure.

3.6 Results and Discussion

The following calculations were carried out for excitation of the P1(5) transition [Or(U)= 184 x

1016 cm2]. Figure 3.5 shows the temporal dependence along the center line of the excitation profile

for (1) the normalized number density inthe directly-excited level, (2) the population fraction in the

laser-coupled levels, and (3) the normalized excitation rate coefficient. The assumed conditions

correspond to atmospheric pressure, a peak center-line saturation parameter Wp" = 10, and no

38
quenching to the vibrational bath level (fb = 0). For convenience, the number density of the

directly-exCited level is normalized so that at peak excitation (t = tp), the normalized population

equals the population fraction 1 ~ ./(0,tp). Hence, from Eq. (3.4),

1_'. g,+g.N=/N_ (1 - ¥)a,o,

= (3._(,)

P P P

(I sat g u (I sat (I 5or

where a Patis the degree of saturation at the temporal and spatial peak of the irradiance pulse.

Figure 3.5 shows that under the above conditions, the population of the upper laser-coupled

level approaches steady state while the excitation rate coefficient is still increasing. At the peak of

the excitation pulse where the LSF signal is monitored, about 92% of the population remains in the

two laser-coupled levels at the center line. Thus for fb ---- 0 and atmospheric pressure, the model

shows that to a good approximation the balanced cross-rate model can be used for OH

measurements.

Figure 3.6 demonstrates the spatial dependence at the temporal peak of the excitation pulse

for (1) the normalized number density in the directly-excited level, (2) the degree of saturation, (3)

the population fraction inthe laser-coupled levels, and (4) the normalized excitation rate coefficient

at the same conditions as in Fig. 3.5. Because of the large value of Wp', the number density in the

directly-excited level remains near its center-line value at substantial lateral distances. As shown

by Eq. (3.26), the spatial profile of _], / a,P=,is dominated by the behavior of c=_t,which approaches

96% at the center line of the spatial irradiance profile. The normalized number density and the

degree of saturation are equivalent at large lateral distances since '/--, 0.

To investigate the effect of pressure on the balanced cross-rate model, we computed the

population fraction remaining in the laser-coupled levels as a function of pressure for a constant

value of the saturation parameter. Figure 3.7 shows the value of 1 - ,./at the temporal and spatial

peak of the irradiance profile for four of the cases summarized in Table 3.3. At lower pressures,

the populations in the vibrational bath level and in the rotational levels of the excited electronic state

increase with increasing pressure. The result is a depletion of the v" = 0 manifold with increasing

pressure, and hence a depletion of the laser-coupled levels.

Figure 3.7 also shows that as pressure is increased, the population Nu + NI = (1 - -/) N o

approaches an asymptotic value which depends on the ratio fb/fv. This assertion is confirmed by

comparing cases C and D, which have different absolute values of fb and fv but the same ratio fb/fv.

39
I

I"

i

i

i

"\

\.

\

J

1 I

2 4 6 8 10

Time (ns)

Figure 3.5 Temporal dependence along the center line for (i) the normalized population,

u(O,t)/a ,P.,, (2) the population fraction in the laser-coupled levels, 1 - ,-/(O,t),and (3)

the normalized excitation rate coefficient, Wlu(O,t)/W _., at conditions corresponding

to atmospheric pressure, a peak center-line saturation parameter of Wp' = 10, and

no quenching to the bath level (fb = 0).

4O
\

I

\

\

\

\

0.2 0.4

Lateral distance (mm)

0.5 0.8

Figure 3.6 Spatial dependence at the temporal peak of the excitation pulse for (1) the normalized

population, N ,(x,tp)/a,P,,, (2) the degree of saturation, eZsat(X,tp), (3) the population

fraction in the laser-coupled levels, 1 - _/(X,tp), and (4) the normalized excitation rate

coefficient, Wlu(X,tp)/W _., at the same conditions as in Fig. 3.5.

41
1.0, j i I J

O. g_ Case

o" 0.8 

v

," B

0.7

0.6

!

5t l I I I

O.

0 4 8

I I I I I

A

i 1 I 1 i

12 16 20

Pressure (otm)

Figure 3.7 Dependence of 1 - ,,/(0,tp), the population fraction at the temporal and spatial peak

of the irradiance profile, on pressure for cases A, B, C, and D (see Table 3.3).

42
Table3.3 Summaryof casesdescribingdepopulationof the laser-coupledlevelsfor

P1(5)excitation.a

Case fb fv Wp' 1 - "),(O,tp) (Ft_(tp))

A 0 -- 10 0.92 0.93

B 0.50 0.25 10 0.71 0.75

C 0.50 0.10 10 0.53 0.58

D 0.25 0.05 10 0.53 0.58

E 0.50 0.10 100 0.52 0.55

a The parameters 1 - -},(0,to) and (Fc(to)) are the respective asymptotic values of the

center-line and spatially-avera_ged populabon fraction in the laser-coupled levels at peak

excitation (see Figs. 3.7 and 3.8).

The asymptotic value is attained when the vibrational bath level and the rotational levels of the

excited electronic state reach a sufficiently high population that the rates for transfer into and out

of the laser-coupled levels are equal. When the transition is well saturated, as happens when Wp'

> 10, the asymptotic value of 1 - "/is insensitive to Wp'; this is borne out by the comparison between

cases C and E of Table 3.3.

Figure 3.8 shows the effect of a Gaussian irradiance profile on the spatially-averaged

population fraction in the laser-coupled levels for cases A, B, and C. The degree of saturation

decreases with increasing distance from the center line of the irradiance profile (see Fig. 3.6);

consequently, the population in the laser-coupled levels away from the center line more closely

represents the unperturbed population in the ground state. Hence, the spatially-averaged

depopulation is less than the depopulation at the center line of the irradiance profile. The resulting

increase in the asymptotic value for the spatially-averaged population in the laser-coupled levels

is detailed in Table 3.3. Because of the greater center-line saturation in case E, the spatial

dependence of esat more closely approximates that resulting from spatially uniform excitation; thus,

the effective population fraction more closely approximates the population fraction along the center

line.

Figure 3.9 shows the asymptotic value of both the spatially-averaged and center-line

population fractions as a function of the ratio fb/fv for Wp" = 10. Depopulation of the laser-coupled

levels clearly becomes more problematic as fb/fv increases; however, the sensitivity of the population

fraction to changes in the ratio fb/fv decreases with larger fb/fv. As fb]fvincreases, population within

v" > 0 increases; depletion of the laser-coupled levels follows since replenishment via rotational

transfer is limited by depletion of v" = 0.

43
/k

V

u__

k/

1.0

0.9

I I I I I

Case A

1 I I I

0.8

B

0.7 -- -

0.6

°.st

0

I I i ,j

4 8

I,, I I I I

12 16 20

Pressure (aim)

Figure 3.8 Dependence of (Fc(tp)), the spatially-averaged population fraction at the temporal

peak of the irradiance profile, on pressure for cases A, B, and C (see Table 3.3). The

population fraction at the center line, 1 - -y(0,tp) (---), from Fig. 3.7 is included for

comparison.

44
t I I

0. B

0.4

i

\

\

\

\

\

\

O.P I I I I I ,I I I I.

-0 2 4 6 8 10

Figure 3.9 Dependence of (Fc(tp)), and 1 - "7(tp) (---), the respective spatially-averaged and

center-line values of the population fraction, on the ratio fb/fv for Wp' = 10.

45
The results in Fig. 3.9 for large fb/fvvalues are inqualitative agreement with those of Campbell

(1984), who used a similar dynamic model to show that prediction of species number densities with

the balanced cross-rate model can result insignificant errors at higher pressures. However, because

Campbell (1984) used lower values of the saturation parameter for many of his cases (e.g., Wp'

1), predicted errors using the two-level model arise from both depopulation of the laser-coupled

levels and a low degree of saturation. Our approach has been to assure that the transition is well

saturated and then to determine the depopulation. The error resulting from the balanced cross-rate

model at the center line, ,/(tp), and averaged throughout the probe volume, 1 - (Fc(tp)), is shown

in Figs. 3.7 through 3.9.

Table 3.4 Sensitivity of the population fraction to changes in rate coefficients for

rotational energy transfer in the ground electronic state.a

fb/fc _'G 1 - 3'(0,tp) (Fc(tp))

0 0.5 0.68 0.72

1.0 0.92 0.93

2.0 1.10 1.09

2 0.5 0.56 0.61

1.0 0.71 0.75

2.0 0.81 0.84

0.5 0.44 0.50

1.0 0.53 0.58

2.0 0.59 0.64

aL'Gis the ratio of the B-parameter in the ground state to that in the excited

electronic state [Eqs. (3.18) and (3.19); Table 3.1]. The parameters 1 - ,/(0,tp)

and (Fc(tp)) are the respective asymptotic values of the center-line and

spatially-averaged population fraction inthe laser-coupled levels at peak excitation

(Wp' = 10; see Figs. 3.7 and 3.8).

Depletion ofthe laser-coupled levels may also occur via reduced rate coefficients for rotational

transfer in the ground electronic state compared to the excited state. Table 3.4 summarizes the

sensitivity of the asymptotic center-line and spatially averaged population fractions to variations in

the rate coefficients for rotational transfer in the ground state. Note that at high pressure,

overpopulation of the laser-coupled level can occur if the influence of the vibrational bath levels is

small (fb/fv _ 0) and if the effective rate coefficient for rotational replenishment of the ground state

is substantially larger than that for rotational depletion in the excited state. At lower pressure, where

45
thetimescale for collisional depopulation is longer than that for excitation (tw), the deviation from

Nu + N/ = _To will be small. At sufficiently high pressure, where the time scale for collisional

depopulation is much shorter than tw, the population fraction in the directly-excited levels reaches

an asymptotic value before the temporal peak of the laser pulse,

Figure 3.10 shows the spatially-integrated, temporal profiles of the normalized population in

the upper laser-coupled level for case A. This normalized population is equivalent to (Fc(tp)) at

peak excitation (t = tp -- 5 ns). When polarization effects are small (Altkorn and Zare, 1984), such

profiles are proportional to the measured fluorescence signal. Because the depopulation for case

A is small, little difference exists in the profiles at the various pressures. At 0.1 atm, the peak of the

fluorescence profile lags the excitation peak; however, as pressure increases, the profiles more

closely follow the excitation pulse.

The spatially-integrated population profiles for case C are shown in Fig. 3.11. The effect of

depopulation of the laser-coupled levels is evident, and as with case A, the profile at 0.1 arm lags

the excitation pulse. However, at 1 atm, the population profile peaks before the excitation pulse.

This behavior occurs when the characteristic time for collisional depopulation of the laser-coupled

levels is comparable to the characteristic time for excitation. When the characteristic collisional

time is much shorter than tw, depopulation of the laser-coupled levels occurs earlier in the irradiance

pulse, as demonstrated by the fluorescence profile at 10 atm.

The effect of depleting the laser-coupled levels is much more distinctive along the center line,

as shown in Fig. 3.12 for case C. As pressure increases and the characteristic time for collisional

depopulation becomes much smaller than tw, the saturated value of Nu + Nj is approached, which

flattens the temporal population profile. The flat temporal profile at 10 arm shows that the center-line

population fraction has reached its asymptotic value (see Fig. 3.7), and no further depopulation of

the laser-coupled levels will occur with increasing pressure.

The effect of depopulation on the excited-state rotational levels at the spatial and temporal

peak of the irradiance profile is shown in Fig. 3.13. For convenience, we show only the populations

in the I:1 levels, and lines are drawn between the rotational-level populations. As with the temporal

profiles described above, the population in the upper laser-coupled level decreases with increasing

pressure. At pressures of 1 atm and above, the relative populations [i.e., N(_/N(u)] are at steady

state. For N' =, 4, the populations have an approximately Boltzmann distribution, but with a

temperature (_1130 K) lower than the ground-state rotational temperature of 2000 K. Similar

47
x

n_

a.

x"

x

"In"

I

I

I

i

I

i

/

I

/

/

/

/

/

I

l atm

I

7

I I I I

\O.I atm

\

X

\

\

\

\

\

\

\

\

\

\

\

\

I0 atm

\

"\

"\

Figure 3.10

2 4 6 13 10

Time (ns)

Temporal profiles of the spatially-integrated, normalized population in the upper

laser-coupled level for case A at pressures of 0.1, 1, and 10 aim.

48
x

x"

v

m

x

A

x

-%

<Z

1.0

O.B

I I I

I

I

I

I

I

/

/

/

/

I

/

/

I I I I I

\

\

atm

\ 0.1 atm

\

\

\

\

\

\

\

\ \

\

"\ \

\

X

%

2 4 6 B i0

Time (ns)

Figure 3.11 Temporal profiles of the spatially-integrated, normalized population in the upper

laser-coupled level for case C at pressures of 0.1, 1, and 10 atm.

49
1.13

0.8

0

<Z

0.4

rl

!

I

I

I

I

I

/

/

/

/

/

/

/

/

I I I

I atm

I0 atm

I I I

" ,,0.Iarm

%

\

\

\

\

\

\

\

\

\

\

\

\

\

2 4 6 8 i0

Time (ns)

Figure 3.12 Temporal profiles of the center-line, normalized population in the upperlaser-coupled

level for case C,at pressures of O.1, 1, and 10 atm.

5O
.m

°m

v

Z

tn

B

13-

m

--l'--

m

--2--

--3--

m

mC m

m

--6--

32

Rotational level (N')

0 5 10

IIIII I I I I I I I I I I

_ \,,_.x,,_atm

"- i"'_...

", I0 atm "-..

\

\

0.1 atmX,,

I I I ! i I I

33 34 35

Energy (crn -_) * 103

\1,

36

w

m

u

m

m

m

Figure 3.13 Rotational-level populations of the F1 component at the spatial and temporal peak

of the irradiance profile for case C at pressures of 0.1, 1, and 10 atm.

51
distributions were obtained by Zizak et al. (1986) for excitation of transitions with N' = 5. At pressures

above -5 atm, where the population fraction in the directly-excited levels has reached its asymptotic

value, the population distributions coincide.

We now use the results of our analysis to make some important observations regarding the

balanced cross-rate model. First, tlSe state-to-state dynamic calculations show that rotational

relaxation in the excited state plays only a small role in direct depopulation of the v" =0 level, even

at high pressures (case A). However, rotational relaxation within the excited electronic state can

play a larger indirect role by increasing the number of pathways for electronic quenching to the v"

> 0 levels. Second, under conditions where fb/fv is small and the rate coefficients for rotational

transfer in the ground state are approximately equal to those of the excited state, the balanced

cross-rate model should remain a good approximation regardless of pressure. Conversely, for large

fb/fv ratios, the balanced cross-rate model becomes a poorer approximation at high pressure. Third,

at sufficiently high pressure the population of the laser-coupled levels attains an asymptotic value,

which is insensitive to both pressure and the saturation parameter. Hence, one would expect that

Eq. (3.3) could be used as a modified balanced cross-rate model if 1 - q exhibited small sensitivity

to both the flame temperature (-1000-2500 K) and the identity of the primary collision partners.

:

For excitation by a nonuniform irradiance profile, Eq. (3.8) shows that the LSF method can be used

at high pressure if .J'(1 - "/)esatdx (and not 1 - ,/alone) displays low sensitivity to the collision

environment.

3.7 Conclusions

We have examined the effect of pressure on the LSF method for measurement of OH

concentration. A numerical model of the excitation dynamics of OH has been developed to explore

the validity of the balanced cross-rate model at higher pressures. Using this model, we have shown

that the depopulation of the laser-coupled levels is sensitive to collisions which depopulate v'" = 0

and to rate coefficients for rotational transfer in the ground state which are smaller than those in

the excited state. In particular, we have shown that the depopulation of v" = 0, and hence the

laser-coupled levels, depends on the probability of (1) electronic quenching to vibrational levels for

which v" > 0 and (2) vibrational relaxation to v" = 0. At sufficiently high pressures, regardless of

the reason for depopulation, the total population of the laser-coupled levels reaches an asymptotic

value, which occurs when the collisionally-excited rotational and vibrational energy levels attain

enough population to balance the population transfer rates into and out of the laser-coupled levels.

52
Whenf_'fv-<1andtherotationaltransferatecoefficientswithinthegroundandexcitedstates

arecomparable, the laser-coupled levels are not significantly depopulated, and therefore the

balanced cross-rate model is a good approximation at all pressures. However, when fb/fv is large,

the depopulation of the laser-coupled levels will be significant at higher pressures, and thus the

balanced cross-rate model will no longer be valid. At sufficiently high pressures, a modified balanced

cross-rate model, Eq. (3.3), could be useful for making measurements of OH concentration if the

asymptotic value of the population fraction is insensitive to temperature and the collisional

environment.

53
CHAPTER 4

EXPERIMENTAL APPARATUS

4.1 Combustion Facility for High-Pressure Flame Studies

4.1.1 Introduction

Measurements of flame species by optical methods, such as laser-induced fluorescence (LIF)

and coherent anti-Stokes Raman spectroscopy (CARS), have proved valuable in elucidating

chemical and physical processes occurring in combustion environments (Eckbreth, 1988). While

much developmental work on optical methods has been done in low pressure (< 1 atm) flames,

most combustors of practical importance operate at high pressure. Since the width of the flame

front decreases with increasing pressure, physical probes are even more likely to perturb the flame

front; hence utilization of optical methods becomes a necessity for many high-pressure studies.

Such measurements could prove useful for a broad range of topics including (1) turbulent flames,

(2) engine knock, (3) pollutant formation (e.g., soot and NO production), and (4) flame extinction

and stability. In this chapter, we describe a high-pressure combustion facility designed for (1) the

development of optical diagnostic methods in high-pressure flames and (2) the study of practical

combustion phenomena by optical methods.

In previous work, Flower and Bowman (Flower and Bowman, 1984; Flower, 1986; Flower and

Bowman, 1986; Flower, 1988) and Edwards et al. (1985, 1987) have described special facilities

designed for optical measurements in high-pressure flames. Flower and Bowman have used laser

scattering and attenuation plus laser-Doppler anemometry to study soot production in laminar and

turbulent d'rffusion flames, Their facility includes a rectangular stainless steel chamber, with an

optical access port on each of the four sides. The vessel is designed to accommodate flames at

pressures to 10 atm, and spatial profiles of the flame are obtained by translating the entire chamber.

Edwards et al. (1987) report LIF measurements of OH and CN in solidpropellant flames at pressures

to 35 atm. The combustor used in this facility is a modification of a high-pressure window bomb,

54
andit includesa servomechanism to keep the surface of the solid propellant at a constant height

during combustion (Edwards et al., 1985). Our design, while emphasizing flexibility and thus allowing

a variety of laser diagnostic methods with laminar or turbulent flames, also stresses low cost byemploying corfimercially available components (where practical) in the facility.

4.1.2 Hlgh-Pressure Faclllty

Our high-pressure combustion facility includes (1) the pressure vessel, (2) the burner

translation system, (3) two flat-flame burners, and (4) the gas control system. To reduce the cost

of the combustion facility, the pressure vessel was constructed from standard stainless steel pipe

(AISI 316, schedule 40). The main body of the pressure vessel (Fig. 4.1) is 109 cm long by 20 cm

ID, with large diameter slip-on flanges welded to either end and blind flanges for the seals. Copper

tubing is coiled around the main body; thus, one can reduce the vessel temperature (if necessary)

by flowing water through the tubing.

Four optical access ports, fabricated from 6.4 cm ID pipe and small-diameter slip-on flanges,

are welded to the main body; the seals are provided by small-diameter blind flanges, each of which

is machined to accommodate a window housing. Each window, 3.8 cm diameter by 1.25 cm thick,

is seated in the housing against an O ring and is kept dry and free of particles by flowing dry nitrogen

through a system of jets in the housing. The inner face (which holds the window housing) of one

blind flange is machined at 10°; thus, for optical measurement techniques such as I_IF,this outer

flange can be used as the laser beam exit port to keep reflected light away from the sampling

volume. On completion, the pressure vessel was hydrostatically tested to 60 atm.

The translation mechanisms are located within the pressure vessel, thus further reducing the

cost of the facility since only the burner and not the entire vessel is moved. The vertical translation

system uses three Unislide assemblies, which are mounted to the bottom blind flange, and a small

stepper motor (SIo-Syn Model M061 -FD02) and a timing belt to drive the three units (Fig. 4.2). The

Unislide assemblies carry a platform (Fig. 4.3) on which the horizontal translation mechanism and

the burner are mounted. Like the vertical system, the horizontal system uses a small stepper motor

(SIo-Syn Model M061 -FD02) and a timing belt to drive the optical translation stage (Newport model

M-420-1S) carrying the burner. The range of movement for the vertical and horizontal systems is

about 11 and 2.8 cm, respectively, while the associated single-step resolution (at 200

steps/revolution) is about 2 and 1 #m, respectively. Two linear variable differential transformers

55
_r

I

Figure 4.1 Cutaway view of the pressure vessel and components,

56
Unislide

Assembly

(lof 3)

Pressure

Tronsducer

Conox __

Connector

(I of 2)

Woler

Trop

\

Pressure

Relief Volve

Figure 4.2 Exploded view of bottom flange and components.

57
Translation Stage

X

0

I/ I

_ Zx

Translation ?? ..sl,:

Platform _o ''

!

i i

I I

Stepper L%.

Motor _

@

Figure 4.3 Exploded view of horizontal translation system.

58
(LVDTs) are usedto monitor the approximate absolute position of the burner; however, to accurately

position the burner relative to the selected zero location, the motors are stepped through a

microcomputer.

In addition to supporting the translation system, the bottom flange supports an electronic

pressure transducer and a pressure relief valve (set for 24 atm) and provides the ports that are

used for electrical wiring and fluid connections. Two Conax connectors are used to bring electrical

signals to and from the vessel. During operation at high pressure (or even atmospheric pressure),

the interior surfaces of the vessel can remain below the dew point, even without cooling the vessel,

and thus water vapor from combustion can condense on these surfaces. Because some of the

water collects on the bottom flange, We had to (1) isolate exposed electrical wiring from moisture

(the wires were stripped to obtain a seal in the Conax connectors) and (2) provide a suitable water

trap at the bottom flange. The former was achieved using a silicon elastomer to fill the dead space

in the electrical access ports where the wires were exposed and water could collect; the latter was

achieved by attaching a closed section of pipe underneath the flange.

The pressure vessel is supported by a steel-frame table; the table also supports optical

breadboards located on either side of the vessel. To provide access to the bottom flange and the

various components, the pressure vessel is moved by a Unistrut trolley and winch system which

mounts to the table. In front of each optical access port is a Lexan shield to protect laboratory

personnel should the windows fail.

Though the vessel was designed to accommodate turbulent flames, we have initially used

only premixed laminar flames. The primary burner (Fig. 4.4) was constructed especially for us by

McKenna Products, Inc. (Pittsburg, CA) and includes a 2.5 cm diameter, water-cooled, sintered

bronze flameholder surrounded by a guard ring, also made of sintered bronze, for isolating the

flame from the ambient gases. The principal advantage of the cooled bronze flameholder is that it

affords a wide range of flow rates for which the flame remains attached to the burner without

sustaining damage; additionally, the cooled plug provides a uniform boundary condition which

results in a flat flame. Radial LIF measurements of the relative OH concentration at pressures to

_12 atm show that the flame is flat typically to within about +10% (see Chapter 5). Originally we

employed a similar McKenna burner ustng a stainless steel flameholder. This design was tried

59
Sintered Bronze

Sintered Bronze Plug

"A

l/

/

/

/

Cooling Lines-

' ' Sleeve / /

#

/

%

Housing

_ Guord Flow Inlet

Burner Gos

Inlet

Figure 4.4 McKenna flat flame burner and guard flow housing.

6O
Hastelloy X Plug

Sleeve

Sintered Metal

Disk

Plug Spacer

O-Ring

Swagelok Fitting

Figure 4.5 Hastelloy flat flame burner.

because a stainless steel plug was assumed to be more durable than the bronze plug; however,

as a result of the low thermal conductivity of the stainless steel, the burner was easily damaged by

the large heat fluxes which result at high flow rates of the fuel and oxidizer.

The secondary burner (Fig. 4.5) is similar in size and shape to the McKenna burner, but it

uses an uncooled hexagonal-pattern plug made of Hastelloy X (a high-temperature, nickel-rich alloy

manufactured by Kentucky Metals, New Albany, IN) for flame stabilization. The low surface area

of this flameholder (as seen by the flame) makes cooling unnecessary; however, the flame can

stabilize below the burner surface since the pore width (--0.8 mm) is not small enough to quench

the flame. Though this burner was difficult to use because of its restrictive operating conditions, it

did prove to be durable; an added advantage is that the large pore size of this flameholder would

allow seeding of the flame.

61
A significant feature of the observed high-pressure premixed laminar flames is flame jitter--low

frequency (-10 Hz) flame oscillations--the amplitude of which increases with pressure for aconstant

mass flow rate of the combustible mixture. Preliminary measurements at -6 atm were made using

a beam derived from a xenon arc lamp. The small-diameter (- 1 mm) beam was first passed through

the flame; the beam cross section was then rotated by 90° so that vertical disturbances such as

flame jitter would deflect the beam along the horizontal axis. The beam was subsequently focused

on the entrance slit of a monochromator, and the beam intensity (passed by the slit), which varied

because of flame jitter, was sampled at 1 kHz. These measurements show that the amplitude

increases, while the frequency of the oscillations decreases, with decreasing mass flow rate of the

combustible mixture.

Flow rates of fuel, oxidizer, diluent, and bath (or guard-ring) gases are metered with four Linde

fJow control modules (models 15C, 14C, 16C, and 18C, respectively) and an assocJa_'ed LJnde

readout and control (ROC) box. For each module, a high-pressure regulator is used to control the

inlet gas pressure, and a back-pressure regulator is used at the exit to limit the pressure drop. The

ROC box is interfaced to an IBM PC-compatible microcomputer via RS 232 ports on the ROC box

and the microcomputer, and a special communications program was written to control the flow

streams (see Appendix A). In addition to displaying the set and read flow rates (and the vessel

pressure), the menu-driven program includes options for (1) setting each flow stream, (2) zeroing

all four streams or just the three streams for the flame, (3) making minor adjustments to individual

streams or combinations of streams (e.g., fuel and oxidizer or fuel, oxidizer, and diluent), (4)

automatically changing the equivalence ratio (according to a prescribed formula), and (5)

automatically changing the flow rates of the combustible gases (according to a prescribed formula)

in response to pressure changes. This last option is useful even with the McKenna burner since

flame stability is enhanced by increasing, with pressure, the mass flow rate of the combustible

mixture. We use a formula based on a description of adiabatic flame speed versus pressure of

CH4-air mixtures (Hjima and Takeno, 1986) to scale the mass flow rate of the combustible mixture.

The pressure within the vessel is controlled with a back-pressure regulator (Fairchild Industrial

Products, Winston-Salem, NC), which is located on the exhaust line, far enough downstream of the

vessel that the gases are sufficiently cool. Typically, during the course of a three-hour experiment,

the vessel pressure was held to within 1% of the set point, with only occasional minor adjustments

made to the regulator. Upstream of the back-pressure regulator on the exhaust line are a condenser

62
andwatertrap;thus,with this trap (and the one underneath the bottom flange), much of the water

produced during combustion is eliminated from the pressure vessel. In parallel with this regulator

is a valve that can handle large flow rates and can quickly depressurize the vessel. A high-pressure

flame is obtained with the following procedure: (1) the burner is lit from an optical access port using

a torch; (2) the port is then sealed, a bath-gas flow rate of 20 to 40 slpm is programmed, and the

pressurizing option on the interfacing program is selected; and (3) the depressurizing valve is shut,

and the back-pressure regulator is adjusted to the desired pressure.

4.1.3 Areas for Improvement

From our experience with the high-pressure combustion facility, we make the following

suggestions for an improved design.

1. Using the condenser and water trap on the exhaust line, the water

was effectively eliminated from the exhaust system; however, for the

pressure vessel a drainage system should be designed to direct the

water collecting on the interior surfaces to the trap beneath the

bottom flange. This would ensure that the accumulation of water

does not interfere with the operation of the burner or the electronic

components. (To prevent water that condensed on the top flange

from falling on the burner, we attached a steel plate to the burner

housing about 15 cm above the burner.)

2. Though the optical translation stage used for horizontal movement

is adequate for most purposes, it does exhibit significant side-play;

for more accurate positioning of the burner, the current translation

stage should be replaced by a system with reduced side-play (for

instance a Newport model M-425-1S stage or a linear bearing/shaft

arrangement).

3. The width of the burner guard ring (Fig. 4.4) should be reduced to

allow a higher velocity of guard flow for the equivalent volumetric flow

of gas. This becomes increasingly important at high pressures, since

gas consumption can be large. Finally, for modelling purposes (i.e.,

providing a tractable boundary condition), the grain size of the

53
sinteredbronzeflameholder(-100 #m) should be reduced, since

this dimension should be small compared to the flame stand-off

distance (Ferguson and Keck, 1979).

4.2 Spectroscopic Equipment

4.2.1 Fluorescence Experiments

For the LIF experiments (Fig 4.6), the second harmonic (at 532 nm) of a Quanta-Ray DCR-3G

Nd:YAG laser is used to pump a PDL-2 dye laser, which includes transversely-pumped oscillator

and preamplifier stages along with a longitudinally-pumped amplifier stage. To produce UV

radiation, the output of the dye laser is sent to a Quanta-Ray Wavelength Extender (WEX-1), where

the light is frequency doubled; the active control circuit of the WEX is used to continuously adjust

the angle of the doubling crystal to obtain the maximum doubled output. For the saturated

fluorescence measurements (Chapters 6 and 7), we used the fast pulse option of the DCR-3G. A

so-called fast pulse was obtained by adjusting the Q-switch delay (relative to the flash-lamp trigger

pulse) while monitoring the laser output. A Q-switch delay was used that resulted in two principal

temporal modes each about 3 ns in width. (A-n_e)_ampie0f the average temporal dependence of

the UV pulse is described below and shown ii_-Fig: 4i10. )

To achieve high conversion efficiency of the 532nm radiation, the dye laser uses a mixture

of Exciton DCM and Sulforhodamine 640 (SR640) dyes. To obtain the optimum mixture, we used

the following procedure.

1. Dye concentrations recommendedby Quanta-Ray for the oscillator

and the amplifier were prepared for both DCM and SR640.

2. Initially, only the DCM solutions were employed, with the PDL-2 lasing

at the wavelength of interest (_620 nm).

3. The mixtures of SR640 for the oscillator and amplifier were then

added to the DCM mixtures (separately, but for both the oscillator

and amplifier) in 50 ml increments while monitoring the laser energy.

This was continued for the oscillator and amplifier until in each case

the laser energy peaked.

Using this procedure, we obtained a laser energy of about 95 mJ/pulse at 620 nm, with an input

energy of about 380 mJ/pulse at 5,32 nm (an efficiency of -25%).

54
OCR-3GI

I

i

i

]JIll ]

PDL-2 ]

Illl

WEX-1

i Trigger

Pv

kfB Lc _:_ _ FB

MOnochromator

A

l I

J Sampling Modules

Computer

Figure 4.6 Schematic for LIF experiments. Components: A - aperture; BD - beam dump; BS -

beam splitter; BSA - beam steering assembly; FB - fluorescence block; L - lens; MA -

image rotating mirror assembly; PD - photodiode; PMT - photomultiplier tube; PP -

Pyrex plate(s); PV - pressure vessel.

65
1,0

0.8-

0

¢-

_0.6-

,e-4

03

@

>

oF-,I

_ 0.4- 0

@

n,"

0.2-

0.0-

l J '1 J J

mooo

0000

0 o

0 o

0 o

O00

0 o

0 o

0 o

O0 °

0 o

0 o

O0 °

l I ! 1 1

0,0 0.1 0,2 0.9

Scan Distance (mm)

Figure 4.7 Integrated irradiance of UV beam measured by scanning a knife edge across the beam

at the focus.

66
c"

Cn

L/3

¢D

>

C_

1.0-

D

0.8-

w

0.6-

m

0.4-

w

0.2-

<>

A

O

A

<>

[]

V

0 -- i arm

-- 3 arm

D -- 6 arm

v 12 arm

0

l

0 30 60 90 120 150

Exit Silt Width (_m)

Figure 4.8 Dependence of fluorescence signal of monochromator B on exit slit width and

pressure.

67
A Pellin-Brocaprismwasusedin the WEX to disperse the visible and UV beams after the

doubling crystal, and a small portion of either the visible or UV beam was then picked off and directed

to the triggering photodiode with a fused silica beam splitter. The UV beam was raised to the

appropriate height with a beam steering assembly; the resulting polarization of the radiation was

vertical. The beam was attenuated when necessary with Pyrex plates and focused over the burner

with a 250 mm focal-length fused silica lens. The approximate spot size of the UV beam over the

burner was measured by scanning a knife edge across the focused beam--which had been

attenuated with a Pyrex plate. The integrated beam irradiance, ILy = f _._f "__ I L( -X',Y ) d .£."C]_',was

then monitored with a photodiode, and an example of a scan is shown in Fig. 4.7. Though ILy shows

good symmetry about the center line, we did observe some nonuniformity in IL(X,y), the irradiance

distribution; at least part of the observed nonuniformity arises in the oscillator of the dye laser. Two

additional factors which led to some nonuniformity in the UV beam were (1) slight damage to the

doubling crystal and (2) damage to a 180° turning prism in the Quanta-Ray Prism Harmonic

Separator (PHS) box (where the 1064 and 532 nm beams are separated).

Fluorescence was collimated with a second 250 mm focal-length lens. In experiments where

two monochromators were used, the first reflector of the image rotating mirror assembly was a

beam splitter, which allowed part of the fluorescence to pass to monochromator A. The remaining

fluorescence was rotated by 90° (with a mirror assembly) and imaged on the entrance slit of

monochromator B. Two Spex 3/4 m Czerny-Turner monochromators were used in the experiments:

(A) a model 1700 which employed a grating blazed a 1 #m (and was used in third order); (B) a

model 1800-11, which employed a grating blazed a 300 nm (and was used in first order).

Monochromator B was converted from a spectrometer by fabricating a plate for mounting the exit

slit; however, the exit plane was slightly off the position of the focal plane, and as a consequence

the image of the entrance slit was blurred at the exit plane. To quantify this effect, the fluorescence

signal was measured as a function of exit slit width for the pressures of interest: 1, 3.1, 6.1, 9.2,

and 12.3 atm. The results for 1,3.1, 6.1, and 12.3 atm are shown in Fig. 4.8; the effect of collisional

broadening is to further broaden the spectral fluorescence profile, and in comparing the

fluorescence signal at different pressures, this broadening must be taken into account.

To align the optics for fluorescence measurements, we devised a simple procedure which

does not require opening the vessel (i.e., taking off any of the flanges). This scheme consists of

the following steps.

68
1. Inthelens-holding mounts outside the optical access ports, we place

iris diaphragms. The lens holders are approximately centered with

respect to the ports. The irises are then set at identical heights using

a cathetometer (and closing the iris to mark the center).

2. We direct the (attenuated) UV beam through the laser entry and exit

ports, using the irises to ensure that the beam passes through the

center of both lens holders (and thus the lenses). Also, at this time

we adjust the horizontal position of the lens holders to ensure that

the beam passes above the center of the burner (when the burner

is centered).

3. Through the opposite ports, we direct the beam from a He-Ne laser.

The irises are again used to ensure that the beam is level and that

it is passing through the center of both lens holders. To ensure the

beam crosses the central chord of the burner, we again adjust the

horizontal position of the lens holders. Finally, we align the

fluorescence optics to so that the He-Ne beam strikes the center of

each optic (including those in the monochromator).

By opening the monochromator slits and making only minor adjustments to the collection optics,

particularly the collection and focusing lenses, we are then able to find a Rayleigh scattering or

fluorescence signal (when the laser is at an appropriate wavelength).

The monochromators employed inexpensive photomultiplier tubes (RCA model 1P28B)

specially-wired for fast response (Harris et al., 1976) for detection of the spectrally-resolved

fluorescence signals. The average temporal response of each PMT was tested using Rayleigh

scattering (Fig. 4.9). These waveforms can be compared to the average temporal signal obtained

with a Texas Instruments TIED56 silicon avalanche photodiode (Fig. 4.10), which has a reported

temporal response of -200 ps (Harris et al., 1980). These waveforms were recorded by repetitively

scanning in time over the signal, using the 200 ps sampling gate of a Stanford Research Systems

fast sampler (SR255), and a scanning voltage supplied by the SR245 computer interface module.

The data was then digitized and displayed with the SR245 using the SR265 software package, which

also controlled the experiment. The average laser pulse shown in Fig. 4.10 has two temporal modes

each with an -2.5 ns FWHM; this average pulse was obtained consistently from day to day without

59
[3

t'-

03

4-.1

03

03

t'-

.r,I

(..

O

43

43

O

O

03

t'-

03

O

>,,

O

rr"

133

I---

(3.

1.0

0.8

0.6

0.4

0.2

OoC

1.0

a,_"_6 1 I I l

0.8

0

> <0.6 or-4

• 0.4

l_iII I|

• _Qe

:. -.

,° ._

• u e

_e

"V

4

Time (nsec)

Figure 4.9 Average temporal response of PMT A and B to UV beam using Rayleigh scattering;

the profiles are averages of 45 (PMT A) and 30 (PMT B) temporal scans.

7O
1.0-

m

tJ

ro_ O. B-

"f4

O9

13

0

-o 0.6-

0

0

r"

l&.

ol O. 4-

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ime

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+1+

I,'

I I I I

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og

m •

om

'...,.,. • .-.-_ ,,',.

o_

lIB

,-_. I" 4.i1+

,.*....#.

QI e

"_ ":k -

O. ! _ # l i I I ,_'_'_4_ -

5 i0 15

Time Cnsec)

Figure 4.10 Average temporal dependence of the UV beam irradiance measured with silicon

avalanche photodiode; the profile is the average of 10 temporal scans.

71
additional adjustment of the Q-switch delay. Both PMTs, which used a 1000 V supply voltage, show

good temporal resolution (Fig. 4.9), though the slower response (compared to that of the fast

photodiode) does result in distortion of the w_veform.

The linearity of the PMTs and the respective circuits was determined using a Rayleigh

scattering signal, which was attenuated with calibrated neutral density filters. The attenuation was

progressively decreased, and the subsequent signal was recorded; the results (Fig. 4.11) show

that both PMTs have a linear range of about 0.5 V or greater.

In addition to the aforementioned PMTs and fast photodiode, two silicon UV-sensitive PIN

photodiodes (Hamamatsu $17722-02) were employed to (1) trigger the detection electronics and

(2) monitor the shot-to-shot UV beam energy. These photodiodes were not fast enough to resolve

the temporal features of the UV pulse, and consequently they were used only to record the laser

energy per pulse rather than the peak laser power. However, because of their large sensitive area,

these photodiodes were especially valuable when it was necessary or helpful to measure the

integrated beam irradiance (e.g., in the experiment where the knife edge was scanned across the

beam). The monitoring photodiode was also used to level and position the burner relative to the

laser beam. For both exercises, an aperture in front of the focusing lens can be used to ensure

that the beam width is small and approximately constant while crossing the burner. To level the

burner, the burner is first translated upward to partially obscure the beam and then translated from

side to side while adjusting its tilt; it is considered level when the photodiode signal is approximately

constant as the burner is translated horizontally. To find the zero vertical position, the burner is

first positioned to totally block the beam. It isthen moved downward until the signal at the photodiode

is half the unblocked value; this is then recorded on the computer as the zero vertical position of

the burner. Though vertical fluorescence profiles taken consecutively (under the same conditions)

show little or no shift, the zero position typically varied 50 to 100 #m from day to day.

The PMT and photodiode signals were recorded with gated integrators; for the saturated

fluorescence experiments, each PMT signal was resolved with the 200 ps sampling gate of a Stanford

Research Systems SR2.55 fast sampler, which was temporally centered at the peak of the

fluorescence pulse using an SR200 gate scanner. The voltage output from the SR255 was then

digitized and stored with the SR245 computer interface module and the SR265 software package.

72
>

v

0

03

0

4J

0

>

D

O

L

U

L

.F-I

El_

,r-I

D

E

O

O

3::

O_

m

X

O.

Io0

0.8

0.6

0.4

0.2

0.0

1.0

0.8

0.6

0.4

0.2

0 D

"d_

0

0

0

I ! !

D

D

0

D

0

0

I I I I I !

0

D

I I I I I i ! ! i t i

0 0.2 0.4 0.6 0.8 1.0

R@ lot i v@ Roy i e i9h Scotter i no

Figure 4.11 Linearity of PMT circuits A {top graph) and B (bottom graph).

73
For both the monitoring photodiode and the PMTs, when wide-band temporal detection was desired

(Chapter 5), we used the SR250 gated integrator and boxcar averager; sampling gates greater than

2 ns could then be selected for detection of the signal.

One of the modifications made to the SR265 software includes a stepper motor interface

package. The package consists of two parts: the first, which was written in FORTRAN to be

compatible to the SR265 software, displays the menu options; the second communicates with the

motor translators through a digital I/0 card. This entailed sending to the motor translator box an

8-bit word, specifying the motor and step direction; this section was written in the C programming

language for greater speed. Some of the features of the package are listed below.

1. The user can move any motor connected to the two translator boxes.

(Up to 16 motors can be addressed.)

2. The user can access a file (supplied by the user), which contains

information on the motors and number of steps (for each motor) to

be moved after each scan. (A scan is defined as a set of samples

taken by the SR245 computer interface.)

3. The user can access a memory file, which keeps track of motor

positions relative to a specified zero. A menu command also allows

the user to send the motor to its zero position with the backlash of

the system automatically removed.

4. The user can specify a motor and the number of steps to be moved

after each sample recorded by the SR2.45 module. Additional options

allow the user to (1) reverse the direction of the motor on each

subsequent scan (to backtrack over the motor's path) or (2) move

the motor back to its zero position before each subsequent scan (so

that the scans can be averaged point by point, for example).

The last option is useful in experiments for which one wants to synchronize the movement of a

stepper motor with data collection. It can be employed, for example, in scanning (1) a knife edge

across the laser beam, (2) the monochromator grating for collection of absorption or fluorescence

spectra, and (3) the grating ofthe dye laser forcollection of excitation spectra. The principal limitation

with this setup is the maximum stepping frequency of about 200 steps/s; however, this is not a

significant limitation for many experiments.

74
4.2.2 Absorption Experiments

Figure 4.12 shows a schematic of the optical layout for the absorption experiments. The

output of a 150-W xenon arc lamp plus two lenses and two apertures were used to produce a

collimated beam, which was directed over the center line of the burner; apertures were also used

after the burner to minimize detected flame emission. By scanning the burner through the beam,

the average beam width was determined to be less than about 200 /=m. A Spex 3/4 m

monochromator, with a grating blazed at 1 #m (monochromator A described above), was used in

3rd order to resolve the absorption spectra. Spectral scans were obtained by using a

specially-designed gearbox (employing an anti-backlash worm gear arrangement) with a 50:1 gear

ratio in conjunction with a stepper motor (SIo-Syn Model M061-FD02, which has a single-step

resolution of 1.8°). This design--which also included a damper to reduce vibration, especially

noticeable at low stepping frequencies--allowed good spectral resolution. Typically, a complete

absorption scan consisted of 21000 or 28000 data points (3 or 4 scans each of 7000 points--a limit

imposed by the SR265 program). Each scan began before the P1(2) line (Dieke and Crosswhite,

1962) and ended beyond the Q1(15) or P1(10) line (see Table 4.1). Each data point is the result of

30 boxcar samples, using the built-in exponential averager to average individual samples. The

computer interface module was then set to sample I in 60 boxcar triggers (with a command in the

SR245 routine), thus resulting in some correlation (albeit a small one) between consecutive data

points. Figure 4.13 gives an example of a typical scan from an atmospheric-pressure flame.

The transmitted light was measured with a PMT using a supply voltage of 700 V; this signal

was processed with the SR250, using an enlarged sampling gate of 75 #s (the gate, normally limited

to 15/_s, was enlarged by adding a capacitor to the sampling circuit of the SR250 module). The

PMT output was connected directly to the SR250 input, which has an input impedance of 1 M_,

and the boxcar output voltage was tested for a linear dependence on the beam intensity using

calibrated neutral density filters to attenuate the beam. Ideally, however, one would use a

current-to-voltage conversion circuit to prevent loading of the PMT circuit.

A significant increase in the signal-to-noise ratio of the absorption measurements was

obtained by repetitively scanning over a portion of the spectrum and averaging the individual scans.

This was accomplished by sending the monochromator stepper motor to its zero position after

each scan--which was done automatically by selecting the appropriate option in the motor interface

menu. Multiple scans could then be run, and the SR265 routine would continually average the

75
Arc

Lamp

L

A

A L(250)

PV

L(250)

Figure 4.12 Schematic of absorption experiments. Components: A - aperture; BF - bandpass

filter; L - lens; MA - image rotating mirror assembly; PMT - photomultiplier tube; PV

- pressure vessel.

76
(s_ ._un "qJm)

0 0

J

OJ

O9

O_

-C:)

m

E

E

v

r

E,I

e_

e-

,5

ee-

"O

E

6

f_

E

eE

2

_-_

"_

e_ ei1

77
Table 4.1 Lines used in absorption analysis.

Line Wavelength (nm)

P1(2) 308.729

Q1(6) 308.824

Q1(8) 309.329

Q2(6) 309.369

Q2(7) 309.552

Q1(9) 309.624

Q2(8) 309.773

Q_(1O) 309.949

P1(5) 310.213

Q2(11) 310.657

P1(6) 310.745

Q2(12) 311.024

Q_(13) 311.113

Q1(15) 312.058

P1(9) 312.485

P1(10) 313.119

results of the current scan with previous scans. An example from an atmospheric-pressure flame

is shown in Fig. 4.14, where two profiles of the strong Q1(6) line are shown: one, a single scan and

the other the average of 5 consecutive scans. Typically, the only observab!e tracking error occurred

in going from the first to the second scan; the remaining scans accurately followed the second

scan.

To aid in data reduction of the absorption spectra, we again modified the SR265 software

package to integrate the absorption profiles; this included the following steps.

1. The user selects a portion of the spectrum that includes the line or

lines of interest from the main window containing, for example, a

7000-point scan; this section of the spectrum is then removed to a

second window.

2. Control is transferred to the second window, and the user is

prompted to make measurements of the baseline by bracketing the

region with two cursors.

78
I I I

308.80 308.84 308.88

Wovelength (nm)

Figure 4.14 Example of improved signal-to-noise ratio in an absorption spectrum obtained by

repetitively scanning over the Q1(6) line in an atmospheric-pressure flame; also

included in the scan is the Q12(6) satellite transition. The multiple-scan profile (A),

which is the average of 5 consecutive scans, has been offset from the single-scan

profile (B) for convenience.

3. The user is then prompted to make the absorption measurement by

again bracketing the region of the spectrum with the two cursors;

the program calculates the absorption integral, using the trapezoidal

rule.

4. Finally, control is returned to the main window and the user is

prompted to exit the analysis loop or select another portion of the

spectrum.

With this software, analysis of absorption spectra is fast and accurate. In particular, with this

approach one does not rely on the triangular approximation [i.e., approximating the profile as a

triangle (Lucht, 1978; Salmon, 1986a)] for integration of absorption profiles. Forthis approximation

79
to be valid, (1) the convolution of the transmission functions of the entrance and exit slits should

approximate a triangular function, (2) the width of this function should be much greater than the

transition linewidth, and (3) the linewidth should have only a small fraction of its total absorption in

the wings of the profile. Consequently, while the triangular approximation can be accurate for a

predominantly Doppler-broadened profile, its accuracy will decrease with increased collisional

broadening.

After having obtained the integrated absorption, the number densities were calculated

employing a FORTRAN routine, which solved the absorption equation (see Appendix B) using the

curve-of-growth method (Lucht, et al., 1978) and fit the data to a Boltzmann curve with a nonlinear

least squares algorithm (Salmon, 1986a). The routine also gives the 95% confidence interval for

the two parameters, temperature and number density; typical uncertainties for the temperature and

number density were 30 to 50 K and 5 to 10%, respectively.

80
CHAPTER 5

LASER-INDUCED FLUORESCENCE MEASUREMENTS OF OH

IN LAMINAR C2Hs/O2/N 2 FLAMES AT HIGH PRESSURE

5.1 Introduction

Measurements of flame species by optical methods, such as laser-induced fluorescence

(LIF), have proved valuable inelucidating chemical and physical processes occurring incombustion

environments (Eckbreth, 1988). Until recently (Edwards et al., 1987; Felton et al., 1988), most work

using LIF has been done in low-pressure (<1 arm) flames, though most combustors of practical

importance operate at high pressure. Since the width of the flame front decreases with increasing

pressure, physical probes are even more likely to perturb the flame front; hence, utilization of optical

methods may be a necessity for many high-pressure studies. Such measurements could prove

useful for the study of a broad range of topics including (1) turbulent flames, (2) engine knock, (3)

pollutant formation (e.g., soot and NO production), and (4) flame extinction and stability. While

high-pressure turbulent combustion environments allow analysis of the complex interaction

between chemistry and the flow field, high-pressure laminar environments should also have an

important role: allowing the study of pressure-dependent flame chemistry. Thus, we have examined

laminar flame structure at high pressure using relative LIF measurements of the OH molecule. We

describe fluorescence profiles at 4 pressures--3.2, 6.3, 9.5, and 12.6 atm--in flat premixed

C2Hs/O2/N2 flames, and we discuss problems associated with high-pressure LIF measurements.

5.2 Experimental Apparatus

Our combustion facility,which is designed forstudy of high-pressure flames by spectroscopic

methods (Chapter 4), includes the following: (1) a pressure vessel constructed from standard

stainless steel piping components (Fig. 5.1); (2) an electronic gas delivery system, which is

interfaced to a microcomputer; (3) a sintered bronze water-cooled burner (2.5 cm in diameter,

constructed by McKenna Products, Inc, Pittsburg, CA), which we used without the guard ring to

8]
allowbetteropticalaccesstotheflame; and (4) an internal x-y burner translation system employing

stepper motors. The range of movement of the vertical and horizontal translation mechanisms is

about 11 and 2.8 cm, respectively, while the associated single-step resolution is about 2 and 1/_m,

respectively. Because the motors are steppedthrough a microcomputer, we can accurately position

the burner.

The optical layout for the LIF experiment is shown in Fig. 5.2. The Quanta-Ray PDL-2 dye

laser is pumped by the frequency-doubled output of a Quanta-Ray DCR-3G Nd:YAG laser; to

produce UV radiation, the output of the dye laser is sent to the Quanta-Ray Wavelength Extender

(WEX-1), where the laser light is frequency doubled. The dye laser is normally tuned to the Q1(8)

transition (,_ = 309.3 nm) of the A2_+-X2]'[(0,0) band (Dieke and Crosswhite, 1962); this line was

chosen for excitation because the Boltzmann fraction of the lower rotational level varies by only

10% over a temperature range of 1000-2600 K (Lucht et al., 1984). For this experiment, the pulse

width and repetition rate of the dye laser were -8 ns and 10 Hz, respectively.

A small portion of the UV beam is first picked off with a quartz beam splitter and sent to a

UV-sensitive photodiode which produces the signal used for triggering the detection electronics.

The beam is then raised to the appropriate height with a beam steering assembly; the resulting

polarization of the radiation is vertical. The beam is attenuated if necessary with Pyrex plates and

then focused over the burner with a 250 mm focal-length fused silica lens giving a focused spot

size of -100/_m. For this experiment, the laser energy after attenuation was -1 mJ/pulse. With

the resulting laser power and the small spot size, we observed partial saturation of the transition,

particularly when using a small temporal sampling gate (e.g., 200 ps). Using saturation

spectroscopy was not our intention for this experiment, however, and we report further on the

saturation behavior of OH at high pressure in Chapters 6 and 7. After leaving the exit port, the

beam is collimated, and another portion is picked off and focused on a pinhole aperture in front of

asecond UV-sensitive photodiode. This photodiode allows us (1) to assess laser power fluctuations

and beam steering and (2) to level and position the burner relative to the laser beam. Though

vertical fluorescence profiles taken consecutively (under the same conditions) show little or no shift,

the zero position typically varied 50 to 100 _=mfrom day to day.

The OH fluorescence is collected with a 250 mm focal-length collimating fused silica lens

through a port adjacent to the beam entrance and exit ports; the optical access ports have a limiting

f-number of about f/9. The laser axis of the fluorescence sampling volume is then rotated from

horizontal to vertical with two mirrors, and the fluorescence isfocused on the entrance slit of a Spex

82
I

I

I

Figure 5.1 Cutaway view of pressure vessel and associated components.

83
DCR-3G

"11 11

PDL-2 ]

!1 11

i

J

I

WEX-1

BD BS

PD

L (250)

L (1_:))

PV

L (250)

' L (250)

Gated

Integrators

Computer

Monochromator

PMT

Figure 5.2 Schematic of LIF experiment. Components: BD - beam dump; BS - beam splitter;

BSA - beam steering assembly; L - lens; MA - image rotating mirror assembly; PD -

photodiode; PMT - photomultiplier tube; PP- Pyrex plate(s); PV- pressure vessel.

84
3/4 meter monochromator. The fluorescence signal is then detected with an RCA 1P28B

photomultiplier, and the resulting electronic signal along with the photodiode signal are processed

with two Stanford Research Systems SR250 gated integrators using sampling gates of 6 and 10 ns

for the photomultiplier and photodiode signals, respectively (the wider gate for the photodiode

reflecting its slower response). The data isthen digitized and stored on an IBM PC using the Stanford

Research Systems SR245 computer interface and the SR265 software package, which we modified

to allow programmed movement of the stepper motors.

5.3 Results and Discussion

A significant feature of the high-pressure flames we observed is flame jitter--low frequency

(-10 Hz) flame oscillations--the amplitude of which increases with pressure for a constant mass

flow rate of the combustible mixture. We also noticed a reduction in flame noise when using a guard

flow (Matsumoto et al., 1982); however, this surrounding flow did not eliminate the flame jitter

observed at high pressures. Measurements of the jitter intensity and frequency at 6.3 arm were

made using a small-diameter beam produced from a xenon arc lamp. The beam was passed

through the flame, and its cross section was rotated by 90° so that vertical disturbances such as

flame jitter deflected the beam along the horizontal axis. The beam was subsequently focused on

the entrance slit of a monochromator, and the intensity was sampled at 1 kHz. The measurements

showed that the amplitude increases, while the frequency of the oscillations decreases, with

decreasing mass flow rate of the combustible mixture.

The flame jitter was reduced by placing a screen about 8 mm above the burner surface. We

note, however, that the problem of flame jitter is exacerbated by the increase in the index of refraction

with pressure; as a result, the laser beam is more likely to be steered away from the fluorescence

collection window (as defined by the monochromator entrance slit) at high pressures by fluctuations

in the gas density. A similar problem is encountered with spatial gradients in the refractive index:

the beam can be displaced relative to the fluorescence collection window as it moves through the

flame. This effect was indeed observed near the flame front (where the temperature gradient is

large) of these high-pressure flames. The problem is perhaps ameliorated by the one-dimensional

geometry of the flame, at least insofar as the laser beam and the entrance slit image are displaced

by the same amount. Even when the beam and slit image do not suffer relative displacement, a

refractive index gradient can still lead to a spatially distorted LIF profile.

85
Rather than collecting fluorescence from the entire (v'=0, v"=0) band we used a

monochromator to isolate appropriate transitions. Although this approach gives a lower

fluorescence signal, it has two advantages: (1) serf-absorption can be reduced through selection

of the detected line; and (2) detection of Rayleigh scattering or scattering from the burner surface

can be eliminated. Though this method proved satisfactory, perhaps a better excitation/detection

scheme for our conditions would include (1,0) excitation and (1,1) wide-band detection (Laurendeau

and Goldsmith, 1989). In addition to satisfying the criteria of minimal serf-absorption and detected

scattering, this method does not require a monochromator, thus yielding a higher fluorescence

collection efficiency.

We now make the following observations regarding the effect of collisions on our relative

fluorescence signals. When rotational equilibrium--that is, steady state of the relative populations

of the rotational levels--in the A2_+(v=0) state of OH is established, the ratio of population in the

directly-excited rotational level to that in the neighboring rotational levels is insensitive to gas

composition and temperature (Smith and Crosley, 1981 ; Zizak et al., 1986). Thus, we expect that

the fluorescence collected from the directly-excited rotational level will be as insensitive to the

collisional environment as fluorescence from the entire (0,0) band. In addition, we expect some

change in the quenching rate at constant pressure through the reaction zone and from flame to

flame insofar as the concentration of quenching species and temperature change. However, as

shown in two previous experiments, over the range of mixture ratios and temperatures expected,

this variation in electronic quenching may not be large. First, Stepowski and Cottereau (1981),

using three low-pressure 03H8/O2 flat flames (equivalence ratios 0.55, 1.0, and 1.25), showed that

for a given flame, the net electronic quenching of OH is approximately constant from the burnt-gas

zone to below the luminous region. Also, at a constant height above the burner, the variation in

quenching rate among the three flames was within about 20% of the maximum value (which was

found in the stoichiometric flame). Second, Schwarzwald et al. (1988) measured electronic

quenching rates of OH in atmospheric-pressure CH4Jair flat flames (equivalence ratios from 0.77

to 1.43). Not surprisingly, the electronic quenching was approximately constant in the burnt-gas

region (y = 0.5 - 20 mm) of each flame; in addition, at a constant height (y = 20 mm), there was no

discemable difference in quenching over the range of equivalence ratios studied.

t#

85
0.0

0

I I l I I

000 •

@

° • •

Q

_o0_O lib I •

lU •

• • III

• •

immIli I

I I I 1 l

5 i0 15 2O 25

Distance From Edge (mm)

Figure 5.3 Horizontal fluorescence profiles 1.5 mm above the burner at (A) 12.6 and (B) 3.2 atm

obtained by detecting the O12(10) transition. The bracketed region denotes the range

of horizontal locations for the vertical profiles in Figs. 5.4-5.9.

87
1.0

_8

._,,4

U3

0.8

0

_J

0.6

0.4

0.2

0.0

0.0

' I

m n • •

• i

&A •

All

• m

v v

V

V

V •

A

T •

• •

v •

j F

• -A

• -B

• -C

- -D

• •

• •

& A A A

V V V

mmm m

& & & A

V V V V v

, l , I , . I _ I

0.5 1.0 1.5 2.0

Distance From Burner (mm)

Figure 5.4 Vertical fluorescence profiles at 3.2 atm. Flow rates of C2H6JO2/N2 (slpm): (A)

0.16/0.75/2.2 (1 atm); (B) 0.29/1.17/3.87; (C) 0.23/0.95/3.42; (D) 0.20/0.87/3.11.

88
.I,,.-I

U3

E)

O

O

_J

..i.a

¢0

1.0

0.8

0.6

0.0

0.0

1 ' I

Do

u_Ru

uu

• IC)

io

[]

[]

I

0

B

UGuui

I L i l L L i I

0.5 1.0 1.5 2.0

Distance From Burner (mm)

Figure 5.5 Vertical fluorescence profiles at3.2 arm.

(E) 0.29/1.17/3.87.

Flow rates of C2H6/O2/N 2 (slpm): (B) and

89

C-J-
For each of the following vertical fluorescence profiles, the monochromator was tuned to

detect the P1(9) transition (._ = 312.5 nm). The entrance and exit slit widths were 30 #m, while the

entrance slit height was 2 mm; the resulting spatial resolution is _,bout 42 #m by 2.9 mm, and the

theoretical spectral resolution is 0.03 nm. For all measurements shown below, each data point is

the average of the fluorescence signal from 600 laser shots. Because serf-absorption of the P1(9)

fluorescence was evident in atmospheric-pressure flames, the burner was positioned horizontally

such that the laser probe was at the near edge of the flame (about 3-5 mm from the edge of the

burner). With this approach, we can reduce the effect of self-absorption on the relative profiles,

and we can probe closer to the burner without blocking portions of the fluorescence signal.

Normally, we did not probe closer than -0.35 mm above the burner surface; when measurements

closer to the surface were desired, we blocked the lower half of the fluorescence cross section to

eliminate vignetting of the fluorescence profile. Using this method, we probed to within -0.2 mm

above the burner. In addition, the flames examined were lean, ranging in equivalence ratio from

about 0.54 to 0.94.

Though monitoring the P1(9) line was satisfactory for the vertical fluorescence profiles, for

horizontal profiles the monochromator was tuned to the O12(10) line (,_ = 316.5 rim); this line has

a much lower absorption cross section (Dimpfl and Kinsey, 1979), and thus fluorescence from this

line is not significantly affected by serf-absorption. Figure 5.3 shows typical horizontal fluorescence

profiles (which have been scaled for convenience) in the burnt-gas region (y = 1.5 mm above the

burner) for flames at 3.2 and 12.6 atm. At this height in these flames, the OH concentration gradient

is small; consequently, the monochromator slits were opened to 140 pm (for the measurement at

3.2 atm) and 200 #m (at 12.6 atm) to collect more photons per laser shot. Though the fluorescence

was primarily from the O12(i 0) line, the P2(14) and the P1(15) lines--which are about equidistant

from the O12(10) line--give a small contribution to the total signal. At both pressures, the profiles

show a rise inthe fluorescence signal at about 1 cm from the burner edge; this nonuniformity, which

was always observed in the horizontal profiles, probably results from a defect in the burner design

or construction. In addition, at 12.6 atm, the photodiode signal decreased near the far edge of the

flame, indicating that the beam was suffering some displacement; the sharp drop in fluorescence

at this edge suggests that beam steering was also distorting the relative concentration profile.

9O
Vertical profiles of the relative OH concentration at 3.2 atm are shown in Figs. 5.4 and 5.5;

profiles B through D were taken consecutively and are compared to profile A from an

atmospheric-pressure flame. At this pressure over a range of flow rates, we were able to probe

within the flame reaction zone, where much of the interesting chemistry takes place; we were aided

in this effort by our ability to probe very close to the burner surface. For adequate resolution near

the flame front of the high-pressure flames, the burner was translated -50 #m after each data point;

away from the flame front the data points are separated by -100 #m. Comparison between the

atmospheric profile and those at 3.2 arm shows, as expected, a significant reduction in the flame

thickness (Williams, 1985). Because the flow rates of fuel and oxidizer are below the values at which

the minimum stand-off distance is obtained, a decrease in their flow rate increases the stand-off

distance (Ferguson and Keck, 1979; Chao and Law, 1988); decreasing the N2 diluent flow rate,

however, has the opposite effect. With the changes in flow rates we find a decrease in the

fluorescence signal. At least part of this reduction is probably due to the lower flame temperature

[which we would expect from a reduction inthe C2H6 and 02 flow rates (Ferguson and Keck, 1979)]

and the concomitant decrease in equilibrium and superequilibrium OH; note, however, that a

decrease in temperature could also lead to an increase in electronic quenching of the excited OH

('Garland et al., 1986; deffries, et al., 1988) and hence a decreased fluorescence yield. An additional

effect of reducing the flow rate of the mixture is that the diameter of the flame decreases slightly;

consequently, when sampling near the edge of the burner, the flame position can change with

respect to the probe volume. This may have happened with profile D, where the fluorescence signal

is lower than expected in comparison to profiles B and C.

After the completion of each profile, the burner was translated back to the initial position (y

= 0.2 ram), with the backlash from the translation system first being removed, and the next set of

measurements was begun. Figure 5.5 demonstrates the repeatability of the measurements; curves

B and E, which have the same flow rate, were taken consecutively. The small decrease in signal

from flame E to B probably results from drift of the laser wavelength from the peak absorption

wavelength.

Vertical OH fluorescence profiles taken consecutively in flames at 6.3 arm are shown in Figs.

5.6 and 5.7. With large reductions in the C2He and 02 flow rates (and a smaller reduction in the N2

flow rate) the flame front moves away from the burner; thus for profiles C and D the reaction zone

is observable. Profiles A, B, and C were taken consecutively, while profile D (Fig. 5.7) was recorded

two days later under the same conditions as C to assess its repeatability. Forthese measurements,

9]
1.0

U]

0.8

0.4

>

°_,_

-_ 02

0.0

0.0

Figure 5.6

• •

• •

• •

!

le,,

t ' I

• -A

• --]3

• --C

O• O

II I O • O o

• mmmmU i mmmm

• • • • • • &

L l = 1 i t i ,,L

0.5 1.0 1.5 2.0

Distance From Burner (mm)

Vertical fluorescence profiles at 6.3 atm. Flow rates of C2Hs/O2/N2 (slpm): (A)

0.38/1.4616.38; (B) 0.29/1.17/5.63; (C) 0.2010.8614.92.

92
_0

• =,--I

1.0

o 0.8

0

o 06

¢)

0

l>

¢;

04

02

0.0

0.0

Z_

&

z_

Z_

Z_

Z_

Z_

_A

L I m 1 , I , I

0.5 1.0 1.5 2.0

Distance From Burner (mm)

Figure 5.7 Vertical fluorescence profiles at 6.3 atm.

(D) 0.20/0.86/4.92.

Flow rates of C2H6/O2/N2 (slpm): (C) and

93
1.0

0.8

0.4

or.-I

_ 02

0.0

0.0

' I ' I ' ! '

• -A

• B

• C

D

OA

&N

IA tO OOoOOotO0 O !

m_n"ulndhmnlnumimll|mm

I i I I i 1 _ I

0.5 1.0 1.5 2.0

Distance From Burner (mm)

Figure 5.8 Vertical fluorescence profiles at 9.5 atm. Flow rates of C2Hs]O2/N2 (slpm): (A)

0.54/3.12/10.3; (B) 0.40/2.58/8.06; (C) 0.40/2.58/8.85.

94
1.0

• p,,,4

r_

o 0.8

(D

0

0.6

E)

0.4

-_ 0.2

0.0

0.0

' I ' I ' I ' I

q,

[]

• @

00 O

mmmmmmm m

, I * I , I _ I

0.5 1.0 1.5 2.0

Distance From Burner (mm)

Figure 5.9 Vertical Fluorescence profiles at 12.6 atm. Flow rates of C2Hs/O2/N2 (slpm): (A)

0.65/2.43/12.2; (B) 0.43/2.20/7.94.

95
the collection cross section was not blocked; thus the initial height above the burner for profiles A,

B, and C is 0.4 mm. For profile D in Fig. 5.7 the initial height is 0.35 mm, and the first 17 points are

separated by only -25 #m. Near the flame front, the shot-to-shot noise of the fluorescence signal

for profiles C and D was larger than would be expected from Poisson statistics; this undoubtedly

is due in part to the large gradients of temperature and concentration in this region. As noted above,

we did observe some displacement of the beam relative to the sampling window. We have made

no attempt in these measurements, however, to quantify or remedy this effect.

Profiles from flames at 9.5 atm, which were taken on the same day (with profiles B and C

taken consecutively), are shown in Fig. 5.8. Starting with flame B we attempted to probe the reaction

zone by slightly increasing the diluent flow rate; the result is shown as profile C. At these conditions,

further increase in the diluent flow rate resulted in a wrinkled flame, indicating that the flame was

near its blow-off limit. As with measurements at 3.2 atm, the collection cross section was blocked

and an initial height of 0.2 mm was used; furthermore, the initial 9 data points are separated by -25

#m. As expected, flames B and C, differing only slightly in the diluent flow rate, have similar levels

of OH in the burnt-gas region. (The flame temperature will decrease with increasing diluent flow,

but only weakly since the flame will stabilize further from the burner where its conductive heat loss

is less.) As was observed in profiles C and D at 6.3 atm, the noise in the fluorescence signal (for

all 3 profiles) at 9.5 atm was significant below about 0.5 ram, where the [OH] gradient is very large.

Because of the higher net reaction rate at greater pressure, equilibration also occurs at smaller

distances from the burner surface (e.g., < 1.5 mm for OH).

In Fig. 5.9, we show the OH measurements for 2 flames at 12.6 atm; the profiles, which were

taken on separate days, have been scaled for convenience. With B the fluorescence cross section

was blocked, while for A it was not. As expected, the larger flow rate acts to spread out the

recombination zone. These profiles also point to a limitation of this particular burner; the flame

stand-off distance may be on the order of the grain size of the sintered metal (-100 #m). Finally,

the flames became increasingly unstable with increasing pressure; because we sought quiescent

conditions in which to make LIF measurements, this is the highest pressure at which we chose to

take data. Nevertheless, higher pressure flames were easily obtained with the McKenna burner.

5.4 Summary

We have presented measurements of relative OH concentration using the LIF method in flat

laminar, lean premixed 02H6/O2/N2 flames at 3.2, 6.3, 9.5, and 12.6 atm. At these pressures, we

96
have measured vertical fluorescence profiles over a range of flow rates of the combustible mixture

and have demonstrated that in some cases the reaction zone can be probed. In comparison to

atmospheric-pressure flames, we observed that at high pressure the reaction zone was small and

accordingly vertical gradients of temperature and concentration could be very large (in the reaction

zone, as well as in the recombination zone). One result of the large gradients was an increase in

the noise of the fluorescence signal even from small flame disturbances. An impediment to making

measurements in these experiments was beam steering (of the laser beam relative to the

fluorescence collection window), which arose from flame oscillations and increased with pressure.

Because we were interested in making measurements under steady, laminar conditions, we chose

not to make measurements in flames above 12.6 arm.

97
CHAPTER6

SATURATEDFLUORESCENCEMEASUREMENTSOFTHEHYDROXYL

RADICALIN LAMINARHIGH-PRESSUREC2H6/O2/N 2 FLAMES

6.1 Introduction

Measurements of flame species by optical methods, such as laser-induced fluorescence

(LIF), have proved valuable in elucidating chemical and physical processes occurring in combustion

environments (Eckbreth, 1988). Fluorescence measurements are relevant to the study of a broad

range of practical combustion topics including turbulent flames, engine knock, pollutant formation,

and flame stability. Linear fluorescence methods are particularly useful for turbulent flames, where

2-D images of relative species concentrations can yield insight into the complex interaction between

chemistry and the flow field. In comparison, laser-saturated fluorescence (LSF), which is currently

limited to point-wise or perhaps 1-D measurements, is attractive because it can provide reliable

absolute species concentrations. Moreover, unlike linear fluorescence, LSF measurements are

insensitive to the rate coefficients for both laser excitation and collisional de-excitation. As a

consequence, in situ calibration of the fluorescence signal is not necessary: a calibration factor

determined in one flame (through techniques such as Rayleigh scattering or absorption) can more

easily be applied to other flames where calibration is more difficult or perhaps impossible [e.g.,

turbulent or sooting flames (Lucht et al., 1984, 1985; Drake et al., 1984, 1985)].

Since LSF was first proposed as a combustion diagnostic (Piepmeier, 1972a; Daily, 1977), it

has been used to detect the diatomic molecules C2 (Baronavski and McDonald, 1977; Mailander,

1978), MgO (Pasternack et al., 1978), CN (Bonczyk and Shirley, 1979; Verdieck and Bonczyk, 1981),

CH (Mailander, 1977; Bonczyk and Shirley, 1979; Verdieck and Bonczyk, 1981; Kohse-Hoinghaus

et al., 1983, 1984; Takubo et al., 1983), OH (Lucht et al., 1978, 1983, 1984, 1985; Kohse-Hoinghaus,

1983, 1984, 1986; Drake etal., 1984, 1985; Salmon and Laurendeau, 1985a, 1985b) and NH (Salmon

et al., 1984) in both subatmospheric and atmospheric flames. Initial experiments (Pasternack et

al., 1978; Bonczyk and Shirley, 1978; Verdieck and Bonczyk, 1981) showed significant disagreement

98
between the fluorescence and independent absorption measurements. Later, however, Lucht et

al. (1983) and Salmon and Laurendeau (1985a) compared LSF measurements of OH concentration

(calibrated using Rayleigh scattering) with independent absorption measurements in low-pressure

(72 torr) laminar H2/O2/Ar flames and demonstrated that saturation can be used to obtain accurate

number densities (+ 15-25%) under these conditions.

In this chapter, we discuss the efficacy of the LSF method for measurement of OH

concentration inhigh-pressure (P > 1 atm) flames. We first describe our efforts to achieve saturation

of an OH transition in a series of C2H6JO2/N2 flames. We then test the adequacy of the balanced

cross-rate model at high pressure. This model was used successfully by Lucht et al. (1983) and

Salmon and Laurendeau (1985a) at low-pressure to relate the population of the laser-coupled

rovibronic level in the excited state to the unperturbed population of the laser-coupled rovibronic

level in the ground state. In essence, the model states that

N,+Nt_N ° o (6.1)

where Nuand NI are the instantaneous populations of the upper and lower laser-coupled rovibronic

levels, respectively, and N o,is the unperturbed population of level I. To evaluate the adequacy of

Eq. (6.1), we compare absorption and calibrated LSF measurements up to a pressure of -6 atm.

We also present absolute OH concentration profiles for lean flames at about 1, 3, 6, 9, and 12 atm;

to our knowledge, these are the first absolute concentration measurements of OH in high-pressure

flames made with LIF.

6.2 Theory

During laser excitation the population of the directly-excited rovibronic level Nu peaks and

Thus, from the rate equation describing the upper laser-coupled steady-state conditions apply.

level (Chapter 3),

N. l (6,2)

Ni gtlg,,+Qos/Ihil=

where gl and gu are the respective degeneracies of levels I and u, and Wju is the rate coefficient for

absorption. Qo_, the effective rate coefficient for collisional depopulation of the directly-excited

level, includes contributions from rotational and vibrational energy transfer, electronic quenching

and spontaneous emission. In general, the population of Nu can be related to N t°by

N.+Nt = (l -y)N °j (6.3)

99
where 1 - ,/is the fraction of the original population remaining in the laser-coupled levels, and N o

is related to the species number density through the Boltzmann fraction. Combining Eqs. (6.2) and

(6.3) gives

N== g_= N_'(] ° -¥)a,o, . (6.4)

g_+gu

where a_t, the degree of saturation, is given by

oz,,, = 1 + g,,l(g,+g,,)]-I "_ .

(6.5)

and W' = Wlu/Q_f is the saturation parameter.

The observed fluorescence signal is given by the integral of the local excited-state population

over the imaged volume; i.e.,

$t= hCVlA/ 4r¢ _, (rlf2) N_(x,y,z)dV . (6.6)

where vf (cm-1) is the frequency of the observed transition, Af (s-1) is the Einstein coefficient for

spontaneous emission, I?(V/W) is the net efficiency of the detection system, and fl (sr) is the solid

angle defined by the collection optics. In this experiment, the image of the monochromator entrance

slit was rotated by 90° so that the slit width was perpendicular to the direction of travel of the beam

(Fig. 6.1). If the dimensions of the slit imaged on the laser beam, H and W, are small compared to

variations in the local excited-state number density, then fNudV = HWfNudx. When N odoes not

vary with the depth of the beam, we can solve for the unperturbed number density via Eq. (6.4) to

obtain

NO g,+g,, 4_St (6.7)

g" hcvtA/(Hhlq_Z)/a(1 - y)a,atdx

g,+g= 4_$t/N °

z

g" hcvtA/(HWq_) fda=,.dx

(6.8)

By rearranging this equation we obtain

f(l - y)_,o, dx

<Fc> " f dx

which represents the spatially-averaged fraction of population remaining inthe laser-coupled levels

(Chapter 3). Note that insofar as W/u is independent of x (e.g., along the beam center line), (Fc)

reduces to 1 - '/.

100
H

\

\

\

\

Laser Beam W Fluorescence

Figure 6.1 Geometry of the fluorescence collection volume.

The parameter I - ./is approximately unity and the balanced cross-rate model is valid when

the population transfer rates into (Rin) and out of (Rout) the laser-coupled levels are balanced, i.e.,

'(R,. - " 0 (6.9) R o=, )dt i

where t = 0 and t = r represent the start of laser excitation and the observation time, respectively.

On the other hand, for the OH molecule with A2_+.--X2]I(0,0) excitation, a likely scenario for

depletion of the laser-coupled levels includes (1) electronic quenching from 2_+(v'=0) to the

zlI(v">0) levels followed by (2) slow vibrational transfer to v" = 0 (Campbell, 1984a; Rensberger

et al., 1989; Wysong et al., 1989). Following the approach used in Chapter 3, the rate coefficient

for quenching from rovibronic level i to the vibrational bath level (a composite of the v" > 0 levels)

is modelled as a fraction fb of the total population leaving rovibronic level i,

Q,(i,b)=f_Q, , (6.10)

101
where we use the notation Qe instead of Qe(O,since we assume that the rate coefficient for electronic

quenching is independent of rotational level i (Kohse-Hoinghaus et al., 1988). Similarly, the rate

coefficient for vibrational transfer from v" > 0 to v" = 0 is expressed as a fraction fv of Qe,

Q_(b)=r_Q, (6.1 l)

When the ratio fb/fv is large, the population of the vibrational bath level will be large at high pressures

(i.e., when a sufficient number of collisions have taken place), and thus it is likely that the

laser-coupled levels will be depleted. Consequently, the balanced cross-rate model will not be

strictlyvalid. However, at sufficiently high pressures, the local depletion 1 - ./reaches an asymptotic

value, which occurs because the coltisionally-excited rotational and vibrational energy levels attain

sufficient population to balance the population transfer rates into and out of the laser-coupled levels

(see Chapter 3). Therefore a modified balanced cross-rate model, Eq. (6.3), could be useful for

making concentration measurements if the spatially-averaged population fraction, (Fc), is

reasonably insensitive to the collisional environment. In other words, by calibrating fluorescence

measurements with a method which gives an absolute concentration (e.g., absorption), (Fc) is

automatically accounted for inthe calibration factor. Fluorescence measurements calibrated with

a method such as Rayleigh scattering (Salmon and Laurendeau, 1985a, 1985b; Kohse-Hoinghaus,

1983, 1984), however, will be in error by 1 - (Fc).

6.3 Experimental Apparatus

Our high-pressure combustion facility includes the following: (1) a pressure vessel

constructed from standard stainless steel piping components (Fig. 6.2); (2) an electronic gas delivery

system, which is interfaced to a microcomputer; (3) a sintered bronze water-cooled fiat-flame burner

(2.5 cm in diameter) surrounded by a guard ring; and (4) an internal x-y burner translation system

employing stepper motors. The range of movement of the vertical and horizontal translation

mechanisms is about 11 and 2.8 cm, respectively, while the associated single-step resolutions are

about 2 and 1 #m. The motors are stepped using a microcomputer, and thus we can accurately

position the burner. Because flow instabilities in the burnt-gas region of the flame increased with

increasing pressure, a screen was attached to the burner housing -8 mm above the burner surface.

This provided a significant improvement in flame stability. Further details of the combustion facility

are given in Chapter 4.

102
I

Figure 6.2 Cutaway view of the pressure vessel and components.

103
DCR-3G

I

' 11 I I

PDL-2 ]

111I

WEX-1

PD

L (250)

PV

---f

Trigger ._ Sampling

E3S Modules

BD BS

i Monoch romator

FB

LI(180)

L (250)

Lc(250)

Computer

Figure 6.3 Schematic for LSF experiments, Components: A - aperture; BD - beam dump; BS -

beam splitter; BSA - beam steering assembly; FB - fluorescence block; L - lens; MA -

image-rotating mirror assembly; PD - photodiode; PMT - photomultiplier tube; PP -

Pyrex plate(s); PV - pressure vessel.

104
The optical layout for the fluorescence measurements is shown in Fig 6.3. The second

harmonic (at 532 nm) of a Quanta-Ray DCR-3G Nd:YAG laser is used to pump a PDL-2 dye laser,

which includes transversely-pumped oscillator and preamplifier stages along with a

longitudinally-pumped amplifier stage. To achieve high conversion efficiency of the 532 nm

radiation, the dye laser employs a mixture of Exciton DCM and Sulforhodamine 640 dyes. Using

this procedure, we obtained a laser energy of -95 mJ/pulse at 620 nm, with an input energy of

-380 mJ/pulse at 532 nm. The output of the dye laser is frequency doubled in the Quanta-Ray

Wavelength Extender (WEX-1). The visible and UV beams are dispersed with a Pellin-Broca prism,

with a portion of the visible beam (not shown in Fig. 6.3) used to trigger the detection electronics.

We obtained as much as 20 mJ/pulse of UV energy at -310 nm, though this value dropped to about

15 mJ/pulse over the course of the experiment. The UV beam was raised to the appropriate height

with a beam steering assembly; the resulting polarization of the radiation was vertical. The UV beam

was also attenuated when necessary with Pyrex plates, and an aperture placed before the focussing

lens was used to block scattered radiation. We used a 250-mm focal-length fused silica lens to

focus the beam over the burner and a second 250-ram focal-length lens to collimate the beam after

the exit port. At the exit port, the vessel window is fixed at a 10° angle so that light reflected from

the window surfaces is directed away from the laser probe volume. Finally, a portion of the beam

was directed to a silicon UV-sensitive PIN photodiode (Hamamatsu S17722-02), which monitored

the shot-to-shot fluctuations of the UV beam energy. Though somewhat slow, this photodiode,

because of its large sensitive area, was especially valuable when measuring the integrated beam

intensity; for example, we employed this photodiode when positioning the burner relative to the

laser beam to determine the burner zero position.

Fluorescence was collimated with another 250-mm focal-length lens and was rotated by 90°

with a mirror assembly; the fluorescence was then focused on the entrance slit of a 3/4 meter

monochromator. For the saturated fluorescence measurements, the slit width and height were 30

#m and 2 ram, respectively; this resulted in a spatial resolution of 42 /_m by 2.9 mm. For

measurements close to the burner surface, we blocked the lower half of the fluorescence beam

prior to the image rotating mirror assembly; thus we could probe close to the burner without

vignetting the fluorescence profile. The Spex 1800-11monochromator employed a specially-wired

RCA 1P28B photomultiplier tube (Harris et al., 1976) with a 1000 V supply voltage for detection of

the spectrally resolved fluorescence signals.

105
.iJ

EL

C)

t--

Q.

1.0

O.B

0.5

0.4

0.2

0.0

B

t

/

.e

.e

•" ,,

° .t•

m 6

7

w

t #

e

t,

dl.

• =•

e_e$

V

I I i i ' x

1.0

O.B

:)

13_

_ O.E

0

0.2

O.C

m

m

m

D

D

m

]

_._o

/.;:"

o:

.! A

_WTm L •

5 10 15 20

Time (ns)

Figure 6,4 Average temporal intensity (30 scans) of the UV beam measured with the

photomultiplier tube using Rayleigh scattering (top); average temporal intensity (10

scans) of the UV beam measured with the avalanche photodiode (bottom).

106
The PMT and photodiode signals were recorded with equipment from Stanford Research

Systems; for the saturated fluorescence experiments, the PMT signal was resolved with the 200 ps

sampling gate of the SR255 fast sampler, which was set at the peak of the fluorescence pulse using

an SR200 gate scanner. The voltage output from the SR255 was then digitized and stored with the

SR245 computer interface module and the SR265 software package, which we modified to allow

programmed movement of laboratory stepper motors. For the PIN photodiode, we used a 10 ns

gate of the SR250 gated integrator and boxcar averager.

_t

The average temporal response of the PMT using Rayleigh scattering is compared in Fig. 6.4

to the average intensity profile obtained with a silicon avalanche photodiode (Texas Instruments

TIED56), which has a temporal response of -200 ps (Harris et al., 1980). These waveforms were

recorded by repetitively scanning in time over the signal, using the 200 ps sampling gate of the fast

sampler (SP,255), and a scanning voltage supplied by the SR245 computer interface module. The

average laser pulse has two temporal modes, each with -2.5 ns FWHM. The relative intensity

profile recorded by the PMT compares well with that from the avalanche photodiode, though the

slower PMT response does result in distortion of the waveform.

The power at the peak of the first temporal lobe can be estimated by dividing the average

energy per pulse by the integrated area under the normalized temporal profile (Fig. 6.4); from this

procedure, using a pulse energy of 15 mJ, we calculate a peak power of -3.3 x 106 W. The

associated maximum UV irradiance (W/cm 2) can be estimated assuming the spatial dependence

of the focused beam is described by an axisymmetric Gaussian function with a FWHM of 110 #m

(see Chapter 4). The approximate spot size of the UV beam at the burner was determined by

scanning a knife edge through the focused beam; though the spatial irradiance profile could not

described perfectly by an axisymmetric Gaussian function, this is a convenient approximation for

extracting the center-line irradiance. The resulting peak irradiance is -2.6 x 10lo W/cm2. By using

this small spot size, we can increase the center-line saturation parameter; however, we also

decrease the total number of excited molecules (integrated throughout the probe volume) and

therefore the fluorescence signal.

I07
6.4 Results and Discussion

6.4.1 Saturation Measurements

For the fluorescence experiments, we used the Qt(8)/Pl(9) excitation/detection line pair.

These lines are suitable since they are isolated from neighboring lines; in addition, the population

of the N" = 8 level varies by only -10% over 11O0to 2600 K (Lucht et al., 1984). To attenuate the

laser intensity, we used Pyrex plates which had been calibrated using Rayleigh scattering. To

account for possible variations in transmission with position, we keyed the plates, and thus we

could place them in the same orientation each time. Because the plates steer the laser beam to

different locations in the flame, the fluorescence focusing lens, If, was positioned to maximize the

signal with each change of attenuation; in addition, a dial gage was used to measure the relative

displacement of this lens, which equals (when multiplied by the system magnification) the

displacement of the beam in the flame. Thus, in obtaining vertical profiles of OH concentration, we

could correct the fluorescence signal, if necessary, for the change caused by beam steering. The

five flames used in this study are described in Table 6.1.

Table 6.1 Description of C2H6/O2/N2 flames used in experiments.

Flame Pressure Equivalence Dilution Total Flow

(atm) Ratio Ratio Rate (slpm)

A 0.98 0.77 3.0 3.15

B 3.1 0.76 3.1 4.61

C 6.1 0.91 3.1 6.45

D 9.2 0.92 3.1 8.21

E 12.3 0.92 3.1 8.21

The saturation curve obtained in the atmospheric-pressure flame is shown in Fig. 6.5. When

plotted on a log-log scale, we observe that partia/saturation is achieved over a large range of laser

powers. In addition, the slope isapproximately constant (within the accuracy of the measurements)

on a log-log plot, even with the laser power attenuated by two orders of magnitude. Hence, over

a wide range of laser attenuation, the sensitivity to laser fluctuations is 0.18 (versus 1 for linear

fluorescence). This is the same sensitivity Salmon and Laurendeau (1985b) report for saturation

of OH in a low-pressure (242 torr) H2/O2/Ar flame.

108
Figure 6.5

m

09

_)

L)

00 0.2 0.4 0.6 0.8 1.0

o

>= 1

I I I

0.2 _,_I i j , , , =,,I j , ,,,I

0.01 0.1 1

Relative Laser Power

Saturation curve for atmospheric C2H6/O2/N2 flame. The solid line shows the

saturation behavior for a simple two-level model using the spatial irradiance function

described by Eq. (6.12).

109
Using a simple two-level model (,,/= 0), the predicted relative saturation curve from Eq. (6.7)

becomes

S t /ct asatdX

, (6.]2)

St'' /aa_o_.mdx

where ,_.m refers to the fluorescence signal at maximum laser power and _sat is given by Eq. (6.5).

As shown in Fig. 6.5, good agreement between the theoretical and experimental saturation curves

results when using the spatial excitation function

w f=

hzl_ [l +(x/w)z] z'z (6.13)

where W _, is the absorption rate coefficient at the beam center line, x is the displacement from the

center line, and w is the beam halfwidth. We should note that with a large center-line saturation

parameter, the slope of the saturation curve is especially sensitive to the wings of the spatial

irradiance profile and not to the spatial irradiance distribution at the central core of the profile, even

though this core contains most of the laser energy.

To obtain a realistic center-line saturation parameter in Eq. (6.5), we used the peak center-line

irradiance ! E= 2.6 x 1010 W/cm2. In addition, we employed a dynamic model (see Chapter 3) with

suitable rate coefficients for electronic quenching and rotational energy transfer to obtain Qeff(where

Qe'4is essentially independent of fv and fb). For the burnt-gas region of an atmospheric C2He/O2/N2

flame, the rate coefficient for electronic quenching, Qe, at -1750 K (as derived from

radiation-corrected thermocouple measurements) was calculated using equilibrium concentrations

of the collision partners and the collision cross sections suggested by Garland and Crosley (1986).

With this procedure, we calculate a relaxation time for electronic quenching of --2.2 ns. This

compares favorably with the value of -2 ns measured by Schwarzwald et al. (1988) in atmospheric

CH4Jair flames.

To estimate the rate coefficients Qr(i,j) for rotational energy transfer, we rely on the observation

of Zizak et al. (1986), that when rotational equilibrium--steady state among the relative rotational-level

populations during the laser pulse--is achieved, the ratio Nu/Nc [where Nc is the population of the

collisionally-excited neighboring rotational levels in the 2_+(v=0) state] is sensitive to the

directly-excited rotational level Ne but apparently insensitive to flame composition and temperature

110
for larger values of Ne. Since the ratio Nu/Nc is determined by the ratio of rate coefficients for (1)

Qr(u), the total rotational energy transfer from level u and (2) Qe, the thermally-averaged electronic

quenching, we can use the ratio Nu/N¢ to estimate Qr(u). For Ne = 8 in the burnt-gas region of a

CH4/air flame, Zizak et al. (1986) found Nu/Nc _ 0.2; modelling the excitation dynamics in a flame,

while using the Qr(i,j)/Qr(u)--the relative distribution of the rate coefficients--deduced by Lucht et al.

(1986) for an H2/O2/N 2 flame (see Chapter 3), we find that a value of Qr(u)/Qe = 8.4 gives Nu]Nc -_

0.2. The resulting effective quenching rate coefficient [Eq. (3.16)] at atmospheric pressure is Qeff

= 2.9 x 109 s'_ at the laser center line.

Table 6.2 Modelling parameters describing Q1(8) laser

excitation and collisional quenching of OH in

an atmospheric flame."

E 15 mJ/pulse

PL 3.3x 106W

] F 2.6 x 10lo W/cm2

uo 32328 cm-1

Av E 0.5 cm-1

Atu 6.399 x 105 s-1

W_ 4.2 x 1013 s-1

Qeff 2.9x 109 s-1

Wp' 15x 103

a The laser energy used is the value estimated to reach

the burner (accounting for optical losses) starting with a

beam energy of 18 mJ/pulse.

Finally, assuming the gain curve of the dye laser is described by a Lorentzian profile which

is much broader than the absorption linewidth width, we can estimate the saturation parameter as

Vl= (g.lg,)lLAl=

V'=_= , (6.14)

Q,tt 4_2hc2v3oAvLQ,H

where uo(cm-1) is the absorption frequency, Au/is the Einstein coefficient for spontaneous emission

from level u to I, and A_ L(cm-1) isthe spectral width (FWHM) characterizing the Lorentzian function.

Equation (6.14) gives a peak saturation parameter Wp' _ 15 x 103. The relevant information is

summarized in Table 6.2.

111
m

03

(..)

tO

03

(b

0

:3

m

LL

>

J_

or"

0.2

2

Relative Laser Power

Figure 6.6 Saturation curves for high-pressure C2Hs/O2/N2 laminar flames. The curve from the

atmospheric flame is shown for comparison.

112
!

¢-

03

O

tO

09

1,._

O

LL

w

rr

1.0

0.5

0

1.0

0.5

0

1.0

0.5

,#

oo

e,_,•

,,,,f 1

I o •

.'.,,...-... .

• eo •

,,,,

e_ •

I t ,

D

•_,, o

eee e •

,..-_

,w e

• e

.7

/

• • ee° • •

•".,',.2" ":'."

¢,

oe ee

--..._.,-..

.,,#

C

I Lm I , I

0

0

ee

,_¥_,_t, ,p °w,"

& " 41,

,z,,,,, >

5 10 15 20

Time (ns)

Figure 6.7 Averagetemporal intensity of fluorescence signal for flamesA (30 scans), C (80scans).

and D (80 scans).

113
FromFig.6.5,weexpectthaipartialsaturationwillalsobeobtainedovera largerangeof

pressures;thisisborneoutinFig.6.6,whichshowssaturationcurvesinthreehigh-pressureflames

(seeTable6.1),comparedto thatobtainedintheatmosphericflame.Thehigh-pressurecurves

showareducedslopeatthehighestlaserpowers;atlowerpowers,thefluorescenceapproaches

linearbehaviorandtheslopeincreases.Sincethelaser-coupledlevelsare progressively depleted

as the laser power is increased, the fluorescence signal does not rise as it otherwise would. Thus,

depletion of the laser-coupled levels results in a decreased slope of the saturation curve, both along

the center line and averaged throughout the probe volume. Because of masking by the wings of

the profile, the spatially-averaged depletion of the laser-coupled levels will always be less than, and

perhaps significantly less than, the value along the beam center line (see Chapter 3).

The effect of saturation on the temporal fluorescence profile is shown for flames A, C, and D

in Fig. 6.7: the profiles are broadened compared to the laser profile (Fig. 6.4). These profiles also

give insight with respect to the depletion of the laser-coupled levels (Salmon and Laurendeau,

1985b). By comparing the relative heights of the two temporal modes, one can estimatethe depletion

of the laser-coupled levels at the second mode relative to that at the first. One would also need (1)

a reliable measurement of the relative intensities of the two laser modes and (2) a saturation curve

to describe the sensitivity of the fluorescence signal to W'. Furthermore, with a dynamic model

similar to the one we have used, one could perhaps estimate (Fc) from the fluorescence profile.

Though we do not have a reliable measurement of the temporal dependence of the laser irradiance

for these cases, we can compare the profiles taken in flames A and D (since the temporal

dependence of the laser was consistent from day to day). From this comparison, we observe that

at the second temporal mode, the laser-coupled levels have undergone a spatially-averaged

depletion of -10% at 9.2 arm relative to the second mode in the atmospheric flame.

6.4.2 Fluorescence/Absorption Measurements

To evaluate the efficacy of the balanced cross-rate model [Eq. (6.1)] for predicting number

densities, we compare calibrated fluorescence measurements at high pressure with those from

absorption. The calibration factor for the high-pressure fluorescence profiles is derived from

absorption measurements in the atmospheric-pressure flame (A in Table 6.1). In this way we use

the balanced cross-rate model implicitly, since we do not calculate absolute concentrations directly

]]4
from the fluorescence voltages. At higher pressures, the difference between the calibrated

fluorescence and absorption measurements represents the depletion of the laser-coupled level

beyond that in the atmospheric flame.

The absorption measurements were performed with a 150-W xenon arc lamp. The

small-diameter beam, which was derived with a set of apertures, entered the high-pressure chamber

through the optical access port opposite to the fluorescence collection port (Fig. 6.3). The same

optics used for fluorescence collection were then used to direct the beam to the monochromator.

The effective absorption beam width (i.e., the dimension in the flame stream-wise direction) was

measured to be < 200/_m by translating the burner through the beam; the dimension in the

horizontal direction was - 1 mm. To accurately calculate the OH number density from the measured

integrated absorption (cm-1),we measured an effective absorption path length using horizontal OH

fluorescence scans (Fig. 6.8). The total number density, NT, at radial position x along the absorption

path is determined from the path-integrated number density by

Nr=_f__Nr(_)d_ , (6.15)

where k_'fr, the effective path length, is derived from the radial dependence of the normalized

fluorescence signal, i.e.,

L_tt = f__ S f(_)/ S /(x)d_ (6.16)

To avoid self absorption--which was evident in the atmospheric flame with the Ql(8)/Pl(9)

excitation/detection scheme--we detected fluorescence from the Ot 2(10) line (while still exciting the

Q1(8) transition). Because ofthe reduced signal resulting from the smaller A-coefficient, we opened

the monochromator entrance and exit slits to 200/_m (250 pm in some cases); consequently, the

P2(14) and P1(15) lines, which are about equidistant from the O12(1(3)transition, provide a small

contribution to the total signal. In doing this, we increased the sensitivity to Q_; however, except

at the burner periphery, where the temperature change is large, the variation in Qeffwith horizontal

position should be small. To ensure that the laser probe was similar in diameter to the absorption

beam, we used a 1-mm slit height; the resulting probe dimensions were 290 (or 360) ._m x 1.4 mm.

Forflames A, B, and C, horizontal scans were made at two or more vertical positions to assess the

variation of L,_frwith distance above the burner. Typically, for the central chord of the burner we

found L,_ffto be --24 mm for x _ -9.5 mm (see Fig. 6.8).

I15
Figure 6.8

m

r-

,m

CO

O

cO

09

O

LL

:>

or1.0 -

05-

o

0 , I

1.0-

0.5 _

O

0 _-

1.0-

o

0.5

O

0 --'

-15

0

0

o

000000000

o oo

oo o

Oo

o

o

o

y = 3.6 mm

, I , I I I

0

o

00o000o

0

00000000

0 o

0 o

J I i

0 0

o

o

y = 2.4 mm o

' l , I _ ,I , L ,

OO

0 o

0000 0o00

0 00000 0°0

y = 1,0 mm

o

I , I ,_. I ,, I ., I ,o

-10 -5 0 5 10 15

Distance From Center (ram)

Relative horizontal OH fluorescence profiles from the atmospheric flame using

Q1(8)/O12(10) excitation/detection as a function of position above the burner surface.

The horizontal position for the vertical profiles is x __-9.5 mm

116
I

E

tJ

(D

O

X

-ro

1.5

1.0

0.5

0

'-''' I'''' I'''' I'"'"' '-"i- i2000

0

O

o %

O

D

_O %

O

O

,A

O

O

O

O

o Fluorescence

[] Abs. (Conc.)

O Abs. (Temp.)

-_- Thermocouple

i , ! I i. i ! i i J i I l I i i i ' I !

1 2 3 4

1500

1000

5OO

Distance from Burner (mm)

,,,/

v

(_

I,,..

t'_

E

t--

Figure 6.9 Calibration of relative OH fluorescence measurements [Q1(8)/O12(10)

excitation/detection] using absorption measurements in atmospheric-pressure

C2Hs/O2/N2 flame (flame A in Table 6.1). Multiple data points (for absorption) at the

same height represent measurements made on different days. Temperatures from

(1) absorption and (2) radiation-corrected thermocouple readings are also shown.

1]7
TheSR265 software package was modified to integrate the absorption profiles (Chapter 4);

with this software, analysis of the absorption spectra is fast and accurate. In particular, one need

not rely on the triangular approximation for spectral integration of an absorption line (Lucht et al.,

i978). This becomes important at higher pressures, since an increasing fraction of the total

absorption occurs in the wings of the profile. When using 10 or more absorption lines (which was

typical in flames A and B), the OH number density and temperature could be calculated by using

the curve-of-growth method (Lucht et al., 1978), and fitting the integrated absorptions with a

nonlinear least-squares algorithm (Salmon, 1986a). This routine also employed the data of Rea et

al. (1987, 1989) for calculation of collisional linewiclths (see Appendix B).

We now compare the calibrated fluorescence measurements in flames B and C with

absorption measurements obtained in these same high-pressure flames. The fluorescence

voltages were calibrated using the atmospheric-pressure flame (A) by comparing the relative OH

fluorescence profile with the absolute number-density profile measured by absorption (Fig. 6.9).

For completeness, we also include OH rotational temperatures calculated from the absorption data

and radiation-corrected temperatures from silica-coated thermocouples (see Appendix C). The

uncertainties in the absorption concentrations reflect contributions from (1) the least-squares fit

(the 2-e uncertainty which includes the temperature uncertainty), (2) the collisional linewidths, and

(3) the path-length measurement. To calculate number densities NTat higher pressure P, we employ

the relation

Nr(P) = ItIB/_(P)/.(P)" SI(P) , (6.17)

where fe (cm3/v) is the calibration factor, Sf(P) is the fluorescence voltage at pressure P, and the

correction factors fB, fo, and fe describe changes in the fluorescence signal due to variations in the

Boltzmann fraction, the effective quenching rate coefficient, and the fluorescence collection

efficiency, respectively. The factor f. accounts for the decrease in detected fluorescence

accompanying increased collisional broadening (see Appendix B), which can cause more

fluorescence to fall outside the spectral detection window. For our experiment, the problem is

perhaps exacerbated by a slight misfocus of the entrance slit image at the exit plane (see Chapter

4); nonetheless, we accounted for this effect by measuring the fluorescence signal as a function

of exit slit width in all five flames. The factor fe is defined as the ratio of fluorescence signals at 30

#m and 90 #m, compared at pressure P and 1 atm (flame A); i.e.,

118
[S/(30 Hrn)/S/(90 llrn)]f

/,= (6.18)

[S/(30 pm)/Sl(90 ltrn)]p

Because of the finite slit width (90 #m), fe probably underestimates the correction factor. When the

detected line is well isolated, this correction factor can be reduced or eliminated by increasing the

exit slit width with respect to the entrance slitwidth.

To adequately evaluate the effect of pressure on the efficacy of the balanced cross-rate model,

we also correct the fluorescence signal for its dependence on Qeff- We thus estimate the change

in Qe_ and then determine fo from the atmospheric-pressure saturation curve. In principle, this

correction factor can be calculated from an in situ measurement, employing the method suggested

by Coltereau (1986); in Chapter 7, we apply this method to our high-pressure laminar flames. The

approach we use here is approximate, since the coupling of the laser and the transition depends

on pressure through the frequency of dephasing collisions (Piepmeier, 1972a, 1972b).

Consequently, while the atmospheric saturation curve represents the sensitivity to laser power, it

only approximates the sensitivity to the collisional environment (see Appendix D). The problem of

calculating fo is made worse when depletion of the laser-coupled levels accompanies the variation

in laser power. Here, we have assumed that at atmospheric pressure, the saturation curve is

unaffected by depletion of the coupled levels, To estimate Qe_, we take the same approach

described above for the atmospheric-pressure flame. We calculate Qe [again based on equilibrium

concentrations of the collision partners and the respective cross sections suggested by Garland

and Crosley (1986)], and we again use Qr(U) = 8.4 x Qe. With the dynamic model, we then calculate

the ratio [Qefl]P/[Qeff]l. Not surprisingly, the calculations show that the variation in [QeN]p/[Qeff]1

is determined primarily by the pressure ratio for these lean flames. While the error in the calculated

value of Qeff might be large, we expect the error in the ratio [Qeff]P/[Qeff]l to be small, since the

flames are similar in equivalence ratio, dilution ratio, and temperature (in the burnt-gas region).

Furthermore, because of saturation, the correction factor fo is not sensitive to errors in [Qeff]P/[Qeff]1.

All of the correction factors for the high-pressure flames are summarized in Table 6.3. For

comparison, the correction factor fo is also calculated from the high-pressure saturation curves;

the difference between the two values for P < 9.2 atm is _<10%.

Figures 6.10 and 6.11 compare fluorescence measurements with absorption measurements

for flames B and C, respectively. In addition, in Fig. 6.12, we show hydroxyl concentration profiles

for flames D and E. in flames B through E, the reaction zone was not observed; however, under

119
03

!

E

O

(D

T=.

X

-IO

I !

<><> <>

I

I _5 _--I-'" I I I

<>

0

1.0 o

0.5

, ! i , ! ,i ! i'..t -_---i-i- _-

t. . ._ ¢

o Fluorescence

[] • Abs. (Conc.)

O Abs. (Temp.)

Thermocouple

O

O O O

0 _ , , _ l , _ _ _ [ i i , , 1 _ _ ' ' I

0 1 2 3 4

Distance from Burner (mm)

20OO

15OO

1000

5OO

v

(D

n3

Q.

E

F--

Figure6.10 Comparison between relative OH fluorescence measurements and absorption

measurements in 3.1 atm C2Hs/O2/N2 flame (flame B in Table 6.1). The open and

closed squares represent absorption measurements using (1) 10 or more _!i_eSand

(2) only the Q1(6) and Q12(6) lines, respectively. Temperatures from absorption and

radiation-corrected therm0coupte readings are also shown.

120
1.5 ''_'' I'''' I'''' I '""""'"l 2000

o')

'E

O

(O

O

X

-r"

O

1.0

0.5

0

c+

DD

[]

0

0

0 o

O Fluorescence

[] Absorption

Thermocouple

0 0 0 0

0

0 i, , , , I , , , , I , • , , I , , , , I

0 1 2 3 4

Distance from Burner (mm)

- 1500

,y,

t.._

t,...

(1)

CL

E

(P

F--

1000

5OO

Figure 6.11 Comparison between relative OH fluorescence measurements and absorption

measurements in 6.1 atm C2H6/O2/N 2 flame (flame C in Table 6.1). The absorption

measurements were made using only the Q_(6) and Q12(6) lines. Radiation-corrected

temperatures from a thermocoupte are also shown.

121
03

!

E

0

¢.o

T=.

0

×

-tO

1.0

0.5

0

•0

0

o

I l I !

0

0

eOo

o Fluorescence (D)

• Fluorescence (E)

-0- Thermocouple

0

0

0

0

0

1500

1000

i,,,, _ , • , , i .... l_ 500

1 2 3 4

Distance from Burner (mm)

v

T=..,

E2.

E

CD

t---

Figure 6.12 Fluorescence measurements for flame D (9.2 atm) and E (12.3, Table 6.1) calibrated

from absorption and fluorescence measurements in flame C. Radiation-corrected

temperatures from a thermocouple are also shown for flame D.

122
Table 6.3

Flame

Correction factors for high-pressure flames.a

[Qeff]P/[Qeff]1 fo fe fB

B 3.2 1.30 1.08 1.00

C 6.6 1.56 1.14 1.00

(I.42)b

D 10.1 1.70 1.20 1.00

(1.,r,3)b

Ec _13.5 1.85 1.22 -1.0

a Quenching rate coefficients and Boltzmann fractions were based on

thermocouple measurements at y = 1 mm.

b Values for fo calculated from the high-pressure saturation data.

cTemperatures were not measured for this flame (though the flow rate is

the same as for flame D); the value of fQis based on the pressure relative to

flame D.

certain conditions at high pressure, we were able to probe beneath the flame front (Chapter 5). For

flames B and C, the fluorescence voltages were calibrated using the atmospheric flame (fc = 1.24

+ 0.06 x 1016 cm-3V-1) and the correction factors shown in Table 6.3. For flames D and E0the

fluorescence signals were calibrated by comparing the relative fluorescence profiles to the

absorption measurements in flame C (fc = 2.92 x 1016 cm-3V-1); the correction factors were then

calculated relative to flame C (rather than relative to flame A).

Figure 6.10 shows good agreement between the absorption and fluorescence

measurements, with the calibrated fluorescence measurements yielding a slightly higher

concentration than the absorption measurements. Three of the absorption measurements

(indicated in the figure) are the result of repetitively scanning over only the Q1(6) and the satellite

Q12(6) transitions (which was made possible by computer control of the scanning process). This

approach was used because flame jitter (which increased with downstream position) and

subsequent beam steering reduced the signal-to-noise ratio of the individual absorption lines; the

effect of flame jitter is especially evident with the absorption temperatures. With the multiple scans,

we increased the signal-to-noise ratio of the absorption measurements, since the Q1(6) line had

the largest absorption of the lines analyzed. To extract the total number density from the integrated

absorption, we used temperatures derived from the radiation-corrected thermocouple

measurements. The OH absorption uncertainties (Appendix C) indicated in Fig. 6.10 include

contributions from the uncertainties in (1) collisional linewidths (2) the effective absorption path

]23
length,(3)the integrated absorption (due to the noise in the profile and baseline) and (2) the

temperature (+50 K). In addition, we show the fluorescence uncertainty, reflecting contributions

from drift of the laser frequency (away from _o) and the uncertainty in calibration and correction

factors.

For flame C, absorption measurements of OH concentration were obtained by averaging over

9 to 34 scans of the Q1(6) and Q12(6) lines at a given height above the burner. At higher pressure,

greater flame instability discouraged us from attempting further absorption measurements. As

shown in Fig. 6.11, the calibrated fluorescence measurements in flame C are about 25% below the

absorption values. This difference is presumably due to depletion of the laser-coupled levels beyond

that in flame A. This conclusion is consistent with results from the high-pressure saturation curves

(Fig. 6.6) and the temporal profiles of fluorescence (Fig. 6.7).

Table 6.4 Input parameters for OH dynamic model.a

W_. 4.2x 1013s-1

Qr(u)/P 3.8 x 109 s-1 atm-1

Qe/P 0.45 x 109 s1 arm-1

fb 0.2

fv 0.1

a In addition to scaling the rate coefficients for rotational

energy transfer in the A;_Z;+ (v'= 0) state, the value of Qr(u)

was also used to scale the Qr(i,j) in the X2]'[(v"=0) state

(see Chapter 3).

Table 6.5 Results of model calculations using the parameters listed in

Table 6.4. The center-line and spatially-averaged

population fractions are values evaluated at the temporal

peak of the excitation pulse.

Pressure (arm) Wp' (Fc) 1 - "7

1 17.4 x 103 0.90 0.85

6 2.96 x 103 0.80 0.67

12 1.48 x 103 0.71 0.52

Further insights on LSF measurements at high pressure can be obtained by employing the

OH dynamic model (see Chapter 3 for details of the model). Input parameters for the model are

listed inTable 6.4. The value offv appears reasonable for ourflame based on recent measurements

124
ofvibrational energy transfer inthe 2]] + state at room temperature (Rensberger et al., 1989; Wysong

et al., 1989). The value of fb is not based on measurements; rather, it was chosen to obtain a large

center-line depletion of the laser-coupled levels. We use Eq. (6.13) to describe the spatial

dependence of the excitation function and a Gaussian quadrature formula to perform the spatial

integration (see Appendix E). The temporal dependence of the excitation pulse is described by a

Gaussian function, with a 2.5 ns FWHM. The remaining input parameters are shown in Table 6.4.

The calculations were performed for flame pressures of 1, 6, and 12 atm, and the results are shown

in Table 6.5.

As noted previously, when (Fc) has a small sensitivity to pressure, Eq. (6.3) can be used to

relate the measured signalto the unperturbed ground-state population. Despite the large center-line

depletion at 12 atm (,7 = 0.48), the relevant spatially-average quantity is [(Fc) p - (Fc)l]/(Fc)l =

-0.21. This is the error one would incur at this pressure in using Eq. (6.3), when calibration is

performed at 1 atm with absorption or some other method yielding an absolute number density.

6.5 Conclusions

In this chapter, we have demonstrated saturation of the Q1(8) transition in the (0,0) manifold

of the OH molecule in high-pressure flames. In particular, we have obtained saturation curves in

C2H6/O2/N2 laminar flames at 1, 6.1, 9.2 and 12.3 arm. Based on these high-pressure curves,

saturation could be attained at pressures > 20 arm in C2Hs/O2/N2 flames. We have also presented

calibrated fluorescence measurements of OH number density at pressures to 12.3 atm; to our

knowledge, these are the first absolute concentration measurements of OH obtained at high

pressure with LIF. To assess the efficacy of the balanced cross-rate model for high-pressure flames,

we have compared LSF measurements, which were calibrated in an atmospheric-pressure flame,

to absorption measurements at 3.1 and 6.1 atm. The high-pressure fluorescence signals were

corrected for both the fluorescence collection efficiency and the finite sensitivity to Q,_. At 3.1 atm

the absorption and fluorescence measurements compare well, with the fluorescence number

densities slightly higher than those from absorption. At 6.1 atm, the concentrations given by the

LSF measurements are ---25% lower than the absorption values, indicating a depletion of the

laser-coupled levels beyond that at atmospheric pressure. The temporal fluorescence waveforms

and the high-pressure saturation curves also suggest a depletion of the laser-coupled levels. The

extent to which the laser-coupled levels continue to deplete with increased pressure is uncertain,

125
and in applying the method to high-pressure flames, it is best to calibrate under conditions similar

to the ones of interest. Nonetheless, we have shown that at moderately high pressures, the LSF

method, when applied to the OH molecule, can give reasonably accurate number densities, even

when calibrating at conditions significantly different from the conditions of interest. We anticipate

that given a reasonable estimate for the finite sensitivity to Qeff (i.e., accuracy within +10% for the

estimated fa), fluorescence measurements accurately calibrated at 1 atm can be applied to flames

at -10 atm with absolute errors within +50%.

126
CHAPTER 7

QUENCHING-INDEPENDENT SATURATED FLUORESCENCE MEASUREMENTS OF THE

HYDROXYL RADICAL IN LAMINAR HIGH-PRESSURE C2H6/O2/N 2 FLAMES

7.1 Introduction

Measurements of flame species by optical methods, such as laser-induced fluorescence

(LIF), have proved valuable inelucidating chemical and physical processes occurring incombustion

environments (Eckbreth, 1988). Fluorescence measurements are relevant to the study of a broad

range of practical combustion topics including turbulent flames, engine knock, pollutant formation,

and flame stability. Linear fluorescence methods are particularly useful for turbulent flames, where

2-D images ofrelative species concentrations can yield insightinto the complex interaction between

chemistry and the flow field. In comparison, laser-saturated fluorescence (LSF), which is currently

limited to point-wise or perhaps 1-D measurements, is attractive because it can provide reliable

absolute species concentrations. Moreover, unlike linear fluorescence, LSF measurements are

insensitive tO the rate coefficients for both laser excitation and collisional de-excitation. As a

consequence, in situ calibration of the fluorescence signal is not necessary: a calibration factor

determined inone flame (through techniques such as Rayleigh scattering or absorption) can more

easily be applied to other flames where calibration is more difficult or perhaps impossible [e.g.,

turbulent or sooting flames (Lucht et al., 1984, 1985; Drake et al., 1984, 1985)].

Since LSF was first proposed as a combustion diagnostic (Piepmeier, 1972a; Daily, 1977), it

has been used to detect the diatomics C2 (Baronavski and McDonald, 1977; Mailander, 1978), MgO

(Pasternack et al., 1978), CN (Bonczyk and Shirley, 1979; Verdieck and Bonczyk, 1981), CH

(Magander, 1977; Bonczyk and Shirley, 1979; Verdieck and Bonczyk, 1981; Kohse-Hoinghaus et

al., 1983, 1984; Takubo et al., 1983), OH (Lucht et ai., 1978, 1983, 1984, 1985; Kohse-Hoinghaus,

1983, 1984, 1986; Drake et al., 1984, 1985; Salmon and Laurendeau, 1985a, 1985b) and NH (Salmon

et al., 1984) in both subatmospheric and atmospheric flames. Initial experiments (Pastemack et

al., 1978; Bonczyk and Shirley, 1978; Verdieck and Bonczyk, 1981) showed significant disagreement

127
between fluorescence and independent absorption measurements. Later, however, Lucht et al.

(1983) and Salmon and Laurendeau (1985a) compared LSF measurements of OH concentration

(calibrated using Rayleigh scattering) with independent absorption measurements in low-pressure

(72 torr) laminar H2/O2/Ar flames and demonstrated that saturation can be used to obtain accurate

number densities (+15-25%) under these conditions.

Because of the lower intensity in the wings of the laser spatial irradiance profile, the

fluorescence signal will always have a finite sensitivity to laser power and quenching. When the

transition is well saturated along the central core of the beam, the sensitivity will be dominated by

the fraction of energy in the wings of the spatial profile. Hence, some error is always incurred when

applying a calibration factor determined in a different collisional environment; the greater the

difference in the effective quenching rate coefficient between the calibration flame and the one of

interest, the greater will be this error.

In this chapter, we describe experimental results using an alternate method first suggested

by Cottereau (1986). This method involves the use of two fluorescence collection geometries for

making quenching-independent measurements using saturated fluorescence. We have applied

the Cottereau approach for concentration measurements of hydroxyl in laminar high-pressure

C2H_O2/N2 flames.

7.2 Theory

steady-state conditions apply.

laser-coupled level, we have

During laser excitation, the population of the directly-excited rotational level peaks and

From the rate equation describing the population of the upper

N_ 1

D= , (7.1)

Ni gllg,,+Q.##lhf.,

where Nu and N# are the respective populations of the upper and lower laser-coupled rotational

levels, gu and gt are the respective degeneracies of levels I and u, and Wtu is the rate coefficient for

absorption. Q_f, the effective rate coefficient for collisional depopulation of the directly-excited

level, includes contributions from rotational and vibrational energy transfer, electronic quenching

and spontaneous emission. In general, the population Nu can be related to N o_,the unperturbed

population of level I, by

N,+N,=(1-y)N ° (7.2)

128
where 1 - ./is the fraction of the original population remaining in the laser-coupled levels, and N (t'

is related to the species number density through the Boitzmann fraction. When the rates of transfer

into and out of the laser-coupled levels are balanced at the observation time r,

o'(R,,-Ro_()dt 0 , (Y.:_)

then I - ./_ 1, and the so-called balanced cross-rate model (Lucht et al., 1980, 1983) is valid. We

note that for OH molecules with XZll(v"=0)---.A2_+(v'=0) excitation, a likely scenario for depletion

of the laser-coupled levels includes population of the v" > 0 levels through (1) quenching from the

ZS+ (`/=0) to the 21"[(,/'>0) levels and (2) slow vibrational transfer to v" = 0 (Rensberger et al., 1989;

Wysong et al., 1989).

The influence of depletion on quantitative LSF measurements has been treated theoretically

and experimentally in Chapters 3 [see also Campbell (1984a)] and 6, respectively. In an experiment

described in Chapter 6, we calibrated fluorescence measurements at high pressure in a flat laminar

atmospheric C2Hs/O2/N2 flame using absorption; we then compared calibrated fluorescence

profiles with absorption profiles in C2H6/O2/N 2 flames at 3 and 6 atm. In the 3-atm flame, the two

measurements showed good agreement, while at 6 atm the fluorescence measurements were

-25% below the absorption measurements. Since the fluorescence values were corrected for their

finite sensitivity to quenching, the -25% disparity at 6 atm presumably arises from a loss of

population from the laser-coupled levels. The saturation curves and the temporal fluorescence

profiles were also found to display qualitative behavior consistent with partial depletion of the

laser-coupled levels.

Combining Eqs. (7.1) and (7.2) gives

N,,= g-i-2--=N°(! - y)a,o, (7.4)

g_-*-g,

where ¢=_t, the degree of saturation, can be defined in terms of the saturation parameter, W' --

Wju/Qeff, by

or

I w

CZ,o, W'+g,,/(g_*-g,) (7.5)

Iv" "/I#_"

a,a ,=l,¢,,IWp. ,.g,,l[Wp.(gt+g,,)] , (7.6)

129
where Wp"is the center-line saturation parameter.

The observed fluorescence signal is given by the integral of the local excited-state population

over the imaged volume; i.e.,

$t hev/A/(rl 4_ f f_) N,,(x, y,z)dV , (7.7)

where vf (cm -I) is the frequency of the observed transition, Af (s-l) is the Einstein coefficient for

spontaneous emission, r/(V/W) is the net efficiency of the fluorescence detection system, and _3is

the solid angle defined by the collection optics. For geometry A (Fig. 7.1), when the image of the

slit width (WA) is small compared to variations in the local excited-stated number density, then

J'NudV -- WAJ'NudAc, where Ac is the cross-sectional area of the laser probe. The measured

fluorescence signal is therefore given by

SIA = hcvlA/(rlAl_'A=QA);A4rc , N=(x,y)d,4, (7.8)

Likewise for geometry B (Fig. 7.1), when the dimensions of the slit imaged on the laser beam, HB

and WB, are small compared to variations in the local excited-state number density, then j'NudV =

HBWBj'NudX. The measured fluorescence signal is thus

S hcv/A t (rlatt , n,) fam.(x)dx (7.9) fn = 4re

If N ois constant throughout the probe volumes, the ratio of the signals is

£

rlAI,dA.OA I " (l-¥)a,=rdAc

S/A

--= ' (7.10)

s, n.n.w.n.;(l -y)a,.td.x"

When the depletion of the laser-coupled levels is small (-/ _ 0) and the spatial dependence

of the saturation parameter corresponds to that of the laser irradiance (i.e., Qeffdoes not vary within

the imaged volume),

ld'(x,y),=l,(x,Y) (7.l I)

t,z p / f

then we can write

. IL }

$t.--2.,] W, ;--'K

StB If'

(7.12)

130
Geometry A

Laser Beam

Fluorescence

\

\

\

\

Geometry B

Laser Beam We Fluorescence

Figure 7.1 Fluorescence collection geometries: top, geometry A; bottom, geometry B.

131
Thus, the ratio of the two signals is a function of the center-line saturation parameter, the spatial

dependence of the laser irradiance, and K, the ratio of detection parameters for the two geometries.

Insofar as the detection parameters and the spatial dependence of the laser irradiance are invariant,

the ratio SfA/SfB will depend only on Wp'. This being the case, the curve of SfA/SfB versus laser

power defines the relative saturation parameter,

I,,','= [ StB.,I , (7.13)

which acts as a quenching calibration function, since Sfg = N o.f_(W/) for g = A, B.

The Cottereau technique is then applied using the following steps.

1. Select a flame and calibrate the fluorescence signals from both

geometries (with measurements from absorption spectroscopy or

Rayleigh scattering, for example).

2. In the calibration flame, generate saturation curves for the two

geometries by varying the laser irradiance, being careful not to

change the spatial dependence of IL. Since the relative laser

irradiance is approximately equivalent to the relative saturation

parameter, Wr', when Qeff is constant, the curve SfA/SfB versus IL

defines the calibration function Wr'(SfA/SfB). This function should be

defined over the range of expected values of Wr'.

3. At the condition of interest, measure SfAand SfB; from the calibration

curve Wr'(SfA/SfB) determine the value of Wr'. With thiS value and

either saturation curve SfA(Wr')or Sfe(Wr'), determine the fractional

change in fluorescence intensity due to the change in the relative

saturation parameter. This value (for geometry A or B) is then used

to correct the fluorescence signal (from geometry A or B) for any

change in the saturation parameter between the calibration flame

and the flame of interest.

Thus, at the condition of interest, the total number density NT can be described by

Nr=S//_[ o. _-[ f, , (7.14)

i

132
where fc (cm3/V) is the calibration factor (determined in step 1), fQ is the quenching correction

factor, which accounts for the fractional change in Wr', and the fi are additional correction factors

(accounting for variations in the Boitzmann fraction, etc.). To illustrate this technique, we consider

Fig. 7.2, where the squares and triangles represent measurements in the calibration flame and the

flame of interest, respectively. In the flame of interest, the measurement of S_A/StB= 0.70 (relative

to SfA/SfB = 1.0 in the calibration flame) gives Wr' = 0.22. From the saturation curves, W/= 0.22

corresponds to quenching correction factors (fQ- 1/Sf for these normalized saturation curves) of

2.13 and 1.49 for geometries A and B, respectively.

7.3 Experimental Apparatus

Our high-pressure combustion facility includes the following: (1) a pressure vessel

constructed from standard stainless steel piping components; (2) an electronic gas delivery system,

which is interfaced to a microcomputer; (3) a sintered bronze water-cooled flat-flame burner (2.5

cm in diameter) surrounded by a guard ring; and (4) an internal x-y burner translation system

employing stepper motors. The range of movement of the vertical and horizontal translation

mechanisms is about 11 and 2.8 cm, respectively, while the associated single-step resolution is

about 2 and 1/_m. The motors are stepped through a microcomputer, and thus we can accurately

position the burner. Because flow instabilities in the burnt-gas region of the flame increased with

increasing pressure (Chapter 5), we attached a screen to the burner housing -8 mm above the

burner surface. This provided a significant improvement in flame stability. Further details of the

combustion facility are given in Chapter 4.

The optical layout for the fluorescence measurements is shown in Fig 7.3. The second

harmonic (at 532 nm) of a Quanta-Ray DCR-3G Nd:YAG laser is used to pump a PDL-2 dye laser,

which includes transversely-pumped oscillator and preamplifier stages along with a

longitudinally-pumped amplifier stage. The output of the dye laser is frequency doubled in the

Quanta-Ray Wavelength Extender (WEX-1), and the visible and UV beams are then dispersed with

a Pellin-Broca prism;though not shown exactly in Fig. 7.3, a portion of the visible beam is then used

to trigger the detection electronics. Forthis experiment we employed -18 mJ/pulse of UV energy.

The UV beam was raised to the appropriate height with a beam steering assembly; the resulting

polarization of the radiation was vertical. The beam was attenuated when necessary with Pyrex

plates, and an aperture placed before the focussing lens was used to block scattered radiation.

133
1.0

0.8

o9_ 0.6

o9

0.4

0.2

n Calibration Flame

A Flame of Interest

|

I I • ! ! I ! J | I

1_ 1 1 1 1 I ! I

o9 J jjTf J

/

0.1 /

f

J

J

f

0.01 0.1

m Geom. A

Geom. B

1

Wr

Figure 7.2 Hypothetical saturation curves and the corresponding quenching calibration curve,

134
DCR-3G

I 1

PDL-2 I

I

II 11

WEX.I

PD

:_ L /_pv

r'n _,

BD S Oll_. _E_

Lf8 Lc_ FB

IMonochromator

Trigger

PMT

Sampling

Modules

Computer

Monochromator

A

I I

Figure 7.3 Schematic for LSF experiments. Components: A - aperture; BD - beam dump; BS -

beam splitter; BSA - beam steering assembly; FB - fluorescence block; L- lens; MA -

image rotating mirror assembly; PD - photodiode; PMT - photomultiplier tube; PP -

Pyrex plate(s); PV - pressure vessel.

135
We used a 250-mm focal-length fused silica lens to focus the beam over the burner and a second

250-mm focal-length lens to collimate the beam after the exit port. At the exit port, the vessel window

is fixed at a 10° angle so that light reflected from the window surfaces is directed away from the

laser probe volume. Finally, a portion of the beam was directed to a silicon UV-sensitive PIN

photodiode (Hamamatsu $17722-02), which monitored the shot-to-shot fluctuations of the UV beam

energy.

Fluorescence was collimated with a 250-mm focal-length lens, and was split with a UV

beam-splitting plate. The fluorescence transmitted by the plate was focused on the entrance slit

of monochromator A. The beam-splitting plate, which had a transmission and reflectance of -30%,

also acted as the first reflector of the image rotating assembly, which rotated by 90° the fluorescence

image; the fluorescence was then focused on the entrance slit of monochromator B. This

arrangement--rather than one with monochromators on either side of the flame--was used so that

the two fluorescence signals would be affected equally by self absorption, which was evident in our

flames. For monochromator A (a Spex 1700), which employed a grating blazed at 1/_m (and was

used in third order), we used an entrance (and exit) slit width and height of 300 #m and 1.2 mm,

respectively. The imaged volume is the disk defined by the width of 500 #m and the diameter dA

of the laser probe (as seen by geometry A). Though the beam width was measured to be about

0.1 mm (see Chapter 4), with saturation, the apparent probe diameter can be much larger (Salmon

and Laurendeau, 1985a). For monochromator B (a Spex 1800-11),which employed a grating blazed

at 300 #m (and was used in first order), we used an entrance slit width and height of 30 #m and 2

mm, respectively, and the associated spatial resolution was 42 #m x 2.9 mm x dB. To increase the

signal for this geometry, we used an exit slit width of 60 #m; this also decreased the sensitivity of

the signal to variations in line broadening concomitant with pressure variations (and noticeable

especially at high pressures). For measurements close to the burner surface, we blocked the lower

half of the fluorescence beam prior to the image rotating mirror assembly; thus we could probe

close to the burner without vignetting the fluorescence profile. The monochromators employed

specially-wired RCA 1P28B photomultiplier tubes (Harris et al., 1976) each with a 1000 V supply

voltage for detection of the spectrally resolved fluorescence signals.

The PMT and photodiode signals were recorded with Stanford Research Systems equipment;

the two fluorescence signals were resolved with the 200 ps sampling gates of two SR255 fast

samplers, which were set at the peak of the respective fluorescence pulses using SR200 gate

136
c

CTI

U3

(0

:_:'l-. PMT A

B _

: ,%o.o:.,.

• °_ .°°a

: \

J

--.d_i | I | I

oee

s." %.

¢ ..

I

! ;

!

e

PMT B

-..._:

I I L

TIED5&

|

J

i I _ _ i

0 5 10 15 20

Tlme (ns)

Figure 7.4 Average temporal irradiance of the UV beam measured with the TIED56 avalanche

photodiode and the photomultiplier tubes for monochromators A and B using Rayleigh

scattering.

137
scanners.Themeasured voltages from the fast samplers were digitized and stored with the SR245

computer interface module and the SR265 software package. Typically, for this experiment we

averaged the fluorescence signal for 600 to 1200 laser shots. For the PIN photodiode we used a

10 ns gate of the SR250 gated integrator and boxcar averager. We note that on the average, only

a small number of fluorescence photons were collected for each laser shot; however, with increases

in focussed beam width, the collection solid angle (n _ 0.006 sr for our experiment), and the

efficiency of some of the optical components (e.g., the beam splitter), single-shot measurements

would be possible.

In Fig. 7.4, the average temporal responses of the PMTs using Rayleigh scattering are

compared to the average intensity profile obtained with a silicon avalanche photodiode (Texas

Instruments TIED56), which has a temporal response of -200 ps (Harris et al., 1980). These

waveforms, which were taken consecutively rather than simultaneously, were recorded by

repetitively scanning in time over the signal, using the 200 ps sampling gate of the fast sampler

(SR255), and a scanning voltage supplied by the $R245 computer interface module. The PMTs

show good temporal resolution, though the convolution of the detector response and the true

temporal profile does result in some distortion of the profile features.

7.4 Results and Discussion

For the fluorescence experiments, we used the Q1(8)/P1 (9) excitation/detection line pair.

These lines are suitable since they are isolated from neighboring lines; in addition, the population

of the N" = 8 level varies by only -10% from 1100 to 2600 K. To attenuate the laser irradiance, we

used Pyrex plates of different thickness; these plates were calibrated against neutral density filters

(inserted in the fluorescence optical train) by using Rayleigh scattering with geometry A, since the

detected signal with this geometry should be insensitive to beam steering caused by the plates.

(We note that Pyrex is not the ideal attenuating material for A __310 nm because the transmission

is a strong function of wavelength.) To account for possible variations in transmission with position,

we keyed the plates, and thus we could put them in the same orientation each time. Because the

plates steer the laser beam to different locations in the flame, the fluorescence focusing lens for

monochromator B, l..fB(see Fig. 7.3), was positioned to maximize the signal with each change of

attenuation; the lens for monochromator A required no adjustment since the probe diameter was

smaller than the slit height. In addition, for lens LfB, a dial gage was used to measure the relative

138
displacement of this lens, which equals (when multiplied by the system magnification) the

displacement of the beam in the flame. Using the vertical fluorescence profile, the saturation curves

could then be corrected for beam displacement. Although the saturation curves are affected by

beam steering, the ratio of the signals SfA/SfB is not affected insofar as Qe, does not vary over the

region probed by the beam.

Because of saturation, the fluorescence signal can also be adversely affected by scattered

or reflected radiation. To block some of this radiation, we placed an iris diaphragm directly before

the laser focussing lens, with the iris opened just wide enough to allow the beam to pass. In addition,

with detection geometry A, we noticed a significant improvement in the vertical resolution of the

atmospheric fluorescence measurements when the window at the laser entry port was removed;

this indicates that the effective probe diameter was increased by the scattered and reflected radiation

from the window. Consequently, we were careful to keep this window clean, thus minimizing the

scattered radiation. This situation could be ameliorated further with anti-reflection coatings on the

windows.

Table 7.1 Description of C2Hs/O2/N2 flames used in experiments.

Flame Pressure Equivalence Dilution Flow Rate

(atm) Ratio Ratio (slpm)

A 0.98 0.77 3.0 3.15

A' 0.98 0.91 3.0 3.2

B 3.1 0.76 3.1 4.6

C 6.1 0,91 3.1 6.45

D 9.2 0.92 3.1 8.2

The C2H6./O2/N 2 flames used in these experiments are listed in Table 7.1. The saturation

curves obtained at atmospheric pressure are shown in Fig. 7.5. Partial saturation is achieved over

a large range of laser powers with both geometries; this is especially evident on the log-log scale

where the sensitivityof the fluorescence signal to laser power is shown to be approximately constant

over two orders of magnitude of IL. Because of the large effective probe diameter for geometry A

and the large vertical gradient in OH concentration, some spatial averaging in the vertical

fluorescence profile was evident in flame A with this geometry. Consequently, to generate the

atmospheric saturation curves (and the quenching calibration curve) we used a richer flame (flame

A'), where the OH concentration gradient was less than for flame A.

139
i

¢...

03

¢.-

(..)

09

O

n

LL

>

Qu

_3

m

n.-

1.0

0.8

0.6

0.4

0.2

0

0

0.1

O Geom. A

• Geom. B

0.2 0.4 0.6 0.8 1.0

O

O

O

O Geom. A

• Geom. B

, , _ _ t ,,,I J . i t ! I I n ol

0.01 0.1 1

Relative Laser Power

Figure 7.5 Saturation curves in an atmospheric C2H6/O2/N2 flame (flame A' in Table 7.1). The

solid lines show the saturation behavior for a simple two-level model using a spatial

irradiance function described by Eq. (7.16), For geometry A, we assume that the

spatial irradiance function is axisymmetric.

140
Table 7.2 Parameters describing laser excitation and

collisional quenching, a,b

E 15 mJ

PL 3.3x 106W

] _ 2.6 x 10lo W/cm 2

W _'u 4.2 x 1013 S"1

vo 32328 cm-1

A/u 6.399 x 105 s-1

Qeff 2.9 x 109 s"1

A/) L 0.5 cm -1

Wp' 15x 103

aThe energy used in the calculation is the value estimated to

reach the burner, accounting for optical losses, when starting

with 18 mJ/pulse.

b At) L denotes the laser spectral width (FWHM).

Using a simple two-level model (,y= 0), the predicted relative saturation curve from Eqs. (7.4)

and (7.7) becomes

S I Iv as°tdV

S /.,,, /va,a_.,,,dV

(7.15)

where Sf,m refers to the fluorescence signal at maximum laser power. For geometry B, good

agreement between the theoretical and experimental saturation curves results when using the

spatial excitation function

w,.= (7.R6)

Wlu(r)= [ 1 + (r/tu)2]2.z '

where W _uis the absorption rate coefficient at the beam center line, r is the radial position, and w

is the beam halfwidth. Calculation of the maximum center-line rate coefficient, W _,, is summarized

in Table 7.2; the resulting maximum saturation parameter is 15 x 103. Estimation of W _, and Wp'

from the laser parameters in Table 7.2 is discussed in detail in Chapter 6. To model the saturation

behavior of geometry A, we again use Eq. (7.16) with the assumption that the excitation profile is

axisymmetric (though we did observe some asymmetry inthe beam profile). The resulting saturation

curve (Fig. 7.5) is in reasonable agreement with the experimental data for geometry A.

141
1...

I.,r'l

u

C

u

tO

m

1,

>

I,. I I I I 1

°IP'& o, Oo

• • g

•_""-'.•?-...i

_e _ ejm

• &

I I:. I 1

i_ "a •

., "_...{2_

I I I I

• - / -, ;::

: : -

iI

°,b •

x., " :.,.

Flame D "_ .,"- Flame D "-.

j Geom. A _,, " Geom. B '_.

.,_-'. .... • ;

' '""'"" ' --":'_'_'.'<,_ i

L .. ,v,_..,. , #..._ ,=... I • ." _" """ I

/ -J_, , , l , ' ,i , Ge m., B ,

0 5 10 15 20 0 5 10 15 20

Tlme (ns)

Figure 7.6 Average temporal intensity of fluorescence signal for flames A (30 scans) and D (80

scans).

| 42
5

4

03

2

©

©

0

©

0.01 0.1 1

Relative Laser Power

Figure 7.7 Quenching calibration curve derived from the atmospheric saturation curves (Fig. 7.5)

inflame A" (see Table 7.1). Multiple data points at the same laser power are repeated

measurements.

143
Figure 7.6 shows temporal fluorescence profiles for the two geometries taken at 1 and 9.2

atm (/lames A and D). As discussed in Chapter 6, depletion of the laser-coupled levels can be

observed (at the second temporal lobe relative to the first) when comparing profiles at 1 and 9.2

atm. This is especially evident with geometry B, where we expect a larger spatially-averaged

depletion of the laser-coupled levels.

In Fig. 7.7, we show SfA/Sfe versus relative laser power obtained from the atmospheric

saturation curves. Though we refer to this curve as the quenching calibration curve, we emphasize

that the corrections derived from the curve take into account variations in laser power as well as

the effective quenching rate coefficient. We now make two observations regarding the quenching

correction curve. First, any depletion of the laser-coupled levels will result in a larger S_A/SfB,since

geometry B (with a smaller contribution from the wings of the fluorescence profile) will show a larger

spatially-averaged depletion than geometry A. Consequently, the measured SfA/SfB yields an

underestimate of the true quenching correction, since a smaller SfA/SfBratio corresponds to a larger

Qeff. Second, the coupling between the laser and the OH molecules depends on (1) the spectral

width of the absorption line relative to that of the laser line and (2) the mode structure of the UV

beam. As the absorption line broadens with increasing pressure (from increased collisional

broadening) and overtakes the spectral width of the laser beam, the molecules will, on the average,

absorb less laser energy (i.e., the coupling between the laser and the transition will become less

efficient). An important consequence is that while the saturation curves describe the sensitivity of

the fluorescence signal to laser power, they show only approximately the sensitivity to collisional

environment. To investigate this difference, we have modelled the excitation process with rate

equations for levels I and u using an approach similar to the one taken by Piepmeier (1972a, 1972b);

we have also included the effect of the spatial excitation profile using Eq. (7.16). With this model,

we calculated the sensitivity of the fluorescence signal to both laser power and pressure. The

results suggest that the Cottereau method provides a good estimate of the quenching correction

factor, fo, which accounts for variations in coupling efficiency as well as quenching and laser power

(Appendix D).

The fluorescence voltages for geometries A and B were calibrated at atmospheric pressure

using flame A by comparing the relative OH fluorescence profiles with a profile of absolute OH

number density derived from absorption measurements (Fig. 7.8). To minimize the effect of self

absorption on the profiles, fluorescence was collected at the near edge of the burner; comparison

144
1.2

1.0

C'3

i

0.8

o

_O

o 0.6

_-_ 0.4

O

0.0

O

' ' I ' _ '" .... '"'1 ' ' ' ' I ' ' ' ' [

,••• o Absorption Fluorescence

•_ • Fluorescence (B)

000000000 •

o o_, z

o o _

8

' _ A I I I I .,L =' ! • • ' ' | * ,I i

0 1 2 3 4

Distance from Burner (mm)

Figure 7.8 Calibration of relative OH fluorescence measurements using absorption

measurements in an atmospheric-pressure C2H6/O2/N2 flame (flame A in Table 7.1).

Multiple data points (for absorption) at the same height represent measurements

made on different days.

145
of the absorption profile with the relative fluorescence profile from geometry B demonstrates that

the fluorescence signal is not measurably affected by self absorption. Comparing the ratios of

S_/JSfBin flames A and A' (see Table 7.3) indicates a slightly larger Qeff for flame A" (relative to A);

consequently, we extrapolated the quenching calibration curve (Fig. 7.7) to obtain the reference

value of Wr"in flame A (where we calibrated the fluorescence voltages with absorption). The effect

of spatial averaging when using geometry A is evident in Fig. 7.8; near the burner, where the OH

concentration varies strongly with position, the fluorescence profiles A and B deviate significantly.

Profile B, because of the small vertical dimension of the sampling volume (42 #m), is not significantly

affected by spatial averaging.

The absorption measurements in Fig. 7.8 were performed with a 150-W xenon arc lamp, and

the effective absorption path length was calculated from horizontal fluorescence scans across the

burner (see Chapter 6). For the absorption measurements in flames A and B, we typically used 10

or more absorption lines and the curve-of-growth method (Lucht et al., 1978) to calculate the total

OH number density. In a few of the absorption measurements at 3.1 arm and all the measurements

at 6.1 atm, we repetitively scanned over the Q1(6) [and the satellite Q12(6)] line. This approach was

used because flame jitter (which increased with pressure) and subsequent beam steering reduced

the signal-to-noise ratio of the individual spectral absorption profiles. With the repetitive scans, we

increased the signal-to-noise of the integrated absorption, since the Q1(6) line had the largest

absorption of the lines analyzed. A significant feature of this approach is that scans affected by

severe noise (e.g., those resulting from arc-lamp fluctuations) can be easily eliminated from the

average. To extract the total number density from the integrated absorption, we used temperatures

derived from silica-coated thermocouple measurements. The uncertainty in the absorption

measurements denoted in Fig. 7.8 reflect uncertainty contributions from (1) the integrated

absorption (cm-1), (2) temperature (3) the collisional linewidths, and (4) the effective absorption

path-length (see Appendix C). In cases where 10 or more lines were used to obtain the total number

density, we calculated the 95% confidence interval, which includes uncertainties from the calculated

temperature and the variation in concentration calculated from the individual lines.

To calculate the number densities NT at a higher pressure P, we used the relation

]46
Table 7.3

Flame

Quenching calibration parameters at maximum

laser power.a, b

S_A/,SfB W,' l/[W,']

A 5.02 1 1

A' 4.87 0.95 1.05

B 3.96 0.42 2.4

(3.2)

C 2.88 0.14 6.9

(6.7)

D 2.24 0.062 16

(lO.2)

=We define Wr" • 1 in flame A.

b The 1/Wr' values in parentheses are estimated from

experimental data describing electronic quenching

(Garland and Crosley, 1986) and rotational energy

transfer ('Zizak et al., 1986; Lucht et al., 1986). See

Chapter 6 for a description of the calculation of this

quantity.

Table 7.4 Correction factors for flames B, C, and D.a,b

Flame fa Geometry A Geometry B

fQ fe fo fe

B 1.00 1.57 1.0 1.21 1.05

(1.30)

C 1.00 2.69 1.0 1.56 1.08

(1.56)

D 1.00 4.17 1.0 1.90 1.09

(1.70)

a The fOBin parentheses are the quantities derived from the estimated

1/Wf" (see note b for Table 7.3).

b The fluorescence calibration factors from flame A are fcA = 0.556 ±

0.028 x 1015 crrr3/V and feB = 2.79± 0.14x 1016 cm-3/V.

NT(P)=t=I,to(P)I,(P).SI(P) , (7.17)

where the correction factors fs and fe describe changes in the fluorescence signal due to variations

in the Bottzmann fraction and the fluorescence collection efficiency, respectively. The factor fe

accounts for the decrease in detected fluorescence accompanying increased collisional

broadening; i.e., with increased collisional broadening more fluorescence will fall outside the

spectral detection window. For geometry A, with the larger spectral width, we assumed fe to be

147
constant; for geometry B, we measured the fluorescence signal as a function of exit slit width in

flames A-D, and the factor fe represents the ratio of signals at 60 #m and 90 pm, compared at

pressure P and 1 atm (flame A); i.e.,

[S;(60 i_rn)/S/(90 I_m)],

= (7.18) J'" [St(60 pm)/Sj(90 prn)]p

Because of the finite slit width WB = 90 pm, this is an underestimate of the correction factor. We

also note that SfA/SfB was calculated subsequent to correcting SfB for increased collisional

broadening. In addition, for all the flames, the quenching correction factor was derived from an

average of several S_A/SfBvalues in the burnt-gas region, where the variation in Q_ should be small.

Averaging these values was not necessary, but it did improve the signal-to-noise ratio of the SfA/SfB

measurement. As discussed above, once SfA/S_e has been calculated, Wr' (see Table 7.3) can be

found from the quenching calibration curve (Fig. 7.7), and the fo can then be determined from the

saturation curves (Fig. 7.5). Values for fB, fQ, and fe for flames B, C, and D are listed in Table 7.4.

The resulting vertical OH concentration profiles for flames B, C and D are shown in Figs.

7.9-7.11. As expected from the measurements described in Chapter 6, the fluorescence and

absorption measurements compare well at 3.1 atm (Fig. 7.9). As at atmospheric pressure,

fluorescence profile A is distorted near the burner surface where the OH concentration is a strong

function of position. At 6.1 atm, the calibrated fluorescence measurements are -25% below the

absorption measurements. This is also the result obtained in Chapter 6, and as we noted above,

it is apparently due to the spatially-averaged depletion of the laser-coupled levels beyond that at

atmospheric pressure. For the measurements at 9.2 atm (Fig. 7.11), we derived fcA and fcB from

the comparison of fluorescence and absorption in flame C (rather than in flame A); the other

correction factors were also referenced to those in flame C. This approach was taken for flame D,

because of the depletion of the laser-coupled levels observed at 6.1 atm.

In addition to the measured Wr" in Table 7.3, we also include the corresponding values

estimated from data describing electronic quenching (Garland and Crosley, 1986) and rotational

energy transfer (Zizak et al., 1986; Lucht et al., 1986; see Chapter 6 for details). The apparent errors

in the estimated Wr' are probably due to (1) uncertainties in the calculation of rotational energy

transfer and (2) omission of the coupling efficiency between the laser and the transition. We also

note that the quenching calibration curve (i.e., SfA/Sfe versus laser power) and thus the measured

Wr' may be affected slightly by some spatial averaging (with geometry A) inflame A'. Nevertheless,

148
1.2

10

08

0

0.6

I"'--'1

o 0.4

Oo_g

00

$

o,-, Absorption

o Fluorescence (A)

• Fluorescence (B)

0 o • o o o

0

I, , , , , I , , , , I , , _ , I

I 2 3

Distance from Burner (mm)

Figure 7.9 Comparison between relative OH fluorescence measurements and absorption

measurements in3.1 arm C2H6/O2/N 2flame (flame B in Table 7.1). The closed squares

represent absorption measurements using the Q1(6) and Q12(6) lines.

149
03

I

¢J

c,O

O

O

I--..,-I

1.2

1.0

0.2

0.0

0

' I ' ' ' ' I ' ' ' ' I

O

O

[]Absorption

o Fluorescence (A)

• Fluoreseenee (B)

[] D

• D

88•I F]

o O 0

• • 0

I I I I, I _ L , L ] i L I * |

1 2 3

Distance from Burner (mm)

Figure 7.10 Comparison between relative OH fluorescence measurements and absorption

measurements in 6.1 atm C2Hs/O2/N2 flame (flame C in Table 7.1). The absorption

measurements were made using multiple scans of the Q1 (6) and Q12(6) lines.

150
C_3

J

O

r,D

O

X

O

1.6

1.4

1.2

1.0

0.8

0.6

0.2

0.0

' i I ' ' ' ' {

O

@

O

o Fluorescence (A)

• Fluorescence (B)

@

@

@@o

°@OOo

• @ •

8

0

i , , * L r, , , , I , , L , i

1 2 3

Distance from Burner (mm)

Figure 7.11 OH fluorescence measurements in a 9.2 atm C2Hs/O2/N2 flame (flame D inTable 7.1).

The fluorescence calibration factor was derived from a comparison of LSF and

absorption measurements in flame C (see Table 7.1).

151
though the difference in the estimated and measured Wr"may be large, the difference in fQ is small

due to saturation (see Tables 7.3 and 7.4). Thus, in some cases one may prefer to apply a quenching

correction factor based solely on the estimated ratio of saturation parameters (which in this case

is close to the pressure ratio). We also note that the Cottereau method is a potential alternative to

the procedure described by Barlow et al. (1989a, 1989b) for absolute concentration measurements

of OH. With this approach, Barlow et al. used two lasers to measure simultaneously (1) the relative

OH concentration using LIF and (2) H2, 02, N2, and H20 concentrations using vibrational Raman

scattering. With the measured concentrations of the OH-collision partners (i.e., H2, 02, N2, and

H20) the OH fluorescence voltages were corrected for variations in the electronic quenching rate

coefficient in a nonpremixed turbulent jet flame (on a shot-by-shot basis) using quenching cross

sections recommended by Garland and Crosley (1986). The Cottereau approach has the

advantages of greater simplicity and an in situ measurement of the quenching correction factor;

however, this method is limited by the accuracy of (1) the balanced cross-rate model and (2) the

saturation and quenching calibration curves.

7.5 Conclusions

We have successfully employed a method for making quenching-independent LSF

measurements of hydroxyl concentration in high-pressure laminar C2Hs/O2/N2 flames. With this

technique, one uses two fluorescence detection geometries; the ratio of the two fluorescence signals

is a function of the quenching rate coefficient and the spatial dependence of the laser irradiance.

As long as the laser spatial irradiance profile is invariant, the ratio of the two fluorescence signals

depends only on (1) the center-line saturation parameter and (2) the coupling efficiency between

the laser and the transition. Using the Cottereau method, the fluorescence signals from either

geometry, which have been calibrated at one condition, can be corrected for their finite sensitivity

to quenching via this in situ measurement. At atmospheric pressure, we have calibrated the

fluorescence signals with absorption measurements; we have also generated the quenching

correction function from the corresponding saturation curves in an atmospheric flame. The

fluorescence voltages from the flames at 3.1, 6.1 and 9.2 atm have been adjusted for changes in

quenching relative to the atmospheric flame, using the experimentally-determined relative

quenching rate coefficients; with this procedure, we have obtained absolute concentration profiles

of OH in high-pressure flames. The Cottereau method is still affected by the inaccuracy of the

152
balanced cross-rate model; moreover, the fluorescence profiles from imaging geometry A are

adversely affected by scattered and reflected light. NonethelesS, Use of this method can further

reduce uncertainty in calibrated fluorescence measurements, especially when attempting to obtain

absolute number densities under flame conditions significantly different than the calibration

condition.

153
CHAPTER 8

CONCLUSIONS AND RECOMMENDATIONS

8.1 Conclusions

In this report, we have focused on the efficacy of the LSF method for measurement of OH

concentration in high-pressure flames. We have investigated theoretically and experimentally the

validity of the ba/anced cross-rate model (Lucht et al., 1980, 1983), which relates the measured

quantity Nu to the unperturbed number density N o. In essence, the model states that the

laser-coupled levels experience approximately no net depletion; i.e.,

N,,+Nt-N ° (8.1)

The utility of this model isthat itrequires no knowledge of the collisional environment; consequently,

fluorescence measurements can be related more easily to the desired species number density.

When this relationship cannot be used due to depletion of the laser-coupled levels and this depletion

cannot be accurately measured, LSF can lose much of its attractiveness over linear fluorescence

methods.

In the course of this work, we have developed a high-pressure combustion facility, which will

be used in future high-pressure combustion studies employing spectroscopic methods. This facility

includes the following: (1) a pressure vessel constructed from standard stainless-steel piping

components; (2) an internal x-y burner translation system employing inexpensive stepper motors

and translation mechanisms; (3) two fiat flame burners; and, (4) an electronic gas control system,

which is interfaced to a microcomputer. Though the vessel was designed to accommodate turbulent

flames, we have used only premixed laminar flames for the present study. To test the facility, we

used the laser-induced fluorescence method to measure relative concentrations of OH in lean

premixed 02Hs/O2/N2 flames at 3.2, 6.3, 9.5, and 12.6 atm. By employing a range of flow rates of

the combustible mixture, we demonstrated that the reaction zone can be probed at these pressures.

In comparison to atmospheric flames, the reaction zone was small and accordingly, the [OH]

gradient was large; we also observed large gradients in the OH recombination zone.

]54
We havealsoperformeda theoreticalfeasibilitystudyon the applicationof LSFto the

measurementof OH concentrationin high-pressureflames. Using a numerical model for the

cotlisional dynamics of the OH molecule under nonuniform laser excitation, we investigated the

effect of pressure on the validity of the balanced cross-rate model and the sensitivity of the

depopulation of the laser-coupled levels to the ratio of rate coefficients describing (1) electronic

quenching to the ground-state vibrational levels for which v" > 0 and (2) vibrational relaxation from

v" > 0 to v" = 0. At sufficiently high pressures under near-saturated conditions, the total population

of the laser-coupled levels reaches an asymptotic value, which is insensitive to the degree of

saturation. When the ratio of electronic quenching to vibrational relaxation is small and the rate

coefficients for rotational transfer in the ground and excited electronic states are nearly the same,

the balanced cross-rate model remains a good approximation for all pressures. When the above

ratio is large, depopulation of the laser-coupled levels becomes significant at high pressures, and

thus the balanced cross-rate model no longer holds. Under these conditions, however, knowledge

of the depletion of the laser-coupled levels could be used to correct the balanced cross-rate model.

We have performed experiments to evaluate the efficacy of LSF for OH concentration

measurements in high-pressure combustion environments. First, we demonstrated that saturation

is possible in high-pressures C2H_O2/N2 flames by generating saturation curves at pressures as

high as _12 atm; these curves suggest that partial saturation can be achieved at pressures > 20

atm. To evaluate the limits of the balanced cross-rate model, we compared absorption and

calibrated LSF measurements at 3.1 and 6.1 arm. The fluorescence measurements were calibrated

with absorption measurements in an atmospheric flame and corrected for their finite sensitivity to

quenching with an estimated quenching rate coefficient. In this way, we compared the

spatially-averaged depletion of the laser-coupled levels (and the effective deviation from the

balanced cross-rate model) at 3.1 and 6.1 atm, to the value at atmospheric pressure. While the

absorption and calibrated fluorescence measurements compare well at 3.1 atm, the OH

fluorescence values are -25% below the concentrations from absorption at 6.1 atm, indicating an

effective error of _25% in the balanced cross-rate model beyond that in the atmospheric flame.

We anticipate that with a reasonable estimate of the quenching correction factor, one can measure

OH concentrations within +50% up to pressures of -10 atm. We have also presented absolute OH

concentration profiles for lean laminar flames at 1, 3.1, 6.1, 9.2 and 12.3 atm; to our knowledge,

these are the first high-pressure absolute concentration measurements of OH performed with UF.

155
Finally,wehaveemployedamethodformakingquenching-independent LSFmeasurements

inourC2H_O2/N2 flames. With this technique, one uses two fluorescence detection geometries;

the ratio of the two fluorescence signals is a function of the quenching rate coefficient and the spatial

dependence of the laser irradiance. As long as the laser spatial profile is invariant, the ratio of the

two fluorescence signals depends only on the relative quenching rate coefficient. Thus, the

fluorescence signals from either geometry, which have been calibrated at one condition, can be

corrected for their finite sensitivity to quenching from this in situ measurement. In this work, we

calibrated the fluorescence signals with absorption measurements at 1 atm and generated the

requisite quenching correction function from saturation curves. The fluorescence voltages from

flames at 3.1, 6.1 and 9.2 atm were adjusted for changes in quenching relative to the atmospheric

flame, using the experimentally-determined correction factor. The resulting absolute OH

concentration profiles agreed well with those determined by the standard LSF methodology.

8.2 Recommendations

For the high-pressure combustion facility, we make the following recommendations for an

improved design.

1. Using the condenser and water trap on the exhaust line, the water

was effectively eliminated from the exhaust system; however, for the

pressure vessel a drainage system should be designed to direct the

water collecting on the interior surfaces to the trap beneath the

bottom flange. This would ensure that the accumulation of water

does not interfere with the operation of the burner or the electronic

components.

2. Though the optical translation stage used for horizontal movement

is adequate for most purposes, it does exhibit significant side-play;

for more accurate positioning of the burner, the current translation

stage should be replaced by a system with reduced side-play (for

instance a Newport model M-425-1S stage or a linear bearing/shaft

arrangement).

156
3. Thewidthofthe burnerguardring(Fig.4.4)shouldbe reducedto

allowahighervelocityofguardflowfortheequivalentvolumetricflow

ofgas.Thisbecomesincreasinglyimportantathighpressures,since

gasconsumptioncanbelarge.Finally,formodellingpurposes(i.e.,

providinga tractableboundarycondition),the grainsizeof the

sinteredbronzeflameholder(-100/_m)shouldbereduced,since

this dimensionshouldbe smallcomparedto the flamestand-off

distance.

WealsonotethatwithLSF(whereonlyasmallamountofthetotalfluorescenceisobserved),

single-shot measurements using our facility were not possible for OH number densities _<1016 cm -3,

because of the small solid angle of fluorescence collection afforded by placing the fluorescence

collection lens outside the pressure vessel. However, single-shot measurements would be more

feasible by mounting the fluorescence collection lens inside the vessel on the window-housing

flange; this could result in a 10 to 20-fold increase in signal. An additional increase in signal can

be obtained by opening the monochromator exit slit; the maximum width, of course, is limited by

the requirement for spectral isolation of the detected transition. This approach also has the

advantage of decreasing the sensitivity of the fluorescence signal to collisional broadening.

Improved flame stability for the flat flame burner would allow absorption measurements at

pressures higher than 6 atm. Consequently, one could further characterize the depletion of the

laser-coupled levels as a function of pressure; this would be useful when trying to apply LSF for

OH measurements at pressures to 20 atm, for example. As noted in Chapter 6, one can potentially

estimate the spatially-averaged depletion of the laser-coupled levels from the temporal fluorescence

profile. This would require an OH dynamic model, albeit a simpler one (using perhaps only a few

energy states) than that described in Chapters 3 and 6. This modelling is of course made easier

when the temporal pulse is distinctive (i.e., containing two or more temporal lobes, which for the

Quanta-Ray Nd:YAG is obtainable through the setting of the Q-switch delay). The necessary input

to the model would include descriptions of the laser temporal and spatial profiles and a rough

estimate of the center-line laser irradiance; the spatial profile could perhaps be obtained from a

saturation curve (as we did in Chapter 6). The spatially-averaged depletion could then be found

by matching the experimental temporal profile with the computational profile for a specific

spatially-averaged depletion.

157
Finally,for the quenching-independent measurements employing the two detection

geometries (Chapter 7), we expect a significant improvement in spatial resolution upon reducing

reflected UV radiation from the windows. This could be accomplished with the appropriate

anti-reflection coatings for the laser entry and exit windows. For the high-pressure facility, an

anti-reflection coating is preferable to a Brewster-angle window, because of the large displacement

of the laser beam accompanying insertion of a Brewster window (thus making the optical alignment

more difficult). In addition, the Cottereau method would be improved with the use of

volume-absorbing neutral density filters appropriate for the UV. This would eliminate much of the

uncertainty in the quenching calibration and saturation curves. With good spatial resolution and

accurate quenching calibration and saturation curves, the Cottereau method is a good alternative

to the method used by Barlow et al. (1989a, 1989b; see also Chapter 2), potentially offering greater

accuracy and reduced complexity for absolute concentration measurements of OH in turbulent

flames.

158
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164
Appendix A - Flow Control Routine

In this appendix, we include a listing of the flow control program described in Chapter 4. The

routine has four major sections, the purposes of which are as follows: (1) the main routine, which

handles the selection of menu options; (2) the display package, which initializes and updates the

primary display (including the flow rates) and handles some I/0 functions; (3) the communications

package, which controls RS232 communications with the Linde Readout-and-Control (ROC) box,

including conversion between ASCII strings and floating-point numbers; and (4) the package for

scaling the flow rates with changes in pressure (see Chapter 4). The routine automatically detects

the graphics display adaptor and will thus work on most IBM PC compatibles. The package was

written using Turbo C and may employ some library functions which are unique to this product.

I X Section 1 */

#include <stdio.h>

#include <conio.h>

#inc[u_ (lath.h>

#_nctude <stdiib.h>

#include <dos.h>

#define LINE 2]

#define NORM 7

#define REVERSE 112

#define ESC 0xlb

#define ON 1

#define OFF 0

#define ]NC I

#define DEC 0

#define ETHNOX ].5

struct text_info initial;

float floe[] = (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0);

float fLoe_tmp[] = (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0);

int ioroc(char, char []);

void cstring(char [], float []);

void led(float []);

void pied(float);

void _)pres_int(int);

void edpres(float *);

void myput(int, int, int, char []);

int mygets(char []);

void increment(int, float);

void fspd_rd(int *);

void fspd_cat(float, float, float *, float *);

void fspd_¢t();

int cursor(int);

165
main()

FILE *frec;

char key. s[lO0], I_f[80"25"2];

in, t, j. direction, fspeed_fite, frec_file, chan.

charmer[5], power = OFF;

fLoaT pressure, pressure old;

float fnc, kO, kl, k2, riO, rf2, phi, phi_trg, phi_stp;

static char mer,J[5][85] = (

<N> <P> <O> <R> <S> <T>

<2> <3> <4> <H>

<2> <3> <4> <5> <6> <H> <I>

<H> <ESC>

<H> <ESC>

(" I'IAIN: <B> <H>

(" SET LOOP: <1>

(" T_J_AK LOOP: <1>

(" MIXTURE LOG°:

(" PRESSURE LOOP:

);

static char

("(1)FUEL (2)OXYGEN

("(1)FUEL (2)OXYGEN

("(1)FUEL

(" (2)OXYGEN

("

("

("

("

("

tabet[19][85] = (

(3)DILUENT (4)BATH

(3)DILUENT (4)BATH (5)FUEL/OX (6)OX/DIL

(5)FUEL/OX

(6)OX/D1L

(3)DILUENT

(4)BATH

<V> <Z> "),

<R> .ESC> "),

<D> <R> <ESC> "),

II} f

")

"},

(7)FUEL/OX/D 1L "},

II} t

II} I

|1) •

II} •

II} I

II) 0

(7)FUEL/OX/D]L "),

(ll÷ ÷ ._ .(..J- ÷ ÷ ÷ .._t ÷ -I- .(- .(, ÷ + ÷ ;t ÷ 'l" "_ "_" ÷ + _ + _ + _ ÷ + + + ÷ + ÷ ÷ + 4 + + II),

(. ........................................ ,,),

(.. READ THE CONTROL VALVE FLOW RATES "),

(If ERROR: A/D CHANNEL FOR PRESSURE SIGNAL HAS NOT BEEN SPECIFIED "> REBOOT "),

(" TARGET EQUIVALENCE RATIO HAS BEEN REACHED "),

(" PRESSURIZE THE VESSEL "),

(=' ZERO THE CONTROL VALVE FLOW RATES "),

(- BOOT UP THE CONTROL PROGRAN "),

(" VENT THE PRESSURE VESSEL "),

(" PRESSURE CHANGE TOO LARGE "> VENT THE PRESSURE VESSEL ")

);

/* Begin the [oop for con, rot of the f[o, rates *1

******************************************************************************

gettextinfo(&in_tial);

gettext(1. I. 80, 25, Lx_f);

disptay( );

_indou(1, 1, 80, 25);

myput(1, 1, REVERSE, menu[O]);

for(;;){

key = getch();

******************************************************************************

/* If 'O' or 'q' has been entered OUIT the program */

if(key == 'O' IIkw == 'q')(

ctrscr();

puttext(l, 1, 80, 25, buf);

gotoxy( i ni t | a [. curx, i ni t i a [. cury);

cursor(ON);

break;

)

******************************************************************************

/* %f 'B' or *b' has been entered BOOT up the program */

166
ifCkey == 'B' lJ key == 'b'){

Joroc('R', s);

cstri_(s, flow);

tedCflow);

myput(lINE, 1, REVERSE, [abel(16]);

/* Get the channel for the pressure transducer */

myput(L%NE+2, I, NORN, "Pressure signal channel (I-6): ");

if(mygets(s) == ON)(

chan= atolls);

if(chan >= 1 &&chan <= 6) (

power = ON;

adpres_int(chan);

adpres(&pressure);

pied(pressure);

)

)

)

/* If 'R' or 'r' has been entered, read and display the */

/* set and measured flow rates and pressure */

e|se if(key == 'R' JJ key == 'r') (

ioroc('R', s);

cstring(s, flow into);

for(i=5; i <= 8 ;i++)

fLowCi-1] = flou_tmp[i-1];

ted(flow);

******************************************************************************

/* Read and display the pressure (if POWER = ON) */

if(pouer == ON)(

a<lpres(&pressure);

pied(pressure);

)

)

** If '$' or 's' has been entered, set the flow rate */

else if(key == 'S' II key == 's')(

myput(1, 1, REVERSE, menu(I]);

/* Get the character and set the CHANNEL[] array */

for(;;){

myput(LINE, 1, REVERSE, (abel(O]);

for(i=1; i <= _ ;i++)

channel(i] = OFF;

key = getch();

if(key >= '1' EJ_ key <= '_')(

9otoxy[1,25);

ctreot();

if(key == 'I')(

channel(I] = ON;

myput(LlNE, 1, REVERSE, lab, t(2]);

)

else if(key == '2'){

charv_t[2] = ON;

myput(L_NE, I, REVERSE, label[3]);

)

167
else if(key == '3')(

chenne[ [3] = ON;

myput(LiNE, 1, REVERSE. label[4]);

)

else if(key == '6')(

channel[4] = ON;

myput(L]ME, 1, REVERSE, label[5]);

)

/* Get and set the flow rates */

myput(L]NE+2, I, NORM, "FLO_ RATE (LPM): ");

if(mygets(s) == ON)(

for(i:1; i <: 4 ;i++)(

if(channel[i] == ON)(

ftou[i-1] = atof(s);

increment(i, ftow[i-1]);

)

)

[ed(fiou);

}

gotoxy(1,25);

ctreo[();

)

/* If 'R' or 'r' has been input read the */

/* flow rates and pressure */

******************************************************************************

else if(key == 'R' II key == 'r')(

iOroc('R', s);

cstring(s, ftoutmp);

for(i=5; i <= 8 ;i+*)

fto_[i-1] = f[o_ trap[i-I];

led(f|o_);

if(pouer == ON)(

adpres(&pressure);

pied(pressure);

)

}

******************************************************************************

/* If ESC is hit, escape from the SET loop */

******************************************************************************

else if(key == ESC)(

myput(1, 1, REVERSE. menu[O]);

break;

)

)

}

******************************************************************************

/* If 'T' or 't' has been entered TUEA[ the control valves */

else if(key == 'T' II key == 't')(

myput(1, 1, REVERSE, mer_[2]);

for(i=O; i <= ¢ ;i++)

channel[i] = OFF;

/* Get the increment character string */

*************************************************************************

168
IWput(LINE+2, 1, NONM,NFLOW RATE INCREMENT (1.0 • INC • 0.0):

if(mygets(s) == ON)(

inc = atof(s);

if(inc < 0 II inc • 1.0)

break;

myput(LINE, 1, REVERSE, [abel[I]);

/* Begin _ncrement loop */

for(;;)(

key = getch();

l_**_*_**__*_**__**_*__**_ _t_**  1

/* If "1" through "7" has been input */

/* set the logic array CHANNEL "/

if(key >= '1' && key <= '7')(

for(i=1; i <= 4 ;i++)

channel [i] = OFF;

if(key == _1')(

channel [1] = ON;

mypul:(LINE, 1, REVERSE, label[2]);

)

etse if(key :: '2 _)(

channel [2] = ON;

myput(LINE, 1, REVERSE, label[3]);

)

else if(key == '3')(

channel [3] = ON;

myput(LlNE, 1, REVERSE, label[4]);

)

else if(key == '6')(

channel [4] = ON;

myput(LINE, 1, REVERSE, tabel[5]);

)

else if(key == '5')(

channel [1] = ON;

charmer [2] = ON;

myput(LINE, 1, REVERSE, Label [6]);

)

else i

)

else i

f(key u '6')(

channel[2] = ON;

channel[3] = ON;

_put(LINE, 1, REVERSE, [abel[7]);

f(key -= '7')(

channet [1] = ON;

channel [2] = ON;

channet [3] = ON;

myput(L]NE, I, REVERSE, Labet[8]);

)

)

/* If 'R _ or *r' has been input */

/* read the ftou rates and pressure */

else if(key -= 'R' I] key == _r')(

myput(LINE+l, 1, REVERSE, [abe[Ill]);

ioroc(_R ', s);

cstring(s, flo__tmp);

fon(_=5; i <= 8 ;i++)

f[oM[i-1] = flou_tmp[i-1];

Led(flow);

,,);

169
if(power == ON){

adpres (&pressure);

pied(pressure);

}

}

**************************************************************************

/* If 'I' or 'i j has been input increment the */

/* f t ous */

/ tt_tCr_ett_ttt _ttttt tedr tQtt _tt_t_tttt_et tete_t_ttt tt e_t t _t_t eeee/

else if(key == 'I' II key == 'i')(

myput(LlNE+l, 1, REVERSE, tabet[9]);

for(i=1; i <= 6 ;i++)(

if(channeL[i] == ON)(

fLow[i-I] = ftou[i-1]*(1 + inc);

increment ( i, fLow[i-I]);

)

)

ted(fto_);

)

**************************************************************************

/* if 'D' or edi has been input decrement the */

/* flows */

else if(key == 'D' ]J key == 'd')(

_ut(LINE*I, 1, REVERSE, tabel[lO]);

for(i=1; i <= 6 ;i++)(

if(channeL[i] == ON)(

fto_[i-1] = fLo_[i-1]*(1 - inc);

increment(i, fto_[i-1]);

)

)

tedCftou);

}

/* If ESC is hit, escape from the Loop */

**************************************************************************

else if(key == ESC)(

myput(1, 1, REVERSE, menu[O]);

break;

}

}

)

)

/* If 'N'or 'm' has been entered, change the equivalerce ratio */

**************************************************************************

else if(key == 'N' l[ key == 'm') (

if(ftou[1] == 0.0 Jl fto_[O] == 0.0)(

myput(LINE+l, 27, REVERSE,

"FLOWRATES CANNOT BE ZERO");

detay(lO00);

break;

)

if(pover == OFF) (

_Wput(LINE, 1, REVERSE, LabeL[12]);

detay(lO00);

break;

)

fspd_rd(&fspeed_fiLe);

if(fspeed_fite == OFF)(

IWput(LINE, 2_, REVERSE,

"FLARE DATA FILE CANNOT BE OPENED");

]70
break;

)

f,yput(1, 1, REVERSE, menu[3]);

/* Check if the A/D channels have been specified */

/* properly. If not, break from the loop */

phi stp = 0.0005;

phi = (f[ou[O]/ftou[1]) * ETHNOX;

sprintf(s, .Equivalence ratio _g_.2f; target value: ", phi);

myput(LlNE, 1, MORN, s);

_f(mygets(s) == OFF)

break;

phi trg = atof(s);

_f(phi_trg <= O)

break;

|f(phi_trg > phi)

direction = INC;

else

direction = DEC;

edpres(&pressure);

fspd cat(pressure, phi, &rfO, &rf2);

kO = f[o_CO]/rfO;

kl = ftou[1]/rfO;

k2 = ftou[Z]/rf2;

phi = phi * phi_stp;

for(;;) (

/* If ESC is hit, exit from NIXTURE option */

if(kbhit() && getch() == ESC) (

fspdcl();

myput(1, 1, REVERSE, menu[O]);

break;

)

/* Execute the logic sequence to step the */

/* equivalence ratio */

**************************************************************************

if(directio_ == INC) (

if(p_i >= phi trg) (

myput(L]NE, 1, REVERSE, Label[Ill);

myput(1, 1, REVERSE, menu[O]);

break;

)

else

else

)

else (

if(phi + phi_stp • phi_trg)

phi = phi_trg;

if(phi + phi_stp <= phi_trg)

phi = phi + phi_stp;

if(phi <= phi trg) (

myput(LIgE, 1, REVERSE, Label[13]);

myput(1, 1, REVERSE, menu[O]);

break;

)

else if(phi - phi_stp < phi trg)

phi = phi_trg;

else if(phi - phi stp >= phi trg)

phi = phi - phi_stp;

171
/* Determine the fLame speed ratio for the *1

/* pressure and equivalence ratio. Update */

I* the fLow array *I

/_***_**************@******_***********************t*****t*****t*******tW/

fspd_cal(pressure, phi, &rfO0 &rf2);

flow[O] = rfO * kO;

flow[l) = f[_[O) * ETHNOX/Ph_;

fl_[2] = flow[l] * k2/kl;

for(i=1; i <= 3; i++)

_ncrement(i, flow[i-l]);

led(flow);

pled(pressure);

kl = flow[1]/(flow[O] + flow[l] + flow[2]);

k2 = fl_[2)/(flow[O] + flow[l) + flow[2]);

@Lay(lO0);

)

)

/* If 'P' or 'p' has been entered, pressurize the vessel */

else if(key == 'P' lJ key == 'p'){

if(flow[O] == 0.0 II fl¢_[1] == 0.0){

nnlput(l [_E+1, Z?, REVERSE,

"FLO_ RATES CANNOT BE ZERO");

break;

}

fspd_rd(&fspeed_file);

if(fspeed_file == OFF)(

myput(LiNE+l, 2_, REVERSE,

"FLARE DATA FILE CANNOT BE OPENED");

delay(t000);

break;

)

if(po_r == OFF_

myput(LINE+l, 1, REVERSE, label[IZ]);

detay(lO00);

break;

)

myput(1, 1, REVERSE, menu[6]);

if( (frec= fopen("flame.rec", "a") ) == NULL)(

frec file = OFF;

myput(L%NE, 1, REVERSE,

"RECORD FILE CANNOT BE OPENED");

deLay(ZOO0);

)

else

frec_file = ON;

fprfntf(frec, "Pressure fuel Oxygen Oiiuenr rfO rfZ_n");

myput(L%NE, 1, REVERSE, Label[14]);

**************************************************************************

/* Begin the loop for |ncreme_ting the flow rates "/

**************************************************************************

#res(&pressure);

phi = flow[O]/flow[1] * ETHNOX;

fspd_cel(pressure, phi, &rfO, &rf2);

kO = flow[O]/rfO;

kl = flow[1]/rfO;

k2 = flow[2]/rf2;

pressure_old = pressure;

for(;;){

if(k_it()){

172
_f((keyegetch()) == ESC)(

fspd_ct();

if(frec file --= OIQ)

fc lose( f rec) ;

myput(1, 1, REVERSE, menu(O]);

break;

)

else if(key-l= 'R' ]l key == 'r')(

ioroc('R _, s);

cstring(s, ftou trap);

for(i=5; i (= 8 ;4÷÷)

floe(i-I] = flow_trap(i-I];

led(f lo_);

)

)

adpres(&pressure) ;

/* Vent if pressure change is 1 atm or more */

if(pressure-pressure oLd )= 1.0 II

pressure-pressure old (= -1.0)(

myput(L]NE, 1, REVERSE, tabe[ [18] );

for(_=l; _ (= 3 ;_+÷)(

ftou[i'l] = 0.0;

increment ( i, ftou[i-1]);

}

ioroc('R _, S);

cstrir_(s, f tou_tmp) ;

for(i=$; i _= 8 ;i++)

ftou[i-1] = f[o_ trap(i-I];

ted(ftou);

break;

)

if(pressure-pressure_old >= 0.1 II

pressure-pressure oLd <= -0.1)(

fspd cat(pressure, phi, &rfO, &rf2);

ftou[O] = (rfO * kO);

ftou[1] = (rfO * kl);

ftou[2] = (rf2 * k2);

for(i=1; 4<= 3; i++)

increment(f,f[ou(i-1]);

led(flou);

pl ed(pressure);

pressure_old = pressure;

ifCfrec_fite == ON)

fprintf(frec,

"_7.4f _7._f _7.4f _7.4f _7.4f _7.4f\n",

pressure, f tow[0], f foul1], f |ot_[2], rfO, rf2);

)

}

)

/ W_11"11_ _/W WW _lilll _llitttt[l'W Wtt llt_llllt _ltllt ttit i _IWWW WW WWW WWWW i W Wllt W WWI W WW WWW WWlt• Ill WWlW W WW_ /

/_ If _V_ or _v_ has been entered vent the pressure vessel */

else if(key == 'V' II key == 'v')(

myput(LINE, 1, REVERSE, Label [17]);

for(i=1; t _= 3 ;i÷÷)(

f[ou[i-1] = 0.0;

|ncrement ( i, ftou[i-1]);

)

ioroc('R _, s);

cstrir_(s, flou trap);

for(i=5; i <= 8 ;i+÷)

]73
flou[i-1] = flo_ tmp[i-1];

led(flow);

delay(500);

)

/* If 'Z _ or 'z' has tbeen entered, zero the control valves */

else if(key == _Z' II key == 'z')(

nfyput(LINE, 1, REVERSE, label[15]);

for(i=1; i <= ¢ ;i++)(

flou[i-1] = 0.0;

increment ( i, flo_[i-1]);

}

ior_('R', s);

cstring(s, flow_tmp);

for(i=5; i <= 8 ;i++)

floe[i-I] = flow_tmp[i-1];

led(ftou);

delay(500);

)

/* Reset the screen */

vindow(1, LINE, 80, 25);

ctrscr();

windoa(1, 1, 80, 25);

)

**************************************************************************

/* End of routineNAIN */

)

#include <conio.h>

#include <stdio.h>

#include <stdtib.h>

#include <dos.h>

#define ON 1

#define OFF

#define ESC

#define NDEC

#define COLLINN 1

#define START

#define _iDTH

#define NORH

#define MAX

#define FULL

#define HALF

#define BLANK

#define ZERO

0

Oxlb

5 /* Number of significnat digits */

/* Starting column */

6 /* _idth of channet info */

7 /* Normal attribute */

BO /* Maximum label length */

219 /* Full square character */

221 /* Half square character */

, , /* Blank square character */

222

void myput(int, int, int, char []);

/* ROUTINE DISPLAY() */

/. */

/* PURPOSE: To Initialize the display */

174
static

("FUEL 0

("OXYGEN 0

("D]LUENT 0

("BATH 0

("PRESSURE 0

);

static

void disptay()

(

tnt l, v_mode, line;

char silO] ;

/* Define the initiatization character strings */

char [abet[5][MAX+l] = (

0.2 0.4 0.6 0.8 1.0 1.2

0.5 1.0 1.5 2.0 2.5 3.0

2 4 6 8 10 12

5 10 15 20 25 30

5 10 15

"),

14"),

35"),

.)

char tick[2][NAX+l] = (

("(LPH) ............................................................... "),

("(ATM) ............................................................... ")

);

cursor(OFF);

ctrscr();

windou(1, 1, 80, 25);

/* Print out header character strings */

for(i=O, fine=START; i <= 4 ;i++, tine=Line+M]DTH)

myput([ine, COLUMN, NORM, Label[i]);

/* Print out tick marks */

for(i=1; i <= 8 ;i++)

tick[O][(lO*i)-l] = 31;

for(i=1; i <= 8 ;i++)

tick[1][(lO*i)-l] = 51;

for(i=O; i <= 4 ;i++)(

fine = (START + 1) + (i * _IDTN);

if(i<:3)

myput(tine, COLUMN, NORM, tick[O]);

etse

myput(tine, COLUNN, NORM, tick[l]);

)

/* End of routine disptay */

)

/* INT MYGETS(CHAR S[]) */

/* */

/* PURPOSE: To fitt a character array until the RETURN key is */

/* entered. At[ characters input are echoed on the */

/* screen until the RETURN key is hit. */

int mygets(ch_r s[])

(

unsigned char i, key;

atruct text.info initiat;

gettextinfo(&tnitiat);

/* Get the character string from the key board */

**************************************************************************

175
r

cursor(ON);

for(imO; i < _X ; ){

if((ke_getch()) == ESC)( /* if escape return

cursor(OFF);

return(OFF);

)

else if(key == '\b'){ /* if backspace backup

if(i >= I)(

putch('\b');

putch(' ');

gotoxy(_nftia(.curx + --f, fnftfaL.cury);

)

else

key = '\OI;

*/

*/

)

else if(key == '\r')( /* if return finished */

s[i] = '\0';

cursor(OFF);

if(i==O)

return(OFF);

return(ON);

)

else( /* else store character */

putch(key);

s(i] = key;

++i;

)

)

/* End of routine MYGETS() */

)

/* VOID NYPUT(INT LIME, INT COLUMN, INT ATTRIB, CHAR $[]) */

/* */

/* PURPOSE: To direct the cursor position and then utile */

/* information to the CRT display */

void myput(int tire, int column, _nt attrib, char s[])

(

int _;

gotoxy(cotumn, [ine);

textattr(ettrib);

Cl0UtS(S);

/* End of routine MYPUT */

textattr(NORM);

)

/* VOID LED(FLOAT FLO_) */

/* */

/* PURPOSE: TO construct the character strings representJng the */

/* flow readings and settings */

void led(f|oat flow[I)

(

int i, j, k, Line, x, bar st[4], bar rd[4];

char temp[lO], s[4] [NAX+1];

static float scale[4] = (100, 40, 10, 4);

176
lftft*********************lb*****t*tt****'&tb********************************_ 1

/* Convert the ftou rates to character strings and put the strings */

/* into the display String, S */

for(i=O, tins=START+2; i <= 3; i++, line=Line+WIDTH)(

s[i][O] = 'S'-

s[i][1] = ':';

gcvt((do_>te) fLow[i], NDEC, temp);

for(j=O; j < NDEC; j++)(

if(temp[j] == '\0 v)

break;

s[i][j+2] = temp[j];

)

for(k:j; k < HDEC+2; k++)

s[i][k+2] = ' ';

s[i][9] = ZERO;

bar_st[f] = fto_[i] * scaLe[i]; /*scaLe flow[i]

barlrd[i] = flow[i+4] * scaLe[i];

/* Construct the flow rate charcter strings given the *l

/* scaled flow rates */

for(j=lO; j <= 79 ;j++)(

x = 2*j - 17;

/* Execute Logic for displaying the measured flow */

if (bar_rd[_] < x && bar_rd[i] >= (x-l))

sLY][j] = HALF;

else if(bar_rd[i] < x)

sLY][j] = BLANK;

else if(bar_rd[i] >: x)

s[i] [j] = FULL;

/* Execute Logic for displaying the set ftou rates */

if (bar_still < x t,& bar st[i] >= (x-2))

s[i][j] = HALF;

)

l*********_*****_*****_*************_***_*_****_***_*****************l

/* Write the string to the screen */

s[i][80] = '\0';

gotoxy(COLUNN, [ ins);

for(j--O; j <= NAX-1 ;j++)

putch(s[i] [j]);

)

I t End of routine LED */

)

I t VO%D PLED(FLOAT PRESSURE) */

/. */

/* PURPOSE: TO construct the character string representing the */

/* pressure */

*/

177
void ptecl(ftoat pressure)

(

ftoat scate = 8;

int f, j, k, x, bar;

char temp[lO], s [HAX+I] ;

/* Initialize the character string for the pressure */

s[O] = 'R';

s[1] = ':';

gcvt((doub{e) pressure, NDEC, tamp);

for(j:O; j • NDEC; j++)(

if(temp[j] == '\O')

break;

ski+2] = temp[j];

)

for(k=j; k • NDEC+2; k++)

s[k÷2] = ' ';

s[9] = ZERO;

bar = pressure * scale;

/* Construct the pressure charcter string given the scaled value */

**************************************************************************

for(i=lO; i <= 79 ;i++)(

x = 2"t - 17;

if(bar • x && bar >-- (x-l))

s[_] = HALF;

else ff(ber • x)

S[_] = BLANK;

else if(bar >= x)

s[i] = FULL;

s[80] = '\0';

gotoxy(COLUNN, START+18);

for(i=O; i <= NAX-1 ;i++)

put ch(s [i] );

/* End of routine PLED */

)

/* INT CURSOR(1NT TOGGLE) */

/* */

/* PURPOSE: To turn the cursor on and off */

#define VIDEO OxlO

#define TOP 6

#define BOT 7

int cursor(int t_gIe)

(

union REGS rags;

regs.h.eh = 1;

_f(t_gte == ON)(

regs.h.ch = TOP;

regs.h.cl = BOT;

)

else if(toggle == OFF)(

regs.h.ch = -TOP;

regs.h.cl = -BOT;

)

178
else

return;

int86(VIOEO, ®B, ®s);

/* End of routine cursor */

)

i t Sectio_ 3 */

#include <stdio.h>

#include <conio.h>

#incLude <stdtib.h)

#include <math.h>

#define THR Ox3f8 I t Transmitter Holding Register address */

#define RBR Ox3f8 /* Receiver Buffer Register address */

_lefine HCR Ox3fc /* Nodem Control Register address */

_define LSR Ox3fd /* Line Status Register address */

_k_efine MAX 80

_fine VAIT 2000

int ioroc(char, char []);

/* VOID CSTRING(CHAR S[], FLOAT *P_FLOg) */

/* */

/* PURPOSE: To convert the character string of numbers */

/* (terminated by a \0) to a floating point array. */

cstring(chmr s[], float *p_ftow)

(

int i, j, k, t;

char tempi5];

static float scale[8] = (0.001, 1, 1, 1, 0.001, 1, 1, 1);

/* Begin the loop to convert the character string to numbers */

**************************************************************************

for(i=O, j:O, t=O; ;i+_)(

if(s[i] == '\0') / t Break if end of string */

break;

/ t If character s[i] is a period or a number store in */

/* character string TEHP */

else ifts/i) == _.* I_ (s[i] >= '0' g s[i] <= '9') )(

temp[j] = s[i];

j++;

)

/* _hen S is a co_ or a carriage return, then it has a */

/* c_tete number. Convert the character string TENP */

/* to an integer, INTGR */

else ff(s[i] == ',' ]] (s[i] == '\n' _ ([ == 3 II t == 7) ) ){

telllp[j] = '\0';

*p_f[o_,i © atof(telp) * scale[l);

p ft_;

j=O;

]79
t÷+;

)

)

1********.********,1.***********, .** *******.*****...*****************/

/* End of routine CSTRING */

**************************************************************************

)

/* ROUTINE IMCRENENT(INT i, FLOAT FLOU) */

I* *I

/* PURPOSE: TO take channel CHAMand flow rate set-point FLOW */

/* cocmvert thm into ASCII characters, and send them */

/* to the ROC box */

void increment(int chan, float flow)

(

char silO], in[lO0];

int i, pad;

static float scale[4] = (1000, 100, 100, 100);

**************************************************************************

/* Send the co¢_trot character _C' and the channet rvJ,ber */

ioroc('C', in);

itoa(chan, s, 10);

ioroc(s[O], in);

/* Send the control character'S' and the new flow rate set-points */

ioroc('S', in);

itoa((int) (flo_*scate[chan-1]), s, 10);

for(i=O; s[i] >= '0_ g s[i] <= '9' ;i++)

p_l=4- i;

for(i=O; i < pad ; i++)

ior_('O', in);

for(i=O; i <= (]-pacl) ;i++)

ior_(s[i], in);

**************************************************************************

/* End of Routine INCRENEMT */

**************************************************************************

)

/* IMT ]OROC(CHAR PROI4PT, CHAR RESPONSE[]) */

/* */

/* PURPOSE: To send the ROC control character and retrieve the ROC */

/* response through the CON1 port. */

**************************************************************************

int ioroc(char prompt, char response[])

(

int i, j;

/* Send the character to the ROC box */

outportb(RCR, Ox01); /* Send the to RTS signal */

while((inportb(LSR) & Ox20) != Ox20 ) /* _ait for hi THRE signal*/

outportb(THR, prompt);

white((inportb(LSR) & Ox60) != Ox60 ) /* aait for hi THRE & TSRE*/

]80
/* Get the character(s) sent in response by the ROC box */

**************************************************************************

outportb(NCR, Ox03); /* Send the hi RTS signet */

for(i=O; i < HAX ;i++)(

/* gait for complete character from ROC box before proceding */

for(j=O; (inportb(LSR) & Ox01) != Ox01; j++)(

if(j • UAIT)(

outportb(NCR, Ox01);

res_se[i] = '\0';

return(i);

)

)

response[i] : inportb(RBR);

)

/* End of routine ioroc */

)

/* Function adget(int channel, float *pvalue) */

/* */

/* Purpose: To get values from the MetraByte A to D converter. */

/* The syntax of the calling statement should be */

/* */

/* edger(channel, &value); */

/* */

/* where channel is the channel (0-15) of the A/D */

/* pvatue is the pointer to value */

**************************************************************************

#include <dos.h>

#defi ne ADC_LO Ox300

#define ADC_H! 0x301

#define STATUS Ox:]02

void adget(int chan, float *pvott)

(

/* Start A/D conversion process. A/D conversion wilt be complete */

/* when the value of the NSB of the status register is low */

outportb(STATUS0 than);

outportb(ADC H!, OxO0);

white((inportb(STATUS) & OxSO) == Ox80)

/* Get the low and high bytes describing the voltage signal. */

*pvott = (float) ( ((inlx)rtb(ADC_H]) << _) & OxffO) +

( (inportb(ADC LO) >> _) & OxOOf) );

*Vvolt = 10.0 * (*pvolt/_096) - 5.0;

/* End of function adget */

)

181
#incLude <conio.h>

#incLude <stdtib.h>

#incLude <stdio.h>

#incLude <math.h>

#define ON 1

#define OFF 0

float max, a[2], b[2], c[2];

FILE *fdat;

/* ROUTINE FSPD_RD(INT *P_FSPEED_FILE) */

/* */

/* PURPOSE: TO read the flame speed data file */

void fspd_rd(int *pfspeed_fiLe)

(

char s[80];

/* Reed the data file FLANE.DAT */

*p_fspeed file = ON;

if( (fdat = fopen("ftame.dat", "r')) == NULL)(

*p fspeed f_te = OFF;

return;

)

fgets(s, 80, fdat);

sscanf(s, " _f _f _f ",&a[O], &aLl], &amax);

fgets(s, 80, fdat);

sscanf(s, " _f _f ",&b[O], &b[1]);

fgets(s, 80, fdat);

sscanf(s, " _f _f ",&c[O], &c[1]);

**************************************************************************

/* End of routine FSPD RD */

**************************************************************************

)

/* ROUTINE FSPD_CL() */

/* *t

/* PURPOSE: TO cLose fLame speed date fiLe */

**************************************************************************

void fspd_ct()

(

fctose(fdat);

/* End of routine FSPD CL */

)

/* ROUTINE FSPD CAL(FLOAT PRESSURE, FLOAT PHI, FLOAT *PFO, FLOAT *PFZ)*/

/* */

/* Purpose: CaLcuLate the fueL and oxydant flow rates */

void fspd_cat(ftoat pressure, float phi, fLoat *pfO, float *pf2)

(

fLoat xsqr, xcbe, phat;

double exp(doubLe);

182
/* Calculmte the various _r_ters and the fuel/oxygen float rate */

xcbe = (phi-amax) * xsqr;

• pfO = 1.0 - a[O] * xsqr - a[1] * xcbe;

phat = b[1] * (1.0 - pressure);

• pfO = *prO * (1.0 + (b[O] - 1) * (1 - exp((doubte) phat ) ) );

/* Catcutate the dituent ftou rate */

phat = c[1] * (1.0 - pressure);

• pf2 = 1.0 + (c[O] - 1) * (1 - exp((doubte) phat) );

/* End of routine FSPD CAL */

183
Appendix B - Absorption Theory and Sensitivity Analysis for Collisional Llnewidths

B.1 Introduction

In this appendix, we first present the theory for absorption measurements. We then

discuss collisional broadening of OH at flame temperatures, and we compile data on the

broadening of A2I]+.-X_II (0,0) transitions of OH based on recent measurements by Rea et al.

(1986, 1989). This data base was used to calculate number densities from absorption

measurements in the flames we described in Chapters 6 and 7. In the final section, we present

calculations of the sensitivity of absorption number densities to line broadening. These

calculations were performed for simulated flames at 1, 3, 6, and 12 atm, with the input

parameters based on the C2H_O2/N2 flames in Chapters 6 and 7.

B.2 Theory

The spectral absorption at the exit slit of the monochromator, A v, is given by (Penner, 1959)

flv._. Iv.(/-)' g([v'- vl)c/v"

A,=]- . (B.I)

v*AV /..(O).g(Fv'-vl)av

•" v -_lv =

where Au* (crnq) is the spectral width of the exit slit, lu.(0) and lu,(L) are the respective spectral

irradiances entering and leaving the absorbing medium, and g(I u' - u I ) is the normalized slit

function for which

_[g(Iv'- vl)av" = I (/9.2)

With broad-band excitation, I_/(0) is approximately constant over the limits of integration, and

therefore

A,, = l- exp - /c('_+v)c/s g(T)c/'r , (B.3)

6v

where r m u' - u and L is the path length. The spectral absorption coefficient k(u) is related to the

normalized line profile Y(u) and the population in the coupled levels, NI and No, by

k(v)=(_2)y(v)[NtB, -N=B.,] , (B.4)

]84
where_0(cma)isthe centralfrequencyof thetransitionand Blu and But (cm3-cml/J-s) are the

respective Einstein coefficients for absorption and stimulated emission. Note that the absorption

coefficient k(v) is integrated over the absorption path to account for variations in the population

and linewidth; also, for electronic transitions under conditions of local thermodynamic equilibrium,

Nu = O.At higher pressures, Y(_,)results from a convolution ofthe collisional and Doppler broadening

profiles; thus, in terms of the nondimensional frequency _"==2 _/(In2) (v - vo)/A_o

= Y(t,:a) )'(_') _AVo

( B )

qr-_AvortJ-, a=+(_-y) =

Here, the Doppler linewidth (FWHM), A_ D, is given by

Av_ = 2v o' (2kTln2) mc 2 '/z , (B.6)

where k is the Boltzmann constant, T isthe translational temperature, and m is the mass of the

absorbing species; V_;a) is known as the Voigt function and also the real part of the complex error

function (Abramowitz and Stegun, 1968; Armstrong, 1967; Hui et al., 1978; Humlicek, 1979).

The broadening parameter,

a= l.j'T_ AvN+Avc , (B.7)

A'v D

describes the relative influences of the two homogeneous processes, natural and collisional

broadening, and the inhomogeneous process, Doppler broadening. The natural linewidth, A_,N,

is the broadening of the transition due to spontaneous emission, while the collisional linewidth,

&uc, is the broadening of the transition due to dephasing collisions; at 1 atm and above for the

hydroxyl radical, collisional broadening is much greater than natural broadening. The collisional

broadening is expressed as a sum of the contributions of the gas constituents; i.e.,

Ave = P E x,' (2¥,) (B.8)

where P is the total pressure, and xi and 2"/i (cm-Vatm) are the mole fraction and broadening

coefficient, respectively, of the i-th constituent. Finally, note that at higher pressures, with the

increased contribution from collisional narrowing, the Voigt profile may not adequately describe the

linewidth (Varghese and Hanson, 1984; Rea et al. 1986).

The effect of the slit function is to spread the profile over a wider range of frequencies; thus

185
A= A_dv= l- Iexp If0' - k('_+v)ds 1g(r)d-r, >dv (B.9)

¢ _ -Av

where the limits of integration, _'1 and v2, are chosen to be sufficiently large to include most of the

line but not adjacent lines. The total energy absorbed, though, remains constant (Penner, 1959),

and hence, for a particular transition, integration over the line profile gives

A= 1 -exp [;o' - k(v)cls ]1"v (B.IO)

I

Thus, as long

unnecessary.

as one integrates over the broadened line, knowledge of the slit function is

The curve-of-growth method represents the solution of Eq. (B.IO) for the parameter K (Lucht

et al., 1978)

K . k(_)L [_-2]N B 2/_-_2_L (B.II) v( ; = ' '° a v o '

as a function of the total absorption and the broadening parameter; if the temperature is known,

the total number density, N T = NI/FIB, can then be found from K. If the total absorption from two

or more energy levels is known, then both the rotational temperature and the total number density

can be .calculated by comparing the measured spectra with the spectra calculated from the

curve-of-growth method (Salmon, 1986a). We note that for weak absorption, f oL k(v)ds < 1, the

integrated absorption A is insensitive to a; however, when f _ k(v)ds > 1, accurate determination

of NT is limited by the uncertainty in a.

B.3 Colllsional Broadening of OH

The principal difficulty in calculating the parameter a lies in determining the temperature

dependence of the linewidth &vc for interactions with the main collision partners. In a

room-temperature experiment at subatmospheric pressure, Engleman (1969) measured

broadening of the A2_+,-X2]-[ (0,0) transitions of OH and found similar linewidths for collisions with

molecules such as 02, N2, and CO2. Moreover, unlike interactions of OH with these collision

partners, those with H20 showed a dependence on OH rotational level. In a later high-temperature

experiment (T _ 1300 K)I Wang et al. (1980) measured the homogeneous linewidths for collisions

with 02 and H20 at subatmospheric pressures, again finding a dependence on OH rotationa! level

for interactions with H20. This behavior, they concluded, is the result of rotational transitions of
H20in near resonance with those of OH. Recently, Rea et al. (1986, 1989) measured collisional

broadening of the electronic transitions of OH by Ar, N 2, H20, and CO2, and fit the temperature

behavior of the broadening coefficients to the exponential relation,

2y,= 2Yo , (B.I2)

which follows from a simple hard-sphere collision model where the exponent is 1/2.

Table B.1 Summary of the reference linewidth coefficients and temperature exponents [from Rea

et al. (1986, 1989)].

J HzO CO2 N2 O2

(Try= 1620 K) (1680 K) (2000 K) (2000 K)

2_0 n 2_o n 23o n 23o n

1.5 0.155 0.9 0.108 1.2 0.050 0.8 0.033 0.8

2.5 0.160 1.0 0.092 1.2 0.047 0.8 0.033 0.8

3.5 0.160 0.9 0.067 1.2 0.045 0.8 0.032 0.8

4.5 0.165 0.7 0.060 1.2 0.043 0.B 0.032 0.B

5.5 0.160 0.6 0.054 1.2 0.042 0.8 0.032 0.8

6.5 0.145 0.4 0.050 1.2 0.040 0.8 0.032 0.8

7.5 0.125 0.35 0.048 1.2 0.039 0.8 0.032 0.8

8.5 0.115 0.35 0.048 1.2 0.038 0.8 0.032 0.8

9.5 0.110 0.35 0.048 1.2 0.037 0.8 0.032 0.8

10.5 0.105 0.25 0.048 1.2 0.037 0.8 0.032 0.8

11.5 0 .1_ 0,2 0 ._8 1.2 O._ 7 0.8 0 ._ 2 0.8 l

12.5 0.095 0.1 0.048 1.2 0.037 0.8 0.032 0.8

13.5 0.095 0.1 0.048 1.2 0.037 0.8 0.033 0.8

14.5 0.090 0.0 0.048 1.2 0.037 O.B 0.033 0.8

15.5 0.090 0.0 0.050 1.2 0.037 0.8 0.034 0.8

Table B.2 Relative (_) and absolute (8) uncertainties in the

broadening coefficient for J -- 5.5 at a flame

temperature of 1800 K [from Rea et al. (1986, 1989)].

Collision Partner _ (23) & (23')

(cm-1/atm)

C02 0.17 0.0085

H20 0.08 0.012

N2 0.12 0.0053

02 0.20 0.0070

]87
The linewidths resulting from OH-Ar and OH-N2 collisions were first measured in a shock tube

over a temperature range of 1400 to 4100 K. A rapid-tuning frequency-doubled ring dye laser was

used to resolve lineshapes behind reflected shock waves in weak mixtures of H2 and 02 diluted

with N2 or Ar; these measurements show a small dependence on rotational level, though this

dependence is within the uncertainty of the measurements. For broadening by H20 and CO2, Rea

et al. (1989) used a flat flame burner and a diffusion burner to assess the low and high-temperature

behavior, respectively, of the collisional linewidths. To estimate the contribution from 02, Rea et

al. assumed that 02 and Ar broaden the OH transitions by the same amount. This hypothesis was

based on the measurements of Engleman (1969) and Shirinzadeh et al. (1985) and was tested

using the measured linewidths and temperature exponent for Ar; the two values compared well and

Rea et al. used the linewidth data for Ar to calculate the small contribution from O2 in their lean

flames.

The 2"/i of the principal collision partners for our lean C2HJO2/N2 flames are listed in Table

B.1. These values are based on the measurements of Rea et al. (1986, 1989); the broadening

behavior of 02 was assumed to be the same as that for Ar. Table B.2 lists the approximate

uncertainties in the 2"/i values, which are based on reported uncertainties for the J = 5.5 rotational

level. Though 2-_(O2_.)was not measured, we have assigned a relative uncertainty of 20%;

nonetheless, the total uncertainty is insensitive to this value since the concentration of Oz is small

in the burnt-gas region.

Table B.3 Total and partial uncertainties in the collisional linewidth for J = 5.5 and the flames A,

B, and C described in Chapters 6 and 7. The collisional linewidth and the associated

total uncertainty [calculated from Eq. (B.13)] are listed under the column labeled Arc.

P

(atm)

/kvc P{_[xi 6(2"7i)]2} 1/'2 P_6xi (2"7i) 6P_xi (2_/i)

(cm-1) (cm -i) (cm-1) (cm -1)

0.98 0.0592 0.0041 0,002 0.0006

+ 0.01 + 0.0046

3.1 0.184 0.013 0.006 0.0083

+0.14 ± 0.017

6.1 0,383 0,0264 0.012 0.0126

±0.20 ± 0.032

]88
In addition to the uncertainties in Table B.2, uncertainties in the pressure and species

concentrations also contribute to the total uncertainty in Z_c. Thus, the total uncertainty is

I ;

Since the mole fractions are correlated (i.e., the sum must equal unity), they cannot be handled

individually, as if they were random errors. Instead, to estimate the uncertainty in AuC due to

uncertainties inthe mole fractions, we have calculated the term P_;xi-(2"_i)for the case where x(C02)

and x(H20 ) are 10% below their expected equilibrium values, and we have assumed that the

unknown species making up this deficit broaden the OH transitions weakly as does At. In estimating

the total uncertainty in the collisional linewidth, we have used flames A, B, and C described in

Chapters 6 and 7. This result and the summary of the terms in Eq. (B.13) are shown in Table B.3.

The values are calculated for the pressure and mole fractions in the absorption measurements.

These calculations for the J = 5.5 rotational level show that the net uncertainty in the collisional

linewidth is < 10%. In general, we expect an uncertainty of -10% in the calculation of AuC for the

lines we have used for absorption measurements in our C2Hs/O2/N2 flames.

B.4 Calculations

For the calculations described below, Eqs. (B.3) and (B.10) were integrated with FORTRAN

routines, which employ Romberg integration and are based on algorithms suggested by Press et

al. (1986). For accurate integration with an infinite limit, the variable transformation x = 1/v was

used to map infinity into zero. Consequently, for integration over the range of zero to infinity, we

have used the relation

/o/(v)dv= /(v)dv+ _1 dx (B.14)

In Figs. B.1-B.4, we show the calculated spectral absorption profiles at pressures of 1,3, 6,

and 12 atm. The spectral profiles are calculated using Eq. (B.3) with (1) infinite spectral resolution

(i.e., _u* -- 0) and (2) the triangular slit function,

189
Table B.4 Values of K and A (as functions of pressure) for three transitions assuming NT = 8 x

1015cm-3. The broadening parameter is calculated using data of Rea et al. (1986, 1989)

and the equilibrium distribution of species in a lean (equivalence ratio = 0.8, dilution

ratio = 3.1) C2H6/O2/N2 flame at 1800 K.

Line K a/P A

(atm-1) (cm-1)

1 atm 3 6 12 atm

P1(2) 0.6916 0.236 0.149 0.159 0.165 0.170

Q1(6) 1.538 0.201 0.274 0.310 0.337 0.360

Qt(13) 0.3836 0.171 0.087 0.090 0.093 0.094

= 0 -Av'>t>Av"

g('r)=T(x) = _2 z- (Av" + r)/(_v" -_v" <r < 0 (B.lo)

= (Av" --t)/(Av') 2 0 <r <Av".

Here, we use a slit width (FWHM) Z_u* = 1 cm-l, which is approximately the value measured from

experimental lines. For all cases, the spectral absorption for the Q1(6) and Q1(13) lines is simulated

using hiT = 8.0 x 1015 cm-3. This OH number density is consistent with values measured

experimentally, and the Q1(6) and Q1(13) lines were, in general, the strongest and weakest lines,

respectively, used to calculate the total number density. In addition, the broadening parameter was

calculated using T = 1800 Kand the collisional coefficients of Reaet al. (1986, 1989); the information

for these lines and the additional P1(2) line is summarized in Table B.4. In each case, the integrated

absorption [A (cm-1)] evaluated from Eq. (B.10) is also shown; we note that one consequence of

the increased collisional broadening is an increase in the integrated absorption.

In Figs. B.5-B.8, we show _NT(Z_uC), the relative uncertainty in N T, due to uncertainties in AuC

of 10% and 20%. These curves are calculated as a function of K since experimentally one has

control over this parameter through choice of the absorption line or through variation of the total

flow rate of the combustible mixture. As the latter is increased (while holding constant the

equivalence and dilution ratios), the flame temperature in the burnt-gas region wilt also increase

(Ferguson and Keck, 1979; Chao and Law, 1988), resulting in a greater OH concentration. As

expected, the relative error increases with increasing K. One surprising result, however, is that for

constant K, the relative error at 12 atm is less than that at 6 atm. For our purposes, the important

conclusion is that for the range of concentrations in our C2H6/O2/N2 flames at 1, 3.1, and 6.1 arm,

the uncertainty in NT due to the uncertainty in Z_vc is small (_<2%).

190
Finally,we note that one source of uncertainty in NTwhich we have not included is absorption

in the wings of the profile that cannot be resolved due to noise. At higher pressures, the influence

of collisional broadening increases, resulting in a larger value for the broadening parameter and

thus a broader line, with a greater fraction of the absorbed energy in the wings. Consequently, for

a constant value of the parameter K, the uncertainty in NT increases, because of a decrease in the

effective signal-to-noise ratio of the profile. From calculations performed by Penner (1959), however,

we expect this contribution to be small for our flames.

191
<

0.4

0.3

0.2

0.1

A

/I

QI(13)

<

0.8

0.6

0.4

0.2

01(6)

A

II

I1

-1 0 1

0 = I I •

-3 -2 2 3

V - V0

Figure B.1 Spectral absorption profiles for the Q1(6) (bottom) and Q1(13) (top) lines for P __ 1

atm, T = 1800 K, and NT = 8 x 1015 cm"3. The solid curve is the convolution of the

true spectral absorption, which is represented by the dashed curve, and a triangular

slit function (&u* = 1 cm-1).

192
0.4

0.3

0.2

0.1

0

Q1(13)

h

0.8

0.6

0.4

0.2

Q1(6)

0 , I I i

-3 -2 2 3

h

-1 0 1

V - V 0

Figure B.2 Spectral absorption profiles for the Q1 (6) (bottom) and Q1(13) (top) lines for P __ 3

atm, T = 1800 K, and NT = 8 x 1015 cm -3. The solid curve is the convolution of the

true spectral absorption, which is represented by the dashed curve, and a triangular

slit function (Av* = 1 cm-1).

]93
0.4

0.3

0.2

0.1

0

Q1(13)

A

/./

0.8

0.6

0.2

Q1(6)

0 I , ,I ,

-3 -2 2 3

A

/

-1 0 1

V - V0

Figure B.3 Spectral absorption profiles for the Q1(6) (bottom) and Q1(13) (top) lines for P __ 6

atm, T = 1800 K, and NT = 8 x 1015 cm-3. The solid curve is the convolution of the

true spectral absorption, which is represented by the dashed curve, and a triangular

slit function (Av* = 1 cm'D.

]94
0.4

0.3

0.2

0.1

0 i!

Q1(13)

/'k

<

Figure B.4

0.8

0.6

0.4

0.2

Q1(6)

0 = , I ] ,

-3 -2 2 3

/'k

i I , I , I ,

-1 0 1

V - V 0

Spectral absorption profiles for the Q1(6) (bottom) and Q1 (13) (top) for P = 12 arm,

T = 1800 K, and NI" = 8 x 10_5 cm-3. The solid curve is the convolution of the true

spectral absorption, which is represented by the dashed curve, and a triangular slit

function (Au* = 1 cm-1).

195
0.10

l.-

Z

w

0.05

0

-0.05

I

J

J

J

J

J

i

l

l

! i

-0.10 ' ....... J ' ' ' ' _'

0.1 1 10

K

FigureB.5 UncertaintyinNTfora=O.2(P__ latm) due to an uncertainty in &_c of +l O% (solid

curve) and +20% (dashed curve).

Ig6
0.10

iZ

_J

0.05

0

-0.05

.,,I _

-0.10 , , , ..... i

0.1 1

\

I ! 1 I I 1

10

K

Figure B.6 Uncertainty in NTfor a = 0.6 (P __3 atm) due to an uncertainty in AuC of +10% (solid

curve) and +20% (dashed curve).

197
0.10

0.05

Z 0

oJ

-0.05

\

\

\

\

\

-010. , , , ..... i , . , , , ,,

0.1 1 10

K

Figure B.7 Uncertainty in NT for a = 1.2 (P = 6 atm) due to an uncertainty in A_,c of +10% (solid

curve) and +20% (dashed curve).

198
0.10

t--

Z

_J

0.05

-0.05

-0.10 , , ..... ,i , , , , , , ,,

0.1 1 10

K

Figure B.8 Uncertainty in NTfor a -- 2.4 (P ,-, 12 atm) due to an uncertainty in A_,c of + 10% (solid

curve) and _+20%(dashed curve).

199
Appendlx C - Error Analysls of Absorption Measurements

The uncertainties in the absorption concentration measurements reflect uncertainties from

(1) the calculation of the integrated absorption (cm-1) from the measured profile, (2) temperature

(3) the line broadening parameter (see Appendix B), and (4) the path-length measurement. In cases

where multiple lines (_>10) are used to calculate the total number density, a statistical analysis is

performed by the absorption program; the 95% confidence interval calculated by the program

includes uncertainties from the calculated temperature and the variation in concentrations of

individual lines. When the OH concentration is derived from scans of only the Q1(6) and the Q12(6)

lines, the uncertainty in the integrated absorption was estimated from the signal-to-noise ratio of

the profile and baseline.

The temperatures were measured subsequent to the OH absorption and fluorescence

measurements using silica-coated thermocouples above the burner center (rather at the burner

edge where the fluorescence measurements were taken). We note that even at high pressures,

evidence of catalytic reactions was observed when uncoated thermocouptes were used. The

temperatures were corrected for radiative losses using an emissivity for silica of 0.22 and the Nusselt

number correlation recommended by Bradley and Matthews (1968); this correlation, which is used

to model convective heat transfer from hot wire anemometers and is described by Hinze (1975)

and Kramers (1946), is given by

Nu=0.42 f'r °2÷0.57Pr °'33 R_ °'s° , (C.I)

where Pr is the Prandtl number and Re is the Reynolds number. The thermocouple is thus modelled

as a cylinder in cross flow, with a diameter equal to that of the thermocouple bead; a computer

program developed by Harris (1985) was used to obtain the corrected temperatures. While the

thermocouple measurements at 3.1 atm employed a thermocouple with a diameter of -170/_m,

the values at 1, 6.1, and 9.1 atm employed a thermocouple with a -100/_m diameter. To make

these measurements, we also removed the flame stabilization screen which was fixed about 8 mm

above the burner. The uncertainty in these temperatures is estimated to be +50 Kfor all the flames.

For the effective path length for absorption, we estimate the uncertainty to be_+1 mm; typically,

the effective path length was -24 ram. This uncertainty accounts for possible errors due to effects

such as beam steering, laser wavelength drift (during the absorption path-length measurement),

and the fluorescence signal-to-noise ratio. Finally, we include the uncertainty in NT from an

uncertainty in the collisional linewidth, ArC, of +10% (see Appendix B).

200
TableC.1 Total absorption uncertainty (molecules/cm3) from the partial values due to

uncertainties in (1) the integrated absorption [6N-r(A)], (2) temperature [6NT(T)],

when not included in the absorption calculation], (3) path length [6NT(L,X t f)], and

(4) the collisional linewidth [SNT(A.tJC) ]. The total concentration and associated

uncertainty are listed under the column labeled NT.

Pressure Position NT 8NT(A)

(arm) (mm)

0.98 1.0 1.057 +0.055

+ 0.072

2.0 0.702 +0.053

+ 0.061

3.0 0.526 +0.028

+0.037

1016 cm.3

,,r

-- ;0.045 ¢0.014

_.0.029 _.0.005

_0.024 ¢0.0O3

3.1 0.6 0.813 +0.074 -- _0.037 ¢0.008

+ 0.083

1.0 0.492 +0.059 -- _0.023 ¢0.003

+ 0.063

1.2 0.434 _+0.010 _+0.008 ¢0.018 ¢0.003

+ 0.022

1.4 0.382 -+0.038 -- _0.017 ; 0.002

± 0.042

6.1 0.6 0.934 +0.044 +0.018 _-0.040 _0.019

_+0.065

1.0 0.616 -+0.037 +0.011 _-0.027 ;0.009

+0.048

1.6 0.445 -+0.037 -+0.007 .T.0.019 ¢0.004

+0.042

Finally, for selected OH absorption measurements, the partial uncertainties for the four

sources listed above have been added in quadrature to obtain the total uncertainty in NT. For the

flames at 1, 3.1 and 6.1 atm, the uncertainties (shown in Figs. 6.9-6.11) are summarized in Table

C.1.

201
Appendix D - Saturation of an Inhomogeneously-Broadened A2_+*-X2_ (0,0) Transition of

OH

In this appendix, we examine the saturation behavior of an A2E+.-X2]-[ (0,0) transition of the

hydroxyl molecule at flame temperatures as a function of pressure. We have modelled the excitation

process with rate equations using an approach similar to the one taken by Piepmeier (1972a, 1972b).

Because fesatdV (where V is the imaged volume) is of principal interest, one need consider only

the two laser-coupled energy levels u and/. Since the rate coefficient for excitation can vary over

the absorption profile, the distribution of molecules among the Doppler intervals will also vary with

frequency. One must then define nu(v) and n/(v), the spectral population in energy levels u and I,

respectively, where

and

N. = n.(v)dv (D.I)

N_ __ nt(v)dv (D.2)

Accompanying the variation of W/u over the absorption profile is a deviation from the

MaxwelI-Boltzmann velocity distribution in the excited state, and thus a net population transfer

between the Doppler intervals of level u is possible. The rate of transfer out of the Doppler interval

of interest is simply QD, the rate coefficient of velocity-changing non-quenching collisions, times

the population nu(v)dv. The rate of transfer into this Doppler interval is equal to QD[Nu - nu(v)dv],

the total rate at which velocity-changing non-quenching collisions occur with molecules outside the

interval, times the probability that a collision will transfer the molecule into the interval. This

probability is given by n °(v)du/N o,where n °(v) and N o,are the respective unperturbed spectral

and unperturbed total populations of level I. The ratio of these populations (times du) is simply the

fraction of the total population in the interval dr, which for a MaxwelI-Boltzmann velocity distribution,

is given by the normalized Gaussian function,

n(v------_)= ° C(v- Vo;AVo) (D .3)

N,o

2 (ln2)'"2

-- A--_v_\_-,/ exp{- tn2[2(v- vo)/Avo] _} ,

202
where AVD (cm-1) is the Doppler width (FWHM). Thus, the net rate of transfer into the frequency

interval v to u + dv is

nO(v)(N =/A ;o,)Qt_-n=(v)Q o (D.4)

where the second-order differential has been dropped. The rate equation for the excited-state

population density nu(v) is then given by

dn.(v) QvnO(v)N,,/N o (v)h' (v)- (D.5) dt = t + n t I,

n.(v)[Qo//+ h',,(v)+ Qt_]

With the spectral population fraction, 1 - _/(v), equal to one, population densities in levels u

and I are related by

n,(v)+n.(v)=n_(v) ; (D.6)

this equation implies that laser excitation does not change the velocity of the molecule. As in Chapter

3, the peak fluorescence signal is of principal interest. Thus, setting Eq. (D.5) to zero and solving

for nu(v) using Eq. (D.6) gives

{ (Qo/Q,n)(N,/N°)+h'v" )-]i-v.}

Note that in setting Eq. (D.5) to zero, we implicitly assume that each nu reaches steady state at the

same time. For each Doppler interval, Wv', the spectral saturation parameter, is given by a

convolution of the spectral energy density, Pv (J/cm3-cm-1), and the homogeneous absorption

Id_=(v) B_. C" &Vc

1_v"= ....Q,H QoH Jo Pv." 2n(v-v" )2 +_,_ v_/2av'_ , (v.8)

profile; i.e.,

where AvC (cm-1) is the collisional linewidth (FWHM) and B/u (cm3-cm-1/J-sec) is the Einstein

coefficient for absorption. When the rate coefficient for excitation is independent of frequency u,

the population nu(u) will also be independent of frequency, and Eqs. (3.4) and (D.7) will then be

equivalent.

One can now solve for the desired quantity, namely Nu, by integrating Eq. (D.7) after

substitution from Eq. (D.3); thus,

N.(g.) a¢

g=+g_

-_ Nl o

g, ).)o I'0c/0,tf "l_°(#Jg')]_-'dV

1 - (QD/Q,H) _0 ® J'QJQ.,,.C,.(g,/g.JJv." C(v- Vo;AVz))

dv

(D.9)

203
Comparing Eqs. (3.4) and (D.9), we observe that o_sat,the degree of saturation, is

g= I *QD/Qe// *[l .(gl/q,)]w y"

a,.,= . (D.IO)

.J:_: (,/7_,,,p(y') dy l - (Qo/Qo/f) ].(Qo_Q.,).[_.(g,_q_)],,

where y = 2 _/(In2) (v - vo)/AVD is the nondimensional frequency. Note that when Wy' < 1, Eq.

(D.10) reduces to

g,+gt f: ( 1/_f-_) exp(- yz) h/y dy (D.II)

_sal = _u

Although the dependence on velocity-changing collisions has disappeared, the degree of saturation

still depends on the integral of the saturation parameter times the transition Doppler profile.

Since we are interested in the spatially-integrated degree of saturation, we have solved the

equation

_V fV gu I .QDIQ,t/-11 • (ql/f.)ilJy" ezs=tdV =

1 __: ('/7_)'_PC'"_) dy - (Q_IQ,/j) l.(QDiQ.tt).[i.(gtlq=)]wy.

dl / (D.I2)

using a 2-D Romberg integration routine, which is similar to the 1-D version employed in Appendix

B and is based on an algorithm suggested by Press et al. (1986). We model the spatial dependence

of the spectral energy density with the axisymmetric function (see Chapters 6 and 7)

p,,(o)

pv(r) = , (D.]3)

[ ] + (r/u,)_] __

where r is the radial position, w is the beam halfwidth, and p,,(0) is the spectral energy density at

the laser beam center line. For the imaged volume, we consider the following two cases (see Fig.

7.1): (1) geometry A, which yields the disk with the differential volume dV = 2_rWArdr; (2) geometry

B, which yields the slab with the differential volume dV = WBHB dr.

To model the spectral distribution of energy in the laser pulse of the Quanta-Ray dye laser,

we have used a series of monochromatic modes (i.e., p,, described with a series of 8-functions)

separated by AVLm; the relative intensity of the modes is given by a Lorentzian function, with a

spectral FWHM AVL = 0.5 cm -1. Thus we have

M

= P0 _ 5(v- vL,,) (D.14)

Pv [2(v-v,)/AvL] 2+ 1 m--,.

with

204
vL_ = vL_ ÷ (m. _vL_) (D, I.'5)

Here, Po (J/cm-3) is the energy density of the central mode, which is located at VLc (cm-1), and VLm

(cm ol) is the frequency of the m-th of 2M+1 modes. The energy density of the m-th mode is thus

given by

P"= [2(v-v.)/AvL]Z+l

P0

[2(m'AvL.,)/Av_]2+l

(z). 16)

or

po

p,. -- (,o. 17)

[2(m' Z_yL,.)/AyL] 2 + 1

in terms of the nondimensional frequency [again using the normalization constant A_:D/2v/(In2)].

Note that this model for saturation is least accurate for small AuC, since the actual nonzero width

of the modes will act to increase the degree of saturation. In addition, a dye laser has a

homogeneously-broadened line profile; consequently, mode competition results in fewer axial

modes than are possible (from the cavity length) being active on each laser pulse. Effects such as

vibration prevent complete mode competition (i.e., the elimination of all but a single mode on each

laser shot). We note that for our laser, the mode spacing determined from the cavity length is

estimated to be 0.038 cm-1.

From Eq. (D.8), the spectral saturation parameter is given by

}

Bt=Po ___ 6(V'- VLm)

"= ._--M Arc dr" (D.18)

h/_ Q,// [2(V'--VLc)IAvL] z+ I 2_(V--V')--7_'_Vc2/2

or in nondimensional form

IVy"- _Avo Q,// " [2(-_--yz_)/Ay¢] .. _....... 2+ 1 (y'-y)2+a2 a :ay" (D.]9)

2t4 7

11Av ,) q,I/ _.-M [2(m • Ayu,,)/Ay, , ]2+ I [y-(y,c+m.

°

AyL,,)]2+a 21

2O5
where • _ _/(in2) _,c/AuD is the broadening parameter (when the contribution from natural

broadening is negligible) and YLc-= 2 v_(In2) (VLc- V0)/AUD goes to zero when the central frequencies

of the transition and the laser spectral profile match. We note that Eqs.(D. 18) and (D. 19) describe

a series of Lorentzian-shaped modes under the envelope of the laser spectral energy distribution

(assumed to be a Lorentzian in this case). As a function of the spectral energy density, the laser

irradiance is given by

_

Iz=c • pvdv (D.20)

=Po.C

/H

E (P,,/Po)

tn--M

Finally, the spectral saturation parameter in terms of the laser irradiance is

t_n-2(g,,/g t)A,,t I L( F )

,_ (1).21) I,I , " ( r ) = ( 4 n2 c2 A v o )v _oQotf

r,,l=_M [2(m. Ayl.2)/byL ] 2. I

r,--M [2(m'AyLm)/ZXyL]2+ 1

where we have used the identity

[y- (y, ÷ rn. AyL,_)]2+ a 2

(g_/gt) A=l

Bi, = (D.22)

8_hv_c

to cast the equation in terms of the Einstein A-coefficient.

To calculate the Doppler and collisional linewidths (see Appendix B), we use a temperature

of 1750 K and the Einstein A-coefficient and frequency of the Q1(8) line. In addition, we estimate

the ratio QD/Qeff by comparing the dephasing collision frequency with the quenching collision

frequency. Here, we assume that collisions which quench the molecule (i.e., change its energy

state) also dephase the molecule. The collision frequency is given by the sum of the rate coefficients

for electronic quenching and vibrational plus rotational energy transfer..Since the rate coefficient

for vibrational energy transfer will be small in the A2I_+ (v=0) state, the net frequency for quenching

collisions is Qe + Qr, the sum of rate coefficients for electronic quenching and rotational relaxation.

Using the procedure described in Chapter 6, we find Qe _ 0.45 x 109 s-l, Qr _ 3.8 x 109 S-1, and

Q_ _ 2.9 x 109 s4 for the burnt gas region of an atmospheric C2H6]O2/N2 flame at T = 1750 K.

206
In comparison, the dephasing collision frequency is fc = 7rcA_c _- 5.3 x 109 s-1 (see Appendix B).

Thus we have QD/Qeff = [fc - (Qe + Qr)]/Qeff _ 0.25. The relevant modelling parameters are

summarized in Table D.I.

Table D.1 Modelling parameters for the

Q1 (8) line at 1750 K.a

IL(0) 2.6 x 1010W/cm 2

a/P 0.20 atm-1

AUD 0.235 cm-1

uo 32328 cm-1

Qe/P 0.45x 109s "1 atm-1

Qr/P 3.8 x 109 s-1 atm-1

Qeff/P 2.9 x 109 s-1 atm -1

QD/Qeff 0.25

a We use the symbol P for pressure.

Figure D.1 shows curves describing the variation in the relative fluorescence signal (which is

proportional to the spatially-integrated degree of saturation in the absence of depletion of the

laser-coupled levels) for the two imaging geometries, versus the broadening parameter. We

consider three cases for the laser spectral energy density: (1) the profile contains 41 modes with

a separation of AVLm = 0.038 cm1 (which is approximately the value calculated from the cavity

length of the dye laser); (2) the profile contains 11 modes with _ULm = 0.152 cm-1; (3) the profile

contains 5 modes with _VLm = 0.38 cm-1. We note that for our flames, the range a = 0.02 to 4

corresponds approximately to a range of pressures of 0.1 to 20 atm. The spectral saturation

parameter was calculated from Eq. (D.21) using a center-line irradiance of IL(0) = 2.6 x 101oW/cm2.

In addition, a ratio of Q_f/P of 2.9 x 109 s-latm-1 was employed to describe the variation of the

quenching rate coefficient with pressure (using a/P = 0.20 atm-1). For these saturation curves to

follow those shown in Chapter 7 (Fig. 7.7), the coupling efficiency between the transition and the

laser must remain constant. However, when (1) the homogeneous linewidth is much narrower than

the separation of the modes and (2) the frequency of Doppler-changing collisions is smaller than

the frequency of quenching collisions, nu(v) retains much of the nonuniformity of the laser spectral

energy distribution, and as a consequence, the coupling efficiency is poor. With increasing _vc,

nu(_,) retains less of the nonuniform distribution of the laser; the coupling efficiency can therefore

increase with increasing pressure. We therefore expect that the relative fluorescence signal will

exhibit a smaller sensitivity to pressure than would be obtained when the coupling efficiency is

207
constant and only Q_ changes. This is shown in Fig. D.1 for small e. However, as A_ c increases

further, this effect isoffset by a decrease inthe absorption atfrequencies near _'o,causing a decrease

inthe coupling efficiency with increasing pressure; consequently, the sensitivity of the fluorescence

signal becomes larger than would be observed solely with increased quenching. In addition, we

note that the relative saturation profile is insensitive to the specific shape of the energy density

spectral profile (e.g., Gaussian or Lorentzian), the width of this profile, and the ratio QD/Qeff

(especially with larger a).

In Fig. D.2, we compare the saturation curves (for imaging geometries A and B) calculated

by varying (1) pressure (i.e., the broadening parameter and the quenching rate coefficient) and (2)

the laser irradlance, while holding constant the broadening parameter and the quenching rate

coefficient. For case (1), we have employed the model with 5 axial modes and Ai,'Lm = 0.38 cm-1;

in addition, we have used aJP = 0.20 atm -1, Qeff/P = 2.9 x 109 s-latm-1 and IL = 2.6 x 101oW/cm 2

to simulate the saturation curve that would be obtained by exciting the Q1(8) line in our C2HJO2/N2

flames and varying the pressure from 1 to 20 atm. For comparative purposes, we used the model

employing only 5 modes, since of the three models studied (see Fig. D.1), it is the least like the

saturation curve generated by varying the laser irradiance. For case (2), we used a = 0.20, Qeff =

2.9 x 109 s-l, and IL x P = 2.6 x 10lo W-atm/crn2 to simulate the saturation curve that would be

obtained by varying the laser irradiance at atmospheric pressure. The resulting curves for case (2)

are almost identical to the ones used in Chapters 6 and 7, where we assumed the that the relative

fluorescence signal is independent of collisional broadening (see Eq. 6.14).

Of particular interest, given the variation in the coupling efficiency with pressure, is the

accuracy with which one can calculate the fluorescence correction factor, fQ--which accounts for

changes in the laser irradiance, the quenching rate coefficient, and the coupling efficiency--from

SfA/SfB, the ratio of the fluorescence signals from the two imaging geometries. With the Cottereau

method (1986), which is discussed in detail in Chapter 7, one uses saturation curves derived by

varying the laser irradiance at constant pressure to generate the quenching correction curve, SfA/SfB

versus the relative saturation parameter (Wr')o The measurement of SfA/SfB under some other

condition is used to calculate Wr', which can then be used to calculate fo from the saturation curve

(for either geometry A or B). In the bottom part of Fig. D.2, we show the quenching correction curves

which result from the saturation curves shown in the top part of the figure. The solid curve represents

the dependence of the ratio SfA/St8 on pressure, while the dashed curve represents the dependence

of SfA]SfBon Wr'. Using Fig. D.2, we can compare the fo calculated from the two sets of curves with

208
the following procedure: (1) for an arbitrary value of SfA/SfBdetermine the corresponding pressure,

P=(Pd)from the solid curve (dashed curve); (2) with Ps (Pd), determine from the solid curves (dashed

curves) of the top graph the value of fQ (where fQ = 1/SI) from the curve describing either geometry.

For the Cottereau method to work effectively, the dashed curves should give approximately the

same correction factor (for the same geometry) as the solid curves, which give the true dependence

of the fluorescence signal on pressure. We have carried out this comparison for several values of

SfA/SfB, and the results are listed in Table D.2. This comparison shows that the Cottereau method

can yield a good estimate of fQ, even though the two sets of saturation curves differ significantly.

Table D.2 Comparison of fQ calculated from the saturation functions where

(1) pressure [f(P)] and (2)the laser irradiance [f(IL)] are varied

(see Fig. D.2). The fQ shown below are the values for geometry

A.a

S_A/SfB f(P) f(IL) c(fQ)

(solidcurve) (dashedcurve)

P (atm) fo P (atm) fQ

0,80 2.34 1.50 2.66 1.57 0.041

0.70 3.62 1.94 4.78 2.05 0.059

0.60 5,75 2.63 9.39 2,80 0.065

0.50 9.58 3.80 20.8 4.05 0.066

th se_(fQ) is the relative error in the fluorescence correction factor from using constant-pressure saturation curves (and the corresponding quenching

correction curve).

209
c_

¢-

C/)

CD

c-

(1)

r_

o9

CD

Ii

0.1

Geom. A

\

Key: AVLm (cm "1)

0.038 _,

0.152 _,

.... 0.380

_... _ Geom. B

" -'-,,,,,_....

•

2 , i 1 1 I I II t Z 1 I t _ ttl

0.1 1

a

Figure D.1 Relative fluorescence signal versus the broadening parameter. The top and bottom

graphs show the variation of the signal for geometries A and B, respectively, when

the spectral laser profile contains (1) 41 modes (separated by 0.038 cm-1), (2) 11

modes (separated by 0.152 cm-1), and (3) 5 modes (separated by 0.38 cm-1).

210
1 Geom. B

t_

¢-.

ED

03

(_

¢J

¢-

CD

CJ

(/)

CD

O

!

LL

:>

CD

rr

0.1

1.0

0.8

0.6

0.4

Geom. A

I I i , ¢ I I & L J

I I0

P (atm)

FigureD.2 Relative fluorescence signals (top) and their ratios (bottom) for geometries A and B

versus pressure. For the solid and dashed curves, we use a laser spectral profile

containing 5 modes (and A/._Lm = 0.38 cm-1). The solid curves were calculated by

varying the pressure, while the dashed curves were calculated by varying the laser

irradiance.

211
Appendix E - Gausalan Quadrature Formula for the Weighting Function W(x) = 1/(1 + x2)

Listed inTable E. 1 are the abscissa (xi) and weights (vi) of a 20-th order Gaussian quadrature

formula for the integral (Salmon, 1986b)

I+X2 '

where 1/(1 + x2) is the weighting function, W(x), and f(x) is some smooth function. Integration of a

function g(x) = W(x)f(x) is then given by

N

For example, with the weights and abscissa listed inTable E. 1 and the function g(x) = 1/[(1 + x2)2],

the error in the integral is -4 x 10-4 A general discussion of quadrature formulas, as well as a

routine for calculation of the weights and abscissa for Gauss-Legendre integration is given by Press

et al. (1986).

Table E. 1 Abscissa and weights for the

Gaussian quadrature formula

describing Eq. (E.1).

xi vi

+O.12079 0.24345

+0.37390 0.26708

+O.66524 O.32198

+ 1.03474 0.42833

+1.55437 0.63422

+2.37541 1.06355

+3.87244 2.09242

+7.20763 5.21265

-I-17.65124 19.93440

+92.64416 237.50059

212
Nahonal AeronauTics and

Space Admmistrahon

1. ReportNo.

NASA CR-185218

4. Title and Subtitle

Report Documentation Page

2. Government Accession No. 3. Recipient's Catalog No.

5. Report Date

Saturated Fluorescence Measurements of the Hydroxyl Radical in

Laminar High-Pressure Flames

7. Author(s)

Campbell D. Caner, Galen B. King, and Normand M. Laurendeau

9. Performing Organization Name and Address

Purdue University

School of Mechanical Engineering

West Lafayette, Indiana 47907

12. Sponsoring Agency Name and Address

National Aeronautics and Space Administration

Lewis Research Center

Cleveland, Ohio 44135-3191

February 1990

6. Performing Organization Code

8. Performing Organization Report No.

None

10. Work Unit No.

506-42-51

11. Contract or Grant No.

NAG3-351

13. Type of Report and Period Covered

Contractor Report

Final

14. Sponsoring Agency Code

15. Supplementary Notes

Project Manager, Valerie J. Lyons, Space Propulsion Technology Division, NASA Lewis Research Center.

16. Abstract

We have investigated theoretically and_experimentally the efficacy of laser-saturated fluorescence (LSF) for OH concentration ,_ ,_,_.-

measurements in high:pressure flames.--Using a numerical model describing the interaction of hydroxyl with: _n°nunif°rm__ __ laser

excitation, we have studied the effect of pressure on the validity of the balanced cross-rate model aid the sensitivity of the

depopulation of the laser-coupled levels to the ratio of rate coefficients describing (1) electronic quenching to 2_ +(v" > 0) and (2)

vibrational relaxation from v" > 0 to v" = 0. At sufficiently high pressures and near-saturated conditions, the total population of the

lair-coupled levels reaches an asymptotic value, which is insensitive to the degree of saturation. When the ratio of electronic

quenching to vibrational relaxation is small and the rate coefficients for rotational transfer in the ground and excited electronic states

are nearly the same, the balanced cross-rate model remains a good approximation for all pressures. When the above ratio is large.

depopulation of the laser-coupled levels becomes significant at high pressures, and thus the balanced cross-rate model no longer

holds. Under these conditions, however, knowledge of the depletion of the laser-coupled levels can be used to correct the model. A

combustion facility for operation up to 20 arm was developed to allow LSF measurements of OH in high-pressure flames. Using this

facility, we achieved partial saturation in laminar high-pressure (< 12.3 atm) C2H6IO2/N 2 flames. To evaluate the limits of the

balanced cross-rate model, we compared absorption and calibrated LSF measurements at 3.1 and 6.1 arm. The fluorescence voltages

were calibrated with absorption measurements in an atmospheric flame and corrected for their finite sensitivity to quenching with (I)

estimated quenching rate coefficients and (2) an in situ measurement from a technique employing two fluorescence detection

eometries Whils the absorption and calibrated fluorescence measurements compare well at 3. I arm, the-OH fluorescence values are

-25% below the absorption measurements_at,6."l atm, indicating an efJ'ec_i_,e error of -25% m the 16alanced cross-rate model, e

:n_:elcTtoe t_altoiltho:_m;;phera_uPr;e;Hr_ofl:c_rn_Sr_n_s Cwali:bh[nat' '°;;n%d a_ preei_:_ tOr tO r::nSl°.n'_le/est_mat_°f the quenching

17. Key Words (Suggested by Author(s))

Diagnostics

Flames

Combustion

Laser fluorescence

18. Distribution Statement

Unclassi fled - Unlimited

Subject Category 35

19 Security Classif (of this report) 20. Security Classif. (of this page) 21. No. of pages

Unclassified Unclassified 22 i

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