AlllOb ,V? CI427

NBS

PUBLICATIONS

NBSIR 83-2641

The Application of Laser-Induced

Rayleigh Light Scattering to the

Study of Turbulent Mixing

U S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Washington, DC 20234

January 1983

. U56

83-2641

1dd3

U S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

national botlact OF STANDARDS

LIBRARY

1

1983

NBSIR 83-2641 jT^

THE APPLICATION OF LASER-INDUCED

RAYLEIGH LIGHT SCATTERING TO THE

STUDY OF TURBULENT MIXING

William M. Pitts Takashi Kashiwagi

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Washington, DC 20234

January 1 983

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director
«*AT’. SO
Table of Contents

' '

i- Page

I* V '

. V

' ' y

.• List of Figures ‘. v

List of Tables vill

* > v » < v u **«...» * * i * * % - v •• Nomenclature lx

Abstract 1

1. INTRODUCTION 2

1.1 Preliminary Remarks 2 1.2 Scalar Measurement Techniques In Turbulent Flow Fields ... A

2. RAYLEIGH SCATTERING 13

2.1 Description of Rayleigh Scattering 13

2.2 Past Uses of Rayleigh Scattering as a Probe in

Turbulent Flow Systems 17

2.3 Expected Signal and Noise Levels for Rayleigh

Scattering Measurements 19

3. TURBULENCE MEASUREMENTS 26

3.1 Nature of Turbulence and Approaches to its

Characterization 26

3.2 Calculational Methods for Properties of the

Concentration Flow Field 28

4. EQUIPMENT AND PROCEDURES 36

4.1 Flow System 36

4.2 Optical System 38

4.3 Detection, Conditioning, and Recording Electronics 39

4.4 Experimental Procedures 41

4.5 Data Analysis 42

5. RESULTS 46

5.1 Nature of Detected Rayleigh Scattering 46

5.2 Time Averaged Properties of the Methane Concentration

Field 48

5.3 Conditional Measurements in the Methane Concentration

Field 54

6. DISCUSSION 58

6.1 Comparisons of Measurements from this Study with Other

Work 58

6.2 Validity of Comparisons with Other Studies 70

iii
Page

6.3 Applicability of Rayleigh Light Scattering as a Scalar

Probe of Turbulent Flow Fields 73

6. A Rayleigh versus Raman Scattering as a Scalar Probe 78

6.5 Final Remarks 79

7. ACKNOWLEDGMENTS 80

8. REFERENCES 81

iv
List of Figures

Page

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Optical arrangement and detection electronics for

laser Rayleigh light scattering measurements

Detected light intensity as a function of position

for a back-illuminated pinhole translated along the

laser beam propagation direction. The symbols

represent data for 0.2 mm (X) and 0.4 mm (<3>) slit

widths

Appearance of data records for time-resolved light

scattering measurements as a function of cut-off

frequency. The measurement volume is located on

the jet axis at z/r

Q = 35. The vertical axis

indicates methane concentrations which are uncorrected for photon statistics. Average methane

concentrations for the entire data sets are indicated by X and the expected RMS fluctuations

(± 1 a) due only to photon statistics are indicated

by the bars

Values of

(

XcH

4)o

/

(

XcH

4)c

^ are

plotted as a function of z/r

4/c

Solid lines are the

results of linear least squares fits for

measurements taken at z/r

Q

_> 20

Values of / X (HX/CHX ' and

(

YcH

4)o

/

(

YcH

4)c

are

plotted as a function of z/r

Q

. Solid lines are the

results of linear least squares fits for

measurements taken at z/r

Q

_> 20

Unmixedness of methane concentration on the jet

centerline in mole and mass fraction terms is

plotted as a function of z/r

Q

The skewness of the methane concentration

distribution on the jet centerline is plotted as a function of z/r

Q

The kurtosis of the methane concentration

distribution on the jet centerline is plotted as a function of z/r

Q

Examples of correlation functions and power spectra

for methane concentration fluctuations at three

different axial downstream distances in a methaneair jet. The cut-off frequency of the amplifier is

set to 4.6 kHz

86

87

88

89

90

91

92

93

94

v
Page

Figure 10,

Figure 11,

Integral time scales (T) on the jet centerline as a function of z/r

Behaviors of X

CH,

and Y

CH, are shown as a function

of nondimensionalized radial distance ( r / r i/2^ f° r a downstream distance of z/r 35 in a methane-air tn«

Figure 12. Experimental values of !( X(

Figure 13.

Figure 14,

Figure 15,

Figure 16,

Figure 17,

'(H),

and

CH '(H).

4 \ 4/c are shown as a function of

4 V 4/c

nondimensionlized radial distance (r/r 1/2 ) for a downstream distance of z/r

Q = 35 in a methane-air

jet. The solid line represents results taken from

the work of Becker et al . [48] for an air-air jet

and the dashed line gives the results of Birch et

al. [23] for a methane-air jet

Intermittency factor (y ) and frequency (f ) as functions of nondimensionalized radial distance

95

jet. Solid lines are results for fits of Eq. (5.5) 96

Skewness values as a function of nondimensionalized

radial distance (r/r^ 2)are s ^own for the methane

concentration distribution at a downstream distance

z/r

Q = 35 in a methane-air jet. Values have been

calculated for entire data records (<$>) and for

conditionally sampled data which are weighted by

the corresponding intermittency functions (X)

Kurtosis values as a function of nondimensionalized

radial distance (r/r^ 2)are shown for the methane

concentration distribution at a downstream distance

z/r

Q = 35 in a methane-air jet. Values have been

calculated for entire data records (<$>) and for

conditionally sampled data which are weighted by

the corresponding intermittency functions (X) ......

97

98

99

Integral time scales as a function of

nondimensionalized radial distance C r / r

1 / 2 ^ are shown for methane concentration fluctuations at a downstream distance z/r

Q = 35 in a methane-air

jet

Example of methane concentration behavior in the

intermittent region of a methane-air jet and the

resulting intermittency function calculated for the

data. Arrows indicate short "bursts" of methane

concentration which do not appear in the

intermittency function due to the averaging

inherent in the calculation of this function

100

101

vi
Page

(r/r^^) for a downstream distance of z/r

Q = 35 In

a metnane-air jet. The solid line is a plot of

Eq. (5.6) for R = 1.6 r^ 2 and = .28 * ^/2

Figure 18. Values of the intermittency factor (y) are plotted

on a probability graph as a function of

nondimensionalized radial distance (r/r^^)* The

solid line is a linear least square fit of all

results except the five points closest to the jet

centerline. The symbols refer to positive (<3>) and

negative (0) values of r

Figure 19. Plots of X„„ and X_„ //X

CH CH, XH)<

are given as a

function of the nondimensionalized radial distance

r/ r

l /2 at a downstream distance z/r

Q = 35 in a methane-air jet. _The corresponding conditionally

sampled values, /X

(

X

ch

4 ) T

and

(

X

CH

4) I

/

(

X

CH

4 )c

> are

indicated by the symbol X

102

103

104

vii
List of Tables

Page

Table 1. Observed and calculated relative errors as a function

of cut-off frequency for the current from a photomultiplier illuminated by a constant intensity

light source 105

Table 2. Experimentally determined constants for Eqs. (5.1)-

(5.4) and asymptotic values for concentration

fluctuation intensity on the jet centerline in mole

and mass fraction terms 106

Table 3. Observed constants for spreading rate behavior

(Eq. 6.1) of axlsymmetrlc jets 107

Table 4. Maximum normalized RMS concentration fluctuation

values and radial locations for various axisymmetric

jets 108

Table 5. Experimental parameters for different jets discussed

in text 109

viii
Nomenclature

B dummy variable

cx

cY V V

X Y

C^, constants for Eqs. (5.1) - (5.4)

c

3

constant for Eq. (6.1)

Ct Craya-Curtet number

D jet exit diameter

f

Y

intermittency frequency

fl focal length

G gain of photomultiplier tube

i photomultiplier current output

1AVG average photomultiplier current output during At'

I total light intensity scattered from two component gas

JL laser output (photons/s)

Xo _o

laser irradiance (W cm ) incident on observation volume

X

l intensity (W sr cm ) of light scattered from a unit

observation volume which is parallel to the electric field

of incident polarized light

X 1

—1 —3 intensity (W sr cm ) of light scattered from a unit

observation volume which is perpendicular to the electric

field of incident polarized light

I(t) intermittency function

K kurtosis (flatness)

1 length of cylindrical observation volume

L number of measurements

M number of gases in a mixture

n index of refraction

N number density of gas

N

o Avogadro's number

N

p

number of photons detected

lx
p

r

r

1 / 2

r e R

R

Re

R

p

R(t)

S

t

T

u

X

X"

Y

z

z o a

a

P Y

Af

At

At'

pressure

integrated current (charge) during At

integrated current (charge) during At'

radial distance from jet centerline

radial distance at which concentration has fallen to 0.5 of

centerline value

effective radius

gas constant; instantaneous distance from outside edge of

jet to centerline

value of R for y = 0.5

Reynolds number

rate of photon detection

correlation function

skewness

time

temperature

velocity

mole fraction

measurement of mole fraction in presence of shot noise

mass fraction

axial downstream distance from jet nozzle exit

virtual origin

gain per dynode in photomultiplier

density ratio - 1

intermittency factor

bandpass of cut-off frequency filter

time period

effective integration time when a cut-off frequency filter

is used

x
e quantum yield of photomultiplier

n c coefficient of optical transmission between observation

volume and detector

n L

coefficient of optical transmission between the laser and

observation volume

X wavelength

y r rth central moment

y ; rth moment

y (r)

rth central factorial moment

y (r)

rth factorial moment

V kinematic viscosity

5 unmixedness

0

2 —1 angular cross section (era sr ) for Rayleigh light

scattering

0

a 90° scattering cross section for air

90° scattering cross section for fuel

a w

wrinkle amplitude

P density; depolarization ratio

T dummy variable for autocorrelation

T integral time scale

0) frequency

fl solid angle for light collection

$ (u) power spectrum

Superscripts

a anisotropic

i isotropic

B average value of B for L measurements

B RMS for fluctuations of B for L measurements

xi
Subscripts

f

j

PC

PF

air

ch4

tur

(B)

c

< B

>o

(b) t

value for air

value for fuel (jet gas)

index for summation

photocount

photon field

value for air

value for methane

value for turbulent flow

value of B on jet centerline

value of B at jet exit

conditionally sampled value of B in turbulent region only

largest value of B in radial direction

xii
The Application of Laser-Induced Rayleigh Light Scattering

to the Study of Turbulent Mixing

Abstract

This work describes the development and characterization of an experimental system employing laser-induced Rayleigh light scattering with digital

data acquisition as a time-resolved, quantitative concentration probe in the

turbulent flow field of a binary gas mixture. Equations for the expected

signal and noise levels are given. Estimates of these parameters for the

experimental system used here are in satisfactory agreement with experiment.

It is demonstrated that the laser Rayleigh light scattering technique provides

measurements having high spatial and temporal resolution for various locations

within the concentration flow field. Measurements at various positions in the

flow field of an axisymmetric methane jet issuing into a slow flow of air are

reported and, where possible, compared with appropriate literature results.

The statistical properties of the turbulent concentration fluctuations are

found to be in good agreement with other independent measurements.

Conditionally sampled measurements are also reported and shown to behave in

the same manner as the limited number of similar measurements in the

literature. The capability of calculating power spectra and correlation

functions for the time behavior of the methane concentration is also demonstrated. Other techniques employed for scalar measurements in turbulent flow

fields are briefly reviewed and the utility of these techniques for

1
measurements in different types of flow systems are discussed in relation to

the Rayleigh light scattering method.

Key words: Axisymmetric jets; flow fields; intermittency ; lasers; ramp-like

structures; Rayleigh scattering; scalars; turbulence; turbulent flow.

1 . INTRODUCTION

1.1 Preliminary Remarks

Despite years of study, a full understanding of turbulent behavior

remains elusive. This is unfortunate since turbulence occurs in many natural

and man-made systems. Turbulent flow is the most effective means of mixing

two or more fluids, and for this reason it is especially important in

combustion and reaction systems where mixing must precede molecular

interactions. For this reason, understanding chemically reacting turbulent

flows is a key to the more effective utilization of natural resources and the

control of pollution. Development of effective turbulence models is essential

for the design and construction of systems which utilize turbulent mixing most

effectively. An understanding of this phenomenon is so critical that

turbulence is often said to be the most important unsolved problem in physics.

We have initiated an experimental program with the long term goal of

enhancing the fundamental understanding of chemically reacting turbulent

flow. Our goal is to generate detailed data which can be used to empirically

describe the behavior of such flows and to provide input for mathematical

models designed to predict their behavior. An approach to the problem has

2
been chosen in which the effects of changes in density and temperature on

turbulent behavior are first isolated and evaluated for a well defined and

widely studied flow configuration. Once the effects of changes in these

parameters are understood, it will be possible to isolate the effects of the

nonlinear coupling which occurs between a turbulent flow and a chemically

reacting system.

The need for an accurate, time-resolved probe of concentration in the

turbulent flow field led us to evaluate several experimental techniques for

their effectiveness for such measurements. These included obtrusive probes,

such as those using hot-wires, and more modern nonobtrusive optical techniques

such as marker nephelometry , Raman scattering, and Rayleigh scattering. A

discussion of the advantages and disadvantages of many of these techniques is

included in Section 1.2. Based on our analysis, we have chosen laser-induced

Rayleigh light scattering as the technique most suited to our particular

measurement requirements. This decision is based on the relative sensitivity

of the technique and its ability to perform nonobtrusive measurements with

high temporal and spatial resolution.

There have been two past studies reported in the literature which

indicated that Rayleigh light scattering might be a suitable probe of

concentration behavior in turbulent flow systems [1,2].* This report

describes the development of such a system and how it is used to perform

scalar measurements and includes a detailed analysis of the spatial and

temporal resolution which can be achieved. A wide variety of properties of

^Numbers in brackets indicate the literature references at the end of the

paper.

3
the behavior of concentration fluctuations for an axisymmetrlc turbulent jet

of methane issuing into air are reported and compared with similar measurements available in the literature. The conclusion of this report is that, for

certain types of flows, Rayleigh scattering is an extremely powerful technique

for turbulent flow field scalar measurements.

In the following section (Section 2) the Rayleigh effect is described and

past applications of the technique for concentration, density, and temperature

measurements in turbulent systems are reviewed. This section also contains an

analysis of expected signal and noise levels. Section 3 describes the nature

of concentration fluctuations which occur in a turbulent flow and how the data

generated by a Rayleigh scattering experiment are analyzed in order to

characterize the concentration field. The experimental system employed for

this study is discussed in Section 4. Results of time- and spatially-resolved

concentration measurements in the flow field of an axisymmetrlc turbulent jet

of methane issuing into a background flow of air are summarized in Section

5. In the final section (Section 6) these measurements are compared with

literature measurements on similar turbulent flows, and the validity of such

comparisons is examined. Finally, the usefulness of the Rayleigh scattering

technique as a concentration probe of turbulent flow systems is discussed.

1.2 Scalar Measurement Techniques in Turbulent Flow Fields

Those properties of a system which only require a magnitude for their

full description (e.g., temperature or concentration) are said to be

scalars. Vector properties (e.g., velocity) must be assigned a direction and

magnitude. In this work we treat the measurement of scalar values with an

emphasis on concentration measurements.

4
Many different measurement techniques have been used to determine the

scalar properties of turbulent flow fields. In this subsection the strengths

and weaknesses of some of these techniques will be discussed with a special

emphasis on comparison with the Rayleigh light scattering measurements to be

described in this work. The following discussion is only illustrative and is

not intended to be a detailed review of measurement techniques for scalar

properties in turbulent flow fields.

Scalar probes can be classified as obtrusive or nonobtrusive depending on

whether or not a physical probe is inserted into the flow field. These two

types of probes can be further classified as direct or indirect. A direct

probe is defined as one which responds to the property under consideration

while an indirect probe is sensitive to a marker present in the flow which is

assumed to be passive (i.e., does not change the flow behavior). A probe is

said to be specific if it responds to the individual components of a gaseous

mixture and nonspecific if it only responds to an overall property of the

system such as temperature or density. Another possible trait of scalar

probes is their ability to characterize fluctuations in real time. That is,

the probe has the ability to repeatedly make determinations of a scalar

variable at a frequency sufficiently high that the property appears constant

during a time equal to the period of the measurement. Obviously, this period

will vary for different flow conditions. The ability to perform real time

measurements is important for intermittency and conditionally sampled

determinations. All of the probes to be discussed in this section have the

capability to make spatially resolved measurements. Using the above definitions, the ideal scalar probe would be nonobtrusive, direct, specific, and

capable of infinite temporal and spatial resolution.

5
Early experiments dealing with the concentration fields of turbulent

flows used various obtrusive probes. Usually these studies only reported

average values for temperature or concentration. Representative of this early

work Is that of Hlnze and van der Hegge Zijnen [3] who used thermocouples and

a capillary connected to a gas analyzer to measure the average temperature and

concentration fields of an axlsymmetrlc free jet. Forstall and Shapiro [4]

used helium as a passive marker to study the spreading of an axlsymmetrlc jet

of air Into a coflowing stream of air. Samples were withdrawn from the flow,

and the helium content was determined by a standard thermal conductivity cell.

Studies by Corrsin and Uberoi [5,6] showed that hot-wires operated in a

low overheat constant current mode could be used to measure average temperature and fluctuation intensities in heated air-air flows. This technique has

been widely applied to heated flows with heat acting as a passive marker of

concentration changes. Chevray and Tutu [7] extended this early work by using

two hot-wires. The first was operated in the low overheat constant current

mode to provide a signal proportional to temperature. The second wire was

used in the constant current mode which responds to changes in both temperature and velocity. Using the output of the first wire to provide the

temperature for the second, the velocity and temperature of the flow could be

obtained simultaneously. Much of the current understanding of flow field

behavior of axlsymmetrlc jets has come from experiments of this type. Despite

the widespread use of these techniques, they often require subtle corrections

and questions remain about their performance for flows with large fluctuation

intensities.

6
There have been attempts to extend the use of hot-wires to direct

concentration measurements in flows of two gases by Way and Libby [8,9] and

McQuaid and Wright [10,11]. In order to perform such measurements, it is

necessary to obtain extensive calibrations before collecting actual data and

to perform detailed data analysis in order to obtain the final concentration

value. The techniques are also subject to the same errors as the hot-wire

experiments described above. Due to these problems, these techniques have not

been widely applied for concentration measurements.

One additional physical probe method will be mentioned. Brown and

Rebollo [12] have described a technique for monitoring the time-resolved

concentration fluctuations in a two component gas flow. This technique also

uses a hot-wire, but places the wire inside a sampling probe which has an

entrance designed to sonically choke the flow so that gas entering passes the

hot-wire at a constant velocity and the response of the hot-wire is only to

the composition of the gas. By performing extensive calibrations, it is possible to obtain highly accurate measurements of concentration in binary

mixtures with high spatial and temporal resolution. It should be noted that

the response of the hot-wire to concentration changes is not linear and a

fitting procedure is required for converting the recorded signals to concentrations.

The lack of simple, reliable, and universal obtrusive probe methods for

scalar measurements in turbulent flows has resulted in efforts aimed at the

development of nonobtrusive techniques. Among these techniques are marker

nephelometry , Raman and Rayleigh scattering, and electron beam fluorescence.

Peterson [13] lists many of the past studies which have used Rayleigh

scattering, Raman scattering, and electron-induced fluorescence.

7
Marker nephelometry is the term given to the technique in which light

scattering from particles is used as a probe of concentration fluctuations.

Since its introduction in 1961 by Rosenswelg et al . [14], this method has

proven to be a very useful probe of real-time turbulent fluctuations as

manifested by the behavior of small particles seeded into the flow. Becker et

al . [15] and Shaughnessy and Morton [16] have described the application of the

technique, and Becker [17] has provided a review. There are questions

concerning the ability of the particles to follow the flow, and possible

coagulation of the particles must be carefully considered. The size of the

particles and the seeding levels within the flow must be carefully controlled. Despite these drawbacks, the technique has been applied to a wide

range of flow problems which include combustion systems. Recently, the

technique has been extended to two dimensions by Long et al . [18]. These

workers use a plane of light to illuminate the particles in the flow field.

Scattered light is focused on the face of a low-light-level television camera

which provides a digitized 2-D image of the field of view. The extension of

the scattering technique from a point measurement to 2-D has the potential for

providing an improved and highly detailed picture of turbulent mixing. At

this stage in its development this technique is not capable of real-time

measurements and averages must be made from large numbers of independent

measurements.

The Rayleigh scattering technique which is described in this work and

marker nephelometry have much in common. Both use light scattering as a probe

and for this reason have the potential for high spatial and temporal resolution. Since the Mie scattering used in marker nephelometry is many orders of

magnitude stronger than scattering from molecules, the laser employed does not

8
need to be nearly as powerful as that required for Rayleigh scattering

measurements. This advantage is offset somewhat by the requirement to seed

the flow with particles. The largest source of noise in the particle

scattering technique is marker shot noise. This is a Poisson-type noise which

occurs because of the low number of particles in the observation volume. The

problem is particularly critical in regions of low concentration. Mie

scattering is so strong that electronic shot noise is seldom observed. Since

Rayleigh scattering occurs from molecules which are present at high number

7 -3

density (—2 . 5 x 10 pm ) , marker shot noise is not a problem, but, as we

will show, electronic shot noise due to the weakness of the scattering is the

major source of uncertainty in scalar measurements. Marker nephelometry

cannot provide temperature information or concentration information for an

isothermal tertiary gas mixture, and for this reason is somewhat limited

compared to Rayleigh scattering as a turbulence scalar probe. The demonstrated ability of marker nephelometry to be used as a 2-D probe is a

significant advance. Our calculations indicate that similar experiments are

feasible using Rayleigh scattering as a probe.

The nonspecificity of Rayleigh scattering or marker nephelometry for

individual constituents of a gas mixture is a serious drawback to their

application in turbulent flows composed of several different gases. The

requirement for techniques sensitive to specific components has led to the

development of Raman scattering and electron-induced fluorescence as flow

field diagnostics.

Raman scattering refers to the inelastic scattering of light by

molecules. The energy of the scattered light is shifted from that of the

9
input source by an amount equal to rotational or vibrational energies of the

molecule with which the light is interacting. Since the rotational or

vibrational energy spacings of molecules differ, it is possible to resolve the

scattered light and identify the molecule with which the light is interacting. The strength of the scattered light is proportional to the number

density of the species present. Since the populations of vibrational and

rotational levels depend on temperature, it is possible to determine the

temperature of gases from the Raman scattering.

The major drawback of the Raman technique is its low intensity. In

general, rotational Raman cross sections are ~100 times smaller than Rayleigh

cross sections, while vibrational cross sections are ~1000 times smaller.

Most experiments use vibrational as opposed to rotational Raman scattering in

order to reduce the resolution required to separate the scattered light from

the incident light and from the scattering due to different molecules. As we

will show in this work, Rayleigh scattering cross sections are just sufficient

to obtain time-resolved measurements for turbulent flows with currently

available laser sources. It is clear that averaging techniques are necessary

in order to apply Raman scattering to scalar measurements in turbulent flow

fields

.

Two approaches have been adopted in order to obtain the averaged scalar

properties of a turbulent flow field using Raman scattering. The first uses

high powered pulsed lasers to induce the scattering. A good discussion of

this method is found in the review paper of Lederman and Bornstein [19]. The

number of photons delivered by these lasers in a time period of 5-20 ns is

large enough to ensure that the number of photons which are Raman scattered

and detected during a single pulse is sufficient for concentration measure10
ments which have only a few per cent relative error (see discussion in

Section 2.3) due to photon statistics. In this manner, a single pulse of the

laser is capable of providing a temperature or concentration measurement.

Unfortunately, these lasers have repetition rates which vary from 0.1 to

several seconds and cannot provide real-time information. In order to obtain

accurate characterization of the average properties of the flow field,

thousands of measurements are repeated and the results are used to obtain

averages, standard deviations, and higher moments of the fluctuating property

which is being investigated. The technique is not capable at its current

level of development of providing temporal information for such quantities as

spectral densities, intermittency functions, or conditionally sampled

measurements. The extent of development of the technique is probably best

represented by the work of Drake et al. [20] who have simultaneously monitored

temperature and nitrogen, hydrogen, and water concentrations in turbulent

diffusion flames. Recently, Webber et al . [21] have demonstrated that twodimensional measurements can be made using Raman scattering induced by a

pulsed laser and imaged onto the face of a low-light-level television camera.

It has been known for a long time that Raman scattering induced by a CW

laser can be used to obtain the average concentration of individual components

within a flow field by collecting the scattering for a long period of time.

However, it was believed that the weakness of the scattering precluded a

determination of the fluctuation behavior. Birch et al . [22,23] have

developed a technique which allows repeated measurements of Raman scattering

for short periods of time to yield this information despite the fact that the

number of photons detected during any single period is so low that the

individual concentration measurements are essentially meaningless. The first

11
paper by these authors described a photon correlation method which allowed a

determination of the average, RMS, and autocorrelation of concentration

fluctuations in a methane jet. In a second report they introduced the

concepts used in Section 3.2 to deconvolute the effects of photon statistics

from concentration measurements. These concepts are valid for the Raman

effect even though the effect is 1000 times weaker than Rayleigh scattering.

By the use of this method, these authors have been able to map out many of the

time-averaged properties of a methane-air jet. This work must be considered a

breakthrough in attempts to apply Raman scattering as a diagnostic for

turbulent flow systems.

The electron-beam fluorescence technique is a nonobtrusive method which

can be considered to be an analog to both Rayleigh and Raman light scattering. The light source is replaced by an electron beam and the detected

light arises from atoms or molecules which are electronically excited by the

electrons. The technique is selective since fluorescence from different atoms

or molecules occurs at different wavelengths which can be resolved. The paper

by Smith and Driscoll [24] contains a good description of the technique and

the signal levels which are expected as density and temperature are changed.

The technique is capable of generating photon detection rates which are

sufficient to perform accurate concentration measurements at rates up to

several hundred kHz. Unfortunately, due to the collisional quenching of

fluorescence which occurs at higher pressures, the technique is only suitable

for low density flows. As pressures approach atmospheric, quenching causes

severe problems in signal levels and calibration. These considerations

indicate that the electron-beam fluorescence technique will be the method of

choice when the density is low. As such, it complements Raman and Rayleigh

scattering scalar measurements which are best used in higher pressure regimes.

12
2. RAYLEIGH SCATTERING

2.1 Description of Rayleigh Scattering

The following discussion of Rayleigh scattering considers the special

case of a vertically polarized laser beam passing through a gas. A suitable

detector of scattered light is located perpendicular to the propagation

direction of the laser and the electric field direction of the light. The

collection optics of the detector are stopped down in such a manner that it

observes only a small volume of space containing the laser beam. This

hypothetical arrangement is very similar to that actually used in most

experiments, including the one reported here. We now give equations

describing the intensity and polarization behavior of scattered radiation

reaching the detector. An excellent discussion of Rayleigh light scattering

is given in the book by McCartney [25]

For the purpose of this work we have assumed that the effects of

rotational Raman scattering are negligible since the cross section for this

process is ~ 100 times smaller than that for Rayleigh scattering. It should

be noted that it may be necessary to include Raman effects in order to

accurately predict observed depolarization ratios.

Rayleigh scattering refers to elastic (no shift in frequency) scattering

of electromagnetic radiation which occurs when the electric field of the

radiation interacts with the electric fields of atoms or molecules. In this

case, we will be interested in visible light, but the equations are also valid

for radiation in the infrared and ultraviolet. The oscillating electric field

13
associated with the electromagnetic radiation induces an oscillating electric

dipole moment within the individual atoms or molecules which constitute the

gas. These induced dipoles generate additional electromagnetic waves which

can propagate in a direction different from that in which the light was

originally traveling. These new waves are the scattered light. The strength

of the induced dipole and hence the intensity of the scattered light can be

directly related to the polarizability of the molecule with which the

radiation interacts. The polarizabilities of different molecules are often

very different so that the strength of Rayleigh scattering can be used to

infer the types of molecules or atoms with which the light is interacting.

The intensity of Rayleigh scattering is often described by defining an

angular cross section for each individual molecule, a, as the scattered power

per unit solid angle (intensity) divided by the incident power per unit area

(irradiance) . For a gas of number density N consisting of isotropic molecules

(all of the elements of the diagonalized polarizability tensor are equal) the

angular cross section is related to the index of refraction by

where the superscript i refers to an isotropic molecule, n is the index of

refraction of the gas, and X is the wavelength of the light. This expression

is derived for an ideal gas assuming n - 1 << 1.

The intensity of Rayleigh scattering from a unit volume of pure gas at a

constant temperature is directly proportional to the number density of the gas

and the irradiance of the incident light source. The polarization of the

( 2 . 1 )

14
scattered radiation can be characterized by defining I

(| as the intensity of

scattered light polarized parallel to the electric field of the incident light

and 1^ as the intensity polarized perpendicular. For an isotropic molecule

these relationships give

I* (90°) = a

i

(90°)NI (2.2)

II o

I*(90°) = 0 (2.3)

where I is the incident laser light irradiance and N is the number density of

the gas.

For anisotropic molecules at least two of the diagonalized elements of

the polarizability tensor are not equal, and an incident radiation field will

induce a dipole moment within the molecule which is, in general, not parallel

to the electric field of the radiation. In this case I * 0. The effects of

molecular anisotropy are usually treated by defining the depolarization ratio

P = Ij/1, (2.4)

and using scattering theory to show that Eq. (2.1) must be modified so that

the anisotropic angular scattering cross section for linearly polarized light

becomes

oa (90°) = 4tt 2

(n - l)

2 (3/(3 - 4p))/(N2

A4

) (2.5)

Using Eq. (2.5) it can be shown that

15
I ( 2 . 6 ) a (90°) «= oa (90°)NI

o and

la (90°) = aa (90°)NpI (2.7)

1 o

Values of p for most molecules are small, but vary over a range from zero to

as large as approximately 0.15.

Since the intensity of light scattered from individual molecules is

additive, the total intensity of Rayleigh scattering from a mixture composed

of M different gases can be written as

Ia

( 9 0° ) = E o

a (90°)X

j J

Iq

Ia (90°) = N( E a“ (90

w

)p X. 1 I M

a no r i r j/ o

( 2 . 8 )

(2.9)

where X. is the mole fraction of gas j and N is the total number

3 M

density, N = E N , of the mixture. By using Eqs. (2.8) and (2.9) along

j = l 3 M

with the condition E X = 1 , the mole fraction of each component in an

j=l J isothermal mixture of three gases can be determined by measurements

^ O 3 0

of 1

1 | (90 ) and 1^(90 ) providing each gas has different values of and p^.

However, if there are more than three gases in the mixture or if the values

of CK and

p^ are not different for each gas, the system will be underdetermined and it will be impossible to solve for individual X^

.

When the system is not isothermal the total number density of a constant

pressure gas mixture is inversely proportional to temperature. In this case,

Eqs. (2.8) and (2.9) can be rewritten as

16
I®(90°) = N

q

(P/RT) ^

l a^(90°)X

j j

I q

1^(90°) = N

q

(P/RT)^ E a

j

(90°)Pj

Q

( 2 . 10 )

( 2 . 11 )

O O where N

Q = Avogadro's number = 6.023 x 10 , P is the total pressure, R is the

gas constant, and T is temperature. Providing the values of o and are

different for each gas and independent of temperature, the maximum number of

properties which can be uniquely determined are the temperature and the mole

fractions of two gases. If should be mentioned that the radiation scattered

by gas molecules is spectrally broadened due to molecular translational motion

(Doppler broadening). An evaluation of the spectral broadening of Rayleigh

scattered light can be used to derive a temperature in a turbulent flow

measurement as shown by Robben [26].

2.2 Past Uses of Rayleigh Scattering as a Probe in Turbulent Flow Systems

Several groups have used Rayleigh scattering as a probe of scalar fields

in turbulent combustion. Since a combustion system contains more than two

gases, the actual quantity measured depends on the conditions of the experiment and assumptions (expected to be very good) must be made to obtain

meaningful results and overcome the nonspecificity of this type of scattering. Robben [26] has argued that the contribution of each atom to Rayleigh

scattering is relatively independent of how it is bonded. This implies that

for a premixed combustion system the total Rayleigh cross section is independent of the degree of reaction and therefore the scattering intensity will be

proportional to the mass density within the observation volume. If the total

number of molecules in the flow does not change significantly as a function of

17
the degree of reaction, the mass density will be proportional to the number

density of the gas. This criterion is found to be nearly true for many

combustion systems and Rayleigh scattering has been used to measure number

density for a variety of turbulent combustion configurations [27-32]

.

If the pressure of the combustion system is constant (an open system) and

the assumption is made that the gas is ideal, the number density is inversely

proportional to temperature. This relation was used by Muller-Dethlef s and

Weinberg [33] to measure temperatures in flame speed experiments. Dibble and

coworkers [34-37] have used this method to measure temperature fluctuations in

turbulent premixed flames and have also demonstrated that the technique can be

extended to turbulent diffusion flames where the fuel and air have been

carefully chosen to have identical Rayleigh scattering cross sections. Uiese

workers [38,39] have also demonstrated a technique in which Rayleigh scattering and laser anemometry are combined to determine density and velocity at

essentially the same time and point in space. Pitz et al . [27] have used

measurements of Doppler profiles to measure temperatures in a hydrogen-air

flame.

Rayleigh scattering has also been used for monitoring the concentration

fluctuations which occur in isothermal turbulent flows [1,2]. In these

experiments, real-time concentration measurements were made for axisymmetric

fuel jets issuing into a slow flow of surrounding air. As long as the

scattering cross sections of the two gases are not the same, a single

measurement of total Rayleigh scattering intensity allows a determination of

the mole fractions of the two components. Equation (2.8) can be rewritten as

18
1(90°) = (a X + a,X.)NI ( 2 . 12 ) a a ff o

where a and a. are the observed 90° scattering cross sections for air and

a r fuel, respectively. As long as the pressure and laser intensity remain

constant, the only unknowns in the equation are Xa and X^. The mass conservation equation

X

a + X

f = 1 (2.13)

provides the second relation necessary for the determination of X

& and X^.

Graham et al. [1] were the first to report Rayleigh scattering measurements of this type. These workers studied the fluctuations which occur in

acoustically forced and unforced jets of methane into air. This work demonstrated that Rayleigh scattering can be used to observe concentration

fluctuations in a turbulent flow system. Later, Dyer [2] used the same

technique to measure the average concentration and RMS concentration fluctuations as a function of position in a jet of propane. This work also included

results of autocorrelation measurements which allowed the integral time scale

(defined in Section 4.5) to be determined for known positions in the turbulent

flow. Simple statistical arguments were provided indicating that measurements

performed in this manner are very accurate.

2.3 Expected Signal and Noise Levels for Rayleigh Scattering Measurements

Equation (2.12) gives the intensity of light scattered in the perpendicular direction from a light source of known I Q

. In order to relate this

19
equation to the signal measured in an experiment it is necessary to include

the effects of the solid angle for the collection optics, optical losses, and

detector efficiency. The following expressions are derived in terras of

photons (or events)/s.

It is important to note that the output of the photomultiplier is a

current and that this output may or may not consist of discrete detection

events. For instance, at low light levels a discriminator/amplif ier combination may be used to detect amplified photoelectron pulses arriving at the

anode of the photomultiplier and counters can be used to relate the number of

detected photons to the light intensity. This photon counting technique is

highly compatible with digital data acquisition. However, at high light

intensities the number of detected photons becomes very large and electronic

detection devices can no longer distinguish individual events. This pulse

"pile-up" leads to nonlinearities in the ratio of detected current pulses to

the actual number of photons reaching the anode of the photomultiplier. In

this case, it is preferable to measure the total current output of the

photomultiplier. If the gain (G) of the photomultiplier is known, the number

of detected photons (N

p

) during a time period (At) is related to the current

(i) by the relation

N

p

= J* idt/(G x 1.6 x

10" 19

) (2.14)

where i has units of amps and the integral represents the total charge

collected during At.

20
The following equation gives the predicted photon detection rate during a

laser Rayleigh scattering experiment when the laser is assumed to have a

cylindrical profile within the observation volume of the collection optics.

R

P = ^L 1 ft n

c

e N

M

Z a j-1

( 2 . 15 )

where

Ip = detected photoelectron rate (photons/s)

1^ = laser output (photons/s)

n T = coefficient of optical transmission between the laser and

Li observation volume

1 = length of observed volume element

ft = solid angle (steradians) of collection for scattered light

= coefficient of optical transmission between observation

volume and detector

e = quantum yield of photomultiplier

M

N E a. X. j-i J J = Rayleigh scattering cross section for gas of total number

density N

21
This equation is based on several assumptions including 1) observations are

made at right angles to the laser beam, 2) polarization effects are absent,

and 3) ft is small enough to avoid considering the angular dependence of

Rayleigh scattering.

In order to obtain an estimate of the number of photons which should be

detected in an actual experiment, Rp has been calculated assuming that

scattering is induced from air by a 7 watt argon ion laser operating at

488 nra. The following parameters have been chosen to approximate those

actually existing in our experimental system.

1^ = 1.72 x 10 19 photons/s

n L

= 0.67

1 = 0.027 cm

ft = 0.189 sr (f/2 collection optics)

M

l

J-l

n c = 0.50

e = 0.14

N = 2.46 x 10 19 cm

-^

OjXj = a AIR = 8.2 x 10 cm^/sr

Using these parameters, the detection rate of photons is calculated to be

Rp = 8.3 x 10 7 photons/s.

The use of Rayleigh scattering as a concentration probe requires an

estimate of the accuracy with which a measurement of a given scattering

intensity can be made during a time period At. Much of the material which

follows is described in detail by Robben [40] in his paper on noise in the

22
measurement of light with photomultipliers. The detection of photons obeys

Poisson statistics, which require that a repeated measurement of the number of

detected photons, Np, from a constant intensity light source during At will

have a variance equal to the average number of photons detected during At.

This requirement is expressed as

Var(Np) = <N

p

> (2.16)

where <N > = lim E Wi The relative uncertainty in a measurement of Np is

P L— J-l

L

given by

Var(Np) 1/2

/ <N

p

> = l/<N

p

> 1/2

= l/<RpAt> 1/2 (2.17)

The uncertainty in optical measurements due to Poisson statistics is sometimes

called electronic shot noise. Equation (2.17) shows that in order to reduce

the relative uncertainty in the measurement of a Rayleigh scattering intensity

it is necessary to lengthen the counting period or to increase Rp by

increasing the intensity of light reaching the detector.

An estimate of the relative uncertainty in the intensity measurement of

Rayleigh scattering from air for the conditions described above can be

obtained by the use of Eq. (2.17). For a one second counting time the

predicted relative uncertainty is only 0.00011. However, for a one microsecond counting time the relative uncertainty is 0.11. Clearly, the minimum

time resolution which can be obtained with Rayleigh light scattering concentration measurements depends on the maximum relative uncertainty which is

tolerable in the experimental measurement.

23
When analog detection of the photomultiplier current output is used, Eq.

(2.17) is modified by combining it with Eq. (2.14) to give

Var(q

t

) 1/2 /<q t > = ((G x 1.6 x 10" 19 )/<q t »

1/2 (2.18)

where q^

= idt'. Equation (2.18) describes the relative uncertainty in the

intensity measurement assuming no additional uncertainty is introduced by the

amplification which occurs along the dynode chain following the release of a

photoelectron at the photocathode of the photomultiplier. In practice, the

amplification of current at each dynode in the chain also obeys Poisson

statistics and an extra term must be included in Eq. (2.18) to represent this

source of noise.

Var(q

t

) 1/2

/<q

t > = ((a/(a - 1))(G x 1.6 x 10

_19

)/<q

t »

1/2

(2.19)

a is the gain per dynode within the photomultiplier and a large number of

dynodes has been assumed. A typical value of a is 5, so the relative noise is

increased by ~1.12 over what it would have been in the absence of amplification noise. Equation (2.19) is for the case where the current from the photomultiplier is integrated for a period At. Often, the current outputs of

photomultipliers are not integrated for a given time period, but are instead

"smoothed" by RC time constant circuits or cut-off frequency filters. In

these cases the integration period must be replaced with an effective time

period, At', which is related to the cut-off frequency by the expression

At' = l/(2Af) where Af is the frequency bandpass of the filter.

Equation (2.19) can be rewritten as

24
Var(qp ( 2 . 20 ) 1/2

/<q^> = ((a/(a - 1))(G x 1.6 x 10

_19 )/<q-» 1/2

where q' = iAVG

At' and iAy G is the average current during At'.

The equations discussed thus far only predict the observed variation in

numbers of detected photons for light from a constant intensity source. In

cases where the light intensity is varying, these equations are no longer

strictly valid. However, for moderate numbers of photocounts, it is found

that the relative error in a single measurement of the integrated light

intensity during a time period At is essentially equal to Eqs. (2.17) or

(2.20) where <RpAt> and <q'> are replaced by RpAt and q', respectively.

There are often other sources of noise in scattering measurements which

can interfere with accurate determinations of Rayleigh scattering intensity,

such as source fluctuations, dark current, and background interference.

Becker et al. [15] and Shaughnessy and Morton [16] have given detailed

discussions of such sources of noise in regards to scattering from particles

(Mie scattering). Similar considerations are expected to be important for

scattering from molecules. For the experiments reported here, we conclude

that electronic shot noise is by far the largest noise factor and that other

noise sources can be disregarded.

For the experiments described here, Rayleigh scattering is used to

produce a time record of concentration fluctuations occurring in a turbulent

flow of fuel (methane) into a slow flow of air. The light which is detected

by the photomultiplier consists of scattering from the molecules within the

flow and background radiation from light scattered by the apparatus and other

25
sources. It Is therefore necessary to deconvolute the scattering due to

actual Rayleigh scattering from background light. We have used a calibration

procedure in which scattering from air and methane are measured before the

turbulent flow of methane into air is initiated. These intensities are

recorded for a relatively long time to ensure that the errors in the measurements are small. The intensity of scattering from the turbulent flow is then

recorded in an identical manner. The mole fraction of methane is then

obtained directly from the relation

X

CH,

(I tur

” I AIR

)/(I

CH,

I AIR) 4 4

( 2 . 21 )

where I tur » *aIR» an<* re ^ er t0 Rayleigh scattering intensities from the

turbulent flow, air, and methane, respectively. This equation can easily be

obtained from Eq . (2.12). Note that each intensity contains contributions

from background radiation, but that the background contribution drops out when

the differences in Eq. (2.21) are taken. The value of each will have an

4 error due to electronic shot noise in the measurement of I tur » Fortunately,

methods exist for statistically compensating for electronic shot noise when

calculating many of the quantities of interest for the turbulent flow. These

techniques are considered in the following section.

3. TURBULENCE MEASUREMENTS

3.1 Nature of Turbulence and Approaches to Its Characterization

In early experimental studies of turbulence most investigators were

primarily concerned with averaged measurements of turbulent quantities. This

26
was due to the widely held belief that turbulent flow was very close to being

a totally random phenomenon and that the only hope for treating it was by the

use of statistical techniques. Such a viewpoint is inherent in the use of the

Reynolds decomposition of the Navier-Stokes equations. A primary hypothesis

of this approach is that turbulence consists of a wide size range of eddies

which are randomly distributed in space and time and that there is a constant

cascade of turbulent energy from larger to smaller eddies. In order to

characterize this structure, such measurements as averages, standard deviations (turbulent intensity), and power spectra were made for the velocity

fluctuations within turbulent flow fields.

Recently this focus has begun to change. Studies such as that of Brown

and Roshko [41] have found that turbulent flows have a highly organized large

scale structure. This has led to a resurgence in the use of visualization

techniques to characterize these structures. The existence of these organized

/

r • large scale structures has also increased the need for such measurements as

intermittency and conditionally sampled statistical measurements which require

time-resolved techniques.

Most past experimental studies have dealt with velocity measurements

within the turbulent flow field. Measurements of scalar quantities such as

temperature and concentration have lagged far behind. The preponderance of

measurements of velocity flow fields is due to the importance of momentum

transfer in theories of turbulence and the availability of sensitive techniques for velocity determination. Accurate methods for scalar quantities are

much less developed than those for velocity. It should be noted that the

transport of heat and mass within turbulent flows is one of the primary

27
reasons for their practical Importance. Furthermore, any theory of turbulence

based on velocity behavior should also be able to predict heat and mass

transport In order to be complete. Clearly, accurate measurements of scalar

flow fields are required.

3.2 Calculatlonal Methods for Properties of the Concentration Flow Field

Our work uses Rayleigh light scattering as a probe of the time-resolved

concentration fluctuations occurring In a turbulent flow. The raw data which

are generated are digitized and stored in the memory of a minicomputer. This

subsection describes how the data are analyzed in order to describe the

properties of the concentration fluctuations at a point in space.

The first requirement is to characterize the statistical distribution of

the concentration fluctuations. We have chosen to do this by use of the

average concentration and the second through fourth central moments of the

distribution. For a series of L noise-free concentration measurements (in

mole fraction terms) the average concentration is given by

measurement. The second and higher central moments of the concentration

distribution are defined as

(3.1)

where X is the average concentration and Xj is the result for a single

r (3.2)

28
where u is the rth central moment of the concentration distribution,

r

The second central moment is called the variance. Often the square root

of the variance (called the standard deviation or root mean square (RMS)) is

reported. In this work the RMS is denoted as X . The third and fourth

central moments are often given in dimensionless terms by dividing them by a

suitable power of the variance. The skewness factor is defined as

S = p 3 /(y

2 )3/2 (3.3)

and the flatness factor or kurtosis as

K=y4/(p

2

) 2

. (3.4)

S and K can be considered as measures of how the experimental distribution

differs from a Gaussian. For a perfect Gaussian S = 0 and K = 3.

In Section 2.3 it was pointed out that there is an electronic shot noise

associated with every measurement of X' using Eq. (2.21). This noise can

CH,

4

lead to large errors in the calculated values of X, S, and K when it is

comparable in size to the intensity changes in Rayleigh scattering due to

concentration fluctuations. Fortunately, Birch et al . [23] have developed a

very effective mathematical method for separating the actual moments of the

intensity fluctuations (due to concentration fluctuations) from the effects of

shot noise. These workers used the earlier results of Pike [42] who had shown

that the moments of the photon number distribution are identical to the

factorial moments of the detected photon distribution.

29
In order to apply the results of Pike [42]

,

the detected Rayleigh

scattering must be given as a series of numbers of detected photocounts, Np,

collected during a time period At. The factorial moments for the distribution

of Np are defined as

where is the rth factorial moment, the subscript PC indicates the

photocount distribution, and = B(B - 1 ) ( B - 2) • • •

[

B

- (r - 1)]

B

!

or -7tz—ry. According to Pike [42]

,

(.B-r;

!

( y (r))pC ( y r)pF (3.6)

where

(p^.)pf are the moments of the photon field distribution. * s the

average number of photocounts during At and for scattering from a turbulent

flow can be denoted I and used in Eq. (2.21) to calculate X . In order

tur tn.

4

to obtain the higher moments for the concentration distribution, the photon

field moments must be converted to central moments using the relation

( y r)pF ( 1)j

(j)(

P r-j)pF(y l)pF (3.7)

and then normalized to include only the scattering from gases in the field of

view of the photomultiplier

P r (3.8)

where I CH,

4

and IAj R are the average numbers of photocounts defined earlier.

30
Power spectra are taken in order to determine the frequencies which

compose the concentration fluctuations. For the case of a continuous function

the power spectrum is defined as the square of the Fourier integral

where $>(w) is the power spectrum. In our experiment, the Rayleigh scattering

intensity is recorded at equally spaced times for a finite period of time. It

can be shown that a very good approximation of $(00 ) can be calculated from

discrete data if the highest frequency in the signal is no larger than one

half of the sampling frequency (the Nyquist sampling theorem [43] ) and the

lowest frequency in the signal is sampled at least five times during the total

data collection time. The calculated power spectrum does tend to be broadened

and "noisy'’ due to digital effects arising from the incomplete transformation. A method known as the Fast Fourier Transform (FFT) due to Cooley and

Tukey [44] is used to quickly calculate the Fourier transform for discrete

data, and a simple complex multiplication then yields $( 00 ). It should be

noted that electronic shot noise is "white." This means that it is a constant

intensity at all frequencies and a power spectrum due to concentration

fluctuations measured by Rayleigh scattering will be built on a flat base due

to shot noise.

A related function of interest is the correlation function, R(t), defined

as

-00 — 2 $(w) = j X(t)e dt (3.9)

R(t) = fl00 x( fc ) x(t + x)dt (3.10)

31
R(t) gives an Indication of the time required for an average eddy to pass a

point in space. In conjunction with Taylor's hypothesis [45]

,

an average eddy

size or length scale can be calculated if the velocity at the point is also

known. The Fourier transform of the correlation function is the power

spectrum

^(w) = r R(x)e

iwT

• dt (3.11) —oo

thus either 0 (a>) or R(x) can be used to describe the period and frequency of

concentration fluctuations and one is easily converted to the other. The

minicomputer used in this study is programmed to calculate R(x) by taking a

FFT of X(t), squaring the complex function which results, and taking the

inverse Hermitian (reverse Fourier transform) of the square. The calculation

of a correlation function from a discrete data set of finite length is subject

to the same constraints as those for calculating Fourier transforms.

All of the functions describing the statistical behavior of the time

dependent concentration fluctuations discussed thus far are averaged for the

entire data set. However, it is well known that turbulent flows display a

property known as intermittency (see Schon and Charnay [46] for a discussion)

which is due to the presence of two distinct fluid behaviors in the instantaneous flow field. The regions where the fluid behavior varies are separated

by a well defined boundary which is small compared to the size of the

regions. The two types of fluid behavior have different statistical behaviors

with regard to the property being measured which allow the location of the

boundary between the two regions to be determined. These distinct regions of

fluid behavior are thought to be due to the presence of large scale structure

32
in the turbulent flow field. In this work we are interested in the intermittency function, I(t), which describes the passage of the turbulent/nonturbulent boundary of the fluid through the observation volume. We have

defined a turbulent region as existing when air has been entrained into the

flow and a nonturbulent region as one where either only air or methane are

present. The following equations can be written to mathematically describe

this concept.

I(t) = 1 when 0 < X (t) < 1 CH

4

I(t) = 0 when X

CH

(t) = 0, X

CR

(t) = 1 4 4

(3.12)

This definition of turbulent intermit tency based on concentration has been

used by several research groups [16,47-49] and also in the similar case of

heated flows where the marker is temperature [50], By simultaneously

monitoring temperature and velocity, Chevray and Tutu [51] demonstrated that

the intermittency function derived by real-time monitoring of a temperature

marker is identical to that found when velocity fluctuations are used.

Even though intermittency is a very simple idea conceptually, in practice

is has proven very difficult to generate a concensus among workers in the

field on an experimental definition. In part, this is due to the wide range

of turbulence variables (e.g., velocity, vorticity, concentration) for which

intermittency measurements have been made and the wide range of experimental

techniques employed. In the case of velocity measurements the problem is

severe since there is fluid motion in nonturbulent regions and it is necessary

to base intermittency decisions on whether or not the velocity fluctuations

33
are characteristic of turbulent flow. This problem has led to detailed

analysis and modeling in an attempt to overcome the problem [52,53]. For

scalar quantities the problem is somewhat simplified since the decision is

usually based on the presence or absence of the scalar (e.g., heat or mass).

For these measurements, the accuracy of the determination of the Interface

location is usually limited by noise in the measurement of the scalar

quantity. An additional difficulty arises due to the finite sampling volume

of most probes. Fluctuations occurring in this volume are averaged and this

can lead to inaccuracies in the determination of the boundary location. Many

different approaches to solving or at least minimizing these problems have

been used. In the experimental section (Section 4.5) we describe a procedure

based purely on statistics and the noise level in the measurement.

Once an intermittency function is obtained it can be used to calculate

several new properties of the flow field. The fraction of time the observation volume spends within the turbulent flow region is defined by the

intermittency factor, y, where

Y = lim f t I(t')dt7t (3.13)

t+co °

For discrete data an approximation of y is calculated by summing the number of

points at which I(t) = 1 and dividing by the total number of points. Clearly,

the accuracy of y will depend on the size of the eddies being observed and the

length of time for which the measurement is made. This point will be

discussed further in later sections. An intermittency frequency, symbolized

f^, can be defined as the average number of times I(t) goes from 0 to 1 during

a one second time period. It is obviously related to the number of large

34
scale structures passing through the observation volume. Unfortunately

values of f^ have proven very difficult to reproduce among different

laboratories. This observation is believed [54] to be due to the presence of

very short bursts of turbulence in the observation volume which do not

ically depending on whether or not they are detected.

Once an intermittency function is obtained, it is natural to use it to

determine the statistical properties of the scalar field in the turbulent

region only (by definition, the scalar quantity should be zero in the

nonturbulent region). Such measurements are known as conditional sampling

since the calculations are only performed when the condition I(t) = 1 is

fulfilled. These conditionally sampled measurements are expected to be much

more representative of turbulent behavior since they are made for turbulent

fluid as opposed to the global measurements which are weighted by the presence

of nonturbulent fluid. The average and moments of the turbulent concentration

fluctuations can be obtained by rewriting Eqs. (3.1) and (3.2) as

(3.14)

and

(3.15)

where

^ are calculated using Eqs. (3.5)-(3.8) when corrections must be

made for electronic shot noise.

35
4. EQUIPMENT AND PROCEDURES

4.1 Flow System

The flow system used for this experiment consists of an axisymmetric jet

of methane issuing into a slow flow of surrounding air. The jet is constructed from a 61 cm length of 6.35 mm I.D. brass tubing (9.5 mm O.D.).

These dimensions ensure that fully developed pipe flow occurs in the tube

before the methane exits the jet. The output end of the tube is sharpened to

a fine edge and the upstream end is connected to a ballast chamber to minimize

pressure fluctuations. Since Rayleigh scattering measurements are extremely

sensitive to interference from particle (Mie) scattering, it is necessary to

enclose the entire flow system to prevent dust particles from reaching the

observation volume. For this reason the jet is centered inside a 10.4 x

10.4 x 61 cm enclosure constructed from 5 mm thick optical crown glass. A

flow of air enters the enclosure from the bottom after passing through a bed

of polystyrene balls and a wire gauze to ensure a homogeneous flow. Flows of

both methane and air are controlled and measured by Fischer and Porter

Flowrator meters. Both flows are prefiltered with 0.3 micron filters to

remove particles. Methane (Matheson Technical Grade, >98%) is obtained from a

cylinder. A regulated, house-compressed air line is the source of air.

The initial stages of this work were plagued with scattering from

particles and unexpected profiles for the concentration field of the methane

2 Certain commercial equipment, instruments, or materials are identified in

this paper in order to adequately specify the experimental procedure. Such

identification does not imply recommendation or endorsement by the National

Bureau of Standards, nor does it imply that the materials or equipment are necessarily the best available for the purpose.

36
jet. Subsequent analysis indicated that the source of the problem was

recirculation within the enclosure. (See Becker et al . [47,55] for a good

discussion of this behavior.) Recirculation occurs when the ability of the

jet to entrain surrounding gas is greater than the amount of surrounding gas

present. In this case gas is drawn from downstream and recirculation eddies

develop. Since the entrainment rate of the jet is proportional to the

Reynolds number (Re), the higher the flow rate the more likely the occurrence

of recirculation. Becker et al . [55] analyzed the likelihood of recirculation

in terms of the Craya-Curtet number Ct. Using their analysis it is possible

to show that recirculation should occur for the initial flow conditions used

in this study. In order to eliminate recirculation, it is necessary to reduce

the difference in flow rates between the air and methane. When this is done

recirculation effects disappear. The absence of such effects is confirmed by

hot-wire velocity profiles which are found to be identical with or without the

enclosure in place. All measurements reported here are for an initial methane

flow velocity of 1022 cm/s and a surrounding air flow velocity of 26.9 cm/s.

These velocities correspond to a Reynolds number of Re = uD/v = 3760 where u

is the difference in initial velocities of the two flows, D is the diameter of

the jet, and v is the kinematic viscosity of methane.

The jet and enclosure are mounted on a lathe bed to allow accurate

positioning of the observation volume in the flow field. Scales mounted on

the lathe bed give positions of the observation volume relative to the center

of the nozzle exit which are accurate to 0.25 mm.

37
4.2 Optical System

Figure 1 shows the optical system used in this study. A Spectra-Physics

Model 171-19 Ar ion laser is operated in the single wavelength mode to produce

a 7 watt output at 488 nra. The laser beam is expanded to 22 mm using a 10X

beam expander from Special Optics and is then focused to a narrow cylinder of

~ 0.035 mm diameter within the system enclosure by a lens (fl = 25 cm). The

position of this focus along the laser beam is determined by a knife edge

test. The approximate length of the cylindrical region over which the focused

laser beam diameter remains constant is 4 mm.

Light scattered from the observation volume is collected and collimated

by an anti-reflection (AR) coated 10.2 cm achromatic lens (f/2) and then

refocused using a 10.2 cm AR coated spherical lens. A set of adjustable slits

is placed at the focal point of the second lens to define the observation

length of the cylindrical region of scattering. The diameter of the volume is

determined by the diameter of the laser beam. By using the laser to backilluminate a 0.025 mm pinhole, it is possible to determine the actual length

of the observation volume by translating the pinhole along the laser beam

path. Figure 2 shows plots of observed intensity versus position along the

laser beam path for slit widths of 0.2 mm and 0.4 mm. The slight asymmetry in

the plots is believed to be due to a minor misalignment of the slits relative

to the optic axis. The origin of the plots is the point of minimum diameter

for the laser beam. For slit widths less than 0.2 mm the same curve was

obtained as for 0.2 mm slits. If it were possible to focus the image of the

pinhole on the slits without distortion, the image size would be 0.025 mm.

Figure 2 shows that this is clearly not the case. Spherical aberration causes

38
the minimum optical resolution to be ~0.27 mm. This results from light

collected at different angles by the collection optics being focused at

different distances from the lens. In order to minimize the length of the

observed volume it is necessary to very carefully position the slits at the

minimum diameter of the focus. The cross section of the focused light where

this minimum occurs is known as the circle of least confusion (see Hecht and

Zajac [56]). As the slits are opened the effects of spherical aberration

become much less noticeable and the observed cylindrical volume has a length

which is nearly equal to the slit width. The minimum volume element which can

be resolved using the current optical system is estimated to be 0.0003 mm .

After passing through the slits, the light is again collimated with a

22.5 mm AR coated lens. It is then filtered by a Promfret Research Optics

narrow bandpass filter centered at 488 nm and having a 1.2 nm FWHM and maximum

transmission of 60%. Finally, a second 22.5 mm lens is used to focus the

scattered light on the photocathode of a photomultiplier tube.

4.3 Detection, Conditioning, and Recording Electronics

The EMI 9781B photomultiplier tube used in this study has a modified S-5

photocathode with a reported quantum efficiency of 0.14. In all experiments

described here the tube was operated at 680 volts. The calibrated gain for

this voltage is reported by the manufacturer as G = 2.4 x 10^.

The output of the photomultiplier is measured in the current mode. A

variable resistor is used to convert the current into a voltage which is fed

to an Ithaco Model 4302 dual filter employed as a low pass 10X amplifier.

39
This filter provides a relatively sharp cut-off frequency which attenuates

frequencies higher than a preset value at 24 dB/octave. Input voltages are

adjusted so that a suitable output voltage (<2 volts) is produced for signal

acquisition. The time response of the electronics is such that the filter

provides all frequency selection and smoothing of the photomultiplier signal.

After conditioning, the PM signal is fed to a 12 bit digitizer of a

Nicolet 1180 data acquisition and processing system. This system is a

minicomputer employing a 20 bit processor unit specially designed for

laboratory use. It is equipped with a wide range of analog to digital (A to

D) and digital to analog (D to A) converters. Our particular instrument has a

40 K memory and is interfaced to a Diablo Model 31 disk drive which allows

1,143,296 20 bit words to be stored on interchangeable disks. Communications

to and from the machine are provided by a teletype, a paper tape reader,

oscilloscope, and digital plotter. Manufacturer supplied software includes

BASIC and FORTRAN compilers and general purpose programs for signal acquisition and analysis.

The digitizer of the minicomputer sequentially samples an input voltage

at a user selected dwell time (3 p sec minimum). The actual digitization is

done by the combination of a rapid sample and hold and a much slower A to D.

The digitized input signal, which is proportional to the smoothed current

output of the photomultiplier, is stored in memory. Data sets as large as

32 K can be recorded in a single scan. At the conclusion of a data collection

cycle the entire data set is transferred to the disk for later analysis.

40
4.4 Experimental Procedures

We have chosen to measure the methane mole fraction using Eq. (2.21).

This equation requires that only relative Rayleigh scattering Intensities and

not absolute quantities be measured. For each turbulence measurement It Is

necessary to measure the scattering Intensity due to methane and air. Data

records of 4096 points are taken for each gas. Software programs are

available for rapidly calculating average Intensities and standard deviations. Statistical analysis Indicates that the relative error due to photon

statistics In these average Intensity measurements Is much less than 1%. An

additional measurement Is made when the enclosure Is filled with helium.

Since the cross section for helium Is only 0.015 of that for air, this

Intensity provides a good estimate of the background Intensity from the

enclosure in the absence of scattering gas. Due to the small size of the

enclosure and the use of glass walls with 4% reflections at each air/glass

interface, the amount of detected light which is not due to Rayleigh

scattering is of the same order as the light scattered from air. This

background light limits how close the observation volume can be placed to the

nozzle because scattering of the background light from the nozzle is quite

strong. By subtracting the background intensity from the intensities observed

when air and methane are in the enclosure, the intensity ratio

I,,u / 1

T

_ = /o ATT_ can be calculated. This ratio is used as a check to

LH, AIK Lh, AIK

4 4

ensure that no systematic errors are being made in the measurements. An

indication of the reproducibility of the measurements can be found in the

average value of a ^ /o = 2.33 ± 0.02 found for ten different data sets ~ CJri , A1

4

recorded on the same day. Actual values of a and a for ambient

Lei. AIK

4

conditions are calculated using Eq. (2.1) and values of n.TM and nrH at 488

41
run taken from tables In McCartney's book [25] and Landolt-Borsteln [57],

“28 2 respectively. The results are o^.

R

= 8.17 x 10 cm /sr and

-27 2 = 1.91 x 10 cm /sr giving a predicted value of 2.34 for aCH

4 4

Agreement between observed and predicted values is excellent. As a final

check of intensity calibrations, a second data set is recorded for air after

the turbulence data have been taken. If the two intensities measured for air

differ by more than 1%, the entire series of measurements is repeated.

Immediately after calibrating the Rayleigh scattering intensity, a

turbulent flow of methane into air enters the enclosure. After allowing a

sufficient period of time for the flow to flush the enclosure and to stabilize, the Rayleigh scattering intensity is measured. The size of the

turbulent data record can be varied, but for the experiments reported here

either 16,384 or 32,768 real-time intensity measurements were recorded and

stored on disk.

4.5 Data Analysis

The properties of the concentration fluctuations discussed in Section 3.2

are calculated at different positions in the flow field. As previously noted,

Rayleigh scattering intensities recorded in the memory of the computer are

only relative values and contain errors due to photon statistics. In order to

apply Eqs. (3.5)-(3.8) for the calculation of concentration moments it is

necessary to know the actual numbers of photons detected. We have used Eq.

(2.17) as a means of providing a calibration factor for changing the relative

intensities into absolute numbers of detected photons. Measurements of

scattering from air and methane provide relative light intensities for two

42
well defined methane concentrations. These measurements also yield the

relative standard deviations. It is worthwhile to note that the ratio of the

standard deviations for the two measurements is found, as expected, to be

inversely proportional to the square root of the intensity ratio. By using

the relative standard deviation for scattering from air and substituting in

Eq. (2.17) it is possible to calculate an effective value for the number of

photons detected during a period equal to the dwell time. This number

provides the calibration factor necessary to scale all of the relative

intensity measurements in the computer memory to numbers of detected

photons. Software has been developed using Eqs. (3.1 ) — (3 . 8) to calculate the

average, standard deviation, skewness, and kurtosis for the turbulent methane

concentration time histories. During software development it was found that

round-off errors severely affected factorial moments calculated using

Eq. (3.5) due to the large magnitudes of the numbers involved. In order to

reduce this error it is necessary to calculate central factorial moments using

These calculations were found to be much less susceptible to round-off errors.

Power spectra of concentration fluctuation data are calculated by first

using routines provided by Nicolet to take the fast Fourier transform and then

applying a complex multiplication to give the power spectrum. Power spectra

(4.1)

and convert these to factorial moments using

(4.2)

43
of entire data sets give high frequency resolution, but result in a large

amount of digital noise. For this reason, the data are broken into smaller

data records of 1024 data points. Fourier transforms for each of these

smaller records are averaged and a power spectrum taken of the average. Even

though the resulting power spectrum has much less frequency resolution, the

digital noise is greatly reduced. This method of calculating power spectra

from digital data has often been applied before. (See Konrad [49] and Cheng

et al . [29] for examples.)

Correlation functions for the turbulent concentration data records are

calculated using a subroutine of Nicolet's general applications package. The

entire data record of 16,384 or 32,768 measurements is treated in a single

calculation. Every data set recorded in this study gave R(t) functions which

could be fit as exponentials. For this case, the Eulerian or integral time

scale (T) can be written as

T = / R( t

)

d x = / e

'

J dr (4.3)

o

J o

which is simply equal to the time constant for the decay of the correlation

function. A linear least squares fit is used to calculate T from the log of

the correlation function.

A simple algorithm has been developed for making intermittency decisions. These decisions are complicated by the relatively large error in the

individual measurements due to Poisson noise. Clearly, the ability to

differentiate turbulent from nonturbulent fluid will depend on the noise

level. As discussed above, this noise level is directly related to such

44
factors as averaging time (cut-off frequency), laser power, and observation

volume. We have chosen to make intermittency decisions based purely on

statistical grounds. The fluid is considered to have become turbulent when

five "independent" intensity measurements fall above the sum of the scattering

intensity for air and one half of the standard deviation in the air

measurement. The number of data points required to equal five independent

measurements is calculated by dividing 5 by the product of the dwell time and

the cut-off frequency. Using the above criterion, the probability that the

gas contains a measurable concentration of methane is 0.997. The gas is

defined as having returned to nonturbulent behavior when the average of five

independent measurements falls below the defined cut-off level. It should be

noted that many other equally valid criteria could be selected to define

intermittency. Even though this prescription for calculating the intermittency function is somewhat arbitrary, it does yield results which are in

agreement with visual inspections of the data and which behave very much like

those reported in the literature. Additionally, it does seem to give results

which are fairly independent of the cut-off frequency used for the experiment.

Intermittency frequencies are calculated by determining the number of

times the intermittency function changes from 0 to 1 during a data record and

dividing by the total collection time for the data record.

Once the intermittency function is available, conditionally sampled

quantities are calculated for the turbulent region. The average methane

concentration, standard deviation, skewness, and kurtosis values for the

turbulent fluid are calculated as described above for the entire data record.

45
All of the above discussion on concentration measurements has been in

terms of volume (or mole) fractions. Often, the concentration fields of

turbulent jets are given in terms of mass fraction concentrations (see Way and

Libby [9] and Birch et al . [23] for examples) in an attempt to allow the

comparison of jets with varying density. The use of mass fractions automatically corrects for differences in jet behavior due to momentum differences

based on density. Birch et al . [23] have given the following approximate

equations for converting mole fraction concentrations into mass fraction terms

Y

CH

4

(a

p + ^CH^V^CI^ +

Y

CH

4

(a

p + ^CH^V^Ct^ + *)

where Y~ is the average concentration of methane in mass fraction terms,

4

Y is the RMS of the methane concentration fluctuations in mass fraction

Lrl

.

4

terms, and is the ratio of densities between pure methane and pure air

minus one (“p

P CH

4

//p AIR

Birch et al. [23] have concluded that there

are no measurable differences using mass or mole fractions for skewness,

kurtosis, correlation functions, or power spectra.

5. RESULTS

5.1 Nature of Detected Rayleigh Scattering

The average current output of the photomultiplier for scattering from air

is measured to be ~13 yamps of which ~55% is due to Rayleigh scattering from

air with the remainder being due primarily to scattered light from the

46
enclosure. Using Eq. (2.14), this corresponds to a photon detection rate of

3.4 x 10 7 photons/s or 1.9 x 10 7 photons/s for the Rayleigh scattering. This

experimental value can be compared with the predicted value of 8.3 x 10 7

photons/s calculated in Section 2.3. Even though the two values differ by a

factor of 4.3, the agreement is considered satisfactory since many of the

parameters substituted in Eq. (2.15) are based on best case estimates.

Additionally, the gain of the photomultiplier may no longer be the same as

originally determined by the manufacturer.

As Eq. (2.20) shows, the relative uncertainty in a current (intensity)

measurement from a photomultiplier is expected to be proportional to the

square root of the cut-off frequency. Measurements of the standard deviation

in detected intensity for a constant intensity source sufficient to generate a

current of 15 yamps were made for three cut-off frequencies. The relative

errors are summarized in Table 1. In each case, the observed relative errors

are ~40% higher than predicted by Eq. (2.20). Much better agreement would be

found if the photomultiplier gain is higher than the value used. Interestingly, a higher gain also leads to significant improvement in the agreement

between the observed and calculated current for Rayleigh scattering from air.

Using the above results, it is possible to estimate the error in an

individual methane concentration measurement when the actual concentration is

XH/ = 0.5. is assumed constant for a time period which is greater than

two times the inverse of the cut-off frequency. Assuming the current detected

for air is 13 yamp and for methane is 22.6 yamp with 5.9 yamp from background

scattered light, the 50% mixture of methane would be expected to give a signal

of 17.8 yamp with relative errors of 0.026, 0.016, and 0.010 for cut-off

47
frequencies of 5700, 2280, and 1140, respectively. Using these values, the

uncertainties in the concentration measurement are calculated to be 4.8, 3.0

and 1.9% of full scale. In actual practice, these values are expected to vary

slightly as a function of operating conditions and methane concentration, but

they represent a good estimate of the accuracy of a single methane

concentration measurement with the experimental parameters of our experiment.

Figure 3 shows three 200 ms recordings of data at the same location in a

turbulent flow of methane into air. These plots are uncorrected for photon

statistics. The only parameter changed from one set of data to the next is

the cut-off frequency of the amplifier which has values of a) 5700, b) 2850,

and c) 1140 Hz. Also included in Fig. 3 are the expected uncertainties in

each concentration measurement based on photon statistics which are extrapolated from measurements of scattering from air. Fluctuations due to turbulent

concentration changes are clearly visible in each plot, but as the cut-off

frequency is decreased the uncertainty in each individual measurement is

visibly reduced. Significantly, when Eq. (3.8) is used to calculate the RMS,

skewness, and kurtosis for the concentration fluctuations, the results for

each of the three 32 K point data sets are in close agreement. This result

indicates that the effects of fluctuations due to electronic shot noise can be

deconvoluted from the time-averaged properties of the concentration

distribution.

5.2 Time Averaged Properties of the Methane Concentration Field

Our goal in this work is to demonstrate the effectiveness of Rayleigh

scattering as a concentration probe in isothermal turbulent flows involving

48
two different gases. As part of this study it is necessary to compare

measured values of time-averaged concentration field properties with similar

measurements made by other workers using different techniques and with the two

past studies using Rayleigh scattering as a probe. For this reason, we have

mapped out the centerline behavior as a function of the axial downstream

distance (z) from the nozzle and the radial behavior (in terms of the distance

r from the centerline) of the jet for one downstream distance (z = 111 mm).

Figure 4 shows a plot of reciprocal methane concentration versus axial

distance which has been nondimensionalized by dividing z by the nozzle radius

r

Q

. Note that the concentration of methane is given in both mole fraction,

X , and mass fraction, Y , terms. The straight lines drawn through the

Ln / CH . 4 4

data points are the results of linear least squares curve fits of the data for

z/rQ

> 20. To facilitate later comparisons, the dependence of mole fraction

concentration on downstream distance is expressed in the form

f

XCH

4)o fC„4)c -

~ *l>0 < 5 ->>

where

(H).

((H). ')

is the concentration of methane at the nozzle exit

, the subscript c indicates measurements on the jet

X IX

centerline, is a constant, and z q

is the virtual origin in mole fraction

terms. A similar equation is used for the mass fraction results

(H)ofcH4)c

' C^-*oY K

where r = r /pTM, /p. T1,\ is an effective radius used by Birch et al. [23] in

e ol CH^ AIR

J an effort to account for density differences between the methane and air.

49
This concept was originally introduced by Thring and Newby [58] and does seem

to provide a good correction for density effects due to differences in

X

temperature (see Wilson and Danckwerts [59]). is found to equal 0.083

IX . * Y

with z = -7.5 r , the fit of Eq. (5.2) gives C. = 0.112 with

o o 1

z 1Y - -2.0 r . o o

Values of the RMS concentration fluctuations as a function of axial

distance are shown in Fig. 5 for both mole and mass fraction representations. These data also seem to fall on straight lines. The two sets of data

are fit to equations of the same form as Eqs. (5.1) and (5.2), namely

and

(hMhX = c*(z ' z °x

)

/r

°

* C^

Z " Z °Y

')/r °

X

The data shown in Fig. 5 gives = 0.286 with z

cl = 0.569 with Z 2Y

= -11.9 r . 2 o o

(5.3)

(5.4)

2X -34.8 r and

o

Often the behavior of RMS turbulent fluctuations is described in terms of

fluctuation intensities. Concentration fluctuation intensity is defined as

the local RMS of the concentration fluctuation divided by the local average

concentration, X /X or Y /Y . Concentration fluctuation intensity is

Url, Cn * Lrl/ L*ri, 4 4 44

often called unmixedness. Figure 6 shows the concentration fluctuation

intensity along the jet centerline in both mole and mass fractions terms.

The behaviors of the skewness and kurtosis factors as a function of z are

shown in Figs. 7 and 8, respectively. Even though there are fairly large

50
errors in the individual measurements, several distinct trends are evident in

these results. The skewness is less than zero over the entire range of z

values investigated. The skewness seems to reach a minimum at z/r^ * 20 and

then gradually increases. Similarly, kurtosis values reach a maximum of ~3.8

near z/r^ “ 20 and then fall to values in the 3 - 3.2 range as z increases.

Note that both measures indicate a non-Gaussian distribution for the turbulent

concentration fluctuations along the centerline of an axisymmetric jet.

Autocorrelation functions and power spectra have been calculated for all

measurements taken along the jet centerline. Figure 9 shows examples of these

functions for three values of z. Note that the frequency spectra are plotted

as a function of log(relative spectral density) versus log(f requency) . All of

these spectra are taken from data recorded with a 4.6 kHz cut-off frequency.

This cut-off frequency appears as a sharp dip in spectral density at high

frequency values. For small values of z (z = 20 mm, z/r Q = 6.3) there is

still some spectral density due to turbulent fluctuations at the point where

the signal is attenuated by the filter. Clearly, some spectral information

will be lost. By the time the flow is monitored at moderate downstream

distances (z = 80 mm, z/r

Q = 25.2) the high frequency portion of the spectral

density due to concentration fluctuations is greatly reduced. A plateau in

the spectral density is evident before the sharp drop due to the filter. This

plateau is the baseline due to the white noise associated with photon

detection statistics. This trend is much more evident further downstream

(z = 159 mm, z/rQ = 50.1) where a wide plateau region is observed. The same

power spectrum also shows a spike at 120 Hz which is an artifact due to a

small frequency oscillation of the laser power. The spike is only observed at

large values of z where the total fluctuation intensity is becoming weaker.

51
Integral time scales have been calculated from the autocorrelation

functions using Eq. (4.3). Figure 10 shows the behavior of these time scales

as a function of z/r

o

. The time scales clearly increase with downstream

distance, but due to the large variations between measurements it is impossible to give the form of the dependence. Birch et al . [23] have shown that the

time scales should increase as the square of the downstream distance. We

attribute the large variations in measured integral time scales to digital

noise which results when the autocorrelation is taken for discrete data

recorded over a relatively short period of time. The digital noise appears as

random fluctuations which result in errors for the exponential fit to the

decay of the function. These fluctuations can be clearly seen in the

autocorrelations shown in Fig. 9.

All of the measurements reported above are for r = 0. We have performed

similar measurements for the radial behavior of the concentration field at

z/r

Q = 35. Figure 11 shows the average methane concentration as a function of

r (normalized by *i/ 2

> radial distance at which the concentration has

decreased to one half of its centerline value). Both mole and mass fraction

concentrations are included. The solid lines are Gaussian-type functions of

the form

where the only independent variables are the centerline concentration and

r 1 / 2

• Values of these two parameters are taken directly from the data. These

curves are in excellent agreement with both sets of data shown in the

figure. Note that the values of ?i /2 used to fit the experimental values in

(5.5)

52
Fig. 11 differ slightly. For mole fraction concentrations r^^/ 2 " 0.108

while the mass fraction results give rj/2^ 2 " 0.104.

The RMS concentration fluctuations normalized by the centerline value are

shown in Fig. 12 in terms of mole and mass fractions. The solid line

represents the results of Becker et al . [48] for an air-air axisymmetric jet

and the dashed line gives the results of Birch et al . [23] in terms of mass

fraction for a methane-air jet. Note that the turbulent intensity initially

r/ r

l /2 = 0.9 while the RMS concentration in terms of mass fraction only

Figures 13 and 14 show plots of the skewness and flatness factors for the

methane concentration fluctuations as a function of r/zr

^

2

• Consistent with

results in Fig. 7, the skewness on the jet centerline has a small negative

value (~ -0.4), but as the measurement volume is moved outward in the radial

direction the values of skewness continuously increase until near the edge of

the jet they reach values greater than 5. As Fig. 14 reveals, the kurtosis

value on the jet centerline is greater than the Gaussian value of 3.

Initially, decreasing values of kurtosis are observed as the value of r is

increased. This trend continues until the kurtosis has dropped to a value

of ~2.5 at r/r ^2 = 0.9. After this minimum there is a rapid rise in kurtosis

value and near the outer wings of the jet values in excess of 30 are

observed. These two figures also include the results for conditional

measurements which are described in the next section.

increases as a function of r. maximum of 1.31 at

reaches a maximum of 1.18 at */ r \/2

= 0.7.

53
Power spectra and autocorrelation functions have been calculated for the

radial measurements. The behavior of the integral time scales is shown in

Fig. 15. Near the Jet centerline the autocorrelation time is 1.5 ms, but as

the measurement volume is moved outward from the centerline of the Jet, a

monotonlc Increase occurs and the Integral time scale Increases to values

greater than 10 ms in the outer region of the Jet. It should be noted that

the signal to noise ratio is greatly reduced for the autocorrelation function

as the edge of the Jet is approached. This is due to the fact that only air

is being monitored for a large fraction of the time. In these regions,

fluctuations are only due to photon statistics, and since these are random

they are uncorrelated and contribute a noisy zero baseline for the autocorrelation of the methane concentration fluctuations which occur during the

fraction of time the fluid is turbulent.

5.3 Conditional Measurements in the Methane Concentration Field

All of the calculations discussed thus far are for total data records.

However, as discussed in Section 3.2, the fluid in the outer regions of the

Jet displays an effect known as interraittency which results in two distinct

types of fluid passing through the measurement volume element. The effect of

int.ermittency is clearly seen in Fig. 16 where the methane concentration as a

function of time is recorded for z/rQ « 35 and r/rjy 2 “ 1*25. During part of

the sweep the methane concentration is zero while distinct "bursts" of mixed

fluid can be observed at other times. It should be noted that these bursts

appear to result in sharp increases of methane concentration when they enter

the measurement volume and that the methane concentration then seems to die

away slowly until nonturbulent fluid is once again present. As discussed

54
later, similar structures have been observed for the passive transport of heat

in air-air jets.

The intermittency function calculated for the displayed portion of

time-dependent methane concentration is also included in Fig. 16. Comparison

of the observed methane concentration with the intermittency function shows

that the algorithm described in Section 4.5 for intermittency determination

gives a function which is in good visual agreement with the actual data.

However, this figure also shows that very short bursts of turbulence (marked

by arrows in the figure) are missed due to the averaging process inherent in

the intermittency determination. It is found that most of the turbulent

bursts are of relatively long duration and therefore we feel that the

calculated intermittency functions are good representations of the actual

behavior of the flow.

The intermittency factor, y, has been calculated as a function of r/ r^^

and the results are shown in Fig. 17 along with the corresponding intermittency frequency, f^. The measurements are based on concentration in terms

of mole fractions. These results are not expected to be very different for

mass fraction concentrations. It should be noted that values of f are low

Y

and that they are subject to very large statistical error due to the few large

scale structures which passed through the observation volume during the 3.3 s

data collection time. This is especially true in the regions of very high or

very low y. The same argument indicates that measurements of y will have

large uncertainties in these regions also.

55
Several parameters can be defined which serve to characterize the

behavior of the lntermlttency function. For Instance, the value of the

normalized radial distance where y 0.5 Is found to be r/

r

^ /

2

" Within

the accuracy of the experiment the maximum of f^ also occurs at r/r

^ ^

2

"

1.6. Previous workers have found that when values of y determined from the

transport of passive markers are plotted versus r/r ^/

2

on probability graphs,

linear curves are found. Figure 18 shows such a plot for the values of

y which are included in Fig. 17. This plot is found to be linear for all

values of y except those where round-off errors in the measurements become

significant. The linearity of this plot requires that the location of the

outer boundary of the Jet be purely random. An equation can be written to

describe the behavior of y in terms of the average radial location of the Jet

edge (R r where y 0.5) and the RMS value for the movement of the Jet edge

- 2 1/2 relative to this value, - ( (R - R) ) [48] • 0 is sometimes called the

"wrinkle amplitude." Using these definitions, the following equation can be

written to describe the r dependence of y

y 0.5 erfc((r - R)//2 a ) (5.6) w

An analysis of the straight line in Fig. 18 gives R 1.6 r^ 2 anc*

- 0.28 *

1 / 2

* A plot of Eq. (5.6) is included in Fig. 17 and the agreement

with experiment is very good.

Using lntermlttency functions such as that shown in Fig. 16, it is

possible to calculate the average and higher central moments for concentration

fluctuations in the turbulent (I(t) 1) regions. These calculations are

performed in terms of mole fraction concentrations. The general behavior is

56
expected to be the same if mass fraction concentrations are used. Figure 19

V(H), shows plots of and

4

with the corresponding conditionally averaged quantities

versus normalized radial distance along

and

/ \ // X \ . As would be predicted, the average methane concentration is

^ CH4/T \

ClVc

higher in the turbulent fluid than for the non-condi tioned average. The

concentration in the turbulent bulges decreases much more slowly than the

overall average concentration with radial distance. The conditionally sampled

RMS fluctuations as a function of normalized radius are decreased compared to

the unconditioned results when y is close to 1. However, as the value

of y decreases there is a crossover point at r/r^y

^ = for which

/x \ / X is greater than 1.

V

CH4/T CH

4

The behaviors of conditionally sampled measurements of skewness and

kurtosis are included in Figs. 13 and 14. The differences between conditionally sampled and overall measurements are striking at large values of r. This

is not surprising, since in this region the fluid is 100% air for a relatively

large fraction of the time and the lower end of the resulting methane

concentration distribution must be cut off at this point. Conditional

measurements indicate that while the skewness is still greater than zero and

the kurtosis is greater than three in the turbulent regions, these parameters

are constant or changing very slowly as a function of r.

57
6. DISCUSSION

6.1 Comparisons of Measurements from this Study with Other Work

The primary goal of this study has been the demonstration of a new

technique for performing spatially- and time-resolved measurements in

turbulent flows. In the course of this work a large amount of data has been

generated which can be analyzed and compared with other work published in the

literature. At the same time, we are confirming some past observations and

reporting some new details of the behavior of the concentration field of an

axisymmetric jet. In most cases, comparisons are made with results for

similar jets of air issuing into air where the concentration field is not

mapped directly, but either heat (small temperature differences) or small

particles are assumed to have been passive markers for concentration fluctuations. There is one detailed study [23] where Raman scattering has been used

to map out the concentration field behavior for a free axisymmetric jet of

methane. Raman scattering is not sensitive enough to allow actual timeresolved measurements such as the intermittency and conditionally averaged

flow parameters reported here. However, by clever analysis of their data, the

authors were able to obtain accurate averaged properties for the concentration

field. Santoro et al . [60] have used the promising new technique of optical

tomography to measure the average concentration radial profile of a 10%

methane in air jet. The results reported in this work are in very good

agreement with all of these past studies, despite the fact that many of the

parameters which might be expected to affect turbulent behavior (e.g.,

Reynolds number and initial flow conditions) vary in the different studies.

The following section (Section 6.2) includes further discussion of this point.

58
Equations (5.1) and (5.2) can be used to compare results of Rayleigh

scattering centerline concentration measurements with those found in other

X IX Y 1Y

studies. Table 2 compares values of , zq

,

, and zq

measured in this

work with past measurements for air-air, methane-air, and propane-air

axisymmetric jets. The data for propane jets is calculated for only the three

X IX

sets of axial data reported by Dyer [2]. and z q

for the data of Birch et

al . [23] are derived from results shown in Fig. 5 of their paper. There is no

obvious relationship between the virtual origins of any of the measurements

summarized in Table 2, but it is interesting that all of the other studies

report positive virtual origins while this work gives negative values.

Bradshaw [61] has argued that such differences are expected and depend on

initial flow conditions. The most significant comparison of our results for

centerline concentration behavior should be with the work of Birch et al . [23]

Y who also studied a methane-air jet. Comparison of values listed in Table 2

shows that our value is ~10% smaller than the value found in the earlier

Y

work. However, these workers noted that the value of C^, varies as the region

of z/rQ for which it is determined is changed. They speculated that this is

due to a slow approach to similarity (where similarity is used here to mean

that the downstream behavior of the centerline concentration can be specified

simply by the reduced variable z/r

Q

). These workers found that a Y determination of over the same region of z/rQ used in this work gave a

value of 0.106 which is in good agreement with our results.

The results listed in Table 2 are probably the most accurate available

for the turbulent concentration fields of axisymmetric jets, but measured

values are so scattered that it is impossible to distinguish whether plotting

mole fraction or mass fraction gives the best agreement for jets of different

59
density gases. Becker et al . [48] reviewed experimental results in the

literature for concentration and passive temperature fields of air-air jets

y and found that even though values seem to cluster near 0.1, the measurements show similar scatter to those given in Table 2. Despite this apparent

X Y

uncertainty in values, it was claimed [62] that a value of equal to 0.1

is a constant for isothermal and combusting jets. Clearly, more careful work

is needed to determine whether or not a density effect is present in these

studies and whether or not the use of the effective radius of Thring and Newby

[58] provides a suitable correction for changes in jet centerline behavior as

the density of the jet gas is changed due to molecular composition.

Table 2 also includes the constants which describe the behavior of RMS

concentration fluctuations on the jet centerline (see Eqs. (5.3) and (5.4)).

The agreement between the slope of the curve for our results in terms of mass

fraction concentration and that found by Birch et al . [23] is excellent.

These workers have concluded that RMS concentration fluctuations approach

similarity faster than the average concentration. This is consistent with our

Y Y finding that values are in better agreement than for the two studies.

This behavior is the opposite of that found for the velocity flow field where

the average flow velocity approaches similarity faster than the RMS

Y fluctuations [63]. Both of the experiments on methane jets give C

^ values

which are in poor agreement with the results of Becker. et al . [48] for an airair jet. It should be noted that no density correction is included in Eq.

(5.4) and we are unaware of any method used to make such corrections for RMS

concentration fluctuations. However, the use of the effective radius concept

would improve the agreement. It is an interesting and as yet unexplained

observation that the virtual origin shifts to more negative values for the RMS

fluctuations as compared to average centerline concentrations.

60
By dividing Eq. (5.1) by Eq. (5.3) and Eq. (5.2) by Eq. (5.4) it is

possible to derive equations which give the concentration fluctuation intensity (?) as a function of z for both mole and mass fraction measurements. For

large values of z, differences in the virtual origins become insignificant

XX Y Y

and £ , = C„/C. and £ = C 0 /C.. Table 2 includes the results of these mole 2 1 mass 2 1 calculations for air-air and methane-air jets. Note that the fluctuation

intensity is relatively independent of whether or not mole or mass fraction

concentrations are used. Table 2 indicates that the asymptotic value of £ is

dependent on density and that it is larger in the case of a methane-air jet as

compared to an air-air jet. Birch et al . [23] reached the same conclusion and

noted that the velocity fluctuation intensity is also greater for the methaneair jet. This trend seems to hold for the limited data reported by Way and

Libby [9] for an axisymmetric jet of helium into air. Even though only two

downstream axial locations were investigated, these authors reported a

value

(

?

He)c/

(

f

He)c of °' 37 at z/r

o “ 40 -

There is a paucity of measurements of skewness and kurtosis in the

concentration fields of axisymmetric jets. The only results of which we are

aware are due to Birch et al . [23], These earlier results do not show the

strong variations in skewness apparent in Fig. 7 for small z/r Q

. Their

results for z/rQ

> 20 have values of S ~ -0.3 and seem relatively constant

over the z/r Q = 20 to 60 range investigated in the current work. Our results

seem to indicate an increase from S ~ -0.6 to S 0.35 over the same range of

z/rQ values. Despite these minor differences, the agreement of these two sets

of measurements must be considered good since each study indicates a negative

skewness (S = 0 for a Gaussian) of approximately the same magnitude on the jet

centerline. Similar agreement is found for the kurtosis measurements

61
summarized in Fig. 8. Both studies find decreasing values of kurtosis which

remain greater than 3 (the Gaussian value) throughout the entire range of z/rQ

values investigated. The behavior of these parameters for air-air flows

marked with heat are also consistent with our measurements [50,64],

At this time it is difficult to compare our power spectra,

autocorrelation, and integral time scale measurements with other such

measurements in the literature. As already noted, our measurements are

susceptible to digital noise and fluctuations due to the short period of time

for which data are collected. The general behavior that we observe for the

power spectra is consistent with the results in the literature where plots of

log(spectral density) versus log(f requency) give a relatively flat region at

low frequencies followed by a rapid fall-off at higher frequencies. We feel

that our data collection and analysis procedures can be modified in order to

obtain more accurate autocorrelation measurements.

The radial profiles of average methane concentration in terms of mole and

mass fractions are shown in Fig. 11. The experimental data are found to obey

the Gaussian form of Eq. (5.5) quite well for values of r/ * 1/2 <1*5. At

larger values of r/r^/2 t*le data seem to fall below the calculated curve, but

definite statements are difficult due to uncertainties in the results arising

from the short sampling times employed. Equations which are exactly equivalent to Eq. (5.5) have been used to model the radial concentration behavior in

air-air [48], methane-air [23], and propane-air [2] jets. In addition,

Shaughnessy and Morton [16] and Santoro et al . [60] have measured radial

concentration profiles for air-air and 10% methane in air-air' jets which are

fit well by Eq. (5.5). For the case of the air-air jet studied by Becker et

al . [48], the authors claimed that at large values of r/r^/2

62
( ^AIR^(^AIr)c ^ ®*®®) t^ie exPerimental data fit was improved by using an

equation which predicts a concentration fall-off with increasing r which is

faster than Gaussian. This is consistent with our observations noted above.

Clearly, the shape of the radial profiles for concentration behavior are

equivalent within experimental error for all axisymmetric jets investigated

thus far. It should be noted that the results for a propane-air jet [2] are

in terms of mole fraction concentrations and those for the methane-air jet

[23] are in mass fraction terms. An analysis of the effect of transforming

from mole fraction to mass fraction on the shape of the concentration radial

profile indicates very little change in the overall shape of the profile, but

the *if 2 values shift to slightly smaller r values for positively buoyant jets

and to larger values for negatively buoyant jets. This can be seen in Fig. 11

where * 1/2 f°r the m°le fraction concentration is 12 mm and for the mass

fraction concentration case is 11.5 mm.

Often the spreading rate of the jet is defined using * 1/2 values. For

sufficient downstream distance the value of r ^/2 *- s f°und to be proportional

to the distance from a virtual origin z q

. This relationship is written as

r l/2

= C

3(

Z - Z o) (6 - U

where the values of C

3 and z Q

will be dependent on whether mole or mass

fraction concentrations are used. Table 3 summarizes values of C

3 obtained

for different jets using various experimental techniques. Dyer [2] claimed

that his value of C

3 indicates the presence of a slight density effect on the

spreading rate of the jet. This conclusion may be correct, but such a

definite statement is difficult to justify based on the limited data of

63
Table 3 which indicate very little difference between the air-air and

methane-air jets.

There does seem to be a density effect when concentration fluctuation RMS

values along the radial direction are considered. Figure 12 shows that the

normalized radial RMS values we observe are in close agreement with the

methane-air results of Birch et al . [23]. One possible means of characterizing this type of measurement for different jets is to compare the values

rs* /v of the maximum ratio of X /X or Y /Y observed and the value of r/r,

/

0 max c max c where it occurs. Table 4 lists the results from a number of different laboratories. Four sets of data are given for air-air jets in which passive

markers were used as concentration probes. Becker et al . [48] and Shaughnessy

and Morton [16] both used light scattering from particles for their measurements. There is very good agreement between these two groups for both

^max^c an<* rmax^r l/2* Antonia at al . [50] and Chevray and Tutu [51] have

also studied air-air jets, but used heated air as a marker. These two groups

of workers are in good agreement, but the results obtained using the two

different techniques are in relatively poor agreement with the particle

measurements which give lower values for X /X and rmov /ri / 0 . It may be

that one of these techniques does not respond to turbulent fluctuations

perfectly or that the markers are not totally passive. Despite this discrepancy, Table 4 shows that the ratio of X /X and Y /Y is greater for both

max c max c methane and propane jets than for air-air jets. Due to the discrepancy in the

results for the air-air jets it is impossible to state whether or not there is

a density effect on the value of rmax/ r i/2*

64
Our results for the skewness and kurtosls of concentration fluctuations

as a function of x/x\/2* shown in Figs. 13 and 14, are in excellent agreement

with the results of Birch et al . [23]. Both the magnitudes of the parameters

and their behavior as a function of r/rj /2 match closely. Our results are

also in good agreement with those of Antonia et al . [50] for an air-air jet.

The rapid increases in both skewness and kurtosls values at the edge of the

jet can be understood when it is noted that the intermittency factor rapidly

falls off at approximately the same values of r where the large increases

occur (compare Figs. 13 and 14 with 17). In this region of the flow field,

periods of time when the methane concentration is zero are averaged with those

when the concentration is nonzero (this can be clearly seen in Fig. 16).

Since the methane concentration cannot be negative, a sharp cut-off in the

concentration distribution exists at the lower end and the skewness and

kurtosls values must increase dramatically as the fraction of time during

which the fluid is pure air increases.

We have been unable to find detailed integral time scale measurements as

a function of r with which to compare the measurements shown in Fig. 15.

However, Dyer [2] did find that T increased from 140 ps to 315 ys on going

from the centerline to * 1/2 * n a propane-air jet.

No measurements of intermittency in the concentration field of an

axisymmetric jet have been reported, but studies using passive markers have

been performed. Becker et al . [48] studied the intermittency function for an

air-air jet where the intermittency decision was based on light scattering

from particles. These workers found that the radial location where

65
Y = 0.5, R, is equal to R/r^^ = 1*78. Using a similar technique, Shaughnessy

and Morton [16] found that R/r^^ was 1 • 52 for an air-air jet with Re 56052

and 1.43 with Re = 31590. Chevray and Tutu [51] have performed detailed

intermittency measurements in a heated air-air jet where the heat acted as a

passive scalar. A value of R/r

J/2 = 1.6 can be inferred from their data. All

of these values must be considered to be in good agreement with our measurement of = 1*6 since the value of R is highly dependent on the observation volume and cut-off constant used. (See discussions in Antonia et al .

[50], Shaughnessy and Morton [16].)

It is difficult to compare our result for the wrinkle amplitude with the

value measured by Becker et al . [48] since these workers found that the value

of on the centerline is given by an equation with a different virtual

origin than However, by assuming large values of z, a value of

a /r, = 0.29 can be derived from their results. This value is in excellent w 1/2

agreement with the value of 0.28 determined in this study. In their study

using heat as a marker, Antonia et al . [50] found that was equal to 0.3r^2

which is also in good agreement with our results.

As noted earlier, the concentration fluctuations in the intermittent

region of the flow show a distinct ramp-like structure which is clearly

visible in Fig. 16. To our knowledge, this is the first observation of such

structures in turbulent flows for an experiment monitoring concentration

fluctuations directly. However, such structures have been found in studies

using heat as a passive marker. As early as 1968 Gibson et al . [65] noted the

presence of this behavior in the wake of a heated sphere where the sharp edge

of the ramp occurred at the upstream end of the turbulent bulge. Similar

66
structures in axi symmetric jets have been found to have the leading edge of

the ramp facing downstream [50]. This observation is consistent with the time

record of methane concentration fluctuations shown in Fig. 16 where the sharp

edges of the ramp-like structures occur at the leading or downstream edge of

the turbulent bulges.

The observation of these ramp-like structures in intermittent regions of

turbulent flows has resulted in a wide range of studies which are beginning to

yield detailed information concerning the behavior of large scale structures. Measurements of nonzero values of skewness in the derivative of

temperature with respect to z, which can be obtained from 3T/3t by use of

Taylor's hypothesis, have been associated with these ramp-like structures.

(See Gibson et al . [66] and Sreenvivasan and Tavoularis [67].) Such observations are important, since one of the predictions of Kolmogorov's concept of

local isotropy [45] is that the skewness of 3T/3z will be zero. As might be

expected, the sign of the derivative is found to depend on the type of flow

configuration. The values are negative when the edge of the ramp faces

downstream and positive when the face is upstream. Relations are being

developed to predict the sign of the derivative based on measurements of

average flow field properties [66,67].

Important clues to the nature of turbulent mixing have been derived from

the work of Chevray and Tutu [51] on heated axisymmetric jets. They used

highly conditioned measurements to obtain average radial velocities near the

beginning and end of the turbulent bulges. These workers have found that the

average direction of fluid flow is away from the center of the jet at the

downstream edge of the bulges. This implies that highly concentrated gas from

67
the center of the jet Is being "shot out" into the surrounding fluid and thus

explains the sharp edge of the ramp. At the upstream end of the ramp the

average flow direction of the fluid is towards the center of the jet. In this

region the surrounding gas is being entrained into the jet and dilutes the jet

fluid leading to the fall-off in concentration as the bulge passes the

observation volume. This proposed mechanism is described in a very lucid way

in the paper by Gibson et al . [66].

Figure 19 shows that, as expected, the concentration of methane in the

turbulent regions is considerably higher than the unconditioned concentration

when the flow is intermittent. This same general behavior has been observed

in similar studies using passively marked air-air jets. Becker et al . [48]

have given a numerical specification for ^^jr^'J'^(^AIr)c

*

For 2*ven r^ r l/2

values their turbulent concentrations are found to be significantly lower than

those indicated in Fig. 19. For instance, at r/r ^2 “ 2, this earlier work

yielded a value of 0.15 for

^ ^aXR^t/(^ ^AIr)c* comParec* with a value of 0.29

taken from Fig. 19. This discrepancy is easily understood by noting that this

earlier work found that the average location of the boundary of the jet occurs

at R/r ^2

= 1*78 as opposed to the value of 1.6 we have measured. Since the

normalized wrinkle amplitude is nearly equal for the two jets, the value

of y at any normalized radius will be larger for the air-air jet. The radial

profiles of concentration are nearly identical, which implies that at any

given radial location the "turbulent fluid" must contain a higher proportion

of low concentration jet fluid and the average concentration in the turbulent

region will be lower. This conclusion is supported by the results of Chevray

and Tutu [51] for a temperature marked jet. These workers found a normalized

value of R/r ^2 which is nearly identical to that reported for the methane-air

68
jet used here. The values of (where it must be remembered it f X

AIR)T/( XAIR)C

is assumed that X

AIR

is proportional to a temperature difference) as a

function of normalized radius are in very good agreement with the current

measurements. For instance, at r/r^2 “ 2 these workers found a value of

(^AIR.)t^(^AIr)c " *- s very close to the value of 0.29 cited

above. Based on these results, the current measurements of conditional

concentrations must be considered in good agreement with the limited data

available in the literature for passively marked air-air jets.

Data available for comparison with the conditional RMS values shown in

Fig. 19 are limited to the studies of Becker et al . [48] and Antonia et al .

[50]. The general behavior of the particle marked air-air jet is similar to

that shown in Fig. 19. Initially, as the mixing becomes intermittent the

values of (xmr) t/(xair) c fall below the value of *air/(xair)

c

. As the value

of r is increased the value of the conditioned RMS again approaches that of

the unconditioned RMS and then becomes larger. The same general behavior is

found for the temperature marked jet. Interestingly, Antonia et al . [50] find

that the value of

^ xAjR^'j^(

X

AIr)c

rema ^ ns very nearly constant across the

entire jet profile in marked contrast to the results of Fig. 19 or the

particle marked air-air jet where the intensity first rises and then falls for

both the conditional and conventional measurements. At this time we can offer

no explanation for this difference, but will note that Antonia et al . [50]

performed their study in a co-flowing stream of air where the velocity ratio

of the jet to surrounding gas was considerably lower than those used in this

study or the free jet used by Becker et al . [48].

69
The only conditionally averaged skewness and kurtosis results of which we

are aware for the radial distribution of concentration fluctuations is the

work of Antonia et al . [50]. These workers find nearly identical behavior for

these two parameters as shown in Figs. 13 and 14. At r values where both the

skewness and kurtosis are rapidly increasing due to intermittency , conditional

measurements remain nearly constant. For both sets of measurements the

conditioned value of skewness is positive and equal to approximately one while

the kurtosis value remains slightly higher than the Gaussian value of three.

6.2 Validity of Comparisons with Other Studies

Up to this point, differences between our experimental flow conditions

and those of studies with which our results are compared have not been

considered in detail. Table 5 summarizes the conditions used in each of these

studies for some of the parameters which might influence the measurements

compared in Section 6.1. The values in the table are given in terms of the

density ratio of the jet fluid to the surrounding air, the ratio of the air

velocity (u^j^ = 0 is a free jet) to the jet velocity, and the Reynolds number

corresponding to the velocity difference between the jet and surrounding flow.

From Table 5 it is clear that the experiments used for comparison

purposes with the results of this work have been performed under widely

varying conditions. Despite these differences in flow conditions, very good

agreement is found between our results and these earlier studies. In

particular, the agreement between our results and those of Birch et al . [23]

is very good, despite the fact that their jet was a free jet with a Reynolds

number four times greater than that used for this work. The large differences

70
in virtual origins recorded in Table 2 also indicate that the initial

conditions at the jet nozzles were very different for the two jets.

It is obvious that the use of an enclosure and a coflow of surrounding

gas must change the concentration field behavior of the axisymmetric jet used

in this study as compared to that of a free jet. As the jet slows down due to

turbulent mixing with its surroundings, it will eventually decay to a velocity

where it must respond to the coflow of air. The jet is also constantly

expanding and will eventually fill the entire enclosure. However, in the

downstream regions of the flow where we have made measurements, the effects of

the coflowing surrounding gas and the enclosure do not seem strong enough to

modify the concentration field in an experimentally verifiable way. This is

consistent with our observation that the velocity behavior of the jet is the

same with and without the enclosure. The radial profile of the jet was

studied at an axial position where the jet has a maximum radius of ~29 mm.

(The outer edge of the jet spends 99.9% of the time within this distance of

the centerline, see Fig. 18.) Since the shortest distance from the jet

centerline to the walls of the enclosure is 50.9 mm, it is not surprising that

the presence of the walls does not modify the behavior of the jet in a

measurable way. The absence of an effect due to the coflowing surrounding

gases on the averaged properties of a jet at comparable downstream distances

to those employed here has been noted by Shaughnessy and Morton [16]. These

workers found that their results for a coflowing air-air jet were in very good

agreement with those of Becker et al . [48] for the corresponding free jet.

Ebrahimi and Kleine [62,68] have given a formula for the variation

y

of with Re which can be written as

71
C* = (1.3(Re/104

) + 6) ( 6 . 2 ) -1

Y

Table 2 compares values of from four different measurements where the

Reynolds number varies from 3770 to 54,000. Using Eq. (6.2), the expected

Y variation in is from 0.154 to 0.077. The results summarized in Table 2

indicate a much smaller variation than this. Based on the results of our

measurements and comparisons with others in the literature, we feel that a Y small Reynolds number effect may be present for values of C^, but that this

Y

effect is hidden by variations in values of due to experimental conditions. Shaughnessy and Morton [16] found very little effect on jet properties

on going from Re = 56,050 to Re = 31,590. However, they did note a small, but

reproducible, decrease in the half-widths of the average velocity, average

concentration, and the normalized value of R as Re was lowered. Antonia _et

al. [50] have reported a similar behavior, but the results may not be

comparable with those of the other jets in Table 5 due to the relatively high

values of uair/ujeT usec* this work. Effects of Re differences on the other

properties of the concentration field evaluated in this study have not been

reported. All of the evidence cited above indicates that while small effects

of Re may be present in these measurements, these effects are not strong

enough to invalidate the comparison of our results with other studies

discussed in Section 6.1.

The effects of density differences on the behavior of the average

concentration field and the RMS have already been discussed in Section 6.1.

The concept of an effective radius used in Eq. (5.2) is expected to compensate

for density differences between jet fluids for comparisons of the axial

behavior of average mass fraction concentration, but the variations in the

72
measured results among different studies are so large that this has not been

verified. A strong effect does appear In the behavior of the RMS concentration fluctuation. Careful studies should be performed to confirm and

characterize this density effect. The presence or absence of effects due to

density differences on the other properties of the flow field reported in this

study cannot be verified due to insufficient data for comparison.

On the basis of the very good agreement of the measured properties of the

concentration flow field from this study and those in other studies and the

lack of experimental evidence indicating strong modifications of the field

(with the possible exception of those due to the effects of jet density), we

conclude that the measurements reported in Section 5.2 and Section 5.3 are

reasonable and give an accurate description of the concentration field of an

axisymmetric jet.

6.3 Applicability of Rayleigh Light Scattering as a

Scalar Probe of Turbulent Flow Fields

In the past, many different measurement techniques have been used to make

scalar measurements in turbulent flow fields. Some of these techniques have

been discussed briefly in Section 1.2. All of these techniques have serious

disadvantages and no one experimental method has dominated the field.

Concentration and temperature measurement methods have lagged far behind the

corresponding velocity measurements where hot-wire and laser anemometry have

provided easily implemented and accurate velocity determinations.

73
This study has been designed to demonstrate the feasibility of using

laser Rayleigh light scattering as a concentration probe in simple turbulent

flow systems. The Rayleigh technique has previously been shown to be a

powerful means of monitoring mass density, number density, and temperature

fields in carefully selected complex turbulent reaction systems (see discussion in Section 2.2). As suggested by the pioneering studies of Graham et al .

[1] and Dyer [2], the work reported here has proven that Rayleigh light

scattering is an excellent technique for performing quantitative time3

(~200 ps) and spatially-resolved (~0.0003 mm ) measurements in a two gas

turbulent flow system. A wide variety of turbulence properties have been

investigated and the results have been shown to be in excellent agreement with

those in the literature which were measured using independent techniques.

A necessary requirement for this technique to have a wide applicability

is that it be useful for a large number of different gas mixtures. One of the

reasons methane was chosen for this study is that it does not have an

unusually strong Rayleigh scattering cross section relative to that of air.

Most gas pairs have scattering cross section ratios at least as large as that

for methane-air, a r /a AT

D

= 2.34, and many are considerably higher. For

Uii , AIK

4

instance, the propane-air combination has a ratio of 13.5. Furthermore, most

gases have scattering cross sections which are the same order of magnitude

(the very small cross section for helium is an exception) as those for air and

methane. This implies that the present experimental arrangement can be used

to study a wide variety of two component turbulent flows with temporal and

spatial resolution comparable to those found for this study. Of course, some

combinations of gases will not be suitable due to their having cross sections

which are nearly identical. In order to determine whether or not a particular

74
binary gas combination is suitable for study, an analysis similar to that

developed in Section 2.3 can be performed. Our results indicate that this

analysis will only provide an order of magnitude estimate of signal and noise

levels, but it should be possible to relate the results of the calculation to

those combinations of gases for which experiments have been previously done in

order to obtain a more accurate estimate of expected signal and noise levels.

Even though the experimental apparatus developed for this study provides

concentration measurements with high spatial and temporal resolution, it is

easy to imagine experiments for which improved signal to noise ratios or

higher temporal and/or spatial resolution would be required. Earlier analysis

in Section 2.3 has shown that by far the most important factor which limits

the Rayleigh light scattering technique is the relative weakness of the

scattering and the resulting noise in the detected signal due to Poisson

statistics. In order to obtain the optimum quality of information from such a

measurement, the researcher is forced to make compromises concerning spatial

and temporal resolution since the signal to noise ratio decreases as the

observation volume and averaging time decrease. As an example, it would be

possible to increase the cut-off frequency used in this work by a factor of 4,

while maintaining a constant signal to noise ratio, by opening the slits to 1

mm. In many cases, observation of turbulent fluctuations within a cylinder of

1 mm length would provide sufficient spatial resolution and the faster

response time would allow higher velocity flows to be investigated.

A second means of improving signal to noise ratios in this type of study

is to increase the intensity of light reaching the detector by improving the

experimental system. This can be accomplished by increasing the laser power

75
within the observation volume and/or improving the transmission and efficiency

of the collection and filtering optics. Even though more powerful CW lasers

are available commercially, the high cost and complexity of such lasers

compared to the system used here does not make this approach to increasing

laser power attractive. However, it is possible to increase the laser power

in the scattering volume by using a multipass mirror system or placing the

observation volume within the laser cavity where laser power levels are

considerably higher. Either of these improvements can be expected to increase

laser intensity levels within the observation volume by factors of 10-100. By

more careful design of the optical system and use of AR coated optical

components throughout, another increase of 2-3 in light reaching the detector

can be expected. The gains in signal to noise ratio are attained by the use

of more complex and costly optical components.

At this point it is proper to consider what types of additional

quantitative scalar measurements can be made in turbulent flows using the

Rayleigh light scattering technique as developed here. It is possible to use

the same apparatus to investigate turbulent mixing of heated or cooled jets of

a single gas issuing into the same gas. The variable which is fluctuating in

this case is temperature. Since changes in temperature result in density

variations (for constant pressure), Eq. (2.10) shows that for a single

component flow the Rayleigh scattering intensity will be inversely

proportional to the absolute temperature. For the case of a heated air-air

flow, the jet would need to be at ~650 K in order to observe signal to noise

levels comparable to those of the methane-air jet. Similarly, a jet cooled to

150 K would provide similar signal levels. Studies such as those outlined

here would provide information concerning turbulent mixing of gases when

temperature differences cannot be considered to be passive.

76
The discussion of Section 2.1 has shown that an analysis of the scattered

Rayleigh light in terms of its polarization components, I

|( and I , yields an

additional independent variable which is characteristic of the molecular

composition. Subject to the constraints on Rayleigh scattering cross sections

and depolarization ratios previously discussed, the measurement of these two

intensities allows the mole fractions of a three component isothermal gas or

the temperature and concentration of a two component nonisothermal system to

be uniquely determined. Since a typical value of p = I^/I

|( is 0.01, the

intensity of the perpendicular component is expected to be ~100 times smaller

than the total scattering intensity. This implies that for the conditions

used in this study that either the time or spatial resolution would have to be

severely sacrificed in order to employ polarized Rayleigh light scattering as

a probe for quantitative measurement of three scalar quantities. However,

methods of significantly increasing the intensity of detected scattered light

have been described above. The use of these techniques would allow intensity

measurements of the polarized components to provide simultaneous values of

three scalar quantities with temporal and spatial resolution similar to those

reported in the current study.

We conclude from the results of this study and the discussions above that

Rayleigh scattering offers a useful and accurate method for quantitative

scalar measurements in many simple flow systems. When its applications to

global measurements discussed in Section 2.2 are included, it is clear that

Rayleigh scattering can become a powerful tool for the analysis of scalar

properties in turbulent flow fields.

77
6.4 Rayleigh versus Raman Scattering as a Scalar Probe

Due to the nature of the techniques, turbulence experimenters will often

be required to choose between Rayleigh and Raman light scattering as nonobtrusive probes for turbulent flow systems. The choice of type of scattering

measurements must be based on the nature of the flow and the properties which

are to be determined. Peterson [13] has indicated in his review that Raman

scattering is widely accepted as a flow diagnostic while experiments using

Rayleigh scattering are not widely used. We feel that this is unfortunate

since there are many experimental conditions for which Rayleigh scattering

should be superior due to its large cross section relative to those for Raman

scattering. For flow systems where either Rayleigh or Raman scattering can be

used, such as the flow studied here, two component heated flows, three

component isothermal flows and the reacting flows described in Section 2.2,

Rayleigh scattering should offer substantial advantages over Raman scattering. Consider the application discussed in this work. Birch et al . [23]

have performed essentially the same study using Raman techniques. These

workers reported point measurements for the average, unmixedness, skewness,

kurtosis, concentration probability functions, and autocorrelation functions

of the methane concentration fluctuations in the jet. Our analysis indicates

that, with the exception of the autocorrelation functions, the measurements

described in Section 5.2 are in excellent agreement and of comparable quality

with those of this earlier work. These workers have not reported the time

required for making a single point measurement in the flow, but since Raman

scattering is expected to be at least 1000 times weaker than Rayleigh

scattering, the time required to obtain a measurement with equivalent signal

to noise should be at least 1000 times longer. This implies a time

78
approaching an hour to make a single measurement which was performed in three

seconds using Rayleigh scattering. These considerations are not only

important from an efficiency viewpoint. In cases where the flow of expensive

gases are being studied it is important to limit experimental time for cost

effectiveness. The above discussion is with regard to CW Raman experiments.

Similar constraints will apply to experiments using pulsed lasers.

When it is noted that Rayleigh scattering also allows time-resolved

studies and that the experimental requirements for Rayleigh scattering are

less stringent (i.e., no spectrometer is required for Rayleigh scattering), it

is clear that Rayleigh scattering is the superior technique for applications

where its use is suitable. Examples where Rayleigh scattering cannot be used

are systems where a large number of different gases must be monitored or where

intense scattering from particles (such as soot) or the apparatus does not

allow the elastic scattering to be observed. In these cases, Raman scattering

provides an excellent alternative.

6.5 Final Remarks

This work has presented a detailed description and investigation of laser

induced Rayleigh scattering as a concentration probe in binary mixtures of

isothermal turbulent flows. It has been demonstrated that the technique can

be used to provide detailed properties concerning the concentration flow

field. In addition, detailed information concerning the concentration field

of an axisymmetric jet has been provided which should aid in a more complete

understanding of turbulent mixing. In the near future we hope to perform

detailed density effect studies on this flow configuration using Rayleigh

scattering as the probe.

79
Even though we feel that Rayleigh scattering has been demonstrated to be

a powerful technique, there are several improvements which would make it more

universally useful for turbulence studies. Among these is the use of

polarization effects to allow an additional scalar property to be measured.

It should also be possible to extend the technique to two dimensions as has

been done for particle nephelometry [18] and Raman scattering [21],

A major conclusion of this paper must be that none of the current

techniques for providing scalar measurements in turbulent flows approximate

those of the ideal probe described at the beginning of Section 1.2. However,

it is also clear that by judicious choice, an experimenter can find techniques

for performing these measurements with an accuracy and detail which has only

been possible recently. In this context, the Rayleigh light scattering

technique evaluated in this paper is an important addition to the turbulence

researcher's arsenal of probes for scalar measurements.

7 . ACKNOWLEDGMENTS

We wish to acknowledge Dr. Bernard McCaffrey of the Center for Fire

Research for performing the velocity measurements reported in this work. We

have also been aided by helpful discussions with Dr. Howard Baum of the Center

for Fire Research and Drs. James McMichael and Patrick Purtell from the Center

for Chemical Engineering.

80
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85
ENCLOSURE

CO

4-1 rC

00

G -H O rH

4-1 -G U oo g •H

4J 0) <D I—i GJ

T3 • to G 4J G u G

0)

G

4J

m s G G G

0) *—i U S 3

01u 10 00 o G G >4-1 G G S H CO

S-1 o 00 G •H G G •H iH O l-i G u G O 4J 4J •H a 4J

4J

G

G

O-t iH

a o G to

f—1 G3

00

•H

U-t

86

PHOTOMULTIPLIER
DISTANCE (MM)

Figure 2. Detected light intensity as a function of position for a backilluminated pinhole translated along the laser beam propagation

direction. The symbols represent data for 0.2 mm (X) and

0.4 mm (£) slit widths.

87
A) 5700 Hz

B) 2850 Hz

.1 -

i 1 1 1 1 i

i i i 0 50 100 150 200

TIME (ms)

Figure 3. Appearance of data records for time-resolved light scattering

measurements as a function of cut-off frequency. The measurement

volume is located on the -jet axis at z/r = 35. The vertical

0 axis indicates methane concentrations which are uncorrected for

photon statistics. Average methane concentrations for the entire

data sets are indicated by X and the expected RMS fluctuations

(+ 1 a) due only to photon statistics are indicated by the bars.

88
(X

ch

,)o/(X

CH4 )c

or

(Y

CH4

)o/(Y

0 20 40 60

z/r0

Figure 4. Values of

(

X

CH

4)o

/

(

XcH

4)c “

d

(

Y

CH

4)q

/

(

Y

CH

4) are plotted as a function of z/r . Solid lines

are the results of linear least squares fits for

measurements taken at z/r > 20.

o —

89
Figure 5. Values of

(

and

are plotted as a function of z/r

Q

. Solid lines

are the results of linear least squares fits

for measurements taken at z/r >_ 20.

90
cn

(/

Ld

Q

LdX

1 1 1 1 nr

*

X

A +*\* i

“

X X

x

X

x* «

X

* *

X

X

5?

It x MOLE FRACTION - X MASS FRACTION

. 4

'

X

1 _i i i i _l

0 10 20 30 40 50 60

Figure 6. Unmixedness of methane concentration on the jet centerline in mole

and mass fraction terms is plotted as a function of z/r . o

91
0 1 0 20 30 40 50 60

z/ro

Figure 7. The skewness of the methane concentration

distribution on the jet centerline is plotted as a function of z/r .

92
lh

in

o

h3

o

00

fO

cotn

K>

CM

K)

o

K)

ooCM

Figure 8. The kurtosis of the methane concentration

distribution on the jet centerline is plotted as a function of z/r .

93
CORRELATION

FUNCTION

TIME (ms)

1 2 3

LOG (FREQUENCY)

Figure 9. Examples of correlation functions and power spectra for

methane concentration fluctuations at three different axial

downstream distances in a methane-air jet. The cut-off

frequency of the amplifier is set to 4.6 kHz.

94
w

Ld

<

o

(/)

Ld

<

Cd

CD

z/r.

Figure 10. Integral time scales (T) on the jet centerline as a function

of z/r . o

95
96
_J 1 1 1 L -2-10 1 2

rA,/2

Figure 12.

•\i Experimental values of X

CH, are

shown as a function of nondimensionlized radial distance

(r/r

1/2 ) for a downstream distance of z/r

Q = 35 in a methane-air jet. The solid line represents results taken

from the work of Becker et al. [48] for an air-air jet

and the dashed line gives the results of Birch et al.

[23] for a methane-air jet.

97
igure 13. Skewness values as a function of nondimensionalized radial distance (r/rj , 2 ) are shown for

the methane concentration distribution at a downstream distance z/r = 35 in a methane-air

jet. Values have been calculated for entire

data records ( 0 ) and for conditionally sampled

data which are weighted by the corresponding

intermittency function (X).

98
KURTOSIS

Figure 14. Kurtosis values as a function of nondimensionalized

radial distance (r/r ,„) are shown for the methane

concentration distribution at a downstream distance

z/r = 35 in a methane-air jet. Values have been

calculated for entire data records ) and for

conditionally sampled data which are weighted by

the corresponding intermit tency functions (X)

99
Figure 15. Integral time scales as a function of

nondimensionalized radial distance (r/ are shown for methane concentration fluctuations at

a downstream distance z/r B 35 in a methane-air

. ^ o

100
0 50 100 150 200

TIME (ms)

Figure 16. Examples of methane concentration behavior in

the intermittent region of a methane-air jet

and the resulting intermittency function

calculated for the data. Arrows indicate short

"bursts" of methane concentration which do not

appear in the intermittency function due to the

averaging inherent in the calculation of this

function.
-2-10 1 2

r/r1/2

Figure 17. Intermittency factor (y) and frequency (f ) as functions of nondimensionalized radial distance,

(r/r ,„) for a downstream distance of z/r = 35 in

a methane-air jet. The solid line is a p?ot of

Eq. (5.6) for R = 1.6 r^^ anc* °w

~ *28 r ^/2*

102
Figure 18. Values of the intermittency factor (y) are plotted on a probability graph as a function

of nondimens ionalized radial distance (r/r-^

2

) The solid line is a linear least square fit of

all results except the five points closest to

the jet centerline. The symbols refer to

positive (^ ) and negative ((3) values of r.

103
- 2-10 1 2

r/r1/2

Figure 19. Plots of X_u and k / \ are given as a

Lri, Lh, l Lh, / 4 4 \ 4/C

function of the nondimensionalized radial distance

r/r at a downstream distance z/r = 35 in a methane-air jet. _The corresponding conditionally

sampled values, ( and are

indicated by the symbol X.

104
Table 1. Observed and Calculated Relative Errors as a Function of Cut-off Frequency for the Current

From a Photomultiplier Illuminated by a Constant Intensity Light Source

Cut-off Frequency (Hz)

Observed Calculated

Relative Error Relative Error

5700 .028 .019

2280 .017 .012

1140 .011 .009

105
Table

2.

Experimentally

Determined

Constants

for

Eqs.

(5.1 )— (5- 4)

Asymptotic

Values

for

Concentration

Fluctuation

Intensity

on

the

Jet

Centerline

in

Mole

and

Mass

Fraction

Terms

CO

O o CM

CO rs O' CM S CM CM |1 CM s • • • Kf o o o o

as u> oOs

CM

CM

CM

CM

>>CM

O

N

Is osIs sO

u

-ac

to

>s CM

CJ

OSsOm

oo

sOH

'O' o X

CM oN

Is 00• stCOI

Is

X CM UuXX

cj

<u

•“5

sO so

00

CM 1 | sr • • O o o o o o

Is Is Is Is o sO CO 00 • • • • CM —

o St 1 iH m

CMm o CM

r-H CM Os Os

*—H

O o • • • o o o o o o o o

Is Is Is Is m m H 00 • • • • 1 CO uo st

CO o st CO

00 OS *-s os o o *—S o • • • • o o O o

Is •H

Is Is < IS •H 1 •H < c 01 < 1 1 e 1 St St to Is 32 32 cx •H cj CJ o <3

is IX

00

CO st

CM <—i

<Uo CO i-l X 4-J 1-1 CO o CO CO 1 1 o o 4-4 | CO 4->| i—i

cu 1 4-1 <u| CM c •

i Is V jC at CO a Is M a> Is 0) CJ Is •H X <u Ps CO Q CO

106
Table 3. Observed Constants for Spreading Rate Behavior

(Eq. 6.1) of Axisymmetric Jets

Concentration

Source Jet Units c

3

z 0

Present Data CH4-Air Mole ,108a

. 105a

0

-9.1r

Mass ,104a

0

.103a -2. Or

Birch et al. [23] CH4-Air Mass .097 0

Santoro et al. [60] 10% CH4-Air Mole .097a

0

Dyer [2] Propane-Air Mole ,086a

0

Becker et al. [48] Air-Air Mole .106 4.8r

aFrom one downstream position

107
Table

A,

Maximum

Normalized

RMS

Concentration

Fluctuation

Values

and

Radial

Locations

for

Various

Axisymmetric

Jets

CM

X9

G

CM o uO CO O' 00 O' o O' r-> oo

• • • • • • • • • o O O o o o o o

l>< o

IX

IX

CO I • I CM

O'

I • I

m

0)Cu

C0a.

t-4 U r* u u M M u M M 32 32 M

•H u 32 32 32 3

1 1 a/ <u c

<u

<u i i 1 1 1 1 c a

Mt Sf sr M M i-l U CO c0 <. s s

o a CH 33 3 32 3

a a. o o

00 u u

z* eu

CO

4-1 CO •ac

o

•H

4-1 O

(—i CO vO M —( <M

*"“1 3 e i—

t

o »—

1

i—

i

O

1—1 4-1 o s

i

1 < 00 M uO u~l CO <• o •

i >—

s

CM 1—

1

z o

——

• 3 u

<u «3 h| 4-1 CM a <0 • H CO

| 3

M 4-1 co| H •a 3 co c0

1

00 3

O 0 4-1 1 00 v\ uS 4-1 C/3 4-> 1 0) 0) i—

i

CO

4-1 3| 1 a CO So CM i—

i

c u JZ •H C0 *—

i

—

(U J3 <u OO c M O

oo O 3 o > U iH

a> U CJ « 4-* a/ 0) M •H 0) J= c X c3

cu CQ sa C/3 <2 CJ £ c0
Table

5.

Experimental

Parameters

for

Different

Jets

Discussed

in

Text o o o o o o o o o O o a> n- o o o o o o o o o 04 pi o o <r o o un o o o

on 0k 0k ON 0k * a •k

m 0k 0k MO CT\ vO •—

CM un 00

CM

m

m cn on CM p—< on

4-i <u

•“) vO on <r cm

CM on cm <r

m -d- on . O O O O on un M • o o • o • • • • • o 3 o o o o o o o 3

t-i 3aQ.

m in MJ CM <r vt 1 i m m ®\ un o o CTi a\ • • • • • • • •

<D

H-j o o o o o a o o U ° CJ o M

•H

O

JM •H

•H •H 4m -h 4m •h •H •H < t4 < M

**

t-l ^ 1 M 1 lj u i u 1 w - i 4-1 M 4-4 U

u

0) 3 i 1 § 3 <u i s >1 « 2 a I 31

a>| ? | 3 i 3

353 5 M

u 1. ° * - 3

g. £ o 00

M P,

co

u £ 3 «

T3

a> co T3

a) 3 2 X * ^

tM3 ^ -H3

4-t t4

CO

X

<u <d

4-1 co

a) 3S 33

M3

—41 c

r—

o P—1 o i—

4-1

O

A 00 un un cn k—

<r o u CM >—

S • •, 3

<U ml • va

m 4J

CJ

A C0 

ml cO | 3

}M

u cO | Pn

H 3 o CO 4-4| co 4-1 1 o £* 1 a> 1 co a> | CO 4J| — <u| ai

4-1 a) | o CM c cO P>> c M u A m 3

<uA

O a> 00

C

U

CO CJ 4-1

u 3 o >

<u

u c a> CJ 3 4-1 (V

M •H CO Pn <u ^3

q

A

Pm pq CO

Q « CO -3

O

109

NBS-114A (rev. 2-«0) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR 2. Performing Organ. Report No. 3. Publication Date REPORT NO.

NBSIR 83-2641 February 1983

4. TITLE AND SUBTITLE

The Application of Laser- Induced Rayleigh Light Scattering to the Study of

Turbulent Mixing

5. AUTHOR(S)

William Pitts and Takashi Kashiwagi

S. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions) 7. Contract/Grant No. NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE S. Type of Report & Period Covered

WASHINGTON, D.C. 20234

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

10. SUPPLEMENTARY NOTES

| | Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bi bliography or literature survey, mention it here)

This work describes the development and characterization of an experimental

system employing laser- induced Rayleigh light scattering with digital data

acquisition as a time-resolved, quantitative concentration probe in the

turbulent flow field of a binary gas mixture. Equations for the expected

signal and noise levels are given. Estimates of these parameters for the

experimental system used here are in satisfactory agreement with experiment.

It is demonstrated the laser Rayleigh light scattering technique does

provide highly spatially- and time-resolved measurements within the

concentration flow field. Measurements at various postions in the flow

field of an axisymmetric methane jet issuing into a slow flow of air are

reported and where possible, compared with appropriate literature results.

The statistical properties of the turbulent concentration fluctuations are found to be in good agreement with other independent measurements.

Conditionally sampled measurements are also reported and shown to behave

j_n the same manner as the limited number of similar measurements in the

literature. The capability of calculating power spectra and correlation

functions for the time behavior of the methane concentration is also

demonstrated. Other techniques employed for scalar measurements in

turbulent flow fields are briefly reviewed and the utility of these

techniques for measurements in different types of flow systems are

12. <E discussed in relation to the Rayleigh light scattering method. words by semicolons)

Axisymmetric jet; concentration flow field; intermittency ; laser; ramp-like

structures; Rayleigh light scattering; scalar probe; turbulence; turbulent flow

13. AVAILABILITY 14. NO. OF

PRINTED PAGES

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