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dissertation entitled

EFFECTS OF 2-D AND 3-D FORCING ON
MOLECULAR MIXING IN A TWO-STREAM
SHEAR LAYER

presented by

Colin G. MacKinnon

has been accepted towards fulﬁllment
of the requirements for

PhD degree in Mechanical Engineering

 
    

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1/” WM“

EFFECTS OF 2-D AND 3-D FORCING ON MOLECULAR MIXING
IN A TWO-STREAM SHEAR LAYER

By

Colin G. M“Kinnon

A DISSERTATION

Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Mechanical Engineering

1998

ABSTRACT

EFFECTS OF 2-D AND 3-D FORCING ON MOLECULAR MIXING
IN A TWO-STREAM SHEAR LAYER

By

Colin G. MacKinnon

It is well known that external 2-D perturbations at frequencies low compared to the
natural roll-up frequency lead to enhanced growth rates in a two-stream shear layer. The
purpose of the present study was to quantify various aspects of the molecular mixing taking
place in such ﬂows. Experimental measurements were obtained for the amount of molecular
mixing and the mixture composition in a chemically reacting turbulent shear layer subjected
to 2-D perturbations, over a range of frequencies and amplitudes. In addition, the effect of
3-D forcing and combined 2-D/3-D forcing on the mixing ﬁeld were studied. The results
show that the fraction of the shear layer width ﬁlled with mixed ﬂuid initially decreases and
then increases with forcing frequency. Somewhat surprisingly, even though the addition of
3-D perturbations did cause spanwise undulations in the mixed ﬂuid amount, the layer width
and the average mixed-ﬂuid concentration, it did not change the trend in the mixed—ﬂuid
fraction found for purely 2-D forcing. This indicates that streamwise vorticity injection does
not necessarily lead to further increases of the mixing enhancement in this study in a liquid
phase, high Schmidt number shear layer.

In a work independent from the above, the need for both mixing and kinematic data
has led to the development of a technique to simultaneously measure velocity and
concentration in a mixing layer. Although the technique is still in an evolutionary stage, the

potential of this approach is demonstrated.

This thesis is dedicated to my parents Norman and Margaret M“‘Kinnon.

iii

ACKNOWLEDGEMENTS

Thanks are due to many people for the completion of this thesis. I am indebted to my
advisor, Dr. Manooch Koochesfahani, for advice and guidance over the last few years. I am
grateful to the other ‘inmates’ - past and present - for helpful discussions and assistance! In
particular Mr. Richard Cohn has served above the call of duty with unceasing patience to all
my questions. Finally, a warm thank-you to all my friends and family everywhere for your

tremendous support.

iv

TABLE OF CONTENTS

LIST OF FIGURES .................................................... vii
LIST OF SYMBOLS ................................................... xii
Chapter 1
INTRODUCTION ................................................ 1
1.1 Background ................................................... 2
1.1.1 The Natural Layer ...................................... 2
1.1.2 Molecular Mixing ...................................... 4
1.1.3 The Forced Layer ....................................... 6
1.2 Extension of Molecular Tagging Velocimetry (MTV) to Mixing Studies . . 12
1.3 Objective .................................................... 13
1.4 Outline ...................................................... 13
Chapter 2
EXPERIMENTAL FACILITY, FLOW DIAGNOSTICS
AND INSTRUMENTATION ...................................... 14
2.1 Shear Layer Facility ........................................... 14
2.2 Forcing Mechanisms ........................................... 16
2.2.1 2-D Forcing .......................................... 16
2.2.2 3-D Forcing .......................................... 17
2.3 Diagnostics .................................................. 17
2.3.1 Passive Scalar Laser-Induced Fluorescence .................. 19
2.3.2 Chemically Reacting Laser-Induced Fluorescence ............ 22

2.3.3 Simultaneous Molecular Tagging Velocimetry (MTV) and LIF . . 25

Chapter 3
TWO-DIMENSIONAL FORCING RESULTS ....................... 27
3.1 Streamwise Evolution at Mid-span ................................ 28

3.2 Spanwise Results ............................................. 31

3.2.1 Amount of Mixed Fluid ................................. 31
3.2.2 Composition of Mixed Fluid ............................. 36
Chapter 4
THREE-DIMENSIONAL F ORCING RESULTS ..................... 39
4.1 Streamwise Flow Structure at Mid-Span ........................... 39
4.2 Spanwise Results ............................................. 40
4.2.1 Amount of Mixed Fluid ................................. 41
4.2.2 Composition of Mixed Fluid ............................. 46
4.3 Discussion of results from Chapter 3 and Chapter 4 .................. 48
Chapter 5
SIMULTANEOUS WHOLE-FIELD MEASUREMENTS
OF VELOCITY AND CONCENTRATION .......................... 55
5.1 Background .................................................. 55
5.2 Experimental Technique ........................................ 57
5.3 Preliminary Results ............................................ 59
CONCLUSIONS ....................................................... 62
APPENDD( ........................................................... 65
1. Bleaching of the Dye ............................................ 65
2. Free Stream Intensity Elimination ................................. 66
REFERENCES ........................................................ 68

vi

LIST OF FIGURES

Figure 1.1.1. Geometry of a shear layer. ...................................... 1
Figure 1.1.2. The mixing transition. ......................................... 6
Figure 1.1.3. Shear layer growth versus x*. ................................... 9
Figure 2.1.1 Schematic of experimental facility. .............................. 15
Figure 2.3.1 Shear layer experimental set-up for passive scalar LIF spanwise imaging
............................................................... 18
Figure 2.3.2 Laser sheet orientations used for shear layer LIF experiments .......... 18
Figure 2.3.3. Optical set-up for chemically reacting LIF. ........................ 22

Figure 2.3.4 Fluorescence vaersus (a) solution pH and (b) base volume fraction, EB. . . 24

Figure 2.3.5 CP versus E with (a) base on high-speed side and acid/dye on low-speed side
and (b) base on low-speed side and acid/dye on high-speed side. ............ 24

Figure 3.1.1. Streamwise flow structure and passive scalar concentration ﬁeld for (a) no
2-D forcing, (b) f = 4 Hz, (c) f = 8 Hz, (d) f = 16 Hz, (e) f = 32 Hz; mid-amplitude,

no 3-D forcing. ................................................... 74
Figure 3.1.2. Unforced shear layer width versus x. ............................. 75
Figure 3.1.3. Comparison of mixing transition with Breidenthal. ................. 76
Figure 3.1.4. Normalized product thicknesses versus x. ......................... 77

Figure 3.2.1. Spanwise ﬂow structure and product concentration ﬁeld with no 2-D
forcing. ........................................................ 78

Figure 3.2.2. Spanwise ﬂow structure and product concentration ﬁeld with 2-D forcing;
f: 4 Hz, x* = 0.77,f/fo= 0.11. ....................................... 79

Figure 3.2.3. Spanwise flow structure and product concentration ﬁeld with 2-D forcing;
f= 8 Hz, x* = l.55,f/fo= 0.21. ....................................... 80

vii

Figure 3.2.4. Spanwise ﬂow structure and product concentration ﬁeld with 2-D forcing;

f= 16 Hz, x*=3.1,f/fo= 0.42. ....................................... 81
Figure 3.2.5. Spanwise ﬂow structure and product concentration ﬁeld with 2-D forcing;

f = 32 Hz, x* = 6.2, f/fo: 0.84. ....................................... 82
Figure 3.2.6 Average product concentration spanwise images for (a) f = 4 Hz, (b) f = 8 Hz,

(c) f = 16 Hz, (d) f = 32 Hz; no 3-D forcing ............................. 83
Figure 3.2.7. Calculated quantities versus 2 at x=17.4 cm; no 3-D forcing. .......... 84
Figure 3.2.8. Span-averaged quantities versus x*; no 3-D forcing. ................ 85
Figure 3.2.9. Spanwise rms quantities versus x*; no 3-D forcing. ................. 86

Figure 3.2.10. Forced mixed-ﬂuid fraction relative to unforced mixed-fluid fraction; no
3-D forcing. ..................................................... 87

Figure 3.2.1]. Average mixed-fluid concentration versus 2 at x = 17.4 cm; no 3-D
forcing. ......................................................... 88

Figure 3.2.12. Span-averaged mean mixed-ﬂuid concentration versus x*; no 3-D
forcing. ........................................................ 89

Figure 3.2.13. Spanwise ms of mean mixed-ﬂuid fraction versus x*; no 3-D forcing. . 90

Figure 3.2.14. Spanwise ﬂow structure and concentration ﬁeld with purely 2-D forcing;
x = 17.4 cm. ..................................................... 91

Figure 3.2.15. Spanwise ﬂow structure and concentration ﬁeld with purely 2-D forcing;
x = 17.4 cm. ..................................................... 92

Figure 3.2.16. Spanwise flow structure and passive scalar concentration field with purely
2-D forcing; x = 17.4 cm. ........................................... 93

Figure 4.1.1. Streamwise ﬂow structure and passive scalar concentration field with 3-D
forcing (LS) for (a) no 2-D forcing, (b) f = 4 Hz, (c) f = 8 Hz, (d) f = 16 Hz,
(e) f = 32 Hz; mid-amplitude. ....................................... 94

Figure 4.1.2. Streamwise flow structure and passive scalar concentration ﬁeld with 3-D
forcing (HS) for (a) no 2-D forcing, 0)) f = 4 Hz, (0) f = 8 Hz, ((1) f = 16 Hz,
(e) f = 32 Hz. .................................................... 95

Figure 4.2.1. Spanwise flow structure and product concentration field in a shear layer
with 3-D (LS) forcing; no 2-D forcing. ................................ 96

viii

Figure 4.2.2. Spanwise flow structure and product concentration ﬁeld in a shear layer

with 2-D/3-D (LS) forcing; f = 4 Hz, x* = 0.77, ﬂfo = 0.11. ............... 97
Figure 4.2.3. Spanwise flow structure and product concentration ﬁeld in a shear layer
with 2-D/3-D (LS) forcing; f = 8 Hz, x* = 1.55, ﬂfo = 0.21. ............... 98
Figure 4.2.4. Spanwise ﬂow structure and product concentration ﬁeld in a shear layer
with 2-D/3-D (LS) forcing; f = 16 Hz, x* = 3.1,f/fo = 0.42. ............... 99
Figure 4.2.5. Spanwise flow structure and product concentration field in a shear layer
with 2-D/3-D (LS) forcing; f = 32 Hz, x* = 6.2, f/fo = 0.84. .............. 100
Figure 4.2.6. Average product concentration spanwise images for (a) f = 4 Hz, (b) f = 8 Hz,
(c) f = 16 Hz, (d) f = 32 Hz; 3-D/LS forcing. ........................... 101
Figure 4.2.7. Calculated quantities versus z at x = 17.4 cm; 3-D(LS) forcing. ....... 102
Figure 4.2.8. Span-averaged quantities versus x*; 3-D(LS) forcing. .............. 103
Figure 4.2.9. Spanwise rrns quantities versus x*; 3-D(LS) forcing. ............... 104

Figure 4.2.10. Spanwise flow structure and product concentration ﬁeld in a shear layer
with 3-D (HS) forcing; no 2-D forcing. ............................... 105

Figure 4.2.11. Spanwise flow structure and product concentration ﬁeld in a shear layer
with 2-D /3-D (HS) forcing; f = 4 Hz, x* = 0.77, ﬂfo = 0.11. .............. 106

Figure 4.2.12. Spanwise ﬂow structure and product concentration ﬁeld in a shear layer
with 2-D /3-D (HS) forcing; f = 8 Hz, x* = 1.55, ﬂfo = 0.21. .............. 107

Figure 4.2.13. Spanwise flow structure and product concentration ﬁeld in a shear layer
with 2-D /3-D (HS) forcing; f = 16 Hz, x* = 3.1,f/fo = 0.42, high amplitude. . 108

Figure 4.2.14. Spanwise flow structure and product concentration ﬁeld in a shear layer

with 2-D /3-D (HS) forcing; f = 32 Hz, x* = 6.2, ﬂfo = 0.84. .............. 109
Figure 4.2.15. Averaged product concentration spanwise images with no 2—D forcing for (a)
no 3—D forcing, (b) 3-D(LS) forcing, and (c) 3-D(HS) forcing .............. 110
Figure 4.2.16. Average product concentration spanwise images for (a) f = 4 Hz, (b) f = 8 Hz,
(c) f = 16 Hz, (d) f = 32 Hz; 3-D/HS forcing. .......................... 111
Figure 4.2.17. Calculated quantities versus 2 at x = 17.4 cm; 3-D(HS) forcing. ..... 112

Figure 4.2.18. Span-averaged quantities versus x*; 3-D(HS) forcing. ............. 113

ix

Figure 4.2.19. Spanwise rms quantities versus x*; 3—D(HS) forcing. .............. 114

Figure 4.2.20. Average mixed-ﬂuid concentration versus z at x = 17.4 cm; (a) 3-D(HS)

forcing, (b) 3—D(LS) forcing. ....................................... 115
Figure 4.2.21. Span averaged mean mixed-ﬂuid concentration versus x*; (a) 3-D(HS)
forcing, (b) 3-D(LS) forcing. ....................................... 116
Figure 4.2.22. Spanwise ms of mean mixed-ﬂuid concentration versus x*; (a) 3-D(HS)
forcing, (b) 3-D(LS) forcing. ....................................... 117
Figure 4.2.23. Spanwise ﬂow structure and product concentration ﬁeld with 2-D / 3-D(HS)
forcing; f = 16 Hz, x* = 3.1, highest amplitude. ........................ 118
Figure 4.2.24. Spanwise ﬂow structure and passive scalar concentration ﬁeld with 2-D/3-D
forcing. ........................................................ 119
Figure 4.2.25. Mixed-ﬂuid fraction versus x* for all cases. ..................... 120
Figure 5.2.1. Laser grids for high density MTV measurements at (a) t = to and
(b)t=to+At. ................................................... 121
Figure 5.2.2. Experimental set-up for combined LIF-MT V measurements .......... 122
Figure 5.2.3. Emission of (a) ﬂuorescence and phosphorescent of MTV triplex and
(b) ﬂuorescence of ﬂuorescein. ..................................... 123
Figure 5.2.4. Timing diagram for combined LIF-MTV measurements. ............ 124

Figure 5.2.5. Sample images for simultaneous concentration/velocity measurements. 125

Figure 5.3.1. Simultaneous concentration field from LIF (top) and velocity/vorticity

ﬁeld from MTV (bottom); no 2-D forcing ............................. 126
Figure 5.3.2. Simultaneous concentration field from LIF (top) and velocity/vorticity

field from MTV (bottom); f = 4 Hz. ................................. 127
Figure 5.3.3. Simultaneous concentration ﬁeld from LIF (top) and velocity/vorticity

ﬁeld from MTV (bottom); f = 8 Hz. ................................. 128
Figure 5.3.4. Compilation of urms data in the plane shear layer. .................. 129
Figure 5.3.5. Compilation of vrms data in the plane shear layer. .................. 130
Figure 5.3.6. Compilation of Reynolds stress data in the plane shear layer. ........ 131

Figure 5.3.7. Normalized profiles of mean velocity. .......................... 132

Figure 5.3.8. Normalized proﬁles of Reynolds stress. ......................... 133
Figure 5.3.9. Normalized proﬁles of average concentration. .................... 134
Figure 5.3.10. Normalized proﬁles of Ems. .................................. 135
Figure 5.3.11. Normalized proﬁles of 3757. ................................ 136
Figure 5.3.12. Normalized proﬁles of 37—57. ................................ 137

xi

Symbol

take

:1:

(1.)...
I...

LIST OF SYMBOLS

Description

dye concentration

low-speed free-stream dye concentration

product concentration

product concentration at ﬂuorescence tum—on threshold
average product concentration

peg diameter

entrainment ratio

forcing frequency

initial roll-up frequency

peg height

pixel intensity

ﬂuorescence intensity

intensity at ﬂuorescence turn on threshold

intensity corresponding to free stream dye concentration
molar concentration

number of absorbing dye molecules at time t

number of absorbing dye molecules at time t=O

number of moles in acid

xii

Rea

Ree

velocity ratio, U2/U,
growth rate parameter, (U 1 - U2)/ (U1 + U2)
Reynolds number, AU él/v

Reynolds number based on momentum thickness at splitter
plate tip, UGO/v

time

time delay

total length of time record

hi gh-speed free-stream velocity
low-speed free-stream velocity
convection speed of large structures
mean streamwise velocity at y
volume of low-speed ﬂuid

volume of high-speed ﬂuid

acid volume

base volume

volume of high-speed, low-speed ﬂuid
streamwise coordinate
dimension-less variable, le/ Uc
transverse coordinate

spanwise coordinate

dye absorption coefﬁcient

consecutive rows below free stream intensity for image
ﬁltering

xiii

EB
Es

pdf

LIF

shear layer 1% thickness
span-averaged layer 1% thickness
mixed-ﬂuid thickness

span-averaged mixed-ﬂuid thickness
product thicknesses

vorticity thickness

shear layer visual thickness

small number

dye molar absorption coefﬁcient
layer momentum thickness

initial layer momentum thickness
smallest scalar diffusion scale
Kolmogorov scale

kinematic viscosity

hi gh-speed ﬂuid volume fraction
base volume fraction

concentration at ﬂuorescence turn on threshold
dye bleaching time constant

vorticity

probability density function

laser induced ﬂuorescence

xiv

Chapter 1

INTRODUCTION

The present work is concerned with mixing in a nominally planar, incompressible
shear layer. This type of ﬂow arises when two ﬂuids of different speeds, which are initially
separated by a thin partition (for example, a splitter plate), merge with each other. A
schematic of the ﬂow conﬁguration is shown in Figure 1.1.1. If the Reynolds number is
sufﬁciently high, intense mixing occurs in the region of the velocity gradient between the
streams. For this reason such shear layers are often called mixing layers. The dramatic
increase in the amount of mixing as the Reynolds number is increased was called the ‘mixing

transition’ by Konrad (1976). This will be discussed in more detail later in the introduction.

 

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W --_ -\ V
U2
U2

Figure 1.1.1. Geometry of a shear layer.

Over the past few decades turbulent mixing layers have been the subject of a great
deal of attention. This is not only because of their occurrence in countless numbers of
naturally-occurring and engineering ﬂows, but also due to their fundamental importance in

the study of free shear ﬂows. In practical applications, shear layers govern the rate of mixing

in combustion chambers, and are also responsible for some of the broadband noise generated
in propulsion systems. The ability to control the mixing, structure and growth of the shear
layer would have a signiﬁcant impact on many engineering applications. The purpose of the
current work is to investigate the ways in which the molecular mixing ﬁeld is affected by

two-dimensional and three-dimensional external perturbations.

1.1 Background
There have been many signiﬁcant experimental and computational works related to
the present study in recent years. These studies fall into three main categories which will be

discussed in the following sections.

1.1.] The Natural Layer

A shear layer which is not subjected to any externally imposed disturbances is often
referred to as a natural shear layer. Probably the most important recent discovery concerning
natural shear layers was made by Brown & Roshko (1971, 1974). They initially wanted to
study the effect of a density difference in their gaseous layer. While they did ﬁnd that large
changes of the density ratio across the mixing layer had a relatively small effect on the layer
spreading angle, they were astonished to ﬁnd that the ﬂow was dominated by large coherent
structures over a wide range of Reynolds numbers. Their shadowgraph pictures also showed
that a ﬁne mesh of small scale three-dimensional motions was superposed on the background
of the large structures.

At about the same time, Winant & Browand (1974) proposed that the primary

mechanism by which the shear layer grows is by the amalgamation of two neighboring

structures into a single larger structure. They called this interaction 'pairing'. In the natural
layer the vortices are irregularly spaced so that when pairings (and other amalgarnations) take
place, the growth of the layer increases, on the average, in a linear fashion. Heman &
Jimenez (1982) have suggested that the pairing process is not the only mode of growth of the
shear layer. Their results indicated that most of the entrainment is achieved during the
normal life of the large spanwise structures, but not during pairing. However, there seems
to be little doubt that most of the entrainment of irrotational ﬂuid into the layer is associated
with the evolution of the large scale structures.

The work of Dimotakis & Brown (1976) showed that the large scale motions
persisted, in a liquid mixing layer, up to Reynolds numbers of 3 x 106 (based on the velocity
of the high-speed stream and the distance from the trailing edge of the splitter plate to the
measurement location). They also pointed out that the dynamics of the shear layer may in
fact be governed by a global 'feedback mechanism'. This mechanism suggests that the
initiation of the layer at the splitter plate tip is coupled with the large scale structures located
farther downstream.

The formation and persistence of the organized two-dimensional structures has been
documented in numerous other investigations (for example, Rebollo, 1973; Browand &
Weidman, 1976; Wygnanski et al., 1979; Browand & Ho, 1983). There is, however, a
secondary structure present in the ﬂow. Miksad (1972) was among the ﬁrst to observe weak
longitudinal vortical structures in his low Reynolds number gaseous layer, and concluded
that 'once a secondary vortex structure is established transition to turbulence occurs'. In the
works of Konrad (1976) and Breidenthal (1978, 1981), plan views of their shear layers

revealed streamwise streaks. Breidenthal interpreted these to be pairs of streamwise vortices

of alternating signs. This was conﬁrmed by the cross-sectional views of Bemal (1981). His
pictures showed structures composed of pairs of counter-rotating streamwise vortices
superimposed on the spanwise vortices. A more recent study by Huang & Ho (1990) has led
to the conclusion that the interactions between the merging spanwise structures and the
streamwise vortices leads to the generation of small scale three-dimensional motions. The
production of small scale motion is regarded to be the mechanism which increases mixing
in the layer, by means of increased interfacial area (Jimenez, Martinez-Val & Rebollo, 1979).

Thus, a simpliﬁed view of the development of the ﬂow in a turbulent shear layer is
given by the following. It is well known that for a shear layer with laminar boundary layers
on the splitter plate, disturbances are ampliﬁed immediately downstream of the plate by
Kelvin-Helmholtz instability. These disturbances grow from the plate tip with a certain
natural frequency which is dependent on the velocity ratio and the initial momentum
thickness, 00, of the layer. These instability waves initially grow exponentially, until they
saturate and large spanwise structures develop. Through the interaction of these structures
with the streamwise vortices, small-scale motions are produced, which subsequently lead to
enhanced mixing within the layer. Prior to the establishment of fully rolled-up vortices
certain aspects of the ﬂow can satisfactorily be described by linear inviscid stability theory
(Michalke, 1965). The ensuing interactions of the primary and secondary vortices resulting
in the fine scale three-dimensional motions need further investigation to enable a more

detailed understanding.

1.1.2 Molecular Mixing

The vast majority of research in shear layers, and shear ﬂows in general, has

concentrated on the momentum transport properties of the ﬂow. Quantities typically
measured include mean and rrns velocities, frequency spectra of the velocity ﬂuctuations,
Reynolds stresses and, more recently, vorticity (Lang, 1985; Foss & Haw, 1990; Foss &
Wallace, 1989; Balint & Wallace, 1989). In contrast, studies concerned with quantifying the
levels of the mixing taking place have been far fewer. Some exceptions are the experimental
works of Konrad (1976), Breidenthal (1978, 1981), Koochesfahani (1984, 1986), Zhang &
Schneider (1995), and Karasso & Mungal (1996, 1997).

Konrad used a concentration sampling probe in a non-reacting gaseous layer to infer
the amount of mixing, whereas Breidenthal used an absorption technique in a chemically
reacting liquid layer to deduce the amount of chemical product. They found that a rapid
increase in the amount of mixing (or chemical product) occurred some distance downstream
of the splitter plate, when the Reynolds number became sufﬁciently large. The increase in
mixing (mixing transition) was attributed to the increase of interfacial area between the two
ﬂuids, which, in turn, was a consequence of the development of small-scale
three-dimensional motions. In Figure 1.1.2 a plot is reproduced from Roshko ( 1990) which
describes the mixing transition. The amount of mixed ﬂuid normalized by the shear layer
width is plotted versus large structure Reynolds number, AU5/u, where AU = U 1'U2a u is the
kinematic viscosity, 6 = AU / ( arr/awn,“ is the vorticity thickness, and U is the mean
velocity. The vorticity thickness is linearly related to the 'visual thickness' of the shear layer,
i.e. the width of the ‘wedge’ containing the large structures. As noted above, Huang & Ho
(1990) related the development of small-scale motions to the interactions between the

streamwise vortices and merging spanwise structures. The computational study of Moser &

 

 

 

 

 

 

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Figure 1.1.2. The mixing transition.

Rogers (1990) found that 'when the flow is sufﬁciently three-dimensional, a pairing can
cause the mixing layer to undergo a transition to small-scale turbulence'. The mixing of a
passive scalar was seen to increase with this small-scale transition.

Koochesfahani (1984) extended the application of laser—induced ﬂuorescence (LIF)
from a ﬂow visualization tool to a mixing diagnostic. In his liquid layer, both chemically
reacting and non—reacting (passive scalar mode) experiments were performed. The main
results were that, during the mixing transition, the amount of mixed ﬂuid increased and that,
at the same time, the dominant mixed-ﬂuid concentration changed. The initial roll-up of the
vortical structures was found to be asymmetric such that the cores contained a large excess
of high-speed ﬂuid. The LIF technique is also used in the present study for both chemical

product measurements and passive scalar measurements.

1.1.3 The Forced Layer
Some of the earlier works in (pre-mixing transition) shear layers (Freymuth, 1966;

Browand, 1966) were undertaken in an attempt to establish a link between the instability of

the ﬂow and the onset of turbulence. However, the researchers found that there was a large
amount of spatial 'jitter' in the ﬂow. This was due to the fact that, in a natural layer,
instability waves in a wide range of frequencies are ampliﬁed, even though there is a
dominant natural frequency. The different phase-speeds of these waves then produced the
irregularity which was observed.

As a remedy for this situation, low—level forcing at about the natural frequency was
applied to the layers. This provided a clear phase reference which allowed more stable
measurements to be made. It was thought that there was no effect on the dynamics of the
ﬂow, other than a decrease in broadband noise. It later became apparent (Oster &
Wygnanski, 1982; Ho & Huang, 1982; Zarnan & Hussain, 1981) that, in fact, external
periodic oscillations at relatively low amplitudes can signiﬁcantly affect the growth rate of
the shear layer, and that the large structures can, to some extent, be controlled by them.

The dramatic effect of two-dimensional forcing on the layer growth rate is illustrated
in Figure 1.1.3, which has been reproduced from Browand & Ho (1983). A representative
segment for the growth rate of a natural layer has been included at the right hand side of this
plot for comparison. The data for this plot were taken from the forced layers of Oster &
Wygnanski and Ho & Huang. The data of Oster & Wygnanski were obtained at a high
Reynolds number, post-mixing—transition layer, while those of Ho & Huang were produced
mainly in pre-mixing-transition experiments. From this ﬁgure it can be seen that, as opposed
to the linear growth found in natural layers, the forced layer experiences three different types
of growth. Initially the growth rate is enhanced, compared to the natural case. Then there
is a period of little or no growth, and ﬁnally the grth approaches that of the natural layer.

This plot shows the normalized growth rate as a function of the parameter,

x" E Raf/Uc ,

ﬁrst introduced by Oster & Wygnanski (1982). This dimension-less parameter encompasses
the effects of the ratio, A = (U ,- 2)/(U,+U2), to which the post—mixing-transition growth rates
are proportional, the forcing frequency, f, the downstream distance, x, and the mean speed

Uc = (U,+U2)/2. The growth of the layer is measured by the momentum thickness,

 

°° -U -U
0 : [(11, )(U 2) dy,
(Ul—U2)2

which, in the plot, has been normalized by Uc / f , the wavelength of the perturbation.
Oster & Wygnanski found that they could segregate the ﬂow into three main parts,

representing the different response characteristics mentioned above. These regions of the

ﬂow were categorized as follows :

I x* < 1 : the growth rate is enhanced by a factor of 2 or more,

II 1 < x* < 2 : the ﬂow forms a periodic array of vortices with passage frequency equal to
the forcing frequency; the growth rate is inhibited in this 'frequency-locked' region,
even reduced to zero; Reynolds stresses are reversed in sign,

[II x* > 2 : relaxation to unforced growth rate.

In the present work the effects on mixing are investigated as x* is increased by raising
the forcing frequency while maintaining a ﬁxed downstream location. Many of the mixing

results in Chapters 3 and 4 are plotted against the x* variable.

      
 
   

 

 

0.2:»
OASI- slope = /
ﬂ 2 d9 ' asmpronc atom"
U 0,10 -- an: Iron ouroncco
6 MIXING LAYER
d6
—=.oa4x
0.05 6):
i 1 .1
3 4 s

_1

O 1 2
x ’ =
Figure 1.1.3. Shear layer growth versus x*.

Ho & Huang (1982) showed how they could manipulate the growth rate and control
vortex merging by forcing the layer at a subharmonic of the most—ampliﬁed (or natural)
frequency. For example, forcing the layer at the ﬁrst subharmonic produced pairing of
neighboring vortices and forcing at the second subharmonic yielded 'tripling'. They also
found that pairing took place at the downstream location where the energy of the
subharmonic mode of the velocity ﬂuctuation reached its peak. This illustrated the
importance of the development of the subharmonic mode of the shear layer to the process of
vortex merging.

Previous work in our lab (Koochesfahani & MacKinnon, 1991) concentrated on the
effects of 2-D forcing on the passive scalar mixing ﬁeld. The forcing frequencies used were
much lower than the natural roll-up frequency (f << f0). It was found that while the total
amount of mixed ﬂuid increased when forcing was applied the amount of mixed ﬂuid per

unit width of the layer remained nearly constant. That is, the increase in mixing was

attributable more to the increased width of the layer rather than to any enhancement in small
scale mixing. If the mixing efficiency were deﬁned as the fraction of the layer ﬁlled with
mixed ﬂuid, the forcing did not in fact result in a more efﬁcient mixer. Later results
(MacKinnon & Koochesfahani, 1994) showed an increase in mixed ﬂuid fraction as x* was
increased by using 2-D forcing at a higher frequency. The implementation of a 3-D
perturbation in the low—speed boundary layer of the splitter plate resulted in signiﬁcant
spanwise variations of the amount of mixed ﬂuid and the average mixed-ﬂuid concentration.
One again, when the amount of mixed ﬂuid was normalized by the local layer width, it was
found that the mixed-fraction fraction increased only for the higher frequency 2-D forcing,
i.e. higher x* values. One of the limitations of the passive scalar technique is that it typically
overestimates the actual amount of mixing, unless the resolution of the measurements is
extremely high (this issue is addressed further in Chapter 2). For a study of this type it is
highly desirable to measure the true extent of mixing. This can be achieved by using LIF in
the chemically reacting mode, as in the present work.

The study of Roberts (1985) is, to the best of our knowledge, the only other
investigation to quantify the amount of chemical product in a liquid shear layer undergoing
imposed 2-D perturbations. Roberts found that the effect of 2-D forcing can signiﬁcantly
alter the amount of chemical product in the layer. In pre-transitional ﬂows there were large
increases in the amount of chemical product in the frequency-locked region. In post-
transitional ﬂows increases were observed only in the very early stages of the enhanced
growth region. The mixing data were obtained using an absorption technique which yields
the integrated chemical product along the line of sight of an illuminating beam/sheet. Thus,

the shear layer width is not available for these measurements. Also, the experiments were

10

conducted at a single stoichiometric mixture ratio, from which it is not possible to
extrapolate the total amount of mixing.

The forced studies cited above have all been concerned with the effects of
two-dimensional forcing on various aspects of the shear layer. However, the intricacies of
the interplay between the large scale spanwise structures and the streamwise vortical
structures have recently received much attention. In order to facilitate studies related to the
origin and evolution of the streamwise structures, several researchers have incorporated 3-D
perturbations in a variety of forms to trigger the generation of these structures. Breidenthal
(1980) was one of the ﬁrst to perform such a study on shear layers and wakes, and utilized
a splitter plate with a spanwise variation of either wedges or serrations at the trailing edge.
His results showed that the shear layer readily developed the typical 2-D structures, and that
further downstream there were no signs of the initial 3-D disturbance. Lasheras, Cho &
Maxworthy (1986) placed a small cylindrical ‘peg’ alternately in one of the splitter plate
boundary layers and found that the resulting horseshoe vortex induced regions of streamwise
vorticity under the straining ﬁeld of the spanwise structures. The streamwise structures were
found to propagate laterally by self-induction. They also noted that whenever streamwise
vorticity ﬁrst appeared, it was always in the braid region between consecutive spanwise
structures. Lasheras & Choi (1988) studied the effects of using two types of sinusoidal
variations (indentations and corrugations) in the trailing edge of the splitter plate. They
concluded that perturbations in the spanwise vorticity, subjected to the large straining ﬁeld
between the primary vortices, are stretched in the axial direction resulting in pairs of
counter-rotating streamwise vortices whose axes are aligned with the direction of maximum

strain. Nygaard & Glezer (1991) have studied the interactions of the spanwise and

11

streamwise vortices and proposed a method by which these interactions lead to the
generation of small scale three-dimensional motions. Bell & Mehta (1990, 1993) have
measured turbulence transport quantities in shear layers with streamwise vorticity injection
from a variety of sources including arrays of vortex generators, arrays of pegs, and
corrugations at the splitter plate. They recorded signiﬁcant changes in properties such as the

layer growth and the Reynolds stress in the far-ﬁeld.

1.2 Extension of molecular tagging velocimetry (MTV) to mixing studios

While most of the discussion so far has concentrated on quantifying various aspects
of the mixing process, the fact remains that scalar mixing data are not sufﬁcient, by
themselves, for providing a detailed understanding of entrainment, whereby irrotational ﬂuid
is inducted into the layer, and mixing in turbulent ﬂows. Additional ﬂow kinematics are
needed for this purpose. In recent years two-component velocity maps have been measured
in many turbulent ﬂows using particle image velocimetry (PIV) or molecular tagging
velocimetry (MTV) approaches. Ongoing developments within our own lab regarding the
MTV technique (Koochesfahani et al., 1996, Gendrich & Koochesfahani, 1997) have
resulted in its successful implementation in shear layer and wake ﬂows, among others.
Although still at an exploratory stage in the present work, the MTV method has been
combined with passive scalar LIF to allow the simultaneous whole-field measurements of
velocity and concentration in a mixing layer. This technique allows the superposition of
vorticity and mixing ﬁelds as well as the non-intrusive measurement of Reynolds ﬂuxes such

as Wand W, quantities which have typically been very difﬁcult to record experimentally.

12

1.3 Objectives

The scarcity of molecular mixing results in forced shear layers motivated the
present effort to quantify (via chemical reaction) the changes in the amount of mixing, the
mixed-ﬂuid fraction and the mixed-ﬂuid composition occurring resulting from external 2-D
perturbations in a shear layer.

Recent works incorporating streamwise vorticity injection mechanisms have reported
signiﬁcant inﬂuences on far-ﬁeld turbulent statistics such as Reynolds stresses, attributed to
the presence of the 3-D perturbations. Prompted by these results as well as our own previous
work in the effects of 3-D forcing on the passive scalar mixing ﬁeld, the present study sought
to quantify the effect of vorticity injection on the molecular mixing ﬁeld in a shear layer.

In a work independent from the above, the need for both mixing and kinematic data
has led to the development of a technique to simultaneously measure velocity and
concentration in a mixing layer. Although the technique is still in an evolutionary stage, the

objective here was to demonstrate the potential of this approach.

1.4 Outline

Chapter 1 details background information relevant to the study of mixing in forced
shear layers. The experimental procedures used are described in Chapter 2. The results for
2-D forcing are presented in Chapter 3, followed by those for 3-D forcing in Chapter 4. The
last section of Chapter 4 contains a discussion and summary of these results. Finally, in
Chapter 5 the technique for the simultaneous acquisition of velocity and concentration
measurements is presented along with some preliminary results. This is followed by a brief

summary of the main conclusions.

l3

Chapter 2

EXPERIMENTAL FACILITY, FLOW DIAGNOSTICS

AND INSTRUMENTATION

The experiments for the present study were conducted using the liquid mixing layer
facility in the Turbulent Mixing Laboratory at Michigan State University. Data were
acquired for a variety of 2-D/3-D forcing conditions in a shear layer using three different
diagnostic procedures. In this chapter the details of the facility, the experimental set-up and

the ﬂow diagnostics are described.

2.1 Shear Layer Facility

The experiments were performed in a gravity-driven, liquid shear layer apparatus, a
schematic of which is shown in Figure 2.1.1. The test-section has a cross-section of 4 cm
(height) x 8 cm (span) and is 35 cm long. The free-stream speeds were nominally U1: 40
curls and U2 = 20 cm/s, giving a velocity ratio of r = 0.5. The initial Kelvin-Helmholtz roll-
up frequency was estimated from long temporal sequences of visual data to be approximately
f0 = 38 Hz. Ho & Huerre (1984) have suggested that the initial most ampliﬁed wavelength
is related to the initial momentum thickness via 10 = 30 60. Utilizing the present value for
f; results in an estimate for the initial momentum thickness, 60 z 0.25 mm.

Water was pumped from the two independent supply tanks up to the overhead tanks,
where in each a constant head was maintained by making use of an overﬂow chamber. In

addition, a constant head was maintained at the outlet of the test section. These measures

14

 

overheadtanks T i‘l

 

 

 

 

 

flow control valves I II If

 

bellows/shaker assembly

   

titration reference chamber splitter plate

test sectIon \

 

 

 

2' supply tanks
//

, / /

 

 

 

 

 

downstream a..—
ﬂow control
valve

 

 

 

 

 

 

 

 

 

 

 

 

 

I II I
Ute drain

Figure 2.1.1 Schematic of experimental facility.
minimized ﬂuctuations of the free-stream speeds which may have arisen as a result of time
dependent boundary conditions at the inﬂow and outﬂow. The ﬂow rates were controlled
by three valves, one in each supply line upstream of the contraction, and one downstream of
the test section. The upper stream was arbitrarin chosen to be the high speed stream for the
shear layer experiments.

The development of the splitter plate boundary layers is an important consideration

for our experiments. As a means to minimize non-uniform upstream conditions, extreme
care was taken during the ﬁlling process to expel as much air as possible from the ﬂow

management screens and straws and from the underside of the splitter plate.

2.2 Forcing Mechanisms
The goal of the current study was to investigate the effects of 2-D and 3-D
perturbations on the mixing ﬁeld in a shear layer and a wake ﬂow. This section describes

the methods used to impose these perturbations.

2.2.1 2-D Forcing

Two-dimensional velocity perturbations have been introduced into shear ﬂows by
many different techniques. For example, Oster & Wygnanski (1982) attached an oscillating
ﬂap at the trailing edge of the splitter plate, Ho & Huang (1982) used rotating valves in the
test section supply lines, Roberts (1985) constructed a variable area oriﬁce plate in the high-
speed supply line, and an oscillating airfoil placed slightly downstream of the splitter plate
tip was used by Koochesfahani (1989). The oscillating airfoil technique was also used more
recently by Katch (1993, 1994) for a mixing study in the same facility as the current
experiments. His conclusions were similar to those in a previous bellows-forced layer in our
lab (Koochesfahani & MacKinnon, 1991), indicating that the source of the 2-D disturbance
is less important than other forcing parameters such as frequency and amplitude. Acoustic
excitation is commonly used in gaseous ﬂows.

In the present case, forcing was applied by means of an oscillating bellows operating
in the high-speed supply line, upstream of the settling chamber. A schematic of the bellows
mechanism and location may be seen in Figure 2.1.1. The motion was controlled by a
magnetic coil vibrator and ampliﬁer system (Vibration Test Systems VTS 50), the input to
which was supplied by a function generator (Hewlett Packard HP3314A). Sinusoidal

motions were used for all of the 2—D forcing cases. Three different relatively low forcing

16

amplitudes were used. The nns perturbation levels in the high-speed free-stream were found

to be less than about 4% for all cases.

2.2.2 3-D Forcing

As mentioned above, researchers have used a variety of ways to introduce 3-D
perturbations into the shear layer. These typically take the form of spanwise modiﬁcations
at the trailing edge of the splitter plate, e.g. wedges or serrations (Breidenthal, 1980),
indentations or corrugations (Lasheras & Choi, 1988), a matrix of surface heater elements
(Nygaard & Glezer, 1991), and arrays of pegs or right-triangular vortex generators (Bell &
Methal, 1990, 1993). In the present case, since it was not possible to modify the splitter
plate, the most convenient method of introducing 3-D perturbations was to place a single
small cylindrical peg (Lasheras et. al, 1986), of diameter 7 mm and height 3 mm, on the
centerline of the splitter plate about 1.5 cm upstream of the tip. The presence of this peg
injected streamwise vorticity of both signs into the ﬂow in the near-ﬁeld region. Since the
strength of the vorticity is expected to depend on the speed of the ﬂow in the vicinity of the
peg, three different conﬁgurations were used: no peg, peg on the low speed side and peg on

the high speed side of the splitter plate.

2.3 Diagnostics

The results in this study have been obtained using three different experimental
procedures: passive scalar laser-induced ﬂuorescence (LIF), chemically reacting LIF and
molecular tagging velocimetry. The former two methods provided a variety of mixing

related information and are described brieﬂy below; further details are available in

17

R951=6000@x=17.4cm

 

laser sheet U1/

/kU2

 

 

 

 

. J. ~

 

  

 

 

 

4cm y
z

 

P99
(D=7.H=3mm)

80m
ﬂamers

Figure 2.3.1 Shear layer experimental set-up for passive scalar LIF spanwise imaging

 

Figure 2.3.2 Laser sheet orientations used for shear layer LIF experiments

Koochesfahani (1984, 1986). The latter, used in conjunction with passive scalar LIF to yield
simultaneous velocity/vorticity and concentration measurements, is introduced here and

discussed further in Chapter 5.

2.3.1 Passive Scalar Laser-Induced Fluorescence

Passive scalar LIF is a particularly useful tool in the study of mixing ﬂows. It is a
non-intrusive technique which provides excellent ﬂow visualization and can also yield
quantitative concentration information, typically over a 2-D plane. Generally, a ﬂuorescent
dye is premixed with one of the mixing streams and becomes visible in the presence of a
laser sheet. A CCD camera then records the ﬂuorescence intensity, from which a
quantitative concentration ﬁeld can be obtained since the ﬂuorescence intensity is known to
be linearly proportional to the local dye concentration at low values of concentration (see c. g.
Koochesfahani, 1984, Appendix A).

In the current experiments water from the low-speed stream is premixed with a
solution of disodium ﬂuorescein dye to an initial concentration of about
C do 2 2x 10'7M (molar concentration). The low-speed ﬂuid subsequently becomes diluted
as it is mixed with the pure ﬂuid from the high speed stream (water). Recording the
ﬂuorescence intensity yields the dye concentration, and therefore the relative concentration
of high speed to low speed ﬂuid in the layer, as can be seen from the following relationships.

The local instantaneous concentration of the dye, Cd, in a sampling volume is given by

where UI and 02 are the volumes of high speed and low speed ﬂuid, respectively, within the

sampling volume. Therefore the normalized concentration of high speed ﬂuid, E , is

19

i.e. the high-speed ﬂuid volume fraction, Ul/(Ul + 02). Note that values of E z 0and
E = 1 correspond to pure low speed ﬂuid and pure high speed ﬂuid, respectively. Other
values of concentration indicate mixed ﬂuid. Concentration pdf’s can then be used to
compute various quantities of interest, such as the mixed-ﬂuid probability and the mixed-
ﬂuid thickness, 6,“.

Illumination was provided by the beam from a 4 watt argon-ion laser (Excel 3000)
which was focused through a converging lens and then passed through a cylindrical lens to
produce a thin laser sheet (about 0.5 mm thick, or 200). A schematic of a typical
experimental set-up for spanwise imaging is shown in Figure 2.3. 1; an inset of the splitter
plate is also shown with the peg on the high speed side. The sheet was imaged in three
spanwise and three streamwise orientations for passive scalar data; the same orientations
were used for the chemically reacting measurements, with the exception that the two
upstream spanwise stations were not utilized. Figure 2.3.2 shows a schematic of these
arrangements. Only a subset of this data has been incorporated into the present work since
the focus here is on mixing effects near the end of the mixing transition.

The ﬂuorescence intensities were recorded by a Sony XC-77RR CCD camera , which
was operating at 60 ﬁelds/s with an exposure time of 1 msec. A N ikkor 50mm f/1.2 lens was
used for streamwise imaging and a Nikkor 35mm f/1.8 lens was used for spanwise imaging.
The camera contains a 2-D array of 768 (horizontal) x 484 (vertical) "pixels", of which 512

x 484 were digitized. In our streamwise imaging experiments, the 4 cm width of the test

20

section was imaged onto about 230 pixels, resulting in a spatial resolution of 170 (H) um x
170 (V) pm. The 512 horizontal pixels correspond to a streamwise range of about 9 cm.

The analog signal from the camera was digitized to 8 bits and stored on hard disk in
real time (60 ﬁelds/sec) by a digital image acquisition system (Trapix 5500) with a capacity
of 4.5 Gb, or almost 10 minutes of data at a resolution of 512 x 512 pixels. Typically, a
sequence of 13 forcing cases was captured in a single automated acquisition. The available
amount of reservoir ﬂuid dictated that each individual forcing case was comprised of 1024
ﬁelds of data (or about 128 Mb). For the lowest forcing frequency (4 Hz) cases this record
length corresponded to the passage of about 70 structures. It is believed that this record
length is sufﬁcient for the present purpose. The amount of useful reservoir ﬂuid was
maximized during the runs by implementing a trigger—controlled data acquisition board along
with a GPIB board to control changes of the forcing frequency and amplitude.

The LIF technique has an important limitation, as noted by Breidenthal (1981), when
used in the passive scalar mode. This technique typically overestimates the amount of mixed
ﬂuid (i.e. it provides an upper bound to the actual molecular mixing). The difficulty arises
when the sampling volume of the measurement apparatus is larger than the smallest mixing
scales, as is usually the case. It is then impossible to determine, within the resolution of the
measuring device, whether or not two ﬂuids are mixed. In the present case the smallest
diffusion (Batchelor) scales are expected to be on the order tens of microns, signiﬁcantly less
than the 170 um spatial scale resolved here. For all the drawbacks of the passive scalar mode
it remains the simplest way to estimate the pdf of the concentration ﬁeld. In order to make
unambiguous mixing measurements the chemically reacting mode of LIF was used to

quantify the mixing results reported here.

21

argon-ion laser

converging lens

 

 

 

 

cylindrical lens

electric stirrer

 

 

 

 

titration reference
chamber

 

 

 

 

I J

._._. splitter plate
tip
[a __._.__._.._. -1- --_.-.._,_._- .1..- .1-“-.. _,..._.,. ._.-..J

Figure 2.3.3. Optical set-up for chemically reacting LIF.

2.3.2 Chemically Reacting Laser—Induced Fluorescence

The chemically reacting mode of LIF (Koochesfahani, 1984, 1986) overcomes the
limitations of its passive scalar counterpart by labeling only those parts of the ﬂow which are
molecularly mixed. This is achieved by exploiting the dependency on the local chemical
environment of the dye’s ﬂuorescence capability. In the present case ﬂuorescein has been
used because of its sensitivity to pH. The chemical reaction is a difﬁrsion-limited, acid (A)-
base (B) reaction of the type A + B —> P with the dye premixed in the acid solution. The
ﬂuorescence is “off” in an acidic environment with pH 3 4. Conversely, above this threshold
the dye ﬂuoresces efficiently in the presence of argon-ion laser illumination. Thus, at a
reaction interface the local pH rises sharply and this is accompanied by a correspondingly
rapid increase in the ﬂuorescence intensity. This ﬂuorescence intensity, If , is proportional

to the chemical product concentration, Cp, where chemical product is deﬁned here as the

22

molecularly mixed ﬂuid whose pH is above the ﬂuorescence threshold. The normalized

product concentration is then given by

CP _ If
(CP)max (If)max ,

 

 

where (Cp )max is the maximum possible product concentration (at ﬂuorescence “tum-on”)
and (If)max is the corresponding maximum ﬂuorescence intensity. Note that (If)max was
available throughout the experiments in the titration reference chamber (see Figure 2.3.3).
A plot of ﬂuorescence intensity versus solution pH is shown in Figure 2.3.4a. For low pH
the ﬂuorescence is effectively ‘tumed-off’ , but as the pH increases above the threshold value
(pH = 4) a rapid increase in ﬂuorescence occurs. The intensity increases with pH until a
maximum is reached, at about pH = 8, after which it remains essentially constant. Figure
2.3% shows the ﬂuorescence intensity as a function of base volume fraction EB = vB/( VA+ lg)
as the volume of base VB is increased during a titration of a ﬁxed volume VA of the acid/dye
solution. Unlike the intensity-pH behavior, which is a characteristic of the dye, the intensity-
EB curve depends on the relative concentrations of acid and dye solutions. The intensity is
close to zero at low pH since the solution is very acidic. As base solution is added, a point
is reached where the pH threshold is crossed and the ﬂuorescence ‘turns on’. After this peak
is reached the addition of more base simply dilutes the dye solution, reducing the
ﬂuorescence intensity linearly, and ultimately to zero. In the experiments when the base
solution is on the high-speed side and the acid/dye solution is on the low-speed side, the
concentration of high-speed ﬂuid, E, at any point in the ﬂow is just the base volume fraction.

Invoking the relationship between CP and 1, given above, we can then obtain the linear

23

150

II (arbitrary units)

50

 

 

lI (arbitrary units)

 

 

150

§

'J
O

 

 

._.__..._.___ ._-_ ._

 

 

0.2

Figure 2.3.4 Fluorescence Lversus (a) solution pH and (b) base volume fraction, EB.
variation in CP versus E, shown in Figure 2.3.5a. When the acid/dye solution is on the high-

speed side this variation is reversed (Figure 2.3.5b). These ‘one-sided’ triangular forms will

be referred to in later chapters. Koochesfahani (1984,1986) has shown that such ‘ﬂip’

experiments, at low and high stoichiometric mixture ratios, can be used to obtain resolution

free estimates for the amount of mixing via the relation, on, = 6m + on .

Time-averaging the normalized product concentration ﬁeld gives rise to proﬁles of

the average product. These are integrated to compute the actual levels of molecular mixing,

Figure 2.3.5 CP versus E with (a) base on high-speed side and acid/dye on low-speed side and

Cdo

Cm

p
'n
n
‘v
'-
u
no.
.1

 

(a)

 

 

ﬁe

 

 

 

 

 

(b) base on low-speed side and acid/dye on high-speed side.

24

Cdo

the so-called product thicknesses, 61,1 and on .

For the chemically reacting experiments the acid and base free-streams were dilute
solutions of sulphuric acid and sodium hydroxide, prepared to pH values of about 3.2 and
12.1, respectively. The effect of density variations between the streams was minimized by
adding a solution of sodium sulphate to the acid stream. The densities were matched to

within a speciﬁc gravity of 0.0005.

2.3.3 Simultaneous Molecular Tagging Velocimetry (MTV) and LIF

The two prior ﬂow diagnostics provide information relating to the ﬂow structure and
mixing ﬁeld (concentration pdf’s, amount of mixing, etc.) in a given ﬂow. However, it is
the structure and dynamics of the vorticity ﬁeld which determine the ﬂow behavior. Using
molecular tagging techniques (Gendrich et al., 1997), based on novel supramolecular designs
at MSU, a method has been developed to simultaneously measure the vorticity ﬁeld,
visualize the structure generated by this ﬁeld, and record the corresponding concentration
ﬁeld. This type of information has not been obtained previously in a non-intrusive manner.
A brief description is given here; further details are available in Chapter 5.

Molecular tagging velocimetry (MTV) is an optical technique typically used to
measure two components of the velocity ﬁeld at many points in a ﬂow at the same time. The
process relies on the long lifetime of certain phosphorescent lumophors. In our application,
a grid of intersecting laser lines “tags” a region of the ﬂow just after the laser ﬁres and is
recorded on a detector. A short time later, a second detector records the displaced grid after
it has been convected a short distance by the ﬂow. A spatial correlation approach then

provides a local displacement vector, which is proportional to the velocity vector, for each

25

intersection point on the initial grid.

By combining MTV with the standard LIF method i.e. by adding dye to one of the
free-streams, and using a third camera, we can measure velocity and concentration at the
same time. The schematic in Figure 5.2.2 displays the experimental set-up for the combined
MTV/LIF runs.

As mentioned in the introduction we note that this technique is still under

development. It has nevertheless provided initial estimates of quantities which are difﬁcult

to measure non-intrusively such as the velocity-concentration correlations u ’ E’ and v ’ E’ ,

where u and v are the streamwise and transverse velocity components, respectively.

26

Chapter 3

TWO-DIMENSIONAL FORCING RESULTS

This chapter describes both qualitative observations from ﬂow visualizations and
quantitative results from the chemically reacting product measurements and properties
derived from these measurements. First, results from the data obtained via streamwise
imaging will be presented which will be followed by spanwise imaging results.

Throughout this chapter we will frequently quote results in terms of the dimension-
less variable introduced in Chapter 1, namely x*=— Axf/ Uc , where A = (U, - U2)/(U, + U2),
x is the downstream distance, and Uc = (U, + U2)/2 where U, and U2 are the high- and low-
speed free-stream velocities, respectively. Recall that Oster & Wygnanksi (1982) identiﬁed
three important ranges for this parameter: 0 < x < 1 represents a region of enhanced growth;
1 < x < 2 refers to the “frequency-locked” region characterized by the passage of equally-
spaced, non-interacting vortical structures; the range x > 2 is associated with the gradual
relaxation to the unforced growth rate. Note that x* is increased by increasing the forcing
frequency at a ﬁxed x location. Whether x* is a truly useful scaling requires that we vary the
x location also. Unfortunately this was not possible in the current facility for the reasons
mentioned in section 3.2.1. For reference, the forcing frequencies normalized by the initial
roll-up frequency, f0 , are f Ifo = 0.11, 0.21, 0.42 and 0.82 for f = 4, 8, 16, and 32 Hz,
respectively.

Due to the sheer volume of data, in certain figures we have elected to show ﬂow

images from only a single 2-D forcing amplitude. This is justiﬁed since, for about 75% of

27

the experiments with forcing, the amplitude was found to have only very minor effects.
Similarly, for readability in some plots we will only include the results of one amplitude.
Additional data are included when necessary to highlight exceptional cases. Summary plots

include data from all forcing conditions.

3.1 Streamwise evolution at mid-span

We ﬁrst discuss the development of the shear layer in the streamwise direction at the
mid-span location. Data were obtained from two different streamwise ﬁelds of view - an
upstream view covering a range of about 2.5 cm (1006,) < x < 11.5 cm (4600,), and a
downstream view covering a range of about 11.5 cm (4600,) < x < 20 cm (8000,). Figure
3.1.1 shows representative instantaneous images of the concentration ﬁeld and the structure
of the ﬂow for various 2-D forcing frequencies. The ﬂow is from right to left. The samples
shown here have been forced at the intermediate amplitude; however, they are also
representative of the ﬂow structure for the other forcing amplitudes. In these images the
high-speed free-stream concentration (£ 2 1) is labeled black and the low-speed free-stream
concentration (5 z 0) is labeled light grey; the mixed ﬂuid concentrations are represented by
darker shades of grey. The result of the Kelvin-Helmholtz instability is clearly seen in these
views, where naturally occurring disturbances in the ﬂow are ampliﬁed immediately
downstream of the splitter plate. One of the most noticeable features of these images is that
the growth of the forced layers is modiﬁed relative to that of the unforced layer. In
particular, for the two lower forcing frequencies f = 4, 8 Hz, we see that their growth is
restricted only by the test-section height at the regions furthest downstream. These views

also highlight the frequency response of the forced shear layer. In each case, the structures

28

being shed near the splitter plate tip, at the natural frequency of the layer, roll around and
amalgamate with each other until the large structure passage frequency, at some distance
downstream, becomes synchronized with the forcing frequency. Notice, for example, the
quadrupling of four small structures at the extreme right side of the 8 Hz case, which
becomes a single much larger structure further downstream. Such ‘collective interactions’
are characteristic for forcing where f / f0 << 1 (Ho & Huang, 1982).

We focus now on the latter third of the downstream view. The downstream location
x = 17.4 cm is labeled for reference since this is the location at which all the spanwise
chemical reaction product measurements were made. At this ﬁxed location we step through
the range of x* (= Axf/ Uc) values 0.77, 1.55, 3.1 and 6.2 by varying the forcing frequencies
f = 4, 8, 16 and 32 Hz, respectively.

The ﬂow regimes categorized by the x* parameter are clearly identiﬁable at this
downstream location - Figure 3.1.1(b) shows the enhanced growth phase (f = 4 Hz, x* =
0.77); the frequency-locked region (f = 8 Hz, x* = 1.55) is depicted in Figure 3.1.1(c); Figure
3.1.1(d) shows the beginning of a period of re-adjustment to the unforced growth rate (f =
16 Hz, x* = 3.1); the ﬂow in Figure 3.1.1(e) resembles the unforced layer, having reached
the re-adjustment stage (f = 32 Hz, x* = 6.2). Before 2—D forcing is applied, Figure 3.1.1(a),
a weak braid region can be seen between the large structures, along with the incursion of
unmixed free—stream ﬂuids into the center of the layer. Much larger structures are seen in
the enhanced growth and frequency-locked cases, together with correspondingly larger and
more penetrative entrainment "tongues" of mostly unmixed ﬂuid. This indicates that although
the layer is wider and has entrained more ﬂuid, much of it is still unmixed. We might

therefore expect that for these two cases the amount of mixed ﬂuid per unit width of the layer

29

would not increase relative to the unforced layer. This qualitative assessment is in agreement
with the plot of mixed-ﬂuid fraction versus x*. to be discussed in the next section. As we
shall see, in fact at x* = 0.77, 1.55, corresponding to the 4 Hz and 8 Hz cases, the mixed-
ﬂuid fraction is lower than for the unforced layer.

In contrast to the other cases in Figure 3.1.1 we see that forf= 16 Hz (x* = 3.1) and,
to a lesser extent f = 32 Hz (x* = 6.2), there is no discernible braid in the vicinity of our
measurement station (x = 17.4 cm). By the latter stages of the downstream view the
organized structures and braid regions appear to have been broken down through a complex
series of interactions. It is interesting to note that the 16 Hz case produced the largest value
of mixed-ﬂuid fraction, followed in value by that of the 32 Hz case (x* = 3.1, 6.2,
respectively, in Figure 3.2.8).

We focus momentarily on the unforced case alone. The shear layer width 6, in the
unforced case was computed at many streamwise locations and is shown in Figure 3.1.2. The
plot includes a range of asymptotic ‘best-ﬁt’ growth rates for unforced shear layers (Brown
& Roshko, 1974) at the present velocity ratio, with which the present data is in nominal
agreement.

Breidenthal’s (1981) plot of chemical product normalized by the local vorticity
thickness versus Rebufor an unforced shear layer is reproduced in Figure 3.1.3 with data
from the present case superposed. We have estimated the vorticity thickness using the ratio
6, / 6,, = 2.1 suggested by Brown & Roshko (1974). Note that Breidenthal’s data were
obtained using two velocity ratios, namely r = 0.76 and r = 0.38. For the present case the
velocity ratio is r = 0.5 and this data falls between the latter two data sets. While the

absolute magnitudes of the normalized product differ, the onset of the mixing transition

30

appears to be bracketed appropriately within Breidenthal’s results. It is also apparent that the
location of our spanwise data measurements (at Red” z 2700) corresponds to a Reynolds
number near the end of the mixing transition.

The normalized product thicknesses for the unforced case is shown in Figure 3.1.4
as a function of downstream distance. This plot shows that a plateau is reached at the
downstream end of the measurements. The values for these two limits for the present case
of r = 0.5 and E, = 0.05 are : 6,,,/6l = 0.208 and 6P2/6, x 0.148. These values are higher than
the limiting product thicknesses of 6,,,/6, 2 0.165 and 6 IQ, = , 0.125 quoted by
Koochesfahani & Dimotakis (1986) obtained from experiments operating at r = 0.38 and E,
= 0.09. Karasso & Mungal (1996) operating at r = .25 and E, = 0.06 report similar values
(6,,,/6, = 0.171, 0.174, 0.179; 6,46, = 0.125, 0.128, 0.132 depending on Re) for their un-
tripped cases. As we shall see in section 3.2 there is an element of spanwise variation in
most of the measured quantities. Other factors potentially contributing to the observed
differences may be due to test-section conﬁnement issues, upstream initial conditions or non-

zero pressure gradient effects. Such areas provide good sources for future study.

3.2 Spanwise Results
This section describes the effects of the 2-D forcing on the amount of mixing and the

composition of the mixed ﬂuid.

3.2.1 Amount of mixed ﬂuid
Spanwise chemically reacting data were acquired at a downstream location

of x = 17.4 cm. This location was chosen as a compromise between completion of the mixing

31

transition and an attempt to minimize the interference of the test-section side walls. This
location corresponds approximately to the third last data point on the mixed ﬂuid fraction
plots of the previous section and as mentioned above is near the end of the mixing transition.

Sample image time series of chemical product concentration CP, are shown in Figures
3.2.1-3.2.5 for the cases of no 2-D forcing, f = 4 Hz, f = 8 Hz, f = 16 Hz, f = 32 Hz using the
intermediate forcing amplitude. Recall that in the Cp, experiments the acid/dye combination
comprises the high-speed free-stream. Since the shear layer rolls up with a bias of high-
speed ﬂuid more signal is obtained in these measurements. In these images the ﬂow is
coming “out of the page” toward the reader and the full cross-section (4 cm x 8 cm) of the
test-section is shown to scale. The images highlight only the regions of the ﬂow which are
molecularly mixed with a local pH above the ﬂuorescence “tum-on” threshold. This is in
contrast to the passive scalar concentration images of the previous section which label one
of the free-streams as well as the ﬂuid which appears to be mixed. The shades of grey in
these images are directly proportional to the normalized product concentration via the grey-
scale map at the bottom of each ﬁgure. The product concentration can be related back to the
high-speed ﬂuid concentration using the ‘triangle’ plots of Figure 2.3.5. The eight images
in each case are progressive in time and are arranged in column sequential order. The At
between successive images is 1/60 second.

The ﬁrst case, that of the unforced ﬂow, shows samples of the braid regions between
larger structures, which contain relatively low levels of mixing (e. g. frame 5), as well as the
cores of larger structures indicated by signiﬁcantly more mixed ﬂuid (e. g. frames 3 and 8).
While the regions of mixed ﬂuid form a highly convoluted interface with the free-streams

they are conﬁned, on the average, to about the middle two-thirds of the test-section height.

32

Regions which may be inferred to contain streamwise vorticity can be seen in each frame,
mostly in the form of ‘mushroom-shaped’ counter—rotating pairs.

In Figure 3.2.2 (f = 4 Hz, x* = 0.77) we are monitoring the passage of a very large
structure. The ﬁrst frame shows the connective braid region between a large structure which
has just passed by and the structure about to come. The core of the structure contains a large
amount of mixed ﬂuid and occupies a correspondingly larger fraction of the test-section
height compared to the cores of the unforced case. One can easily imagine a temporally
periodic variation in the amount of mixed ﬂuid synchronized to the forcing frequency. In
fact, due to the large amount of free-stream ﬂuid and the low amount of mixing
accompanying the braid regions, the probability of ﬁnding mixed ﬂuid at the centerline (y
= 0) is lower than that of the unforced case. Secondary streamwise structures appear to be
randomly distributed throughout many of the frames.

The f = 8 Hz, x* = 1.55 case is shown in Figure 3.2.3. In this sequence we see the
core of a large structure, then the braid region which is followed in turn by the passage of the
next core. Once again, the cores exhibit a substantial amount of mixed ﬂuid and occupy a
large fraction of the test-section height. An interesting feature of this series of images is that
many of them display a crude spanwise periodicity of the secondary streamwise structures
(see, for example, the last two images).

Turning our attention to the f = 16 Hz, x* = 3.1 case of Figure 3.2.4 we can
immediately notice a lack of a braid region in any of the frames. There is a large amount of
mixed ﬂuid in every frame. A time average of the product concentration ﬁeld would be
expected to yield a much larger amount of mixed product than in any of the previous cases.

This is borne out in the mixed-ﬂuid plot discussed below. Also, the ﬂow structure in this

33

series looks as though it has a different character from the preceding cases - there seems to
be less contrast or variation in the product concentration and the ﬂow has the appearance of
being more ‘lumpy’.

Figure 3.2.5 (f = 32 Hz, x* = 6.2) shows ﬂow patterns somewhat reminiscent of the
unforced case, but once again without the presence of braid structures. The shear layer is
evidently thinner here compared with the other forced cases.

In determining the amount of product a large number of images like those just
discussed are averaged. Line proﬁles are then extracted at many spanwise locations. These
proﬁles are then normalized according to the procedures outlined in Chapter 2. The amount
of mixed product 6,,, or 6P2 is then the area under the normalized proﬁles. The proﬁles are
also used to estimate the shear layer width, 6,. The average CPl product images for the
forced cases are shown in Figure 3.2.6. As before the lighter greys indicate higher product
concentrations. We can see the larger layer widths for the lower two frequencies compared
to those of the f = 32 Hz (x* = 6.2) case, for example. There is evidence of weak three-
dimensionality in the center (vertically) of the layer for f = 16 Hz (x* = 3.1), as well as much
weaker corrugations at the upper and lower edges of the layer for f = 4, 8 Hz (x* = 0.77,
1.55). The unforced case is shown in Figure 4.2.15 for comparison with the ‘unforced’ peg
cases.

We now quantify the amount of mixed ﬂuid in the layer. Using the procedure
referred to above the mixed ﬂuid thickness, 6m = 6,,, -I- 6,,,, was acquired for all the forcing
cases at many points in the spanwise z-direction, along with the visual thickness, 6,, so that
the mixed-ﬂuid fraction, 6,,I / 6,, could be computed. The results are summarized in Figure

3.2.7 for the intermediate forcing amplitude cases.

34

In terms of the amount of mixed ﬂuid shown in Figure 3.2.7(a) the 16 Hz case
consistently has the highest values. This is followed at signiﬁcantly lower values at f = 32
Hz. Lower again are the f = 4, 8 Hz cases which show only marginally more mixed ﬂuid
than the unforced case.

The shear layer width is plotted in Figure 3.2.7(b). As noted from the instantaneous
and averaged product concentration images, the 4 and 8 Hz cases have the largest layer
widths. When the amount of mixed ﬂuid is normalized by the local layer width these two
cases then naturally produce the lowest levels of the mixed-ﬂuid fraction as shown in part
(c). The unforced layer and the 32 Hz cases show comparable layer widths and consequently
their respective mixed-ﬂuid fractions retain the same relative magnitudes as their mixed ﬂuid
thicknesses. The largest value of mixed-ﬂuid fraction is attained by the 16 Hz case, with a
width just larger than the unforced case but a much greater mixed-ﬂuid thickness.

In order to characterize each case in the simplest possible way the various quantities
described above have been averaged across the span and the results are plotted in Figure
3.2.8 versus the dimension-less variable x*. In addition, all of the forcing amplitudes have
been incorporated into these plots so that the effect of the forcing amplitude can now be
quantified. In this plot ‘al' refers to the highest amplitude, and ‘a3' to the lowest. The
corresponding spanwise rms ﬂuctuations for each quantity follow in Figure 3.2.9.

The span-averaged plots shown in Figure 3.2.8 conﬁrm the trends just described from
the plots of the spanwise variation of 6,,,(z), 6,(z) and (6m /6, )(z). The most noticeable feature
of the span-averaged mixed-ﬂuid plot (ﬁgure 3.2.8(a)) is that the variation in forcing
amplitude has a small effect on the amount of mixed ﬂuid with the exception of the x* = 3.1

(f = 16 Hz) cases. At this frequency the ﬂow exhibits a strong sensitivity to very small

35

changes in forcing amplitude. The reason for this sensitivity is not clear from the present
study. Also, at x* = 3.1, these cases are the only ones which reﬂected signiﬁcant changes in
the shear layer width. In contrast, the mixed-ﬂuid fraction is not nearly as sensitive to
forcing amplitude.

The rms ﬂuctuations plotted in Figure 3.2.9 indicate that compared to the unforced
layer the two highest x* regions display the largest levels of ﬂuctuations in each of the three
quantities. The lowest amplitude component at x* = 3.1 shows the greatest ﬂuctuations.
This may be due to the higher amplitude forcing inducing a more two-dimensional behavior.
Qualitative conﬁrmation may be seen in Figure 3.2.6(c,a3). These plots will be compared
later with their counterparts from the experiments with 3-D forcing.

The ﬁnal plot in this section (Figure 3.2.10) shows the mixed-ﬂuid fraction for each
forcing case as a percentage of the mixed-ﬂuid fraction from the unforced case. On a per-
unit-layer-width basis the intermediate amplitude case at x* = 3.1 displays approximately

35% more mixing than the unforced case.

3.2.2 Composition of mixed ﬂuid

We turn our attention now to the composition of the mixed ﬂuid. This is an important
part of any mixing control strategy; it is clearly undesirable if an attempt at mixing control
produces enhanced mixing but at an unwanted mixture composition. The results which
follow are based on the same spanwise chemically reacting LIF image data as the previous
section.

Insight into the composition of the mixed ﬂuid by is revealed by computing the

average concentration of the mixed ﬂuid, €M(z), which is shown (Koochesfahani, 1984, 86)

36

to be given by

where 6,,, and 6,2 are the product thicknesses from measurements at high and low
stoichiometric mixture fractions, respectively. EM(z) represents, at a given z-location, the
average mixed-ﬂuid concentration across the extent of the layer in the y—direction.

Figure 3.2.11 shows the variation of EM(z), over almost 90% of the span, for the 2-D
forcing cases at the intermediate amplitude. The most noticeable feature here is that the f =
16 Hz case shows a different type of behavior from the other cases. Whereas the unforced
layer and f = 4, 8, 32 Hz (x*=0.77, 1.55, 6.2) exhibit little spanwise variation, the mixed-ﬂuid
concentration at f = 16 Hz (x*=3. 1) shows a large decrease across most of the span. In other
words, €M(z) is almost invariant with x* until some point above x* = 1.55, where it becomes
signiﬁcantly modiﬁed, and ﬁnally returns to an invariant state sometime before reaching x*
= 6.2. A value of 0.5 corresponds to a 1:1 mixture of high-speed stream to low-speed stream
ﬂuid. At some 2 locations 5,, is below 0.5, indicating that more low-speed ﬂuid is mixed on
average!

A further averaging of €M(z), with respect to 2, yields the span-averaged mixed-ﬂuid
concentration, E—M-. This quantity is plotted in Figure 3.2.12 for all of the forcing amplitudes
and conﬁrms the description just given. Note that it is only one of the amplitudes at x* = 3.1
which produces the dramatic effect of altering the average concentration from that of the
unforced ﬂow, a z 0.59, to a value of a: 0.5. That this is indeed dramatic is apparent

when one considers that the imposed forcing on the shear layer, with one free-stream twice

37

the speed of the other, has resulted in a 1:1 mixture composition usually attributed to that of
a wake ﬂow with equal speeds! The spanwise rrns concentration ﬂuctuations are shown in
Figure 3.2.13 and depict, as we might expect, the highest values for x* = 3.1 (f = 16 Hz).

As qualitative conﬁrmation of this drop in concentration we include in Figure 3.2.14
and Figure 3.2.15 sample images within the x*= 1.55 and x* = 3.1 regimes from the two
chemical product experiments. To interpret the intensities represented in these images we
recall that the product concentration Cp, is related to the high-speed ﬂuid concentration E via
the ‘triangle’ plots in Figure 2.3.5 . Figure 3.2.14 shows samples from the high
stoichiometric mixture fraction experiment; thus increasing Cp, values correspond to
increasing E values. In comparing the two images the lower image for the most-part contains
darker shades of grey than the upper image. This corresponds to lower concentrations as
indicated in the span-averaged mixed-ﬂuid concentration plot. A similar effect is seen in
Figure 3.2.15 which shows samples from the low stoichiometric mixture fraction (Cm)
experiments. However, in this case it is the lighter greyscales (lower image) which
correspond to lower concentrations, according to the “calibration” plot in Figure 2.3.5.

A third pair of samples in Figure 3.2.16 conﬁrms the above conclusions in perhaps
a more dramatic fashion. These images were obtained from the passive scalar LIF technique,
Which highlights the two free-streams as well as the mixed ﬂuid. The high-speed ﬂuid
concentration is labeled according to the colormap at the bottom of the figure. At x* = 1.55
the mixture is mostly yellow corresponding to relatively high concentrations, whereas at x*

= 3.1 the dominant color is green indicating midrange high-speed ﬂuid concentrations.

38

Chapter 4

THREE-DIMENSIONAL FORCING RESULTS

This chapter describes the results of the effects of combined 2-D/3-D forcing on the
mixing ﬁeld and the composition of mixed ﬂuid. The 3-D forcing takes the form of
streamwise vorticity injection near the tip of the splitter plate due to the presence of a small
cylindrical disturbance element, or ‘peg’, in one of the two splitter plate boundary layers.
Two sets of experiments were conducted - those with the peg in the low-speed boundary
layer and those with the peg in the hi gh-speed boundary layer. Qualitative observations from
ﬂow visualizations as well as quantitative results from the chemically reacting product
measurements and properties derived from these measurements are presented. The type of
3-D forcing used is indicated in ﬁgure captions and legends etc. by the use of either of the
abbreviations “LS” or “HS”, referring to whether the disturbance element is on the low- or
high-speed side of the splitter plate, respectively. The word ‘unforced’, in quotes, is used in
reference to the ﬂows for which the peg is present, but which do not have imposed 2-D

forcing.

4.1 Streamwise Flow Structure at Mid-Span

Sample streamwise ﬂow images acquired using passive scalar ﬂow visualization for
the case of 3-D forcing in the low-speed boundary layer are shown in Figure 4.1.16. As in
the previous chapter the upstream and downstream views are created from two independent

sets of experiments and, in general, the two images selected in each pair are not necessarily

39

in phase. In comparing these views with the case of no 3-D forcing we see that the same type
of large scale features are present. Before 2-D forcing is applied we can see braid regions
accompanied by mostly unmixed free-stream ﬂuid connecting the larger structures. The
downstream views at f = 4, 8 Hz correspond to the enhanced growth and frequency-locked
regions, respectively. The layer is wider in both cases but clearly contains a large amount of
unmixed ﬂuid. In the region of re-adjustment to the unforced growth rate, the f = 16, 32 Hz
cases show very little braid structure.

There are some subtle differences, however, compared to the no-peg case. Beginning
at the farthest upstream locations, the interface between the high- and low-speed streams is
much less sharply deﬁned and appears to contain more small scale structures and more
mixed ﬂuid. These additional disturbances in the ﬂow structure are attributed to the presence
of the peg.

The peg’s inﬂuence on the ﬂow structure appears even greater when the source of the
3-D forcing is in the high-speed boundary layer, as can be seen in Figure 4.1.17. As for the
two previous cases, the various x* regimes are clearly identiﬁable, and we may infer similar
conclusions regarding the amount of mixing taking place. However, although the large scale
structures are still evident, they appear to have less free-stream ﬂuid associated with them
and the cores appear to be more well-mixed than in the previous case. The spanwise views
in the next section will illustrate further the signiﬁcant disturbances caused, in particular, by

the peg on the high-speed side of the splitter plate.

4.2 Spanwise Results

First we describe the effects of the 3-D forcing on the amount of mixed ﬂuid which

40

results. This is followed by an account of the forcing effects on the composition of the

mixed ﬂuid.

4.2.1 Amount of mixed ﬂuid

Short time—sequences of chemically reacting (Cm) ﬂow visualization images are
shown in Figures 4.2.1 - 4.2.5 for the case of 3-D forcing on the low-speed side of the splitter
plate. The sequences shown were obtained using 2-D forcing at the intermediate amplitude.
The overall ﬂow behavior is similar to the cases without 3-D forcing from the previous
chapter. In particular, the alternating passage of braid regions and core regions is easily
inferred for the cases of no 2-D forcing, f = 4 Hz (x* = 0.77) and f = 8 Hz (x* = 1.55) in
Figures 4.2.1-4.2.3. The higher frequency cases (x* = 3.1, 6.2) once again show a lack of any
braid structure (Figures 42.4-42.5). There is, however, an interesting structural difference
in the vicinity of the center-span which is noticeable in Figures 4.2.1 - 4.2.3. The ﬁrst two
frames in Figure 4.2.1 show good examples of the feature in question. These frames show
the layer almost separated into two regions of mixed ﬂuid in the vicinity of z = 0. The effect
is not quite so strong but is nonetheless still present for f = 4, 8 Hz. More solid conﬁrmation
of this observation is available in the time-averaged product images of Figure 4.2.6. A
distinct “indentation” into the lower edge of the shear layer in the averaged images can be
seen for essentially all of the cases except f = 16 Hz, about which it is difﬁcult to make the
same conclusion. It is speculated, albeit in an over-simpliﬁed way, that the streamwise
vorticity in the legs of the horseshoe vortex generated by the peg has remained sufﬁciently
coherent to cause, on the average, an up«wash of low-speed ﬂuid near the center-span of the

layer. Images from a low speed shear layer shown later in section 4.3 indicate the same

41

relative sense of vorticity portrayed by this argument.

Various quantities of interest have been computed by extracting proﬁles from the
average product images at many z-locations. The results are plotted in Figures 4.2.7-4.2.9.

The mixed-ﬂuid thickness (6",), visual thickness (6,) and mixed-ﬂuid fraction (6,,/6,)
are shown in Figure 4.2.7 for the subset consisting of the intermediate forcing amplitude.
The mixed ﬂuid thickness plot depicts an undulating variation across the span with less
mixed ﬂuid in the central portion of the test-section compared to off-center regions
particularly for the cases of no 2-D forcing, and f = 4, 8 Hz. The regions with less mixed
ﬂuid coincide with the regions of the “indentations” in the average product images. As in
the previous chapter, the two higher frequency cases show more mixing than the other cases.

The layer widths, 6,, in general show less signiﬁcant variations across the span than
the mixed-ﬂuid thickness. The two higher frequency cases have widths comparable to that
of the ‘unforced’ case, all of which are narrower than those for f = 4, 8 Hz.

The mixed-ﬂuid fraction, 6,,/6,, shows more mixing per unit width of the layer for
the two higher frequency cases than the ‘unforced’ case, which in turn has larger values than
the two lower frequency cases. The two peaks in the f = 16 Hz case have resulted from
locally relatively high mixing levels coupled with slightly smaller layer widths, and are
expected to be related to the signature of the peg.

The observations just described are very similar to those which resulted when there
was no 3-D disturbance. This fact is better illustrated by the span-averaged versions of the
three quantities just presented, depicted in Figure 4.2.8. The plots in this ﬁgure essentially
parallel those in Figure 3.2.8., both in terms of trends and magnitudes. The only exceptions

are due to the high sensitivity displayed by the two larger amplitude f = 16 Hz cases in the 6;

42

and6; plots. Once again, the mixed-ﬂuid fraction shows little sensitivity to forcing
amplitude.

In comparing these three plots with similar plots from the no-peg case it is clear that,
in spite of the modiﬁcations noted above due to 3-D (LS) forcing, at a given x* location we
have not in fact achieved either more mixing or more mixing per unit width of the layer. In
fact, within this comparison, the largest value of mixed-ﬂuid fraction appears for a case
without 3-D perturbation.

The spanwise rms plots of the same three variables are shown in Figure 4.2.9. The
‘unforced’ and f = 4, 8 Hz cases in the rms 6m plot show much higher rms ﬂuctuations than
their no-peg counterparts. The ‘unforced’ layer width 6, rms is only moderately higher than
for the no-peg case. All other cases, however, show ﬂuctuations more or less comparable
to those without 3-D forcing. Once again the x* = 3.1 (f = 16 Hz) cases show a greater

sensitivity to forcing amplitude.

We turn our attention now to the case when the 3-D disturbance element is placed on
the high-speed side of the splitter plate. This is the case which shows the largest increase in
the amount of mixed ﬂuid, although not in the mixed-ﬂuid fraction.

Sample time series of instantaneous chemical product images (C9,) are shown in
Figures 4.2.10—4.2.14. Each set except for f = 16 Hz (x* =3.1) shows data acquired with the
intermediate 2-D forcing amplitude; the 16 Hz set, having been forced at the highest
amplitude, is depicted here because it resulted in the largest amount of mixed ﬂuid which
was recorded in the current experiments, as well as providing signiﬁcant mixed-ﬂuid

composition effects. In the ﬁrst set (Figure 4.2.10), that of the ‘unforced’ case, we can still

43

distinguish braid regions and large structure core regions. There is perhaps also evidence of
a counterpart to the 3-D (LS) forcing ‘indentation’ seen earlier in this section, but on the
opposite side of the shear layer, commensurate with the change in sign of the streamwise
vorticity. For example, near the center-span portion of frames 1, 6 and 7 there appears to
have been an incursion of unmixed ﬂuid on the upper side of the shear layer. While one
could draw attention to many similar features across the span, the existence of a repeatable
effect at this location is borne out by the time averaged product image. Figure 4.2.15(c)
shows the ‘unforeed’ average product image for this case, and includes the analogous images
from the cases of no 3-D forcing and 3-D (LS) forcing for comparison in parts (a) and (b),
respectively.

Returning to the time series data, the f = 4, 8 Hz cases indicate the passage of large
coherent structures connected by relatively quiescent braids, along with a lot of seemingly
energetic small scale activity. These cases also show a well deﬁned “wiggle” in their average
product images in Figure 4.2.16. Additionally, there appear to be counter-rotating vortical
structures thrust towards the bottom side of the test-section in many of the frames. These
features, too, are repeatable enough to show up in the average product images.

For the ﬁnal two cases, f = 16, 32 Hz (x* = 3.1, 6.2) we are not surprised at the lack
of appearance of a braid structure. The 16 Hz case indicates a particularly large amount of
mixed ﬂuid. As mentioned earlier, this case in fact produced the largest average mixed-ﬂuid
thickness from all of the current experiments. The average product images for this case,
Figure 4.2.16(c), show a much more signiﬁcant degree of contortion than all the other cases.
This must be attributed to the disturbance element on the hi gh-speed side of the splitter plate.

We now discuss the mixing related quantities computed from the average product

images. The mixed-ﬂuid thickness plotted in Figure 4.2. 17(a) shows a much larger amount
of mixed ﬂuid for the 16 Hz case relative to the other cases. The remaining cases have
comparable levels of mixed ﬂuid and show a well-deﬁned reduction in mixed ﬂuid over
about the middle third of the test-section span. All of the profiles show some degree of
undulation. The layer width plot in Figure 4.2.17(b) also shows an undulatory nature, with
relative peaks near the center-span, for each of the proﬁles. As in the previous cases the
widths associated with the f = 4, 8 Hz are larger than the “unforced” and 32 Hz cases; the 16
Hz case is wider this time having been forced at the highest amplitude.

The mixed-ﬂuid fraction (Figure 4.2.17(c)) shows widely varying proﬁles for the two
highest frequencies. The ‘unforced’ case has a greater mixed-ﬂuid fraction than that at the
two lower frequencies; all cases show a relative drop in value at locations near their mid-
sections compared to those closer to the side-walls.

These results are summarized in the span-averaged plots of Figure 4.2.18. The trends
are very similar to those of the no 3-D forcing and 3-D (LS) forcing conditions. An exception
for the span-averaged mixed-ﬂuid thickness is that it is not only the highest amplitude case
at x* = 3.1 which has a large value - the lowest amplitude case has a relatively high value,
also. Compared to the ‘unforced’ case, forcing at f = 16 Hz and at high amplitude has
resulted in over 50% more span-averaged mixed ﬂuid. However, as we can see from the
span-averaged mixed-ﬂuid fraction plot, on a per unit layer width basis, we do not in fact
achieve greater mixing efﬁciency.

The rrns variations across the span of 6m, 6, and (6m / 6,) are shown in Figure 4.2.19.
The mixed-ﬂuid rrns values are much higher compared to those when 3-D forcing is absent

(Figure 3.2.9). The rrns ﬂuctuation in the ‘unforced’ 3-D (HS) case is more than twice the

45

corresponding value when there is no 3-D forcing. When 2-D forcing is applied in addition
there are signiﬁcant increases in rms variation at each x* location. It is clear that the peg is
exercising a strong spanwise inﬂuence on the mixing ﬁeld.

Making similar comparisons for the rrns ﬂuctuation in shear layer width shows that
the “unforced” 3-D (HS) case has only slightly higher variations than the unforced, no peg
case. Also, very large ﬂuctuation levels are found for the two lower amplitude 16 Hz, 3-D
(HS) cases. The ﬂuctuations in the mixed-ﬂuid fraction are found to be greatest for the high

amplitude 16 Hz 3-D (HS) case, followed closely by the 32 Hz 3-D (HS) cases.

4.2.2 Composition of mixed ﬂuid

In this section we describe the effects of the 3-D forcing on the average mixed ﬂuid
concentration, EM. Figures 4.2.20 (a) and (b) shows the spanwise variation of this quantity
for the 3-D (HS) and 3-D (LS) forcing cases, respectively. Again the high amplitude f = 16
Hz case is plotted here (part (a)), whereas the intermediate amplitude is used for the
remaining cases. When the source of the disturbance is on the high-speed side of the splitter
plate a well-deﬁned ‘wiggle’ in EM is found across the span for each forcing case. This
wiggle is expected to be due to the signature of the streamwise vorticity generated by the peg.
The cases of no 2-D forcing, f = 4, 8, and 32 Hz essentially coincide, showing a lower mixed-
ﬂuid concentration near mid-span and higher concentrations at off—center spans locations.
For f = 16 Hz the trend just described completely reverses, indicating a very signiﬁcant
modiﬁcation of the interplay between the spanwise and streamwise structures. Similar
results, although not as dramatic, are found for the case of 3-D (LS) forcing (Figure

4.2.20(b)). It is interesting here that the wiggle patterns show the same characteristics

46

regardless of whether the peg is on the high-speed or low-speed side of the splitter plate,
since one would expect a reversal in the sign of the streamwise vorticity when the peg
location is switched.

The span-averaged versions of these proﬁles are shown in Figure 4.2.21. Both plots
show similar trends, with the exception of the variations at x* = 3.1 (f = 16 Hz). It is
apparent that the zone around x* = 3.1 is highly sensitive to the forcing amplitude in terms
of mixture composition modiﬁcations. The spanwise rrns ﬂuctuations in EM are shown in
Figure 4.2.22. For 3-D forcing on the low-speed side (Figure 4.2.22(b)), these variations are
comparable to those with no peg. In contrast, the 3-D (HS) case of Figure 4.2.22(a) shows
signiﬁcant increases in the levels of ﬂuctuation for all forcing cases.

The next two ﬁgures give qualitative conﬁrmation of the spanwise variation in
concentration. Figure 4.2.23 shows two instantaneous chemical reaction images forced at
f = 16 Hz (x* = 3.1). Figures 4.2.23(a) and (b) show product concentration Cp, and CP2
images, respectively. We note from the triangle plots of Figure 2.3.5(b) that the CP, product
concentration increases as the hi gh-speed ﬂuid concentration increases. On the other hand
an increase in CP2 product concentration indicates a decrease in the high-speed ﬂuid
concentration (Figure 2.3.5(b)). We can see a bright patch near the center of the product
concentration ﬁeld in the upper image of Figure 4.2.23 ﬂanked on both sides by darker
shades of grey. The colormap shows this to be a ‘low-high-low’ product concentration
variation across the span. The actual high-speed ﬂuid concentration is then also ‘low-high-

9

low . The same effect is seen in Figure 4.2.23(b). This time the product variation across
the span is seen to be ‘high-low-high’. Referring once again to the triangle plots of Figure

2.3.5 we ﬁnd the high-speed ﬂuid concentration variation to be ‘low-high-low’. A sample

47

image pair from the low-speed 3-D forcing passive scalar experiments is shown in Figure
4.2.24. Here the high-speed ﬂuid concentration may be read directly from the colormap
shown. The upper image (f = 4 Hz, x* = 0.8) has a ‘yellow-green-yellow’ variation across
the span indicating a ‘high-low-high’ high-speed ﬂuid concentration, in agreement with
Figure 4.2.20. The lower image indicates a high-speed ﬂuid concentration variation which
is the reverse of that just described, also in agreement with Figure 4.2.20.

In summary, while the presence of the 3-D disturbance does indeed have a deﬁnite
effect on the structure of the ﬂow, the total amount of mixing, ﬂuctuations in the mixing
field and undulations in the average mixed-ﬂuid concentration, it does not lead to more
efﬁcient mixing, i.e. on a per unit layer width basis. This is reﬂected in Figure 4.2.25 which
indicates that the highest mixed-ﬂuid fraction recorded during these experiments was
obtained from a case without 3-D forcing. The main message here is that data from purely
2-D forcing and from combined 2-D/3-D forcing (regardless of forcing amplitude) all follow
a similar trend. The mixed-ﬂuid fraction initially decreases and is lower than the unforced
case in the range x* < 2.0. Mixing enhancement relative to the unforced case then increases
beyond x* > 2.0 until it reaches a peak and begins to reduce. However mixing enhancement
over the unforced case is maintained at least until x* = 6. A discussion of the main

observations from Chapters 3 and 4 follows in the next section.

4.3 Discussion of results from Chapter 3 and Chapter 4
One of the goals of the present work was to attempt to answer the question of whether
or not the injection of streamwise vorticity into a turbulent shear layer enhances molecular

mixing. The work was motivated by previous passive scalar results in our lab

48

(Koochesfahani & MacKinnon, 1991, MacKinnon & Koochesfahani, 1994) and the
turbulence measurements involving vorticity injection (e. g. Bell & Mehta, 1990, 1993). Our
earlier passive scalar study showed that 2—D forcing of a shear layer (f << f0 ), while
increasing the total amount of mixed ﬂuid in correspondence with the enhanced shear layer
spreading, did not in fact lead to more efﬁcient mixing, deﬁned in terms of the mixed-ﬂuid
fraction. Our latter work found that enhanced mixing efﬁciency could be achieved by
forcing at a higher frequency (x* z 3). It was expected that a further enhancement of the
small scale mixing could take place in the presence of increased turbulent transport due to
injected streamwise vorticity at the splitter plate tip. At the same time, higher 2-D forcing
frequencies were added to the list of forcing parameters. Contrary to our expectations,
essentially the same trends, including‘magnitudes, were found in the mixed-ﬂuid fraction,
6m/ 6,, versus x* for purely 2-D forcing and combined 2-D/3-D forcing. In other words, the
injected streamwise vorticity and the resulting increased turbulent transfer did not further
increase the mixing efﬁciency over the trends found for purely 2-D forcing.

While surprising and somewhat counter-intuitive, a similar result concerning the
latter effect has been reported previously. Karasso & Mungal (1997) have recently
investigated the effects of stabilizing and de-stabilizing streamwise curvature on the
concentration ﬁeld in mixing layers at post-mixing transition conditions. Curvature tends
to produce streamwise vortical structures of the Taylor-G6rtler type. Chemical product
measurements were made in straight and curved shear layers; in the latter, both stable (Uinner
< Uoum) and unstable (Uinner > UM“) velocity conﬁgurations were used. They cite the work

of Plesniak et al. (1994), who performed velocity measurements in both stable and unstable

curved layers and found that well-organized spatially stationary streamwise vorticity was

49

generated, which produced signiﬁcant spanwise variations in the mean velocity and Reynolds
stress distributions (although the source was attributed more to the ampliﬁcation of small
incoming disturbances than to the Taylor-G6rtler instability). In addition, Plesniak et al.
reported that for the unstable layer the vorticity thickness, peak streamwise vorticity and
primary Reynolds stress were higher than those for the stable and straight layers. Meanwhile,
the product measurements of Karasso & Mungal showed that both the mixed-ﬂuid fraction
and the average mixed-ﬂuid concentration remained constant regardless of whether the
stable, unstable or straight ﬂow conﬁguration was used. The experiments which are cited
above suggest caution in relating the enhancement of momentum mixing with that of
molecular mixing.

It is well-known (Breidenthal, 1980, Koochesfahani & Dimotakis, 1986) that the
mixed-ﬂuid fraction above the mixing transition depends on the Schmidt number, Sc 5 u/D,
deﬁned as the ratio of the diffusion coefﬁcient of momentum to that of mass. The apparent
similarity between the 2—D and combined 2-D/3-D forcing in the present study may be a
further effect of this parameter. Schmidt numbers for liquids are typically about three orders
of magnitude larger than for gases, on account of the very low mass-diffusion coefﬁcients
for liquids. In gases, Schmidt numbers are on the order of unity, indicating comparable
diffusion of mass and momentum. It appears that the small scale motions which are
presumably generated due to the injected streamwise vorticity are simply not small enough
to have any effect at the molecular level. A natural and interesting extension of the current
work would therefore be to repeat the present experiments in a gas phase shear layer. In this
regard, the effects of a variety of spanwise perturbations on the turbulent momentum

transport properties have been well documented recently by Bell & Mehta (1993). They

50

found that the introduction of an array of cylindrical pegs in the high-speed side boundary
layer not only generated a regular array of counter-rotating vortex pairs but also affected the
layer growth rate and turbulence properties in the far-ﬁeld. Strong, although somewhat
different, effects were also found when an array of vortex generators, was the source of
spanwise perturbation.

What seems somewhat ironic here is that a mechanism has been found which
enhances mixing efﬁciency, the source of which appears to lie in the two-dimensional nature
of the (relatively high) forcing frequency. The contribution of the braids to the overall
mixing product in liquid shear layers is generally considered to be small, the mixing being
conﬁned to a thin interface undergoing a diffusion-limited reaction, while that of the cores
is significantly larger. It is speculated that by destroying the braid structures a dramatic
increase in mixing takes place. This may be related to forcing at a frequency close to the
subharmonic of the fundamental roll-up frequency (ﬂfo= 0.42). The computational instability
analysis of Monkewitz (1988) states that, ‘the development of the subharmonic, leading
eventually to pairing or shredding, crucially depends on its phase relation with the
fundamental’. We note here that there is still a lot of room for improvement in terms of
mixing enhancement - the largest value of the mixed-ﬂuid fraction (6m / 6,) which was
recorded during the current experiments is approximately 0.5, i.e. on the average only about
half of the shear layer width contains mixed ﬂuid.

The 3-D perturbation does, however, have a deﬁnitive effect on the development of
the shear layer. The spanwise undulations seen for the peg cases in the mixed ﬂuid
thickness, 6,,,(z), the shear layer width 6,(z), and the average mixed-ﬂuid concentration,

5,,(2), can all be attributed to the presence of the 3-D perturbation. As a means to help

51

visualize the types of streamwise structures generated by the peg, included in Figure 4.3.1-2
are passive scalar LIF samples from a low-speed shear layer with a peg in the low-speed side
boundary layer. The signature of the peg is readily apparent in these images. Notice also the
predominance of the middle peak of low-speed (light grey) free-stream ﬂuid. Qualitatively,
this is the result of the induced velocity from the streamwise vorticity in the legs of the
horseshoe vortex generated by the peg. It is expected that the sense of this induced motion
will change as the peg is moved to the high-speed side of the splitter plate. This provides a
simplistic and qualitative reasoning for the ‘indentations’ discussed in section 4.2. It is
interesting to see in Figure 4.3.2 that when 2-D forcing is applied how the number of
streamwise structures increases dramatically. This reason for this will be clearer after the
following description. Volumetric iso-concentration surfaces composed from these images
are shown in Figure 4.3.3 and provide a perspective view of the 3-D structure of the ﬂow.
Lasheras et al. (1986) performed an experiment in a low-speed shear layer, utilizing
a chemical reaction with a pH sensitive marker to visualize the instantaneous interface
between the two streams, and to analyze the origin and development of three-dimensional
streamwise vorticity. They conﬁrmed earlier ﬁndings that the layer is composed of counter-
rotating pairs of streamwise vortices and stated that these structures were the result of the
unstable response of the layer to 3-D perturbations in the upstream conditions. Further, they
found that the streamwise vorticity was always seen to form ﬁrst on the braids between
consecutive spanwise structures and then to propagate into their cores. They proposed a
mechanism to explain their structural observations. Their argument is modiﬁed for the
present case and is schematically represented in Figure 4.3.4. The 3-D perturbation would

result in a ‘kink’ of the axis of the primary spanwise vorticity, as shown at (a). The positive

52

strain would then stretch the kink in the streamwise direction producing a pair of counter-
rotating streamwise vortices (b). At the base of the kink the vortex lines would be lifted
upward due to the inﬂuence of the streamwise vorticity. The vertical shear and/or strain
would then orient the vortex axis in the axial direction, to be acted upon by the positive strain
(c). This effect would continue to magnify as well as to propagate in the spanwise direction.
While it is understood that the above description is necessarily an over-simpliﬁcation, it is
felt that the basic features of this mechanism are relevant to the present case.

It is intriguing to note that the orientation of the spanwise trends in €M(z) observed
in the peg cases are preserved regardless of whether the 3-D disturbance is in the high-speed
or low-speed boundary layer. One might expect that a mirror-image of the initial streamwise
vorticity (as the peg changes sides) would be revealed as a mirror-image of the ‘wiggle’ in
the spanwise concentration plots at each forcing frequency. The reason for the observed
behavior is not yet clear.

The large reduction in span-averaged mixed-ﬂuid concentration at f = 16 Hz (x* =
3.1), was particularly noticeable for the case with no 3-D forcing. An explanation may be
attempted solely on the basis of quasi 2-D structures. Dimotakis (1986) has related the
entrainment into the shear layer to the upstream/downstream asymmetry of the large scale
structure spacing. The 2-D forced layer at x* = 3 has already passed through the frequency
locked region 1 < x* < 2. This region is characterized by equally-spaced large structures. The
upstream/ downstream symmetry of the large structure spacing in this region would imply
a unity entrainment ratio. Because there is a delay between ﬂuid entrainment and ultimate
mixing, at some value of x* beyond 2, the mixture concentration is expected to decrease

toward that corresponding to 1:1 mixing, namely 5 = 0.5. While this picture may seem

53

consistent with our results, the intriguing question is why the frequency-locked region should
affect the mixture composition at all - the nearly zero growth rate in this region implies
almost no additional ﬂuid is entering the layer.

In closing, we note that it may be tempting in certain applications to use low
frequency forcing (f << f0 , x* < 2) to enhance the spreading rate of a shear layer in the hope
of achieving better mixing. This work suggests that more efﬁcient mixing would occur if

no forcing were used at all.

54

Chapter 5

SIMULTANEOUS WHOLE-FIELD MEASUREMENTS

OF VELOCITY AND CONCENTRATION

The previous two chapters have concentrated on measurements of the amount of
mixing in a forced shear layer along with the changes in the mixed ﬂuid composition which
result from the forcing. However, the ﬂow behavior which leads to the various mixing
effects is not well understood. Since it is the structure and dynamics of the vorticity ﬁeld
which determine the mixing ﬁeld in these ﬂows, additional knowledge of the ﬂow
kinematics in the form of velocity and vorticity ﬁelds is needed to learn more about the
dynamics of the mixing processes taking place. The subject of the present chapter is a
description of a novel technique to acquire simultaneous non-intrusive velocity and
concentration data over a plane in a two-stream liquid flow. Preliminary results of whole-
field velocity Ivorticity maps with corresponding concentration ﬁelds are presented along
with point measurements of turbulent statistics such as velocity-concentration correlations.
The experiments discussed below took place with the help of Mr. R. Cohn, whose assistance
is gratefully acknowledged. Many of the details described here have recently been presented
at the 13‘h US. National Congress of Applied Mechanics (Koochesfahani & MacKinnon,

1998).

5.1 Background

There exists an extensive body of literature on turbulent statistics in many types of

55

ﬂows involving mean and/or ﬂuctuating measurements of either velocity components or
scalar quantities (e. g. temperature, concentration). Studies involving both velocity and scalar
measurements are far more limited. One of the earliest was the pioneering study by Keagy
& Weller (1949). Their results in a helium jet included proﬁles of mean velocity using a
Pitot probe and mean concentration using a sampling probe. Following a suggestion from
Corrsin, Way & Libby (1970, 1971) developed a two-sensor hot-wire probe capable of
monitoring ﬂuctuations of one velocity component and of concentration in a low-speed
helium jet. Antonia et al. (1975) and Chevray & Tutu (1978) produced results involving two
ﬂuctuating velocity components and temperature ﬂuctuations using a cold-wire sensor
mounted on an X-wire probe in heated air jets. More recently, the advent of optical
diagnostics such as LDV, LIF and particle scattering techniques have presented new
opportunities for the non-intrusive simultaneous acquisition of multiple ﬂow variables.
Owen (1976) used a combination of LDV and LIF to measure velocity and concentration
correlations in a co-axial liquid jet. Stamer (1983) and Dibble & Schefer (1983) acquired
velocity, density, and species concentration via LDV/Mie scattering and LDV/Raman
scattering, respectively, in a diffusion ﬂame. Such works have led to important information
on velocity/scalar correlations for modeling in the Reynolds averaged conservation
equations. All of the above investigations, however, have incorporated single point
measurements. One of very few studies involving simultaneous planar measurements is that
of Frank, Lyons & Long (1996), who have combined particle-image velocimetry (PIV) and
LIF to record two velocity components as well as concentration in gas-phase ﬂows. The
present work monitors two components of velocity and concentration in liquid-phase ﬂows.

It’s advantage stems from the fact that, in contrast to all of the above non—intrusive

56

techniques, the use of seeding particles is not required. Seed particles have the potential to
contaminate either the velocity (e. g. out of plane motion) or the concentration measurements

or to lose neutral buoyancy (in reacting ﬂows).

5.2 Experimental Technique

The shear layer facility used for the mixing measurements was also used for the
simultaneous velocity/concentration measurements. As before, the free-stream speeds were
set to U, z 40 cm/s and U2 z 20 curls, and the same forcing frequencies were used. The
procedure for the simultaneous measurement is a combination of two non-intrusive
techniques - molecular tagging velocimetry (MTV) for the velocity data and laser-induced
ﬂuorescence (LIF) for the concentration data. For a detailed description of various MTV
approaches including the one used here the reader is referred to Koochesfahani et al. ( 1996),
Gendrich et al. (1997). Brieﬂy, the MTV procedure used is as follows.

A three component phosphorescent compound (l-Ber - GB-CD - ROH) is premixed
in the entire shear layer facility. Details of this complex may be found in Ponce et al. (1993).
The molecules of the triplex become long lifetime tracers (e'l lifetime z 4 ms) when excited
(‘tagged’) by photons. The source of the excitation is a pulsed laser (Lambda Physik LPX
220i, wavelength 308 nm), which is used to tag the regions of interest. The laser beam is
converted via a beam-splitter, mirrors and ‘beam-blockers’ into a two-dimensional grid of
thin laser lines. An example of the resulting tagged grid is shown in Figure 5.2.1(a). An
initial image of the grid is recorded at time t = to , just after the laser ﬁres. The tagged
molecules comprising the laser grid are then convected by the ﬂow. A short time (At) later,

within the lifetime of the tracer, the phosphorescent luminescence from the grid is recorded

57

by a second camera. A sample of a distorted grid is shown in Figure 5.2.1(b). Using a
spatial correlation technique, for each intersection point of the grid the displacement between
its initial and ﬁnal locations is computed. Knowing the time between images allows the
resulting two-dimensional displacement ﬁeld to be converted to a velocity ﬁeld. Two
cameras, triggered At apart, are used to acquire the initial and displaced images of the grid.
The two camera system is adopted to minimize the effects of variations in the initial grid
pattern (e.g. laser beam pointing instability, vibration of the optics, etc.) which would be
misinterpreted as ﬂow velocity ﬂuctuations.

The concentration measurement is facilitated by premixing a solution of ﬂuorescein
with the reservoir ﬂuid of only one of the free-streams, as in the LIF method discussed
earlier. Both reservoirs have the phosphorescent triplex premixed to enable velocity
measurements over the whole ﬁeld of view. The ﬂuorescence intensity ﬁeld at t = to gives
the concentration ﬁeld. This is recorded by a third camera viewing the opposite side of the
test-section from the MTV cameras. A schematic of the set-up is shown in Figure 5.2.2.

The issue of cross-talk between the MTV and LIF signals is a relevant one, but can
be shown to be almost negligible. Consider the two emission spectra in Figure 5.2.3. In part
(a) of this ﬁgure the ﬂuorescence and phosphorescence emissions of the MTV triplex are
shown to occur over the approximate ranges 300-400 nm and 460-700 nm, respectively. Part
(b) shows that the ﬂuorescein emission occurs above about 490 nm. We ﬁrst consider the
effect of the MTV signal on the LIF measurement. It is clear that the ﬂuorescence emission
of the MTV triplex is spectrally well separated from that of the ﬂuorescein and can easily be
ﬁltered out. We note here that the quantum efﬁciency of the triplex phosphorescence (I)c =

0.035, about 1/30th that of the ﬂuorescence of the ﬂuorescein. Thus the triplex

58

phosphorescence is easily dominated by the LIF signal. The effect of the relatively weak
phosphorescence emission can be reduced to negligible levels by reducing the exposure of
the LIF detector (1 us in the present case). Further, the triplex compound does not absorb and
re-emit ﬂuorescein’s emissidn. As for the effect of the LIF signal on the MTV measurement
- the ﬂuorescence emission from ﬂuorescein decays to near zero levels well before the pair
of MTV images are acquired. A timing chart is sketched in Figure 5.2.4 and shows the
relative positions of the laser pulse and the triggering of the three cameras.

For the work described here two types of data were acquired:
1) a low density grid (i.e. thick grid lines spaced relatively far apart) was used for the actual
combined MTV/LIF measurements, and
2) a relatively high density of laser grid lines was used to acquire purely velocimetry data.

It was felt that the thicker grid lines of the lower density grid would provide better
ﬂow visualization with which to compare the MTV vorticity ﬁelds, and also reduce potential
errors in the concentration ﬁeld due to laser pointing variations. This, of course, leads to a
trade-off in spatial resolution. However, in future experiments it is expected that the spatial
resolution will be increased signiﬁcantly. A sample of the three images required for a
combined MTV/LIF measurement is shown in Figure 5.2.5. The top image show the
concentration ﬁeld due to the ﬂuorescein acquired by the LIF camera. The lower two images
display the initial laser grid pattern due to the MTV triplex and it’s subsequent distortion At

later acquired by the two MTV cameras.

5.3 Preliminary Results

The following results have been extracted from the ﬁrst application of the combined

59

MTV/LIF procedure. As noted above, the study is still somewhat exploratory in nature in
the sense that certain parameters remain to be optimized (e. g. spatial resolution, LIF
exposure, laser beam pointing stability). However, it is believed that the results obtained
demonstrate that the technique is capable of producing quantitative two-dimensional
concentration/vorticity ﬁelds as well as turbulent statistics such as velocity-scalar Reynolds
ﬂuxes.

The first three figures (5.3.1-5.3.3) provide examples of the combined two-
component velocity measurements and concentration in a shear layer with no forcing, and
forcing at f = 4 Hz and f = 8 Hz, respectively. These ﬁgures display the concentration ﬁeld
(upper image) aligned horizontally with the velocity ﬁeld/vorticity contours (lower image).
The mean convection speed has been subtracted from the velocity ﬁeld. Stagnation points
are seen between adjoining large structures and the regions of vortical motion inferred by the
concentration measurements appear to closely track the vorticity ﬁeld from the MTV
measurements.

Next some turbulence point statistics are presented from the high-density grid data.
While such data are available at many grid intersections, only transverse proﬁles at a single
x-location (x 2 15.5 cm) near the mid-point of the grid are reported here. Figures 5.3.4-6
show the present data of maximum normalized um, vans, and —;’_v_’ versus Re 60 along with
data compiled from the literature on unforced plane shear layers. In each case the present
datum point falls within the scatter of the existing data, and provides some initial validation
of the velocity measurements. Proﬁles of the mean streamwise velocity plotted using
similarity coordinates are shown in Figure 5.3.7, where Uc = (U ,+U2)/2 is the mean free-

stream speed and y, is the transverse co-ordinate at which this value occurs in the mean

60

profiles. An increase in the shear layer width, 6,,, at f = 4 Hz is clearly seen relative to the
unforced case. The width at f = 8 Hz appears to be very similar to that of the unforced layer.
We note that it remains to be shown how 6, varies with 6,,, in forced shear layers. The
present technique is capable of providing such information. Proﬁles of the Reynolds stress — W
are plotted in ﬁgure 5.3.8. The familiar bell-shaped proﬁle is seen in the unforced case,
while the f = 4 Hz case shows much larger intensities, indicative of more organized motions.
The Reynolds stress intensity drops signiﬁcantly at f = 8 Hz. Oster & Wygnanski (1982)
show a qualitatively similar drop with streamwise distance at a ﬁxed frequency in one of
their plots. The average concentration and its rrns variation in the y-direction are shown in
Figure 5.3.9-10. The mean concentration at f = 8 Hz case shows a ﬂat region in the middle
of the layer consistent with ﬂow visualizations indicating the passage of structures in the
frequency—locked x* regime with fairly well-mixed cores. The rrns concentration proﬁles
have a double-humped nature indicating greater variation at the edges of the shear layer. The
streamwise and lateral velocity-concentration Reynolds ﬂuxes 37—57 and W are shown in
Figures 5.3.11-12. Unfortunately we have not found this type of data for shear layers in the
literature, and therefore quantitative comparisons cannot be made. However, qualitative
arguments may be made for the signs of the correlations.

It is evident that the simultaneous application of both the MTV and LIF techniques
yields more information than each separately. The non-intrusive combined measurement of
the two-dimensional velocity/vorticity ﬁeld along with the concentration ﬁeld and structural
information is expected to be a useful tool in ﬂow studies concerned with mixing and mixing

enhancement.

61

CONCLUSIONS

Chemically reacting and passive scalar measurements of the structure and mixing
field were performed in a turbulent two stream mixing layer undergoing 2-D and combined
2-D/3-D perturbations. The majority of the work presented has focused on quantifying the
amount of molecular mixing and the mixture composition as a function of the dimension-
less variable x* = hf / Uc , which was varied by changing the frequency at a ﬁxed
downstream location, near the end of the mixing transition. Both streamwise and spanwise

measurements were made. A summary of the main conclusions is as follows.

0 When 2-D forcing is applied, the amount of molecular mixing, quantified by the
mixed-ﬂuid thickness, 6,,, increases by varying degrees relative to that of the

unforced layer at all frequencies and amplitudes used.

0 If the mixing efﬁciency is deﬁned as the fraction of the layer occupied by mixed
ﬂuid, i.e. the mixed-ﬂuid fraction, 6,,/6,, results indicate that mixing efﬁciency is
increased only for x* 2 2. A peak is reached at some point beyond x* = 2, but mixing
enhancement appears to continue until at least x* = 6. It is speculated that the
destruction of the braid regions connecting the large spanwise structures is
responsible for the increase in mixing efﬁciency. This may be a related to forcing at
a frequency close to the subharmonic. An important result is that below x* = 2, the

mixing efﬁciency is decreased relative to the unforced case. Thus low frequency (f

62

<<f,,) forcing is not recommended if enhanced mixing efﬁciency is a goal.

The mixture composition also was affected by 2-D forcing. While there was little
variation between the other cases, at x* = 3.1, the span-averaged mixed-ﬂuid
concentration, a, decreased to approximately 0.5, suggesting a signiﬁcant
modification to the entrainment and mixing process. This value indicates a 1:1
mixture ratio of high-speed to low-speed ﬂuid, more characteristic of a wake ﬂow
with equal speeds rather than a shear layer with one stream twice the speed of the

other.

The 3-D perturbations caused a spanwise undulation in the mean mixed-ﬂuid
concentration, EM(z). The nature of the ‘wiggle’ was the same for the cases of no 2-D
forcing, f = 4, 8 and 32 Hz. At f = 16 Hz the nature of the wiggle reversed, for
reasons which are still unclear. Interestingly, the character of these wiggles was
preserved regardless of whether the source of the 3-D forcing was on the high- or

low-speed side of the splitter plate.

While the span-average mixed-ﬂuid concentrations-E; , for the majority of cases
with 3-D forcing were unchanged or showed slight increases relative to their

‘unforced’ cases, a tendency towards lower values was found at x* = 3.1.

The presence of a 3-D disturbance in either of the boundary layers of the splitter plate

also caused undulations of the amount of mixed ﬂuid and the layer width. Somewhat

63

surprisingly the trends of the mixed-ﬂuid fraction versus x* did not change compared
to that for purely 2—D forcing. That is, the presence of the 3—D perturbation did not

further increase the mixing efﬁciency over levels for purely 2—D forcing.

It is often speculated that increased three-dimensional motions should lead to an
increase in interfacial surface area and hence yield enhanced mixing efﬁciency. This
is not borne out by the present work and may be a reﬂection of the Schmidt number
in the current liquid phase experiments. This result has potential ramiﬁcations in
liquid applications where increased mixing enhancement is sought through the use
of streamwise vorticity injection mechanisms. Further study is needed in this area,
in particular a repeat of the current work in gas phase ﬂows would be highly

illustrative.

A novel technique has been presented for the simultaneous non-intrusive
measurement of two velocity components and concentration in a plane, along with
preliminary results. It is expected that this approach will be a useful tool in ﬂow

studies concerned with mixing and mixing enhancement.

APPENDIX

1. Bleaching of the Dye

Continuous exposure to an excitation source results in a loss of absorption efﬁciency
of the ﬂuorescein dye due to a process known as photo-bleaching. Bleached dye molecules
do not absorb the laser light, the effect of which is an apparent reduction in dye

concentration. The number of absorbing dye molecules decays exponentially in time as

(Koochesfahani, 1984)

where no is the number of molecules absorbing at time t = 0, n is the number of molecules
absorbing at time t, and 1,, is the bleaching time constant. 12,, is a function of the dye used,
the laser photon ﬂux (the number of photons per unit area per unit time), and the dye
absorption cross section. Koochesfahani (1984) calculated a value of 1,, = 20 s for his
experiments, indicating that only 37% of the dye molecules would still be absorbing after 20
seconds. Thus bleaching effects can be very signiﬁcant.

However, the problem of bleaching is greatly reduced in ﬂowing systems. If the dye-
bearing ﬂuid passes through the laser sheet in a time much less than 1:b bleaching becomes
negligible. The titration reference chamber is more sensitive to bleaching because the same
ﬂuid remains in the chamber throughout the experiment. Bleaching is reduced, though, by
continuously circulating the ﬂuid and by making the volume of ﬂuid covered by the laser

sheet much smaller than the total volume of the chamber. To minimize bleaching effects

65

further, the intensity of the chamber near the start of each experiment was used as the
normalization constant (If)m,.
2. Free Stream Intensity Elimination

Ideally, the ﬂuorescent intensities in both free streams are zero. In reality the free-
stream which carries the acid/dye solution has nonzero intensity. Typically, values of about
4-8 counts were recorded in the acid/dye stream compared with (L )max = 200. Although
these values are small, they cannot be neglected and measures were taken to effectively
‘ﬁlter’ out the acid/dye free-stream contribution to 6,,, and 6m.

From an acquired image sequence it is straightforward to identify the acid/dye free-
stream intensity values present. Once the maximum value has been determined, one possible
method to eliminate the free stream contribution is simply to threshold all intensities at or
below this value to zero in each image of the sequence. This method is limited by the fact
that it may eliminate the contribution of some real phenomena. Nelson (1996) improved
upon this technique in the following way. Each column in each image was read and
processed separately by the computer. When the intensity along the column fell below the
free stream value for a specified number of consecutive rows the intensities were set to zero.
This method reduces the possibility of actual product being ﬁltered out. The ﬁltering
process will identify the nonzero intensity contribution from the acid/dye stream and set these
intensities to zero.

The number of consecutive rows, y, needed before intensities were set to zero had
to be determined before processing. Setting y too low may result in eliminating real features,

while setting y too high can allow some free-stream intensity to remain unﬁltered. However,

66

Nelson (1996) has demonstrated that for highly mixed ﬂows, such as those in the present

experiments, the product thickness is almost totally insensitive to changes in y.

67

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73

 

20.0 cm 17.4 cm x = 2.5 cm

Figure 3.1. 1. Streamwise ﬂow structure and passive scalar concentration ﬁeld for (a) no 2—D forcing,
(b) f: 4 Hz, (c) f = 8 Hz, (d) f = 16 Hz, (e) f = 32 Hz; mid-amplitude, no 3-D forcing.

74

Shear layer width 61 (cm)

4.0

3.5

3.0 1
2.5 '-

2.0 '

1.5

1.0

0.5

 

v r‘v v

v'vwvw‘r

 

 

 

’ ‘
’
’ ‘
----- slope .1111 K I , ’ .
I ’ ‘

—— slope .l3x , ,
X—X 5ppresentdata X/x’ ,I’

 

 

 

x (cm)

Figure 3.1.2. Unforced shear layer width versus x.

75

 

1.0

 

D
O
A

0.8 r = 0.38

0.6

r = 0.76

 

r=0.5,present data

 

l6

 

0.4

0.2

.........................

 

 

 

 

 

Figure 3.1.3. Comparison of mixing transition with Breidenthal.

76

 

Nil-unlined product thlchrea

0.4

0.1:

 

 

 

 

 

 

 

 

—— pans
— yr.l48 ’W ‘
O—---O6n/6 V/V -
- 51 ’2’ 1
V- 4891, r V/V
’ :e—e—e— ,
v’ Yr"
(’0’ l
0’
l
3 6 9 12 15 18 21

Figure 3.1.4. Normalized product thicknesses versus x.

77

 

Figure 3.2.1. Spanwise ﬂow structure and product concentration field with no 2-D forcing.

78

 

Cp,=0 CP,=1

Figure 3.2.2. Spanwise ﬂow structure and product concentration ﬁeld with 2-D forcing; f = 4 Hz,
x* = 0.77,f7f,,= 0.11.

79

 

Figure 3.2.3. Spanwise ﬂow structure and product concentration ﬁeld with 2-D forcing; f = 8 Hz,
x* = l.55,f7f°= 0.21.

80

 

Figure 3.2.4. Spanwise ﬂow structure and product concentration ﬁeld with 2-D forcing; f: 16 Hz,
x* = 3.1,ﬂfo= 0.42.

81

 

Figure 3.2.5. Spanwise ﬂow structure and product concentration field with 2-D forcing; f = 32 Hz,
117* = 6.2,ﬂf,,= 0.84.

82

@588 Die. 0: MN: mm ":3 .NE 2 “:8 .NE w "~28 .NE v ":8 c8 83:: 8:55am :osabcoocoo 835a owmco>< .©.N.m 85mm

 

 

 

 

(an)

Layer Width, 8' (en) Amount of Mixed Fluid, 8

Mixed Fluid Fraction, 5_ I 5'

No 3-D forcing

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2.0 4 , . , . 4
I 3
1.5 l A
0- )~ 1 ’ --e
“4“ 1
(a)
05 I-- "If-32112 ----
- I .---—-.f=16llz
I V--—-Vf=8llz .
[3 ----- Ella-4H: ,
. , G--——-Ounforced q
0 r L l #4 1 n
.4 .2 o 2 4
2 (b)
at
l l-- "If-32H: —-—---
' O—--—-Of=ronz
' V-r—-Vf=8ﬂz ..
' B ----- 0’34“! 4
- G——-Ounforced ,
0 1 r 1
.4 .2 o 2 4
0" *1 1 I T v I
i ,
i
*i i ’w
I ~ I \ A
. 0’ '~ l - s .
I, ‘ \--..~ r.~¥ ," i \.
l

M H

. 6‘ e—G‘e—
“‘s-‘wﬂtM—‘givkﬁf ' (C)

 

 

 

 

 

 

 

 

0.2 ~
l-- "Ila-32112
” .—--—-.f-l£ﬂz
V“—'Vf'3ﬂl
' [3 ----- {Bf-MHz
L G——-O unforced
o L i
4 -2 0 2 4

Z (cm)

Figure 3.2.7. Calculated quantities versus 1 at #174 cm; no 3-D forcing.

84

No 3.1) Forcing

 

 

 

 

 

 

 

L6 v - - - . - -
Unforced
v-—-v-3
14> '3 """ 43-2
' —— e1
[3‘ G- -O
’ x
I \\
’ \
I \\
’ x
X \‘
le' 1.21 , x, (a)
I 9‘ \
,’ / \“\ ‘-
l / \\\ ‘\‘ l
I / \ \
I \ s
I, / \'\ \
Mir ’1‘: /,/-/ ’<8
/ ‘\~ /'/o
O" 1
i
0.8 ‘ ‘4 ‘ ‘ A
0 l 3 4 5 6 7
4 v v - -
l
1
31 a “*3; --------
\ “~—-_ --------
‘\ ‘T“-_:‘
\ I

lsr 2 . ‘ (b)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Unforced
v—-—-Va3
l . [3 ----- {In
G——-O at
o A g A A AA A gA
l 2 3 4 5 6 7
00‘ I I
Unforced
v—-—-v-3
I:-I ----- Eli-2
0.5 ; G——-O e]
l [Ii ‘~‘\~‘~-
— I “‘
o I 9“ “~
~ 0.4 . ~~_ “a- (C)
I -
so I” NEE
./
1 _/
0.3 §}_—::
0.2 r‘ ‘ ‘ A ‘ - * rt ‘
1 2 3 4 5 6 7

x.

Figure 3.2.8. Span-averaged quantities versus x*; no 3-D forcing.

85

No 3-D Forcing

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.20 . ' . rm
Unforced
3‘33
0.15 G—-—-€)al I
IR‘\~
m / \‘\
E . e———--—“?77 .
a. 0.10 I / ............ \‘V (a)
// ,E"”
/Z/’
0.05’ / r .
/,-
1
0 A4 A A A A A A A A
0 1 2 3 4 S 6 7
0.4 r '
Unforced
v—-——-Va3 ‘
0.3L [3 ----- an
G——-€) a]
In ‘\‘ 4
§_ 0.2- ’ \~\‘ . (b)
I /G~~....__‘ \‘
/ / ,B --------- T _?.>.-..\_:_§
/ ,e
//’,’
0.1 . ~ -” .
o g A A A A
0 l 2 3 5 6 7
0.06 . v . .
Unforced
V--—-V&3
13 ----- 43:2
0.04 ' G———O I]
a
E
E'- 7%\::I;- ....... (C)
no. I’: __;:;>.;;§
,/’/9——
0.02 >
I
o + A A A A
l 2 3 4 5 6 7
x.

Figure 3.2.9. Spanwise rrns quantities versus x*; no 3-D forcing.

86

 

 

 

 

 

 

 

 

 

1.4 - - - -
. l
r t
g P
.3:
5 1.2~
‘0“
\
E
83
\
E 1
E
2:- 1.0r
‘5
1‘3 1
0.8--_..----.----
0 2.5 5.0 7.5

X*

Figure 3.2.10. Forced mixed-ﬂuid fraction relative to unforced mixed-ﬂuid fraction; no 3-D
forcing.

87

 

1.0 I I I l I I l I l T r I l I I

0.8 r -

l

o... _ W‘éU-‘jftfmja

 

 

 

’0'
.0? t -..- -Q/‘ t
\e"' ‘\

0.4 - ./. -I

i I-- ---.f=32Hz ‘
.—--—-.f=16Hz

0.2 F V"—'Vf=3HZ _
E1 ----- -Elf=4Hz

. G-———€)Unforced .

0 I I I l I I I l I I I l I I I
-4 -2 0 2 4
Z(cm)

Figure 3.2.11. Average mixed-ﬂuid concentration versus z at x = 17.4 cm; no 3-D forcing.

88

0.7

 

 

 

 

p
06 $.11. -—"_ ——-- l-I-a
. Ad—77 ~_§_?-_ -'t
I

 

 

 

 

 

 

 

 

 

 

 

 

. . j,
\ ’1
\ ’l
\ ’l
\ ,’
\ ,V
b \ I’
\ I!
0.5 i
Unforced,
v—-—-v a3
13 ----- 43:12
G———Oal
0.4 ee-
0 1 2 3 4 5 6 7
x*

Figure 3.2.12. Span-averaged mean mixed-ﬂuid concentration versus x*; no 3-D forcing.

89

 

v v v v ' v v v v V v v v v ' v v v v ' v v v v v v v v v ﬁ'ﬁ v v v

 

 

 

 

0.06
-———-— Unforced
v—-—-Va3 ‘
13 ----- £1212

0.04 : G—-——€) a1

a i &
\\\
E /’ ~\
A: I \\
t5" ,’ ﬁx‘ \
I \
/I’/ ‘\.
0.02- ’ \- ‘x
[l/ \‘\‘\‘
_ G.___ l’ \‘E
—-—- v
0 ..................................
0 1 2 3 4 5 6
X*

Figure 3.12.13. Spanwise rms of mean mixed-ﬂuid fraction versus x*; no 3-D forcing.

90

 

f=8Hz;x* z1.55

 

Figure 3.2.14. Spanwise ﬂow structure and concentration ﬁeld with purely 2-D forcing; x = 17.4
cm.

91

 

f=8Hz;x* z 1.55

 

Figure 3.2.15. Spanwise ﬂow structure and concentration ﬁeld with purely 2-D forcing;
x = 17.4 cm.

92

 

Figure 3.2.16. Spanwise ﬂow structure and passive scalar concentration ﬁeld with
purely 2-D forcing.

93

 

20.0 cm 17.4 cm x = 2.5 cm

Figure 4.1.1. Streamwise ﬂow structure and passive scalar concentration ﬁeld with 3-D forcing (LS)
for (a) no 2—D forcing, (b) f = 4 Hz, (c) f = 8 Hz, (d) f = 16 Hz, (e) f = 32 Hz; mid-amplitude.

94

 

20.0 cm 17.4 cm x = 2.5 cm

Figure 4.1.2. Streamwise flow structure and passive scalar concentration ﬁeld with 3-D forcing (HS)
for (a) no 2-D forcing, (b) f = 4 Hz, (c) f = 8 Hz, (d) f = 16 Hz, (e) f = 32 Hz.

95

 

CP1=0 Cpl=l

Figure 4.2.1. Spanwise ﬂow structure and product concentration ﬁeld in a shear layer with 3-D
(LS) forcing; no 2-D forcing.

96

 

Figure 4.2.2. Spanwise ﬂow structure and product concentration ﬁeld in a shear layer with 2-D/
3-D (LS) forcing; f = 4 Hz, x* = 0.77,f/f0 = 0.11.

97

 

Figure 4.2.3. Spanwise flow structure and product concentration field in a shear layer with 2-D/
3-D (LS) forcing;f = 8 Hz, x* = 1.55,f/f0 = 0.21.

98

 

Figure 4.2.4. Spanwise flow structure and product concentration ﬁeld in a shear layer with 2-D/
3-D (LS) forcing;f = 16 Hz, x* = 3.1,ﬂf0 = 0.42.

99

 

Figure 4.2.5. Spanwise flow structure and product concentration ﬁeld in a shear layer with 2-D/
3-D (LS) forcing;f = 32 Hz, x* = 6.2,f/f; = 0.84.

$588 wdmé .NE mm H as A3 .NE 2 "x 3 .NE w ".28 .Nm v ">3 c8 mome_ 0&3:wa :ouabcoocoo 8355 owﬁo>< .cdé oSwE

  

101

(cm)

Layer Width, 5' (cm) Amount of Mixed Fluid. 5

Mixed Fluid Fraction, 5_ I 5’

3.1) forcing (LS)

 

2.0 r

Y T

 

1.5

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

' i 1
0.5 I" ".f=32H1__-..1
* .---—-.f=1681 ..
r v—-—-Vf-snz .
r [3 """ ﬂf=4ﬂl
.. G——-Ounforced
L 4 g 4 l n
0-4 2 o 2 4
‘ l r I F l 1
g l
l
v m g i
b ‘ .. __ _, .. - ‘. g _ -_ . ,IV
3 1&1” ’8’ \Qﬁj ﬁﬁ/érg‘ﬂxam
\ 9’ - , /.
o—V-HJ'EaE-iz‘ *3? .‘e
s.’ ,.’ .
2
1
1
1 .-- "lien“:
t O—----Of=16nz
’ V"—'Vf=8ﬂl
r [3 ----- Elf=4ﬂz
L- G——-Oun!orced
g L L 1 L
04 2 o 2 4
0.6 r r l r , I T
P i l I
L- i ,Q\ .‘
I \ 1 ll \
-O/ \‘ I / ‘x\ .'1 i
”l: _.‘ M- v" \
0.4 ”—1": l’ - - I-l I’G-OAB
- E"E;%; ka’G‘ evggi/a—GK:
. ’E‘W' ' '[ ,
s .
0.2 !
.-- ---.f=32llz J
.---—-.f=loﬂz
V--—-Vf=8ﬂz y
B ----- {EL/=4“:
G———Onnforced J
o . . . . . l
-4 -2 0 2 4
Z(cm)

(a)

(b)

(C)

Figure 4.2.7. Calculated quantities versus 2 at x = 17.4 cm; 3-D(LS) forcing.

102

3-D Forcing (LS)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.6 ' ' ' ' ' ‘ * '
l
Unforced
V--—-V'3
14» [3 ----- Em .
. o-——-Oal
9\
, / \\
.6' My / \\ ‘ (a)
\\
E ..... \
x ....... \
‘--~--:>
-l'ﬁ
1.0» -——-—-""' ‘
g! -—’__—__V.——'"
l
0.8 4 ‘ ‘ ‘4 ‘ ‘
0 1 3 4 5 6 7
4 - e. - a
3’ §Fﬁ~ —-~—e\
> \\\ l
\ \“ \\M\
L“! """""" :_"_;_-::.=-';*‘E
\"’-’
I'd- 2 (b)
* Unforced ‘
v—-—-v-3
1 > El ----- {1&2
o A g A A L A
0 l 3 4 5 6 7
0.6 l
1 l
r Unforced,
a-as .
0.5 G——-O-l
"' i ---=~’“‘=--—--
2, 0.4 ﬁt ”Kw-sic. (C)
CO

 

 

0.3

 

0.2

 

\-
-.._...- a,

 

 

 

 

 

 

 

 

x.

Figure 4.2.8. Span-averaged quantities versus x*; 3-D(LS) forcing.

103

3-D Forcing (LS)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.20 a .2 #2.- .-- .32- -- - T --
’ i
l Unforced 4
> 3:13;: 1
0.15) G——-O!1 1
1
9“
E // ~\\\‘ -
' 0.10 r / ,x’ﬁﬂ ‘ (a)
/ ../—g"‘ *
l ﬁr”
/
0.05) 1
o A A 4 g; P
0 l 2 3 5 6 7
0.4 ﬂ - f r -
Unforced
v—-——v-3
03’ t3 ----- 43-2
G——-O a]
Q
E L \\\ T
0.2 V \ 1 b
- \
//’ \‘\\\
/’ "O‘B --------------- :\‘\\a
0.1 - (34g! .
Q,” 1
[3
o ‘ A A A . A_¥ A A
0 l 2 3 4 5 6 7
(Loaﬁ--. . - . . .1- V, a,
Unforced
v—-—-v-3 1
l3 ----- 43:2
0'04’ CL“ G———O I1 ‘
H II, “--.‘~ <
E I, K‘.‘ ““s“
2- ”/ \§§“\“ (C)
I E:‘
'3 ‘\"§
0.02 -
l
o AAAAAAAAAAAAAAA A
0 l 2 3 4 5 6 7
xt

Figure 4.2.9. Spanwise rms quantities versus x*; 3-D(LS) forcing.

104

 

CP1=0 Cpl=1

Figure 4.2.10. Spanwise flow structure and product concentration ﬁeld in a shear layer with 3-D
(HS) forcing; no 2—D forcing.

105

 

CP1=0 CP1=1

Figure 4.2.11. Spanwise ﬂow structure and product concentration ﬁeld in a shear layer with 2-D
/3-D (HS) forcing; f = 4 Hz, x* = 0.77,f/fo = 0.11.

106

 

Figure 4.2.12. Spanwise ﬂow structure and product concentration ﬁeld in a shear layer with 2-D
/3—D (HS) forcing;f = 8 Hz, x* = 1.55,f7fo = 0.21.

107

 

Figure 4.2.13. Spanwise ﬂow structure and product concentration ﬁeld in a shear layer with 2-D
/3-D (HS) forcing; f = 16 Hz, x* = 3.1,f7f0 = 0.42, high amplitude.

108

 

Figure 4.2.14. Spanwise ﬂow structure and product concentration ﬁeld in a shear layer with 2-D
/3-D (HS) forcing;f = 32 Hz, x* = 6.2,ﬂfo = 0.84.

109

(a)

(b)

(c)

 

Figure 4.2. 15. Averaged product concentration spanwise images with no 2-D forcing for (a) no 3-D
forcing, (b) 3-D(LS) forcing, and (c) 3-D(HS) forcing.

110

@588 mEQAH ”NE mm MK v .Nm 2 “~28 .NI w MR .NE v ">3 5% mamas: 023.3% 5:328:00 835cm omﬁo>< .3 .m.v oczmﬁ

 

 

 

 

3-D forcing (HS)

 

 

 

 

 

 

 

 

 

 

 

2.0 ji. 1 1 r ; t r
l- \
l I \
. ' , 4
A I‘\\ / ! ‘\
5 1.5 ’ H I 3 ‘
V. ’7 ‘\ ,o’ \ ‘ i ---Q
.g. ‘ I g I,—
2
a
E
'3
.5
2
E
5 2
E 0.5 --- --..f.32liz
r- i .-"—'.f=1‘Hz -1
. V"—'Vf=3“'
r- l B ---- 6’34“!
; G——-Ounforoed
of l I .
4 -2 0 2 4

 

 

 

 

Layer Width, 81 (cm)
H

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 I-- ---If=32nz--—~--
t .—--—-.f=lollz .
r V'"—‘Vf'3ﬂl
. [3 ----- {Bf-4H!
_ G-——-Onnforced
o 1 a L 1
4 -2 o 2 4
0.6 1 ’ f
l l
‘. [/T‘.
4' ~ ' n
.. . I- ’
3 I’ * $.a—O‘ ,‘ ,+ “h
“1' °°"‘“’7’ ' ‘n ‘\ "i‘ 1 AV-
“ . "ﬁ-Gﬁk “I —I. u’ ”’13-?
g “315' .‘9‘6 5 ﬁ—V’
h r V- B. 7: :28“ _ -
2 v4; -El--£E| 9— I
l
B 0.2 !
~25 I" ".1.-328:
. ._-——-.f-16Hz
V--—-Vf-"h
13 ----- El“!!!
L G-——-Onnforced
o - . . a l .
.4 -2 o 2 4
Z(cm)

(a)

(b)

(C)

Figure 4.2.17. Calculated quantities versus 2 at x = 17.4 cm; 3-D(HS) forcing.

112

IO

Figure 4.2.18. Span-averaged quantities versus x*; 3-D(HS) forcing.

3-D Forcing (HS)

 

 

 

 

 

 

 

 

 

 

 

1.6 - - - - -
Unforced
V--—-VI3
1.4. R 13 ----- 1:1-2
/ \ G-——-Oal
/ \
/ \
/ \
\
1.2 / EL- \
/ ,’V\‘“- \
/ I’/ \“‘~ \
I, I \:~\\‘ \
/ ,z/ “*3 1
to M U
0.8 L ‘ ‘ r e
1 2 3 4 5 6 7
4 - - - a
.1.—7sz~-—6\
3» 8' “ ‘ ‘
2 >
Unforced
‘ v—-—-Va3
1 . [3 ----- £142
G--—-Oal
o A A A A L L
o 1 2 3 4 s 6 7
0.6 I
1 l
Unforced
§'—1¥13
0'5 G—--Oal
/G-\\ ,
o4 //B\wiaa._
’ /
/
,
E‘ y/
0.3 G,"
0.2
o 1 2 3 4 s 6 7

 

 

 

 

 

 

 

 

 

 

 

 

 

 

x.

113

(a)

(b)

(c)

ﬁrms

6‘ runs

(8. / 8') ms

34) Forcing (HS)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.20 ﬁ a ﬁ
\“:~\\...:\
\‘\ 'h-u
0.15 » *‘szg
,/
//
I
{:—Vf
Saba
Unforced
0.05 ’ V--_-V‘3
B ----- {El-2
G—--O I1 ‘
l
0 - -
1 2 3 4 s 6 7
0.4 -
T.
/’I ‘\§\ Unforced
” ‘ Vu—"Vﬂ
,’ \ 13 ----- 13:2
0.3 h I], \\ G——-O .1
. \\
/.' x.
H
/’I
I], \
0.2» /’I /9\\\ \ (b)
II, // \\\\\ $§
‘/ \\
a? F
01’ ’(/ [I
0 - . 1 a - - a
0 1 2 3 4 s 6 '7
0.06 f - v
/ ~“‘7’%
/ '/'/v"
/ '/
004 > / "’ i
. / V "”
// ’/
13”
’/’l” (C)
9N:- z”” i
0.02 » VB
Unforced
V--—-VI3
El ----- {III
G--—-Oal
0 L1 . - .
l 2 3 4 S 6 '7

x0

Figure 4.2.19. Spanwise rms quantities versus x*; 3-D(HS) forcing.

114

1.0

 

0.8 r

0.6: ragat-‘Ubi-ziWE “Egg—:51“

0.4 1

.-- ---.f=32Hz *
.—--—-.f=16Hz
0.2L V—-—-Vf=8Hz
[3 ----- 43f=4HZ
G——-€)Unforced l

 

 

 

 

 

 

 

0 - - A n - A A a . 2 A n A A .
-4 -2 0 2 4
Z(cm)
1.0 - - - . - - - . . . - 4
i
0.8 +
0.6- Mﬁgmiii
M: r \““.._./‘ \. ,. (b)
0.4- 1
I-- ---.f=32 Hz
.‘--—-.f= 16H!
0.2~ V—-—-Vf=8Hz
13 ----- Bf=4Hz
G———O Unforced
0 A A A a A - - n A . A n - - -
-4 -2 0 2 4

Z (cm)

Figure 4.2.20. Average mixed-ﬂuid concentration versus z at x = 17.4 cm; (a) 3-D(HS)
forcing, (b) 3-D(LS) forcing.

115

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.7
f 1
0.6 M. ................ _0_ ‘ _
e: \ :‘\~ __,‘_z:'—‘=’-:ig——
L \ ‘\ \ —-—-"""'"':'—=_’—— // 4
\ ‘\ V": ————— /
2 r ‘B" ///'
“" 1 \ ,/ (a)
\ //
8'
0.5 .
-— Unforced‘
V--—-Va3
l3 ----- £1 a2
G———O a1
0.4 LL-1 --+A ----i----iaL4-
0 l 2 3 4 5 6 7
x.
0.7
l
e—:-=—= \\'—-—V—--—--—--—---——-,—...e
0.6 ‘ § /:;,4’
\\ {’¢',v
\§ / ”"
i ‘F "f", * (b)
u: ’ '9'” ‘
0.5 .
Unforced‘
v—-—-v as
B ----- B82 1
G———O a1
0.4LA1-1
0 1 2 3 4 5 6 7
x4

Figure 4.2.21. Span averaged mean mixed-fluid concentration versus x*; (a) 3-D(HS) forcing,
(b) 3-D(LS) forcing.

116

 

 

 

 

 

 

 

 

 

 

0% ---ﬁﬁ---- vvrfr fﬁ-
Unhwaﬂ
» V—-—-Va3 1
,G\ [3 ----- -[E]a2
0-04' / \\ G———Oal
/ V\ \\
E ///B_ ‘\‘ \\\
A // z’ ----- k-___ \ ‘ (a)
“2 /’ ” \3““‘\~
V g/ \- s
0.02» 87/ -
o ..................................
0 1 2 3 4 5 6 7
x*
006 - .. -,.f. rv~fﬁ .- -- r»#
Unﬁwaﬂ
v—-—-Va3
13 ----- {m
004- G}-—-—€)al
a 1
.. ,13~--\ , (b)
A / “~
1 I’ ‘~-“
0.02‘ I, ___,-.———*"';—:;”g§
a, /’/V ’l”
aAi’n/ 74/9,,
0 ..................................
0 1 2 3 4 5 6 7
X*

Figure 4.2.22. Spanwise ms of mean mixed-ﬂuid concentration versus x*; (a) 3-D(HS)
forcing, (b) 3-D(LS) forcing.

117

CPLPZ = 1

   

CPm = 0

 

Figure 4.2.23. Spanwise ﬂow structure and product concentration ﬁeld with 2-D / 3-D(HS)
forcing; f = 16 Hz, x* = 3.1, highest amplitude.

118

 

Figure 4.2.24. Spanwise ﬂow structure and passive scalar concentration ﬁeld with
2—D/3-D (LS) forcing.

119

8/5

0.6

0.4 .

0.3

0.2

 

:v—u—w a3;HS
0.5»

: x———><a3;Ls
&-—-a a2;Ls 5:2:

-_- ---I 112018

 

.—--—-. al;HS

 

’6 ----- -€Bal;LS ,5
’V--—-V 83
El ----- E a2
» G——-O a1

 

 
 
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

X*

Figure 4.2.25. Mixed-ﬂuid fraction versus x* for all cases.

120

 

 

 

Figure 4.3.1. Spanwise passive scalar structure and concentration ﬁeld in a low speed shear
layer with 3-D(LS) forcing and no 2-D forcing.

121

 

Figure 4.3.2. Spanwise passive scalar structure and concentration ﬁeld in a low speed shear
layer with 3-D(LS) forcing and 2-D forcing at f = 8 Hz.

122

 

 

 

5130641
with 3D!

 

 

(a)

(b)

 

Figure 4.3.3. Volumetric rendering of iso-concentration surfaces in the low speed shear layer
with 3-D(LS) forcing along with (a) no 2-D forcing and (b) f = 8 Hz.

123

(a)

(b)

Figure 4.3.4. Mechanism for axial vorticity generation.

124

LIF Image

MTV Image Pair

MTV: Image of tagged regions
at 1 = to,

 

MTV: Image of tagged regions
at t = to + At.

 

Figure 5.2.5. Sample images for simultaneous concentration/velocity measurements.

125

 

1.5

d

y(cm)
O
IllIIllIlllllIIIIIIIIIIIIIIIIIIIII

 

 

Figure 5.3. 1. Simultaneous concentration ﬁeld from LIF (top) and velocity/vorticity ﬁeld
from MTV (bottom); no 2-D forcing

126

 

> >—>> > >> 5 b
..v->1>~>+ >7>7>7> b

1.5

V D V VD}, >»> 5
7.7»7'777> >7»>~>~"§
V ' 7 V V b b h »‘ g
'7' 7'. p‘ ‘ ‘ .‘ ‘

A

“‘<<7¢.‘.<<V‘VV
VVVVV‘»‘~<7»<7‘*‘7‘~<7<
‘7‘»1<~< Q»‘ < <74
<»<r‘~<r< ‘7‘ ‘7‘ <

VVVV»< ﬂ ‘

x
,V.
,V
V
V.
‘,
‘3
<
‘

y(cm)
a
I'llIllllIIIIIlIllIIIlIIIIIIIIIITI

 

 

Figure 5.3.2. Simultaneous concentration ﬁeld from LIF (top) and velocity/vorticity field
from MTV (bottom); f = 4 Hz.

127

 

rjlilllllIIllW’TT'IIIT'IIIIIIIIT'I!

 

 

Figure 5.3.3. Simultaneous concentration ﬁeld from LIF (top) and velocity/vorticity field
from MTV (bottom); f = 8 Hz.

128

u'/AU

0.20

 

0.18

 

0.16

v v v vvvwv
. . . . ...
. . .
.
I
............................ J........,...... .,..,.....,.,q
..
..
.
.
.
t
.
............................
.‘I
.
.

 

 

0.14

................................

 

 

 

0.12

 

 

0.10

 

 

0.08 i ‘

 

 

p ........................................................................
I I
p ............... - .........................................................
.. u
. . 1
n. .
U' '
.i .
I l
b ............... - ...........................................................
. ........
. .
. . .
. . .
. ..... 0 .
LAALL A A AAAAAA A A

‘onqmobaeo

A

Present

Balint & Wallace 1989
Patel 1973

Liepmann & Laufer 1947
Spencer & Jones 1971
Browand 81 Latigo 1978
Winant & Browand 1974
Browand & Weidman 1976
Wygnanski 81 Fiedler 1970

. ......
PLJAAAAI

 

Re=AU6wlv

GI

106

Figure 5.3.4. Compilation of urms data in the plane shear layer.

129

v'/AU

0.20

 

.................................

‘
d

 

0.18

0.16

.................................

 

0.14

.............................

ODHJCDDB$O

.............................

V"""

I I V T‘T'UI

Present

Balint 8 Wallace 1989
Patel 1973

Liepmann 81 Laufer 1947
Spencer 8 Jones 1971
Browand 8 Latigo 1978
Browand 81 Weidman 1976
Wygnanski 8 Fiedler 1970

 

0.12

...........................

.............................

.............................

 

 

 

 

p ....................... 1 ........................................................ 4
0.10 T T _ u f I I
b ......................................... '..i ....... A ............ l .......... i, ............ i ..... l.l.l..|q
008 A A A AAAAA A A A AA A A A AAAAA A A A AAAAA
o

 

 

 

 

 

Re=AU8m/v

Figure 5.3.5. Compilation of vrms data in the plane shear layer.

130

«wvmmz

 

0.014

0.012 i

oumobao,

V 'V""'

Present

Patel 1973

Liepmann 8 Laufer1947
Spencer 8 Jones 1971
Browand 8 Latigo 1978
Browand 8 Weidman 1976
Wygnanski 8 Fiedler 1970

 

 

0.010

 

0.008

............................

..............................

.............................

 

0.006

 

 

 

 

 

 

0.004

Re=AU8w/v

Figure 5.3.6. Compilation of Reynolds stress data in the plane shear layer.

131

C

(u-u )/AU

0.8

0.6

0.4

0.2

 

 

 

 

 

 

 

 

 

 

 

 

 

 
 

 

v—--—V F=8Hz

 

 

 

B---E] F=4Hz """
9—0 Unforced

 

 

 

 

 

 

 

 

 

 

 

-0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08
( Y - Yc) / x

Figure 5.3.7. Normalized proﬁles of mean velocity.

132

- u'v' / (AU)2

 

0.020 ,

r V. Y r
.................................................. V—-—VF=8HZ

B---E]F=4Hz .
G—OUntorced.

 

0.015

 

0.010

 

0.005 i

 

 

 

 

 

\

 

  

 

 

 

 

 

 

 

-0.10 -0.08 -0.06 -0.04 -0.02 0 0.02

(Y-chx

0.04 0.06 0.08 0.10

Figure 5.3.8. Normalized proﬁles of Reynolds stress.

133

éavg

 

 

 

 

  

 

 

[3——-E]F=4Hz

 

 

 

 

 

 

G—O Unforced

 

 

0 i i
-0.12 -0.08 -0.04 0
( Y - Yc ) / x

0.04 0.08 0.12

Figure 5.3.9. Normalized proﬁles of average concentration.

134

0.8

0.6

 

 

 

V-———-V F=8Hz .

[3—--E] F=4Hz
G—eUnforced

 

 

 

 

 

 

 

 

 

 

 

 

-0.

08

-0.

04

0.04

Figure 5.3.10. Normalized proﬁles of Ems.

135

ut/MU)

 

0.04 .

.................

..................

.................

....................................

_B---B
o———e

Unforced ‘

F=4Hz

1

 

002

 

 

 

002

 

 

................

.................

.................

.................

.................

 

 

................

....................

....................

..................

 

 

 

 

0

(YBYJ/X

Figure 5.3.11. Normalized proﬁles of 175’.

136

- v'§'/ (AU)

 

0.04 ,

..................

................

.................

.................

...............

..................

 

 

 

 

 

 

 

 

..................

 

...................

 

. ................. B---BF=4H2
§ G——€)Unforced1

 

 

 

 

Figure 5.3.12. Normalized proﬁles of v ’E’ .

0

(Y-Yc)/X

137

 

"I111111111110“