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thesis entitled

STRUCTURE AND MIXING IN A
LOW REYNOLDS NUMBER FORCED WAKE
IN A CONFINING CHANNEL

presented by

KIRK E . NELSON

has been accepted towards fulfillment
of the requirements for

MS degree in Mech. Engr.

 

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TO AVOID FINES Mum on or bdoro duo duo.

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STRUCTURE AND MIXING IN A
LOW REYNOLDS NUMBER FORCED WAKE
IN A CONFINING CHANNEL
By

Kirk E. Nelson

A THESIS

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

MASTER OF SCIENCE

Department of Mechanical Engineering

1996

ABSTRACT
STRUCTURE AND MIXING IN A
Low REYNOLDS NUMBER FORCED WAKE
IN A CONFINING CHANNEL
By

Kirk E. Nelson

The mixing field of a forced, low Reynolds number (Ree z 100) splitter plate wake is studied
using chemically reacting laser induced fluorescence. Results indicate that forcing one free
stream at high amplitude greatly increases the amount of scalar mixing downstream. At the
farthest downstream location investigated the wake forced at 9% amplitude exhibits about
sixteen times more chemical product than the unforced wake at the same location. Three-
dimensionality originating from the test section side walls is primarily responsible for this
increase in mixing. Marked three-dimensionality resulting in increased mixing is also

observed in a higher Reynolds number wake flow.

Two additional wake flows, one employing a false wall in the test section and another using
a peg near the splitter plate tip, are also studied. Both flows produce streamwise vorticity
providing other examples of no-slip boundaries leading to wake three-dimensionality and

increased mixing.

ACKNOWLEDGMENTS

This thesis would not have been possible without the help of numerous individuals. First
on the list is my advisor, Dr. Manooch Koochesfahani. His advice, knowledge, and guidance
throughout my Master’s research has been invaluable. I am also indebted to Drs. J .F. Foss
and M. Zhuang for reviewing this manuscript. Thanks to everyone in the lab, past and
present: Greg Ambrose, Steve Beresh, Rich Cohn, Chuck Gendrich, Greg Katch, Scott
Krueger, F igen Lacin, Bernd Stier, and especially Colin MacKinnon whose mastery of the

shear layer facility made things much easier for me.

My parents, Paul and Brenda Nelson, deserve special thanks for putting up with me all these

years. The patience and companionship of my family and friends is also greatly appreciated.

The experimental facilities and image acquisition system used for this study were purchased

with funding provided by the Air Force Office of Scientific Research.

iii

TABLE OF CONTENTS

LIST OF TABLES ..................................................... vii
LIST OF FIGURES .................................................... viii
LIST OF SYMBOLS ................................................... xvi
Chapter 1. INTRODUCTION .............................................. 1
1.1 Natural Shear Layers and Wakes ................................... 3

1.2 Forced Shear Layers and Wakes ................................... 6

1.3 Mixing in Shear Layers and Wakes ................................. 9

1.4 Objectives of the Current Work ................................... 13
Chapter 2. EXPERIMENTAL FACILITY AND INSTRUMENTATION .......... 15
2.1 Experimental Facility ........................................... 15

2.2 Forcing Mechanism ............................................ 17

2.3 Diagnostics ................................................... 17

2.4 Data Reduction ................................................ 21
Chapter 3. RESULTS FOR THE LOW SPEED WAKE ........................ 26
3.1 Streamwise Results ............................................ 26

3.1.1 Flow Visualization ..................................... 26

3.1.2 Calculated Quantities ................................... 34

3.1.3 Factors Leading to Variation in Streamwise Data ............. 37

iv

3.2 Spanwise Results .............................................. 40

3.2.1 Flow Visualization ..................................... 41

3.2.2 Calculated Quantities ................................... 46

3.3 Comparison of Streamwise and Spanwise Data ...................... 52

3.4 Comparison with Previous Nonreacting LIF Data ..................... 55

3.5 The Low Speed Wake: A Summary ............................... 56
Chapter 4. RESULTS FOR THE HIGHER SPEED WAKE ..................... 58
4.1 Streamwise Results ............................................ 58

4.1.1 Flow Visualization ..................................... 59

4.1.2 Calculated Quantities ................................... 60

4.2 Spanwise Results .............................................. 61

4.2.1 Flow Visualization ..................................... 61

4.2.2 Calculated Quantities ................................... 64

Chapter 5. RESULTS FOR THE FALSE WALL AND PEG CASES .............. 66
5.1 False Wall Cases .............................................. 66

5.1.1 False Wall atx=0cm .................................. 68

5.1.2 False Wall at x = 3.5 cm ................................. 69

5.2 Peg Cases .................................................... 71

5.2.1 Discussion ............................................ 73

Chapter 6. CONCLUSIONS .............................................. 75
APPENDIX A. Notes on the Chemically Reacting LIF Technique ................ 78
A] Chemical Properties of Fluorescein Dye ............................ 78

A.I.I pH Dependence ........................................ 78

A. 1.2 Bleaching ............................................ 79

AZ Product Concentration Measurement .............................. 80
APPENDIX B. Image Processing .......................................... 82
B.1 Free Stream Intensity Elimination ................................. 82
B.2 Camera ‘Offset’ Correction ...................................... 84
APPENDIX C. Effects of Free Stream Speed on Wake Development .............. 87
APPENDIX D. Predicting ES ............................................. 90
D] Standard Method .............................................. 90
D2 Additional Concerns ........................................... 90
APPENDIX E. Line Plots of E( y) ....................................... 92
APPENDIX F. Effects of Three-Dimensionality .............................. 93
LIST OF REFERENCES ................................................. 95

vi

LIST OF TABLES

Table 1. Spanwise data for the unforced, low speed wake. ..................... 53
Table 2. Spanwise data for the low speed wake forced at 2%. .................. 53
Table 3. Spanwise data for the low speed wake forced at 5%. .................. 53
Table 4. Spanwise data for the low speed wake forced at 9%. .................. 54
Table 5. Comparison of Am/A for nonreacting and reacting LIF. ................ 56
Table 6. Spanwise data for the higher speed wake. ........................... 65
Table C. 1. Calculated data for various wake free stream speeds. .................. 88

vii

Figure 1.

Figure 2.

Figure 3.

Figure 4.

Figure 5.
Figure 6.
Figure 7.
Figure 8.

Figure 9.

Figure 10.

Figure 11.

Figure 12.

Figure 13.

Figure 14.

LIST OF FIGURES

(a) Geometry of a shear layer. (b) Geometry of a wake. .............. 98

Examples illustrating the resolution problem of nonreacting LIF. All
three cases would be considered uniformly mixed at 1:1. .............. 98

Simultaneous plan and side views of the highly mixed wake

(Roberts, 1985). .............................................. 99
Downstream evolution of the mixed-fluid fraction (MacKinnon &

Koochesfahani, 1993). ......................................... 99
Schematic of the shear layer facility .............................. 100
CP versus 5,, for a chemically reacting LIF experiment. .............. 100
Schematic of the optical arrangement (not to scale) .................. 101
Setup for (a) streamwise and (b) Spanwise imaging. ................. 101
Graphical explanation of 6,, and 6,. .............................. 102

(a) Sample instantaneous and (b) average chemically reacting LIF
images for the low speed unforced wake at z = 0.0 cm. .............. 103

(a) Sample instantaneous and (b) average chemically reacting LIF
images for the low speed wake forced at 2%. z = 0.0 cm ............. 104

(a) Sample instantaneous and (b) average chemically reacting LIF
images for the low speed wake forced at 5%. z = 0.0 cm ............. 105

(a) Sample instantaneous and (b) average chemically reacting LIF
images for the low speed wake forced at 9%. z = 0.0 cm ............. 106

(a) Sample instantaneous and (b) average chemically reacting LIF
images for the low speed unforced wake at z = +0.8 cm. ............. 107

viii

Figure 15.

Figure 16.

Figure 17.

Figure 18.

Figure 19.

Figure 20.

Figure 21.

Figure 22.

Figure 23.

Figure 24.

Figure 25.

Figure 26.
Figure 27.
Figure 28.
Figure 29.
Figure 30.

Figure 31.

(a) Sample instantaneous and (b) average chemically reacting LIF
images for the low speed wake forced at 2%. z = +0.8 cm. .......... 108
(a) Sample instantaneous and (b) average chemically reacting LIF
images for the low speed wake forced at 5%. z = +0.8 cm. .......... 109

(a) Sample instantaneous and (b) average chemically reacting LIF
images for the low speed wake forced at 9%. z = +0.8 cm. .......... 110

(a) Sample instantaneous and (b) average chemically reacting LIF
images for the low speed unforced wake at z = -0.8 cm ............... l 11

(a) Sample instantaneous and (b) average chemically reacting LIF

images for the low speed wake forced at 2%. z = -0.8 cm. ........... 112
(a) Sample instantaneous and (b) average chemically reacting LIF
images for the low speed wake forced at 5%. z = -O.8 cm. ........... 113
(a) Sample instantaneous and (b) average chemically reacting LIF
images for the low speed wake forced at 9%. z = -O.8 cm. ........... 114
(a) Sample instantaneous and (b) average chemically reacting LIF
images for the low speed unforced wake at z = -2.0 cm. ............. 115
(a) Sample instantaneous and (b) average chemically reacting LIF
images for the low speed wake forced at 2%. z = -2.0 cm. ........... 116
(a) Sample instantaneous and (b) average chemically reacting LIF
images for the low speed wake forced at 5%. z = -2.0 cm. ........... 117
(a) Sample instantaneous and (b) average chemically reacting LIF
images for the low speed wake forced at 9%. z = -2.0 cm. ........... 118
Calculated quantities versus x at z = 0.0 cm. (a) 6,, (b) 6,,, (c) 6,,/6,. . . . 119
Calculated quantities versus x at z = +0.8 cm. (a) 6,, (b) 6,,, (c) 6,,/6,. . . 120

Calculated quantities versus x at z = -O.8 cm. (a) 6,, (b) 6,,, (c) 6,,/6,. . . . 121
Calculated quantities versus x at z = -2.0 cm. (a) 6,, (b) 6,,, (c) 6,,/6,. . . . 122
6,, versus forcing amplitude for various x at midspan (z = 0.0 cm). ..... 123

A6P/Aamplitude versus forcing amplitude for various x at midspan
(z = 0.0 cm) ................................................. 123

ix

Figure 32.

Figure 33.

Figure 34.

Figure 35.

Figure 36.

Figure 37.

Figure 38.

Figure 39.

Figure 40.

Figure 41.

Figure 42.

Figure 43.

Figure 44.

Figure 45.

Mean 6,, versus x and 5% amplitude error boundaries at z = 0.0 cm for
(a) 5% and (b) 9% forcing amplitude. Symbols indicate experimental
data points .................................................. 124

Mean 6,, versus x and 5% amplitude error boundaries at z = +0.8 cm for
(a) 5% and (b) 9% forcing amplitude. Symbols indicate experimental
data points .................................................. 125

Mean 6,. versus x and 5% amplitude error boundaries at z = -0.8 cm for
(a) 5% and (b) 9% forcing amplitude. Symbols indicate experimental
data points .................................................. 126

Mean 6,, versus x and 5% amplitude error boundaries at z = -2.0 cm for
(a) 5% and (b) 9% forcing amplitude. Symbols indicate experimental
data points .................................................. 127

Effect of e scaling on midspan data. (a) unsealed, (b) e s 0.10,
(c) best e. .................................................. 128

Instantaneous spanwise chemically reacting LIF images of the unforced
low speed wake at x = 4 cm. C ,, > 0.10 mapped to white ............. 129

Instantaneous spanwise chemically reacting LIF images of the low speed
wake forced at 2%; x = 4 cm. C : > 0.10 mapped to white. ........... 130

Instantaneous spanwise chemically reacting LIF images of the low speed
wake forced at 5%; x = 4 cm. C ,3 > 0.25 mapped to white. ........... 131

Instantaneous spanwise chemically reacting LIF images of the low speed
wake forced at 9%; x = 4 cm. C :> 0.25 mapped to white. ........... 132

Instantaneous spanwise chemically reacting LIF images of the unforced
low speed wake at x = 8 cm. C : > 0.20 mapped to white ..... , ........ 133

Instantaneous spanwise chemically reacting LIF images of the low speed
wake forced at 2%; x = 8 cm. C 2‘ > 0.20 mapped to white. ........... 134

Instantaneous spanwise chemically reacting LIF images of the low speed
wake forced at 5%; x = 8 cm. C ,3: > 0.40 mapped to white. ........... 135
Instantaneous spanwise chemically reacting LIF images of the low speed

wake forced at 9%; x = 8 cm. C ,3 > 0.40 mapped to white. ........... 136

Instantaneous spanwise chemical];I reacting LIF images of the unforced
low speed wake at x = 12 cm. C P > 0.50 mapped to white ............ 137

Figure 46.

Figure 47.

Figure 48.

Figure 49.

Figure 50.

Figure 51.

Figure 52.

Figure 53.

Figure 54.

Figure 55.

Figure 56.

Figure 57.

Figure 58.

Figure 59.
Figure 60.
Figure 61.

Figure 62.

Instantaneous spanwise chemically reacting LIF images of the low speed

wake forced at 2%; x = 12 cm. C : > 0.50 mapped to white. .......... 138
Instantaneous spanwise chemically reacting LIF images of the low speed
wake forced at 5%; x = 12 cm. c,1“> 0.50 mapped to white. .......... 139
Instantaneous spanwise chemically reacting LIF images of the low speed
wake forced at 9%; x = 12 cm. C : > 0.50 mapped to white. .......... 140
Instantaneous spanwise chemically reacting LIF images of the unforced

low speed wake at x = 16 cm. C P > 0.50 mapped to white ............ 141
Instantaneous spanwise chemically reacting LIF images of the low speed
wake forced at 2%; x = 16 cm. C ,1“ > 0.50 mapped to white. .......... 142
Instantaneous spanwise chemically reacting LIF images of the low speed
wake forced at 5%; x = 16 cm. C : > 0.50 mapped to white. .......... 143
Instantaneous spanwise chemically reacting LIF images of the low speed
wake forced at 9%; = 16 cm. C : > 0.50 mapped to white. .......... 144
Instantaneous spanwise chemically reacting LIF images of the unforced

low speed wake at x = 24 cm. C P > 0.60 mapped to white ............ 145
Instantaneous spanwise chemically reacting LIF images of the low speed
wake forced at 2%; x = 24 cm. C : > 0.60 mapped to white. .......... 146
Instantaneous spanwise chemically reacting LIF images of the low speed
wake forced at 5%; x = 24 cm. C ,1“ > 0.60 mapped to white. .......... 147
Instantaneous spanwise chemically reacting LIF images of the low speed
wake forced at 9%; x = 24 cm. C ,1“ > 0.60 mapped to white. .......... 148
5? distribution of the low speed wake at (a) x = 4 cm, (b) x = 8 cm,

(c)x= 12 cm, (d)x= 16cm, (e)x=24cm. ....................... 149
C ,1“ distribution of the low speed wake at (a) x = 4 cm, (b) x = 8 cm,

(c)x= 12 cm,(d)x= 16cm, (e)x=24cm. ....................... 150
Calculated quantities versus 2 at x = 4 cm. (a) 6,, (b) 6,,, (c) 6,,/6,. ..... 151
Calculated quantities versus 2 at x = 8 cm. (a) 6,, (b) 6,,, (c) 6,,/6,. ..... 152
Calculated quantities versus 2 at x = 12 cm. (a) 6,, (b) 6,,, (c) 6,,/6,. . . . . 153
Calculated quantities versus 2 at x = 16 cm. (a) 6,, (b) 6,,, (c) 6,,/6,. . . . . 154

xi

Figure 63.

Figure 64.

Figure 65.

Figure 66.

Figure 67.

Figure 68.

Figure 69.

Figure 70.

Figure 71.

Figure 72.

Figure 73.

Figure 74.

Figure 75.

Figure 76.

Figure 77.

Figure 78.

Calculated quantities versus 2 at x = 24 cm. (a) 6,, (b) 6,, (c) 6,,/6,. . . . . 155
Normalized product area A,/A, versus x from spanwise data for all

forcing conditions. ........................................... 156
Comparison of mean streamwise data with spanwise data at z = 0.0 cm;

(a) 6,, (b) 6,. ............................................... 157
Comparison of the mixed-fluid fraction from reacting and nonreacting

LIF. ...................................................... 158

(a) Sample instantaneous and (b) average chemically reacting LIF images
for the higher speed unforced wake at z = +0.8 cm. ................. 159

(a) Sample instantaneous and (b) average chemically reacting LIF images
for the higher speed forced wake at z = +0.8 cm. ................... 160

(a) Sample instantaneous and (b) average chemically reacting LIF images
for the higher speed forced wake at z = -0.8 cm ..................... 161

(a) Sample instantaneous and (b) average chemically reacting LIF images
for the higher speed unforced wake at z = -2.0 cm. .................. 162

(a) Sample instantaneous and (b) average chemically reacting LIF images
for the higher speed forced wake at z = -2.0 cm. ................. . . . . 163

Calculated quantities versus x for the unforced higher speed wake.
(a) 6,, (b) 6,, (c) 6,,/6,. ........................................ 164

Calculated quantities versus x for the forced higher speed wake.
(a) 6,, (b) 6,, (c) 6,,/6,. ........................................ 165

Instantaneous spanwise images of the forced higher speed wake at

x= 4 cm. C, > 0.10 mapped to white. .......................... 166
Instantaneous spanwise images of the forced higher speed wake at
x= 8 cm. C, > O. 20 mapped to white. .......................... 166
Instantaneous spanwise images of the forced higher speed wake at
x= 12cm. C,>.050mappedtowhite. ......................... 167
Instantaneous spanwise images of the unforced higher speed wake at

= 16 cm. C, > O. 50 mapped to white. ......................... 167
Instantaneous spanwise images of the forced higher speed wake at
x= 16 cm. C, >0.50 mapped to white. ......................... 168

xii

Figure 79.

Figure 80.

Figure 81.

Figure 82.

Figure 83.

Figure 84.

Figure 85.

Figure 86.

Figure 87.

Figure 88.

Figure 89.

Figure 90.

Figure 91.

Figure 92.

Figure 93.

Figure 94.

Instantaneous spanwise images of the forced higher speed wake at
x = 24 cm. C :3 > 0.60 mapped to white. ......................... 168

CE distribution of the higher speed wake at (a) x = 4 cm, (b) x = 8 cm,
(c)x=12cm,(d)x=16cm,(e)x=24 cm. ....................... 169

Calculated quantities for the higher speed wake. (a) 6,, (b) 6,, (c) 6,,/6,. 170

Schematic of the test section with the false wall mounted at (a) x = 0 cm,
and(b)x=3.5 cm ............................................ 171

LIF images at x = 1.8 cm of the wake with the false wall mounted at
x = 0 cm; (a) 5% forcing, (b) 9% forcing. ......................... 172 .

LIF images at x = 4 cm of the wake with the false wall mounted at
x = 0 cm; (a) 5% forcing, (b) 9% forcing. ......................... 173

LIF images at x = 8 cm of the wake with the false wall mounted at
x = 0 cm; (a) 5% forcing, (b) 9% forcing. ......................... 174

LIF images at x = 16 cm of the wake with the false wall mounted at
x = 0 cm; (a) 5% forcing, (b) 9% forcing. ......................... 175

LIF images at x = 24 cm of the wake with the false wall mounted at
x = 0 cm; (a) 5% forcing, (b) 9% forcing. ......................... 176

LIF images at x = 1.8 cm of the wake with the false wall mounted at
x = 3.5 cm; (a) 5% forcing, (b) 9% forcing. ....................... 177

LIF images at x = 4 cm of the wake with the false wall mounted at
x = 3.5 cm; (a) 5% forcing, (b) 9% forcing. ....................... 178

LIF images at x = 8 cm of the wake with the false wall mounted at
x = 3.5 cm; (a) 5% forcing, (b) 9% forcing. ....................... 179

LIF images at x = 16 cm of the wake with the false wall mounted at
x = 3.5 cm; (a) 5% forcing, (b) 9% forcing. ....................... 180

LIF images at x = 24 cm of the wake with the false wall mounted at
x = 3.5 cm; (a) 5% forcing, (b) 9% forcing. ....................... 181

Illustration of the splitter plate tip with the peg mounted on the upper
surface (not to scale). ......................................... 182

Instantaneous spanwise images of the unforced peg wake at x = 16 cm. . 183

xiii

Figure 95.

Figure 96.

Figure 97.

Figure 98.

Figure 99.

Figure 100.

Figure 101.

Figure 102.

Figure A.1.

Figure A.2.

Figure A.3.

Figure A.4.
Figure A.5.

Figure 3.1.

Figure 3.2.
Figure B.3.
Figure 8.4.

Figure B.5.

Instantaneous spanwise images of the peg wake forced at 2%;
x = 16 cm. ................................................. 184

Instantaneous spanwise images of the peg wake forced at 5%;
x = 16 cm. ................................................. 185

Instantaneous spanwise images of the peg wake forced at 9%;
x = 16 cm. ................................................. 186

Instantaneous spanwise images of the unforced peg wake at x = 24 cm. . 187

Instantaneous spanwise images of the peg wake forced at 2%;
x = 24 cm. ................................................. 188

Instantaneous spanwise images of the peg wake forced at 5%;
x = 24 cm. ................................................. 189

Instantaneous spanwise images of the peg wake forced at 9%;
x = 24 cm. ................................................. 190

Effect of the peg on wake structure. (a) Sample experimental image,
(b) illustration of streamwise vorticity sign and approximate strength. . . 191

Fluorescence intensity versus pH behavior of fluorescein dye. ........ 192

Representative curve of fluorescence intensity versus
base volume fraction .......................................... 192

Effects of dye bleaching in the titration reference chamber for 2 W and

3 W laser power. ............................................ 193
C, (5; £5) for a fast, irreversible reaction. ......................... 193
CP (EB; 55) for a chemically reacting LIF experiment. ................ 194
Schematic of a wake flow and intensity profiles along the dashed line

for raw data and data that has been filtered. ....................... 195
6,(y), z = 0.8 cm, x = 6.0 cm, unforced. .......................... 195
6,(y), z = 0.8 cm, x = 14 cm, 5% forcing. ......................... 196
6,,(y), z = -0.8 cm, x = 21 cm, 9% forcing. ........................ 196
Intensity versus exposure time for the Sony CCD camera. ............ 197

xiv

Figure 8.6.

Figure C.1.

Figure C.2.
Figure C.3.
Figure E.1.
Figure E.2.
Figure E.3.
Figure E.4.

Figure E.5.

Figure F.1.
Figure F2.

Figure F3.

(a) Example 1, (EB) plot for a camera with zero black level offset.
(b) 1, (£3) plot for a camera with negative black level offset. .......... 197

Chemically reacting LIF images of a wake at different free stream
speeds. Uo = (a) 7.17, (b) 8.50, (c) 8.77, (d) 9.94, (e) 11.54,

(I) 11.56 cm/s. .............................................. 198
6,,/6, versus x for various wake free stream speeds. ................. 199
6,,/6, versus x' for various wake free stream speeds .................. 199
C—:( y) profiles at various x and 2 locations; unforced. ............... 200
CE( y) profiles at various x and 2 locations; 2% forcing amplitude. ..... 201
C?( y) profiles at various x and 2 locations; 5% forcing amplitude. ..... 202
C—:-( y) profiles at various x and 2 locations; 9% forcing amplitude. ..... 203

C?( y) profiles for the higher speed wake at various x and 2 locations.
-- forced -------- unforced. ..................................... 204

2“,, versus x from spanwise imaging for 5% and 9% forcing amplitude. 205
V k versus x from spanwise imaging for 5% and 9% forcing amplitude. 205

pea

Model illustrating streamwise vortex evolution (a) low x, (b) high x. . . . 206

XV

Symbol

paogov>_>3>>

’8

P)max

10
*

3|
{-

O.

bk.»

5‘00

LIST OF SYMBOLS

Description (page or Figure of first reference)

test section cross-sectional area (12)

mixed-fluid area (12)

1% area (24)

product area (23)

instantaneous dye concentration (19)

free stream dye concentration (22)

product concentration (18)

product concentration at fluorescence turn on threshold (18)

normalized product concentration (22)

mean normalized product concentration (23)

peg diameter (71)

forcing frequency (6)

wake natural roll up frequency (6)
gravitational acceleration (19)
peg height (71)

pixel intensity (19)

xvi

w

w: >z

:3

corrected pixel intensity (22)

fluorescence intensity (18)

intensity at fluorescence turn on threshold (18)

intensity corresponding to flee stream dye concentration (22)
intensity flom uniform concentration reference image (22)
acid dissociation constant (91)

intensity correction scaling factor (22)

molarity of the acid solution (90)

molarity of the base solution (90)

number of absorbing dye molecules at time t (79)

number of absorbing dye molecules at time t = 0 (79)
number of moles of acid (90)

probability of pure lower stream fluid (12)

probability of pure upper stream fluid (12)

probability of mixed fluid (12)

Reynolds number based on momentum thickness at the splitter
plate tip: UGO/v (6)

Richardson number: Eg—f (19)

pH

0

time (22)

time between fields (41)

total length of time record

wake flee stream velocity (Fig. 1)

shear layer high speed stream velocity (Fig. 1)

xvii

shear layer low speed stream velocity (Fig. 1)

mean streamwise velocity at y (Fig. 1)
three-dimensionality propagation velocity (94)

acid volume (78)

base volume (78)

streamwise coordinate (Fig. l)

nondimensional streamwise coordinate: xflU0 (39)
transverse coordinate (Fig. 1)

spanwise coordinate (Fig. 8)

spanwise location of 6,, maxima (94)

dye absorption coefficient (19)

consecutive rows below flee stream intensity for image
filtering (83)

wake 1% thickness (24)

span-averaged wake 1% thickness (51)

mixed-fluid thickness (24)

product thickness (23)

span-averaged product thickness (51)

product thickness referenced to the upper flee stream (24)
product thickness referenced to the lower flee stream (24)
velocity/flequency correction factor (39)

dye molar absorption coefficient (19)

change in molarity due to reaction (91)

xviii

53
is

momentum thickness (xvii)

initial wake roll up wavelength (39)

kinematic viscosity (xvii)

fluid concentration (81)

base volume flaction (18)

concentration at fluorescence turn on threshold (Fig. 6)
fluid density (19)

density difference between the two fluid streams (19)
mean fluid density (19)

dye bleaching time constant (7 9)

vorticity (3)

xix

Chapter 1

INTRODUCTION

This study is concerned with the mixing field resulting flom forcing a confined wake.
Wakes resulting flom a splitter plate are a special case of a two-stream shear layer, which is
illustrated in Figure 1a. A two-stream shear layer arises when two fluid streams of different
velocity interact downstream of a thin interface—-for example a splitter plate. A wake results

when the two fluid streams have the same velocity, as shown in Figure lb.

Both wakes and shear layers occur in many natural and manmade phenomena. Chemical
lasers and combustors are two important applications. Both applications rely on the mixing
of reacting species; therefore, methods either to enhance or to control molecular mixing in

shear layers and wakes are of paramount importance.

Wakes are inherently unstable and shed vortices flom the splitter plate tip at high enough
Reynolds number. One result of this vorticity is an increase in the length of the passive
scalar interface between the two fluids, thus an increase in chemical reaction and combustion
downstream. For relatively low Reynolds number, though, the vorticity is not strong enough
to elicit strong mixing. Introducing an external perturbation into one or both streams,

however, can introduce stronger vorticity that results in not only a further increase in

2
interface area, but also an amplification of three-dimensionalin in the flow due to vortex
stretching and reorientation. This three-dimensionality is accompanied by an increase in

small scales and a dramatic increase in molecular mixing compared with the unforced wake

(Roberts, 1985; MacKinnon & Koochesfahani, 1993).

Experimenters have used two primary methods to introduce three-dimensionality into the
nominally two-dimensional wake flow. The first method relies on a spanwise periodic
disturbance to generate streamwise vorticity (e.g., Meiburg & Lasheras, 1988; Weygandt &
Mehta, 1995). The second method relies on the interaction of the spanwise vortices with the
flow facility side walls to generate streamwise vorticity (e.g., Roberts, 1985; MacKinnon &
Koochesfahani, 1993). This second method was used for the present study and required
oscillating one approach stream at sufficiently high amplitude to generate strong spanwise

vorticity.

The purpose of this study is to measure the molecular mixing in a wake using an acid-base
reaction between the two flee streams and a pH sensitive dye. More specifically, the present
study investigates how the interposition of a nominally two-dimensional disturbance of
varying amplitude affects the downstream evolution and mixing in the wake. The following
sections give a historical summary of the work to date related to the present study. This
historical research can be divided into three areas: natural shear layers and wakes, forced
shear layers and wakes, and mixing in shear layers and wakes. The final section of Chapter

1 discusses the specific goals of the present study.

1.1 Natural Shear Layers and Wakes

The study of wakes dates back several decades. In 1954 Roshko showed that coherent
vortical structures exist in the wakes of two-dimensional bodies at moderate to high
Reynolds number. These observations were confirmed and expanded by Townsend (1956),
Taneda (1959), and Morkovin (1964). Many of these early investigators noted periodic
signals in hot wire data that suggested some kind of random secondary structure. Grant
(1958) concluded that the turbulent wake, after first being dominated by an essentially two-
dimensional Ka'rman vortex street, began to develop three-dimensionality as counterrotating
vortices inclined to the wake. The onset of three-dimensionality also appeared to be coupled
to turbulence transition. Cimbala et al. (1988), using smoke-wire visualization, also
observed three-dimensionality in the wake of a circular cylinder. Their plan views of a
Re = 150 wake Show three—dimensionality downstream of x/d = 100. Three-dimensionality
seems to occur at lower x/d for higher Reynolds number (Re = 190), where the wake

becomes turbulent, although the investigators never suggest this in their report.

Hayakawa & Hussain (1989) conjectured that three-dimensionality should exist even in the
near field of a turbulent wake. Their experiments, in fact, proved this by finding significant
three-dimensionality in the moderately near field (x/d = 20) of a turbulent (Re = 1.3 X 10")
cylinder wake. These investigators, using X-wire rakes, found concentrations of transverse
vorticity (toy) with strengths and scales comparable to the spanwise vorticity (0),) . Based
on these and earlier observations, they concluded that their data showed strong three-

dimensionality in the wake caused by longitudinal ‘ribs’ formed in the braid regions

connecting the spanwise structures.

Recently, Williamson (1992) has extensively studied wake three-dimensionality. Williamson
and his colleagues initially noted the presence of spot-like ‘vortex dislocations’ that appeared
at random locations in the wake of a circular cylinder. These dislocations were caused by
adjacent spanwise vortex cells shedding at difl‘erent flequency causing a localized
discontinuity in the spanwise structure. To study these structures in a controlled manner,
Williamson triggered the vortex dislocations by placing a ring of larger diameter at a fixed
location on the cylinder. This created a localized difference in shedding frequency, and
effectively triggered symmetric vortex dislocations downstream of the ring. Excellent flow
visualization photographs clearly show the stretching and reorientation of the primary vortex
tubes caused by the dislocation. Williamson concluded that the vortex dislocations are an
essential element in wake transition. Also, the similarity of the vortex dislocations to
structures observed in shear layers (see Browand & Troutt; 1980, 1985) suggests that they

may be a feature common to all shear flows.

Interest in shear layers and wakes produced by splitter plates was spurred by the results of
Brown & Roshko (1971, 1974). Their shadowgraph pictures show the presence of large,
coherent, spanwise structures developing flom the splitter plate tip and convecting
downstream. Dimotakis and Brown (1976) furthered this research by showing that these
structures persist up to high Reynolds number: 3 X 10‘ based on the high speed stream

velocity and downstream distance. Another finding was that these large structures play an

5

important role in the entrainment process. The structures pull initially irrotational fluid into

the shear layer where rapid mixing then occurs.

Konrad (1976), in a gas layer, and Breidenthal (1978, 1981), in a liquid layer, used methods
to investigate the molecular mixing in shear layers. These researchers found a dramatic
increase in mixing at some distance downstream of the splitter plate that seemed coupled to
the presence of a streamwise disturbance. Breidenthal suggested that the streamwise
structures were pairs of counterrotating streamwise vortices. Furthermore, he postulated that
these structures were responsible for increased small-scale motions in the shear layer.
Streamwise structures of this type had previously been observed by Bradshaw ( 1966) and
Miksad (1972). Most of these researchers observed the streamwise structures in plan view.
Bernal (1981), however, was the first to observe the streamwise structures in cross-sectional

view of the mixing layer.

Because the streamwise structures seemed to be coupled to the rapid increase in mixing led
to a more thorough investigation of their origin and characteristics. Lasheras, et a1. (1986)
concluded that the streamwise vortices originated flom upstream disturbances. The
streamwise structures appeared first in the braid regions connecting the cores of the spanwise
structures, then propagated to the cores themselves. Bernal & Roshko (1986) also concluded
that the streamwise vortices originated flom available upstream disturbances. Also, by
studying the onset of the structures under many flow characteristics they found that the

critical Reynolds number for the streamwise structures decreased with the shear layer

6

velocity ratio. In other words, wake flows exhibit more three-dimensionality than shear

layers.

1.2 Forced Shear Layers and Wakes

Some early results flom forcing a shear layer are reported in Ho & Huang (1982) and Oster
& Wygnanski (1982). These researchers showed that forcing the shear layer at its natural
frequency, or a subharrnonic of its natural flequency, would lead to very different growth
characteristics compared with the unforced case. In addition, Oster & Wygnanski showed

that changing the forcing amplitude would also alter the shear layer development.

This work was extended by Roberts (1985) who studied wakes forced at several flequencies
by oscillating one fluid stream. Roberts’ forcing method, it should be pointed out, was
effectively the same as the present study. His chemically reacting laser induced fluorescence
(LIF) photographs of a Re, = 160 wake show some very interesting results. The unforced
flow exhibits a “somewhat tenuous Karman vortex street with mixing occurring on a thin
interface” (Roberts, 1985). Forcing the flow at a frequency close to its natural flequency (in
his study, f = 4.4 Hz; f, = 5 Hz) results in a more organized version of the natural flow. The
interface becomes more tightly rolled-up, suggesting increased vorticity. Forcing at less than
the natural flequency (f = 1.7 Hz) produces a double Karman vortex street: structures form
at a frequency close to the natural flequency and are modulated at the forcing frequency.
The tendency for amalgamation of these structures in a shear layer (see Ho & Huang, 1982)

is not seen in Roberts’ wake photograph. In cases where the forcing flequency is higher than

7

the natural flequency (f = 6.5, 9.8 and 10.75 Hz) a noticeable breakdown in the large
structures is seen. Also evident is a dramatic increase in the amount of product (mixing)
accompanying the breakdown. The highest forcing flequency also shows a new, larger scale
vortex street downstream of the breakdown. Plan views of the wake at this Reynolds number
show the test section side walls are largely responsible for introducing three-dimensionality

into the flow.

In contrast to Roberts, MacKinnon & Koochesfahani (1993) examined the effects of
changing the forcing amplitude. Their experiments investigate a Ree == 100 wake forced at
near its natural flequency (f = f, = 6 Hz). Forcing was achieved by oscillating one fluid
stream using an electromagnetic bellows mechanism—the same mechanism used in the
present work. Using the nonreacting LIF technique they found that increases in the forcing
amplitude led to dramatic changes in both the resulting flow structure and the amount of
molecular mixing achieved. Like Roberts, they also observed that wake/side wall interaction

led to the formation of streamwise vorticity and the resultant increased mixing.

Another, perhaps more direct, method of introducing streamwise vorticity into wakes and
shear layers is perturbing the flow at or near the splitter plate tip. Lasheras & Choi (1988),
studying a shear layer, and Meiburg & Lasheras (1988), studying a wake, both used this type
of forcing. To produce streamwise vorticity they used splitter plates with tips either
corrugated (vertical undulation) or indented (horizontal undulation) at various flequencies

and amplitudes. Both investigations employed a test section 9 cm high x 25 cm wide to

8

intentionally de-emphasize side wall effects. They concluded that in this forcing
configuration, the Kelvin-Helmholtz instability developed first, leading to the familiar nearly
two-dimensional spanwise vortex structures. The secondary streamwise instability
developed from the strain field existing in the braid regions of the primary structures.
Because the spanwise vortex tubes remain essentially two-dimensional during the
development of streamwise vorticity, the investigators concluded that the two instabilities

are nearly independent of one another.

A similar approach was used by Nygaard and Glezer (1991 ). They used a heater mosaic on
the splitter plate surface to impose spanwise disturbances into a shear layer. Their research
shows that the streamwise vortices resulting flom the upstream perturbation are accompanied
by distortions in the mean streamwise velocity field. These distortions result in spanwise-
periodic flow regions where perturbations are amplified and subsequently break down to
small-scale motion. Nygaard and Glezer believe this breakdown leads to mixing transition

farther downstream.

Although investigators have used many methods to force wakes and shear layers two
characteristics seem universal: forcing alters the Structure and development of these flows,
and three-dimensionality (as streamwise vortices) is instrumental in enhancing the mixing

in these flows.

1.3 Mixing in Shear Layers and Wakes

Most of the studies of shear layers and wakes to date have concentrated on the transport
properties of these flows, such as the velocity fields, the vorticity fields, the Reynolds
stresses, etc. A much smaller body of work exists related to the actual mixing properties of
these flows. However, mixing is an important feature of these flows especially in

combustion and chemical reactions.

Koochesfahani (1984) built on the foundation laid out first by Konrad (1976) and
Breidenthal (1978, 1981) using a new technique: laser induced fluorescence. Although the
chemically reacting version of LIF was incorporated on a limited basis, Koochesfahani’s
work primarily employed the passive scalar, nonreacting version of LIF. In nonreacting LIF
one fluid stream is premixed with a fluorescent dye that becomes diluted downstream of the
splitter plate due to mixing with the other fluid stream. A laser is used to excite the dye and
the resulting fluorescence is recorded. The average concentration within a finite sampling
volume, for example that imaged in one pixel, is the ratio of fluorescence at that point to the
flee stream fluorescence. As noted by Breidenthal (1981), the passive scalar technique will
always overestimate mixing if the recording device is unable to resolve the smallest mixing
scales of the flow. Consider, for example, the situation illustrated in Figure 2. Imagine that
each of the three large rectangles represents one imaging pixel. In each case the average
concentration in the three large rectangles is the same, but only one of these cases is
uniformly mixed at 1:1. The nonreacting LIF technique would consider all of the cases in

Figure 2 to be mixed 1:1 (cf. Koochesfahani & Dimotakis, 1985). Despite its limitations,

10

the nonreacting LIF technique remains a quick and simple method for finding the

concentration field of a shear layer or wake.

Roberts (1985) extended the use of LIF to study the mixing in forced shear flows. One of
his test cases, a moderate Reynolds number wake (Ree = 160) forced at 9.8 Hz (about twice
the natural flequency), clearly showed an increase in mixing over the unforced case. Passive
scalar LIF measurements at the wake centerline found a mixing increase of more than an

order of magnitude for the highly mixed case over the unforced flow.

Roberts attributed much of this product increase to the streamwise vorticity generated by
reorientation of the spanwise vortex structures near the side walls of the test section. Figure
3, reproduced flom Roberts (1985), shows this side wall effect very clearly in plan view.
Moving downstream, the regions of the wake exhibiting the most mixing convect away flom
the side walls toward midspan. These highly mixed regions eventually merge at the test
section midspan. Downstream of this location the greatest mixing in the wake is
concentrated in about the central one-third of the test section. A single cross-stream image
of the same flow as in Figure 3 taken at x = 12 cm, although somewhat blurry, shows
evidence of pairs of counterrotating streamwise vortices. Roberts proposed that the no-slip
condition imposed on the flow at the side walls caused the spanwise structures to be tipped
in the walls’ boundary layers. This tipping produces pairs of streamwise vortices with
opposite signs. Mutual induction of these vortices cause them to move away flom the side

walls. The vortex pairs move toward midspan quickly at first, but begin to slow as they

11

approach the vortex pair originating flom the other side wall. Eventually an equilibrium
condition is reached where no further spanwise displacement is observed. The result is a
wake that is highly mixed in the center of the test section, but with virtually no mixing near

the side walls (Roberts, 1985; Roberts & Roshko, 1985).

Intrigued by the highly mixed flow caused by the side wall/vortex interaction, Roberts
conducted an experiment to test the effect of the wall boundary layer thickness on the wake
development. To do this, he placed a false side wall within the test section. A triangular
notch was cut into the false wall so that its leading edge was 3 cm upstream of the splitter
plate tip. With this setup the boundary layer had only developed for 3 cm at the tip of the
splitter plate for the false wall, in contrast to approximately 60 cm for the test section true
walls. Phenolphthalein flow visualization photographs revealed that although the flow was
no longer symmetric, the vortex tipping process still occurred on the false wall. From these
observations Roberts concluded that a no-slip condition alone was sufficient to reorient the

spanwise vorticity, and thus, produce a highly mixed wake flow (Roberts, 1985).

Roberts’ work contains much useful information. Unfortunately, it does not provide much
quantitative data, especially dealing with wake flows. The first investigation concentrated
on quantifying the mixing field of a forced wake is that of MacKinnon and Koochesfahani
(1993). This study uses the nonreacting (passive scalar) LIF technique to investigate the
sensitivity of Ree = 100 wake flows to forcing amplitude. In contrast to Roberts’ work,

MacKinnon and Koochesfahani kept a fixed forcing flequency (the natural wake roll-up

12
flequency f = f;) while varying the forcing amplitude. Cross-stream (spanwise) flow image
sequences were recorded at five distinct downstream x locations. At each location the wake
was forced at three different forcing amplitudes (velocity perturbation RMS amplitude)
corresponding to 1.6%, 5.6%, and 9.1% of the flee stream flow speed. Besides the forced

cases, the unforced wake was investigated for comparison.

Quantities of interest were calculated by statistically evaluating the image sequences. The
primary statistical tool used in nonreacting LIF is the probability density function (pdf) of
the concentration field. Other quantities can be calculated flom the pdf, such as the total
mixed-fluid probability Pm(y, z), and the probabilities of finding fluid flom either the lower
or upper flee streams P0(y, z) and P,(y, 2). Another quantity, the mixed-fluid area Am, can
be found flom the span-averaged pdf. Dividing Arn by the test section cross-sectional area
A results in the flaction of the test-section occupied by mixed fluid. A plot of Am/A as a
function of downstream distance, reproduced flom MacKinnon and Koochesfahani (1993),
is shown in Figure 4. Notice that the value of the mixed-fluid flaction Am/A can be as high
as 41% for the wake forced at 9.1% amplitude at a downstream distance of x = 24 cm. This
value represents more than an order of magnitude increase over the unforced case at the same

location.

The work of MacKinnon and Koochesfahani conclusively proves that forcing a wake,
especially at high amplitude, can drastically increase the amount of molecular mixing

downstream. It does not, however, provide mixing data that can be considered reliable on

13

an absolute basis. Their investigation used the nonreacting LIF method, which always
provides an upper bound on the actual amount of mixing. To get reliable mixing

measurements using LIF it is necessary to use the chemical reaction method.

1.4 Objectives of the Current Work

It is the objective of this report to provide quantitative data on the actual amount of chemical
product in a Ree z 100 wake perturbed at various forcing amplitudes. All product
calculations are based on the reacting LIF technique; therefore, they are not subject to the
inherent limitations of the nonreacting technique. Mixing measurements are calculated flom
image sequences with a laser sheet illuminating the xy-plane (streamwise imaging) and the
yz—plane (spanwise imaging) at several locations. These measurements are the chemically
reacting LIF analogs of the measurements of MacKinnon & Koochesfahani (1993), which
were performed in the same flow facility using the same forcing method. In addition, mixing

measurements are made for a higher Reynolds number wake flow in a similar manner.

In addition to the quantification of the mixing field in the wake, this work provides
significant information regarding the structure of the forced wake in the form of flow images.
Pictures illustrating the forced wake at different amplitudes in both streamwise and spanwise
views are included. Additionally, passive scalar, spanwise flow images are presented for
two extensions to the base flow situation. The first extension uses a thin vertical plate
mounted in the test section downstream of the splitter plate tip. This vertical plate is similar

to Roberts’ ‘false wall.’ The second extension uses a small cylindrical peg mounted on the

14

upper surface of the splitter plate to produce a secondary, three-dimensional disturbance in
the wake. These two extensions are investigated to further examine the effects of forcing,

especially no-slip boundaries, on the structure and mixing of the wake.

Chapter 2

EXPERIMENTAL FACILITY AND INSTRUMENTATION

All of the experiments used for this study were performed in the Turbulent Mixing
Laboratory’s small liquid shear layer facility. Experiments executed in this facility have
previously been reported by Koochesfahani & MacKinnon (1991), MacKinnon &
Koochesfahani (1993), and Katch (1994). The present study is based on results flom both
streamwise and spanwise imaging. This chapter will explain the experimental facility,

forcing mechanism, diagnostics, and data reduction used for these two imaging setups.

2.1 Experimental Facility

All of the experiments were performed in the gravity-driven, liquid, two-stream shear layer
facility illustrated in Figure 5. Fluid for the two streams was pumped flom two 210 L barrels
into overhead, constant head supply tanks placed approximately 2.5 m above the test section.
These overhead tanks were connected to the contraction by flexible hoses. Beyond the
splitter plate tip, the two streams mix in the test section and exit the facility through a hose
discharging into a downstream, constant head dump tank. The acrylic test section used in

this study had inside dimensions of 4 cm (height) X 8 cm (width) X 32 cm (length).

The flow rate through the facility was controlled by three valves: one each along the two

15

16

fluid supply lines upstream of the contraction, and one downstream of the test section. Two
separate wake speeds were investigated: U0 = 10 cm/s and U0 = 20 cm/s. Throughout this
report the nominally 10 cm/s wake and the 20 cm/s wake will be termed the ‘low speed’ and
‘higher speed’ wakes, respectively. The Reynolds number Ree based on the momentum
thickness at the splitter plate tip has been previously determined flom LDV data to be
approximately 100 for this facility for the low speed wake. MacKinnon & Koochesfahani
(1993) found these conditions result in a natural Karman roll-up flequency of about 6 Hz.
The present investigation found the value to be closer to 7 Hz. Uniform, laminar flow was
ensured in both streams by using a series of honeycombs and fine screens upstream of the
contraction. Extreme care was taken in filling the test section to reduce bubbles and air

pockets that could upset the symmetry and flow characteristics of the approach streams.

A titration reference chamber was placed on top of the test section during each experiment.
The chamber was required because, unlike nonreacting LIF, the maximum intensity (If)mam
is not available in the test section during the experiments. The titration reference chamber
is a rectangular glass container with an adjustable cover. Before each experiment the
chamber was filled with 1.5 L of fluid flom the acid/dye supply reservoir. Fluid flom the
base reservoir was then added until the intensity maximum was achieved. During the
titration and the experimental runs the fluid in the reference chamber was continuously
mixed with an electric stirrer to ensure both a uniform mixture and to reduce the effects of

dye photobleaching (see Appendix A).

17
2.2 Forcing Mechanism
Forcing was achieved by an oscillating bellows mechanism positioned in the upper stream
supply line slightly upstream of the honeycombs and screens (see Figure 5). The motion of
the bellows was controlled by a magnetic coil vibrator and amplifier (Vibration Test Systems

VTS 50) that received its input flom a function generator (Hewlett Packard HP3314A).

The bellows input signal for all the low speed wake forced cases was set at a flequency of
6 Hz; the same forcing flequency used by MacKinnon & Koochesfahani (1993). The higher
speedwake was forced at a frequency of 12 Hz. In each case, the input waveform was
symmetric and sinusoidal. The forcing amplitude was varied flom case to case. The low
speed wake was forced with amplitudes corresponding to velocity perturbations of about 2%,
5%, and 9% RMS of the flee stream velocity. These values were found flom previous LDV
data (MacKinnon & Koochesfahani, 1993). A linear variable differential transformer
(LVDT) and a linear velocity transformer (LVT) were available to monitor the bellows’

position and velocity.

2.3 Diagnostics
The principle diagnostic tool used in this study was chemically reacting laser induced
fluorescence. As noted in the introduction, the chemically reacting mode of LIF does not

suffer flom the resolution problems present in the nonreacting LIF technique.

Chemically reacting LIF is an extension of the nonreacting LIF technique described in §1.3.

18

Reacting LIF uses a diffusion-limited. acid-base reaction of the type A + B -+ P between the
two flee streams. One flee stream fluid is premixed with an acid, in this study sulfuric acid
(H2804), and the other stream is premixed with a base: sodium hydroxide (NaOH). A
fluorescent dye is also premixed with the acid. The dye used for this study was disodium
fluorescein. This dye exhibits strong greenish fluorescence when excited by an argon-ion
laser, but only if it is in an alkaline environment (see Appendix A). Because of this, initially
the fluorescence is ‘turned off’ with the dye in the acidic stream. When the two streams mix.
the acid-base reaction is initiated and the pH increases with a corresponding sharp and rapid
increase in the fluorescent intensity. Using this technique the dye becomes a marker for
chemical product. Figure 6 illustrates product concentration C, versus base volume flaction

5,. The fluorescence behaves in a similar fashion leading to the relation

(3 1
P = f (2.1)
(CP)max (12mm:

 

 

Equation 2.1 is the basis for all product calculations. The fact that the product concentration
is proportional to fluorescence is the fimdamental premise used in chemically reacting LIF.
The presence of fluorescence indicates product generation and, thus, molecular mixing.
Because fluorescence is only observed when mixing has occurred there is no overprediction
of mixing flom time-averaged data—which is the primary limitation of the nonreacting LIF

technique. These concepts are discussed more thoroughly in Appendix A.

For this study fluorescein dye was mixed with the acid stream at a concentration of

19

approximately 2 X 10’7 M (moles/L). Koochesfahani (1984) measured the absorption
coefficient a of fluorescein dye to be 0.157 cm" for a dye concentration Cd = 1 x 10" M.
The absorption coefficient scales with the dye concentration as a = 80Cd where e 0 is the dye
molar absorption coefficient. The dye concentration used in this study is a factor of 50 more
dilute than Koochesfahani’s. Thus, an absorption coefficient a = 3.14 x 10'3 cm " is
expected. Attenuation of the fluorescent intensity at a distance y is given by I = Ioe’”. In the
worst case——the entire test section filled with fluorescent dye—the difference in fluorescent
intensity would be about 1.2% between the top and bottom of the test section. Based on

these calculations, attenuation was considered negligible.

Effort was also taken to ensure that the two fluid streams had equal density. Addition of acid
and base to the two fluid streams could sufficiently change the density to the point where
buoyancy effects could no longer be neglected. Buoyancy effects can be evaluated using the

Richardson number, Ri, defined as

 

(2.2)

where Ap is the density difference between the two flee streams, g is the acceleration due to

gravity, 6 is a representative wake dimension, and E = (p1 + p2) / 2 is the mean fluid

density. In this study, sodium sulfate (Na2804) was added to the stream with the density
deficit whenever a sufficient density difference was measured. In each experiment the

densities of the two streams were matched to within a specific gravity of 0.0005. Therefore,

20

in the worst case—the wake filling the entire test section height—the largest possible Ri is
0.02, based on 6 = 4 cm and U0 = 10 cm/s. Koop & Browand (1979) found buoyancy effects

could be neglected for Ri < 0.05 based on the vorticity thickness of a shear layer at x = 1 cm.

A Lexel model Excel 3000 argon-ion laser operating in light mode (i.e., constant power) was
used as the light source. The power requirements varied from experiment to experiment, but
generally values of 3-3.5 W were necessary. The optical setup is illustrated in Figure 7. As
shown, the beam was passed through a converging lens, then through a cylindrical lens to

produce a laser sheet. This configuration produced a sheet that was about 0.5 mm thick.

The streamwise imaging arrangement is shown in Figure 8a. One camera was used to image
the test section and the titration reference chamber simultaneously. For these experiments
a Sony XC-77RR CCD camera was used. The camera has a resolution of 480 (vertical) X
512 (horizontal) pixels, and was operated with an exposure time of 1 ms. Either Nikkor 50
mm f/1.2 or 58 mm f/1.2 lenses were mounted on the camera with an orange filter (number
15) to eliminate scattered laser light. Standard video flaming rate (30 flames/s or 60 fields/s)
was digitized to 8 bits and recorded onto hard disk in real time by an image acquisition
system (Recognition Concepts, Inc. TRAPIX-5500). For each individual case, a total of512
flames (1024 fields) were captured requiring 128 MB of disk space. This corresponds to the
passage of about 100 structures for the low-speed wake, and 200 structures for the higher

speed wake.

21

Figure 8b illustrates the arrangement used for spanwise imaging. As a result of the facility
geometry, an additional camera (not shown in Figure 8b) was needed to image the titration
reference chamber. The Sony XC-77RR was used to image the test section. The same
settings and lenses were used as those for streamwise imaging (except the x = 24 cm cases,
where a 35 mm f/1.7 lens was used). An NEC TI-24A CCD camera was used to photograph
the titration reference chamber. The titration chamber and test section were not imaged
simultaneously in spanwise experiments because of acquisition limitations. Instead, the

titration reference chamber was imaged between experimental runs.

Similar spatial resolutions for both streamwise and spanwise imaging were obtained. The
test section height of 4 cm was imaged onto about 250 vertical pixels. Thus, the entire test
section span of 8 cm could be imaged onto 500 pixels. The corresponding resolution was
160 X 160 pm. For streamwise imaging only 8 cm of the test section streamwise extent
could be imaged at one time. Therefore, three different camera/laser sheet positions were

required to cover the x range of interest (x = 5-24 cm).

2.4 Data Reduction

The LIF technique relies on the fact that the ratio of the product concentration C, at any
location to its value at fluorescence turn on (C,),,,,,, is the same as the ratio of the fluorescent
intensity I, at that location to its maximum value (If)max (Equation 2.1). Because of this, it is
imperative that any nonuniformities in either the laser sheet or the camera (i.e., nonuniform

pixel response or black level ‘offset’) be removed. This was accomplished by first adding

22

each camera’s offset to all nonzero intensities (see Appendix B) and then dividing all images
by a uniform dye concentration reference image. The reference image was generated at the
end of each experiment by running the facility in closed-loop mode until a condition of
uniform dye concentration resulted throughout the test section. In practice, this was
accomplished by letting the facility run continuously for approximately one hour. For the
reference images, the titration reference chamber was emptied and refilled with the uniform
dye concentration fluid. This was acheived, of course, without altering the positions of the

cameras, laser sheet, test section, or reference chamber.

Each flame in an image sequence was then corrected pixel-by-pixel using the formula

CO"

I
= k— (2.3)
Ircf

where 160,, is the corrected pixel intensity, k is a scaling factor (usually selected to produce
peak intensity values close to the original values), I is the original pixel intensity, and I", is
the fluorescent intensity of the same pixel flom the reference image. Intensities in the

titration reference chamber were corrected in the same manner.

The corrected intensities could then be used to calculate the normalized product

concentration C,*, defined as

C I
C:(x,y,z,t) = —P = —f (2.4)
Cdo Ifa

23

where 1,, = (If),,,,,/[1 - ES] flom Figure 6 and Equation 2.1.

The wake’s development is best illustrated by evaluating time-averaged quantities. The

normalized, time-averaged product concentration at each location in the wake is defined as

:dt (2.5)

O'—3‘~i
O

7 l
C , (x, y,z) = ;-
where T is the length of the time record. C ,1“ can be calculated flom experimental image

sequences by taking the corrected average intensity (at each pixel) over the entire sequence

and dividing by the normalization intensity 1,,

It is customary to quantify the amount of mixing product across the wake using the product

thickness 6, (e.g., Breidenthal, 1981; Roberts, 1985) . Product thickness is defined as

41!:

5,.(x,z) = Cid, y, z)dy (2.6)

Integrating 6, across the test section span results in the total amount of product at a

downstream distance x. This quantity is called the product area A, and is defined as

A,(x) = f6,(x,z)dz (2.7)

The product thickness has units of length, but it is not a physical distance. The wake,

24

however, does have a physical width. One way to quantify this width would be to measure
the thickness of the wake flom time exposure or time-averaged images. This method has
been used in the past and is called the visual thickness of a wake or shear layer (Roberts,

1985). Another way to quantify the wake width is to define a 1% thickness 6,. The one

percent thickness is the distance between the points where C ,2.“ has fallen to 1% of its

maximum value on the top and bottom sides of the wake. Other investigators have found

that the 1% thickness and the visual thickness are often nearly equivalent (Koochesfahani,

1984). Figure 9 illustrates the definitions of 6, and 6l graphically.

The wake 1% area A, can be evaluated by integrating 6, across the test section span

9”

A105) 3 Jf 5,(x,z)dz (2.8)

Defining a normalized product thickness 6,/6, is also useful. The normalized product
thickness is thus the product per unit width of the wake, and can be thought of as a measure

of mixing efficiency. Likewise, a normalized product area can be defined as A,/A,.

Figure 4, discussed in §1.3, uses a quantity called the mixed-fluid area Am. In nonreacting
LIF the mixed-fluid thickness 6,,, is calculated by finding the area under the mixed-fluid pdf,
Pm. Am is then found by integrating 6,,, across the test section span. It can also be shown that
6,,, = 6,, + (5,2 where 6 ,, and 6 mare the product thicknesses referenced to the upper and lower

flee streams, respectively (Koochesfahani & MacKinnon, 1991). In the present study, the

25
dye was always carried in the upper stream, thus 6, = 6,,. Finding 6,2 by flipping the upper
and lower streams so that the acid/dye is in the lower stream is possible, but would require
each experiment to be performed twice: once with the dye in the upper stream, and once with
the dye in the lower stream. If it is assumed that the wake flow is symmetric and, thus, has
a unity entrainment ratio—which appears valid at least for highly mixed cases (see

MaeKinnon & Koochesfahani, 1993)—then 6,, = 6,2 and 6,,, = 26, leading to Am = 2A,.

Chapter 3

RESULTS FOR THE LOW SPEED WAKE

This chapter presents visual and quantitative results for the low speed (Uo = 10 cm/s) wake.
This flow was forced at a flequency f = 6 Hz at amplitudes corresponding to approximately
2%, 5%, and 9% RMS of the flee stream speed U0. The unforced wake at these flow

conditions was also studied for comparison.

3.1 Streamwise Results

Streamwise data for the low speed wake were obtained for a total of four complete spanwise
planes: 2 = 0.0 cm (also referred to as ‘midspan’), z = +0.8 cm, 2 = -0.8 cm, and z = -2.0 cm.
To cover the complete streamwise range of interest, x z 5 - 25 cm, three separate laser sheet

positions were required.

3.1.1 Flow Visualization

Figures 10-25 are chemically reacting LIF images of the low speed wake. For each case
sample instantaneous images and images averaged over the entire sequence (1024 fields) are
shown. The streamwise (x) range of each image is indicated below the images. The
transverse range covered in each image is y = -1.8 to 1.8 cm. Note that the images are
presented at actual size. Each page illustrates a single forcing condition and flow in each

image is flom right to left. Colors used in the images are directly related to the normalized

26

27

product concentration through the colormap shown at the bottom of each Figure.

2 = 0.0 cm (midspan)

Figure 10 shows the unforced wake at the test section midspan (z = 0.0 cm). The mixing
interface appears as a thin, sinuous line. Weak spanwise vorticity originating flom the
splitter plate tip (not shown in these images) causes the waviness of the interface. The
interface gradually grows in amplitude and starts to crest in the central image (x = 12-19 cm).
The highest x locations seem to show a ‘bunching’ effect—the waves appear compressed in
the streamwise direction. This may lead to eventual pairing of the structures farther
downstream, similar to the pairing observed in shear layers (e. g., Winant & Browand, 1974).
Overall, the unforced wake has a much more random development than the forced cases to
be described next. Events such as the ‘bunching’ evident in the high x image of Figure 10a
seem to occur randomly, possibly as a result of some external, unintentional disturbance.
Figure 10b, the average image, shows the overall low level of mixing achieved in the
unforced case. The wake increases in width moving downstream, but shows very little

increase in mixing throughout the streamwise range shown.

Figure 11, images of the wake at midspan with 2% forcing, shows the wake has a more
periodic, repeatable structure compared with the unforced case. The gap between x = 11 cm
and x = 14.5 cm is an actual gap in the acquired data. The forcing clearly alters the flow
leading to a more rapid, organized roll-up of the interface. Another interesting feature is

shown in Figure 11b. After initially increasing in width (6,), like the unforced case, the 2%

28

forced case width levels off—and perhaps decreases a little—before increasing again for
higher x. The high x (19 cm s x s 25 cm) image of Figure 11b, in particular, shows definite
streaks of higher intensity fluid. These streaks are caused by the same features of the
structures passing in nearly identical positions throughout the image sequence.
Discontinuities do exist between average images acquired for different laser positions (see,
for example, the center and left image in Figure 11b). Each image contains data flom a
different experimental run, therefore the flow and forcing conditions can be slightly different
from image to image. The effects of various flow parameters on the development of the

wake will be addressed later in this report.

The 5% forcing case is shown in Figure 12. The structures appear more tightly rolled up
than the 2% case and a ‘dot’ of mixed fluid appears in the center of each structure above the
wake centerline. This dot is most likely caused by the C, versus 5, behavior of the dye.
Product concentrations are at their peak for E, near Es (see Figure 6), so wake regions with
a large excess of upper stream fluid appear bright in the flow images. The cores of the
vortices shed flom the upper surface of the splitter plate are probably this type of wake

region.

The roll-up continues as the structures move downstream, and eventually (the high x image
of Figure 12a) the structures take on a teardrop shape. Figure 12b shows a pattern similar
to that seen in Figure 11b: the width of the wake is fairly constant in the range x = 8-15 cm

then begins to increase for x > 15 cm.

29

Figure 13 shows midspan images of the wake at 9% forcing amplitude. The structures
resulting flom this highest forcing condition are characterized by a distinct ‘mushroom’
appearance at low x. In contrast to the lower forcing cases, 9% forcing causes the vortex
cores to be centered very close to the wake centerline. Structures resulting flom vortices
shed flom the top surface of the splitter plate are, like the 5% case, characterized by a dot of
fluid at the vortex cores. In fact, the structures originating flom the top surface of the splitter
plate (-m,) appear more rolled-up than those originating flom the bottom surface (+(o, ).
Moving downstream, the vortex structures in Figure 13a grow and begin to exhibit large
amount of mixed fluid in their cores. This highly mixed fluid is a direct result of three-
dimensionality in the flow. By the time the wake has reached the third image (x = 19 cm)
it has grown to fill the entire height of the test section and the original spanwise vortex
structure is completely absent. The average images, Figure 13b also show this development.
The wake width increases constantly moving downstream. The breakdown to three-

dimensionality observed in the center image of Figure 13a translates to the highly mixed
condition evident in Figure 13b. C_: values are flactionally higher in the upper half of the

test section in the high x image of Figure 13b, although the entire wake is well-mixed on

average.

2 = +0.8 cm
Slightly off-center there are some subtle differences. Figure 14 shows the unforced low
speed wake at z = +0.8 cm. The instantaneous images, Figure 14a, show a pattern very

similar to the midspan images. The average images, Figure 14b, show some differences

30

flom the unforced midspan cases (Figure 10b). For one thing, the wake is clearly narrower
off midspan. Also the average images in Figure 14b are not as continuous across the three
images as the midspan average images were. It has already been mentioned that the unforced
cases seem more random than the forced cases, thus the discontinuities across the images
may stem partly flom the more random nature of the unforced wake. Also, the overall

product concentration levels are so low for the unforced wake that small intensity decreases

can cause C ,1,“ to be mapped to black in the images.

Figure 15 depicts the 2% forced wake at z = +0.8 cm. Its basic structure is much the same
as the midspan case, Figure 11. Once again, the average images show that the wake width
remains fairly constant downstream after initially growing for low x. Another feature of
Figure 14b is the presence of streamwise nonuniformities. Careful examination of the low
x image reveals a herringbone-like pattern. These nonuniformities can be seen in several
other time-averaged images, as well. Briefly, the framing rate of the camera is such that the
image from the eleventh field will be slightly out of phase with the image flom the first
field. After some large number of fields, the entire phase of the wake will have been covered
and the entire process repeats. If the mixing interfaces are very thin, it is possible that the
interfaces may ‘miss’ columns and these columns will appear black in the average images.
The nonuniformities are a direct result of the digitization and are only seen for flows with

little mixing, thus should not greatly affect calculated mixing quantities.

At 5% forcing, shown in Figure 16, there are substantial differences from the midspan case.

31

After developing similarly to the midspan case for low x, the upper (49,) vortex structure
stretches and the uppermost band of the interface begins to jut out over the top of the like-
signed, downstream vortex. The lower (+002) vortex structures appear to continue
downstream largely unchanged. Recall that the midspan wake with 5% forcing exhibited a
teardrop shaped structure at high x—this structure is entirely absent flom the z = +0.8 cm
case. These differences suggest that there is some three-dimensionality in the wake at this

downstream distance.

The 9% forcing case at z = +0.8 cm, shown in Figure 17, is also slightly different flom the
midspan case. The characteristic mushroom shape develops initially, but three-
dimensionality is observed at earlier x than the midspan case. Also, the wake growth rate
seems slightly lower. The wakedoes not fill the entire test section until well into the far left
instantaneous image (x = 22 cm). Also, even though the wake is well mixed at high x, the
streamwise periodicity is still preserved. Although three-dimensionality appears to be
responsible for the increase in mixing, three-dimensionality does not seem to destroy the
primary spanwise structure of the wake. It is likely, judging flom the high x image of Figure
17a, that the streamwise periodic structure is destroyed when the spanwise rollers move into
the boundary layers at the top and bottom of the test section. The average images (Figure
17b) show development much like the midspan case: constant growth and an increase in

mixing until the wake fills the entire test section.

32

z = -0.8 cm

In general, the structure of the wake at z = 08 (Figures 18-21) is very similar to the structure
at z = +0.8 cm. This implies that the wake is symmetric about the z = 0 cm plane. One
notable exception, however, is Figure 20. At low x, the structure of the wake forced at 5%
is similar whether the plane of the laser sheet is at z = 0.0 cm (Figure 12), z = +0.8 cm
(Figure 16), or z = -0.8 cm (Figure 20). The high x images, however, are different. There
are at least two possible explanations for this. Either the wake is slightly asymmetric or the

differences may be the result of case to case flow variations and not the result of wake

asymmetry at all.

z = -2.0 cm

The structure of the wake midway between the nridspan and the wall of the test section is
substantially different florn the structure near the midspan. Many of the differences can be
attributed to the presence of three-dimensionality at smaller x locations. The unforced case,
shown in Figure 22, develops in its usual manner: initially a sinuous line of gradually
increasing amplitude moving downstream. Well downstream, however, an interesting
pattern is observed. Streams of fluorescent product appear to break off the main interface
and protrude well above and below the wake centerline. Although it is possible that these
structures are, in fact, not connected to the rest of the interface, it is more probable that three-
dimensionality has moved a portion of the interface out of the plane of the laser sheet. The
existence of these structures is also seen in the high x average image of Figure 22b. Near the

centerline there is a narrow band of mixed fluid, then bands above and below the centerline

33

that are separated by regions of largely unmixed fluid. There is a large discontinuity
between the mid x and high x images in Figure 22b, but the overall product concentration

levels are so low the discontinuity probably does not significantly affect product thickness

results.

The structure of the wake forced at 2% amplitude, Figure 23, is also similar to the midspan
case for low x. Downstream at x > 18 cm, though, a slightly different structure arises where
the spanwise vortices are ‘stacked.’ Structures of opposing vorticity are clearly above and
below the wake centerline with a region of more highly mixed fluid between them. This
suggests three-dirnensionality-in the wake downstream of x = 18 cm. Despite the differences
seen in the instantaneous images, the average images are similar to the midspan cases,

although there is more product downstream.

The wake at 5% forcing amplitude, Figure 24, shows three-dimensionality for x > 12 cm.
The highly mixed, three-dimensional fluid is initially confined to the vortex cores, but
gradually encompasses most of the wake as it moves downstream. The ‘stacked’ vortex
pattern observed in the 2% case is also seen here. The average images of Figure 24b show

that the wake is much more well-mixed, but narrower, than the corresponding midspan case.

Figure 25, 9% forcing amplitude, shows perhaps the most interesting wake development.
The instantaneous images of Figure 25a show the wake becomes three-dimensional very

early (x z 7 cm) leading to a fairly well-mixed condition by x = 11 cm. Moving

34

downstream, though, the wake narrows slightly and there is a large decrease in product. This
development is especially striking when viewing the image sequence in real time: the wake
appears to ‘unmix’ as it moves downstream. Actually, what is really occurring is the region
of strong mixing is moving out of the laser sheet plane with increasing downstream distance.

Spanwise images will show this phenomenon more clearly.

3.1.2 Calculated Quantities

Figures 26-29 present the results calculated flom the streamwise average images in Figures
10-25. 6, and 6 both consider only the transverse region y = -1.8 to +1.8 cm, thus the
maximum value of 6, is 3.6 cm. Each Figure contains data flom several experimental runs
that are marked identically for clarity. Different symbols indicate different forcing

conditions only.

2 = 0.0 cm (midspan)

Figure 26 presents the calculated data for the low speed wake at midspan. The development
of 6, for all forcing conditions is plotted in Figure 26a. Many of the features in the flow
images are also seen in this plot. The unforced wake is very narrow for low x and its width
increases continuously moving downstream. The wakes forced at 2% and 5% show initial
growth for low x, then each enters a region of virtually fixed 6, before resuming growth at
higher x. The wake forced at 9%, on the other hand, shows no reduction in growth rate. The

wake forced at 9% increases in width until it has filled the entire test section (6, = 3.6 cm).

35

Figure 26b depicts the development of the product thickness 6, for each forcing condition
at z = 0.0 cm. The clear pattern emerging flom this graph is that increasing the forcing
amplitude drastically increases mixing, especially at high x. At x = 24 cm, the wake forced
at 9% has a product thickness a factor of 40 higher than the unforced wake at the same
location. Normalized product thickness curves are shown in Figure 26c. Increases in forcing
amplitude are accompanied by large increases in the amount of normalized product. The 9%
forcing case approaches a value of 6,/6, '2 0.42, close to the value of 0.5 for perfect 1:1

mixing.

Figures 26b and 26c, in particular, Show significant data spread for the 9% forcing condition.
Keep in mind that each individual forcing condition shows data flom at least three
experiments (low, mid, and high laser sheet locations). In some cases there is also a
redundancy in data for a certain laser sheet position. The middle laser sheet location (x z 12-
20 cm), for example, shows data flom three different 9% forcing cases. Each individual case
is easy to recognize on the plots. Because each plot shows data flom many experiments, it
is not surprising that discontinuities and data spread are common in Figures 26-29. Slight
variations in the forcing amplitude are the most probable reason for discrepancies between

data sets and will be discussed further in §3.1.3.

z = +0.8 cm
Figure 27a illustrates 6, versus x for each forcing amplitude at z = +0.8 cm. 6, values are

similar between the midspan and z = +0.8 cm cases. The product thickness (Figure 27b) is

36

also similar except for the 9% forcing case. At 9% forcing 6, is higher than at the midspan
for low x, but its ultimate level is considerably lower. The reduction in 6, at high x also

results in a decrease in normalized product thickness (see Figure 27C).

2 = -0.8 cm

Results for z = -0.8 cm are shown in Figure 28. The wake width 6, is very sinrilar to both
the midspan and z = +0.8 cm cases. The product thickness increases very quickly for 9%
forcing and reaches an ultimate value of about 6, = 1.5 cm at x = 24 cm. This is close to the
value found at midspan. The normalized product thickness reaches an ultimate value of

about 0.41 at x = 24 cm, again close to the nridspan value.

2 = -2.0 cm

As was the case in the flow images, the calculated quantities at z = -2.0 cm are quite different
flom their midspan counterparts. Figure 29a shows the development of 6, versus x. Both
the 2% and 5% forced cases show development similar to the midspan cases. The 9%
forcing case, though, is substantially different. For 9% forcing, 6, is close to its value at the
midspan for x = 5 cm. However, after initially growing in width more quickly than the
nridspan case, the width at z = -2.0 cm reaches a maximum value at x = 12 cm, then begins
to decrease for higher x. Another feature evident in Figure 29a is the large jump in 6, for the
middle laser sheet location of the unforced wake. This discontinuity is also evident in the

corresponding flow image, Figure 22b.

37

The product thickness for the unforced case, shown in Figure 29b, is much more continuous
than 6,. The overall levels of mixing are so low that the increased width apparently does not
greatly affect 6,. The downstream evolution of 6, is quite striking for the 9% amplitude
case. 6, rises very quickly for 9% forcing, but reaches a maximum at x = 10.5 cm, then
begins to fall. The maximum value of the product thickness is 6, = 0.62 cm, only 40% of
the maximum attained at the midspan. In fact, both the 2% and 5% forcing cases eventually
show more product than the 9% forcing case at high x. Normalized product thickness,
Figure 29c, shows similar trends. The cases with lower forcing amplitude have higher 6,./6,

than the 9% amplitude case for high x due to their increased amount of product.

3.1.3 Factors Leading to Variation in Streamwise Data

As noted above, the data in Figures 26-29 often do not collapse onto a single curve. These
figures all contain data measured flom several different experimental runs. Although the
experiments are nominally identical, there are several factors that may vary slightly between
runs. Flow properties that may vary include the flee stream velocities of the two streams,
the forcing frequency, and the forcing amplitude. This section discusses the extent each of

these factors can affect the calculated wake data.

Error in Forcing Amplitude
Figures 26b-29b show that the product thickness of the wake is strongly dependent on the
forcing amplitude. Because of this, a small error in setting the forcing amplitude can

translate into significant variations in the measured 6, Based on the method used for setting

38

the forcing amplitude (monitoring the bellows velocity trace with an oscilloscope), a 5%

error in forcing amplitude is considered reasonable.

Since data are available for the wake at several forcing flequencies, it is possible to estimate
the error introduced by forcing the wake at amplitudes slightly different flom a nominal
value. The first step is to plot 6, versus forcing amplitude for several x locations. One
example is provided in Figure 30. The data points in Figure 30 are the mean values of the
6, data at z = 0.0 cm (Figure 26). The solid lines connecting the points in Figure 30 were
generated using a third order curve fit to the data points. The slope of these lines, shown in
Figure 31, shows the sensitivity of 6, to variation in forcing amplitude. The x = 19 cm
curve, for example, passes through A6,/Aamp = 0.44 at 8.5% forcing amplitude. Thus, a
35% error in setting the forcing amplitude would produce an error in 6, of 0.44 X (8.5 X

0.05) = $0.187 cm. This corresponds to a 16% uncertainty in 6, at this location.

Figures 32-35 are plots of mean 6, (solid lines) versus x showing a :t5% error envelope in
the forcing amplitude (dashed lines) for the cases forced at 5% and 9% amplitude. The error
envelope was determined using data similar to Figure 31. Experimental data sets are shown
by various symbols. The Figures Show that a 15% amplitude error band can account for

most of the variation among the various data sets at the same nominal conditions.

Error in Free Stream Speed and Frequency

The downstream evolution of the product thickness may be expected to scale in terms of a

39

nondirnensional streamwise parameter x* defined as

x = —U_ (3.1)

where A is the forcing wavelength of the wake. With this scaling, changes in forcing
flequency and flee stream velocity result in a perceived expansion or compression of x*. The
total uncertainty contributed by the flee stream velocity and the forcing flequency can be
lumped into a single parameter 6. Thus, x* can be rewritten as x* = xf(1 + e)/U,, to account

for variation flom the nominal values of flequency and flee stream velocity.

The first step in rescaling the data using the e correction factor is to pick one data set as a
‘baseline.’ All other data sets for the same forcing amplitude and 2 locations are then scaled
using different values of 6 until they fit the baseline data set optimally. Data can be forced
to fit very well if no constraints are put on 6. From a practical point of view, though, the
combined speed/flequency error is not expected to be large. The flee stream velocities can
be monitored accurately with the flow meters and the forcing flequency' is dialed into a
function generator. Based on this, a total error of less than 5% is expected (in contrast, the
effects of much larger variations in the flee stream speed are discussed in Appendix C).
Therefore, a more reasonable method of rescaling is to allow 6 to fall within a certain,
constrained, range. Thus, for a i5% total error the difference between the maximum and
minimum values of 6 should differ by no more than 0.10. Figure 36 shows a representative

example of e rescaling. Figure 36a shows 6, versus x* for data with no rescaling. Figure

40

36b shows the same data rescaled such that A6. 5 0.10, and Figure 36c shows the data
rescaled without any constraints on e. The data can be forced to fit very well if no
constraints are placed on 6 (see Figure 36c), but results are nearly as good if e is constrained

to :l:5% (Figure 106b).

In conclusion, some of the variation between data sets can be accounted for by uncertainty
in the forcing flequency and the flee stream velocity. However, both of these parameters can
be set quite accurately during an experiment. Thus, these parameters may account for a little
variation between data sets, but the majority of the variation can be attributed to error in

setting the forcing amplitude.

3.2 Spanwise Results

Streamwise imaging allows observation of the downstream evolution of the wake both
visually and quantitatively. Unfortunately, only a thin slice of the wake span is seen at one
time. Spanwise imaging, on the other hand, allows the entire cross-section of the wake to
be viewed in one experiment. Spanwise viewing allows several vital questions to be
answered. For example, what flaction of the test section is occupied by mixed fluid for each

forcing condition?

Because of this, spanwise data for the low speed wake were acquired at five different x
locations: x = 4, 8, 12, 16, and 24 cm. One difficulty with this imaging setup is light flom

the laser sheet must pass through much more fluid than for streamwise imaging (typically

41

about 30 cm for spanwise imaging compared with 4 cm for streamwise imaging) before
reaching the camera lens. The chemical reaction between the two streams results in index
of reflaction variations, thus possible optical problems, in the test section. For this reason,
data flom streamwise imaging is considered more accurate—especially at low x. However,
spanwise imaging is the only method that allows the entire test section to be imaged
simultaneously, and for this reason spanwise data were collected. Comparisons of

streamwise and spanwise data will be presented later.

3.2.] Flow Visualization

Figures 37-56 are chemically reacting LIF images of the low speed wake. Each Figure
contains a total often images corresponding to one complete forcing cycle of the wake. The
images are separated in time by At = 1/60 s and the sequence proceeds down the left column,
then down the right column. Thus, the first image in the sequence is in the upper left
position and the last image is in the lower right. The range in each image is approximately
2 = -3.9 to +3.9 cm and y = -1.9 to +1.9 cm. The greyscale mapping varies and is indicated
by the colorbar shown in each Figure. The lowest value of C,* that has been mapped to

white is noted in the caption of each Figure.

x = 4 cm
The unforced wake at x = 4 cm is depicted in Figure 37. Like the streamwise images of the
unforced wake at low x, the spanwise views show a single, thin mixing interface between the

two fluid streams. The interface is nearly two dimensional, although there appears to be

42

some slight distortion near the test section side walls. The intensity levels are also very low.

a feature common to many of the spanwise cases at low x.

The 2% forcing case is shown in Figure 38. Once again, the intensity levels are quite low
and it is difficult to discern some of the features of the flow. However, a single interface is
evident in each image. Unlike the unforced case, the interface moves considerably in the y
direction flom image to image. Also, the presence of three-dimensionality is clearly seen
near the edges of the images. Three-dimensionality is even more well defined in Figure 39,
the 5% forcing case. There appear to be several streamwise vortices near both sides of the
images. The middle part of the test section is two-dimensional and exhibits a more
convoluted interface than the unforced and 2% forcing eases. Figure 40, 9% forcing, is
somewhat similar—streamwise vortices near the sidewalls connected by a nearly two-
dirnensional central region. The intensity values in the regions of streamwise vorticity are

considerably higher than in the two-dimensional central region.

x = 8 cm

The unforced wake at x = 8 cm, Figure 41, shows the three-dimensionality first observed at
x = 4 cm more clearly. Like at x = 4 cm, there is a single, nearly two-dimensional interface
over most of the test section span. Near the walls, though, there is definite vertical

displacement of the interface indicating streamwise vorticity.

At 2% forcing amplitude, Figure 42, there is considerable change compared to the same case

43

at x = 4 cm. Although the intensities are still low, there is much more activity in the center
of the test section, also the three-dimensionality near the side walls is more evident. The
major difference in Figure 43, 5% forcing, is the overall intensities are substantially higher
than they were at x = 4 cm indicating more cherrrical product at x = 8 cm than upstream. In

addition, the overall width of the wake has increased.

9% forcing, shown in Figure 44, is the most dramatic illustration of the streamwise vortex
structures yet seen. Two areas of high mixing can be observed in each image, while the
central portion of the test section continues to show the passage of the tightly rolled-up
spanwise structures. Careful examination of the central portion of each image shows the
passage of the braid regions that connect the core regions followed approximately two or

three images later by the passage of the core regions themselves.

x = 12 cm

Figure 45, the unforced wake at x = 12 cm, illustrates the behavior of the wake with
increasing downstream distance. The wake is no longer twocdimensional: there is
considerable variation across the test section span. The unforced wake still shows only a
single mixing interface, though. The 2% forced wake shown in Figure 46 is a more
developed version of the same case at x = 8 cm, as is the case for 5% forcing, Figure 47.
Although the central portions of the images in Figures 46 and 47 are still primarily two-

dimensional, there is some spanwise undulation of the interfaces beginning to appear.

44

A large portion of the wake forced at 9%, shown in Figure 48, is dominated by streamwise
structures. Tightly rolled-up spanwise mixing interfaces are still evident (e.g., the fourth
image in the right-hand column), but at x = 12 cm three-dimensionality is starting to
encroach all the way to the middle of the test section. Despite the presence of the well-mixed
streamwise vortices across most of the structure, there are still areas in the center of the test

section with little or no mixing evident.

x = 16 cm

The structure of the unforced wake at x = 16 cm, Figure 49, is quite similar to the structure
at x = 12 cm. The interface moves more in the transverse direction flom image to image,
however, and one image (bottom right) shows a partial second interface below the primary
interface. This shows that the wake is starting to crest, at least sporadically, at this x
location. Streamwise vorticity near the side walls tends to distort the mixing interface into
a ‘horseshoe’ shape. The 2% and 5% forcing cases, Figures 50 and 51, are similar to the
same cases at x = 12 cm. Three—dimensionality is still primarily confined to near the two
side walls, but there is some indication of increased waviness to the spanwise interfaces in
the center of the test section. The wake width is close to its value at x = 12 cm for these two
forcing cases. This agrees well with the observations flom streamwise imaging (Figures 11-

12).

The 9% forcing amplitude case at x = 16 cm is shown in Figure 52. Streamwise structures

completely dominate the wake structure. The last vestiges of the spanwise vortex structures

45

can be seen as a very faint, thin interface at either the top or bottom of the images, depending
on the location in the forcing cycle. Although the entire center of the test section shows
three-dimensionality at certain times, the streamwise structures originating flom each side
wall can still be discemed—there is still a small area at the very center of the test section that
can contain unmixed fluid. Also, the regions near the test section side walls have very little

mixing.

x = 24 cm

The structure of the unforced wake at x = 24 cm, Figure 53, exhibits up to three mixing
interfaces in the center of the test section. This indicates that at x = 24 cm, the unforced
wake crests fairly consistently. The 2% and 5% forcing cases are presented in Figures 54
and 55. Three-dimensionality, especially in the 5% case, appears to be gradually moving

toward the center of the test section.

Figure 56 depicts the 9% forcing amplitude case at x = 24 cm. At this point, all of the mixed
fluid occupies the central portion of the test section, and fills the test section’s entire vertical
extent. Unlike at x = 16 cm, the streamwise structures flom each side of the test section are
no longer distinguishable. There are, however, large streamwise vortex structures on each
side of the mixed region above the test section centerline (see the last three images). It is
interesting that although the fluid in the center of the test section is very well mixed, the

regions near the test section side walls are virtually devoid of mixed fluid.

46
Average Images
Images averaged over the entire sequence are presented for each spanwise case in Figures

57-58. The images are pseudocolored using the colormap at the bottom of each Figure.

These images are, in fact, plots of 359,2) , thus the Figures show the downstream evolution

of the mean, normalized product concentration for each forcing amplitude. Traditional line

plots showing a subset of the data flom Figures 57-58 are included in Appendix E.

Figure 57 shows 530,2) for the unforced wake (left column) and the wake forced at 2%

(right column). CE(y,z) for the wake forced at 5% (left column) and 9% (right column) are

presented in Figure 58. The general trends for each case are an increase in width and mixing
as the wake moves downstream. The regions of strongest mixing, especially in the 5% and

9% forcing cases, move toward the center of the test section with increasing x.

3.2.2 Calculated Quantities

With the data flom Figures 57-58, it is now possible to study the spanwise variation of
several wake quantities. A subset of the column data flom the images in Figures 57-58 have
been used to generate the plots in Figures 59-63. These Figures show 6,(z), 6,(z), and
6,/6,(z) for the five x locations studied. Like the streamwise cases, only the region y = -l .8
to +1.8 cm was used for the calculations, thus the maximum possible value for 6, is 3.6 cm.
Note: a common range has been used for 6, in Figures 59-63 (0-4 cm). The ranges for 6 ,and

6,./6, vary between Figures to enhance the detail.

47

x = 4 cm

The wake 1% thickness across the test section span for each forcing condition is shown in
Figure 59a. At this low x location the wake tends to have a uniform width across the central
portion of the test section with marked variation near the side walls. This pattern occurs
regardless of the forcing condition. The 5% and 9% forced cases exhibit nearly identical
thicknesses, with the 2% case showing slightly lower 6, and the unforced case showing a
much lower value of 6, . The product thickness is shown in Figure 59b. The unforced wake
and wake subjected to 2% forcing amplitude show nearly identical (low) 6,. The 5% forcing
case is similar in the middle portion of the test section, but exhibits a marked increase in
product thickness near the side walls. The 9% forcing case also shows this increase near the
side walls, but the amount of product is also significantly larger in the center of the test
section compared to the other cases. Note that the regions of increased product correspond
to the areas occupied by streamwise vortices (see Figures 3940). The normalized product
thickness across the span for all forcing cases is shown in Figure 59c. The unforced wake
has the highest values of 6,./6, in the central portion of the test section as a result of its very

low values of 6,. Overall values of 6,./6, are very low for all forcing conditions, though.

2: = 8 cm

Data flom the x = 8 cm laser sheet location are presented in Figure 60. One characteristic
of these data, as well as data farther downstream, is the pronounced symmetry between the
two halves of the test section. Also, both the wake width 6, and product thickness 6, drop

to zero near the test section walls. The areas with the largest amount of mixing are always

48

away flom the side walls at this location and farther downstream.

Figure 60a shows that 6, is similar in the middle of the test section for the three forced cases
with the unforced case showing a thickness roughly a factor of two lower. Although 6, is
still fairly uniform in the central portion of the test section for each case, there is some
evidence of the beginning of spanwise variation. Figure 60b shows the product thickness
across the test section span for each case. 6, tends to be constant in the center of the test
section for all cases, however the 5% and 9% forcing cases both show well defined 6, peaks
on either side of the test section centerline. In both cases the peaks have moved away flom
the test section side walls, echoing the behavior of the streamwise vortices in Figures 4344.
Figure 60c shows the variation in 6,./6, across the test section for each forcing condition.
Overall levels of normalized product have increased for all forced cases compared with the

x = 4 cm data.

x = 12 cm

The salient characteristic in Figure 61a, 6, versus 2 at x = 12 cm, is the increased width of
the wake forced at 9% compared with the 2% and 5% cases. In fact, the 2% and 5% forcing
cases have a width very similar to that observed at x = 8 cm. The unforced wake is still
considerably narrower, but it has doubled in width since x = 8 cm. Product thickness, Figure
61b, has increased for all the forced cases. Also, all three forced cases show clear 6, maxima
on each side of the test section centerline. The product thickness peaks for the 9% forcing

case have moved about 5 mm inward flom their positions at x = 8 cm and, as a consequence,

49

there is no longer a region of nearly constant 6, in the center part of the test section. The
maximum normalized product thickness, Figure 61c, has increased to about 0.26 for the 9%
forcing case, compared to 0.19 at x = 8 cm. Similar increases are also seen for the other

forcing cases.

x = 16 cm

6, for the 2% and 5% forcing cases at x = 16 cm, shown in Figure 62a, continue to remain
at a virtually fixed level in the center of the test section. The unforced case is still growing,
and by x = 16 cm it is nearly as thick as the 2% and 5% forcing cases. The wake forced at
9% amplitude has a width of just above 3.0 cm in the middle of the test section, but its width
falls off quite sharply at about 2 = d: 1.0 cm. The product thickness, too, is concentrated near
the center of the test section (see Figure 62b) for 9% forcing. At x = 16 cm, the 6, maxima
have moved to locations of z z $0.6 cm. A very narrow region of reduced product thickness
is evident at the test section center, which agrees well with the images in Figure 52. The
other forced conditions and the unforced condition show profiles similar to those at lower
x locations, but with increased overall values. The normalized product thicknesses for all
cases are plotted in Figure 62c. An increase in normalized product is evident for each case
compared with locations further upstream. For example, the maximum 6,./6, for 9% forcing

at x = 16 cm is about 0.32, 23% higher than at x = 12 cm.

50

x = 24 cm

The wake 1% thickness across the test section at a position 24 cm downstream of the splitter
plate tip is shown in Figure 63a. 6, for the unforced wake has finally reached a value very
close to the wake forced at 2% in the center portion of the test section. The width of the 2%
forcing case is still about the same as it was at x = 12 cm, but there are regions of increased
width at z = +3.0 cm. The 5% forcing case, on the other hand, is clearly wider than it was
upstream. 9% amplitude forcing results in the wake filling the entire vertical extent of the
test section over the central 2.5 cm of the test section span. The wake thickness drops
sharply outside this region. However, there are shoulders with a width 6, z 1.1 cm located
about 2.3-3.0 cm flom midspan. These shoulders show up well in the mean concentration
field image (Figure 58). The ‘double hump’ profile of the product thickness at lower x is
absent flom the 9% forcing case at x = 24 cm (Figure 63b). The product thickness no longer
decreases at midspan, resulting in a profile with a single peak. The maximum 6, for the 9%
forcing case is nearly 1.5 cm, which compares well with streamwise results. 6, peaks on
either side of midspan are still evident for the lower forcing amplitudes. The product
thickness has increased moving downstream, though. Peak 6, for the 5% amplitude case is
0.61 cm at x = 24 cm compared with 0.39 cm at x = 16 cm. Midspan values of 6,/6, (Figure
63c) are about 0.09, 0.15, and 0.38 for the 2%, 5%, and 9% forcing cases, respectively.
These are all significantly higher than at x = 16 cm, where the values were 0.04, 0.10, and

0.17.

As noted above, the peak values of 6, for the forced wake move away flom the side walls

51

and into the central portion of the test section for increasing x. The regions of the wake with
the most product are also strongly three-dimensional. Examination of Figures 59-63 reveals
that the regions of three-dimensionality move away flom the side walls quickly for low x,
but begin to slow moving downstream. In addition, the regions of three-dimensionality in
the higher forcing amplitude cases convect away flom the side walls faster than the regions

in the lower amplitude cases. Appendix F discusses this phenomenon in greater detail.

Span-Averaged and Integrated data

Figures 59-63 show that 6, and 6, are often strongly dependent on 2. Stating a single value
of 6, at the midspan, for example, does very little to explain the overall behavior of the wake.
There are several ways that the large body of data in Figures 59-63 can be pared down to
elicit a much smaller body of data that quantifies the extent and amount of mixing across the
entire cross-section of the wake. For example, integrating 6, and 6, across the test section
span results in the product area A, and the 1% area A, (see Equations 2.7 and 2.8). A, is a
measure of the total amount of chemical product in the wake at a downstream distance x.
A, is a measure of the total area occupied by mixed fluid at x. From these two quantities a
normalized product area can be defined as A,/A,. This is a measure of the chemical product
per unit area of the wake and can be interpreted as the mixing efficiency. Similarly, A,/A

represents the product area as a flaction of the total test section area.

All of the above quantities represent some type of area. Two useful quantities with units of

length are the span-averaged 1% thickness (6,) and the span-averaged product thickness (6 ,l,

 

52

which are found by dividing A, and A,, by the width of the test section.’

Tables 1-4 summarize these data for each forcing amplitude and the unforced wake. These
Tables represent the fulfillment of one of the primary goals of this investigation: to quantify
the downstream evolution of the mixing field under different forcing conditions. Several
interesting observations can be made flom the data in Tables 1-4. For example, there is 10.4
times more normalized product at x = 24 cm for the wake forced at 9% amplitude than for
the unforced wake. The data for the normalized product area A,/A, at each forcing condition
is plotted in Figure 64. The efficiency of the mixing increases with downstream distance and
forcing amplitude, except for the unforced flow which shows its highest A,/A, at x = 4 cm
due to a very small value of A, (1.53 cmz). The maximum value of normalized product area

is A,/A, = 0.250 for the 9% forced wake at x = 24 cm (see Table 4).

3.3 Comparison of Streamwise and Spanwise Data

A caveat was stated at the beginning of §3.2 stating streamwise imaging is thought to be
slightly more accurate’than spanwise imaging. At this point, data are available flom both of
these imaging configurations. Therefore, these data can be compared to determine the extent

of any differences observed.

 

I The quantities 6, and 6, were calculated using the region y = -1.8 to +1.8 cm and z = -3.6 cm to +3.6
cm, thus all span-averaged and integrated quantities use these limits. The “width of the test section” is
therefore 7.2 cm, not the physical value of 8.0 cm. Likewise, the test section area used for calculations was
A = 25.92 cm2 (3.6 cm X 7.2 cm) not the physical value of 32 cm2 (4 cm X 8 cm).

53

Table 1. Spanwise data for the unforced, low speed wake.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

x (cm) A, (cm’) A, (cmz) (6,) (cm) (6,) (cm) A,,/A A,/A,

4 1.53 0.060 0.213 0.008 0.002 0.039

8 4.30 0.058 0.597 0.008 0.002 0.013

12 8.67 0.110 1.204 0.015 0.004 0.013

16 11.04 0.153 1.533 0.021 0.006 0.014

24 10.92 0.266 1.517 0.037 0.010 0.024
Table 2. Spanwise data for the low speed wake forced at 2%.

x (cm) A, (cm’) A, (cm’) (6,) (cm) (6,) (cm) A,,/A A,/A,

4 7.77 0.058 1.079 0.008 0.002 0.007

8 1 1.24 0.077 1.561 0.011 0.003 0.007

, 12 13.29 0.485 1.846 0.067 0.019 0.036

16 13.88 0.830 1.928 0.115 0.032 0.060

24 14.50 1.817 2.014 0.252 0.070 0.125
Table 3. Spanwise data for the low speed wake forced at 5%.

x (cm) A, (cm’) A, (cr‘n’) (6,) (cm) (6,) (cm) A,,/A A,/A,

4 10.73 0.156 1.490 0.022 0.006 0.015

8 13.00 0.537 1.806 0.075 0.021 0.041

12 14.01 1.337 1.946 0.186 0.052 0.095

16 14.43 1.770 2.004 0.246 0.068 0.123

24 16.04 2.888 2.228 0.401 0.111 0.180

 

54

Table 4. Spanwise data for the low speed wake forced at 9%.

 

 

 

 

 

 

x (cm) A, (cm’) A, (cmz) (6,) (cm) (6,) (cm) A,/A A,,/A,
4 10.50 0.470 1.458 0.065 0.018 0.045

8 13.78 1.341 1.914 0.186 0.052 0.097

12 15.00 2.528 2.083 0.351 0.098 0.169

16 15.99 3.283 2.221 0.456 0.127 0.205

24 16.41 4.102 2.279 0.570 0.158 0.250

 

Data flom a representative spanwise location (2 = 0.0 cm) are shown in Figure 65 for the 5%
and 9% amplitude cases. The sold line marks the mean data flom the streamwise imaging
cases. Differences between the streamwise and spanwise data in Figure 65 are typical of
other spanwise locations. Usually the spanwise data agrees well with the streamwise data.
6, values flom the spanwise data show an approximately equal probability of being above
or below the streamwise data, but stay close to the streamwise data. 6, values for the
spanwise data are also close to the streamwise mean, but are always lower than the
streamwise values. The differences ranges flom 5% (x = 24 cm, 9% forcing) to 22% (x =
16 cm, 9% forcing). However, the extreme discrepancy of 22% is in a region of rapid

growth in 6,.

Interestingly, the assertion that spanwise imaging may be less accurate at low x is not
supported by the data. Figure 65 does not suggest any magnification in the differences

between streamwise and spanwise data for low x.

55

3.4 Comparison with Previous Nonreacting LIF Data

MacKinnon & Koochesfahani (1993) used nonreacting LIF to measure the downstream
evolution of the mixed-fluid flaction A,,, for several forcing amplitudes. The present data can
be compared to previous nonreacting data if the assumption is made that the wake entrains
the same amount of fluid flom the top and bottom streams, leading to the conclusion A,,, =
2A, (see §2.4). This assumption is supported, at least in highly mixed cases, by both Roberts

(1985) and MacKinnon & Koochesfahani (1993).

Figure 66 is a comparison of A,,/A based on nonreacting LIF (MacKinnon & Koochesfahani)
with A,,/A calculated with reacting LIF (the present study) using the assumption A,,, = 2A,.
The unforced and 9% forcing cases are shown in Figure 66; complete data are provided in
Table 5. As expected, the nonreacting technique always overpredicts the amount of mixing.
However, the difference in the two techniques is much greater at low x. For example, A,,/A
at x = 24 cm and 9% forcing is 1.31 times higher for the nonreacting data compared with the
reacting data. At x = 4 cm, the nonreacting data is 6.81 times higher for the same forcing
conditions. This behavior makes sense. The problem with nonreacting LIF is it labels
unmixed fluid as mixed due to resolution limitations (Figure 2). If there is more actual
mixed fluid present in the wake, the nonreacting technique would be expected to mislabel
less fluid. In other words, the nonreacting LIF technique is completely accurate in the limit

that all fluid is actually mixed.

56

The order of magnitude increase in mixing for the forced flow compared with the unforced
flow observed at x = 25 cm (Roberts, 1985) and x = 24 cm (MacKinnon & Koochesfahani,
1993) is also supported in the present data. At x = 24 cm, A,,/A is 15.8 times higher for the

wake forced at 9% than for the unforced wake.

Table 5. Comparison of A,,/A for nonreacting and reacting LIF.

 

nonreacting

 

 

x (cm)

1.8

 

 

 

 

12
16
24

 

 

 

 

 

 

 

 

 

 

 

 

3.5 The Low Speed Wake: A Summary

Results have been presented for both streamwise and spanwise imaging of the low speed
wake. These results comprise a primary goal of this study. The data show that forcing the
wake at high amplitude greatly enhances the resultant mixing downstream. The wake forced
at an amplitude of 9% exhibited more than an order of magnitude increase in product

compared with the unforced case at x = 24 cm.

57

Data measured flom spanwise and streamwise imaging are similar. The product thicknesses,
though, measured flom spanwise viewing are about 10% lower than the same cases measured

flom streamwise viewing. This discrepancy seems independent of streamwise location.

As expected, comparison with previous data measured flom nonreacting LIF shows that the
nonreacting method overpredicts the amount of mixing. The overprediction is more
pronounced for low x, where there is little mixing. Overprediction can be as low as 31% for

the most highly mixed flow studied.

Chapter 4

RESULTS FOR THE HIGHER SPEED WAKE

This section presents visual and quantitative results for a higher speed (U o = 20 cm/s) wake.
This flow was studied to see what differences in wake growth and structure occur at higher
Reynolds number. Higher speed wake experimental data was recorded only when there was
additional fluid remaining in the facility’s supply reservoirs after the low speed runs were
completed. However, there is a substantial data set for the unforced higher speed wake and
the higher speed wake forced at 12 Hz with < 1% RMS amplitude. Note that the observed
natural roll-up frequency for the higher speed wake was about 17 Hz. Thus, f / j; = 0.7 for

the higher speed wake compared with f / j; z 0.9 for the low speed wake.

4.1 Streamwise Results

Streamwise results for the higher speed wake exist for several locations. Experimental runs
were performed for the forced higher speed wake at z = 0.0 cm (high x), z = +0.8 (low, mid,
and high x), z = -0.8 cm (low and mid x), and z = -2.0 cm (low, mid, and high x). Runs for
the unforced higher speed wake were done at z = +0.8 cm (rrrid and high x), and z = -2.0 cm

(mid and high x).

58

59

4.1.] Flow Visualization
Images of the higher speed wake are presented in Figures 67-71. These figures use the same
format as the images of the low speed wake (Figures 10-25), including the color mapping.

Missing images represent gaps in the recorded data.

The unforced higher speed wake (see Figures 67 and 70) is characterized by a narrow,
somewhat unstructured vortex street with periodic regions of more highly mixed fluid. There
is considerably more activity than was observed for the low speed wake (see, for example
Figure 10). Examination of the average images reveals that the unforced higher speed wake,

like the low speed wake, grows slowly as it moves downstream.

The forced higher speed wake exhibits a much different structure flom the unforced wake,
even at the very low forcing amplitude studied (Figures 68, 69, and 70). The wake width is
considerably larger for the forced wake and the structure is more periodic. The forced higher
speed wake closely resembles the low speed wake forced at 2% (see Figure 11), however,
like the unforced higher speed wake there are periodic regions of higher intensity mixed
fluid. A good example of this can be seen in the mid x image in Figure 69. The average
images in Figures 68, 69, and 71 show an increasing wake width moving downstream. The
region of constant wake width seen in the low speed wake forced at 2% is not evident in the

higher speed forced wake.

60

4.1.2 Calculated Quantities

The quantities calculated flom streamwise imaging of the higher speed wake are shown for
the unforced and the forced cases in Figures 72 and 73, respectively. 6, for the unforced
higher speed wake (Figure 72a) increases gradually moving downstream. The wake is
slightly wider at z = -2.0 cm than at z = +0.8 cm. The same basic pattern appears in the
product thickness, Figure 68b. The product thickness of the wake half way between nridspan
and the sidewall (z = -2.0 cm) is about 2.6 mm at x = 24 cm. The value at the same x
location for z = +0.8 cm is 1.7 mm. The normalized product thickness for the unforced

higher speed wake is plotted in Figure 72c.

The 1% thickness for the forced higher speed wake is shown in Figure 73a. 6, is relatively
uniform at all four spanwise (2) laser sheet positions and the wake width increases with
increasing x. The forced wake is considerably thicker than the unforced wake. At x = 24
cm, the forced wake thickness is about 2.8 cm compared to 2.3 cm for the unforced wake (at
z = -2.0 cm). The product thickness for the forced wake, Figure 73b, shows a considerable
spread in the data. At x = 24 cm, the product thickness varies flom 1.8 mm to 3.1 mm due
to the highly three—dimensional behavior of the higher speed wake (which will be seen in the
spanwise images). These values are similar to the product thicknesses for the unforced
higher speed wake. The normalized product thickness for the forced higher speed wake,
Figure 73c, ranges flom 0.065 to 0.110 at x = 24 cm. 6,/6, values for the unforced wake at
this location fall within this range, but in general the unforced higher speed wake has slightly

more normalized product than the forced wake. This is because the unforced wake shows

61

a similar amount of product, but it carries it in a narrower width.

4.2 Spanwise Results
The forced higher speed wake was imaged at five streamwise locations: x = 4, 8, 12, 16, and

24 cm. In addition, the unforced higher speed wake was imaged at x = 16 cm.

4.2.1 Flow Visualization

Chemically reacting LIF images of the forced higher speed wake are presented in Figures 74-
76 and 78-79. The unforced higher speed wake at x = 16 cm is shown in Figure 77. Each
Figure contains a total of five images corresponding to one complete forcing cycle of the
wake. The images are separated in time by At = 1/60 s. The range covered in each image
is approximately 2 = -3.9 cm to +3.9 cm and y = -l .9 cm to +1.9 cm. The greyscale mapping
for each Figure is indicated below the images. The lowest value of C,* that has been mapped

to white is noted in the caption of each Figure.

x = 4 cm
One forcing cycle of the forced higher speed wake at x = 4 cm is shown in Figure 74.
Overall intensities are very low, but a relatively narrow structure can be seen that varies

greatly across the test section span.

x=8cm

The structure of the higher speed wake is more clear in Figure 75. The fluorescent interfaces

62

have a decided corrugated appearance, suggesting a series of streamwise vortices across the
test section span. The regions of highest mixing seem to be near each side wall which is

similar to the pattern observed in the low speed wake.

x = 12 cm
This development is even more evident in Figure 76, the forced higher speed wake at x = 12

cm. A series of structures, apparently streamwise vortices, distort the fluorescent mixing
interface across the test section span. Higher C if values associated with the streamwise

structures near the side walls suggest that the structures near the walls may have originated
flom reorientation of the spanwise vortex structures in the side walls’ boundary layer. If this
is true, the streamwise vortices in the central part of the test section must have originated

flom some other mechanism.

x = 16 cm
The single spanwise unforced higher speed wake case is shown in Figure 77. The width of
the unforced wake is lower than the forced cases. The highest intensities are near the side

walls, similar to the forced wake cases.

The forced higher speed wake at x = 16 cm is shown in Figure 78. The structure of the wake
here is much the same as it was further downstream. The streamwise structures have

radically stretched and distorted the spanwise wake cross-section.

63
x = 24 cm
Further evidence of this is seen in Figure 79, the higher speed forced wake at x = 24 cm. The
wake is highly three-dimensional across the entire test section. Even at this downstream

location, though, the intensities near the test section side walls are higher than in the central

part of the test.

The streamwise vortices often contain a significant amount of well-mixed fluid and may
extend well above or below the primary extent of the wake. The presence of periodic regions
of mixed fluid seen in some of the streamwise images of the higher speed wake (see, for
example, Figure 69) can probably be attributed to these streamwise structures moving into

the plane of the laser sheet.

Average Images

Time-averaged images (C—,;(y,z) images) of the spanwise higher speed wake are presented

in Figure 80. These images have been pseudocolored using the same colormap as the
streamwise images of Figures 67-71. The average images show the development of
streamwise vorticity even at low x. These images, especially at x = 16 and 24 cm, show that
the streamwise structures occur at discrete spanwise positions—they are certainly not
random. A total of seven streamwise structures across the test section span are seen for both
the unforced and forced wake indicating a spanwise spacing of about 1.1 cm. In addition,
these average images show that the streamwise vortices nearest the side walls contain the

largest amount of mixed fluid, similar to what was seen in the instantaneous images. The

64

images in Figure 80 form the basis for the calculated data below.

4.2.2 Calculated Quantities

Conventional line plots of C ,1“ extracted flom Figure 80 at several spanwise (2) locations

and each streamwise location studied are presented in Appendix E. Plots of 6,, 6,, and 6,/6,
measured flom Figure 80 are shown in Figure 81. Figure 81a indicates that the wake width
increases with increasing x. Also, the width shows more variation across the test section
(due to the streamwise structures) at higher x locations. 6, for the unforced wake at x = 16

cm is about 65-70% of its value for the forced wake at the same x location.

The product thickness of the wake, Figure 81b, also increases moving downstream. The
peak product thicknesses are near the test section side walls, which agrees with the
instantaneous flow images. 6, for the unforced wake is, again, slightly lower than the forced
wake at x = 16 cm. The decrease in product thickness is offset by the reduction in wake
thickness resulting in nearly identical normalized product thicknesses for the unforced and
forced wake at x = 16 cm (Figure 81c). Peak values of 6,/6, greater than 0.20 are achieved

by the higher speed forced wake at x = 24 cm.

Span averaged and integrated data
Span averaged and integrated data for the higher speed wake are presented in Table 6. Data
for both the unforced and forced wake are shown at x = 16 cm and are indicated as “(uf)” and

“(f)” in the Table. Substantial growth in both the 1% area and product area are seen with

65

increasing downstream distance. The maximum value of A,/A, is 0.127 at x = 24 cm. This
is similar to the value seen for the low speed wake forced at 2% amplitude at the same

location (A,/A, = 0.125).

In summary, the higher speed wake shows a downstream evolution similar to the low speed
wake. There is a clear increase in both the area occupied by the wake and the amount of
mixed product in the wake. Forcing the wake at small amplitude did not noticeably increase
the amount of normalized product. Regions of streamwise vorticity near the side walls. as
in the low speed wake, exhibited the strongest levels of mixing in the wake. In addition,
however, the higher speed wake showed pronounced three-dimensionality in the central
portion of the test section even at low x. It is suggested that the three-dimensionality in the
center of the test section is the result of a mechanism separate flom the mechanism that

produced the structures nearest the side walls.

Table 6. Spanwise data for the higher speed wake

 

 

 

 

 

 

 

x (cm) A, (cm’) A, (cm’) (6,) (cm) (6,) (cm) A,IA A,/A,
4 9.23 0.059 1.247 0.008 0.002 0.006
8 13.23 0.131 1.838 0.018 0.005 0.010
12 16.07 0.772 2.232 0.107 0.030 0.048
16 (uf) 11.43 0.876 1.588 0.122 0.034 0.077
16(1) 17.57 1.307 2.440 0.182 0.050 0.074
24 19.73 2.504 2.740 0.348 0.097 0.127

 

Chapter 5

RESULTS FOR THE FALSE WALL AND PEG CASES

5.1 False Wall Cases

Chapters 3 and 4 both showed that the regions of the wake showing the most mixing were
dominated by streamwise vortices. It is also clear that much of the streamwise vorticity is
generated flom the side walls of the test section. What is not known is the exact mechanism
responsible for this vorticity generation. It has been postulated in this study, and also in
Roberts (1985), that the streamwise vorticity is generated by the primary spanwise vortex
street being stretched and reoriented—’tipped’— in the side walls’ boundary layers. Another
possibility, though, is that at least some of this vorticity results flom comer vortices
generated in the boundary layers upstream of the splitter plate tip. One way to test Roberts’
vortex tipping hypothesis is to insert a false side wall into the test section at midspan. Comer
vortices are not possible flom the false wall, hence generation of streamwise vorticity flom

the false wall implies reorientation of the spanwise vortices.

Roberts (1985) discusses an experiment preformed in this fashion. A false wall was inserted
into the test section such that its leading edge was at a location approximately 3 cm upstream
of the splitter plate tip. His results suggest that the vortex tipping process still occurs on the

false wall, thus he concluded that a nO-slip boundary condition alone was sufficient to

66

67

generate streamwise vorticity in the wake.

The present investigation is an extension of Roberts’ work. Several experiments were
conducted with a vertically oriented plate (false wall) inserted in the test section. The false
wall was placed such that its leading edge was either flush with the splitter plate tip
(x = 0 cm) or a short distance downstream (x = 3.5 cm). A schematic of this setup is shown
in Figure 82. The false wall was thin, about 0.5 mm, and the leading edge was rounded off
to minimize flow separation. The false wall was positioned at midspan across the entire
transverse extent of the test section. Nonreacting LIF image sequences were acquired at five
x locations: x = 1.8, 4, 8, 16, and 24 cm. At each of these locations the wake was forced at

5% and 9% amplitude.

Images are presented in the same format as previous spanwise data: ten images for each case
corresponding to one complete forcing cycle. Each image shows only one-half of the test
section (i.e., the test section span between the side wall and the false wall). During the
experiments the camera was focused on the half of the test section that produced the best
image quality. The images to follow have been processed so that the false wall is always at
the left edge of each image and the true side wall of the test section is always at the right

edge.

68

5.1.1 False Wall at x = 0 cm

Figures 8387 are images of the wake with the false wall’s leading edge at x = 0 cm. With
the laser sheet at x = 1.8 cm, Figure 90, the wake has already begun to roll-up and shows
streamwise vorticity near the side wall for both 5% and 9% forcing. There is little evidence
of any streamwise vorticity near the false wall. This indicates that at least a portion of the

streamwise vorticity near the side wall is generated upstream of the splitter plate tip.

Figure 84, the wake at x = 4 cm, reveals a much different structure. Streamwise vortices are
well defined at both the side wall and the false wall. The vortical structures nearest the side
wall are larger than those at the false wall, which gives the wake a somewhat slanted
appearance. This appearance is even more pronounced in Figure 85, x = 8 cm. The upper
edge slants downward toward the false wall for both the 5% and 9% forcing amplitude cases.
Figures 86 and 87, images of the wake at x = 16 cm and x = 24 cm, Show evolutions similar
to cases without the false wall. The streamwise vorticity, and as a result mixing, move away
flom the side walls—both the true side wall and the false wall—into the central portion of
the test section. Both the 5% and 9% forced wakes are quite well-mixed at

x = 24 cm.

In conclusion, at least part of the streamwise vorticity near the side wall is generated
upstream of the splitter plate tip. This is based on the earlier development and subsequent
increased size of the streamwise vortex structures near the side wall. However, streamwise

vorticity is generated flom the false wall. This shows that Roberts’ vortex tipping

69

mechanism is at least partially responsible for streamwise vorticity production in the wake.

5.1.2 False Wall at x = 3.5 cm

Images acquired with the false wall’s leading edge at x = 3.5 cm are presented in Figures 88-
92. With this configuration the wake reaches the false wall at a distance equal to about two
forcing wavelengths downstream of the splitter plate tip. Thus, the vortex street has some

time to develop before impacting the plate.

Figure 88 shows images of this wake configuration at x = 1.8 cm. This is upstream of the
false wall, therefore the structure of the wake is the same as if the plate was not there. There
are clear streamwise vortex structures in the far right of each image with a relatively two-
dirnensional structure away flom the true side wall. Several small streamwise disturbances
can be discerned across the span, however. These disturbances must have originated
upstream and become amplified as the wake moved downstream. At x = 4 cm (Figure 89)
the streamwise structures are clearly larger in amplitude. At this laser sheet position, the
wake has just reached the false wall and it is still difficult to recognize any change in the
wake due to the plate. The influence of the false wall is definitely felt at x = 8 cm, Figure
90. Streamwise vortices are evident near the false wall for both 5% and 9% forcing. The
slanted appearance of the wake first seen with the false wall at x = 0 cm also appears for the

two cases in Figure 90.

By x = 16 cm (Figure 91) the wake has developed much more. The streamwise vortices

70

originating flom the side walls have moved farther into the test section center than those
originating flom the false wall resulting in a wake structure skewed toward the center of the
test section (i.e., the left-hand side of the images). This is particularly obvious for 9%
forcing amplitude. Another feature in Figure 91 is the apparent disappearance of the
previously observed streamwise structures. Because the images in Figure 91 are flom the
left half of the test section and the images in Figures 88-90 are flom the right half of the test
section, it is probable that the streamwise structures are the result of upstream disturbances

(bubbles or particles) in the right half of the test section.

Figure 92, x = 24 cm, is also flom the left half of the test section. Both the 5% and 9%
forcing cases show a considerably different structure than the same cases with the false wall
beginning at x = 0 cm. The 9% forcing case is highly mixed over approximately the left two-

thirds of the images, with very little mixing near the true side wall of the test section.

These results suggest that streamwise placement of the false wall does not affect the
development of streamwise vorticity. Although the structure of the wake is different near
the false wall, streamwise vorticity does develop. Based on these results, it appears that any
no-slip boundary (producing a velocity gradient au/az) in the test section will result in the
generation of streamwise vorticity. Although no mixing measurements were evaluated, it
appears that this three-dimensionality may also lead to an enhancement in mixing

downstream.

71

5.2 Peg Cases

The results for the false wall suggest that any no-slip boundary will produce streamwise
vorticity downstream by stretching and reorienting the primary spanwise vorticity. Many
other forms of disturbance could be imposed on the wake both upstream or downstream of
the splitter plate tip. One such disturbance is a three-dimensional body placed within the
boundary layer near the splitter plate tip. This is clearly much different from the false wall.

Would it, too, produce streamwise vorticity downstream?

This question was answered by performing a series of experiments with a small cylindrical
peg (d = 7 m, h = 1 mm) placed on the upper surface of the splitter plate approximately
5 cm upstream of the splitter plate tip (x = -5.0 cm). This configuration is illustrated in
Figure 93. Note that the Reynolds number based on the peg diameter and U0 = 10 cm/s is
about 700, thus it is possible that the peg may shed vortices. Image sequences were acquired
for the unforced flow and the flow forced at 2%, 5%, and 9% RMS of the flee stream speed

U0 = 10 cm/s at streamwise locations x = 16 and 24 cm.

Data collected flom these experiments are not analyzed quantitatively in this report. Because
of this, the experimentally simpler nonreacting LIF technique was used for all the peg cases.
Instantaneous flow images are presented for each forcing condition studied. The format for
these images is the same as that used for the chemically reacting spanwise images: ten

consecutive images separated temporally by At = 1/60 s.

72

x = 16 cm

Instantaneous flow images for the peg wake at x = 16 cm are presented in Figures 94-97.
Figure 94, the unforced wake, shows a wavy interface between the two fluid streams. There
is a noticeable indentation in the center of the test section apparently resulting flom the peg
upstream. Despite this, the unforced peg wake is not dramatically different in structure flom
the unforced wake without the peg (Figure 49). With 2% forcing applied, Figure 95, there
is a definite change in the wake structure. The peg results in the appearance of streamwise
vortices on either side of nridspan both above and below the wake centerline. Similar trends
can be seen in the wake forced at 5%, Figure 96. Again, there are pairs of counterrotating
streamwise vortices resulting flom the peg upstream. In certain cases the influence of the
peg seems to nearly cut the wake in half (see, for example, the fourth image in the leftth
column). Figure 97 shows the structure of the peg wake with 9% forcing. With this forcing
amplitude the peg affects the structure of the wake so radically that it is completely different
flom the same wake without the peg seen in Figure 52. The structure of the peg wake is also
highly asymmetric with respect to the z-axis. Much of the activity appears to be constrained
to the upper half of the test section, although the wake actually impacts the bottom wall of
the test section at certain locations. Another interesting feature is the small counterrotating
streamwise vortex pair that appears ‘hanging’ below the wake at midspan. Notice that the

core of this structure always appears black, indicating pure fluid flom the upper flee stream.

73

x = 24 cm

The unforced peg wake at x = 24 cm is shown in Figure 98. There is significantly more
activity here than at x = 16 em, but the overall structure is still very similar to the same wake
without the peg (see Figure 53). The peg wake forced at 2%, Figure 99, is also similar to the
same wake without the peg, Figure 54. However, the peg clearly alters the structure near
midspan. As at x = 16 cm, the wake forced at 5% (Figure 100) appears nearly severed at
midspan and it is incredibly symmetric. Comparison with the same flow without the peg,
Figure 55, shows that the peg has significantly altered the wake structure. With a 9% forcing
amplitude applied, Figure 101, the peg wake at x = 24 cm becomes very highly mixed. As
was seen with this forcing amplitude upstream, there is significant asymmetry with respect
to the z-axis. The wake impacts the bottom of the test section regularly, but still does not
appear to reach the test section top wall. The small counterrotating vortex pair is still evident
near midspan in several images, but is generally less pronounced than it was further

upstream.

5.2.1 Discussion

Figures 94-101 Show that placing a small three-dimensional disturbance upstream of the
splitter plate tip generates streamwise vorticity downstream. Although these data were nOt
quantitatively anayzed, it appears that the additional streamwise vorticity generated by the

peg may also lead to an enhancement of mixing.

A sample image flom the peg wake is shown in Figure 102a. This image is flom x = 16 cm

74

at 5% forcing amplitude and is the same image shown in the bottom left comer of Figure 96.
The dominant features in the center of the test section are the opposite signed, paired
streamwise vortices both above and below the z-axis. This image is well downstream of both
the splitter plate tip and the peg, so it is difficult to establish the exact origin of the structures
present. It is clear, though, that the streamwise vortices near midspan are a direct result of
the peg. A simplified sketch showing the relative strengths and signs of the streamwise
vortices is given in Figure 102b. An explanation of the mechanism resulting in this structure
is beyond the scope of this report. However, the reader is referred to Lasheras et a1. (1986)
for an excellent discussion on the development and mechanics of streamwise vorticity in
shear flows. Although their paper deals specifically with shear layers, many of the structures

are strikingly similar to those observed in the present work.

In summary, both no-slip boundaries studied (the false wall and the peg) resulted in the
production of streamwise vorticity in a low Reynolds number wake flow. Since streamwise
vorticity is responsible for increased mixing in the wake, inserting a false wall or peg into

the flow may also increase the level of mixing achieved.

Chapter 6

CONCLUSIONS

The structure and mixing of a forced, liquid phase splitter plate wake have been studied with
both streamwise and spanwise imaging using chemically reacting LIF. The low speed wake
(Uo = 10 cm/s) was examined at 2%, 5%, and 9% forcing amplitude in addition to the
unforced case. A higher speed wake (U0 = 20 cm/s) was studied on a more limited basis for
both unforced and low amplitude forcing cases. Additional data were acquired using the
nonreacting LIF technique for two different base flow situations. One of these situations
used a vertically oriented thin plate (false wall) placed at the test section rrridspan. The
second situation used a small cylindrical peg placed on the upper surface of the splitter plate.

The following conclusions are supported by data flom these experiments.

Forcing the low speed wake, especially at high amplitude, at a frequency near the natural
wake roll-up frequency greatly increases scalar mixing downstream. Streamwise vorticity
originating flom the side walls of the test section is the primary mechanism resulting in this
increase in mixing. At x = 24 cm there is about 40 times as much product at midspan for the
wake forced at 9% amplitude as for the unforced wake. The highly mixed wake, however,
is concentrated in the center of the test section with the regions near the side walls showing
almost no mixing. Because of this, the total amount of product integrated across the test

section span for the 9% forcing case is only about 16 times higher than the unforced case.

75

76
Although chemically reacting LIF is expected to produce accurate measurements of mixing
product, several factors can contribute to uncertainty in the data. Uncertainty in forcing
flequency and flee stream velocity contribute to a perceived expansion or compression of the
nondimensionalized streamwise coordinate x*. Also, small errors in the forcing amplitude
cause a shift in 6, (and 6,). These errors can be significant. For example, a 5% error in
setting the forcing amplitude (i.e., forcing the flow at 9.5% instead of 9%) at midspan will
result in a 17% error in the product thickness. Therefore, it is extremely important to set and

monitor the flow parameters as accurately as possible.

Previous results have been reported for the same wake conditions, but using nonreacting LIF.
Based on the current results, nonreacting LIF overpredicted mixing at x = 24 cm with 9%
forcing by 31%. Larger discrepancies were found between the data at low x (x = 4 and 8
cm). At x = 4 cm the wake with 9% forcing exhibited 6.81 times as much mixed fluid using

the nonreacting technique.

The higher speed (U, = 20 cm/s) wake exhibited behavior different flom the low speed wake.
Spanwise images show that the high speed wake, both unforced and with a small amount of
forcing applied, is highly three-dimensional across its entire span. Stronger streamwise
VOl'tices are observed near the side walls similar to those seen in the low speed wake.
However, there are also a series of smaller streamwise vortices in the central portion of the
test section. It is suggested that these smaller vortices are generated flom a mechanism
different flom the vortices nearest the side walls. The low speed wake, conversely, showed

0Illy weak three-dimensionality in the center of the test section (except the highest forcing

77
amplitude) even at high x. Forcing the high speed wake at low amplitude resulted in an
increase in wake width of about 30%, but did not significantly alter the amount of product

across the wake.

Images with the false wall mounted in the test section at x = 0 cm and x = 3.5 cm show that
the reorientation and stretching of the spanwise vortices is responsible for some streamwise
vorticity in the wake. Streamwise vortices are observed near the false wall even at x = 4 cm
with the false wall mounted so that its leading edge touches the splitter plate (x = 0 cm). The
streamwise vortices near the true wall are stronger, though, suggesting that another
mechanism contributes to the generation of streamwise vorticity, as well. When the plate is
mounted with its leading edge at x = 3.5 cm, corresponding to approximately two forcing
wavelengths, the wake proceeds unaffected at midspan until it impacts the false wall.
Downstream of this point streamwise vortices begin to appear near the false wall. Therefore,

production of streamwise vorticity is not dependent on the location of the false wall.

Another source of three-dimensional disturbances was studied by placing a small cylindrical
peg on the upper surface of the splitter plate upstream of the tip. Wake images Show the peg
greatly affects the structure of the wake downstream, especially for higher amplitude forcing.
The peg introduces counterrotating streamwise vortices near the test section midspan. These
vortices increase the overall three-dimensionality of the wake and split the wake into two
symmetric halves. No quantitative measures of mixing were attempted, but it is possible the

streamwise vorticity generated by the peg increases the overall level of mixing in the wake.

APPENDICES

APPENDIX A

Notes on the Chemically Reacting LIF Technique

A.1 Chemical Properties of Fluorescein Dye

A.1. 1 pH Dependence

An important characteristic of fluorescein dye is its pH dependence. F luorescein dye
fluoresces efficiently when excited by an argon-ion laser, but only when it is in an
environment with a pH 2 4. A plot of recorded fluorescence intensity versus solution pH is
shown in Figure A. 1. For low pH the fluorescence is effectively ‘turned off,’ but as the pH
increases above the threshold value (pH z 4) a rapid increase in fluorescence occurs. The
intensity increases with increasing pH until a maximum is reached. This intensity maximum
corresponds to pH 2 8. For pH > 8 the intensity remains virtually constant at the maximum

value.

During the experimental runs the fluorescein dye was premixed with the acidic stream. The
acidic stream had a pH < 4, so initially the fluorescence was turned off. Reaction with the
basic stream resulted in an increase in pH and a corresponding rise in the fluorescent
intensity as shown in Figure A. 1. By titrating the base solution into the acid/dye solution,

the intensity as a function of the base volume flaction EB = vB / (vA + vB) was determined.

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79

A typical plot is shown in Figure A.2. Unlike the intensity-pH behavior, which is a
characteristic of the dye, the intensity-EB curve depends on the relative concentrations of the
acid and base solutions. The intensity is zero for low EB and rises sharply near the intensity
turn on threshold ES. After the peak fluorescent intensity is reached addition of more base
merely dilutes the solution, thus the intensity should decrease linearly to zero for EB
approaching unity. It is desirable to keep the value of ES close to zero so that nearly all the
reaction product fluoresces. For the present study 65 was generally in the range EB = 0.06-
0.07. This required acid and base concentrations of approximately 0.2 mM and 5.8 mM,

respectively.

A.1.2 Bleaching

Excitation of fluorescein dye over time results in a loss of absorption efficiency due to a
process known as photobleaching. Bleached dye molecules do not absorb the laser light
resulting in a perceived reduction in dye concentration. The number of absorbing dye

molecules decays exponentially in time as

(A.1)

where n, is the number of molecules absorbing at time t = 0, n is the ntunber of molecules
absorbing at time t, and 1:, is the bleaching time constant. 1', 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). Koochesfahani (1984) calculated a value

80

of t, z 20 s for his experiments. meaning that only 37% of the dye molecules would still be

absorbing after 20 seconds. Obviously bleaching problems can be 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 t, 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. A plot of measured fluorescent
intensity versus time for the titration reference chamber is shown in Figure A3. A curve fit
to Equation A.1 results in 1:, = 6329 s for 2 W laser power and 4329 s for 3 W laser power.
The maximum laser power used in any experiment was 4 W, so a worst case of t, = 3200
s is expected. The laser was blocked between the experimental runs, so it is estimated that
the reference chamber was exposed to laser light for 300 s at most. Even so, this represents
about a 7% drop in the chamber intensity between the start and finish of the experiment. To
minimize bleaching effects, the intensity of the chamber near the start of each experiment

was used as the normalization constant (If)max.

A.2 Product Concentration Measurement
Chemically reacting LIF analysis is based on a one-step, infinitely fast, reversible reaction
of the type A + B _. P. For this reaction the product concentration C, is dependent on the

two reactant concentrations. If the reactants A and B are carried in two fluid streams at

81

concentrations of C, , and C2,. respectively, the product concentration C, is defined as

C05 for€<€s

C,(€;€S) = {C;,(1 _ E) for 5 > ,5 (A2)

(see Figure A.4) where E is the volume flaction of reactant C2, and ES is the stoichiometric
mixing ratio (Koochesfahani, 1984). In a chemically reacting LIF experiment, with the
acid/dye as one reactant and the base as the other, C, versus 8, is as shown in Figure A5.
The right triangle shape of Figure A5 is similar to Figure A2 and the fluorescence intensity

can be used to estimate the product concentration by using the relation

C” = If (A.3)
(CP)max (If max

 

 

where (C,),,,,,, is the maximum possible product concentration, I, is the fluorescence
intensity, and (If),,,,ax is the maximum fluorescence reached at the fluorescence threshold
(Koochesfahani & Dimotakis, 1986). Note that (11),,ax is available throughout the experiment

in the titration reference chamber.

APPENDIX B

Image Processing

B.1 Free Stream Intensity Elimination

Ideally, the fluorescent intensities in both flee streams will be zero. In reality the upper
stream, carrying the acid and dye, has nonzero intensity. Typically, values of about 5-7
counts were recorded in the upper stream compared with (I, )max z 200. Although these
values are small, they cannot be neglected and measures were taken to effectively ‘filter’ out

the upper flee stream contribution to 6, and 6,.

From the acquired image sequences it is a simple task to identify the upper flee stream
intensity values present. Once the maximum value has been determined, one possible
method to eliminate the flee stream contribution is simply to set all intensities at or below
this value to zero in each image of the sequence. The problem with this method is it may
also eliminate the contribution of some real phenomena. Because of this, an improved
method was used. Each column in each image was read and processed separately by the
computer. If the intensity along the column fell below the flee 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. An example of this process is illustrated in

Figure B. 1. Pure fluid flom each of the two streams is labeled differently in the simulated

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83

streamwise flow image in Figure B. 1. Mixing occurs on the thin interface indicated by the
white band connecting the two fluid streams. Along the column shown by the dashed line
in the flow image, the unprocessed intensity profile will resemble that shown in the plot
labeled “Raw data.” There are sharp intensity spikes at the mixing interface and regions of
low intensity and zero intensity corresponding to fluid flom the upper and lower streams.
respectively. The filtering process will identify the nonzero intensity contribution flom the
upper stream and set all these intensities to zero, as shown in the plot labeled “Filtered data”

in Figure 3.1.

The number of consecutive rows y needed before intensities were set to zero had to be
determined before processing. Setting 1 too low may result in eliminating real features,
while setting 7 too high can allow some flee stream intensity to remain unfiltered. Selecting
the value of y is made even more difficult because different flows are affected differently by
it. Figure 3.2 shows the effect of varying y on an unforced wake at low x. The actual case
shown is at z = 0.8 cm, x = 6 cm. The solid line marked “unprocessed data” shows the
calculated 6, without any processing. Note that this value is about an order of magnitude
higher than the processed values, shown as circles. For this case there is a slight increase in
6, moving flom y = 1 (i.e., all intensities less than or equal to the maximum flee stream
value are set to zero) to y = 2, but further increase in y shows very little change. This is

expected for this case because the mixing interface is a single wavy line (see Figure 14).

Figure 8.3, on the other hand, is very sensitive to y. The case depicted in Figure B3 is the

84

wake at z = 0.8 cm, x = 14 cm forced at 5% (see Figure 16), which is a tightly rolled up
vortex street. For this case the solid line indicating unprocessed data shows about a 40%
increase in 6, compared with y = 2, much closer than the order of magnitude difference seen
in Figure B.2. The reason for the gradual increase in 6, with increased consecutive rows is
coupled to the structure of this flow. Increasing 7 causes the filtering algorithm to miss
regions of upper flee stream fluid between the tightly spaced interfaces. Unfortunately, for
such cases it is difficult to know what value of y is ‘correct.’ Spacing of the interfaces in the
flow images suggest y in the range 2-4 should give satisfactory results in all cases.

Therefore, 7 = 3 was used for each case in this report.

Figure B.4 illustrates the effects of varying y for a highly mixed case. The case illustrated
is at z = -0.8 cm, x = 21 cm and is forced at 9% amplitude (see Figure 21). For the highly
mixed wake the product thickness is almost totally insensitive to changes in y. In fact, the
data in Figure 8.4 suggest that filtering has very little effect whatsoever—the solid line
indicating unprocessed data is at essentially the same 6, as the filtered cases. This suggests
that when the wake is highly mixed the probability of finding pure upper stream fluid is

small.

B.2 Camera ‘Ofl'set’ Correction
An important factor to consider in LIF is the black level offset of the camera used. Consider
the data shown in Figure 8.5, which is a plot of intensity versus exposure time for the Sony

XC-77RR CCD camera used in the present study. Ideally, as exposure time approaches zero

85

(i.e., no light) the recorded intensity should approach zero. Extrapolating the data in Figure
8.5 shows that this camera has an intensity offset of about -5. That is, at zero exposure the
true intensity would be -5 counts. In practice, this translates to the recorded intensity being
zero though there is a finite amount of light exciting the CCD array. The problem this causes
is illustrated in Figure 8.6. If Figure B.6a is the intensity versus EB behavior of a camera
with zero offset, a camera with a finite negative offset would record 1, (5,) as shown in
Figure B.6b. Of course, the negative intensities are recorded by the digitizer as zero, so the
net effect is a perceived lower overall intensity level. This in itself is not a problem, but
errors arise when the intensities are divided by the reference value 1],. If, for example, a
camera with zero offset recorded an intensity value of 50 at some location and the value of
I f, recorded by the same camera was 200, the normalized value at this location would be
50/200 = 0.25. A camera with an offset of -5 would record the intensity at the same location

as 45 with 1,, = 195 producing a normalized value of 45/195 = 0.23, a 7.7% error.

To eliminate the error caused by camera offset, the offset value for the camera used in each
experiment (i.e., 5 for the Sony camera) was added to all nonzero intensities in each image.
The offset was also added to the intensities in the titration reference chamber to correct the
values of (If)max and 9,. Note that the camera offset can also be positive, that is a finite
intensity is recorded even for zero light. This problem can be corrected in the same manner
by subtracting the offset value from each image. In fact, a positive offset may be desirable
because it does not lose any intensity data, which negative offsets do (the portion of the

Curve where If< 0 in Figure B.6b).

86

Another way to eliminate offset problems is altering the camera hardware itself. Many
cameras provide a pedestal level adjustment that changes the black level offset. This

approach, however, was not employed in the present study.

APPENDIX C

Effects of Free Stream Speed on Wake Development

The differences between the development of wakes with flee stream speeds of U, = 10 cm/s
and U, = 20 cm/s have already been discussed. Likewise, how uncertainty in flee stream
speed can stretch or compress the nondimensional streamwise coordinate x* has been
documented. This appendix will discuss exactly how changes in flee stream speed affect

wake development.

A series of experiments was performed with various wake flee stream speeds. All other flow
parameters were fixed throughout the experiments. Six different wake speeds were used
ranging flom U, = 7.17 cm/s to U, = 11.56 cm/s. Each case was forced identically with a
frequency of 6 Hz and an amplitude representing 9% RMS of the flee stream speed for a
U, = 10 cm/s wake. Instantaneous chemically reacting LIF images for each of the six cases
are presented in Figure C1. The streamwise range in each image is x = 7.5 cm to x = 13.0
cm. Free stream speed clearly has a major impact on the development of the wake. At lower
speed the wake is dominated by three-dimensionality (Figure C. l a—C. 1 c), at higher speed the

flow is much less three-dimensional and narrower (Figure C.1d-C. l f).

Data calculated for the six cases are shown in Table Cl 6,, 6,, and 6,/6, are given for each

87

88

wake speed in addition to data normalized by the nominal case U, = 9.94 cm/s. These values
are calculated as 6,‘ = 6,/(6,),,,,,, , 6,‘ = 6,/(6,),,,,,,, and [6,/6,]' = [6,/6,]/[6,/6,],,,m. The
lowest speed wake studied, U, = 7.17 cm/s, had 2.33 times as much normalized product as
the nominal case. In contrast, the highest speed cases, U, = 1 1.54 cm/S and U, = 1 1.56 cm/s,

had only 58% and 71% as much product as the nominal case.

Table C. 1. Calculated data for various wake flee stream speeds.

 

 

 

 

 

 

 

U, (cm/s) U,/U2 5, (cm) 6, (cm) 6,“ 6,’ [6,/6,]’
7.17 1.01 0.549 3.19 2.95 1.27 2.33
8.50 0.96 0.461 2.86 2.47 1.13 2.18
8.77 0.98 0.463 2.85 2.49 1.13 2.20
9.94 1.01 0.186 2.52 mm -----
1 1.54 0.98 0.101 2.34 0.54 0.93 0.58
1 1.56 1.13 0.128 2.42 0.69 0.96 0.71

 

The discrepancy in the two highest speed cases is most likely due to their differences in
velocity ratio U,/U, as shown in the second column of Table C.1. Ideally, a wake is
achieved when U,/U, = 1. With the exception of one case, the velocity ratios are within i4%
0f the ideal wake condition. The last case shown (U, = 11.56 cm/s) has flee stream
Velocities of U, = 12.24 cm/s and U, = 10.88 cm/s resulting in a velocity ratio U ,/U2 = 1.13.
This case is better classified as a shear layer and results in a 23% increase in normalized
Pl‘Oduct thickness compared to a wake with nearly identical flow speed (U, = l 1.54 cm/s).
Interestingly, although the shear layer contains significantly more product than the wake, the

tWC) flows have very similar structures (see Figures C.1e and 1). Besides these two cases the

89

effect of the velocity ratio was not systematically studied. In the experiments in this report

the velocity ratio was kept in the range 0.95-1.05 and significant shear layer effects are not

expected.

A plot of 6,/6, versus x for each case is shown in Figure C2. The variation in the data
between cases is reduced some by nondimensionalizing the x axis as x* = xf/U,, as
illustrated in Figure C.3. Changing the flee stream speed of the wake also changes the

natural roll-up flequency and the forcing amplitude percentage. Thus, the data should not

be expected to collapse perfectly.

In the low speed wake cases reported in the main body of this report the flee stream speeds
were set as accurately as possible. In each experiment these speeds were within 0.05 cm/s

of the nominal value U, = 10 cm/s. Therefore, variations in wake width and product due to

speed differences should be negligible.

APPENDIX D

Predicting E,

It is often convenient to know the approximate value of E, before an experiment begins.
Fortunately, ES occurs very near neutralization (i.e., when the solution pH = 7). Thus, 5, can

be predicted using basic chemistry.

D.1 Standard Method

Consider a fixed volume of acid 0A of molarity M A being titrated with a base of molarity MB.
Initially, the number of moles of acid is given by nA = vAMA. At neutralization n, will be
exactly balanced by the number of moles of base, that is nA - (bk/I3 = 0. Therefore, the
volume of base 0,3 that must be titrated to neutralize the acid is given by vB = nA / M,3 and E,

can be found as E, = v,,/ (v, + 0,).

D.2 Additional Concerns
This method works if the acid has only one hydrogen ion (e. g., HCl). In the present
investigation, HZSO, was used. The second hydrogen ion in sulfuric acid also partially

dissociates in the reaction HSO, ,4 H ’ +S042— .

90

91

The general expression for the dissociation constant for this reaction is

___ 1H’1iSOi‘1
[H5041

 

= 0.012 (D1)

The dissociation equation can be rewritten in terms of the acid molarity M A as

K, = ——E— = 0.012 (13.2)

where C indicates the change in molarity due to the reaction.

Now, let M' = K, / M A. Equation D.2 can be rewritten as

 

1 +,/(1+M‘)2 + 4M‘ -(1+M‘)
2

 

(c + MA) = M, (D3)

The partial dissociation of the second hydrogen ion can now be accounted for by replacing

M A with the expression above for (C + M A) in §D. 1.

APPENDIX E

Line Plots of CEO)

Conventional line plots containing a subset of the data in Figures 57-5 8, the time-averaged

spanwise images, are presented in Figures E. 1-E.4. These plots show the transverse (y) C?

profiles of the wake at each streamwise (x) position studied for five spanwise positions on the

positive 2 side of the test section. Profiles flom the negative 2 side are expected to be similar

due to symmetry.

Similar line plots for the higher speed wake are provided in Figure E.5. Data in these plots

are a subset of the data in Figure 80. C ,3: Profiles at each streamwise position are given for

a total of five spanwise positions. At x = 16 cm, the unforced profiles are shown as dashed

lines.

92

APPENDIX F

Effects of Three-Dimensionality

The ‘tipping’ of spanwise vortices in the side walls’ boundary layers was first noted by
Roberts (1985). He observed regions of three-dimensionality in a forced wake that
resulted in strong mixing. Photographs of the wake in plan view showed that this three-
dirnensionality was the result of the spanwise vortices being stretched and reoriented in
the sheared regions near the test section side walls. A single spanwise image confirmed
that the regions of three-dimensionality were, in fact, pairs of counterrotating streamwise
vortices. Later, Koochesfahani & MacKinnon (1993) studied the effects of this three-
dimensionality more extensively. Like Roberts, they found that the streamwise vortices
tend to convect away from the side walls as the wake moves downstream. In addition,
their images show the three-dimensionality is more pronounced at high amplitude forcing.
This causes the streamwise structures to convect toward the middle of the test section

more quickly.

Similar results were found in the present work. For high amplitude forcing, the regions
of three-dimensionality move away from the side walls very quickly. This can be seen
in both spanwise flow images (Figures 37-56) and in the plots of measured product

thickness (Figures 59b-63b). The peak values of 6, are at the regions of strongest mixing

93

94

and, hence, within the regions of streamwise vorticity. Because of this, the streamwise
evolution of the three-dimensionality can be tracked by plotting the spanwise (2) location
of the 6, maxima z”, as a function of x. This has been done for the wake forced at 5%
and 9% amplitude in Figure F .1. Notice that z,,,,,, hence three-dimensionality, convects
away from the side walls more quickly for the 9% amplitude case. The three-

dimensionality propagation velocity V,,,, can be found using

DU (F.1)

Figure F2 is a plot of V,,,, versus x. The streamwise vortices move away from the side

walls fairly quickly at first, but begin to slow as they move downstream.

This behavior seen in Figures RI and F .2 is exactly what is expected. The three-
dimensionality initially moves away from the side walls due to the velocity induced by
the streamwise vortices, shown in Figure F .3a. As the three-dimensionality moves toward
the center of the test section, though, V,,,, decreases due to the opposite-signed vortices
associated with the other side wall, as illustrated in Figure F.3b. The model shown in
Figure F .3 was originally proposed by Roberts (1985). Thus, the data in Figures El and

F2 quantitatively support Roberts’ hypothesis.

LIST OF REFERENCES

LIST OF REFERENCES

Bernal, L. P. (1981), “The coherent structure of turbulent mixing layers,” Ph.D. Thesis,
California Institute of Technology.

Bernal, L. P. and Roshko, A. (1986), “Streamwise vortex structure in plane mixing
layers,” Journal of Fluid Mechanics, Vol. 170, pp. 499-525.

Bradshaw, P. (1966), “The effect of initial conditions on the development of a flee shear
layer,” Journal of Fluid Mechanics, Vol. 26, pp. 225-236.

Breidenthal, R. E. (1978), “A chemically reacting turbulent shear layer,” Ph.D. Thesis,
California Institute of Technology.

Breidenthal, R. (1981), “Structure in turbulent mixing layers and wakes using a chemical
reaction,” Journal of Fluid Mechanics, Vol. 109, pp. 1-24.

Browand, F. K. and Troutt, T. R. (1980), “A note on the spanwise structure in the two-
dimensional mixing layer,” Journal of Fluid Mechanics, Vol. 97, pp. 771-781.

Browand, F. K. and Troutt, T. R (1985), “The turbulent mixing layer: geometry of large
vortices,” Journal of Fluid Mechanics, Vol. 158, pp. 489-509.

Brown, G. L. and Roshko, A. (1971), “The effect of density difference on the turbulent
mixing layer,” Turbulent Shear Flows; AGARD-CP-93, pp. 1-12.

Brown, G. L. and Roshko, A. (1974), “On density effects and large structure in turbulent
mixing layers,” Journal of Fluid Mechanics, Vol. 64, pp. 775-816.

Cimbala, J. M., Nagib, H. M., and Roshko, A. (1988), “Large structure in the far wakes of
two-dimensional bluff bodies,” Journal of Fluid Mechanics, Vol. 190, pp. 265-298.

Dimotakis, P. E. and Brown, G. L. (1976), “The mixing layer at high Reynolds number;
large-structure dynamics and entrainment,” Journal of Fluid Mechanics, Vol. 78,
pp. 535-560.

Grant, M. L. (1958), “The large eddies of turbulent motion,” Journal of Fluid Mechanics,
Vol. 4, pp. 149-190.

95

96

Hayakawa, M. and Hussain, F. (1989), “Three-dimensionality of organized structures in a
plane turbulent wake,” Journal of Fluid Mechanics, Vol. 206, pp. 375-404.

Ho, C-M. and Huang, L-S. (1982), “Subharmonics and vortex merging in mixing layers,”
Journal of Fluid Mechanics, Vol. 119, pp. 443-473.

Katch, G. J. (1994), “Mixing of species in a two-stream shear layer forced by an
oscillating airfoil,” MS Thesis, Michigan State University.

Konrad, J. H. (1976), “An experimental investigation of mixing in two-dimensional
turbulent shear flows with applications to difl’usion-limited chemical reactions,”
Ph.D. Thesis, California Institute of Technology.

Koochesfahani, M. M. (1984), “Experiments on turbulent mixing and chenrical reactions
in a liquid mixing layer,” PhD. Thesis, California Institute of Technology.

Koochesfahani, M. M. and Dimotakis, P. E. (1985), “Laser-induced fluorescence
measurements of mixed fluid concentration in a liquid plane shear layer,” AIAA
Journal, Vol. 23, pp. 1700-1707.

Koochesfahani, M. M. and Dimotakis, P. E. (1986), “Mixing and chemical reactions in a
turbulent liquid mixing layer,” Journal of Fluid Mechanics, Vol. 170, pp. 83-112.

Koochesfahani, M. M. and MacKinnon, C. G. (1991), “Influence of forcing on the
composition of mixed fluid in a two-stream shear layer,” Physics of Fluids A,
Vol.3, pp. 1135-1142.

Koop, C. G. and Browand, F. K. (1979), “Instability and turbulence in a stratified fluid with
shear,” Journal of Fluid Mechanics, Vol. 93, pp. 135-159.

Lasheras, J. C., Cho, J. S., and Maxworthy, T. (1986), “On the origin and evolution of
streamwise vortical structures in a plane, flee shear layer,” Journal of Fluid
Mechanics, Vol. 172, pp. 231-258.

Lasheras, J. C. and Choi, H. (1988), “Three-dimensional instability of a plane flee shear
layer: an experimental study of the formation and evolution of streamwise vortica,”
Journal of Fluid Mechanics, Vol. 189, pp. 53-86.

MacKinnon, C. G. and Koochesfahani, M. M. (1993), “Three-dimensional structure and
mixing of a forced wake inside a confined channel,” AIAA 93-0658.

Meiburg, E. and Lasheras, J. C. (1988), “Experimental and numerical investigation of the
three-dimensional transition in plane-wakes,” Journal of Fluid Mechanics, Vol.
190, pp. 1-37.

97

Miksad, R. W. (1972), “Experiments on the nonlinear stages of flee-shear-layer
transition,” Journal of Fluid Mechanics, Vol. 56, pp. 695-719.

Morkovin, M. V. (1964), “Flow around circular cylinders—a kaleidoscope of challenging
fluid phenomena,” ASME Symposium on Fully Separated F lows, pp. 102-118.

Nygaard, K. J. and Glezer, A. (1991), “Evolution of streamwise vortices and generation of
small-scale motion in a plane mixing layer,” Journal of Fluid Mechanics, Vol. 231,
pp. 257-301.

Oster, D. and Wygnanski, I. (1982), “The forced mixing layer between parallel streams,”
Journal of Fluid Mechanics, Vol. 123, pp. 91-130.

Roberts, F. A. (1985), “Effects of a periodic disturbance on structure and mixing in
turbulent shear layers and wakes,” Ph.D. Thesis, California Institute of
Technology.

Roberts, F. A. and Roshko, A. (1985), “Effects of periodic forcing on mixing in turbulent
shear layers and wakes,” A1AA-85-05 70.

Roshko, A. (1954), “On the development of turbulent wakes flom vortex streets,” NA CA
Report 1191.

Taneda, S. (1959), “Downstream development of the wakes behind cylinders,” Journal of
the Physical Society of Japan, Vol. 14, pp. 843-848.

Townsend, A. A. (1956), Structure of Turbulent Shear Flow, Cambridge University Press.

Weygandt, J. H. and Mehta, R. D. (1995), “Effects of streamwise vorticity injection on a
plane turbulent wake,” AIAA Journal, Vol. 33, pp. 86-93.

Williamson, C. H. K. (1992), “The natural and forced formation of spot-like ‘vortex
dislocations’ in the transition of a wake,” Journal of Fluid Mechanics, Vol. 243, pp.
393-441.

Winant, C. D. and Browand, F. K. (1974), “Vortex pairing: the mechanism of turbulent
mixing layer growth at moderate Reynolds number,” Journal of Fluid Mechanics,
Vol. 63, pp. 237-255.

98

 

 

 

 

 

 

   

 

 

(a)
U0
My)
0))
U0
Figure 1. (a) Geometry of a shear layer. (b) Geometry of a wake.
mixed 1:1 pure fluid from stream] pure fluid from stream]
interface mixed 1:1 pure fluid from stream 2

pure fluid from stream 2

Figure 2. Examples illustrating the resolution problem of nonreacting LIF. All three
cases would be considered uniformly mixed at 1:1.

 

 

 

 

 

 

05 T I T 1 I 1 1 l l I l I Y T I l 1 I l I V lfi'
r _
r- .
1 9—0 amp=9.l% -
l' V—7 unforced ‘
0.4 r —
0.3 — ‘
S i Z
<= : :
0.2 — —
0.1 _ ‘
E ,, _ M i

0 1 W 1 1 1 l 1 1 ‘1’ 1 1 1 l 1 1 1 1

0 5 IO 15 20 75

x (cm!

Figure 4. Downstream evolution of the mixed-fluid fraction (MacKinnon &
Koochesfahani. 1993).

100

   
  
 
 
 
  

overhead tanks

upstream flow control valves

bellows/shaker assembly
titration reference chamber
test section
n/
’ll
U

 

 

 
 
   
     

supply tanks
\

 

 

 

downstream
g. ’_'\ flow control
valve

 

 

 
 

dump tank

 

 

 

 

Figure 5. Schematic of the shear layer facility.

Cdo
(CP)max - - -

C1453; gs)

 

 

 

EB

Figure 6. CP versus EB for a chemically reacting LIF experiment.

101

     
 
 
  

argon-ion laser beam

converging lens

cylindrical lens

electric stirrer

 

 

 

titration reference chamber I
1:

test section

1........_-_.. ............

Figure 7. Schematic of the optical arrangement (not to scale).

laser sheet

 

 

 

 

 

 

 

 

 

 

 

/
U0/ 2
1/ U0
(a) /
l X
o
T y CCD camera
2
laser sheet
Uo /
1/ U0
(b) "
y
2
CCD Camera

Figure 8. Setup for (a) streamwise and (b) spanwise imaging.

102

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l I

I I

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‘0 3 0.0-II
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I
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E?

Figure 9. Graphical explanation of 6p and 61.

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5? (cm)

5,15,

0.4

0.3

0.2

0.1

 

 

 

 

 

 

T T Y I I T U f ! I I 4
1 ”j (a)
_ . . O 9% Forcing -—
.. (Pd) V 5% Forcing ‘
_ D 2% Forcing A
_ dppod) 0 Unforced q
1 1 1 1 l 1 1 1 l 1 1
0 10 20 30
I T I I I I U I I I I
- 0 9% Forcing | 1
- V 5% Forcing -__-- ”___ __ __d
» U 2% Forcing ~gl0. %
_ 0 Unforced .. 3. _J

 

 

 

 

IIITIIITTIIirTIITTIITlrIr
i'

 

lllJlllllllllllLllllllll

(b)
I r r r 1 I 1 I T I I
' 9% Forcing ;
V 5% Forcing
D 2% Forcing ”0......“-
0 Unforced 0' j.
o
(C)

 

 

 

La)
C

Figure 26. Calculated quantities versus x at z = 0.0 cm. (a) 6,, (b) 5?, (c) 6,,/61.

 

 
 
 
  

 

 

 

 

 

 

   

 

 

4 f I fir I v I I I I I I I I I
0 9% Forcing :
V 5% Forcing _
D 2% Forcing _
0 Unforced
3 —.
"é; .
V 2 _ ,_ l
'0‘ _
I 1
l _ , , _
0 L 1 l
0 30
l V V I I V I V l T l
0 9% Forcing _
l 5 V 5% Forcing , W, . , 7 7, _
' D 2% Forcing
0 Unforced . _
i
E ’ i
0-
0° I
,,_4
l
30
0.5 I I I I I I I I I l I I I T _
r 0 9% Forcing :
E V 5% Forcing —
0.4 D 2% Forcing ’ “ ‘ , ' * *fi
: O Unforced ’. if... :
0.3 h 7.9 W '

I—I — ’ w
«o _ _
‘25. _ ° 0.. I -

_ 0 . s

0-2 r .“ ." ’" i

_ . ‘ v _

0.1 — °. W : .“I ‘

r _

1 a

‘ OI... ‘

0 ..~..

0 10 20 30

Figure 27. Calculated quantities versus x at z = +0.8 cm. (a) 61, (b) 61,, (c) 5pm,.

(3)

(b)

(C)

 

 

 

 

 

 

 

   

 

 

 

4 f ' I [ I j fl I l l I I fir
” W i
3 _ , , , ,. , . , _
E W ‘
v 2 _ 7 . I 7 . 7, 77 —I
0°. » l was I (a)
1 __ , o 7 7 7 9 9% Forcing V _-
, qp, V 5% Forcmg ~
_ O ‘ D 2% Forcing _
s ed) 0 Unforced _
_ 000 I
0 L 1 1 1 l l 1 l 1 l 1 l 1 1
0 10 20 30
I I I I l I l I l I ff T T
0 9% Forcing J
1. V 5% Forcing . __ ,, , ,, g
5 , D 2% Forcing pm ‘
_ 0 Unforced .° _
E
8 (b)
be.
; 0 9% Forcing _
— V 5% Forcing ‘ 1
Q4 — D 2% Forcing pm a
i O Unforced .0 Z
_ . <
, o _
0.3 L“ ' ' .0” ' " F
to" : 0 :
,3. - . _ (C)
0.2 1 7 7 - 7 7 7 7 W7 v 7‘
: ‘ . IVVV -
: ,4" w :
0.1 - 1 M j 5
r ’0’ " vvvv W 4
I. ‘ l i
0 ’ . :3 PW 1011mm . J ‘
0 IO 20 30

Figure 28. Calculated quantities versus x at z = -0.8 cm. (a) 6], (b) 61,, (c) 6,,/61.

 

 

 

 

 

 

   
   

 

 

 

 

 

 

4 *I I l T I fl I fi fi I F *I I T
I 0 9% Forcing «
I V 5% Forcing ~
* U 2% Forcing ~
3 I O Unforced ‘ * “ -, " " r
A l' d
E >- _.
v 2 ~ _I a
“a F 1 1)
1 ~ “
_ lo :
I 000 I
L M i
O 1 1 L 1 l 1 1 1 1 l 1 1 1 1
0 IO 20 30
I I I I I T T fi I T I I T
w 0 9% Forcing 1
1.5 ~ V 5% Forcing a
c D 2% Forcing 1
_ O Unforced -
A I “
g 1.0 r " ‘ —
1 I i (b)
(O "‘ -I
r— ‘ —l
0.5 ~ ~
L :1 AV "" 7 V A
0 __J, Ead‘u’i‘nfi-een: . . 1 . . - 1 A . . 1,
0 10 20 30
0.5 .. I I I I l T I I I l I I I a d
: 0 9% Forcing :
* V 5% Forcing 1
0'4 f C] 2% Forcing :
_ O Unforced 1
0.3 ” :
oo— _ _
1 _ _ (C)
‘0 I-
0.2 f I i
0.1 .. _-
0 i 1 1
0 30

 

Figure 29. Calculated quantities versus x at z = -2.0 cm. (a) 5], (b) 6?, (c) 6p/61.

123

 

 

 

 

 

 

 

 

 

 

 

I I I I I I I I
_ 3* x=25 ' _
'3 x=23
1.5 ' o x=21 .1 7..
’ + x—l9
.. A x
L. ' X
' x
A i- V x
E 1.0 ” U x
3 - 0 x
a.
(o 1-
0.5 —- ~-
I
O
O 2 4 6 8

forcing amplitude (%)

Figure 30. 6], versus forcing amplitude for various x at midspan (z = 0.0 cm).

 

08 I I T I I I I I I I I I I I I I I I I

ASP/Aamplitude (cm)

 

 

 

 

 

 

 

 

 

 

 

forcing amplitude (%)

Figure 31. Aop/Aamplitude versus forcing amplitude for various x at midspan
(z = 0.0 cm).

124

 

 

 

 

 

 

 

 

 

 

0 6 T I I i I I I f I I l I I I
F —1
""""" 5% amp error boundary 7
” _ mean data 1 1
0.4 _ ._
A — —I
E
V _ — a
m (1
co
0.2 " “ ‘
O I J J
0 30
x (cm)
I I I I I I I I I I I I I I
— """"" 5% amp error boundary q
1 5 _ —— mean data a
A
E l.0 *“ 2
3 7 7 (b)
O.
m '- —1
0.5 H " “
0 1 1 u 1 l 1 1 1 1 l 1 1 1 1
0 10 20 30

x (cm)

Figure 32. Mean 5,, versus x and 5% amplitude error boundaries at z = 0.0 cm for (a) 5%
and (b) 9% forcing amplitude. Symbols indicate experimental data points.

125

 

 

 

 

 

 

 

 

 

05 I I I I I I I I I I I I I I
r o
_ """""" 5% amp error boundary 0 1
~ _ meandata . J
0.4 ~ - A- ~
’- '1
A 0.3 — —-
E i I
8 (a)
n. h 5
oo _ a
0.2 — r
I- —I
0.1 F —
0 l l l
0 30
x (cm)
F I I I I I I I I I I I I I
— -1
a """"" 5% amp error boundary - .1
1 5 _ —— mean data m g . fl
’5‘ 1.0 —~ ~
0 _ a
a. (b)
oo I s
0.5 _ r
>— —I
1 I
r- ~
0 L _,l-____1.___
0 30

 

x (cm)

Figure 33. Mean 61, versus x and 5% amplitude error boundaries at z = +0.8 cm for
(a) 5% and (b) 9% forcing amplitude. Symbols indicate experimental data
points.

126

 

 

 

 

 

 

 

 

 

O 6 I I I I I I T I ' I I I I r
""""" 5% amp error boundary 1 o "
e —— mean data ; . a
0.4 I“ _
E h +
o
‘2. ~ ~ (a)
to
0.2 ” _1
F- "I
O 1 1 1 J 4
0 30
x (cm)
I I I l r T I I ‘ I I I r I
""""" 5% amp error boundary d
—— mean data 4
I a
A
E 1.0 m _4
U
h -1
E- 1 (b)
0.5 e , g
I _I
O L l l L
0 3O

 

x (cm)

Figure 34. Mean 5,, versus x and 5% amplitude error boundaries at z = -0.8 cm for
(a) 5% and (b) 9% forcing amplitude. Symbols indicate experimental data
points.

127

 

 

 

 

 

 

 

 

 

 

0.6 I I I I I I I I 77 I I I I I
I """""" 5% amp error boundary , u 4
F — mean data ' I
0.4 F" ‘
A ’— _l
E
x; '- " (a)
00 __ _
0.2 P ‘
0 g l 1 1
0 30
x (cm)
I I— I— I I 1— I I I I I I I 1
0.8 _ -------- 5% amp error boundary ’”
— mean data
0.6 F ' J
E __ A
V (b)
00“ 0.4 — —
0.2 * F
L _i
O 1 1 1 L i 1 1 1 1 l 1 1 1 1
0 10 20 30
x (cm)

Figure 35. Mean 6,, versus x and 5% amplitude error boundaries at z = -2.0 cm for
(a) 5% and (b) 9% forcing amplitude. Symbols indicate experimental data

points.

E 1.0
3
G-
00
0.5
o
1.5
E 1.0
3
D-
00
0.5
0
1.5
E 1.0
3
Q-
00

0.5

 

I— CZIQi «
. [flog 1
_ ,. 93! _
t OI a

1 fig 1 ~ (a)

 

 

 

 

 

 

 

 

 

4 1 1 1 a 1 1 1 l 1 1 1 1 J 1 1 1 1
0 5 IO 15 20
T T I I I I I I I I 7
: v—-~-v 5:0.07 1
[3—---+:1 e=0.07
” ‘- """ 0 £=0.()7 E
I I~~~~~I e=-0.03 «
_ G """" 0 £=0.00(baselinc) .1
1 1 (b)
l l l 1 l l l l 1 L 1 l L 1 J l l l l
O 5 10 IS 20
I I I I T I T I I I I I I I r j I I I
_ V“"V 8:0.09 1
C*—‘-"9 €=0.07
” G- ---- 0 e=0.10 ~05 n
‘ I'" '3 €=-0.05 “ fl. 4
c G """" 0 €=0.()0(basclinc) ‘53 q

‘ (C)

 

 

 

x* = xf(1+e)/UO

Figure 36. Effect of e scaling on midspan data. (a) unsealed, (b) A6 3 0.10, (c) best e.

 

Figure 37. Instantaneous spanwise chemically reacting LIF images of the unforced low
speed wake at x = 4 cm. C .3 > 0.10 mapped to white.

_n

3

 

O n
‘5‘. 'l"' o

C

Figure 38. Instantaneous spanwise chemically reacting LIF images of the low speed
wake forced at 2%; x = 4 cm. C : > 0.10 mapped to white.

131

 

Figure 39. Instantaneous spanwise chemically reacting LIF images of the low speed
wake forced at 5%; x = 4 cm. C : > 0.25 mapped to white.

 

Figure 40. Instantaneous spanwise chemically reacting LIF 1mages of the low speed
wake forced at 9%; x= 4 cm. CP > 0. 25 mapped to white.

 

Figure 41. Instantaneous spanwise chemically reacting LIF images of the unforced low
speed wake at x = 8 cm. C 3' > 0.20 mapped to white.

 

Figure 42. Instantaneous spanwise chemically reacting LIF images of the low speed
wake forced at 2%; x = 8 cm. C 1: > 0.20 mapped to white.

 

0 C: 1

Figure 43. Instantaneous spanwise chemically reacting LIF images of the low speed
wake forced at 5%; x = 8 cm. C If > 0.40 mapped to white.

136

 

0 c,, 1

Figure 44. Instantaneous spanwise chemically reacting LIF images of the low speed
wake forced at 9%; x = 8 cm. C I: > 0.40 mapped to white.

 

Figure 45. Instantaneous spanwise chemically reacting LIF images of the unforced low
speed wake at x = 12 cm. C ,5 > 0.50 mapped to white.

3

0°

 

'1 u—‘

' ”I

 

* I

0 c,, 1

Figure 46. Instantaneous spanwise chemically reacting LIF images of the low speed
wake forced at 2%; x = 12 cm. C 1: > 0.50 mapped to white.

139

 

0 c: 1

Figure 47. Instantaneous spanwise chemically reacting LIF images of the low speed
wake forced at 5%; = 12 cm. C ,,* > 0.50 mapped to white.

140

 

Figure 48. Instantaneous spanwise chemically reacting LIF 1mages of the low speed
wake forced at 9%; x— - 12 cm. CP > 0. 50 mapped to white.

1

4

 

*

0 CF 1

Figure 49. Instantaneous spanwise chemically reacting LIF images of the unforced low
speed wake at x = 16 cm. G: > 0.50 mapped to white.

 

Figure 50. Instantaneous spanwise chemically reacting LIF images of the low speed
wake forced at 2%; x = 16 cm. c: > 0.50 mapped to white.

143

 

Figure 51. Instantaneous spanwise chemically reacting LIF images of the low speed
wake forced at 5%; x = 16 cm. C : > 0.50 mapped to white.

144

 

Figure 52. Instantaneous spanwise chemically reacting LIF images of the low speed
wake forced at 9%; x = 16 cm. C P > 0.50 mapped to white.

 

Figure 53. Instantaneous spanwise chemically reacting LIF images of the unforced low
speed wake at x = 24 cm. C : > 0.60 mapped to white.

146

 

Figure 54. Instantaneous spanwise chemically reacting LIF images of the low speed
wake forced at 2%; x = 24 cm. C ,3," > 0.60 mapped to white.

147

 

Figure 55. Instantaneous spanwise chemically reacting LIF images of the low speed
wake forced at 5%; x = 24 cm. C ,, > 0.60 mapped to white.

148

 

Figure 56. Instantaneous spanwise chemically reacting LIF images of the low speed
wake forced at 9%; x = 24 cm. C : > 0.60 mapped to white.

149

 

unforced

   

.; 1. .
.‘l
at. _

0 C; 1

2% forcing

Figure 57. C—; distribution of the low speed wake at (a) x = 4 cm, (b) x = 8 cm,
(c) x = 12 cm, (d) x = 16 cm, (e) x = 24 cm.

150

 

 

5% forcing 9% forcing

Figure 58. CT: distribution of the low speed wake at (a) x = 4 cm, (b) x = 8 cm,
(0) x = 12 cm, ((1) x =16 cm, (e) x = 24 cm.

151

(a)

 

 

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AW 13
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. _ _ _ b . 1F — _ _ . _ p _ LL . _ _ e _ if p L

5 0 5 0 5 0 5 0

J 1. 0. J l 0.

0 O O 0 0 0

2 (cm)

4 cm. (a) 6,, (b) 6,,, (c) 6P/51.

Figure 59. Calculated quantities versus 2 at x

152

 

 

 

 

 

 

 

 

 

4 fl 1 f f l 1 1
— F """ ' 9% Forcing 1
» V1‘11V 5% Forcing <
- 131145 2% Forcing «
3 — G """" 0 Unforced ~
«0 > ‘ -
. 1 " 99W -
- T) .0 -
l 1 i l} "
h , 0 o O .. .. o \"0 ‘
' '1. a" 00000 9Q 1111-
0 111’: 1 1 l 1 1 1 l 1 1 1 l 1 1
-4 -2 0 2 4
0.5 _ T 1 I I I l I I 7 1 Y j I 1 <
: 3 0— ----- 0 9% Forcing 3 ‘
_ ‘1 V #V 5% Forcing ; :
04 _ 1 - v 1!.) . B—-—»—E] 2%Forcing r 1 1,, , ,__‘
- _ 1 § 0 -------- o Unforced _
_ , ‘1‘ ’ . ..
: 11 ‘ ,9 *1 :
A 0.3 — -‘ 1 :1 9 ~
E — :l b ‘1 \ _
3 . y (1', 1 1, ' .1 F
no“ - W1? 1 5 0" f «
0.2— 116"" "’1' ‘ ‘1“ 1 ‘ "'“ 1 '91” 1‘
' 1 1 b. E .z‘ 11‘; 1
I 1' f1 ‘ . g '. .—r 0' 1 i
: I 1‘ “ 1
_ Y :1 V . [‘1‘ 1‘ u
0.1 1"“17’47'1 t ‘ ' * 1 1 ' ' ‘ 1‘ 2117' 1
’ 1' 1 § 1 ‘-_ 1 “
‘ 1. W'VW‘V‘Vq‘i‘U‘Q‘V‘Vvv—afl 11 1
1- ‘ ‘J—O
01.12.12,... 11 :fifia-afifiaei; .1 ...“...
-4 -2 0 2 4
0.20 I r I I Y x 1 1 1 1 1 I 1 1 1
1 .1 <
: ‘, .1 “““ 0 9% Forcing , _
, , . Vn—‘V 5% Forcing -“. _
P ," 1'1 I3—'—"€l 2% Forcing (. g
1— ’: O O ........ 0 rc : .1 —
0.15 .- . 0
L- / 1‘. il ‘1 1
_ 7'1 o ‘1 1'1 _
- 1’11 9 111 .
1. 1 ; \
0°— _ I,‘ if! ‘1'.I ‘ 9 ‘
‘35. 0101 PW ’ 011 1 ’0‘ ‘1?’ A
“ ‘ -'1 ‘- ' WY
1 1" 1". h. ‘ ‘1 1 1
> 1 j 1 ‘-. 1 r1 1 _
> “11'? 1~o--0~a 0 . Y1; _
o.05~-1‘-' 7 ,1;- ,1
_ :1; i will}-
_ Y1"GW‘,VVVV‘VV9-V-vvv\é}7 1"?
_ ' o- o, 1
“ img 8.3. 8: 9“} 818$; 8 ‘3 O ”9““?
0
-4 -2 4

Figure 60. Calculated quantities versus 2 at x = 8 cm. (a) 61, (b) 61,, (c) 6,,/5,.

 

 

 

 

0
2 (cm)

(a)

(b)

(C)

153

 

 

 

 

 

 

 

 

 

 

4 E r fi' 1 l r ‘1’ 1 Y Y ' ' I 1 ‘ 1
g —————— O 9% Forcing ‘
_ 1:1-—"V 5% Forcing ‘
» 1:1—--—-—E] 2% Forcing -
3 _ 0 -------- O Unforced a
' ‘1
_ f~o -*' "N. 1’ _
A — \R~ ‘ ‘
E L V’v-‘W1 7 L
14.-T 2 L #f ‘8 {1:3 ‘5? —§1§\1!F‘§’35:v E} a . \Q — (a)
4’ I\ \
» 1‘! O 8
’ _ o W
c $1 1,1 .9. O O o~e---oNev-010'0'0' 0‘9 I". \-I‘
_ {I 1 ‘1 ,9. \l‘ ‘
1 : Ion; _—
1 1.50 b: i
1 31‘ "-._| M
_ ,‘ '1 8
0 SR! 1 1 l 1 1 1 l 1 l ' 1 l ‘ la
4 -2 0 2 4
10 f . . 1 ' I V
5 g— ----- O 9% Forcing
v—-——V 5% Forcing
_ ; 13—.—»-a 2% Forcing
0.8 o -------- O Unforced _
1 ‘N' i-Vl
0.6 — ’ “ J 1. —
a ’ “ 9 1.
o ‘ "1 "I I\‘
v — 1 ’ " 4
1°“- ‘ a1“ , 5‘ (b)
0.4 — ».. i o‘ ’1‘ _
o, ‘1 ‘4. Ex
_ 1 ‘ ' ‘ 4
188%; ‘ ' ’ W 11
02 ‘ . x 51 8:1 1
- 11;]: ' KV-‘v- «11143—4? #11”? 9”? fi‘
. I, 1 \ ‘
'fi-G-B a-B—B- 121—1}- E -El—E+— B %
0 10106990100€>O1 10M€>01 1““-
-4 -2 0 2 4
0.5 ' ‘ ‘ l I l I l
: o— ----- O 9% Forcing :
_ v——--‘V 5% Forcing 1
0.4 H :1—»—~-E1 2% Forcing F
: G -------- O Unforced :
0.3 f 8
m— p -
.2“ : h 9 V‘ : (c)
0.2 — 7 1? ‘1 1 ' 1" I i _
_ .9 *1. " J’v 8
- o ‘ 8 I, ‘ 2“ \ Z
, 1887311 ‘1! "W <71; ‘
. V W I V‘ I . 7 H
01_ 8W J’ Vv—Avv—v—v-JV V'VV/ ‘21; V V _
> I A 21/ ‘ q ’I0 -
_ 5+ 5 -3. 43 13 {Ha - 183—1343' ‘1 ‘8 8
o ‘ mfg-.0 -8- 0 81,0 ~80. 0"?“0'07“? ‘
-4 ~2 2 4
2 (cm)

Figure 61. Calculated quantities versus 2 at x = 12 cm. (a) 5], (b) 61,, (c) 61461.

81 (cm)

SP (cm)

5H5:

Figure 62. Calculated quantities versus 2 at x = 16 cm. (a) 6,, (b) 6,,, (c) 6,,/6,.

 

 

 

 

 

 

 

 

 

 

 

 

 

4 f I j r Y 7 V [fl j I I I 77 r
__ 4
3 b I ' \ n
._ ’[X '\.. "
* Erik ’s “- BEE) r
2 h WWwFVW ‘VV ‘3‘??- Big; E {13‘1va —
L ‘7? 91,50“ 3 3/8‘ gig" 5” 1‘ ~
P I" 1.5.0.2..0 G .o o o 0 0- 0 O 5 ll 4
Li X 0 O l i
" il‘,‘ \‘ i i V
* IL‘L) o ------- C 9% Forcing 5‘ Q'l i. 1
l h .f Vflnv 5% Forcing “\ 1 V
F .1 [Em—"El 2% Forcing "i ', ‘
L- I G """"" 0 Unforced ’1'. ‘
r [L [bi L
L .1 L
0 till 1 L l 4 L 1 l l i 1 1 1 l 1 T
-4 -2 0 2 4
15 r I T T r r l I I I I I n I
b i O ------ C 9% Forcing ‘
* V——”‘V 5% Forcing A
c ”___.43 2% Forcing A
G -------- O Unforced 4
1.0 b “’ ‘ T fi "’ ' V
~ I b. ‘ 6
’— ." \Q . :I
:1
~ Q
0.5 P
0.4
O 2 4
0.5 r I r I 1 1 r 1 r T [ 7 7
: 0 ----- ‘ 9% Forcing :
. V—-“‘V 5% Forcing ~
0.4 _, D—“"El 2% Forcing
: 0 """"" O Unforced :
_ -4
.— ‘q A
0.3 ~ "'u .s‘ ‘
P I. Q ’ -
C 9 .d i
L ,.' 6‘ ; h\ 4
I
: VVV" ’ ivy \ :
_ yfl jvvv 9% R o
0.1 :_ I I" \V‘VVFV‘V"V- V'V'VI I Xi’jggv '1
- .' BEBB‘B—B'Bfi—R{T—C}-Bflifl b- OLE/3V u
-4 -2 0 2 4
2 (cm)

(a)

(b)

(C)

51 (cm)

5,. (cm)

51151

Figure 63. Calculated quantities versus 2 at x = 24 cm. (a) 51, (b) 6,,, (c) 6,,/61.

155

 

 

 

 

 

 

 

 

 

 

 

 

4
3
'b 1 7 =
2 ='_. = 7 i
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- {1? EFF-El 2% Forcing ; i -
» If 0 """" 0 Unforced 1 \1‘ a
_ / l h. ‘
0 i 1 l u 1 1 l 1 1 1 i 1 1 m
—4 -2 0 2 4
]_S I r I I ?.T T v V v i l I r
_ , \ _
§ """ 9% Forcing I .~.
. V*‘--V 5% Forcing 5 "’fl a
G — ‘9 2% Forcing I O\
— e ------- Unfo a. a
‘ " J
1, \.
1.0 3 l.‘ b_\ _
- I: 1‘ _
P \ ‘1
ll, ‘
, .‘V 2‘. 4
_ ’VVK‘, V\ /R 3' ”RV _
0.5 ~ V7 I” N 1
- l
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0,5 . . i , . . i , . . T , . . ,
* 0 """ . 9% Forcing <
3 V“'—*7 5% Forcing A
> [3"—"'9 2‘1? Forcing <
0.4 , 0"" 0 Unforced . A
_ [I ‘0 0.”. _
0 3 h ‘d 3‘ i
.. I. -. _.
~ 6
- r l‘. _
> o’ '3 a
- / g F\ V
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2 (cm)

(a)

(b)

(C)

 

 

 

 

0.3 I I I I T I I I I I I I I I l I I I I i I y I r
- ’ """ 5 9% forcing ; a
_ Vu—V 5% forcing 1.x".
‘3‘—"EI 2% forcing “Ix“
L O """" 0 unforced ,,,-r"' 1
i ‘g' ’
I— ‘./ ,/ IN _4
—‘ I. ///
< h ’/ //// —4
\a. / I],
< ” /’ //” ‘
.— / ///V '/ "
I // ‘/
/ // /
’_ ~ I L _ /. _‘
0.1 ,1 , [V /
~ / // /'/ _
/ / /// g /'/'
h / // /./B —1
/ /-
'— /V/ ‘/' -<
~“ y/I/ /a/I?
._ ’1’ — ___________________ O _‘
V “g/t/u.-. G O -----------
0 l 1 1 Q‘mI‘TT‘ 1 l 1 1 1 1 J 1 1 1 1 i 1 1 1 1
0 5 IO 15 20 25
x(cm)

Figure 64. Normalized product area A,,/Al versus x from spanwise data for all forcing
conditions.

 

 

 

 

 

 

 

 

   
  

 

 

 

4 7 I I I i I I I I i I I I I
' 1
3 — _
E ”" -L
3 2 — V._ (a)
w~ h— .1
_ I _
c
1 F mean streamwise data
~ ' I 9% spanwise data
- g 5 5% spanwise data
0 l I 1 1 i 1 1 1 1 i 1 1 1 1
0 IO 20 30
x (cm)
I l l I I l l l l I l I l I
b mean streamwise data ‘ _
l 5 __ I 9% spanwise data _
' 5 5% spanwise data
_ _
E 1.0 — . _ (b)
0
v '- —<
D...
oo — a
0.5 h ‘ ‘ r
i— -L
r -
O l l l
0 30

x (cm)

Figure 65. Comparison of mean streamwise data with spanwise data at z = 0.0 cm;
(a) 61, (b) 6,,.

 

0.5 ' I ' ' ' ' ' ' T ' ' ' I I I I I I I I I I I T

H reacting. 9%

‘ """ ‘ nonreacting.9%

_ 0—0 reacting. unforced

04 _ G """" 0 nonreacting. unforced _ _, .—"'

A/A

 

 

 

 

x (cm)

Figure 66. Comparison of the mixed fluid fraction from reacting and nonreacting LIF.

159

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4 T I I I I I T I I I I I I
” ° 2 = -2.0 cm ‘
_ U z = +0.8 cm ‘
3 F —1
I. q
A
E '- 00000000 1
8 2 — 00006309000 ‘
00— b 0000 W ~
1 ” _
0 1 1 1 l 1 1 1 1 l 1 L 1 1
O 10 20 30
I T I I I T fir I I I I I I
L z = -2.0 cm 4
1.5 ’ U z = +0.8 cm ‘
F q
l— —I
E 1.0 _ r
0
v P -4
0-
oc ~ 8
i- .4
0.5 *‘ M
l- o —1
0 L 1 l l i W 1 1
O 10 20 30
05 I I I I I I I I I I I I r
_ 0 z = -2.0 cm .
0 4 Z O z = +0.8 cm ‘
. ’- _J
>- ‘1
3 1
0.3 ” 4
.— r J
3 ‘ ‘
0.2 — -
~ I
1
>— 00 -1
0.] — 0°"<> *
5 W “
0 1 1 1 l 1 1 1 1 41 1 1 4 1
0 10 20 30
x (cm)

Figure 72. Calculated quantities versus x for the unforced higher speed wake. (a) 5,,

(b) 5p, (C) 51151-

(a)

(b)

(C)

 

 

4 I I I I T I I I Ifi I I I
- -1
* ° z=-20cm J
: V z=-08cm :
3* U z=+08mn 1
" 0 z=00cm ‘
.— -J
E — gs ~ ‘ 4
£52 — 1f§i° “ (a)
°°" ’ HEW ‘

 

 

 

 

 

 

 

_ ‘1
l ‘ +
~ 1
O 1 1 1 1 l 1 1 1 1 l 1 1 1 1
O 10 20 30
I I I I I I I I I I I I I I
~ 0 z=-20cm 1
1.5 — v z=-O.8cm “
: D z=+0.8cm :
P 0 z=ODcm _
E 1.0 ~ . ~ - H
U +— —4
1 (b)
00 L H
05 H W 1
J
30

 

 

O4

0:3q o
N
ll
be
0
B

03
g (C)
to

02

01

1LL111111111LLL1111111L1

ITTIWIIIWIIIITIIIITIIIIII

 

 

 

0
L»
O

 

Figure 73. Calculated quantities versus x for the forced higher speed wake. (a) 5,,
(b) 5p, (C) W51-

 

   

a:

0 C P 1
Figure 74. Instantaneous spanwise images of the Figure 75. Instantaneous spanwise images of the
forced higher speed wake at x = 4 cm. forced higher speed wake at x = 8 cm.

c: > 0.10 mapped to white. c: > 0.20 mapped to white.

 

Figure 76. Instantaneous spanwise images of the Figure 77. Instantaneous spanwise images of the
forced higher speed wake at x = 12 cm. unforced higher speed wake at x = I6
C: > 0.50 mapped to white. cm. Cp > 0.50 mapped to white.

168

 

Figure 78. Instantaneous spanwise images of the Figure 79. Instantaneous spanwise images of the
forced higher speed wake at x = 16 cm. forced higher speed wake at x = 24 cm.
C: > 0.50 mapped to white. C: > 0.60 mapped to white.

 

 

forced

 

*

CP

unforced E i
0

1

Figure 80. C—:distfibufion of the higher speed wake at (a) x = 4 cm, (b) x = 8 cm,
(c) x = 12 cm, (d) x =16 cm, (e) x = 24 cm.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

      

 

 

   

 

 

 

’5‘ _
oo— _ (a)
4
E - (b)
Ig‘ _
4
_ _ I I I I l -
- i H x: Acm "
- i BTB‘i‘fcmfm'fw’l -
0.20 ‘— ‘ :; 2cm _-:
— X= Cm .1
- X=‘ Cl'll ..
0.15 ~ 1
0°.— : j (C)
«3" : I
0.10 _— __
0.05 E -:
o 1 l
.4 -2 0 2 4

Figure 81. Calculated quantities for the higher speed wake. (a) 6,, (b) 6,,, (c) 6,,/5,.

l7l

laser sheet / false wall
1,!

/

 

 

 

 

 

 

 

 

 

 

 

 

 

1
laser sheet
/ /
/ /
false wall x
I y
z (b)

 

 

Figure 82. Schematic of the test section with the false wall mounted at (a) x = 0 cm, and
(b) x = 3.5 cm.

172

 

 

(a) (b)

Figure 83. LIF images at x = 1.8 cm of the wake with the false wall mounted at x = 0 cm;
(a) 5% forcing, (b) 9% forcing.

173

 

 

(a) (b)

Figure 84. LIF images at x = 4 cm of the wake with the false wall mounted at x = 0 cm;
(a) 5% forcing, (b) 9% forcing.

174

 

 

(a) (b)

Figure 85. LIF images at x = 8 cm of the wake with the false wall mounted at x = 0 cm;
(a) 5% forcing, (b) 9% forcing.

175

 

 

(a) (b)

Figure 86. LIF images at x = 16 cm of the wake with the false wall mounted at x = 0 cm;
(a) 5% forcing, (b) 9% forcing.

176

 

 

(a) (b)

Figure 87. LIF images at x = 24 cm of the wake with the false wall mounted at x = 0 cm;
(a) 5% forcing, (b) 9% forcing.

l
-

(a)

 

   

 

 

I

l I II I. I

 

 

(b)

Figure 88. LIF images at x = 1.8 cm of the wake with the false wall mounted at
x = 3.5 cm; (a) 5% forcing, (b) 9% forcing.

178

 

 

(a) (b)

Figure 89. LIF images at x = 4 cm of the wake with the false wall mounted at x = 3.5 cm;
(a) 5% forcing, (b) 9% forcing.

179

 

 

(a) (b)

Figure 90. LIF images at x = 8 cm of the wake with the false wall mounted at x = 3.5 cm;
(a) 5% forcing, (b) 9% forcing.

180

 

 

(a) (b)

Figure 91. LIF images at x = 16 cm of the wake with the false wall mounted at x = 3.5cm;
(a) 5% forcing, (b) 9% forcing.

181

 

 

(a) (b)

Figure 92. LIF images at x = 24 cm of the wake with the false wall mounted at
x = 3.5 cm; (a) 5% forcing, (b) 9% forcing.

182

 

Figure 93. Illustration of the splitter plate tip with the peg mounted on the upper surface
(not to scale).

 
 

183

Figure 94. Instantaneous spanwise images of the unforced peg wake at x = 16 cm.

184

 

Figure 95. Instantaneous spanwise images of the peg wake forced at 2%; x = 16 cm.

185

 

Figure 96. Instantaneous spanwise images of the peg wake forced at 5%; x = 16 cm.

186

 

Figure 97. Instantaneous spanwise images of the peg wake forced at 9%; x = 16 cm.

187

 

 

Figure 98. Instantaneous spanwise images of the unforced peg wake at x = 24 cm.

188

 

Figure 99. Instantaneous spanwise images of the peg wake forced at 2%; x = 24 cm.

189

 

Figure 100. Instantaneous spanwise images of the peg wake forced at 5%; x = 24 cm.

190

 

Figure 101. Instantaneous spanwise images of the peg wake forced at 9%; x = 24 cm.

191

(a)

 

 

 

(b)

 

 

 

 

 

Figure 102. Effect of the peg on wake structure. (a) Sample experimental image,
(b) illustration of streamwise vorticity sign and approximate strength.

 

 

 

 

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— 1
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5 ~ _
r— O —<
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0 1 1 MAML 1 1 I 1 1 L I 1
0 4 8 12
Solution pH

Figure A. 1. Fluorescence intensity versus pH behavior of fluorescein dye.

 

 

 

 

150 I I I I I I I I I
. _
1— OO _1
o
’5‘ 100 *— " 0 ‘ ' ‘ —
'E t _
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I: _ a
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0 is 02 0.4 06 08 10
53

Figure A.2. Representative curve of fluorescence intensity versus base volume fraction.

 

 

 

 

|.l I I I I I I I I I I I I
L. : d
e 3 w: m0 = e ”4329 ‘
e 2 w: [/10 = e ”6329 _
l 0 '\:‘_ O > 1-—I
1.. a ? O —4
a . O _
— V V V0 O . ‘ .4
_ , , _
“a 09 ”— ' O o ' """
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_ a O 0 d
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_ V , O . e O I
1- ' v I . -I
_ V v _
0.8 +— v d
e v v V , a
0.7 1 1 I 1 1 1 1 I 1 1 1 1
0 300 600 900 1200
time (s)
Figure A.3. Effects of dye bleaching in the titration reference chamber for 2 W and 3 W
laser power.
C20

CP(€; 53)

Figure A.4. CP(€; £3) for a fast, irreversible reaction.

 

 

 

Es

194

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53

Figure A.5. CP(§B; £5) for a chemically reacting LIF experiment.

195

 

 

 

 

 

 

 

—

>
_> >
Raw data Filtered data

E Upper Stream Fluid
: Mixed Fluid
- Lower Stream Fluid

Figure B. 1. Schematic of a wake flow and intensity profiles along the dashed line for
raw data and data that had been filtered.

 

 

 

 

 

1.25 F—‘fi 1 1 1 I 1 1 1 1 j—I¥ u“—1——1 **
.. unprocessed data ~
1.00 F
0.75 — a
E a 1
E, g _
n- _ a
"° e I
0.50 " I
0.25 P a
I— O O O O O
I—
0 ;1_;4F_1._1_‘1 gm-%,li+ _1_1 7;
0 10 20 '40
I

Figure B.2. 6P(y), z = 0.8 cm, x = 6.0 cm, unforced.

196

 

 

 

 

 

 

 

 

 

 

0.3 1 T 1 4 1
unprocessed data
I
' E
0.2 , 1 O _
O O
o O O O
E
3
co“ 1
0.1 _
o . 1 1 1
IO 20 30
Y
Figure 8.3. 6p(y), z = 0.8 cm, x = 14 cm, 5% forcing.
2.0 I I I I I I I I
1.5 AA ,{A A A A ~~-~-unprocesseddata ..... .. ‘7
U UV U U U U «
g -
V 10 — fl
0-
w —1
0.5 — a
0 1 I 1 I 1 1 1 I

Figure B.4. 6P(y), z = -O.8 cm, x = 21 cm, 9% forcing.

Intensity (arbitrary units)

200

150

100

50

197

 

 

 

 

 

' I I I I 1 I I r I I I ' l I 1 I 1
: y = +99311 -519, R: 1.57. max dev:3.20 :
I a
L- . -1
— .1
/ 1 1 1 1 I 1 1 1 1 I 1 1 1 I 1 1 1 1 I
0.5 1.0 1.5 2.0
Shutter Speed (ms)

Figure B.5. Intensity versus exposure time for the Sony CCD camera.

 

 

 

£13 1

(a)

 

 

 

Eu 1

(b)

Figure B.6. (a) Example IKEB) plot for a camera with zero black level offset.
(b) 11(513) plot for a camera with negative black level offset.

198

 

Figure C. 1. Chemically reacting LIF images of a wake at different free stream speeds.
= (a) 7.17, (b) 8.50, (c) 8.77, (d) 9.94, (e) 11.54, (0 11.56 cm/s.

0.3

0.2

51451

0.1

0.3

0.2

51451

0.1

199

 

 

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V""V 11.56cm/s
0- ----- 0 11.54 cm/s
"" " 9.94 cm/s
A———A 8.77 cm/s
+-- -- -+ 850ch

a -------- e 7.17cm/s fiéj
at“

1 61.. T
- ~--e>-. ..e...
,..e---6 fig @ «9

139-~69 .
a. ,1/ I“.

 

 

 

 

 

 

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,3 VIV’ ' o
. -I' ,v’ 3" ‘
iggiltiii-cwf‘. 1
1 1 1 I 1 1 1 1 1
7 9 ll 13 15
x (cm)
Figure C.2. 5,1/6l versus x for various wake free stream speeds.
I I 7 I I I I I I I T I I fl I
9 """" ‘9 7.17cm/s 4
+“' “' ‘+ 8.50 cm/s
A———A 8.77 cm/s a
'“ ‘I 9.94 cm/s
" """ . 11.54 cm/s ‘
v—---v 1156ch > 1 , Affi4 ,_ —
A” , ’
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Aqfiu’ ‘13-’59 3’ 9 £19 {9 Gang}
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t
x = xf/Uo

Figure C.3. 5P/1‘5l versus x* for various wake free stream speeds.

200

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P- \\ \\ —I
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0 5 10 15 20 25
x(cm)

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x (cm)

Figure F .2. Vpeak versus x from spanwise imaging for 5% and 9% forcing amplitude.

206

 

 

 

 

 

 

 

one

 

 

 

Figure F.3. Model illustrating streamwise vortex evolution. (a) low x, (b) high x.

(a)

(b)

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