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A STUDY OF TURBULENCE PRODUCTION AND MODIFICATION IN
BOUNDARY LAYERS USING A NEw PHOTOCHROMIC VISUALIZATION
TECHNIQUE

presented by

Chin—Chou Chu

has been accepted towards fulfillment
of the requirements for

Ph. D Mechanical Engineering

' degree in

mi gar

Major professor

Date December 30, 1987

 

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[ _

 

A STUDY OF TURBULENCE PRODUCTION AND MODIFICATION IN

BOUNDARY LAYERS USING A NEW PHOTOCHROMIC VISUALIZATION
TECHNIQUE

by

Chin-Chou Chu

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Mechanical Engineering

1987

ABSTRACT
A STUDY OF TURBULENCE PRODUCTION AND MODIFICATION IN

BOUNDARY LAYERS USING A NEW PHOTOCHROMIC VISUALIZATION
TECHNIQUE

A major extension of Laser Induced Photochemical Anemometry (LIPA) has
been developed that enables the velocity components and their gradients over a two-
dimensional domain of a fluid flow to be measured. As a result, the transverse vorticity
component and the strain rate as well as the Reynolds stresses in the interrogation
plane can be determined. Calibration depends only on a time and a length scale.
Comparison of measurements with the exact solution in a Stokes’ layer indicates that
the technique’s accuracy can be predicted by classical error analysis and that it is
comparable or better than that achievable with the best single point probe techniques.
Using the LIPA technique we have quantified several complicated turbulent and
- unsteady flows which include the skin friction measurement on compliant surfaces and
both temporal and spatial information pertaining to the velocity distributions, spanwise
vorticity distributions, and streamwise vorticity distributions associated with the vortex
ring/ moving wall interaction model Of the turbulence production process. The results Of
this study extend our understanding Of turbulence production and modification

concerning boundary layers and also provide a rational basis for boundary layer control.

ACKNOWLEDGEMENTS

On completion of this dissertation, I have reached the end Of my formal

education. I would like to acknowledge the advice and support Of a number Of people.

I would like to acknowledge the support of the Office of Naval Research, grant
monitor: Dr. Reischman; and the Air Force Office Of Scientific Research, grant

monitor: Dr. J. McMichael, for their support in the completion of this work.

I particularly express my gratitude to R. E. Falco, my advisor, for all his

assistance and guidance throughout my Ph.D. program.

I would like to give many thanks to the committee members: John Foss, David
Yen, Richard Bartholomew, and Daniel Nocera. In particular, John Foss gave me quite
a few constructive comments on my thesis, and Richard Bartholomew helped me a lot

in computer graphics.

The following people provided specific help which I appreciated: Frank
Cummings’ contribution to the experimental facilities, Mary Cline’s proof-reading and
typing, Joe Klewicki’s advice on my first draft of the thesis, Sean Hilbert’s fabrication Of
the beam divider, Kue Pan’s help in computer graphics, and Chuck Gendrich’s

digitization of the circulation.

Many thanks to John Bracy and Scott Wixom, for their assistance in the early
stages of my thesis. Also, many thanks to James Chang, YOO Seoung-Chool, Nasser
Rashidnia, Michael Hetherington, and Jeff Zenas for their friendship.

Finally, thanks to the Eastman Kodak CO. for their cooperation in preparing the

photochromic chemicals and providing the information shown in Fig. 2.1.

TABLE OF CONTENTS

 

 

 

 

 

 

 

 

 

page
LIST OF FIGURES viii
LIST OF TABLES xv
LIST OF SYMBOLS xvi
CHAPTER
1. INTRODUCTION 1
2. LASER INDUCED PHOTOCHEMICAL ANEMOMETRY (LIPA) .................. 4
2.1 Introduction 4
2.1.1 Photochromic chemical, light source and working fluid
2.2 Technical details 5
2.2.1 Optical configuration
2.2.1.1 Single tracer technique
2.2.1.2 Grid tracing technique
2.3 Algorithms to obtain fluid dynamic quantities - __ 8
2.3.1 Single tracer technique
2.3.2 Grid tracing technique
2.4 Calibration and error analysis .................... 10
2.5 Summary and comments 11

3. EXPERIMENTAL DETERMINATION OF DRAG MODIFICATIONS DUE
TO ELASTIC COMPLIANT SURFACES USING QUANTITATIVE
VISUAL TECHNIQUES _ 13

3.1 Introduction - 13

 

 

iv

 

3. Experimental details 14
.2.1 Kerosene channel facility

.22 Flow documentation in kerosene channel

.2.3 Compliant surfaces

.24 Surface responses on compliant coatings

.2.5 Direct shear stress measurement on the walls

3.3 Results 18
3.3.1 Flow documentations in kerosene channel
.3.1.1 Velocity profiles
.3.1.2 Pressure measurement
Surface responses of compliant coatings in turbulent channel flow
Shear stress measurements at walls - both stiff and compliant surface
.3.3.1 Results obtained from photochromic technique
3.3.3.2 Skin friction measurement on stiff surface by hot-film anemometry
3.3.4 Surface response on compliant surfaces associated with wall shear stress
measurement
3.3.5 Observed wave patterns on compliant surfaces

 

3
3
.2
.3
3

3.4 Discussion 23

 

3.5 Conclusion 26

. NEW UNDERSTANDING OF THE INTERACTIONS ASSOCIATED

WITH TURBULENCE PRODUCTION: A VORTEX RING MOVING

WALL INTERACTION MODEL OF THE TURBULENCE RODUCI'ION
MECHANISM NEAR WALLS 27

4.1 Introduction 27
4.1.1 Back ound
4.1.2 New oundary layer Observations in the
Turbulence Structure Laboratory, Michigan State
University

 

 

 

4.2 Vortex ring/moving wall interaction model -- - 31
4.2.1 Vortex rin / moving wall simulation
of the turbu ence production process

4.2.2 Experimental details
4.2.2.1 Experimental apparatus
4.2.2.1.] Ring generating system .
4.2.2.1.2 Moving belt system
4.2.2.1.3 Control system
4.2.2.2 Visualization and recording
4.2.2.2.1 Two-view flow
visualiztion
4.2.2.2.2 Three-view flow
visualization

 

4.3 Results of the interactions based on two-view
flow visualization 35

 

4.3.1 Evolution Of model
4.3.1.1 Vortex ring moves towards wall
(fast ring, Ur/Uw > 0.45)
4.3.1.2 Vortex rin moves towards wall
(slow ring, r/Uw < 0.35)
4.3.1.3 Vortex ring moves awa from wall
(fast ring, Ur Uw > 0.60
4.3.1.4 Far field e ect
4.3.1.5 Vortex up? moves awa from wall
(slow n'ng, r Uw < 0.45,)
4.3.1.6 Summary 0 interaction
4.3.2 Scaling associated with the interactions
4.3.2.1 Streak spacing
4.3.2.2 Streak length
4.3.2.3 Wavelength associated with wavy
instability
4.3.3 Stability consideration
4.3.3.1 Ring stability
4.3.3.2 Streaks stability
4.3.3.3 Comparison

4.4 Results based on three-view visualization
4.4.1 Slow ring moves toward the wall
4.4.2 Fast ring moves away from the wall

 

4.5 Implication for turbulent boundary layer
4.5.1 Connection between vortex ring/ moving
wall description and the typical eddy/

wall layer interaction
4.5.1.1 Outer region
4.5.1.2 Inner region
4.5.1.3 Inner/ outer region interaction
4.5.2 Streaks spacing
4.5.3 Vortical motions associated with
Streaky structure
4.5.4 Implications for drag modification

4.6 Summary and comment

 

. QUANTITATIVE REFINEMENT OF THE VORTEX RING/ MOVING
WALL INTERACTION MODEL

 

5.1 Introduction

 

5.2 Stokes’ layer measurement
5.2.1 Introduction
5.2.2 Experimental details
5.2.3 Results
5.2.4 Discussion and summary

5.3 Vortex ring measurement

 

-41

43

48

51
51

-51

54

.1 Introduction
.2 Experimental details
.3 Results
.4 Discussion and summary

w visualization 1n kerosene tank

56

 

.1 Introduction

.2 Experimental details

.3 Results

4. 4 Discussion and summary

AAA; bibs»

5.5 Velocity distribution associated with the
vortex ring / moving wall interaction

59

 

5.5.1 Introduction

5. 2 Experimental details

.5 .3 Results

5.4 Discussion and summary
5. Streamwise vorticity measurement associated with

5.

5

5.

6

the vortex ring/movmg wall interaction

63

 

6.1 Introduction
6. 2 Experimental details
6. 3 Results
6. 4 Discussion and summary
Summ

5.

67

 

5.
5.
5.
5.
7
5.

ummary
7.1 The photochromic technique- an
accurate and owerful technique
5.7.2 Further un erstanding of turbulence
production rocess through the
vortex ring moving wall interaction

6. CONCLUSION AND FURTHER COMMENT

69

 

6.1 Conclusion

69

 

6.2 Further comment

71

 

FIGURES
APPENDIX A

72
168

 

BIBLIOGRAPHY

vii

....... .. 173

LIST OF FIGURES

Fig. 2.1 The associated absorption and emission spectrum Of the
photochromic chemical used in this study

 

Fig. 2.2 A schematic of the stretching of the photochromic
line in shear flow

 

Fig. 2.3 The dependence of the quality of photochromic line
on its orientation in shear flow

 

Fig. 2.4 A schematic of experimental configuration for one
of the laser beam orientations

 

Fig. 2.5 The divergence characters of the laser beam after a
F-500mm convex lens

 

 

Fig. 2.6 The specular reflection from the beam divider
Fig. 2.7 A photo of the beam divider

 

Fig. 2.8 A photo of the output Of the divider showing the
F raunhofer diffraction

 

Fig. 2.9 A sketch of the optical configuration for generating
a grid in Fig. 2.10 (a)

 

Fig. 2.10 A demonstration Of the grid; 3) shortly after the
laser pulse, b) 0.4 seconds later

 

Fig. 2.11 Algorithm to Obtain the wall shear stress using
photochromic technique

72

73

74

75

76
77
78

79

80

81

 

Fig. 2.12 Procedure for conversion of the displacement of a

 

grid box to velocities

Fig. 2.13 Decomposition of the velocities used to calculate
the circulation around a grid box

Fig. 3.1 A schematic Of the kerosene channel flow facility

 

Fig. 3.2 The dependence of the shear modulus Of gelatin on
the concentration of gelatin and water m1xture

 

viii

82

83

-84

85

86

Fig. 3.3 A sketch of the experimental configuration used to
capture the surface deformation under the turbulent
channel flow

 

Fig. 3.4 The optical configuration of the wall shear stress
measurement experiment

 

 

 

Fig. 3.7 The turbulent intensity profiles

 

 

R60 3 1200

 

 

both and coating thickness

 

 

Fig. 3.13 The combination of Fig. 3.13 (a) through (c)
regardless of thickness

 

compliant surface

 

Fig. 3.15 The comparison of transverse length scale of

 

 

 

Fig. 3.17 A photo showing the triangular-shaped waves

 

87 -
_ 88
Fig. 3.5 A close-up of the technique used for the wall shear
stress measurement on compliant surfaces 89
Fig. 3.6 The mean velocity profile over a stiff surface.( The
centerline velocity is 0.341 m/sec yielding R g a 1200) 90
91
Fig. 3.8 The pressure distribution along the kerosene channel at 92
Fig. 3.9 The onset boundary for different compliant coatings 93
Fig. 3.10 The de endence Of the occurrence of each element on
- 94
Fig. 3.11 The histogram of the skin friction Obtained from
1205 samples over the reference stiff surface 95
Fig. 3.12 The histograms of the skin friction associated with
3, 19 and 30 mm compliant coatings - - 96
97
Fig. 3.14 A photo of the pocket-like depressions formed on the 3mm
- - 98
depressions in compliant surfaces with the
pocket footprints made on a solid surface - 99
Fig. 3.16 The comparison of the time between pocket-like
depressmns in compliant surfaces with that
Obtained from boundary layer and channel flows -_ 100
_ 101
Fig. 3.18 A photo of the quasi two-dimensional large-scaled waves . 102
Fig. 3.19 A comparison of the visual phenomena on compliant
surfaces with the flow visualization in the near 103

wall region Of channel flow by Yoda (1982) ...............

 

Fig. 4.1 Two pockets and a pair of streaks as seen in wall slit
visualization of a turbulent boundary layer using
smoke as the contaminant in air, the slit is at
the top of the photo and the flow is from top to
bottom. (Falco 1981)

 

Fig. 4.2 The basic idea behind the simulation. Performing
a Galilean transformation on the vortex
ring/ moving wall interaction makes in a model
of the turbulent boundary production rocess;
(a; instantaneous turbulent boundary ayer;
b simulated vortex ring/ wall shear layer

 

Fig. 4.3 A schematic of the side view and end view of the
experimental ap aratus used in the vortex
ring/ moving w simulations

 

Fig. 4.4 A schematic of the three-view visualization system;
note that only the end view was illuminated

 

by the laser sheet

Fig. 4.5 Sketches of the four types of local vortex
ring/ moving wall interactions (see text for explanation)

Fig. 4.6 Streaks form from the stretching of the lifted
hairpin for Ur/Uw a 0.8

 

 

Fig. 4.7 Six photos of a vortex ring/ moving wall interaction for Ur/Uw < 0.35
when the ring moves toward the wall at a 3 degree angle.
Both plan and side views are shown. The ring and the wall
are moving to the right and only the wallward side Of the
ring has dye in it. The interaction results in a air of
long streaks, a pocket and its associated hairpm lift-up,
which then gets partially ingested into the ring

 

Fig. 4.8 Hairpins form over streaks

 

Fig. 4.9 Four photos of a vortex ring/moving wall interaction for Ur/Uw> 0.45
when the ring is moving away from the wall at a 2.5 degree angle.
Both plan and side views are shown. The ring and the wall are
moving to the right. A hairpin forms first. The long stable
streaks which also form, come closer and closer together,
indicating that the streamwise vorticity which caused them
are of Opposite sign. This evolution leads to "pinch-Ofl" and

 

the creatron of a new vortex ring

Fig. 4.10 Same conditions as Fig. 4.9, except that the wall layer is very
thin. We obtain long stable streaks and a long stretched
hairpin which does not inch-off over 2500 wall layer
distance of the facili . e time between each photo is
approximately 50 w units

 

104

105

106

107

108

109

110
111

112

113

Fig. 4.11 Four photos of the evolution for 6 /D > .15. In this case a pocket
does not form, and it a ars that the hairpin has been

 

generated by the initi vortex ring/wall interaction

Fig. 4.12 Four photos of the interaction for 6 /D < .15. In this case
pinch-off of a portion Of the lifted hairpin does occur,
creating a new small vortex ring

 

Fig. 4.13 The dependence of the formations and evolutions Of streaks on 6 / D
and Ur/Uw for D"' > 250 and a 3 gegree incidence angle.
The indicated boundaries between ' erent evolutions are
approximate

 

Fig. 4.14 The dependence of the formations and evolutions of streaks on 6 / D
and Ur/U for rings moving away from the wall at 2.5 degrees.
6 / D now plays a much more important role, and long streaks
are generated over the entire speed ratio range studied

 

Fig. 4.15 The dependence of the streak spacing in wall units on the size of
the vortex rin in wall units, for an incidence angle of
3 degrees an Ur/U = .31. The thickness of the wall layer

 

(in wall units) is shown next to each data point

Fig. 4.16 The dependence of the streak spacing on the speed ratio and angle ........

Fig. 4.17 The non-dimensionalized streamwise wavelength that sets in as
a function of 6 1' for different Ur/Uw and angles

 

Fig. 4.18 A comparison between ring and streak stability the Of a three
degree ring moving towards the wall

 

Fig. 4.19 The dependence of the time to instability of the streaks on the
wall Eyer thickness (both quantities are non-dimensionalized
by w layer variables) for three degree incidence rings

Fig. 4.20 (a) A photo of a hairpin vortex in three-view flow visualization;
(b) A sketch of the vortical motion of the hairpin vortex;
note that the arrows indicate the sign Of rotation

 

Fig. 4.21 Four 4photos of the three-view visualization; each photo is

 

10 t apart

Fig. 4.22 A conceptual picture describing the spatial relationship of
the formation of visual features Observed in the vortex
ring/ moving wall interaction includin the main hairpin vortex,
secondary hairpin vortices, long stre , and pocket; the arrows
indicate the local flow direction

 

Fig. 4.23 A photo showing the laser illuminated end view flow visualization
for a fast ring moving away from the wall. The observed long

114

115

116

117

118

119

120

121

- 122

123

124

126

streaks were just the legs Of the lifted h ' in vortex;

the were one unit. The dye marker actu 1y concentrated

wi ' the streamwise vortices. The sign of the vorticity shown
in Fig. 4.23 (b) is consistent with that associated with the

hairpin vortex shown in Fig. 4.20 (b)

- 127

 

Fig. 4.24 The conceptual picture summarizing the s atial evolution of the
vortex ring/moving wall interaction for r/Uw> 0.6 when

128

 

the vortex ring moves away from the wall

 

Fig. 4.25 Comparison among several investigators’ observations

Fig. 4.26 The distribution Of D+ Obtained from the diameter of the typical
eddies of a turbulent boundary layer at R 9 at 1176, superimposed
upon the streak spacing Obtained for various size rings

129

130

 

Fig. 4.27 (a) The vortical motions associated with the observed streaky
structure in vortex ring/ moving wall simulation;
(b) The counter-rotatmg pair hypothesized by many
investigators

131

 

Fig. 5.1 A schematic Of experimental a paratus Of the Stokes’ layer
measurement; the moving be t system is similar
to what was used in water tank

132

 

Fig. 5.2 The optical configuration for generating the photochromic grid ......

Fig. 5 .3 The flow chart of the control system of the Stokes’ layer
measurement. The best orientation of the incident
laser beam is also shown in this figure

............. 133

134

 

Fig. 5.4 Two photos from the result which are 0.05 seconds apart; these
photos were taken for U = 12.7 cm/sec and belt running
time t = 5.25 seconds; the belt moved from right to left

135

 

Fig. 5.5 The non—dimensional velocity profile for two belt running speeds

where the solid line represents the exact solution -

136

 

Fig. 5.6 Results of the velocity gradient au/ay Obtained from double
differentiation and of the spanwise vorticity obtained
from circulation approach are shown in this figure
where they are compared with the exact solution
(represented by solid line). Everything is, nondimensionalized
by the similarity variables Of the exact solution.

............. 137

 

A check of continuity equation is also shown in this figure

Fig. 5.7 A schematic of the experimental configuration used to generate
and measure the vortex ring

..... 138

 

Fig. 5.8 The flow chart of the control system for vortex ring measurement

xii

............ 139

Fig. 5.9 Two photos of the result which are 0.07 seconds apart -

 

Fig. 5.10 The instantaneous velocities distribution along two axes of the ring ...........

Fig. 5.11 The instantaneous circulation distribution of the ring, which also
shows the results obtained by Sullivan et al. (1973) or
different Reynolds numbers and shows Hill’s exact
solution of a spherical vortex

 

Fig. 5.12 The instantaneous vorticity distribution over a vortex ring

 

Fig. 5.13 A set of photos with both top view and side view describing
the time evolution of vortex ring/ moving wall interactions
in the conditions of U /U = 0.26, 3 degree of incident

angle, 6 /D = 0.18 and U‘y= 15.5 cm/sec

 

Fig. 5.14 By sending a single photochromic tracer parallel to the moving
wall at y+ at 16 we obtained the visual result of the
interaction shown in this figure, which is the same
as that obtained from the h drogen bubble technique by many

other researchers, such as et al.(1971) and Smith et al.(1983) ...........

 

Fig. 5.15 The locations of velocity measurement

 

Fig. 5.16 The details of the optical configuration

Fig. 5 .17 The time evolution of the streamwise velocity distribution at
the measurement oints. The dotted lines represent the
undisturbed velocrty profiles of the Stokes’ layer

 

Fig. 5.18 The constant velocity lines in y-z plane

 

Fig. 5.19 The velocity defect or gain with respect to the undisturbed wall
layer shown in (a). These sets of data had been converted
to the turbulent boundary layer point of view by performing
the Galilean transformation

 

Fig. 5.20 A photo of the optical configuration and the orientation of the
laser beam

 

 

Fig. 5 .21 The side view of the data acquisition and lighting system

Fig. 5.22 The result of the streamwise vorticity measurement. Those photos
are selected from the same sequence of movie in one
experiment. Two photos of each set were 0.02 seconds
apart which corresponded to 0.5t+ apart

 

Fig. 5.23 The contour plots of the instantaneous streamwise vorticity

distribution ...............

 

Fig. 5.24 The instantaneous Reynolds stress distribution

 

xiii

140
141

142
143

144

145
146
147

148
150

152

154
155

- 156

158
161

Fig. 5.25 A iphoto taken 0.02 seconds before t=6.8 seconds (shown in
ig. 5.25 (a)) indicates that a pair of counter-rotating

streamwise vortices formed from the wall and moved upward-

 

Fig. 5.26 The time evolution of total circulation Of the strong vortex
(the region with positive sign in Fi .5.23 (c)-(e);
and the titrntfi e;olution( 3f the tot circulation of
one le 0 e airpin e region with negative sign in
Fig. 5.53 (c)-(e))

Fig. 5.27 A sketch of the pocket vortex (Falco 1980b)

 

Fig. 5.28 The sketch of possible merging process

 

Fig. A1 The undistorted and distorted mesh
Fig. A2 An example of the error analysis

 

xiv

164

_- 165

166
167
171

.. 172

LIST OF TABLES

TABLE 1 Local skin friction reduction
TABLE 2 Skin friction measurement from hot-film

 

TABLE 3 Physical scales associated with the
pocket-like depressions

 

TABLE 4 Characteristics of triangular-shaped waves

20
21

22

o-Ng<c:

U)

LIST OF SYMBOLS

Area
Circumference
Skin friction coefficient, (Van/ay)/(o.5 U612)
Ring bubble diameter (dye marked region)
Inner diameter of the orifice

Shear modulus
Flow speed/ surface wave speed .

Reynolds number based on momentum thickness
Average time duration of a single event

Average time between events

Velocity of vortex ring in streamwise direction
Velocity of moving wall

Channel centerline velocity

Boundary layer free stream velocity

Convection velocity of Typical eddy

Convection velocity of pocket-like depression
Total velocity (vector)

Transverse length scale of pocket-like depression
Streaks spacing

Normal displacement of compliant surface

Displacement

Time

Spatial coordinates

Velocity components in x,y, and z-direction
Friction velocity, Rial/79y")

Stokes’ layer thickness

Vorticity

Shear stress

Shear strain
y / 2177f

Kinematic viscosity

Momentum thickness

Partial derivative

Circulation

Grid spacing

Finite interval
Wavelength

Non-dimensional by wall layer unit, :2 / 11,,
Non-dimensional time, t(Uw/D0)
Non-dimensional vorticity, w(6 /Uw)

(an/6y): Non-dimensional au/ay, (an/ay)(6 /Uw)
(av/6y). Non-dimensional av/ay, (av/ay)(6 /Uw)

xvii

CHAPTER 1
INTRODUCTION

A large number of fluid flows are difficult to measure. Examples include flows
with moving boundaries, reversed flows, flows with unsteady velocity and temperature
gradients, and flows in complicated geometries. In a wider class of flows only a limited
amount of information can often be obtained, due to the limitations of the
measurement techniques. Development of classical techniques has been underway for
years in attempts to understand complicated fluid problems. The state of the art hot-
wire anemometry such as Foss’ vorticity probe (see Foss 1984) and Wallace’s nine-wire
probe (see Wallace 1986) have made it possible to acquire one point vorticity
measurements; however, these techniques must invoke the Taylor’s hypothesis and are
limited to flows with an appropriate mean component relative to the fluctuation.
Recently, Lang’s (1985) four-spot LDA technique eliminated the intrusive problem,
and, in principle, the need for Taylor’s hypothesis and an appreciable mean velocity
component. However, this technique still yields only one point, one component vorticity
measurements. For many flow problems, it is desirable to obtain simultaneous multi-
point measurements. These include understanding the coherent motions in many
turbulent and unsteady flows, and the study of mixing in internal combustion engines.
Furthermore, quantitative Lagrangian information cannot be obtained by these
techniques. Thus, a technique which is able to provide the flow field information
simultaneously over a region is currently needed. Laser Induced Photochemical
Anemometry (LIPA) is considered a most promising technique to meet our need for
the fluid dynamics measurement because it is a visual, non-intrusive, and quantitative

technique, which is simple to set up and calibrate.

The objective of the present study is to demonstrate LIPA as a powerful tool in
turbulent and unsteady flow problems and to extend our understanding of turbulence
production and modification in boundary layers. It is hoped that the information gained
will lead to a rational basis for boundary layer control. Thus, this study is a combination
of both the technical development of LIPA and its application towards understanding

the basic physics of the bursting process in turbulent boundary layer flows.

In chapter 2 the LIPA technique, a non-intrusive technique, will be discussed.
This technique was first developed by Hummel and his co-workers (1967). With the
advent of high powered excimer lasers, use of highly efficient photochemicals, and new
optical designs, we are able to obtain important fluid quantities such as velocity and
vorticity over a two-dimensional domain of a complicated fluid flow. The first topical
study, which is discussed in Chapter 3, is to use the simplest application of LIPA to
quantitatively measure the change of the skin friction in a turbulent channel flow which
results fi'om the motion of a compliant surface. The study of the surface deformation
observed on the compliant surfaces leads to the next topic, the origin of the turbulence
production in boundary layers. Several investigators (Kline et al. 1967, Corino and
Brodkey 1969, Offen and Kline 1975, Falco 1978, 1979, 1980, Smith 1978) have
presented some possible mechanisms which are responsible for the production process
in the near wall region of boundary layer flows. Based upon the research which has
been carried out by F alco (1974, 1977, 1979, 1980 and 1983), Lovett (1982), and Signor
(1982), it has been shown that the turbulence production mechanism near a wall is
closely related to the formation and evolution of a localized flow module which is
created in the wall region of a turbulent boundary layer as the result of the interactions
Of vortex-ring-like eddies with the viscous sublayer. Further study of the vortex

ring/moving wall interaction model of this process will be discussed in Chapter 4. This

2

model successfully simulates the turbulence production process and provides all visual
features observed in the wall region of a turbulent boundary layer such as pocket (Falco
1979), a pair of low speed streaks (Runstadler et al. 1963, Offen and Kline 1975,
Oldaker and Tiederman 1977, Smith 1978, Falco 1980) with the spacing about 100 wall
layer units, and hairpin liftup (Falco 1982, Acarlar and Smith 1984). It also reveals the
vortical motions associated with the streaky structure. To quantify the fluid quantities in
such a complicated three-dimensional unsteady flow, we apply the LIPA technique. We
make use of LIPA measurements of vorticity and velocity in a Stokes’ layer in order to
demonstrate the accuracy of the LIPA technique. The ability of this technique is
revealed by the measurements of vortex ring flows. Measurements of the vortex
ring/ moving wall interaction in chapter 5 reveal many details of the vortex ring/ moving
wall interaction model and shed new light on how production takes place in the
bursting process in the boundary layer flows. The physical evidence includes the
velocity field associated with the bursting process, the characteristics of the low speed
streaks, and the time evolution of the streamwise vorticity associated with the streaky

structure.

CHAPTER 2
LASER INDUCED PHOTOCHEMICAL ANEMOMETRY (LIPA)

2.1 Introduction

Hummel and his co-workers (1967) first exploited the phenomena of
photochromism (Brown 1971). Photochromism is attributed to atoms or molecules
‘ which are stable or metastable in two states and which possess different molecular or
electronic configurations; i.e., having distinguishably different absorption spectra.
Certain external excitations can cause the atoms to shift between the two states.
Discovering this fact, Popovich and Hummel (1967) and Seely et al. (1975) used a single
line of uv radiation to excite an organic liquid in which a certain amount of
photochromic chemical had been dissolved. They were able to follow the discolored
time line and measure one component of velocity in flows with one predominant
direction of motion. Today, with the advent of highly powered uv lasers, advanced
optical designs and new chemicals, we are able to extend this technique to more

complicated flows.
2.1.1 Photochromic chemical, light source and working fluid

The chemical used in this study was Kodak 1,3-Trimethyl-8-nitrospiro[2-H-1-
benzopyran-2,2’-indoline]. Fig. 2.1 shows the associated absorption and emission
spectrum of this chemical. We excited it at 351nm using pulses of 20ns duration
produced by a Tachisto Excimer laser running on XeF with approximately 100 mj
output and repetition rate being adjustable from 0.1 to 100 Hz. The laser beam was 3 x
20 mm at the exit and had a divergence of 6 mrad half angle. The chemical was

dissolved in the working fluid, kerosene; we found that when the chemical was excited,

it reflected blue light for a certain period of time which depended on the power of the
excitation and the concentration of the chemical. Generally speaking, higher laser
intensity results in a longer trace length and a darker trace color; higher chemical
concentration results in a shorter trace length, a longer trace lifetime and also a darker
trace color. For each experiment we controlled the concentration of the chemical to let
the fluid be tagged long enough to move appreciably, so that we could obtain the
required information. Usually, the concentration of the chemical ranged between 5 to
15 ppm. Since the working fluid had a low electrical conductivity, 5 ppm of anti-static
agent, Shell-Sol 71, was added to increase the conductivity of the kerosene to avoid
building up an electrostatic charge. The addition of the anti-static agent also increased
the polarity of the testing fluid, and thus the equilibrium between the two molecular
states was shifted toward the colored side. Therefore, the lifetime of the photochromic
traces increased with the concentration of the anti-static agent. In principle, for the
velocities of our experiments, we needed to follow the photochromic lines for only a

fraction of a second to obtain the required information.

2.2 Technical details

In practice, we need only to follow one visual photochromic time line to obtain
one velocity component in the flows with one predominant flow direction, and also to
obtain the velocity gradient within the viscous sublayer of a turbulent boundary. .
However, to measure two components of the velocity in a flow using the visualization,
we must tag and follow specific fluid particles. The simplest way to do this is to have
two photochromic lines intersect. That intersection defines a point in the flow which we
can follow. To measure a spatial gradient, we must simultaneously mark two points in

the flow. In addition, we need several points and must use interpolation to measure a

spatial gradient in a prescribed direction. Thus, creation of a grid of marked
intersecting fluid lines would allow us to simultaneously measure velocities and
gradients in the plane on which the grid is generated. Furthermore, by integrating the
velocity component along each grid box we are able to obtain instantaneous circulation
and vorticity distribution in the plane of the recording media. Accordingly, we catalog
the applications into two groups: single tracer technique and grid tracing technique. All

the technical details and the applications of these techniques are given below.
2.2.1 Optical setup

2.2.1.1 Single tracer technique

Liang (1984) applied this technique to study the spatial growth of a Stokes’ layer.
For some applications, we need only one photochromic line to define the velocity
gradient au/ay on the wall in a turbulent boundary layer and the velocity profiles in the
unsteady flows with one predominant flow direction. However, due to the rectangular
shaped cross-section of the laser beam, it depends on the local flow conditions and the
orientation of the laser beam to get the best quality of the photochromic time line . For
example, if we would like to obtain the velocity distribution of a two-dimensional
boundary layer, the photochromic time line shown in Fig. 2.2 (a) will, of course, result
in a higher resolution image than that shown in Fig. 2.2 (b). In other cases, such as
measuring the mean velocity distribution in the spanwise direction of the same flow
field, the orientation of the laser beam shown in Fig. 2.3 (a) will result in a better image
than that shown in Fig. 2.3 (b), even though the photochromic time line is less dense in
color; however, its reduced sensitivity to the local shear force of the flow will keep the

photochromic time line itself from smearing.

Fig. 2.4 shows the experimental configuration for one of the laser beam
orientations. The convex lens was a fused silica lens, 38.2 mm in diameter, 500 mm in

6

focal length, and with a transmission higher than 90% at 351 nm wavelength. The lens
thinned the laser beam from 20 x 7 mm down to 0.056 x 0.160 mm at the focal point.
Fig. 2.5 shows the divergence characters of the laser beam after a F-500mm convex

lens.

2.2.1.2 Grid tracing technique

To enable us to measure important fluid quantities over a two-dimensional
domain of a fluid flow, we have generalized the technique to uniquely tag specific
points in the flow on a specific grid which can be used to obtain two velocity
components and the spatial gradients of these components at a large number of points

in a flow field.

We sought a method of dividing a laser beam into ’n’ beams where ’n’ would be
10, using a static device. In doing so, we sought to lose as little light as possible. Thus, a
special divider was designed by Prof. Falco, which appears as an oversized blazed
reflecting grating; the step size ’a’ is approximately 2 mm. The incident laser beam was
directed at a shallow angle (15 degrees) to the plane of the grating. Because the facets
are so much larger than a wavelength of light, we expected to primarily see specular
reflection. The separation of the specularly reflected portions of the beam was
determined by the difference of the angle of incidence and the blaze angle, and the
grating step width and spacing as shown in Fig. 2.6. A photo of the actual beam divider
is shown in Fig. 2.7. It was fabricated by individually fixing aluminum coated mirrors to
a machined base. Apart from diffraction effects, no incident laser energy would be lost.
As expected, diffraction effects were exhibited in a far-field case, that is, Fraunhofer
diffraction (see Hecht and Zajac). A photo of the output of the beam divider using a
Helium Neon laser is shown in Fig. 2.8. We can see the specularly reflected beams and

the superimposed diffraction pattern. When experiments were performed with the

7

Excimer laser at 351 nm in the near-field, the diffraction pattern was not observed
(Fresnel diffraction). For all experiments using the photochromic grid tracing
technique, we have to make sure to locate the test area away from the effect of far-field

diffraction.

Fig. 2.9 presents a schematic representation of the optical setup for making a
grid in Fig. 2.10 (a). The beam splitter is made by Newport Co. and designed for 351 nm
wavelength. Again, the focal length of the convex lens is 500 mm. Note that the
orientation of the laser beam is also based upon the same principle mentioned in the
previous section. The arrangement of the optical set for different flow measurements

will be discussed in Chapter 5.

2.3 Algorithms to obtain fluid dynamic quantities

2.3.1 Single tracer technique

The technique to measure the velocity component by a single incident beam
path is to measure the displacement between two tracers along the mean flow direction
and to divide this distance by the time interval between the two tracers. (The time
interval is the reciprocal value of the laser pulsing rate.) Fig. 2.11 shows one example of
wall shear stress measurement in the turbulent channel flow where t1 and t2 represent
two instantaneous photochromic tracers in the near wall region. We choose YO within
the sublayer and measure the distance between t1 and t2 which is As; we know the time
interval At between two tracers, then the velocity V will be As / At at yo; furthermore, the
velocity gradient at the wall can be approximated as V/yO. This procedure can be used

to calculate the displacement, velocity, and the velocity gradient.

2.3.2 Grid tracing technique

The two photos in Fig. 2.10 show the grid generated by the optical configuration
shown in Fig. 2.9, which are 0.4 seconds apart, taken by a still camera with a motor
drive. The mesh size is the order of 1 mm. From the distortion of the grid in Fig. 2.10
(b) in comparison to the one in Fig.2.10 (a), (one laser pulse, two photos with At apart)
we can calculate all the kinematic quantities of the flow in the plane of the film. Note
that, in practice, we would not use a second image which has distorted as much as Fig.

2.10 (b); this is only used to illustrate the procedure.

For convenience, we choose any one ’grid box’ in Fig. 2.10 (a) which, if the mesh
size is small enough, can be thought as of as a textbook ’fluid particle’ in a flow at time t
= 0. This fluid particle is shown using solid lines in Fig. 2.12 (a). As this particle moves
with the flow, it may undergo several motions such as translation, rotation, and
deformation. The dashed lines in Fig. 2.12 (a) show the same fluid particle after a short
time interval, At. Because we know the history of this specific fluid particle, we can
compute the velocity of each corner by taking the time derivative of displacement As
associated with each point, that is, As/At. The deduction procedures are shown in Fig.
2.12 (b). Note that V is designated as the velocity at point 1 which is then positioned at
the midpoint between point 1’ and point 1". Fig. 2.13 shows the velocity vectors deduced
from Fig. 2.13. Actually, a fluid particle moving in a general three-dimensional flow
field may have motions about all three coordinate axes; however, we limit the

discussion to the projection of this motion onto the plane of the photos which is parallel

to the initial plane of the grid.

To obtain velocity gradients, vorticity, and strain rates from the velocities, we
must differentiate across the distance of a grid box. Thus, for a given flow, the grid mesh

must be small enough to resolve the smallest scales of motion.

An alternative method can be used if we are interested in the vorticity. Using the

9

definition of the circulation 1‘,
r = fc V ads (1)
and Gauss’ theorem to relate the surface integral to an area integral,

P = fwa'dA (2)

we can obtain the vorticity component normal to the film plane, (02, from a grid
box of arbitrary shape, with circumference C and area A. The velocity component V-ds
in Eq.(1) is estimated by forming the average of the corner velocity components (see
Fig. 2.13). The dividing of I‘ in eq.(2) by the area of the grid box results in the average
vorticity at the centroid of this fluid particle. This approach has the advantages of
avoiding a second differentiation (i.e. the differentiation of V with respect to x or y) of
the experimental data.

Thus, by following the distortions of a single grid box we can obtain the
velocities, circulation, vorticity and even the Reynolds stress and strain rates, if desired,
over that small area. By doing this for the other grid mesh points, we can obtain the
important fluid dynamic quantities at many locations over a two-dimensional field in a

fluid flow simultaneously.

2.4. Calibration and error analysis

The calibration of this technique depends only on a time and a length scale. In
principle, we need only to have a known length scale on the film and the time interval

between two films, so we are able to calculate displacement, velocity, and etc.

As far as the designated accuracy of the grid tracing technique is concerned, let

us consider the grid box in Fig. 2.10 (a). Let us assume that the grid mesh is spaced 6

10

m
if

II I a
Ni n9

 
 
 

and that a worse case line movement between images is 1/2 the mesh width. After time
At, standard analysis (see Taylor 1972 as well as Falco and Chu 1987) shows that the

uncertainty in estimating the vorticity z is

6wz = (1/At)(66/e)

to first order in e. The details of this analysis are shown in Appendix A. As an
example of the designed accuracy of our experiments, if we produce 100 pm lines on a
grid of mesh of 1 mm, and our error in reading the center of the lines is 10%, we obtain
6 e /e = 0.01. For At = 0.01 sec, the uncertainty in the measurement is l/sec. This is
better than has been possible with a hot-wire probe, and is comparable with the most

sophisticated four-spot laser doppler measurements (see Lang 1985).

2.5 Summary and comments

1. A non-intrusive, visual, and quantitative technique has been developed, by
which we are able to measure the instantaneous fluid dynamic quantities such as

velocity, vorticity, and circulation over a two-dimensional domain of a fluid flow.

2. The vorticity obtained by the photochronric grid tracing technique is the
average vorticity of a small area instead of the true vorticity at one point because
vorticity is a point function. All the measured vorticity mentioned in chapter 5 will
represent the average vorticity of each small grid box. The direction of the average

vorticity is normal to the image plane.
3. The calibration depends only on a time and a length scale.

4. Analytically, the designed accuracy is better than that with hot-wire probes,
and is comparable with the most sophisticated four-spot LDA measurement.

11

5. The algorithms of obtaining fluid dynamic quantities involves the linear
approximation. Thus, the distortion of the photochromic time line cannot be too much;

usually we keep the edges of each grid box as straight as possible.

6. The ability and accuracy of this technique and the possible human errors will

be tested and discussed in following chapters through the all applications in this study.

7. Further discussion and comments and improvements will be in Chapter 5 & 6.

12

CHAPTER 3
EXPERIMENTAL DETERMINATION OF DRAG MODIFICATIONS DUE TO

ELASTIC COMPLIANT SURFACES USING QUANTITATIVE VISUAL
TECHNIQUES

3.1. INTRODUCTION

Over the past few years there has been a renewed interest in the possibility of
lowering skin friction drag caused by turbulent boundary layers through the use of
compliant surfaces. These are surfaces that will deform under the shear stress and
pressure fluctuations created by turbulence. This deformation can Iesult in significant
changes in flow properties. It has been suggested that this ability to deform the surface
may inhibit the process by which turbulence is produced, thus lowering the drag. The
detailed mechanism by which this will occur is not yet completely understood. To
determine whether or not a compliant surface reduces the skin friction drag, only three
types of measurement are possible: momentum balances, drag balances and obtaining
au/ay at the wall with a non-disturbing measurement technique. Drag balance
measurements have been made by several investigators for PVC based visco-elastic
surfaces such as Hansen et al. (1974). On the whole, these show an increase in drag
that has been attributed to the formation of static divergence waves in the surface.
Recently, elastic surfaces have been investigated (Gad-el-Hak 1984). These
experiments showed the formation of smaller and faster waves. However, no drag
measurements have yet been attempted. In principle, no matter how accurate the drag
balance measurement is, it cannot give instantaneous shear stress information, which
will be needed to determine what aspects of the turbulence production process are

interfered with by various wall mechanisms. Although the surface hot-film technique

13

,3. :1le
. ‘fi‘
if you.

.‘ l 9
film
YEW

”VJ?

Judi-v

‘ i
r E“
on. ‘

and hydrogen bubble technique are available to get the instantaneous information, yet,
the problems of surface interference, buoyancy problems, and flow disturbance
problems are still not solved, which make the results questionable. Thus, a non-
intrusive wall shear stress measurement technique is needed, which can give accurate
results. The photochromic technique can do this. We present the results of skin
friction measurements made on an almost elastic (very low damping) compliant surface.
The measurements were made possible by using the single tracer technique. It enabled
us to visualize the instantaneous velocity profile in the viscous sublayer region and thus
to measure the velocity gradient at the wall directly even though the surface is moving

(see the discussion in the chapter about the error analysis).

3.2. EXPERIMENTAL DETAILS

Experiments were performed in a recirculating channel flow facility, which
included 1) overall deformations of the compliant surfaces under turbulent channel
flows at fluid to surface wave speed ratios, K, from 0 to 2.2; and 2) measurements of
the local skin friction on both stiff surface and compliant surfaces under the identical

flow conditions.
3.2.1 Kerosene channel flow facility

A turbulent channel flow was developed in the 5.49 m by 0.4572 In by 0.1524 in
test section of a recirculating liquid flow facility, in which deodorized kerosene was used
as the working fluid. The rectangular channel was designed with a 0.4 degree decline
angle along the flow direction to remove any air bubble in the channel. The flow was
driven by a 2 HP DC motor with a solid state power supply turning an axial pump. The

flow was tripped by two 6.35 mm diameter threaded rods which were mounted at the

14

top and the bottom plate of the channel separately. The trip rods were located 6.35 cm
downstream of a 20 mesh screen which was at the downstream end of a precise hex
honeycomb. The test section hatch (50.8 cm by 25.4 cm) was fitted at the bottom plate
and was 4.19 In downstream of the trips. Two viewing windows (45.72 cm by 15.24 cm)
were mounted on the side walls of the channel at the test section. A 19 mm quartz laser
access window was mounted flush with the top wall of the channel, allowing
measurements to be made 38 cm downstream of the leading edge of the test hatch. Fig.

3.1 shows a scheme of the experimental apparatus.

The use of approximately 500 gallons of kerosene necessitated some safety
precautions. Ten parts per million of the antistatic agent, Shell 71 solution, were added
to prevent dangerous electrical charge buildup since the channel was typically run for
several hours such that the kerosene reached equilibrium state with ambient
temperature before measurements were made. The channel, storage tank and all
associated equipment were grounded, and all pump motors were shielded. To achieve
high quality of hot-fihn measurement; a filter made by Flow Tech Co. was also used to

eliminate any particles in the kerosene bigger than 0.5 microns.
3.2.2 Flow documentation in kerosene channel

Velocity profiles were taken using a TSI cylindrical hot-film probe, 1210-20W,
and a DISA anemometer, 55M01. The probe was bent into a five degree of pitch angle
in order to get several measurements in the near wall region. The probe was calibrated
at the center line of the kerosene channel flow by the photochromic single tracer
technique. We averaged about 100 velocity values fi'om photos which were taken by a
Nikon camera with a micro lens and a motor drive during the probe sampling period. In
all, there were ten velocity points calibrated between 0.015 m/sec. and 0.366 m/sec.
The laser pulsing rate for each velocity calibration was set from 2 Hz to 25 Hz.

15

 

The two-dimensionality of the channel flow was checked from the static
pressure drop measurements made at the quarter, half and three-quarter spanwise
points every foot along its length. An open type kerosene manometer was used for those

measurements. The details of the pressure measurement is also shown in Fig. 3.1.
3.2.3 Compliant surfaces

The compliant surfaces were made of Knox unflavored gelatin, which has been
found to exhibit nearly elastic properties (see Hunston, Yu and Bullman 1984). Shear
moduli G of compliant surfaces were obtained through the relationship 7 = G x y
where r was the applied shear stress and 1 was the shear strain carefully measured by a
telescope. Fig. 3.2 shows the dependence of the shear modulus of gelatin on the
concentration of gelatin and water mixture. The concentration is counted as the
percentage of the weight of the powder gelatin in the water mixture. The gelatin was
put in a refrigerator at 40 degrees F for six hours after it was prepared in the special
tray; then we measured the shear modulus of the gelatin prior to testing it in the
kerosene channel. The special trays could be inserted into the test section hatch,
allowing various thicknesses to be tested. 3 mm, 19 mm and 30 mm thick surfaces were
studied, which corresponded from 6 to 60 times the viscous sublayer thickness at Re 9 a

1200. The trays were 48 cm long in the streamwise direction and 22 cm wide in the

spanwise direction.
3.2.4 Surface responses on compliant coatings

Preliminary experiments were conducted to study overall surface motion
characteristics of compliant surfaces under the turbulent channel flows at different
Reynolds numbers. Taking advantage of the total internal reflection at the interface

between compliant surface and kerosene (because the index of refraction of the

16

kerosene is greater than that of the gelatin), we were able to study the spatial pattern of
the surface motions by visualizing the light which shone through the rear viewing
window and was totally reflected at the interface. We set up a 16 mm REDLAKE high
speed movie camera looking through one of the viewing windows with a 25 degree pitch
angle with respect to the tested surface to capture the surface deformation under the
turbulent channel flow. The sketch of the experimental apparatus is shown in Fig. 3.3.
The surface deformation was recorded on EASTMAN KODAK EKTACHROME 7250
film. The framing rate varied from 100 to 400 frames/second, depending on the
channel flow speed. The recorded movie was projected on a 90 by 90 cm diffused glass
through a 16 mm PHOTO OPTICAL DATA ANALYZER which has the function of
single frame advancing. By the superimposed calibration scale we could obtain length
scales, time scales, frequencies of occurrence, and velocity scales associated with

various deformation patterns.
3.2.5 Direct shear stress measurement on the walls

3.2.5.1 Measurement technique and set-up

The photochromic single tracer technique was used to measure the wall shear
stress on both stiff and compliant surfaces. The laser pulses passed through the laser
access window and intersected the bottom plate on the tested surfaces. Fig. 3.4 shows
the optical set-up of this experiment. The laser beam was thinned by a 500 mm focal
length convex lens to 150 pm at the tested wall. The photochromic time lines were
viewed through a short range Questar telescope which enabled us to resolve the
motions in the viscous sublayer and its adjacent region, typically, the field of view was 5
mm by 3 mm. The data was recorded by a 35 mm Photosonic high speed movie camera
on Kodak T'RI-X 400 film. We photographed at a framing rate that allowed two fresh

photochromic time lines to be recorded on each frame. The rate of the laser pulse was

17

high enough to have a negligible motion of the compliant surface between two pulses.

The aluminum and gelatin surfaces were reflective enough to result in a sharp
reflection of the photochromic time line. The point at which the actual photochromic
time line and its image met uniquely defined the instantaneous position of the surface.
This fact was used both to define the distance above the surface, and to quantify the
instantaneous motion of the surface. We measured the velocity at a constant distance
(y"' at 4, where the u, was obtained from the hot-film measurement for stiff surface)
from the surface, whether it was fixed or moving, by simply measuring the distance
between two lines at our chosen distance above the current position of the wall and
dividing it by the time between two pulses. Thus, the au/ay or wall shear stress value
could be obtained from each frame. Fig. 3.5 shows a close-up of this technique used for
wall shear stress measurements on compliant surfaces. In those experiments, a laser
pulse rate of 75 Hz and camera framing rate of 25 frames/ second were used. All films

were analyzed on a NAC motion film analyzer which is accurate to 0.05 mm.
3.3. Results

3.3.1 Flow documentation in kerosene channel

3.3.1.1 Velocity profiles

The standard deviation of the calibration of the hot-film probe was 0.003 m/ sec.
Fig. 3.6 shows the mean velocity profile over a stiff surface at the same streamwise
location used for the photochromic measurements taken under conditions which lead to
skin friction reduction on the compliant surfaces. The centerline velocity was 0.341
m/sec yielding Re 9 as 1200. The plot follows the Coles (1968) law of the wall. Fig. 3.7
shows the turbulent intensity profiles which match those of Eckelmann (1974).

18

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at.

3.3.1.2 Pressure measurement

The result of the pressure measurement at Re 9 z 1200 is shown in Fig. 3.8,
which indicated that there was an even pressure distribution in the spanwise direction
of the channel flow and there was a smooth pressure gradient along the channel flow

direction.
3.3.2 Surface responses of compliant coatings in turbulent channel flow

Preliminary experiments were performed to classify the surface responses of the
gelatin at different values of flow speed/ surface wave speed, K, for three coating
thicknesses. Fig. 3.9 shows the stability boundary for the onset of class B waves for both
gelatin and PVC plastisols obtained by Gad-el-Hak et a1 (1984). It indicates that the
onset value of K of wave-like motion for both materials strongly depends on the coating
thickness. The current visual observations of 3, 19 and 30 mm thick coatings showed
that the first response of all three coatings was with local, three-dimensional, small
scale, randomly oriented, and short lived deformations at approximately the same value
of K, 0.6, instead of being a wave-like response. This onset response is different from
that of the wave-like motion and hasn’t been observed by other investigators. The

insensitivity of coating thickness to this onset response supported these observation.

As we increased the values of K, we observed the change of the characteristics of
the surface responses. The three-dimensional, micro-scaled, and short-lived pocket-like
depression (Falco 1980 b), the intermittency of triangular-shaped waves, and the large-
scaled quasi two-dimensional waves are the basic elements which constituted the
surface responses of the compliant surfaces. The occurrence of each element strongly
depended upon the values of K and on the coating thickness. Fig. 3.10 shows the

dependence of the occurrence of each element on both K and coating thickness.

19

Gad-el-Hak et. al. (1984) showed that wave-like motion on the compliant
coatings did increase the drag. It appears that the beneficial range of surface motions
might occur between our current onset condition and the onset of the wave-like motions

(class B waves).
3.3.3 Shear stress measurements at walls - both stiff and compliant surface

3.3.3.1 Results from photochromic technique

We performed experiments to measure the wall shear stress in the possibly
beneficial range suggested from the visual results in sec. 3.3.2. The wall shear stresses
were obtained using the photochromic single tracer technique at 4.31 m downstream of
the trip rod, with centerline velocity 0.341 m/sec yielding Re 6 g 1200. The
measurement conditions associated with each different thickness are also shown in Fig.
3.9. Table 1 lists the statistical results of the local skin friction coefficient on both stiff

and compliant surfaces.

 

 

TABLE 1
Local skin friction coefficienth
surface K mean s.d. skewness flatness
STTFF 0.004324 0.001277 0.670 3.629

 

COMPLIANT overall 0.003966 0.001295 0.685 3.413
3 mm 1.58 0.003950 0.001310 0.760 3.687
19 mm 1.37 0.003976 0.001255 0.500 2.880
30mm 1.33 0.003973 0.001333 0.810 3.661

 

Figure 3.11 shows the histogram of the skin friction obtained from 1205 samples
over the reference stiff surface. The curve is a lognormal distribution, which has the
same mean and standard deviation as the experimental result shown in Table 1. Fig.
3-12 (a) through (c) are the histograms of the skin friction associated with 3, 19 and 30

20

LCCO

U‘i -,.

THIN
its)

M
w an.
.

m.

mm compliant coatings. The curves are also lognormal distributions. If we combine Fig.
3.12 (a) through (c) regardless of thickness, then we will have the histogram shown in
Fig. 3.13. Comparing the stiff surface (Fig. 3.11) versus the compliant surfaces (Fig.

3.13), we have an 8% reduction in skin fiiction coeficient.

3.3.3.2 Skin friction measurement on stifl' surface by hot-film anemometer

Table 2 shows the results of local skin friction, Cf, obtained from the hot-film
measurement under the same flow conditions which led to skin friction reduction on
compliant surfaces. The results obtained from the photochromic technique are also

shown in Table 2 as reference.

TABLE 2

Cf measurement from hot-film

 

# of measurement Cf (Clauser) Cf (Newton)

 

 

1 0.00460 0.00379
2 0.00455 0.00388
3 0.00455 0.00376
average 0.00457 0.00381

 

Photochromic technique 0.00432

 

3.3.4 Surface response on compliant surfaces associated with the wall shear stress
measurement

Visual observation showed that three-dimensional, short-lived pocket-like
depressions, which are of the order of Taylor microscale, formed on the compliant
surfaces (see Fig. 3.14 photo) at the same flow condition at which we conducted the
wall shear stress measurement. Those depressions were the major Observed response

WhiCh showed up randomly on the compliant surfaces and were bordered by crests that

21

extended above the mean level of the undisturbed surfaces. Table 3 lists the physical
scales associated with the pocket-like depressions. Those data were obtained from the

16 mm movie mentioned in sec. 3.2.4.

Fig. 3.15 shows the comparison of transverse length scale of depressions in
compliant surfaces with the pocket footprints made on a solid surface. (cf. Yoda, F alco,
and Emmerling). The comparison of the time between depressions in compliant
surfaces with the time between pocket-like foot prints obtained from boundary layer

and channel flows is shown in Fig. 3.16 (Lovett, Eckelmann, and Thomas).

TABLE 3

Physical scales associated with the pocket-like depressions

 

thickness 3 mm 19 mm 30 mm average

K 1.55 125 1.25
lo w+ 1.92:0.04 1.92:0.04 1.962004 1.932004
d+ 30.2tl.8 27.8:18 33213.8 30.4:25
T + 35815.4 33.4:445 30915.4 33.4451
(112/U1 0.59:0.07 0.62:0.07 05910.05 06020.05
max. (19 1.2 y+ 1.6 y+ 1.6 y+ 1.5 y+

K used in Cf
measurement 1.58 1.37 1.33

 

 

 

3.3.5 Observed wave patterns on compliant surfaces

When the value of K was over 1.2 (for thinner coating), groups of three-
dimensional triangular-shaped waves were observed intermittently. Fig. 3.17 is a photo
showing this kind of wave. This phenomenon strongly depends on the thickness of the
compliant coatings. It appeared at relatively lower values of K for thicker coatings. For
3 111m coating it existed at K between 1.2 and 2.1. As K was below 1.8, the pocket-like

22

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o
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"\

depressions dominated the overall picture. However, those triangular-shaped waves
were dominant when K was over 1.8. Table 4 shows the wavelength, half angle, wave
speed, and wave numbers associated with the triangular-shaped waves in 3 mm coating

at two different value of K.

As the value of K was increased, the wave patterns became quasi-two-
dimensional and approached two-dimensionality for thicker coatings. Those waves were
the large-scale waves with large amplitudes traveling at about 50% of the channel
center-line velocity, they looked like the class B waves which were observed by Gad-el-
Hak et al. Fig. 3.18 shows a photo of these quasi two-dimensional large-scaled waves.

TABLE 4

Characteristics of the triangular-shaped waves

 

flow speed / surface wave speed, K 1.80 2.07
wavelen h/ coating thickness 2.89 «£0.35 3.50:0.31

 

half an e (de ee) 46.7i3.0 52.1133
wave velocrty flow velocity 0.73 $0.02 0.721.003
wave numbers 2.43 t0.56 3.34:0.80

 

3.4. Discussion

The lateral scale of the pocket-like depressions is about 60 times the height of
the surface movement, so that if a probe was positioned in the wall, it would severely
inhibit these motions of the compliant surface. The photochromic technique is a
reliable tool to obtain the wall shear stress on compliant surfaces nonintrusively and

accurately.

The average reading uncertainty obtained from different readers during the data
1' Cduction process through a motion film analyzer was 3%, which was mainly a result Of

23

human error. Through the use of digital image processing equipment, this uncertainty
can be reduced. The maximum error associated with the au/ay measurement caused by'
the movement of compliant surface was 4%. This error was estimated by the maximum
vertical displacement on compliant surfaces between two photochromic time lines. It is
reasonable to use the lognormal distribution to estimate the mean of the error which is
due to the surface movement because the wall shear stress has a lognormal distribution.

Thus, the mean of the error in calculating au/ay is about 1.5%.

Results of hot-film measurement were different from those obtained using the
photochromic technique. The result obtained using Clauser plot based on Coles (1968)
universal law is about 5% higher than that obtained using the photochromic technique.
The reason for this difference may possibly be attributed to measurement error or the

favorable pressure gradient of the channel flow which was not fully developed.

The value of rms(au/6y)/mean(au/ay) was 0.295 on the stiff surface
measurement; this indicates that the measurement was in agreement with several

investigators such as Mitchell & Hanratty (1966) and Eckelmann(1974).

In comparing the two histograms in Fig. 3.11 and Fig. 3.13, the compliant
surfaces did change the characteristics of the statistical results on skin friction
distribution. Interestingly, it shows that only the high probability events have been

changed and the skewness and flatness almost stay the same.

The only other study of elastic surfaces known to the author is that of Gad-e1-
Hak et al.(1984). He found that two-dimensional waves set in at values of K
(approximately 3.5, for a 3 mm thick surface) higher than those for which we found a
three-dimensional pattern. The reason for the differences are not known, but earlier,

Falco, Chu and Wiggert (1983) also observed a three-dimensional pattern developed in

24

1'th ‘
{.4. .

Swag;

[in Na»
A

I

“A . T
i?

-341 1

“‘3‘.”
, t ,
Isn‘...‘
h

176301

1
”Wing.

N‘km‘ :

"fa
“- 5

I" r
3111!
Us Ji\

the same compliant material in a water channel test before the onset of large amplitude

waves of the type found by Gad-el-Hak et al.

It appears that the response we have found is a response of the surface to the
microscale eddies of the turbulence, which, at least in these preliminary experiments,
does lead to skin friction reduction. More evidence on this is shown in Table 3; the
length scales, the velocity scales and the time scales associated with the pocket-like
depressions correlate very well with those of the bursting process in a turbulent channel
flow and boundary layer flow. Fig. 3.15 and Fig. 3.16 show a very good agreement
among the comparisons. Fig. 3.19 shows the further comparison between the visual
phenomena on compliant surfaces and the flow visualization in the near wall region of

channel flow by Yoda (1981). Apparently, they look similar.

Interestingly, we obtained almost the same amount of skin friction reduction for
three different thickness coatings at the operating conditions. It may suggest that the
characteristics of turbulence being modified during the interaction with the compliant
surfaces has weak dependence on the thickness of the coating, when the operating value
of K is slightly above our current onset boundary and is significantly below the onset
boundary of class B waves. If this modification were created by wave motions on
compliant surfaces, then the dependence on the coating thickness should be

pronounced.

From Fig. 3.9 we also can see that for thinner coatings there is a wider range of
three-dimensional surface deformation before the onset of quasi-two-dimensional
surface motions. Thus, thinner coatings should have a wider operating range over
Which skin friction reductions are possible. Further experiments are needed to

determine the range of applicability of these results.

As far as the triangular-shaped waves are concerned, their half angles,
25

wavelengths and wave numbers increased as the value of K went up. Eventually, the
half angles reached to 90 degrees and the waves became two-dimensional, which had
large amplitude and wavelength spreading over the whole compliant surface. Those
large scale waves were close to class B waves observed by Gad-el-Hak et al., which

travelled at about 50% of the channel center line velocity.
3.5. Conclusions

1. A non-intrusive quantitative photochromic single tracer technique has been
used to measure the skin friction both on a stiff surface and on compliant surfaces. The

error of this technique is about 4.5% plus sampling error.

2. Eight percent (8%) skin friction reduction has been found on low damping

elastic gelatin.

3. Histograms of skin friction distribution are lognormal for both stiff and

compliant surfaces.

4. The observed onset response on currently used compliant surfaces was local,
three-dimensional, small scale, and short lived deformation at approximately the same

value of K, 0.6, for three different thicknesses.

5. In conditions which lead to skin friction reduction, the surface responses show
the characteristics of turbulence. The measured length scale, time scales and velocity
scale associated with the observed pocket-like depressions correlate very well with

those of the bursting process in wall bounded turbulent flows.

26

CHAPTER 4
NEW UNDERSTANDING OF THE INTERACTION ASSOCIATED WITH

TURBULENCE PRODUCTION: A VORTEX RING/MOVIN G WALL INTERACTION
MODEL OF THE TURBULENCE PRODUCTION MECHANISM NEAR A WALL

4.1 Introduction

In the previous chapter we studied the surface responses of the compliant
surfaces associated with the skin friction measurement and compared those with the
bursting process in wall bounded turbulent flows visually (see Fig. 3.19) and
quantitatively (see Table 3, Fig. 3.15, and Fig. 3.16). We concluded that at low forcing
levels where Cf reduction was found, the response of compliant surfaces is a response to
turbulence. Accordingly, we ask ourselves a question, "What mechanism is responsible
for creating pocket-like deformations on compliant surfaces and also for rearranging a
dye marker to create the structural features in the near wall region of rigid wall
bounded turbulent flows (see Fig. 3.19)?" We focus on this point in this chapter and the

following chapter.

There is a need to construct both experimental and numerical simulations of the
turbulence production process near walls, because of the difficulty of isolating
mechanisms when experiments are conducted in the boundary flows. A good simulation
must embody the essential features of the production process. Several investigators
(Kline et al. 1967, Corino and Brodkey 1969, Offen and Kline 1975, Falco 1978, 1979,
1980, Smith 1978) have presented some possible mechanisms which are responsible for
the production process in the near wall region of boundary layer flows. In this chapter
we present a moderately extensive review of the important structural features
associated with the wall region events as well as the new boundary layer observations

27

observed in Turbulence Structure Laboratory, Michigan State University (Falco, Lovett,
and Signor), that helps complete the picture of structural feature interactions. Then we
present the vortex ring/moving wall simulation experiments that model all of the
important properties.
4.1.1 A review of the important structural features associated with the wall region
events in boundary layer flows

Turbulent boundary layer structure that should be modeled includes the long
streaks (Runstadler et al. 1963), the pockets (Falco 19803, 1980b), the hairpins (Falco
1982, Acarlar and Smith 1984), the Typical eddies (Falco 1977, 1983), and coherent
regions of streamwise vorticity and/ or streamwise vortices. Basically, these structural
features have been shown to be associated with the production process, but the
formation of the structures and the interactions are not completely understood. A
number of investigators have studied the formation of low speed streaks. Oldaker and
Tiederman (1977) observed that a pair of low speed streaks formed as a result of the
response to what appeared to be a sequence of local high speed outer region eddies
interacting with the wall and aligned along a streamwise direction. The path left by the
outer region disturbances clearly formed a high speed streak. Falco (1980a) observed
the formation of low speed streaks in pairs by a similar mechanism. Although low speed
streaks are often observed to exist singly, care must be taken when interpreting low
speed streak formation, because once formed the low speed streaks can persist for very
long times (Smith and Metzler 1983), and the undisturbed passive dye marked region

will simply convect into the observation zone.

Since the mid fifties, it has been suggested that long counter rotating streamwise
vortices exist in the wall region and that pairs of these vortices produce a gathering of

wall layer dye between them that we see as the low speed streaks. A high speed streak

28

would be the result of high speed fluid being induced towards the wall between a pair of
these streamwise vortices rotating the other way. A number Of authors have suggested
causes for these streamwise vortices. Currently, the most popular suggestion is that
they are the ’legs’ of hairpin vortices that are also observed in the wall region.
However, as Acarlar and Smith (1984) have pointed out, it is very hard to understand
how the hairpin legs could extend upstream as far as would be necessary to produce
streaks of length x+ = 0(1000). Thus, there is still no experimental evidence
supporting the various rational physical hypotheses describing the formation of long
streaks.

Another feature of the wall region structure is the frequent rearrangement of
marker that moves it away from a local region, leaving a scoured ’pocket’ of low marker
concentration. Fig. 4.1 shows two pockets as seen in a layer of smoke marked sublayer
fluid. Pockets are footprints of outer region motions that interact with the wall. Falco
( 1980a) showed that they start out as a movement of wall layer fluid away from a
location as a high speed outer region eddy (a typical eddy, discussed below) nears the
wall. The interaction results in the footprint opening up into a developed pocket shape.
Fluid is seen to lift-up from the downstream end of the pocket, and take on the

characteristics of a hairpin vortex (Falco 1982).

Vortex lines are constantly being bent in turbulent boundary layers. Although
flow visualization of a passive contaminant cannot be used to observe vorticity directly,
dye marked features in the wall region that appear to be hairpin vortices have been
observed by Falco ( 1982) and Smith et al. (1983). We have Observed hairpins appearing
to form over individual streaks. The streak is seen to become lumpy, and one of the
lumps grows and a hairpin emerges from it. Acarlar and Smith (1984) have also

observed hairpins growing over simulated streaks, and, it appears, in a turbulent

29

boundary layer.

The microscale coherent motions observed across a turbulent boundary layer,
which are similar to laminar vortex rings embedded in a shear flow, are called Typical
eddies. They have been studied by Falco (1974, 1977, 1982, 1983), who showed that
they contribute significantly to the Reynolds stress in the outer part of the boundary
layer, and that they are the excitation eddies that create the pockets. Experiments using
two mutually orthogonal sheets of laser light enabled F alco (1980b) to determine, as far
as the smoke marking allows, that the coherent feature was a ring, as opposed to a

portion of a hairpin vortex, as suggested by Head and Bandyopadhyay (1981).

Both types of hairpin creation mechanisms described above can produce
hairpins that can pinch-off and form new vortex rings. Falco (1983) showed visual
evidence of a hairpin lifting from the downstream end of a pocket, contorting and
pinching off to form a new vortex ring-like typical eddy. This pinch-off mechanism has
also been clearly shown to occur in the calculations of Moin et al. (1986) mentioned

above.

Many investigators have noted the presence of streamwise vortices in the wall
region. Almost without exception, the vortices have been of short extent (Praturi and
Brodkey 1978, Falco 1980b, Smith 1982). A number of investigators have suggested that
streamwise vortices of much greater extent exist in the wall region essentially laying just
above the wall in pairs, which are responsible for the creation of both low and high
speed streaks. This evidence is of a statistical nature, usually from correlation
measurements. However, no one has ever observed them, and recent calculations of
turbulent channel flow using the full Navier-Stokes equations (Kim 1986) have shown
that the eddies which have streamwise vorticity are not elongated in the streamwise

direction.
30

4.1.2. New boundary layer observations 1n the Turbulence Structure Laboratory,
Michigan State University

The major discovery is that as a typical eddy convects over the wall, it causes an
interaction that results in the formation of a pair of long streaks. If the typical eddy is
convecting towards the wall, when it gets close enough, it will create a pocket, and have
one of four types of interactions defined below. The creation of the long streaks occurs

even when the typical eddies are quite distant from the wall, well into the log region.

Observations mentioned above have indicated that hairpin vortices can form as a
result of pocket evolution and as a result of lumping instability of existing low speed
streaks. They also found that there were occurrences where neither of these
mechanisms appeared to be the cause. They also identified another mechanism that can
result in the formation of hairpin vortices. When a typical eddy is moving away from the
wall at a shallow angle and when it is moving relatively slowly, say Uc/Uoo <0.4, it will
create a pair of long very stable streaks that trail behind a hairpin vortex that lifts up
slowly. The eddy can be as far from the wall as indicated above, and thus, will convect
appreciably downstream before the hairpin will be noticed. It may convect out of the
field of view, leaving the observer with the impression that the formation of the hairpin

did not involve the coherent motion.

Thus, only one coherent motion, interacting with the wall, is necessary to create
both the long streaks and the pockets; since the remaining structures found in the wall
region are related to these two structures. The visual results suggested that the typical

eddy be responsible for the onset of the turbulent production process.

4.2 Vortex Ring/Moving Wall Interaction Model

4.2.1 Vortex ring/moving wall simulation of the turbulence production process
31

Accordingly, we can simulate the interaction of a typical eddy with the wall
region of a turbulent boundary layer by creating a vortex ring and having it convect
towards or away from a moving wall. Fig. 4.2 shows the basic idea behind the
simulation. The vortex ring can be aimed at or away from the wall at shallow angles.
Both the wall and the ring move in the same direction. The Reynolds numbers based
upon the initial ring velocity and diameter of the dyed ring bubble, D, ranges between
600 and 2000. When created away from walls, these rings remain stable to azimuthal
instabilities over durations longer than those used in the interaction experiments. By
performing a Galilean transformation on the simulation, we recover the essential

aspects of the typical eddy wall region interaction in a turbulent boundary layer flow.

For convenience, we have used an impulsively started moving belt. It has the
advantages of being an exact solution of the Navier-Stokes equations (Stokes’ first
problem), and therefore is well defined. Furthermore, the velocity profile is
approximately linear in the wall region which is similar to the mean velocity profile of
the viscous sublayer of a turbulent boundary layer. It is relatively easy to match the
friction velocity in these simulations with those found in low Reynolds number

turbulent boundary layers.
4.2.2 Experimental details

4.2.2.1 Experimental apparatus

Experimental simulations were performed in a water tank which is 40.5 cm deep
by 32.4 cm wide by 243.8 cm long. Fig. 4.3 shows the side view and end view of the
experimental apparatus which includes a vortex ring generating device, a moving belt

and driving arrangement, a synchronizing timer, and visualization recording devices.

4. 2. 2. 1.1 Vortex ring generating device

32

The vortex ring generating device includes a constant head reservoir from which
fluid, which could be dyed, passes through a solenoid valve whose opening time could
be varied, and an orifice of prescribed size (see Fig. 4.3 items 1,2,3). The constant head
reservoir (item No. 1) is filled with a mixture of 10 ppm Fluorescent Sodium Salt Sigma
No. F-6377, green dye and water solution. As the solenoid valve (No. 2) opens, a slug of
dyed fluid is released from the orifice (3) by the pressure head, and rolls up into a
vortex ring. Three different inner diameters of the orifice have been used; 2.54 c111, 1.27
cm, and 0.95 cm. The size and speed of the vortex ring generated depends upon both
the height of the dye reservoir and the opening duration time of the solenoid valve for a

fixed orifice. The details have been presented in Liang (1984).

4. 2.2.1.2 Moving belt and driving device

The wall upon which the vortex ring interacted is a moving belt (4) made Of
transparent plastic which has a smooth surface. Two ends of the belt are joined together
to form a loop, which circulates around two rollers (5) as shown in Fig. 4.3. The width of
the belt is 17.8 cm; and the distance between the two rollers is 152.4 cm. The test
section is at 76.2cm downstream from one of the rollers, giving us a Stokes’ layer for
this distance (if the belt is run longer in time, the leading edge effects begin to enter
into the problem). This width/length ratio is sufficient to prevent the disturbances
generated in the corners from reaching the center of the belt at the test section.
Therefore, the wall layer flow on the moving belt could be considered one-dimensional.
One of the rollers is driven by a 1/4 HP DC motor (6). The speed of the belt is
adjustable within the range of 2.5 cm/Sec. to 22.9 cm/sec. The belt reaches a constant
speed very soon (within a second) after power is turned on. This short acceleration
period allows us to consider the belt to be impulsively started. As the belt moves, a
Stokes’ layer builds up on the belt. A mixture of red food coloring and water is used to

mark the wall layer for visualization. The belt is covered with dye before each run

33

during a ’dye run’ using a dye injector near the leading roller of the belt, shown in Fig.

4.3 (7). The fluid is allowed to come to complete rest before each ’data run’.

4.2.21.3 Control system

The opening duration time of the solenoid valve, and the time delay between the
onset of the belt movement and release of the vortex ring are controlled by a 115
VAC/60 Hz timer designed in the laboratory. Since the thickness of the Stokes’ layer,
6, is a function of the square root of the belt run time, that is, 6 = 4.0 J'Vt', by carefully

adjusting the time delay, we can adjust 6 / D as desired.

4.2.2.2 Visualization and recording
4.2221 Two-view visualization

The primary visual data consisted of simultaneous plan and side view time
resolved images which were collected using a standard video camera, a VCR, and a
monitor, and are shown in the end view of Fig. 4.3. The side view was often illuminated
by a laser sheet emitted from an 8 W Coherent CR-8 Supergraphite Argon Ion Laser.
The visual data were analyzed on a high resolution monitor with a superimposed

calibrated scale, using the slow motion capabilities of the recorder.

A 35mm Photo-Sonic movie camera and a 16mm Redlake high speed movie
camera were also used to record high resolution images of the interactions on Kodak
ASA 400 color negative film and Kodak Ektachrome 7250 film respectively. The data

acquisition system is the same as that shown in Fig. 4.3

4.2.2.22 Three-view visualization

A simultaneous three-view data acquisition system was designed in order to
resolve the vortical structure associated with the vortex ring/ moving wall interaction in
the plane which is perpendicular to the mean flow direction Fig. 4.4 shows the scheme

of the three-view visualization system; note that only the end view was illuminated by

34

the laser sheet. The image of the laser illuminated end view was sent to the top view
collecting mirror through a front coating flat mirror. This is shown in both views of the

set-up in Fig. 4.4.

4.3 Results of vortex ring/moving wall interactions based on two-view flow
visualizations

We will describe the model in terms of the velocity ratios and spatial
relationships of the simulation. Later in the discussion, we will invoke the Galilean

transformation to relate the findings to the turbulent boundary layer case.
4.3.1 Evolutions of the model

4.3.1.1 Fast rings (Ur/Uw > 0.45) moving towards the wall with a shallow angle (3, 6,
and 9 degree)

Interactions which result from these rings have been described by Liang et al.
(1983). They result in the formation of a pocket, and varying degrees of lift-up of wall
layer fluid. The interactions have been divided into four types. Fig. 4.5 shows sketches
of the four types of interactions. Type I results in a minor rearrangement of the wall
layer fluid; followed by the ring moving away from the wall essentially undisturbed.
Type II (same as described for boundary layer interactions) results in a well defined lift-
up of wall layer fluid, which takes on a hairpin configuration. This fluid does not get
ingested into the ring, and the ring moves away from the wall as a perturbed but stable
ring. The hairpin has been observed to pinch-off or just move back down towards the
wall and lose its identity. Type 111 results in a lifted hairpin of wall layer fluid which gets
ingested into the ring, resulting in a chaotic breakdown of both the lifted hairpin and
the vortex ring, as the vortex ring is moving away from the wall. Type IV also initiates a

hairpin vortex, but in this case the hairpin vortex is ingested into the ring on a much

35

shorter timescale, and the ring and lifted wall layer fluid both breakdown while the ring

is very close to the wall.

Liang et al. used vortex rings with D+ > 250 and a + between 20 and 50, and
they observed only the above four types of interactions. Current experiments indicate
that if D+ < 150 and 6 1' is between 20 and 50, we can also obtain the four types of
interactions noted above, but, in addition, we found that long streaks also formed. In
these cases, a hairpin grew out of the open end of the pocket, its legs stretched and a
pair of streamwise streaks formed along the hairpin legs (see Fig. 4.6). The streaks grew
to several hundred wall units. This observation is in contrast to the suggestions of a
number of investigators that a lifted hairpin vortex would induce a single streak to form

between its legs.

4.3.1.2 Slow rings (Ur/Uw < 0.35) moving towards the wall at a shallow angle (3, 6,
and 9 degree)

These initial conditions result in a pair of long low speed streaks, x+ = 0(1000),
a pocket, and hairpins which induce themselves and portions of the streaks to lift-up.
Fig. 4.7 shows six photos of this happening prior to the onset of a Type III interaction.
We can see the formation of the pair of low speed streaks, followed by the formation of
the pocket, and the associated hairpin lift-up, then partial ingestion of the pocket
hairpin. The ring later breaks up. The streaks that form under these conditions become
wavy and slowly breakdown resulting in additional lift-up and transport. Hairpins have
been observed to form over these streaks (see Fig. 4.8). The initial conditions are two-
dimensional. The moving belt is started from rest, so that the layer approximates a
Stokes’ layer. These streaks have obviously not formed as the result of the pre-existence
of streamwise vortices, but spanwise vorticity has been distorted to give a streamwise
component, and it is clear from the Navier Stokes equations that new streamwise

vorticity has also been generated at the wall.

36

4.3.1.3 Fast rings (Uer > 0.45) moving away from the wall at a shallow angle (less
than 3 degrees)

These initial conditions result in a hairpin vortex which is linked to the
distributed streamwise vorticity that has formed a pair of long, very stable, low speed
streaks. A pocket is not observed. The evolution of the hairpin in this case has been
observed to lead to the pinch-off of this hairpin, forming a vortex ring, and another
hairpin. Fig. 4.9 shows four photos of the evolution leading to the creation of a new
vortex ring. The long stable streaks which form come closer and closer together,
indicating that the streamwise vorticity which caused them, and which is of Opposite
sign, is being stretched and brought very close together. Diffusion is accelerated, and
the vorticity is redistributed into a vortex ring and a hairpin loop. Fig. 4.10 shows long
stable streaks and a long stretched hairpin which does not pinch-off over the distance
available due to size limitations of the experimental facility--more than 2500 wall layer
units. There are two initial conditions that may cause this kind of long stretched
streamwise vorticity to evolve into a hairpin: 1) 6 / D is very small; 2) the ring is far away
from the wall. Further study concerning the effects of ring to wall distance is needed.
4.3.1.4 Far-field effect (fast ring, Ur/Uw > 0.6, moves away from the wall at a shallow
angle)

The far field effect could happen even though the edge of the lower lobe of the
vortex ring is around 120 y+ above the wall. A long stretched hairpin was observed to
form which had the same shape as that shown in Fig. 4.10, however, the spacing

between the two legs became narrower as the distance between the ring and the wall

became larger.

4.3.1.5 Slow rings (Ur/Uw < 0.45) moving away from the wall at a shallow angle (less
than 3 degree)

These initial conditions result in a hairpin from which a pair of long stable low
speed streaks emerge. A pocket is also not observed. The phenomenon of hairpin

37

pinch-off, for this case, appears to depend upon 6 /D. If 6 /D < 0.15 we get pinch-off,
but only a part of the fluid involved in the hairpin is observed to pinch-off and form the
ring. If 6 /D is greater, and the ring moves away from the wall without ingesting any
wall layer fluid (Type I or II), the lifted hairpin appears to do very little. Fig. 4.11 shows
four photos of the evolution for 6 / D > 0.15. In this case a pocket does not form, and it
appears that the hairpin has been generated by the initial vortex ring/wall interaction,
and that a pair of streamwise vortices-which could be called its legsutrail behind,
creating the streak pair. Pinch-off does not occur. Fig. 4.12 shows four photos of the
interaction for 6 /D < 0.15. In this case pinch-off of a portion of the lifted hairpin does

occur creating a new small vortex ring.

4.3.1.6 Summary of interactions

A summary of the vortex ring/wall interactions which result in streak formation
and evolution is shown as a function of the parameters Ur/Uw 6 /D, and ring angle in
Fig. 4.13 and 4.14. Fig. 4.13 shows the dependence of the formations and evolutions of
streaks on 6 /D and Ur/Uw for D+ > 250 and a 3 degree incidence angle. The
indicated boundaries are between different evolutions and are approximate; additional
data are necessary to precisely locate their positions. The available information suggests
that the streak development is essentially not dependent upon 6 / D. Furthermore, the
long streaks are only observed to form for speed ratios less than approximately 0.35.
Fig. 4.14 shows the dependence of the formations and evolutions of streaks on 6 / D and
Ur/UW for rings moving away from the wall at 2.5 degrees. 6 /D now plays a much

more important role, and long streaks are generated over the entire speed ratio range

studied.
4.3.2 Scaling associated with the vortex ring/moving wall interactions

From our perspective of a turbulence production model, the streak spacing,

38

streak length and wavelength of the streak instability are quantities of interest.

4.3.2.1 Streak spacing

Fig. 4.15 shows the dependence of the non-dimensional streak spacing on the
size of the non-dimensional vortex ring, for an incidence angle of 3 degrees and Ur/UW
= 0.31. The thickness of the wall layer (in wall units) is shown next to each data point.
The streak spacing, Z1”, is within 10% of the ring diameter for wall layer thicknesses
between 20 and 50 wall units. Results shows that decreasing Ur/Uw will decrease the
average streak spacing relative to the ring size for fixed incidence angles. Furthermore,
increasing the incidence angle of the vortex ring will increase the average streak spacing
for a given ring size and speed ratio. Fig. 4.16 shows the dependence of the streak

spacing on the speed ratio and angle.

4.3.2.2 Streak length
Measurements show that streak lengths greater than x+ = 500 were obtained
for many of the interactions in ranges where the streaks are stable ( for rings with D+

= 100, streaks as long as x+ = 1000 were found ).

4.3.2.3 Wavelength associated with wavy streak instability
Fig. 4.17 shows the non-dimensionalized streamwise wavelength that sets in as a
function of 6 + for different Ur/UW The wavelength is the same order as the ring

diameter. It decreases as the ring/wall speed ratio.
4.3.3 Stability considerations

4.3.3.1 Vortex ring stability
Some additional data has been obtained, which confirms and extends the results
of Liang (1984), showing that the boundary between stable ring wall interactions (Types
I and H), and unstable interactions (Types HI and IV) depends upon 6/D. Fig. 4.18
39

shows a stability map of the interactions for 3 degree rings. We can see that for low
ring/wall speed ratios, the ring stability depends primarily upon the relative thickness of
the wall layer and the size of the ring; for thicker wall layers or smaller rings, the
interactions are more stable. Furthermore, the shallower the incidence angle the more

stable the interaction.

4.3.3.2 Stability of the streaks

Fig. 4.19 shows the dependence of the time onto instability (i.e. the time from
the formation of the streaks to the first observation of the wavy instability) of the
streaks which exhibited wavy instability on the wall layer thickness (both quantities are
non-dimensionalized by wall layer variables) for 3 degree incidence rings. We can see
that for each convection velocity ratio, there is a value of 6 + above which the time to

instability becomes much longer.

4.3.3.3 Comparison between ring and streak stability

Both the rings and the streaks are more stable when the wall layer is thicker. Fig.
4.18 shows a comparison of the stability boundaries of a three degree ring moving
towards the wall, with the stability boundary of streaks formed by those same rings. The
streak stability boundary has generally the same shape; stable rings will, in general,
correspond to stable streaks, except for a small range of 6 /D. The ring stability curves

and the streak stability boundary curves for different size rings collapse when plotted

this way.

The streak formation boundaries in this figure represent the boundaries between
conditions that will enable a pair of long streaks to form. For 6 /D below the
boundaries, we have a very unstable situation in which the fluid in the region around
the eddy seems to rearrange itself into the beginnings of a streak, but the streak pair is
not stable, and immediately breaks up. For 6 /D values above the boundaries, a pair of

40

long streamwise streaks form. However, once formed, the streaks are susceptible to
breakdown by the wavy or lumpy instabilities noted above, where the time to instability
is a function of angle, convection velocity, and the instantaneous wall layer thickness

(for example, see Fig. 4.19).

4.4 Results of the vortex ring/moving wall interactions based on three-view
visualization

By accessing the laser illuminated end view we were able to realize the
streamwise vortical structure associated with the vortex ring/ moving wall interaction.
We will discuss the interactions which were observed the most in the turbulent layer,
that is, the interactions in which a pair of long streaks were observed as being either

stable or unstable.

4.4.1 Slow rings (Ur/Uw < 0.35) moving towards the wall with a shallow angle (3
degree)

The conditions of the case discussed here are shown as point ’A’ in Fig. 4.18.
These initial condition result in a main hairpin, a pair of low streaks x"’ = 0(1000), a
pocket, and hairpins induce themselves and portions of the streaks to lift-up. By sending
the laser sheet to different locations we were able to resolve the vortical structure at

different parts of the interaction.

The main hairpin was observed to form first; the sign of the hairpin vortex is
shown in Fig. 4.20. Evidently, it was a vortex loop; the core is about 5-10y+ and the
distance between two legs was about 50-60 2"" in the spanwise direction. This hairpin
vortex was the wall layer fluid induced and lifted up by the lower lobe of the vortex ring.
After the hairpin vortex was lifted up from the wall, it was stretched and diffused. The
visual evidence showed that this hairpin vortex lasted about 50 t+. Even though we still

41

can visual the organized dye marker associated with the lifted hairpin at the later stage
of the vortex ring/ moving wall interaction, however, the laser illuminated end view

suggested that there was not much vortical motion in this hairpin vortex.

Fig. 4.21 shows the evolution of the vortex pair which was observed to be
associated with the streaky structure. There are 10 t+ between photos. As this vortex
pair induced itself up, it was getting bigger and bigger and its size could be about 25-30
z+ extending about 200-300 11* in the near wall region (y"' < 10). The three-view
visualization showed that even before the streamwise vorticity, x, rolled into vortices,
the top view had already shown the wall layer dye marker being gather together to form
streaks (see Fig. 4.21 (b)). After. the vortex» pair was observed to form, it induced itself
up and broke up. This quick lifting and breakup lasted only about 20 t+. Mainly, the
dye marker associated with the observed breakup was from this vortex pair. Only the
top view could not tell the difference between the streamwise vortices and the long
streaks. Fig. 4.21 (b) shows clearly the evidence of the formation of the secondary

hairpin vortices over streaks; especially in the region near the pocket.

Three-view visualization also showed that as the pocket vortex (Falco 1980b)
entered into the viewing window (laser illuminated end view), suddenly, the lifted
vortex pair was turned inward in the rotating direction of the pocket vortex (Falco
1980b). This inward motion caused the lifted vortex pair to break-up. However, there
was no dye marker present in the vortical structure of the pocket vortex. One possible
reason for this may be due to the dye marker which had been pushed away to form

streaks in the earlier stage of the interaction.

Based upon the results of three-view visualization on vortex ring/moving wall
interaction model, we summarize the interaction into one picture. Fig. 4.22 shows a
conceptual picture describing the spatial relationship of the formation of visual features

42

observed in the vortex ring/moving wall interaction including the main hairpin vortex,
secondary hairpin vortices, long streaks, and pocket; the arrows indicate the flow
direction.

4.4.2 Fast rings (Uer > 0.6) moving away from the wall with a shallow angle (less
than 3 degree)

Fig. 4.23 (a) is a photo showing the laser illuminated end view visualization
under the those initial conditions. The observed long streaks were just the legs of the
lifted hairpin vortex; they were one unit. The dye marker actually concentrated with the
streamwise vortices. The sign of the vorticity shown in Fig. 4.23 (b) is consistent with
that associated with the hairpin vortex shown in Fig. 4.20 (b). Fig. 4.24 shows the
conceptual picture summarizing the spatial evolution of this type of vortex ring/ moving

wall interaction.
4.5 Implications for turbulent boundary layers

4.5.1 Connection between vortex ring/wall layer description and the typical eddy/wall
layer interaction
4.5.1.1 Outer region of turbulent boundary layer

To interpret the results of the vortex ring/moving wall interactions in terms of
turbulent boundary layer interactions, we must perform a Galilean transformation on
the velocity field. Our interpretation of the simulation has been to identify the Stokes’
layer with the viscous wall region which extends to y+ approximately 30-50. The mean

velocity at this height is approximately 70 - 80% of Ugo. Thus,

UTE/U00 = a(1 -Ur/Uw)

where ’a’ represents the outer region velocity defect which we can not simulate

43

(20-30%). Thus, in thinking about the implications for the turbulent boundary layer,
basically high speed ratios in the simulations correspond to low convection velocities of

the typical eddies in the boundary layer.

4.5.1.2 Inner region of turbulent boundary layer

As far as the shear condition in the near wall region is concerned, we can
estimate the velocity gradient at the wall by using the exact solution of Stokes’ layer.
The velocity of the moving wall used in the vortex ring/moving wall interactions ranges
from 0.076 m/sec to 0.152 m/sec which corresponds to 0.65 to 0.25 Ur/Uw or 0.35 to
0.75 UTE/Uno’ and the belt running time is between 2 and 6 seconds: resulting in the
ratio of the friction velocity to the wall velocity, “r/Uw is between 5.5% and 3.5%.
This range of the friction velocity is very close to what is found in low Reynolds number
boundary layer flows. However, due to the unsteady nature of the Stokes’ layer, for each
fixed velocity of the moving wall, the percentage of u,,/UW decreases monotonically
during each experiment. This variation in u 1. / Uw is approximately 1% over the course
of any given experiment. This is slightly different from the real situation in the near wall
region of turbulent boundary layer where the friction velocity is stochastically

stationary.

4.5.1.3 Inner/outer region interaction

As a result, we expect the typical eddies that emerge from wall layer fluid
(through a pinch-off of lifted hairpin vortices, for example) to have a low convection
velocity. Since these are moving away from the wall, they will correspond to fast rings
moving away from the wall. These exhibit long streak formation which is stable, and
pinch-off, depending upon the thickness of the wall layer. We do see long stable low
speed streaks in the boundary layer (Falco 1980), and we have limited evidence of
hairpin pinch-Off (Falco 1983). On the other hand, typical eddies that are convecting

44

towards the wall will be of relatively high speed, and thus simulated by low speed vortex
rings moving towards the wall. These will produce long streaks which go unstable
(undergoing either wavy or lumpy instabilities), short streaks which go unstable, and
pockets in all cases. Again we see all these events in the turbulent boundary layer. Fig.
4.25 shows a comparison with what were observed by Offen, Kline (1975) and Smith
(1978). The similarity is apparent.

The wide range of interactions that can be simulated using the vortex
ring/moving wall experiments are not all admitted by the turbulent boundary layer with
equal frequency. Some are not admitted at all. The range of the parameters (angle, wall
layer thickness, convection velocity) found in the boundary layer are limited, and in all
cases they have skewed probability distributions (towards higher values) that are
approximately lognormal. When these distributions are used to determine the events

that are most probable, we begin to see what to expect.
4.5.2 Spacing between streaks

Fig. 4.26 shows the distribution of D+ obtained from the diameter of the typical
eddies of a turbulent boundary layer at Rea z 1176 (Falco 1974), superimposed upon
the streak spacing obtained for various size rings. When the simulation outcomes are
conditioned by the probabilities of scales found in this boundary layer, we see that the
simulation gives a most likely streak spacing of approximately 100 wall units. This is an
important quantitative test of the quality of the simulation, for although the average
streak spacing is 2+ = 100, all observations of streak pairs have also shown their

spacing to be approximately this value.
4.5.3 The vortical motions associated with the streaky structure

The three-view visualization realized the vortical motions associated with the
45

streaky structure in the vortex ring/moving wall interaction (see Sec. 4.3.4). We may
interpret as follows. When the coherent motion moves towards the wall from the outer
region, the pressure gradient at the wall in the spanwise direction will cause the
creation of the streamwise vorticity and roll up into vortices later on. The size of the
counter-rotating streamwise vortices observed to be associated with each streak
resulted from the vortex ring/moving wall interaction (see Fig. 4.21) is very much
different from the familiar sketch of the counter rotating vortices (see Fig. 4. 27) in

turbulent boundary layers which was hypothesized by many investigators.

Some investigators hypothesized that the lifted hairpin vortices found in the wall
region of the turbulent boundary layers were responsible for the formation of the low
speed streaks. However, this phenomenon was not observed in the vortex ring/ moving
wall interaction simulation. The main hairpin is observed to form due to the interaction
between the lower lobe of the vortex ring and the wall layer fluid; its strength depends
on how close the ring can approach (this is just what was defined as four Types of
interaction). This lifted hairpin will not last long enough to form such a long streak
which is about 1000 x+. Because soon after it is lifted, it may either get ingested into
the lower lobe of the ring and lose its coherence or stay in the low shear region.
However, in the second case the two legs of the hairpin are too far apart (see Sec.
4.3.4.1) as well as too far away from the wall (the tip of the hairpin will reach as far as
40 y+), it is not possible to form a streak between the legs; and the laser illuminated
end view indicates that even if this lifted hairpin does not get ingested into the vortex
ring it will not keep its coherence over 30 t+ . Some interactions (Fig. 4.8 and 4.21 for
examples) do result in the formation of the secondary hairpin vortices over streaks, this
phenomena is a consequence of the viscous effect between the two vortices of each
streamwise vortex pair and is not the initiator of the formation of the streaks. This is
also shown clearly in the conceptual picture in Fig. 4.22.

46

As mentioned in Sec. 4.3.4.2, the fast vortex ring moves away from the wall
which corresponds to the vortex ring moving away fi'om the wall with low convection
velocity in the turbulent boundary layer. The observed long streaks are just the legs of
the lifted hairpin vortex; they are one unit. The dye marker actually concentrated with
the streamwise vortices. Thus, this type of interaction should not be confused with the

typically assumed non-vortical structure of streaks.

We have very limited information about distributions of this type for the angles
of incidence and/ or movement away fi'om the wall, for the convection velocity, and for
the instantaneous wall layer thickness, but the evidence indicates that the frequency of
occurrence of many of the interactions which we can simulate is quite low in the
turbulent boundary layer. Often these interactions are very intense. Thus, the conditions
in the boundary layer that exist which keep their probability low are likely to be
essential to the maintenance of the measured values of the drag. We need to explore
ways to further limit the occurrence of the violent breakups if we are to pursue a
rational program of drag reduction (and noise reduction) in the boundary layer. The
model allows us to isolate a specific high drag producing event, and carefully study the
parameters that it depends upon. We are currently building the sample sizes necessary

to more accurately obtain the distributions mentioned above.
4.5.4 Implications for drag modifications

As we have seen, small changes in the parameters of typical eddy size, incidence
angle, convection velocity, and wall layer thickness can alter the evolutions that result
when a typical eddy interacts with the wall. Changes in any of these variables which
cause a cross over in the boundaries (such as those shown in Fig. 4.18), will result in a

change in the drag at the wall.

Consider, for example, the angle of incidence. If we can change the strength Of
4

the large scale motions, say, by outer layer manipulators, we can easily change the angle
of a typical eddy that is moving towards the wall, and may even be able to change the
direction if it is at a shallow angle, so as to make it move away from the wall. This will
affect the stability of both the local eddy wall interaction (interactions of Type I-IV),
and the stability of the streaky structure which is created, as well as the formation of
new typical eddies via the pinch-off process. Thus, we can affect not only the local drag,

but alter the drag downstream by directly interfering with the cyclic production process.

Modifications to the wall that result in small changes in the effective wall region
thickness, for example, NASA riblets, will also have an effect on the drag. If increases in
wall region thickness above the critical thicknesses can be made (see for example, Fig.
4.18), streaks are more likely to remain stable. Furthermore, the local interactions

(Types I-IV) will also tend to be of Type I and 11. Thus, the drag can also be reduced.
4.6 Summary and Comment

New boundary layer observations in the Turbulence Structure Laboratory,
Michigan State University have suggested that long low speed streaks are formed in
pairs as the result of the interactions of microscale very coherent vortex ring-like eddies
(typical eddies) propagating over the wall. Depending upon the distance from the wall,
the angle of incidence of the eddy with the wall (both magnitude and sign), the
convection velocity of the eddy, and the local thickness of the viscous wall region,
different structural features can evolve out of the evolution. The extent of the distance
over which a typical eddy could interact with the wall and wall layer flow was a surprise,
but means that many coherent microscale eddies that are in the logarithmic region and

further out take part in the production process.

The vortex ring/moving wall simulation incorporates all Of the evolutions and
48

structural features associated with the turbulence production process. Besides, the
results of the three-view visualization present the similar vortical structure associated
with the low speed streaks found in the near wall region of turbulent boundary layers.
The vortex ring/ moving wall simulation dramatically demonstrates that the pre—existing
streamwise vortices are not réquired to produce streamwise streaks. When the streak
spacings obtained in the simulation are conditioned by the probability of occurrence of
typical eddy scales found in the boundary layer, we see that the simulation provides the
correct streak spacing (approximately 100 wall units). Other possible outcomes of the
simulation need to be weighed by the measured probabilities of occurrence of the
angles, convection velocities, and length scales of the typical eddies in the turbulent
boundary layer to enable us to obtain a picture of the most probable forms' of the
interactions, and to gain insight into the causes of the interactions which occur with
lower probability, that may contribute significantly to the transport. It appears that
turbulent boundary layer control leading to drag reduction can be realized by fostering
the conditions suggested by the simulations which will increase the probability of having

stable interactions.

All the results discussed in this chapter are from the flow visualization of the
vortex ring/ moving wall interaction simulations. Flow visualization, however, can only

give partial information at best. The three major reasons for this are:
a) flow visualization is strictly valid only in highly energetic motions,

b) flow visualization has characteristics to leave vortical remnants which may

lead to incorrect conclusions about the flow kinematics, and

c) the conventional flow visualization techniques are valid for only short time,

since once the dye marker has been removed from a given region no information about

49

the kinematics in that region may be obtained.

Thus, in order to verify the conclusion drawn from the flow visualization and to
answer some questions which were not answered through the flow visualization such as
the initial conditions in the vortex ring/ moving wall interactions: vorticity distribution
over the Stokes’ layer and vorticity distribution associated with the vortex ring, the
velocity distribution associated with the streaky structure, and the streamwise vorticity
distribution associated with the streaky structure, it was necessary to make quantitative
measurements. The Laser Induced Photochemical Anemometry (LIPA) technique was

accessed in this quantification. The results of which are given in the following chapter.

50

CHAPTER 5

QUANTITATIVE REFINEMENT OF THE VORTEX RING/MOVING WALL
INTERACTION MODEL

5.1 INTRODUCTION

As mentioned in chapter 4, the vortex ring/ moving wall interaction model
provided a conceptual picture (shown in Fig. 4.22) describing the spatial information of
all visual features observed in the wall region of wall bounded turbulent flows. The flow
shown in Fig. 4.22 is completely unsteady and three—dimensional. The best existing
probe techniques are not enough in helping us to answer the questions listed in the
conclusion of chapter 4. To the author’s knowledge, the photochromic techniques are
the unique techniques that enable us to measure nonintrusively the instantaneous fluid
dynamic quantities such as velocities, vorticity, circulation, and strain rates over a two-

dimensional domain in such a flow field.

We applied both single tracer technique and grid tracing technique to quantify
the vortex ring/moving wall interaction model. First, we measured the Stokes’ layer
flow and also checked the accuracy of the grid tracing technique. Then, we applied
those techniques to more complicated measurements associated with the Type II
interaction of the vortex ring / moving wall simulation including:

a) vortex ring flow,
b) velocity distributions in the wall region, and

c) streamwise vorticity distribution in the wall region.

5.2 STOKES’ LAYER MEASUREMENT

51

5.2.1 Introduction

In this section we first discuss the measurement of a Stokes’ layer which was
approximated by a rapidly started moving belt and was used to simulate the viscous wall
layer in the vortex ring/moving wall interaction mentioned in chapter 4. Although the
Stokes’ layer flow is the simplest unsteady flow, the measurement is somewhat difficult;
so far no measurement has yet been made. Since the Stokes’ layer flow is one-
dimensional in space (only has diffusion in y-direction), an exact solution of the Navier-
Stokes equations is available. By applying the photochromic grid tracing technique we
were able to obtain the instantaneous velocity distribution, velocity gradients, and
vorticity distribution across the layer and were also able to test the accuracy of this

technique against the exact solutions.
5.2.2 Experimental details

Fig. 5.1 presents the schematic representation of the setup of Stokes’ layer
measurement; the moving belt system is similar to what was used in the water tank.
The width of the belt is 17.8 cm, and the distance between the rollers is 152.4 cm with
the test position 90 cm downstream of the leading roller. All experimental data were
obtained before the leading edge effects reached the test position. Furthermore, the
aspect ratio is sufficient to prevent the disturbances generated in the corners from
reaching the center of the belt when the data were taken. Therefore, the wall layer flow
measured was one-dimensional. The working fluid was deodorized kerosene in which
10 ppm of the photochromic chemical was dissolved. Fig. 5.2 shows the optical set-up
for generating the photochromic grid. Because only spanwise vorticity components were
to be measured, the depth of field looking into flow was not crucial. The best
orientation for the incident beam is also shown in Fig. 5.2.

Fig. 5.3 shows the flow chart of5 the control system of the Stokes’ layer
2

measurement. Time delay # 1 initiates the excimer laser to generate a photochromic
grid as well as calculating time (t) involved in the exact solution of Stokes’ layer, while
time delay # 2 initiates the data acquisition system which includes a 35 mm high speed
Photo-Sonic movie camera and background lighting. Usually we start the movie camera
2.5 seconds prior to the data acquisition because the surge time of the camera to its full
speed is 1.5 second. The data were recorded on Kodak Tmax ASA 400 film through a
micro lens at 200 frames per second. The films were analyzed on a NAC motion film

analyzer which is accurate to 0.05 mm.
5.2.3 Results

Fig. 5.4 shows two photos fi'om the result of the Stokes’ layer measurement
which are 0.05 seconds apart; these photos were taken under conditions with Uw = 12.7
cm/sec and belt running time t = 5.25 seconds; the belt moved from right to left. Fig.
5.5 shows the non-dimensional velocity profile for two belt running speeds; the solid
line represents the exact solution. Results of the velocity gradient au/ay obtained from
double differentiation and of the spanwise vorticity obtained from circulation approach
are shown in Fig. 5.6, where they are compared with the exact solution. Everything is
non-dimensional by the similarity variables of the exact solution. In theory, the spanwise
vorticity “z is equal to -(au/6y) in Stokes’ layer since av/ax is equal to zero. Because
the flow is one-dimensional, incompressible, and does not change with the streamwise
coordinate, x, the continuity equation reduces to av/ay = 0. A check of this across the
Stokes’ layer is also shown in Fig. 5.6. The mean value of (av/6y). across the layer is -

0.011 and the standard deviation is 0.095, which corresponds to 1 / second.
5.2.4 Discussion and Summary
By applying the photochromic grid tracing technique, we obtained the

53

instantaneous velocity distribution and, for the first time, the vorticity distribution
across the Stokes’ layer. There is an agreement among the velocity profiles in Fig. 5.5
except in the vicinity of the edge of the Stokes’ layer. This may be caused by the free
surface effect, the small disturbance from the driving system, and the reading error. The
errors involved in the calculation of velocity gradient, the vorticity distribution and the
check of continuity equation are of similar magnitude. The absolute value of the error is
i2/sec which is consistent with the design error analysis. The deviation of the
experimental profile in the near wall region is a consequence of the grid mesh being too
large (the largest mesh in vertical direction in Fig. 5.4 is about 0.15 6) to adequately
resolve the large value of the gradient au/ay. On the whole, the results are very
encouraging, which indicates that by using the exact solutions of Stokes’ layer we can
estimate the velocity, velocity gradient and spanwise vorticity distribution associated
with the undisturbed viscous wall layer for different belt speeds in the vortex
ring/moving wall interactions as long as the leading edge effect of the belt does not

reach the test position.

The demonstrated accuracy of the photochromic grid tracing technique in
Stokes’ layer measurement is more than adequate for many fluid dynamic problems. As
speed increases 100-fold the accuracy can, in principle, be maintained, since the
calibration depends only on a time and a length scale. There is further room for
improvement through the use Of high resolution image processing. At present, this
technique is accurate enough to apply to more complicated flow measurements which

will be mentioned in the following sections in the chapter.
5.3. VORTEX RING MEASUREMENT

5.3.1 Introduction
54

The second item to be quantified in the vortex ring/wall interaction is the vortex
ring, the sOurce of the excitation. The vortex ring represents a class of flow fields that
are of particular importance in turbulent and unsteady flow. Several techniques had
been attempted to measure the detailed structure of the vortex ring. The hydrogen
bubble technique was attempted by Maxworthy (1972), but the results were inaccurate
due to strong axial gradients and associated radial velocities. Hot wire measurements
are hampered by probe interference and difficulty of calibration. Recently, numerous
investigators such as Sullivan and Widnall (1973), Maxworthy (1977) and Didden (1979)
used a two-component laser doppler velocimeter (LDV); although this technique has
taken care of the intrusive problem, it is still a single point measurement, and can only
be used to get the circulation distribution, not the local vorticity. By using the
photochromic grid tracing technique we can obtain instantaneous velocity distribution
and vorticity distribution, allowing us to gain deeper understanding of the dynamics of

vortex ring flow.
5.3.2 Experimental details

The experimental set-up used to generate and measure the vortex ring is shown
in fig. 5.7. The same ring generating system applied in the water tank was used. The
flow chart of the control system for vortex ring measurement is shown in Fig. 5.8. In
order to match the Reynolds number of the vortex ring which was used in the vortex
ring/moving wall interaction in the water tank, a 19mm inner diameter orifice was
used. The kerosene in the reservoir was dyed with chlorophyll to mark the vortex ring
(Fig. 5.9 shows the lower half of ring marked with the dye). This enabled us to easily
locate the frames that needed to be analyzed. The flow was axisymmetric, so that we
needed only to align our grid through an axis of symmetry and to measure the flow in

half of the ring. The measuring window was at four ring bubble diameters downstream

55

of the exit of the orifice.
5.3.3 Results

Fig. 5.9 shows two photos of the result which are 0.07 seconds apart. The
instantaneous velocities distributed along two axes of the ring are shown in Fig. 5.10.
The instantaneous circulation distribution of the ring is shown in Fig. 5.11, which also
shows the results obtained by Sullivan et al. (1973) for different Reynolds numbers
along with the Hill’s exact solution of a spherical vortex, although there is no solution
existing for the experimentally generated rings. Through the circulation approach we

obtained the instantaneous vorticity distribution over a ring, which is shown in Fig. 5.12.
5.3.4 Discussion and summary

The vorticity distribution obtained from the photochromic technique is the
instantaneous vorticity distribution associated with a vortex ring and no use of Taylor’s
hypothesis is required. To know the time evolution of a vortex ring we must simply
generate the photochromic grid at different locations downstream of the orifice or use

the moving grid generating system to follow a vortex ring.

Comparing the vorticity and circulation distributions with those obtained by
Sullivan et al. (shown in Fig. 5.11 and Fig. 5.12) shows clearly the Reynolds number
dependency, even though the ring generating systems are different. Interestingly, the
comparison also shows that the circulation distribution associated with the low

Reynolds number vortex ring is closer to that of the Hill’s spherical vortex.

5.4 FLOW VISUALIZATION IN KEROSENE TANK

5.4.1 Introduction

56

By using the photochromic grid tracing technique we are able to quantify the
Stokes’ layer flow and the vortex ring flow separately. These are the two initially
independent flow fields. To gain insights into their interaction, in other words, to obtain
the optimal spatial and temporal information about interactions such as the strength of
the streamwise vorticity associated with the streaky structure and how the streamwise
vorticity changes with the time, we must have an overview of the interaction to
determine where and when to make the measurements. Thus, flow visualization is
needed to make sure that: 1) the same experiments can be repeated in the kerosene
tank (required to use photochromic chemical) at the same Reynolds number, and 2) the
measurement window is optimal, that is, we will measure most of the events of interest

at the chosen position and time.
5.4.2 Experimental details

The experimental apparatus for flow visualization in the kerosene tank had the
same arrangement and control system as that used in the water tank (see Fig. 4.3), but
the scales and materials were different. The width of the moving belt was 17.8 cm; the
inner diameter of the orifice was 1.9 cm and its center was located 3.8 cm above the
wall. The incident angle of the vortex ring was set at 3 degrees with respect to the
moving belt. The plate which supported the moving belt was Teflon, a kerosene
resistant material. The kerosene in the reservoir was dyed with chlorophyll to mark the
vortex ring. As far as the dye marker in the wall layer is concerned, we gently injected
the chlorophyll dyed kerosene by a syringe to cover some part of the belt before each

run and waited long enough to let the injected dye settle.

The primary visual data consisted of plan and side view time resolved images
which were collected by using a 35 mm Photo-Sonic movie camera with a micro-lens on
Kodak Tri-X 400 ASA film. The side view was illuminated by a 300 watt flood light

57

diffused through a white color filter. The top view was illuminated by two 300 watt
flood lights from underneath and the white teflon plate worked as a white color filter.

The frame rate of the movie camera was 20 frames / sec.
5.4.3 Results

Fig. 5.13 shows one set of photos with both top view and side view describing the
time evolution of vortex ring/moving wall interactions in the conditions of Ur/Uw =
0.26, 3 degrees of incident angle, 6 /D at 0.18 and UW = 15.5 cm/sec. The non-
dimensional ring diameter was 120 wall layer units. These pictures show clearly the
same features which were visualized in the Type II interaction in the water tank under
the same flow condition. A pair of streaks with spacing 140 wall layer units were
observed, which is consistent with that shown in Fig. 4.21. Besides, the hairpin liftup and
pocket also were observed. This consistency gave us confidence that no appreciable
changes during startup resulted because of the factor of two increase in viscosity.
Through the evolution of the interaction we were able to locate the position where the

photochromic tracer or grid will be sent.

By sending a single photochromic tracer parallel to the moving wall at y+ a 16
we obtained the visual result of the interaction shown in Fig. 5.14 which is the same as
that obtained from the hydrogen bubble technique used by many other researchers,
such as Kim et al.(1971) or Smith et al.(1983).

5.4.4 Discussion and summary

The result of the flow visualization of the vortex ring/moving wall simulation in
kerosene tank showed the same features which were observed in the Type II interaction
in the water tank. Those visual results also provided the information to locate the
optimal position for the vleocity measurement. Furthermore, the vortex ring/moving

58

wall interaction model could produce the same visual features which were visualized
through the hydrogen bubble technique in the near wall region of wall bounded

turbulent flows.

5.5 VELOCITY DISTRIBUTION ASSOCIATED WITH THE VORTEX RING/
MOVING WALL INTERACTION

5.5.1 Introduction

Even though the flow visualization in the vortex ring/ moving wall interaction
model did show clearly the formation of a pair of streaks, it did not provide information
on the characteristics of the streaks except for the spacing between the streaks. If the
model is good, the velocity measurement (temporal and spatial information) will show
quantitatively the same as that measured and observed in turbulent boundary layers.
These measurements will be able to provide insights into how the viscous wall layer
responds to the disturbance from the vortex ring during the interaction Based upon the
results obtained from the flow visualization in the kerosene tank, we figured out that if
measurements are conducted only in one fixed location, then the location is 25.4 cm
(i.e. x/D = 8) downstream of the exit of the orifice, where we will be able to monitor
the major events of the interaction. In these measurements the photochromic tracer
technique was used; it is the only technique available to obtain the velocity distribution
precisely and efficiently for this particular flow field. We can generate photochromic
tracers either perpendicular (in x-y plane) or parallel to the wall (in x-z plane) and

obtain the associated velocity distribution in the mean flow direction.
5.5.2 Experimental details
We repeated the same experiment as we did for flow visualization in the

59

kerosene tank in Sec. 5.4. Fig. 5.15 shows the locations of measurement. Because we
could only record one photochromic tracer for each run in the spanwise direction (2-
direction), we needed to repeat the same experiment several times to obtain the whole
information in the z-direction. The high repeatibility of vortex ring/moving wall
interaction did provide the reliability to put the measurements together from different
runs ( the variance of the velocities of the vortex ring and the moving belt are less than
5% for different runs). We only measured half of the flow field as shown in Fig. 5.15,
because the flow field was symmetric about the center line (see Fig. 5.15 also). A
special optical apparatus was designed for this purpose; a movable carriage which was
controlled precisely by a threaded rod carried a set of optical components including one
500 mm focal lens and two reflecting mirrors to accurately guide the laser light beam to
the measuring positions. Fig. 5.16 shows the details of the optical configuration. The
Excimer laser was set to pulse 10 times per second and the 35 mm Photo-Sonic movie
camera was also set at 10 frames per second. We synchronized the belt running system
and data acquisition system. As the switch was turned on, the belt, camera, background
lighting (a 300 watt flood light) and movie camera started simultaneously. The
instantaneous time lines which represented the instantaneous velocity distribution in
the streamwise direction were recorded on T-MAX 400 ASA film through a micro-lens.
The films were processed with Microdol-X at 70 degrees F for 10 minutes and were
digitized by a NAC film analyzer. For each frame we could measure the non-

dimensional velocity components, U(y)/Uw, at different y positions.

5.5.3 Results

We analyzed the data for each measurement point and obtained the spatial and

temporal velocity information of the wall layer as follows:

a) Fig. 5.17 (a) through ((1) show the time evolution of the non-dimensional

60

streamwise velocity distribution at the measurement points. The dotted lines represent
the undisturbed velocity profiles of the Stokes’ layer. The visual information
corresponding to Fig. 5.17 is shown in Fig. 5.13; the arrows indicate the measured

location.

b) Fig. 5.18 (a) through (d) show the time evolution of the constant streamwise
velocity lines in y-z plane. Again, the dotted lines represent the constant velocity levels
of the undisturbed Stokes’ layer.

5.5.4 Discussion and summary

Fig. 5.17 shows that the wall layer fluids are accelerated, decelerated, and then
lifted up. The results shown in Fig. 5.18 indicate that there is a distinct region of high
momentum fluids being pumped away from the wall. As the results shown in Fig. 5.18
are compared with those obtained from flow visualization shown in Fig. 5.13, we found
that the long streaks observed by the flow visualization in the vortex ring/ moving wall
interaction simulation (discussed in Sec. 4.3.1.2, 4.4.1 and 5.4) were the high speed
region. This phenomenon also confirms what was observed in the three-view flow
visualization in Sec. 4.4.1 (see the laser illuminated end view in Fig. 4.21), where a pair
of counter-rotating streamwise vortices associated with each streak was observed. The
pair of counter-rotating streamwise vortices pumped the high momentum fluids away
from the wall. Again, the width of each streak is also about 30 2+ (see the hump in Fig.
5.18 (c)).

As theOresults shown in Fig. 5.17 and 5.18 were observed from the point of view
of the turbulent boundary layer by performing the Galilean transformation (see Fig.
5.19), we see clearly that the vortex ring/moving wall interaction model can simulate

the characteristics of the low speed streaks observed in wall bounded turbulent flows.

61

The data shown in Fig. 5.19 represent the velocity defect or gain with respect to the
undisturbed wall layer (i.e the layer after performing the Galilean transformation
shown in the lower half of Fig. 5.19 (a)) at different y+. The characteristics of the low

speed streks found in Fig. 5.18 and 5.19 are listed as follows:

a) the spacing (distance between the peak of humps)
is about the size of the vortex ring (see Fig. 5.18(c),
5.19(c) and Fig. 4.26); note that the ring bubble

diameter in this measurement was 3.18cm (1 1/4 in);

b) the region and the percentage of the velocity
defect is clearly shown; for example, a 30 % of

velocity defect is found at y+ = 15 (Fig. 5.19(c));

c) the width of each streak (if it is defined as the
region in which the velocity defect is over 10 %)
is about 30 2+ at y+ = 10 (Fig. 5.19 (c) and is

about 20 2+ at y+ = 10; and
d) the extent of coherent liftup may reach about y+ =
40 (see Fig. 5.18 and 5.19).
These results compare well with those obtained from turbulent boundary layer

flows. (see Smith & Metzler 1983)

Besides, the results shown in Fig. 5.18 precisely define the spanwise location of

the test window for measurement of the streamwise vorticity associated with the streaky

structure.

62

5.6. STREAMWISE VORTICITY MEASUREMENT ASSOCIATED WITH THE
VORTEX RING MOVING WALL INTERACTION

5.6.1 Introduction

From the result of the three-view visualization of the vortex ring/ moving wall
interaction in water tank, we observed the vortical structure associated with the streaks,
which showed that a pair of counter-rotating streamwise vortices accompanied each
single streak in the later stage of the streak formation. This phenomenon is similar to
what was found by Blackwelder and Eckelmann (1979). The morphological comparison
was mentioned in Sec. 4.5.3. Blackwelder and Eckelmann ( 1979) studied the vortex
structures associated with the bursting process as defined by VITA and estimated the
streamwise vorticity by using hot-film sensors and flush mounted wall elements. They
found that the streamwise vorticity was one order of magnitude less than that of
spanwise vorticity and the middle of the vortex structures lay approximately at y+ = 20-
30. In this section, we quantify the streamwise. vorticity associated with the streaky
structure in Type H interaction of the vortex ring/ moving wall simulation such that we
may have further comparison with the information obtained from the turbulent
boundary layers. By using the photochromic grid tracing technique we are able to
obtain the spatial and temporal information on streamwise vorticity distribution as well

as on the Reynolds stress distribution.
5.6.2 Experimental details

The same experiment which was conducted in Sec. 5.4 and in Sec. 5.5 was
repeated in this section. The initial conditions of this vortex ring/moving wall

interaction result in a Type II interaction: the incident vortex survives and the pair of

streaks break up.

63

The test area, located at the same position which is 25.4 cm downstream of the
exit of the orifice. Because the test area of the photochromic grid tracing technique is
limited, we adjusted it to cover a single streak and its adjacent area. It covered from 25
to 80 z"' from the center line of the flow and up to 40 y+ from the moving wall. Fig.
5.20 shows the optical configuration and the orientation of the laser beam. In this
experiment we took advantage of the test area being close to the side window of the
kerosene tank, so that we could adjust the laser beams in the grid to be almost
orthogonal. This kind of optical arrangement will provide better resolution in the
direction which is perpendicular to the wall than that of the diamond shape grid box

used in vortex ring and Stokes’ layer measurements.

The side view of the data acquisition and lighting system is shown in Fig. 5.21
including the Photosonic 35 mm movie camera, one 300 watt projector light bulb, and
white color filter. A Fl.2 Nikon lens and a 2.0 x QUANTARAY 7 ELEMENT Auto
Tele Converter were used to magnify the image; the background lighting was set at 60%
of the output through a potentiometer and was concentrated by a convex lens. The
repetition rate of the excimer laser was 2.5 Hz, that is, a fresh photochromic grid was
generated every 0.4 seconds. The images were recorded at 50 frames / second on Kodak
400 Tmax films and were processed in Microdol-X for 10 minutes at 70 F. The film was
digitized through the NAC film analyzer.

5.6.3 Results

Fig. 5.22 (a) and (b) show the results of the streamwise vorticity measurement,
the first photo of each set shown in Fig. 5.22 was photographed at 6.8 and 7.6 seconds
respectively after belt started, which corresponded to t. = 55.3 and 61.8 respectively.
Those photos are selected from the same sequence of movie in one experiment. Two
photos of each set were 0.02 second apart which corresponded to 0.5 t‘l’ apart.

54

Following the procedures mentioned in Chapter 2, the data were deduced from
each set of the photos and the corresponding contour plots of the instantaneous

streamwise vorticity distribution were obtained, which are shown in Fig. 5.23.

Fig. 5.24 (a) through (1) represent the instantaneous Reynolds stress

distributions which were also obtained from the same data base as that of Fig. 5.23 (a)

through (f).

5.6.4 Discussion and summary

In the early stage (see Fig. 5.23 (a) and (b)) of the formation of streamwise
vortices, the maximum value (O(1/sec.)) is about the noise level of this technique. Even
at this moment the visualization already shows the nicely-formed streaks at the test area
(Fig. 5.23 (a)-(d) almost correspond to the vortical structure shown in the end views of
Fig. 4.21 (a)-(d)). It means that even though the level of the streamwise vorticity is very
low, it is able to gather the dye marker together to form streaks. However, the velocity
information (see Fig. 5.17 (d)) shows that the velocity profile in the mean flow direction
appears to have a very strong defect in spanwise direction, that is, it has a very big

au/az.

As we follow the time evolution of the streamwise vorticity distribution shown in
Fig. 5.23 (a) and (b), a pair of counter-rotating streamwise vortices induced themselves
up to about y+ = 20, their strength, “’x’ was about 0.19. which is about one order of
magnitude less than the spanwise vorticity (the mean spanwise vorticity, 022., in the wall
layer was about 1.04). A photo taken 0.02 second before t. = 58.6 (shown in Fig. 5.25
(a)) indicates that a pair of counter-rotating streamwise vortices formed from the wall
and moved upward. The old photochromic dye marker showed a blurry region in the

vicinity of the wall. It means that the fluid in this blurry region has relatively higher

65

speed because it comes from the near wall region and has high momentum. If we look
at this from the point of view of the turbulent boundary layer, this is just the low
momentum fluid ejected from the near wall region; this argument is also supported by
the velocity measurement shown in Fig. 5.17 (c) and (d) (sliced view of velocity
distribution in x-z plane shows the corresponding low momentum region). As soon as
the edge of the pocket reached the measuring window (it started shortly before t. =
55.3, evidence of this came from the result of visualization both in the water tank and in
the kerosene tank; see Fig. 4.21 (b)), this pair of streamwise vortices was dominated by
the pocket vortex which may come from the bending of existing spanwise vorticity (see
the difference between Fig. 5.23 (c) and (d)). The results show that the contribution
from aw/ay and av/az are almost equal; it may suggest this bending of an existing
vortex line from the spanwise direction to the streamwise direction. The fast outward
spreading of the edge of the pocket suggested that there was a strong pressure

perturbation from the incident vortex ring and a strong aw/ay contributed to wx.

The maximum “’2 associated with the vortex ring used in this interaction was
35 / sec and the maximum measured wx was about 15 / sec which corresponded to about

1 / 2 of the “’2 existing in the wall layer. The ratio (wx/wz )max is about 0.43.

The total circulation of the strong vortex (the region with positive sign shown in
Fig. 5.23) increased dramatically from t‘ = 58.6 to t. = 65.1, which is shown in Fig.
5.26. The turning of the direction of the pocket vortex (see Falco 1980b) to the
streamwise direction (i.e. the streamwise vorticity component will increase) is a possible
reason for the increase of the circulation (see Fig. 5.27). And the area of this strong
vortex may be caused by the shape of the pocket vortex as well as the viscous diffusion.
It separated about 20 t+ between t. = 58.6 and t. = 65.1; the viscous diffusion can do

something within 20 t+. This also can explain the decreasing of the peak value of the

66

streamwise vorticity o; fiom 1.47 to 0.83 within 20 t+ (see Fig. 5.23 (d) and (o).

The vorticity contours also show the strength of the hairpin which was originally
the pair of streamwise vortices associated with each single streak. One leg Of this
hairpin merged with the pocket vortex and the hairpin vortex was as a whole unit
induced by the pocket vortex (Fig. 5.28 shows the possible merging process). Fig. 5.23
(c)-(e) shows the time evolution of this emerging. Fig. 5.26 also shows the total
circulation of one leg of this hairpin vortex (the region with negative sign shown in Fig.
5.23). The maximum strength of the streamwise vorticity, wx', associated with this lifted
hairpin was about 0.62. and the associated instantaneous Reynolds stress vw/uTuT was
low compared with that associated with pocket vortex (see Fig. 5.24 (d), Reynolds stress
distribution). This means that the Reynolds stress associated with the streaky structure
was low and was about 30% of that of the pocket vortex. Thus, we have a detailed
breakdown of the contrlhutions of the long streaks and the pockets to streamwise

vorticity and the Reynolds stress produced by it.

5.7 Summary

5.7.1 The photochromic technique - an accurate and powerfirl technique

Data derived by the photochromic technique has been used throughout this
chapter. Using a photochromic mesh of small enough size, instantaneous fluid dynamic
quantities over a two-dimensional field can be measured. The predicted accuracy
through the classical error analysis described in Chapter 2 has been confirmed in the
Stokes’ layer measurement. Using this technique we have quantified the velocity and
vorticity distributions of the two originally independent fluid flows (i.e. the Stokes’ layer

and the vortex ring) of the vortex ring/moving wall interactions. We have also

67

measured both temporal and spatial information pertaining to the velocity
distributions and streamwise vorticity distributions associated with the vortex
ring/ moving wall interaction.
5.7.2 Further understanding of turbulence production process through the vortex
ring/ moving wall interaction model

The visual and photochromic technique derived results of the vortex
ring/ moving wall interaction simulation indicate that this model not only demonstrates
qualitative agreement with the near wall boundary layer phenomena but also
quantitatively captures the correct kinematical magnitudes associated with this
phenomena. This was demonstrated in the velocity measurements associated with the
vortex ring/moving wall interaction in that the characteristics of the low speed streaks
were fully revealed. Furthermore, the model studies show that the streamwise vorticity
associated with the streaky structure is about one order of magnitude less than the
mean spanwise vorticity. We realized that the pocket vortex plays a very important role
through the streamwise vorticity measurements. The pocket vortex is apparently
responsible for the instability of the streaks, and it is the major contributor to the
Reynolds stress. The secondary hairpin vortices which formed on the low speed streaks

are not as important, in terms of both vorticity and Reynolds stress, as the pocket

vortex.

68

CHAPTER 6
CONCLUSION AND FURTHER COMMENT

6.1 Conclusion

As addressed in chapter 1 this study is a combination of both the technical
development of LIPA technique and its application towards understanding the basic
physics of the bursting process in turbulent boundary layer flows. The major findings of

this two phase experimental study can be summarized as follows:

1) A major extension of LIPA (Laser Induced Photochemical Anemometry)
that enables the instantaneous velocity, velocity gradient, vorticity, and Reynolds stress
to be obtained over a two-dimensional domain of a fluid flow has been developed and
demonstrated. Calibration depends only upon a time and a length scale. Comparison of
measurements with the exact solution in a Stokes’ layer indicates that its accuracy can
be predicted by classical analysis, and is comparable or better than that achievable with
the best single point probe techniques. Furthermore, the LIPA is not restricted to
slowly varying flows as are so many flow visualization techniques. Using the LIPA
technique we have also quantified both temporal and spatial information pertaining to

the velocity distributions and streamwise vorticity distributions associated with the

vortex ring/ moving wall interaction.

2) The LIPA technique has been applied to measure the local skin friction on
bOth a stiff surface and a compliant surface. Eight percent skin friction reduction has
been found on low damping elastic gelatin at Re 9 as 1200. At the skin fiiction reduction

conditions the observed onset surface deformation on the compliant surfaces was local,

69

three-dimensional, small scale, and short lived. This was found at approximately the
same value of K, 0.6, for three different coating thicknesses. Results show that at
conditions which lead to skin friction reduction, the surface response is a response to
turbulence. The measured length scale, time scale, and the velocity scale associated
with the observed pocket-like depressions correlate very well with those of the bursting

process in wall-bounded turbulent flows.

3) The vortex ring/ moving wall simulation incorporates all the evolutions and
structural features associated with the turbulence production process. It dramatically
demonstrates that streamwise vortices are not required to produce streamwise streaks.
When the streak spacing obtained in the simulation is conditioned by the probability of
occurrence of typical eddy scales found in the boundary layer, we see that the
simulation provides the correct streak spacing (approximately 100 wall layer units). It
also appears that turbulent boundary layer control leading to drag reduction can be
realized by fostering the conditions suggested by the simulations which will increase the

probability of having stable interactions.

4) The visual and LIPA technique derived results of the vortex ring/ moving wall
interaction simulation indicate that this model not only demonstrates qualitative
agreement with the near wall boundary layer phenomena, but also quantitatively
captures the correct kinematical magnitudes associated with this phenomena. This was
demonstrated in the velocity measurements associated with the vortex ring/ moving wall
interaction, in that the characteristics of low speed streaks were fully revealed.
Furthermore, the model studies show that the streamwise vorticity associated with the
Streaky structure is about one order of magnitude less than the mean spanwise vorticity.
And finally, the model studies also realize that the secondary hairpin vortices formed on

the low speed streaks are not as important, in terms of both vorticity and Reynolds

70

stress, as the pocket vortex.
6.2 Further comment

1) The calibration of the LIPA technique depends on only a time and a length
scale; there is further room for improvement. In practice, determining the intersecting
points of the grid lines is limited by the grain size of the film used, and the distortion of
the developing process. Improvements in the grain limitation can be made by using a
large format still camera With a shuttering mechanism that will enable a double
exPosure of the grid to be made on one plate. Image processing techniques have also

been demonstrated to increase the accuracy and repeatability of the results.

2) Orrrent limitations of the LIPA technique include the need to work in organic
liquids, which are required to dissolve the chemicals, and available penetration of the
laser beam into the liquid. The way to generalize this technique to be used in popular
fluid media is ongoing at the Turbulence Structure Laboratory, Michigan State
University. This ongoing research includes the study of new chemicals which can be

used for water, and the scanning technique which can be used to improve the

Penetration problem.

3) The ’moving’ LIPA technique can be used to obtain the Lagrangian

information in many turbulent and unsteady flows. Its future is very promising!

71

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76

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81

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88

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W A V E . P D L
0 10 20 so
12 + : : : I .L : : : I I : : : I : ; 12
.1- ‘I-
10 - ..._ 10
d -r-
5 - -- 5
Gad-el-Hak et al. ‘
¢ A... PVC PLASTISOL ~-— 5
4 -— unth— ‘
\‘I I \‘I ,
_ / Gad_el_Hak CURRENT ..EASLRET.ENTS
2 "" . ELASTIC COATING CURRENT "" 2
o ONSET
a; E flEl
0 : I : : I : t : : I : : : : I : i o
0 10 20 50

COATING THICKNESS (mm)

Fig. 3.9 The onset boundary for different compliant coatings.

93

SURFACE RESPONSE

 

 

 

 

W A V E . P D L
o 10 20 so
3 1 1 1 1 I 1 1 1 I ‘ 1 1 1 1 l 1 1
I T T T T I I 1 T r I l I l 1 l I
v-
A
D \
[fl "' \ QUASI Two DIMENSIONAL WAVES
% -- ‘ x
\
E - ‘ ‘
< ' “~
‘
3 ‘*~-----
-I-
E
I II-
3 0 POCKET s TRIANGULAR WAVES
5 \ ° °
ur- \ \
a ‘ fi— ‘ ‘ '\ ‘ d-
% ._ POCKET ‘-~-___
3 ___________
a «I ‘3' ------ a- ——————— —a
V '0-
x
q-
o 1 1 1 L l l J L l [ l L 1 L l 1 ' o
I Y I T r T 1’ r I I I I ‘1 T ' fl I
o to 20 30

COATING THICKNESS (mm)

Fig. 3.10 The dependence of the occurrence of each element on both K and coating
thickness.

94

 

 

 

 

 

 

 

 

0.3 1‘
STIFF SURFACE
P(Cf) 1205 points
. MEAN 0.004324
S.DEV. 0.001277
SK.F. 0.670
FL.F. 3.629
0.2 '
0.1 "
Cf

Fi . 3.11 The histogram of the skin friction obtained from 1205 samples over the
re erence stiff surface.

95

NC!)

0.2

Fig. 3.12 The histograms of the skin friction associated with 3, 19 and 30 mm compliant

coatings.

 

 

 

mun SWAG!

1-.

W

5.00].

SKJ.
FLJ'.

 

 

 

 

 

3:8 pour.-

100197!
0.0013!)
0.310
3. 661

 

 

 

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cf

mum sum:
19 n. 662 when

"M'
E‘s-E
335

 

 

 

 

 

O. ”3’76
0. ”1235
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2.3.0

 

 

 

K

 

 

 

 

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mun sauna
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/

 

 

 

 

\

0.003990
0.”!309
0.760
3.67.

 

 

 

K

 

p

‘f

 

 

 

 

 

 

 

 

 

 

 

0.3 - COMPLIANT SURFACES
TOTAL: 1224 points
MEAN 0.003966
P(Cf) S.DEV. 0.001295
SK.F. 0.685
FL.F. 3.413
0.2 P
0.1 -
Cf

Fig. 3.13 The combination of Fig. 3.13 (a) through (c) regardless of thickness.

97

 

 

Fig. 3.14 A photo of the pocket-like depressions formed on the 3mm compliant surface.

98

w+

TRANSVERSE LENGTH SCALE OF POCKET

 

 

 

 

0 500 1000 1500 2000
l 1 1 1 l 1 ' l 1 I 1 1 0 l I l 1 l 1 ' 1 0
100 I I I I I I I I I l I I I I T I I T I I I I 100
I I
1‘:
up v .. if
db ‘ J
:J
D I:
+
O PRESENT WORK (COMPLIANT SURFACE)
‘ El YODA (CHANNEL)
V PALCO (BOUNDARY LAYER) -
-- A EMMERLING (1973) I ~
.. W.
I I . I I
O I I I I I I I I I I T I I I I I I I l I o
o 500 1000 1500 2000
Re

Fig. 3.15 The comparison of tranverse length scale of depressions in compliant surfaces

with the pocket footprints made on a solid surface.

99

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.. Pt... SKI

 

101

 

 

Fig. 3.18 A photo of the quasi two-dimensional large-scaled waves.

102

100 WALL UNIT

DYE SLIT

SI _
I
I

 

 

3mm COMPLIANT SURFACE

YODA (1981.)

t surfaces with the flow

da (1981).

Ian

1
“If;

henomena on co
lization in the near wall region of channel flow by

'alp

VlSll

f the

omparlson 0

Fig. 3.19 A c
“51.18

POCKET STREAKS POClKET

 

Fig. 4.1 Two pockets and a pair of streaks as seen in wall slit visualization of a
turbulent boundary layer usmg smoke as the contaminant in air, the slit is at the top of
the photo and the flow is from top to bottom. (Falco 1981)

104

     
     

[NSF-\NTANHKS

; ()lJIHl FIXJ

  

V0! IE‘
RING - LIKE EDDY

 

on (ovum
MOVING WALL

 

'1 , Simulated vortex rinywall shear layer

Fig. 4.2 The basic idea behind the simulation. Performin a Galilean transformation on
the vortex ring/movin wall interaction makes in a mode of the turbulent boundary
production process; (a instantaneous turbulent boundary layer; (b) simulated vortex
ring/wall shear layer.

105

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Fig. 4.6 Streaks form from the stretching of the lifted hairpin for Ur/Uw = 0.8.

109

 

Fig. 4.7 Six photos of a vortex nng{ moving wall interaction for Ur/Uw< 0.35 when the
ring moves toward the wall at a 3 egree angle. Both plan and side views are shown.
The ring and the wall are moving to the right and only the wallward side of the ring has
dye in it. The interaction results 1n a pair of long streaks, a pocket and its associated
hairpin lift-up, which then gets partially ingested into the ring.

110

 

Fig. 4.8 Hairpins form over streaks.

111

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113

 

 

Fig. 4.11 Four photos of the evolution for 6 / D > .15. In this case a pocket does not
form, and it appears that the hairpin has been generated by the initial vortex ring/wall
interaction.

114

 

Fig. 4.12 Four Epotos of the interaction for 6 /D < .15. In this case pinch-off of a
portion of the ' ted hairpin does occur, creating a new small‘vortex ring.

115

b/D

 

 

0.3 III—
*’ l I :
l I |
I I I
l I
I12 -u- I I I
I
I LONG I SHORT I
I STREAKS ISTREAKS' POCKET ONLY
1- . : a : 1 I
I POCKET . pocxsr'
I I :
0.1 "F- I |
I I I '
I I '
I I '
«I. I i I
1 J 1 l 1 I l I i l 1 | 1 l 1 I
0" ' I ' I I I ' I T I I I *"I I 1* ‘1
011 112 114 115 115
Ur / UW

Fig. 4.13 The dependence of the formations and evolutions of streaks on 6 /D and
U / U for D+ > 250 and a 3 degree incidence angle. The indicated boundaries
bertween different evolutions are approximate.

116

 

 

0.3 7—
.1- I '
' I
| l r17
| I I:
0.2 -~ LONG STREAKS I ,
I I l
E I I
I PINCH-OFF
do .I. ___________ .J g I)
: LONG STREAKS I
I /
LONG STREAKS I I
SMALL PINCH-OFF I ,
I
I ll
.. ' __________ .J
l
' LONG STRETCHED HAIRPIN
_.L l 1 l l 1 I 1 l l J 1 1 L l l J; I
0" I I ' I I ' I ' I . I ' I * I . *I . I
oo 02 0A 06 on In
Or / uw

Fig. 4.14 The dependence of 6 / D on U / U for rings moving away from the wall at 2. 5
degrees. 6 / D now plays a much more important role, and long streaks are generated
over the entire speed ratio range studied.

117

 

 

 

325 .1- 0+ A .329

275 -- 037.0

225 -l-

Z+

.. 3.6
175 ‘I 46. 3 “$7355?

125 -— '53?”

7s --

 

25 75 125 175 225 275 325

Fig. 4.15 The dependence of the streak spacing in wall units on the size of the vortex
ring in wall units, for an incidence angle of 3 degrees and Ur/Uw = .31. The thickness
of the wall layer (in wall units) is shown next to each data point.

118

2+

350 '-

o
,U U '0.31
300-I- 6 '1"

  
  
 

3°, 11 u =0.31
m __ r/ I.

200 -r-
O
3 . Ur/Uw 80.22

150 ‘1-

lOO -—

 

so L I l l l l l l I I

50 1 00 l 50 200 250 300 350 400

Fig. 4.16 The dependence of the streak spacing on the speed ratio and angle.

119

1.5

1.4

1.3

1.2

1.1

 

1.0

X/D

0.9

4.

°-° 3°, "1"”. . 0.22
+
0.7 \

00°

. L . . l
25 30 35 4O 45 50

d

Fig. 4.17 The non-dimensionalized streamwise wavelength that sets in as a function of
6 for different Ur/Uw and angles.

120

OIIEI

 

STABLE INTERACTIONS
LONG STREAKS

     

 

| I
. &
POCKET l SHORT STREAKS I
I & I POCKET
| POCKET I
_ STREAK | I
STABILITY I I
BOUNDARY I I
A \ I I
b \
i L
STABILITY I
BOUNDARY I I
|
I I

' UNSTABLE INTERACTIONS

I-

I.
F"

0.1 0.2 0.3 0.4 0.5 0.6

Fig. 4.18 A comparison between ring and streak. satbility the of a three degree ring
moving towards the wall.

121

200 --

../.._,

I +

-r 3°, ur/uw - 0.31

1.0 -b

1” -b O
3 , Ur/Uw' 0.22

/
...‘L / /

1'4-

 

 

120 -I-
- L 1 . 1 1 _1
‘°° ' I ‘ I ' r I I F I
25 so 35 +0 45 so

5+

Fig. 4.19 The dependence of the time to instability of the streaks on the wall layer
thickness (both quantities are non-dimensionalized by wall layer variables) for three
degree incidence rings.

122

. end view

J

_

 

 

 

(b) X

Fig. 4 .20 (a) A photo of a hairpin vortex in three-view flow visualization;
(b ) A sketch of the vortical motion of the hairpin vortex;
note that the arrows indicate the sign of ratation

123

     

plan view

I.)
side View

g 21 Four photos of the three-View visualization; each photo is 10 t + apart.

124

   
   

L .

-‘ ~x new“. ~«74191‘“|Iw

     
     
 

am...

«2
V ?

 
 

 

 

Fig. 4.21 Cont.

VORTEX RING

HAIRPIN

 

   

‘ SECONDARY HAIP IN

 

Fig. 4.22 A conceptual picture describing the spatial relationshi of the formation of
visual features observed in the vortex ring/ moving wall interact1on including the main
h ' in vortex, secondary hairpin vortices, long streaks, and pocket; the arrows indicate
the ocal flow direction.

126

 

 

Fig. 4.23 A photo showing the laser illuminated end view flow visualization for a fast
ring moving away from the wall. The observed long streaks were just the legs of the
lifted hairpin vortex; thegere one unit. The dye marker actually concentrated within
the streamwise vortices. e sign of the vorticity shown in Fig. 4.23 (b) is consistent with
that associated with the hairpin vortex shown in Fig. 4.20 (b).

127

 

VORTEX RING

HAIRPIN

 

 

Fig. 4.24 The conceptual picture summarizin the spatial evolution of the vortex
ring/ moving wall interaction for Ur/Uw> 0. when the vortex ring moves away from the
wall.

128

    

Win mgm-w.mn .... . . . a

1.. Chu (1987)

trailing vortices kinked region

C / S

 

1

i

\

Q

\ speed
wall Q 3'1, front

\ '

R

\

\

\

‘ direction of motion —.

End View Plan View

~c. Smith (1978)

Fig. 4.25 Comparison among several investigators’ observations.

129

 

 

 

 

 

 

 

 

 

 

 

 

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325 - - ° 32. 9
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. 42 .
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75 -
I I I . I . 1 I
25 l I I I I I
25 75 I 25 1 75 225 275 525
D4-

Fig. 4.26 The distribution of D+ obtained from the diameter of the typical eddies of a

turbulent boundary layer at R 9 = 1176, superimposed upon the streak spacing obtained
for various size rings.

130

 

 

 

Fig. 4.27 (a) The vortical motions associated with the observed streaky structure in
vortex. ring/ moving wall simulation; (b) The counter-rotating pair hypothesized by
many investigators.

131

LASER

 

 

 

 

 

 

 

 

 

 

P

 

SIDE VIEW

Fig. 5.1 A schematic of experimental apparatus of the Stokes’ layer measurement; the
moving belt system is similar to what was used in water tank.

132

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134

 

 

 

Fig. 5. 4 Two photos from the result which are 0. 05 second apart; these photos were
taken for UW =12. 7 cm/ sec and belt running time t= 5. 25 seconds; the belt moved
from right to Wleft.

135

STOKES LAYER VELO. DISTR.

° 0...O...417fp0:+ 0.404fptt-waulcyuap

3.”

2.00 “+-
2.40

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(U/Uw)-1-ERF(n)

$133.55 The nondimensionalized velocity profile for two belt running speeds where the
id line represents the exact solution.

136

3.0

 

 

 

 

-p- IT-
.4..
2.5 --
2.0 ---
4..
A.
1.5 --
2E
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1.0 ---
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0.5 -2..
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-3.0 —2.5 —2.0 —1.5 - .0 - .5 0.0 0.5
t t

w or (an/8y) or (av/33’)m

Fig. 5.6 Results of the velocity gradient au/ay obtained from double differentiation
and of the spanwise vorticity obtained from circulation a proach are shown in this
figure where they are compared with the exact solution (Eepresented by solid line).
Everything is nondimensionalized by the similarity variables of the exact solution. A
check of continuity equation is also shown in this figure.

137

 

DYE :
I nesenvom
'

SOLE CHO
.996

 

L

 

 

 

 

ORIFICE

 

 

 

Fig. 5.7 A schematic of the experimental configuration used to generate and measure
the vortex ring.

138

 

 

 

 

 

 

 

 

 

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1 —

 

139

 

Fig. 5.9 Two photos of the result which are 0.07 second apart

140

 

 

 

 

Lagrangian

/x]

 

\
\
/\
\ Eulerian

 

 

 

 

 

 

 

 

1 2 U/Ur

 

plane 2 = 0

Fig. 5.10 The instantaneous velocities distribution along two axes of the ring.

141

CIRCULATION DISTRIBUTION

...w W .D.. Hill‘s. ARM at at.

1.20

1.“

0.00

0.00

I‘/ I},

0.40

0.20-

 

 

Fig. 5.11 The instantaneous circulation distribution of the ring, which also shows the
results obtained by Sullivan et al. (1973) for different Reynolds numbers and shows
Hill’s exact solution of a spherical vortex.

142

 

 

 

 

 

mam-01 Y 1m: meant-01

X mm:

L l
[MIR FD! -Zl.flll II sum mm mm I 5.1111!)

Fig. 5.12 The instantaneous vorticity distribution over a vortex ring.

143

 

V . u:‘vrfllf‘wwx§<ryi-t n

 

Fig. 5.13 Four sets of photos with both top view and side view describing the time
evolution of vortex rin / moving wall interactions in the conditions of Ur/Uw = 0.26, 3
degree of incident an e, 6/D = 0.18 and Uw = 15.5 cm/sec.

144

 

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147

2.00 12* = 24.4 (t = 3.0 sec.)

I.“ - MEASUREMENT POINTS

- y / (2 x SORTWO)

'I

 

'1 -y /(2xsonrm»

 

 

(U /U°)-I-ERF('I.)

Fig. 5 .17 The time evolution of the streamwise velocity distribution at the measurement
pomts. The dotted lines represent the undisturbed velocity profiles of the Stokes’ layer.

148

t* = 44.7 (t = 5.5 see.)

a. m w a

a.

Sarcomxs\xr e.

 

1.2

 

(U luau-Emu)

t* = 57.0 (t = 7.0 sec.)

 

. a w a

8358 x $\ A .. ...

 

1.2

1.0

0..
(U /UO) - I — EM-‘(M

0.4

0.0

Fig. 5.17 Cont.

149

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VON)

tram WALL

Y(IN)

CONST. u, at t*

24.4 (3.0 sec)

2+ from CENTER UNE

0.0 21.5 lo]

0.0 0.4

611.5 36 107.5

undisturbed
u/U.

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0.0 l""
0.0 0.2

  

 

a ' ’
. I I I I IIII III IIII
o 'U'III'U'U'I'U'U'I'IIIUIII

Z(in) from CENTER LINE

Fig. 5.18 The constant velocity lines in y-z plane.

150

32.5 (4.0 sec)

U
N

U
O

[9

WM W01! +A

TNM W04} +A

Y(|N) from WALL

from WALL

Y(IN)

CONST. u, at t* = 44.7 (5.5 sec)

Z+fromCENTERUNE

 

0.0 [8.4 36.8 55.2 73.6 92
I L, l l l l l l
I I I I I I T I :
0.0 -
u/UU

 

0.5-1

II

0.4 -=

1‘3

IIII IIIIIIIII IIII II I IIIIIII III
II'III IIIIIIIIII'IIIIIIIII'I I'IIIII'II

 

n
v

0.2

 

1

1p1r1u b In 1' In 0

 

»- :99 01:15:14:

 

b

0.0'

p

o

a

K, I...
I

a“
qp

9..

o

.-
p

II)

:: -‘-

0

b
c:
in

I :
IIIII IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIJ
II I

IJII
I'I'IIIIIII
.—
GD
0

h;

g-pppoo o -'.) a
”new“ m... u
I

CONST. u, at t* = 57.0 (7.0

2+ from cans! UNE
0.0 17.5 14.3 52.2

 

0.0 0.2 0.‘ 0.0
2611) from CENTER LINE

Fig. 5.18 Cont.

151

69.6

{-55.2

III'III IIII'II
a;
CD
CD

 

  

87

WM W01} +A

TNM W013 +A

z+mcmrmuuz

 

  
  

 

 

 

 

 

 

 

0.0
I I I I I I I I J I l L I I l I I I I I
‘0. I I r I I r r I I I l I i j I I I I 4 'J
«1-
0.0 {E- 0.0
I: 0.0
°‘ 1:
g 0.4 1} M
° ‘3 1:- M
5 ..
A 0-0 .:' 0.0
a ..
A -0.2 1:- '44
£15 0‘ 11‘5- -0.4
I J J I I J I d -
"1° T . i I i ' 1 . I ' I ' I . I . I I I r 1.0
0.0 0.1 0.2 0.3 0.6 0.0 0.0 0.1 0.0 0.0 1.0
2(h) from CENTER LNE
2+ from 08115! LINE
0.0
l l I l I _L I l_.j l L I L L L l IL I I
I” i r ‘I T I I Ifi T l I ‘ I I I r I [fl 1 in
u + ‘3' I"
y = 5 i t* = 32.5 :1:
15 1:: z;
0.4 20 V 1- 0.4
b
25 0 q:
.. 0.2 {— 0.2
a n
1: ..
"\.- 7’ d.
A u _ at-.. _—‘ M
3 2:
A -0.2 .1; .03
a --
I, Z:
:5 -0.‘ 1:- -'0.4
. -P
a -0.0 1:- -0.0
:I—
-0.0 1:- -0.0
all-
L J_I I I 4 I I I I l I I I I L l I 1
TI.“ I U I I I I T t T I I I I I r I 1 r ‘ r “Io.
0.0 0.1 0.2 0.3 0.4 0.0 0.0 0.7 0.0 0.0 1.0

200) fromCENTERUNE

Fig. 5.19 The velocity defect or gain with respect to the undisturbed wall layer shown in
(a). These sets of data had been converted to the turbulent boundary layer point of view
by performing the Galilean transformation.

152

z+mcanatms

 

t‘k

uuuu‘uawaa

ig.-(035

y

A: 9.53 dd»

0.1 u o.-
zai) mama:

030.30.40‘“

0.1

2?me

 

 

 

y

 

\i“
= l
0.0

30 A
35
40

y

\ ._
A, .. u
w”, .
\\.

1 l 1
l l l
0.1 0.3 0.6

A
I

l
1
0.

 

u a a a a a a a I
.3: .18.. 5 mA... Sta: .3!

200 mm“

Fig. 5.19 Cont.

153

 

 

Fig. 5.20 A photo of the optical configuration and the orientation of the laser beam.

154

.829? wEEw: can 537433 8% 2: mo 33> 03m 2: “NW .wE

<I< ZOHHUmmImmcxo

 

3MH> MDHm ABDOMV

 

 

 

<xmz<u
mH>ox
.5: mm

 

t UZH%=UH4

r . DJ _. :6

> azu—

 

 

 

 

 

155

 

y+

t=6.8sec
(t'=55.3)

 

 

t = 6.82890

 

Fig. 5.22 The result of the streamwise vorticity measurement. Those photos are selected
from the same se uence of movie in one experiment. Two photos of each set were 0.02
second apart whic corresponded to 0.5t apart.

156

y?

t= 7.6sec
(t°=68.3)
- O

 

 

t = 7.625»

 

Fig. 5.22 Cont.

157

 

 

w.(l/se<=)

. ( mg: 0.0965 0)..)

(a)

t’= 48.8

 

 

 

 

 

(b)

 

t°= 55.3

 

 

 

Fig. 5 .23 The contour plots of the instantaneous streamwise vorticity distribution.

158

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(e

(

)

f)

 

L

 

 

 

 

1
l

conu- -o.~-OIII It‘ll-01mm.

2+ 75 mu 11m amt tum.- mun-en

Gal-C m

 

l

/,
r \\$\/
Q‘»

. f..—

r-

 

rig/Rt? KR 15°

3‘ ""“_\ \
.. 0

///fl\

l\‘\.__,./€'./"" ,- \ \ “

3. ‘-4O

°' « t'-55.3
' > (a)
7 .

  
 

 

Cl /’
O I ’ I
O
A

  

 

 

75 CH!” m :0!

 

I 0

TI 0.2mm cum IM' (ELM-0| 30
um: awa-or I "Om: 0.01III-0I

Fig. 5.24 The instantaneous Reynolds stress distributions obtained from Fig. 5.22 (a)-

(0-

161

 

 

 

 

 

 

 

 

 

3'0

1 1
mm U 0.11m
mam-m

l l
I" 1.01m C.” I

too)
I mm: (Lu-0| 1 Ill":

1
CM" F- -Z.

l
75

Fig. 5.24 Cont.

162

 

 

 

 

 

 

t'- 68.3

(f)

 

 

 

 

Fig. 5.24 Cont.

163

 

 

    

\ EX

 

“f ’//////////////////////////////////A
(b)

Fig. 5.25 A photo taken 0.02 second before t=6.8 seconds (shown in Fig. 5.25 (a))
Indicates that a pair of counter-rotating streamwise vortices formed from the wall and
moved upward.

164

CIRCULATION VS TIME

300.0

200.0 (+)

 

 

( - )
mo \
" —a
58.6 61.8 65.1 c*
L I A I I J
0.0 r y : l = I I I l
u 7.2 7.8 3.0 3.4

t (SEC)

Fig. 5.26 The time evolution of total circulation of the strong vortex (the region with
positive sign in Fig.5.22 (c)-(e); and the time evolution of the total circulation of one leg
of the hairpin (the region with negative sign in Fig. 5.22 (c)-(e)).

165

WINDOW OF MEASUREMENT
LAB. COORDINATES

POCKET VORTEX

 

 

 

 

 

 

 

Fig. 5 .27 A sketch of the pocket vortex (F alco 1980b).

166

, pocket
hairpin vortex

Q
I I, I
.I

.————>>

 

 

 

Fig. 5.28 The sketch of possible merging process.

167

APPENDIX

APPENDIX A

ERROR ANALYSIS OF THE PHOTOCHROMIC GRID TRACING TECHNIQUE
FOR THE MEASUREMENT OF VORTICITY

Consider a unit of the mesh (see Fig. A1). The corners of the undistorted mesh
are defined as points 1a to 4a in counterclockwise rotation. We will assume that the
mesh is spaced 6 and that a worse case line movement between images is 1/2 the mesh
width. After time At the mesh square will move to position 1b to 4b. The vorticity
“’2 = av/ax - au/ay

=(Y1a'y1b)/At '(Yza'YZbVAtu
(x2a‘x1a)
(xla-xlb)/At - (x4a-x4b)/At
(Y4a'y1a)

 

 

where,

Yla 'Ylb = An = 1/2 e
y2a 'Y2b = Am = 1/2 6
y4a'y1a = AYm = 6
Xla-le =AXI = 1/26
X4a-X4b = AXH = 1/2 E
x2a"‘1a = AxIII = 6

I2 - I1 = AI

_(AyI - AyH)/At - (AXI - AXII)/At

O wz

 

AxIII AYIII

The uncertainty in the measurement of vorticity (6 wz) is thus,

168

(6wz)2 = (awz/aAyI - 6Ay1)2 + (awz/aAyH - 6Ayn)2
+ (awz/aAym - 6Aym)2 + (awz/anI - W92

+ (awz/ann . 6Axn)2 + (awz/anm . alum?
+ (awz/am - 6At)2
Estimates of the magnitudes of the terms are:

awz/am = -«Ay1-Ayn)/Axnp/<At)2
+ ((Axl - Axn)/AymV(At)2
= -<(1/2 e - 1/2 eve/(At)2
g0
awz/aAyI = l/At . Axm a l/At . e
6wz/6Ayn = -1/At . Axm z l/At . e
awz/aaym = ((AxI - Axn)/At)/(Aym)2 a (1/2e -1/2e>/At - e2
2 0
3%,/an1 = -1/At - Aym as -1/m - e
anal/BAX“ = l/At . Aym a l/At . e
5wz/3Axm = -((AY1'AY11)/At)/(Axm)2 g'(1/2€ '1/2€)/At ' 62
a 0

Therefore 6 “’z squared is equal to :

(5.092 = (5.5/26m)2 + (ac/261302 + o + (66/26At)2
+ (6:5/2asAt)2 + (66/26AI)2 + 0 + O
= 4 (66/26At)2

Finally,

Swz = (1/At)(6e/e) to the first order in e.

169

For example, (see Fig. A.2) assume that
a) meshing spacing = 1000 pm
b) line width = 100 pm
c) 10% reading error in reading the center of the 100 pm line, i.e. 6 c = 10 pm;
66/6 = 0.01
if At = 0.01 second (between two frames), we will have
6002 = (1/AI)(6€/6) = l/sec.

170

4b 3b

 

 

 

 

 

 

 

 

4a 3a
‘ 1b b
la 23
*1/26 ‘4
Y
x

Fig. A.1 The undistorted and distorted mesh

171

mom

| I

<— 1000M“

Fig. A.2 An example of the error analysis

172

BIBLIOGRAPHY

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176