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An Experimental Study of the Sub-Critical Flow past a Circular Cylinder Fitted with a Single-Start Helical Surface
Wire
by
Lavanya Murali
A thesis submitted in conformity with the requirements for the degree of Master of Applied Science
Aerospace Engineering University of Toronto
© Copyright by Lavanya Murali 2017
ii
An Experimental study of the Sub-Critical Flow Past a Circular
Cylinder with a Single Start Helical Surface Wire
Lavanya Murali
Master of Applied Science
Aerospace Engineering
University of Toronto
2017
Abstract
This study experimentally investigates the structure of the flow past a circular cylinder fitted with
a helical wire perturbation using Particle Image Velocimetry (PIV) and Hydrogen Bubble Flow
Visualization (HBFV). Dual shear layers having the same sign of vorticity are observed when the
helical wire passes from angular locations between 35 and 55 with respect to the forward
stagnation point. Such shear layers have been recorded in the literature for the three-start helical
wire type protrusions, and have been attributed to interactions induced by the presence of multiple
wires. This work shows, however, that a single wire is sufficient to produce this behavior. HBFV
images and the divergence of the 2-D velocity field measured using PIV show that a portion of the
incoming flow arriving at the wire is diverted along the length of the wire, which later is observed
to intermittently turn and flow over the wire, thus influencing the flow downstream of the cylinder.
Finally, the swirling vortices induce streamwise vortical patterns and disrupt the Karman vortex
tube.
iii
Acknowledgments
I would first like to thank my advisor, Dr. Alis Ekmekci for her guidance and support throughout
this research. Under her tutelage, I have learned many transferable and technical skills, which have
helped me grow into a better professional. I would like to thank the members of my research
committee Dr. Zingg, Dr. Lavoie, Dr. Steeves and Dr. Nair, whose recommendation during the
research assessment committee meetings helped me understand this work better. I thank Dr. Gülder
for reviewing this thesis at a short notice and for providing valuable suggestions for improving the
quality of this work. I thank Dr. Gottlieb for the several hours of discussion we had on science
and beyond, which stimulated my curiosity to understand the world in general. I also would like
to thank Dr. Sullivan for all the beneficial inputs he gave on my research.
I would like to thank my colleagues at the experimental fluid labs for the help they have provided
in helping me set up the experiments. I would like to thank LiLex Industries in Toronto, who
helped me in building the experimental model in a short period.
Apart from gaining valuable experience in doing research, UTIAS has given me friends for life,
who made my time here, one of the most memorable periods of my life. Thank you, Sandipan,
Bharat, Martin, Vishal and Maciej for all the discussions, adventures and encouragement!
I am fortunate to have family and friends who extended their continuous support throughout this
work. I particularly thank my parents and parents-in-law whose support catalyzed this work. To
Arun, who has been my source of inspiration, my critic and my strongest pillar of support, thank
you!
Finally, I would like to dedicate this work to my spiritual Gurus, whose teachings have inspired
me to lead a life of contentment, and, to my beloved late grandpa, who was instrumental in making
me a strong and independent woman, and whose dream it was to see me as a proud engineer.
iv
Table of Contents
Abstract ........................................................................................................................................... ii
Acknowledgments .......................................................................................................................... iii
Table of Contents ........................................................................................................................... iv
List of Tables ................................................................................................................................ vii
List of Figures .............................................................................................................................. viii
List of Symbols ............................................................................................................................ xiii
List of Abbreviations ................................................................................................................... xiv
1 Introduction ................................................................................................................................ 1
1.1 Motivation ........................................................................................................................... 1
1.2 Practical applications .......................................................................................................... 2
1.3 Literature Review ................................................................................................................ 2
1.3.1 Flow past a stationary rigid cylinder in sub-critical regime ................................... 2
1.3.2 Behavior of the flow past a rigid cylinder during VIVs ......................................... 4
1.3.3 Techniques used in the control of the flow past a cylinder ..................................... 6
1.3.4 Surface protrusions ................................................................................................. 7
1.3.5 Flow past helical surface protrusions .................................................................... 10
1.3.5.1 Helical strakes......................................................................................... 10
1.3.5.2 Helical wires ........................................................................................... 11
1.4 Objective ........................................................................................................................... 16
1.5 The layout of the thesis ..................................................................................................... 16
2 Experimental Methodology ...................................................................................................... 18
2.1 Flow facility ...................................................................................................................... 18
2.2 Model configuration .......................................................................................................... 20
2.3 The set-up of the experimental model .............................................................................. 21
v
2.4 Coordinate system and the fields of view ......................................................................... 22
2.5 Experimental set-up for different fields of view ............................................................... 23
2.6 Experimental techniques ................................................................................................... 27
2.6.1 Hydrogen bubble aided flow visualization (HBFV) ............................................. 27
2.6.1.1 Operation ................................................................................................ 28
2.6.2 Particle Image Velocimetry (PIV) ........................................................................ 28
2.6.2.1 The principle ........................................................................................... 28
2.6.2.2 Operation ................................................................................................ 28
2.6.2.3 Data acquisition ...................................................................................... 28
2.6.2.4 Image processing .................................................................................... 29
2.6.2.5 Data processing ...................................................................................... 30
2.6.2.6 Boundary generation............................................................................... 31
2.7 Calculation of flow properties .......................................................................................... 33
2.7.1 Velocity ................................................................................................................. 33
2.7.2 Vorticity ................................................................................................................ 33
2.7.3 Time-averaged functions ...................................................................................... 34
3 Results and Discussions ........................................................................................................... 35
3.1 Flow behavior in the X-Y plane ........................................................................................ 35
3.1.1 Patterns of the time-averaged streamwise velocity 𝑢𝑥
𝑈∞⁄ in the near wake
region .................................................................................................................... 36
3.1.2 Patterns of time-averaged and instantaneous fields of spanwise vorticity 𝜔𝑧𝐷
𝑈∞⁄ in the near-wake region .......................................................................... 38
3.1.3 Patterns of time-averaged and instantaneous fields of spanwise vorticity 𝜔𝑧𝐷
𝑈∞⁄ in the shear layer region .......................................................................... 46
3.1.4 Patterns of time-averaged and instantaneous 𝜕𝑢𝑥
𝜕𝑥+
𝜕𝑢𝑦
𝜕𝑦 contours in the shear
layer region ........................................................................................................... 49
vi
3.2 The flow behavior in the Z-X plane .................................................................................. 52
3.3 Flow behavior in the Y-Z plane ........................................................................................ 55
3.4 Discussion ......................................................................................................................... 56
4 Recommendations for Future Work ......................................................................................... 59
4.1 Future work with the current experimental model ............................................................ 59
4.2 Future work that can be performed on models different than the one used in the current
work for analyzing the flow behavior with cylinder movement ....................................... 61
4.3 Experimental set-up for forced oscillation experiments: two possible test rig designs .... 62
5 Appendix A .............................................................................................................................. 64
References ..................................................................................................................................... 70
vii
List of Tables
Table 1.1 Classification of different flow regimes based on the flow characteristics and Strouhal
number (St) variation with respect to the angular position of the wire (), based on Figure 1.1
(taken from Joshi (2016)) . Each fundamental angle (1) and (2) is referred according to the findings
by Nebres and Batill (1993) and Ekmekci and Rockwell (2010) respectively. ............................. 8
Table 1.2 Review of the literature on the studies conducted on helical -wire type surface
perturbations in order to find the optimum configurations which will help curb VIVs. .............. 12
Table 2.1 Values of the free-stream velocities, the resolution of the camera lens used, the field of
view of the plane, the pulse separation time, the magnification factor of the PIV image, and the
resolution of the data for different experiments are tabulated. ..................................................... 19
viii
List of Figures
Figure 1.1 Variation of the prevailing Strouhal number (St) of the velocity fluctuations in the wake
of the cylinder as a function of the angular position () of the single spanwise wire for a wire
diameter d= 0.0625D and Reynolds number of 10,000. The fundamental wire locations θt, θc, θm,
θ𝑟 and θ𝑏 are plotted as per the findings of Nebres and Batill (1993), while the critical angle
locations of θ𝑐1 and θ𝑐2 are plotted as per Ekmekci and Rockwell (2010) findings. Figure adapted
from Joshi (2016). ........................................................................................................................... 7
Figure 2.1 Experimental model: A circular cylinder fitted with a single helical wire type surface
protrusion. The cylinder’s diameter is (D)= 50.8 mm and length is (L)= 533 mm, diameter of the
surface wire is (d) = 3.125 mm, and the pitch of the helix is (P) = 152.4 mm. ............................ 20
Figure 2.2 (a) The cylinder – endplate configuration, and (b) the rotary mount and the uni-
directional traverse system. ........................................................................................................... 21
Figure 2.3 The coordinate system that was used to characterize the flow. Fields of visualization
are also highlighted in the sketches. ............................................................................................. 23
Figure 2.4 PIV Experimental set-ups in X-Y plane is shown. the camera is placed underneath the
water channel, the light source is placed on the side of the water channel and the plane of
illumination is parallel to the base of the water channel. The top right part of the image is the
sectional view of the X-Y plane. ................................................................................................... 24
Figure 2.5 Hydrogen bubble flow visualization experimental set-ups for Y-Z plane is shown.
Here, the camera is placed on the side of the water tunnel facing the mirror, the light source is
placed beneath the water channel and the plane of illumination is parallel to the span of the cylinder
and is formed behind it. ................................................................................................................ 25
Figure 2.6 For the Z-X plane, (a) PIV experimental set-up and (b) hydrogen bubble experimental
(HBFV) set-up is shown. In this plane, for both type of experimental set-ups, the camera (CCD for
PIV, video camera for HBFV) faces the cylinder, the light source (laser for PIV and LED lights
for HBFV) is placed below the water channel and the plane of illumination is parallel to the span
of the cylinder and on one side of the cylinder. ............................................................................ 26
ix
Figure 2.7 Figure (a) depicts the passive boundary (pink lines) generated over the data file for Z-
X plane. Figure (b) depicts the final PIV output file (vector field) in Z-X plane. It can be noted that
the vectors within this boundary in Figure (b) are not removed, and is used as part of the flow. 31
Figure 3.1 Contour patterns of non-dimensionalized time-averaged streamwise (X-direction)
velocity, ⟨ux⟩
U∞⁄ , is plotted in the near-wake region at different wire angular locations. The solid
lines represent positive values of ⟨𝑢𝑥⟩, while the dashed lines represent negative values. Here, the
minimum and incremental values of normalized-time-averaged streamwise velocity are
|⟨ux⟩
U∞⁄ |
min= 1.6 and |
⟨ux⟩U∞
⁄ | = 0.04. ............................................................................. 36
Figure 3.2 The non-dimensionalized vortex formation length L𝑓
D⁄ as a function of the wire angle
(𝜃) for the single-helical-wire (purple curve), the single-straight-wire-fitted (orange curve) and
plain (green curve) cylinders. The Reynolds number for all the experiments is 10,000. The wire-
to-diameter ratio for helical and straight wire fitted cases is d = 0.0625D. .................................. 37
Figure 3.3 Contours of time-averaged normalized spanwise (X-Y plane) vorticity |⟨ωz⟩|D
U∞⁄ in
the near-wake region for selected wire angular locations θ. Absolute values of the time-averaged
vorticity are plotted in each image in order to assimilate the amount of asymmetry in the flow (in
terms of vorticity asymmetry angle). The yellow straight line helps to measure the vorticity
asymmetry angle. The purple vertical line indicates the total wake width at X = 0.5D location,
while the violet line indicates the total wake width measure at X = 0.75D location. ................... 39
Figure 3.4 The non-dimensionalized instantaneous spanwise vorticity 𝜔𝑧𝐷
𝑈∞⁄ in the near-wake
region is plotted for different instants of data acquisition, each separated by half a nominal period
of a Karman cycle (Tn) in each row. Here, the data is shown for θ=35°,42° and 50° angular
locations, each presented in a different column. Here, the value of Tn is 20 frames, or in other
words, 1.38 s. ................................................................................................................................ 41
Figure 3.5 Figures (a), (b) and (c) illustrate the definition of the vortex formation length (Lf ), the
vorticity asymmetry angle ( ) and the total (WT) and lower (WL) wake width respectively. Figures
(d), (e) and (f) show the measurement of the two vorticity asymmetry angles (∅1 and ∅2), two
x
total wake widths (WT1 and WT2 ) and two lower wake widths (WL1 and WL2). In figure (c), the
wake width calculations are done at two different downstream locations: X= 0.5D (purple line)
and X (violet line) = 0.75D. .......................................................................................................... 42
Figure 3.6 (a) The variation of vorticity asymmetry angle ϕ relative to the wire angle 𝜃 is plotted.
The value of 𝜃 ranges from 𝜃 = 0° to 180°. (b) The presence of two asymmetric angles for =
41, 42 and 43. The two value of asymmetry angles can be attributed to the presence of same
strength vorticity in both the dual shear layers on the wire side. .................................................. 43
Figure 3.7 The variations of wake widths W and WL relative to the wire angle 𝜃 are plotted in
figure (a) and (c) at X= 0.5D and 0.75D respectively. The graphs (b) and (d) depict the change in
the value of the wake width relative to the wire angle 𝜃 at X= 0.5D and 0.75D, respectively. The
value of 𝜃 ranges from θ = 0° to 180° and X = 0 is considered as the cylinder center along the
streamwise (X-axis) direction. ...................................................................................................... 46
Figure 3.8 Contours of time-averaged normalized spanwise (X-Y plane) vorticity |⟨ωz⟩|D
U∞⁄ in
the shear layer region at selected wire angular locations θ. . ........................................................ 47
Figure 3.9 The normalized instantaneous spanwise vorticity ωzD
U∞⁄ from the shear layer region
is given at selected instants in time, each separated by half the period of a nominal Karman cycle
(Tn) in each row. Here, the data is shown for 𝜃 = 35°, 42° and 50° wire angular locations, each
presented in a different column. The value of Tn is 20 frames, which corresponds to 1.38 s. ..... 48
Figure 3.10 Contours of time-averaged negative variation of 𝑢𝑧 in the Z-direction, (i.e., - 𝜕𝑢𝑧
𝜕𝑧),
χDU∞
⁄ , in the shear layer region for selected wire angular locations, θ. Here the value of χ is
nondimensionalized with the free stream velocity (U∞) to diameter of the cylinder (D) ratio. .. 49
Figure 3.11 Negative of the instantaneous variation of 𝑢𝑧 in the Z-direction,(i.e.,− 𝜕𝑢𝑧
𝜕𝑧),
χDU∞
⁄ ,
from the shear layer region is plotted for different instants in time, each separated by half the period
of a nominal Karman cycle (Tn) in each row. Here, the value of χ is nondimensionalized with the
free stream velocity (𝑈∞) to diameter of the cylinder (D) ratio. Each column represents the wire
xi
angular location,θ, at which the data is plotted. The data is shown for θ = 35°, 42° and 50° wire
angular locations. The value of Tn is 20 frames, which corresponds to 1.38 s. ............................ 50
Figure 3.12 (a) The normalized values of the time-averaged cross-stream (Z-X plane) vorticity
⟨ωy⟩DU∞
⁄ in the down stream region of Z-X plane at a distance of Y = 0.75D. (b) A snapshot of
the flow field from the hydrogen bubble visualization experiments, indicating the formation of two
opposite-sign vortices extending in the streamwise direction (marked in green for clarity). The
location where the cross-stream vorticity (𝜔𝑦) and the two vortices occur is marked by an arrow
(in red). Here, for PIV data, the minimum and incremental values of contours are
|⟨ωy⟩D
U∞⁄ |
𝑚𝑖𝑛= 10 and ∆ |
⟨ωy⟩DU∞
⁄ | = 0.3. ....................................................................... 53
Figure 3.13 The instantaneous snapshots of the flow in the Z-X plane at two different instants in
time. In case A, at θ > 90°, the flow continues to move along the wire and in case B, at θ < 90°,
the flow is deflected downstream of the wire in the streamwise X-direction. .............................. 54
Figure 3.14 Formation of streamwise vorticity 𝜔𝑥 very close to the cylinder surface is shown at
different instances in time using HBFV technique. The imaging plane is at X=0.50D, where X is
measured from the cylinder center. Here, Reynolds number is 5,000. ......................................... 55
Figure 3.15 The formation of the streamwise vorticity 𝜔𝑥 very close to the projection of the
cylinder surface on the Y-Z plane is shown at different instances in time using the hydrogen bubble
visualization. The imaging plane is at X = 0.50D, where X is measured from the cylinder center.
Here, Reynolds number is 10,000. ................................................................................................ 55
Figure 4.1 Variation of the Strouhal number with the wire angle, θ, is plotted for a cylinder fitted
with (a) single-start helical wire, and (b) single straight wire case (Joshi, 2016). Here, 𝜃 is measured
from 0° to 360°. The results were obtained from CTA measurements at ReD = 10,000. For both
cases, the wire-to-diameter ratio was d= 0.0625. The location of the hot-wire probe and orientation
of the cylinder during the course of experiments is illustrated in top right corner. ...................... 59
Figure 4.2 The conceptual design # 1 for the forced-vibration experiments using slider-crank
mechanism. ................................................................................................................................... 62
xii
Figure 4.3 The conceptual design # 2 for the forced-vibration experiments using linear actuators.
....................................................................................................................................................... 63
Figure 5.1 The non-dimensionalized vortex formation length (Lf ) is plotted for different wire
angular locations. .......................................................................................................................... 64
Figure 5.2 The vorticity asymmetry angle () is plotted for various angular locations. Here the
angle made by the yellow straight line is used as a measure of asymmetry. The values are plotted
on the contour plots of normalized time-averaged absolute values of |⟨ωz⟩|D
U∞⁄ . ................... 65
Figure 5.3 Values of total wake width WT are plotted at a distance of X = 0.5D for different angular
locations ranging from = 0 to 180. Here the purple straight line is used as a measure of WT. The
values are plotted on the contour plots of normalized time-averaged absolute values of
|⟨ωz⟩|DU∞
⁄ . .................................................................................................................................. 66
Figure 5.4 Values of lower wake width WL are plotted at a distance of X = 0.5D for different
angular locations ranging from = 0 to 180. Here the purple straight line is used as a measure of
WL. The values are plotted on the contour plots of normalized time-averaged absolute values of
|⟨ωz⟩|DU∞
⁄ . .................................................................................................................................. 67
Figure 5.5 Values of total wake width WT are plotted at a distance of X = 0.75D for different
angular locations ranging from = 0 to 180. Here the violet straight line is used as a measure of
WT. The values are plotted on the contour plots of normalized time-averaged absolute values of
|⟨ωz⟩|DU∞
⁄ . . ................................................................................................................................ 68
Figure 5.6 Values of lower wake width WL are plotted at a distance of X= 0.75D for different
angular locations ranging from = 0 to 180. Here the violet straight line is used as a measure of
WL. The values are plotted on the contour plots of normalized time-averaged absolute values of
|⟨ωz⟩|DU∞
⁄ . . ................................................................................................................................ 69
xiii
List of Symbols
Symbols Description 2 P vortex wake mode 2 pairs of vortices being shed in each half cycle
2 S vortex wake mode 2 single vortices being shed in each half cycle
2 T vortex wake mode 2 triplet of vortices being shed in each half cycle
𝑐𝑠𝑦𝑠 System damping
d Diameter of the helical wire
D Diameter of the cylinder 𝑑
𝐷⁄ Wire-cylinder diameter ratio
𝑓𝑐ℎ𝑎𝑛𝑛𝑒𝑙 Frequency of the water channel
𝑓𝐾 Karman shedding frequency
𝑓𝑆𝐿 Shear layer frequency
H Height of the strake
k Spring stiffness
L Length of the cylinder
Lf Vortex formation length 𝐿
𝐷⁄ Aspect ratio
𝑚𝑑 Mass of the displaced fluid
𝑚𝑠𝑦𝑠 Mass of the system
𝑚∗𝜁 Mass-damping parameter
N Number of sample points acquired using PIV.
P Pitch of the helix
P* Localized pitch
𝑅𝑒𝐷 Reynolds number defined with respect to the cylinder diameter
St Strouhal number
Su Autospectral density of the fluctuating streamwise velocity
t Thickness of strake
𝑇𝑛 Nominal period of vortex shedding.
𝑈∞ Free stream velocity
𝑢𝑥 Velocity component in the X-direction
𝑢𝑦 Velocity component in the Y-direction
𝑢𝑧 Velocity component in the Z-direction
WT, WT1 and WT2 Total wake width
WL, WL1 and WL2 Lower wake width 𝛿
𝐷⁄ Thickness of the unperturbed boundary layer
Δ𝑇 Laser pulse separation time
𝜃 Angular position of the wire in the X-Y plane, with respect to the flow.
𝜃𝑡 , 𝜃𝑐, 𝜃𝑚, 𝜃𝑟 and 𝜃𝑏 Fundamental angles defined by Nebres and Batill (1993)
𝜃𝑐1 and 𝜃𝑐2 Critical wire angles, as defined by Ekmekci (2006) and Ekmekci and Rockwell
(2010, 2011)
Vorticity asymmetry angle
𝜒 Quantity to determine if there is any loss or gain of fluid volume per unit time in the
X-Y plane, i.e. any variation of 𝑢𝑧 across the X-Y plane. In other words, a measure of
the rate of injection or rejection of fluid volume into the X-Y plane.
𝜔𝑥 Vorticity component in the Y- Z plane
𝜔𝑦 Vorticity component in the Z- X plane
𝜔𝑧 Vorticity component in the X- Y plane
xiv
List of Abbreviations
CTA Constant Temperature Anemometry
FFT Fast-Fourier Transformations
HBFV Hydrogen bubble assisted flow visualization
PIV Particle Image Velocimetry
SDPIV Stereoscopic Digital PIV
V3V Volumetric 3-component Velocimetry
VIVs Vortex-Induced Vibrations
1
1 Introduction
This chapter provides the motivation, the related review of literature and the summary of the
scope of this thesis. In the literature review, the behavior of the flow past a stationary rigid
cylinder in sub-critical regime is discussed first. Then the flow past rigid cylinders subjected to
motion is briefly summarized, followed by different forms of control methods, with a focus on
various helical surface protrusions used to curb the vortex-induced vibrations. Finally, the
chapter concludes with a summary of the scope of this project.
1.1 Motivation
When the drag on a body is dominated by pressure or form drag as opposed to viscous drag, the
body is termed as a bluff body (Bearman, 1984). A popular example of a bluff body is a circular
cylinder. There have been numerous studies conducted to analyze the flow over circular
cylinders for various conditions over the past several decades due to its complexity and practical
importance in real engineering applications. The long term goal of the current study is to improve
the understanding of the control of vortex-induced vibrations (VIVs). VIV is a phenomenon that
occurs in many engineering situations, and can be viewed as the response of the body to periodic
irregularities in the flow past the body. Circular cylinders placed in fluid flows periodically
discharge vortices that induce an uneven pressure distribution around the cylinder generating
uneven forces and vibrations that act on the bluff body. These vibrations may have small or large
amplitudes, and can result in the failure of the structure over a period of time or instantaneously.
Small vibration amplitudes lead to fatigue or fretting wear in the long term and can lead to
structural loss. When the frequency of the flow matches the natural frequency of the cylinder,
resonance may occur, which may lead to damage in the cylinder structure in a short period of
time. Generally, VIVs are controlled by methods that aim to attenuate large vibration amplitudes
and mitigate the vortex shedding frequency. This study aims to understand the behavior of the
flow over a fixed circular cylinder when a passive control method, in the form of single wire
wound helically over the surface, is employed.
2
1.2 Practical applications
VIVs are encountered in many engineering applications. It is an important source of fatigue
damage for offshore oil production risers and mooring lines (Pantazopoulos, 1994). Also, tall
and slender chimney stacks, high-rise buildings, bridges, aircraft control surfaces, rocket launch
pads, antennas etc., are susceptible to such vibrations due to wind flow (Blevins, 1990;
Naudasher and Rockwell, 2005; Padoussis, Price and de Langre, 2011). Therefore, it is necessary
to understand, model and control VIVs.
1.3 Literature Review
Literature on vortex-induced vibrations is vast and continuously growing, both on fundamental
issues and on its prediction and control. Particularly, there is a need to understand experimentally
the physics behind different control measures. Comprehensive reviews related to the formation
and prediction of VIVs have been written, most prominently by Bearman (1984, 2009, 2011),
Blevins (1990), Naudasher and Rockwell (2005), Sarpkaya (2004) and Williamson and
Govardhan (2004, 2008).
1.3.1 Flow past a stationary rigid cylinder in sub-critical regime
The study of the flow behavior during VIVs on a circular cylinder begins with understanding the
flow in its canonical form, i.e., the flow past a stationary circular cylinder. Numerous studies
have analyzed the flow past a stationary cylinder, with detailed studies of the wake region
conducted by Gerrard (1966), Blevins (1990), Zdravkovich (1990, 1996), and Williamson
(1996), to name a few. Of the many parameters that affect the flow behavior, Reynolds number
plays a dominant role. As the Reynolds number increases from low to high, the flow past a
stationary rigid circular cylinder exhibits a series of flow regimes (Khoury, 2012). The
experiments in this study were conducted at a single value of Reynolds number equal to 10,000.
This value of Reynolds number lies in the sub-critical flow regime whose characteristics are
explained below.
When a stationary rigid cylinder is placed in the sub-critical fluid flow regime, laminar boundary
layer forms on either side of the stagnation point. An adverse pressure gradient causes the
boundary layers to detach from the body forming shear layers that trail from the surface of the
3
cylinders. The shear layers are periodically shed from the upper and lower halves of the cylinder,
generating a regular vortex pattern of alternate shedding, called Karman vortex shedding. As this
shedding process is a result of the transformation of the flow from a steady to an oscillating
behavior, the flow may be understood as a Hopf bifurcation, whose length scales with the
cylinder diameter. In this regime, the cylinder wake becomes three-dimensional in nature
(Williamson, 1996; Wei and Smith, 2006) and involve interactions of the boundary layer,
separating free shear layer and the wake (Williamson, 1996).
At the sub-critical flow regime, the laminar boundary layers separate at about 80 degrees aft of
the nose of the cylinder. The free shear layer separates in laminar state but becomes highly
unstable and transitions eventually to turbulent state, giving rise to small scale vortices (referred
to as Helmholtz vortices). These small-scale vortices are developed by the action of a Kelvin-
Helmholtz mechanism which arises when there is a difference in velocity between two fluids.
The sizes of the vortices scale with the thickness of the separating shear layer, which is generally
a small fraction of the cylinder diameter. In order to be visible, small-scale vortices in the shear
layer need to develop and then undergo significant amplification. The small-scale vortices in the
shear layer influence the strength of the shear layers (the maximum magnitude of the vorticity
in the shear layer) and also affect the drag acting on the body. Bloor (1964) pioneered the work
on predicting the frequency of these small-scale shear-layer vortices as 𝑓𝑆𝐿
𝑓𝐾⁄ ≈ 𝑅𝑒𝐷
32⁄ , where
𝑓𝑆𝐿 shows the shear layer frequency and 𝑓𝐾 is the Karman frequency. However, it was not until
the work by Prasad and Williamson (1997) that a comprehensive and a clear understanding was
developed to predict the frequency of this instability with respect to the critical Reynolds
number. They derived the relationship between the shear layer frequency and Karman frequency
for Reynolds number up to 105
as the power law 𝑓𝑆𝐿
𝑓𝐾⁄ = A × (𝑅𝑒𝐷)P, where, A = 0.0235 and
P = 0.6742. In the sub-critical flow regime, as Reynolds number increases, the turbulent
transition point in the separating shear layers moves gradually upstream. This, in turn, affects
the shear layer interactions downstream of the cylinder, thus weakening the ability of the Karman
vortex to draw fluid into the formation region. Hence, the formation region is shrunk to balance
the entrained fluid and the vortices roll-up closer to the cylinder. The combined effect of the
reduction in strength of shear layer, which reduces the Strouhal number (St) value, and the
4
decrease in the vortex formation region, which favors an increase in St value, produces a
cancellation making the St almost constant (Anderson and Szewczyk, 1997). Also, in the sub-
critical flow regime, the pressure fluctuations around the cylinder vary considerably. The base
suction and Reynolds stresses increase, while the fluctuating lift reaches its maximum values
only in the upper subcritical range, where the formation of vortices takes place immediately
behind the cylinder.
1.3.2 Behavior of the flow past a rigid cylinder during VIVs
The vortex shedding process gives rise to an uneven pressure distribution between the upper and
lower surfaces of the cylinder, generating periodic, fluctuating lift and drag forces that are
exerted on the cylinder. The fluid flow and the structural vibrations are coupled through the force
exerted on the structure by the fluid. The structure exerts an equal and opposite force on the fluid.
The structure's force on the fluid can synchronize vortices in the wake and produce large
amplitude vibrations.
When a rigid cylinder is allowed to move, either forcibly or freely, the vortices are shed in
symmetric pairs and arrange in a staggered pattern some distance downstream of the cylinder
(Sarpkaya, 2004). This symmetric shedding is induced by the motion of the body, which
strengthens the vortices and gives rise to a force in phase with the body velocity. As the structure
displaces, its orientation to the flow changes and the fluid force may change, giving rise to many
modes of vortex shedding patterns, at a combination of different amplitudes of cylinder vibration
and reduced velocity (which is equal to the ratio of the free stream velocity to the product of the
frequency of the cylinder and the cylinder diameter) (Williamson and Govardhan, 2004, 2008).
When the frequency of the vortex shedding approaches one of the natural frequencies of the
cylinder, vibrations due to fluctuating lift forces may be enhanced in the transverse direction (the
Y-axis, direction perpendicular to both the flow direction and cylinder axis). Alternatively,
vibrations due to fluctuating drag forces occur in the streamwise direction (the X-axis, direction
along the flow direction and perpendicular to the cylinder axis) when one of the natural
frequencies is close to twice the shedding frequency. In either case, the phenomenon is termed
as lock-in or synchronization of vortex shedding. In the lock-in regime, the amplitude of the
cylinder vibrations reaches a critical threshold which, in turn, may affect the integrity of the
5
structure. The measurements of the fluctuating forces acting on the cylinder, the variation of the
response graphs in conjunction for different flow parameters, and the study of the cylinder
motion and its effect on the flow behavior have been an area of research for several years.
When a rigid cylinder is forced to vibrate perpendicular to the flow, the fluid dynamic forces exerted
on the body become magnified due to the oscillations, and through a non-linear interactive process,
the vibration of the body can be increased still further and can have large effect on the vortex
shedding. Williamson and Roshko (1988) conducted a flow visualization study over a wide range of
oscillation frequencies and amplitudes at various Reynolds number with the rigid cylinder motion
starting from rest. They observed various vortex-shedding patterns depending on the excitation
conditions and observed a shedding pattern with two vortex pairs per cycle apart from the normal
Karman vortices.
Khalak and Williamson (1996, 1997a, 1997b, 1999) considered a rigid cylinder with low mass-
damping parameter value, 𝑚∗𝜁, where 𝑚∗ = 𝑚𝑠𝑦𝑠
𝑚𝑑⁄ , 𝜁 =
𝑐𝑠𝑦𝑠
2√𝑘𝑚𝑠𝑦𝑠⁄ ( 𝑚𝑠𝑦𝑠 is the mass of
the system, 𝑚𝑑 is the mass of the displaced fluid, 𝑐𝑠𝑦𝑠 is the system damping, k is the spring stiffness)
that is allowed to vibrate freely in transverse direction. They noticed that there are two distinct
stable wake patterns which may form, depending on the amplitude and frequency of oscillation:
one with two single vortices shed per cycle, denoted as a `2S’ mode, and another with two pairs
of vortices per cycle, denoted as a `2P’ mode.
For an elastically mounted rigid cylinder, free to respond only in the streamwise direction, each
time a vortex shedding occurs, a weak fluctuating drag is developed at roughly half the flow
speed required for transverse vibration, resulting in a very low amplitude oscillation in
streamwise direction. Although the in-line amplitudes are typically only about a third of the
transverse amplitudes, they occur at double the frequency and so their contribution to restricting
fatigue life can be substantial (Williamson and Govardhan, 2004). In practical applications, the
cylinder is free to oscillate in both transverse and streamwise direction due to vortex shedding
occurring in all directions normal to the cylinder axis. Depending on the ratio of natural
frequencies, an elastically mounted rigid cylinder may also vibrate simultaneously in the in-line
and transverse directions. As the natural frequency ratio was increased, there were concurrent
changes in the amplitude profiles. The studies demonstrated a set of response branches, wherein,
6
for mass ratio values (m*) greater than or equal to 6, the vibrations in transverse direction
contributed to the change in flow behavior whereas the streamwise vibrations did not affect the
flow. For values of m* below 6, significant vibrations in streamwise direction resulted in a new
response branch, which yielded large amplitudes. Also, this response corresponded with a new
periodic vortex wake mode, “2T” mode, comprising a triplet of vortices being formed in each
half cycle (Jauvtis and Williamson, 2003, 2004; Williamson and Jauvtis, 2004).
1.3.3 Techniques used in the control of the flow past a cylinder
When VIV occurs, there is fluctuating pressure acting on the cylinder. As the cylinder vibrates
through a moving fluid, hydrodynamic forces act on it. Many measurements of various flow
characteristics and its effects on vortex shedding have revealed that the amplitude of the vortex
shedding and its corresponding drag will, in fact, affect the integrity of the cylinder
(Pantazopoulos, 1994; Branković and Bearman, 2006). Hence, it is very critical to control the
amplitude of resonant vortex-induced vibration, the associated magnified drag and the vortex
shedding frequency so that resonance can be delayed. There are two methods employed to
mitigate VIVs: (1) active methods and (2) passive methods. In active flow control methods, the
object and the instabilities are continuously monitored and the input is given to modify the flow.
Such methods involve a more dynamic means of altering the flow by means of feedback control
mechanisms in terms of power input to introduce external disturbances to the flow field. In
passive methods, the geometry of the cylinder is modified by appending geometric protuberances
such as shrouds, spars, fairings, helical stakes etc. to control the instability (Zdravkovich, 1981;
King and Weaver, 1982; Blevins, 1990; Choi, Jeon and Kim, 2008; Kumar, Sohn and Gowda,
2008). Zdravkovich (1981) further classified passive methods into three categories based on their
influence on the flow characteristics. Passive methods that affect the boundary layers and/or
separated shear layers (creating artificial turbulence in the flow layers) were grouped as surface
protrusions. Methods that affect the entrainment layers were classified as shrouds. The third type,
termed as near-wake stabilizer methods, affect the interaction between two separating shear
layers downstream of the cylinder. Choi, Jeon and Kim (2008) al so classified the control
methods into three types of feedback control mechanisms: (i) passive controls, which are
actuators without any power input; (ii) active open-loop controls, which are actuators with power
input but do not use sensors; and (iii) active closed-loop controls, which are actuators with power
7
input and also use sensors. These flow control methods do not completely annihilate vortex
shedding, but weaken and delay the process causing VIVs. The scope of this thesis is to study
the behavior of the flow past a rigid stationary cylinder fitted with a single helical surface wire.
1.3.4 Surface protrusions
As summarized by Zdravkovich (1981), a surface protrusion on a cylinder can influence the
shear layer separation characteristics, thus providing a passive hydrodynamic means for altering
vortex shedding. The geometry and the location of the surface protrusion can be selected to cause
artificial turbulence in the separated shear layer. Omnidirectional (3-D) surface protrusions (as
opposed to unidirectional protrusions) can disorganize the vortex coherence along the length of
the cylinder (i.e. the vortex tube), thereby reducing fluctuating lift forces. The simplest flow
geometry that can be employed to understand the effect of the protrusion on the boundary layers
is the flow past a single spanwise wire (trip wire) attached along the span of a circular cylinder.
This fundamental understanding of the flow past a two-dimensional structure can help in
elucidating the flow behavior of more complex three-dimensional structures, such as the flow
past a cylinder with a helical surface protrusion.
Figure 1.1 Variation of the prevailing Strouhal number (St) of the velocity fluctuations in the wake of the cylinder
as a function of the angular position () of the single spanwise wire for a wire diameter d= 0.0625D and Reynolds
number of 10,000. The fundamental wire locations 𝜃𝑡, 𝜃𝑐, 𝜃𝑚, 𝜃𝑟 and 𝜃𝑏 are plotted as per the findings of Nebres
and Batill (1993), while the critical angle locations of 𝜃𝑐1, and 𝜃𝑐2 are plotted as per Ekmekci and Rockwell (2010)
findings. Figure adapted from Joshi (2016).
8
Nebres and Batill (1993) performed an experimental study of the flow around a cylinder with a
single straight spanwise wire in a wind tunnel. When the cylinder was placed in a uniform cross
flow, the Strouhal number (St) was shown to be a function of the angular position, θ, of the
perturbation, the perturbation size, and the Reynolds number. Figure 1.1 plots the variation of
Strouhal number (St) with respect to angular position of the perturbation (). The fundamental
wire locations, 𝜃𝑡, 𝜃𝑐, 𝜃𝑚, 𝜃𝑟 and 𝜃𝑏, as identified by Nebres and Batill (1993), correspond to
the transition of the boundary layer and/or changes in its separation characteristics with respect
to the increasing wire angle, allowing classification of the flow behavior into distinct regimes,
which are presented in Table 1.1.
Regime Characteristics of the flow
I 0 t(1)
The flow separates at the wire and reattaches to the cylinder surface. A laminar
boundary layer is formed after the final separation point. St remains constant
and at its reference value.
II
t(1) c
(1)
The flow reattaches to the cylinder surface downstream of the flow separation
at the wire. A turbulent boundary layer with delayed final separation point is
formed. St gradually increases to reach its maximum value at c (Nebres and
Batill, 1993).
c1(2)
The flow oscillates between being attached to the cylinder surface (steady
attachment) and nonattachment (steady separation) to the cylinder surface after
being separated from the wire. Significant extension in the streamwise length
of the time-averaged near-wake structure and mitigation of the spectral
amplitude of the velocity fluctuations, associated with the Karman frequency,
occurs. St varies from being maximum to a value lower than the reference
value.
III c(1) r
(1) The flow is completely separated from the wire and does not reattach to the
cylinder downstream. The St dropped sharply to its minimum value.
c2(2)
Range of angles where, placing the wire amplifies the spectral amplitude of the
velocity fluctuations and also a significant contraction in the streamwise length
of the time-averaged near-wake structure occurs. St is lower than the reference
value.
c(1) m
(1) Spacing between the shear layers is increased. St number decreases to reach its
minimal value.
m(1) St reaches its minimum value.
m(1) b
(1) Spacing between the shear layers is decreased. St number gradually increases.
r (1) At this position, there is a secondary increase in St.
IV b(1) 180
The wire is in the base region of the cylinder and has no significant effect on
the flow.
Table 1.1 Classification of different flow regimes based on the flow characteristics and Strouhal number (St)
variation with respect to the angular position of the wire (), based on Figure 1.1 (taken from Joshi (2016)) . Each
fundamental angle (1) and (2) is referred according to the findings by Nebres and Batill (1993) and Ekmekci and
Rockwell (2010) respectively.
9
Ekmekci (2006) and Ekmekci and Rockwell (2010, 2011) greatly enhanced the understanding
of the effects of a single spanwise wire considered by Nebres and Batill (1993) by employing
the cinematic technique of PIV to determine the flow characteristics for different wire diameter
(d) to cylinder diameter (D) ratios = 0.029, 0.012 and 0.005 at a constant Reynolds number of
10,000. The surface wires considered included small-scale (d = 0.005D and 0.012D) and large-
scale (d = 0.029 D) wires, which was defined based on the measure of the d/D ratio relative to
the thickness of the unperturbed boundary layer forming between circumferential locations of 5º
to 75º from the forward stagnation point of the cylinder. For both, the large-scale and the small-
scale wires, two critical angular locations, θc1 and θc2 were identified. These critical angles are
indicated in Figure 1.1 along with the fundamental angles as defined by Nebres and Batill (1993).
When the wire was attached at those critical angles, either the most significant extension
(at θc1) or the most significant contraction (at θc2) occurred in the streamwise length of the
time-averaged near-wake structure with respect to the reference case. For a range of angles,
asymmetry in the near wake structure was observed, due to the early onset of the shear layer
instability in the wire-side shear layer as compared to a normal flow on the smooth side.
Furthermore, the autospectral density of the streamwise velocity component, Su, was examined
over a number of points in the near wake of the cylinder fitted with the wire at the two critical
angles, θc1 and θc2, and also at a reference angle, θ = 120° for both wire scales. In the case of
the large-scale wire, for the reference angle, a pronounced spectral peak at the characteristic
Karman frequency (𝑓𝐾) was observed at all points, and the influence of the wire was found to be
insignificant. Therefore, the reference case corresponded to a wire-uninfluenced scenario. At the
first critical angle θc1 , the wire attenuated the spectral amplitudes of velocity fluctuations at the
Karman frequency (𝑓𝐾) considerably relative to the reference case, while at the second critical
angle θc2, it significantly amplified the Karman instability. It was also noted that the small-scale
wires showed no significant change in the strength of the Karman instability at both the critical
wire locations θc1 and θc2.
An important observation made by Ekmekci (2006) and Ekmekci and Rockwell (2010, 2011)
was that, at the location of the first critical angle (θc1), for both the large-and small scale wire
types, the wire-side shear layer underwent bistable oscillations at irregular time intervals. This
resulted in two different modes, one that involved a reattachment of the separated shear layer to
10
the cylinder surface after separating from the wire, and another that did not exhibit reattachment
of the separated shear layer after flow separation at the wire. The switching between the two
stable modes near the separation region from the wire, resulted in a broad spectral peak with a
low central value, which was one order less than the Karman frequency. Thus, the first critical
wire location, θc1, acts as a transition angle between regimes II and III mentioned in Table 1.1.
1.3.5 Flow past helical surface protrusions
Among all the passive control methods that are based on the use of a surface protrusion
technique, helical surface protrusions have been adopted extensively in suppressing VIVs in
many practical applications. The flow behavior past the helical surface protrusions and hence,
their effectiveness in suppressing VIVs, depend mainly on the design parameters of the
protrusion, such as (a) the protrusion shape, which can, for example, be a strake (a thin sharp
edged rectangular plate) or a wire (a plate with rounded edges and near-circular cross-section),
and (b) the geometric properties of the protrusion (e.g. the height L, the thickness t or wire
diameter d, and the pitch P of the helix), relative to the diameter D of the bare cylinder.
1.3.5.1 Helical strakes
Studies conducted by Scruton and Walshe (1963), Ruscheweyh (1981), Allen, Henning and Lee
(2004), Bearman and Branković (2004); Branković and Bearman (2006), Constantinides and
Oakley (2006), Korkischko and Meneghini (2010, 2011), Zhou et al. (2011) and the review by
Zdravkovich (1981) suggest that three helical strakes with a pitch (P) in a range of 4D to 5D and
height (H) equal to 0.1D for experiments conducted in air and 0.2D for experiments conducted
in water (Korkischko and Meneghini, 2010, 2011) were most effective in suppressing VIVs. The
flow visualization experiment conducted by Zhou et al. (2011) showed the formation of small-
scale vortical structures in the wake of the cylinder, which do not roll-up or interact with each
other, thus mitigating regular vortex shedding. While visualization in the spanwise direction
showed that vortices are generated initially, they were broken down and dislocated quickly. At
the same time, the vortices also swirled as they evolved downstream. Zhou et al. (2011)
concluded that the occurrence of vortex dislocations was responsible for the variations of peak
frequency (Strouhal number) in the streamwise and spanwise direction. A numerical analysis
conducted by Constantinides and Oakley (2006) suggested that the strakes completely
11
suppressed VIVs over the lock-in range of a bare cylinder. They found that the flow usually
separates at the tip of the strake, and when tip of the strake is aligned with the flow, separation
is partially controlled by the cylinder surface. The separated flow induced a three-dimensional
flow behind the cylinder, breaking the vortex coherence along the span of the cylinder and the
vortices shed were disorganized. In an experimental study using stereoscopic PIV, Korkischko
and Meneghini (2010, 2011) found that the presence of a Kelvin-Helmholtz instability (small-
scale vortices) in the separating shear layers decreased the vortex formation length, and this
gradually decreased the St value as the base suction value increased. The three-dimensional flow
profile indicated that the positive shear layer induces negative flow and the negative shear layer
generated positive flow along the spanwise direction. Also, the strong vortical structures in the
streamwise direction combined with the periodic deflection of the spanwise vorticity disrupted
the correlated vortex shedding. For a cylinder allowed to vibrate freely, the efficiency of the
helical strakes depended strongly on the mass-damping parameter, and below a certain value of
this parameter, the amplitudes of the oscillations increased to magnitudes comparable to those
of a plain cylinder (Ruscheweyh, 1981). When the reduced velocity became greater than 5, the
cylinder experienced the lock-in behavior, and 2S (2 single vortices) and 2P (2 pairs of vortices)
shedding modes were visible albeit with small amplitude values (Bearman and Branković, 2004;
Branković and Bearman, 2006).
1.3.5.2 Helical wires
The flow behavior for a cylinder fitted with helical wires is similar to that of cylinders fitted with
helical strakes; however, the location of flow separation region and interaction of separated shear
layers with the flow are noticeably different. In the case of cylinders with helical wire
protrusions, studies concentrated on understanding the effect of the protrusions on the flow
structure in addition to their impact on VIVs. Price (1956), Nakagawa., Fujino. and Arita. (1959),
Weaver (1959, 1964), Nakagawa (1965), Lubbad et al. (2007) and Lubbad, Lo̸set and Moe
(2011) performed measurements on freely vibrating cylinders and suggested the optimal
parameters that help mitigate VIVs. The geometry and flow configurations along with the results
from these various studies are summarized in Table 1.2.
12
Nakagawa.
,Fujino.
and Arita.,
1959;
Nakagawa,
1965
Geometry: Rigid cylinders were allowed to
vibrate freely using a cantilever arrangement.
ReD: 1.5 × 105 to 1.5 × 106 and d = 0.004 D
Cylinder # of
Wire
Angle the
wires are
tuned (from
end to end)
Pitch
angle/
Pitch
A 8 180° π2⁄
B 4 90° π8⁄
C 4 45° π16⁄
D 1 - 250 mm
The value of the maximum amplitude of
vibrations doubled when Cylinder A was used,
magnitude was similar when Cylinder D was
employed and completely suppressed when
Cylinder B and Cylinder C where used when
compared to the plain cylinder case.
During the study of wake fluctuations, assessed
using the power spectrum of lift force, Cylinder D
had no effect, Cylinder A enhanced the spectrum
with a high peak detected at the value were
Karman shedding is observed, Cylinder B and
Cylinder C were effective in reducing the power
spectrum even though oscillatory behavior from
wake fluctuations were noticed.
The wires induced turbulence and further
disrupted the regularity of the phase of the
periodic vortex shedding along the span.
Price, 1956
Geometry: Freely vibrating rigid cylinders with
different surface protrusions.
ReD = 4340 and d = 0. 023D
Cylinder A: Cylinder with 3 tripping wires
placed parallel to the cylinder axis at 0°, −60°
and 60°.
Cylinder B: Cylinder helically wound with 3
wires with Pitch (P)=20D.
The amplitude of Cylinder A was as that of a plain
cylinder while the maximum amplitude of
Cylinder B was reduced to 1.5D from 2.5D.
Concluded that neither of these two
configurations was effective in curbing the
amplitudes and that shrouds were better in
mitigating VIVs than helical surface protrusions.
Weaver
(1959,
1964),
Geometry: Stationary rigid cylinders, rigid and
freely vibrating cylinders and flexural
cylinders.
ReD = 1.0 ×104 to 1.0 × 106 and d = 0. 023D
The cylinder and wire diameters ranged from
38.1 mm to 254 mm. For every cylinder, a
combination of various wire windings, diameter
and pitch was employed for both stationary and
freely vibrating cylinder case.
Number of starts: 1, 2, 4, 8 and 16.
Pitch range: 6D- 20D.
The maximum reduction of the fluctuating lift
force occurred for 4 wire case for a wire diameter
range d = D 16⁄ - D 8⁄ and effective pitch range 8D
– 16D; minimum at d = 3 32⁄ D with an optimum
pitch (P) = 12D.
The fluctuating lift force was not sensitive to pitch.
Lubbad et
al., 2007;
Lubbad,
Lo̸set and
Moe, 2011
Geometry: Rigid cylinder, freely vibrating in
transverse and streamwise directions.
ReD = 2400 to 24000 and d = 0.06D – 0.2D
Number of starts: 1, 2 and 3.
Pitch range: 2.5D to 10D.
The surface roughness of the wire may moderately
affect the efficiency of VIV mitigation while
variation in pitch values did not show any effect.
The frequency ratio (ratio between the natural
frequency in transverse and streamwise direction)
affects the cylinder response considerably.
Higher amplitude of vibrations was obtained for
low frequency ratio and the lock-in range became
wider for high frequency ratio.
The optimum configuration where, the amplitude
was effectively reduced by 96% in transverse
direction and 97% in the streamwise relative to a
plain cylinder, was a cylinder wound with 3 wires
of d= 0.15D with an optimum pitch (P) = 5D. Table 1.2 Review of the literature on the studies conducted on helical -wire type surface perturbations in order to
find the optimum configurations which will help curb VIVs.
13
Majority of the studies listed in Table 1.2 were characterization studies to determine the
conditions under which VIVs would be suppressed. Recently, more detailed experiments have
been conducted by Nebres and Batill (1992), Nebres, Nigim and Batill (1992), Lee and Kim
(1997), Chyu and Rockwell (2002), Saelim (2003) and Ekmekci (2014) for fixed cylinders fitted
with helical wire protrusions, but again, only a few of these studies attempted to unearth a
mechanistic understanding of the flow modifications that lead to this suppression.
Nebres and Batill (1992) and Nebres, Nigim and Batill (1992) initially conducted experiments
on a stationary cylinder embedded with the optimum configuration (as recommended by Weaver
(1959, 1964)) of pitch P = 12D, number of starts = 4, and wire diameter d = 0.09D at Reynolds
number, ReD = 10,000 to understand the characteristics of the wake region. Later, this study was
expanded to include the effect of pitch on the wake region at the same Reynolds number. In the
second study, they used the same cylinder-wire configuration but employed three different pitch
values, which were P = 8D, 12D and 16D. They found that the vortex formation length, defined
as the point from the cylinder surface where the RMS value of the hot-wire signal became
maximum, was 2.5 times longer than the formation length of a plain cylinder. This increase in
vortex formation length was associated with the periodic variation in boundary layer separation
along the span of the cylinder, as well as to the near-wake properties such as shear layer
transition, entrainment, diffusion and thickness of the helical wire. The extension of vortex
formation region may influence the unsteady surface pressures and further, influence VIVs.
Finally, they suggested that the periodically varying orientation of the perturbations had a very
significant effect on the separation points and the overall flow field.
Lee and Kim (1997) studied the flow characteristics of a controlled wake of a stationary cylinder
with a 3-start helical wire for two different pitch values. The wire diameter was d = 0.075D. The
experiments were conducted for a range of Reynolds number ranging from 5,000 to 50,000. The
first cylinder, Cylinder A, had a pitch P = 5D, and the second cylinder, Cylinder B, had a pitch
= 10D. For Cylinder A, at Reynolds number of 10,000, the wake structures were similar to that
of a plain cylinder but with a slightly elongated vortex formation region. At Reynolds number
of 25,000, the wake structures were difficult to observe. For Reynolds number greater than or
equal to 25,000, the wake shrinks abruptly and vortices are suppressed. For Cylinder B, the wake
remained suppressed for the entire Reynolds number range investigated, the width of wake was
14
narrow and the vortex formation region was barely discernible. From the flow visualization
experiments, it was shown that the surface protrusions made the near wake to have periodic
spanwise variation relative to the geometry of the surface protrusions, which was associated with
the lateral surface flow motion along the cylinder’s surface. The iso-pressure contours were
found to be varying along the span which resulted in the spanwise flow along the model surface.
With an increase in Reynolds number, the spanwise pressure gradient on the model surface was
observed to change the surface flow towards the spanwise direction, eventually suppressing large
vortex formation. They concluded that the surface protrusions elongate the vortex formation
region and decrease the dominant vortex shedding frequency, but shrink the wake width which
increased the velocity deficit in the wake.
Chyu and Rockwell (2002) performed PIV in three orthogonal planes, and highlighted the
instantaneous vorticity and velocity patterns obtained under optimal configurations (P = 4.5D, d
= 0.1D at Reynolds number, ReD = 10,000) on a cylinder with a three-start helical wire type
surface protrusion. In their experiments, X-axis was the axis along the flow direction, Z-axis was
along the span of the cylinder and the Y-axis was the axis perpendicular to both the flow direction
and the span of the cylinder. The presence of a dual-vorticity layer on one side (two adjacent
layers of like vorticity) and the formation of small-scale concentrations of shear layer vortices
were highlighted in the X-Y plane. The wake pattern in the Y-Z plane at a distance of 2D away
from the cylinder revealed counter-rotating pairs of small-scale streamwise vorticity (𝜔𝑥)
concentrations at each crest of the helical perturbations. Along the span of the cylinder, in the Z-
X plane, the instantaneous velocity and transverse vorticity data showed that the helical
perturbation produced a spatially periodic pattern of wake-like flows at the crest of the helical
protrusion. In each wake-like region, patterns of nearly zero, or even negative flow, were
generated. The patterns of velocity and vorticity of a typical wake-like region showed widely
separated layers of opposite sense, which were bound by a low velocity region and contained
small-scale concentrations of vorticity. In these respects, a given wake-like region resembled the
very near-wake from a two-dimensional bluff body. Hence, they concluded that the existence of
the wake-like regions along the span of the cylinder and the generation of the counter-rotating
streamwise vorticity modified the near-wake structure, thus presumably precluding the
formation of Karman vortices (rollup of small-scale shear layer vortices into large-scale clusters)
15
in the near-wake region.
Saelim (2003) extended the investigations of Chyu and Rockwell (2002) to a lower ReD value of
160 and characterized the instantaneous and averaged flow patterns in three orthogonal planes
in the near-wake using PIV. Each cylinder was helically wound with three wires each with a
diameter d = 0.0625D, and the localized pitch P* [Pitch (P) / Number of wires] for both cases
was 4D. At Reynolds numbers of 10,000, the vortex formation length (the distance from the
center of the cylinder to the point of intersection of the two separated shear layers, downstream
of the flow) and the width of the wake (W) (the distance between the two shear layers at the
midpoint of the vortex formation distance) is much greater than the plain cylinder case due to
the superposition of asymmetrical contributions from the upper and lower regions of the wake.
At low Reynolds numbers, three-dimensional structure of the near-wake undergoes a well-
defined transformation with increasing distance from the base. At high Reynolds numbers, the
three-dimensional structure patterns are less deterministic but show a spanwise spatial
periodicity.
Ekmekci (2014) recently conducted a comparative study of the flow behavior between a circular
cylinder fitted with a single, straight, spanwise wire, and a circular cylinder fitted with three
wires wound helically around its surface. The wire diameter, in both cases, was a small-scale
wire (d = 0.012D), whose length scale was much smaller than the boundary layer thickness. For
the analysis, while the cylinder fitted with a spanwise wire was placed such that the wire was at
60º with respect to the forward stagnation point (which was the location of the critical wire angle
(θc1) for a small-scale wire with d = 0.012D), the three-start helical wires were made to pass at
+60º, -60º and 180º at the cross-section of PIV visualization (the two helical wires symmetrically
passed the critical angle location). For both cylinder-wire configurations, it was found that a
bistable phenomenon was observed at the critical wire angle location (θc1) and that both
configurations had an insignificant effect on the strength of the Karman instability. For a
cylinder-spanwise wire combination, large amount of near-wake distortion is observed on the
wire side, due to a relatively early onset of shear layer instability, caused due to the perturbation
of the shear layer by the wire, relative to the shear layer on the smooth side. However, for a
cylinder-helical wire combination, the near-wake structure was perfectly symmetric due to the
onset of transition on both shear layers in that plane. The time-averaged characteristics show
16
consistent trends for the cylinder-spanwise wire and the cylinder-helical wire configurations in
the plane where the wire(s) is (are) at the critical angle. For both cases, the near-wake bubble is
extended in the streamwise direction by nearly an identical amount, and both configurations
show reduction in the peak magnitudes of Reynolds stress and RMS velocity fluctuations.
1.4 Objective
Though the literature on helical configuration is vast and growing, the issue of why certain
helical configurations attenuate oscillations, while others turn out to be detrimental, has remained
largely unresolved. A detailed study of the flow past a fixed cylinder fitted with a single-start
helical wire for a fixed wire to cylinder diameter ratio and pitch can lead to the elucidation of
the physics of flow control through helical devices. This thesis examines, using PIV analysis and
hydrogen bubble-aided flow visualization (HBFV), the fundamental case of flow past a cylinder
with a single-start helical surface wire (see Figure 2.1 and section 2.2 for details). The diameter
and localized pitch of the cylinder match the optimum configuration suggested in the studies of
Chyu and Rockwell (2002) and Saelim (2003) for the subcritical Reynolds number of 10,000.
The study aims to understand the flow properties in all the three planes of visualization: X-Y, Y-
Z and X-Z, where X-axis is along the flow direction, Z-axis is along the span of the cylinder and
the Y-axis is the axis perpendicular to both the flow direction and the span of the cylinder. The
PIV experiments were conducted in X-Y and X-Z planes, while the HBFV experiments were
conducted in X-Z and Y-Z planes. The flow profiles deduced in the Y-Z and Z-X planes will
help detect the behavior of the flow along the span of the cylinder. In the X-Y plane, various
wake properties are analyzed. Finally, an attempt will be made to correlate the flow behavior at
various planes to understand the complete flow topology for the single helical wire configuration
in question.
1.5 The layout of the thesis
In Chapter 2, an overview of the experimental set-up, and the quantitative and qualitative
measurement techniques employed (consisting of PIV and hydrogen bubble flow visualization)
are explained. The findings from both measurement techniques and the summary of major
conclusions are discussed in Chapter 3. Finally, Chapter 4 presents the recommendations for
future work. Also presented is a brief overview of the designs that can be used to mount the
17
cylinder to make it either a freely vibrating rigid cylinder or a cylinder forced to vibrate under
prescribed amplitudes and frequencies. These designs can guide future experiments in the group.
18
2 Experimental Methodology
This chapter explains the experimental methods and techniques used to analyze the flow inside
the water channel. A brief overview of the flow facility, design of the model, its set-up in the
water channel, and the experimental set-up in different planes are discussed. For the study of the
flow over the helical-wire-wound cylinder, two different sets of experimental techniques were
employed. First, the flow was qualitatively visualized using the hydrogen bubble visualization
technique, and then, Particle Image Velocimetry was used to analyze the quantitative flow
properties. The principle of each technique and its operation in the present study has also been
elucidated in this chapter. The chapter concludes with a brief description of the flow properties
that are used in the present study.
2.1 Flow facility
All experiments were conducted in a re-circulating water channel at the Experimental Fluid
Dynamics Laboratory located at the University of Toronto Institute for Aerospace Studies. The
tunnel, designed by Engineering Laboratory Design Inc., has a capacity of approximately 2820
Gallons (10,675 L) of water. The water channel can be used in either a free-surface test section
mode (test section without top covers) or in a fully-covered tunnel mode (test section with top
covers). All the experiments were conducted at flow Reynolds number equal to 10,000. To avoid
fluctuations in the value of the Reynolds number, due to temperature change, the water
temperature was frequently measured over the course of the experiment and the free-stream
velocity was adjusted accordingly. The flow turbulence intensity, which is characterized by hot
film anemometry, was found to be less than 0.5% for the free-surface test section mode and less
than 0.4% for the fully-covered tunnel mode (Aydin, 2013).
A single stage, axial flow, 3 blade propeller pump with discharge elbow is used to generate the
flow. A transistor inverter type variable speed motor control regulates the RPM of the pump.
The input frequency for the motor is varied, according to the necessary flow speed, within a
range of 0-60 Hz. A remote control station, located adjacent to the test section regulates the
motor RPM, measured as channel frequency, which in turn regulates the flow velocity at the test
section. The input channel frequency (𝑓𝑐ℎ𝑎𝑛𝑛𝑒𝑙) is related to the free-stream velocity (U∞)
19
through equation 2.1 (for free-surface test section mode) or through equation 2.2 (for fully-
covered tunnel mode), which are established from a linear curve-fit for the channel:
U∞ = 1.892 + 13.076 ∗ 𝑓channel ( 2.1)
U∞ = 6.200 + 12.538 ∗ 𝑓𝑐ℎ𝑎𝑛𝑛𝑒𝑙 ( 2.2)
Free
stream
velocity
(U∞)
(m/s)
Camera
Lens
(mm)
Field of
visualization
(in terms of D)
Laser pulse
separation
time (∆T)
(μs)
Magnification
factor (MF)
(pixel/mm)
Vector
Resolution
(∆x, ∆y)
(mm, mm)
Z-X Plane
Y = 0.75D 0.176 50 4.88 D × 3.63 D 2500 6.46 (2.48, 2.48)
X-Y Plane
Shear Layer 0.182 105 1.75 D × 1.31D 2000 17.97 (0.89, 0.89)
Near Wake 0.179 50 2.97 D × 2.21 D 2000 10.61 (1.51, 1.51)
Table 2.1 Values of the free-stream velocities, the resolution of the camera lens used, the field of view of the plane,
the pulse separation time, the magnification factor of the PIV image, and the resolution of the data for different
experiments are tabulated.
Table 2.1 lists the values of all free-stream velocities that were measured for different
experimental planes. In the present work X axis shows the streamwise direction, Y shows the
cross-flow direction and Z shows the spanwise direction. It must be noted here that the
differences in free-stream velocities, despite having a constant Reynolds number of ReD =
10,000, for different planes is due to the temperature variations in the tunnel, as each set of
experiments were performed on different days. The flow is initially distributed to the inlet
plenum by a perforated cylinder. It then passes through a settling chamber that has a flow
conditioning unit composed of one polycarbonate plastic honeycomb section and three stainless
steel screens, and finally through a 6:1 contraction section before entering the test section. The
test section sidewalls and the floor are fabricated using clear acrylic material (to allow optical
access to the flow). The test section is structurally supported by five frames made from fabricated
structural steel. The test section is 60.96 cm wide, 76.20 cm high and 5.0 m long. The flow
leaving the test section then enters the return plenum where a stainless steel turning vane system
divides and directs the flow, through pipes, to the filter system. The filter system includes a 0.5
HP circulating pump, a stainless steel filter housing and replaceable activated carbon particle
20
filter cartridges, which help in removing contaminants from the water. The water, thus filtered,
is recirculated back to the inlet plenum. A horizontal traverse system is attached to the base of
the water channel which runs parallel to the test section. This traverse allows mounting of the
camera or laser equipment under the test section.
2.2 Model configuration
The circular cylinder (shown in Figure 2.1) used in this study was made of a hollow anodized
aluminum rod of diameter (D) = 50.8 mm and length (L) =533 mm. The aspect ratio of this
cylinder L/D =10.49 is larger than the minimum value classified by Norberg (1994) in order to
avoid flow instabilities. An extruded anodized aluminum rod of diameter (d) = 3.125 mm was
bent in a helical pattern with a pitch of P = 152.4 mm (3D), and welded to the surface of the
main cylinder. The ratio of the wire diameter (d) to the cylinder diameter (D) is d = 0.0625D,
which, from boundary layer theory, is larger than the unperturbed boundary layer thickness (𝛿)
of a circular cylinder at the Reynolds number of ReD = 10,000, and therefore, can be classified
as a large scale wire (Aydin, 2013).
Figure 2.1 Experimental model: A circular cylinder fitted with a single helical wire type surface protrusion. The
cylinder’s diameter is (D)= 50.8 mm and length is (L)= 533 mm, diameter of the surface wire is (d) = 3.125 mm,
and the pitch of the helix is (P) = 152.4 mm.
P
Holder
D
Wire
Cylinder Model
L U
∞
21
The cylinder configuration was similar to that of Saelim (2003) cylinder model, except for the
number of wires employed. Also, the wire diameter employed in this study was greater than that
used in experiments conducted by Ekmekci (2014). To avoid reflections from the metal cylinder
and wire while illuminating the flow field, a coat of black, acrylic paint was uniformly applied
to the entire cylinder model. A holder made of a hollow anodized aluminum rod was used to
connect the cylinder to the rotational mount.
2.3 The set-up of the experimental model
In all the experiments, the model was placed at the center of the width of the channel and was
always anchored rigidly in a vertical direction, relative to the flow.
Figure 2.2 (a) The cylinder – endplate configuration, and (b) the rotary mount and the uni-directional traverse
system.
The cylinder supports were secured onto a rotary mount (as shown in Figure 2.2 (b)), which in
turn was supported on a unidirectional traverse system that was placed atop the water channel
and spanned the width of the channel. The rotary mount was used to rotate the cylinder along its
longitudinal axis to obtain data at different wire angular positions relative to the flow direction
while keeping the plane of visualization fixed. The cylinder was confined in between two
rectangular end plates (as shown in Figure 2.2 (a)) to reduce the three-dimensional effects caused
due to the wall and to facilitate quasi-two-dimensional flow past the model. In a prior
Top End
Plate
Bottom
End Plate
Cylinder
Model
(a)
Rotary
Mount Uni-directional
Traverse system
Cylinder
Holder
(b)
22
investigation conducted by Khoury (2012), different types of end-plate designs were tested to
study the spanwise flow behavior in the cylinder wake using quantitative flow measurement
techniques. This study recommended an optimum end configuration for cylinders. This
configuration involved two endplates with a sharp leading edge, one at the bottom and the other
at the top end of the cylinder. In the present study, this configuration was followed along with
the suggested endplate dimensions by Khoury (2012). Each end-plate was 7.5D in length, 12D
in width and 12 mm in thickness, was made from acrylic and beveled at the leading edge with
an angle of 23.6°. These end- plates spanned the entire width of the channel. The bottom end-
plate was supported by 90-mm-thick stainless steel bars, while the top end-plate was fastened to
the top-cover. Also, as suggested by Khoury (2012), the distance between the cylinder axis and
the leading edge of the endplates was 3D. For this configuration, the blockage ratio based on the
cylinder diameter was 8.3%.
2.4 Coordinate system and the fields of view
A right-handed Cartesian coordinate system was used to represent the flow characteristics. The
free-stream flow direction is along the X-axis. The Z-axis is along the longitudinal axis of the
cylinder, and the Y-axis represents the direction that is perpendicular to both the flow direction
and the longitudinal cylinder axis. Figure 2.3 depicts the three different planes of view that was
used to analyze the flow, namely, the X-Y plane (Figure 2.3 (a), the Y-Z plane (Figure 2.3 (b))
and the Z-X plane (Figure 2.3 (c)) In the X-Y plane figure (Figure 2.3 (a)), the top right corner
shows the sectional cuts of the cylinder at that particular planar location. In this thesis, the free
stream velocity is designated as 𝐔∞ and the components of the velocity in X, Y and Z direction
will be represented as 𝒖𝒙, 𝒖𝒚 and 𝒖𝒛 respectively. The vorticity components normal to the Y-Z,
Z-X and X-Y planes are represented as 𝝎𝒙, 𝝎𝒚 and 𝝎𝒛, respectively.
23
Figure 2.3 The coordinate system that was used to characterize the flow. Fields of visualization are also highlighted
in the sketches.
2.5 Experimental set-up for different fields of view
The flow over a helical cylinder is three dimensional in nature. In order to visualize and analyze
the flow characteristics efficiently, the flow needs to be analyzed in three different planes of
view. In this thesis, the PIV technique was employed to study the flow behavior in the X-Y and
Z-X planes, while the hydrogen bubble flow visualization (HBFV) technique was used to
examine the flow in the Z-X and Y-Z planes. Both the hydrogen bubble flow visualization and
PIV techniques require a light source to illuminate the field of interest and a camera for recording
the flow. The location of the light source and camera remain the same for both of these
24
techniques in a given plane of study. The hydrogen bubble visualization technique used in this
study employs an array of LED lights for illumination and a video camera to record the flow
field. The PIV, on the other hand, employs Nd: YAG laser as the light source, and a CCD camera
to record the flow field images.
Figure 2.4 PIV Experimental set-ups in X-Y plane is shown. the camera is placed underneath the water channel,
the light source is placed on the side of the water channel and the plane of illumination is parallel to the base of the
water channel. The top right part of the image is the sectional view of the X-Y plane.
As seen in Figure 2.4, the X-Y plane was studied at the mid-section of the cylinder, i.e., at a
distance of 𝐿 2⁄ from the bottom end of the cylinder. For the analysis of this plane, only the PIV
technique was used. This plane provided information on the vortex-shedding characteristics for
various wire angles θ (achieved by rotating the cylinder around its longitudinal axis to desired
locations using a motorized rotary system). The wire angle is defined as the angle the wire makes
with respect to the most forward point of the circular cylinder. Two fields of view were analyzed
in the X-Y plane: the shear-layer view and the near-wake view (see top right inset in Figure 2.4).
In the shear layer view, the flow behavior closer to the cylinder surface, i.e., the area closer to
the separated shear layers on the wire side of the cylinder, was studied. The near-wake view
25
allowed analysis of the interaction of the separated shear layer emanating from either side of the
cylinder, and in turn, helped in understanding the flow behavior downstream of the cylinder.
Experiments for the shear-layer view were conducted for a range of angles, from θ = 0° to θ =
180°. For the near-wake view case, the range of angles varied from θ = 0° to θ = 360°. Table 2.1
provides information about the camera lenses used to capture the shear-layer and near-wake
views in this plane. The light source (laser) for this set of experiments was placed on one side of
the water channel with the help of a traverse system and arranged such that the light entered from
the side wall (along the Y-axis direction) and illuminated the midsection of the cylinder. The
recording camera (CCD camera) was placed underneath the water channel, and the height and
camera settings were adjusted to give the best possible image and video of the plane of
illumination.
Figure 2.5 Hydrogen bubble flow visualization experimental set-ups for Y-Z plane is shown. Here, the camera is
placed on the side of the water tunnel facing the mirror, the light source is placed beneath the water channel and
the plane of illumination is parallel to the span of the cylinder and is formed behind it.
26
Figure 2.5 shows the hydrogen bubble flow visualization set-up used in the Y-Z plane. This plane
provides an understanding of the cross-stream structures and the behavior of the flow
downstream of the cylinder. Experimentally, as there was no optical access to visualize this
plane, a mirror was placed far-downstream from the cylinder and was used to assess the flow
patterns closer to the cylinder. As mentioned above, only hydrogen bubble visualization was
conducted in this plane. The visualization was conducted for a range of downstream planar
locations, along the flow direction (X-axis), measuring from X = 0.56D to X = 3D, where X =
0D is the cylinder center as seen from Y-Z plane. The light source (LED light) was placed
underneath the water channel, and was adjusted for different downstream positions. The camera
(video camera) was placed on the side of the water channel, facing the mirror, and was adjusted
to image the flow reflected from the mirror. Here, the light source illuminated the region behind
the cylinder and was parallel to its span (along Z-axis).
Figure 2.6 For the Z-X plane, (a) PIV experimental set-up and (b) hydrogen bubble experimental (HBFV) set-up is
shown. In this plane, for both type of experimental set-ups, the camera (CCD for PIV, video camera for HBFV)
faces the cylinder, the light source (laser for PIV and LED lights for HBFV) is placed below the water channel and
the plane of illumination is parallel to the span of the cylinder and on one side of the cylinder.
27
Understanding the formation of the vortex tube and the generation of the cross-stream structures
was the primary aim while studying the flow in the Z-X plane. Figure 2.6 (a) depicts the
experimental set-up used in the Z-X plane for the PIV experiment and Figure 2.6 (b) depicts the
experimental set-up used in same plane for the hydrogen bubble visualization experiment. Both
PIV and hydrogen bubble experiments were conducted at a distance of Y = 0.75D (where Y-axis
is in the cross-stream direction and Y = 0D is the cylinder center in Z-X plane). Table 2.1
describes the camera lens used during the PIV experiment and the corresponding size of the field
of view that was generated at the Z-X plane. The light source (laser for PIV and LED light for
HBFV) for this set of experiments was placed beneath the water channel. The camera (CCD for
PIV and video camera for HBFV) was fixed on the side of the water channel facing the span of
the cylinder.
2.6 Experimental techniques
The hydrogen bubble aided flow visualization (HBFV) technique, which is a qualitative study,
and the Particle Image Velocimetry (PIV), which is a quantitative measurement technique for 2-
D velocity fields, were employed in this work. These different techniques allowed us to
understand the flow behavior comprehensively, as each of them identified different flow features
and complemented each other. All the PIV experiments were conducted in the fully covered
tunnel mode. For HBFV, a single top cover of the channel, far-upstream of the cylinder, was
removed to place the equipment necessary to generate the hydrogen bubbles.
2.6.1 Hydrogen bubble aided flow visualization (HBFV)
Water is a transparent medium and its motion remains invisible to the human eye during direct
observations. However, by using flow visualization techniques, the motion of fluids can be
recognized. One of the techniques of flow visualization is hydrogen bubble technique, where
hydrogen bubbles are introduced into the flow. Many studies have been conducted to optimize
the experimental parameters required to effectively conduct the flow visualization experiment.
A detailed explanation of the working principle of this method may be found in Aydin (2013)
and Joshi (2016), and, only the configuration used for the present study is mentioned here.
28
2.6.1.1 Operation
For all flow visualization experiments, a 300-mm length and 5-micron diameter stainless steel
wire was attached to copper prongs, which acted as an anode. A thin copper rod acts as an
cathode. The copper prongs were placed upstream of the cylinder and were designed such that
its presence did not influence the flow. The anode was placed significantly downstream of the
cylinder and close to the cylinder wall, thus leaving the downstream flow characteristics
unperturbed, and also minimizing wall boundary effects. The copper prongs were attached to a
traverse system that could translate the prongs along the Y axis To visualize the flow in Y-Z and
Z-X planes, the stainless-steel wire that was attached to the copper prongs was arranged to be
parallel to the Z-axis (see Figure 2.5 and Figure 2.6 (b)). A set of seven LED flash lights were
electrically powered by 5.8 V to supply illumination. A constant voltage of 85 V was maintained
using a voltmeter to produce a thick sheet of hydrogen bubbles inside the water channel. A Canon
Vixia HF R30 video camera with 30 frames per second acquisition rate and a shutter speed of
1/30 second was used to capture the flow behavior.
2.6.2 Particle Image Velocimetry (PIV)
Particle Image Velocimetry (PIV) is a non-intrusive flow velocity measurement technique
(Raffel et al., 2007). Details of this quantitative flow visualization technique are as follows:
2.6.2.1 The principle
The PIV technique records the local fluid velocity, in terms of position and time, of small tracer
particles introduced into the flow.
2.6.2.2 Operation
There are various steps involved while performing a PIV experiment. Each experiment involves
the use of following procedures in order to obtain the velocity data.
1. Data Acquisition
2. Image processing
2.6.2.3 Data acquisition
For each of the experimental planes mentioned earlier, the lights and camera were set-up
according to the procedure mentioned in section 2.5. Nearly neutrally buoyant hollow glass
29
spheres of diameter 10 μm and specific density of 1.08 were added to the flow in sufficient
concentrations to act as tracer particles. The particles trace the motion of the fluid and act as
transmitters of information in the form of scattered light. Each experimental plane within the
flow was illuminated by means of a Nd:Yag laser which had a wavelength of 532 nm and a
maximum energy output of 200 mJ/pulse. The laser system fired at 14.5Hz rate, which
corresponds to the maximum operating frequency of the laser. The thickness of the laser sheet
was kept at approximately 1mm. For improved velocity vector output, a spherical lens with
1000-mm diameter focal length and a cylindrical lens with a 50-mm diameter focal length were
used. The cylindrical lens was used to spread the beam in only one direction, thereby generating
a laser sheet from the laser beam while the spherical lens was used to project the laser sheet to
the desired thickness. For optimum displacement value, it is important to accurately choose the
pulse separation value (Δ𝑇) for the laser. The values of Δ𝑇 that were used in the experiments,
fields of view obtained from the camera settings, and the values of the magnification factor and
vector resolution can be found in Table 2.1 for the X-Y and Z-X experimental planes.
The light scattered by the tracer particles were recorded via a high-quality lens on two separate
frames (two consecutive single-exposure images) using a Powerview 2 MP CCD camera
manufactured by TSI Inc. resulting in an effective pixel size of 1,600 pixels X 1,200 pixels and
a vector field grid size of 99 vectors x 73 vectors. A model 610035 synchronizer, manufactured
by TSI Inc., was used to synchronize the timing between the laser pulses and the camera shutter
open time through a PC desktop computer at an acquisition rate of 14.5 Hz. After development,
the photo-graphical PIV recording is digitized by means of a scanner, the output of the camera
is transferred to the memory of a computer directly by means of a frame grabber. A TSI 4G
Insight® software was used to control the data acquisition settings.
2.6.2.4 Image processing
Image analysis is performed on the raw PIV images so that important information embedded in
these images can be extracted and analyzed using image-processing methods. In PIV
experiments, image analysis procedure involves the evaluation of raw PIV images and
enhancement of data.
30
For evaluation of the raw PIV images, each image was divided into small subareas called
interrogation areas. The correlation function is an algorithm that sums the particle image matches
at all pixel displacement peaks caused by the contribution of many pairs. The Hart Correlation
technique was used to obtain the local displacement vectors of the tracer particles between frame
A and frame B. Starting from a large interrogation area, the local correlation value is iteratively
obtained through successive approximations of local displacements using increasingly smaller
regions of interrogation. This correlation technique was used to improve processing speed and
accuracy, and eliminate any spurious vectors. A Gaussian peak fit function, which locates the
peak with sub-pixel accuracy, was used to detect the peak in the cross-correlation map for
obtaining the displacement vector. A recursive Nyquist grid algorithm is used to reduce the
number of spurious vectors as well as to increase the final resolution of the vector field. In this
algorithm, the image is first examined for an interrogation size of 64 pixels x 64 pixels. Each
interrogated area is then divided into four smaller areas of size 32 pixels x 32 pixels where the
cross-correlation technique is again performed using the initial velocity data obtained from the
larger interrogated area. The process of interrogation is repeated for all interrogation areas of the
PIV recordings with the interrogation window overlap ratio of 50%. The evaluation of raw PIV
images was processed in the Insight 4G ® software built by TSI Inc.
2.6.2.5 Data processing
2.6.2.5.1 Vector validation test
The second part of image analysis involves the enhancement of the evaluated PIV images.
During cross-correlation procedure lost pairs due to in-plane and out-of-plane motion, or low
seeding density caused low correlation signal strength lead to spurious vectors. Spurious vectors
happen when the highest correlation peak is due to random pairing of particle images producing
the highest correlation peak. These vectors have extremely large values with respect to its nearby
vectors and need to be removed. A PIV vector validation software, CLEANVEC®, was used to
remove the spurious velocity vectors from the evaluated PIV images. The software applied two
tests on each velocity vector within the image. (i)Vector Global Validation test: This is a filter
that detects vectors outside a user-specified range for velocity components, and this velocity
range is applied to the whole velocity field. (ii) Vector Local Validation test: This is a filter that
uses the vectors in the neighborhood of each vector to calculate a reference vector for validation.
31
A dynamic median operator was introduced in the filter where the velocity components of the
reference vector are the median value of all vectors in the neighborhood. When the difference
between the current vector and the reference vector is greater than the user-defined tolerance,
the current vector becomes invalid. These invalid vectors are then removed which leads to empty
grid spaces.
2.6.2.5.2 Data conditioning
The empty grid spaces in the data field that are created by the cleansing of spurious vectors and
the vectors just outside the masked out boundary area are replaced with artificially created
vectors using another-in-house software MatProcess (coded in 2014 by Phil McCarthy). This
algorithm uses a singular value decomposition method on a system of linear equations for a
bilinear least square fit based on 5 nearest neighboring vectors to generate vectors. Also, this
software applies a data smoothing value of 1.3 which replaces every vector in the velocity field
by its Gaussian-weighted mean of the neighbor vectors in order to minimize noise in the data
prior to the calculation of velocity moments.
2.6.2.6 Boundary generation
After the vectors are conditioned, a boundary is then placed onto each data file. This boundary
resembles the exact location and shape of the solid cylinder model used, and can be used either
as a passive or an active boundary.
Figure 2.7 Figure (a) depicts the passive boundary (pink lines) generated over the data file for Z-X plane. Figure
(b) depicts the final PIV output file (vector field) in Z-X plane. It can be noted that the vectors within this boundary
in Figure (b) are not removed, and is used as part of the flow.
(a) (b)
32
When a passive boundary is used (as depicted in Figure 2.7), the vectors inside the boundary are
treated as part of the flow field and the boundary only represents the shape and location of the
model during the experiments. The boundary includes the entire contour of the cylinder
configuration, including the visible and invisible part of the helical wire.
Figure 2.8 Figures (a) and (c) denote the active boundary (pink line), used in the X-Y plane case. (a) depicts the
near-wake region and (c) depicts the shear-layer region, which are drawn along the shape of the cylinder model
and include a poorly illuminated region (caused due to model obstruction of the laser light) and the perspective of
the wire associated with the camera settings. Figures (b) and (d) denote the final processed images, where the active
boundary blanks out the area where the data may become ambiguous.
When an active boundary is applied (as shown in Figure 2.8), the vectors inside it are nullified
to avoid data misinterpretation. The active boundary also masks out the wire’s perspective and
shadow regions, obtained as a result of camera settings and light illuminating the cylinder,
respectively. In this study, passive boundaries are generated for the experiments in Z-X plane
data set, while for the X-Y plane, in both shear-layer and near-wake views, active boundaries are
used.
(a) (b)
(c) (d)
33
2.7 Calculation of flow properties
A detailed analytical description of each parameter is described in Ekmekci (2006). In this
section, a brief note of all the parameters used in this study is mentioned. All the parameters
were computed using the in-house PIV MatProcess and PIVAnalysis software coded in
MATLAB®. The final output file was visualized and interpreted using TecPlot®, and the figures
were assembled and labeled in CorelDraw®. The initial conditions required for computations
were derived from Table 2.1.
2.7.1 Velocity
The measure of the displacement of a particle from one frame to another frame (cross-correlation
function) over the time Δ𝑇 (the time taken by the particle to move from one frame to another)
gives the velocity vector. Therefore, from image analysis,
Velocity = (Pixel displacement*(
mm
pixel))
ΔT ( 2.3)
The velocity field obtained from PIV measurements can be used to estimate various other flow
properties by means of differentiation and integration.
2.7.2 Vorticity
Vorticity is defined as 𝛁 × 𝐕 and its component in the X-Y plane, for example, can be calculated
as
ωz=∂uy
∂x-∂ux
∂y ( 2.4)
where, 𝑢𝑥 and 𝑢𝑦 are the components of velocity in the X and Y directions, respectively. For
flows near boundaries, finite difference methods were used to compute the partial derivatives
required for the vorticity calculation. For the flow, inside, since derivatives are sensitive to
noise, vorticity was calculated by choosing a small rectangular contour around which the
circulation is calculated from the velocity field using a trapezoidal numerical integration rule.
The local circulation is then divided by the enclosed area to arrive at an average vorticity for
the sub-domain. Hence a vorticity at a point (i, j) within the enclosed area, in the X-Y plane,
can be expressed as
34
ωz (i,j)= 1
4δxδyΓ(i,j)=
1
4δxδy∮ v⃗ .dl⃗⃗ ⃗l(x,y)
( 2.5)
2.7.3 Time-averaged functions
The time-averaged flow properties help to interpret the behavior of the flow field over a period
of time. Each component of velocity and vorticity was time-averaged using the following
formula. For example, the time-averaged X-component velocity value was calculated from
equation:
<u(x,y)> = 1
N∑ un(x,y),
Nn=1 ( 2.6)
while, the time-averaged vorticity value for the X-Y plane was calculated from equation
<ωz(x,y)> = 1
N∑ ωzn
(x,y).Nn=1 ( 2.7)
where N is the total number of PIV images acquired.
35
3 Results and Discussions
In this section, the experimental results are presented with the aim of understanding the effects
of a single-start helical wire wound around a circular cylinder in subcritical flow. The wire
diameter was d = 0.0625D, the pitch was P = 3D and the Reynolds number of the flow was
maintained at a value of ReD = 10,000. The flow fields were investigated in three orthogonal
planes: X-Y, Z-X and Y-Z, and the results from these planes are discussed in sections 3.1, 3.2
and 3.3, respectively. As mentioned in Chapter 2, hydrogen bubble flow visualization (HBFV)
and particle image velocimetry (PIV) were employed to delineate the flow fields. The PIV
experiment was conducted in X-Y and Z-X planes, while the HBFV experiment was dine in Y-
Z and Z-X planes. The PIV analysis aided the understanding of instantaneous and time-averaged
flow properties in terms of contours of vorticity concentrations and components of velocity. It
also allowed the study of the wake properties in terms of wake width, vorticity asymmetry angle
and vortex formation length. The HBFV technique provided a qualitative perspective of the flow
field. This section ends with the discussion on the results, given in section 3.4.
3.1 Flow behavior in the X-Y plane
The PIV experiments in the X-Y plane were done in two different regions: near wake and shear
layer, to understand the flow behavior accurately (as mentioned earlier in section 2.5). One way
of interpreting the results in this plane is to imagine that the sampling done at each angle
corresponds to a particular height in the given pitch, so that the range of angles from θ = 0° to
θ = 360° covers the entire pitch of the helix. Therefore, even though the experiment was
performed with a fixed position of the illuminating laser plane for different angles by rotating
the cylinder, the results at a given angle are the fields at that X-Y plane where the wire intersects
the plane at that wire angle. Note that, to aid the interpretation of each figure, the plane where
the experiment is conducted and the field of view employed in the experiment are illustrated on
the top left and top right corners, respectively. The angle θ in the experiments discussed in this
section is measured from the negative X-axis, and is positive for anti-clockwise angles with
respect to this axis. In the discussions that follow, the shear layer originating on the wire side of
the cylinder is termed as the wire-side shear layer, while the one occurring on the smooth side is
called the smooth-side shear layer.
36
3.1.1 Patterns of the time-averaged streamwise velocity ⟨ux⟩
U∞⁄ in the
near wake region
Figure 3.1 Contour patterns of non-dimensionalized time-averaged streamwise (X-direction) velocity, ⟨𝑢𝑥⟩
𝑈∞⁄ , is
plotted in the near-wake region at different wire angular locations. The solid lines represent positive values of ⟨𝑢𝑥⟩,
while the dashed lines represent negative values. Here, the minimum and incremental values of normalized-time-
averaged streamwise velocity are |⟨𝑢𝑥⟩
𝑈∞⁄ |
𝑚𝑖𝑛= 1.6 and |
⟨𝑢𝑥⟩𝑈∞
⁄ | = 0.04.
37
Figure 3.1 depicts the patterns of time-averaged normalized streamwise velocity ⟨𝑢𝑥⟩
𝑈∞⁄ of the
near-wake structure for selected angular positions of the wire (from 𝜃 = 0° to 180°). Please refer
to Figure 5.1 to see the ⟨𝑢𝑥⟩
𝑈∞⁄ contours at more wire angular positions. The solid lines
correspond to positive values and the dashed lines correspond to negative values of ⟨𝑢𝑥⟩. From
these images, the vortex formation length, 𝐿𝑓, a prominent wake characteristic that quantifies
downstream vortex extension, can be deduced. The vortex formation length (𝐿𝑓) is defined as
the distance from the most downstream boundary of the cylinder (X = +0.5D) to the point in the
downstream direction on the X-axis where the streamwise velocity is zero (see Figure 3.5(a) for
pictorial representation of Lf) [60]. In each image in Figure 3.1, the value of 𝐿𝑓 is indicated in
the top right corner, and the angle 𝜃 is indicated in the bottom right corner.
Figure 3.2 The non-dimensionalized vortex formation length (𝐿𝑓
𝐷⁄ ) as a function of the wire angle (𝜃) for the
single-helical-wire (purple curve), the single-straight-wire-fitted (orange curve) and plain (green curve) cylinders.
The Reynolds number for all the experiments is 10,000. The wire-to-diameter ratio for helical and straight wire
fitted cases is d = 0.0625D.
38
For the helical-wire-fitted case, the variation of 𝐿𝑓
𝐷⁄ with θ is shown separately in Figure 3.2.
The values of 𝐿𝑓
𝐷⁄ for the plain and straight-wire-fitted cylinders [from the study of Joshi [38]]
are also shown in this figure for comparison purposes only. For both straight-wire fitted and
plain cylinder cases, the Reynolds number employed was 10,000. The wire-to-cylinder diameter
ratio of the straight-wire-fitted case is d = 0.0625D, which is the same as the wire diameter ratio
of the single-start-helical-wire-fitted cylinder considered here. From the Figure 3.2, it is evident
that the vortex formation length is always larger for the cylinder fitted with the single start helical
wire than the vortex formation length of a smooth cylinder and the vortex formation length of
cylinder fitted with the straight wire at any angle.
3.1.2 Patterns of time-averaged and instantaneous fields of spanwise
vorticity ωzD
U∞⁄ in the near-wake region
In Figure 3.3, the time-averaged patterns of the near-wake structure are plotted in terms of
absolute values of normalized spanwise vorticity |⟨𝜔𝓏⟩|𝐷
𝑈∞⁄ for selected angular positions of
the wire from 𝜃 = 0° to 180°. The color bar showing the different contour levels of |⟨𝜔𝓏⟩|𝐷
𝑈∞⁄
is given below the figure.
An important observation that can be made from Figure 3.3, is the formation of dual, wire-side
shear layers between 𝜃 = 35° and 𝜃 = 55°. This phenomenon was first observed by Chyu and
Rockwell (2002) for the three-start helical wire geometry in the X-Y sectional cuts of the wires.
In their study, they performed the analysis at three different angular locations. At one such
location, they noticed the formation of dual shear layers on the upper surface of the cylinder.
They postulated that the reason for this dual layer structure occurrence is apparently associated
with: (i) separation from a section of the helical perturbation on the fore surface of the cylinder
and (ii) separation from the section of the perturbation. In the current study, the dual shear layers
begin to form at 𝜃 = 35° and continues till 𝜃 = 55°. As there is only one single wire in the
present case, the reason behind the formation of dual vorticity layers cannot be that suggested
by Chyu and Rockwell (2002). At 𝜃 = 35°, the dual vorticity layer is such that the layer closer
to the cylinder has stronger time-averaged vorticity levels.
39
Figure 3.3 Contours of time-averaged normalized spanwise (X-Y plane) vorticity |⟨𝜔𝓏⟩|𝐷
𝑈∞⁄ in the near-wake
region for selected wire angular locations 𝜃. Absolute values of the time-averaged vorticity are plotted in each
image in order to assimilate the amount of asymmetry in the flow (in terms of vorticity asymmetry angle). The yellow
straight line helps to measure the vorticity asymmetry angle. The purple vertical line indicates the total wake width
at X = 0.5D location, while the violet line indicates the total wake width measure at X = 0.75D location.
40
As 𝜃 is increased, the time-averaged vorticity of the dual layers shift such that the vorticity in
the layer closer to the cylinder gets weaker, while it gets stronger in the layer further away from
the cylinder. Eventually the vorticity of the two layers balance out and become nearly equal at
𝜃 = 42°. When the wire angle 𝜃 is increased further, the strengths of the vortices in the dual
layer reverse: that is, the shear layer away from the cylinder becomes stronger while the one
closer to the cylinder gets weaker. Finally, the dual layer structure disappears past 𝜃 = 55°.
The occurrence of the dual shear layer phenomenon can be further elucidated by studying the
instantaneous patterns of spanwise vorticity 𝜔𝑧𝐷
𝑈∞⁄ over a period of time. In Figure 3.4,, the
instantaneous patterns of the near-wake structure are shown in terms of the normalized spanwise
vorticity 𝜔𝑧𝐷
𝑈∞⁄ for three different angular positions of the wire, at 𝜃 = 35°, 42° and 50°, at
selected time instants. For a plain cylinder in the subcritical flow regime, small-scale vortical
structures should form in the separated shear layers (as mentioned in section 1.3.1). Studies done
by Chyu and Rockwell (2002) suggest that clusters of such small-scale vortices modify the near-
wake flow field. Likewise, it can be seen from Figure 3.4 that these small scale vertical clusters
are also formed for a single-start helical wire. The color bar showing the levels of the
𝜔𝑧𝐷𝑈∞
⁄ contours is given at the bottom of Figure 3.4. The same levels are used for all the images
for ease of comparison. A nominal period, 𝑇𝑛, was obtained through a Fast-Fourier
Transformations (FFT) analysis conducted on 1,000 images at three locations downstream of the
cylinder. The instantaneous images in Figure 3.4 were selected at one half of this nominal period,
𝑇𝑛2⁄ . Note that the dual wire-side shear layers display vorticity of same sign. At 𝜃 = 35°, the
occurrence of the same sign dual shear layer is sporadic, and when the dual shear layer does
occur, the frequency of occurrence of the shear layer further away from the cylinder is weak
compared to the one that forms closer to the cylinder. At 𝜃 = 42°, the same sign, dual shear
layers are almost always present in the flow structure along with a weak shear layer of opposite
sign in between them. At 𝜃 = 50°, the dual shear layers are noticeable however, when the dual
shear layers does not form, the shear layer that forms closer to the cylinder occurs less frequently
in comparison to the one that forms further away from the cylinder.
41
Figure 3.4 The non-dimensionalized instantaneous spanwise vorticity 𝜔𝑧𝐷
𝑈∞⁄ in the near-wake region is plotted
for different instants of data acquisition, each separated by half a nominal period of a Karman cycle (Tn) in each
row. Here, the data is shown for θ=35°,42° and 50° angular locations, each presented in a different column. Here,
the value of Tn is 20 frames, or in other words, 1.38 s.
42
These trends agree well with the results deduced from the time-averaged results of Figure 3.3,
and are evidenced much more clearly in the supplementary videos of the instantaneous non-
dimensionalized 𝜔𝑧𝐷
𝑈∞⁄ given for the three angles: Movie 01 (𝜃 = 35°), Movie 02 (𝜃 = 42°)
and Movie 03 (𝜃 = 50°).
Figure 3.5 Figures (a), (b) and (c) illustrate the definition of the vortex formation length (Lf ), the vorticity
asymmetry angle ( ) and the total (WT) and lower (WL) wake width respectively. Figures (d), (e) and (f) show the
measurement of the two vorticity asymmetry angles (∅1 and ∅2), two total wake widths (WT1 and WT2 ) and two
lower wake widths (WL1 and WL2). In figure (c), the wake width calculations are done at two different downstream
locations: X= 0.5D (purple line) and X (violet line) = 0.75D.
From Figure 3.3, one can deduce two important wake characteristics: the vorticity asymmetry
and the wake width. The vorticity asymmetry angle 𝜙 is a measure of the disproportionateness
between the wire-side and smooth-side shear layers caused by the presence of the wire. It aids
in the identification of the early development of transition in the wire-side shear layer (Ekmekci
and Rockwell, 2010, 2011). Figure 3.5 (b), pictorially defines the vorticity asymmetry angle. The
following procedure was adopted to determine 𝜙: First, two vorticity level curves of equal
magnitude were identified in the wire-side and plane-side shear layers. The angle made by the
line segment (yellow straight lines in Figure 3.3, Figure 3.5 (b) and Figure 5.2) joining the
rightmost extremes of these vorticity level curves with the Y-axis, was defined as the vorticity
asymmetry angle 𝜙. The selection of the magnitude of the vorticity for the level curves was
43
critical to illustrate the asymmetry clearly. As may be seen from Figure 3.5 (b), for small values
of vorticity (for example those shown via red color contour lines), the line segment is nearly
vertical and relatively insensitive to the wire angle 𝜃, while for large values (for example those
shown via green color contour lines), contour levels can be absent on the wire-side shear layer.
Hence, a moderate contour level of |⟨ωz⟩|D
U∞⁄ = 6.7 was chosen to delineate the asymmetry
clearly.
Figure 3.6 (a) The variation of vorticity asymmetry angle 𝜙 relative to the wire angle 𝜃 is plotted. The value of 𝜃
ranges from 𝜃 = 0° to 180°. (b) The presence of two asymmetric angles for = 41, 42 and 43. The two value of
(b)
(a)
44
asymmetry angles can be attributed to the presence of same strength vorticity in both the dual shear layers on the
wire side.
The variation of the vorticity asymmetry angle 𝜙is shown in Figure 3.3for selected wire angular
positions from the angular range 𝜃 = 0° to 180° (please refer to Figure 5.2 to see the vorticity
contours depicting the vorticity asymmetry angles for more angular locations). The vorticity
asymmetry angle increases from a small value (close to 𝜙 ≈ 6°) at 𝜃 = 0° to a significantly large
value of 𝜙 ≈ 29° at 𝜃 = 41°, fluctuates between 𝜃 = 40° and 55°, and then gradually decreases
up to about 𝜃 = 90°, beyond which it decreases monotonically, reversing sign at 𝜃 = 120°. For
𝜃 between 41° and 43°, with our definition of the vorticity asymmetry angle, it is possible to
even define two values of 𝜙 ( 𝜙1 and 𝜙2 see Figure 3.5 (d) for definition) due to the dual shear
layer phenomenon identified previously, see Figure 3.6 (b). In theory, it should be possible to
obtain two values of 𝜙 for the entire range of angles over which dual shear layers occur (𝜃 =
35° to 55°). However, due to the limitations in selecting the vorticity contour level defining 𝜙
that were explained above, only a single value of 𝜙 could be measured for the remaining angles
in the dual shear layer range.
From Figure 3.6 (a), it can be deduced that the strongest evidence of asymmetry occurs from
𝜃 = 30° through 90° due to the distortion induced by the wire in the shear layer region, with the
maximum distortion occurring at 𝜃 = 42°. A comparison of this trend with the measurement of
𝜙for the cylinder fitted with a straight wire of same diameter and the same Reynolds number
(Joshi, 2016) reveals that, for a straight wire perturbation, the asymmetry manifests most strongly
only over a smaller range of wire angles, while for the helical wire perturbation, the asymmetry
is spread over a wider range of angles, possibly due to the three-dimensional effects of the helical
perturbation.
The second characteristic that can be deduced from Figure 3.3 is the width of the wake W, which
is defined (Saelim, 2003) as the difference in the Y coordinates of the maxima in the time-
averaged vorticity of the separating shear layer formed on either side of the cylinder, at a fixed
X location. Alternatively, it is the length of the vertical line segment connecting the locations of
these maxima. The pictorial representation of the measurement of the non-dimensionalized total
wake width 𝑊𝑇 = 𝑊 𝐷⁄ is shown in Figure 3.5 (c). Here, the non-dimensioanlized total wake
45
width (𝑊𝑇) can further be divided into upper half (𝑊𝑈) and lower half (𝑊𝐿) (see Figure 3.5 (c)
for definition) wake width relative to the cylinder center line (Y=0), where 𝑊𝑇 = 𝑊𝑈 + 𝑊𝐿.
Here, 𝑊𝑇 and 𝑊𝐿 were evaluated at two different streamwise distances: X = 0.5D and 0.75D.
Please refer to Figure 5.3 and Figure 5.4 for the vorticity contours depicting the 𝑊𝑇 and 𝑊𝐿 values at
X = 0.5D and Figure 5.5 and Figure 5.6 for depicting 𝑊𝑇 and 𝑊𝐿 values at X = 0.75D respectively
for various wire angles. Figure 3.7 depicts the variation of the non-dimensionalized total wake
width (WT
D⁄ ) and lower half of the wake width (WL
D⁄ ) with the wire angle () for X = 0.5 D [in
subfigures (a) and (b)] and X = 0.75D [in subfigures (c) and (d)]. Subfigures (a) and (c) show
the total wake width WT
D⁄ (green curve), and also the lower half of the wake width WL
D⁄ (red
curve), since the upper and lower halves of the wake width can be different due to the asymmetry
arising from the wire-side shear layer. The asymmetry is evinced more clearly in the plots of the
difference, (2WT-WL )
D⁄ , given in subfigures (b) and (d). As evident from the graphs, the value
of the wake width is found to be nearly identical at the two downstream distances. However,
their values greatly exceed those of the plain cylinder case [shown with dotted lines in subfigures
(a) and (c)]. Both WT
D⁄ andWL
D⁄ values remain constant from 𝜃 = 0° through 𝜃 = 30°. For 𝜃 =
35° through 55°, in the dual-shear layer formation angular range, eachWT
D⁄ and WL
D⁄ curve
splits into two subcurves (WT1
D⁄ ,
WT2D
⁄ and WL1
D⁄ ,
WL2D
⁄ , see Figure 3.5 (e) and Figure 3.5
(f) for definitions) and throughout this bifurcated range, the values of the wake widths for each
sub-curve remain relatively constant. Beyond 𝜃 = 55°, as 𝜃 increases, the values of WT
D⁄ and
WLD⁄ decrease gradually, and remain constant after 𝜃 = 120°. Since the variation in the wake
width with the wire angular position is an indicator of a spanwise three-dimensionality in the
flow (Chyu and Rockwell, 2002), there is a significant flow variation between a fairly large range
of angles, 𝜃 = 35° and 𝜃 = 120°, and this range coincides with that of the significant vorticity
asymmetry angles.
To understand the behavior of the flow closer to the cylinder surface, the shear layer region is
examined in detail, next.
46
Figure 3.7 The variations of wake widths W and WL relative to the wire angle 𝜃 are plotted in figure (a) and (c) at
X= 0.5D and 0.75D respectively. The graphs (b) and (d) depict the change in the value of the wake width relative
to the wire angle 𝜃 at X= 0.5D and 0.75D, respectively. The value of 𝜃 ranges from 𝜃 = 0° to 180° and X = 0 is
considered as the cylinder center along the streamwise (X-axis) direction.
3.1.3 Patterns of time-averaged and instantaneous fields of spanwise
vorticity ωzD
U∞⁄ in the shear layer region
Figure 3.8 shows contours of the time-averaged spanwise vorticity in non-dimensional form for
selected wire angles in the shear layer region. Consistent with the observations made in the near
wake region, same sign dual vorticity layers can be clearly observed in the shear-layer region
between the angular range of 𝜃 = 35° and 𝜃 = 55° on the wire side. In the dual shear layer, the
vorticity layer that is further away from the cylinder has weaker vorticity in comparison to the
layer that is closer to the cylinder at the beginning of this range of angles (close to 35°), but at
𝜃 = 42°, the two shear layers become equal in vorticity strength, and beyond 𝜃 = 42°, the layer
away from the cylinder becomes stronger than the other one.
47
Time sequences of the instantaneous vorticity contours are depicted for the wire angles of 𝜃 =
35°, 42° and 50° in Figure 3.9. This information is available in much greater detail in the
supplementary videos Movie 04, Movie 05 and Movie 06 for wire angles of 𝜃 = 35°, 42° and
50°, respectively. Apart from the formation of the dual shear layer, another shear layer of lower
strength and opposite sign is found to occur in between the two same-sign shear layers. Dual
shear layer formation could be the result of the three-dimensional flow from another layer.
Figure 3.8 Contours of time-averaged normalized spanwise (X-Y plane) vorticity < 𝜔𝑧 > 𝐷
𝑈∞⁄ in the shear layer
region at selected wire angular locations 𝜃.
48
Figure 3.9 The normalized instantaneous spanwise vorticity 𝜔𝑧𝐷
𝑈∞⁄ from the shear layer region is given at
selected instants in time, each separated by half the period of a nominal Karman cycle (Tn) in each row. Here, the
data is shown for 𝜃 = 35°, 42° and 50° wire angular locations, each presented in a different column. The value of
Tn is 20 frames, which corresponds to 1.38 s.
49
3.1.4 Patterns of time-averaged and instantaneous ∂ux
∂x+
∂uy
∂y contours in
the shear layer region
Figure 3.10 Contours of time-averaged negative variation of 𝑢𝑧 in the Z-direction, (i.e., - 𝜕𝑢𝑧
𝜕𝑧⁄ ),
𝜒𝐷𝑈∞
⁄ , in the
shear layer region for selected wire angular locations, 𝜃. Here the value of 𝜒 is nondimensionalized with the free
stream velocity (𝑈∞) to diameter of the cylinder (D) ratio.
50
Figure 3.11 Negative of the instantaneous variation of 𝑢𝑧 in the Z-direction, (i.e., − 𝜕𝑢𝑧
𝜕𝑧⁄ ),
𝜒𝐷𝑈∞
⁄ , from the
shear layer region is plotted for different instants in time, each separated by half the period of a nominal Karman
cycle (Tn) in each row. Here, the value of 𝜒 is nondimensionalized with the free stream velocity (𝑈∞) to diameter of
the cylinder (D) ratio. Each column represents the wire angular location, 𝜃, at which the data is plotted. The data
is shown for 𝜃 = 35°, 42° and 50° wire angular locations. The value of Tn is 20 frames, which corresponds to 1.38
s.
51
To determine if there is any variation of 𝑢𝑧 across the X-Y plane, the quantity 𝜒 =𝜕𝑢𝑥
𝜕𝑥+
𝜕𝑢𝑦
𝜕𝑦
was computed. For incompressible fluids, the continuity equation requires that 𝜕𝑢𝑥
𝜕𝑥+
𝜕𝑢𝑦
𝜕𝑦=
−𝜕𝑢𝑧
𝜕𝑧 holds. Therefore, if 𝜒 is positive at any point in the X-Y plane,
𝜕𝑢𝑧
𝜕𝑧 is negative at that point,
that is, 𝑢𝑧 is slowed down in the +Z direction, and the difference in the fluid volume is redirected
into the X-Y plane. On the other hand, if 𝜒 < 0, then 𝜕𝑢𝑧
𝜕𝑧> 0, that is, the fluid motion in the +Z
direction is sped up, and the fluid required for this acceleration is drawn from the given X-Y
plane at the position where 𝜒 is computed. Thus, positive values of 𝜒 imply injection of fluid
volume into the X-Y plane, while negative values imply rejection of fluid volume from the plane.
For two-dimensional flows in the X-Y plane, where the Z-component of velocity 𝑢𝑧 is absent, 𝜒
is identically zero.
Figure 3.10 shows the time-averaged variation of non-dimensionalized 𝜒𝐷
𝑈∞⁄ in the wire-side
shear layer region for selected wire angles between θ = 0° and 180°. The flow is not two
dimensional, as evidenced by the significant, non-zero values of 𝜒. There are two key regions of
non-zero 𝜒: the region just upstream of the wire and close to the cylinder, where 𝜒 < 0, and the
region immediately downstream of the wire, where 𝜒 > 0. These regions are prominently
observed for the angles between 30° and 120°. The presence of a region of negative 𝜒 just
upstream of the wire indicates that the incoming flow along the X-axis is diverted away from the
plane in the +Z direction when it approaches the wire. The maximum value of 𝜒 upstream of the
wire increases as θ is increased and attains a maximum at about 42°, before decreasing with
further increase in θ and becoming negligible near 90°. This suggests that the diversion of the
incoming flow in the +Z direction is most pronounced at the θ = 42° wire location in the X-Y
plane.
The time sequences of 𝜒𝐷
𝑈∞⁄ images, given in Figure 3.11, and the videos Movie 07 through
Movie 11 for angles θ = 0°, 35°, 42°, 50° and 90°, respectively, reveal more details. Even
though many time averaged images have almost no 𝜒 level in the separated shear layer
downstream of the cylinder, the instantaneous images convey a non-zero 𝜒 signal over this area
(compare, for example, the time-averaged and instantaneous images of 𝜒 for θ = 50°). This
52
implies that, in the separated shear layer downstream of the cylinder, there are regions that
alternate between positive and negative values of 𝜒 and cancel each other out when time
averaged. Fluid, therefore, is continuously going in and out of the X-Y plane in the shear layer
downstream of the cylinder at these angles, again confirming the significant three dimensionality
of the flow.
To complement the PIV findings in the X-Y plane, which have been discussed so far, and to
visualize the complete three-dimensional flow behavior, hydrogen bubble visualization
experiments were conducted in Y-Z and Z-X planes. These are discussed next.
3.2 The flow behavior in the Z-X plane
The experiments in the Z-X plane allow the understanding of the flow behavior along a given
pitch (see section 2.5 for the description of the experimental set-up for this set of experiments).
Figure 3.12 shows the contour patterns of time-averaged normalized cross-stream vorticity
(⟨𝜔𝑦⟩𝐷
𝑈∞⁄ ) measured using PIV, accompanied by an instantaneous picture obtained from a
hydrogen bubble experiment focusing on the Z-X plane. Both PIV and hydrogen bubble images
in this plane were taken at a distance of Y = 0.75D. Video of the flow field visualized with
hydrogen bubbles is also provided in the Movie 12. Figure 3.12 and the hydrogen bubble
visualization video (Movie 12) illustrate the formation of two counter-rotating vortices that
extend along the flow direction starting on the wire. In their investigations on three-start helical
strakes fitted on a freely vibrating cylinder, Zhou et al. (2011) also observed similar swirling
patterns in the Z-X plane, albeit they started forming further downstream of the cylinder,
whereas, in the present experiments involving a single-start helical wire, these swirling patterns
are observed to start on the wire and extend downstream as can be seen from Figure 3.12 (b) and
Movie 12. It can be noted that the wake-like pattern reported previously by Chyu and Rockwell
(2002) for a stationary cylinder fitted with a three-start helical wire configuration in the Z-X
plane was not found to occur in the present case. Also, the PIV image, given in Figure 3.12 (a)
shows that these cross-stream vortices tend to occur for wire angles that begin at about 𝜃 = 70°
to 80° and thicken in the range of 𝜃 = 40° to 135°.
53
Figure 3.12 (a) The normalized values of the time-averaged cross-stream (Z-X plane) vorticity ⟨𝜔𝑦⟩𝐷
𝑈∞⁄ in the
down stream region of Z-X plane at a distance of Y = 0.75D. (b) A snapshot of the flow field from the hydrogen
bubble visualization experiments, indicating the formation of two opposite-sign vortices extending in the streamwise
direction (marked in green for clarity). The location where the cross-stream vorticity (𝜔𝑦) and the two vortices
occur is marked by an arrow (in red). Here, for PIV data, the minimum and incremental values of contours are
|< 𝜔𝑦 > 𝐷
𝑈∞⁄ |
𝑚𝑖𝑛= 10 and ∆ |
< 𝜔𝑦 > 𝐷𝑈∞
⁄ | = 0.3.
Movie 12, taken from hydrogen bubble visualization experiments in the Z-X plane, confirms
some features that have already been seen and predicted from the PIV images taken in the X-Y
plane. First, it was noted that the flow in the shear layers observed in the X-Y PIV images was
not two dimensional, and the fluid appeared to flow in and out of the plane. This is captured in
the hydrogen bubble video Movie 12. Second, a diversion of the incoming flow at the upstream
end of the wire was predicted in the level curves and videos of the parameter 𝜒 between the wire
54
angles of 30° and 120°. This can be clearly seen in the videos (Movie 12); a stream of fluid
flows along the upstream end of the wire. To the incoming flow, the portion of the wire between
the angles of 30° and 90° acts as an inclined ledge that tends to deflect the flow along the wire
surface. The hydrogen bubble video images, selected instants of which are given in Figure 3.13,
also reveal that the flow along the wire is more complicated than the X-Y PIV images suggest.
As can be seen in the video (Movie 12), beyond 90°, the flow either continues along the length
of the wire (Case A in Figure 3.13), or is pushed downstream of the wire in the streamwise
direction (Case B in Figure 3.13). That is the flow tends to go between being in case A and case
B intermittently.
Figure 3.13 The instantaneous snapshots of the flow in the Z-X plane at two different instants in time. In case A, at
𝜃 > 90°, the flow continues to move along the wire and in case B, at 𝜃 < 90°, the flow is deflected downstream of
the wire in the streamwise X-direction.
55
3.3 Flow behavior in the Y-Z plane
Figure 3.14 Formation of streamwise vorticity ⟨𝜔𝑥⟩ very close to the cylinder surface is shown at different instances
in time using HBFV technique. The imaging plane is at X=0.50D, where X is measured from the cylinder center.
Here, Reynolds number is 5,000.
Figure 3.15 The formation of the streamwise vorticity ⟨𝜔𝑥⟩ very close to the projection of the cylinder surface on
the Y-Z plane is shown at different instances in time using the hydrogen bubble visualization. The imaging plane is
at X = 0.50D, where X is measured from the cylinder center. Here, Reynolds number is 10,000.
56
The experimental set-up for this set of experiments was described earlier in section 2.5. Figure
3.14 and Figure 3.15 show the instantaneous hydrogen bubble visualization images of the flow
in the Y-Z plane at four different instants in time at a distance of X = 0.50D at Reynolds number
of 5,000 and 10,000, respectively. Note that here X is measured from the cylinder center and the
flow is coming out of the plane of the image towards the reader. Also, see Movie 13 for Reynolds
number of 5,000 and Movie 14 for Reynolds number of 10,000. In the plain and straight-wire-
fitted cylinder cases, one expects the flow structure at X = 0.50D to be invariant in the Z-
direction. However, with the helical wire type perturbation, it can be observed from the results
in the Y-Z plane that there is significant deviation from this invariance, and one can distinguish
finite-size counter-rotating pairs of vorticity concentrations. Such a vortex pair is observed to
occur at two locations very close to the projection of the cylinder surface on the Y-Z plane of
visualization. As the plane of visualization moves away from the cylinder in the downstream
direction, the streamwise vorticity tends to be more concentrated near the cylinder center as can
be observed in Movie 15, Movie 16 and Movie 17, which respectively correspond to the Y-Z
planes at X = 1 D, 2D and 3D.
3.4 Discussion
The long term objective of this project, as explained in the introduction, is to understand why
only certain helical surface perturbations (number of wires, wire diameters, helical pitch)
suppress VIVs at a given Reynolds number. This thesis is a stepping stone in that direction, and
studies the behavior of the flow past a single-start helical wire wrapped around a circular cylinder
in three different orthogonal planes, namely X-Y, Y-Z and Z-X. This sub-section compares the
present findings with the results of prior published work, and highlights the new findings of this
research.
An important characteristic of the flow in the X-Y plane is the vortex formation length, 𝐿𝑓.
Stretching of the downstream vortex has been related in the past to the suppression of vortices,
which results from the mitigation of momentum transport through the center region of the wake
(Lee and Kim, 1997). In the case of the cylinder fitted with a single-start helical wire, 𝐿𝑓was
found to vary along the span of the cylinder, depending on the angular location of the wire facing
the approach flow. Also, the value of 𝐿𝑓 for the single-start-helical-wire-fitted cylinder was
57
found to be larger than 𝐿𝑓 of the straight-wire-fitted and plain cylinders. This trend is consistent
with the values obtained by studies conducted by Saelim (2003) on a three-start helical wire
model. In the study conducted by Saelim (2003), at a Reynolds number of 10,000 , for (P = 3D
and d = 0.0625D), the value of 𝐿𝑓 was noticed to be significantly greater than the value of 𝐿𝑓 for
the plain cylinder case. It was seen in our studies that, with only a single-start helical wire, 𝐿𝑓,
on an average, was noticeably larger than the straight wire and plain cylinder case. This suggests
that even a single-start helical wire can lead to a strong modification in the flow field and hence
possibly the stress distributions that may influence the vibration behavior of the cylinder it is
wound around. Measurement of vorticity asymmetry angle, 𝜙, suggests that similar to the
straight wire case, the near-wake asymmetry occurs only at a range of angles in case of the single-
start helical wire. The wake widths, 𝑊𝑇 and 𝑊𝐿, are found to be larger than the plain cylinder
case with greater variation occurring over the range of wire angles θ = 30° to 120°. The width
of the lower half of the wake (𝑊𝐿) is found to be greater than the value of half of the total width
of the wake (𝑊𝑇
2⁄ ) for angles θ = 35° to 55°, due to the asymmetry in the flow caused by the
early transition to turbulence in the wire-side shear layer.
Lee and Kim (1997) reported that the variation of iso-pressure contours along the span resulted
in a spanwise flow. In this study, from the continuity equation, the variation of the spanwise
velocity component, 𝑢𝑧, with the Z-coordinate was computed. The time-averaged value of this
variation showed that there exists a finite Z-direction flow next to the cylinder surface and that
the flow was moving in and out of the plane in the shear layers prominently in the angle range 𝜃
= 30° to 120°. The hydrogen bubble visualization videos in the Z-X plane conclusively showed
that this is indeed the case, with the incoming flow in this range of angles being diverted along
the upstream surface of the wire. This diverted flow intermittently went between two behaviors
beyond 𝜃 = 90°: (1) at some instants, it continued along the length of the wire, and (2) at other
instants, it was pushed downstream of the wire in the streamwise direction. This rich and detailed
description of the flow is unavailable in prior work. A second distinctive feature in the hydrogen
bubble visualization videos in the Z-X plane is the observation of swirling vortices emanating
from the wire. The hydrogen bubble visualization results in the Y-Z plane also show streamwise
vortical structures. Presumably, the vortical structures seen in the Z-X plane manifest themselves
58
also as the streamwise vortical structures in the Y-Z plane. The distinct asymmetry, the increase
in the vortex formation length and the variation of the wake width in selected wire angular range
in the X-Y plane are presumably associated with the flow behavior in Z-X plane at the same
ranges. It is, however, unclear whether the bi-stable oscillations of the shear layers in the X-Y
plane or the out-of-plane motion of the flow or the three-dimensional geometry of the model
itself which is contributing to such variations in the flow field structure.
A closer examination of the time-averaged and instantaneous PIV images of the shear layer
region in the X-Y plane revealed that, in the wire angle range of 𝜃 = 35° to 55°, there are two
wire-side shear layers having the same sign of vorticity, separated by a small region of vorticity
of opposite sign. In the flow near the near-wake region, Chyu and Rockwell (2002) also reported
the formation of same sign dual shear layers at a given angle for a fixed cylinder fitted with a
three-start helical wire at a Reynolds number of 10,000. They postulated that the occurrence of
the dual shear was the result of the separation from upstream and downstream wires. Also, the
dual shear layer pattern is evident in the measurements of three-start-helical-strake-fitted-
cylinder experiments, conducted by Korkischko and Meneghini (2011) at ReD = 1,000, even
though they have not mentioned this explicitly. It is not possible to comment definitively on the
origin of the dual shear-layer phenomenon observed on the wire-side PIV images in the X-Y
plane. One may question whether this phenomenon is related to the bistable shear layer
oscillations observed by Ekmekci (2014). The existence of the bistable shear-layer oscillations
could not be confirmed in the present work because the large size of the wire wrapping around
the cylinder prevented optical access to the flow region close the cylinder surface. Nevertheless,
the bistable shear layer oscillations can be ruled out from being the source of the dual shear-layer
phenomenon because the instantaneous images of the flow suggest that the two shear layers on
the wire side can occur simultaneously; this does not happen in the bistable oscillation case,
where the flow is either reattaching or separating from the cylinder surface. An alternative source
for the existence of two shear layers on the wire side may be the flow of fluid in the Z-direction,
which was in fact evidenced by the non-zero values of 𝜒 in this region. This flow could be
associated with the second shear layer. However, this possibility needs to be substantiated with
further experimental data.
59
4 Recommendations for Future Work
This chapter discusses possible improvements for this work and makes recommendations for
future directions of investigation.
4.1 Future work with the current experimental model
Figure 4.1 Variation of the Strouhal number with the wire angle, 𝜃, is plotted for a cylinder fitted with (a) single-
start helical wire, and (b) single straight wire case (Joshi, 2016). Here, 𝜃 is measured from 0° to 360°. The results
were obtained from CTA measurements at ReD = 10,000. For both cases, the wire-to-diameter ratio was d= 0.0625.
The location of the hot-wire probe and orientation of the cylinder during the course of experiments is illustrated in
top right corner.
It is known that the increase in the vortex formation length occurs concomitantly with a decrease
in the Strouhal number (which is the dimensionless frequency of the Karman vortex shedding).
The Strouhal number for different wire angles was measured in the present work by placing a
hot filament probe at the X = 4.3D, Y = 3D position. These results are shown on the left hand
60
side of Figure 4.1. The right hand side of this figure also provides the Strouhal number variation
with the wire angle for a single-wire-fitted cylinder (taken from the work of Joshi (2016)). For
both the case studies, the wire-to-diameter ratio was d=0.0625D and the Reynolds number
employed was 10,000. Surprisingly, there is barely any change in the Strouhal number with wire
angle for the single-start helical wire case, unlike the straight wire perturbation geometry which
has a pronounced minimum and a maximum (the right-hand side of Figure 4.1) when the probe
is set at exactly the same position. In the future, the probe can be placed closer to the cylinder to
examine the Strouhal number variation in greater detail.
In this work, no force or stress measurements were performed to examine the effect of the helical
wire perturbation on the drag and lift forces acting on the cylinder. In the future, suitable
transducers can be employed to measure these forces, and thus directly confirm the role of the
wire on modifying VIVs.
The Reynolds number and the geometry were kept constant in this work. In future work, the
Reynolds number can be varied from 5,000 to 50,000 (following Lee and Kim (1997)). The
influence of the pitch of the helix and the wire diameter can also be examined by repeating the
experiments of the present work for single-start-helical-wire-wound cylinders with systematic
variation of these geometrical parameters.
In this thesis, the quantity 𝜒 = −𝜕𝑢𝑧
𝜕𝑧⁄ was calculated from the PIV images collected from the
X-Y plane to determine the possibility of fluid being added or removed from a given X-Y plane.
The time-averaged value of 𝜒, calculated for different wire angles (which correspond to different
X-Y planes), presents an opportunity to understand the complete, time-averaged 3-D velocity
field only from X-Y PIV data. The time-averaged quantity ⟨𝜒⟩ = −𝜕⟨𝑢𝑧⟩
𝜕𝑧⁄ can be obtained
from a given PIV image as a function of X and Y, as was done in this work. If the PIV data is
taken for different wire angles for small angle differentials, one obtains ⟨𝜒⟩ as a function of X,
Y and Z. ⟨𝑢𝑧⟩ can then be obtained at every X-Y location by integrating the definition of ⟨𝜒⟩ as
⟨𝑢𝑧⟩(𝑋, 𝑌) = ⟨𝑢𝑧0⟩(𝑋, 𝑌) + ∫ ⟨𝜒⟩(𝑋, 𝑌, 𝑍) 𝑑𝑍
𝑍
𝑍0, where ⟨𝑢𝑧0
⟩(𝑋, 𝑌) is the time averaged Z-
velocity at the location (𝑋, 𝑌, 𝑍0). Note that ⟨𝜒⟩ is periodic in Z, and the periodicity of ⟨𝑢𝑧⟩
requires that the integral ∫ ⟨𝜒⟩(𝑋, 𝑌, 𝑍) 𝑑𝑍𝑃
0 is identically zero, where P = Pitch of the helix. The
61
X-Y plane PIV data already provides ⟨𝑢𝑥⟩(𝑋, 𝑌, 𝑍) and ⟨𝑢𝑦⟩(𝑋, 𝑌, 𝑍), and thus the reconstruction
of the 3-D velocity field requires only the knowledge of the velocity ⟨𝑢𝑧0⟩ at only one axial
position Z0 for every combination of X and Y. Thus, it is possible to reconstruct the entire, 3-D
time-averaged velocity field only from the X-Y PIV data collected at regularly and finely spaced
θ intervals. This approach can be validated by comparison with ⟨𝑢𝑧0⟩ data obtained directly from
the Z-X and Y-Z PIV data. The process of finding ⟨𝑢𝑧⟩ by this procedure and validating it will
be implemented in the future.
The three-dimensional nature of the flow field can be elucidated much more clearly using
Volumetric 3-Component Velocimetry (V3V) and Stereoscopic Digital PIV (SDPIV). These
techniques make use of two or more cameras, which capture the flow field in more than one
plane at a given time. These avenues can be explored in the future.
4.2 Future work that can be performed on models different than the one used in the current work for analyzing the flow behavior with cylinder movement
This study was conducted on a rigid stationary cylinder. However, in practical applications, the
cylinder can move relative to the flow. In order to gain a representative model of the actual
scenario, it is recommended to study the flow field while including the cylinder motion. The
cylinder can either be allowed to move freely with the forcing of the flow (free-vibration case)
or the cylinder motion can be manipulated by an outside source (forced-vibration case). In the
case of the helical-wire type surface protrusions, earlier studies (see section 1.3.2) were
conducted under free-vibration conditions for a range of Reynolds number, wire-to-cylinder
diameter (d/D) ratio and pitch, mainly to find the optimum configuration that suppressed VIVs.
Also, it was shown that a single-start helical wire (Nakagawa., Fujino. and Arita., 1959;
Nakagawa, 1965; Lubbad et al., 2007; Lubbad, Lo̸set and Moe, 2011) did not suppress VIVs. In
this scenario, it would be interesting to see the complete flow profile using the experimental
techniques used in this study (i.e., PIV and hydrogen bubble visualization) and compare it with
the stationary case.
Another interesting case study that can be investigated is the effect of controlled motion of a
cylinder fitted with a single-start helical wire type surface protrusion on the flow. This study can
62
help in characterizing the different flow structures that are obtained at a combination of
oscillation frequencies and amplitudes for different Reynolds numbers, wire-to-cylinder
diameter (d/D) ratios and pitches of the helix. In the following section, a brief description of two
possible designs for the experimental set-up that can be used for forced-oscillation experiments
is given.
4.3 Experimental set-up for forced oscillation experiments: two possible test rig designs
Experiments on helical-wire-fitted cylinders undergoing forced oscillations can be pioneering in
terms of studying the effects of structural vibrations on the flow control. For such experiments,
the cylinder is to be forced to vibrate at a particular frequency and amplitude. An oscillation
frequency range of 0.2 Hz to 5 Hz would be suitable if one aims to study the effects of cylinder
vibrations at the Karman vortex shedding frequency (𝑓𝑘) as well as at the shear layer frequency
(𝑓𝑠𝑙). Oscillation amplitudes over a large range from 0.1D to 2D (where D is the diameter of the
cylinder) can be considered.
Figure 4.2 The conceptual design # 1 for the forced-vibration experiments using slider-crank mechanism.
One possible design for forced-vibration tests is shown in Figure 4.2. This design makes use of
a slider-crank mechanism, which has been in use for many high speed applications such as
63
automobile engines. In such a system, a crank with holes drilled at different locations from the
center would provide the option of changing the oscillation amplitudes to different values. A rod
connects the crank to the linear slider, using pin joints or cam rollers. This rod would translate
the rotational motion of the crank plate to the linear motion of the slider. The motor is a DC
brushless motor with a controller. The major drawback of this type of a design is that amplitudes
as small as 0.1D cannot be achieved, however, higher amplitudes are easily possible. A possible
substitution to the crank is to make use of cam-shaft assemblies which are also readily available.
Figure 4.3 The conceptual design # 2 for the forced-vibration experiments using linear actuators.
Another possible design for forced-vibration tests is shown in Figure 4.3. It makes use of linear
actuators/slides which are readily available in the market. The major drawback of this type of a
design is that speeds as high 8 Hz may not be reached as travelling at that speed may heat the
lead screw and nut.
64
5 Appendix A Supplementary Figures
Figure 5.1 The non-dimensionalized vortex formation length (Lf ) is plotted for different wire angular locations.
65
Figure 5.2 The vorticity asymmetry angle () is plotted for various angular locations. Here the angle made by the
yellow straight line is used as a measure of asymmetry. The values are plotted on the contour plots of normalized
time-averaged absolute values of |⟨𝜔𝑧⟩|𝐷
𝑈∞⁄ .
66
Figure 5.3 Values of total wake width WT are plotted at a distance of X = 0.5D for different angular locations
ranging from = 0 to 180. Here the purple straight line is used as a measure of WT. The values are plotted on
the contour plots of normalized time-averaged absolute values of |⟨𝜔𝑧⟩|𝐷
𝑈∞⁄ .
67
Figure 5.4 Values of lower wake width WL are plotted at a distance of X = 0.5D for different angular locations
ranging from = 0 to 180. Here the purple straight line is used as a measure of WL. The values are plotted on
the contour plots of normalized time-averaged absolute values of |⟨𝜔𝑧⟩|𝐷
𝑈∞⁄ .
68
Figure 5.5 Values of total wake width WT are plotted at a distance of X = 0.75D for different angular locations
ranging from = 0 to 180. Here the violet straight line is used as a measure of WT. The values are plotted on the
contour plots of normalized time-averaged absolute values of |⟨𝜔𝑧⟩|𝐷
𝑈∞⁄ .
69
Figure 5.6 Values of lower wake width WL are plotted at a distance of X= 0.75D for different angular locations
ranging from = 0 to 180. Here the violet straight line is used as a measure of WL. The values are plotted on the
contour plots of normalized time-averaged absolute values of |⟨𝜔𝑧⟩|𝐷
𝑈∞⁄ .
70
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